Journal of Mechanical Engineering 2017 7-8

http://www.sv-jme.eu

63 (2017) 7-8

Since 1955

Papers

417

Luka Skrinjar, Janko Slavič, Miha Boltežar: Absolute Nodal Coordinate Formulation in a Pre-Stressed Large-Displacements Dynamical System

426

Kozhikkatil Sunil Arjun, Rakesh Kumar: LBM Analysis of Micro-Convection in MHD Nanofluid Flow

439

Florent Bunjaku, Risto V. Filkoski, Naser Sahiti: Thermal Optimization and Comparison of Geometric Parameters of Rectangular and Triangular Fins with Constant Surfacing

447

Hao Feng, Qungui Du, Yuxian Huang, Yongbin Chi: Modelling Study on Stiffness Characteristics of Hydraulic Cylinder under Multi-Factors

457

Tomaž Berlec, Mario Kleindienst, Christian Rabitsch, Christian Ramsauer: Methodology to Facilitate Successful Lean Implementation

466

Hong Seok Park, Duc Viet Dang, Trung Thanh Nguyen: Development of a Servo-Based Broaching Machine Using Virtual Prototyping Technology

Journal of Mechanical Engineering - Strojniški vestnik

Contents

7-8 year 2017 volume 63 no.

Strojniški vestnik Journal of Mechanical Engineering

Strojniški vestnik – Journal of Mechanical Engineering (SV-JME) Aim and Scope The international journal publishes original and (mini)review articles covering the concepts of materials science, mechanics, kinematics, thermodynamics, energy and environment, mechatronics and robotics, fluid mechanics, tribology, cybernetics, industrial engineering and structural analysis.

The journal follows new trends and progress proven practice in the mechanical engineering and also in the closely related sciences as are electrical, civil and process engineering, medicine, microbiology, ecology, agriculture, transport systems, aviation, and others, thus creating a unique forum for interdisciplinary or multidisciplinary dialogue.

The international conferences selected papers are welcome for publishing as a special issue of SV-JME with invited co-editor(s).

Editor in Chief Vincenc Butala

University of Ljubljana, Faculty of Mechanical Engineering, Slovenia

Technical Editor Pika Škraba

University of Ljubljana, Faculty of Mechanical Engineering, Slovenia

Founding Editor Bojan Kraut

University of Ljubljana, Faculty of Mechanical Engineering, Slovenia

Editorial Office University of Ljubljana, Faculty of Mechanical Engineering SV-JME, Aškerčeva 6, SI-1000 Ljubljana, Slovenia Phone: 386 (0)1 4771 137 Fax: 386 (0)1 2518 567 info@sv-jme.eu, http://www.sv-jme.eu Print: Papirografika Bori, printed in 300 copies Founders and Publishers University of Ljubljana, Faculty of Mechanical Engineering, Slovenia University of Maribor, Faculty of Mechanical Engineering, Slovenia Association of Mechanical Engineers of Slovenia Chamber of Commerce and Industry of Slovenia, Metal Processing Industry Association President of Publishing Council Branko Širok

University of Ljubljana, Faculty of Mechanical Engineering, Slovenia

Vice-President of Publishing Council Jože Balič

http://www.sv-jme.eu

63 (2017) 7-8

University of Maribor, Faculty of Mechanical Engineering, Slovenia

Since 1955

Strojniški vestnik Journal of Mechanical Engineering

Journal of Mechanical Engineering - Strojniški vestnik

Slavič, Miha Boltežar: rdinate Formulation in a Pre-Stressed ts Dynamical System

7-8 year 2017 volume 63 no.

Cover: The image presents the experimental setup used at the pre-stressed rigid-flexible multibody system. Two forcemeters and a high-speed camera were used to measure the pre-stress forces, the contact forces and the kinematics.

The validated numerical model of the electric circuit breaker was used to perform parameter sensitivity analysis where the switch-off time was shown to reduce to approx. 30 %.

Image Courtesy: Laboratory for dynamics of machines and structures, Faculty of Mechanical Engineering, University of Ljubljana Askerceva 6, 1000 Ljubljana, Slovenia, EU www.ladisk.si

ISSN 0039-2480 © 2017 Strojniški vestnik - Journal of Mechanical Engineering.

All rights reserved. SV-JME is indexed / abstracted in: SCI-Expanded, Compendex, Inspec, ProQuest-CSA, SCOPUS, TEMA. The list of the remaining bases, in which SV-JME is indexed, is available on the website.

International Editorial Board Kamil Arslan, Karabuk University, Turkey Hafiz Muhammad Ali, University of Engineering and Technology, Pakistan Josep M. Bergada, Politechnical University of Catalonia, Spain Anton Bergant, Litostroj Power, Slovenia Miha Boltežar, UL, Faculty of Mechanical Engineering, Slovenia Franci Čuš, UM, Faculty of Mechanical Engineering, Slovenia Anselmo Eduardo Diniz, State University of Campinas, Brazil Igor Emri, UL, Faculty of Mechanical Engineering, Slovenia Imre Felde, Obuda University, Faculty of Informatics, Hungary Janez Grum, UL, Faculty of Mechanical Engineering, Slovenia Imre Horvath, Delft University of Technology, The Netherlands Aleš Hribernik, UM, Faculty of Mechanical Engineering, Slovenia Soichi Ibaraki, Kyoto University, Department of Micro Eng., Japan Julius Kaplunov, Brunel University, West London, UK Iyas Khader, Fraunhofer Institute for Mechanics of Materials, Germany Jernej Klemenc, UL, Faculty of Mechanical Engineering, Slovenia Milan Kljajin, J.J. Strossmayer University of Osijek, Croatia Peter Krajnik, Chalmers University of Technology, Sweden Janez Kušar, UL, Faculty of Mechanical Engineering, Slovenia Gorazd Lojen, UM, Faculty of Mechanical Engineering, Slovenia Thomas Lübben, University of Bremen, Germany Janez Možina, UL, Faculty of Mechanical Engineering, Slovenia George K. Nikas, KADMOS Engineering, UK José L. Ocaña, Technical University of Madrid, Spain Miroslav Plančak, University of Novi Sad, Serbia Vladimir Popović, University of Belgrade, Faculty of Mech. Eng., Serbia Franci Pušavec, UL, Faculty of Mechanical Engineering, Slovenia Bernd Sauer, University of Kaiserlautern, Germany Rudolph J. Scavuzzo, University of Akron, USA Arkady Voloshin, Lehigh University, Bethlehem, USA General information Strojniški vestnik – Journal of Mechanical Engineering is published in 11 issues per year (July and August is a double issue).

Institutional prices include print & online access: institutional subscription price and foreign subscription €100,00 (the price of a single issue is €10,00); general public subscription and student subscription €50,00 (the price of a single issue is €5,00). Prices are exclusive of tax. Delivery is included in the price. The recipient is responsible for paying any import duties or taxes. Legal title passes to the customer on dispatch by our distributor.

Single issues from current and recent volumes are available at the current single-issue price. To order the journal, please complete the form on our website. For submissions, subscriptions and all other information please visit: http://en.sv-jme.eu/.

You can advertise on the inner and outer side of the back cover of the journal. The authors of the published papers are invited to send photos or pictures with short explanation for cover content.

We would like to thank the reviewers who have taken part in the peerreview process.

The journal is subsidized by Slovenian Research Agency.

Strojniški vestnik - Journal of Mechanical Engineering is available on http://www.sv-jme.eu, where you access also to papers’ supplements, such as simulations, etc.

Information for Authors All manuscripts must be in English. Pages should be numbered sequentially. The manuscript should be composed in accordance with the Article Template given above. The maximum length of contributions is 10 pages. Longer contributions will only be accepted if authors provide juastification in a cover letter. For full instructions see the Information for Authors section on the journal’s website: http://en.sv-jme.eu .

SUBMISSION: Submission to SV-JME is made with the implicit understanding that neither the manuscript nor the essence of its content has been published previously either in whole or in part and that it is not being considered for publication elsewhere. All the listed authors should have agreed on the content and the corresponding (submitting) author is responsible for having ensured that this agreement has been reached. The acceptance of an article is based entirely on its scientific merit, as judged by peer review. Scientific articles comprising simulations only will not be accepted for publication; simulations must be accompanied by experimental results carried out to confirm or deny the accuracy of the simulation. Every manuscript submitted to the SV-JME undergoes a peer-review process.

The authors are kindly invited to submit the paper through our web site: http://ojs.svjme.eu. The Author is able to track the submission through the editorial process - as well as participate in the copyediting and proofreading of submissions accepted for publication - by logging in, and using the username and password provided.

SUBMISSION CONTENT: The typical submission material consists of: - A manuscript (A PDF file, with title, all authors with affiliations, abstract, keywords, highlights, inserted figures and tables and references), - Supplementary files: • a manuscript in a WORD file format • a cover letter (please see instructions for composing the cover letter) • a ZIP file containing figures in high resolution in one of the graphical formats (please see instructions for preparing the figure files) • possible appendicies (optional), cover materials, video materials, etc.

Incomplete or improperly prepared submissions will be rejected with explanatory comments provided. In this case we will kindly ask the authors to carefully read the Information for Authors and to resubmit their manuscripts taking into consideration our comments.

COVER LETTER INSTRUCTIONS: Please add a cover letter stating the following information about the submitted paper: 1. Paper title, list of authors and their affiliations.

2. Type of paper: original scientific paper (1.01), review scientific paper (1.02) or short scientific paper (1.03).

3. A declaration that neither the manuscript nor the essence of its content has been published in whole or in part previously and that it is not being considered for publication elsewhere.

4. State the value of the paper or its practical, theoretical and scientific implications.

What is new in the paper with respect to the state-of-the-art in the published papers? Do not repeat the content of your abstract for this purpose.

5. We kindly ask you to suggest at least two reviewers for your paper and give us their names, their full affiliation and contact information, and their scientific research interest.

The suggested reviewers should have at least two relevant references (with an impact factor) to the scientific field concerned; they should not be from the same country as the authors and should have no close connection with the authors.

FORMAT OF THE MANUSCRIPT: The manuscript should be composed in accordance with the Article Template. The manuscript should be written in the following format: - A Title that adequately describes the content of the manuscript.

- A list of Authors and their affiliations.

- An Abstract that should not exceed 250 words. The Abstract should state the principal objectives and the scope of the investigation, as well as the methodology employed. It should summarize the results and state the principal conclusions.

- 4 to 6 significant key words should follow the abstract to aid indexing.

- 4 to 6 highlights; a short collection of bullet points that convey the core findings and provide readers with a quick textual overview of the article. These four to six bullet points should describe the essence of the research (e.g. results or conclusions) and highlight what is distinctive about it.

- An Introduction that should provide a review of recent literature and sufficient background information to allow the results of the article to be understood and evaluated.

- A Methods section detailing the theoretical or experimental methods used.

- An Experimental section that should provide details of the experimental set-up and the methods used to obtain the results.

- A Results section that should clearly and concisely present the data, using figures and tables where appropriate.

- A Discussion section that should describe the relationships and generalizations shown by the results and discuss the significance of the results, making comparisons with previously published work. (It may be appropriate to combine the Results and Discussion sections into a single section to improve clarity.)

- A Conclusions section that should present one or more conclusions drawn from the results and subsequent discussion and should not duplicate the Abstract.

- Acknowledgement (optional) of collaboration or preparation assistance may be included. Please note the source of funding for the research.

- Nomenclature (optional). Papers with many symbols should have a nomenclature that defines all symbols with units, inserted above the references. If one is used, it must contain all the symbols used in the manuscript and the definitions should not be repeated in the text. In all cases, identify the symbols used if they are not widely recognized in the profession. Define acronyms in the text, not in the nomenclature.

- References must be cited consecutively in the text using square brackets [1] and collected together in a reference list at the end of the manuscript.

- Appendix(-icies) if any.

SPECIAL NOTES Units: The SI system of units for nomenclature, symbols and abbreviations should be followed closely. Symbols for physical quantities in the text should be written in italics (e.g. v, T, n, etc.). Symbols for units that consist of letters should be in plain text (e.g. ms-1, K, min, mm, etc.). Please also see: http://physics.nist.gov/cuu/pdf/sp811.pdf .

Abbreviations should be spelt out in full on first appearance followed by the abbreviation in parentheses, e.g. variable time geometry (VTG). The meaning of symbols and units belonging to symbols should be explained in each case or cited in a nomenclature section at the end of the manuscript before the References.

Figures (figures, graphs, illustrations digital images, photographs) must be cited in consecutive numerical order in the text and referred to in both the text and the captions as Fig. 1, Fig. 2, etc. Figures should be prepared without borders and on white grounding and should be sent separately in their original formats. If a figure is composed of several parts, please mark each part with a), b), c), etc. and provide an explanation for each part in Figure caption. The caption should be self-explanatory. Letters and numbers should be readable (Arial or Times New Roman, min 6 pt with equal sizes and fonts in all figures).

Graphics (submitted as supplementary files) may be exported in resolution good enough for printing (min. 300 dpi) in any common format, e.g. TIFF, BMP or JPG, PDF and should be named Fig1.jpg, Fig2.tif, etc. However, graphs and line drawings should be prepared as vector images, e.g. CDR, AI. Multi-curve graphs should have individual curves marked with a symbol or otherwise provide distinguishing differences using, for example, different thicknesses or dashing.

Tables should carry separate titles and must be numbered in consecutive numerical order in the text and referred to in both the text and the captions as Table 1, Table 2, etc. In addition to the physical quantities, such as t (in italics), the units [s] (normal text) should be added in square brackets. Tables should not duplicate data found elsewhere in the manuscript. Tables should be prepared using a table editor and not inserted as a graphic.

REFERENCES: A reference list must be included using the following information as a guide. Only cited text references are to be included. Each reference is to be referred to in the text by a number enclosed in a square bracket (i.e. [3] or [2] to [4] for more references; do not combine more than 3 references, explain each). No reference to the author is necessary.

References must be numbered and ordered according to where they are first mentioned in the paper, not alphabetically. All references must be complete and accurate. Please add DOI code when available. Examples follow.

Journal Papers: Surname 1, Initials, Surname 2, Initials (year). Title. Journal, volume, number, pages, DOI code.

[1] Hackenschmidt, R., Alber-Laukant, B., Rieg, F. (2010). Simulating nonlinear materials under centrifugal forces by using intelligent cross-linked simulations. Strojniški vestnik - Journal of Mechanical Engineering, vol. 57, no. 7-8, p. 531-538, DOI:10.5545/svjme.2011.013.

Journal titles should not be abbreviated. Note that journal title is set in italics.

Books: Surname 1, Initials, Surname 2, Initials (year). Title. Publisher, place of publication.

[2] Groover, M.P. (2007). Fundamentals of Modern Manufacturing. John Wiley & Sons, Hoboken.

Note that the title of the book is italicized.

Chapters in Books: Surname 1, Initials, Surname 2, Initials (year). Chapter title. Editor(s) of book, book title. Publisher, place of publication, pages.

[3] Carbone, G., Ceccarelli, M. (2005). Legged robotic systems. Kordić, V., Lazinica, A., Merdan, M. (Eds.), Cutting Edge Robotics. Pro literatur Verlag, Mammendorf, p. 553576.

Proceedings Papers: Surname 1, Initials, Surname 2, Initials (year). Paper title. Proceedings title, pages.

[4] Štefanić, N., Martinčević-Mikić, S., Tošanović, N. (2009). Applied lean system in process industry. MOTSP Conference Proceedings, p. 422-427.

Standards: Standard-Code (year). Title. Organisation. Place.

[5] ISO/DIS 16000-6.2:2002. Indoor Air – Part 6: Determination of Volatile Organic Compounds in Indoor and Chamber Air by Active Sampling on TENAX TA Sorbent, Thermal Desorption and Gas Chromatography using MSD/FID. International Organization for Standardization. Geneva.

WWW pages: Surname, Initials or Company name. Title, from http://address, date of access.

[6] Rockwell Automation. Arena, from http://www.arenasimulation.com, accessed on 200909-07.

EXTENDED ABSTRACT: When the paper is accepted for publishing, the authors will be requested to send an extended abstract (approx. one A4 page or 3500 to 4000 characters). The instruction for composing the extended abstract are published on-line: http://www.sv-jme.eu/informationfor-authors/ .

COPYRIGHT: Authors submitting a manuscript do so on the understanding that the work has not been published before, is not being considered for publication elsewhere and has been read and approved by all authors. The submission of the manuscript by the authors means that the authors automatically agree to transfer copyright to SV-JME when the manuscript is accepted for publication. All accepted manuscripts must be accompanied by a Copyright Transfer Agreement, which should be sent to the editor. The work should be original work by the authors and not be published elsewhere in any language without the written consent of the publisher. The proof will be sent to the author showing the final layout of the article.

Proof correction must be minimal and executed quickly. Thus it is essential that manuscripts are accurate when submitted. Authors can track the status of their accepted articles on http://en.sv-jme.eu/.

PUBLICATION FEE: Authors will be asked to pay a publication fee for each article prior to the article appearing in the journal. However, this fee only needs to be paid after the article has been accepted for publishing. The fee is 240.00 EUR (for articles with maximum of 6 pages), 300.00 EUR (for articles with maximum of 10 pages), plus 30.00 EUR for each additional page. The additional cost for a color page is 90.00 EUR. These fees do not include tax.

Strojniški vestnik -Journal of Mechanical Engineering Aškerčeva 6, 1000 Ljubljana, Slovenia, e-mail: info@sv-jme.eu

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8 Contents

Contents Strojniški vestnik - Journal of Mechanical Engineering volume 63, (2017), number 7-8 Ljubljana, July-August 2017 ISSN 0039-2480 Published monthly

Papers Luka Skrinjar, Janko Slavič, Miha Boltežar: Absolute Nodal Coordinate Formulation in a Pre-Stressed Large-Displacements Dynamical System Kozhikkatil Sunil Arjun, Rakesh Kumar: LBM Analysis of Micro-Convection in MHD Nanofluid Flow Florent Bunjaku, Risto V. Filkoski, Naser Sahiti: Thermal Optimization and Comparison of Geometric Parameters of Rectangular and Triangular Fins with Constant Surfacing Hao Feng, Qungui Du, Yuxian Huang, Yongbin Chi: Modelling Study on Stiffness Characteristics of Hydraulic Cylinder under Multi-Factors Tomaž Berlec, Mario Kleindienst, Christian Rabitsch, Christian Ramsauer: Methodology to Facilitate Successful Lean Implementation Hong Seok Park, Duc Viet Dang, Trung Thanh Nguyen: Development of a Servo-Based Broaching Machine Using Virtual Prototyping Technology

417 426 439 447 457 466

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 417-425

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 417-725 © 2017 Journal of Mechanical Engineering. All rights reserved. c 2017 Journal of Mechanical Engineering. All rights reserved.

DOI:10.5545/sv-jme.2017.4561 Original Scientific Paper — DOI:10.5545/sv-jme.2017.4561

Original Scientific Paper

Received for review: 2017-05-04 Received for review: 2017-05-04 Received revised form: 2017-05-25 Received revised form: 2017-05-25 Accepted for publication: 2017-06-02 Accepted for publication: 2017-06-02

Absolute Nodal Coordinate Formulation in a Pre-Stressed Large-Displacements Dynamical System Luka Skrinjar1 , Janko Slaviˇc2 , Miha Boltežar2 1

2

ETI Elektroelement d. d., Slovenia University of Ljubljana, Faculty of Mechanical Engineering, Slovenia

The design process for dynamical models has to consider all the properties of a mechanical system that have an effect on its dynamical response. In multi-body dynamics, flexible bodies are frequently modeled as rigid, resulting in non-valid modeling of the pre-stress effect. In this research a focus on the pre-stress effect for a flexible body assembled in a rigid-flexible multibody system is presented. In a rigid-flexible assembly a flexible body is modeled with an absolute nodal coordinate formulation (ANCF) of finite elements. The geometrical properties of the flexible body are evaluated based on the frequency response and compared with the experimental values. An experiment including the pre-stress effect and large displacements is designed and the measured values of the displacement are compared to the numerical results in order to validate the dynamical model. The pre-stress was found to be significant for proper numerical modeling. The partially validated numerical model was used to research the effect of different parameters on the dynamical response of a pre-stressed, rigid-flexible assembly.

Keywords: ANCF, pre-stress, multibody system, measurement Highlights

• • • •

A numerical model of a rigid-flexible multibody system is used in the analysis of kinematic properties during switch-off.

A flexible body is modeled with the Absolute Nodal Coordinate Formulation to include the pre-stress effect.

The influence of different parameters on the switch-off time and the contact distance is investigated.

The numerical model was validated and shows good agreement with the experimental values.

0 INTRODUCTION

When modeling dynamical systems the proper material and contact properties of the numerical model are crucial for simulating an accurate dynamic response.

One of the properties to be considered is the effect of pre-stress on rigid and flexible bodies, as it can have a significant impact on the dynamical response of multibody mechanical systems.

The modeling of deformable bodies in a multibody system can be done using a floating frame of reference (FFR) [1], which is based on the classic finite element (FE) method that is widely used in a variety of applications [2] and [3]. While in a floating frame of reference formulation a mixed set of absolute reference and local elastic coordinates are used, in the absolute nodal coordinate formulation (ANCF) only absolute coordinates are used, which include global displacement and global vector gradients [4].

The ANCF is a non-incremental method and it has been used for solving many different problems in mechanics, such as vehicle components [5] and [6], the modeling of belt drives [7], railroad applications [8], bio-mechanics [9] and also in the field of digital image correlation (DIC) [10]. The main features of the ANCF are a constant mass matrix, zero centrifugal

and Coriolis inertia forces and the possibility for exact modeling of rigid-body movement.

The modeling of the pre-stress effect on bodies in mechanical systems is an interesting research topic in civil-engineering applications [11], where the static [12] and dynamic responses of structural elements are considered [13]. The effect of pre-stress is introduced to the ANCF finite elements to create an accurate model of a leaf spring, where pre-stress is evaluated based on the known geometrical states in the undeformed and deformed configurations that define the vector of absolute nodal coordinates [14]. In [15] the effect of the non-dimensional axial pre-stress of eigenfrequencies on a simply supported beam is researched. The pre-stress effect is included in the model of a flexible multibody belt-drive [16], where the belt-drive is modeled with ANCF two-dimensional shear deformable beam elements that account for the longitudinal and shear deformations.

When modeling mechanical systems [17–20] a validation is needed to evaluate the results from the numerical model, this can be done using different methods of validation. Numerical results can be compared to: measured values of a real engineering application [21], measured values of a custom-designed experimental setup [22] or to another

*Corr.

University of Ljubljana, Faculty of Mechanical Engineering, Aškerˇceva 6, 1000 Ljubljana, Slovenia, miha.boltezar@fs.uni-lj.si *Corr.Author’s Author’sAddress: Address: University of Ljubljana, Faculty of Mechanical Engineering, Aškerčeva 6, 1000 Ljubljana, Slovenia, miha.boltezar@fs.uni-lj.si

417 417

StrojniĹĄki vestnik - Journal 63(2017)7-8, 417-425 StrojniĹĄki vestnik - JournalofofMechanical Mechanical Engineering Engineering 63(2017)7-8, 417-725

numerical result [23] in order to validate the numerical model. The measured values of the external and contact forces that result in a pre-stressed state of the rigid-flexible assembly during the experiment are used to build the dynamical model with the pre-stress effect.

The objective of our manuscript is the application of the ANCF method to a real, pre-stressed, rigid-flexible assembly to model the large rotation and displacement problem in the dynamics of a multibody system, where the dynamic response of a mechanical system is investigated. Measurements are made to evaluate the actual dynamical properties of the mechanical system. A comparison between the numerical results and the measured data is presented.

This manuscript is organized as follows. Section 1 gives the theoretical background for the absolute nodal coordinate formulation and a generalized force vector is introduced. In addition, the formulation of the equations of motion for multibody systems assembled from rigid and flexible bodies is presented. In Section 2 the numerical model of a circuit-breaker assembly is presented. The experimental results are compared to the numerical ones in Section 3. Finally, the last Section draws the conclusions.

The ANCF is a non-incremental, finite-element method that can be used to describe large rotations and large deformations in applications of multibody system dynamics [24–26]. The formulation uses a position vector and gradient vectors as the nodal coordinates. The beam elements, based on an absolute nodal coordinate formulation, can be specified as Euler-Bernoulli or shear deformable and have been intensively used in two- and three-dimensional beam applications [27] and [28].

The general motion of a two-dimensional j-th beam finite element can be described with the vector field [29]: r j (x,t) =

rxj ryj

= S j (x) e j (t) ,

(1)

where r is the global position vector of an arbitrary point on the element, S is the global shape function that depends on the Lagrangian coordinates and e is a vector of time-dependent coefficients that consist of the absolute position and slope coordinates of each node in an element. In this paper a planar gradient deficient [25] Euler-Bernoulli beam element is used [30–32], Fig. 1.

418 418

b)

Fig. 1. Position vector and slopes in the planar absolute nodal coordinate beam finite element: a) undeformed and b) deformed reference configuration

The vector of the element nodal coordinates e for a Euler-Bernoullli finite element is given by e = e (t) = [e1 . . . e8 ]T .

(2)

The vector of the nodal coordinates includes the global displacements [4]: r1 = r(0) = [e1 e2 ]T ,

r2 = r(L) = [e5 e6 ]T ,

(3)

and the global slopes of the element nodes that are defined as [33]:

1 THEORETICAL BACKGROUND

a)

r1x =

∂ r1 (0) ∂ r2 (L) = [e3 e4 ]T , r2x = = [e7 e8 ]T . (4) ∂x ∂x

For this element the shape function S is a 2 Ă— 8 matrix and is defined as [25]: S = [S1 I

S2 I

S3 I

S4 I]T ,

(5)

where I is a 2 Ă— 2 identity matrix and S1 . . . S4 can be written as [34]:

S1 = 1 − 3Ξ 2 + 2Ξ 3 , S2 = l Ξ − 2Ξ 2 + Ξ 3 , (6)

S3 = 3Ξ 2 − 2Ξ 3 , S4 = l −Ξ 2 + Ξ 3 ,

where Ξ = x/L is the only coordinate of the element with length L. Only one gradient vector can be defined at the node and the shear strain is assumed to be zero.

As a consequence, the cross-section is assumed to remain perpendicular to the element’s center line.

1.1 Multibody Dynamics

The virtual work of the external force F j applied at an arbitrary point P defined by the coordinates xPj on the j-th finite element can be written as [1] and [29]:

T T T δWej = F j δ rPj = F j S j xPj δ e j = Qej δ e j . (7)

Skrinjar, L. - Slaviˇc, J. - BolteŞar, M.

Absolute Nodal Coordinate Formulation in a Pre-Stressed Large-Displacements Dynamical System

Strojniški vestnik - Journal Engineering63(2017)7-8, 63(2017)7-8, 417-425 Strojniški vestnik - JournalofofMechanical Mechanical Engineering 417-725

For example, the virtual work Eq. (7) due to the distributed gravity of the finite element can be obtained using the shape function, Eq. (5) as: δWgj

=

δWgj

=

j

[0 − ρg] S j δ e j , (8)

L 1 L 1 0 0− δ e j . (9) −mej g 0 0 2 12 2 12 V

The gravitational force vector acting at the element nodal coordinates can be expressed as:

L 1 L T 1 j j 0 0 0 − . (10) Qg = −me g 0 2 12 2 12 1.2 Equations of Motion

A mechanical system is an assembly of rigid and deformable bodies that are connected with kinematic constraints to achieve the design requirements [1].

The kinematic constraint equations that describe the mechanical joints between the bodies as well as time-dependent, user-defined motion trajectories are defined in terms of the vector of generalized coordinates of the system, q, and time t as: C (q,t) = 0,

(11)

where C is the vector of constraint equations. The vector q includes the generalized coordinates of the rigid and flexible bodies of the system, where flexible bodies are described with the absolute nodal coordinates vector e.

The constraint forces are included in the equations of motion with the use of Lagrange multipliers and the equations of the system have the form: Mq¨ = Qe − Qs − CTq λ ,

(12)

where M is a symmetric mass matrix of the multibody system and includes rigid and deformable bodies, Cq is the Jacobian matrix of kinematic constraints Cq = ∂ C/∂ q, q¨ is the vector of accelerations of the multibody system, Qe is a vector of all the applied external forces, including the contact forces, spring forces and gravitational forces, Qs is a vector of elastic strain forces developed only for the deformable bodies, and λ is the vector of Lagrange multipliers. Eq. (12) and the second time derivative of Eq. (11) can be written together in the augmented form [25]:

Qe + Qg − Qs q¨ M CTq , (13) = λ Qd Cq 0 where Qd is the vector that absorbs all the terms of the acceleration constraint equations that depend only

on the velocities [35]. The vector of accelerations q¨ can then be integrated forward in time to obtain the velocities q˙ and coordinates q [36].

For the i-th deformable body (that is assembled from ne number of ANCF finite elements) the mass matrix and the force vectors are presented in details in Section 4 [25].

The effect of pre-stress is introduced to the rigid or ANCF flexible body with the external force applied to the flexible body using Eq.(7) and the force magnitude and direction must be defined, although this rapidly decreases to zero during the time integration.

2 THE NUMERICAL MODEL OF A PRE-STRESSED RIGID-FLEXIBLE ASSEMBLY

A real mechanical system of a pre-stressed rigid-flexible assembly of a residual current circuit breaker (RCBO) is used in the experimental setup, Fig. 2, and also for the numerical model’s validation, Fig. 3. The mechanical system is assembled from an inertially fixed pin, a rigid body, a point mass, a flexible body and a pre-stressed helical compression spring. The helical compression spring is mounted between the inertially fixed housing and the flexible body. The rigid body with a slot is in contact with the pin via a pin-slot clearance joint [37]. An electric cable connects the terminal with the flexible body and if the flexible body is in contact with the static contact the circuit breaker is switched ON and conducts an electric current.

The assembly’s pre-stressed state results from the accumulation of the potential energy in the pre-stressed helical springs and the elastic strain energy in the flexible body. To speed-up the electrical switch, the potential energy due to the pre-stress is used. Details about the numerical model are presented next.

2.1 Numerical Model

An inertially fixed rigid pin body is connected to a rigid slot body with a pin-slot clearance joint [37].

The moving contact part is modeled as three separate bodies, e.g., a rigid slot body, a contact pad as a mass point and a flexible body as a beam based on ANCF. In Fig. 3 the flexible beam is modeled with two ANCF finite elements and three nodes, e.g., i = 1 and n = 2. The rigid connection is used to mechanically couple the rigid slot body and the flexible body [38]. A pre-stressed helical compression steel spring is attached between the flexible beam body and the ground [35]. The body coordinate system marked with the upper-script number of the body coincides

Absolute Nodal Coordinate Formulation in a Pre-Stressed Large-Displacements Dynamical System

Skrinjar, L. – Slavič, J. – Boltežar, M.

419 419

StrojniĹĄki vestnik - Journal 63(2017)7-8, 417-425 StrojniĹĄki vestnik - JournalofofMechanical Mechanical Engineering Engineering 63(2017)7-8, 417-725

with a body center of mass for the rigid body, while the body coordinate system for the flexible body is positioned at the first node of a body’s mesh.

At the initial position of the moving contact different forces are applied to keep it in a stationary position, e.g., the force of a helical compression spring, the contact force between a pin and a slot, the pre-stressed contact force between a moving contact and a fixed contact, Fc , and the external pre-stressed force F2 (t). The flexible body vibrates continuously under gravity if there is no damping.

During a dynamical simulation only the spring force is continuous and the contact force between the pin and the slot is present when the contact is detected.

The geometrical and mass properties used for the numerical model of the multibody system are summarized in Table 1. The initial position and the orientation values of the i-th body are marked as qi0 and the initial velocity vector, q˙ i0 , of the multibody system is zero. The vector q20 for the flexible body only defines the position and the orientation of the body’s local coordinate system, which is used to transform the absolute nodal coordinate of the flexible body, while the actual values depend on the number of ANCF finite elements used, e.g., for 2 Euler-Bernoulli ANCF finite elements the vector q20 has 3 nodes and each node has 2 vectors (one position and one gradient vector), which in total equals 12 components of the vector q20 .

A helical compression spring is attached to the s s housing (ground) at position uP = 0, uP,y and onto the body 2. For a flexible body (i = 2) the spring position is defined as L2 = 18.5 mm, see Fig. 3, and for a rigid body (i = 2) the spring position is u2P = [6.5, 0.] mm.

Dynamical simulations of the numerical model are performed with custom-written software [39], which automatically generates the equations of motion and uses numerical integration techniques to solve them, Eq. 12.

2.2 Free-Free Response of the Rigid-Flexible Assembly

Fig. 2. A pre-stressed rigid-flexible assembly with contact conditions - the experimental setup

In order to validate the equivalent geometry and stiffness properties of the rigid-flexible assembly a measurement of the bending natural frequencies was made, Fig. 5. A Polytec PDV 100 vibrometer was used to measure the response of the flexible part of the assembly; the impact excitation was introduced via a miniature PCB Piezotronics’s impulse hammer model 084A14. The data acquisition was made using a NI 9234 24-bit data-acquisition card with a sampling rate at 51.2 kHz and 512 samples were acquired during the measurement.

In the numerical model (Fig. 4), all the contacts were removed to obtain the free-free T conditions and the external force F0 (t) = 0, Fy0 (t) was applied, where Fy0 (t) is: Fy0 (t)

Fig. 3. A pre-stressed rigid-flexible assembly with contact conditions - the dynamical model

420 420

=

F0 sin 0

Ď€ tF

t ,

if t ≤ tF

,

(14)

F0 = 4 N represents the force amplitude for the selected time interval [0, tF = 0.1] ms and the simulation end time is tn = 100 ms.

Table 2 shows the parameters that were used in the model to obtain the natural frequencies

Skrinjar, L. - Slaviˇc, J. - BolteŞar, M.

Absolute Nodal Coordinate Formulation in a Pre-Stressed Large-Displacements Dynamical System

Strojniški vestnik - Journal Engineering63(2017)7-8, 63(2017)7-8, 417-425 Strojniški vestnik - JournalofofMechanical Mechanical Engineering 417-725

Table 1. Properties of the multibody system

i mi [10−3 kg] J i [10−9 kg m2 ]

qi0 [mm, mm, deg] q˙ i0 [mm, mm, deg]/s

rigid slot body 1 0.473 3.38

flexible body 2 1.3 /

rigid body 2 1.3 66.58

contact pad 3 0.346 /

[−3.15, 0.6, 14.8]

[−5.6, −15.4, 83.6]

[−4.2, −3, 83.6]

[−5.6, −15.4, /]

0

0

Fig. 4. A free-free rigid-flexible assembly

[40] at the free-free boundary conditions shown in Table 3. Table 3 compares the ANCF model to the modal analysis results using the commercial software ANSYS (BEAM188 elements) and the experimental results.

Table 2. Properties of a rigid-flexible assembly Property length L [mm] height h [mm] width w [mm] density ρ [kg/m3 ] Young’s modulus E [GPa]

Exp. 4600 0

0

amplifier (Brüel & Kjaer Nexus 2692 was used). When the pre-stress string on the Endevco 2312 side was instantly cut, the static contact forces were taken from the measured dynamic force. The data was acquired with the NI 9234 (24-bit) card at a sampling frequency of 51.2 kS/s per channel.

During the experiment the motion of the rigid-flexible assembly was recorded with a Photron FASTCAM SA-Z high-speed camera. A frame rate of 67200 fps at a resolution of 384 × 640 pixels was used.

Each pixel corresponded to 47 µm for the measured assembly. A digital image correlation (DIC) [23] and [41] was applied to the high-speed camera images to obtain the kinematics of the assembly. An image from recorded sequence is presented in Fig. 6.

3.1 Results

The pre-stressed forces Fx2 and Fc were measured when the string was instantly cut and are shown in Table 4.

Value 25 1.1 5.2 8940 127

Table 4. Measured pre-stressed forces Measured force Fx2 [N] 11.77 Fc [N] 2.92

Table 3. Bending natural frequencies [Hz] of the rigid-flexible assembly at free-free boundary conditions

1st bending frequency [Hz] Error [%]

0

ANCF 4724 -2.62

ANSYS 4971 -7.46

3 THE EXPERIMENT

The experimental setup is shown in Fig. 2. Two pre-stress contact forces were measured during the experiment: the PCB 218C was used to acquire the change of contact force on one side (the force Fx2 in the model), while the Endevco 2312 was used on the other (the force Fc in the model). The latter was also used to apply the pre-stress via a string, see Fig. 2.

Both sensors are charge-type and require a charge

The kinematics of the position vector of node 0 in the x (i.e., e0x ) and y (i.e., e0y ) direction obtained from the DIC are shown in Figs. 7 and 8, respectively. Finally, the trajectory of node 0, e0 , is shown in Fig. 9. The experimental results are compared to the numerical results obtained using two numerical models: the deformable rigid-flexible assembly presented in Section 2 and a rigid assembly.

The rigid assembly was similar to the flexible-rigid assembly, but the "flexible body” (Fig. 3) was modeled as rigid and therefore not able to accumulate the potential energy due to the pre-stress.

The performance of the electric circuit breaker is evaluated based on several criteria, one that has to be considered is the speed of the contact to break the electric circuit, e.g., to move away as quickly as possible. Fig. 7 shows that a distance of approximately 2 mm is guaranteed at approximately 1.75 ms after

Absolute Nodal Coordinate Formulation Pre-Stressed Large-Displacements Dynamical System Skrinjar, L.in –a Slavič, J. – Boltežar, M.

421 421

Strojniški vestnik - JournalofofMechanical Mechanical Engineering 417-725 Strojniški vestnik - Journal Engineering63(2017)7-8, 63(2017)7-8, 417-425

Fig. 5. Measurement of bending natural frequencies of the rigid-flexible assembly for free-free boundary conditions

Fig. 7. A x coordinate of a node 0, e0x , on a flexible body and comparison with a rigid body and experimental values

Fig. 6. An image recored with high-speed camera at experiment time t =

0.98 ms

Fig. 8. A y coordinate of a node 0, e0y , on a flexible body and comparison with a rigid body and experimental values

the movement is started. Once the numerical model is partially validated it can be used to research the parameter’s influence. Fig. 10 shows the comparison of the x coordinate of node 0, e0x , for different values of the pre-stress force, the parameter of torsional stiffness 422

422

ct and the location of the attached helical spring usP,y .

From the results it follows that a doubled pre-stress and a decreased stiffness ct and a change in the attachment of the helical spring usP,y from 0 mm to −1 mm would

Skrinjar, L. - Slaviˇc, J. - Boltežar, M.

Absolute Nodal Coordinate Formulation in a Pre-Stressed Large-Displacements Dynamical System

Strojniški vestnik - Journal Engineering63(2017)7-8, 63(2017)7-8, 417-425 Strojniški vestnik - JournalofofMechanical Mechanical Engineering 417-725

Fig. 9. A trajectory of a node 0, e0y , on a flexible body and comparison to a rigid body and measured values

result in 2 mm of distance in approximately 0.6 ms, which is approximately 1/3 of the current switch-off time.

mechanical system is evaluated with digital image processing of a high-speed camera capture. The dynamical model is partially validated with the experimental results. The significance of the modeling of flexible bodies in the case of pre-stress is shown.

A good agreement between the measurement and the rigid-flexible model is achieved for x coordinate (Fig. 7) while for the fully rigid assembly model the value of final position is properly simulated. The main difference in the both numerical models is in flexible body and the hybrid rigid connection between rigid slot and flexible body that is achieved with a simple revolute joint with additional torsional spring. For the circuit breaker function the y coordinate is not as important as x coordinate; however it is shown that measured values of y agree well with the numerical values for the rigid-flexible model, while the rigid model gives inappropriate results after time approx. t = 1.26 ms, see Fig. 8. The point trajectory of both numerical models, see table 1, significantly divergate at the end of simulation.

Based on the partially validated numerical model it is clear that a significant decrease in the switch-off time for the electrical contact is possible.

ACKNOWLEDGMENT

The authors acknowledge the partial financial support from the Slovenian Research Agency (research core funding No. P2-0263 and J2-6763).

A APPENDIX coordinate of a node 0, e0x , on a flexible body for different

Fig. 10. A x values of prestress effect

4 CONCLUSIONS

In this work a pre-stressed rigid-flexible dynamical system based on a real mechanical system and a flexible body is modeled with an absolute nodal coordinate formulation. The dynamical system is assembled from rigid and flexible bodies that are interconnected with kinematic constraints.

First, the bending frequency of the rigid-flexible assembly is measured and based on the measured data an equivalent geometry is designed to achieve equal stiffness properties, including the eigenfrequency. This geometry of the flexible body is then used in a multibody system to model the dynamics and to evaluate the dynamic response of the pre-stressed rigid-flexible assembly.

The dynamics of the

The flexible body can be assembled from multiple ANCF finite elements and evaluated mass matrix and force vectors of the flexible body (continuum) are obtained from mass matrices and force vector of finite elements as [35]: Mi

ne

=

∑ Bi j

T

Mi j Bi j ,

(15)

∑ Bi j

T

Qisj ,

(16)

∑ Bi j

T

Qiej ,

(17)

j=1 ne

Qis

=

Qie

=

j=1 ne j=1

where Bi j is a constant Boolean matrix describing the element connectivity conditions [25]. The Boolean matrix includes zeros and ones and maps the element coordinates to the body coordinates. The Boolean matrix of the finite element always has a number

Absolute Nodal Coordinate Formulation in a Pre-Stressed Large-Displacements Dynamical System

Skrinjar, L. – Slavič, J. – Boltežar, M.

423 423

Strojniški vestnik- Journal - JournalofofMechanical Mechanical Engineering 417-725 Strojniški vestnik Engineering63(2017)7-8, 63(2017)7-8, 417-425

of rows equal to the number of finite element nodal coordinates and a number of columns equal to the number of nodal coordinates of the flexible body.

For two ANCF finite elements of Euler-Bernoulli type, as presented in Fig. 11, the boolean matrix of size 8 × 12 for each element is defined as:   1 0 0 0 0 0 0 0 0 0 0 0  0 1 0 0 0 0 0 0 0 0 0 0     0 0 1 0 0 0 0 0 0 0 0 0     0 0 0 1 0 0 0 0 0 0 0 0   B0 =   0 0 0 0 1 0 0 0 0 0 0 0     0 0 0 0 0 1 0 0 0 0 0 0     0 0 0 0 0 0 1 0 0 0 0 0  0 0 0 0 0 0 0 1 0 0 0 0 

     B1 =      

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0

1 0 0 0 0 0 0 0

0 1 0 0 0 0 0 0

0 0 1 0 0 0 0 0

0 0 0 1 0 0 0 0

0 0 0 0 1 0 0 0

0 0 0 0 0 1 0 0

0 0 0 0 0 0 1 0

0 0 0 0 0 0 0 1

           

Fig. 11. Element connectivity

REFERENCES

REFERENCES

[1] A. A. Shabana. Dynamics of Multibody Systems.

Cambridge University Press, 2005.

[1] Shabana, A.A. (2005). Dynamics of Multibody Systems, [2] V Alankaya and F Alarçin. Using sandwich composite Cambridge University Press. shells for fully pressurized tanks on liquefied petroleum [2] Alankaya, V., Alarçin, F. (2016). Using sandwich composite gas carriers. Strojniški Vestnik/Journal of Mechanical shells for fully tanks on liquefied petroleum gas Engineering,pressurized 62(1):32–40, 2016. carriers.

Strojniški vestnik Journal of Mechanical Engineering, [3] N. O. Chibueze, C. V. Ossia, and J. U. Okoli.

On the DOI:10.5545/sv-jme.2015.2611. vol.

62, no.of1, Steel p. 32-40, Fatigue Catenary Risers. Strojniški vestnik [3] Chibueze, Ossia, C. V., Okoli, J.U. (2016).

On the fatigue of - JournalN.O., of Mechanical Engineering, 62(12):751–756, steel catenary risers. Strojniški vestnik - Journal of Mechanical 2016.

DOI:10.5545/svvol. 62,Definition no. 12, p.of 751-756, [4] Engineering, A. A. Shabana.

ANCF Finite Elements. jme.2015.3060.

Journal of Computational and Nonlinear Dynamics, 10(5):054506, 2015. Definition of ANCF finite elements.

[4] Shabana, A.A. (2015).

[5] Journal M. A. ofOmar, A. A. Shabana, A. M.Dynamics, Mikkola, vol.

W. 10, Y. Computational and Nonlinear Loh, R. Basch.

Multibody System Modeling DOI:10.1115/1.4030369. no.

5, p.and 054506, of Leaf Journal of Vibration and Basch, Control, [5] Omar, M.A.,Springs.

Shabana, A.A., Mikkola, A.M., Loh, W.Y., R. 10(11):1601–1638, 2004.

(2004).

Multibody System Modeling of Leaf Springs. Journal

424

424

Control, vol.Q.10, no.and 11,A.p.A.16011638, [6] ofM.Vibration Patel, G.and Orzechowski, Tian, Shabana.

A new multibody system approach for tire modeling DOI:10.1177/1077546304042047. usingM.,ANCF finite elements.

Proceedings of theA [6] Patel, Orzechowski, G., Tian, Q., Shabana, A.A. (2016).

Institution of system Mechanical Engineers, Part K: using Journal of new multibody approach for tire modeling ANCF Multi-body Dynamics, 0(0):1–16, 2015. of Mechanical finite elements.

Proceedings of the Institution ˇ [7] Engineers, G. Cepon andK:M. Boltežar.

Dynamics of a belt-drive Part Journal of Multi-body Dynamics, vol. 230, system using DOI:10.1177/1464419315574641. a linear complementarity problem for the no. 1, p. 69-84, belt-pulley contact description. Journal of Sound and [7] Čepon, G., Boltežar, M. (2009). Dynamics of a belt-drive Vibration, 319(3-5):1019–1035, 2009. system using a linear complementarity problem for the belt[8] J.-H. Seo, S.W. Kim, I.-H. Jung, T.-W. Park, J.-Y. pulley contact description. Journal of Sound and Vibration, vol.

Mok, Y.-G. Kim, and J.-B. Chai. Dynamic Analysis 319, no. 3-5, p. 1019-1035, DOI:10.1016/j.jsv.2008.07.005. of a Pantograph-Catenary System Using Absolute [8] Seo, J.-H.,Coordinates.

Kim, S.W., Jung, I.-H., Park, System T.-W., Mok,Dynamics, J.-Y., Kim, Nodal Vehicle Y.-G., Chai, J.-B. (2006).

44(8):615–630, 2006. Dynamic analysis of a pantographsystem coordinates.

[9] catenary F. M. Gantoi, M. A.using Brown,absolute and A. A.nodal Shabana.

ANCF Vehicle System Dynamics, vol.

44, no.

8, p. 615–630, Finite Element/Multibody System Formulation of the DOI:10.1080/00423110500373721.

Ligament/Bone Insertion Site Constraints. Journal of [9] Gantoi, F.M., Brown, Shabana, A.A. (2010).

ANCF finite Computational andM.A. Nonlinear Dynamics, 5(3):031006, 2010. element/multibody system formulation of the ligament/ [10] bone M. Langerholc, Slaviˇc, andJournal M. Boltežar.

Absolute insertion siteJ. constraints. of Computational Nodal Coordinates in Digital and Nonlinear Dynamics, vol. 5, Image no. 3, Correlation. p. 031006, Experimental Mechanics, 53(5):807–818, 2013.

DOI:10.1115/1.4001373.

[11] Langerholc, A. Ayoub M.,and F. C. Filippou. M. (2013).

Finite-Element [10] Slavič, J., Boltežar, Absolute Model for Pretensioned Concrete Girders. nodal coordinates in digitalPrestressed image correlation.

Experimental (April):401–409, Mechanics, vol. 53, 2010. no. 5, p. 807–818, DOI:10.1007/s11340[12] 012-9691-4.

A. Akl, M. Saiid Saiidi, and A. Vosooghi. Deflection of in-span hinges inF.C. prestressed concrete box girder [11] Ayoub, A., Filippou, (2010). Finite-Element Model bridges during construction. Engineering Structures, for Pretensioned Prestressed Concrete Girders. Journal 131:293–310, 2017. of Structural Engineering, vol. 136, no. 4, p. 401-409, [13] A. Mordak and Z. Z. Manko.

Effectiveness of DOI:10.1061/(ASCE)ST.1943-541X.0000132.

Post-tensioned Prestressed Concrete Road Bridge [12] Akl, A., Saiid Saiidi, Vosooghi, A. (2017).under Deflection of inRealization in theM.,Light of Research Dynamic span hinges in prestressed concrete box girder bridges during Loads. Procedia Engineering, 156:264–271, 2016.

Structures, 293-310, [14] construction.

Z. Yu, Y. Engineering Liu, B. Tinsley, andvol.A.131, A. p.Shabana.

DOI:10.1016/j.engstruct.2016.11.003.

Integration of Geometry and Analysis for Vehicle [13] Mordak, Manko, Z.Z.Continuum-Based (2016). Effectiveness postSystem A., Applications: LeafofSpring tensioned roadofbridge realization inand the and Tireprestressed Assembly.concrete Journal Computational Nonlinear Dynamics, 10(3):1–17, light of research under dynamic loads.2015.

Procedia Engineering, 264–271, [15] vol.

P. 156, G. no.

Gruber, K. DOI:10.1016/j.proeng.2016.08.296.

Nachbagauer, Y. Vetyukov, and J. Z., Gerstmayr.

A novel director-based Bernoulli-Euler [14] Yu, Liu, Y., Tinsley, B., Shabana, A.A. (2015).

Integration finiteand element nodal applications: coordinate ofbeam geometry analysisinforabsolute vehicle system formulation freeleaf of geometric continuum-based spring andsingularities. tire assembly.Mechanical Journal of Sciences, 4(2):279–289, 2013.

Computational and Nonlinear Dynamics, vol. 10, no. 3, p. ˇ [16] 1–17, G. Cepon, L. Manin, and M. Boltežar. Introduction of DOI:10.1115/1.4031151. damping into the flexible multibody belt-drive model: A [15] Gruber, P.G., Nachbagauer, K., Vetyukov, Y., Gerstmayr, J. numerical and experimental investigation. Journal of (2013). A novel director-based Bernoulli-Euler beam finite Sound and Vibration, 324(1-2):283–296, 2009. element in absolute nodal coordinate formulation free of [17] R. G. Rinaldi, L. Manin, C. Bonnard, A. Drillon, geometric singularities. Mechanical Sciences, vol. 4, no. 2, p.

H. Lourenco, and N. Havard. Non Linearity of the DOI:10.5194/ms-4-279-2013.

279-289, Ball/Rubber Impact in Table Tennis: Experiments and [16] Čepon, G., Manin, L., Engineering, Boltežar, M. (2009).

Introduction Modeling.

Procedia 147:348–353, 2016.of into the belt-driveand model: [18] damping S. Baglioni, F. flexible Cianetti,multibody C. Braccesi, D.M.A numerical and experimental investigation.

Journal of Sound De Micheli. Multibody modelling of N DOF robot arm DOI:10.1016/j. and Vibration, 324,manufacturing. ni. 1-2, p. 283-296, assigned to vol. milling Dynamic analysis jsv.2009.02.001. and position errors evaluation. Journal of Mechanical [17] Rinaldi, R.G., Manin, L., Bonnard, C., Drillon, A.,2016.

Lourenco, H., Science and Technology, 30(1):405–420, (2016).Stefan Non linearity of the in [19] Havard, Lionel N.Manin, Braun, andball/rubber Damien impact Hugues.

Modelling the Belt –andEnvelope Interactions during table tennis: experiments modeling. Procedia Engineering, the147, Postal Mail Conveying by a Sorting Machine.

DOI:10.1016/j.proeng.2016.06.307. vol. p. 348-353, StrojniškiS.,vestnik - Journal of Mechanical [18] Baglioni, Cianetti, F., Braccesi, C., De Engineering, Micheli, D.M. 62(7-8):463–470, 2016. of N DOF robot arm assigned to (2016).

Multibody modelling

Skrinjar, L. - Slaviˇc, J. - Boltežar, M.

Absolute Nodal Coordinate Formulation in a Pre-Stressed Large-Displacements Dynamical System

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 417-425

milling manufacturing. Dynamic analysis and position errors evaluation. Journal of Mechanical Science and Technology, vol. 30, no. 1, p. 405-420, DOI:10.1007/s12206-015-1245-0.

[19] Manin, L., Braun, S., Hugues, D. (2016). Modelling the belt – envelope interactions during the postal mail conveying by a sorting machine. Strojniški vestnik - Journal of Mechanical Engineering, vol. 62, no. 7-8, p. 463-470, DOI:10.5545/svjme.2016.3770.

[20] Wolfsteiner, P., Pfeiffer, F. (2000). Modeling, simulation, and verification of the transportation process in vibratory feeders.

Journal of Applied Mathematics and Mechanics - Zeitschrift für Angewandte Mathematik und Mechanik, vol. 80, no. 1, p.

35-48, DOI:10.1002/(SICI)1521-4001(200001)80:1<35::AIDZAMM35>3.0.CO;2-X. [21] Bayoumy, A.H., Nada, A.A., Megahed, S.M. (2014). Methods of modeling slope discontinuities in large size wind turbine blades using absolute nodal coordinate formulation.

Proceedings of the Institution of Mechanical Engineers Part K-Journal of Multi-Body Dynamics, vol. 228, no. 3, p. 314-329, DOI:10.1177/1464419314528319.

[22] Čepon, G., Manin, L., Boltežar, M. (2011). Validation of a flexible multibody belt-drive model. Strojniški vestnik - Journal of Mechanical Engineering, vol. 57, no. 7-8, p. 539-546, DOI:10.5545/sv-jme.2010.257.

[23] Langerholc, M., Slavič, J., Boltežar, M. (2013). A thick anisotropic plate element in the framework of an absolute nodal coordinate formulation. Nonlinear Dynamics, vol. 73, no. 1-2, p. 183-198, DOI:10.1007/s11071-013-0778-y.

[24] Shabana, A.A. (1998). Computer implementation of the absolute nodal coordinate formulation for flexible multibody dynamics. Nonlinear Dynamics, vol. 16, no. 3, p. 293-306, DOI:10.1023/A:1008072517368.

[25] Shabana, A.A. (2008). Computational Continuum Mechanics.

Cambridge University Press, Cambridge, DOI:10.1017/ cbo9780511611469.

[26] Shabana, A.A. (1996). Finite element incremental approach and exact rigid body inertia. Journal of Mechanical Design, vol.

118, no. 2, p. 171-178, DOI:10.1115/1.2826866.

[27] Nachbagauer, K., Gruber, P., Gerstmayr, J. (2013). A 3D shear deformable finite element based on the absolute nodal coordinate formulation. In: Samin, J.C., Fisette, P. (eds.) Multibody Dynamics. Computational Methods in Applied Sciences, vol. 28, p. 77-96, Springer, Dordrecht, DOI:10.1007/978-94-007-5404-1_4.

[28] Gerstmayr, J., Irschik, H. (2008). On the correct representation of bending and axial deformation in the absolute nodal coordinate formulation with an elastic line approach. Journal

of Sound and Vibration, vol. 318, p. 461-487, DOI:10.1016/j. jsv.2008.04.019.

[29] Omar, M.A., Shabana, A.A. (2001). A two-dimensional shear deformable beam for large rotation and deformation problems.

Journal of Sound and Vibration, vol. 243, no. 3, p. 565-576, DOI:10.1006/jsvi.2000.3416.

[30] Escalona, J.L. (1998). Co-ordinate formulation to multibody system dynamics. Journal of Sound and Vibration, vol. 214, p.

833-851, DOI:10.1006/jsvi.1998.1563.

[31] Berzeri, M., Shabana, A.A. (2000). Development of simple models for the elastic forces in the absolute nodal co-ordinate formulation. Journal of Sound and Vibration, vol. 235, no. 4, p.

539-565, DOI:10.1006/jsvi.1999.2935.

[32] Maqueda, L.G., Shabana, A.A. (2009). Numerical investigation of the slope discontinuities in large deformation finite element formulations. Nonlinear Dynamics, vol. 58, no. 1-2, p. 23-37, DOI:10.1007/s11071-008-9458-8.

[33] Shabana, A.A. (1997). Definition of the slopes and the finite element absolute nodal coordinate formulation. Multibody System Dynamics, vol. 1, no. 3, p. 339-348, DOI: [34] Shabana, A.A., Hussien, H., Escalona, J.L. (1998). Application of absolute nodal coordinate formulation to large rotation and large deformation problems. Journal of Mechanical Design, vol. 120, no. 2, p. 188-195, DOI:10.1115/1.2826958.

[35] Shabana, A.A. (2009). Computational Dynamics, 3rd Edition.

Wiley, Chichester.

[36] Hussein, B., Negrut, D., Shabana, A.A. (2008). Implicit and explicit integration in the solution of the absolute nodal coordinate differential/algebraic equations. Nonlinear Dynamics, vol. 54, no. 4, p. 283-296, DOI:10.1007/s11071007-9328-9.

[37] Skrinjar, L., Slavič, J., Boltežar, M. (2016). A validated model for a pin-slot clearance joint. Nonlinear Dynamics, vol. 88, no.

1, p. 131-143, DOI:10.1007/s11071-016-3234-y.

[38] Sugiyama, H., Shabana, A.A. (2004). On the use of implicit integration methods and the absolute nodal coordinate formulation in the analysis of elasto-plastic deformation problems. Nonlinear Dynamics, vol. 37, no. 3, p. 245-270, DOI:10.1023/B:NODY.0000044644.53684.5b.

[39] Skrinjar, L., Turel, A., Slavič, J. (2016). DyS. From https:// github.com/ladisk/DyS, accesed on 2017-05-04.

[40] Braccesi, C., Cianetti, F., Tomassini, L. (2016). Fast evaluation of stress state spectral moments. International Journal of Mechanical Sciences, vol. 127, p. 4-9, DOI:10.1016/j. ijmecsci.2016.11.007.

[41] Gorjup, D., Slavič, J., Boltežar, M. (2016). PyDIC. From https:// github.com/ladisk/pyDIC, accesed on 2017-05-04.

Skrinjar, L. – Slavič, J. – Boltežar, M.

425

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 426-438 © 2017 Journal of Mechanical Engineering. All rights reserved.

DOI:10.5545/sv-jme.2016.4248 Original Scientific Paper

Received for review: 2016-12-06 Received revised form: 2017-04-24 Accepted for publication: 2017-05-22

LBM Analysis of Micro-Convection in MHD Nanofluid Flow Arjun, K.S. – Kumar, R. Kozhikkatil Sunil Arjun* - Rakesh Kumar

Department of Mechanical Engineering, Indian Institute of Technology (ISM) Dhanbad, India The lattice Boltzmann-Bhatnagar-Gross-Krook method was used to simulate Al2O3-water nanofluid to find the effects of Reynolds, Rayleigh and Hartmann numbers, slip coefficient, nanoparticle volume fraction and axial distance on forced convection heat transfer in MATLAB. The ranges of studied Reynolds number, Rayleigh number, magnetic field strength, nanoparticle volume concentration and slip coefficient include 200 ≤ Re ≤ 4000; 103 ≤ Ra ≤ 106; 0 ≤ Ha 90; 0 ≤ φ ≤ 2%; 0.005 ≤ B ≤ 0.02, respectively. The results show that increasing Reynolds number and nanoparticle volume fractions improve heat transfer in the 2D microtube under laminar, turbulent, slip and temperature jump boundary conditions. Decreasing the values of slip coefficient decreases the temperature jump and enhances the Nusselt number. A critical value for the Rayleigh number (105) and magnetic field strength (Ha 10) exists, at which the impacts of the solid volume fraction and slip coefficient effects are the most pronounced. The pressure drop shows a similar type of enhancement in magnitude, as observed in the case of the Nusselt number. However, application of nanofluids for low Reynolds numbers is more beneficial, and the effect of volume fractions are more pronounced in comparison to slip coefficient, though the effects are marginal.

Keywords: magneto-hydrodynamics, Nusselt number, lattice Boltzmann method, microtube, slip coefficient Highlights • A novel effective forced convection heat transfer of Alumina-water nanofluid in a microtube was proposed, incorporating the effects of laminar, turbulent, slip and temperature jump boundary conditions.

• Effects of the migration of nanoparticles, Ra, nanoparticles volume fraction, Ha and external magnetic field strength and its effect on the thermal characteristics of the system were analysed using MATLAB based on LBM. • At critical values for Ha and Ra, the impacts of solid volume fraction and slip coefficient are the most pronounced.

• Nanofluid with 2 % volume fraction at low Re and slip coefficient can increase heat transfer.

• Model predictions compared with the earlier experimental studies, proved the validity of the proposed 2D model of fluid flow, useful for qualitative post processing including particle tracing and animations.

0 INTRODUCTION The external magnetic field can suppress or enhance the heat transfer of nanofluid flowing through a micro-channel by adjusting its orientation and magnitude. CFD simulate flow conditions that are not reproducible during experimental tests that are too large, remote, or small. Considering the difficulties of experimental techniques to determine extremely low permeability, the lattice Boltzmann method is easier to implement, computationally efficient over conventional computational fluid dynamics (CFD) and more capable for the simulation of micro, slip and transition regimes, and large complex flows and interactions between different phases, based on its intrinsically mesoscopic kinetic nature. Expensive computation and complex mathematical procedure of molecular dynamics and direct simulation Monte Carlo, as well as the inability of Navier-Stokes for simulation of flow in transition and free molecular regimes, have encouraged the use of lattice Boltzmann methods (LBM) [1]. It is a finite difference method, and the Navier-Stokes equations can be recovered with a proper choice of the collision operator.

426

The information theory with measures to quantify information contents is based on the notion of causal states as stochastic spatio-temporal patterns capturing the dynamics of a local neighbourhood and applicable to structured time-dependent spatial data.

Causal states that feature unusual behaviour over time intervals can then be quantified. When flows become more complex, 2D hydrodynamic modelling provides a better indication of extents and characteristics. 3D models are difficult to create and more difficult to read. 2D model distributes the fluid more effectively throughout the area and has the ability to allow for variance within the XY plane of elevation and material roughness. When it is anticipated that there will be a significant interaction between flow paths or breakout from channels, a 2D hydrodynamic model will provide a more comprehensive indication of characteristics throughout the study area.

Magnetorheological fluid film bearings are evaluated for an SAE-10 W lubricant with controllable properties and magnetic particles aligned into chains, capable of excitement as Magnetorheological fluid, in which a magnetostatic field affects the apparent viscosity [2]. Thermal conductivity enhancement and thermomagnetic convection in devices using magnetic

*Corr. Author’s Address: Indian Institute of Technology (ISM), Dhanbad-826004, India, arjun@mece.ism.ac.in

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 426-438

nanofluids are capable of controlling its flow and heat transfer process via an external magnetic field [3]. The noncovalent surface coating of CNT’s with magnetite nanoparticles composite based magnetorheological fluid possesses an increased sedimentation stability, larger saturation critical stresses, and faster response to time- varying magnetic fields better than ferrofluids and conventional magnetorheological fluids do [4].

The heat transfer of a heat pipe filled with a ferrofluid, stabilized by citrate ions, was enhanced by about 13 % [5]. The heat transfer in the electrorheological fluids considering the microconvection transport is numerically solved on a flat layer, and it is concluded that the internal rotations of elementary particles intensify heat transfer [6]. The increase in particle volume fraction and magnetic field strength may increase the thermal conductivity of the magnetorheological fluid, a smart material with the capability of changing reversibly from liquid to near solid state under the presence of external magnetic fields [7]. Nano-sized magnetic particle-based Ferro Fluid is a magnetic colloidal suspension of two different nano-sized magnetic particles, dispersed in a carrier liquid; it has improved shear thinning, elevated dynamic moduli and thermo-rheological complexity due to a long chain-like structure under the influence of an applied magnetic field [8].

The lattice Boltzmann method [9] originated from Ludwig Boltzmann’s kinetic theory of gases.

Gases/fluids can be imagined as consisting of a large number of small particles with random motions, and the exchange of momentum and energy is achieved through particle streaming and billiard-like particle collision. The number of particles is reduced and confined to the nodes of a lattice in LBM. For a 2D model, known as the D2Q9, a particle is restricted to stream in nine possible directions, including one staying at rest; these velocities are referred to as the microscopic velocities. For each particle on the lattice, a discrete probability distribution function is associated, which describes the probability of streaming in one specific direction. The macroscopic fluid density is defined as the summation of microscopic particle distribution functions and the macroscopic velocity is an average of microscopic velocities, weighted by the distribution functions.

There is no report of magneto-hydro-dynamics (MHD) mixed convective heat transfer of nanofluids in a vertical microtube, except a theoretical study of fully developed convective heat transfer of nanofluid under a uniform magnetic field using a modified Buongiorno’s model [10]. Studies on the convective heat transfer of nanofluids in microducts are limited.

The heat transfer of non-Newtonian nanofluids in a microtube rises with an increase in volume fraction but decreases with an increase in diameter [11].

Theoretical and experimental convective heat transfer analysis of stable magnetic nanofluids in a microtube under an external magnetic field [12] for velocity, temperature, pressure, pressure drop, and flow drag is reported. The well-known differences of microflows from macroscopic ones are slip velocity and temperature jump on the solid–fluid boundaries. For liquid microflows, a slip flow regime can be observed [13] and hence, Navier–Stokes and particle based methods including LBM can be applied. Convective heat transfer characteristics of microscale flows for optimum design of thermal systems operating at low Re are reported [14]. Compressibility is the dominant factor in high-speed microtube flows, and the rarefaction effect is important for low speed flows in microtubes with relatively low Mach number and high Knudsen number [15].

Use of an internal energy distribution function gives stable results [16] as it considers pressure work and viscous heat dissipation [17] and thus the most stable thermal LBM method. Raisi et al. [18] simulated Cu–water nanofluid in a microchannel for both slip and no-slip conditions, ignoring temperature jump effects and applying the classic Navier–Stokes equations. Theoretical results of fluid flow in slip flow regimes or nanofluid flow simulation using LBM in a single or multi-phase mixture model has been reported [19]. Few studies of nanofluid simulation in microchannels using LBM [20] and [21] have ignored slip velocity and temperature jump effects, except in [1]. An accurate understanding of convection heat transfer of nanofluids in a microtube in the slip flow regime and the effect of temperature jump is not yet available in the literature.

Particular attention was given to the effects of temperature jump and slip velocity with different solid volume fractions of nanofluid in the slip flow regime using LBM. We have investigated the effects of migration of nanoparticles and its effect on the thermal characteristics of the system. We have also analysed the effects of governing parameters such as Ra, nanoparticles volume fraction, Ha, and external magnetic field strength. 2D model of fluid flow used in this study can be used for qualitative post processing including particle tracing and animations.

1 PROBLEM AND NUMERICAL DETAILS We have used a steel microtube (thickness 50 µm, length 10 mm and internal diameter 100 µm) as

LBM Analysis of Micro-Convection in MHD Nanofluid Flow

427

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 426-438

shown in Fig. 1 to study numerically, using the double population LBM–BGK (Bhatnagar–Gross– Krook) model. The BGK model is one of the most popular lattice Boltzmann methods for simulating the convection heat transfer. In this, hydrodynamic and thermal parameters of fluid flow are estimated using density momentum (f) and internal energy density (g) distribution functions. A computer simulation has been developed and written using MATLAB software. Most of the existing LBM–BGK models can be viewed as compressible schemes to simulate incompressible fluid flows. The compressible effect might lead to some undesirable errors in numerical simulations. In this paper, an LBM–BGK model without compressible effect is designed for simulating incompressible flows. The incompressible Navier–Stokes equations are recovered from this incompressible model. The results agree well with the analytic solutions and the results of previous studies.

are studied for different values of slip coefficient, B = 0.005 to 0.02 along the axial distance 0.25 to the full length of the duct. Here, τ is the dimensional relaxation time; fi (x, t) is the density distribution function for the particle moving with discrete velocity Ci at position x and time t; fie (x, t) and gie (x, t) are the local equilibrium distribution functions that have an appropriately prescribed functional dependence on the local hydrodynamic properties. C = (3rTm) – 1/2 (Tm is the mean value of temperature). ∆t is the lattice time step which is set to unity, τf and τg are the relaxation times for the flow and temperature fields, respectively.

The hydrodynamic and thermal Boltzmann equations are written as follows [25] and [26].

∂gi ∂g + ciα i = Ω( gi ) − f i Z i = ∂t ∂xa

Fig. 1. Geometry of microtube

Let u and T be the velocity and temperature profiles at the inlet. The wall temperature is set to Tw = 2 Ti with the wall surfaces subjected to a uniform heat flux of 5000 W/m². As the length of the microtube is long enough, we will obtain fully developed hydrodynamic and thermal conditions rapidly in the turbulent regime, and Re is small. Since the tube is small, tube wall thickness is comparable to the inner diameter, and the heat conduction in the wall along the axis direction may be important. The ratio of axial conduction to the tube inside convection is less than 0.02 and thus can neglect it. The simulated nanofluid is a dispersion of nanoparticles of Alumina with a mean diameter of 23 nm in pure water. We assume it pt be an incompressible Newtonian fluid with negligible radiation effect and in laminar and turbulent flow regime. The size of nanoparticles in this study is small enough to be considered as a homogenous flow as reported in the corresponding recent works [22] to [24].

The effect of Re 200 to 4000 with Ra 103 to 6 10 under the influence of Ha 0 to 90 are noted. The effects of the nanoparticle volume fraction (φ = 0 % to 2 %) are investigated for forced convection. The slip velocity, temperature jump, and their effects 428

∂f i ∂f 1 + ciα i = Ω ( f ) = − ( f i − f i e ) , (1) ∂t ∂xα τf

= 0.5 | c − u |2 Ω( f i ) − f i Z i = −

( gi − gie ) − f i Z i , (2) τg

where u = (u, v) and Ω are the macroscopic velocity vector and collision operator, respectively.

We have applied the D2Q9 lattice model (Fig. 2) to the present study. Microscopic discretized velocities are:

i −1 i −1   Ci =  cos π , sin π  , when i = 1 to 4, (3) 2 2  

 π π  i − 5 i − 5 Ci = 2  cos  π +  , sin  π +  , 4 4   2  2  when i = 5 to 8, (4)

C0 = (0, 0). (5)

Fig. 2. D2Q9 lattice

The discrete heat dissipation and equilibrium distribution functions are:

Arjun, K.S. – Kumar, R.

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 426-438

δ u ∂u  Z i = ( ciα − uα )  α + ciα α  , (6) δ t ∂xα  

2  9 ( ci ⋅ u ) 3u 2  f i = ωi ρ 1 + 3 ( ci ⋅ u ) + −  , (7) 2 2   e

4 1 1 i = 0,1,…, 8; ω0 = ; ω1,2,3,4 = ; ω5,6,7 ,8 = , 9 9 36 1  1.5 + 1.5 ( c1,2,3,4 ⋅ u ) +  (8) g1e,2,3,4 = ρ e  , 2 2 9  +4.5 ( c 1, 2 ,3, 4 ⋅ u ) − 1.5u  

g5e,6,7 ,8 =

 3 + 6 ( c5,6,7 ,8 ⋅ u ) +  1  . (9) ρe  2 2 36  +4.5 ( c ⋅ 1 5 u u − . ) 5 6 7 8 , , ,  

We have simulated the collision and streaming steps in LBM to overcome difficulty in solving implicit forms as a modified discrete distribution function for density-momentum ( f̃i ), fi ( x + ci ∆t , t + ∆t ) − fi ( x, t ) =

=−

∆t  fi ( x, t ) − f i e ( x, t )  , (10)  2τ f + 0.5∆t  ∆t ( f i − f i e ), fi = f i + 2τ f

(11)

and that for internal energy ( g̃i ), g i ( x + ci ∆t , t + ∆t ) − g i ( x, t ) = =−

τ g ∆t ∆t  g i ( x, t ) − gie ( x, t )  − f i zi , (12) τ g + 0.5∆t τ g + 0.5∆t g i = gi +

∆t ∆t gi − gie ) + f i zi . (13) ( 2τ g 2

The top and bottom boundaries are adiabatic. We have estimated the unknown inlet and outlet thermal distribution functions, satisfying the equilibrium conditions and improving the accuracy using the known inlet temperature profile and non-equilibrium bounce back model, normal to the boundary [27].

We have an applied specular reflective bounce back model (combination of bounce back and specular boundary condition) to determine the slip velocity in LBM, in this work. For example, for the bottom wall, we have estimated the unknown distribution functions by Eqs. (14) and (15). The tangential momentum accommodation coefficient is a parameter in determining the degree of the slip and represents the average tangential momentum exchange between the fluid molecules and the solid boundary. This coefficient is primarily dependent on the roughness

of the wall surface and its energetic attraction of fluid molecules, and is near unity for most engineering applications [28]. The accommodation coefficient rises as the wall-fluid attraction strength increases [29]. We have chosen the effect of the energy accommodation coefficient in reducing the slip flow as 0.3 corresponding to the temperature values used in this study to maintain the mass flow rate as per [30]. In addition, after fixing the slip coefficient as 0.2 being the bottom plot as per [30], we have obtained the value of accommodation coefficient r, as the sum of the coefficients is unity.

For the different microtubes with various roughnesses, the curves of thermal performance are close to each other. This indicates that although within the 10-mm length range of microtube, the roughness effect on thermal performance exists as an enhancement in nature, flow resistance also increases and the overall thermal performance does not change much. For the same mass flow rate, an increase in roughness will decrease flow area, leading to increased flow velocity and subsequently reduced heat exchange efficiency [31]. The presence of surface roughness reduces boundary slip for flow in microtubes. The decrease in roughness height or increase in Knudsen number can lead to large wall slip for gas flow in microchannels [32]. The microtubes cannot express the comprehensive effects of roughness and boundary slip on MHD nanofluid flow behaviour and heat transfer characteristics.

At low shear rates, the slip length has desired consistency with the Navier model. At high shear rates, the Navier condition fails and boundary condition will be nonlinear even though the liquid remains Newtonian. This phenomenon is just like the Knudsen number rule for linear slip condition of Navier–Stokes equations in dilute gases. f2̃ = f4̃ ,

(14)

̃ = r f7,8 ̃ + (1–r) f̃8,7 . f5,6

(15)

For the D2Q9 model and the horizontal wall boundary with the flow on its upside as shown in Fig. 2, we note that the distribution functions at α is 2, 5 and 6 directions, indicating that the flow field from outside the wall are unknown. The distribution functions at α is 1, 3, 4, 7 and 8 are known because they stream from the points in the flow field. In the diffuse scattering boundary condition, the unknown distribution functions can be determined from the known distribution functions. For the wall boundary as shown in Fig. 2, we have simplified the temperature

LBM Analysis of Micro-Convection in MHD Nanofluid Flow

429

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 426-438

jump for the bottom wall as below in LBM, based on the internal energy distribution function:

g 2,5,6 =

3 e g 2,5,6 ( ρω , uω , eω ) ( g 4 + g 7 + g 8 ) . (16) ρω e

The dot products of the wall normal vector n and the lattice velocities at α is 1 and 3, are zero. We have also calculated the top wall temperature jump similarly.

In previous works in which the temperature jump of nanofluid was not taken into account, Nu = knf / kf (∂θ/∂Y) w with θ = (T − Tc)/(Th − Tc). In the present work, the effect of even a small value of temperature jump results in the temperature gradient between the wall and adjacent fluid layer. At this state, Nu approaches asymptotically a constant value along the microtube walls, the outlet Nu at the outlet domain of a microtube.

DH ( ∂T / ∂y )w Nu = ( knf / k f ) , (17)

Tw − Tbulk

at 107 < Ra <109 for turbulent flow using 2 % Al2O3water nanofluid at Re 200.

Re = ρnf unf DH /µnf .

3 RESULTS AND DISCUSSION The effects of the dimensionless slip coefficient on Nu along the microtube wall are shown in Figs. 3 to 5 at Ra = 104, Re = 200 and B = 0.005 to 0.02 for φ = 0 % to 2 %. Nu has the largest value at the entrance with axial distance 0.25-microtube length and then starts to decrease and Nu increase with φ. We have observed that the increase of solid concentration leads to the enhancement of heat transfer; such enhancements are due to the increase of the effective thermal conductivity with the increase of solid volume fractions of nanoparticles. Significant values of temperature jump were observed, especially around the entrance region, and have the greatest temperature gradient near the wall.

(18)

Calculation of pressure is:

c2 ρ . (19) 3 For natural convection, the Raleigh number is: p=

Ra = gβ L3 Pr/ν2, where Pr = ν/χ .

(20)

In the simulation, Boussinesq approximation applied to the buoyancy force term, as in [33]:

Fi = 3ωi ρ g β∆T . (21)

Fig. 3. Effect of slip coefficient on Nu (φ = 0 %)

The external magnetic field only influences the force term, where new parameter added to the buoyancy force term as:

Fi = Fix + Fiy,

(22)

Fix = 3ωi ρ [A (ν sinθ cosθ – u sin2θ)],

(23)

Fiy = 3ωi ρ [gβ ΔT + A (u sinθ cosθ – ν cos2θ)], (24)

where A is the adjustable coefficient, θ is the magnetic field orientation, β is the thermal expansion coefficient, and g is the gravitational acceleration. The convergence criterion is that the relative changes of the variables between two successive iterations are less than 10−6 %.

We have applied the Large Eddy Simulation model in the LBM, with the total viscosity affecting the relaxation time. The effect of the magnetic field was shown only in the force term, which is added to the collision process and investigated for Ha 0 to 90 430

Fig. 4. Effect of slip coefficient on Nu (φ = 1 %)

Observations show that a larger dimensionless slip coefficient corresponds to larger slip velocity as well as temperature jump on the walls, especially at the entrance region. With a larger dimensionless

Arjun, K.S. – Kumar, R.

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 426-438

slip coefficient, the temperature gradient decreases compared to places where the dimensionless slip coefficient is smaller; consequently, Nu will have a lower value. The temperature gradient between the nanofluid particles on the wall and their neighbouring ones adjacent to the wall decreases with a larger dimensionless slip coefficient, and as a result, Nu would have the lesser value of recent cases. Thus, Nu results obtained near the walls have higher accuracy if we consider the temperature jump. Further, the decrease in Nu is a result of the augmented thermal energy transfer from the wall to the fluid. The nanoparticles hit the wall, absorb thermal energy, reduce the wall temperature, and mix back with the bulk of the fluid. Since the inclusion of nanoparticles enhances the effective thermal conductivity of the nanofluid, the decrease in the Nu is more remarkable where the conduction regime prevails (Ra 104). Thus, the Nu decreases by increasing x, regardless of the volume concentration.

mean nanofluid thermal conductivity when the ratio of Brownian and thermophoretic diffusivities is 0.5, which can be useful for designing nanoparticles for high-energy carriers [37].

We have presented Nu at the outlet with different values of φ, Ra at 103 to 106 and Re 200 in Fig. 6, which indicates the effect of using nanofluid volume fractions and Ra to increase the heat transfer rate.

When the Ra is larger than 105, the Nu near the heated wall decreases significantly. For a fixed Ra, solid volume fractions can affect the enhancement of heat transfer. By adding 2 % Al2O3 nanoparticles by volume, the Nu increases about 17 % at Ra = 104 from 103, a slight decline of enhancement to 8 % at Ra = 105 (but with the highest value of 18.95), but decreases significantly to 33 % when Ra increases to 106. This means that there is a critical value of Ra of Al2O3-water nanofluid for the performance of heat transfer enhancement in terms of the Nu and identified as 105 in this study.

Fig. 5. Effect of slip coefficient on Nu (φ = 2 %)

Fig. 6. Effect of nanofluid volume fractions and Ra on Nu (B = 0.005)

Most of the previous reports ignored the temperature jump [18], [34] and [35] except [36].

Decreasing the values of slip coefficient increases the wall slip velocity, temperature jump values, convective heat transfer coefficient; consequently, the Nu at each axial position as well as for all volume fractions of nanofluid. In the present study, thermal enhancement up to 30 % to 32 % could be achieved by decreasing the slip coefficient with the increase of the volume fraction from 0% to 2%. This finding is in agreement with the results of [36]. In low Re number laminar forced convection flows (Re = 1 to 10), the Brownian force has a significant effect on flow and heat transfer characteristics, thermophoresis may be neglected, and Nu and convection heat transfer coefficient significantly increase [37]. We have captured the maximum Nu based on the bulk

We have observed the suppression of the fluid velocity and hydrodynamic boundary layer thickness owing to the retarding effect of increased Lorenz force, by imposing the magnetic field in terms of increasing Ha at low Ra from 103 to 104.

The intensity of convection weakens significantly, and the domination of the conduction mode of heat transfer makes the isotherms parallel to each other and maximizes stream function value. The Ra compares buoyancy forces to viscous forces. For lower Ra, viscous forces dominate over buoyancy forces to maintain the conduction regime with small and stable disturbances in the fluid and negligible thermosolutal convection effects on macrosegregation. As conduction is the dominant mechanism alone up to Ra 104, Nu is minimum compared to that at Ra 105. As the

LBM Analysis of Micro-Convection in MHD Nanofluid Flow

431

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 426-438

Ra increases up to 105, the role of the convection in heat transfer becomes more significant. Consequently, the thermal boundary layer thickness becomes thinner.

A rise in velocity gradients leads to a shear stress augmentation at the walls, enhancing the pressure drop. The slip velocity has an increasing trend with the velocity gradient. Thus, momentum closer to the walls enhances and leads to a rise in the convective heat transfer compared to lower Ra. There is a critical Rayleigh number for heat transfer enhancement of applying nanofluids; beyond the critical value, the enhancement rate will be reduced. At critical Ra, the thermal diffusivity is high, and heat moves rapidly through it by conduction relative to its volumetric heat capacity. We have obtained the maximum value of Nu at Ra 105 compared to higher Ra. The transition from conduction to convection mode of heat transfer change is noticed at Ra 105 and saturation happens at this Ra, which corresponds to critical Ra. A similar conclusion was obtained in [29].

The mutual effects of the buoyancy and inertia determine flow inside a microtube. These forces run parallel to each other; their directions are opposite for positive values of mixed convective parameters. At Ra of 106, a similar flow pattern as at Ra 105 is observed, but with a greater thermal gradient. The increase in mixed convective parameter intensifies the buoyancy force, which leads to a rise of the momentum near the walls and due to a constant mass flow rate inside the microtube, the velocity in the core region reduces. An increase in mixed convective parameter also reduces the absolute amplitude of the concentration profile in the core region and enhances the concentration near the walls. Above a critical Ra, buoyancy forces become important, disturbances grow, and a dominant convection regime is established. Here, the effects of thermosolutal convection on macro segregation become significant. The momentum in the core region moves toward the walls, so does the nanoparticle concentration. Hence, the near wall velocity gradients increase with increasing Ha, enhancing the slip velocity. An upward trend of the velocity at the wall and a reversed behaviour for that in the core region of the microtube, with increasing mixed convective parameter is established. This causes the temperature near the heated wall to decrease significantly. For Ra 106, Nu decreases in comparison to Ra 105.

The existence of a critical Ra value of 105 for the performance of heat transfer enhancement in terms of the normalized average Nu has been reported [37] and [38] in an enclosure filled with Al2O3-water nanofluid.

Using 1% of Alumina nanoparticles leads to an increase of almost 32% of outlet Nu at Ra = 105.

432

This increase would be over 34 % for using 4 % of Alumina-water nanofluid. Similar conclusions were already reported [30] and [38]. However, we have observed the effect of volume fractions more pronounced than slip coefficient. Flow behaviours and the average rate of heat transfer in terms of the Nu as well as the thermal conductivity of nanofluid is effectively changed with the particle volume fraction and particle diameter with a fixed Ra [39]. The mean Nu increased with increase in Ra [40]. The flow and heat transfer characteristics of Al2O3-water nanofluid in the square cavity are more sensitive to viscosity than to thermal conductivity [41].

The impact of the nanoparticle volume fraction on Nu is small when 104 < Ra > 105 and negligible at all other Ra values of the investigation (Fig. 6).

This indicates that there exist a critical Ra, at which the impact of nanoparticle volume fraction on Nu becomes small, and negligible when Ra is below and above this critical Ra. The profiles of Nux for Ra values 103 to 106 along the microtube wall at Re 200 and B = 0.005 for φ = 0.02 is given in Fig. 7. Nux has larger values at the entrance and then start to decrease asymptotically along the walls and approach constant values for all Ra values. As Ra increases from 103 to 104, Nux increases significantly, then at Ra 105, the enhancement decreases and at Ra 106, Nux values decreases to a minimum and lower than those at Ra 103. Hence, Ra 105 is the critical Ra that determines the impact of nanoparticle volume fraction on Nu at a constant Re and dimensionless slip coefficient.

Fig. 7. Nux at x = 0.2L, B = 0.005 for φ = 0.02

Fig. 8 shows the effect of different Ra and Ha on the Nu at Re 200 using 2 % nanofluid. Nu decreases with increasing Ha but not monotonously. The value of Nu rises in a weak magnetic range up to Ha 10. For Ha above 10, Nu decreases. For a fixed mean velocity of flow, in the perpendicular sectors, the electric

Arjun, K.S. – Kumar, R.

StrojniĹĄki vestnik - Journal of Mechanical Engineering 63(2017)7-8, 426-438

conduction hindered and the flow velocity accelerated while relatively decelerated in the parallel sectors.

Fig. 8. Effect of Ha and Ra (B = 0.005, Ď&#x2020; = 2 %)

Therefore, the local mean temperature in the perpendicular sector is lower than the bulk temperature. The electric current pattern established near the edges between the Hartmann walls and the isothermal walls, which combined with the imposed magnetic field, assists the buoyant flow and contrast the viscous forces exerted by the walls. Only for Ha > 10 did the decelerating effects of the Lorentz forces near the central regions of the walls become dominant and both peak velocities and Nu decreased with Ha. The experimental result of the heat transfer presented the singularity that Nu rises in a weak magnetic flux density, though it decreases with increasing magnetic flux density as a whole trend [42]. Tagawa and Ozoe [43] found that a weak magnetic field (Ha 100 to 200) slightly enhanced heat transfer, causing the average Nu to increase by 5 % to 7 %, and to enhance the peak velocity attained near the hot and cold walls. Tagawa and Ozoe [44] also confirmed the moderate increase in heat transfer for Ha 100 to 200 in liquid gallium at Ra 106. Ha = 10 and Ra = 105 were the best combination with an enhancement up to 3 % Nu. The critical values for the Ra and magnetic field orientation, at which the impacts of the solid volume fraction and magnetic field effects are the most pronounced are reported [30]. The present study is in partial agreement with the finding that when the external magnetic field strength is increased, the average flow drag rises as does the average heat transfer rate [12]. In addition, for smaller nanoparticles, as magnetic field strength intensifies, the peak of the velocity profile near the walls is increased and that at the core region it is decreasing with the enhanced heat transfer rate [10]. The advantage of nanofluids in heat

transfer enhancement in the presence of a magnetic field is reported [44]. As the magnetic field strength intensifies, the peak velocity profile near the walls is increased, and the peak velocity profile in the core region is decreased [10].

When the magnetic field is strengthened (higher Ha), so does the retarding force, while the peak of the velocity profile in the core region decreases and the velocity profile becomes uniform. The momentum in the core region moves toward the walls, near wall velocity gradients increase, enhancing the slip velocity. The fluid temperature also increases in the fluid due to the additional heating owing to the resistance of fluid flow. These result in an increase in heat transfer rate inside the microtube. The stronger the magnetic field strength, particle-particle and particle-wall interaction will be greater leading to greater clogging in the microtube and greater pressure required to move the fluid through the microtube. The effect is greater closer to the inlet.

However, when the flow strength reaches a certain level (Re 2500), the pressure needed to move the fluid through the microtube will reach a saturation value with respect to the corresponding value of Nu (Fig 9). Nu and the pressure drop increases consecutively with Re, with highest Nu enhancement of 610 % at Re 4000 using 2 % Al2O3-water nanofluid in comparison to that at Re 200 using water (Figs.

9 and 10). The application of nanofluids for low Re seems to be highly beneficial in comparison to higher Re. The pressure drop shows a similar enhancement in magnitude only. The average Nu increases with an increase in Re and nanofluid volume concentration as well as a decrease in nanoparticle size [45] and [46].

The enhancement of heat transfer is reported to be around 22 % using the 1 % Al2O3-water nanofluid compared to the water and has a higher friction factor than water does [47].

Fig. 9. Effect of Re on Nu and pressure drop

LBM Analysis of Micro-Convection in MHD Nanofluid Flow

433

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 426-438

4 VALIDATION AND GRID INDEPENDENCE We have conducted mesh testing to ensure grid independence. Calculations of different mesh cases were carried out in 2 % Al2O3-water nanofluid of Ra = 106, B = 0.005 and Re = 50. Having studied grid independence to evaluate the heat transfer of nanofluid in the microtube in terms of the average Nu as shown in Table 1, the grid independence was ensured, and a lattice with 800×14 nodes found appropriate for the next computations.

Table 1. Results of grid independence test Grids (x direction) 700 900 800 700 700 900 800 800 800 900

Grids (y direction) 12 10 12 10 14 14 14 16 18 18

Grid nodes

Average Nusselt No.

8400 9000 9600 7000 9800 12600 11200 12800 14400 16200

16.68662 16.11631 15.45408 14.99470 13.96442 13.95444 13.95020 12.14082 11.46672 10.55592

The dependency of the grid on a microtube is performed and shows an excellent agreement between the Nu results in the Re range relevant for the present study (200 to 4000). The y+ values are much smaller than 1 (0.054, 0.063, and 0.051, respectively). For a laminar flow, the results match very well with each other, under the condition that y+ ≤ 1 recommended for high accuracy. For the 900 × 14 mesh, y+ > 1 is observed for Re around 50000. Around this Reynolds number, the Nu starts diverging from the expected solution and leads to increasingly wrong results, strongly underestimating Nu. The same effect appears for the 800×14 mesh for Re > 41000. The 800×16 mesh shows good agreement with the Nu results until Re > 52000.

For further validation, we have compared the proposed LBM for incompressible fluid simulation results with the experimental results of [48]. Fig. 10 shows that the comparisons are in excellent agreement with the maximum deviation of less than 6 %.

Fig. 11 shows the dimensionless velocity profiles, at different φ = 0 to 0.04 along the microtube wall at x = 0.2 L for B = 0.005 and y = 0 to 1. The fully developed velocity condition is observed after a short entrance length of x = 0.03 L. The slip coefficient leads to generate the slip velocity at Y = 0 and Y = 434

1 which is well obvious in Fig. 11. However, it has the maximum value at the entrance and then decreases along the microtube. In contrary of usual macro scale flows in tubes, the maximum value of velocity (1.48) is less than 1.5 in a fully developed region due to slip velocity on the walls. It can be seen from the figure that with the increase in volume fraction, the velocity curves become closer to the y-axis. The velocity curve becomes shrunk compared with the pure fluid. It is observed that the increase of solid concentration leads to enhanced effective thermal conductivity and the decrease of velocity.

Fig. 10. Comparison of simulated and experimental data [48]

Fig. 11. Velocity profiles at φ = 0 to 0.04

Fig. 12 shows the dimensionless temperature profiles along the microtube wall at x = 0.2 L for B = 0.005 and φ = 0.02 as a function of y. The minimum value of nanofluid temperature (1.99) is less than 2 in the fully developed region due to temperature jump. Fig. 12 represents the temperature jump generated. However, there is a very small value of the temperature jump in the fully developed region.

Arjun, K.S. – Kumar, R.

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 426-438

cavity. Thus, when Ha is increased to 30, it is found that the vortices are no more symmetric. This occurs due to the presence of magnetic field, which gives rise to the Lorentz force and tries to retard the convection.

When Ha is increased to 60 and 90, isotherms are almost parallel that is Hartmann number acts against convection inside the cavity. Increasing Ha further (Ha = 90) reduces the strength of the vortex, and the eyes of the vortices are shifted to the bottom region of the cavity.

5 CONCLUSIONS Fig. 12. Temperature profiles (x = 0.2 L, B = 0.005, φ = 0.02)

Fig. 13. Effect of Ha and Ra on Nu (B = 0.005, φ = 2 %) for turbulent flow

Fig. 13 shows the average Nu for different Ra and Ha for turbulent flow. The trend of enhancement of average Nu with the Ha is not the same at various Ra. Heat transfer augmentation takes place at Ra 107 to 109 by Ha 0 to 10, while it commences dropping from Ha 30 to 90. Similar heat transfer enhancement of a magnetic field at Ha 25 and retarding effect from Ha 25 to 100 at the Ra 107 and 109 in a square cavity was reported [49]. For Ha = 0 and 10, the isotherms pattern is like a plume, indicating strong convection as expected, since Ra is higher than 105. In the absence of a magnetic field (Ha = 0), the isoconcentration curves are symmetric and almost uniformly distributed in the entire enclosure. However, the isoconcentration curves become asymmetric in the presence of a magnetic field. An increased Hartmann number, i.e. a stronger magnetic field, diminishes the flow strength within the cavity. The magnetic susceptibility due to the applied magnetic field over a moving fluid creates a Lorentz force that has the tendency to oppose the flow; consequently, streamlines weaken inside the

The present paper investigates the magnetic field applied to forced convection laminar and turbulent heat transfer in a microtube filled with Al2O3-water nanofluid. This has been simulated by MATLAB based LBM-BGK method. The effects of Re, Ra, nanoparticle volume fraction, Ha, slip coefficient and axial distance on the characteristics of flow and heat transfer have been examined. The major findings of this paper are: • The Nu and pressure drop increase with the Re. However, the application of nanofluids for low Re seems to be highly beneficial in comparison to higher Re. • The increase of volume fraction of Al2O3 nanoparticles in water enhances the heat transfer in the microtube at various Ra. However, there is a critical Ra for heat transfer enhancement while using nanofluids, beyond which the enhancement rate will be reduced. The heat transfer of nanofluid increases with the increase of Ha for a fixed Ra and nanoparticle volume fraction up to a lower Ha and thereafter the heat transfer decreases. A critical lower Ra pronounces the effect of Ha. • The larger value of slip coefficient corresponds to a higher temperature jump and lower heat transfer. Nanofluid with 2 % volume fraction at low values of slip coefficient can increase heat transfer in a microtube. However, the effect of volume fractions more pronounced compared to slip coefficient.

• The impact of nanoparticle volume fraction on Nu is small when 104< Ra >105 and negligible at all other Ra values of the investigation.

• Heat transfer augmentation takes place with turbulent flow at all Ra by Ha up to 10 while it drops from Ha above 30.

• Decreasing the axial distance enhances the Nusselt number.

LBM Analysis of Micro-Convection in MHD Nanofluid Flow

435

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 426-438

7 NOMENCLATURES c ∆x /∆t, Microscopic velocity vector, [ms−1] DH = 2h Hydraulic diameter, [m] e Internal energy density, [J m−3] F External force term, [N] h Height of microtube, [m] k Thermal conductivity coefficient, [Wm−1K−1] Pr Prandtl number, [-] α, χ Thermal diffusivity, [m2 s−1] β Slip/thermal expansion coefficient, [K−1] ν Kinematic viscosity, [m2 s−1] ρ Density, [kg m−3] ∆P Pressure drop, [Pa] ∆x lattice spacing, [-] ∆T Temperature difference , [K] e Equilibrium f Base fluid i Inlet flow, lattice directions α x–y geometry components δu lattice step u, [-] δt Time step t, [-] ωi Weighting factor, [-] 8 REFERENCES [1] Karimipour, A., Esfe, M.H., Safaei, M.R., Semiromi, D.T., Jafari, S., Kazi, S.N. (2014). Mixed convection of copper–water nanofluid in a shallow inclined lid driven cavity using the lattice Boltzmann method. Physica A: Statistical Mechanics and its Applications, vol. 402, p. 150-168, DOI:10.1016/j. physa.2014.01.057.

[2] Bompos, D.A., Nikolakopoulos, P.G. (2016). Experimental and analytical investigations of dynamic characteristics of magnetorheological and nanomagnetorheological fluid film journal bearing. Journal of Vibration and Acoustics, vol. 138, no. 3, p. 1-7, DOI:10.1115/1.4032900.

[3] Nkurikiyimfura, I., Wang, Y., Pan, Z. (2013). Heat transfer enhancement by magnetic nanofluids - A review. Renewable and Sustainable Energy Reviews, vol. 21, p. 548-561, DOI:10.1016/j.rser.2012.12.039.

[4] Samouhos, S., McKinley, G. (2006). Carbon nanotube– magnetite composites, with applications to developing unique magnetorheological fluids. Journal of Fluids Engineering, vol.

129, no. 4, p. 429-437, DOI:10.1115/1.2436581.

[5] Nakatsuka, K., Jeyadevan, B., Neveu, S., Koganezawa, H. (2002). The magnetic fluid for heat transfer applications.

Journal of Magnetism and Magnetic Materials, vol. 252, p.

360-362, DOI:10.1016/S0304-8853(02)00683-2.

[6] Mokeev, А.А., Gubarev, S.A., Korobko, E.V., Bedik, N.A. (2013). Microconvection heat transfer in electrorheological fluids in rotating electric field. Journal of Physics: Conference Series, vol. 412, conf. 1, 13th International Conference on Electrorheological Fluids and Magnetorheological Suspensions, p. 1-13, DOI:10.1088/17426596/412/1/012008.

436

[7] Rahim, M.S.A., Ismail, I. (2015). Review of magnetorheological fluids and nanofluids thermal behaviour. The 3rd International Conference on Mechanical Engineering Research, Pahang, p.

1-10, DOI:10.1088/1757-899X/100/1/012040.

[8] Shah, K., Choi, S.B., Choi, H.J. (2015). Thermorheological properties of nano magnetorheological fluid in dynamic mode: experimental investigation. Smart Materials and Structures, vol. 24, no. 5, DOI:10.1088/0964-1726/24/5/057001.

[9] Begum, R., Basit, M.A. (2008). Lattice Boltzmann Method and its Applications to Fluid Flow Problems. European Journal of Scientific Research, vol. 22, no. 2, p. 216-231.

[10] Malvandi, A., Ganji, D.D. (2014). Magnetohydrodynamic mixed convective flow of Al2O3–water nanofluid inside a vertical microtube. Journal of Magnetism and Magnetic Materials, vol.

369, p. 132-141, DOI:10.1016/j.jmmm.2014.06.037.

[11] Niu, J., Fu, C., Tan, W. (2012). Slip-flow and heat transfer of non-Newtonian nanofluid in a microtube. PLoS ONE, vol. 7, no.

5, p. 1-9, DOI:10.1371/journal.pone.0037274.

[12] Lo, K.J., Weng, H.C. (2015). Convective heat transfer of magnetic nanofluids in a microtube. Smart Science, vol. 3, no.

2, p. 56-64, DOI:10.1080/23080477.2015.11665637.

[13] Goodarzi, M., Safaei, M.R., Karimipour, A., Hooman, K., Dahari, M., Kazi, S.N., Sadeghinezhad, E. (2014). Comparison of the finite volume and lattice Boltzmann methods for solving natural convection heat transfer problems inside cavities and enclosures. Abstract and Applied Analysis, vol. 2014, p. 1-15, DOI:10.1155/2014/762184.

[14] Cetin, B., Zeinali, S. (2014). Analysis of heat transfer and entropy generation for a low-Peclet-number microtube flow using a second-order slip model: an extended-Graetz problem.

Journal of Engineering Mathematics, vol. 89, no. 1, p. 13-25, DOI:10.1007/s10665-014-9704-7.

[15] Tang, K., Huang, J.L., Jin, T., Wu, M.X. (2015). An experimentbased comparative investigation of correlations for microtube gas flow. Sadhana, vol. 40, no. 2, p. 537-547, DOI:10.1007/ s12046-014-0326-6.

[16] He, X., Chen, S., Doolen, G.D. (1998). A novel thermal model for the lattice Boltzmann method in incompressible limit.

Journal of Computational Physics, vol. 146, no. 1, p. 282-300, DOI:10.1006/jcph.1998.6057.

[17] D’Orazio, A., Corcione, M., Celata, G.P. (2004). Application to natural convection enclosed flows of a lattice Boltzmann BGK model coupled with a general-purpose thermal boundary condition. International Journal of Thermal Sciences, vol. 43, no. 6, p. 575-586, DOI:10.1016/j.ijthermalsci.2003.11.002.

[18] Raisi, A., Ghasemi, B., Aminossadati, S.M. (2011). A numerical study on the forced convection of laminar nanofluid in a microchannel with both slip and no-slip conditions. Numerical Heat Transfer, Part A: Applications, vol. 59, no. 2, p. 114-129, DOI:10.1080/10407782.2011.540964.

[19] Guo, Y., Qin, D., Shen, S., Bennacer, R. (2012). Nanofluid multiphase convective heat transfer in closed domain: Simulation with lattice Boltzmann method. International Communications in Heat and Mass Transfer, vol. 39, no. 3, p. 350-354, DOI:10.1016/j.icheatmasstransfer.2011.12.013.

[20] Ay, C., Young, C.-W., Young, C.-F. (2012). Application of lattice Boltzmann method to the fluid analysis in a rectangular micro

Arjun, K.S. – Kumar, R.

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 426-438

channel. Computers & Mathematics with Applications, vol. 64, no. 5, p. 1065-1083, DOI:10.1016/j.camwa.2012.03.025.

[21] Yang, Y.-T., Lai, F.-H. (2011). Numerical study of flow and heat transfer characteristics of alumina-water nanofluids in a microchannel using the lattice Boltzmann method. International Communications in Heat and Mass Transfer, vol. 38, no. 5, p. 607-614, DOI:10.1016/j. icheatmasstransfer.2011.03.010.

[22] Takabi, B., Shokouhmand, H. (2015). Effects of Al2O3-Cu/ water hybrid nanofluid on heat transfer and flow characteristics in turbulent regime. International Journal of Modern Physics C, vol. 26, no. 4, DOI:10.1142/S0129183115500473.

[23] Kakaç, S., Pramuanjaroenkij, A. (2016). Analysis of convective heat transfer enhancement by nanofluids: single-phase and two-phase treatments. Journal of Engineering Physics and Thermophysics, vol. 89, no. 3, p. 758-793, DOI:10.1007/ s10891-016-1437-1.

[24] Takabi, B., Salehi, S. (2014). Augmentation of the heat transfer performance of a sinusoidal corrugated enclosure by employing hybrid nanofluid. Advances in Mechanical Engineering, vol. 6, DOI:10.1155/2014/147059.

[25] Chapman, S., Cowling, T.G. (1999). The Mathematical Theory of Non-uniform Gases. 3rd ed., Cambridge University Press, Cambridge.

[26] Sajjadi, A.H., Kefayati, R. (2015). Lattice Boltzmann simulation of turbulent natural convection in tall enclosures.

Thermal Science, vol. 19, no. 1, p. 155-166, DOI:10.2298/ tsci120105066s.

[27] Alamyane, A.A., Mohamad, A.A. (2010). Simulation of forced convection in a channel with extended surfaces by the lattice Boltzmann method. Computers & Mathematics with Applications, vol. 59, no. 7, p. 2421-2430, DOI:10.1016/j. camwa.2009.08.070.

[28] Arya, G., Chang, H.-C., Maginn, E.J. (2003). Molecular simulations of Knudsen wall-slip: effect of wall morphology.

Molecular Simulation, vol. 29, no. 10-11, p. 697-709, DOI:10.1080/0892702031000103257.

[29] Dellar, P.J. (2002). Lattice kinetic schemes for magnetohydrodynamics. Journal of Computational Physics, vol. 179, no. 1, p. 95-126, DOI:10.1006/jcph.2002.7044.

[30] Succi, S. (2002). Mesoscopic modeling of slip motion at fluidsolid interfaces with heterogeneous catalysis. Physical Review Letters, vol. 89, no. 6, p. 064502-1-064502-4, DOI:10.1103/ PhysRevLett.89.064502.

[31] Xing, Y., Zhi, T., Haiwang, L., Yitu, T. (2016). Experimental investigation of surface roughness effects on flow behavior and heat transfer characteristics for circular microchannels.

Chinese Journal of Aeronautics, vol. 29, no. 6, p. 1575-1581, DOI:10.1016/j.cja.2016.10.006.

[32] Zhang, C., Chen, Y., Deng, Z., Shi, M. (2012). Role of rough surface topography on gas slip flow in microchannels.

Physical Review E, vol. 86, no. 1, p. 016319, DOI:10.1103/ PhysRevE.86.016319.

[33] Aminossadati, S.M., Raisi, A., Ghasemi, B. (2011). Effects of magnetic field on nanofluid forced convection in a partially heated microchannel. International Journal of Non-Linear Mechanics, vol. 46, no. 10, p. 1373-1382, DOI:10.1016/j. ijnonlinmec.2011.07.013.

[34] Kalteh, M., Abbassi, A., Saffar-Avval, M., Harting, J. (2011).

Eulerian–Eulerian two phase numerical simulation of nanofluid laminar forced convection in a microchannel.

International Journal of Heat and Fluid Flow, vol. 32, no. 1, p.

107-116, DOI:10.1016/j.ijheatfluidflow.2010.08.001.

[35] Karimipour, A., Nezhad, A.H., D’Orazio, A., Esfe, M.H., Safaei, M.R., Shirani, E. (2015). Simulation of copper–water nanofluid in a microchannel in slip flow regime using the lattice Boltzmann method. European Journal of Mechanics - B/Fluids, vol. 49, p. 89-99, DOI:10.1016/j.euromechflu.2014.08.004.

[36] Ahmed, M., Eslamian, M. (2015). Laminar forced convection of a nanofluid in a microchannel: effect of flow inertia and external forces on heat transfer and fluid flow characteristics.

Applied Thermal Engineering, vol. 78, p. 326-338, DOI:10.1016/j.euromechflu.2014.08.004.

[37] Yang, C., Li, W., Sano, Y., Mochizuki, M., Nakayama, A. (2013).

On the anomalous convective heat transfer enhancement in nanofluids: a theoretical answer to the nanofluids controversy.

Journal of Heat Transfer, vol. 135, no. 5, p. 545041-545049, DOI:10.1115/1.4023539.

[38] Zhou, W., Yan, Y. (2014). Lattice Boltzmann simulation of magnetic field effects on nanofluid. 4th Micro and Nano Flows Conference. University College London, London.

[39] Taher, M.A., Lee, Y.W., Kim, H.D. (2013). Heat transfer enhancement of Cu-H2O nanofluid with internal heat generation using LBM. Open Journal of Fluid Dynamics, vol. 3, p. 92-99, DOI:10.4236/ojfd.2013.32A015.

[40] Mliki, B., Abbassi, M.A., Guedri, K., Omri, A. (2015). Lattice Boltzmann simulation of natural convection in an L-shaped enclosure in the presence of nanofluid. Engineering Science and Technology, an International Journal, vol. 18, no. 3, p.

503-511, DOI:10.1016/j.jestch.2015.04.008.

[41] He, Y., Qi, C., Hu, Y., Qin, B., Li, F., Ding, Y. (2011). Lattice Boltzmann simulation of alumina-water nanofluid in a square cavity. Nanoscale Research Letters, vol. 6, p. 184-191, DOI:10.1186/1556-276X-6-184.

[42] Miyazaki, K., Inouet, H., Kimotott, T., Yamashita, S., Inoue, S., Yamaoka, N. (1986). Heat transfer and temperature fluctuation of lithium flowing under transverse magnetic field.

Journal of Nuclear Science and Technology, vol. 23, no. 7, p.

582-593, DOI:10.1080/18811248.1986.9735026.

[43] Tagawa, T., Ozoe, H. (1997). Enhancement of heat transfer rate by application of a static magnetic field during natural convection of liquid metal in a cube. Journal of Heat Transfer, vol. 119, no. 2, p. 265-271, DOI:10.1115/1.2824219.

[44] Tagawa, T., Ozoe, H. (1998). Enhanced heat transfer rate measured for natural convection in liquid gallium in a cubical enclosure under a static magnetic field.

Journal of Heat Transfer, vol. 120, no. 4, p. 1027-1032, DOI:10.1115/1.2825886.

[45] Malvandi, A., Safaei, M.R., Kaffash, M.H., Ganji, D.D. (2015).

MHD mixed convection in a vertical annulus filled with Al2O3– water Nanofluid considering nanoparticle migration. Journal of Magnetism and Magnetic Materials, vol. 382, p. 296-306, DOI:10.1016/j.jmmm.2015.01.060.

[46] Kalteh, M., Abbassi, A., Saffar-Avval, M., Frijns, A., Darhuber, A. Harting, J. (2012). Experimental and numerical investigation of nanofluid forced convection inside a wide microchannel

LBM Analysis of Micro-Convection in MHD Nanofluid Flow

437

StrojniĹĄki vestnik - Journal of Mechanical Engineering 63(2017)7-8, 426-438

heat sink. Applied Thermal Engineering, vol. 36, p. 260-268, DOI:10.1016/j.applthermaleng.2011.10.023.

[47] Salman, B.H., Mohammed, H.A., Munisamy, K.M., Kherbeet, A.S. (2014). Three-dimensional numerical investigation of nanofluids flow in microtube with different values of heat flux.

Heat Transfer-Asian Research, vol. 44, no. 7, p. 599-619, DOI:10.1002/htj.21139.

[48] Salman, B.H., Mohammed, H.A., Kherbeet, A.S. (2014).

Numerical and experimental investigation of heat transfer

438

enhancement in a microtube using nanofluids. International Communications in Heat and Mass Transfer, vol. 59, p. 88100, DOI:10.1016/j.icheatmasstransfer.2014.10.017.

[49] Sajjadi, H., Kefayati, G.H.R. (2014). MHD turbulent and laminar natural convection in a square cavity utilizing lattice Boltzmann method. Heat Transfer-Asian Research, vol. 45, no.

8, p. 795-814, DOI:10.1002/htj.21191.

Arjun, K.S. â&#x20AC;&#x201C; Kumar, R.

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 439-446 © 2017 Journal of Mechanical Engineering. All rights reserved.

DOI:10.5545/sv-jme.2016.4276 Original Scientific Paper

Received for review: 2016-12-15 Received revised form: 2017-05-06 Accepted for publication: 2017-06-06

Thermal Optimization and Comparison of Geometric Parameters of Rectangular and Triangular Fins with Constant Surfacing Bunjaku, F. – Filkoski, R.V. – Sahiti, N. Florent Bunjaku1 – Risto V. Filkoski2 – Naser Sahiti3,*

1 University

of Prishtina “Hasan Prishtina”, Faculty of Education, Kosova “Sts Cyril and Methodius”, Faculty of Mechanical Engineering, Macedonia 3 University of Prishtina “Hasan Prishtina”, Faculty of Mechanical Engineering, Kosova 2 University

This paper presents an optimization model of fins of rectangular and triangular profiles, based on a constant value of the transverse cutting surface, as well as the optimization of the ratio of efficiency of both fin profiles. The optimization model is based on the analytical and numerical simulation of the heat flux through fins in order to derive relevant thermo-physical parameters of the investigated fin profiles.

The optimization of both fin profiles is carried out for different fin materials based on constant heat transfer coefficient and for different fin materials based on variable heat flux. The efficiency of fins as relevant fin goodness parameter is also analysed and the optimal values of the ratio of fin efficiency of both profiles is graphically presented and the optimal value estimated. Numerical simulation of fin models is carried out by using ANSYS/Fluent software.

Keywords: fins, heat flux, optimisation, geometrical parameters, rectangular and triangular profile, fin efficiency Highlights • This paper presents an analytical and numerical analysis of heat transfer through finned heat exchanging surfaces.

• The model of optimisation of the finned systems is based on the determination of optimal dimensions of fin profile related to maximal values of heat flux through fins.

• Optimal fin thickness corresponding to the maximal heat flux as function of fin conductivity and heat transfer coefficient are presented.

• Examples of temperature fields of rectangular and triangular fins are presented.

• The efficiency of the rectangular and triangular fins is analysed, and the optimal value of corresponding ratio is presented.

0 INTRODUCTION Substantial improvements in energy efficiency in many industrial fields can be achieved by employing more effective heat transfer surfaces. The most effective heat transfer enhancement can be achieved by using fins as elements for heat transfer surface area extension [1] and [2]. Kraus et al. [3] have offered a detailed discussion of the mathematical models related to the optimization of finned systems with various profiles, such as rectangular, triangular, etc. Mokheimer [4] has analysed the efficiency of the fins for the constant and variable heat transfer coefficient for various profiles depending on the local temperature. The results have shown that the assumption of constant heat transfer coefficient through fins, results in a considerable underestimation of the fin efficiency.

Pardeep et al. [5] have estimated the heat flux of a cylindrical heat exchanger with a system of rectangular and triangular fins and the comparison of temperature surfaces was carried out depending on the length of the fins. Moitsheki et al. [6] have developed a model that describes the profile of the temperature of one longitudinal fin with various profiles, as well

as the effects of thermal gradient conductivity, thermal conduction, and the coefficient of heat transfer.

Toner and Kilic [7] have numerically analysed the temperature and the efficiency of rectangular and triangular fins, and the optimal dimensions have been calculated as a function of the Biot number.

Lindstedt and Kaj [8] have analysed analytically and numerically the thermal performance for some shapes of fins, such as rectangular, triangular and trapezoidal, and the comparisons between fins have been presented. A particularly interesting model related to the optimization of finned surfaces through so-called thermal transmitting matrix was presented

by Arthur [9]. In the work of Farzaneh et al. [10], a multi-objective optimization model is presented.

By using the genetic algorithm, the optimization of geometrical parameters of the fins was done for six various profiles. Taler and Duda [11] and Taler [12] have presented two-dimensional temperature distribution with analytical solutions for various profiles. Rek et al. [13] have used CFD simulation to analyse a heating oven, since the CFD is a common numerical technique, which is applied in many simulations in different research studies. Bonefačić et al. [14] have applied CFD software for modelling of

*Corr. Author’s Address: University of Prishtina, Faculty of Mechanical Engineering, Prishtina, naser.sahiti@uni-pr.edu

439

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 439-446

an empty room without internal heat sources, with the aim of predicting heat balance and thermal comfort parameters. The study of Raisi [15] investigates natural convection cooling of a heat source that produces uniform heat flux, placed on the bottom of a cavity, filled with non-Newtonian power-law fluid. Filkoski et al. [16] have presented several case studies of analysis of different thermal systems with the application of the CFD technique, emphasizing its potential for research and for engineering educational purposes, which is demonstrated with practical examples and interpretation of test results in connection with certain specific issues.

The current paper provides an optimization of cross cutting geometry of rectangular and triangular fin forms in order to find the optimal geometry related to maximal heat flux. The optimization is based on analytical and numerical analysis based on CFD code ANSYS/Fluent and corresponding results are presented in tables and figures. The optimization is carried out for different fin materials and different heat transfer coefficient for both fin types. Further, the authors provided an optimization of the ratio of fin efficiency of both fin profiles as a function of fin characteristic parameter N. To the best knowledge of the authors, analysis of various aspects of fins in the literature has been carried out in an essentially analytical way.

d 2θ

dx

2 OPTIMIZATION MODEL FOR RECTANGULAR FINS The primary issue concerning the effectiveness of the heat exchangers is the methodology of intensifying the heat transfer, which would lead to optimal heat exchanger design.

The differential equation that describes the phenomenon of heat transfer through fins (Fig. 1) is given in the following form: 440

− m 2θ = 0, (1)

where θ = T – Tfluid is the temperature difference between the temperature of fins’ surface (T) and the temperature of the surrounding air (Tfluid), m = 2h / kδ the characteristic finned parameter, h the heat transfer coefficient and k the thermal conductivity of the fin material.

The boundary conditions of the problem are:

θ = θb

for

x = b;

 ∂θ  −k   = h2θtip  ∂x  x=0

1 COMPUTATIONAL MESH AND SIMULATION PROCEDURE For the current computational model, a fine structured grid was created with elements numbering between 4005 and 6732 for the rectangular fins, and between 3298 and 4094 for triangular fins. As a solution method, the SIMPLE algorithm for velocity-pressure coupling was employed. The pressure field was discretized with a second order scheme whereas for the velocity and temperature field the second order upwind discretization scheme was applied. The convergence criteria for residuals of continuity and momentum equations was set to 10-6 and 10-8 for the energy equation.

2

for

x = 0. (2)

Fig. 1. The profile of rectangular fin

With θb is given the temperature difference at the base of the fin; h2 and θtip respectively are the heat transfer coefficient and the temperature difference at the top of the fin.

By considering the boundary conditions in Eq. (2) and taking h2 = 0 for simplifying the problem, i.e. the thermal flux at the top of the fin is neglected, the solution of the differential equation, Eq. (1), based on [3], is obtained in this form:

θ ( x) =

θb cosh mx , (3) cosh mb

 dθ  Q 0 = −k ⋅ S   = kδ mLθb tanh(mb). (4)  dx  x=0

By replacing b and m in Eq. (4), the following is obtained:

(

)

Q 0 = A ⋅ δ 1/ 2 ⋅ tanh B ⋅ δ −3/ 2 , (5)

where the parameters A and B are defined as:

Bunjaku, F. – Filkoski, R.V. – Sahiti, N.

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 439-446

A = θ b L 2h ⋅ k ; B = S

2h . (6) k

According to the adopted optimisation model, for (dQ0/dδ) = 0, based on [17], the following transcendental equation is obtained:

tanh ( u ) − 3u + 3u ⋅ tanh 2 ( u ) = 0, (7)

where u=Bδ–3/2.

The solution of Eq. (7) is uopt = 1.419, and for the optimal thickness and height of a rectangular fin the following applies: 1/ 3

δ opt ,

 S2 ⋅h  =   k 

 S ⋅k  ; bopt , =   . (8)  h  1/ 3

In the following, the optimisation of the considered finned system is implemented, by adopting the surface of transversal cutting of the fin (S = δb) as a constant value, and by simulating corresponding values of the heat flux through fins of for various materials (steel, aluminium and copper) and various ratios of δ and b. The results for heat flux are presented in terms of fin thickness δ (Fig. 2).

geometry depends only on fin thickness (fin height b) whereas fin efficiency depends on fin thickness but also on fin material. While increasing of fin efficiency with increasing of fin thickness (reducing fin height) for copper is faster for low values and, in that way, reaches faster an apparently constant value, increasing of fin efficiency over fin thickness for steel is slower.

This means that in the case of copper fins, benefits related to increasing fin efficiency with increasing fin thickness diminishes faster due to reducing of convective heat transfer area, and this means that the maximal value of heat transfer flux is faster achieved for fins of cupper material compared with fins of materials with lower conductivity (aluminium, steel) A further analysis performed in the present work is on identifying the optimal thickness of the fin as a function of the heat transfer coefficient (Fig. 3). In this case, the subject of analysis is only the aluminium finned heat transfer surface, given that the analysis would be the same for other types of materials.

Fig. 3. Heat flux through rectangular fins as function of thickness (δ) for the Aluminium material Fig. 2. Heat flux through rectangular fins as function of the fin conductivity (k) and fin thickness (δ)

From the diagram in Fig. 2, it can be noted that the generated heat flux increases at the beginning, up to a maximal value and later it decreases, by increasing the thickness of the fin (δ). Furthermore, the diagram shows that for all three types of fin materials (steel, aluminium, copper) the optimal thickness of the fin profile can be identified. Regarding the graph in Fig. 2, it should be noted that maximal values for heat flux in Figs. 2 and 7 are related to a trade-off between the convective heat transfer area and fin efficiency.

It should also be noted that for constant fin length (L) convective heat transfer area for particular fin

From Fig. 3, it can be noted that for the same value of the fin thickness (δ) for fins characterized with a higher convection heat transfer coefficient (h), higher values for the heat flux are obtained.

The efficiency of the finned surface is defined as the ratio between the actual heat flux and heat flux that could be ideally obtained. For the rectangular fin, the efficiency is determined according to the following expression:

Q kmδθb tanh(mb) tanh( N ) , (9) η =  re = = Qid hbθb N

where N = mb = 2h / kδ ⋅ b is the characteristic dimensionless finned parameter.

Thermal Optimization and Comparison of Geometric Parameters of Rectangular and Triangular Fins with Constant Surfacing

441

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 439-446

Values obtained by numerical simulations and analytical values for various materials are presented in Table 1 and Fig. 4.

Table 1. Analytical and numerical values for rectangular fins Rect.

Steel

Aluminium

Copper

k = 16.27 W/(mK) k = 202.4 W/(mK) k = 387.6 W/(mK) h = 25 W/(m2K) h = 25 W/(m2K) h = 25 W/(m2K) Q [W] Q [W] Q [W] No Fins’ dim. [mm]

Anal.

Num

Anal.

Num

Anal.

Num

1

10.82

10.80

38.15

38.22

52.47

52.59

1 x 250

2 1.75 x 143 14.32

14.34

47.29

47.53

58.96

59.34

3

15.35

47.80

48.11

57.27

57.70

2 x 125

15.31

4 2.5 x 100

17.09

17.16

46.13

46.56

51.91

52.44

5

20.87

21.17

30.14

30.82

30.77

31.48

5 x 50

6 7.5 x 33.4 18.84

19.35

21.92

22.68

22.08

22.85

7

17.09

17.87

18.60

17.93

18.67

10 x 25

16.51

Fig. 5 presents a temperature profile of an Al rectangular fin, carried out by means of ANSYS/ Fluent software. Similar temperature profiles were obtained in the other cases that are presented in Table 1. The simulation for other materials (steel and copper) is done in the same way, and the results are presented in Table 1.

3 OPTIMIZATION MODEL FOR TRIANGULAR FINS We the triangular fins, we deal with changeable fin profile (Fig. 6). In the current analysis, the fin temperature gradient change in the orthogonal direction of the transversal cut is neglected, meaning that a one-dimensional temperature field within the fin profile is analysed.

Fig. 6. The profile of a triangular fin

Fig. 4. Comparison of analytical and numerical results for heat flux for various materials of rectangular fins

From Fig. 4 it is obvious that a better results agreement is achieved for fins with smaller thicknesses, whereas with increasing of fin thickness the results agreement is lower. This is because for the analytical solution the problem is considered to be one dimensional whereas a three-dimensional model is applied for the numerical solution.

The differential equation describing the heat transfer through triangular fins, is given in the following form:

x

d 2θ dθ + − m 2bθ = 0, (10) dx 2 dx

where the characteristic finned parameter (m) is defined according to [3], while b is the fin height.

The boundary conditions that apply are:

θ = θb

for

x = b,

 ∂θ  −k   = 0 for  ∂x  x=0

x = 0. (11)

Eq. (10), is a modified Bessel differential equation which solution is:

Fig. 5. Numerical prediction of temperature profile of rectangular fin of the Al material by taking the constant surface S = 0.00025 m2

442

θ = C1I 0 (2m bx ) + C2 K 0 ( 2m bx ), (12)

where I 0 (2m bx ) is a modified function of the first type, of the sequence 0 and with the module 2m bx ,

Bunjaku, F. – Filkoski, R.V. – Sahiti, N.

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 439-446

while K 0 (2m bx ) is a modified function of the second type, of the sequence 0 and with modulation 2m bx .

Integration constants C1 and C2 are determined as per boundary conditions:

for

for

dθ = 0, dx x = b is θ = θb . (13)

x = 0 is

The first boundary condition means that the thermal flux at the top of the trapezoidal fin can be ignored, while the second boundary condition shows that the temperature difference at the base of the fin is equal to θb.

By replacement of values of constants C1 and C2 in Eq. (12) following form of the expression for the temperature field of the triangular fin is obtained:

θ ( x) = θb

I 0 (2m bx ) . (14) I 0 (2mb)

the triangular fin model is implemented by adopting the fin profile surface S = δb/2, as a constant surface, by simulating respective values of the heat flux for various materials (steel, aluminium, copper).

As in the case of the respective rectangular models, it can be noted that, by increasing the fin thickness (δ), the heat flux through fins is increased up to a maximal value and then it is decreased, Fig. 7.

Further, the graphical presentation of the behaviour of heat flux for all three types of materials shows that in all the cases, the optimal fin thickness can be clearly identified.

Again, in similarity to analyses of rectangular fin profile, the optimal triangular fin thickness is presented as a function of the heat transfer coefficient (Fig. 8). In the corresponding case, the results only for Al fins are presented, since the analyses of finned surfaces made from other materials can be performed in the same way.

The heat flux through triangular fin may be expressed by:

2hLθb ⋅ I1 (2mb)  dθ  Q = k ⋅ S  . (15)  = m ⋅ I 0 (2mb)  dx  x=b The optimal thickness of trangular fin is estimated based on methodology similar to that used for rectangular fins. The surface of transverse cutting of the fin is S = δb/2 and by replacing the fin height b = 2S/δ in Eq. (15), the following expression is obtained:

−3/ 2

I (B ⋅δ ) Q = A ⋅ δ 1/ 2 ⋅ 1 , (16) I 0 ( B ⋅ δ −3/ 2 )

Fig. 7. Heat flux through triangular fins as function of the fin conductivity (k) and fin thickness (δ)

where:

A = L ⋅ θb 2hk ; B = 4 S 2h / k . (17)

According to the adopted optimisation model, for (dQ0 / dδ) = 0 based on [17], following transcendental equation is obtained:

4 I1 (u ) ⋅ I 0 (u ) − 3uI 02 (u ) + 3uI12 (u ) = 0. (18)

By solving this equation, the optimal value of the variable u is found to be uopt=2.619.

Hence, following optimal dimensions of the triangular fin are obtained: 1/ 3

δ opt , ∆

1/ 3  S2 ⋅h   S ⋅k  b = 1.671 ; . = 1 197 opt , ∆  h  . (19)  k     

In the following, similarly to the previously presented optimization model of the rectangular fins,

Fig. 8. Heat flux through triangular fins as function of thickness (δ)

Values obtained by numerical simulations and analytical values for various materials are presented in Table 2 and Fig. 9.

Thermal Optimization and Comparison of Geometric Parameters of Rectangular and Triangular Fins with Constant Surfacing

443

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 439-446

Table 2. Analytical and numerical values for triangular fin Steel Tria.

No 1 2 3 4 5

Fins’ dim. [mm] 2x125 2.5x100 5x50 7.5x33.4 10x25

Aluminium

Copper

k = 16.27 W/(mK) k = 202.4 W/(mK) k = 387.6 W/(mK) h = 25 W/(m2K) h = 25 W/(m2K) h = 25 W/(m2K) Q [W] Q [W] Q [W] Anal.

Num.

Anal.

Num.

Anal.

Num.

14.47 15.84 18.46 16.50 13.72

14.49 15.87 18.67 16.90 14.29

42.77 42.00 28.29 19.64 14.89

42.96 42.24 28.66 20.16 15.54

52.23 48.45 29.07 19.81 14.94

52.46 48.74 29.46 20.34 15.59

Fig. 10. Numerical presentation of temperature field in triangular fin for Aluminium material by taking the constant surface S = 0.000125 m2

4 OPTIMIZATION OF THE RATIO OF EFFICIENCY OF TRIANGULAR AND RECTANGULAR FIN PROFILES From Eq. (9) and (20), the expression for the ratio of efficiency of triangular and rectangular fin profiles is derived as:

η∆ I (2 N ) 1 = ⋅ 1 . (21) η tanh( N ) I 0 (2 N )

Minimal value of the mentioned ratio is determined according to the following relation:

Fig. 9. Comparison of analytical and numerical results for heat flux for various materials of triangular fins

The same explanation regarding matching of values obtained analytically and numerically, provided in relation to Fig. 4, is valid also for Fig. 9.

The temperature profile resulting from the heat flux transferred through the Aluminium fins, by changing the geometrical parameters of the fin profile, but by keeping the transversal surface of the fin constant, is presented in Fig. 10. The same methodology is completely applicable for analysis of fins of other materials presented in Table 2 and Fig. 9.

Fig. 10 presents the temperature field obtained from numerical simulation by application of the programme ANSYS/Fluent for the Aluminium fin models, as for the conditions given in Table 2. The results obtained with the CFD simulations of the finned surfaces of other materials are similar and in the frame of the expectations.

The efficiency of the finned heat exchanging surface with triangular fin profile is given with the following relation:

444

η=

1 I1 (2 N ) ⋅ . (20) N I 0 (2 N )

η  d  ∆  tanh( N ) I (2 N )(2 I (2 N ) − I1 (2 N ) ) 0 0  η  = N − 2 dN tanh ( N ) I 02 (2 N ) I1 (2 N ) (1 − tanh 2 ( N )) I 0 (2 N ) + 2 tanh( N ) I1 (2 N )  tanh 2 ( N ) I 02 (2 N )

= 0. (22)

The extreme point of this ratio depending on the characteristic finned parameter N is determined via the graphical solution of the transcendental Eq. (22).

Fig. 11 shows that for the value N = 1.701, the first derivate of this ratio is equal to zero.

Fig. 11. Graphical solution of the transcendental Eq. (22)

The minimal value of the ratio of fin efficiencies for the characteristic finned parameter N = 1.701 is:

Bunjaku, F. – Filkoski, R.V. – Sahiti, N.

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 439-446

 η∆    = 0.89 for N = 1.701. (23)  η min The graphical presentation of efficiencies of rectangular and triangular fin profiles, as well as the ratio of both efficiencies, is provided in Fig. 2.

Fig. 12. Comparison of the fin efficiency of analysed fins

From Fig. 12, it can be noted that the efficiency of rectangular fins is higher than the efficiency of the triangular fins, but from the view point of the heat flux transfer and the compactness of the design the triangular fin profiles are more favourable.

5 CONCLUSIONS This paper provides the results of optimization of the heat transfer rate of rectangular and triangular fin profiles, in terms of estimation of the optimal fin thickness and fin height. The optimization of geometrical parameters of the finned heat exchanging surfaces for various fin models is carried out by taking constant values of the surface of transversal cutting of the fins, respectively of the volume of fins of various materials. For both fins of rectangular and triangular profiles analysed, and for different fin materials, optimal thickness and height are identified, respectively.

Optimal fin thickness for various fin models and materials (steel, aluminium and copper) is presented in tables and figures. It may be concluded that for optimal thickness of the fins, the heat flux through rectangular fins is higher for 11 % to 13 % compared to that through triangular fins, depending on the fin material, while the volume of rectangular fins is two times larger than the volume of the triangular fins. This means that the major part of heat flux is transferred from the fin part close to fins base since

the influence of the fin convection area fare from the fin base is less effective.

The current optimisation model based on adaption of S = const., respectively the comparison of Eq. (8) and Eq. (19) indicates that the ratio of optimal thickness of the analysed fin profiles is (δopt,Δ/δopt,□) = 1.671, while the ratio of optimal fin heights is (bopt,Δ/bopt,□) = 1.197. The optimal geometrical parameters of the fins determined here might serve as a practical tool for engineers involved in designing of fined heat transfer surfaces.

In the current paper, it is also shown that the ratio of the efficiency of triangular and rectangular fins reaches a minimal value for a certain value of the characteristic parameter of the finned N. Finally, it may be concluded that both optimisation models are very important because they can be used to estimate the optimal geometry of fin profiles, which would result in the highest heat flux through fins for a given fin volume, given fin material expenditure.

6 NOMENCLATURES h b I k L m N S T

heat transfer coefficient, [W/(m2K)] fin height, [m] modified Bessel function of the first kind thermal conductivity, [W/(mK)] fin length, [m] fin performance parameter, [m−1] characteristic parameters of the fin cross-sectional or profile area, [m2] temperature, [K]

Greek symbols δ fin thickness, [m] θ temperature difference [K] φ fin effectiveness η fin efficiency Subscripts b base of fin fluid surrounding air re real id ideal Δ triangle form □ rectangular form 7 REFERENCES [1] Sahiti, N. (2015). Interrelation between pin length and heat exchanger performance. Applied Thermal Engineering, vol. 91, p. 946-952, DOI:10.1016/j.applthermaleng.2015.08.089.

Thermal Optimization and Comparison of Geometric Parameters of Rectangular and Triangular Fins with Constant Surfacing

445

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 439-446

[2] Sahiti, N., Bunjaku, F., Krasniqi, D. (2013). Assessment of single phase convection heat transfer enhancement. Journal of Trends and the Development of Machinery and Associated Technology, vol. 17, no. 1, p. 133-136.

[3] Kraus, A., Aziz, A., Welty, J. (2002). Extended Surface Heat Transfer. John Wiley & Sons, New York.

[4] Mokheimer, E.M. (2003). Heat transfer from extended surfaces subject to variable heat transfer coefficient. Heat and Mass Transfer, vol. 39, no. 2, p. 131-138, DOI:10.1007/ s00231-002-0338-3.

[5] Pardeep, S., Harvinder, l., Baljit Singh, U. (2014). Design and Analysis for Heat Transfer through Fin with Extensions.

International Journal of Innovative Research in Science, Engineering and Technology, vol. 3, no. 5, p. 12054-12061.

[6] Moitsheki, R.J., Rashidi, M.M., Basiriparsa, A. (2015). Analytical solution and numerical simulation for one-dimensional steady nonlinear heat conduction in a longitudinal radial fin with various profiles. Heat Transfer—Asian Research, vol. 44, no. 1, p. 20-38, DOI:10.1002/htj.21104.

[7] Toner, M., Kilic, A. Onat, K. (1983). Comparison of rectangular and triangular fins when condensation occurs. Wärme - und Stoffübertragung, vol. 17, no. 2, p. 65-72, DOI:10.1007/ BF01007220.

[8] Lindstedt, M., Lampio, K., Karvinen, R. (2015). Optimal shapes of straight fins and finned heat sinks. Journal of Heat Transfer, vol. 137, no. 6, p. 061006, DOI:10.1115/1.4029854.

[9] Snider, A.D.S. (1982). Mathematical techniques in extended surface analysis. Mathematical Modelling, vol. 3, no. 3, p.

191-206, DOI:10.1016/0270-0255(82)90024-0.

[10] Farzaneh Hajabdollahi, F., Rafsanjani, H.H.. Hajabdollahi, Z., Hamidi, Y. (2012). Multi-objective optimization of pin fin to

446

determine the optimal fin geometry using genetic algorithm.

Applied Mathematical Modelling, vol. 36, no. 1, p. 244-254, DOI:10.1016/j.apm.2011.05.048.

[11] Taler, J., Duda, P. (2006). Solving Direct and Inverse Heat Conduction Problems. Springer, Berlin, DOI:10.1007/978-3540-33471-2.

[12] Taler, D. (2014). Fins of straight and circular geometry, Encyclopedia of Thermal Stresses, (Hetnarski, R.B., ed), Springer, Dordrecht, p. 1670-1683, DOI:10.1007/978-94-0072739-7_383.

[13] Rek, Z., Rudolf, M., Zun, I. (2012). Application of CFD simulation in the development of a new generation heating oven. Strojniški vestnik - Journal of Mechanical Engineering, vol. 58, no. 2, 134-144, DOI:10.5545/sv-jme.2011.163.

[14] Bonefacić, I., Wolf, I., Franković, B. (2015). Numerical modelling of thermal comfort conditions in an indoor space with solar radiation sources. Strojniški vestnik - Journal of Mechanical Engineering, vol. 61, no. 11, 641-650, DOI:10.5545/sv-jme.2015.2493.

[15] Raisi, A. (2016). Natural convection of non-Newtonian fluids in a square cavity with a localized heat source. Strojniški vestnik - Journal of Mechanical Engineering, vol. 62, no. 10, p. 553564, DOI:10.5545/sv-jme.2015.3218.

[16] Filkoski, R.V., Chekerovska, M., Bunjaku, F. (2016). Research and education in thermal and power engineering with support of CFD technology. International Conference REMOO “Science and Engineering for Reliable Energy”.

[17] Milincic, D. (1989).

Heat Transfer.

Naučna knjiga, Beograd. (in Serbian)

Bunjaku, F. – Filkoski, R.V. – Sahiti, N.

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 447-456 © 2017 Journal of Mechanical Engineering. All rights reserved.

DOI:10.5545/sv-jme.2017.4313 Original Scientific Paper

Received for review: 2017-01-09 Received revised form: 2017-04-11 Accepted for publication: 2017-05-29

Modelling Study on Stiffness Characteristics of Hydraulic Cylinder under Multi-Factors Hao 1 South

Feng, H. – Du, Q. – Huang, Y. – Chi, Y. – Qungui Du1 – Yuxian Huang3 – Yongbin Chi1

Feng1,2,*

China University of Technology, School of Mechanical & Automotive Engineering, China 2 Liugong Machinery Co., Ltd, R&D Center, China 3 Purdue University, Herrick Laboratories, School of Mechanical Engineering, USA

For a complex mechanical system driven by hydraulic cylinders, the dynamic response characteristics of the mechanical system are significantly affected by the stiffness characteristics of hydraulic cylinders. This paper comprehensively studies the impacts of various factors on the stiffness characteristics of the hydraulic cylinders, including the oil bulk modulus, the air content in the hydraulic oil, the axial deformation of the piston rod, the volume expansion of the cylinder barrel, the volume expansion of the metal pipes and the flexible hoses, and the deformation of the hydraulic cylinder sealing. By combining the theoretical analysis and the experimental results, the level of each impacting factor was quantified, and the stiffness model of the hydraulic cylinder was established. Finally, comparative analysis of the stiffness was conducted by taking the experimental hydraulic cylinder as an example; it was verified that the calculated results of the proposed hydraulic cylinder stiffness model approximated the experimental results. Compared with stiffness models presented in current literature, the average accuracy was improved by more than 15 %.

Keywords: hydraulic cylinder stiffness, bulk modulus, air content in hydraulic oil, hydraulic system Highlights • A new stiffness model of the hydraulic cylinder was established, which incorporated factors of the compressibility of the oil, the axial deformation of the piston rod, the volume expansion of cylinder barrel, and the volume expansion of flexible hoses.

• The level of each impacting factor on the hydraulic cylinder stiffness was analysed: the compressibility of the oil is about 80 %, the volume expansion of the cylinder barrel is about 10 %, the axial deformation of the piston rod is about 6 %, and the volume expansion of flexible hoses is about 3 %. The impact of either the volume expansion of metal pipes or the sealing deformation is very small.

• Experimental tests proved that the content of the air in the hydraulic oil influences both the hydraulic cylinder stiffness and the bulk modulus significantly, but only at a low pressure level (P < 6 MPa).

• Tests proved that the change of the hydraulic cylinder stiffness is nonlinear. When the pressure P < 6 MPa, the degree of nonlinearity is relatively high. However, when the pressure is P > 6 MPa, the stiffness approaches to linearity.

0 INTRODUCTION Hydraulic cylinders are widely used in mechanical systems to drive loads. However, their stiffness characteristics significantly affect the characteristics of system dynamics [1] to [4]. Several studies have been carried out to date. For example, Dai [5], Wang and Wu [6] and Khalil [7] proposed the stiffness model described by Eq. (1). Laceklis-Bertmanis et al. [1] also adopted the aforementioned stiffness model to solve the vibration problem in a hydraulic hitch-system.

However, when Zhong and Yunxin [8] calculated the dynamic response of a pump truck boom using Eq. (1), the impact of the axial deformation of the piston rod on the stiffness was also considered. Recently, the mathematical model of the hydraulic cylinder stiffness was established by Jiang et al. [9] and the flexibility of the fluid supply circular tubes was considered via the volume modulus of the circular tube. Meanwhile, the tests also demonstrate that the stiffness of the

hydraulic cylinder is significantly impacted by the flexibility of the circular fluid supply tubes:

 A12 A22  K = Eo  +  , (1) V1 + VL1 V2 + VL 2 

where K is the stiffness of the hydraulic cylinder system, Eo is the oil bulk modulus, A1 and A2 are the effective area of the head chamber and the rod chamber, V1 and V2 are the volume of the head chamber and the rod chamber, and VL1 and VL2 are the fluid line volume on the head chamber and on the rod chamber, respectively.

Most of the mathematical models for the stiffness calculation provided in the mentioned literature only considered the influences of certain factors.

The compressibility of the hydraulic oil, the axial deformation of the piston rod, and the flexibility of

the fluid supply circular tube were included, while the influences of the air content in the oil, the volume expansion of the cylinder barrel, and the hydraulic cylinder sealing were neglected. In this

*Corr. Author’s Address: South China University of Tech., School of Mechanical & Automotive Eng., Wu Shan Road 381, GuangZhou, China, fenghao2005@163.com

447

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 447-456

paper, the stiffness characteristics of the hydraulic cylinder are fully analysed by comprehensively considering the compressibility of the hydraulic oil, the air content in the oil, the axial deformation of the piston rod, the volume expansion of the cylinder barrel, the volume expansion of the metal pipes, the volume expansion of the flexible hoses, and the hydraulic cylinder sealing.

1 STIFFNESS MODELLING A hydraulic cylinder system mainly consists of the cylinder barrel, the hydraulic oil, the piston sealing, the rod sealing, the piston rod, the flexible hose, and the metal pipe, as shown in Fig. 1.

determined by calculating the axial stiffness of the rod. The axial stiffness of the piston rod Kr is:

Kr =

where Ar is the rod cross-sectional area, Lr is the length of the piston rod, and E is Young’s modulus for the material of the piston rod. The axial stiffness of the piston rod is determined by its length and its rod cross-sectional area.

2.2 Cylinder Barrel Expansion Stiffness The cylinder barrel expansion stiffness is produced by the movement of the piston rod, Δx , when the barrel of the hydraulic cylinder is expanded in the radial direction under a pressure change ΔP. The formula for a steel cylinder radial deformation ΔD due to a pressure change ΔP is [10]:

Fig. 1. A hydraulic system: 1 cylinder barrel, 2 hydraulic oil, 3 piston sealing, 4 rod sealing, 5 piston rod, 6 flexible hose, 7 metal pipe

The main factors affecting the hydraulic cylinder stiffness are the hydraulic oil stiffness Ko , the piston rod axial stiffness Kr , the cylinder barrel expansion stiffness Kc , the metal pipe expansion stiffness Kp , the flexible hose expansion stiffness Kh , and the sealing ring deformation stiffness Ks . The net stiffness can be regarded as the sum of the reciprocals of the stiffness of the individual component. Thus, the net stiffness K of the hydraulic cylinder system can be calculated using Eq. (2): 1 1 1 1 1 1 1 = + + + + + . (2) K Ko K r Kc K p K h K s

The stiffness modelling of each of the factors will be discussed in the next section.

2 STIFFNESS MODELLING OF EACH INFLUENCING FACTOR 2.1 Axial Stiffness of the Piston Rod In general, the piston rod is a type of solid and cylindrical steel rod, and its stiffness can be 448

EAr , (3) Lr

∆D =

 D∆P  D12 + D 2 + υb  , (4)  Eb  D12 − D 2 

where Eb is Young’s modulus for the cylinder barrel, vb is the Poisson ratio for the cylinder barrel, and D1 and D are the outer and inner diameters of the cylinder barrel, respectively.

D12 + D 2 = λc as the expansion coefficient.

D12 − D Then, Eq. (4) can be simplified as: Set

∆D =

D∆P ( λc + υb ). (5) Eb

The volume expansion ΔVc1 for the head chamber of the cylinder barrel under a pressure change ΔP is:

∆Vc1 =

π D∆DL1 . (6) 2

According to the formula of the spring stiffness Ksp = df / dx, as well as Eqs. (5) and (6), the cylinder barrel expansion stiffness Kc1 caused by the expansion of the head chamber is given by:

K c1 =

∆P1 A1 ∆P1 A12 Eb A1 1 , (7) = = ⋅ ∆S ∆Vc1 2 L1 λc + υb

where ΔP1 is the pressure change in the head chamber, and L1 is the effective length of the head chamber.

Due to the difference between the cylinder effective cross-sectional area and the effective elongation, the stiffness calculations in terms of the deformation of the cylinder barrel between the head

Feng, H. – Du, Q. – Huang, Y. – Chi, Y.

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 447-456

chamber and the rod chamber are different. Therefore, the cylinder effective cross-sectional area and the effective elongation of the rod chamber are defined as A2 and L2, while A1 and L1 in Eq. (7) are replaced by A2 and L2. Then the stiffness, Kc2 , of the rod chamber in terms of the deformation of the cylinder barrel can be obtained as:

Kc 2 =

Eb A2 1 . (8) ⋅ 2 L2 λc + υb

2.3 Metal Pipe Expansion Stiffness

Set

The metal pipe expansion stiffness is produced by the movement of the piston rod, Δx, when the metal pipe is expanded in the radial direction under a pressure change ΔP. The method to calculate the stiffness caused by the volume expansion of the metal pipe is the same as that of the cylinder barrel. Which, according to Eq. (4), can be derived as the radial deformation, ΔDp , of the metal pipe’s inner diameter:  D p ∆P  D 2p1 + D 2p  2  , (9) ∆D p = υ + p  E p  D p1 − D 2p 

where Ep is Young’s modulus for the metal pipe, vp is the Poisson ratio for the metal pipe, and Dp1 and Dp are the outer and inner diameters of the metal pipe.

D 2p1 + D 2p

= λ p as the expansion coefficient D 2p1 − D 2p of the metal pipe. Then, the volume expansion, ΔVp , of the metal pipe under a pressure change ΔP is: Set

∆V p =

π D p ∆D p L p 2

, (10)

where Lp is the length of the metal pipe.

Thus, the stiffness Kp caused by the expansion deformation of the metal pipe in the head chamber end is:

Kp =

anticorrosive rubber layer. The radial expansion of the flexible hose is nonlinear but small under a pressure change ΔP. Hypothesis: i) The change in the radial direction is small and approximately linear. ii) An equivalent radial elasticity modulus, Eh , can be used to describe its small expansion. Eh can be determined through experimental and theoretical methods.

Therefore, the method for calculating the volume expansion of the hose is the same as that for the metal pipe.

2 E p A12 ∆PA1 . (11) = ∆V p / A1 π D p2 L p λ p + υ p

(

)

2.4 Flexible Hose Expansion Stiffness The flexible hose expansion stiffness is produced by the movement of the piston rod, Δx, when the flexible hose is expanded in the radial direction under a pressure change ΔP. The flexible hose is composed of an inner rubber layer, a medium steel wire winding, and an exterior

Dh21 + Dh2

= λh as the expansion coefficient of Dh21 − Dh2 the flexible hose. Where Dh1 and Dh are the outer and the inner diameter of the flexible hose. Therefore, the stiffness, Kh , influenced by the expansion of the flexible hose in the head chamber end is:

Kh =

2 Eh A12 , (12) π Dh2 Lh ( λh + υ )

where Lh is the length of the flexible hose.

Since the flexible hose is a type of multi-layer composite material, its complex properties need to be determined with the combined theoretical and experimental methodology. According to Eq. (2), the stiffness of the hydraulic cylinder without the flexible hose, Knohose , is: 1 1 1 1 1 1 = + + + + . (13) K nohose K o K r K c K p K s

According to Eq. (2), the stiffness of the hydraulic cylinder with the flexible hose Kwithhose is: 1 K withhose

=

1 1 1 1 1 1 + + + + + . (14) Ko ' K r Kc K p Kh K s

By subtracting the Eq. (13) from the Eq. (14), the stiffness influenced by the volume expansion of the flexible hose and the compressibility of the oil in the flexible hose is given by:

1 K withhose

−

1 K nohose

=

1 K oilhose

+

1 . (15) Kh

According to Eq. (15), the stiffness, Kwithhose , of the hydraulic cylinder with the flexible hose and the stiffness, Knohose , of the hydraulic cylinder without the flexible hose can be measured. By combining Eqs. (12) and (15), the equivalent elasticity modulus of the flexible hose can be derived.

Modelling Study on Stiffness Characteristics of Hydraulic Cylinder under Multi-Factors

449

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 447-456

2.5 Stiffness of Hydraulic Oil According to the formula of the hydraulic oil’s stiffness in [5] and [6], the stiffness, Ko , influenced by the hydraulic oil can be composed of the hydraulic oil’s stiffness of the rod chamber and the head chamber.

 A12 A22  K o = Eo  +  . (16)  V1 + VL1 V2 + VL 2 

The oil bulk modulus Eo in Eq. (16) is influenced by the air content and the pressure of the fluid. There is a great deal of literature devoted to the study on the bulk modulus considering the influence of air content [14] to [17]. The oil bulk modulus Eo considering the different air content rates and work pressures can be describe in Eq. (17), [16] and [17]. pa 1/ n ) p a + p Eo = Eo' ⋅ , (17) p1a/ n 1 + α ⋅ Eo ' ⋅ n ⋅ ( pa + p )( n+1)/ n 1+ α ⋅ (

stiffness, Ks , on the stiffness mathematical model can be neglected.

wherein Eo' is the oil bulk modulus without air content α is the relative air content in oil under the atmospheric pressure; pa is the atmospheric pressure; p is the working pressure, and n is the isentropic coefficient (n = 1.4).

Fig. 2. The detailed section view of piston sealing

3 EXPERIMENTAL TEST To measure the hydraulic cylinder stiffness, the equivalent elasticity modulus, Eh , of the flexible hose in Eq. (12) and the bulk modulus Eo of the oil in Eq. (16), and to verify Eq. (2) of the hydraulic cylinder’s stiffness mathematical model, the experimental study is carried out with the locked head chamber of the hydraulic cylinder. Moreover, the rod chamber of the cylinder is connected to the oil tank, shown in Fig. 3.

2.6 Stiffness Influenced by Sealing Deformation An external load impact will induce the axial reciprocating vibration of the hydraulic cylinder, so the seal ring will also follow in the reciprocating motion of the cylinder. Take the experimental hydraulic cylinder as an example in which a T-type bonded seal ring is used. The piston diameter is 160 mm, the groove diameter is 145 mm, and the side clearance of the groove is 0.2 mm. As shown in Fig. 2, the piston rod is subjected to an external force Fext , and the rod chamber side is the high-pressure. When pushing the piston, the axial displacement of the seal ring, Δx , is about 0.2 mm, and the extrusion output of the oil is 0.436 ml, corresponding to a calculated piston’s displacement of 0.06 mm. Note that the stiffness variation of the hydraulic cylinder influenced by the displacement of the seal ring is very small.

The step seal and the V-seal are two commonly adopted seals on the piston rod side. Moreover, the force exerted on the seal is unidirectional, and the self-deformation of the sealing is very small: so much so that the influence of the sealing ring deformation 450

Fig. 3. Schematic of Experiment Setup: 1 platform, 2 loading hydraulic cylinder (LHC), 3 trolley, 4 magnetostrictive sensor, 5 draw wire displacement sensor, 6 experimental hydraulic cylinder (EHC), 7 vent valve, 8 cut-off valve, 9 flexible hose, 10 cut-off valve

Fig. 3 shows the experimental setup. The loading hydraulic cylinder (LHC) 2 and the experimental hydraulic cylinder (EHC) 6 are installed on the platform 1 and connected by the trolley 3. Two displacement sensors 4 and 5 are installed on the experimental hydraulic cylinder. The displacement sensor 4 is a high-precision magnetostrictive sensor that measures the compressive displacement variation of the hydraulic cylinder during the test, while the displacement sensor 5 is a draw-wire displacement sensor that measures the hydraulic cylinder stroke. Pb is the pressure of the head chamber in the experimental hydraulic cylinder 6. Pa and Ta are the P and T port

Feng, H. – Du, Q. – Huang, Y. – Chi, Y.

StrojniĹĄki vestnik - Journal of Mechanical Engineering 63(2017)7-8, 447-456

of the loading hydraulic cylinder 2. Pb and Tb are the P and T port of the experimental hydraulic cylinder 6. A flexible hose 9 is installed between the cut-off valves 8 and 10. Meanwhile, the discharge and intake of the air are carried out through the vent valve 7, so that the influences of the different air contents on the stiffness of the hydraulic cylinder can be qualitatively studied. For easy air discharging, lower the height of the connecting trolley 3 to tilt the experimental hydraulic cylinder 6 and the air vent port 7 on the highest location of the hydraulic cylinder. Fig. 4 shows the actual testing devices. The technical data of the experimental setup is shown on Table 1. The residual volume Vr in Table 1 refers to the oil volume in the tested air exhaust equipment and the hydraulic cylinder that cannot be calculated via the stroke.

can be released as the undissolved gas. Then the air is discharged through the vent valve 7.

Table 1. Technical data of the experimental setup Name

Value

Cylinder barrel inner diameter [m]

0.16

Cylinder barrel outer diameter [m]

0.194

Piston rod diameter [m]

0.08

Piston rod length [m]

1.13

Cylinder maximum stroke [m]

0.815

Flexible hose inner diameter [m]

0.025

Flexible hose outer diameter [m]

0.043

The length of flexible hose [m] The hydraulic oil type The piston seal on the measuring hydraulic cylinder The residual volume, Vr

2 L-HM46 Glyd Ring

[m3]

0.001

Five states are considered for evaluating the factor related to the hydraulic cylinder stroke: the following elongations of 0.138 m, 0.228 m, 0.381 m, 0.456 m, and 0.536 m, respectively, and they are measured through the displacement sensor 5.

The setup is carried out according to the factors related to the fluid line state, the air content, and the stroke before loading. During testing, the pressure Pb of the testing hydraulic cylinder 6 and the compressive displacement of the displacement sensor 4 are acquired and collected in real time.

4 RESULTS AND DISCUSSION Fig. 4. The actual experimental setup

The oil leakage test must be done before the stiffness testing of the hydraulic cylinder. The test standards are the ISO standard [18] and [19]. The oil leakage caused by the piston seal must be less than 0.5 ml/min under the pressure of 1.5 times working pressure, and the pressure should be maintained for 2 min.

Two conditions are considered for the state of the flexible hose: with or without the flexible hose, which is controlled through the cut-off valve 8, shown in Fig. 3.

Three different states are qualitatively considered for the air content: air content 0 is not considered in the discharged air; air content 1 is considered in the discharged air at the first time; and air content 2 is considered in the discharged air at the second time. By using the dissolving and releasing principle of the air in the hydraulic oil [11] and [12], and after multiple cyclic loading and unloading tests, the dissolved gas

4.1 Analysis of Bulk Modulus & Influence Factors To measure the oil bulk modulus and to qualitatively study the impact of the air content on the bulk modulus, the measured pressure and the displacement data are analysed according to the following conditions: (1) The flexible hose is neglected; (2) For the big elongation of the hydraulic cylinder and plenty of hydraulic oil, the elongation of the hydraulic cylinder is taken as 0.536 m. (3) Consider the three different states of the air content. Because the amount of air discharges in the third test and afterwards is so small that it can be omitted, only the air discharges in the first two tests are considered in the data analysis and discussions. After data processing, the curve of the pressure-volume variation of the oil is obtained, and it is shown in Fig. 5.

From Fig. 5, the relation between the pressure and the volume variation is nonlinear, and the nonlinearity is particularly obvious at a low pressure. When the pressure P > 6 MPa, the relation becomes linear. At

Modelling Study on Stiffness Characteristics of Hydraulic Cylinder under Multi-Factors

451

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 447-456

low pressure, the air content is obvious. When the pressure P > 6 MPa, the slopes under three states of the air content are approximately balanced, showing that the air influence on the bulk modulus is small at this time.

Therefore, the larger the air volume in the hydraulic oil is, the bigger ΔVair would be, leading to the increase of ΔV, so the bulk modulus is small.

Fig. 5. The pressure-volume variation curve

According to the literatures [13] and [14], the oil’s bulk modulus can be expressed as the tangent modulus or secant modulus. Thus, the tangent modulus and the secant modulus of the data in Fig. 5 are analysed, and the curve of the relation between the bulk modulus and the pressure is obtained and it is shown in Fig. 6.

The figure highlights that: The bulk modulus of the hydraulic oil is nonlinear. When the pressure P < 6 MPa, the bulk modulus is greatly influenced by the air content, and the gradient of the variation is big. However, when the pressure P > 6 MPa the air amount influences the bulk modulus less, and the linearity is obvious.

Since the working pressure of the hydraulic cylinder in a mechanical system is usually higher than 6 MPa and considering that the secant bulk modulus is commonly adopted for transient variation of the stiffness Eo = 1.49e9 Pa is taken according to Fig. 6, which is a value relatively approximated to the results given by Bureček in [16].

(2) At the three states of the air amount, the tangent bulk modulus is small because the tangent bulk modulus is calculated by ΔPi and ΔVi , which are near the tangential direction, for examples: ΔPi = Pi+1 – Pi–1 and ΔVi = Vi+1 – Vi–1. Therefore, the relative pressure and the volume variation are used to calculate the bulk modulus, but the influence of the accumulated amount of the volume compression is not considered.

(3) At the three states of the air amount, the difference of the secant bulk modulus is obvious because the secant modulus is adopted to calculate ΔPi = Pi+1 – P0 and ΔVi = Vi+1 – V0 , while the compressed volume of air ΔVair is included in ΔVi. 452

Fig. 6. The pressure-volume variation curve

4.2 Stiffness Analysis of Hydraulic Cylinder and Influence Factors To measure the stiffness of the hydraulic cylinder and to qualitatively study the influence of the air content on the stiffness, measured pressure and displacement data are analysed according to the following conditions: (1) The flexible hose is considered. (2) For a large elongation of the hydraulic cylinder and plenty of hydraulic oil, the elongation of the hydraulic cylinder is taken as 0.536 m. (3) Consider the three states of air content. After the data was processed, the curve of the hydraulic cylinder force-compressive displacement variation is obtained as shown in Fig. 7. The displacement in Fig. 7 was measured directly, while the piston force in Fig. 7 was converted from the measured pressure.

From Fig. 7, the curve approximates a pressurevolume variation curve of Fig. 5, showing that the characteristic of the hydraulic oil is the main factor for determining the stiffness of the hydraulic cylinder.

After processing the data of the hydraulic cylinder force and displacement in Fig. 7, and obtaining the hydraulic cylinder’s stiffness-pressure curve shown in Fig. 8, it shows that at low pressure P < 6 MPa, the amount of air greatly influences the hydraulic cylinder stiffness while the nonlinearity is obvious and the gradient of the stiffness variation is big. When the

Feng, H. – Du, Q. – Huang, Y. – Chi, Y.

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 447-456

pressure P > 6 MPa, the influence of the air amount on the stiffness is small, while the linearity is obvious and the gradient of the stiffness variation is small.

Fig. 7. The force-compressive displacement variation curve

4.3 Stiffness under Different Elongations and Analysis of Influence Factors To measure the hydraulic cylinder stiffness under different elongations and to research the influence of the elongation on that stiffness, the measured pressure and displacement data are analysed according to the following conditions: (1) The flexible hose is considered. (2) The hydraulic cylinder elongations are 0.138 m, 0.228 m, 0.381 m, 0.456 m, and 0.536 m, respectively. (3) Neglect the state of the air content and take the state without discharging air. After data processing, the hydraulic cylinder force and compressive displacement variation curve is obtained as shown in Fig. 9.

Under different elongations, the stiffness is clearly changed. As shown in Fig. 9, there is intersection between stroke curves at 0.138 m, 0.228 m and 0.318 m, which indicates that when the stroke of the hydraulic cylinder and the amount of the cylinder liquid volume are too small, other factors during the test including “the clearance of the hydraulic cylinder” or “the deformation of the rubber sealing” will have greater impact on the stiffness of the hydraulic cylinder than the air does. However, this phenomenon only occurs when the pressure is smaller than 2.5 MPa, and the results are normal when the pressure is greater than 2.5 MPa.

Fig. 8. The stiffness-pressure variation curve

Calculate the equivalent elasticity modulus of the hose based on the example of the experimental hydraulic cylinder. According to Fig. 8, under a stroke of 0.536 m and a pressure of 16 MPa, the value of the measured hydraulic cylinder stiffness without hose is Kwithouthose = 4.7e7 N/m, and the value of the measured hydraulic cylinder stiffness with hose is Kwithhose = 4.24e7 N/m. Based on Eq. (18), the stiffness generated by the hose hydraulic oil is Khose_oil = 6.14e8 N/m. By substituting these stiffness values into Eq. (16), and calculating with Eq. (12), the value of the equivalent elasticity modulus of the hose is Eh = 1.78e10 Pa. The equivalent elasticity modulus of the hose inferred in this way is smaller than the elasticity modulus of steel Esteel = 2.06e11 Pa, but is bigger than the bulk modulus of the hydraulic cylinder Eo = 1.49e9 Pa.

Fig. 9. The force-compressive displacement variation curve under different elongations

To further analyse the relation between the stiffness and the different elongations of the hydraulic cylinder, the data in Fig. 9 were processed and the stiffness-elongation curve obtained, as shown in Fig. 10. The figure highlights that: (1) The stiffness reduces dramatically with the increase of the cylinder

Modelling Study on Stiffness Characteristics of Hydraulic Cylinder under Multi-Factors

453

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 447-456

elongation. (2) When P < 6 MPa, the gradient of the variation is big. When P > 6 MPa, the variation gradient of the hydraulic cylinder stiffness under each elongation is very small, and the linearity is obvious.

According to the above analysis, the influence of cylinder sealing and the expansion of the metal pipe can be neglected during the hydraulic cylinder stiffness calculation. Therefore, the hydraulic cylinder stiffness calculation model Eq. (2) can be simplified as follows: 1 1 1 1 1 = + + + . (18)

K Ko K r Kc K h The levels of influence of each factor is given based on the experimental hydraulic cylinder. Since different hydraulic cylinder structures have different sizes, the levels need to be demonstrated according to Eqs. (2), (3), (7), (11), (12), and (16). After that, accept or reject each factor according to the accuracy requirements of the hydraulic cylinder stiffness.

4.5 Comparative Analysis of Different Stiffness Models

Fig. 10. The stiffness-elongation variation curve

4.4 Level of Influence Analysis of Various Factors To obtain the level of influence of the various factors on the hydraulic cylinder stiffness, the experimental hydraulic cylinder can be taken as an example.

According to Eqs. (2), (3), (7), (11), (12), and (16), the values of the hydraulic cylinder stiffness and the stiffness produced by each factor can be calculated respectively. Then the percentage of the stiffness produced by each factor relative to the hydraulic cylinder stiffness is also calculated. The level of influence of various factors on the hydraulic cylinder stiffness can thus be obtained and the results are shown in Table 2. It is concluded that: (1) the stiffness produced by the expansion of the metal pipe is small and can be neglected; (2) The influences of the flexible hose expansion stiffness, the axial stiffness of the piston rod and the cylinder barrel expansion stiffness on hydraulic cylinder stiffness cannot be neglected, especially for a short elongation of the hydraulic cylinder.

Table 3. The error analysis of two models

Table 2. The Level of influence of various factors

L [m] 0.138 0.228 0.381 0.456 0.536

Ko [%] 72.90 77.42 81.68 83.00 84.09

Kr [%] 10.05 7.74 5.56 4.89 4.33

Kc [%] 10.81 10.04 9.31 9.08 8.89

Kp [%]

Kh [%]

0.50 0.39 0.28 0.25 0.22

6.24 4.80 3.45 3.03 2.69

L in table 2 is the hydraulic cylinder elongations.

454

Eq. (1) and Eq. (18) proposed in this paper can be adopted to calculate the stiffness as an example for experimental hydraulic cylinders. After comparing and analysing the test results, as shown in Fig. 11, the errors between these two models, and test results are summarized in Table 3.

From Fig. 11 and Table 3 the calculated results of the stiffness model raised in this paper are better than those reported in the literature, and the average accuracy is improved by more than 15 %. Meanwhile, it is proven that: (1) when the elongation of the hydraulic cylinder is small, the stiffness error obtained when only considering the compressive deformation of hydraulic oil is very large, and the error reaches up to 40 %; (2) When the elongation of the hydraulic cylinder is sufficiently large, only the compressive deformation stiffness of the hydraulic oil needs to be considered. However, since the hydraulic cylinder is usually working in a reciprocating motion, the influences of the cylinder barrel expansion stiffness, the axial stiffness of the piston rod, and the flexible hose expansion stiffness cannot be neglected in the dynamic characteristic investigation of the hydraulic cylinder system or mechanical system.

Stroke [m] 0.138 0.228 0.381 0.456 0.536 Average Error

Feng, H. – Du, Q. – Huang, Y. – Chi, Y.

Error of the model from Eq. (1) [%] 40.76 29.63 15.35 9.18 11.23 21.23

Error of the new model proposed by this paper [%] 2.61 0.37 -5.78 -9.39 -6.47 -3.73

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 447-456

influenced by the air content, while the nonlinearity is obvious and the variation gradient is large. However, when the pressure P > 6 MPa, the bulk modulus and the hydraulic cylinder stiffness are subtly influenced by the air content, while the linearity is obvious and the variation is small.

6 ACKNOWLEDGEMENTS

Fig. 11. The comparative analysis of theoretical and experimental hydraulic cylinder stiffness

5 CONCLUSIONS To improve the calculation accuracy of the hydraulic cylinder stiffness, this paper comprehensively considered the influences of various factors on the stiffness of the hydraulic cylinder, and proposed a new stiffness model of the hydraulic cylinder whose calculation accuracy is higher than that in the published literature, which was proven by the tests.

Meanwhile, the influences of different air contents on the bulk modulus and the hydraulic cylinder stiffness, as well as the influences of different elongations of the hydraulic cylinder on stiffness were experimentally investigated. The main research conclusions are as follows: The compressive deformation of the hydraulic oil, the axial deformation of the piston rod, the expansion deformation of the cylinder barrel, and the expansion deformation of the flexible hose need to be considered for a hydraulic cylinder stiffness.

While other factors like the air content in the oil, the expansion deformation of the metal pipe, and the seal of the hydraulic cylinder can be ignored.

The level of influence of each factor on the hydraulic cylinder stiffness is the following: the compressive deformation of the hydraulic oil about 80 %, the expansion deformation of the cylinder barrel is about 10 %, the axial deformation of the piston rod is about 6 %, and the expansion deformation of the flexible hose is about 3 %. Due to substantial differences for cylinders of different sizes, the ratio of the impact generated by various factors on the cylinder stiffness provided above is only applicable to the specific cases discussed in the paper.

When the pressure P < 6 MPa, the bulk modulus and the hydraulic cylinder stiffness are greatly

This work is supported by the China National Key Technology R&D Program “Lightweight technology research and application on typical construction machinery” (2011BAF11B01). The authors wish to thank China National Earthmoving Machinery Engineering Research Center for providing experimental support. The authors also wish to thank Aaron Becker, Hydraulics Chief Engineer, North America New Technology R&D, LiuGong Machinery Ltd, for his valuable suggestions. Many thanks also go to the reviewers of this paper for their helpful comments.

7 REFERENCES [1] Laceklis-Bertmanis, J., Kakitis, A. Kronbergs, E., Repsa, E., Smits, M. (2010). Pressure oscillation in hydraulic hitchsystem during implement transport. Žemės Ūkio Inžinerija, Mokslo Darbai, vol. 42, no. 2/3, p. 22-31.

[2] Vollmer, F., Murrenhoff, H. (2002). Hydraulic linear actuators with high dynamic load stiffness. SAE Technical Paper, no.

2002-01-1496, DOI:10.4271/2002-01-1496.

[3] Tomski, L., Uzny, S. (2011). A hydraulic cylinder subjected to Euler’s load in aspect of the stability and free vibrations taking into account discrete elastic elements. Archives of Civil and Mechanical Engineering, vol. 11, no. 3, p. 769-785, DOI:10.1016/S1644-9665(12)60115-0.

[4] Uzny, S. (2009). Free vibrations and stability of hydraulic cylinder fixed elastically on both ends. PAMM, vol. 9, no. 1, p.

303-304, DOI:10.1002/pamm.200910125.

[5] Dai, Y.F. (1999). The stiffness calculation of hydraulic cylinder.

Nonferrous Metals Design, vol. 26, no. 1, 61-63. (in Chinese) [6] Wang, L., Wu,B. (2007). Nonlinear dynamic characteristics of moving hydraulic cylinder. Journal of Mechanical Engineering, vol. 43, no. 12, p. 12-19, DOI:10.3901/jme.2007.12.012. (in Chinese) [7] Khalil, M.K.B. (2009). Interactive analysis of closed loop electro-hydraulic control systems. 13th International Conference on Aerospace Sciences & Aviation Technology, no.

ASAT-13-HC-01.

[8] Zhong, Z., & Yunxin, W. U. (2013). An equivalence method of the hydraulic cylinders in modal analysis of boom of truck mounted concrete pump. Machine Tool & Hydraulics, vol. 41, no. 7, p. 5-8 (in Chinese) [9] Jiang, W., Luo, X., Chen, X. (2016). Influence of structural flexibility on the nonlinear stiffness of hydraulic system.

Modelling Study on Stiffness Characteristics of Hydraulic Cylinder under Multi-Factors

455

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 447-456

Advances in Mechanical Engineering, vol. 8, no. 8, DOI:10.1177/1687814016663806.

[10] Lei Tianjue (1998). The New Hydraulic Engineering Handbook, Beijing: Beijing Institute of Technology Press.

[11] Cho, B.H., Lee, H.W., Oh, J.S. (2002). Estimation technique of air content in automatic transmission fluid by measuring effective bulk modulus. International Journal of Automotive Technology, vol. 3, no. 2, p. 57-61.

[12] Ericson, L., Palmberg, J.O. (2008). Measurement of free air in the oil close to a hydraulic pump. Proceedings of the JFPS International Symposium on Fluid Power, vol. 2008, no. 7-3, p.

647-652, DOI:10.5739/isfp.2008.647.

[13] Manring, N.D. (1997). The effective fluid bulk-modulus within a hydrostatic transmission. Journal of Dynamic Systems, Measurement, and Control, vol. 119, no. 3, p. 462-466, DOI:10.1115/1.2801279.

[14] Fei, S., Kong, D. (2011). Bulk modulus measurement of hydraulic oil based on drop-hammer calibration device.

456

International Conference on Electric Information and Control Engineering, p. 213-216, DOI:10.1109/ICEICE.2011.5778375.

[15] Yang, H., Feng, B., Gong, G. (2011). Measurement of effective fluid bulk modulus in hydraulic system. Journal of Dynamic Systems, Measurement, and Control, vol. 133, no. 6, p.

061021, DOI:10.1115/1.4004783.

[16] Bureček, A., Hružík, L., Vašina, M. (2015). Determination of undissolved air content in oil by means of compression method. Strojniški vestnik - Journal of Mechanical Engineering, vol. 61, no. 7-8, p. 477-485, DOI:10.5545/sv-jme.2015.2471.

[17] Petrović, R., Živković, M., Rong, W.Z., Rakić, D., Slavković, R. (2014). Influence of air content entrained in fluid of a vane pump with double effect operating parameters. Tehnički vjesnik – Technical Gazette, vol. 21, no. 2,p. 401-407.

[18] Hydraulic fluid power - cylinders acceptance tests (ISO 10100:2001 + amd 1:2012).

[19] Hydraulic cylinder (JB/T 10205-2010). (in Chinese)

Feng, H. – Du, Q. – Huang, Y. – Chi, Y.

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 457-465 © 2017 Journal of Mechanical Engineering. All rights reserved.

DOI:10.5545/sv-jme.2017.4302 Original Scientific Paper

Received for review: 2017-01-03 Received revised form: 2017-04-07 Accepted for publication: 2017-06-16

Methodology to Facilitate Successful Lean Implementation Berlec, T. – Kleindienst, M. – Rabitsch, C. – Ramsauer, C. Tomaž Berlec1,* – Mario Kleindienst2 – Christian Rabitsch2 – Christian Ramsauer2 1University

of Ljubljana, Faculty of Mechanical Engineering, Slovenia 2Graz University of Technology, Austria

The implementation of lean production in a company is a transformation of the whole company’s culture. To achieve such a lean culture, the role and support of management are decisive. This paper introduces a newly defined model and methodology with an interview guide which helps to distinguish a supportive from a non-supportive management team when introducing lean production, and helps to decide if a step needs to be repeated, improved, or the next step can be initiated. The methodology is especially suitable for small and medium-sized enterprises (SME’s), because of their lack of human resources, where this model was also tested.

Keywords: corporate culture, lean production, management learning, interview guide, critical success factors Highlights • A model and methodology which helps to distinguish the level of management support when introducing lean production was defined.

• After each finished step an interview needs to be done, based on which the next step by lean production implementation is decided.

• Beside the needed lean production knowledge, special attention is paid to management support.

• This model is developed and especially suitable for SME’s because of their lack of human resources.

0 INTRODUCTION The basic principles and practices of the Toyota production system (TPS) have been discussed for decades. Sugimori et al. [1] published one of the first scientific papers on this topic.

The practice now known as lean production (LP) has been changing and developing from a simple set of practices to the complexity of an entire lean business system [2] and [3]. As a result, knowledge and understanding about the theory behind LP is also evolving in [2] and [4].

In this research paper [5] the authors identify four key main factors that are critical for the implementation of lean manufacturing within small and medium-sized enterprises (SMEs), which are: leadership and management, finance, skills and expertise, and the culture of the recipient organisation.

These four factors are defined, but least had been improved on the field of management support.

Pay [6] stated that there are four major reasons companies fail to achieve benefits through lean implementation. The first is that senior management is not committed to and/or doesn’t understand the real impact of ‘lean.’ The second reason is that senior management is unwilling to accept that cultural change is required for lean to be a success. The third reason is that the company lacks the right people in the right positions, and the last reason is that the company has chosen lean as their process improvement

methodology when a different process improvement program – or none at all – would have been the better choice. Based on Pay [6] these four major reasons for failure needs to be avoided or detected soon enough to prevent damage and LP failure.

Papers [7] to [9] identified a lack of senior leadership focus and complacency as barriers to lean manufacturing implementation.

A methodology for implementing lean manufacturing strategies was proposed which is able to systematically identify manufacturing waste, select appropriate lean tools, identify relevant performance indicators, achieve significant performance improvement, and establish lean culture in the organisation [10]. A management commitment transformation plan and the formation of a lean team should be enough to initiate a lean culture.

But initiation of a lean culture is not sufficient, management needs to consistently stay supportive and not only at the start of LP implementation. A lean team cannot implement LP if management support is not absolute. Detection of unsupportive management should be done soon enough.

The creation of a lean culture is one of the greatest challenges awaiting the prospective lean implementers, since a considerable degree of organisational learning skills are needed [11]. This is why the LP implementation progress should be measured, and all employees have to be educated regarding LP.

*Corr. Author’s Address: University of Ljubljana, Faculty of Mechanical Engineering, Aškerčeva 6, SI-1000 Ljubljana, Slovenia, tomaz.berlec@fs.uni-lj.si

457

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 457-465

Herzog and Tonchia [12] presented an instrument for measuring the degree of lean implementation in manufacturing, based on a survey within 72 SMEs in Slovenia. They divided lean into eight lean issues with 24 lean variables, on which a company should be focused by implementing lean.

In the research [13] organisational culture and lean practices were investigated in correlation to successful and unsuccessful lean implementation. The authors concluded that a successful lean plant has a higher institutional collectivism, future orientation, human orientation, use of small group problem-solving, development of supplier partnership, customer involvement, adoption of continuous improvement, and lower assertiveness in comparison with unsuccessful lean plant. The results also indicate, that in order to implement lean management successfully it is fundamental to go beyond lean management technicalities by adopting soft practices and nurturing the development of an appropriate organisational culture profile.

To overcome the human resource barriers in successful lean implementation, the authors [14] identified a connection between barriers and performance measures. A framework to overcome each barrier was suggested.

The book [15] gives managers and executives the means how to maximise employee potential by increasing the improvement power. It also defines the people-related approaches and practices needed to alter any cultural dynamic. The authors stated, that everyone needs to learn and improve, and has to be involved. They suggest a five-year plan to make a long-lasting change requiring evolution of organisation, culture, and behavior.

In the research [16] the authors stated, that selecting the right person for the adoption of lean manufacturing in an industry will reduce the ambiguity, time consumption, and computation time.

They proposed based on the TOPSIS-Simos method to identify a lean resourced employee in the industry.

A literature review on lean implementation and organisational transformation was done by [17], where the authors came to the conclusion that lean implementation is a transformational process, requiring organisational level support and changes.

They also noticed that challenges and issues of lean implementation signify a lack of understanding of the organisational culture necessary for lean transformation.

Lean success factors were identified in the doctoral thesis of Pearce [18], including the extent of a business manager’s own knowledge, which impacts 458

the success or failure of an LP implementation. It turned out, that the main problems are the manager’s knowledge and support for LP implementation.

Based on Pentlicki [19], who developed a deeper understanding of the barriers faced by SMEs and the strategies required for the successful implementation of lean manufacturing, senior leaders have varying definitions of their roles in leading lean manufacturing implementation [20], have differing perspectives regarding the degree of leadership knowledge required for successful lean manufacturing implementation.

They also struggle to expand lean manufacturing implementation into support departments such as engineering, purchasing, administrative functions, and sales. This means that all employees need to learn about lean, regardless of where in the company they work. However, the learning process needs to be different for management than for all other employees, which is taken into account in our new model.

In the paper [21] the authors propose a motivational lean game to successfully overcome the communication and motivation problems between management and other employees.

The paper [22] offers managers a better understanding of the relationship and impact that some of the most essential lean methods have on the performance of their operations, based on which managers will be able to take better and more effective decisions about the implementation of lean methods.

Kull et al. [23] stated that the successful use of lean manufacturing practices requires more than the use of tools. It depends on a nation’s culture, as well as the company culture. The culture in a company depends on an example of the management, and a culture change is a long process which can be made

by LP with management support.

A manager’s role has changed radically with the implementation of LP [24]. The focus on managerial tasks has changed from managing processes to developing and coaching people. Hence the manager’s role is to give clear direction for change situations [25].

Mostafa et al. [26] stated that by LP implementation the focus should be on human and technical factors in a parallel manner all times. The expert team building, lean monitoring, and controlling should also be included in the LP implementation.

Drew et al. [27] are convinced that by implementing a sustainable operational improvement, three aspects need to be taken into account: the operating system, the management infrastructure, and the mind-sets and behaviors of the staff. In our

Berlec, T. – Kleindienst, M. – Rabitsch, C. – Ramsauer, C.

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 457-465

proposed model we tried to integrate all these three aspects.

A number of studies have been conducted to understand or identify the factors that affect the process of implementing LP. Among the factors that influence LP implementation, 55 % of the studies mention the importance of management support and/or commitment. However, none of them clearly describes criteria to distinguish a supportive from a non-supportive management team. Marodin and Saurin [28], listed main factors that affect LP implementation. The most important are: • managerial support and commitment, • the ability, experience, and knowledge to conduct the lean implementation process, • an organisational culture receptive to changes.

According to Anvari et al.’s [29] ranking of the most critical success factors (CSFs) in order of importance are management and leadership, and followed by organisational culture. From this we can conclude, that the main focus has to be on management and leadership.

Scherrer-Rathje et al. [30] mention the following CSFs: management commitment, management support, lean team autonomy, an employee’s autonomy to make process improvements, information transparency, and an employee’s early as possible involvement in lean.

According to [30], a lean project should also be introduced from the top down, because the bottom-up case requires too many resources. Besides that, open discussion with employees is very important, because if management leaves them in the dark, they do not know the lean goal they are expected to achieve. They need to see the whole picture of lean, and not only their work, because they can then position their work in the whole lean picture. They also proved that it is very important to implement lean on a small unit first (pilot project), where success is guaranteed, and then implement it slowly over the whole company. If the pilot project is a failure, lean implementation in the eyes of the employees is over.

Motivated by the failure rate of lean implementation in SMEs in Vietnam, the authors [31] proposed a new application model of lean management by recognising the role of human resources development in the lean implementation steps.

In the research [32] an empirical evidence for the important role of management support and communication by lean implementation was provided.

Based on the literature review, we can conclude that management support is outstanding as the most critical success factor in the implementation of LP. Considering the fact that the whole organisational culture has to change, and all employees need to go through the lean learning process and participate in the lean implementation, it is very important to have proper human resources especially in management and people leading LP implementation in the company.

These are the reasons why we decided to build a model to facilitate successful lean implementation and define the criteria to distinguish between supportive and non-supportive management teams.

1 THE MODEL TO FACILITATE SUCCESSFUL LEAN IMPLEMENTATION LP implementation is a strategic activity within a given organisation supported by management, as well as by other employees, and which will succeed only through joint action.

According to Womack and Jones [3] five lean principles (specify value from the customers perspective, map the value stream, make the valuecreating process flow, implement pull system, strive for perfection as the goal) are known for lean implementation, which will be the fundamental basis of our model.

As stated, management support is crucial for LP implementation, which depends on lean culture.

Based on these assumptions, we propose a model that will clearly show the state of management support in the company early enough to prevent the failure of LP implementation.

In order to be able to commit to a LP implementation, managers and other employees need to obtain lean knowledge, which is obtained not only through teaching, but also with training, observation, and experience – all of which together can be described as lean learning.

There is a difference if the decision for lean implementation was decided by stockholders (owners) or by management supported by stockholders. If the decision or idea originates from management, then there is already the first positive impulse and the start of the lean implementation is much easier.

If the decision came from the stockholders in the form of a command, managers will not feel safe and managerial resistance should be expected.

The proposed model for the methodology to facilitate successful lean implementation in SME’s consists of five steps combined with lean learning for

Methodology to Facilitate Successful Lean Implementation

459

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 457-465

Fig. 1. The model to facilitate successful lean implementation

management and employees, which is shown in Fig. 1.

As seen in Fig. 1, all employees (at the managerial and operational levels) need to go through a lean learning process. In the beginning, all employees need to learn a lot of LP where the employees on the operational level are the focus for LP usage, and also on the managerial level on the usage with a focus on mentoring and encouraging operational employees. So besides the normal workshops, managerial employees need to have additional learning workshops.

In each step all the employees should grow in terms of LP knowledge based on workshops and practical deployment in their environment. This is why we make an interview after each step to check the practical knowledge, to see the management support, to avoid problems, and to resolve outstanding problems. The basis of a lean implementation is the step where the value is specified from the customer point of view. After completing this first step, the company needs to check the main points with employees using a proposed interview guide (IG).

2.1 Interview Guide 1 – Specify Value (IG 1) 1.

2.

3.

4.

460

What is the basic idea of lean philosophy?

Why is lean production useful to our company?

What are our customers willing to pay for?

What is your specific value-added?

5. Is the communication between employees and management satisfactory and the management support sufficient to implement LP? The purpose of this first IG is to check whether all employees understand the basic principles of LP and the relationship of LP to the overall success of the company. By asking basic questions that every employee has to answer in his/her personal context, we enable individual answers – this is necessary because the great range of employee tasks in a manufacturing organisation make uniform answers difficult. The learning objective here is that the individual contribution to the overall system can be identified and valued by every employee.

Based on IG, we additionally want to facilitate successful lean implementation besides the general goal – a lean culture, which is the basis for perfection.

We recommend fulfilling the IG in the form of qualitative interviews, which are performed separately with managerial and operational levels. Besides that, each interviewee needs to give an assessment from 0 % to 100 % (Table 1) of his knowledge and his understanding after completing each step. This assessment needs to be consistent with the score given by interviewer. After finishing all the interviews the average assessment is calculated.

The interview scale is proposed based on proportional and cardinal scale [33] and grade scale used for knowledge evaluation process at the faculty.

The interviewer gives an objective grade based on his knowledge and experience.

Berlec, T. – Kleindienst, M. – Rabitsch, C. – Ramsauer, C.

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 457-465

Table 1. Interview scale Percentage 1% to 50% 50% to 60% 60% to 70% 70% to 80% 80% to 85% 85% to 90% 90% to 95% 95% to 100%

Description Ignorance of the principles of lean High lack of knowledge, large uncertainties Lack of knowledge, less clarity A slight lack of knowledge, not sovereign A slight lack of knowledge, sovereign A slight shadow in knowledge, but still satisfactory The knowledge in its field reliable The knowledge is reliable on the whole company area

Table 1 shows the interview scale from 0 % to 100 %, where percentages under 50 % mean negative feedback, over 85 % positive feedback and between 50 % and 85 % mean a shortage of lean knowledge or communication.

After a comparison of the results from both groups (managerial and operational levels), a decision can be made whether to proceed to the next step or not based on the proposed model (Fig. 1).

If the feedback from the IG is positive (over 85 %) and the difference between the answers of managerial and operational levels is low, the step to the next level can be started.

If the feedback of the IG is negative (under 50 %) (lack of management support, low lean knowledge, bad communication, etc.), the same step needs to be repeated from the start.

In the case that the feedback is not negative and not positive (between 50 % and 85 %), then the shortcomings have to be addressed first (with additional lean learning, with communication, etc.), and only then the next step can be initiated. In this case, the main thread is that the lean learning at all levels has to be repeated, where the loss of the valuable time cannot be avoided. This is why lean learning, the confirmation that all employees understand the lean philosophy, and know how to use it is very important from the beginning.

The same procedure with the IG described above should be followed after each step has been completed as shown in the model in order to facilitate successful lean implementation (Fig. 1). All questions in the IG are changed according to the additional step in the model, except one question remains the same in all IG through the whole LP implementation: “The communication between employees and management works well and management support is sufficient to implement LP,” since management support is critical for LP implementation according our experience and the literature review in section 1.

After step two has been completed the next Interview Guide can be started.

2.2 Interview Guide 2 – Value Stream (IG 2) 1. What is a value stream and the main idea behind it?

2. What are the value-adding activities and waste in general, and when thinking about your own workplace?

3. What does the current value creation process in your company look like?

4. What does your individual contribution to the whole value stream (supply chain, value add, preand post- process steps) look like?

5. Is the communication between employees and management satisfactory and the management support sufficient to implement LP? The goal of the IG 2 is to check whether people understand the basic idea and their individual contribution to the value stream, and if they can distinguish between value adding and non-value adding activities in their own workplace and, of course, testing for management support.

Again interviewee needs to give an assessment from 0 % to 100 % consistent with the score given by interviewer. After finishing all the interviews the average assessment is calculated.

If the average assessment is between 50 % and 85 % that means, that not all employees understand the value stream principle, and a new learning cycle for value streams needs to be done before proceeding to the next step. If the average assessment is under 50 %, this step needs to be repeated.

Besides further theoretical explanation for employees and management combined with the practical input on their own workplace, management needs to think if they communicate the principles correctly and if the chosen training method is appropriate and meaningful for everybody. We suggest the use of lean learning factories as a proven method to train the key lean principles.

Learning factories represent a realistic company environment, for example an assembly area.

Within this area, typical problems related to lean implementation and almost all relevant methods and tools within the lean philosophy can be elaborated.

Within the neutral training environment of the learning factory, workers can experience the lean philosophy and its aftermath in practice. Furthermore, it is recommended to build interdisciplinary teams that do the training in the learning factory together.

There should be people from all hierarchy levels and

Methodology to Facilitate Successful Lean Implementation

461

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 457-465

intra-organisational disciplines mixed up in order to create an exchange of ideas, problems, and thoughts that would help the organisation to improve lean implementation results. Such a learning factory has been in existence since early 2014 at the Institute of Industrial Management and Innovation Research at Graz University of Technology.

After all conditions from step 2 are met, that means that average assessment is over 85%, step 3 – the flow can be carried out. When the third step is finished, the next IG (IG 3) is proposed.

2.3 Interview Guide 3 – Flow (IG 3) 1. I understand the necessary requirements to introduce flow.

2. I understand advantages of flow principle.

3. I can transfer theory to practice (flow in my area/ company).

4. I understand limitations of flow within my company and the relevant background.

5. I receive the right amount of information at the right time to successfully complete my tasks.

6. Is the communication between employees and management satisfactory and the management support sufficient to implement LP? The idea behind IG 3 is to ask the basic questions that will clearly show whether the principles of flow production are understood from both the management level and operative level workers.

It is particularly important for operative level workers to understand the advantages of the flow principle. As very often the introduction of flow principles leads to repetitive tasks and workers tend to be less motivated performing these tasks, an awareness of the importance of this principle for the whole company is crucial.

The fourth question is aimed at the limitations of flow and the relevant background, and why flow is not always applicable. This question is intended to initiate thinking processes in all employees in order to help them come up with new innovative ideas on how to overcome these limitations. The fifth question aims to discover whether workers are provided with the right information. Since very important fragments of the flow principles are also the preparation and allocation of relevant information, this question is exceedingly important.

The procedure with assessment percent is the same as by the previous steps.

If the understanding of the managerial and operational levels on the flow principle is sufficient (average assessment over 85 %), and management 462

support is satisfactory, the fourth step – pull can be initiated.

This does not mean that the flow principle has to work a hundred percent, in the meaning of KAIZEN it never will, but the fundamental basis should be introduced in the company environment.

After step four, the last IG is proposed.

2.4 Interview Guide 4 – Pull (IG 4) 1. I understand where the pull system helps to overcome the limitations of flow.

2. I still see potential for further pull implementation, 3. The lean culture is an important part of the company.

4. Is the communication between employees and management satisfactory and the management support sufficient to implement LP? Pull production can be seen as a facilitator of the flow principle. Producing according to the demand of the next process step should help keep stocks low and prevent over-production. In this step, a lot of strategic considerations have to be kept in mind. This is why, in our point of view, extensive management involvement is indispensable in this step. Only the combination of strategic considerations from management level and operative improvement potentials from an operative level can lead to success and a move towards step number 5.

It is very important that the transition to lean manufacturing and lean culture is made at all levels and in all areas of the company, and not only in production (as often seen), because only then can the lean culture in a company be developed.

Since lean implementation never ends because we strive for perfection, we can talk about the plan– do–check–act (PDCA) circle.

The proposed model to facilitate successful lean implementation is very suitable for SMEs, because of the shortage of people in SMEs for implementing LP. This helps them to keep a good overview over the LP implementation, and have quick and timely reactions if the LP implementation turns away from the optimal path. The use of this model also helps them to raise the rate of success of the LP implementation.

The same model can be also used in a big company to keep a good overview of LP implementation and to focus on the main problems by LP implementation.

3 SIMULATION AND RESULTS The proposed model to facilitate successful lean implementation was tested in two SMEs. The first

Berlec, T. – Kleindienst, M. – Rabitsch, C. – Ramsauer, C.

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 457-465

Table 2. An example of answers on IG 1 of one interviewee Question What is the basic idea of lean philosophy?

Why is lean production useful to our company?

What are our customers willing to pay for?

What is your specific value-added?

Is the communication between employees and management satisfactory and the management support sufficient to implement LP? Interviewee’s assessment (from 0 % to 100 %) Interviewer assessment (from 0 % to 100 %)

Answer The basic idea is the elimination of waste in the company.

Maximise customer value while minimising waste.

Things are getting more organised, Quality performance is better, we have fewer defects and rework and lower levels of Inventory.

Only for the added-value to the product. For example, for the final product, but not for the transport and the rework.

Injection molding of parts.

Yes, the management supports the LP implementation. We have daily 10-minute morning meetings to address and solve some problems. So the communication now is much better than before the start of LP implementation.

95 % 90 %

company, which we will call ‘Company A,’ has 90 employees and works in an automotive industry. They are specialised in the injection molding of multicomponent products, and in the complex injection molding of thin-walled products. They have just started the first step of lean implementation.

The second company, referred to as ‘Company B,’ has 208 employees, and is also working for an automotive, electrical, and mechanical industry. They work on special wiring harness with sensor technology, injection molded technical plastic products, and metallizing products. They expanded rapidly for the last seven years, and started the lean implementation a year ago, so we tried our model in the middle of an existing process of the lean implementation process.

First, the interdisciplinary lean core teams were built in both companies, based on [34], where the core team size depends on company size, theme, and project. The core team consists of six members in Company A and eight members in Company B which were acquainted with the model and the Interview Guides. After completing the first step in company A and the third step in company B, the interviews were made. On average, five minutes were necessary for an interview because of the individual answers, for the interviewer to get an overview of the knowledge, and the consisting problems.

In Table 2, an example of IG 1, after Company A finished the first step is presented.

Based on the answers of employees, and the management, interviewee’s, and interviewer assessment which were all over 90 %, we can conclude that the company is ready to go to the second step – value stream.

In company B we also tried our model from the first step, although the company was already in the flow phase. However, they have some problems in

implementing this phase. This is why we checked if they have any deficits in knowledge, and based on that, problems with LP implementation. So first we went over the IG 1, based on which we got an assessment by 95 %. Then we used the IG 2, the company reached 80 %. After analysing the results, we can conclude that the employees have a lack of communication and knowledge about the value stream. That is why we made a weekend workshop on value streams.

The same problems regarding communication and knowledge were solved in this workshop. After this workshop the company continued with the LP implementation, which went much more smoothly.

After a month we repeated the IG 2 and they reached 95 %.

Based on these two different examples in different stages, we can conclude, that our model helps to facilitate successful lean implementation, because it shows the problems of managerial support, communication, and knowledge. These problems, when they are recognised, can be solved very fast and easily. But normally these problems are not recognized, and if the company waits too long, the problems increase and the LP implementation will be unsuccessful.

4 CONCLUSION Based on the literature review and the lack of the timely detection of management support by LP implementation, a new model was proposed to facilitate successful lean implementation in SMEs. The model consists of five steps: specify value; value stream; flow; pull and perfection, combined with lean learning for management and employees and supported by four interview guides; and conducted after each step of the LP implementation plan with a

Methodology to Facilitate Successful Lean Implementation

463

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 457-465

strong emphasis on knowledge, management support and communication.

With the help of the proposed model, a company can monitor and simultaneously verify the LP implementation and can immediately react to a small sign of poor knowledge or lack of management support that is critical to the LP implementation, and which was tested in two different companies.

The IG are meant as a guide for interviews after each step defined by the model, based on which the company can easily conduct a review after each step, before the LP implementation deviates from the right path of successful LP implementation and growth of healthy lean culture.

Beside the needed knowledge, special attention is paid to management support with a question that is asked after each step, since management support can be quickly forgotten after dealing with new, possibly hidden production problems.

This proposed model accompanied by the IG is a ‘simple guide’ that needs to be followed by a company that is implementing LP. With the help of the proposed model and the four IG, a company will have a much higher success rate than without them.

This model is developed and especially suitable for SMEs because of their lack of human resources.

However, the model can also be used for a large scale industries, where they have a department for lean implementation or at least one employee for this task, but with the help of the proposed model, a company can monitor and simultaneously verify the LP implementation and can immediately react to a small sign of poor knowledge or a lack of management support that is critical to the LP implementation.

Our future research will continue with the proposed idea by upgrading the model for the implementation of agile manufacturing and agile manufacturing.

5 REFERENCES [1] Sugimori, Y., Kusunoki, K., Cho, F., Uchikawa, S. (1977). Toyota Production System and Kanban System Materialisation of Just-in-time and Respect-for-human System. International Journal of Production Research, vol. 15, no. 6, p. 553–564, DOI:10.1080/00207547708943149.

[2] Hines, P., Holweg M., Rich N. (2004). Learning to Evolve. A Review of Contemporary Lean Thinking. International Journal of Operations & Production Management, vol. 24, no. 10, p.

994–1011, DOI:10.1108/01443570410558049.

[3] Womack, J.P., Jones, D.T. (2003). Lean Thinking: Banish Waste and Create Wealth in Your Corporation, (2nd ed.), Free Press, New York.

464

[4] Papadopoulou, T.C., Özbayrak, M. (2005). Leanness: Experiences from the Journey to Date. Journal of Manufacturing Technology Management, vol. 16, no. 7, p.

784–807, DOI:10.1108/17410380510626196.

[5] Achanga, P., Shehab, E., Roy, R., Nelder, G. (2006). Critical Success Factors for Lean Implementation within SMEs. Journal of Manufacturing Technology Management, vol. 17, no. 4, p. 460–471, DOI:10.1108/17410380610662889.

[6] Pay, R. (2008). Everybody’s Jumping on the Lean Bandwagon But Many Are Being Taken for a Ride, Industry Week, from http://www.industryweek.com/companies-amp-executives/ everybodys-jumping-lean-bandwagon-many-are-being-takenride, accessed on 2015-6-29.

[7] Atkinson, P. (2010). Lean is a Cultural Issue. Management Services, vol. 54, no. 2, p. 35–41.

[8] Pirraglia, A., Saloni, D., Van Dyk, H. (2009). Status of lean manufacturing implementation on secondary wood industries including residential, cabinet, millwork, and panel markets.

Bio Resources, vol. 4, no. 4, p. 1341–1358.

[9] Turesky, E.F., Connell, P. (2010). Off the Rails: Understanding the Derailment of a Lean Manufacturing Initiative.

Organisation Management Journal, vol. 7, no. 2, p. 110–132, DOI:10.1057/omj.2010.14.

[10] Karim, A., Arif-Us-Zaman, K. (2013). A methodology for effective implementation of lean strategies and its performance evaluation in manufacturing organizations.

Business Process Management Journal, vol. 19, no. 1, p.

169–196, DOI:10.1057/omj.2010.14.

[11] Rymaszewska, A.D. (2014). The challenges of lean manufacturing implementation in SMEs. Benchmarking: An International Journal, vol. 21, no. 6, p. 987–1002, DOI:10.1108/BIJ-10-2012-0065.

[12] Herzog, V.N., Tonchia, S. (2014). An instrument for measuring the degree of lean implementation in manufacturing. Strojniški vestnik – Journal of Mechanical Engineering, vol. 60, no. 12, p. 797–803, DOI:10.5545/sv-jme.2014.1873.

[13] Bortolotti, T., Boscari, S., Danese, P. (2015). Successful lean implementation: organizational culture and soft lean practices. International Journal of Production Economics, vol.

160, p. 182–201, DOI:10.1016/j.ijpe.2014.10.013.

[14] Rane, A.B., Sunnapwar, V.K., Rane, S. (2016). Strategies to overcome the HR barriers in successful lean implementation.

International Journal of Procurement Management, vol. 9, no.

2, p. 223–247, DOI:10.1504/IJPM.2016.075266.

[15] Jekiel, C.M. (2011). Lean Human Resources: Redesigning HR Processes for a Culture of Continuous Improvement.

Productivity Press, New York.

[16] Balaji, K., Senthil Kumar, V.S. (2016). Evaluation and selection of lean resourced employee in the manufacturing industries using the TOPSIS-Simos method. Proceedings of the Institution of Mechanical Engineers, Part B, Journal of Engineering Manufacture, DOI:10.1177/0954405416635069.

[17] Yadav, O.P., Nepal, B.P., Rahaman, M.M., Lal, V. (2017).

Lean implementation and organizational transformation: A literature review. Engineering Management Journal, vol. 29, no. 1, p. 2-16, DOI:10.1080/10429247.2016.1263914.

Berlec, T. – Kleindienst, M. – Rabitsch, C. – Ramsauer, C.

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 457-465

[18] Pearce, A. (2014). Lean Thinking and the Factors Necessary for Its Success, PhD thesis, University of Canterbury, Christchurch.

[19] Pentlicki, J.H. (2014). Barriers and Success Strategies for Sustainable Lean Manufacturing Implementation: A Qualitative Case Study, PhD thesis, University of Phoenix, Phoenix.

[20] Boyle, T.A., Scherrer-Rathje, M., Stuart, I. (2011). Learning to be Lean: The Influence of External Information Sources in Lean Improvements. Journal of Manufacturing Technology Management, vol. 22, no. 5, p. 587–603, DOI:10.1108/17410381111134455.

[21] Herakovic, N., Metlikovic, P., Debevec, M. (2014). Motivational lean game to support decision between push and pull production strategy. International Journal of Simulation Modelling, vol. 13, no. 4, p. 433–446, DOI:10.2507/ IJSIMM13(4)4.275.

[22] Belekoukias I., Garza-Reyes J.A., Kumar, V. (2014). The impact of lean methods and tools on the operational performance of manufacturing organisations. International Journal of Production Research, vol. 52, no. 18, p. 5346–5366, DOI:10.1 080/00207543.2014.903348.

[23] Kull, T.J., Yan, T., Liu, Z., Wacker, J.G. (2014). The moderation of lean manufacturing effectiveness by dimensions of national culture: Testing practice-culture congruence hypotheses.

International Journal of Production Economics, vol. 153, p.

1-12, DOI:10.1080/00207543.2014.903348.

[24] Poksinska, B., Swartling, D., Drotz, E. (2013). The daily work of lean leaders - lessons from manufacturing and healthcare.

Total Quality Management & Business Excellence, vol. 24, no.

7-8, p. 886–898, DOI:10.1080/00207543.2014.903348.

[25] Heath, C., Heath, D. (2010). Switch: How to Change Things When Change is Hard, Crown Publishing, New York.

[26] Mostafa, S., Dumrak, J., Soltan, H. (2013). A framework for lean manufacturing implementation. Production &

Manufacturing Research, vol. 1, no. 1, p. 44–64, DOI:10.1080 /00207543.2014.903348.

[27] Drew, J., McCallum, B., Roggenhofer, S. (2004). Journey to Lean: Making Operational Change Stick, Palgrave Macmillan, London, DOI:10.1057/9781403948410.

[28] Marodin. G.A., Saurin, T.A. (2013). Implementing lean production systems: Research areas and opportunities for future studies. International Journal of Production Research, vol. 51, no. 22, p. 6663–6680, DOI:10.1080/00207543.201 4.903348.

[29] Anvari, A.R., Norzima, Z., Rosnah, M.Y., Hojati, S.M.H., Ismail, Y. (2010). A comparative study on journey of lean manufacturing implementation. Asian International Journal of Science and Technology in Production and Manufacturing Engineering, vol.

3, no. 2, p. 77–85.

[30] Scherrer-Rathje, M., Boyle, T.A., Deflorin, P. (2009). Lean, take two! Reflections from the second attempt at lean implementation. Business Horizons, vol. 52, no. 1, p. 79–88, DOI:10.1016/j.bushor.2008.08.004.

[31] Nguyen, D.M. (2015). A new application model of lean management in small and medium-sized enterprises.

International Journal of Simulation Modelling, vol. 14, no. 2, p.

289-298, DOI:10.2507/IJSIMM14(2)9.304.

[32] Worley, J.M., Doolen, T.L. (2006). The role of communication and management support in a lean manufacturing implementation. Management Decision, vol. 44, no. 2, p.

228–245, DOI:10.1108/00251740610650210.

[33] Götze, U., Northcott, D., Schuster, P. (2015). Investment Appraisal: Methods and Models. Springer-Verlag, Berlin Heidelberg, DOI:10.1007/978-3-662-45851-8.

[34] Rihar, L., Kušar, J., Gorenc, S., Starbek, M. (2012). Teamwork in the Simultaneous Product Realisation. Strojniški vestnik - Journal of Mechanical Engineering, vol. 58, no. 9, p. 534– 544, DOI:10.5545/sv-jme.2012.420.

Methodology to Facilitate Successful Lean Implementation

465

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 466-475 © 2017 Journal of Mechanical Engineering. All rights reserved.

DOI:10.5545/sv-jme.2017.4384 Original Scientific Paper

Received for review: 2017-02-07 Received revised form: 2017-04-07 Accepted for publication: 2017-06-06

Development of a Servo-Based Broaching Machine Using Virtual Prototyping Technology Park, H.S. – Dang, D.V. – Nguyen, T.T. Hong Seok Park1 – Duc Viet Dang1,* – Trung Thanh Nguyen2

1University 2Le

of Ulsan, School of Mechanical and Automotive Engineering, South Korea Quy Don Technical University, Faculty of Mechanical Engineering, Viet Nam

Predicting machine tool performance at the design stage is one way to resolve the time issue and achieve cost savings. The objective of this paper was to develop a new non-hydraulic broaching machine using a servo motor, ball screw, and roll element linear guide using virtual prototyping technology. First, we developed a multi-body simulation model (MBS) of a servo-based broaching machine to investigate its dynamic behaviour. Then, an adaptive sliding mode proportional-integral-derivative (PID)-based controller (ASMPID) was proposed to conduct the broaching process. We then performed a co-simulation between the mechanical structure and virtual controller to investigate the ram body trajectory and identify the optimal control parameters. Finally, we manufactured a prototype machine to evaluate the simulation results and determine the benefits of the new system. Our results indicated that the proposed model, which includes a mechanical structure and intelligent controller, effectively improved broaching machine design. Therefore, this work is expected to improve the prototyping efficiency of new broaching machines.

Keywords: broaching machine, servo motor, ball screw, virtual prototype technology, multi-body simulation, adaptive sliding mode control Highlights • A new broaching machine that uses a servo motor, ball screw, and roll element linear guide has been developed to replace hydraulic components.

• A multi-body model of the new broaching machine that includes a control system model was established to generate a virtual prototype machine.

• The proposed adaptive sliding mode PID-based controller effectively eliminates external disturbances in the non-linear system during the broaching process.

• The experimental results show that the servo-based broaching machine can eliminate the disadvantages of a traditional machine and increase product quality.

0 INTRODUCTION Broaching is widely used in industrial applications to machine various features on internal surfaces, including key ways, noncircular holes, and firtree slots on turbine discs. This operation has several benefits when machining conditions are appropriately selected, including high productivity, compatible surface integrity, and ensured geometrical accuracy. Unfortunately, conventional broaching machines, which use a hydraulic system, have many disadvantages, such as noisy operation, excessive energy consumption, low productivity, and large footprint required for installation (Fig. 1). The hydraulic pump is the dominant source of noise and consumes 60 % to 80 % of the total energy. Therefore, the development of a new broaching machine without a hydraulic system is desirable.

The optimization of broaching has attracted the attention of many researchers. Klocke et al. [1] investigated the effects of cutting-edge geometries on the process forces, chip formation, and tool wear mechanisms. The surface quality was analysed under 466

various machining parameters in real processing time [2] to [4]. However, no one has investigated the interaction between the mechanical structure of the machine and its controller under working conditions.

Consequently, an effective approach to predict machine performance before physical prototyping is urgently needed.

Usually, a physical prototype is used in the design stage to produce and evaluate new machine models.

However, this method is slow and expensive [5].

Fortunately, many publications have indicated that virtual prototyping approaches using well-defined material properties, numerical models, and controllers can accurately analyse, simulate, and investigate real machine behaviour. Dai et al. [6] developed a virtual prototype model for a remotely operated seabed tracked vehicle to optimize and support the control system without the need for expensive hardware prototyping. Likewise, virtual prototyping of industrial equipment has been proposed to investigate dynamic behaviour in the initial stage [7] to [9]. All these studies demonstrated that virtual prototyping

*Corr. Author’s Address: School of Mechanical and Automotive Eng., University of Ulsan, 93 Daehak-ro, Nam-gu, Ulsan 44610, South Korea, vietnarime@gmail.com

StrojniĹĄki vestnik - Journal of Mechanical Engineering 63(2017)7-8, 466-475

technology is a powerful tool for simulating and optimizing machine tool characteristics.

conducted to identify the machine tool behaviour and stress distribution. Then, an intelligent controller was designed and integrated with the mechanical model to construct a virtual prototype of our new broaching machine. A co-simulation was performed to evaluate the controller functionality. Finally, the physical machine was manufactured to perform broaching operations and verify that the design requirements were met.

2 CONCEPTUAL DESIGN OF A SERVO-BASED BROACHING MACHINE

Fig. 1. A conventional broaching machine using a hydraulic unit

To overcome the limitations of hydraulic systems, we developed a new broaching machine using a servo motor, ball screw, and roll element linear guide based on virtual prototyping technology. We found that the interaction between the mechanical structure and the controller, along with external disturbances in processing time, contributed to the machine tool efficiency. Consequently, the development of a robust approach for describing machine tool behaviour and generating optimal control parameters is an important area of research.

In this paper, the scientific methodology used to resolve these issues is first introduced. Next, the concept for a new broaching machine and mechanical model are presented. The multi-body rigid-flexible model and control system are then described.

Subsequently, the co-simulation results of the virtual broaching machine and the physical prototype are discussed. Finally, we draw conclusions and suggest future research.

A servo-based broaching machine was developed based on a 7.5-ton hydraulic version currently used to manufacture the internal surface of automotive components such as hubs, inner races, and sleeves (Fig. 3 [10]). The machine has five key systems: a feed drive, controller, slider, frame, and tool brush. The configuration of the servo-based broaching machine is shown in Fig. 4, and the specifications are listed in Table 1. In the proposed concept, the servo-driven axis and ball screw are mounted on the machine frame.

The sliding system, which includes the table lift, tool brush, and linear guide, performs the broaching motions. The closed-loop principle is applied to control the feed driving movements. As a result, the new servo-based broaching machine can offer high productivity, appropriate stiffness, improved accuracy, noise reduction, and a smaller footprint than the traditional one can.

1 RESEARCH METHODOLOGY The framework proposed for the development of a new broaching machine based on a multi-body simulation (MBS) model and an intelligent virtual controller is shown in Fig. 2. We formulated the problem and designed the mechanical structure based on specific requirements. Next, an MBS model of the new machine was developed to represent the actual mechanical system and to determine the body relationships, degrees of freedom, space missions, joint types, and geometric constraints in an integrative model. Subsequently, a dynamic simulation was

Fig. 2. The framework for developing a servo-based broaching machine

Development of a Servo-Based Broaching Machine Using Virtual Prototyping Technology

467

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 466-475

The working principle of the servo-based broaching machine can be divided into the following steps: Step 1: A work piece is transferred to the ram body and is clamped using the jig system.

Step 2: The retrieving head-system-mounted tool moves down to perform the broaching process. This motion is conducted with the support of the lift servo motor, ball screw, and linear ball-bearing guide.

Step 3: The tool is engaged by the pulling head system, and the ram body is then moved to the highest position required for broaching the desired shapes. The retrieving head system is moved after the machining cycle is complete.

Step 4: The ram body is moved to the bottom of the machine, and the machined part is removed. The retrieving head system is moved down, and a new machining cycle can then begin.

3 DEVELOPMENT OF A MULTI-BODY MODEL 3.1 The Equations of Motion for a Flexible Multi-Body System A multi-body dynamic model can be created using variations of mechanical principles, such as the energy conservation law, the Newton-Euler equation, the Lagrange equation, the Hamilton principle, and the Kane equation. Among these approaches, the Lagrange equation has been widely applied to build forward or inverse kinematics model [11] and [12].

A flexible body can be considered as a collection of nodes in a finite element model, and deformation can be seen as a linear superposition of mode shapes.

Fig. 4. The configuration of a servo-based broaching machine

Fig. 5 illustrates the position of a particle P0i and a node on flexible body i, where point Pi is the new  position of node P0i according to vector u if when body i is deformed. The global reference frame of body i is represented using the Cartesian coordinates

x, y, and z. r ( x y z ) is the origin vector for the position of the local reference coordinate system (xi, yi, zi) for body i. Its direction, expressed in Euler angles, is π = (ϕ θ ψ ) . The deformation of the flexible body depicted by generalized coordinates is  T q = {q1 q2 ... qm } .

Table 1. Specifications of the new broaching machine Specifications Cutting power [N] Main stroke [mm] Lift stroke [mm] Cutting speed [mm/s] Return speed [mm/s] Main servo motor [kW] Lift servo motor [kW]

Value 80000 1235 700 100 200 14 4

Fig. 3. The main machined parts in the new broaching machine

468

Fig. 5. Location and orientation of points in a flexible body

Therefore, the generalized coordinates of the flexible body can be expressed as:

ξ = {x y z , ϕθψ , qi (i = 1,..., m)}T = { r π q}, (1)

where m is the number of model coordinates. The location vector of node Pi in a global reference frame  can be defined by the vector rPi as follows:

Park, H.S. – Dang, D.V. – Nguyen, T.T.

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 466-475

      rPi = r + Ai u ip = r + Ai (u0i + u if ), (2)

where Ai denotes the transformation matrix from the local coordinate system to the global coordinate system, which is expressed in terms of four Euler  parameters. u pi is the position vector of point Pi given  the body’s local coordinate system. u0i is the position i of point P0 in a non-deformed state of body i in a  local coordinate system. u if is the direction vector of point Pi on a deformed body with respect to point P0i on a non-deformed body.  u if = Φ p q. (3)

Φp is the supposed deformation mode matrix for the motion’s degree of freedom on node Pi. The velocity of node P0i can be expressed as:

v p = [I − Ai (u 0i + u if ) B Ai Φ p ]ξ , (4)

where I and the tilde symbol present the identity matrix and skew symmetric matrix, respectively.

Matrix B is defined as a first-order derivative of a Eulerian angle relative to time or the angular velocity transition matrix. Consequently, the kinetic energy in the flexible body can be expressed as:

T=

1 1 ρν Tν dV = ξT M (ξ )ξ, (5) 2∫ 2

where ρ and M are the mass density and flexible-body mass matrix, respectively. The potential energy of the flexible body is:

1 W = Wg (ξ ) + ξ T K ξ , (6) 2

Substituting the calculated values for T, W and G into Eq. (8) gives the flexible body differential equation of motion using the Lagrange multipliers method: T

1  ∂M   M ξ + M ξ −  ξ + Kξ + f g + 2  ∂ξ  T

 ∂ψ  (9) + Dξ +   λ = Q,  ∂ξ  where fg , ξ , and ξ are the gravity force and first and second derivatives of the generalized coordinates of the flexible body, respectively.

3.2 Modelling the Multi-Body Rigid-Flexible System of the New Broaching Machine The framework for the rigid-flexible coupling dynamics analysis is illustrated in Fig. 6. First, the 3D machine model with component characteristics was designed based on the conceptual design. The machine tool parts are divided into two key bodies, rigid and flexible, depending on their working functionalities.

ANSYS software was used to discretize the components into a small grid and generate modal neutral files. Next, the rigid and flexible bodies were imported into the ADAMS software by means of a Parasolid file in the *.x_t format and a modal neutral file in the *.mnf format, respectively. The driving modes of the joints were then specified for predetermined motions. Finally, we performed a dynamic simulation to evaluate the characteristics of the conceptual design.

where K is a generalized stiffness matrix corresponding to mode coordinate q. Damping force depends on the generalized modal velocity and can be deduced from:

1 Γ = qT Dq, (7) 2

where G and D represent the energy dissipation function and constant symmetry matrix, respectively.

Due to interactions between the components, the kinetic equation can be inferred from [12]:

 d  ∂L  ∂L ∂Γ  ∂ψ T + +   −  λ − Q = 0 , (8)  dt  ∂ξ  ∂ξ ∂ξ  ∂ξ   ψ = 0

where L = T – W, ψ, λ, and Q are the Lagrange term, constraint equation, Lagrange multiplier, and generalized forces, respectively.

Fig. 6. Flowchart modelling the rigid-flexible coupling

The proposed rigid-flexible multi-body model of a servo-based broaching machine is shown in Fig. 7.

Development of a Servo-Based Broaching Machine Using Virtual Prototyping Technology

469

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 466-475

The ram body deforms under the working conditions that occur during processing. Therefore, it is necessary to model this component as a flexible body. The CAD model of the ram body was thus transferred to the FA software ANSYS. The material properties, unit type, unit attributes, and mesh parameters were defined before meshing. Two connection points in ANSYS were specified to generate the relationships between the flexible body and other components. The modal neutral file (*.mnf file) was generated using the interface between ANSYS and ADAMS. The other components (base frame, cutting tool, and frame column) were modeled as rigid bodies due to their low deformation during processing and were assigned mass and inertia matrices as illustrated in Table 2.

information about the 10 maximum stress nodes is shown in Table 3. The maximum stress is less than the allowable value, and the ram body meets the strength requirement. In other words, the designed machine is safe in terms of dynamic behaviour. Therefore, the developed model can be used to simulate, analyse, and validate the machine functionality.

Fig. 8. Stress distribution in the new broaching machine Table 3. Details associated with the maximum stress on the ram body

Fig. 7. Rigid-flexible coupling model Table 2. Parameter values used to model the broaching machine Parts

Material

Cutting tool SKH-55 Workpiece SCr420H1 Rambody Steel Frame Steel Base Cast-Iron

Mass [kg] 35.4 4 897.2 3559 2313

Ixx [kg∙m2] 4.661 0.007 99.922 5077.47 1005.525

Iyy [kg∙m2] 4.661 0.007 106.038 5093.63 633.586

Izz [kg∙m2] 0.02 0.013 32.5 452.47 1518.337

The simulation of the rigid-flexible model was conducted to investigate the machine behaviour under working conditions using: 1000 steps in 20 s intervals.

The Von Mises stress distribution in the ram body during processing is illustrated in Fig. 8. Detailed 470

Hot spot 1 2 3 4 5 6 7 8 9 10

Stress [MPa] 103.515 99.0346 98.0287 97.6758 93.0629 91.8174 91.2342 89.9963 89.845 88.9793

Node 3324 49 50 51 1196 765 1174 711 52 53

Time [s] 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8 1.8

X [mm] -1806.36 -1841.61 -1818.6 -1794.12 -1951.36 -1961.36 -1951.36 -1941.36 -1771.11 -1752.35

Y [mm] 489.718 738.663 730.289 730.289 423.195 418.86 410.812 418.86 738.663 754.401

Z [mm] -76.8091 -399.309 -399.309 -399.309 -174.94 -168.451 -168.404 -168.451 -399.309 -399.309

4 DEVELOPMENT OF AN INTELLIGENT CONTROLLER 4.1 Controller Design The proportional-integral-derivative (PID) control method is widely applied in linear systems due to its simplicity and effectiveness. This method is insensitive to parameter changes, including proportional gain KP, integral gain KI, and derivative

Park, H.S. – Dang, D.V. – Nguyen, T.T.

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 466-475

gain KD. Furthermore, self-tuning controller gains can improve potential applications of the PID control [13] and [14]. In addition, the sliding mode control (SMC) is a popular strategy to deal with uncertain control systems [15] to [17]. The main advantage of the SMC method is its robustness against parameter variations and external disturbances. Therefore, combining an adaptive SMC with a PID controller (ASMPID) is an intelligent choice for updating PID gains and adapting to non-linear systems [18] and [19]. Here, we propose an ASMPID controller to investigate the ram body position of a servo-based broaching machine (Fig. 9).

4.2 Interaction between the Mechanical Model and Control System The mechanical structure and control system communicate through an exchange of state variables.

In this work, the control design was developed based on ADAMS/Control and MATLAB/Simulink, as depicted in Fig. 10a. The input and output signals represent the main servo motor torque and ram body position, respectively. These parameters were first defined in the ADAMS model to generate the state variable. After that, the virtual mechanical model was exported to the MATLAB/Simulink environment to complete the interaction (Fig. 10b). As mentioned above, the new broaching machine was considered to be a system with a single input and output. The statespace equation for the ram body displacement can be expressed as follows:

x1 (t ) = x2 (t ), x2 (t ) = f ( X ) + b( X )u + d (t ), (10) T

where X = ( x1 , x2 ) is a state variable vector that represents the position of the ram body. f(X ) and b(X ) are nonlinear functions. d(t) is the bounded lumped disturbance, including parameter variations and external disturbances, u represents a control signal.

As shown in Eq. (10), the sliding surface can be defined as:

s = e + λ e, (11)

where e = xd – x, and xd, x, and λ are the desired position, measured position, and positive constant, respectively. x in Eq. (11), gives Substituting x2 (t ) = 

uPID =

ds T where A = [ K P K I K D ] , B = [ s ∫ s ] , and ε is the dt appropriate error.

The control signal u of the controller is determined as: u = uPID + uh = AB + uh , (14)

P K I K  D ] represents the estimated where A = [ K values of vector A, and uh is the signal of the auxiliary controller.

Substituting Eq. (14) into Eq. (12) yields s = xd − f ( X ) − b( X )[ AB + uh ] − d (t ) + λ e = A B + b( X )ε − b( X )u , = b( X ) (15) h

where A = A − A is the estimation error.

To prove the stability of the system, we used a Lyapunov function: 1 1 2

V = s2 + A . (16) 2 2γ The derivative of Eq. (16) yields: i 1 i V = ss+ AA= γ i

i

1 = s (b( X ) AB + b( X )ε − b( X )u h ) + AA= γ = ( sb( X ) B +

1 i A ) A + sb( X )ε − b( X )u h s ≤ 0 . (17) γ

From Eq. (17), we have: ( sb( X ) B + i

i

1 i A ) = 0. γ

A = − A = −γ sb( X ) B. Hence, The three PID gains (KP, KI, and KD) are updated on-line by the following adaptive laws: i

i

t

i

ds P = γ sb( X ) s , K K I = γ sb( X ) ∫ s, K D = γ sb( X ) .(18) dt 0

Considering Eq. (17): V = sb( X )ε − b( X )u h s ≤ 0.

With the auxiliary controller, uh = η sgn(s); the sign function is:  1 if s > 0  sgn( s ) =  0 if s = 0 . (19) −1 if s < 0 

Therefore, we have:

s =  xd − f ( X ) − b( X )u − d (t ) + λ e. (12)

The control effort u of the PID controller is determined as:

1 [  xd − f ( X ) − d (t ) + λ e] = AB + ε , (13) b( X )

V = sb( X )ε − b( X )η sgn( s ) s ≤ ≤ sb( X )ε − b( X )η s < b( X ) s ( ε − η ) < 0

⇒η > ε .

Development of a Servo-Based Broaching Machine Using Virtual Prototyping Technology

(20) 471

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 466-475

Fig. 9. Control scheme for ram body movement

a)

b) Fig. 10. The principle of connection between ADAMS and MATLAB/Simulink; a) inputs and outputs in ADAMS and MATLAB, and b) interactions between the mechanical structure and controller

Eq. (17) proves that the sliding surface is stable.

The control torque of the main servo motor in the new broaching machine is shown in Eq. (14).

5 SIMULATION RESULTS We performed a co-simulation that integrated the MBS model and the ASMPID controller. The tracking performance of the ram body is shown in Fig. 11a, in which the reference value (REF) was derived based

a)

472

on the ram body trajectory. The simulation results revealed that the overshoot and settling time were near zero. Furthermore, the steady state error was satisfied with stable control criteria, and external disturbances were eliminated. Additionally, the ram body velocity was close to the design specification, as shown in Fig. 11b. Therefore, the proposed ASMPID controller is a robust approach to optimizing system parameters and eliminate disturbances.

b) Fig. 11. Co-simulation results; a) tracking performance of the ram body, and b) ram body velocity Park, H.S. – Dang, D.V. – Nguyen, T.T.

StrojniĹĄki vestnik - Journal of Mechanical Engineering 63(2017)7-8, 466-475

6 PHYSICAL PROTOTYPING The hardware for the new broaching machine was developed based on the 3D CAD model, and the results are described in Sections 3 and 5. The base frame, frame column, and ram body are illustrated in Fig. 12. We selected a THK ball screw (HBN10025S7.5RRG2 +3055LC5) for its high load capacity, low torque fluctuation, low noise, and low long-term maintenance (Fig. 13a). The permissible axial force is approximately 179 kN to ensure rigidity under broaching forces. The linear guide has balls that roll in four rows, LM rails, and an LM block (model SHS45LR4KKHHC0E+2460LPI) to replace the traditional sliding guides (Fig. 13b). The main servo (A06B-0275-B410 with 14 kW power) generated the ram body movements, and the tool lift servo motor (A06B-0247-B400 with 4 kW) controlled the broaching tool motions. The machine controller is implemented using the algorithm proposed in Section 4.

operating noise decreased by approximately 29 %, and the required working floor area decreased by about 30 % compared to the hydraulic-driven machine.

Furthermore, the product quality criteria, including perpendicularity, concentricity, and true position, improved by around 49 %. The broaching force tested in the processing time is shown in Fig. 15. The small error between the simulation and experimental results demonstrates that the proposed approach is feasible and can be effectively used in machine tool design.

a)

a)

b) Fig. 13. Components purchased for the machine; a) ball-screw, b) linear guide

b) Fig. 12. Prototyped mechanical parts; a) machine frame, and b) ram body

The broaching process was conducted to verify the simulation results in terms of the ram body velocity and broaching forces, as illustrated in Fig. 14. Moreover, the noise level and product quality also were investigated in order to verify the machine performance. The results indicate that the new broaching machine adequately meets the quality criteria and design specifications (Table 4). The

Fig. 14. Physical prototype of the new broaching machine

Table 4. Experimental confirmation Performance specifications Co-axiality of the broach tool [mm] Broaching speed [mm/s] Return speed [mm/s] Machine noise [dB] Broaching force [N] Perpendicularity of the part [mm] Concentricity of the part [mm] True position [mm]

Conventional machine 0.05 135 235 80 100000 0.08 0.08 0.5

Desired values in the machine 0.04 100 200 60 80000 0.06 0.06 0.3

Measured values 0.03 100 200 56.9 81800 0.042 0.044 0.254

Development of a Servo-Based Broaching Machine Using Virtual Prototyping Technology

Standard KS B ISO 6779 Test report Test report KS I 5004 Test report KS B ISO 6779 KS B ISO 6779 KS B ISO 6779

473

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 466-475

9 REFERENCES

Fig. 15. Broaching force in processing time

7 CONCLUSIONS In summary, this work presented the development of a new broaching machine based on an MBS and the implementation of modern control technology. The MBS model was developed to investigate the machine dynamic behaviour as a function of processing time.

ASMPID was proposed and integrated into the synthesis model. The co-simulation was performed to investigate the dynamic machine tool behaviour and to obtain the optimal control parameters for eliminating system disturbances. The prototyped machine was implemented to conduct the broaching process and evaluate the simulation results. The following conclusions can be drawn from this investigation.

1. Based on conceptual ideas, a new broaching machine was developed using a servo motor, ball screw, and roll element linear guide.

2. The simulation results indicate that the virtual prototyping model is safe in terms of dynamic behavior, satisfies the specifications, and has stable control criteria.

3. The ASMPID controller effectively eliminates external disturbances in this non-linear system during the broaching process.

4. The experimental results show that the new broaching machine can eliminate the disadvantages of a traditional machine and increase the product quality.

8 ACKNOWLEDGEMENTS This work was supported by an Institute for Information & Communications Technology Promotion (IITP) grant funded by the Korean government (MSIP) (B0101-16-1081, Development of ICT-based software platform and service technologies for medical 3D printing applications).

474

[1] Klocke, F., Vogtel, P., Gierlings, S., Lung, D., Veselovac, D. (2013). Broaching of Inconel 718 with cemented carbide. Production Engineering, vol. 7, no. 6, p. 593-600, DOI:10.1007/s11740-013-0483-1.

[2] Schulze, V., Zanger, F., Krauße, M., Boev, N. (2013). Simulation approach for the prediction of surface deviations caused by process-machine-interaction during broaching. Procedia CIRP, vol.8, p. 252-257, DOI:10.1016/j.procir.2013.06.098.

[3] Kishawy, H.A., Hosseini, A., Moetakef-Imani, B., Astakhov, V.P. (2012). An energy based analysis of broaching operation: Cutting forces and resultant surface integrity. CIRP Annals - Manufacturing Technology, vol. 61, no. 1, p. 107-110.

DOI:10.1016/j.procir.2013.06.098.

[4] Zanger, F., Boev, N., Schulze, V. (2014). Surface quality after broaching with variable cutting thickness. Procedia CIRP, vol.

13, p. 114-119, DOI:10.1016/j.procir.2014.04.020.

[5] Mandić, V., Ćosić, P. (2011). Integrated product and process development in collaborative virtual engineering environment.

Technical Gazette - Tehnički vjesnik, vol. 18, no. 3, p. 369-378.

[6] Dai, Y., Zhu, X., Chen, L.S. (2016). A mechanical-hydraulic virtual prototype co-simulation model for a seabed remotely operated vehicle. International Journal of Simulation Modelling, vol. 15, no. 3, p. 532-541, DOI:10.2507/ IJSIMM15(3)CO11.

[7] Zivanovic, S., Glavonjic, M., Milutinovic, D., (2015). Configuring a mini-laboratory and desktop 3-axis parallel kinematic milling machine. Strojniški vestnik - Journal of Mechanical Engineering, vol. 61, no. 1, p. 33-42, DOI:10.5545/svjme.2013.1619.

[8] Dai, Y., Pang, L., Chen, L., Zhu, X., Zhang, T. (2016) A new multi-body dynamic model of a deep ocean mining vehiclepipeline-ship system and simulation of its integrated motion.

Strojniški vestnik - Journal of Mechanical Engineering, vol. 62, no. 12, p. 757-763, DOI:10.5545/sv-jme.2015.3211.

[9] Tesic, Z., Stevanov, B., Jovanovic, V., Tomic, M., Kafol, C. (2016). Period batch control - a production planning system applied to virtual manufacturing cells. International Journal of Simulation Modelling, vol. 15, no. 2, p. 288-301, DOI:10.2507/ IJSIMM15(2)8.337.

[10] Korea Broach Manufacture Corporation. (2017). from http:// www.broachmc.co.kr/, accessed on 2016-10-02.

[11] Ambrósio, J.A.C., Gonçalves, J.P.C. (2001), Complex flexible multibody systems with application to vehicle dynamics.

Multibody System Dynamics, vol. 6, no. 2, p. 162-182, DOI:10.1023/A:1017522623008.

[12] Shabana, A.A. (2014). Dynamics of Multibody Systems, 4th ed., Cambridge University, Cambridge.

[13] Guclu, R. (2006). Sliding mode and PID control of a structural system against earthquake. Mathematical and Computer Modelling, vol. 44, no. 1-2, p. 210-217, DOI:10.1016/j. mcm.2006.01.014.

[14] Leva, A. (1993). PID autotuning algorithm based on relay feedback. IEEE Proceedings D - Control Theory and Applications, vol. 140, no. 5, p. 328-337, DOI:10.1049/ipd.1993.0044.

Park, H.S. – Dang, D.V. – Nguyen, T.T.

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, 466-475

[15] Wang, W., Yi, J., Zhao, D., Liu, D. (2014). Design of a stable sliding-mode controller for a class of second-order underactuated systems. IEE Proceedings - Control Theory and Applications, vol. 151, no. 6, p. 683-690, DOI:10.1049/ ip-cta:20040902.

[16] Young, K.D., Utkin, V.I., Özgüner, Ü., (1999). A control engineer’s guide to sliding mode control. IEEE Transactions on Control Systems Technology, vol. 7, no. 3, p. 328-342, DOI:10.1109/87.761053.

[17] Zinober, A.S.I. (1994). Variable Structure and Lyapnuov Control, Springer-Verlag, Berlin, DOI:10.1007/BFb0033675.

[18] Chang, W.-D., Yan, J.-J. (1994). Adaptive robust PID controller design based on a sliding mode for uncertain chaotic systems. Chaos Solitons & Fractals, vol. 26, no. 1, p. 167-175, DOI:10.1016/j.chaos.2004.12.013.

[19] Kuo, T.C., Huang, Y.J., Chen, C.Y., Chang, C.H. (2008). Adaptive sliding mode control with PID tuning for uncertain systems.

Engineering Letters, vol. 16, no. 3, p. 311-315.

Development of a Servo-Based Broaching Machine Using Virtual Prototyping Technology

475

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8 Vsebina

Vsebina Strojniški vestnik - Journal of Mechanical Engineering letnik 63, (2017), številka 7-8 Ljubljana, julij-avgust 2017 ISSN 0039-2480 Izhaja mesečno

Razširjeni povzetki (extended abstracts) Luka Skrinjar, Janko Slavič, Miha Boltežar: Metoda absolutnih vozliščnih koordinat v prednapetem dinamskem sistemu z velikimi pomiki Kozhikkatil Sunil Arjun, Rakesh Kumar: Analiza mikrokonvekcije v toku MHD-nanofluida po metodi LBM Florent Bunjaku, Risto V. Filkoski, Naser Sahiti: Toplotna optimizacija in primerjava geometrijskih parametrov pravokotnih in trikotnih reber z enako površino Hao Feng, Qungui Du, Yuxian Huang, Yongbin Chi: Modeliranje togosti hidravličnega cilindra ob upoštevanju več faktorjev Tomaž Berlec, Mario Kleindienst, Christian Rabitsch, Christian Ramsauer: Metodologija za uspešno uvajanje vitke proizvodnje Hong Seok Park, Duc Viet Dang, Trung Thanh Nguyen: Razvoj stroja za posnemanje s pomočjo tehnologije virtualnih prototipov Osebne objave

SI 61 SI 62 SI 63 SI 64 SI 65 SI 66 SI 67

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, SI 61 © 2017 Strojniški vestnik. Vse pravice pridržane.

Prejeto v recenzijo: 2017-05-04 Prejeto popravljeno: 2017-05-25 Odobreno za objavo: 2017-06-02

Metoda absolutnih vozliščnih koordinat v prednapetem dinamskem sistemu z velikimi pomiki Luka Skrinjar1 – Janko Slavič2 – Miha Boltežar2 2 Fakulteta

1 ETI

Elektroelement d.d., Slovenija za strojništvo, Univerza v Ljubljani, Slovenija

Cilj raziskave je izdelava veljavnega numeričnega modela mehanskega podsestava stikalnega mehanizma, ki je vgrajen v kombinirano električno zaščitno stikalo, za določitev dinamskega odziva sistema z vključitvijo prednapetja. Prednapetje v dinamskem sistemu zagotavlja potencialno energijo, ki se v trenutku proženja stikalnega mehanizma začne pretvarjati v kinetično in tako zagotovi energijo za hiter odklop električnega tokokroga.

Prekinitev električnega tokokroga je izvedena z odmikom komponente gibljivega kontakta od nepomičnega kontakta.

Raziskava se osredotoča na modeliranje prednapetja v dinamskem sistemu, ki je sestavljen iz togih in prožnih teles, kjer so prožna telesa podvržena velikim pomikom. Modeliranje prožnih teles je v okviru metode absolutnih vozliščnih koordinat - AVK, ki omogoča enostavno vključitev prožnih teles v sistem gibalnih enačb in ustrezno obravnava velike pomike ter zagotavlja konstantno masno matriko prožnega telesa, ki je sestavljeno iz več AVK končnih elementov Predstavljena je izdelava numeričnega modela dinamskega sistema sestavljenega iz togih in prožnih teles.

Predstavljen je pristop k modeliranju gibljivega kontakta, ki je v dinamskem smislu sestavljen iz togega telesa z režo, prožnega telesa modeliranega v okviru teorije AVK in masne točke. Celoten dinamski model vključuje prožno telo, masno točko in tlačno vzmet. Prožno telo je povezano z osjo preko kinematične povezave »čep-vreži-z-zračnostjo«, ki poleg rotacije zagotavlja tudi ustrezno translacijo med telesoma. Tlačna vzmet je vgrajena med ohišje, ki je nepomično vpeto, in prožnim telesom.

V prvi fazi so določene geometrijske lastnosti prožnega telesa na osnovi rezultatov meritev odziva točke na gibljivem kontaktu – hitrosti. Nato je z ustreznimi geometrijskimi lastnosti določen odziv numeričnega modela.

Veljavnost geometrijskih lastnosti numeričnega modela je delno potrjena z določitvijo prve upogibne lastne frekvence. V drugi fazi je dinamski model prožnega telesa uporabljen kot podsklop dinamskega modela stikalnega mehanizma, kjer je veljavnost delno preverjena na osnovi obdelave meritev s hitro kamero.

Numerični model stikalnega mehanizme je nato uporabljen za raziskavo vpliva različnih parametrov na samo funkcijo; predvsem na razdaljo med gibljivim in nepomičnim kontaktom. Primerjava numeričnih rezultatov na osnovi dinamskih modelov glede na rezultate meritev predstavi, da se rezultati togo-prožnega dinamskega modela bolje skladajo z rezultati meritev kot rezultati popolnoma togega dinamskega modela. Vpliv prednapetja v numeričnem modelu je pomemben, saj se dinamski odziv med togo-prožnim sistemom in popolnoma prožnim sistemom znatno razlikuje.

Vsebina raziskave je osredotočena na modeliranje dinamskega odziva mehanskega podsestava v stikalnem mehanizmu s poudarkom na vključitvi prednapetja. Za določitev vrednosti dejanskih sil, ki zagotavljajo prednapetje v obravnavanem mehanskem sistemu, je izvedena meritev z dvema eno-osnima silomeroma. Mehanski sistem je prednapet, kar predstavlja vklopljen položaj stikalnega mehanizma, in nato v trenutku prožen s prerezom vrvice – odstranitve sile prednapetja. S ciljem validacije izdelanega numeričnega modela je gibanje mehanskega podsestava od vklopljenega položaja do izklopljenega položaja posneto s hitro kamero. Na osnovi posnete sekvence slik so z uporabo metode digitalne korelacije slik določene kinematične lastnosti točke na gibajočem-se telesu.

Doprinos raziskave je veljaven numerični model mehanskega podsestava, ki je vgrajen v sklop stikalnega mehanizma kombiniranega električnega zaščitnega stikala. Takšen model je lahko uporabljen za izboljšanje delovanja obravnavanega podsestava v stikalnem mehanizmu s ciljem zagotoviti kakovostnejše delovanje med odklopom električnega toka. Na primeru je predstavljena tudi možnost potencialne izboljšave dinamskega odziva s spremembo vpetja vzmeti na ohišju.

Ključne besede: metoda absolutnih vozliščnih koordinat, dinamski sistem, prednapetje, meritve

*Naslov avtorja za dopisovanje: Univerza v Ljubljani, Fakulteta za strojništvo, Aškerčeva 6, 1000 Ljubljana, Slovenija, janko.slavic@fs.uni-lj.si

SI 61

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, SI 62 © 2017 Strojniški vestnik. Vse pravice pridržane.

Prejeto v recenzijo: 2016-12-06 Prejeto popravljeno: 2017-04-24 Odobreno za objavo: 2017-05-22

Analiza mikrokonvekcije v toku MHD-nanofluida po metodi LBM Arjun; K.S. – Kumar, R. Kozhikkatil Sunil Arjun* - Rakesh Kumar

Oddelek za strojništvo, Indijski inštitut za tehnologijo (ISM), Dhanbad, Indija

V obstoječi literaturi ni mogoče najti podrobnejše obravnave prenosa toplote s konvekcijo in vpliva temperaturnega skoka za drseči tok nanofluida v mikroceveh. V tem članku je predstavljena študija vpliva temperaturnega skoka in hitrosti na površini pri različnih volumskih deležih trdne snovi za nanofluid v režimu drsečega toka, opravljena po metodi LBM. Nanofluid Al2O3-voda je bil simuliran v paketu MATLAB po metodi Boltzmann-Bhatnagar-Gross-Krook za določitev vpliva Reynoldsovega, Rayleighovega in Hartmannovega števila, drsnega koeficienta, volumskega deleža nanodelcev in aksialne razdalje na prisilni prenos toplote s konvekcijo. Preučeno je bilo vedenje nanofluida v razponu Reynoldsovega števila 200 ≤ Re ≤ 4000, Rayleighovega števila 103 ≤ Ra ≤ 106, jakosti magnetnega polja 0 ≤ Ha ≤ 90, volumske koncentracije nanodelcev 0 ≤ φ ≤ 2 % in drsnega koeficienta 0,005 ≤ B ≤ 0,02.

V članku je predstavljena študija vpliva magnetnega polja na vsiljeni laminarni in turbulentni prenos toplote s konvekcijo v mikrocevi, napolnjeni z nanofluidom Al2O3-voda. Simulacija je bila opravljena po metodi LBMBGK v paketu MATLAB. Preučen je vpliv Re, Ra, volumskega deleža nanodelcev, Ha, drsnega koeficienta in aksialne razdalje na lastnosti toka in prenosa toplote. Hidrodinamični in toplotni parametri toka fluida so ocenjeni s funkcijo porazdelitve gostote vztrajnostnega momenta (f) in gostote notranje energije (g). Raziskan je vpliv Re v razponu od 200 do 4000 in Ra v razponu od 103 do 106 pri vrednostih Ha od 0 do 90. Preučen je tudi vpliv volumskega deleža nanodelcev (φ = 0 % do 2 %) na prisilno konvekcijo. Raziskani so hitrost na površini, temperaturni skok in njun vpliv pri različnih vrednostih drsnega koeficienta B = 0,005 do 0,02 v aksialni smeri od četrtine do konca kanala.

Iz rezultatov je mogoče sklepati, da se s povečevanjem Reynoldsovega števila in volumskega deleža nanodelcev izboljšuje prenos toplote v 2D-mikroceveh pri robnih pogojih laminarnega toka, turbulentnega toka, drsečega toka in temperaturnega skoka. Z zmanjševanjem vrednosti drsnega koeficienta se zmanjšuje vpliv temperaturnega skoka in povečuje vpliv Nusseltovega števila. Obstajata kritični vrednosti za Rayleighovo število (105) in jakost magnetnega polja (Ha = 10), pri katerih je najbolj izražen vpliv volumskega deleža trdnih delcev in drsnega koeficienta. Povečanje tlačnega padca je podobno kot pri Nusseltovem številu. Ker so nanofluidi uporabnejši pri majhnih Reynoldsovih številih, je vpliv volumskega deleža močnejši kot vpliv drsnega koeficienta, čeprav so ti vplivi pravzaprav marginalni.

Delovni mediji za praktično tehnično uporabo so običajno podvrženi faznim spremembam, zato bo eno od prihodnjih raziskovalnih področij v okviru tega projekta tudi toplotna analiza pulzirajočega multifaznega toka. Opraviti bo mogoče tudi termohidrodinamično analizo za pulzirajoče turbulentne tokove z zelo velikim Reynoldsovim številom in za tokove z majhnim Reynoldsovim številom. Stena cevi je lahko v praksi na konstantni temperaturi, ali pa je ogrevana le delno. V prihodnje bodo zato obravnavane tudi te posebne okoliščine, predstavljeno delo pa bo motivacija in kažipot za nadaljnje delo.

Predlagan je nov in učinkovit način prenosa toplote s prisilno konvekcijo za nanofluid aluminij-voda v mikrocevi ob upoštevanju robnih pogojev laminarnega toka, turbulentnega toka, drsečega toka in temperaturnega skoka. Vpliv migracije nanodelcev, vrednosti Ra, volumskega deleža nanodelcev, vrednosti Ha in jakosti zunanjega magnetnega polja na toplotne lastnosti sistema je bil preučen po metodi LBM s paketom MATLAB. Vpliv volumskega deleža trdne snovi in drsnega koeficienta je največji pri kritičnih vrednostih Ha in Ra. Prenos toplote je izboljšan pri nanofluidu z volumskim deležem trdne snovi 2 % ter pri majhnih vrednostih Re in drsnega koeficienta.

Ključne besede: magnetohidrodinamika, Nusseltovo število, mrežna Boltzmannova metoda, mikrocev, drsni koeficient, mikrokonvekcija, nanofluid

SI 62

*Naslov avtorja za dopisovanje: Oddelek za strojništvo, Indijski inštitut za tehnologijo (ISM), Dhanbad, Indija, arjun@mece.ism.ac.in

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, SI 63 © 2017 Strojniški vestnik. Vse pravice pridržane.

Prejeto v recenzijo: 2016-12-15 Prejeto popravljeno: 2017-05-06 Odobreno za objavo: 2017-06-06

Toplotna optimizacija in primerjava geometrijskih parametrov pravokotnih in trikotnih reber z enako površino Florent Bunjaku1 – Risto V. Filkoski2 – Naser Sahiti3,* 1 Univerza

v Prištini “Hasan Priština”, Pedagoška fakulteta, Kosovo sv. Cirila in Metoda, Fakulteta za strojništvo, Makedonija 3 Univerza v Prištini “Hasan Priština”, Fakulteta za strojništvo, Kosovo 2 Univerza

Za izboljšanje pasivnega prenosa toplote na mestih z manjšim koeficientom prenosa toplote se običajno uporabljajo rebra različnih oblik. Povečevanje prenosa toplote z rebri in prisilno konvekcijo je dobro raziskano in dokumentirano v dostopnih virih, vpliv reber različnih oblik na izboljšanje naravne konvekcije, npr. pri radiatorjih za ogrevanje prostorov, pa je slabše raziskan in podatki o tem niso na voljo. Članek zato podaja odgovore na nekatera vprašanja o vplivu geometrije in materiala reber ter koeficienta prenosa toplote na toplotni tok z naravno konvekcijo.

Cilj analize je preučitev pogojev, ki zagotavljajo maksimalen prenos toplote pri omejenem materialu oz. volumnu reber. Analiziran je vpliv geometrije oblike reber enake površine na toplotni tok z naravno konvekcijo in rezultati so prikazani grafično. Optimizacija je opravljena z analitično in numerično simulacijo toplotnega toka ob predpostavki, da je koeficient prenosa toplote po površini rebra konstanten. Pri analizi geometrije preseka reber sta bila privzeta določena vrednost koeficienta prenosa toplote in material reber za ugotavljanje optimalne debeline reber, ki zagotavlja maksimalen prenos toplote.

Analizirani sta bili dve vrsti geometrije reber, in sicer pravokotna in trikotna. Analiza je pokazala, da je za optimalno debelino reber potreben kompromis med površino za konvektivni prenos toplote in učinkovitostjo reber iz različnih materialov (jeklo, aluminij in baker). Optimalna debelina reber pri materialih z večjo toplotno prevodnostjo je manjša, kar pomeni večjo izgubo toplote zaradi reber, kjer se zmanjšuje površina za konvektivni prenos toplote. V nadaljnji analizi je bila določena optimalna debelina reber za različne vrednosti koeficienta prenosa toplote. Vnovič se je izkazalo, da je mogoče določiti optimalno debelino reber za vsako vrednost koeficienta prenosa toplote. Večji ko je koeficient prenosa toplote, večji je toplotni tok. Določen je tudi toplotni tok po dolžini reber pravokotnega in trikotnega preseka za različne materiale in pri različnih vrednostih koeficienta prenosa toplote. Pri rebrih s pravokotno geometrijo so bile v primerjavi z rebri s trikotno geometrijo dosežene za 11 % do 13 % večje vrednosti toplotnega toka.

Iz tega sledi, da se večji del toplote prenaša prek dela rebra, ki je bližje osnovi, saj je vpliv konvekcijske površine rebra dlje od osnove manjši. Poudariti je treba, da so nekoliko večje vrednosti toplotnega toka pri pravokotnih rebrih povezane tudi z dvakrat večjim volumnom kot pri trikotnih rebrih.

Optimalni geometrijski parametri reber kot predmet te študije so lahko praktično orodje za inženirje, ki se ukvarjajo z oblikovanjem rebrastih površin za prenos toplote. Pomen optimizacijskih modelov, predstavljenih v tem članku, je v možnosti praktične uporabe pri iskanju optimalne geometrije profilov reber za največji toplotni tok pri danem volumnu oz. potrošku materiala. Podobne analize v literaturi običajno temeljijo na analitičnem pristopu, medtem ko so analize v tem članku podprte z obširnimi numeričnimi simulacijami modelov.

Ključne besede: rebra, toplotni tok, optimizacija, geometrijski parametri, pravokoten in trikoten profil, učinkovitost reber

*Naslov avtorja za dopisovanje: Univerza v Prištini “Hasan Priština”, Fakulteta za strojništvo, Priština, Kosovo, naser.sahiti@uni-pr.edu

SI 63

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, SI 64 © 2017 Strojniški vestnik. Vse pravice pridržane.

Prejeto v recenzijo: 2017-01-09 Prejeto popravljeno: 2017-04-11 Odobreno za objavo: 2017-05-29

Modeliranje togosti hidravličnega cilindra ob upoštevanju več faktorjev Hao 1Tehniška

Feng, H. – Du, Q. – Huang, Y. – Chi, Y. – Qungui Du1 – Yuxian Huang3 – Yongbin Chi1

Feng1,2,*

univerza Južne Kitajske, Fakulteta za strojništvo in avtomobilsko tehniko, Kitajska 2Liugong Machinery Co., Ltd, Razvojno-raziskovalno središče, Kitajska 3Univerza Purdue, Herrickovi laboratoriji, Fakulteta za strojništvo, ZDA

Togost hidravličnih pogonskih cilindrov močno vpliva na dinamični odziv kompleksnih mehanskih sistemov. Za postavitev točnega modela dinamike hidromehanskega sistema so potrebni točni podatki o togosti hidravličnih cilindrov. Večina matematičnih modelov za računanje togosti v dostopni literaturi se omejuje le na nekatere izbrane faktorje: upoštevajo stisljivost hidravličnega olja, aksialne deformacije batnice in upogljivost okrogle cevi za dovod olja, medtem ko so vsebnost zraka v olju, volumski raztezek ohišja cilindra in deformacije tesnil hidravličnega cilindra zanemarjeni. Na voljo je le malo literature, ki bi obravnavala vpliv teh izpuščenih faktorjev na točnost hidravličnega cilindra. V predstavljeni študiji je bil zato s kombinacijo teoretične analize in eksperimentalnih preizkusov celovito preučen vpliv več različnih faktorjev na togost hidravličnega cilindra, vključno s stisljivostnim modulom olja, vsebnostjo zraka v hidravličnem olju, aksialnimi deformacijami batnice, volumskim raztezkom ohišja cilindra, volumskim raztezkom kovinskih in gibkih cevi ter deformacijami tesnil hidravličnega cilindra.

Na koncu je postavljen in preverjen nov model togosti hidravličnega cilindra. Njegova povprečna točnost je v primerjavi z modeli togosti v literaturi izboljšana za več kot 15 %. Eksperimentalni preizkusi so obenem potrdili, da vsebnost zraka v hidravličnem olju pomembno vpliva na togost hidravličnega cilindra in na stisljivostni modul, vendar samo pri manjših tlakih (p < 6 MPa). Preizkusi so tudi pokazali, da je sprememba togosti hidravličnega cilindra nelinearna. Pri vrednostih tlaka p < 6 MPa je stopnja nelinearnosti razmeroma visoka, pri tlakih p > 6 MPa pa se karakteristika togosti približa linearni funkciji. Na primeru eksperimentalnega hidravličnega cilindra je bil kvantificiran vpliv posameznih faktorjev na togost hidravličnega cilindra: 80 % stisljivost olja, 10 % volumski raztezek ohišja cilindra, 6 % aksialne deformacije batnice in približno 3 % volumski raztezek gibkih cevi. Vpliv volumskega raztezka kovinskih cevi in deformacije tesnil je zelo majhen.

Opisani vpliv različnih faktorjev na togost hidravličnega cilindra je zaradi pomembnih razlik med cilindri različnih velikosti veljaven samo za specifični primer, ki ga obravnava članek. Opravljena je bila tudi kvalitativna analiza togosti hidravličnega cilindra, na katero vpliva vsebnost zraka v olju.

Za prihodnje raziskave tako ostaja še kvantitativna analiza tega vpliva.

Točnost izračuna togosti hidravličnega cilindra po matematičnem modelu, ki je v članku, je boljša od točnosti modelov v literaturi. Novi model togosti je zato pomemben in praktično uporaben za izboljševanje točnosti modelov dinamike hidrodinamskih sistemov.

Ključne besede: togost hidravličnega cilindra, stisljivostni modul, vsebnost zraka v hidravličnem olju, ekvivalentni modul elastičnosti gibke cevi, hidravlični cilinder, hidravlični sistem

SI 64

*Naslov avtorja za dopisovanje: Tehniška univerza Južne Kitajske, Fakulteta za strojništvo in avtomobilsko tehniko, Wu Shan Road 381, GuangZhou, Kitajska, fenghao2005@163.com

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, SI 65 © 2017 Strojniški vestnik. Vse pravice pridržane.

Prejeto v recenzijo: 2017-01-03 Prejeto popravljeno: 2017-04-07 Odobreno za objavo: 2017-06-16

Metodologija za uspešno uvajanje vitke proizvodnje Berlec, T. – Kleindienst, M. – Rabitsch, C. – Ramsauer, C. Tomaž Berlec1,* – Mario Kleindienst2 – Christian Rabitsch2 – Christian Ramsauer2 1Univerza

v Ljubljani, Fakulteta za strojništvo, Slovenija univerza v Gradcu, Avstrija

2Tehnična

Osnovni principi in metode vitke proizvodnje so znani že desetletja. Pregled literature in praksa pa kažeta, da uvedba metod vitke proizvodnje ni tako enostavna, kot se zdi na prvi pogled, saj veliko podjetji preneha z uvajanjem predno dosežejo pričakovane rezultate, oziroma željenih rezultatov sploh ne dosežejo, čeprav so izvedli projekt uvajanja do konca. Implementacija vitke proizvodnje v podjetje ne pomeni le prenos in uporabo obstoječih metod vitke proizvodnje v podjetje, temveč transformacijo kulture celotnega podjetja, ki pa ni izvedljiva čez noč, ampak gre za daljši proces, v katerem morajo sodelovati vsi zaposleni.

Pri transformaciji kulture podjetja iz klasične v vitko, igrata odločilno vlogo podpora vodstva in znanje zaposlenih. Zato je odločilnega pomena, da se sproti spremlja pridobljeno znanje zaposlenih o vitkosti, se odpravljajo nastale težave in spremlja podpora vodstva, saj se le tako lahko pravočasno sprejme ukrepe, popravi oziroma odpravi napake in pomanjkljivosti ter projekt uvedbe vitke proizvodnje uspešno pelje do cilja. Za uspešno uvajanje vitke proizvodnje je bila razvita metodologija (model) podprta z vodenimi intervjuji, ki so v pomoč pravočasnemu odkrivanju podpore oziroma ne-podpore vodstva ter znanja zaposlenih pri uvajanju vitke proizvodnje. Model je sestavljen iz petih korakov: določitev ciljnih vrednosti, toka vrednosti, toka materiala in informacij, prehoda na vlečni način proizvodnje in popolne vitke proizvodnje, v kombinaciji z vitkim učenjem vodstva in zaposlenih. Po končanju vsakega koraka uvedbe vitke proizvodnje je potrebna izvedba vodenega intervjuja zaposlenih z vprašalnikom. Na osnovi rezultata intervjuja, se tim, ki uvaja vitko proizvodnjo odloči za nadaljevanje na naslednji korak v primeru zadovoljivih rezultatov (nad 85 %), za dodatna izobraževanja, boljšo podporo vodstva in odpravo nejasnosti v primeru srednjega rezultata (med 50 % in 85 %) oziroma za ponovitev že narejenega koraka uvedbe vitke proizvodnje v primeru slabega rezultata (pod 50 %). Za vodilo pri izvedbi intervjuja so pripravljena vprašanja, ki pokrivajo vsa potrebna področja v določenem koraku, vedno pa je dodano še vprašanje o komunikaciji ter podpori med zaposlenimi in vodstvom. Na ta način, lahko podjetje nadzira in simultano preverja implementacijo vitke proizvodnje, saj le s sprotnimi intervjuji po vsakem koraku, lahko hitro odkrije in odpravi pomanjkljivosti, kot so neznanje, pomanjkanje podpore vodstva, ter se tako izogne neuspehu pri uvedbi vitke proizvodnje. Metodologija je bila testirana v dveh podjetjih, ki proizvajata komponente za avtomobilsko industrijo. Prvo podjetje je bilo z uvedbo vitke proizvodnje na začetku (pri prvem koraku), drugo podjetje pa vitko proizvodnjo uvaja že dobro leto in glede na predlagani model zaključuje drugi korak uvedbe.

V obeh podjetjih so bili formirani jedrni timi s šestimi člani v prvem in osmimi člani v drugem podjetju. Člani tima so bili seznanjeni z modelom in vprašalniki. V prvem podjetju je bil po končanju prvega koraka izveden in ovrednoten intervju z rezultatom nad 90 %, na osnovi katerega je bila sprejeta odločitev, da podjetje lahko nadaljuje z drugim korakom uvedbe. Ker v drugem podjetju po zaključku prve faze ni bil izveden vodeni intervju in ker so se začele pojavljati težave pri uvedbi, se je jedrni tim odločil, da izvede najprej intervju po prvem koraku. Rezultat intervjuja je bil 95 %. Nato se izvedli še intervju po drugem koraku uvedbe in dosegli 80 %.

Po analizi rezultatov je bilo ugotovljeno pomanjkanje komunikacije in znanja iz vrednostnega toka. Izvedena je bila učna delavnica na tematiko vrednostnega toka za poenotenje znanja in odpravo težave s komunikacijo. Po učni delavnici je podjetje nadaljevalo z uvedbo vitke proizvodnje, ki je potekala veliko bolj gladko. Po enem mesecu je bil intervju ponovljen, podjetje pa je doseglo 95 %. Na osnovi različnih primerov v različnih stopnjah uvedbe vitke proizvodnje, lahko zaključimo, da je model ustrezen, saj pravočasno identificira problem podpore vodstva, komunikacije in znanja. Če so problemi identificirani pravočasno, jih je možno hitro in enostavno rešiti. Z odlašanjem, pa se problemi povečujejo. Ignoriranje pa praviloma pripelje do neuspešne uvedbe vitke proizvodnje.

Predlagana metodologija je posebej primerna za mala in srednja podjetja, kjer zaradi pomanjkanja kadra za uvajanje vitke proizvodnje, dodelijo zaposlenemu poleg obstoječih nalog še uvajanje vitke proizvodnje. Brez težav pa se uporabi tudi v velikem podjetju, kjer imajo zaposlene kadre, odgovorne izključno za uvedbo vitke proizvodnje.

Nadaljnje raziskave gredo v smeri nadgradnje vitkosti z agilnostjo in leagilnostjo.

Ključne besede: kultura podjetja, vitka proizvodnja, učenje managementa, intervju, kritični faktorji uspeha *Naslov avtorja za dopisovanje: Univerza v Ljubljani, Fakulteta za strojništvo, Aškerčeva 6, 1000 Ljubljana, Slovenija, tomaz.berlec@fs.uni-lj.si

SI 65

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, SI 66 © 2017 Strojniški vestnik. Vse pravice pridržane.

Prejeto v recenzijo: 2017-02-07 Prejeto popravljeno: 2017-04-07 Odobreno za objavo: 2017-06-06

Razvoj stroja za posnemanje s pomočjo tehnologije virtualnih prototipov Hong Seok Park1 – Duc Viet Dang1,* – Trung Thanh Nguyen2 1 Univerza

2 Tehniška

v Ulsanu, Šola za strojništvo, Južna Koreja univerza Le Quy Don, Fakulteta za strojništvo, Vietnam

Cilj predstavljenega dela je bil razvoj novega stroja za posnemanje s servomotorjem, krogličnim vretenom in linearnimi vodili kot nadomestilom za hidravlični pogon. Konvencionalni hidravlični stroji za posnemanje imajo vrsto slabosti, kot so hrupnost, velika raba energije in majhna produktivnost, zasedejo pa tudi veliko prostora. Za odpravo teh pomanjkljivosti je bil razvit nov stroj za posnemanje brez hidravličnega sistema. Članek predstavlja razvojni proces, vključno s simulacijskimi metodami in eksperimentalno validacijo stroja za posnemanje s servopogonom.

Za prihranek pri stroških, povezanih z eksperimenti, je bila uporabljena tehnologija za virtualno izdelavo prototipov, vključno z modelom za simulacijo več teles (MBS) in pametnim krmilnikom. Na podlagi koncepta je podan predlog mehanske konstrukcije novega stroja za posnemanje. Nato je bil za simulacijo novega stroja razvit model z več telesi, ki predstavlja mehanski sistem ter omogoča določitev odvisnosti med telesi, prostostnih stopenj, vrste zgibov in geometrijskih omejitev v enem integriranem modelu. Z dinamično simulacijo sta bila identificirana vedenje obdelovalnega stroja in porazdelitev napetosti. Adaptivni PID-krmilnik z drsnim režimom vodenja (ASMPID) je bil zasnovan in integriran z mehanskim modelom za oblikovanje virtualnega prototipa novega stroja za posnemanje. Funkcionalnost krmilnika je bila ocenjena s simulacijo. Končno je bil izdelan še fizični stroj za preučitev operacij posnemanja in potrditev izpolnitve projektnih zahtev.

Stroj za posnemanje s servopogonom je bil razvit na podlagi simulacije več teles (MBS) in sodobne tehnologije krmiljenja. Rezultati simulacije kažejo, da je virtualni prototip varen v smislu dinamičnega vedenja, izpolnjuje specifikacije in ima stabilne regulacijske kriterije. Krmilnik ASMPID učinkovito odpravlja vplive zunanjih motenj na ta nelinearni sistema med obdelavo. Rezultati eksperimentov so pokazali, da je razviti model z mehansko konstrukcijo in krmilnikom primeren za konstruiranje strojev za posnemanje. Novi stroj lahko odpravi slabosti tradicionalnih strojev in izboljša kakovost obdelave.

Kljub uporabnosti simulacijskih modelov konstrukcije stroja in virtualnega krmilnika je treba pred fizičnimi eksperimenti nujno preučiti tudi kakovost izdelkov. Napovedovanje kakovosti obdelovancev s pomočjo tehnologij virtualnih prototipov bo zato predmet nadaljnjega dela.

Novost te študije je predlog novega stroja za posnemanje s servomotorjem, krogličnim vretenom in linearnimi vodili, ki odpravlja pomanjkljivosti hidravličnih strojev. Raziskava je pokazala, da predlagani virtualni prototip z mehansko konstrukcijo in pametnim krmilnikom uspešno izboljšuje zasnovo stroja za posnemanje. Delo je zato lahko pomemben prispevek k učinkovitejši izdelavi prototipov novih strojev za posnemanje.

Ključne besede: stroj za posnemanje, servomotor, kroglično vreteno, tehnologija virtualne izdelave prototipov, simulacija več teles, adaptivno krmiljenje z drsnim režimom

SI 66

*Naslov avtorja za dopisovanje: Univerza v Ulsanu, Šola za strojništvo, 93 Daehak-ro, Nam-gu, Ulsan 44610, Južna Koreja, vietnarime@gmail.com

Strojniški vestnik - Journal of Mechanical Engineering 63(2017)7-8, SI 67 Osebne objave

DOKTORSKI DISERTACIJI

Na Fakulteti za strojništvo Univerze v Mariboru je obranil svojo doktorsko disertacijo: ● dne 20. junija 2017 mag. Boštjan OGRIZEK z naslovom: »Zasnova inteligentnega sistema celovite obdelave podpornih informacij za razvoj novih aparatov« (mentor: prof. dr. Borut Buchmeister); V industrijski praksi je vedno večja težnja po izboljšanju razvojnega procesa. Eden izmed razlogov je želja po končnem dobičku na izdelani aparat. Drug razlog je porast količine različnih razvojnih podjetij ter posledično tudi konkurence na globalnem trgu.

Sam razvoj traja od prve ideje za nov izdelek pa vse do njegove ukinitve. V tem času poteka veliko aktivnosti, ki se izvajajo z željo po končnem uspehu izdelka na trgu. Vendar pa se, tako kot je to znano iz drugih panog, v obilici konkurence pogoji za uspeh zaostrijo.

To pomeni, da v primeru podobnega napredka ter delovanja podjetij le ta celovito gledano ne morejo ustvariti večje konkurenčne prednosti na trgu. Če je v razvoj vloženih preveč resursov to pomeni, presežek investicije ter vpliv na končno ceno izdelka. V koliko je vloženih resursov premalo je lahko končni rezultat nepopoln izdelek, ki ga trg na dolgi rok zavrne. Tako je za optimalen razvoj izdelka potrebna optimalna pot, ki sočasno zmanjša resurse na optimalno raven prav tako pa zagotovi prepotrebno končno kakovost.

V doktorski disertaciji smo zbrali podatke o različnih aparatih za pripravo napitkov za namene raziskovanja v področju snovanja inteligentnega podpornega sistema za razvoj aparatov. Iz zbranih podatkov smo izluščili predvidene pomembne karakteristike, ki smo jih zapisali v različne table za kasnejše delo. Zaradi samega tipa delovanja smo za kreiranje podpornega sistema uporabili metodologijo nevronskih mrež. S pomočjo le teh smo na podlagi podatkov iz obstoječe baze znanja kreirali podporne mehanizme, ki smo jih kasneje umestili v naš podporni sistem. Podporni sistem smo zastavili modulno, saj je bil že začetni namen možnost kasnejših enostavnih nadgradenj v primeru novih dognanj ter učenja iz

lastnih primerov. Kreirane nevronske mreže so bile tekom razvoja sistema tudi testirane ter kakovostno ovrednotene. Podporni sistem je bil kreiran s pomočjo implementacije šestih podpornih področij.

Ta področja so bila izbrana iz različnih vej razvoja aparatov. Končni sistem je bil zasnovan z miselnostjo hitre pomoči ter enostavnostjo uporabe končnega odjemalca.

Rezultati testiranja podpornega sistema so pokazali ustreznost metodologije za namen razvoja aparatov. Dokazali smo, da je mogoče razviti podporni sistem s pomočjo nevronskih mrež, ki pomaga pri obdelavi podpornih informacij. Prav tako smo s pomočjo rezultatov ponudili možnosti za dodatne raziskave ter razvoj v smeri inteligentnih sistemov za podporo tekom razvoja različnih izdelkov. * Na Fakulteti za strojništvo Univerze v Ljubljani je obranil svojo doktorsko disertacijo: ● dne 23. junija 2017 Boštjan JURJEVČIČ z naslovom: »Eksperimentalno modeliranje pnevmatskega transporta premogovega prahu z uporabo elektrostatične merilne metode« (mentor: izr. prof. dr. Andrej Senegačnik); V delu je predstavljen razvoj celovite merilne metode za določevanje karakteristik pnevmatskega transporta premogovega prahu z vrinjenimi elektrostatičnimi sondami. Na laboratorijskem preizkuševališču smo pri nadzorovanih pogojih raziskali ključne vplivne veličine na izmerjene vrednosti ter ocenili merilno negotovost metode.

Mreža paličnih elektrostatičnih sond je bila uspešno vgrajena v transportno-mlevni sistem realne termoelektrarne za določanje razporeditve masnega toka premogovega prahu po kanalu, za določevanje kakovosti mletja in za statistično kontrolo obratovanja v realnem času.

SI 67

Strojniški vestnik – Journal of Mechanical Engineering (SV-JME) Aim and Scope The international journal publishes original and (mini)review articles covering the concepts of materials science, mechanics, kinematics, thermodynamics, energy and environment, mechatronics and robotics, fluid mechanics, tribology, cybernetics, industrial engineering and structural analysis.

The journal follows new trends and progress proven practice in the mechanical engineering and also in the closely related sciences as are electrical, civil and process engineering, medicine, microbiology, ecology, agriculture, transport systems, aviation, and others, thus creating a unique forum for interdisciplinary or multidisciplinary dialogue.

The international conferences selected papers are welcome for publishing as a special issue of SV-JME with invited co-editor(s).

Editor in Chief Vincenc Butala

University of Ljubljana, Faculty of Mechanical Engineering, Slovenia

Technical Editor Pika Škraba

University of Ljubljana, Faculty of Mechanical Engineering, Slovenia

Founding Editor Bojan Kraut

University of Ljubljana, Faculty of Mechanical Engineering, Slovenia

Editorial Office University of Ljubljana, Faculty of Mechanical Engineering SV-JME, Aškerčeva 6, SI-1000 Ljubljana, Slovenia Phone: 386 (0)1 4771 137 Fax: 386 (0)1 2518 567 info@sv-jme.eu, http://www.sv-jme.eu Print: Papirografika Bori, printed in 300 copies Founders and Publishers University of Ljubljana, Faculty of Mechanical Engineering, Slovenia University of Maribor, Faculty of Mechanical Engineering, Slovenia Association of Mechanical Engineers of Slovenia Chamber of Commerce and Industry of Slovenia, Metal Processing Industry Association President of Publishing Council Branko Širok

University of Ljubljana, Faculty of Mechanical Engineering, Slovenia

Vice-President of Publishing Council Jože Balič

http://www.sv-jme.eu

63 (2017) 7-8

University of Maribor, Faculty of Mechanical Engineering, Slovenia

Since 1955

Strojniški vestnik Journal of Mechanical Engineering

Journal of Mechanical Engineering - Strojniški vestnik

Slavič, Miha Boltežar: rdinate Formulation in a Pre-Stressed ts Dynamical System

7-8 year 2017 volume 63 no.

Cover: The image presents the experimental setup used at the pre-stressed rigid-flexible multibody system. Two forcemeters and a high-speed camera were used to measure the pre-stress forces, the contact forces and the kinematics.

The validated numerical model of the electric circuit breaker was used to perform parameter sensitivity analysis where the switch-off time was shown to reduce to approx. 30 %.

Image Courtesy: Laboratory for dynamics of machines and structures, Faculty of Mechanical Engineering, University of Ljubljana Askerceva 6, 1000 Ljubljana, Slovenia, EU www.ladisk.si

ISSN 0039-2480 © 2017 Strojniški vestnik - Journal of Mechanical Engineering.

All rights reserved. SV-JME is indexed / abstracted in: SCI-Expanded, Compendex, Inspec, ProQuest-CSA, SCOPUS, TEMA. The list of the remaining bases, in which SV-JME is indexed, is available on the website.

International Editorial Board Kamil Arslan, Karabuk University, Turkey Hafiz Muhammad Ali, University of Engineering and Technology, Pakistan Josep M. Bergada, Politechnical University of Catalonia, Spain Anton Bergant, Litostroj Power, Slovenia Miha Boltežar, UL, Faculty of Mechanical Engineering, Slovenia Franci Čuš, UM, Faculty of Mechanical Engineering, Slovenia Anselmo Eduardo Diniz, State University of Campinas, Brazil Igor Emri, UL, Faculty of Mechanical Engineering, Slovenia Imre Felde, Obuda University, Faculty of Informatics, Hungary Janez Grum, UL, Faculty of Mechanical Engineering, Slovenia Imre Horvath, Delft University of Technology, The Netherlands Aleš Hribernik, UM, Faculty of Mechanical Engineering, Slovenia Soichi Ibaraki, Kyoto University, Department of Micro Eng., Japan Julius Kaplunov, Brunel University, West London, UK Iyas Khader, Fraunhofer Institute for Mechanics of Materials, Germany Jernej Klemenc, UL, Faculty of Mechanical Engineering, Slovenia Milan Kljajin, J.J. Strossmayer University of Osijek, Croatia Peter Krajnik, Chalmers University of Technology, Sweden Janez Kušar, UL, Faculty of Mechanical Engineering, Slovenia Gorazd Lojen, UM, Faculty of Mechanical Engineering, Slovenia Thomas Lübben, University of Bremen, Germany Janez Možina, UL, Faculty of Mechanical Engineering, Slovenia George K. Nikas, KADMOS Engineering, UK José L. Ocaña, Technical University of Madrid, Spain Miroslav Plančak, University of Novi Sad, Serbia Vladimir Popović, University of Belgrade, Faculty of Mech. Eng., Serbia Franci Pušavec, UL, Faculty of Mechanical Engineering, Slovenia Bernd Sauer, University of Kaiserlautern, Germany Rudolph J. Scavuzzo, University of Akron, USA Arkady Voloshin, Lehigh University, Bethlehem, USA General information Strojniški vestnik – Journal of Mechanical Engineering is published in 11 issues per year (July and August is a double issue).

Institutional prices include print & online access: institutional subscription price and foreign subscription €100,00 (the price of a single issue is €10,00); general public subscription and student subscription €50,00 (the price of a single issue is €5,00). Prices are exclusive of tax. Delivery is included in the price. The recipient is responsible for paying any import duties or taxes. Legal title passes to the customer on dispatch by our distributor.

Single issues from current and recent volumes are available at the current single-issue price. To order the journal, please complete the form on our website. For submissions, subscriptions and all other information please visit: http://en.sv-jme.eu/.

You can advertise on the inner and outer side of the back cover of the journal. The authors of the published papers are invited to send photos or pictures with short explanation for cover content.

We would like to thank the reviewers who have taken part in the peerreview process.

The journal is subsidized by Slovenian Research Agency.

Strojniški vestnik - Journal of Mechanical Engineering is available on http://www.sv-jme.eu, where you access also to papers’ supplements, such as simulations, etc.

Information for Authors All manuscripts must be in English. Pages should be numbered sequentially. The manuscript should be composed in accordance with the Article Template given above. The maximum length of contributions is 10 pages. Longer contributions will only be accepted if authors provide juastification in a cover letter. For full instructions see the Information for Authors section on the journal’s website: http://en.sv-jme.eu .

SUBMISSION: Submission to SV-JME is made with the implicit understanding that neither the manuscript nor the essence of its content has been published previously either in whole or in part and that it is not being considered for publication elsewhere. All the listed authors should have agreed on the content and the corresponding (submitting) author is responsible for having ensured that this agreement has been reached. The acceptance of an article is based entirely on its scientific merit, as judged by peer review. Scientific articles comprising simulations only will not be accepted for publication; simulations must be accompanied by experimental results carried out to confirm or deny the accuracy of the simulation. Every manuscript submitted to the SV-JME undergoes a peer-review process.

The authors are kindly invited to submit the paper through our web site: http://ojs.svjme.eu. The Author is able to track the submission through the editorial process - as well as participate in the copyediting and proofreading of submissions accepted for publication - by logging in, and using the username and password provided.

SUBMISSION CONTENT: The typical submission material consists of: - A manuscript (A PDF file, with title, all authors with affiliations, abstract, keywords, highlights, inserted figures and tables and references), - Supplementary files: • a manuscript in a WORD file format • a cover letter (please see instructions for composing the cover letter) • a ZIP file containing figures in high resolution in one of the graphical formats (please see instructions for preparing the figure files) • possible appendicies (optional), cover materials, video materials, etc.

Incomplete or improperly prepared submissions will be rejected with explanatory comments provided. In this case we will kindly ask the authors to carefully read the Information for Authors and to resubmit their manuscripts taking into consideration our comments.

COVER LETTER INSTRUCTIONS: Please add a cover letter stating the following information about the submitted paper: 1. Paper title, list of authors and their affiliations.

2. Type of paper: original scientific paper (1.01), review scientific paper (1.02) or short scientific paper (1.03).

3. A declaration that neither the manuscript nor the essence of its content has been published in whole or in part previously and that it is not being considered for publication elsewhere.

4. State the value of the paper or its practical, theoretical and scientific implications.

What is new in the paper with respect to the state-of-the-art in the published papers? Do not repeat the content of your abstract for this purpose.

5. We kindly ask you to suggest at least two reviewers for your paper and give us their names, their full affiliation and contact information, and their scientific research interest.

The suggested reviewers should have at least two relevant references (with an impact factor) to the scientific field concerned; they should not be from the same country as the authors and should have no close connection with the authors.

FORMAT OF THE MANUSCRIPT: The manuscript should be composed in accordance with the Article Template. The manuscript should be written in the following format: - A Title that adequately describes the content of the manuscript.

- A list of Authors and their affiliations.

- An Abstract that should not exceed 250 words. The Abstract should state the principal objectives and the scope of the investigation, as well as the methodology employed. It should summarize the results and state the principal conclusions.

- 4 to 6 significant key words should follow the abstract to aid indexing.

- 4 to 6 highlights; a short collection of bullet points that convey the core findings and provide readers with a quick textual overview of the article. These four to six bullet points should describe the essence of the research (e.g. results or conclusions) and highlight what is distinctive about it.

- An Introduction that should provide a review of recent literature and sufficient background information to allow the results of the article to be understood and evaluated.

- A Methods section detailing the theoretical or experimental methods used.

- An Experimental section that should provide details of the experimental set-up and the methods used to obtain the results.

- A Results section that should clearly and concisely present the data, using figures and tables where appropriate.

- A Discussion section that should describe the relationships and generalizations shown by the results and discuss the significance of the results, making comparisons with previously published work. (It may be appropriate to combine the Results and Discussion sections into a single section to improve clarity.)

- A Conclusions section that should present one or more conclusions drawn from the results and subsequent discussion and should not duplicate the Abstract.

- Acknowledgement (optional) of collaboration or preparation assistance may be included. Please note the source of funding for the research.

- Nomenclature (optional). Papers with many symbols should have a nomenclature that defines all symbols with units, inserted above the references. If one is used, it must contain all the symbols used in the manuscript and the definitions should not be repeated in the text. In all cases, identify the symbols used if they are not widely recognized in the profession. Define acronyms in the text, not in the nomenclature.

- References must be cited consecutively in the text using square brackets [1] and collected together in a reference list at the end of the manuscript.

- Appendix(-icies) if any.

SPECIAL NOTES Units: The SI system of units for nomenclature, symbols and abbreviations should be followed closely. Symbols for physical quantities in the text should be written in italics (e.g. v, T, n, etc.). Symbols for units that consist of letters should be in plain text (e.g. ms-1, K, min, mm, etc.). Please also see: http://physics.nist.gov/cuu/pdf/sp811.pdf .

Abbreviations should be spelt out in full on first appearance followed by the abbreviation in parentheses, e.g. variable time geometry (VTG). The meaning of symbols and units belonging to symbols should be explained in each case or cited in a nomenclature section at the end of the manuscript before the References.

Figures (figures, graphs, illustrations digital images, photographs) must be cited in consecutive numerical order in the text and referred to in both the text and the captions as Fig. 1, Fig. 2, etc. Figures should be prepared without borders and on white grounding and should be sent separately in their original formats. If a figure is composed of several parts, please mark each part with a), b), c), etc. and provide an explanation for each part in Figure caption. The caption should be self-explanatory. Letters and numbers should be readable (Arial or Times New Roman, min 6 pt with equal sizes and fonts in all figures).

Graphics (submitted as supplementary files) may be exported in resolution good enough for printing (min. 300 dpi) in any common format, e.g. TIFF, BMP or JPG, PDF and should be named Fig1.jpg, Fig2.tif, etc. However, graphs and line drawings should be prepared as vector images, e.g. CDR, AI. Multi-curve graphs should have individual curves marked with a symbol or otherwise provide distinguishing differences using, for example, different thicknesses or dashing.

Tables should carry separate titles and must be numbered in consecutive numerical order in the text and referred to in both the text and the captions as Table 1, Table 2, etc. In addition to the physical quantities, such as t (in italics), the units [s] (normal text) should be added in square brackets. Tables should not duplicate data found elsewhere in the manuscript. Tables should be prepared using a table editor and not inserted as a graphic.

REFERENCES: A reference list must be included using the following information as a guide. Only cited text references are to be included. Each reference is to be referred to in the text by a number enclosed in a square bracket (i.e. [3] or [2] to [4] for more references; do not combine more than 3 references, explain each). No reference to the author is necessary.

References must be numbered and ordered according to where they are first mentioned in the paper, not alphabetically. All references must be complete and accurate. Please add DOI code when available. Examples follow.

Journal Papers: Surname 1, Initials, Surname 2, Initials (year). Title. Journal, volume, number, pages, DOI code.

[1] Hackenschmidt, R., Alber-Laukant, B., Rieg, F. (2010). Simulating nonlinear materials under centrifugal forces by using intelligent cross-linked simulations. Strojniški vestnik - Journal of Mechanical Engineering, vol. 57, no. 7-8, p. 531-538, DOI:10.5545/svjme.2011.013.

Journal titles should not be abbreviated. Note that journal title is set in italics.

Books: Surname 1, Initials, Surname 2, Initials (year). Title. Publisher, place of publication.

[2] Groover, M.P. (2007). Fundamentals of Modern Manufacturing. John Wiley & Sons, Hoboken.

Note that the title of the book is italicized.

Chapters in Books: Surname 1, Initials, Surname 2, Initials (year). Chapter title. Editor(s) of book, book title. Publisher, place of publication, pages.

[3] Carbone, G., Ceccarelli, M. (2005). Legged robotic systems. Kordić, V., Lazinica, A., Merdan, M. (Eds.), Cutting Edge Robotics. Pro literatur Verlag, Mammendorf, p. 553576.

Proceedings Papers: Surname 1, Initials, Surname 2, Initials (year). Paper title. Proceedings title, pages.

[4] Štefanić, N., Martinčević-Mikić, S., Tošanović, N. (2009). Applied lean system in process industry. MOTSP Conference Proceedings, p. 422-427.

Standards: Standard-Code (year). Title. Organisation. Place.

[5] ISO/DIS 16000-6.2:2002. Indoor Air – Part 6: Determination of Volatile Organic Compounds in Indoor and Chamber Air by Active Sampling on TENAX TA Sorbent, Thermal Desorption and Gas Chromatography using MSD/FID. International Organization for Standardization. Geneva.

WWW pages: Surname, Initials or Company name. Title, from http://address, date of access.

[6] Rockwell Automation. Arena, from http://www.arenasimulation.com, accessed on 200909-07.

EXTENDED ABSTRACT: When the paper is accepted for publishing, the authors will be requested to send an extended abstract (approx. one A4 page or 3500 to 4000 characters). The instruction for composing the extended abstract are published on-line: http://www.sv-jme.eu/informationfor-authors/ .

COPYRIGHT: Authors submitting a manuscript do so on the understanding that the work has not been published before, is not being considered for publication elsewhere and has been read and approved by all authors. The submission of the manuscript by the authors means that the authors automatically agree to transfer copyright to SV-JME when the manuscript is accepted for publication. All accepted manuscripts must be accompanied by a Copyright Transfer Agreement, which should be sent to the editor. The work should be original work by the authors and not be published elsewhere in any language without the written consent of the publisher. The proof will be sent to the author showing the final layout of the article.

Proof correction must be minimal and executed quickly. Thus it is essential that manuscripts are accurate when submitted. Authors can track the status of their accepted articles on http://en.sv-jme.eu/.

PUBLICATION FEE: Authors will be asked to pay a publication fee for each article prior to the article appearing in the journal. However, this fee only needs to be paid after the article has been accepted for publishing. The fee is 240.00 EUR (for articles with maximum of 6 pages), 300.00 EUR (for articles with maximum of 10 pages), plus 30.00 EUR for each additional page. The additional cost for a color page is 90.00 EUR. These fees do not include tax.

Strojniški vestnik -Journal of Mechanical Engineering Aškerčeva 6, 1000 Ljubljana, Slovenia, e-mail: info@sv-jme.eu

http://www.sv-jme.eu

63 (2017) 7-8

Since 1955

Papers

417

Luka Skrinjar, Janko Slavič, Miha Boltežar: Absolute Nodal Coordinate Formulation in a Pre-Stressed Large-Displacements Dynamical System

426

Kozhikkatil Sunil Arjun, Rakesh Kumar: LBM Analysis of Micro-Convection in MHD Nanofluid Flow

439

Florent Bunjaku, Risto V. Filkoski, Naser Sahiti: Thermal Optimization and Comparison of Geometric Parameters of Rectangular and Triangular Fins with Constant Surfacing

447

Hao Feng, Qungui Du, Yuxian Huang, Yongbin Chi: Modelling Study on Stiffness Characteristics of Hydraulic Cylinder under Multi-Factors

457

Tomaž Berlec, Mario Kleindienst, Christian Rabitsch, Christian Ramsauer: Methodology to Facilitate Successful Lean Implementation

466

Hong Seok Park, Duc Viet Dang, Trung Thanh Nguyen: Development of a Servo-Based Broaching Machine Using Virtual Prototyping Technology

Journal of Mechanical Engineering - Strojniški vestnik

Contents

7-8 year 2017 volume 63 no.

Strojniški vestnik Journal of Mechanical Engineering