Journal of Mechanical Engineering 2013 2

http://www.sv-jme.eu

59 (2013) 2

Strojniški vestnik Journal of Mechanical Engineering

Since 1955

Contents

Papers

71

Luka Knez, Janko Slavič, Miha Boltežar: A multi-axis biodynamic measuring handle for a human hand-arm system

89

Aleksander Preglej, Igor Steiner, Sašo Blažič: Multivariable Predictive Functional Control of an Autoclave

97

Eda Okutan, Sedat Karabay, Tamer Sınmazçelik, Egemen Avcu: A Study on the Derivation of Parametric Cutting Force Equations in Drilling of GFRP Composites

106

Irina Stefanova Aleksandrova, Gancho Nenkov Ganev: Combined Cutting-deforming Taps

112

Simon Štampar, Saša Sokolič, Gorazd Karer: Nonlinear Control of a Hybrid Batch Reactor

Chi-Hsiang Chen, Yung-Cheng Wang, Bean-Yin Lee: The Effect of Surface Roughness of End-Mills on Optimal Cutting Performance for High-Speed Machining

124

Journal of Mechanical Engineering - Strojniški vestnik

Jianping Li, Songyong Liu, Changlong Du: 81 Experimental Research and Computer Simulation of Face Grind-hardening Technology

2 year 2013 volume 59 no.

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 Editorial Office University of Ljubljana (UL) Faculty of Mechanical Engineering SV-JME Aškerčeva 6, SI-1000 Ljubljana, Slovenia Phone: 386-(0)1-4771 137 Fax: 386-(0)1-2518 567 E-mail: info@sv-jme.eu, http://www.sv-jme.eu

Print DZS, printed in 450 copies

Founders and Publishers University of Ljubljana (UL) Faculty of Mechanical Engineering, Slovenia University of Maribor (UM) Faculty of Mechanical Engineering, Slovenia Association of Mechanical Engineers of Slovenia Chamber of Commerce and Industry of Slovenia Metal Processing Industry Association Cover: When operating hand tools, vibrations excite the human hand, leading to vibration diseases and injuries. To improve the safety of workers, the vibration transmissibility to the hand is being researched. Since there is currently a lack of viable experimental data, used to develop dynamic models, a special measuring handle was developed. The handle measures triaxial vibration transmissibility to several parts of the hand and enables the development of validated dynamical models.

Image Courtesy: LADISK, Faculty of Mechanical Engineering, University of Ljubljana.

International Editorial Board Koshi Adachi, Graduate School of Engineering,Tohoku University, Japan Bikramjit Basu, Indian Institute of Technology, Kanpur, India Anton Bergant, Litostroj Power, Slovenia Franci Čuš, UM, Faculty of Mech. Engineering, Slovenia Narendra B. Dahotre, University of Tennessee, Knoxville, USA Matija Fajdiga, UL, Faculty of Mech. Engineering, Slovenia Imre Felde, Obuda University, Faculty of Informatics, Hungary Jože Flašker, UM, Faculty of Mech. Engineering, Slovenia Bernard Franković, Faculty of Engineering Rijeka, Croatia Janez Grum, UL, Faculty of Mech. Engineering, Slovenia Imre Horvath, Delft University of Technology, Netherlands Julius Kaplunov, Brunel University, West London, UK Milan Kljajin, J.J. Strossmayer University of Osijek, Croatia Janez Kopač, UL, Faculty of Mech. Engineering, Slovenia Franc Kosel, UL, Faculty of Mech. Engineering, Slovenia Thomas Lübben, University of Bremen, Germany Janez Možina, UL, Faculty of Mech. Engineering, Slovenia Miroslav Plančak, University of Novi Sad, Serbia Brian Prasad, California Institute of Technology, Pasadena, USA Bernd Sauer, University of Kaiserlautern, Germany Brane Širok, UL, Faculty of Mech. Engineering, Slovenia Leopold Škerget, UM, Faculty of Mech. Engineering, Slovenia George E. Totten, Portland State University, USA Nikos C. Tsourveloudis, Technical University of Crete, Greece Toma Udiljak, University of Zagreb, Croatia Arkady Voloshin, Lehigh University, Bethlehem, USA President of Publishing Council Jože Duhovnik UL, Faculty of Mechanical Engineering, Slovenia 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 magazine. 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.

ISSN 0039-2480 © 2013 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.

The journal is subsidized by Slovenian Book Agency.

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

Instructions for Authors All manuscripts must be in English. Pages should be numbered sequentially. The maximum length of contributions is 10 pages. Longer contributions will only be accepted if authors provide justification in a cover letter. Short manuscripts should be less than 4 pages. For full instructions see the Authors Guideline section on the journal’s website: http://en.sv-jme.eu/.

Please note that file size limit at the journal’s website is 8Mb. Announcement: The authors are kindly invited to submitt the paper through our web site: http://ojs.sv-jme.eu. Please note that file size limit at the journal’s website is 8Mb. The Author is also able to accompany the paper with Supplementary Files in the form of Cover Letter, data sets, research instruments, source texts, etc. 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.

Please provide a cover letter stating the following information about the submitted paper: 1. Paper title, list of authors and affiliations.

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

3. A declaration that your paper is unpublished work, not considered elsewhere for publication.

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?

5. We kindly ask you to suggest at least two reviewers for your paper and give us their names and contact information (email).

Every manuscript submitted to the SV-JME undergoes the course of the peer-review process.

THE FORMAT OF THE MANUSCRIPT The manuscript should be written in the following format: - A Title, which adequately describes the content of the manuscript.

- An Abstract 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.

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

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

- A Theory or experimental methods used.

- An Experimental section, which should provide details of the experimental set-up and the methods used for obtaining the results.

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

- A Discussion section, which 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 the clarity).

- Conclusions, which should present one or more conclusions that have been drawn from the results and subsequent discussion and do not duplicate the Abstract.

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

Units - standard SI symbols and abbreviations should be used. 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.)

Abbreviations should be spelt out in full on first appearance, e.g., variable time geometry (VTG).

Meaning of symbols and units belonging to symbols should be explained in each case or quoted in a special table at the end of the manuscript before References.

Figures must be cited in a consecutive numerical order in the text and referred to in both the text and the caption 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.

Pictures may be saved in resolution good enough for printing in any common format, e.g. BMP, GIF or JPG. However, graphs and line drawings should be prepared as vector images, e.g. CDR, AI. When labeling axes, physical quantities, e.g. t, v, m, etc. should be used whenever possible to minimize the need to label the axes in two languages.

Multi-curve graphs should have individual curves marked with a symbol. The meaning of the symbol should be explained in the figure caption.

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 caption as

Table 1, Table 2, etc. In addition to the physical quantity, e.g. t (in italics), units (normal text), should be added in square brackets. The tables should each have a heading. Tables should not duplicate data found elsewhere in the manuscript.

Acknowledgement of collaboration or preparation assistance may be included before References. Please note the source of funding for the research.

REFERENCES A reference list must be included using the following information as a guide. Only cited text references are included. Each reference is referred to in the text by a number enclosed in a square bracket (i.e., [3] or [2] to [6] for more references). 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. All non-English or. non-German titles must be translated into English with the added note (in language) at the end of reference. 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 crosslinked simulations. Strojniški vestnik - Journal of Mechanical Engineering, vol. 57, no. 7-8, p. 531-538, DOI:10.5545/sv-jme.2011.013.

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

Please add DOI code when available and link it to the web site.

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. 553-576.

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 2009 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 2009-09-07.

EXTENDED ABSTRACT By the time the paper is accepted for publishing, the authors are requested to send the extended abstract (approx. one A4 page or 3.500 to 4.000 characters). The instructions for writing the extended abstract are published on the web page http://www.sv-jme.eu/ information-for-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 and 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 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 fast. Thus it is essential that manuscripts are accurate when submitted.

Authors can track the status of their accepted articles on http://en.svjme.eu/.

PUBLICATION FEE For all articles authors will be asked to pay a publication fee 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 300.00 EUR (for articles with maximum of 10 pages), 20.00 EUR for each addition page.

Additional costs for a color page is 90.00 EUR.

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2 Contents

Contents Strojniški vestnik - Journal of Mechanical Engineering volume 59, (2013), number 2 Ljubljana, February 2013 ISSN 0039-2480 Published monthly

Papers Luka Knez, Janko Slavič, Miha Boltežar: A Multi-Axis Biodynamic Measuring Handle for a Human Hand-Arm System Jianping Li, Songyong Liu, Changlong Du: Experimental Research and Computer Simulation of Face Grind-hardening Technology Aleksander Preglej, Igor Steiner, Sašo Blažič: Multivariable Predictive Functional Control of an Autoclave Eda Okutan, Sedat Karabay, Tamer Sınmazçelik, Egemen Avcu: A Study on the Derivation of Parametric Cutting Force Equations in Drilling of GFRP Composites Irina Stefanova Aleksandrova, Gancho Nenkov Ganev: Combined Cutting-deforming Taps Simon Štampar, Saša Sokolič, Gorazd Karer: Nonlinear Control of a Hybrid Batch Reactor Chi-Hsiang Chen, Yung-Cheng Wang, Bean-Yin Lee: The Effect of Surface Roughness of End-Mills on Optimal Cutting Performance for High-Speed Machining

71 81 89 97 106 112 124

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 71-80 © 2013 Journal of Mechanical Engineering. All rights reserved.

DOI:10.5545/sv-jme.2012.709

Received for review: 2012-07-20 Received revised form: 2012-11-27 Accepted for publication: 2012-12-06

A Multi-Axis Biodynamic Measuring Handle for a Human Hand-Arm System Knez, L. – Slavič, J. – Boltežar, M. Luka Knez – Janko Slavič* – Miha Boltežar

University of Ljubljana, Faculty of Mechanical Engineering, Slovenia The biodynamic response method is increasingly being used to study the human hand-arm system and vibration-induced injuries that affect the hand. Most measurements are made in the dominant forearm direction of excitation, but recently research has turned to multi-axis measurements as well as excitation. This study looks at a new instrument handle that measures the biodynamic responses at the palm and the fingers in multiple directions and, at the same time, removes the need to stop the test and change the orientation of the handle. In addition to the biodynamic response, the sensors inside the handle are able to measure the static push and grip forces simultaneously and therefore remove the need for an additional force plate or force sensor at the handle base, which is typically used to measure the push force.

The apparent mass of the handle was measured in order to determine the usable frequency range of the system. Additionally, the apparent mass distribution along the hand was investigated and it was found that the apparent mass distribution along the hand varies with frequency.

Keywords: biodynamic response, human hand-arm system, multi-axis measurement, apparent mass distribution, instrument handle

0 INTRODUCTION For health reasons, a great deal of research has been done in the field of vibration transmissibility from the excitation source to the user’s hands [1]. The measurement techniques that are most frequently used are the ISO 10819 [2] standardized method and − as an alternative to the standardized method − the driving-point, biodynamic-response method [3] and [4].

The standardized ISO 10819 method measures the vibration transmissibility to the hands when the user wears anti-vibration gloves. The method uses a special adapter, which contains a miniature accelerometer that is held in the palm of the hand.

The operator holds a vibrating handle, which then simulates the hand-tool excitations. To keep the measurements as realistic as possible, the grip and push forces are also measured and it is the operator’s task to keep them within the prescribed limits. The grip force is measured at the handle itself and the push force is usually measured at the handle-shaker interface or with a force plate located under the operator. The vibration transmissibility to the hand is derived from accelerations measured at the adapter and at the reference point in the handle.

However the adapter can cause measurement errors; therefore, other methods have been developed.

One of the recent and most promising methods used for determining the vibration transmissibilities and the dynamic properties of the hand is the biodynamicresponse method, researched among others by [3] to [8]. The method requires simultaneous measurements of the dynamic motion and forces at the handhandle interface and eliminates the need for a palm

adapter. A comparison between the standardized and biodynamic methods made by Dong et al. [6] shows that the biodynamic method performs better than the standardized method. The method has also been improved to measure the biodynamic responses separately at the palm and at the fingers [3] and [9].

There are various types of vibration sources that excite the hands in multiple directions; the ISO 5349-1 [10] and ISO10068 standards [11] denote those directions as the Xh-, Yh- and Zh-axis. The forearm direction or Zh-axis is the dominant direction in the operation of several tools [12] and [13]; however, there are certain tools that excite strongly in more axes (e.g., chain-saw, hand grinder, etc. [13]). To protect the user from the hazards of using such tools, research must be conducted for multiple axes. Recently, Dong et al.

[14] carried out a multi-axis study where the system used can excite and measure the hand responses simultaneously in all three orthogonal directions. The researched approach requires the simultaneous use of three shakers and, to measure the fingers after the palm measurements are completed, the test needs to be stopped and the handle rotated by 180 degrees.

This study researches a measuring system that is used for the biodynamic response measurements of the hand-arm system (HAS) at the palm and at the fingers for all three directions. The design of the system enables concurrent measurements of both the palm and the fingers, therefore removing the need to rotate the handle. The same sensors that are used for the dynamic response measurements are also used for the measurement of the static grip and push forces.

Since both static forces are measured in the handle itself, the force plate, which is commonly used to measure the push force, is no longer necessary.

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

71

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 71-80

The hand is a complex system of tissues, muscles and bones, and its parts differ in terms of mass and strength. As a result, some parts of the hand might be more susceptible to vibrations than others. The distribution of the apparent mass along the hand was, therefore, examined in an effort to clarify this.

The manuscript is organized as follows. The basics of biodynamic theory are presented in Section 1. Section 2 covers the instrumental handle and its dynamic characterization, the measuring setup and some details about multi-axis signal acquisition and processing. The results of the apparent mass of the HAS are shown in Section 3 for the Zh- and Yh-axis of excitation and the distribution of the apparent mass along the hand is also presented.

1 THEORETICAL BACKGROUND The theory used to derive the biodynamic response of the HAS is only briefly presented here; it is explained in detail by Dong et al. [3]. A biodynamic system is characterised by the apparent mass (AM), the mechanical impedance (MI), and the apparent stiffness (AS). In this study only the AM will be used, which is defined as: F AM = , (1)

A where F is the dynamic force of the hand, and A is the dynamic acceleration at the hand-handle interface.

These parameters must be measured simultaneously in the direction of excitation. The reader should note that the MI and the AS can be computed from the AM data.

In the frequency domain, the biodynamicresponse parameters can be computed from:

Z ( w) =

G fm ( w )

Gmm ( w )'

, (2)

where Z(ω) represents any of the biodynamic-response parameters, Gfm is the cross-spectrum of the force and the dynamic motion (acceleration for the AM, velocity for the MI or displacement for the AS), and Gmm is the auto-spectrum of the dynamic motion. The results obtained are mathematically complex:

Z (ω ) = Z Re (ω ) + Z Im (ω ) ⋅ j , (3)

where ZRe(ω) is the real component of the result, Zlm(ω) is the imaginary component and j = −1.

The measured dynamic force F is a combination of the biodynamic force and the inertial force of the 72

handle. For the biodynamic response of the hand ZHand it is therefore necessary to deduct the effect of the measuring handle ZHandle from the total (handle and hand) biodynamic response ZTotalHand:

Z

Hand

(ω ) = Z TotalHand (ω ) − Z Handle(ω ) . (4)

For the biodynamic response of the palm or the fingers the biodynamic parameters must be measured separately at the palm and at the fingers. The AM at the fingers AMFingers is therefore computed as: AM Fingers (ω ) =

= AM TotalFingers (ω ) − AM HandleFingers (ω ) , (5)

where AMTotalFingers is the total AM (with the human hand on the handle) and AMHandleFingers is the AM of the handle measured (without the human hand on the handle) at the fingers' side of the handle. A similar procedure is applied for the biodynamic response of the palm. If necessary, the biodynamic response of the gloved hand can also be evaluated, see, for example, Dong et al. [3] for details.

2 APPARATUS 2.1 The Measuring Handle A system capable of measuring in all three axes (Xh, Yh and Zh) has been developed [15] and is based on the research of Dong et al. [6] and [3] and Shibata et al. [4]. A measuring handle, with a diameter of 40 mm and a length of 110 mm, was made as shown in Fig. 1.

The handle consists of an upper and lower stainlesssteel cover, each with a 3-axis accelerometer attached.

The upper cover is used for the palm and the lower for the finger measurements. Each cover is screwed onto two 3-axis force sensors and the force sensors are screwed onto an aluminum frame. A circular plate is welded onto the bottom of the aluminum frame where it can be fixed onto an electrodynamic shaker.

The 3-axis force sensors, Kistler 9317B type, are used to measure the biodynamic forces in all three directions. The vector forces shown in Fig. 1 are labelled as P1 and P2 for the palm side and F1 and F2 for the finger side. These vector forces are measured in the hand’s coordinate system shown in Fig. 1. The piezoelectric force transducers together with the Kistler 5073 charge amplifiers can measure the dynamic, as well as the quasi-static grip and push forces. Therefore, every force signal measured by the sensors contains dynamic as well as static components of the forces, which are obtained by appropriate

Knez, L. – Slavič, J. – Boltežar, M.

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 71-80

a)

b) Fig. 1. The measuring handle: a) a sketch of the handle; b) a photograph of the handle

signal processing (see Sections 2.2 and 2.3). The selected charge amplifier also has a low zero-drift, which is approximately 0.25 N/min. To measure the dynamic accelerations in all three directions, two 3-axis accelerometers, Brüel & Kjaer 4524B type, are used. The vector accelerations are denoted as AP and AF for the palm and finger sides, respectively.

The accelerometers are attached to the middle of each cover, as suggested by Adewusi et al. [16].

2.2 Identifying the Apparent Mass The details of the signal processing of the measured forces and accelerations are shown in Fig. 2. To obtain the force at the fingers, the forces F1 and F2 are first summed:

F = F1 + F2 . (6)

This summation was made for each segment (2500 samples per segment, resulting in 0.25 s).

The sampling frequency was 10-kHz and a low-pass filter of 20-kHz was used. The force at the fingers F and the acceleration vector at the finger side AF are transformed into the frequency domain. The Hamming window was used and the 2500 samples resulted in a 4-Hz frequency resolution.

If the AM with the human hand on the handle (specifically the fingers) is measured, then the subscript ‘’TotalFingers’’ is used; if the handleonly (finger side) is measured, the subscript ‘’HandleFingers’’ is used. As discussed later, measurements with the hand on and without the

A Multi-Axis Biodynamic Measuring Handle for a Human Hand-Arm System

73

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 71-80

Fig. 2. Flowchart of the dynamic forces F and the accelerations A and the quasi-static grip Fg and push forces Fp

hand on the handle are required. Here, the hand-onhandle equations will be discussed in detail, but a similar approach is used for the handle only. The frequency-domain forces and accelerations when the hand is on the handle are denoted as F TotalFingers and A TotalFingers , and the AM per segment i is obtained as:

AM TotalFingers ,i =

F TotalFingers , (7) A TotalFingers

where the division needs to be performed for each Xh, Yh and Zh axis separately (at the element level).

The AM of the fingers on the handle is obtained by segment averaging (100 averages have been used, where the segments overlapped at 50%):

and time-domain acceleration AP. 2.3 Identifying the Push and Grip Forces In addition to the dynamic forces, the static push and grip forces, as defined in ISO 10819, need to be measured. As these forces are always in the Zh-axis of the hand, only the forces in this particular direction need to be processed. As can be seen in Fig. 2, the grip force Fg is the summation of the forces F1,Zh and F2,Zh (Zh is used to denote the component of the vector in the Zh direction). To obtain the static component, the measured samples are averaged in the time-domain (the averaging period was 0.25 s, which corresponds to 2500 measured samples):

1 100 ∑AM TotalFingers ,i . (8) 100 i =1

Finally, as discussed in the theoretical section, from measurements of the handle only and the handle with the hand, the biodynamic response of the fingers can be identified from Eq. (4).

For the biodynamic response of the palm, the palm-side apparent mass AMPalm is required. A similar approach to the finger side is used, but it is based on the time-domain summation at the palm side:

74

AMTotalFingers =

P = P1 + P2 (9)

Fg = Mean ( F1,Zh + F2 ,Zh ) . (10) Similarly, the push force Fp is obtained:

(

)

Fp = Mean P1,Zh + P2 ,Zh − ( F1,Zh + F2 ,Zh ) . (11)

2.4 Identifying the Apparent Mass Distribution at the Fingers and the Palm This study also looks at the AM distribution along the hand. For this reason, four hand regions have been defined (Fig. 3): the upper finger side (thumb, index and middle finger), the lower finger side (pinky and

Knez, L. – Slavič, J. – Boltežar, M.

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 71-80

ring finger), the upper palm side, and the lower palm side.

The force exerted by any part of the hand is distributed to both of the force sensors; however, the change in the dynamic response is dependent on the position of the hand-part with regards to the handle. The apparent mass calculated from the forces therefore gives additional information on the F j TotalFingers dynamics of the hand, specifically which part of the hand exerts more force on the handle.

Similarly, the dynamic acceleration A TotalFingers

Fig. 3. The hand gripping the handle, divided into four areas, measured with four force sensors

by:

is obtained from AF. A single accelerometer is used for both the upper and lower sides since the frequency range of interest (10 to 500 Hz) is sufficiently below the first natural frequency of the system (550 Hz).

Rigid motion of the handle cover can therefore be assumed and the measured acceleration is equal for both sides of the hand (j = 1, 2). The differences compared to the apparent mass are measured via the dynamic forces.

A similar approach is used for the palm AM distribution:

RPalm =

The AM distribution at the finger side is estimated

RFingers =

AM1,Fingers AM 2 ,Fingers

, (12)

where AMj,Fingers are the AM vectors at the upper (j = 1) and lower (j = 2) finger sides, respectively. The division in Eq. (12) needs to be performed for each Xh, Yh and Zh axis separately (at the element level).

The AM vectors AMj,Fingers are obtained by subtracting the AM measured at the handle only, AMj,HandleFingers, from the AM measured when the hand is on the handle, AMj,TotalFingers: AM j ,Fingers = AM j ,TotalFingers − AM j ,HandleFingers . (13) The AM values are evaluated similarly for each and direction as in Eq. (8), except that the forces F 1TotalFingers are not summed but used separately, i.e.: F 2TotalFingers F j ,TotalFingers AM j ,TotalFingers = , (14)

A F ,TotalFingers is the AM when the hand is on the handle. are obtained from the Fj The dynamic forces F j TotalFingers by frequency-domain averaging and the procedure is similar to that described in Section 2.2, except that 5000 samples were used and resulted in a 2-Hz resolution.

AM1,Palm AM 2 ,Palm

. (15)

2.5 Experimental Setup The experimental setups used in this study are illustrated in Fig. 4. For the Zh-axis measurements the handle was fixed on an LDS V555 electrodynamic shaker that was tilted in the appropriate direction.

For the Yh-axis measurements a larger LDS V875 electrodynamic shaker was used. With a proper experimental setup the biodynamic responses in the Xh direction could also be measured.

During the measurements the handle was subjected to a broadband random vibration with a power spectral density (PSD) of 5 (m/s2)2/Hz in the frequency range 10 to 500 Hz. 2.6 Dynamic Characterization of the Handle The instrument handle is a dynamical system and as such has its own dynamic properties, which are determined using modal testing [17] to [19]. For proper results, the measurement system’s natural response should be well outside the measurement range. For this reason the AM of the handle was measured for the Zh and Yh directions of the excitation in order to determine the usable frequency range.

Fig. 5 presents the AM at the palm and Fig. 6, the AM at the fingers.

A Multi-Axis Biodynamic Measuring Handle for a Human Hand-Arm System

75

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 71-80

a)

b)

Fig. 4. Experimental setup for excitation in the: a) Zh direction; b) Yh direction

Fig. 5. Apparent mass response of the handle measured at the palm (- Zh direction; - - - Yh direction)

There are slight differences between the response of the handle for the Zh- and Yh- axis. The reason for the differences was found in the structural dynamics of the measuring system, because the handle’s dynamic properties are dependent on the direction of 76

the excitation. The fundamental resonant frequency of the handle in the Zh-axis was measured at 572 Hz, while in the Yh-axis it was found at 550 Hz. Although the rigidity of the handle was assumed, the peak in the Yh-axis has a larger influence on the measurements

Knez, L. – Slavič, J. – Boltežar, M.

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 71-80

Fig. 6. Apparent mass response of the handle measured at the fingers (- Zh direction; - - - Yh direction)

Fig. 7. Apparent mass of the subject for Zh-axis excitation (- palm; - - - fingers)

than the one in the Zh-axis. This results in a slightly different apparent mass of the handle.

3 RESULTS AND DISCUSSION The results of the measuring system are presented in this section − specifically the AM of the HAS − and a comparison with previous research is made. Only one subject was used, since the focus of the research is on the handle itself and not on inter- and intra-subject differences. The experimental procedure is based on the procedure described in the ISO 10819 standard and Dong et al. [3], and is the same for both directions of excitation. The research on posture by Aldien et al.

[20] and Adewusi et al. [21] was also considered.

The biodynamic response of the handle alone was measured first and afterwards one subject held the handle with his bare hand. The subject was given all

the relevant instructions prior to the measurements.

The grip force was 30 N and the push force was 50 N throughout the measurement. Both forces were constantly displayed on a monitor, as indicated in Fig. 8.

The AM was identified using Eq. (8). The subject’s AM was measured three times for each direction of the excitation and the results were then averaged to minimize the inter-subject differences.

The measurement frequency range chosen was from 10 to 500 Hz, in accordance with the excitation subjected to the handle, see Section 2.

3.1 The Biodynamic Response of the HAS in the Zh- and Yh- axis The measurements in the dominant Zh-axis were made first. Fig. 7 shows the resulting AM of one subject

A Multi-Axis Biodynamic Measuring Handle for a Human Hand-Arm System

77

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 71-80

measured at the palm and at the fingers. The results are comparable to those reported by Dong et al. [6] and Concettoni and Griffin [8].

The values of the amplitude measured at the palm agree well with the one reported by Dong et al. [6].

Both results show a nearly constant magnitude of 1.1 kg from 10 to 30 Hz and a resonance peak was observed in both studies at around 450 Hz with a magnitude of 0.4 kg.

Concettoni and Griffin [8] measured the apparent mass of a hand pushing down on a vibrating plate with different coupling conditions. Their study found two frequency ranges where finger resonances are expected (10 to 16 Hz and 50 to 90 Hz), depending on the dynamic properties of the measured subject. The data presented in this study agrees with their findings, with a peak at 16 Hz and two more at 75 and 90 Hz. The Yh-axis of excitation was also investigated.

The results are presented separately for the palm and the fingers in Fig. 8.

3.2 Apparent Mass Distribution at the Hand This section presents the result of the Zh-axis excitation and the Zh-axis AM distribution, only.

However, other axes could be researched similarly, as discussed in the following.

The AM distribution at the fingers RFingers,Zh (Eq. (12)) and the palm RPalm,Zh (Eq. (15)) are shown in Figs. 9 and 10. If the upper and lower sides of the fingers/palm were equally loaded the AM distribution and would be close to 1. However, from Figs. 9 and 10 it is clear that this is not the case. The are two distinct frequency regions (20 to 40 Hz and 80 to 100 Hz) where the upper fingers take up to 45% more

load. At frequencies close to 10 Hz the measurements show that more load is taken by the lower fingers.

The palm AM distribution shows a different trend: when the excitation is in the frequency range 10 to 60 Hz the lower palm side takes more load; however, from 60 Hz onward, the upper side of the palm is loaded more (up to 80%). Above approximately 200 Hz the AM distribution is close to 1 for the finger as well as for the palm side.

4 CONCLUSIONS A novel handle for assessing the biodynamic characteristics of a human hand-arm system has been developed. The use of a hand-held adapter is not required and, in addition to the palm, measurements of the fingers can be made concurrently. All of the sensors are located inside the handle; therefore, a force plate or a force sensor at the shaker-handle interface, used for measuring the push force, are not required.

Since the handle is fitted with 3-axes sensors, it is capable of measurements in all three hand directions (Zh, Yh, Xh).

The results of the AM for the bare hand are presented for the Zh- and Yh-axis of excitation. The results matched with those observed by other researchers. The distribution of the apparent mass of the hand was also researched to examine the load on different parts of the hand. The results confirmed that the hand is not uniformly loaded, as the apparent masses were found to vary by up to 200 Hz. The thumb, index, and middle fingers, on average, exert more force on the handle than the ring and the pinky finger, resulting in a higher apparent mass. The palm side has a mixed trend: the lower part of the palm produces a higher apparent

Fig. 8. Apparent mass of the subject for Yh-axis excitation (- palm; - - - fingers)

78

Knez, L. – Slavič, J. – Boltežar, M.

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 71-80

Fig. 9. Apparent mass relations between the upper and lower parts of the hand (fingers side)

Fig. 10. Apparent mass relations between the upper and lower parts of the hand (palm side)

mass below 60 Hz, but at higher frequencies the trend changes and the upper part is more loaded.

5 REFERENCES [1] Griffin, M.J. (1990). Handbook of Human Vibration.

Academic Press, London.

[2] ISO-10819:1996. Mechanical Vibration and ShockHand-Arm Vibration-Method for the Measurement and Evaluation of the Vibration Transmissibility of Gloves at the Palm of the Hand. International Organization for Standardization, Geneva.

[3] Dong, R.G., Welcome, D.E., McDowell, T.W., Wu, J.Z. (2006). Measurement of biodynamic response of human hand-arm system. Journal of Sound and Vibration, vol. 294, no. 4-5, p. 807-827, DOI:10.1016/j. jsv.2005.12.047.

[4] Shibata, N., Hosoya, N., Maeda, S., (2008).

Establishment of one-axis vibration test system for

measurement of biodynamic response of human handarm system. Industrial Health, vol. 46, no. 6, p. 629634, DOI:10.2486/indhealth.46.629.

[5] Dong, R.G., Welcome, D.E., McDowell, T.W., Wu, J.Z. (2009). Methods for deriving a representative biodynamic response of the hand-arm system to vibration. Journal of Sound and Vibration, vol. 325, no.

4-5, p. 1047-1061, DOI:10.1016/j.jsv.2009.04.006.

[6] Dong, R.G., Rakheja, S., McDowell, T.W., Welcome, D.E., Wu, J.Z., Warren, C., Barkley, J., Washington, B., Schopper, A.W. (2005). A method for assessing the effectiveness of anti-vibration gloves using biodynamic responses of the hand-arm system. Journal of Sound and Vibration, vol. 282, no. 3-5, p. 1101-1118, DOI:10.1016/j.jsv.2004.03.069.

[7] Dong, R.G., Wu, J.Z., Welcome, D.E. (2005). Recent advances in biodynamics of human hand-arm system. Industrial Health, vol. 43, no. 3, p. 449-471, DOI:10.2486/indhealth.43.449.

A Multi-Axis Biodynamic Measuring Handle for a Human Hand-Arm System

79

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 71-80

[8] Concettoni, E., Griffin, M. (2009). The apparent mass and mechanical impedance of the hand and the transmission of vibration to the fingers, hand, and arm.

Journal of Sound and Vibration, vol. 325, no. 3, p. 664678, DOI:10.1016/j.jsv.2009.03.033.

[9] Dong, R.G., McDowell, T.W., Welcome, D.E., Warren, C., Wu, J.Z., Rakheja, S. (2009). Analysis of antivibration gloves mechanism and evaluation methods.

Journal of Sound and Vibration, vol. 321, no. 1-2, p.

435-453, DOI:10.1016/j.jsv.2008.09.044.

[10] ISO-5349-1:2001.

Mechanical Vibration – Measurement and Evaluation of Human Exposure to the Hand-Transmitted Vibration – Part 1: General Requirements.

International Organization for Standardization, Geneva.

[11] ISO-10068:1998. Mechanical Vibration and ShockFree, Mechanical Impedance of the Human Hand-Arm System at the Driving Point. International Organization for Standardization, Geneva.

[12] Dong, R.G., Welcome, D.E., McDowell, T.W., Wu, J.Z., Schopper, A.W. (2006). Frequency weighting derived from power absorption of fingers-hand-arm system under z(h)-axis vibration. Journal of Biomechanics, vol. 39, no. 12, p. 2311-2324, DOI:10.1016/j. jbiomech.2005.07.028.

[13] Stelling, J., Dupuis, H. (1996). Different acute effects of single-axis and multi-axis hand-arm vibration. International Archives of Occupational and Enviromental Health, vol. 68, no. 4, p. 236-242, DOI:10.1007/BF00381434.

[14] Dong, R.G., Welcome, D.E., Xu, X.S., Warren, C., McDowell, T.W., Wu, J.Z., Rakheja, S. (2012).

Mechanical impedances distributed at the fingers and palm of the human hand in three orthogonal directions.

80

Journal of Sound and Vibration, vol. 331, no. 5, p.

1191-1206, DOI:10.1016/j.jsv.2011.10.015.

[15] Knez, L., Slavič, J., Boltežar, M. (2011). Vibration transmissibilities of the human hand arm system exposed to Zh- and Yh- axes vibration. Proceedings of the Kuhljevi dnevi conference, p. 97-104.

[16] Adewusi, S.A., Rakheja, S., Marcotte, P., Boileau, P.E. (2008). On the discrepancies in the reported human hand-arm impedance at higher frequencies.

International Journal of Industrial Ergonomics, vol. 38, no. 9-10, p. 703-714, DOI:10.1016/j. ergon.2007.12.004.

[17] Ewinsm, D.J. (2000). Modal Testing Theory, Practice and Application – Second Edition. Research studies press ltd., Baldock, Hertfordshire.

[18] Maia, N.N.M., Silva, J.M.M. (1997). Theoretical and Experimental Modal Analysis. Research studies press ltd., Taunton, Somerset.

[19] Česnik, M., Slavič, J., Boltežar, M. (2009). Spatialmode-shape identification using a continuous wavelet transform. Strojniški vestnik - Journal of Mechanical Engineering, vol. 55, no. 5, p. 277-285.

[20] Aldien, Y., Marcotte, P., Rakheja, S., Boileau, P.E. (2006). Influence of hand-arm posture on biodynamic response of the human hand-arm exposed to z(h)axis vibration. International Journal of Industrial Ergonomics, vol. 36, no. 1, p. 45-59, DOI:10.1016/j. ergon.2005.07.001.

[21] Adewusi, S.A., Rakheja, S., Marcotte, P., Boution, J. (2010). Vibration transmissibility characteristics of the human hand-arm system under different postures, hand forces and excitation levels. Journal of Sound and Vibration, vol. 329, no. 14, p. 2953-2971, DOI:10.1016/j.jsv.2010.02.001.

Knez, L. – Slavič, J. – Boltežar, M.

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 81-88 © 2013 Journal of Mechanical Engineering. All rights reserved.

DOI:10.5545/sv-jme.2012.695

Received for review: 2012-07-04 Received revised form: 2012-09-17 Accepted for publication: 2012-11-21

Experimental Research and Computer Simulation of Face Grind-hardening Technology Li, J. – Liu, S. – Du, C. Jianping Li* – Songyong Liu – Changlong Du

China University of Mining & Technology, College of Mechanical and Electrical Engineering, China The influence of technical parameters on face grind-hardening surface hardness and hardened layer depth were determined by systematic experimental studies on technological parameters, such as grinding methods and grinding parameters, which provides a reference for choosing reasonable parameters in face grind-hardening processing. By FEA simulation of the grinding temperature field using ANSYS software, the variation in temperature at different points on the workpiece surface and the temperature field dynamic states are determined.

The simulation results are consistent with the experimental values, which indicates that the simulation method is feasible for studying face grind-hardening.

Key words: face grinding, grind-hardening, surface hardness, hardened layer depth, FEA simulation, ANSYS software

0 INTRODUCTION Research on face grind-hardening technology has not been reported to date. However, peripheral grinding and cylindrical grind-hardening technologies have been extensively researched since “grind-hardening” was proposed by the Brinksmeier [1] in 1994. The major works on this topic are as follows: (1) Research on the feasibility of grind-hardening and the metallographic structure of the hardened layer [2] to [5].

(2) Research on the influence parameters of the grind-hardening effect [6] to [10].

(3) Research on the temperature field and heat source model by the simulation method [11] to [14].

(4) Research on the performance of surface hardening [15] to [16].

With the popularization and application of the “grinding hardening” technology, it was found that “grinding hardening” technology is influenced and limited [17] to [20]. Based on an analysis of the above, face grind-hardening technology was studied by experiments and simulation.

grinding wheel slowly with a certain speed vf, until all the allowance was rubbed away.

Grinding Wheel Workpiece

ns

Surface

Chuck

Computer

x

Infrared Thermometer Lathebed

a) Grinding Wheel Surface

vf

1 EXPERIMENTAL METHOD According to the different modes of feeding, face grinding in the test can be divided into (1) one-way face grinding and (2) creep feed entry type, as shown in Fig. 1.

(1) One-way face grinding type: the workpiece was directly ground by the grinding wheel end; the grinding allowance was removed totally in one time step.

(2) Creep feed grinding method, i.e. horizontal grinding: the workpiece was cut into by the

z

nw

ns

nw Workpiece

Revolving Top

Lathebed

b) Fig. 1. Schematic diagram of the grinding system; a) one-way face grinding type, and b) creep feed entry type

*Corr. Author’s Address: China University of Mining & Technology, College of Mechanical and Electrical Engineering, Xuzhou, Jiangsu 221116, China, 13505205658@163.com.

81

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 81-88

In order to compare the hardened effects under the two grinding methods, random access points on the workpiece surface were measured. Fig. 4 shows the hardened hardness curve comparison. As can be seen from the graph, the hardness of the surface quenching in a one-way entry type is uniform, while in the creep feed entry type it has large fluctuations.

The C45E4 steel in the quenched and tempered state was used as the test material; the surface of the workpiece shape is shown in Fig. 2, which is an annular surface (stepped shaft shoulder face).

0 R2

0 R5

5 R2

R2 5

5 Table R3 1. Test parameters (1) Grinding mode

Fig. 2. Grinding surface shape and size of workpiece (mm)

One-way face grinding Creep feed

Grinding wheel speed vs [m/s]

Grinding depth ap [mm]

Workpiece speed nw [r/min]

Feed rate vf [mm/s]

30

0.3

90

-

30

0.3

90

0.3

2 EXPERIMENTAL RESULTS AND ANALYSIS The face grind-hardening experiment was carried out under different grinding parameters. The results in Fig. 3 show that if the grinding parameter selection is suitable, after the end grind-hardening process, the surface of the workpiece presented some obvious conventional quenching characteristics, which formed a certain depth of the hardened layer, and the hardened surface layer had similar hardness distribution in the depth direction.

Fig. 4. Quenching hardness curve comparison at different points on the workpiece surface

Fig. 3. Hardness distribution curve in the depth direction of the workpiece hardened layer

2.1 Influence of Grinding Methods on Hardening Effect The experimental research was focused on the grindhardening effect of two grinding methods. The test parameters of both are shown in Table 1.

82

Fig. 5. Hardened layer depth curve comparison along the radius direction

Li, J. – Liu, S. – Du, C.

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 81-88

Fig. 5 shows the hardened depth curve comparison along the radial direction. As can be seen from the graph, the hardened layer depth varies as the radius increases. Namely, it decreases with radius in one-way face grinding and it increases in creep-feed grinding.

Fig. 6 shows two different grinding methods’ grinding wheel effect cross checker, i.e. creepfeed (Fig. 6a), and one-way face grinding (Fig. 6b).

With creep feed (Fig. 6a), the grinding wheel cuts into from the outer edge of the workpiece and the workpiece’s external region has a long grinding time, thereby accumulating a high level of thermal energy, so that the temperature extends to a large depth and the hardened layer is thick. At the feed, the hardened layer has its maximum depth, while in the return place, as the heating time is too short, the depth of the hardened layer decreases rapidly. One-way face grinding (Fig. 6b) resulted in a large grinding area, a high metal removal rate, and increasing hardened surface roughness, at the same time the wheel face contact radius curvature resulted in the grinding zone’s different heat source intensity, therefore the surface hardness and depth of hardened layer appear uneven. With greater workpiece contact width, the surface hardening effect distribution is more notable.

a)

b)

a) b) Fig. 6. Two different grinding methods’s grinding wheel effect cross checker; a) creep feed entry type, and b) one-way face grinding type

2.2 Influence of Grinding Dosage on Hardening Effect The influence of grinding dosage on the hardening effect is remarkable, as different grinding dosages provide different grinding results. In the experiment, the feed rate, grinding speed and grinding depth were varied; the testing parameters are shown in Tables 2, to 4.

Fig. 7 shows the relationship between the grinding factors and the hardening effect. From Fig. 7 it is clear hardened hardness and hardened layer depth decrease as the feeding rate increases, and increase as the depth of grinding and wheel speed increase, however the magnitude of change is different.

c) Fig. 7. Comparison of relationships between influencing factors and the hardening effect; a) influence of feed rate on the hardening effect, b) influence of grinding depth on the hardening effect, and c) Influence of grinding speed on the hardening effect Table 2. Test parameters (2) Workpiece number 1 2 3 4 5

Grinding speed vm [m/s] 30 30 30 30 30

Experimental Research and Computer Simulation of Face Grind-hardening Technology

Grinding depth ap [mm] 0.3 0.3 0.3 0.3 0.3

Feed rate vf [mm/s] 0.1 0.2 0.3 0.4 0.5

83

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 81-88

Table 3. Test parameters (3) Workpiece number 6 7 8 9 10

Grinding speed vm [m/s] 30 30 30 30 30

Grinding depth ap [mm] 0.1 0.2 0.3 0.4 0.5

Feed rate vf [mm/s] 0.3 0.3 0.3 0.3 0.3

Grinding depth ap [mm] 0.3 0.3 0.3 0.3 0.3

Feed rate vf [mm/s] 0.3 0.3 0.3 0.3 0.3

Table 4. Test parameters (4) Workpiece number 11 12 13 14 15

Grinding speed vm [m/s] 29.0 29.5 30.0 30.5 31.0

It can be seen that the grinding depth has the most significant effect on the hardened hardness, followed by the feed rate, while the effect of grinding velocity is the least pronounced (Fig. 7a). Grinding depth (Fig. 7b) and feed rate (Fig. 7a) have a significant impact on the hardened layer depth, but the grinding speed’s impact is not significant (Fig. 7c). Generally, the hardenability change is more obvious than the depth of the hardened layer. Therefore, in order to get a better face hardening effect in a certain range (stable influence region), the grinding depth should be increased and the feed rate reduced.

Using one group of test conditions for an example simulation, the grinding process parameters as shown in Table 5 can be calculated as shown in Table 6.

Table 6. Simulation parameters Simulation parameters Total heating power q [Nm/s] Source area A [mm2] Time of grinding arc ts [s] Heat intensity qm [W/m2]

Value 5760 117.809 0.111 4.156×107

3.2 FEA Process of ANSYS When the workpiece goes into the grinding area during the process of grinding, its surface temperature rises rapidly and when the workpiece leaves the grinding area, the temperature drops quickly. Since the temperature field changes with time, we used the transient analysis in ANSYS [23] to [26].

3.2.1 Establishment of a Finite Element Model For finite element analysis, we use the element type Solid70 unit, since the workpiece surface is directly affected by the heat effect, which causes a significant temperature gradient, which needs high precision.

Therefore, the surface meshing is more detailed on the surface, as shown in Fig.8.

3 FEA SIMULATION OF THE GRINDING TEMPERATURE FIELD The temperature effect is the most direct factor of phase change, which plays a decisive role on the hardening effect of the workpiece surface material [21] and [22]. Therefore, the grinding temperature analysis is important for improving the workpiece surface hardening effect. Since the temperature measurements during the test are relatively complicated, FEA simulation of the grinding temperature field was performed.

3.1 Grinding Conditions Table 5. Grinding process parameters Grinding process parameters Maximum speed of grinding wheel vs [m/s] Rotational speed of workpiece nw [r/min] Grinding depth ap [mm] Grinding method Room temperature [ºC]

84

Value 30 90 0.5 Directly face grinding, without coolant 20

Fig. 8. Mesh results

Fig. 9. Heat source model load (step 1)

3.2.2 Loading of Heat Source During the grinding hardening process, the contact area between the grinding wheel and the workpiece is regarded as the heat source. Along with the rotation of the workpiece, the heat source on the workpiece surface moves in a circular motion. Since ANSYS does not support a direct moving load, we discretized the movement of heat source. This is the method applied when applying temperature load: the workpiece remains motionless, while the load moves along the circumferential direction.

In the simulation process, the contact area between the circular workpiece and grinding wheel

Li, J. – Liu, S. – Du, C.

StrojniĹĄki vestnik - Journal of Mechanical Engineering 59(2013)2, 81-88

a) 0.111 s

b) 0.222 s

c) 0.333 s

d) 0.444 s

e) 0.555 s

f) 0.666 s Fig. 10. Temperature field distribution cloud pictures

takes up 1/60 of the whole work area, therefore, the heat load is divided into six steps to be loaded.

Each load step’s load time is the time the grinding wheel goes through a single grinding arc length (0.111 s). As the radial dimension of the workpiece is relatively small, the radius of curvature effects can be ignored and the heat intensity can be seen as uniform distribution. As shown in Figs. 9 and 10, the uniform heat source model is loaded to the surface of the workpiece, so that the heat source moves along the surface of the workpiece.

3.2.3 Simulation Results and Analysis Through the finite element simulation, we can determine the grinding temperature field distribution and its variation with time.

Fig. 10 shows the distribution of the temperature field. When the wheel goes through the grinding zone, the surface temperature of the workpiece rapidly rises up to a maximum of 1200 degrees, therefore the heat source location forms a local high temperature, while the workpiece at a certain depth reaches the surface

Experimental Research and Computer Simulation of Face Grind-hardening Technology

85

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 81-88

quenching temperature requirements, by increasing depth and reducing the temperature rise. With the movement of the heat source to the next grinding region, the temperature of the previous grinding region began to drop rapidly, while the grinding area began to heat up and the process proceeds in this way.

After grinding of the workpiece surface was finished, the area underwent a heating and cooling process, so as to realize the end surface hardening.

Consider the first grinding zone as an example of the grinding process: at 0.111 s (Fig. 10a), the top workpiece temperature rose quickly to 1178 ºC, as the wheel moved, the regional temperature decreased rapidly, at 0.222 s (Fig. 10b) the temperature dropped to 563 ºC, at 0.333 s (Fig. 10c) it dropped to 279 ºC, and at 0.444 s (Fig. 10d) the temperature dropped slowly to 200 ºC. This shows that the surface has undergone two stages of cooling, (1) rapid cooling above 300 ºC and (2) slow cooling below 300 ºC, in accordance with the cooling rate’s generating martensite.

Fig. 11 shows the single-point surface temperature curve. From the chart we can see that when the heat source moved into position, the temperature rose rapidly and reached 1100 ºC; when the heat source was removed, the temperature dropped to 500 ºC, then continued to decrease at a relatively slow rate. This is because in the process of cooling, the temperature gradient is high at first, since the substrate has fast heat conduction. With heat input to the substrate, the temperature gradient decreases and the cooling rate becomes slower. However, the cooling process took a short time, which is consistent with experimental measurements of the temperature curve (Table 7).

From the temperature variation we can see that the workpiece temperature dropped from the highest value to below 300 ºC in just 0.3 s. Accordingly, we can predict that the workpiece material showed a martensitic transformation.

Fig. 12 shows the temperature curves of a set of points on the workpiece surface along a circumferentially arranged direction. From the chart we can see that at the observed points the heating and cooling process occurred as shown in Fig. 11, and the variations were essentially the same, although the time it took to reach the highest temperature was dependant on the workpiece entry time. However the highest temperatures were very similar, showing that the workpiece surface can achieve a consistent hardening effect, and will not experience differences due to the duration of contact with the heat source.

86

Fig. 13 shows the contour map of the grinding hardening temperature field along the workpiece depth.

Fig. 11. Single-point surface temperature curve

Temp 1. φ = 60º; Temp 2. φ = 120º; Temp 3. φ = 180º; Temp 4. φ = 240º Fig. 12. Each point temperature change curve of the workpiece surface along the circumference direction

Fig. 13. The grinding temperature field isotherm

From Fig. 13 it can be seen that the points at different depths have different temperatures. The surface has the highest temperature, which decreases

Li, J. – Liu, S. – Du, C.

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 81-88

with increasing depth; the heat becomes lower, the temperature drops and eventually stabilizes at lower values. Thus the surface of the workpiece has reached the austenitizing temperature, while the inside of the workpiece still maintains a relatively low temperature, which is similar to the traditional surface quenching temperature field distribution.

3.3 Validation of the Simulation Results A comparison of several groups of the measured temperature values with the simulation value is shown in Table 7. It is clear that the error value floats between 1.95 and 8.05%. The maximum error is 8.05, meeting the requirements of general engineering prediction accuracy. The results show that the loading of the uniformly distributed source model conforms to the objective situation. These results also prove that the finite element numerical simulation of the temperature field has high accuracy, therefore we can use the simulation method to forecast the hardening effect. This can also be regarded as the basis for the selection and design of grind-hardening technology parameters, which are important in grinding hardening test research.

Table 7. Comparison between simulation values and measured values Test number 1 2 3 4 5 6 7 8

Measured [°C] 856.3 889.2 911.6 935.7 964.5 1029.3 1132.6 1186.8

Simulation [°C] 894.56 921.37 953.12 1010.98 983.26 1101.74 1190.52 1242.20

Error [%] 4.47 3.51 4.55 8.05 1.95 7.04 5.11 4.66

(2) On the grinding wheel surface, different radii have a different line speed, which results in different heat source intensity. Therefore, different grinding widths will cause different distributions of the grinding hardening effect: One-way face grinding has high grinding efficiency, but can cause the distribution of quenching hardness and depth of hardened layer. Adopting creep-feed grinding will provide a uniform hardened layer.

However, quenching hardness and the depth of the hardened layer both decrease with increased feed rate, and increase with the depth of grinding and grinding speed, in which the grinding depth has the most significant impact, this is followed by feed rate, while the impact of grinding speed is the least pronounced.

(3) ANSYS software was used for transient analysis of the face grinding temperature field. With simulation the dynamic process of the end face grinding hardening was observed and the temperature variation with time was calculated for different points on the workpiece surface during the hardening process. The distribution of the temperature field of the surface layer under different depths was obtained under different time and temperature conditions. The simulation results are consistent with the experimental measurements, indicating the effectiveness of the simulation method.

5 ACKNOWLEDGEMENT Financials support for this work was provided by the National Natural Science Foundation of China (Project No. 51005232), the Jiangsu postdoctoral fund (Project No. 1101106C) and China’s postdoctoral special funding (Project No. 201104546); all are gratefully acknowledged.

4 CONCLUSIONS

6 REFERENCES

In this paper, we use the end face grinding method for a grinding hardening experiment study on C45E4 steel and through the measurement and analysis of the microstructure, surface hardness and hardened layer depth, we can draw the following conclusions: (1) During the face grinding hardening process, on the surface layer of the workpiece the metallographic structure changes and a certain thickness of martensite structure forms. This verifies the feasibility of the face grinding hardening technology.

[1] Brinksmeier, E., Brockhoff, T. (1994). Randschichtwarmebehandlung durch schleifen [J]. Heat Treatment and Materials, vol. 49, no. 5, p. 327-330.

[2] Zarudi, I., Zhang, L.C. (2002). Mechanical property improvement of quenchable steel by grinding. Journal of Materials Science, vol. 37, no. 2, p. 3935-3943, DOI:10.1023/A:1019671926384.

[3] Zarudi, I, Zhang, L.C. (2002). Modelling the structure changes in quenchable steel subjected to grinding.

Journal of Materials Science, vol. 37, no. 2, p. 4333434, DOI:10.1023/A:1020652519141.

[4] Zhang, L.C. (2007). Grind-hardening of steel surfaces: a foce review. International Journal of Abrasive

Experimental Research and Computer Simulation of Face Grind-hardening Technology

87

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 81-88

Technology, vol. 1, no. 1, p. 33-36, DOI:10.1504/ IJAT.2007.013847.

[5] Konstantios, S., George, T., Stavros, D. (2007).

Environmental impact assessment of grind-hardening process. The International Journal of Advanced Manufacturing Technology, vol. 12, no. 5, p. 338-345.

[6] Chryssolouris, G., Tsirbas, K., Salonitis, K. (2005).

An analytical, numerical and experimental approach to grind hardening. Journal of Manufacturing Process, vol. 7, no. 1, p. 1-9, DOI:10.1016/S15266125(05)70076-1.

[7] Salonitis, K., Tsoukanta, G., Stavropoulos, P. (2006).

Process forces modelling in Grind hardening.

Proceedings of the 9th CIRP International Conference, vol. 13, no. 9, p. 295-302.

[8] Salonitis, K., Chryssolouris, G. (2007). Cooling in grind-hardening operations. International Journal of Manufacturing Technology and Management, vol. 33, no. 3, p. 285-297, DOI:10.1007/s00170-006-0467-9.

[9] Salonitis, K., Chryssolouris, G. (2007). Thermal analysis of grindhardening process. International Journal of Manufacturing Technology and Management, vol. 12, no. 1, p. 72-92, DOI:10.1504/ IJMTM.2007.014143.

[10] Salonitis, K., Chondros, T., Chrysolouris, G. (2008).

Chryssolouris, G Grinding wheel effect in the grind-hardening process. International Journal of Manufacturing Technology and Management, vol. 38, p. 48-58, DOI:10.1007/s00170-007-1078-9.

[11] Tsirbas, K., Mourtzis, D., Zannis, S. (2004).

Chryssolouris G Grind hardening modeling with the use of neural networks. Proceedings of AMST International Conference on Advanced Manufacturing, vol. 25, no.

10, p. 13-18.

[12] Youssef, H.A., Al-Makky, M.Y., Abd-Elwahab, M.M. (2003). Evaluation of a proposed neural network predictive model for grind-hardening. Alexandria Engineering Journal, vol. 42, no. 4, p. 411-417.

[13] Fricker, D.C., Pearce, T., Harrison, A.J.L. (2004).

Predicting the occurrence of grind hardening in cubic boron nitride grinding of crankshaft steel. Journal of Engineering Manufacture, vol. 218, no. B, p. 13391356, DOI:10.1243/0954405042323577.

[14] Michael, F., Kompella, S., Chandrasekar, S. (2009).

Measurement of temperature field in surface grinding using infrared imaging system. Journal of Tribology, vol. 125, no. 2, p. 377-383.

[15] Zarudi, I., Zhang, L.C. (2002). A revisit to some wheel-workpiece interaction problems in surface

88

grinding. International Journal of Machine Tools & Manufacture, vol. 42, no. 8, p. 905-913, DOI:10.1016/ S0890-6955(02)00024-X. [16] Prekel, H. (2003). Automatic detection of surface properties of grind-hardening layer using infrared image. International Journal of Machine Tools & Manufacture, vol. 41, no. 6, p. 103-114.

[17] Contuzzi, N., Campanelli, S.L., Ludovico, A.D. (2011).

3D Finite Element Analysis in the Selective Laser Melting Process. International Journal of Simulation Modelling, vol. 10, no. 3, p. 113-121, DOI:10.2507/ IJSIMM10(3)1.169.

[18] Tamizharasan, T., Senthil Kumar, N. (2012).

Optimization of cutting insert geometry using DEFORM-3D: Numerical simulation and experimental validation. International Journal of Simulation Modelling, vol. 11, no. 2, p. 65-76, DOI:10.2507/ IJSIMM11(2)1.200.

[19] Gostimirović, M., Sekulić, M., Kopač, J., Kovač, P. (2011). Optimal control of workpiece thermal state in creep-feed grinding using inverse heat conduction analysis. Strojniški vestnik - Journal of Mechanical Engineering, vol. 57, no. 10, p. 730-738, DOI:10.5545/ sv-jme.2010.075.

[20] Rabiey, M., Walter, Ch., Kuster, F., Stirnimann, J., Pude, F., Wegener, K. (2011). Dressing of hybrid bond CBN wheels using short-pulse fiber laser. Strojniški vestnik - Journal of Mechanical Engineering, vol. 58, no. 7-8, p. 462-469, DOI:10.5545/sv-jme.2011.166.

[21] Yang, G., Han, Z.T., Du, C.L. (2008). The Experimental Study and Theoretical Analysis of the External Cylindrical Grinding and Surface Hardening Technology. China University of Mining and Technology, Xuzhou.

[22] Ma, Z., Han, Z., Du, C. (2009). The Experimental Research on Grinding Hardening and Computer Simulation. China University of Mining and Technology, Xuzhou.

[23] Ma, Z., Han, Z. Du, C. (2008). The numerical simulation of the transverse feed grinding temperature field. Manufacturing Technology & Machine Tool, vol.

10, p. 40-42.

[24] Deng, F. (2010). The Self-Study Manual of ANSYS10.0.

People’s Posts and Telecommunications Press, Beijing.

[25] Zhang, G., Hu, R., Chen, J. (2007). ANSYS10.0 Thermodynamics Finite Element Analysis Example Tutorial. Mechanical Industry Press, Beijing.

[26] Kang, S., Chen, X., Wang, C. (2010). The Entry of ANSYS. China Electric Power Press, Beijing.

Li, J. – Liu, S. – Du, C.

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 89-96 © 2013 Journal of Mechanical Engineering. All rights reserved.

DOI:10.5545/sv-jme.2012.617

Received for review: 2012-05-25 Received revised form: 2012-11-08 Accepted for publication: 2012-11-15

Multivariable Predictive Functional Control of an Autoclave Preglej, A. – Steiner, I. – Blažič, S. Aleksander Preglej1,* – Igor Steiner1 – Sašo Blažič2

2 University

1 INEA d.o.o., Slovenia of Ljubljana, Faculty of Electrical Engineering, Slovenia

This paper presents the predictive functional control of an autoclave, which is designed, tested and compared in uni- and multivariable manners. The control of the autoclave is based on our previously developed mathematical model for an autoclave, where we dealt with the heat-transfer and pressure-changing processes. First, we presented the principles of the predictive control algorithm, which are easy to understand. Next, the basic principles of predictive control were extended to a multivariable manner, so we presented the control law of the multivariable predictive algorithm. Furthermore, we depicted the suggested tuning rules for both control algorithms, which normally give satisfactory results, considering the trade-off between robustness and performance. We implemented both predictive algorithms in the linearized and simplified autoclave model, where we applied faster tuning rules due to the need for faster closed-loop responses. For comparison we also designed and applied a classical compensating PI controller. The results show superior performance of the multivariable predictive approach. All three algorithms rise similarly quickly, but then the PI and the simple predictive controller slowly approach the desired value due to slower tuning because of the very noisy manipulated variable. The interactions in the autoclave model are not very strong, therefore by the interactions influence rejection, both predictive algorithms show similar performances, while the PI approach performs much worse. The multivariable predictive approach also proves its superior performance by the interactions influence rejection when controlling the processes with stronger interactions. We can conclude that the autoclave should be controlled as one multivariable process using a multivariable predictive functional approach.

Keywords: predictive control, multivariable control, autoclave, temperature, pressure, interactions

0 INTRODUCTION The control of the autoclave is designed on the basis of a mathematical model of the autoclave developed in [1], where the paper deals with the various types of heat transfer, basic heat-transfer equations, heattransfer coefficients, heat flow, forced convection, conduction, thermal resistance, specific theories about dimensionless numbers like the Nusselt, Reynolds and Prandtl numbers, etc. The other process treated mathematically is pressure changing. The focus is the process inside the autoclave, which can be more simply described as heating, cooling and changing the pressure. Most of the used data are real and obtained from the autoclave manufacturer, but where this was not possible, the method of the model’s response fitting to the measured data was used. At the end of the paper we conclude that the designed model is usable for a variety of process control, due to the obtained very similar simulated and real process responses, considering some simplifications and using a curvefitting procedure.

The similar heat transfer problems like natural and enhanced convection were studied in [2] and even more specific problems like radiation, conduction, and also natural and forced convection mechanisms were studied in [3]. In [4] the authors focus on the issue of heat treatment, where heat transfers were calculated using methodology based on inverse heat transfer,

and similarly the inverse problem was used in [5] to approximate heat conduction.

In a real process, temperature and pressure control are treated as two independent control loops. The temperature is controlled continuously with two predictive functional controllers (PFCs) and pulse-width modulation of the heating with electrical heaters and cooling with a water cooler and an analogue valve. The pressure is discretely controlled with pressure increasing through the onoff valve and pressure decreasing through two on-off valves of different sizes. The advantage of predictive control is that it is simple to understand and easy to tune [6]. Predictive control [7] and [8] is based on a forecast of the process output signal at each sampling instant, where the forecast can be made implicitly or explicitly, based on a controlled process model. In the next step the control is selected such that it brings the predicted process output signal back to the reference signal in a way that minimizes the control error in the area between certain time horizons. Predictive control normally provides good performance, so it is not surprising that it is increasingly used in the industry [9] to [14].

First, the predictive functional control algorithm was developed for linear systems and then the basic idea was extended to nonlinear systems [15] to [20].

An example of industrial use of fuzzy predictive control is proposed in [21] to [23], where new Takagi-Sugeno proportional-integral predictive fuzzy

*Corr. Author’s Address: INEA d.o.o., Stegne 11, 1000 Ljubljana, Slovenia, aleksander.preglej@inea.si

89

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 89-96

controllers (PI-P-FCs) to speed control a class of servo systems are presented.

Like most industrial plants, the autoclave also exhibits a multivariable nature, which means that it has at least two inputs, two outputs and more than one variable that have to be controlled. In many cases more than one input variable is coupled with the outputs. The interactions between the temperature and the pressure in the autoclave cannot be neglected, so they were taken into account. Multivariable process control is well known and it was extensively studied in [24] and [25]. The fundamental principles of predictive functional control [7] were applied and extended to the multivariable case in [27]. In comparison with classical multivariable approaches, the main advantage of multivariable predictive functional control (MPFC) is in its simple design and high-quality control performance.

In the paper the predictive functional control of an autoclave in uni- (PFC) and multivariable (MPFC) manners is presented. The performances of both predictive algorithms are compared to the classical compensating PI approach. The results show the advantage of using the MPFC controller for multivariable autoclave processes.

The paper is organized as follows: in Section 1 the details of the autoclave model are given. In Sections 2 and 3 the univariable and multivariable predictive functional control are introduced, and in Section 4 controller tuning rules for both predictive control algorithms are presented. The implementation of both predictive control algorithms and the compensating PI approach is depicted in Section 5 and the results are collected in Section 6. Finally, the conclusions are drawn in Section 7.

An autoclave is a pressure vessel in a cylindrical form [1] where composite semi-products are heated at selected temperatures and under high pressure, and so under the applied conditions become harder and therefore of a higher quality. In the autoclave the working pressure is up to 7 bar and the working temperature is up to 180 °C. The autoclave is made of stainless steel and isolated with mineral wool and an isolating aluminium coat. The volume of the autoclave is 5600 litres. The autoclave is heated with electrical heaters with a power up to 110 kW and cooled with an inner cooler with a power up to 73 kW using cooling water. The pressure in the autoclave is increased and decreased by a flow of compressed air. A centrifugal ventilating

(

)

2 θ p.set = argmin  ∑ y process − ymodel  . (1)   In Eq. (1) the following notations are included: θp.set is the set of parameters, yprocess the real process output and ymodel is the mathematical model output.

The set of parameters, which were optimized using mentioned method, consists of the coefficients in Nusselt numbers calculations x and q, metal and coat masses mme and mc, metal and mineral wool thicknesses lme and lw, air circulation velocities u and v, and surface between the air in the autoclave and the metal Same by the autoclave heating model.

By the autoclave cooling model the set of optimized parameters consists of the volume flow of the cooling water Φcwi, cooler surface Scwa, heattransfer coefficient between the cooling water and the air in the autoclave Kcwa, and again metal thickness lme

1 DETAILS OF THE AUTOCLAVE MODEL

90

fan on the back of the autoclave with a water-cooled mechanical axle washer and an electromotor drive outside the autoclave provide the air circulation.

The mathematical model of the autoclave’s heating is built using heat flows and energy-balance equations, where the heat-transfer coefficients, areas of thermal conductivity, resistances of thermal conductivity, material masses, specific heat capacities, thermal conductivities, convection coefficients, characteristic lengths and Nusselt numbers are defined.

In addition to the influence of the conductance on the heat transfer, forced convection is also significant.

The delay with the heating is 30 s.

The cooling process is very similar to the heating process. The only difference is the source, which is heaters for heating and a cooler for cooling. All the other heat flows are the same. The mathematical model of the autoclave’s cooling is again built using heat flows and energy-balance equations, where similar parameters and coefficients are defined. The delay with the cooling is also 30 s.

The pressure in the autoclave is increased with compressed air through the entry on-off valve and decreased by letting the air out through two exit onoff valves of different sizes. The valves are modelled as analogue valves, where both exit valves are considered as a single valve with a larger dimension.

The mathematical model of the pressure changing is built using mass flows and mass-balance equations.

The delay with the pressure changing is 1 s.

Some of the model parameters were first estimated and then optimized with the method of the model’s response fitting to the measured data with the criterion function of the sum of squared errors, described with symbols as follows:

Preglej, A. – Steiner, I. – Blažič, S.

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 89-96

and surface between the air in the autoclave and the metal Same.

The set of optimized parameters by the autoclave pressure changes model consists of nonlinearity Knl and the valve constants Kin and Kout.

2 PREDICTIVE FUNCTIONAL CONTROL Since they are natural and can be rapidly understood, the basic principles of PFC control are very solid and easy to understand [9]. The algorithm is based on the explicit use of a dynamic process model to predict the future process-output behaviour over a finite horizon and to evaluate control actions in order to minimize the chosen cost function.

For each time constant the optimal control sequence according to the criterion is obtained, but only the first element is used and applied.

The control goal is to determine the future control action so that the predicted output trajectory coincides with the reference trajectory, which is given in the form of the reference model. The single coincidence point (horizon) is assumed and is called the coincidence horizon (H). The prediction is calculated using the known strategy of mean level control under the assumption of constant future manipulated variables u(k) = u(k + 1) = ... = u(k + H – 1).

The main idea of the PFC is the equivalence of the objective increment of the process Δp and the model output increment Δm, from which the control law of the PFC is obtained:

(1 − a ) ( w ( k ) − y ( k )) + y ( k ) , (2) u (k ) = b b 1− a ) ( 1− a 1− a H r

m

H m

m

m

m

m

where am can be written as am = e –Ts/Tm, in which Tm is the model time constant and Ts stands for the sampling time, and ar can be written as ar = e–Ts/Tr, in which Tr is the reference model time constant. Furthermore, bm is the model gain, w is the reference signal, y is the process output and ym is the process model output.

If the process has a time delay, the control law is modified according to Smith’s predictor principle [26]:

(1 − a ) ( w ( k ) − y ' ( k )) + y ( k ) , (3) u (k ) = b b 1− a ) ( 1− a 1− a H r

m

H m

m

m

m

m

where y′(k) = y(k) + ym(k) - ymd(k), in which ymd is the delayed model output.

3 MULTIVARIABLE PREDICTIVE FUNCTIONAL CONTROL The basic principles of predictive functional control were extended to the multivariable manner [27]. The problem of delays in the plant is circumvented by constructing an auxiliary variable that serves as the output of the plant if there are no delays present. A discrete undelayed process model must be given in the state-space form with the matrices Am, Bm and Cm:

xm ( k + 1) = Am xm ( k ) + Bm u ( k ) , y m ( k ) = C m xm ( k ) , 0

(4)

where xm is the model state vector, u is the model’s input and ym0 is the undelayed model output.

The control goal is the same as in Section 2 and the reference trajectory is again given in the form of the reference model. The prediction is also calculated using the known strategy of mean level control under the assumption of constant future manipulated variables.

Next, we can obtain the H-step-ahead prediction of the undelayed model:

ym0 ( k + H ) = Cm  AmH ⋅ xm ( k ) + M AIB ⋅ u ( k )  , (5)  

where MAIB = (AmH – I)(Am – I)–1Bm, in which I is identity matrix.

The reference model is given as:

xr ( k + H ) = Ar ⋅ xr ( k ) + Br w ( k ) , yr ( k ) = Cr ⋅ xr ( k ) ,

(6)

where xr is the reference model state vector, w is the reference signal and yr is the reference model output.

The matrices Ar, Br and Cr of the reference model must satisfy the equation: −1

Cr ( I − Ar ) Br = I , (7)

which enables reference trajectory tracking due to a unity gain for each channel. If a first-order reference model is used its matrices become diagonal.

Furthermore, we can choose Cr = I and so it must be Br = I – Ar. The reference-model prediction can then be given as:

(

)

yr ( k + H ) = ArH yr ( k ) + I − ArH w ( k ) , (8)

where a constant and bounded reference signal w(k + i) = w(k), i = 1, ..., H is assumed.

If the main idea of the MPFC is taken into account, the reference-trajectory tracking yr(k + i) = yp0(k + i), i =1, ..., H, next equalise the

Multivariable Predictive Functional Control of an Autoclave

91

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 89-96

objective increment vector Δp and the model output increment vector Δm:

yr ( k + H ) − y 0p ( k ) = ym0 ( k + H ) − ym0 ( k ) , (9)

and do some further calculations, we obtain the control law of the MPFC controller:

((

)

)

u ( k ) = G0−1 I − ArH e '' ( k ) + M AC xm ( k ) , (10)

where e′′(k) = w(k) – yp(k) + ym(k), MAC = = ArHCm – CmAmH and G0 = Cm(AmH – I)(Am – I)-1Bm. The control law is realizable if G0 is nonsingular, which is true when the plant is stable, controllable and observable. In other words, the MPFC control law can only be implemented for stable open-loop systems.

4 CONTROLLER TUNING RULES Predictive functional controllers are quite easy to tune because there are just a few parameters to set. The first requirement is to have the plant model. With the PFC this means having a model time constant Tm, a model gain Km and a model delay Dm. On the other hand, with the MPFC this means having the model written in the undelayed discrete state-space form with the matrices Am, Bm and Cm. From here on only two controller parameters need to be tuned. With the PFC these are the reference model time constant Tr and the coincidence horizon H. With the MPFC these are the discrete reference model matrix Ar and again the coincidence horizon H. Note that the coincidence horizon H must always be an integer value.

We investigated the predictive functional controller’s behaviour and performance using the different parameter settings on various simple and complex models.

With the PFC we took into account the results from [6] and tested their relevance. Using these settings the control performance was good, so we used the Tr rule and the bit fastened H rule, which we can combine in Tr = Tm / 10 and H = round(Tr / (2Ts)).

In addition, with the MPFC we examined the findings from [27], where the stability of the control algorithm regarding the parameter H was studied. If H is less than the maximum relative degree ρ of the model (H < ρ), the matrix G0 becomes singular and the control law is not applicable. When H is equal to ρ (H = ρ) the obtained closed-loop control is stable only if all the open-loop transmission zeros are inside the unit circle. And when H tends to infinity (H→∞) 92

the system matrix of the closed-loop system Ac goes to Am, from which it can be concluded that a stable control law could always be obtained for open-loop stable systems, even if some open-loop transmission zeros are outside the unit circle when a suitable coincidence horizon is used.

The discrete reference model matrix Ar can be, using Eq. (7) and further assumptions, easily presented as a diagonal matrix of the reference model time constants in a continuous time:  ar1 0 K 0  0 a 0  r2 K Ar =  , (11)

 M M O M    0 K arm  0 where m stands for the number of model states, arm is the state matrix (A), which in this case is a constant, of the discretized with Ts continuous time state-space model with A′ = –1 / Trm, B′ = 1 / Trm, C′ = 1 and D′ = 0.

Following that we can give the tuning rules for MPFC parameters like Trm = Tmm / 2.5 and H ≥ ρ, where Tmm is the continuous time constant of the mth reference transfer function.

H ≥ ρ is valid for stable open-loop systems with all open-loop transmission zeros inside the unit circle.

If some open-loop transmission zeros are outside the unit circle, the setting H > ρ must be used.

In general, these tuning rules are default settings, which normally give satisfactory results, considering the trade-off between the robustness and performance of the controlled system. If our requirements are different, we can also set it higher or lower. However, caution is needed as a lower Tr or Trm means a more tightened and faster control loop, and so the closedloop can become unstable. A lower H also means a more tightened and faster control loop, so a lot of noise can be propagated through the system. The lower limit for H is one, because normally the models have a maximum relative degree equal to one. A higher H propagates less noise through the system, but also slows down the control loop.

5 IMPLEMENTATION For the implementation of the control algorithms we had to linearize and simplify the built multivariable mathematical model of an autoclave [1]. A sampling time (Ts) of 1 second was used. Univariable predictive control is designed based on a first-order transfer function of a process. We used the following approximations:

Preglej, A. – Steiner, I. – Blažič, S.

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 89-96

Gheat ( s ) =

0.0485 −30 s e , (12) 63034 s + 1

G press ( s ) =

4.01e5 −1s e , (13) 288s + 1

where Gheat is the first-order transfer function of the heating process and Gpress is the pressure-changing process transfer function.

From the transfer functions in Eq. (12) and (13) we can easily obtain the model parameters for the time constant, gain and delay, which are Tmh = 63034, Kmh = 0.0485 and Dmh = 30 for the heating process, respectively, and Tmp = 288, Kmp = 4.01e5 and Dmp = 1 for the pressure-changing process, respectively.

For the reference-model time constant the tuning rules suggest Tr = Tm / 10 and H = Tr / 2, but the specialty of the real time autoclave process and the customer demands required faster closed-loop responses. Real-time experiments showed that the best results are obtained with the controller parameters Trh = 180 and Hh = 90 for the heating process. The realtime pressure changing is discretely controlled, but for the purpose of the simulation and the comparison with the MPFC control, we also designed the PFC with the controller parameters Trp = 11.5 and Hp = 6.

Since the difference between the heating and cooling processes is in fact only the source (the heaters by heating and the cooler by cooling), we used the same model to which we applied different source values. In spite of the controller limits, this refers to the heating from 0 to 110 kW of the heaters power and for the cooling from 0 to –73 kW of cooler power. With the pressure-changing process for the pressure increasing we used the controller limits from 0 to 100 of inlet valve opening and for the pressure decreasing from 0 to –100 of outlet valve opening. The same source values and controller limits were used by the MPFC algorithm.

Multivariable predictive control is designed based on an undelayed continuous two-inputs twooutputs state-space model with matrices Am = aij; i, j = 1, …, 5, Bm = bij; i = 1, …, 5, j = 1, …, 2, and Cm = cij; i = 1, …, 2, j = 1, …, 5, where a11 = –2.914, a12 = 0.024, a13 = 2.887, a14 = 4.25e–5, a15 = 1e–6, a21 = 1.57e–4, a22 = –1.57e–4, a31 = 1.89e-2, a33 = –1.89e–2, a41 = 1.02e–5, a44 = –1.02e–5, a51 = 0.05, a55 = –3.5e–3, b11 = 2.5e–4, b52 = 1400, c11 = 1, c25 = 1 and all others are zero. These matrices are then used in the discrete form.

From the previously mentioned state-space model we estimated the time constants Tm1 = 63034 and Tm2 = 288. For the mth reference model time constant the tuning rules suggest Trm = Tmm/2.5, but

again faster closed-loop responses are required. The simulation experiments showed that the best results are obtained with the controller parameters Tr1 = 40 and Tr2 = 6, which can be transformed to the following discrete reference model matrix Ar:

0  0.9753 Ar =  . (14) 0.8465  0

For the second controller parameter H the tuning rules suggest H ≥ ρ, where ρ is 1 by the autoclave model. However, as mentioned above, a lower H means a tighter and faster control loop, so a lot of noise is propagated through the system. Again, simulation experiments showed that the best results are obtained with Hmpfc = 10.

For the comparison we also designed the classical compensating PI controller with the transfer function GR = KR(TR s + 1) / (TR s), where KR is the compensator gain and TR is the compensator time constant.

We used a compensator which zero cancels the system pole (TR = TP) and so we get the openloop transfer function GOL = (KP KR) / (TP s), where TP is the system time constant and KP is the system gain. The closed-loop transfer function is then GCL = ((TP / KP / KR)s + 1) – 1, from which the compensator gain using the system gains from Eqs. (12) and (13) can be determined in following equation:

KR =

1 , (15) K Pα

where α is a coefficient between 0 and 1, which tells us by how much the compensated system is speeded up (a lower α means a faster system).

As was stated previously, the compensator time constant is equal to the system time constant, which is 63034 by the temperature control regarding Eq. (12) and by the pressure control regarding Eq. (13) is 288. α by the temperature control equals 0.0045, which gives a compensator gain KRt = 4.582e3, and further, α by the pressure control equals 0.42, which gives a compensator gain KRp = 5.938e–6.

6 RESULTS We applied the same amount of white noise (with different variance for the temperature and pressure signals) to all three algorithms simulations on the system outputs. The simulation experiment, which lasted 8000 seconds, was carried out in the following steps:

Multivariable Predictive Functional Control of an Autoclave

93

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 89-96

•

we increased the pressure from atmospheric pressure (1 bar) to 5 bar at time 50 s, next, we increased the temperature from room temperature (24 °C) to 150 °C at time 1500 s, then, we decreased the pressure to 3 bar at time 3000 s, next, we again increased the pressure to 5 bar at time 4000 s, next, we decreased the temperature back to room temperature (24 °C) at time 5000 s, and finally, we decreased the pressure back to atmospheric pressure (1 bar) at time 6000 s.

• • • • •

pressure change on the temperature here is minimal, so the disturbance cannot be seen in Figs. 1 and 2.

Fig. 3. PI, PFC and MPFC PC; pressure set point in bars (magenta), PI (blue), PFC (red) and MPFC response (green line)

Fig. 1. PI, PFC and MPFC performance comparison (PC); temperature set point in °C (magenta), PI (blue), PFC (red) and MPFC response (green line) Fig. 4. PI, PFC and MPFC PC; PI (blue), PFC (red) and MPFC (green line) inlet/outlet valve opening in %

Fig. 2. PI, PFC and MPFC PC; PI (blue), PFC (red) and MPFC (green line) heating/cooling power in kW

In Fig. 1 (temperature step responses) very similar responses of the PI and PFC algorithms can be observed, which rise relatively quickly but then very slowly approach the desired temperature. On the other hand, the MPFC algorithm is similarly quick, but it also reaches the desired value a lot more quickly than the other two algorithms. PI and PFC are tuned more slowly due to the very noisy manipulated variable during quicker tuning. In Fig. 2 the comparable noisy power manipulated variables of all three algorithms are presented. It is clear that the manipulated variable of the MPFC algorithm holds a little longer at the high/low limit, which explains reaching the desired temperature more quickly. The influence of the 94

In Fig. 3 (pressure step responses) we can see very similar responses of the PFC and MPFC algorithms, which quickly reach the desired pressure and also reject the influence of the temperature change on the pressure reasonably well, which can be seen around the times 1500 and 5000 s. On the other hand, the PI algorithm response is significantly slower, especially with the cooling, and also the rejection of the temperature change disturbance is much worse than with the other two algorithms. Again, in Fig. 4 the comparable noisy valve opening manipulated variables of all three algorithms are presented, where the PI manipulated variable is the least noisy, but also it does not reach the higher PFC and MPFC peaks for good temperature-change disturbance rejection.

7 CONCLUSIONS For the needs of the classical compensating PI, univariable and multivariable predictive functional control system design we used a previously built mathematical model of an autoclave, which was linearized, then written in multivariable state-space

Preglej, A. – Steiner, I. – Blažič, S.

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 89-96

model form and further simplified to two univariable first-order transfer-function models.

With the implementation of the PI, PFC and MPFC algorithms we followed the controller tuning rules and, where necessary, we used modified, faster rules.

The main advantage of the proposed MPFC algorithm is in the simple design, even in the case of delayed systems. In the results the MPFC approach proved its purpose because it showed the best performance. It allowed the fastest tuning, while the other two approaches performed with very noisy (not usable) manipulated variables at the same tuning speed.

As mentioned in the conclusions in [1], the interactions between the temperature and the pressure were taken into account. It can be said that also with the interactions disturbance rejection the MPFC showed superior performance, although the interactions in the autoclave model are not quite so strong. However, before implementing the MPFC approach to the autoclave model, we tested it on several simulated examples, where the interactions were much stronger.

A direct comparison of the performance of the PFC and MPFC showed that the MPFC performs better with the interactions’ disturbance rejection. In any case it can be concluded that the autoclave should be controlled as one multivariable process using a multivariable control approach, for example, MPFC. As mentioned above [1], the autoclave model will also have to be additionally validated for the other real operating conditions and due to the very different regimes of operation some fuzzy-control approach, like the fuzzy-model-based multivariable predictive functional control (FMBMPC), should be implemented.

8 ACKNOWLEDGEMENTS The operation part was financed by the European Union, European Social Fund. The operation implemented in the framework of the Operational Programme for Human Resources Development for the Period 2007 to 2013, Priority axis 1: Promoting entrepreneurship and adaptability, Main type of activity 1.1.: Experts and researchers for competitive enterprises.

9 REFERENCES [1] Preglej, A., Karba, R., Steiner, I., Škrjanc, I. (2011).

Mathematical model of an autoclave. Strojniški vestnik

- Journal of Mechanical Engineering, vol. 57, no. 6, p.

503-516, DOI:10.5545/sv-jme.2010.182.

[2] Venko, S., Vidrih, B., Pavlovič, E., Medved, S. (2012).

Enhanced heat transfer on thermo active cooling wall. Strojniški vestnik - Journal of Mechanical Engineering, vol. 58, no. 11, p. 623-632, DOI:10.5545/ sv-jme.2012.436.

[3] 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, p. 134-144, DOI:10.5545/sv-jme.2011.163.

[4] Taraba, B., Duehring, S., Španielka, J., Hajdu, Š.

(2012). Effect of agitation work on heat transfer during cooling in oil ISORAPID 277HM. Strojniški vestnik Journal of Mechanical Engineering, vol. 58, no. 2, p.

102-106, DOI:10.5545/sv-jme.2011.064.

[5] Gostimirović, M., Sekulić, M., Kopač, J., Kovač, P. (2011). Optimal control of workpiece thermal state in creep-feed grinding using inverse heat conduction analysis. Strojniški vestnik - Journal of Mechanical Engineering, vol. 57, no. 10, p. 730-738, DOI:10.5545/ sv-jme.2010.075.

[6] Dovžan, D., Škrjanc, I. (2009). Self-tuning algorithms for predictive functional controller. Electrotechnical Review, vol. 74, no. 4, p. 205-210.

[7] Richalet, J. (1993). Industrial application of model based predictive control. Automatica, vol. 29, no. 5, p.

1251-1274, DOI:10.1016/0005-1098(93)90049-Y. [8] Gerkšič, S., Strmčnik, S., Boom, T.V.D. (2008).

Feedback action in predictive control: an experimental case study. Control Engineering Practice, vol. 16, no.

3, p. 321-332, DOI:10.1016/j.conengprac.2007.04.012.

[9] Dovžan, D., Škrjanc, I. (2012). Control of mineral wool thickness using predictive functional control. Robotics and Computer-Integrated Manufacturing, vol. 28, no.

3, p. 344-350, DOI:10.1016/j.rcim.2011.10.004.

[10] Qin, S.J., Badgwell, T.A. (2003). A survey of industrial model predictive control technology. Control Engineering Practice, vol. 11, no. 7, p. 733-764, DOI:10.1016/S0967-0661(02)00186-7.

Poignet, P. (2005).

Predictive [11] Vivas, A., functional control of a parallel robot. Control Engineering Practice, vol. 13, no. 7, p. 863-874, DOI:10.1016/j.conengprac.2004.10.001.

[12] Karer, G., Škrjanc, I., Zupančič, B. (2008). Selfadaptive predictive functional control of the temperature in an exothermic batch reactor. Chemical Engineering and Processing, vol. 47, no. 12, p. 23792385, DOI:10.1016/j.cep.2008.01.015.

[13] Škrjanc, I. (2008). Self-adaptive supervisory predictive functional control of a hybrid semi-batch reactor with constraints. Chemical Engineering Journal, vol. 136, no. 2/3, p. 312-319, DOI:10.1016/j.cej.2007.04.012.

[14] Likar, B., Kocijan, J. (2007). Predictive control of a gas-liquid separation plant based on a Gaussian process model. Computers & Chemical Engineering,

Multivariable Predictive Functional Control of an Autoclave

95

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 89-96

vol. 31, no. 3, p. 142-152, DOI:10.1016/j. compchemeng.2006.05.011.

[15] Clarke, D. (1994). Advances in Model-Based Predictive Control. Oxford University Press, New York.

[16] Škrjanc, I., Matko, D. (2000). Predictive functional control based on fuzzy model for heat-exchanger pilot plant. IEEE Transactions on Fuzzy Systems, vol. 8, no.

6, p. 705-712, DOI:10.1109/91.890329.

[17] Blažič, S., Škrjanc, I. (2007). Design and stability analysis of fuzzy model-based predictive control – a case study. Journal of Intelligent and Robotic Systems, vol. 49, no. 3, p. 279-292, DOI:10.1007/s10846-0079147-8.

[18] Dovžan, D., Škrjanc, I. (2010). Predictive functional control based on an adaptive fuzzy model of a hybrid semi-batch reactor. Control Engineering Practice, vol. 18, no. 8, p. 979-989, DOI:10.1016/j. conengprac.2010.04.004.

[19] Causa, J., Karer, G., Núñez, A., Sáez, D., Škrjanc, I., Zupančič, B. (2008). Hybrid fuzzy predictive control based on genetic algorithms for the temperature control of a batch reactor. Computers & Chemical Engineering, vol. 32, no. 12, p. 3254-3263, DOI:10.1016/j. compchemeng.2008.05.014.

[20] Škrjanc, I., Matko, D. (2001). Fuzzy predictive functional control in the state space domain. Journal of Intelligent and Robotic Systems, vol. 31, p. 283-297, DOI:10.1023/A:1012011010623.

96

[21] Precup, R.-E., Preitl, S., Faur, G. (2003). PI predictive fuzzy controllers for electrical drive speed control: methods and software for stable development.

Computers in Industry, vol. 52, no. 3, p. 253-270, DOI:10.1016/S0166-3615(03)00130-1.

[22] Precup, R.-E., Preitl, S. (2004). Optimisation criteria in development of fuzzy controllers with dynamics. Engineering Applications of Artificial Intelligence, vol. 17, no. 6, p. 661-674, DOI:10.1016/j. engappai.2004.08.004.

[23] Precup, R.-E., Preitl, S., Korondi, P. (2007). Fuzzy controllers with maximum sensitivity for servo systems.

IEEE Transactions on Industrial Electronics, vol. 54, no. 3, p. 1298-1310, DOI:10.1109/TIE.2007.893053.

[24] Rosenbrock, H.H. (1970).

State-space and Multivariable Theory. Thomas Nelson and Sons Ltd, London.

[25] Maciejowski, J.M. (1989). Multivariable Feedback Design. Addison-Wesley, Workingham.

[26] Smith, O.J.M. (1957). Close control of loops with dead time. Chemical Engineering Progress, vol. 53, no. 1, p.

217-219.

[27] Škrjanc, I., Blažič, S., Oblak, S., Richalet, J. (2004).

An approach to predictive control of multivariable time-delayed plant: Stability and design issues. ISA Transactions, vol. 43, no. 5, p. 585-595, DOI:10.1016/ S0019-0578(07)60170-0.

Preglej, A. – Steiner, I. – Blažič, S.

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 97-105 © 2013 Journal of Mechanical Engineering. All rights reserved.

DOI:10.5545/sv-jme.2012.774

Received for review: 2012-08-31 Received revised form: 2012-11-16 Accepted for publication: 2013-01-14

A Study on the Derivation of Parametric Cutting Force Equations in Drilling of GFRP Composites Eda Okutan – Sedat Karabay – Tamer Sınmazçelik – Egemen Avcu Eda Okutan* – Sedat Karabay – Tamer Sınmazçelik – Egemen Avcu University of Kocaeli, Department of Mechanical Engineering, Turkey The aim of the present work is to derive machine force equations in the drilling of [0°/+45°/90°/–45°] oriented glass fiber reinforced polymeric matrix composites (GFRP). The novelty is in the use of the Shaw and Oxford model, which was initially developed for metals, for GFRP composites. The machining was performed on the GFRP samples using 118° point angle drills under dry conditions. During machining, drill torques and thrust force fluctuations were recorded using a dynamometer–amplifier–computer combination with different feed rates and drill diameters. The collected data were then analysed using mathematical models to investigate the empirical relationships between the essential parameters. The cutting forces in the drilling of GFRP materials were calculated using empirical equations and the results were compared with the measured data to verify the accuracy of the derived equations for the drilling of glass fiber reinforced polymer matrix materials. Moreover, the whole surface morphology of the drilled GFRP samples was examined by optical microscope and scanning electron microscope (SEM).

Keywords: glass fiber reinforced polymer (GFRP), machinability, surface morphology, thrust force, drill torque, empirical equation

1 INTRODUCTION Glass fiber reinforced polymer matrix (GFRP) composite materials offer superior properties such as high specific strength, high specific modulus of elasticity, high damping capacity, good corrosion resistance, good tailoring ability, excellent fatigue resistance, good dimensional stability and a low coefficient of thermal expansion [1] to [8]. Hence, they are used in many fields, such as the automotive, aerospace, sporting goods, marine, chemical industry, electrical industry, etc. [5], [6], [8] and [9]. In these fields, the drilling of GRFP composite materials is generally needed for the joining of composite structures. However, drilling of GFRP implies coping with problems that are not encountered when machining other conventional materials. The drilling of GFRP composite materials may lead to widespread damage and may cause many problems, such as fiber delamination, fiber breakage, fiber pull out, stress concentration, thermal damage, microcracking, etc. due to the inhomogeneity and anisotropic nature of GFRP composite materials [4], [5] and [10]. These problems cause aesthetic problems, but may also compromise the mechanical properties of the finished part [4]. For this reason, numerous researchers have investigated the GFRP drilling process and reported the factors that affect the quality of the finished part. Hence, many researchers have investigated the influence of these factors in the drilling of GFRP composites [5] to [7] and [9] to [12]. Moreover, many researchers have investigated the effects of various parameters (cutting speed, feed rate, point angle, thrust force, cutting tool geometry, etc.) particularly on the delamination behavior of GFRP composites [13] to [17]. In addition to these studies, some researchers

have investigated the modelling of the drilling of materials. Unfortunately, most of the models developed for metals have proved to be unsuitable for composites, as the cutting mechanism is different [17] to [20]. In the literature survey on machining it was observed that only the action of the cutting lips and the chisel edge are generally considered in modelling, however in the machining stage several types of damages observed in composite drilling are directly related to cutting force and torque. In particular, the structural damages mentioned above can be related to the thrust force during drilling. The presence and extension of the different kinds of damage depend on the composite material characteristics, tool geometry and material, and the process parameters [21] to [25].

The damage is particularly detrimental to the residual mechanical properties and significantly reduces the composite performance in use. Consequently, special care should be given to avoid the generation of defects during drilling. Therefore, it is particularly important when modelling the cutting action to derive analytical equations that predict the machining forces as a function of process parameters.

In the present work, the aim is to derive machine force equations for the drilling of GFRP composites.

Thus, GFRP composite material was drilled in a specially designed drilling system and drill torques and thrust force fluctuations were recorded using a dynamometer–amplifier–computer combination with different feed rates and drill diameters. The appropriate model for drilling GFRP was chosen and its performance tested on GFRP. The experimental data were examined using mathematical models to investigate the empirical relationships between essential parameters. The cutting forces in the drilling of GFRP materials were calculated using empirical

*Corr. Author’s Address: Department of Mechanical Engineering, Umuttepe Campus, Kocaeli, Turkey avcuegemen@gmail.com

97

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 97-105

equations and the results were compared with the measured data to verify the accuracy of the derived equations for the drilling of glass fiber reinforced polymer matrix materials. Moreover, following investigation of the test data for the derivation of empirical equations, hole surface morphology of GFRP samples were investigated using an optical microscope and scanning electron microscope (SEM).

2 EXPERIMENTAL PROCEDURES 2.1 Specimen Preparation and Mechanical Properties In this study, [0°/+45°/90°/–45°] oriented glass fiber reinforced polymer matrix composite samples were used. Samples were cut to 200×37×10 mm rectangles from 200×200×10 mm plates. Properties of the laminate are presented in Table 1. The polymeric matrix material is an orthophtalic polyester and composite laminates were produced using the vacuum assisted resin transfer molding technique.

Table 1. Properties of composite samples Fiber type Glass

Density [g/m3] 940

Number of laminates 14

Hardness of Brinell 43.1 HB

2.2 Equipments and Machine Tools Used in the Test Set-up In the experiment, an Arsenal PK–40 drilling machine was used. Properties of the drill machine are shown in Table 2.

Table 2. Feed rates and angular speed of main shaft of drilling machine Trade name of drilling machine Main drill shaft speed-range Automatic feed rate of drill shaft Main drive power

Arsenal PK–40 5 to 1500 rev/min 0.1 to 0.40 mm/rev 2.2 kW

Other equipment used in addition to the drilling machine are four axes piezoelectric type Kistler drill dynamometers and their auxiliary devices for measuring machining forces. Thus, the measurement set up combination consists of a Kistler–9272 drill dynamometer, Kistler–5070A amplifier and computer. When machining, the signal produced by the dynamometer related to the thrust force and torque is transferred by RS–232 connection to the computer.

The data acquisition process is performed using a program called as DynoWare written by Kistler Co. In the drilling of GFRP samples, DIN 338 HSS drills 98

with a right hand helical form and 118° point angle with four different diameters were used.

2.3 Drilling Process of GFRP Samples Tests were performed without using any coolant in the drilling operation. The revolution of the drill machine spindle was set at a constant speed of 265 rpm. Machining of the GFRP samples was performed with different diameters of drills and different feed rates. The drilling force measurement plan for GFRP material is shown in Table 3. To minimize vibration during machining, ythe drill dynamometer was fixed to the table of the machine table rigidly without distorting the sensitive parts of the device. Then, all connections between the stations for measuring and data acquisition were made. Drill studies were performed by using the drill force measurement plan.

Each drill was worked with samples at four different feed rates.

Table 3. Drill force measurement plan Spindle rpm [rev/min] 265 265 265 265

Drill diameter [mm] 4 6 8 10

Feed Rate [mm/rev] 0.10 0.10 0.10 0.10

0.16 0.16 0.16 0.16

0.25 0.25 0.25 0.25

0.40 0.40 0.40 0.40

These combinations were repeated five times on the GFRP samples. The collected results were then analyzed using the DynoWare–Kistler data acquisition program. Mean values of the fluctuation curve due to thrust force and torque were determined and the tabulated data were used to investigate the empirical equations.

3 RESULTS AND DISCUSSIONS 3.1 Derivation of Drill Torque Equation on GFRP A cutting model for drilling was chosen to study the empirical equations related to the forces in a drilling process performed on GFRP. We chose to use Shaw and Oxford’s drill model. Since this model was originally used on metal cutting parameters, it was not clear from the outset whether the model would be suitable for detection of the cutting forces on GFRP. Thus, the study also tests the validity of the proposed model. Using Eq. (1) and the collected test data, the empirical torque equation with respect to drill diameter and drill feed rate was determined [26] and [27]. In Eq. (1), a is evaluated by the relationship

Eda Okutan – Sedat Karabay – Tamer Sınmazçelik – Egemen Avcu

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 97-105

between the specific cutting energy, u and f·d [26].

For a given GFRP material, s is considered a constant in order to simplify the complex calculations.

Fig. 2. Drill torque versus to drill feed rate on GFRP

Fig. 1. Specific energy u versus f·d in drilling

The slope of the curves in Figs. 4 and 5 are as 0.42 and 0.51, respectively. The ratio [c/d], which is the ratio of length of the chisel edge to drill diameter, taken as a constant (0.213) for the drills used in the experiments [26].

The test data is checked using Eq. (1) to see whether there is a correlation between the measured and calculated values using the [26] to [30].

c 1 − ( )2 Md s 2 a f 1− a f 0.8 d + K ( c ) 2 − a ], (1) [ 1.2 = K6 7 1+ a 3 d d HB d d 1 + ( c )a d

where Md is drill torque, [N·cm], HB Brinell hardness of GFRP samples, [kg/mm2], f feed rate, [mm/rev], d drill diameter, [mm], S the average distance between imperfections in the material, [mm] and a, K6, K7 constants.

Specific cutting energy is defined as given in Eq. (2) [24] to [25]:

U=

8Md . (2) f d2

Fig. 1 shows the use of the test results on the evaluation of specific cutting energy versus (f·d) drawn in logarithmic scale. From the slope of the regression curve, the a value was determined to be a = 0.31.

After determination of drill torque data, “feed rate versus drill torque” and “drill diameter versus drill torque” graphics were drawn on a logarithmic scale to find out the relationship between of them. The graphics are shown in Figs. 2 and 3, respectively.

Fig. 3. Drill torque versus to drill diameter on GFRP

Consequently Eq. (1) can be transformed into a simplified form as given in Eq. (3) by substituting these numerical values.

or

M d = K8 f 0.42 d 0.51 , (3) M d = K 9 H B f 0.42 d 0.51 . (4)

In Fig. 1, the value of the specific energy on the vertical line cut by the regression curve shown to be around 390 N/mm2. Using this value, Eqs. (5) to (7) can be derived for the drill torque in GFRP.

= U

8Md 390 , (5) = f d 2 ( f d )0.31

A Study on the Derivation of Parametric Cutting Force Equations in Drilling of GFRP Composites

99

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 97-105

= Md

390 f d 2 = 48.75 f 0.69 d 1.69 , (6) 8 ( f d )0.31

0.42 0.51 M d K= d 48.75 f 0.69 d 1.69 . (7) = 8 f

By inserting material hardness into Eqs. (7) and (8), the final Eq. (9) can be determined.

K8 48 = .75 f 0.27 d 1.18 K 9 H B , (8) =

K 9 = 1.131 f 0.27 d 1.18 . (9)

Eq. (9) is then inserted in Eq. (4). Thus, the required drilling torque on glass fiber reinforced polyester composite material can be derived as given in Eq. (10).

Fig. 4. Thrust force versus feed rate

M d = 0.131 H B f 0.69 d 1.69 . (10)

3.2. Derivation of the Drill Thrust Force Equation on GFRP With the help of dimensional analysis, Shaw and Oxford’s parametric relation for drill thrust force is presented in Eq. (11) [26].

c 1− 1− a Tv c 2a f d [ + K14 ( )1− a ] + = K13 S d d 2 HB d 1+ a (1 + c ) a d c 2 + K12 ( ) , (11) d

Fig. 5. Thrust force versus drill diameter

where Tv is axial force [daN], K12, K13, K14 are constants and a = 0.31.

In the Eq. (11), the value of a has been calculated to be a = 0.3. Moreover s, which is the distance between imperfections in the material, is taken to be a constant value (s = 1) for simplification. The thrust force equation can then be defined by Eq. (12).

c 1− Tv c f 0.69 d + K14 ( )0.69 ] + = K15 1.31 [ c 0.31 d d 2HB d (1 + ) d c + K12 ( ) 2 .

(12) d

After performing machining, the collected data related to thrust force are plotted in logarithmic scale and the corresponding graphs are drawn with combinations of “Thrust force versus to feed rate” and “Thrust force versus to drill diameter” in Figs. 4 and 5, respectively.

100

Fig. 6. Graphic representation of the relationship between {

T 2

v

d HB

} vs {

f 0.69 } d 1.31 .

The measured data are input into the thrust force Eq. (12). Then the relationship between the

Eda Okutan – Sedat Karabay – Tamer Sınmazçelik – Egemen Avcu

StrojniĹĄki vestnik - Journal of Mechanical Engineering 59(2013)2, 97-105

T

f 0.69 } can be determined as d 2 HB d 1.31 shown in Fig. 6. The equation of the line in Fig. 6 has been derived as given in Eq. (13). The equation for this line defines teh â&#x20AC;&#x153;thrust forceâ&#x20AC;? in drilling of GFRP samples.

parameters {

v

} vs {

Tv = 2.7576 H B f 0.69 d 0.69 + 0.009 H B d 2 [ N ]. (13) 3.3 Comparison of the Theoretical Results and Experimental Results

measured and theoretical values is around 5% and this is an acceptable level for this kind of handmade artificial materials. In Fig. 8, the variation between the experimental and theoretical drill trust values of the samples drilled with 10 mm drills seems greater compared to the samples drilled with 4mm, 6mm, and 8mm drills. The reason for this result can be explained by the higher probability of encountering imperfections, due to the inhomogeneous nature of the GFRP composites, with the increase in the tool diameter.

In this section, the theoretical results of the drill torque and thrust values were calculated by using derived empirical equations as a function of feed rate and drill diameter. The results were then compared with the experimental records. In Figs. 7 and 8 comparisons of the theoretical and empirical data on drill torques and thrust force are given as a function of feed rate and drill diameter.

Fig. 8. Comparison of experimental (a) and theoretical (b) drill thrust values as a function of feed rate and drill diameter

3.4 Investigation of Hole Surface Morphology of Drilled GFRP Samples

Fig. 7. Comparison of experimental and theoretical drill torque values as a function of feed rate and drill diameter

Machining of composite materials differs significantly in many respects from machining of conventional metals and their alloys. In the machining of composites, the material behavior is not only nonhomogeneous and anisotropic, but it also depends on diverse reinforcement and matrix properties, as well as on the volume fraction of matrix and reinforcement. The tool encounters, alternatively, matrix and reinforcement materials, whose response to machining can be entirely different. Graphics shows good correlations between the measured and calculated values. Nominal fluctuation of the

The important topic in the machining of a composite material is to detect real hole entry defects, the circular defect and damage from a heat source in the wall of the hole, the lamination at the exit hole. Therefore, following analysis of test data for the derivation of empirical equations, hole surface morphology of GFRP samples was investigated by using an optical microscope and scanning electron microscope (SEM). From the various machining operations, a brief summary of drilling performance and defects has been presented below, with views of the samples.

As expected, all forms of defects occurred as shown in Figs. 9 and 10. In Fig. 9, the exit side of the tools from the samples with delaminated fibers are shown.

As seen in Figs. 9a, b, c and d, limited delaminations were observed on the drilling surfaces. Such limited delaminations may not cause remarkable defects in GFRP composites. However, for further understanding of delaminations and cutting effects in GFRP holes,

A Study on the Derivation of Parametric Cutting Force Equations in Drilling of GFRP Composites

101

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 97-105

a) b)

c) d)

Fig. 9. View of exit side of the drilled GFRP samples machined by: (a) 4 mm drill, (b) 6 mm drill, (c) 8 mm drill and (d) 10 mm drill

samples were cut from the axis of the tool, and then the surfaces cut by the lips of the drills are shown in Fig. 10 with the help of a SEM. The polyester matrix and glass fibers can be seen clearly in Figs. 10a and b. Good adhesion between the matrix and fibers is observed in these figures. In Fig. 12c and d, fiber tips broken during the drilling process are shown.

As seen in Figs. 10c and d, fibers were broken in a brittle manner during the drilling process. However, they remained embedded in the polyester matrix and limited delaminations were observed. From Figs.

9 and 10, we can conclude that glass fibers have a strong adhesion to the polyester matrix. Thus, it has been determined that surface quality and dimensional ovality are at an acceptable level for mechanical connecting using bolts.

102

4 CONCLUSIONS From the above study on the derivation of empirical equations related to GFRP using a conventional drill, the following results can be summarized.

1) It was determined that when the drill diameter and feed rate are increased while machining GFRP, the thrust force and drill torque increase.

This result also verifies that if the drill diameter is increased then the un–deformed chip material volume increases. This means that for processing of continuous chip formation at high feed rates, a higher power requirement is demanded by the tool to get rid of cutting, friction and extrusion forces. This creates high torque and thrust forces in the machining operations.

2) In this study, the model we used, which was developed for metals by Shaw and Oxford, showed very good accordance with the derivation of the empirical relationship for the drilling of

Eda Okutan – Sedat Karabay – Tamer Sınmazçelik – Egemen Avcu

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 97-105

a) b)

c) d)

Fig. 10. SEM photos of; (a) vertical cut of the drill holes and (c) view surfaces of drilled GFRP samples under different magnifications

glass fiber reinforced oriented “0°/+45°/90°/45°” in the polymer matrix composite. As a conclusion, the equations presented below can be used to estimate the machining forces on drilling operations for the defined composites. The empirical equations for torque and thrust forces are given below; Torque equation: M d = 0.131 H B f 0.69 d 1.69 [ N cm ] , Thrust force equation: Tv = 2.7576 H B f 0.69 d 0.69 + 0.009 H B d 2 [ N ].

3) Comparing the measured and empirical results for drilling forces, some differences have been determined. These differences are unavoidable due to the microstructure of the GFRP. Not surprisingly, the machining characteristics of the composite materials with a non-isotropic nature

results in fluctuations compared to homogenous and isotropic or quasi- isotropic materials.

Therefore, cutting force fluctuation should be expected from the machining of these kinds of materials. However, these differences are not that important for estimating the level of machining forces by empirical equations as empirical equations give approximate values to engineers not exact ones. Finally by tolerating some of the deviations, the derived empirical relations for similar types materials can be used effectively to give some design and constructive ideas.

4) In this study, the main aim was to determine the relationship between cutting forces and the essential parameters of the machining tool.

Additionally, machined hole quality and damage development due to drill feeding of the material were also very important. Delamination of the

A Study on the Derivation of Parametric Cutting Force Equations in Drilling of GFRP Composites

103

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 97-105

fibers occurred at the exit side of the holes, although it was determined that surface quality and dimensional ovality are at an accepted level for mechanical connecting with bolts. Surface quality and roughness of the machined holes are due to structural discontinuities in the GFRP. Discontinuities of the artificial materials were also determined to be essential reasons for the force fluctuations.

5) Chisel edge length relative to drill diameter is indicative of delamination of GFRP due to increasing thrust force [31]. This effect also can be seen somewhat in the Fig. 8 by increases in the mesured thrust force rather than by the calculated data for the same cutting parameters.

6) Structural parts made of composite frequently have to be drilled in the structural, aircraft and automobile industries. However, little is known about the conditions between the drilling tool and material. This study aimed to show whether the model verified for ferro-alloys can be used for pre-estimation of drilling forces in the machining of GFRP composites. It has been proven that drilling forces applied to construction parts designed for the structural and machine industry can be easily determined. This will help to prevent excessive force application during these processes in order to prevent damage to composite structures.

5 REFERENCES [1] Abrao, A.M., Faria, P.E., Rubio, J.C., Reis, P., Davim, J.P. (2007). Drilling of fiber reinforced plastics: A Review. Journal of Material Processing Technology, vol. 186, no. 1-3, p. 1-7, DOI:10.1016/j. jmatprotec.2006.11.146.

[2] Tsao, C.C., Hocheng, H. (2007). Effect of tool wear on delamination in drilling composite materials.

International Journal of Mechanical Sciences, vol. 49, no. 8, p. 983-988, DOI:10.1016/j.ijmecsci.2007.01.001.

[3] Arul, S., Vijayaraghavan, L., Malhotra, S.K., Krishnamurthy, R. (2006). The effect of vibratory drilling on hole quality in polymeric composites.

International Journal of Machine Tools and Manufacture, vol. 46, no. 3-4, p. 252-259, DOI:10.1016/j.ijmachtools.2005.05.023.

[4] Davim, J.P., Rubio, J.C., Abrao, A.M. (2007). A novel approach based on digital image analysis to evaluate the delamination factor after drilling composite laminates.

Composite Science and Technology, vol. 67, no. 9, p.

1939-1945, DOI:10.1016/j.compscitech.2006.10.009.

[5] Palanikumar, K. (2010). Modeling and analysis of delamination factor and surface roughness in drilling GFRP composites. Materials and Manufacturing

104

Processes, vol. 25, no. 10, p. 1059-1067, DOI:10.1080/10426910903575830.

[6] Arul, S., Samuel, R., Vijayaraghavan, L., Malhotra, S.K., Krishnamurthy, R. (2006). Modeling and Optimization of Process Parameters for Defect Toleranced Drilling of GFRP Composites. Materials and Manufacturing Processes, vol. 21, no. 4, p. 357365, DOI:10.1080/10426910500411587.

[7] Latha, B., Senthilkumar, V.S. (2009). Analysis of thrust force in drilling glass fiber-reinforced plastic composites using fuzzy logic. Materials and Manufacturing Processes, vol. 24, no. 4, p. 509-516, DOI:10.1080/10426910802714688.

[8] Ramkumar, J., Malhotra, S.K., Krishnamurthy, R. (2002). Studies on drilling of glass/epoxy laminates using coated high-speed steel drills. Materials and Manufacturing Processes, vol. 17, no. 2, p. 213-222, DOI:10.1081/AMP-120003531.

[9] Palanikumar, K., Prakash, S., Shanmugam, K. (2008).

Evaluation of delamination in GFRP composites.

Materials and Manufacturing Processes, vol. 23, no. 8, p. 858-864, DOI:10.1080/10426910802385026.

[10] Faraz, A., Heymann, T., Biermann, D. (2011).

Experimental investigations on drilling GFRP epoxy composite laminates using specialized and conventional uncoated cemented carbide drills. Materials and Manufacturing Processes, vol. 26, no. 4, p. 609-617, DOI:10.1080/10426911003636969.

J.Z., Chen, J.C. (2009).

Surface [11] Zhang, roughness optimization in a drilling operation using the taguchi design method. Materials and Manufacturing Processes, vol. 24, no. 4, p. 459-467, DOI:10.1080/10426910802714399.

[12] Bhatnagar, N., Singh, I., Nayak, I. (2004), Damage investigation in drilling of glass fiber reinforced plastic composite laminates. Materials and Manufacturing Processes, vol. 19, no. 6, p. 995-1007, DOI:10.1081/ AMP-200034486.

[13] Gaitonde, V.N, Karnik, S.R., Rubio, J.C., Correia, A.E., Abrao, A.M., Davim, J.P. (2008). Anaylsis of parametric influence on delamination in high-speed drilling of carbon fiber reinforced plastic composites. Journal of Materials Processing Technology, vol. 203, no. 1-3, p.

431-438, DOI:10.1016/j.jmatprotec.2007.10.050.

[14] Rubio, J.C., Abrao, A.M., Faria, P.E., Correia, A.E., Davim, J.P. (2008). Effects of high speed in the drilling of glass reinforced plastics: Evaluation of the delamination factor. International Journal of Machine Tools & Manufacture, vol. 48, no. 6, p. 715-720, DOI:10.1016/j.ijmachtools.2007.10.015.

[15] Abrao, A.M., Rubio, J.C., Faria, P.E., Davim, J.P. (2008). The effects of cutting tool geometry on thrust force and delamination when drilling glass fibre reinforced plastic composite. Materials and Design, vol. 29, no. 2, p. 508-513, DOI:10.1016/j. matdes.2007.01.016.

[16] Davim, J.P., Reis, P., Antonio, C.C. (2004). Drilling fiber reinforced plastics (FRPs) manufactured

Eda Okutan – Sedat Karabay – Tamer Sınmazçelik – Egemen Avcu

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 97-105

by hand lay-up: influence of matrix (Viapal VUP 9731 and ATLAC 382-05). Journal of Material Processing Technology, vol. 155-156, p. 1828-1833, DOI:10.1016/j.jmatprotec.2004.04.173.

[17] Mauch, C.A., Lauderbaugh, L.K. (1990). Modeling the drilling processs – An analytica model to predict thrust force and torque, computer modeling and simulation of manufacturing processes. ASME Production Engineering Division, vol. 48, p. 59-65.

[18] Armarego, E.J.A., Wright, J.D. (1984). Predictive models for drilling thrust and torque—a comparison of three flank configurations. Ann CIRP, vol. 33, no. 1, p.

5-10, DOI:10.1016/S0007-8506(07)61368-7.

[19] Ehmann, K.F., Kapoor, S.G., DeVor, R.E., Lazoglu, I. (1997). Machining process modeling: A review.

Journal of Manufacturing Science and Engineering, vol. 119, no. 4B, p. 655-659, DOI:10.1115/1.2836805.

[20] Chandrasekharan, V., Kapoor, S.G., DeVor, R.E. (1995). A mechanistic approach to predicting the cutting forces in drilling: with application to fiberreinforced composite materials. ASME Journal of Engineering for Industry, vol. 117, no. 4, p. 559-570, DOI:10.1115/1.2803534.

[21] El-Sonbaty, I., Khashaba, U.A., Machaly, T. (2004).

Factors affecting the machinability of GFR/epoxy composites. Composite Structures, vol. 63, no. 3-4, p.

329-338, DOI:10.1016/S0263-8223(03)00181-8.

[22] Tagliaferri, V., Caprino, G., Diterlizzi, A. (1990). Effect of drilling parameters on the finish and mechanical properties of GFRP composites. International Journal of Machine Tools and Manufacture, vol. 30, no. 1, p.

77-84, DOI:10.1016/0890-6955(90)90043-I. [23] Caprino, G., Tagliaferri, V. (1995). Damage development in drilling glass fibre reinforced plastics. International Journal of Machine Tools and Manufacture, vol. 35, no. 6, p. 817-829, DOI:10.1016/0890-6955(94)00055-O.

[24] Di Ilio, A., Tagliaferri, V., Veniali, F. (1991).

Cutting mechanisms in drilling of aramid composites. International Journal of Machine Tools and Manufacture, vol. 31, no. 2, p. 155-165, DOI:10.1016/0890-6955(91)90001-J. [25] Veniali, F., Di Ilio, A., Tagliaferri, V. (1995). An experimental study of the drilling of aramid composites.

ASME Journal of Energy Resources Technology, vol.

117, no. 4, p. 271-278, DOI:10.1115/1.2835423.

[26] Shaw, M.C., Oxford, C.J. (1957). On the drillings of metals: II. The torque and thrust in drilling. Transaction of. ASME, vol. 79, p. 139-148.

[27] Karabay, S. (1986). Design and Construction of a Strain-Gage Type Drill Press Dynamometer and Investigation of Drilling Characteristics of MKEK Ç-1020-Steel. MSc. Thesis, Middle East Technical University, Ankara.

[28] Langella, A., Nele, L., Maio, A. (2005). A torque and thrust prediction model for drilling composite materials. Composite Part A, vol. 36, no. 1, p. 83-93.

[29] Fernandes, M., Cook, C. (2009). Drilling of carbon composites using a one shot drill bit. Part II:Empirical modelling of maximum thrust force. International Journal of Machine Tools & Manufacture, vol. 46, no.

1, p. 76-79. DOI:10.1016/j.ijmachtools.2005.03.016.

[30] Fernandes, M., Cook, C. (2006). Drilling of carbon composites using a one shot drill bit. Part II: Empirical modelling of maximum thrust force. International Journal of Machine Tools & Manufacture, vol. 46, no.

1, p. 70-75, DOI:10.1016/j.ijmachtools.2005.03.015.

[31] Tsao, C.C., Hocheng, H. (2003). The effect of chisel length and associated pilot hole on delamination when drilling composite material. International Journal of Machine Tools & Manufacture, vol. 43, no. 11, p. 10871092, DOI:10.1016/S0890-6955(03)00127-5.

A Study on the Derivation of Parametric Cutting Force Equations in Drilling of GFRP Composites

105

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 106-111 © 2013 Journal of Mechanical Engineering. All rights reserved.

DOI:10.5545/sv-jme.2012.721

Received for review: 2012-08-01 Received revised form: 2012-12-05 Accepted for publication: 2013-01-14

Combined Cutting-deforming Taps Aleksandrova, I.S. – Ganev, G.N. Irina Stefanova Aleksandrova* – Gancho Nenkov Ganev Теchnical University of Gabrovo, Bulgaria Enhancement of the efficiency and quality of internal thread forming requires continuous improvements in the design of the tools used and optimization of their body geometry. A new design for cutting-tightening taps with enhanced strength and reliability for forming thread surfaces by combining the methods of cutting and plastic deformation are proposed in this paper. An experimental study of torque was carried out during thread forming employing the designed combined tool and the major factors having an effect on the tool serviceability were defined. An algorithm for designing cutting-tightening taps has been proposed, which guarantees a minimum torque in thread forming.

Keywords: threads, methods of machining, combined cutting-deforming tap

0 INTRODUCTION Quality parameters of threads when machining depend both on material properties and on a number of technological factors: method and arrangement of shape-forming, tool structure and geometry, as well as cutting conditions [1] to [10]. The technology employed for making threaded parts has to provide a set of geometrical parameters and characteristics of the state of the surface layer, thus determining the performance characteristics of the threaded connection dependent on its functional purpose.

Thread surfaces – external or internal – are obtained by three principal methods: cutting, plastic working, and a combined method [2] to [5], [7], [8], and [11] to [15]. The two latter methods have a number of advantages as regards guaranteeing the major quality characteristics of all types of threaded connections. This is attributed to the greater hardness of the surface layer of the thread turns, the positive effect of surface compressive stresses, stable high accuracy, and low roughness of surfaces. Тhe use of combined machining and plastic deformation of external threads is widespread and is the prevailing method used for a number of fastener threaded parts [8]. For internal threads, having lower manufacturing producibility, these working methods, regardless of their obvious advantages, find limited application.

It is known that over 60% of the parts of modern machines and mechanisms have threaded holes.

Making internal threads, especially of small sizes, is a manufacturing problem, owing to the insufficient strength and reliability of the tools (taps) used. The design and use of new tool materials, the application of optimum technological equipment and new kinds of lubricating-cooling agents do not solve the problems of highly productive, quality manufacturing of internal threads. Continuous improvement in tap design, geometry optimization of tap bodies, and 106

improvement of manufacturing technology of taps is necessary, since these are the most widely used tools for machining internal threads.

The objective of this paper is the structural and technological development and experimental study of a new design of cutting-deforming taps which have enhanced strength and reliability, combining both methods of formation – cutting and plastic deformation. By creating these taps, opportunities are offered for intensifying the internal thread forming process accompanied by quality improvement. The objective of this paper has been formulated on the basis of comparison, analysis and quality evaluation of advantages and disadvantages of methods and tools for making internal threads with diameters ranging from 1 to 16 mm (Table 1).

1 DESIGN AND STUDY OF COMBINED CUTTING-DEFORMING TAPS 1.1 Analysis of the Possibilities for Enhancing the Strength of Taps In order to determine tap, it is necessary to take into account the shape and size of the operating tool elements as a geometric body, as well as the size and character of change in the forces affecting tool wear.

During internal thread forming, taps are mainly subjected to torsional loads and sometimes to bending loads (when the hole and tool axes are displaced).

Therefore, tangential stresses are most dangerous for taps occurring where the tool tends to be twisted by the applied torque. The destruction (breaking) of these tools depends mainly on the size of the maximum torque and on their cross-section.

To determine the size of the crushing torque, special test specimens of high-speed steel HSS with a hardness of НRC 63 were made. One of the specimens has a cross-section of three-sided relieved profile of chipless tap with an M8 ground thread with the

*Corr. Author’s Address: Technical University of Gabrovo, 4 H. Dimitar St, Gabrovo, Bulgaria, irina@tugab.bg

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 106-111

following dimensions: inside diameter d1 = 6.65 mm; outside diameter d = 8.144 mm; mean diameter d2 = 7.30 mm; height of relieving k = 0.48 mm. The crosssection of the test specimen is Sn1 = 29.175 mm2; and it is determined according to the relationship [4]: Sn1 =

( d1 − k )2 π 4

− Ak 2π , (1)

where A = 1 is a constant for the three-sided relieved tap. Таble 1. Quality evaluation of methods and tools for cutting internal threads Parameters

Tapping

Geometric accuracy of thread Degree of roughness of thread Strength properties of threads Applicability to various materials Manufacturing producibility of tool Output Tool life Strength of the bearing section of the tool

satisfactory

Threading with fluteless taps (by plastic deformation) good

satisfactory

good

satisfactory

good

good good

low (for working metals with high plasticity) satisfactory

low short low

good satisfactory good

The second specimen is a conventional M8 thread-cutting tap. Due to the complicated profile of the cross-section of the thread-cutting taps, universally valid formulae for calculating its area are not available in literature. However, the area can be determined graphically in the AutoCAD environment and it is Sn2 = 10.2 mm2.

After loading the test specimens the following results were obtained for the breaking torque Md and failure tangential stresses τ: • for the chipless specimen М8; Md1 = 65.6 Nm; τ1 = 670 MPa; • for specimen М8 with chip flutes; Md2 = 21.7 Nm; τ2 = 640 MPa. The relationship between the determined values of the breaking torques for chipless and thread-cutting taps characterizes the common safety margin (Eq. 2), since the determined values for failure stresses were approximately identical:

= KS

M d1 65.6 = = 3.023. (2) M d 2 21.7

The analysis made shows that the chipless tap is over three times stronger than the conventional thread-cutting tap. This led us to the idea of designing a tap with a forming part, which encloses a cutting part that removes the whole or most of the additive as in conventional thread-cutting taps, and a tightening part, which through plastic deformation finishes and strengthens the thread. The calibrating part of the tap is shaped as chipless fluteless taps and thus the tool strength is significantly enhanced.

1.2 Design of Thread-tightening Taps with Enhanced Strength In accordance with the theoretical-experimental anlaysis, a combined cutting-deforming (threadtightening) tap was designed, which encloses a forming part that has a length of lf and a calibrating part. The cross-sections of the forming and calibrating parts are shaped and relieved as chipless taps (Section e-e) (Table 2), which enhances the tool strength. On the front part of the tap at length ls, a certain number of chip flutes with the geometry required for cutting are made. The forming part (lf) of the tap consists of two zones: cutting – having a length of lc and tightening - having a length of ld, shaped at angles χr1 and χr respectively, where χr1 ≥ χr (Table 2). The lengths of the cutting and tightening parts are determined by the location of point Т (the point where the chip flute inclined at angle λ intersects the axial plane of the tap) and by the length of the forming part, lf. The teeth positioned in front of point Т (Section a-a) are cutting with a positive clearance angle defined by the relieving on the flank. The teeth positioned after point Т (Section b-b), are tightening owing to their negative clearance angle shaped by the rising slope of the relieving curve of the preceding tooth of the tap.

Depending on the position and length of the chip flutes with regard to the forming part with length lf and the size of angle λ, various arrangements are possible (Table 2), which define the tap as cutting or cutting-tightening.

1.2.1 Taps with Inclined Chip Flutes λ > 0° and Variable Rake γ along the Chip Flute If lf ≥ lc and diameter d0 of the preliminary drilled hole is within: d2 ≥ d0 ≥ d1, the tap is cutting-tightening.

For thread diameters less than dT (Table 2), the tap is cutting.

If lf < lc, the tap is cutting and part of the calibrating teeth is also cutting. The tool differs from conventional cutting taps mainly in that there are no

Combined Cutting-deforming Taps

107

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 106-111

chip flutes on its calibrating part, which significantly enhances its strength and reduces the chance of breaking.

The cutting part with angle χr1 is additionally relieved (Section f-f, Table 2).

If lc = ls > lf , the tap is cutting.

1.2.2 Taps with Straight Chip Flutes (λ = 0°) and Invariable Rake along the Chip Flute

1.3 Experimental Study of the Designed Thread-tightening Taps

If lc = ls ≤ lf and diameter d0 of the preliminary drilled hole is within: d2 ≥ d0 ≥ d1, the tap is cutting-tightening.

The internal thread forming process employing the designed cutting-deforming taps and their

Таble 2. Taps – geometrical and structural elements Shapes of the forming part of the tap cylindrical taper

Type of tap

Deforming (chipless) tap: The forming part lf is relieved with a height of k at angle χr.

Inclined chip flutes at angle λ

> 0°

Cutting-deforming tap: • lc ≤ lf ; d2 ≥ d0 ≥ d1; d3 = d0 – δ; • angle γ is variable (γ ≥ 0) for the forming part lf .

Cutting tap: • lc > lf ; d3

= d0 – δ;

• angle γ is variable:

γ = arcsin

2ai . di Straight chip flutes (λ

= 0°)

Cutting-deforming tap: • lc ≤ lf ; d2 ≥ d0 ≥ d1; • cutting part lc is relieved with a height of k at angle χr1; • tightening part ld is relieved with a height of k at angle χr.

Cutting tap: • lc ≥ lf ; d0 ≥ d1; d3 = d0 – δ; • cutting part lc is relieved with a height of k at angle χr1; • chip flute length ls ≥ lf .

108

Aleksandrova, I.S. – Ganev, G.N.

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 106-111

serviceability depend on a great number of factors, which can be divided into two large groups: • Factors determined by the tool structure: pitch p and diameter d of the thread, lengths of cutting and tightening parts lc and ld, number of flutes, geometrical elements of the forming part (inclination angle of the chip flute λ, rake angle γ, clearance angle α, angles of cutting and tightening parts χr1 and χr), and the arrangement for manufacturing the forming part; • Factors determined by the type of machining: material to be machined (hardness, chemical composition, and structure), thread length, type of hole – blind or through, diameter of the preliminary drilled hole d0, plastic deformation additives vs. cutting additives ratio (η [%]), lubricating-cooling liquid type, intensity and feeding method in the cutting zone, machining conditions, etc.

Preliminary experimental studies of the serviceability of the designed cutting-deforming tap have been conducted. The maximum torque Mbmax in thread forming is taken to be a parameter for evaluating serviceability. For strength reasons, Mbmax should be deliberately kept at a minimum, especially if taking into account that the cross-section of the tap is limited by the thread diameter.

Four thread-tightening taps M8 with three flutes (z = 3) of high-speed steel HSS have been made for conducting the study. Their design parameters are listed in Table 3.

The studied taps operate under identical conditions and the ratio of additives for plastic deformation to additives for cutting is (Table 2, Table 3):

2

 d − dT  η =  100 = 17.5%  d − d2 

(3)

Таble 3. Еxperimental conditions No.

λ [grad]

1 2 3 4

0 3 6 9

lc [mm] 10.5 10.05 5.7 3.8

χr [grad] 2 2 2 2

χr1 [grad] 2.45 2.54 4.5 6.76

d = 8.144–0.02 mm; d2 = 7.323–0.02 mm; d3 = 6.9 mm; γmax = 10°; k = 0.48 mm; d0 = 7+0.03 mm; dT = 7.8 mm; lc =

d3 sin γ max (λ > 0°) 2tg λ

 ( 2d T − d − d1 ) tg λ  χ r1 = arctg  .  ( d + d1 − dT ) sin γ max 

The material machined is steel C45 and Castrol Carecut ES1 thread oil was used as a lubricatingcooling liquid. The length and diameter of the through holes being worked are respectively: l0 = 13 mm; and d0 = 7+0.03 mm. The torque is measured at a purpose stand for torque testing Мicrotap at constant speed of rotation n = 315 min–1.

Four experiments were conducted and during each experiment four observations were made. The character of the torque variations at λ = 0° is shown in Fig. 1, and at λ > 0° in Fig. 2. The measured values of maximum torque Mbmax are presented in Table 4.

The analysis of the experimental results obtained shows that the magnitude of the maximum torque during thread forming depends on the length of the cutting part of the designed thread-deforming tap and that Mbmax decreases as the length increases. This

Fig. 1. Torque during working with thread-tightening taps with straight chip flutes (λ = 0°) Combined Cutting-deforming Taps

109

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 106-111

is explained by the increasing thickness of the layer being cut hz by one cutting tooth: hz =

( d T − d3 ) p 2lc z

= ( 0.0178 ÷ 0.0493) mm. (4)

Therefore, when the ratio of additives for plastic deformation to additives for cutting η is set, it is necessary for the length of the cutting part of the tap to be at a maximum. Таble 4. Experimental results n

λ = 0°

Mbmax λ = 3°

dT = d − 0.1 η ( d − d 2 ) is 2. The diameter determined (Table 2).

3. The diameter of the preliminary drilled hole d0 = d + d1 – dT is determined.

4. The diameter of the tap front d3 = d0 –(0.05 ÷ 0.1) is determined.

5. The length of the cutting part lc =

is determined, i.e. the cutting part angle χr1 should be as small as possible.

[Nm]

λ = 6°

λ = 9°

1 2 3 4

7.80 9.60 8.40 6.00

8.25 8.40 7.65 9.00

9.75 12.55 13.95 12.90

17.55 18.15 16.65 17.25

M bmax

7.95

8.33

12.28

17.4

The algorithm of designing cutting-tightening taps is the following: 1. The ratio of additives for plastic deformation and additives for cutting is assumed to be η [%].

dT − d 3 → max 2tg χ r1

2 CONCLUSION Тhe possibility of increasing tap strength by designing combined tools with enhanced strength and reliability, and forming thread surfaces by combining the methods of both cutting and plastic deformation, has been backed by theoretical and experimental arguments. A new combined cuttingdeforming tap has been designed. Its forming part encloses two zones: a cutting zone, which removes the larger part of the additive as conventional thread cutting taps do, and a tightening zone, which by

a)

b) Fig. 2. Torque during working with thread-tightening taps with inclined chip flutes: а) λ = 3°; b) λ = 6°

110

Aleksandrova, I.S. – Ganev, G.N.

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 106-111

plastic deformation further forms and strengthens the thread. The cross-sections of the forming and calibrating parts are shaped and relieved as chipless taps and that significantly enhances the tool strength, creating the conditions needed to enhance the quality of the machined thread. The expected higher quality is related to the fact that the final thread forming, which determines its accuracy and roughness, is achieved by plastic deformation and depends primarily on the manufacturing technology of the tap and its accuracy.

An experimental study of the torque when forming the thread employing the designed combined cutting-deforming taps has been conducted and the major factors having an effect on their serviceability have been defined.

An algorithm for designing cutting-tightening taps has been proposed that ensures minimum torque while forming the thread.

3 REFERENCES [1] Аndonov, I. (2001). Material Cutting. Softtrade, Sofia. (in Bulgarian) [2] Ivanov, V. (1983). Chipless Taps - Design, Technology and Exploitation. PhD thesis. Rousse University Printing, Rousse. (in Bulgarian) [3] Ivanov, V. (1998). Cutting Tools. Rousse University Printing, Rousse. (in Bulgarian) [4] Меnshakov V., Urlapov, G., Sereda, V. (1976). Chipless Taps. Mashinostroenie, Moscow. (in Russian) [5] Prokofev, А. (2000). Progressive Technological Methods of Enhancing Thread Connection Quality.

Reference Book. Engineering Journal, vol. 35, no. 2, p.

9-12. (in Russian) [6] Prokofev, А. (2006). Теchnological equipment for obtaining performance properties of thread connections.

In: Suslov, А., Fedorov, V., Gorlenko, О. et al. Теchnological Equipment and Enhancing Performance Properties of Parts and Their Connections, Маshinostroenie, Моscow, p. 334-394. (in Russian)

[7] Prokofev, А. (2008). Теchnological Equipment and Enhancing Performance Properties of Thread Connections, PhD Thesis. Bryansk State Technical University, Bryansk. (in Russian) [8] Suslov, А. (1999). Development of scientific bases of working high-accuracy internal threads. In: Suslov, А., Steshkov, А., Prokofev, А. (ed.). Present Problems of Quality Enhancement of Mechanical Engineering Production, p. 128-129. (in Russian) [9] Olinda de Carvalho, A. Brandão, L., Panzera, T., Lauro, C. (2012). Analysis of form threads using fluteless taps in cast magnesium alloy (AM60). Journal of Materials Processing Technology, vol. 212, no. 8, p. 1753–1760, DOI:10.1016/j.jmatprotec.2012.03.018.

[10] Stéphan, P., Mathurin, F. Guillot, J. (2012).

Experimental study of forming and tightening processes with thread forming screws. Journal of Materials Processing Technology, vol. 212, no. 4, p. 766–775, DOI:10.1016/j.jmatprotec.2011.10.029.

[11] Ivanov, V., Kirov, V. (1997). Rolling of Internal Threads: Part 1. Journal of Materials Processing Technology, vol. 72, p. 214-220.

[12] Niţu, E., Iordache, M., Marincei, L., Charpentier, I., Le Coz, G., Ferron, G., Ungureanu, I. (2011). FEmodeling of cold rolling by in-feed method of circular grooves. Strojniški vestnik - Journal of Mechanical Engineering, vol. 57, no. 9, p. 667-673, DOI:10.5545/ sv-jme.2010.244.

[13] Fromentin, G.G., Poulachon, A., Moisan, Julien, B., Giessler, J. (2005). Precision and surface integrity of threads obtained by form tapping. CIRP Annals Manufacturing Technology, vol. 54, no. 1, p. 519-522, DOI:10.1016/S0007-8506(07)60159-0.

[14] Fromentin, G., Bierla, A., Minfray, C., Poulachon, G. (2010). An experimental study on the effects of lubrication in form tapping. Tribology International, vol. 43, no. 9, p. 1726-1734, DOI:10.1016/j. triboint.2010.04.005.

[15] Bhowmick, S., Lukitsch, M., Alpas, A. (2010). Tapping of Al–Si alloys with diamond-like carbon coated tools and minimum quantity of lubrication. Journal of Materials Processing Technology, vol. 210, no. 15, p.

2142-2153, DOI:10.1016/j.jmatprotec.2010.07.032.

Combined Cutting-deforming Taps

111

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 112-123 © 2013 Journal of Mechanical Engineering. All rights reserved.

DOI:10.5545/sv-jme.2012.619

Received for review: 2012-06-01 Received revised form: 2012-12-04 Accepted for publication: 2012-12-14

Nonlinear Control of a Hybrid Batch Reactor Štampar, S. – Sokolič, S. – Karer, G. Simon Štampar1,* – Saša Sokolič1 – Gorazd Karer2

¹ Metronik d.o.o., Slovenia ² University of Ljubljana, Faculty of Electrical Engineering, Slovenia This paper introduces a new class of advanced control algorithms for batch-reactor temperature control where a nonlinear PI controller with a feed-forward part in a cascade combination with a P controller is used. The main goal of the algorithm is to optimize production by lowering the costs of the temperature control and increasing the quantity and quality of the chemical, biological, pharmaceutical, food and beverage products produced in these reactors. The algorithm is designed to cope with the constraints and the mixed discrete and continuous nature of the process by manipulating variables for heating and cooling. The stability and robustness of the control algorithm is proven through the Popov Stability Criterion. The simulation results of the proposed algorithm show much better performance compared to a conventional cascade PI control structure, which is most commonly used in industry. Furthermore, the study also shows real-time implementation on a bioreactor using the proposed algorithm.

Keywords: nonlinear process control, cascade control, batch reactor, temperature control

0 INTRODUCTION These days the use of batch reactors in the chemical, pharmaceutical, food and beverage industries is very common. According to some statistics, 50% of all production processes in industry are batchtype processes [1]. The term batch reactor is used for a variety of process operations, such as chemical reactions, product mixing, batch distillation, crystallization, solid dissolution, and polymerization.

In some cases these reactors have specific, roledependent, names, such as crystallizer or bioreactor.

A typical batch reactor consists of a vessel and a heating ̶ cooling system. The authors in [2] and [3] recognize that, because of the versatility, drastic changes in the pre-described temperature, mixed continuous and discrete hybrid nature of the batch reactor, a rapid and precise temperature control is hard to achieve, especially with conventional PI control algorithms, which are most commonly used in the process industry. Today, forced by competitiveness and the optimization of production costs, we strive to lower the costs of the temperature control and increase the quantity and quality of the products produced. To achieve better temperature control, which is essential for a large number of reactors, an improvement in the control algorithm was made by using a nonlinear PI controller in a cascade. Another important aspect of the control algorithm is the simplicity of the design and implementation, because these are widely used in real processes, spatially on low-cost hardware implemented by process engineers. The batch reactors we are dealing with are of a hybrid and nonlinear nature, because of the discrete heating−cooling mediums and the continuous position of the analogue valve.

112

Over the last three decades in the fields of modelling, simulations and temperature control of batch reactors, a lot of research and development has been carried out. This is reflected in many published studies in the field of advanced control principles for the temperature control of batch reactors. In [4], a historical review of the development of control algorithms is presented. Surveys with examples and explanations of the theoretical and mathematical background for the following fields are given: optimal control [5] to [7]; internal model control [8] to [11]; predictive control [12] and [13]; adaptive control [14] and [15]; nonlinear control [16] to [20]; fuzzy-modelbased controls [21] and [22]. Some of the advanced control algorithms are already used in industry, but most of them are only presented in scientific studies. From the conclusions of these reports we can summarize that the use of advanced control algorithms – because of the higher quality, quantity and lower cost requirements – are increasingly necessary. Therefore, a lot of improvement is possible in this field, especially if the advanced algorithm is implemented in a real process.

The most promising concepts in the field of adaptive control are [23] to [28]. The authors in [28] developed a self-tuning adaptive control, whose performance meets the required strict temperature tolerances in the polymerization reactor. The field of optimal control is represented by [29] to [33] and the field of predictive control by articles [34] to [37]. More recently, the model predictive functional control (PFC) scheme has been commonly used for the temperature control of the batch reactor’s content, as seen in [38] to [40]. In the field of nonlinear control the authors in [41] developed a new nonlinear observer-based controller for the control of a continuous stirred tank

*Corr. Author’s Address: Metronik d.o.o., Stegne 9a, 1000 Ljubljana, Slovenia, simon.stampar@metronik.si

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 112-123

reactor with recycle. As mentioned before, this paper introduces a new class of advanced control algorithm, where a nonlinear PI controller with a feed-forward part in a cascade combination with a P controller is used. The main goal of the proposed algorithm is fast and exact reference temperature tracking and a fast disturbance rejection. What is more, with this algorithm the number of heating−cooling medium switchings, and consequently their consumption, should be as low as possible.

A good process model is needed for the development and testing of the proposed algorithm.

The authors in [42] to [45] discuss different types of batch reactors, which are used in the chemical, biological, pharmaceutical, food and beverage industries. They also present different modelling techniques for these reactors. Our choice for the development and testing of the proposed algorithm is a theoretical model for the process of heating and cooling the reactor’s content. In the literature, a number of papers and books have been published that discuss the construction of a theoretical model, such as in [46]. The basic theoretical models of a batch reactor are described in [46] to [49]. These works contain theoretical models for different types of batch reactors and discuss the basis of heat conduction between the reactor’s jacket, the reactor’s core and to the reactor’s surroundings.

The author in [50] presents a two-stage modelling concept for an industrial heat exchanger using prior knowledge of the process and recorded data. Similar to this approach, a detailed nonlinear theoretical model for the heating and cooling of a hybrid batch reactor was successfully developed in [51]. We also decided to use this theoretical model for the development and testing of our proposed algorithm.

For this new class of control algorithms a stability and robustness analysis also has to be conducted.

The stability-analysis problem for this process with a nonlinear feedback control algorithm is formulated using the Lur’e problem, which belongs to the group of Lyapunov functions, as described in [52] to [54].

In this particular case we use a sub-class of the Lur’e system studied by Popov, as described in [55] to [58].

A comparison is made to show the performance advantages of this algorithm according to a conventional cascade PI control.

This paper also contains an implementation of this algorithm on a real process. In order to show the flexibility of the proposed algorithm, it is implemented on a slightly different type of batch reactor, i.e., a bioreactor. The goal of temperature control is to achieve fast and, more particularly,

precise temperature control with fast disturbance rejection over a long time period (weeks). The maximum allowed temperature tolerance is ±0.2 °C. Exceeding the tolerance can harm the product quality or even destroy livings cells in the bioreactor, as these are very sensitive to temperature.

The paper is organized in the following way: the first section describes the theoretical model of the batch reactor; the second section contains a detailed description of the proposed algorithm; the third section contains a stability and robustness analysis of the proposed algorithm; the forth section contains the simulation results of the proposed algorithm and a comparison with a conventional PI controller; in the last section an implementation example of this algorithm on a real bioreactor is shown. Finally, we make some concluding remarks.

1 THE HYBRID BATCH REACTOR MODEL The hybrid batch reactor, described in [50], is made of stainless steel and serves to prepare solvents that are used in drug production. Its capacity is 630 liters. The temperature control (heating and cooling) of the reactor’s content is performed via pipes wrapped around the wall of the reactor. The heating and cooling occurs via these pipes with a heating− cooling medium (water 50% and glycol 50%) at three different temperatures Tin: Tin1 = –25 °C, Tin2 = 5 °C and Tin3 = 140 °C. The right medium for temperature control is chosen according to the output of the control algorithm. The different input mediums cannot be mixed with each other. Additional adjustment in the control algorithm is made with an analogue valve, which determines the amount of fresh medium pumped into the reactor’s jacket.

The scheme of the hybrid batch reactor is shown in Fig. 1.

Fig. 1. Scheme of the hybrid batch reactor

The reactor’s core temperature T is controlled by the jacket inlet temperature, Tjin, and the reactor’s

Nonlinear Control of a Hybrid Batch Reactor

113

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 112-123

jacket temperature, Tj. The authors in [50] simplified the reactor’s jacket as a flat plate connected to the reactor’s core with a surface S. The heat transfer between the reactor’s core and the jacket is defined by the highly nonlinear overall thermal conductivity U. While the parameters m and c define the mass and heat capacity of the reactors core content, the parameters mj and cj define the mass and heat capacity of the medium mixture in the reactor’s jacket. Other parameters used in the theoretical model are as follows: Φ is the flow of the heating−cooling medium; vv (range between 0 and 100%) is the position of the analogue valve that represents the ratio between the fresh input heating−cooling medium Tin and the reflux of the heating−cooling medium Tj. So the theoretical model is defined by the first law of thermodynamics, the conservation of energy, as in [46] and [49], (Eqs. (1) to (3)).

T jin = vvTin + (1 − vv ) T j , (1)

mjc j

dT j dt

(

)

= Φc j T jin − Φc j T j − US T j − T , (2) mc

dT = US T j − T . (3) dt

(

)

The authors in [50] determined that the process of heating and cooling the reactor’s contents is highly nonlinear in terms of its parameters. Therefore, the authors developed a complex and detailed nonlinear theoretical model.

Due to the nonlinearities of the theoretical model described in [50], we used this detailed model for the development and testing of the advantages of the proposed algorithm in comparison with a conventional cascade PI algorithm.

2 THE NONLINEAR ALGORITHM As already described in the introduction, for the control of the reactor’s core and jacket temperature we introduce a new class of advanced control algorithm where a nonlinear PI controller with a feedforward part in a cascade combination with a P controller is used.

While the internal proportional term controls the reactor’s jacket temperature, the external nonlinear control loop controls the reactor’s core temperature.

The goal of the control law is to achieve fast and exact reactor-core reference-temperature tracking.

It is also very important to optimize the costs of the temperature control. For this reason the number of on/ off valve switchings should be as low as possible. With 114

this restriction we minimize the amount of heating− cooling medium used and extend the lifecycle of the equipment.

The main contribution of the new control algorithm is in the external nonlinear control loop.

The nonlinear control contains a feedback and feedforward part. The feedback part RFB is made of a modified nonlinear hyperbolic function N(e) with an additional conventional PI controller. The output of the control uFB(t,e) is shown in Eq. 4.

t   u FB ( t , e ) = N ( e )  kcp e ( t ) + kci ∫ e (τ ) dτ  , (4)   0  

 p+q−2 N ( e ) = 1 + ( k0 − 1)  ,  ( p + q )   

where e(t) is the difference between the reference temperature rt(t) and the reactors core temperature T(t). N(e) is a modified hyperbolic function, where p = exp(k1·e(t)) and q = exp(–k1·e(t)). This function is bounded between 1 (e = 0) and k0 (e = ∞). The proportional kcp and integrating part kci define the PI parameters of the proposed algorithm where the integrating part kci serves in steady-state error reduction. The error can be caused by heat losses to the reactor’s surroundings, disturbances in the system, heating the reactor’s content from mixing and especially endothermic and exothermic reactions, etc.

The main idea of this algorithm is that with a larger error e(t) the output of the control action increases much faster than with a conventional PI controller. Such a type of control gives us a large controller output when the reactor’s temperature is far from the reference temperature (very fast reference temperature tracking) and a small controller output when it is near the reference temperature (smaller than with a conventional PI controller, and consequently fewer heating−cooling medium switchings). This reduces the heating−cooling medium consumption and extends the equipment’s lifecycle. To provide such a type of response the modified hyperbolic function parameters are determined as k0 = 100 and k1 = 0.2.

The feed-forward part adds the reference temperature to the controller output. The combination of the feedback and feed-forward provides us with a large feedback controller output plus a reference temperature when we are far from the reference and a small feedback controller output plus a reference temperature when we are near the reference. This combination can be employed because we can predict

Štampar, S. – Sokolič, S. – Karer, G.

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 112-123

that the reactor’s core and jacket temperature will be approximately equalized in the steady state.

Before the output of the external nonlinear part can be used for the internal controller reference we have take some limitations into account. The output has to be limited between the highest jacket temperature allowed Tjmax and the lowest jacket temperature allowed Tjmin. In the case where that limit is exceeded we also have to freeze the integrating part to avoid windup.

We can now define the nonlinear control uc(t,e) with the feedback and feed-forward parts for the whole operating range, as shown in Eqs. (5) and (6). t   uc ( t , e ) = N ( e )  kcp e ( t ) + kci ∫ e (τ ) dτ  + rT ( t ) , (5)   0  

uc ( t ,e ) ; T jmin < uc ( t ,e ) < T jmax    uc ( t , e ) =  T jmin ; T jmin ≥ uc ( t ,e )  . (6)   uc ( t , e ) ≥ T jmax  T jmaxx ;  The internal controller of this algorithm is a conventional feedback proportional controller Rj, which controls the reactor’s jacket inlet temperature uj(t) (Eq. (7)).

u j ( t ) = k jp e j ( t ) , (7)

where ej(t) is the difference between the nonlinear control output uc(t,e) and the reactor’s jacket Tj(t) temperature; kjp is the proportional gain.

In the end, the decision logic for the choice of the input heating−cooling medium is defined. First, on the basis of the previous input heating−cooling medium Tin(t–), the position of the mixing valve is calculated from Eq. (1) as follows:

vv ( t ) =

u j (t ) − T j (t )

( )

Tin t − − T j ( t )

. (8)

So the decision logic DL is defined as follows: if Tin(t–) = Tin1 and vv(t) < –δ then Tin(t+) = Tin2 if Tin(t–) = Tin2 and vv(t) < –δ then Tin(t+) = Tin3 (9) if Tin(t–) = Tin2 and vv(t) > 1+δ then Tin(t+) = Tin1 if Tin(t–) = Tin3 and vv(t) < –δ then Tin(t+) = Tin2 In the decision rules, the parameter δ defines the dead zone involved in the switchings of the heating− cooling medium. A control scheme for the proposed algorithm is shown in Fig. 2. The parameters Gc and Gj are the transfer functions that represent the dynamics of the heating and cooling of the reactor’s jacket and core.

Before testing the proposed algorithm we include some limitations in the switchings between the heating−cooling media. First, it is important that only one medium at a time is used. We also have to consider the equipment protection against deformation due to high-temperature changes in the reactor’s jacket. So, no direct heating−cooling medium change from Tin1 to Tin3 and vice versa is allowed. To optimize the cooling of the reactor’s core we consider that the medium Tin1 = –25 °C is used only if the reactor’s core temperature is low enough T(t) < 30 °C. This limitation stems from the fact that the heat transfer between the reactor’s jacket and core is much smaller because of a thick film that is formed on the walls inside the reactor’s jacket, as described in [50].

3 STABILITY AND ROBUSTNESS ANALYSIS FOR THE NONLINEAR ALGORITHM The dynamics of the batch reactor’s heating and cooling are approximately represented by two firstorder transfer functions for the reactor’s core Gc (Eq. (10)) and jacket Gj (Eq. (11)), as developed in [50].

The first relates the reactor’s core temperature T to the control input Tj given by:

Gc ( s ) =

K Gc T( s ) 1 = = , (10) T j ( s ) TGc s + 1 1660 s + 1

Fig. 2. Control scheme for the proposed algorithm Nonlinear Control of a Hybrid Batch Reactor

115

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 112-123

where TGc represents the time constant for the first order process of heating and cooling the reactor’s core and KGc its gain.

The second relates the reactor’s jacket temperature Tj to the control input uj given by:

Gj (s) =

Tj ( s)

=

K Gj

=

1 , (11) 35s + 1

(

)

controller GR, with a time constant TIMC as the tuning parameter (Eq. (14)).

GR ( s ) =

GIMC ( s )

1 − GIMC ( s ) Gc ( s )

=

TGc KGcTIMC

 1  1 +  . (14) T Gc s  

The parameters for the batch reactor’s temperature control are determined heuristically and are TIMC = 335 for the external loop and kjp = 2 for the where TGj represents the time constant for the first proportional part of the internal loop. So, the order process of heating and cooling the reactor’s parameters for the conventional PI controller are jacket and KGj its gain.

1 TGc = 3 ⋅10−3 . kcp = 5 and kci = So the closed-loop process of heating and cooling = KGcTIMC KGcTIMC the reactor’s core and jacket employs the cascade algorithm with the nonlinear PI controller and a proportional term. The nonlinear controller does not 3.2 Popov Stability Criterion employ the feed-forward part, because the stability analysis is made just on the closed-loop process.

For the stability analysis of our process we can now To investigate the absolute stability of the apply the Popov Stability Criterion. The Popov plot closed-loop process W(s) (Eq. (12)), we combine the examines W(jω), which consists of the plot ReW(jω) linear parts of the nonlinear algorithm (Eq. (5)), the against ωImW(jω), where ω is a parameter between proportional controller (Eq. (7)), and the two first(0,∞); Re and Im refer to the real and imaginary parts order transfer functions of the heating and cooling of of the plot. From this plot the range of the allowed the reactor’s jacket (Eq. (10)) and core temperature values for the nonlinear part of the control algorithm (Eq. (11)): can be determine by retaining closed-loop stability.

For a better understanding of the Popov Stability     K Gc kcp s + kci K Gj k jp  . (12) W (s) =   Criterion a graphical interpretation is given as follows:  TGj s + 1 + K Gj k jp   s (TGc s + 1)    The closed-loop system is absolutely stable if the  Popov plot P(jω) = Re[W(jω)]+ jωIm[W(jω)], ω ≥ 0 The closed-loop process W(s) is a third-order lies to the right of the line that intercepts the point transfer function, which separates out the nonlinear 1 1 − + j 0 with slope as shown in Fig. 3. part of the nonlinear control algorithm. k γ u j (s)

TGj s + 1

3.1 Control Algorithm Parameters (Linear Parts) The parameters for the PI controller are determined through the internal model control (IMC) approach.

The standard IMC design scheme is proposed in [8].

The IMC design is, in the ideal case, the inverse of the process model Gc–1(s) . In the ideal case, inversion can lead to an unstable controller in the case of unstable zeros in the model. In our case the inversion is made by the so-called H2 optimality criterion, as in [8]. The only tuning parameter for the IMC design procedure GIMC is the time constant TIMC (Eq. (13)), which defines the desired closed-loop behavior.

GIMC ( s ) = Gc

−1

TGc s + 1 1 = .(13) (s) (TIMC s + 1) KGc (TIMC s + 1)

With the assumption that the process model is equivalent to the real process we get a conventional PI 116

Fig. 3. Popov plot

3.3 Stability Analysis To apply the Popov Criterion to the system, we need to compute the intersection of the Popov plot W(jω)

Štampar, S. – Sokolič, S. – Karer, G.

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 112-123

with the real axis. From Eq. (12) we can obtain the real (Eq. (15)) and imaginary (Eq. (16)) parts as follows:

( ) , (15) (b − ω ) + ω a −c ( ( k a − k ) ω + k b ) ω Im W ( jω ) = , (16) (b − ω ) + ω a Re W ( jω ) =

−c1 kcpω 2 − kcp b1 + kci a1

1

2

2

1

we calculate the stability condition through the interval of possible values for the dynamics of the reactor’s core (Eq. (10)) and jacket (Eq. (11)).

cp 1

1

2

ci

2

2

2 1

2

2

ci 1

2 1

where: TGc + TGj + KGj k jpTGc = 8.63 ⋅10−2 , a1 = TGcTGj b1 =

(1 + KGj k jp ) = 5.16 ⋅10−5 and

c1 =

( KGc KGj k jp ) = 3.44 ⋅10−5 .

Fig. 4. Popov plot for stability analysis

TGcTGj

TGcTGj

So the Popov plot of W(jω) for the parameter  c1 kcp b1 − kci a1 −c ( k b )  1 ci 1  , ω = 0 starts at the point  2   b1 b12   and for the parameter ω = ∞ terminates at the point (0,0). By investigating the process stability – with the parameters a1, b1, c1 > 0 and kcp, kci > 0 – two distinct cases are possible, depending on the value of the parameters kcp and kci. a) kcp / kcp < a1.

In this case ωImW(jω) is always negative for ω ≥ 0. This means that the Popov plot of W(jω) remains always entirely in the third and fourth quadrants and does not cross the real axis.

Therefore we can easily construct a straight line with a non-negative slope passing through the origin, such that the Popov plot is entirely to the right of this line. From the above conclusions it is obvious that the range of the nonlinear gain is (0,∞). The Popov plot starts at point (–0.001,–0.002) for the parameter ω = 0 and terminates at point (0,0) for the parameter ω = ∞ (Fig. 4). b) kcp / kcp ≥ a1.

With the parameters specified for the temperature control of the batch-reactor content we meet the criterion for Popov stability in case a).

(

)

To analyse the stability of the proposed control algorithm in the case of process model uncertainties,

First, it is given that the time constant of the reactors core temperature TGc varies from 100 to 3000. By following the rules written in case a) we can conclude that the controlled process is stable for the whole interval of possible values for the parameter TGc. In the second process model uncertainty, it is given that the time constant of the reactors jacket temperature TGj varies from 10 to 300. Again by following the rules written in case a) we can conclude that the controlled process is stable for the whole interval of possible values for the parameter TGj. 3.4 Robustness Analysis In many cases in industry, the controller output has a delayed impact on the temperature in the reactor’s core. This is because of the delays in the position changes of the analogue and on/off valves.

To prove the robustness of the control algorithm in such cases we add an additional first-order process to the system GA, which simulates the actuator’s delays.

1

GA ( s ) = , (17) TA s + 1 where TA represents the time constant for the first order process that simulates the actuator’s delays.

For the robustness analysis of the closed-loop process W(s) (Eq. (18)), we combine the following: the linear parts of the nonlinear algorithm; the proportional controller; the two first-order transfer functions of the heating and cooling of the reactors

Nonlinear Control of a Hybrid Batch Reactor

117

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 112-123

jacket and core temperature; and the first-order transfer function that represent the actuator delays.  KGj k jp W (s) =  2  TGj TGA s + TGA s + TGj s + 1 + K Gj k jp   K Gc   kcp s + kci  ⋅  .  (T s + 1)   s   Gc 

 ⋅   (18)

By increasing the actuator delay TA from 10 to 180 seconds, the maximum allowable nonlinear gain kmax decreases from 128 to 35 (Fig. 5).

To apply the Popov Criterion to prove the robustness of the proposed algorithm, we need to compute the crossing of the Popov plot W(jω) with the real axis. From Eq. (18) we can obtain the real (Eq. (19)) and imaginary (Eq. (20)) parts as follows: ReW ( jω ) =

(

b2 = c2 = d2 =

(

ω 2 ω 2 − b2

ω ImW ( jω ) =

where a2 =

)

ω 2 d 2 kci − a2 d 2 kcp − b2 d 2 kci + d 2 c2 kcp

) + (ω a

(

2

2

2 − c2

)

)

2

ω 4 d 2 K cp + ω 2 a2 d 2 kci − b2 d 2 kcp − d 2 c2 kci

(

ω 2 ω 2 − b2

) + (ω a 2

2

TGj TA + TGj TGc + TGcTA TGj TGcTA

TGj + TA + TPc + TGc KGj k jp T j TcTA 1 + KGj k jp TGj TGcTA

2

− c2

)

2

, (19)

From the robustness analysis we can conclude that with longer actuator delays the proposed algorithm may lead to an unstable temperature control. To avoid this we consider the modified hyperbolic function limitation by reducing the parameter k0 to kmax. So, with knowledge of the actuator delay, the upper limit of the nonlinear gain can be precisely defined.

The Popov plot for the above process with an actuator delay of TA = 20 seconds starts at point (–0.0023, –0.0020) for the parameter ω = 0 and terminates at point (0, 0) for the parameter ω = ∞ (Fig. 6).

= 7.92 ⋅10−2 ,

= 4.30 ⋅10−3 ,

= 2.58 ⋅10−6 and

KGj KGc k jp

= 1.72 ⋅10−6 .

TGj TGcTA

Fig. 5. Maximum allowed nonlinear gain according to the actuator delay

, (20)

Now we have to find the crossover frequency where the process crosses the real axis in the Popov plot ωImW(jω) = 0. By solving the Popov-plot crossover frequency we obtain one suitable solution ω0. The value of W(jω) at the crossover is then obtained (Eq. (21)).

ReW ( jω0 ) =

(

)

ω0 2 d 2 kci − a2 d 2 kcp − b2 d 2 kci + d 2 c2 kcp 2

(

2

ω0 ω0 − b2

) ( 2

+ ω0 2 a2 − c2

)

2

.(21)

The equation above indicates that the Popov plot crosses the negative real axis at the frequency ω0.

Therefore, the maximum allowable nonlinear gain can be determined (Eq. (22)), as described in [55].

kmax = −

1 , Re W ( jω0 )

Fig. 6. Popov plot for the robustness analysis

(22)

4 SIMULATIONS In this section, the proposed algorithm was tested by simulating the theoretical model of the batch reactor

118

Štampar, S. – Sokolič, S. – Karer, G.

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 112-123

developed in [50]. The main goal of the study was to achieve rapid and exact reference-temperature tracking, a good disturbance rejection, and a minimal number of the heating−cooling medium switchings. The low switching ratio minimizes the amount of heating−cooling medium used, extends the equipment’s lifecycle, and lowers the costs of temperature control.

For the simulation we assume some disturbances as they appear in the real process. There is a disturbance in the prefabricated heating−cooling media. Because of the sensor noise we consider disturbances in the reactor’s jacket temperature Tj and the reactor’s core temperature T. The initial values are: reactor’s jacket temperature Tj(0) = 0 °C, reactor’s core temperature T(0) = 0 °C, and mass of the reactor’s contents m(0) = 550 kg. At time t = 400 min we took into account the addition of 80 kg of chilled water, which cools the reactor’s content down by 10 °C. At this time, a simulation of a continuous endothermic reaction was also started and this lasted until the end.

The parameters for the proposed algorithm with the external nonlinear controller and the internal proportional controller are k0 = 100, kcp = 5, kci = 3·10–3 and kjp = 2.

The dead zone of the switchings of the heating− cooling medium was chosen to be δ = 20.

The simulation results are shown in Figs. 7 to 9. Fig. 7 shows the batch reactor’s core temperature T and the changing reference temperature rT; Fig. 8 shows the batch reactor’s jacket temperature Tj; and Fig. 9 shows the position of the continuous valve.

industry cases the PI control algorithm is used for the batch reactor’s temperature control.

Fig. 8. Reactor’s jacket temperature with the proposed algorithm

Fig. 9. Position of the continuous valve with the proposed algorithm

5.1 Simulations for the Cascade PI Controller The simulation results using a conventional cascade PI controller are given in this subsection. The control scheme is presented in Fig. 10. Different sets of PI parameters were compared. While a “rapid” PI results in rapid reference-temperature tracking and many heating-cooling medium switchings, a “slow” PI results in fewer heating−cooling medium switchings but much slower reference-temperature tracking than with the proposed algorithm. For the sake of comparison, we adjusted the parameters so that the PI controller achieved approximately the same switchings ratio. The dead zone of the switchings of the heating−cooling medium is the same as with the proposed algorithm, δ = 20.

The parameters for the conventional cascade controller with an external PI – C and internal PI – J controller are kcp = 5, kci = 3·10–3, kjp = 5 and kci = 2.5·10–2 .

5.2 Comparison of the Simulation Results

Fig. 7. Control of the reactor’s core temperature with the proposed algorithm

To show the advantages of the proposed algorithm we compared it to a conventional cascade PI control.

This comparison was chosen because in almost all

As seen from the simulation results using the proposed control algorithm (Figs. 7 to 9) and the PI control algorithm (Figs. 11 to 13) both control approaches give us approximately the same heating−cooling medium switchings. Nevertheless, it is obvious that the proposed algorithm gives us a much faster and more precise reference-temperature tracking than the cascade PI control algorithm. The control performance

Nonlinear Control of a Hybrid Batch Reactor

119

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 112-123

Fig. 10. Cascade PI control

The result for the proposed control algorithm is RMSDSQ = 4.3012 °C and for the PI control algorithm RMSDPI = 4.8700 °C. From the simulation results we can conclude that the proposed algorithm ensures a much better performance, i.e., reference-temperature tracking, than the PI control approach. The number of heating−cooling medium switchings with the proposed algorithm is also smaller with only 24, rather than the 29 seen with the conventional cascade PI algorithm.

Another indicator for the longevity of the equipment is the total movement (TM) of the analogue valve that is calculated in Eq. (24). The total movement for the proposed algorithm is 29.73 and for the PI algorithm it is 47.77. Again, the proposed algorithm gives us the better result. The movement of the analogue valve is reduced by 40% compared to the conventional cascade PI algorithm.

Fig. 11. Control of the reactor’s core temperature (PI)

Fig. 12. Reactor’s jacket temperature (PI)

is measured using only the root-mean-square deviation for both algorithms (Eq. (23)).

RMSD =

2

i =1:n

n

where n is the number of measurements.

120

,

∑ ( vv ( i ) − vv ( i − 1) ) .

(24)

i = 2:n

5 REAL PROCESS-TEMPERATURE CONTROL

Fig. 13. Position of the continuous valve (PI)

∑ ( rT ( i ) − T ( i ) )

TM = vv (1) +

(23)

In addition, in order to prove the effectiveness of the proposed algorithm, its implementation on a real process is shown. To show the flexibility of this algorithm it is implemented on a slightly different type of batch reactor, i.e., a bioreactor. The bioreactor is made of stainless steel. It consists of a tank, with a capacity of 40 litres, and a heating−cooling system, which is made of a single external cooling jacket.

The heating and cooling is done through the jacket with water at two different temperatures Tin1 = 17 °C, Tin2 = 60 °C. The water for the temperature control is chosen based on the output of the control algorithm.

The input waters cannot be mixed with each other.

An additional adjustment from the control algorithm is made with an analogue valve, which defines the amount of fresh water pumped into the reactor’s

Štampar, S. – Sokolič, S. – Karer, G.

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 112-123

jacket. The approximate scheme of the bioreactor is the same as in Fig. 1. It differs only in the number of heating−cooling inputs.

The goal of this temperature control is to achieve fast and, more particularly, precise temperature control with a fast disturbance rejection for very long time periods (weeks or months). The maximumallowed temperature deviation is ±0.2 °C. Exceeding the tolerance can harm the product quality or even destroy the living cells in the bioreactor, which are very sensitive to temperature. Those living cells are the main component of the end product therefore, lack of temperature control could result in large financial losses. Due to the high sensitivity to temperature, the reactor’s jacket temperature is limited to between 42 and 20 °C. The parameters for the proposed algorithm are k0 = 100, kcp = 1, kci = 2·10–3 and kjp = 3.5.

The results from the real-time temperature control of the bioreactor are shown in the Figs. 14 to 16. The reference reactor’s core temperature changes from 37 to 20 °C and back to 37 °C. Then it remains at 37 °C for several weeks.

Fig. 14. Real-time bioreactor core-temperature control with the proposed algorithm

the criterion for a less than ±0.2 °C core-temperature deviation.

Fig. 16. Real-time position of the continuous valve

6 CONCLUSION The main idea of this study was to develop a new control algorithm that provides us with rapid and precise reference-temperature tracking, a good disturbance rejection, and a minimum number of heating−cooling medium switchings.

A new class of advanced control algorithms was developed for temperature control, where a nonlinear PI controller with a feed-forward part in a cascade combination with a P controller is employed. The obtained results showed that the proposed algorithm meets the desired criteria and more. According to the other advanced control principles, the main advantage of the algorithm is in the analytical expression of the control law, which enables its use in real-time control and can be implemented on lowcost hardware by process engineers, who do not have as much knowledge in the field of advanced control algorithms. The stability of the proposed algorithm was successfully studied using the Popov stability criterion. A comparison with a conventional cascade PI controller showed better performance, fewer heating−cooling medium switchings, and less analogue valve movement. This reduces the costs of temperature control by using less heating−cooling medium and extends the lifecycle of the equipment.

The implementation example on a real process, where the temperature of a bioreactor’s content is controlled, shows excellent performance and meets the criterion for a less than ±0.2 °C core-temperature deviation.

7 ACKNOWLEDGEMENTS

Fig. 15. Real-time bioreactor jacket-temperature control with the proposed algorithm

The real process data from the bioreactor for the temperature control with the proposed algorithm provides us with excellent performance data and meets

Operation part financed by the European Union, European Social Fund.

8 REFERENCES [1] Bratina, B., Tovornik, B., Sokolič, S. (2011). Industrial software tools for system operation analysis and

Nonlinear Control of a Hybrid Batch Reactor

121

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 112-123

optimization. Automatization in industry and Economy, from: http://www.aig.si/11/images/stories/clanki/Avto_ Procesov_Daljinsko/AP4_Bozidar_Bratina_N.pdf, accessed on 2012-06-01.

[2] Loeblin C., Perkins, J.D., Srinivasan, B., Bonvin, D. (1999). Economic performance analysis in the design of on line batch optimization system. Journal of Process Control, vol. 9, no. 1, p. 61-78, DOI:10.1016/S09591524(98)00034-1.

[3] Juba, M.R., Hamer, J.W. (1986). Progress and challenges in batch process control. Chemical Process Control, vol. 3, p. 139-183.

[4] Ray, W.H. (1983). Multivariable Process Control - A Survey. Computers & Chemical Engineering, vol. 7, no. 4, p. 367, DOI:10.1016/0098-1354(83)80019-2.

[5] Robinson, A.C. (1971). A survey of optimal control of distributed-parameter systems. Automatica, vol. 7, no.

3, p. 371-388, DOI:10.1016/0005-1098(71)90130-0.

[6] Feichtinger, G., Hartl, R.F., Sethi, S.P. (1994).

Dynamic optimal control models in advertising: Recent developments. Management Science, vol. 40, no. 2,p.

195-226, DOI:10.1287/mnsc.40.2.195.

[7] Sargent, R.W.H. (2000). Optimal control. Journal of Computational and Applied Mathematics, vol. 124, p.

361-371, DOI:10.1016/S0377-0427(00)00418-0.

[8] Morari, M., Zafiriou, E. (1989). Robust Proces Control, Prentice Hall, Englewood Clifs.

[9] Economou, C.G., Morrari, M., Palsson, B.O. (1986).

Internal model control: Extension to non-linear systems. Industrial & Engineering Chemistry Process, vol. 25, no.2, p. 403-411, DOI:10.1021/i200033a010.

[10] Xie, W.F., Rad, A.B. (2000). Fuzzy adaptive internal model control. IEEE Transactions on Industrial Electronics, vol. 47, no. 1, p. 193-202, DOI:10.1109/41.824142.

[11] Hussain, M.A., Kershenbaum, L.S. (2000).

Implementation of an inverse-model-based control strategy using neural networks on a partially simulated exothermic reactor. Chemical Engineering Research and Design, vol 78, no. 2, p. 299-311, DOI:10.1205/026387600527167.

[12] Garcia, C.E., Morari, M. (1989). Model predictive control: Theory and practice: A survey. Automatica, vol. 25, no. 3, p. 335-348, DOI:10.1016/00051098(89)90002-2.

[13] Qina, S.J., Badgwell, T.A. (2003). A survey of industrial model predictive control technology. Control Engineering Practice, vol. 11, no. 3, p. 733-764, DOI:10.1016/S0967-0661(02)00186-7.

[14] Seborg, D.E., Edgar, T.F., Shah, S.L. (1986). Adaptive control strategies for process control: A survey.

American institute of Chemical Engineers Journal, vol.

32, no. 6, p. 881-913, DOI:10.1002/aic.690320602.

[15] Astrom, K.J., Wittenmark, B. (1997). A survey of adaptive control applications, Dynamic modeling control applications for industry workshop. IEEE Industry Applications Society, vol. 1, p. 649-654.

122

[16] Bequette, B.W. (1991). Nonlinear control of chemical processes: A review. Industrial & Engineering Chemistry, vol. 30, p. 1391-1413, DOI:10.1021/ ie00055a001.

[17] Isidori, A. (1995). Nonlinear Control Systems. Springer Verlag, London.

[18] Chen, L., Bastin, G., Van Breusegam, V. (1995). A case study of adaptive nonlinear regulation of fedbatch reactors. Automatica, vol. 31, no. 1, p. 55-65, DOI:10.1016/0005-1098(94)00068-T. [19] Pringle, T.C., MacGregor, J.E. (1997). Nonlinear adaptive temperature control of multi-product, semibatch polymerization reactors, vol. 21, no.12, p. 13951409, DOI:10.1016/S0098-1354(97)00013-6.

[20] Freeman, R.A., Kokotović, P.V. (1996). Robust nonlinear control design: State-space and Lyapunov techniques. Systems & Control, Birkhauser, Boston, DOI:10.1007/978-0-8176-4759-9.

[21] Sugeno, M. (1985). An introductory survey of fuzzy control. Information Sciences, vol. 36, no. 1-2, p. 5983, DOI:10.1016/0020-0255(85)90026-X. [22] Precup, R.E., Hellendoorn, H. (2011). A survey on industrial applications of fuzzy control. Computers in Industry, vol. 62, no. 3, p. 213-226, DOI:10.1016/j. compind.2010.10.001.

[23] Karer, G., Škrjanc, I., Zupančič, B. (2008). Selfadaptive predictive functional control of the temperature in an exothermic batch reactor. Chemical Engineering and Processing, vol. 47, no.12, p. 23792385, DOI:10.1016/j.cep.2008.01.015.

[24] Chen, L., Bastin, G., Van Breusegam, V. (1995). A case study of adaptive nonlinear regulation of fedbatch reactors. Automatica, vol. 31, no. 1, p. 55-65, DOI:10.1016/0005-1098(94)00068-T. [25] Louleh, Z., Cabassud, M., Le Lann, M.V. (1999). A new strategy for temperature control of batch reactors: Experimental application. Chemical Engineering Journal, vol. 75, no. 1, p. 11-20, DOI:10.1016/S13858947(99)00073-X. [26] Xaumier, F., Le Lann, M.V., Cabassud, M., Casamatta G. (2002). Experimental application of nonlinear model predictive control: temperature control of an industrial semi-batch pilot-plant reactor. Journal of Process Control, vol.12, no. 6, p. 687-693, DOI:10.1016/ S0959-1524(01)00057-9.

[27] Le Lann, M.V., Cabassud, M., Le Lann, M.V., Casamatta, G. (1992). Adaptive control of a multipurpose and flexible semi-batch pilot plant reactor.

Computers & Chemical Engineering, vol. 16, no. 9, p.

837-848, DOI:10.1016/0098-1354(92)80036-9.

[28] Vasanthi, D., Pranavamoorthy, B., Pappa, N. (2012).

Design of a self-tuning regulator for temperature control of a polymerization reactor. ISA Transactions, vol. 51, no. 1, p. 22-29, DOI:10.1016/j.isatra.2011.07.009.

[29] Chang, J.-S., Hseih, W.Y. (1995). Optimization and control of semibatch reactors. Industrial & Engineering Chemistry Research, vol. 33, no. 2, p. 545-556, DOI:10.1021/ie00041a015.

Štampar, S. – Sokolič, S. – Karer, G.

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 112-123

[30] Cuthrell, J.E., Biegler, L.T. (1989). Simultaneous optimization and solution methods for batch reactor control. Computer and Chemical Engineering, vol. 13, no. 1-2, p. 49-62, DOI:10.1016/0098-1354(89)89006-4.

[31] Luus, R., Okongwu, O.N. (1999). Towards practical optimal control of batch reactors. Chemical Engineering Journal, vol. 75, no. 1, p. 1-9, DOI:10.1016/S13858947(99)00019-4.

[32] González-Figueredo, C., Ayala, O.R., Aguilar, S., Aroche, O., Loukianov, A., Sánchez, A. (2011). Optimal temperature tracking of a solid state fermentation reactor. Computer Aided Chemical Engineering, vol.

29, p. 839-843, DOI:10.1016/B978-0-444-537119.50168-1.

[33] Hosen, M.A., Hussain, M.A. (2012). Optimization and control of polystyrene batch reactor using hybrid based model. Computer Aided Chemical Engineering, vol. 31, p. 760-764, DOI:10.1016/B978-0-444-595072.50144-X. [34] Foss, B.A., Johansen, T.A., Sorensen, A.V. (1995).

Nonlinear predictive control using local models-applied to a batch fermentation process. Control Engineering Practice, vol. 3, no. 3, p. 389.396, DOI:10.1016/09670661(95)00012-J. [35] Clarke D. (1994). Advances in Model-Based Predictive Control. Oxford Science Publication, Oxford.

[36] Karer, G., Škrjanc, I., Mušič, G., Zupančič, B. (2007). Hybrid fuzzy model-based predictive control of temperature in a batch reactor. Computers and Chemical Engineering, vol. 31, no. 12, p. 1552-1564, DOI:10.1016/j.compchemeng.2007.01.003.

[37] Lakshmanan, N., Arkun, Y. (1999). Estimation and control of batch processes using multiple models.

International Journal of Control, vol. 72, no. 7-8, p.

659-675, DOI:10.1080/002071799220849.

[38] Richalet, J. (1993). Industrial application of model based predictive control. Automatica, vol. 25, no. 5, p.

1251-1274, DOI:10.1016/0005-1098(93)90049-Y. [39] Škrjanc, I., Matko D. (2001). Fuzzy predictive functional control in the state space domain. Journal of Intelligent and Robotic System, vol. 31, no. 1-3, p. 283297, DOI:10.1023/A:1012011010623.

[40] Škrjanc, I. (2008). Self-adaptive supervisory predictive functional control of a hybrid semi-batch reactor with constraints. Chemical Engineering Journal, vol. 136, no. 2-3, p. 312-317, DOI:10.1016/j.cej.2007.04.012.

[41] Di Ciccio, M.P., Bottini, M., Pepe, P., Foscolo, P.U. (2011). Observer-based nonlinear control law for a continuous stirred tank reactor with recycle. Chemical Engineering Science, vol. 66, no. 20, p. 4780-4797, DOI:10.1016/j.ces.2011.06.038.

[42] Pulley R.A. (1986). Batch Process Modeling. Springs Laboratory, Herts.

[43] Luyben, W.L. (2007) Chemical Reactor Design and Control. John Wiley & Sons, Inc., Hoboken, DOI:10.1002/9780470134917.

[44] Jakobsen, H.A. (2007) Chemical Reactor Modeling, Springer-Verlag, Berlin.

[45] Caccavale, F., Pierri, F., Iamarino, M., Tufano, V. (2011). Control and Monitoring of Chemical Batch Reactors. Springer Verlag, London, DOI:10.1007/9780-85729-195-0.

[46] Preglej, A., Karba, R., Steiner, I., Škrjanc, I. (2011).

Mathematical Model of an Autoclave. Strojniški vestnik - Journal of Mechanical Engineering, vol. 57, no. 6, p.

503-516, DOI:10.5545/sv-jme.2010.182.

[47] Fowler, A.C. (1997). Mathematical Models in the Applied Sciences. Cambridge University Press, Cambridge.

[48] Cuthrell, J.E., Biegler, L.T. (1989). Simultaneous optimization and solution methods for batch reactor control. Computer and Chemical Engineering, vol. 13, no. 1-2, p. 49-62, DOI:10.1016/0098-1354(89)890064.

[49] Ingham, J., Dunn, I.J., Heinzle, E., Prenosil, J.E. (1994).

Chemical Engineering Dynamics: Modelling with PC Simulations. VCH Verlagsgesellschaft, Weinheim, DOI:10.1002/9783527616015.

[50] Dragan, D. (2011). Fault Detection of an Industrial Heat-Exchanger: A Model-Based Approach. Strojniški vestnik - Journal of Mechanical Engineering, vol. 57, no. 6, p. 477-484, DOI:10.5545/sv-jme.2010.128.

[51] Štampar, S., Sokolič, S., Karer, G., Žnidaršič A., Škrjanc, I. (2011). Theoretical and fuzzy modelling of a pharmaceutical batch reactor. Mathematical and Computer Modelling, vol. 53, no. 5-6, p. 637-645, DOI:10.1016/j.mcm.2010.09.016.

[52] Montagner, V.F., Oliveira, R.C.L.F., Calliero, T.R., Borges, R.A., Peres, P.L.D., Prieur, C. (2009). Robust absolute stability and nonlinear state feedback stabilization based on polynomial Lur’e functions.

Nonlinear Analysis, vol. 70, no. 5, p. 1803-1812, DOI:10.1016/j.na.2008.02.081.

[53] Sastry, S. (1999). Nonlinear Systems: Analysis, Stability and Control. Interdisciplinary Applied Mathematics, Springer-Verlag, Berlin, Heidelberg.

[54] Georgiou, T.T., Smith, M.C. (1997). Robustness analysis of nonlinear feedback systems: An input– output approach. Transactions on Automatic Control, vol. 42, no. 9, p. 1200-1221, DOI:10.1109/9.623082.

[55] Arcak, M., Larsen, M., Kokotovic, P. (2003). Circle and Popov criteria as tools for nonlinear feedback design.

Automatica, vol. 39, no.4, p. 643-650, DOI:10.1016/ S0005-1098(02)00276-5.

[56] Krstić, M., Kanellakopoulos I., Kokotović P. (1995).

Nonlinear and Adaptive Control Design. John Wiley & Sons, New York.

[57] Popov, V.M. (1960). Criterion of quality for non-linear controlled systems. Preprints of the First IFAC World Congress, Moscow, p. 173-176.

[58] Homayoun, S. (1998). A new class of nonlinear pid controllers for robotic applications. Journal of Robotic System, vol. 15, no. 3, p. 161-181, DOI:10.1002/ (SICI)1097-4563(199803)15:3<161::AIDROB4>3.0.CO;2-O.

Nonlinear Control of a Hybrid Batch Reactor

123

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 124-134 © 2013 Journal of Mechanical Engineering. All rights reserved.

DOI:10.5545/sv-jme.2012.677

Received for review: 2012-06-26 Received revised form: 2012-12-03 Accepted for publication: 2013-01-14

The Effect of Surface Roughness of End-Mills on Optimal Cutting Performance for High-Speed Machining Chen, C.H. – Wang, Y.C. – Lee, B.Y. Chi-Hsiang Chen1,* – Yung-Cheng Wang2 – Bean-Yin Lee3

1Institute

of Mechanical and Electro-Mechanical Engineering, National Formosa University, Taiwan of Mechanical Engineering, National Yunlin University of Science & Technology, Taiwan 3Department of Mechanical and Computer-Aided Engineering, National Formosa University, Taiwan 2Institute

In this study, the effect of surface roughness of end-mills on the cutting performance of high-speed machining has been investigated. A novel optimization design approach of the processing parameters for the high-speed cutting of the DIN 1.2344 tool steel has been also proposed. The characteristics indices of cutting performance selected for this investigation are tool life and metal removal rate. The processing parameters include the surface roughness of the relief face of an end-mill, cutting speed, feed per tooth, axial cutting depth, and radial cutting depth. The process is integrated using multiple performance indices. Consequently, the optimal combination of processing parameters is determined by performing grey relational analysis. The analysis results indicate that the effect of cutting speed and feed per tooth are significant for multiple performance characteristics. Additionally, the surface roughness of the relief face of an end-mill essentially affects the surface roughness of the processed workpiece. Due to a slight effect on the cutting performance characteristics of rough machining, a surface roughness of the relief face of 0.43±0.02 μm for grinding conditions can be used to improve tool grinding efficiency. Verification experiments revealed that the proposed optimization design approach to the processing parameters brings about improvements of 9.1 min in tool life, 1200 mm3/min in metal removal rate, 230616 mm3 in total metal removal volumes, and 0.044 μm in average surface roughness of the workpiece with highspeed cutting.

Keywords: high-speed cutting, grey relational analysis, surface roughness, end-mill

0 INTRODUCTION Developments in machine tools tend towards high speed technology, including high-speed machining (HSM) and high-speed cutting (HSC), especially in high speed end milling applications [1] and [2].

High speed technology applications in machine tools are characterised by a high feeding speed, low axial and radial cutting depth, increased metal removal rate, simplified processing, and reduced costs. The thermal effect of workpieces is insignificant since cutting chips remove most of the heat induced by processing, and hence cutting oil is seldom used. This trend contributes to environmental protection efforts.

Only a small amount of cutting fluid is available to lubricate green cutting. The primary deformation zone is significantly heated and bears the cutting force.

Therefore, major green cutting methods include tool materials, coating technology, tool geometry design, chip control, coefficient of tool-face friction with the workpiece, and selection of cutting. Green cuttingrelated developments and applications depend on technological advances in machinery and cutting tools.

The grinding precision of cutting tools is determined by the surface roughness of the rake face and relief face, in which precision essentially affects the surface roughness of a workpiece and the tool life during high-speed milling. Generally, a cutting tool manufacturer evaluates the quality of grinding, 124

first, with respect to the surface finish of end-mill, and then with by the geometrical profile. The surface finish, which influences the abrasion of the endmill, lubrication, accuracy, and tool life expectancy, depends on the surface roughness of the rake face and relief face.

As the most important and the final procedure in manufacturing, grinding of cutting edges is also critical in determining geometrical shapes, cutting performance, wear on the cutting edge, and tool life [3]. Shaji and Radhakrishnan [4] analysed the grinding parameters with respect to surface characteristics, e.g., wheel, workpiece, processing, and mechanical parameters. Yin et al. [5] examined ultraprecision grinding of cemented carbides from a microstructure perspective. Kwak [6] diagnosed errors in surface grinding processing by Taguchi and response surface methods. Nguyen et al. [7] simulated impact parameters of the precision grinding process.

Owing to its efficiency and systematic approach, the Taguchi method has been extensively adopted in parameter design and experimental planning [8]. Despite its application in optimizing process parameters [9] to [13], the Taguchi method is unsatisfactory for handling multiple performance characteristics. In this study we attempt to derive an efficient solution to overcome the above problem.

Grey relational analysis based on the Taguchi method can be adopted to elucidate the complex relationship among the designated performance

*Corr. Author’s Address: National Formosa University, 64 Wunhua Road, Huwei, Yunlin 632, Taiwan, explorer5270@gmail.com

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 124-134

characteristics. Through this analysis, a grey relational grade is favorably defined as an indicator of the multiple performance characteristics for evaluation.

Grey relational analysis is a highly effective means of analysing processes with multiple performance characteristics [14] to [18].

This paper is schemed as follows. In Section 1, we will describe the analysis method. Then, in Section 2, the importance of the surface roughness of the relief face in the workpiece will be investigated. In Section 3 the optimal experimental design and results will be summarized. Section 4 and 5 will describe, the result analyses, discussions and conclusions.. The end-mill with a the-lower-the-better condition can produce improved machining quality and tool life. Therefore, in this study, processing parameters are estimated by adding in the surface roughness of the relief face of an end-mill to the other other processing parameters, which include cutting speed, feed per tooth, axial cutting depth and radial cutting depth. Moreover, the characteristics of the cutting performance are the tool wear rate and the metal removal rate, which belong to the multiple performance characteristics. How to optimize the HSC process based on grey relational analysis and an analysis of cutting performance characteristics in end-milling for HSC are discussed in detail.

1 ANALYSIS METHODS 1.1 Signal-to-Noise Ratio The Taguchi method is a simple and effective solution for parameter design and experimental planning [19].

In this method, the signal-to-noise (S/N) ratio is used to represent a performance characteristic in which the largest value of the S/N ratio is required. The three S/N ratios are the lower-the-better, the higher-thebetter, and the nominal-the-better. The S/N ratio with a lower-the-better characteristic can be illustrated as follows:

 n  ηij = −10 log  1n ∑ yij2  . (1)  j =1   

The S/N ratio with a higher-the-better characteristic can be expressed as follows:  n 1  ηij = −10 log  1n ∑ 2  ,

 j =1 yij    where yij is the ith experiment at the jth test and n is the total number of the tests, in this study n = 2.

1.2 Grey Relational Analysis Grey relational analysis initially generates data preprocessing to normalize the raw data. Here, the S/N ratio is linearly normalized in the range between 0 and 1, which is also called grey-relational generating [20].

The normalized S/N ratio xij for the ith performance characteristic in the jth experiment can be described as follows:

xij =

ηij − min j ηij max j ηij − min j ηij

, (3)

where i = 1, …, m; j = 1, …, n. m denotes the number of experimental data items and n represents the number of parameters, with m = 18 and n = 2 in this study. Basically, the larger normalized S/N ratio corresponds to the better performance and the bestnormalized S/N ratio is equal to unity.

In gray relational analysis, the evaluation of the relevancy between two systems or two sequences is defined as the gray relational grade. The local gray relation measurement refers to a situation in which only one sequence follows data preprocessing. The gray relation coefficient ζij for the ith performance characteristics in the jth experiment can be expressed as follows:

ζ ij =

mini min j xi0 − xij + ζ maxi max j xi0 − xij xi0 − xij + ζ maxi max j xi0 − xij

, (4)

where xi0 is the ideal sequence for the ith performance characteristic; xij represents the comparability sequence; ζ refers to the distinguishing coefficient, which is defined in the range 0 ≤ ζ ≤ 1, in this study ζ = 0.5.

The grey relational grade is a weighting-sum of the grey relational coefficients. It is defined as follows:

γj =

1 m ∑ β k ζ ij , m k =1

m

∑ βk

k =1

= 1, (5)

where γj is the grey relational grade for the jth experiment, βk denotes the weighting value of the kth performance characteristic, and m the number of the performance characteristic. The gray relational grade γj represents the level of correlation between the ideal sequence and the comparability sequence. In other words, optimization of the complicated multiple performance characteristics can be converted into the optimization of a single grey relational grade.

The Effect of Surface Roughness of End-Mills on Optimal Cutting Performance for High-Speed Machining

125

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 124-134

2 THE IMPACT OF SURFACE INTEGRITY OF THE END-MILL ON THE HSM

Table 1. Material properties of DIN 1.2344 Properties Tensile Yield Strength Young’s modulus Elongation Hardness Machinability rating

The grinding parameters (grit size of the diamond wheel, grinding speed, and feed speed) will directly affect the surface roughness of tool grinding. The dimensional accuracy and surface roughness of the rake face and the relief face will determine the precision of the cutting tool, which will influence the cutting performance of high-speed milling as tool wear, tool life, and surface roughness of the workpiece. Therefore, in this section, the importance of the surface roughness of the relief face in the workpiece will be investigated.

Experiments are performed on a Papars B8 CNC machining center by upward milling operation with compressed air. Fig. 1 schematically depicts the HSC process.

The material compositions of DIN 1.2344 (Hitachi metals DAC) contain 0.39% C, 1.0% Si, 0.4% Mn, 5.15% Cr, 1.4% Mo, 0.8% V, 0.03% P, and 0.01% S, with dimensions of 200×100×100 mm.

Table 1 shows the workpiece material properties. The typical uses of the material are hot work applications including pressure die casting tools, extrusion tools, forging dies, hot shear blades, stamping dies, and plastic moulds. End-mills with the same geometrical parameters are ground with different grinding parameters by a 5-axis CNC grinder (TOPWORK TG-5 Plus). TiAlN coating carbide end-mills with 4 flutes are also ground. The end-mills have the following dimensions: diameter of 8 mm, helix angle of 35°, radial rake angle of 8°, radial relief angle of 12°, axial rake angle of 4°, axial relief angle of 8°, end angle of 1.5°, and nose radius of 0.5 mm.

Geometrical dimensions, e.g. diameter, radial rake angle, radial relief angle, axial rake angle and axial relief angle etc. can be measured using a 5-axis CNC measuring machine (Zoller genius 3). The processing parameters are the surface roughness of the relief face (R), cutting speed (V), feed per tooth

Value 536.67 MPa 333.89 MPa 210000 MPa 24.93 % 12±1 HRC 48 %

Fig. 1. High-speed milling method

Fig. 2. Geometrical parameters of an end-mill (F), axial cutting depth (Da), and radial cutting depth (Dr). Fig. 2 illustrates the surface roughness of the relief face of an end-mill. The configurations of the processing parameters are listed in Table 2.

Table 2. Cutting - experimental layout and results No 1 2 3 4 5 6

126

R [μm] 0.32 0.18 0.41 0.31 0.42 0.29

V [m/min] 251.32 251.32 351.85 351.85 452.38 452.38

Experimental layout F [mm/tooth] 0.06 0.06 0.02 0.02 0.10 0.10

Da [mm] 1.0 1.0 1.0 1.0 1.0 1.0

Dr [mm] 0.75 0.75 1.00 1.00 0.50 0.50

Chen, C.H. – Wang, Y.C. – Lee, B.Y.

Experimental results Cutting Time Average surface roughness [min] of workpiece [μm] 166.86 0.199 185.84 0.068 79.12 0.251 90.06 0.164 71.46 0.190 74.24 0.101

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 124-134

The experiment ends if flank wear (VB) reaches 0.2 mm (ISO 3002/1). The measurement equipment for surface roughness is a Surfcorder SEF-3500 (Kosaka Laboratory). The described measurand of surface roughness is the arithmetic mean deviation of the surface roughness profile (Ra). In practice, the measurement was performed using an interval of 0.08 mm, a sampling length of 0.4 mm, and a feeding speed of 0.1 mm/s. The experimental results are listed in Table 2.

2.1 Grinding Dimensional Accuracy The radius of end mills, whose relief face will vary with different grinding conditions, have been finished according to different grinding conditions. After the end-mill has cut the workpiece for 1 minute and 150 minutes (cutting parameter: V = 251.32 m/min,

F = 0.06 mm/tooth, Da = 1.0 mm, Dr = 0.75 mm), flank wear with better surface roughness will be less than that of the cutting tool with worse surface roughness, as shown in Figs. 3a, b and 4a, b.

2.2 The Relationship between the Relief Surface Roughness and the Surface Roughness of the Processed Workpiece The relationship between the relief surface roughness and the surface roughness of the processed workpiece using HSC is illustrated in Fig. 5a, where the x axis signifes the cutting time and the y axis denotes the surface roughness of the workpiece. The diagram reveals that coverage of the cutting surface roughness of the workpiece will be smaller and steady, if the relief surface roughness becomes small. By contrast, the coverage of the cutting surface roughness of the workpiece will be larger and unsteady, if the relief

Fig. 3. The flank wear of the peripheral cutting edge in the end-mill with a cutting time of 1 min. for DIN 1.2344 tool steel; a) Ra = 0.18 μm, b) Ra = 0.32 μm

Fig. 4. The flank wear of peripheral cutting edge in the end-mill with a cutting time 150 min. for DIN 1.2344 tool steel; a) Ra = 0.18 μm, b) Ra = 0.32 μm The Effect of Surface Roughness of End-Mills on Optimal Cutting Performance for High-Speed Machining

127

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 124-134

a) Relief face Ra=0.32(μm)

0.40 0.30 0.20 0.10 0.00

0.40 0.30 0.20

50

100

150

200

0.00

Cutting time (min)

Relief face Ra=0.42(μm)

0.50

Relief face Ra=0.31(μm)

0.10

0

c)

0.60

Relief face Ra=0.41(μm)

0.50

Relief face Ra=0.18(μm)

Ra (μm)

Ra (μm)

0.50

b)

0.60

Ra (μm)

0.60

Relief face Ra=0.29(μm)

0.40 0.30 0.20 0.10

0

20

40

60

80 100

Cutting time (min)

0.00

0

20

40

60

Cutting time (min)

80

Fig. 5. Effect of cutting time on the surface roughness of the workpiece; a) cutting parameters: V = 251.32 m/min, F = 0.06 mm/tooth, Da = 1.0 mm, Dr = 0.75 mm; b) cutting parameters: V = 351.85 m/min, F = 0.02 mm/tooth, Da = 1.0 mm, Dr = 1.0 mm; c) cutting parameters: V = 452.38 m/min, F = 0.1 mm/tooth, Da = 1.0 mm, Dr = 0.5mm

surface roughness becomes large. The difference between both average surface roughnesses is 0.131 μm. As shown in Figs. 5b and c, even under other cutting conditions, the experiments still result in the same outcome. Thus it has been proved that the relief surface roughness is an important parameter in highspeed milling.

3 EXPERIMENTAL DISIGN AND RESULTS 3.1 Experimental Design The influences of the surface roughness of the relief face on the cutting performance using HSC and the optimal level determination of processing parameters will be analysed. The cutting performance of the end-mill for HSC is relevantly correlated with the processing parameters (the surface roughness of the relief face (A), cutting speed (B), feed per tooth (C), axial cutting depth (D), and radial cutting depth (E)), which are regarded as controllable factors in the study. The selected processing parameters and their assigned value of the level are listed in Table 3. Here, the grinding parameters of A1 (0.23±0.03 μm) in this study are as follows: grit size of the diamond wheel = M25, grinding speed = 1650 m/min, and feed speed = 600 mm/min. The same parameters of A2 (0.43±0.02 μm) are as follows: grit size of the diamond wheel = D46, grinding speed = 1650 m/min, and feed speed = 900 mm/min. The tool grinding times are 621 and 405 s. Here A1 and A2 indicate the roughnesses of the tool coated with TiAlN after grinding.

128

Table 3. Processing parameters and their levels Symbol Processing parameter Level 1 Level 2 Surface roughness of A 0.23±0.03 0.43±0.02 the relief face [μm] Cutting speed B 251.32 351.85 [m/min] Feed per tooth C 0.02 0.06 [mm/tooth] Axial cutting depth D 0.50 1.00 [mm] Radial cutting depth E 0.50 0.75 [mm]

Level 3

452.38 0.10 1.50 1.00

Selecting the orthogonal array involves the total degree of freedom of the processing parameters.

The degree of freedom is defined as the number of comparisons among the process parameters required to optimise the parameters. Here one processing parameter is available for 2 levels and four processing parameters are suitable for 3 levels. This experimental arrangement does not consider the interaction among the processing parameters. The freedom of the processing parameter is the level minus one. Here, the total freedoms are 9 so the L18 orthogonal array is utilized for the experimental plan. Table 4 shows the configuration of processing parameters according to the L18 orthogonal array.

The tool life and wear rate of the cutting edge are analysed. The cutting performance can be evaluated according to the wear rate, which can be classified as peripheral and end wear rate. The metal removal rate governs the removal volume during cutting. A high metal removal rate is generally better, but decreases the tool life. Therefore, in this study an optimal method for processing parameters with a minimum

Chen, C.H. – Wang, Y.C. – Lee, B.Y.

StrojniĹĄki vestnik - Journal of Mechanical Engineering 59(2013)2, 124-134

wear rate and maximum metal removal rate has been proposed. The peripheral wear rate (TWR1), end wear rate (TWR2), and metal removal rate (MRR) are defined in the following equations. average width of flank wear of peripheral cutting edge TWR1 = , (6)

cutting time average width of flank wear of end cutting edge TWR 2 = , (7) cutting time

MRR =

total metal removal volums . (8) cutting time

3.2 Experimental Results Based on the experimental layout as illustrated in Table 4, the experiments are performed in series and each specific experiment is repeated two times. The procedures are described as follows: 1. The overhang length of the tools is selected at a fixed value of 20 mm.

2. The tool dynamic under test is required to be less than 0.02 G.

3. The eperiment ends if flank wear (VB) reaches 0.2 mm (ISO 3002/1).

The cutting duration and volume of metal removal are then calculated. Peripheral and end flank wear quantity are measured using a OLYMPUS STM5-BDZ microscope. According to Eqs. (6) to (8), flank wear and metal removal rate can be analysed, with those results listed in Table 4.

4 ANALYSES AND DISCUSSION The optimisation issue of multiple performance characteristics is analysed by using the grey relation method. Optimal design of processing parameters is described as follows: 1. Experimental results converted into S/N ratio.

2. Normalization of S/N ratio.

3. Analysis of grey relation coefficient.

4. Calculation of grey relation grade.

5. Analysis of variation (ANOVA).

6. Determination of optimal level of processing parameters.

7. Conduct confirmation experiments.

4.1 Optimal Combination of the Processing Parameters Performance characteristics are first converted into the S/N ratio using the Taguchi method. Using S/N

Table 4. Experimental layout and results Experimental layout No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

A

B

C

D

E

Cutting Time [min]

0.24 0.20 0.20 0.22 0.25 0.22 0.23 0.21 0.25 0.42 0.45 0.42 0.45 0.42 0.43 0.45 0.42 0.45

251.32 251.32 251.32 351.85 351.85 351.85 452.38 452.38 452.38 251.32 251.32 251.32 351.85 351.85 351.85 452.38 452.38 452.38

0.02 0.06 0.10 0.02 0.06 0.10 0.02 0.06 0.10 0.02 0.06 0.10 0.02 0.06 0.10 0.02 0.06 0.10

0.50 1.00 1.50 0.50 1.00 1.50 1.00 1.50 0.50 1.50 0.50 1.00 1.00 1.50 0.50 1.50 0.50 1.00

0.50 0.75 1.00 0.75 1.00 0.50 0.50 0.75 1.00 1.00 0.50 0.75 1.00 0.50 0.75 0.75 1.00 0.50

140.39 188.53 156.05 141.40 53.03 98.98 80.55 44.19 43.18 119.69 194.43 170.29 79.12 76.59 98.98 37.62 53.03 74.24

1 12.77 8.12 13.83 13.58 30.08 15.48 23.25 47.92 40.99 16.19 9.86 7.60 24.90 22.78 18.36 52.89 33.80 29.27

Experimental and analysis results Flank wear rate [mm/min]Ă&#x2014;10-4 TWR1 TWR2 2 1 13.77 8.05 9.30 6.62 13.95 9.52 12.96 8.82 30.55 22.58 15.36 13.23 22.47 14.87 46.85 24.38 40.53 41.11 16.13 10.95 9.76 8.49 7.66 11.52 23.86 11.98 22.07 15.44 18.41 15.81 53.82 23.86 33.71 21.17 28.76 15.90

The Effect of Surface Roughness of End-Mills on Optimal Cutting Performance for High-Speed Machining

2 8.08 6.55 9.97 8.59 22.77 14.04 15.15 23.14 41.46 10.42 8.59 10.26 13.30 15.90 15.81 23.39 21.45 16.47

MRR [mm3/min] 200 1800 6000 450 3600 4500 800 5400 4000 1200 600 3000 1200 2700 2250 1800 2400 4000

129

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 124-134

Table 5. Optimization process of processing parameters No 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Sequences of S/N ratio TWR1 TWR2 MRR -22.47 -18.13 46.02 -18.84 -16.37 65.11 -22.85 -19.78 75.56 -22.46 -18.80 53.06 -29.63 -27.11 71.13 -23.76 -22.70 73.06 -27.18 -23.53 58.06 -33.51 -27.52 74.65 -32.21 -32.32 72.04 -24.17 -20.58 61.58 -19.83 -18.63 55.56 -17.66 -20.77 69.54 -27.74 -22.06 61.58 -27.02 -23.90 68.63 -25.29 -23.98 67.04 -34.54 -27.47 65.11 -30.57 -26.57 67.60 -29.25 -24.18 72.04

Normalized S/N ratio TWR1 TWR2 MRR 0.72 0.89 0.00 0.93 1.00 0.65 0.69 0.79 1.00 0.72 0.85 0.24 0.29 0.33 0.85 0.64 0.60 0.92 0.44 0.55 0.41 0.06 0.30 0.97 0.14 0.00 0.88 0.61 0.74 0.53 0.87 0.86 0.32 1.00 0.72 0.80 0.40 0.64 0.53 0.45 0.53 0.77 0.55 0.52 0.71 0.00 0.30 0.65 0.24 0.36 0.73 0.31 0.51 0.88

quantity, optimal performance and minimal variance can be designed. A longer tool life generally implies a higher metal removal rate and better cutting performance. Therefore, the wear rate should be at a minimum and the metal removal rate should be at a maximum. The results in Table 4 are substituted in Eqs. (1) and (2). Table 5 lists the S/N ratio of TWR1, TWR2, and MRR. The S/N ratio can be used for performance analysis. Moreover, a higher S/N ratio should improve the performance characteristics. Based on Eq. (3), the S/N ratio in Table 5 can be normalized for a better comparison. To compare with the original sequences (ideal sequences / (1, 1, 1)), they should be converted into grey relational coefficients by Eq. (4) so that the quantities range from 0.33 to 1. A higher relationship with a distinguishing coefficient leads to a higher distinguishing coefficient. The distinguishing coefficient is normally 0.5. By using Eq. (5), Table 5 shows the grey relation grade of multiple performance characteristics. According to this table, the grey relation grade of the second group is at the maximum (0.82), implying that its multiple performance characteristic is the optimum result in 18 groups.

The grey relational grade for each level of the processing parameters is summarised and shown in Table 6. In addition, the total mean of the grey relational grade for the 18×2 experiments is also calculated to be 0.596. Basically, the larger the grey relational grade, the better the multiple performance characteristics. However, the relative importance 130

Grey relational coefficient TWR1 TWR2 MRR 0.64 0.82 0.33 0.88 1.00 0.59 0.62 0.70 1.00 0.64 0.77 0.40 0.41 0.43 0.77 0.58 0.56 0.86 0.47 0.53 0.46 0.35 0.42 0.94 0.37 0.33 0.81 0.56 0.65 0.51 0.79 0.78 0.42 1.00 0.64 0.71 0.46 0.58 0.51 0.47 0.51 0.68 0.53 0.51 0.63 0.33 0.42 0.59 0.40 0.44 0.65 0.42 0.51 0.81

Grey relational grade

Orders

0.60 0.82 0.77 0.60 0.54 0.66 0.48 0.57 0.50 0.58 0.67 0.78 0.52 0.56 0.56 0.45 0.49 0.58

7 1 3 6 13 5 17 10 15 9 4 2 14 12 11 18 16 8

among the processing parameters for multiple performance characteristics still needs to be known, so that the optimal combinations of the processing parameter levels can be determined.

4.2 Analysis of Variance Variance analysis is employed to determine the influence of processing parameters on multiple performance characteristics by a statistical method.

Additionally, the F test and P test are performed to verify which end-mill for HSC process parameters significantly affects the performance characteristics.

A P-value < α represents a significant difference.

In addition, a larger F-value and a smaller P-value indicate more significant differences. In this study, the value of α is 0.05. Table 7 demonstrates that cutting speed (B) and feed per tooth (C) significantly affect the multiple performance characteristics, i.e. tool life and metal removal rate, because their corresponding F ratio is greater than 4.46, corresponding to the ratio of F0.05 (2, 8) and P-value less than 0.05. The surface roughness ratio of the relief face is 3.87% from the results of variance analysis, therefore, this parameter is inconspicuous in terms of the influence of the cutting performance characteristics. The relative error is 9.57% so that in this experiment there are no important factors neglected. The results are thus satisfactory. Based on the above discussion, the optimal processing parameters are as follows: the

Chen, C.H. – Wang, Y.C. – Lee, B.Y.

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 124-134

Table 6. Response table for the grey relational grade Symbol Processing parameter Level 1 A Surface roughness of relief face 0.616 B Cutting speed 0.703 C Feed per tooth 0.537 D Axial cutting depth 0.570 E Radial cutting depth 0.591 Total mean value of the grey relational grade = 0.596

Level 2 0.575 0.572 0.607 0.620 0.630

Level 3

Max-Min 0.041 0.191 0.106 0.051 0.063

0.512 0.643 0.598 0.567

Ranking 5 1 2 4 3

Table 7. Results of the analysis of variance Symbol Processing parameter Degree of freedom Sum of square A Surface roughness of relief face 1 0.008 B Cutting speed 2 0.114 C Feed per tooth 2 0.035 D Axial cutting depth 2 0.008 E Radial cutting depth 2 0.012 Error 8 0.019 Total 17 0.195 F0.05(1,8) = 5.32, F0.05(2,8) = 4.46

Mean square 0.008 0.057 0.018 0.004 0.006 0.002

F value 3.238 24.459 7.498 1.668 2.553

P value 0.110 0.000 0.015 0.248 0.139

Contribution [%] 3.87 58.52 17.94 3.99 6.11 9.57 100.00

Table 8. Confirmation test results

Optimal Initial Final gain

Processing combination A1B1C3D2E2 A2B1C2D3E1

Tool life [min] 178.53 169.43 9.10

Total metal removal volumes [mm3] 535600 304970 230630

surface roughness of relief face at level one 0.23±0.03 μm, cutting speed at level one 251.32 m/min, feed per tooth at level three 0.1 mm/tooth, axial cutting depth at level two 1.0 mm, and radial cutting depth at level two 0.75 mm.

4.3 Verification Experiments After the optimal level of the processing parameters is obtained, improvement of the performance characteristics must then be verified by using these optimal processing parameters. Table 8 compares the results of the confirmation experiments using the optimal processing parameters (A1, B1, C3, D2, E2) obtained by the proposed method with those of the initial processing parameters (A2, B1, C2, D3, E1), as provided by Li-Hsing Precision Tool Manufacturing Company.

According to Table 8, tool life is defined as the total cutting time before the breakage of cutting edge of the tool or as the flank wear of cutting edge reaches 0.2mm (ISO 3002/1). This table also reveals a 5.37% increase in the tool life (i.e. from 169.43 to 178.53 min), a 75.62% increase in the total metal removal volumes (i.e. from 304974 to 535600 mm3),

Metal removal rate [mm3/min] 3000 1800 1200

Average surface roughness of workpiece [μm] 0.058 0.102 0.044

a 66.67% increase in the metal removal rate (i.e. from 1800 to 3000 mm3/min), and a 43.14% decrease in the average surface roughness of workpiece (i.e. from 0.102 to 0.058 μm). Figs. 6a and b show the effects of cutting time on flank wear of the cutting edge under the conditions of the initial processing parameters compared with those of the final optimal processing parameters. Consequently, the verification tests reveal that the proposed algorithm for solving the optimal processing parameters decrease the average surface roughness of the workpiece and increases both the tool life and metal removal rate.

4.4 Influence of Cutting Performance on the Surface Roughness of the Relief Face The ranges of surface roughness of the relief face for this study are from 0.23±0.03 to 0.43±0.02 [μm].

Fig. 7 shows the integrity of the cutting edge enlarged 200 fold by microscope (OLYMPUS STM5-BDZ).

In addition, it recognizes the integrity of the surface roughness of the relief face on the cutting edge of the difference. Importantly, Table 6 indicates that the surface roughness of the relief face using gray relational grade analysis for the difference is 0.041. In

The Effect of Surface Roughness of End-Mills on Optimal Cutting Performance for High-Speed Machining

131

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 124-134

a)

Flank wear (mm)

0.25 0.20 0.15 0.10 0.05 0.00

0

70

140

210

Cutting time(min)

Initial design Experimental No.12 Optimal design

0.25 0.20 0.15 0.10

Initial design Experimental No.12 Optimal design

0.40 0.30 0.20 0.10

0.05 0.00

c)

0.50

Ra (μm)

Initial design Experimental No.12 Optimal design

b)

0.30

Flank wear (mm)

0.30

0

70

140

210

Cutting time (min)

0.00

0

70

140

210

Cutting time(min)

Fig. 6. Effect of cutting time on cutting performance; a) flank wear of the peripheral cutting edge, b) flank wear of the end cutting edge, c) surface roughness of the workpiece a)

b)

Fig. 7. The cutting edge integrity of surface roughness of the relief face; a) Ra=0.23 μm, b) Ra=0.43 μm

Table 7, it can be seen that the surface roughness ratio of the relief face reveals a 3.87% difference from the results of the variance analysis.

By comparing the results of the optimal processing parameters (A1 B1 C3 D2 E2) with those of the No.12 experimental processing parameters (A2 B1 C3 D2 E2), there is a 4.84% increase in tool life (i.e. from 170.29 to 178.53 min). From Figs. 6a to c, the effect of cutting time on flank wear of the cutting edge and surface roughness of workpiece under the conditions of comparing the No.12 experimental processing parameters with those of the final optimal processing parameters can be summarized. Therefore, the surface roughness of the relief face parameter is inconspicuous in terms of the influence of the cutting performance characteristics. There are two explanations for this result.

First, Figs 6a and b demonstrate that the surface roughness of the relief face has no significant 132

influence on flank wear in HSC before 135 min of continuous cutting. In addition, as indicated in the Fig. 6c, the surface roughness of the relief face will essentially affect the surface roughness of the processed workpiece, i.e. with 48.21% decrease in the average surface roughness of workpiece (from 0.112 to 0.058 μm). However, the smaller surface roughness of the relief face (0.22 μm) will induce less flank wear and less surface roughness of the workpiece.

In terms of tool grinding, the surface roughness of relief face for this study will be set at 0.23±0.03 and 0.43±0.02 μm and the corresponding tool grinding times are 621 and 405 s, respectively. As mentioned above, grinding with the surface roughness of relief face at level 1 (0.23±0.03 μm) for the end-mill will lead to a 53.33% increase in grinding cost, but only a 4.84% increase in tool life. Due to a slight effect on cutting performance characteristics of the rough

Chen, C.H. – Wang, Y.C. – Lee, B.Y.

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 124-134

machining, A2 grinding conditions can be used to improve tool grinding efficiency.

5 CONCLUSIONS From the above descriptions and analyses, the optimal processing parameters of DIN 1.2344 tool steel will be determined by grey relational analysis. Clearly, the optimal results are only given under conditions of HSC in DIN 1.2344 tool steel. The results can be summarized as follows.

1. The surface roughness of the relief face levels are set at 0.23±0.03 and 0.43±0.02 μm for this study. According to the variance analysis results, the surface roughness of the relief face of an endmill slightly influences rough machining in HSC for DIN 1.2344 tool steel. In addition, it will essentially affect the surface roughness of the workpiece, there being a decline of 0.054 μm in the average surface roughness of workpiece (i.e. from optimal processing parameters to No.12 experimental processing parameters). Therefore, A2 grinding conditions (grit size of diamond wheel = D46, grinding speed = 1650 m/min, and feed speed = 900 mm/min) can be used to improve tool grinding efficiency.

2. Based on an analysis of variance, the major controllable factors significantly affecting multiple performance characteristics, i.e. tool life and metal removal rate, are cutting speed and feed per tooth with a desired total contribution of 76.46%.

3. The optimal combination obtained from the proposed method is the processing condition with a surface roughness of the relief face of 0.23±0.03 μm, cutting speed of 251.32 m/min, feed per tooth of 0.1 mm/tooth, axial cutting depth of 1.0 mm, and radial cutting depth of 0.75 mm. The corresponding verification tests indicate an improvement of 9.1 min in tool life, 1200 mm3/min in metal removal rate, 230616 mm3 in total metal removal volumes, and 0.044 μm in average surface roughness of workpiece from the initial parameters to the optimal parameters.

6 REFERENCES [1] Li, L., He, N., Wang, M., Wang, Z.G. (2002). High speed cutting of Inconel 718 with coated carbide and ceramic inserts. Journal of Materials Processing Technology, vol. 129, no. 1-3, p. 127-130, DOI:10.1016/S09240136(02)00590-3.

[2] Dolinsek, S., Sustarsic, B., Kopac, J. (2001). Wear mechanisms of cutting tools in high speed cutting process. Wear, vol. 250, no. 1-12, p. 349-356, DOI:10.1016/S0043-1648(01)00620-2.

[3] Malkin S. (1989). Grinding Technology: Theory and Applications of Machining with Abrasives. Society of Manufacturing Engineers, Michigan.

[4] Shaji, S., Radhakrishnan, V. (2003). Analysis of process parameters in surface grinding with graphite as lubricant based on the Taguchi method. Journal of Materials Processing Technology, vol. 141, no. 1, p. 51-59, DOI:10.1016/S0924-0136(02)01112-3.

[5] Yin, L., Spowage, A.C., Ramesh, K., Huang, H., Pickering, J.P., Vancoille, E.Y.J. (2004). Influence of microstructure on ultraprecision grinding of cemented carbides. International Journal of Machine Tools and Manufacture, vol. 44, no. 5, p. 533-543, DOI:10.1016/j. ijmachtools.2003.10.022.

[6] Kwak, J.S. (2005). Application of Taguchi and response surface methodologies for geometric error in surface grinding process. International Journal of Machine Tools and Manufacture, vol. 45, no. 3, p. 327-334, DOI:10.1016/j.ijmachtools.2004.08.007.

[7] Nguyen, T.A., Butler, D.L. (2005). Simulation of precision grinding process, Part 2: Interaction of the abrasive grain with the workpiece. International Journal of Machine Tools and Manufacture, vol. 45, no. 11, p.

1329-1336, DOI:10.1016/j.ijmachtools.2005.01.006.

[8] Park, S.H. (1996) Robust Design and Analysis for Quality Engineering. Springer, London.

[9] Dhavlikar, M.N., Kulkarni, M.S., Mariappan, V. (2003).

Combined Taguchi and dual response method for optimization of a centerless grinding operation. Journal of Materials Processing Technology, vol. 132, no. 1-3, p.

90-94, DOI:10.1016/S0924-0136(02)00271-6.

[10] Korkut, I., Kucuk, Y. (2010). Experimental analysis of the deviation from circularity of bored hole based on the taguchi method. Strojniški vestnik - Journal of Mechanical Engineering, vol. 56, no. 5, p. 340-346.

[11] Çiçek, A., Kıvak, T., Samtaş, G. (2012). Application of taguchi method for surface roughness and roundness error in drilling of AISI 316 stainless steel. Strojniški vestnik - Journal of Mechanical Engineering, vol. 58, no.

3, p. 165-174, DOI:10.5545/sv-jme.2011.167.

[12] Motorcu, A.R. (2010). The optimization of machining parameters using the taguchi method for surface roughness of AISI 8660 hardened alloy steel. Strojniški vestnik - Journal of Mechanical Engineering, vol. 56, no.

6, p. 391-401.

[13] Saglam, H., Yaldiz, S., Unsacar, F. (2007). The effect of tool geometry and cutting speed on main cutting force and tool tip temperature. Materials and Design, vol. 28, p. 101-111, DOI:10.1016/j.matdes.2005.05.015.

[14] Lin, J.L., Lin, J.F. (2006). Grey theory applied to evaluate the tribological performance of the a-C:H(N) coating films prepared by differing the nitrogen content and the film thickness. The International Journal of

The Effect of Surface Roughness of End-Mills on Optimal Cutting Performance for High-Speed Machining

133

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, 124-134

Advanced Manufacturing Technology, vol. 27, no. 9-10, p. 845-853, DOI:10.1007/s00170-004-2294-1.

[15] Panneerselvam, K., Pradeep, K. Asokan, P. (2012).

Optimization of end milling parameters for glass fiber reinforced plastic (GFRP) using grey relational analysis. Procedia Engineering, vol. 38, p. 3962-3968, DOI:10.1016/j.proeng.2012.06.453.

[16] Ilo, S., Just, Ch., Xhiku, F. (2012). Optimisation of multiple quality characteristics of hardfacing using greybased taguchi method. Materials and Design, vol. 33, p.

459-468, DOI:10.1016/j.matdes.2011.04.050.

[17] Sahoo, A.K., Baral, A.N., Rout, A.K., Routra, B.C. Multi-objective optimization and predictive modeling of

134

surface roughness and material removal rate in turning using grey relational and regression analysis. Procedia Engineering, vol. 38, p. 1606-1627.

[18] Palanikumar, K. (2011). Experimental investigation and optimisation in drilling of GFRP composites.

Measurement, vol. 44, p. 2138-2148, DOI:10.1016/j. measurement.2011.07.023.

[19] Ross, P.J. (1988). Taguchi Techniques for Quality Engineering. McGraw-Hill, New York.

[20] Deng, J.L. (1989). Introduction to Grey system.

The Journal of Grey System, vol. 1, no. 1, p. 1-24.

Chen, C.H. – Wang, Y.C. – Lee, B.Y.

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2 Vsebina

Vsebina Strojniški vestnik - Journal of Mechanical Engineering letnik 59, (2013), številka 2 Ljubljana, februar 2013 ISSN 0039-2480 Izhaja mesečno

Razširjeni povzetki člankov Luka Knez, Janko Slavič, Miha Boltežar: Večosni biodinamični merilni ročaj za merjenje sistema dlan-roka Jianping Li, Songyong Liu, Changlong Du: Eksperimentalna raziskava in računalniška simulacija tehnologije brusilnega utrjanja Aleksander Preglej, Igor Steiner, Sašo Blažič: Multivariabilno prediktivno funkcijsko vodenje avtoklava Eda Okutan, Sedat Karabay, Tamer Sınmazçelik, Egemen Avcu: Izpeljava parametričnih enačb za rezalno silo pri vrtanju polimerov, ojačenih s steklenimi vlakni Irina Stefanova Aleksandrova, Gancho Nenkov Ganev: Orodja za kombinirano izdelavo navojev z odrezavanjem in preoblikovanjem Simon Štampar, Saša Sokolič, Gorazd Karer: Nelinearno vodenje temperature hibridnega šaržnega reaktorja Chi-Hsiang Chen, Yung-Cheng Wang, Bean-Yin Lee: Vpliv površinske hrapavosti steblastih rezkarjev na optimalno zmogljivost visokohitrostnega odrezavanja

SI 15 SI 16 SI 17 SI 18 SI 19 SI 20 SI 21

Osebne vesti Diplomske naloge

SI 22

V spomin prof. dr. Francu Schweigerju

SI 24

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, SI 15 © 2013 Strojniški vestnik. Vse pravice pridržane.

Prejeto v recenzijo: 2012-07-20 Prejeto popravljeno: 2012-11-27 Odobreno za objavo: 2012-12-06

Večosni biodinamični merilni ročaj za merjenje sistema dlan-roka Luka Knez – Janko Slavič* – Miha Boltežar Univerza v Ljubljani, Fakulteta za strojništvo, Slovenija Metoda biodinamičnega odziva se vse pogosteje uporablja za raziskovanje vpliva vibracij na človeške roke ter za proučevanje vibracijskih bolezni, ki prizadenejo roko. Kot pove že ime, pride do nastanka vibracijskih bolezni takrat, kadar je roka ali njen del daljše časovno obdobje izpostavljena vibracijam. Prenosnost vibracij v posamezne dele roke, ki jih s skupno besedo poimenujemo sistem dlan-roka, razberemo iz dinamskih lastnosti rok, merjenih na dlani, pri prstih ter naprej po roki do rame. Večina meritev se izvaja le v glavni smeri vzbujanja, t.j. v smeri podlakti, pred kratkim pa se je začelo raziskovati tudi večosno vzbujanje rok. Merilni ročaji, ki bi bili sposobni meriti biodinamične odzive rok v več smereh, so še v fazi razvoja, zato je to področje še bolj ali manj neraziskano.

Ta članek predstavlja nov merilni ročaj, ki meri biodinamični odziv ločeno na dlani in pri prstih za več smeri vzbujanj. Ena od prednosti razvitega ročaja je sočasna meritev biodinamičnega odziva dlani in prstov, zato ni več treba ustavljati meritve in spreminjati položaj ročaja, kot je bilo običajno pri do sedaj razvitih napravah. Poleg samega biodinamičnega odziva lahko zaznavala v ročaju merijo tudi kvazi statične sile. Meritve statične pridržalne in delovne sile so bistvenega pomena, saj omogočajo primerjavo podatkov, dobljenih z različnimi merilnimi metodami, prav tako pa se lahko preučuje vpliv velikosti teh dveh sil na prenosnost vibracij v roko. Z zaznavali, vgrajenimi v ročaju, lahko merilni sistem poleg pridržalne sile, ki jo običajno zajemamo na samem ročaju, meri tudi delovno silo. Tako ni več potrebe po plošči s silomeri, ki se običajno uporablja za merjenje delovne sile.

Razviti pristop poenostavi postopek merjenja, hkrati pa zmanjša tudi možnosti napak, ki se lahko pojavijo pri meritvah.

Za določitev uporabnega frekvenčnega področja, v katerem razviti merilni sistem meri zanesljivo, je bila najprej podrobno preverjena dinamična masa samega ročaja. Ta se namreč ne sme bistveno spreminjati, dokler se ne približa kateremu od resonančnih vrhov lastne dinamike ročaja. Na podlagi meritev je bilo dokazano, da se ročaj lahko uporablja za biodinamične meritve v razponu od 10 do 500 Hz. V to frekvenčno področje sodi večina ročnih orodij, ki običajno vzbujajo roke in povzročajo poškodbe.

Roka ima kompleksno anatomijo, sestavljeno iz raznih tkiv, mišic in kosti, ki imajo različne materialne in posledično tudi dinamske lastnosti. Nekateri deli roke so torej občutljivejši na vibracije kot drugi, v okviru te raziskave pa je bila zato izmerjena tudi porazdelitev dinamične mase po roki za podrobnejšo preučitev obremenjenosti roke. Ugotovljeno je bilo, da je porazdelitev dinamične mase odvisna od frekvence, iz česar sklepamo o različni občutljivosti posameznih delov roke na vibracije.

Meritve so bile zaradi omejitev opreme sicer opravljene le v dveh od treh možnih smeri vzbujanja, vendar predstavljeni ročaj omogoča sočasen zajem v vseh treh medsebojno pravokotnih smereh. Zagotoviti je treba le ustrezen vzbujevalni sistem. S predstavljenim ročajem se lahko preuči vpliv večosnega vzbujanja na roko, kar je bilo do sedaj težko izvedljivo, predvsem zaradi pomanjkanja merilnih podatkov. V bodoče je treba tudi raziskati, ali ugotovitve, ki so jih raziskovalci dobili z vzbujanjem v smeri podlakti, veljajo za vse smeri vzbujanja.

Ključne besede: biodinamični odziv, sistem dlan-roka, večosne meritve, porazdelitev dinamične mase, merilni ročaj, ločeno merjenje dlani in prstov

*Naslov avtorja za dopisovanje: Univerza v Ljubljani, Fakulteta za strojništvo, Aškerčeva 6, 1000 Ljubljana, Slovenija, janko.slavic@fs.uni-lj.si

SI 15

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, SI 16 © 2013 Strojniški vestnik. Vse pravice pridržane.

Prejeto v recenzijo: 2012-07-04 Prejeto popravljeno: 2012-09-17 Odobreno za objavo: 2012-11-21

Eksperimentalna raziskava in računalniška simulacija tehnologije brusilnega utrjanja Jianping Li* – Songyong Liu – Changlong Du Kitajska univerza za rudarstvo in tehnologijo, Fakulteta za strojništvo in elektrotehniko, Kitajska

Brusilno utrjanje je nova tehnologija, ki izkorišča toploto pri brušenju za martenzitno transformacijo in utrjanje površine obdelovanca med procesom brušenja z dvigom površinske temperature Ac3, ki mu sledi hitro hlajenje.

Uporaba nove tehnologije omogoča skrajšanje proizvodnih ciklov, izboljšanje delovne učinkovitosti in zmanjšanje proizvodnih stroškov z združitvijo operacij brušenja in površinske toplotne obdelave, to pa prinaša velike družbene in gospodarske koristi.

Brusilno utrjanje je tehnologija površinskega utrjanja z izkoriščanjem toplote, ki se sprošča pri brušenju.

Tehnologija omogoča površinsko utrjanje na brusilnih strojih. Kot ekološki in visokoučinkovit postopek obdelave ima velik potencial pri strojni obdelavi. Raziskava predstavlja eksperimente, računalniške simulacije in napovedi učinkov brusilnega utrjanja, zato je uporabna kot vodič pri osvajanju tehnologije in popularizaciji tehnologije v praksi.

Glede na način podajanja je operacije brušenja v preizkusu mogoče razdeliti na (1) enosmerno čelno brušenje in (2) globoko brušenje.

(1) Enosmerno čelno brušenje: neposredno brušenje obdelovanca s čelom brusa; dodatek za brušenje se v celoti odstrani v enem koraku.

(2) Globoko brušenje oz. horizontalno brušenje: brus počasi zarezuje v obdelovanec s hitrostjo vf, dokler ni odstranjen ves dodatek za brušenje.

Pri preizkusih je bilo uporabljeno poboljšano jeklo C45E4, površina obdelovanca pa je bila v obliki prstana (bok prehoda stopničaste gredi). Enota je mm.

Izvedeni so bili eksperimenti brusilnega utrjanja z jeklom C45E4 pri različnih pogojih. Metalografske preiskave, analiza površinske trdote in meritve globine utrjenega sloja kažejo, da je prišlo do martenzitne transformacije na površini obdelovanca in da je nastal utrjen površinski sloj določene debeline. S tem je potrjena uporabnost tehnologije brusilnega utrjevanja.

S sistematično eksperimentalno raziskavo tehnoloških parametrov kot so velikost kontaktne površine, smer brušenja, parametri brušenja in hladilna tekočina je mogoče opredeliti zvezo med tehnološkimi parametri in trdoto brusilno utrjene površine ter globino utrjenega sloja za izbiro primernih parametrov obdelave z brusilnim utrjanjem.

Točke na različnih oddaljenostih od površine brusa imajo različno obodno hitrost, zato je spremenljiva tudi intenzivnost toplotnih virov. Spremenljiva brusilna širina zato povzroči spremenljivo porazdelitev učinka brusilnega utrjanja: Enosmerno čelno brušenje ima visoko učinkovitost brušenja, vendar lahko povzroči spremenljivo porazdelitev trdote in globine utrjenega sloja. Globoko brušenje daje enakomeren utrjen sloj, trdota in globina utrjenega sloja pa se zmanjšujeta s povečevanjem podajanja, oziroma povečujeta z globino in hitrostjo brušenja. Največji vpliv ima globina brušenja, ki ji sledi podajanje, najmanj izražen pa je vpliv hitrost brušenja.

Na podlagi značilnosti čelnega brušenja in porazdelitve temperaturnega polja je bil opredeljen model toplotnega vira za čelno brušenje. S simulacijo temperaturnega polja pri brušenju po metodi končnih elementov v programski opremi ANSYS je bila ugotovljena spremenljiva temperatura točk na površini obdelovanca in dinamična stanja temperaturnega polja. Rezultati simulacije se ujemajo z eksperimentalnimi vrednostmi, s tem pa je potrjena primernost simulacijske metode za preučevanje brusilnega utrjanja.

Nova tehnologija omogoča skrajšanje proizvodnih ciklov, izboljšanje delovne učinkovitosti in zmanjšanje proizvodnih stroškov z združevanjem operacij brušenja in površinske toplotne obdelave, to pa prinaša velike družbene in ekonomske koristi. Ker je bil čas raziskave kratek, ostajajo številni vidiki (način brušenja, vplivni faktorji in vzorci, temperatura in sile med procesom ipd.) neraziskani.

Ključne besede: čelno brušenje, brusilno utrjanje, eksperimentalna študija, temperaturno polje, površinska trdota, globina utrjenega sloja, simulacija MKE, programska oprema ANSYS

SI 16

*Naslov avtorja za dopisovanje: Kitajska univerza za rudarstvo in tehnologijo, Fakulteta za strojništvo in elektrotehniko, Xuzhou, Jiangsu 221116, Kitajska, 13505205658@163.com.

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, SI 17 © 2013 Strojniški vestnik. Vse pravice pridržane.

Prejeto v recenzijo: 2012-05-25 Prejeto popravljeno: 2012-11-08 Odobreno za objavo: 2012-11-15

Multivariabilno prediktivno funkcijsko vodenje avtoklava Preglej, A. – Steiner, I. – Blažič, S. Aleksander Preglej1,* – Igor Steiner1 – Sašo Blažič2

2 Univerza

1 INEA d.o.o., Slovenija v Ljubljani, Fakulteta za elektrotehniko, Slovenija

V prispevku je predstavljeno prediktivno funkcijsko vodenje avtoklava na uni- (PFC) in multi- (MPFC) variabilen način. Vodenje je načrtano na podlagi zgrajenega matematičnega modela avtoklava, kjer smo se ukvarjali s procesi prehoda toplote in spreminjanja tlaka z delovnim območjem temperature do 180 °C in tlaka do 7 bar.

Najprej smo zapisali enostavne osnovne principe prediktivnega vodenja. Algoritem temelji na eksplicitni uporabi dinamičnega modela za napoved prihodnjega izhoda procesa čez končni horizont in določitev prihodnje regulirne akcije tako, da minimizira izbrano kriterijsko funkcijo. Regulirna akcija poskrbi, da napovedani izhod procesa sovpada z referenčno trajektorijo, ki je podana v obliki referenčnega modela. Glavna ideja prediktivnega vodenja je izenačitev spremembe izhoda procesa in spremembe izhoda modela, od koder dobimo regulacijski zakon.

Nadalje smo predstavili regulacijski zakon prediktivnega vodenja, razširjen za multivariabilne (MV) sisteme.

Problem zakasnitev procesa se zaobide s pomožno spremenljivko izhoda nezakasnjenega procesa, zato model nezakasnjenega procesa podamo v diskretnem MV-prostoru stanj. Ostali principi so enaki univariabilnemu (UV) prediktivnemu vodenju, kjer se referenčni model prav tako poda v obliki diskretnega prostora stanj.

V nadaljevanju smo povzeli pravila za nastavljanje parametrov obeh prediktivnih regulatorjev, ki običajno dajejo najboljše rezultate glede na kakovost vodenja in robustnost. Prva zahteva je poznan model procesa, ki ga v primeru PFC lahko zapišemo s časovno konstanto, ojačenjem in zakasnitvijo, v primeru MPFC pa v obliki diskretnega prostora stanj s sistemsko, vhodno in izhodno matriko. Od tukaj najprej je treba podati le dva parametra; prvi je referenčni model, ki je v primeru PFC podan z želeno časovno konstanto sistema, v primeru MPFC pa v obliki diskretnega prostora stanj, kjer podamo le sistemsko matriko. Drugi parameter je horizont, v katerem želimo, da se zaprtozančni odziv sistema čim bolj prilega referenčnemu odzivu. Zaradi enostavnosti je tudi ta parameter povezan s prvim parametrom.

Oba prediktivna algoritma smo implementirali na linearizirana in poenostavljena modela avtoklava, za primerjavo pa smo načrtali in implementirali tudi klasičen PI-kompenzator. Rezultati kažejo izredno učinkovitost pristopa MPFC. Sicer imajo odzivi z vsemi tremi algoritmi podobno hiter dvižni čas, vendar se odziva pri PI in PFC precej počasneje približata želeni vrednosti zaradi počasnejše nastavitve regulatorjev, saj so bili izhodi regulatorjev pri hitrejših nastavitvah zelo nemirni. Križne povezave MV-sistema sicer pri modelu avtoklava niso močne, zato se pri izničenju vplivov interakcij oba prediktivna algoritma izkažeta podobno, medtem ko PIalgoritem deluje precej slabše. Pri modelih z močnejšimi križnimi povezavami pa pristop MPFC pokaže svoje bistvene prednosti pred pristopom PFC pri izničenju vplivov interakcij in tako lahko zaključimo, da je proces avtoklava smiselno voditi z algoritmom MPFC. Možnosti za nadaljnje delo se kažejo v mehkem pristopu k vodenju avtoklava, saj ima le-ta široko delovno področje in zelo različne režime delovanja, zato se model procesa v različnih delovnih točkah lahko razlikuje.

Smiselno bi bilo razviti mehki model avtoklava po celotnem delovnem področju in za vodenje uporabiti multivariabilni prediktivni funkcijski algoritem na podlagi mehkega modela (FMBMPC).

Pri prikazanem postopku implementacije MPFC vodenja avtoklava je kljub MV-naravi procesa poudarek na enostavnosti. Večina klasičnih MV-pristopov vodenja zahteva komplicirano načrtovanje in implementacijo, zaradi česar je MV-vodenje nepriljubljeno v industrijskem okolju. Klasični UV-pristopi pa pogosto slabo izničijo vplive interakcij MV-sistema. Predstavljeni pristop k vodenju MPFC pa je enostaven tako za načrtovanje kot tudi za implementacijo, zato bi bil primeren za preizkus in uporabo na realni MV-napravi v industriji. Tako je predstavljeni pristop lahko uporaben za strokovnjake, ki se ukvarjajo z vodenjem kompleksnejših procesov MV-narave, hkrati pa je algoritem relativno enostavno razširljiv za vodenje MV-procesov na podlagi mehkega modela, kar še dodatno razširi njegovo uporabnost.

Ključne besede: prediktivno vodenje, multivariabilno vodenje, avtoklav, temperatura, tlak, križne povezave

*Naslov avtorja za dopisovanje: INEA d.o.o., Stegne 11, 1000 Ljubljana, Slovenija, aleksander.preglej@inea.si

SI 17

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, SI 18 © 2013 Strojniški vestnik. Vse pravice pridržane.

Prejeto v recenzijo: 2012-08-31 Prejeto popravljeno: 2012-11-16 Odobreno za objavo: 2013-01-14

Izpeljava parametričnih enačb za rezalno silo pri vrtanju polimerov, ojačenih s steklenimi vlakni Eda Okutan – Sedat Karabay – Tamer Sınmazçelik – Egemen Avcu Eda Okutan* – Sedat Karabay – Tamer Sınmazçelik – Egemen Avcu Univerza v Kocaeliju, Oddelek za strojništvo, Turčija

V članku je predstavljena izpeljava enačb za sile pri vrtanju polimerov, ojačenih s steklenimi vlakni, usmerjenimi pod kotom 0°/+45°/90°/–45° (GFRP).

Vrtanje v kompozitni material GFRP je bilo opravljeno s posebej zasnovanim vrtalnim sistemom, dinamika vrtalnega navora in potisne sile pri različnih podajalnih hitrostih in premerih vrtanja pa je bila zajeta s pomočjo dinamometra, ojačevalnika in računalnika. Opredeljen je bil model za vrtanje GFRP in preizkušena je bila njegova veljavnost. Eksperimentalni podatki so bili ovrednoteni z matematičnimi modeli, ki določajo empirične povezave med ključnimi parametri. Rezalne sile pri vrtanju GFRP so bile izračunane na osnovi empiričnih enačb, rezultati pa so bili nato primerjani z rezultati meritev za verifikacijo izpeljanih enačb. Preučena je bila tudi morfologija površine lukenj v vzorcih GFRP s pomočjo povečave pod optičnim mikroskopom in vrstičnim elektronskim mikroskopom (SEM).

Obdelava je bila izvedena na vzorcih GFRP. Med obdelavo sta bila merjena navor in potisna sila pri različnih podajalnih hitrostih in premerih vrtanja s pomočjo kombinacije dinamometra, ojačevalnika in računalnika.

Eksperimentalni podatki so bili nato ovrednoteni z matematičnimi modeli, ki določajo empirične povezave med ključnimi parametri. Rezalne sile pri vrtanju GFRP so bile izračunane na osnovi empiričnih enačb, rezultati pa so bili nato primerjani z rezultati meritev za verifikacijo izpeljanih enačb.

Izkazalo se je, da se ob povečevanju premera svedra in podajalne hitrosti pri obdelavi GFRP povečata potisna sila in vrtalni navor. Rezultati tudi potrjujejo, da se s povečevanjem premera svedra povečuje količina materiala nepreoblikovanih odrezkov.

Primerjava izmerjenih in empiričnih rezultatov za sile pri vrtanju kaže določene razlike. Takšnim rezultatom se ni mogoče izogniti zaradi mikrostrukture GFRP. Ni presenetljivo, da se pri obdelavi kompozitnih materialov neizotropne narave kažejo večja nihanja kot pri obdelavi homogenih, izotropnih ali kvaziizotropnih materialov.

Te razlike pa niso zelo pomembne za ocenjevanje velikosti sil pri obdelavi z empiričnimi enačbami. Empirične enačbe namreč ne dajejo natančnih vrednosti, ampak le orientacijske vrednosti. Izpeljana empirična razmerja so ob upoštevanju določenih odstopanj za materiale podobne vrste primerna za prve faze snovanja in konstrukcije.

Glavni cilj te študije je bil poiskati povezave med rezalnimi silami in ključnimi parametri obdelovalnega stroja. Zelo pomembne so tudi kakovost površine izvrtine in poškodbe, ki nastanejo ob podajanju svedra v material.

Na izstopni strani lukenj se je sicer pojavila delaminacija, ugotovljena pa je bilo, da sta kakovost površine in dimenzijska natančnost luknje sprejemljiva za mehanske zveze z vijaki. Kakovost in hrapavost površine obdelanih lukenj sta posledica nezvezne zgradbe GFRP. Te nezveznosti v umetnih materialih so tudi ključni razlog za nihanja sile.

V gradbeništvu, letalski in avtomobilski industriji se pogosto pojavlja potreba po vrtanju v konstrukcijske dele iz kompozitov, le malo pa je znanega o interakciji med vrtalnim orodjem in materialom. Študija osvetljuje vprašanje, ali je verificirani model za železove zlitine uporaben tudi za prvo oceno rezalnih sil pri obdelavi kompozitov vrste GFRP. Izkazalo se je, da so sile pri vrtanju v dele gradbenih in strojnih konstrukcij enostavno določljive. Konstruktorjem so tako na voljo praktične informacije za preprečevanje čezmerne sile, ki bi lahko poškodovale kompozitne konstrukcije.

Shawov in Oxfordov model, ki je bil razvit za kovine, je tako inovativno uporabljen na GFRP. Ključne besede: GFRP, obdelovalnost, morfologija površine, potisna sila, vrtalni navor, empirična enačba

SI 18

*Naslov avtorja za dopisovanje: Univerza v Kocaeliju, Oddelek za strojništvo, Umuttepe Campus, Kocaeli, Turčija, avcuegemen@gmail.com

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, SI 19 © 2013 Strojniški vestnik. Vse pravice pridržane.

Prejeto v recenzijo: 2012-08-01 Prejeto popravljeno: 2012-12-05 Odobreno za objavo: 2013-01-14

Orodja za kombinirano izdelavo navojev z odrezavanjem in preoblikovanjem Aleksandrova, I. – Ganev, G. Irina Stefanova Aleksandrova* – Gancho Nenkov Ganev

Tehniška univerza v Gabrovem, Oddelek za opremo in tehnologije v strojništvu, Bolgarija

Izdelava notranjih navojev, zlasti navojev manjših dimenzij, predstavlja tehnološki problem zaradi nezadostne trdnosti in zanesljivosti uporabljenih orodij (navojnih svedrov). Snovanje in uporaba novih orodnih materialov ter vključevanje optimalne tehnološke opreme in novih vrst hladilno-mazalnih tekočin ne rešuje izziva visokoučinkovite in kakovostne izdelave notranjih navojev. Zato so nujne nenehne izboljšave zasnov navojnih rezkarjev, optimizacija geometrije teles teh orodij in izboljšave tehnologije izdelave navojnih svedrov, ki so najbolj razširjeno orodje za izdelavo notranjih navojev. Članek obravnava konstrukcijski in tehnološki razvoj ter predstavlja eksperimentalno študijo nove zasnove orodij za izdelavo navojev z odrezavanjem in preoblikovanjem, ki zagotavlja izboljšano trdnost in zanesljivost.

V članku je predstavljena teoretična in eksperimentalna obravnava možnosti izboljšanja trdnosti navojnih svedrov z zasnovo kombiniranih orodij z izboljšano trdnostjo in zanesljivostjo, ki izoblikujejo površino navojev s kombinacijo postopkov odrezavanja in plastičnega preoblikovanja. Na osnovi opravljene teoretičnoeksperimentalne analize je bilo zasnovano novo kombinirano orodje za izdelavo navojev z odrezavanjem in preoblikovanjem. Telo orodja je sestavljeno iz dela za preoblikovanje in dela za umerjanje. Prerez delov za preoblikovanje in umerjanje je za večjo trdnost orodja oblikovan kot pri navojnih svedrih brez odrezkov.

Na sprednji strani orodja je določeno število žlebov za odrezke z geometrijo, ki je potrebna za odrezavanje.

Preoblikovalni del orodja je sestavljen iz dveh področij: področja za odrezavanje, ki odstrani več materiala kot običajni navojni svedri, in področja za plastično preoblikovanje, ki navoj dodatno oblikuje in utrdi. Odvisno od položaja in števila žlebov za odvod odrezkov na preoblikovalnem delu in kota žlebov so opredeljene različne konfiguracije, ki določajo, ali deluje orodje samo z odrezavanjem ali z odrezavanjem in preoblikovanjem.

Izvedena je bila eksperimentalna študija zmogljivosti orodja za odrezavanje in preoblikovanje navojev, pri čemer je bila zmogljivost ovrednotena s parametrom maksimalnega navora pri preoblikovanju. Za namen študije so bila izdelana štiri orodja za odrezovanje/preoblikovanje navojev iz hitroreznega jekla, dimenzije M8 in s tremi žlebovi. Kot žlebov za odvod odrezkov je bil λ = 0, 3, 6, 9°, s čimer je bila dosežena različna dolžina dela orodja za odrezavanje. Orodja so delovala pod enakimi pogoji, razmerje med odstotkom dodatka za plastično preoblikovanje in dodatka za odrezavanje je bilo konstantno (η = 17,5%). Opravljena analiza rezultatov eksperimenta je pokazala, da je navor pri preoblikovanju navoja odvisen predvsem od dolžine rezalnega dela orodja za izdelavo navojev, pri čemer navor pada z naraščajočo dolžino. Ko je določeno razmerje dodatkov za plastično preoblikovanje in odrezavanje η , mora biti dolžina rezalnega dela orodja maksimalna.

Na osnovi opravljene analize eksperimentalnih rezultatov in opredelitve glavnih dejavnikov, ki vplivajo na zmogljivost orodij za izdelavo navojev z odrezavanjem in preoblikovanjem, je predlagan algoritem za snovanje teh orodij. Predlagani algoritem zagotavlja minimalen navor med preoblikovanjem navoja ter vključuje opredeljevanje kombinacije konstrukcijskih in geometrijskih elementov orodja ter maksimalno dolžino oz. minimalni kot rezalnega dela.

V članku so predstavljena nova orodja za izdelavo navojev z izboljšano trdnostjo in zanesljivostjo. Navoj izoblikujejo s kombinacijo postopkov odrezavanja in plastičnega preoblikovanja. Predlagani algoritem za snovanje teh orodij je pogoj za snovanje in izdelavo orodij z veliko zmogljivostjo. Kombinirano orodje omogoča intenzivnejše preoblikovanje notranjega navoja in izboljšanje kakovosti navoja.

Ključne besede: navoji, postopek obdelave, orodje za kombinirano odrezavanje/preoblikovanje navoja, zmogljivost, navor pri preoblikovanju navoja, algoritem snovanja

*Naslov avtorja za dopisovanje: Tehniška univerza v Gabrovem, Oddelek za opremo in tehnologije v strojništvu, 4 H. Dimitar St, Gabrovo, Bolgarija, irina@tugab.bg

SI 19

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, SI 20 © 2013 Strojniški vestnik. Vse pravice pridržane.

Prejeto v recenzijo: 2012-06-01 Prejeto popravljeno: 2012-12-04 Odobreno za objavo: 2012-12-14

Nelinearno vodenje temperature hibridnega šaržnega reaktorja Štampar, S. – Sokolič, S. – Karer, G. Simon Štampar1,* – Saša Sokolič1 – Gorazd Karer2

¹ Metronik d.o.o., Slovenija ² Univerza v Ljubljani, Fakulteta za elektrotehniko, Slovenija

V tem članku je predstavljen nov koncept vodenja temperature šaržnega reaktorja z nelinearnim PI-regulatorjem.

Na področju vodenja temperature šaržnega reaktorja obstaja veliko različnih naprednih algoritmov za vodenje, ki pa se zaradi kompleksnosti in zahtevnosti parametriziranja v praksi niso izrazito uveljavili.

Glavni cilj tega algoritma je izboljšati hitrost in natančnost vodenja temperature ter doseči hitro kompenzacijo motenj, ki so posledica endotermnih in eksotermnih reakcij v šaržnih reaktorjih. Ti reaktorji se v večini premerov uporabljajo za proizvodnjo različnih tipov produkta, zato se njihova dinamika lahko zelo razlikuje od produkta do produkta. Natančno in hitro vodenje temperature takih tipov reaktorjev je težko doseči zaradi velikih sprememb želene temperature, motenj, ki vplivajo na proces, ter mešane zvezne in diskretne (hibridne) narave procesa.

Večina industrijskih šaržnih reaktorjev za vodenje temperature uporablja konvencionalne PI- in PID-regulacijske algoritme, ki pa ne omogočajo optimalnega vodenja temperature, vsaj ne na celotnem območju delovanja regulatorja. Zaradi tega in zaradi čedalje višjih ter strožjih zahtev po konkurenčnosti in optimizaciji stroškov proizvodnje, ki nam jih narekujejo globalni trgi, si prizadevamo znižati stroške vodenja temperature ter povečati kvaliteto in kvantiteto produktov z razvojem in uporabo naprednih algoritmov za vodenje.

Nelinearna komponenta algoritma nam zagotovi, da se z večanjem razlike (napake) med referenčno temperaturo in temperaturo v jedru reaktorja izhod regulacijskega algoritma povečuje veliko hitreje kot s konvencionalnim PI-regulatorjem, ki je najpogosteje uporabljen regulacijski algoritem za vodenje temperature šaržnih reaktorjev v industrijskem okolju. Zato nam takšen način vodenja omogoča velik regulirni izhod, ko smo daleč od referenčne temperature (zelo hitro sledenje referenčni temperaturi), in majhen regulirni izhod, ko smo blizu referenčnega signala (manjši kot s konvencionalnim PI-regulatorjem, kar posledično povzroča manj preklopov med grelno-hladilnimi mediji).

Pri razvoju nelinearnega PI-regulatorja smo veliko pozornosti posvetili njegovi enostavni zasnovi ter možnosti enostavne implementacije na krmilniški nivo. Zaradi široke uporabe šaržnih reaktorjev, predvsem v farmacevtski, kemični, prehrambeni in biološki industriji, mora biti algoritem za vodenje zasnovan tako, da ga lahko hitro in brez težav implementirajo procesni inženirji, ki nimajo veliko znanja na področju naprednih regulacijskih algoritmov.

Velika prednost tega algoritma je tudi v tem, da lahko njegovo stabilnost obravnavamo s kriterijem Popova, kar pri ostalih naprednih algoritmih predstavlja veliko težavo. Zato smo v članku dokazali stabilnost po Popovu pri odstopanju parametrov modela od realnega procesa ter analizirali robustnost algoritma. Analiza robustnosti je pomembna, saj se v realnem procesu lahko pojavi vrsta sistemov, ki dodajo red sistemu, kar povzroča, da izhod vodenja vpliva na temperaturo vsebine reaktorja z zakasnitvijo.

Rezultati simulacij so pokazali prednost predlaganega nelinearnega PI-algoritma v primerjavi s konvencionalnim kaskadnim PI-regulatorjem. Z identičnim referenčnim signalom smo s predlaganim algoritmom dosegli veliko hitrejše in natančnejše vodenje ter manjše število preklopov med grelno-hladilnimi mediji.

Učinkovitost algoritma smo dokazali tudi z implementacijo algoritma v industrijskem okolju, in sicer na bioreaktorju. Glavni cilj vodenja temperature je bilo v tem primeru hitro ter predvsem natančno njeno vodenje za dolge časovne intervale. Natančno vodenje je v tem primeru še posebej pomembno, saj lahko nihanje temperature za več kot ±0,2 °C poškoduje ali pa celo uniči žive celice v bioreaktorju.

Ključne besede: nelinearno vodenje procesov, kaskadno vodenje, šaržni reaktor, vodenje temperature

SI 20

*Naslov avtorja za dopisovanje: Metronik d.o.o., Stegne 9a, 1000 Ljubljana, Slovenija, simon.stampar@metronik.si

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, SI 21 © 2013 Strojniški vestnik. Vse pravice pridržane.

Prejeto v recenzijo: 2012-06-26 Prejeto popravljeno: 2012-12-03 Odobreno za objavo: 2013-01-14

Vpliv površinske hrapavosti steblastih rezkarjev na optimalno zmogljivost visokohitrostnega odrezavanja Chen, C.H. – Wang, Y.C. – Lee, B.Y. Chi-Hsiang Chen1,* – Yung-Cheng Wang2 – Bean-Yin Lee3

1Institut

za strojništvo in elektromehaniko, Nacionalna univerza Formoze, Tajvan za strojništvo, Nacionalna univerza za znanost in tehnologijo Yunlin, Tajvan 3Oddelek za strojništvo in računalništvo, Nacionalna univerza Formoze, Tajvan

2Institut

Razvoj obdelovalnih strojev gre v smeri visokohitrostnih tehnologij, ki vključujejo visokohitrostno rezkanje (HSM) in visokohitrostno odrezavanje (HSC), zlasti pri visokohitrostnih aplikacijah s steblastimi rezkarji.

Razvoj ekološko sprejemljivih tehnologij in aplikacij odrezavanja je odvisen od tehnološkega napredka pri strojih in rezalnih orodjih. Natančnost brušenja rezalnih orodij določa površinsko hrapavost cepilne ploskve in proste ploskve, ta pa vpliva na površinsko hrapavost obdelovanca in življenjsko dobo orodja med visokohitrostnim rezkanjem. Kakovost površine, ki vpliva na abrazijo steblastega rezkarja, mazanje, natančnost in pričakovano življenjsko dobo, je odvisna od površinske hrapavosti cepilne ploskve in proste ploskve. Dimenzijska natančnost in površinska hrapavost cepilne ploskve in proste ploskve določata natančnost rezalnega orodja in s tem zmogljivost orodja pri visokohitrostnem rezkanju, ki se kaže v obrabi in življenjski dobi orodja ter v površinski hrapavosti obdelovanca. Brušenje rezalnih robov kot najpomembnejši in končni korak izdelave orodja je kritičnega pomena za določanje geometrijske oblike, zmogljivosti odrezavanja, obrabe rezalnega roba in življenjske dobe orodja.

V študiji so ocenjeni parametri obdelave z upoštevanjem površinske hrapavosti proste ploskve steblastega rezkarja. Predlagan je tudi nov pristop k optimizaciji parametrov visokohitrostnega odrezavanja orodnega jekla DIN 1.2344. Za preučevanje zmogljivosti odrezavanja sta bila izbrana karakteristična parametra življenjska doba orodja in stopnja odvzema materiala. Med procesnimi parametri so površinska hrapavost proste ploskve steblastega rezkarja, rezalna hitrost, podajanje na zob, aksialna globina rezanja in radialna globina rezanja. Več parametrov zmogljivosti zagotavlja integralno obravnavo procesa, optimalna kombinacija parametrov obdelave pa je nato določena s sivo relacijsko analizo. Predlagana je metoda za določanje optimalnih parametrov obdelave, ki dajejo minimalno obrabo orodja in maksimalno stopnjo odvzema materiala. Maksimalna ocena sive relacije je v drugi skupini (0,82), kar pomeni, da so zmogljivosti te skupine optimalne med 18 skupinami. Vpliv parametrov obdelave na več karakteristik zmogljivosti je statistično določen z analizo variance. Opravljena sta bila tudi F-test in P-test, s katerima je bilo ugotovljeno, kateri parametri procesa HSC značilno vplivajo na karakteristike zmogljivosti. Analiza variance kaže, da sta glavna dejavnika, ki značilno vplivata na karakteristike zmogljivosti kot sta življenjska doba orodja in stopnja odvzema materiala, rezalna hitrost in podajanje na zob, s skupnim prispevkom 76,46%. Relativna napaka je 9,57%, zato v eksperimentu ni bil zanemarjen noben pomemben dejavnik. Površinska hrapavost proste ploskve je bila v tej študiji nastavljena na 0,23±0,03 in 0,43±0,02 μm. Čas brušenja orodja je bil 621 oz. 405 sekund. Rezultati analize variance kažejo, da površinska hrapavost proste ploskve steblastega rezkarja nekoliko vpliva na grobo visokohitrostno obdelavo orodnega jekla DIN 1.2344.

Pomembno vpliva tudi na površinsko hrapavost obdelovanca z zmanjšanjem povprečne površinske hrapavosti obdelovanca za 0,054 μm (razlika med optimalnimi parametri procesa in parametri procesa št. 12). Kot je bilo omenjeno zgoraj, brušenje proste ploskve steblastega rezkarja do hrapavosti prve stopnje 0,23±0,03 μm povzroči 53,33-odstotno povečanje stroškov brušenja, a samo 4,84-odstotno podaljšanje življenjske dobe orodja. Pogoji brušenja A2 (zrnavost diamantnega koluta D46, hitrost brušenja 1650 m/min in hitrost podajanja 900 mm/min) lahko torej izboljšajo učinkovitost brušenja orodja. Optimalna kombinacija, ki jo pokaže predlagana metoda, je površinska hrapavost proste ploskve 0,23±0,03 μm, rezalna hitrost 251,32 m/min, podajanje 0,1 mm/zob, aksialna globina rezanja 1,0 mm in radialna globina rezanja 0,75 mm. Eksperimenti so potrdili, da predlagani pristop k optimizaciji parametrov obdelave prinaša izboljšanje življenjske dobe orodja za 9,1 minute, stopnjo odvzema materiala 1200 mm3/min, celotno količino odvzetega materiala 230.616 mm3 in povprečno površinsko hrapavost obdelovanca 0,044 μm po visokohitrostnem odrezavanju.

Ključne besede: optimizacija, visokohitrostno odrezavanje, siva relacijska analiza, površinska hrapavost, steblasti rezkar, brušenje orodja

*Naslov avtorja za dopisovanje: Institut za strojništvo in elektromehaniko, Nacionalna univerza Formoze, 64 Wunhua Road, Huwei, Yunlin 632, Tajvan, explorer5270@gmail.com

SI 21

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, SI 22-24 Osebne objave

Diplomske naloge

DIPLOMIRALI SO Na Fakulteti za strojništvo Univerze v Ljubljani so pridobili naziv univerzitetni diplomirani inženir strojništva: dne 23. januarja 2013: Simon MALOVEC z naslovom: »Razvojno vrednotenje pokrova alternatorja glede na utrujanje« (mentor: prof. dr. Marko Nagode); Martin VOVK z naslovom: »Postavitev in primerjava 3+2 in 5-osne simultane tehnologije robotske obdelave prostih površin« (mentor: doc. dr.

Franci Pušavec, somentor: prof. dr. Janez Kopač); dne 25. januarja 2013: Klemen DERMOTA z naslovom: »Učinkovita raba in obnovljivi viri energije v pivovarski industriji« (mentor: prof. dr. Vincenc Butala); Pavel SIMONČIČ z naslovom: »Razvoj konstrukcije izolatorja za vzorčenje in pripadajočega transportnega vozička« mentor: izr. prof. dr. Jernej Klemenc); Miha URH z naslovom: »Možnost uporabe duroplastov pri nabrizgavanju izolacij« (mentor: prof. dr. Karl Kuzman); Aleš VRHOVNIK z naslovom: »Analiza vplivnih parametrov pri mazanju ter njihov vpliv na izbor vrste maziva za mazanje kotalnih ležajev« (mentor: prof. dr.

Mitjan Kalin): dne 28. januarja 2013: Matjaž PIRIH z naslovom: »Lasersko dolbenje sintranega jedra feritne dušilke« (mentor: prof. dr.

Janez Možina); Miha PRELOVŠEK z naslovom: »Spletna storitev za statistično kontrolo procesov« (mentor: prof. dr. Alojz Sluga); Šimen ŠKRLEP z naslovom: »Adaptivno vodenje žarka vlakenskega laserja z galvo sistemom in soosno postavljeno kamero« (mentor: prof. dr. Janez Možina); Gašper ŠUBIC z naslovom: »Strukturna analiza krila brezpilotnega letala« (mentor: izr. prof. dr. Tadej Kosel, somentor: doc. dr. Boris Jerman); dne 29. januarja 2013: Blaž BEDENČIČ z naslovom: »Optimizacija delovanja sistemov daljinskega ogrevanja« (mentor: prof. dr. Alojz Poredoš); David FRÖHLICH z naslovom: »Napoved kavitacijskih tlačnih pulzacij na prototipni izvedbi naprave za čiščenje odpadne vode« (mentor: prof. dr.

Branko Širok); Andreja POLJŠAK z naslovom: »Konstrukcijska zasnova visokotlačnega parnega kotla na lesno SI 22

biomaso« (mentor: izr. prof. dr. Andrej Senegačnik, somentor: prof. dr. Franc Kosel). * Na Fakulteti za strojništvo Univerze v Mariboru so pridobili naziv univerzitetni diplomirani inženir strojništva: dne 31. januarja 2013: Marko KOLARIČ z naslovom: »Vpliv mreže na izračunane tokovne karakteristike v vbrizgalni šobi« (mentor: prof. dr. Breda Kegl, somentor: asist. Blaž Vajda); Matjaž PŠENIČNIK z naslovom: »Modeliranje proizvodnega sistema s programom Robot Studio« (mentor: izr. prof. dr. Karl Gotlih, somentor: doc. dr.

Tomaž Vuherer); Miha VALENTE z naslovom: »Konstruiranje vozička naprave za meritev zaostalih napetosti« (mentor: prof. dr. Nenad Gubeljak). * Na Fakulteti za strojništvo Univerze v Mariboru so pridobili naziv magister inženir strojništva: dne 30. januarja 2013: Matjaž BUKŠEK z naslovom: »Projektiranje in konstruiranje preskusne naprave za preskušanje zobnikov« (mentor: prof. dr. Srečko Glodež, somentor: doc. dr. Janez Kramberger); Jure ŠTREKELJ z naslovom: »Parametrično modeliranje artikulatorja« (mentor: izr. prof. dr. Miran Ulbin, somentor: doc. dr. Aleš Belšak). * Na Fakulteti za strojništvo Univerze v Ljubljani so pridobili naziv diplomirani inženir strojništva: dne 10. januarja 2013: Nejc BOGATAJ z naslovom: »Doseganje kakovosti obdelave pri odrezavanju ulitka iz aluminija« (mentor: prof. dr. Janez Kopač); Jernej JANČAR z naslovom: »Podpora operacijam hidroagregatov: storitvena podpora v luči vzdrževanja« (mentor: prof. dr. Alojz Sluga, somentor: doc. dr. Drago Bračun);

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, SI 22-24

dne 11. januarja 2013: Blaž KOKOVICA z naslovom: »Analiza aerodinamskih lastnosti toka na izstopu iz šobe pršilnika fitofarmacevtskih sredstev« (mentor: izr. prof. dr. Marko Hočevar, somentor: prof. dr. Branko Širok); Marko NIKOLIĆ z naslovom: »Določitev porabe goriva in izpustov onesnažil osebnega vozila gnanega s trigorivnim Ottovim motorjem« (mentor: izr. prof. dr. Tomaž Katrašnik). *

Na Fakulteti za strojništvo Univerze v Mariboru so pridobili naziv diplomirani inženir strojništva: dne 31. januarja 2013: Matjaž HAFNER z naslovom: »Optimiranje izdelave bagerske ročice« (mentor: izr. prof. dr. Borut Buchmeister, somentor: doc. dr. Marjan Leber); Simon KAMPUŠ z naslovom: »Zasnova tehnološkega postopka za izdelavo priključnih cevi filtra« (mentor: izr. prof. dr. Ivan Pahole); Zvonko KOLAR z naslovom: »Uporaba CAD/ CAM orodij pri izdelavi zahtevnih elementov iz pločevine« (mentor: izr. prof. dr. Ivan Pahole).

SI 23

Strojniški vestnik - Journal of Mechanical Engineering 59(2013)2, SI 22-24

V spomin prof. dr. Francu Schweigerju

V snežnem januarju se je tiho poslovil od nas spoštovani prof. dr. Franc Schweiger. Profesorja sem osebno spoznal med študijem na Fakulteti za strojništvo, Univerze v Ljubljani leta 1978, bil je moj mentor pri diplomi in kasneje tudi na magistrskem in doktorskem študiju. Z njegovim delom pa sem se prvič seznanil že v srednji šoli pri prebiranju člankov objavljenih v Strojniških vestnikih. Vse do njegove upokojitve leta 1995 sva tesno sodelovala, zadnjič na skupnem raziskovalnem projektu v sodelovanju s Fakulteto za strojništvo in Litostrojem. Naj mi bo dovoljeno, da v imenu fakultete ter svojem imenu orišem življensko pot profesorja.

Rojen je bil 4. oktobra 1926 v Gotni vasi pri Novem mestu. Med vojno je bil bolničar v partizanski bolnišnici, obiskoval je gimnazijo v Ljubljani in Kočevju ter maturiral leta 1945. Po vojni se je vpisal na Oddelek za strojništvo Tehniške fakultete Univerze v Ljubljani, kjer je leta 1953 diplomiral. Po študiju se je za krajšo dobo zaposlil v kranjski Iskri, leta 1954 pa je nastopil službo v Inštitutu za turbinske stroje v Ljubljani. Tu je njegovo delo obsegalo raziskave na področju mehanike fluidov turbinskih strojev in naprav.

V letu 1960 se je znanstveno izpopolnjeval v državnem inženirskem laboratoriju (National Engineering Laboratory) v Glasgowu v Veliki Britaniji.

Decembra leta 1962 je bil na Univerzi v Glasgowu, Oddelek za aeronavtiko in mehaniko fluidov, izvoljen za raziskovalca, kjer je leta 1965 doktoriral z delom »Tok v centrifugalnih črpalkah delujočih pri delnih pretokih« (Flow in Centrifugal Pump Working at Part Capacity). Po doktoratu je raziskoval aerodinamične pojave v laboratoriju Univerze v Cardiffu v Veliki Britaniji, od koder se je leta 1968 vrnil v domovino.

Tu je na Inštitutu za turbinske stroje prevzel Oddelek za teoretično mehaniko fluidov.

Leta 1972 je bil izvoljen za izrednega, leta 1980 pa za rednega profesorja na Fakulteti za strojništvo Univerze v Ljubljani za predmet Hidravlični stroji. Tu je ostal do upokojitve leta 1995.

SI 24

Znanstveni opus profesorja Schweigerja obsega študij tokovnih razmer v črpalkah, merjenje velikih pretočnih količin, nestacionarne pojave v hidravličnih cevnih sistemih in statistično analizo vodnih turbin.

Izsledke svojih raziskav je predstavil na mednarodnih znanstvenih srečanjih, na katerih je tudi vodil sekcije in bil član znanstvenih odborov. Svoja dela je objavljal v Strojniškem vestniku in mednarodnih revijah.

Posebno odmevna je serija petih člankov s področja statistične analize vodnih turbin, ki so bili objavljeni v International Water Power & Dam Construction.

V svoje raziskovalno delo je vključeval študente ter kolege z univerz, inštitutov in industrije.

Pomembno področje profesorjeve ustvarjalnosti je bilo njegovo sodelovanje v mednarodnih združenjih. Leta 1969 je bil imenovan v šesto delovno skupino Mednarodne elektrotehniške komisije IEC (International Electrotechnical Commission). V delovni skupini je sodeloval pri izdaji predpisov za merjenje pretoka na hidroagregatih. Pri tem je vodil pripravo predpisov za tlačno-časovno metodo merjenja pretokov. Bil je tudi član strokovne komisije za regulacijo in pretoke JUREMA, mednarodnega združenja za hidravlične raziskave IAHR (International Association for Hydraulic Research) in ameriškega združenja strojnih inženirjev ASME (American Society for Mechanical Engineers).

Pedagoško področje profesorja Schweigerja je obsegalo dodiplomski in podiplomski študij. Bil je mentor mnogim diplomantom, magistrantom in doktorantom. Naloge kandidatov so bile tesno povezane s problemi iz industrije, posebej tistih v Litostroju in Turboinštitutu. Profesor je vzpostavil stike s številnimi tujimi univerzami.

Delo profesorja Schweigerja na pedagoškem, strokovnem in znanstveno-raziskovalnem področju je pustilo globok pečat generacijam inženirjev za kar smo mu hvaležni in ga bomo ohranili v trajnem spominu.

Izr. prof. dr. Anton Bergant

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 Editorial Office University of Ljubljana (UL) Faculty of Mechanical Engineering SV-JME Aškerčeva 6, SI-1000 Ljubljana, Slovenia Phone: 386-(0)1-4771 137 Fax: 386-(0)1-2518 567 E-mail: info@sv-jme.eu, http://www.sv-jme.eu Print DZS, printed in 450 copies Founders and Publishers University of Ljubljana (UL) Faculty of Mechanical Engineering, Slovenia University of Maribor (UM) Faculty of Mechanical Engineering, Slovenia Association of Mechanical Engineers of Slovenia Chamber of Commerce and Industry of Slovenia Metal Processing Industry Association Cover: When operating hand tools, vibrations excite the human hand, leading to vibration diseases and injuries. To improve the safety of workers, the vibration transmissibility to the hand is being researched. Since there is currently a lack of viable experimental data, used to develop dynamic models, a special measuring handle was developed. The handle measures triaxial vibration transmissibility to several parts of the hand and enables the development of validated dynamical models.

Image Courtesy: LADISK, Faculty of Mechanical Engineering, University of Ljubljana.

International Editorial Board Koshi Adachi, Graduate School of Engineering,Tohoku University, Japan Bikramjit Basu, Indian Institute of Technology, Kanpur, India Anton Bergant, Litostroj Power, Slovenia Franci Čuš, UM, Faculty of Mech. Engineering, Slovenia Narendra B. Dahotre, University of Tennessee, Knoxville, USA Matija Fajdiga, UL, Faculty of Mech. Engineering, Slovenia Imre Felde, Obuda University, Faculty of Informatics, Hungary Jože Flašker, UM, Faculty of Mech. Engineering, Slovenia Bernard Franković, Faculty of Engineering Rijeka, Croatia Janez Grum, UL, Faculty of Mech. Engineering, Slovenia Imre Horvath, Delft University of Technology, Netherlands Julius Kaplunov, Brunel University, West London, UK Milan Kljajin, J.J. Strossmayer University of Osijek, Croatia Janez Kopač, UL, Faculty of Mech. Engineering, Slovenia Franc Kosel, UL, Faculty of Mech. Engineering, Slovenia Thomas Lübben, University of Bremen, Germany Janez Možina, UL, Faculty of Mech. Engineering, Slovenia Miroslav Plančak, University of Novi Sad, Serbia Brian Prasad, California Institute of Technology, Pasadena, USA Bernd Sauer, University of Kaiserlautern, Germany Brane Širok, UL, Faculty of Mech. Engineering, Slovenia Leopold Škerget, UM, Faculty of Mech. Engineering, Slovenia George E. Totten, Portland State University, USA Nikos C. Tsourveloudis, Technical University of Crete, Greece Toma Udiljak, University of Zagreb, Croatia Arkady Voloshin, Lehigh University, Bethlehem, USA President of Publishing Council Jože Duhovnik UL, Faculty of Mechanical Engineering, Slovenia 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 magazine. 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.

ISSN 0039-2480 © 2013 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.

The journal is subsidized by Slovenian Book Agency.

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

Instructions for Authors All manuscripts must be in English. Pages should be numbered sequentially. The maximum length of contributions is 10 pages. Longer contributions will only be accepted if authors provide justification in a cover letter. Short manuscripts should be less than 4 pages. For full instructions see the Authors Guideline section on the journal’s website: http://en.sv-jme.eu/.

Please note that file size limit at the journal’s website is 8Mb. Announcement: The authors are kindly invited to submitt the paper through our web site: http://ojs.sv-jme.eu. Please note that file size limit at the journal’s website is 8Mb. The Author is also able to accompany the paper with Supplementary Files in the form of Cover Letter, data sets, research instruments, source texts, etc. 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.

Please provide a cover letter stating the following information about the submitted paper: 1. Paper title, list of authors and affiliations.

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

3. A declaration that your paper is unpublished work, not considered elsewhere for publication.

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?

5. We kindly ask you to suggest at least two reviewers for your paper and give us their names and contact information (email).

Every manuscript submitted to the SV-JME undergoes the course of the peer-review process.

THE FORMAT OF THE MANUSCRIPT The manuscript should be written in the following format: - A Title, which adequately describes the content of the manuscript.

- An Abstract 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.

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

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

- A Theory or experimental methods used.

- An Experimental section, which should provide details of the experimental set-up and the methods used for obtaining the results.

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

- A Discussion section, which 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 the clarity).

- Conclusions, which should present one or more conclusions that have been drawn from the results and subsequent discussion and do not duplicate the Abstract.

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

Units - standard SI symbols and abbreviations should be used. 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.)

Abbreviations should be spelt out in full on first appearance, e.g., variable time geometry (VTG).

Meaning of symbols and units belonging to symbols should be explained in each case or quoted in a special table at the end of the manuscript before References.

Figures must be cited in a consecutive numerical order in the text and referred to in both the text and the caption 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.

Pictures may be saved in resolution good enough for printing in any common format, e.g. BMP, GIF or JPG. However, graphs and line drawings should be prepared as vector images, e.g. CDR, AI. When labeling axes, physical quantities, e.g. t, v, m, etc. should be used whenever possible to minimize the need to label the axes in two languages.

Multi-curve graphs should have individual curves marked with a symbol. The meaning of the symbol should be explained in the figure caption.

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 caption as

Table 1, Table 2, etc. In addition to the physical quantity, e.g. t (in italics), units (normal text), should be added in square brackets. The tables should each have a heading. Tables should not duplicate data found elsewhere in the manuscript.

Acknowledgement of collaboration or preparation assistance may be included before References. Please note the source of funding for the research.

REFERENCES A reference list must be included using the following information as a guide. Only cited text references are included. Each reference is referred to in the text by a number enclosed in a square bracket (i.e., [3] or [2] to [6] for more references). 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. All non-English or. non-German titles must be translated into English with the added note (in language) at the end of reference. 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 crosslinked simulations. Strojniški vestnik - Journal of Mechanical Engineering, vol. 57, no. 7-8, p. 531-538, DOI:10.5545/sv-jme.2011.013.

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

Please add DOI code when available and link it to the web site.

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. 553-576.

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 2009 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 2009-09-07.

EXTENDED ABSTRACT By the time the paper is accepted for publishing, the authors are requested to send the extended abstract (approx. one A4 page or 3.500 to 4.000 characters). The instructions for writing the extended abstract are published on the web page http://www.sv-jme.eu/ information-for-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 and 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 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 fast. Thus it is essential that manuscripts are accurate when submitted.

Authors can track the status of their accepted articles on http://en.svjme.eu/.

PUBLICATION FEE For all articles authors will be asked to pay a publication fee 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 300.00 EUR (for articles with maximum of 10 pages), 20.00 EUR for each addition page.

Additional costs for a color page is 90.00 EUR.

http://www.sv-jme.eu

59 (2013) 2

Strojniški vestnik Journal of Mechanical Engineering

Since 1955

Contents

Papers

71

Luka Knez, Janko Slavič, Miha Boltežar: A multi-axis biodynamic measuring handle for a human hand-arm system

89

Aleksander Preglej, Igor Steiner, Sašo Blažič: Multivariable Predictive Functional Control of an Autoclave

97

Eda Okutan, Sedat Karabay, Tamer Sınmazçelik, Egemen Avcu: A Study on the Derivation of Parametric Cutting Force Equations in Drilling of GFRP Composites

106

Irina Stefanova Aleksandrova, Gancho Nenkov Ganev: Combined Cutting-deforming Taps

112

Simon Štampar, Saša Sokolič, Gorazd Karer: Nonlinear Control of a Hybrid Batch Reactor

Chi-Hsiang Chen, Yung-Cheng Wang, Bean-Yin Lee: The Effect of Surface Roughness of End-Mills on Optimal Cutting Performance for High-Speed Machining

124

Journal of Mechanical Engineering - Strojniški vestnik

Jianping Li, Songyong Liu, Changlong Du: 81 Experimental Research and Computer Simulation of Face Grind-hardening Technology

2 year 2013 volume 59 no.