Journal of Mechanical Engineering 2012 3

58 (2012) 3

http://www.sv-jme.eu

Strojniški vestnik Journal of Mechanical Engineering

Since 1955

Papers

147

Matjaž Ramšak: Radio Controlled Sailplane Flight: Experimental and Numerical Analysis

156

Hamidreza Salimi, Bahador Saranjam, Ahmad Hoseini, Mohsen Ahmadzadeh: Use of Genetic Algorithms for Optimal Design of Sandwich Panels Subjected to Underwater Shock Loading

165

Adem Çiçek, Turgay Kıvak, Gürcan Samtaş: Application of Taguchi Method for Surface Roughness and Roundness Error in Drilling of AISI 316 Stainless Steel

175

Ali Movaghghar, Gennady Ivanovich Lvov: Theoretical and Experimental Study of Fatigue Strength of Plain Woven Glass/Epoxy Composite

183

Mezid Muhasilovic, Jožef Duhovnik: Cfd-Based Investigation of the Response of Artificial Ventilation in the Case of Tunnel-Fire

191

Ning Fang, P Srinivasa Pai, Nathan Edwards: Tool-Edge Wear and Wavelet Packet Transform Analysis in High-Speed Machining of Inconel 718

203

Tino Stanković, Mario Štorga, Dorian Marjanović: Synthesis of Truss Structure Designs by NSGA-II and NodeSort Algorithm

213

Yong-Bin Liu, Lin Zhu, Tien-Chien Jen, Ji-Wen Zhao, Yi-Hsin Yen: Numerical Analyses to Investigate the Feasibility and Effectiveness in Using Heat Pipe Embedded End Mills

Journal of Mechanical Engineering - Strojniški vestnik

Contents

3 year 2012 volume 58 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.

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Editor in Chief Vincenc Butala University of Ljubljana Faculty of Mechanical Engineering, Slovenia Co-Editor Borut Buchmeister University of Maribor 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 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: Top figure presents a geometrical model of Disk Launch Glider made by Catia. The background is the photograph of Ribniško Pohorje which is perfect for thermal soaring in spring time. Middle figures are results of numerical simulations made by Computational Fluid Dynamic.

The streamlines at different angle of attack are plotted. At right figures the recirculation zone is clearly visible. At bottom photograph the real radio controlled DLG is in author’s hand.

Image courtesy: Institute for Power, process and environmental enginerring, Faculty of Mechanical Engineering, University of Maribor, Slovenia

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Strojniški vestnik - Journal of Mechanical Engineering 58(2012)3 Contents

Contents Strojniški vestnik - Journal of Mechanical Engineering volume 58, (2012), number 3 Ljubljana, March 2012 ISSN 0039-2480 Published monthly

Papers Matjaž Ramšak: Radio Controlled Sailplane Flight: Experimental and Numerical Analysis Hamidreza Salimi, Bahador Saranjam, Ahmad Hoseini, Mohsen Ahmadzadeh: Use of Genetic Algorithms for Optimal Design of Sandwich Panels Subjected to Underwater Shock Loading Adem Çiçek, Turgay Kıvak, Gürcan Samtaş: Application of Taguchi Method for Surface Roughness and Roundness Error in Drilling of AISI 316 Stainless Steel Ali Movaghghar, Gennady Ivanovich Lvov: Theoretical and Experimental Study of Fatigue Strength of Plain Woven Glass/Epoxy Composite Mezid Muhasilovic, Jožef Duhovnik: CFD-Based Investigation of the Response of Mechanical Ventilation in the Case of Tunnel-Fire Ning Fang, P Srinivasa Pai, Nathan Edwards: Tool-Edge Wear and Wavelet Packet Transform Analysis in High-Speed Machining of Inconel 718 Tino Stanković, Mario Štorga, Dorian Marjanović: Synthesis of Truss Structure Designs by NSGA-II and NodeSort Algorithm Yong-Bin Liu, Lin Zhu, Tien-Chien Jen, Ji-Wen Zhao, Yi-Hsin Yen: Numerical Analyses to Investigate the Feasibility and Effectiveness in Using Heat Pipe Embedded End Mills

147 156 165 175 183 191 203 213

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)3, 147-155 DOI:10.5545/sv-jme.2009.153

Paper received: 2009-11-05, paper accepted: 2012-02-07 © 2012 Journal of Mechanical Engineering. All rights reserved.

Radio Controlled Sailplane Flight: Experimental and Numerical Analysis Ramšak, M. Matjaž Ramšak* Faculty of Mechanical Engineering, University of Maribor, Slovenia The article deals with numerical and experimental analysis of radio controlled sailplane flight. A Computational Fluid Dynamics programme, Ansys CFX, is used for the determination of aerodynamic forces. Photogrammetry is used for the measurement of speed and glide angle using a video camera. The article presents a comparison of the computed and measured glide ratios.

Keywords: computational fluid dynamics, photogrammetry, aerodynamics, glide ratio

0 INTRODUCTION Flying an airplane was, and is still, one of the most frequent wishes of children, but this wish comes true in real life only for a minority. In contrast to flight simulators, the radio controlled (RC) airplanes are real and within easy reach for everyone. While doing experiments using large scale planes is not easy or cheap (and can also be dangerous), RC planes are ideal for exploring the aerodynamic laws. This is the main idea and motivation for the presented work.

There are many publications dealing with real scale aircraft aerodynamics [1], but we could not find any articles dealing with small scale planes. When comparing large and small scale plane aerodynamics there is a fundamental difference in the Reynolds number value range. With using numerical modelling this is generally not the problem. The problem, however, is experimental analysis. In our case the sailplane weights only 320 grams, thus preventing the installation of any sensors. This is the main reason for using photogrammetry.

The structure of the article is as follows. In the Introduction, the modelling assumptions and physical background are explained briefly. Forces and the glide ratio are defined. At the end of the section the sailplane model is introduced. In the first section the experimental procedure is explained. The numerical modelling is described briefly in the second section.

Results and discussion are the topic of the last section.

The article finishes with conclusions.

In this manner the force equilibrium can be written simply as:   R = Weight , (1)

where R is the resultant aerodynamic force. In the absence of a motor thrust these two forces are the only forces acting on the sailplane. It is an elementary procedure to decompose the resultant aerodynamic force into its components, called Lift and Drag. Drag force is defined as being in a direction opposite to the velocity. In this manner, the lift is defined as being in a normal direction to the velocity upwards, see Fig. 1. We would like to emphasise an easily mismatched mind pattern dealing with simulations as a result of a steady flight constraint. Of course, in the real flight the angle of attack dictates everything. Bearing in mind the assumption of a steady flight, AoA is just a variable without an influence on the glide angle and velocity, which are both defined as a constant.

Variations of AoA produce different magnitude of lift and drag without changing their direction. In the numerical model this results in a different weight of artificial sailplane being modelled. In the experiment the weight is a constant value. This means that the AoA relation can be varied by changing the position of the centre of gravity.

0.1 Assumption of a Steady Flight The object of the research is the steady flight of a sailplane. The assumption of a steady flight determinates a constant velocity, constant Glide Angle (GA) and constant Angle of Attack (AoA), see Fig. 1.

Fig. 1. Forces acting on sailplane during a steady flight

Using elementary trigonometry functions the relation between glide angle GA and forces is:

*Corr. Author’s Address: University of Maribor, Faculty of Mechanical Engineering, Smetanova 17, 2000 Maribor, Slovenia, matjaz.ramsak@uni-mb.si

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Strojniški vestnik - Journal of Mechanical Engineering 58(2012)3, 147-155

sin GA =

Drag Lift , cos GA . (2) = Weight Weight

A well-known aviation term, Glide ratio also known as the glide number or finesse for unpowered flights, or a lift to drag ratio for powered flight, is simply deduced as:

Glide Ratio =

Lift 1 = . (3) Drag tan GA

Glide ratio refers to the distance a sailplane will move forward for a lost altitude value of unit distance.

From the energy point of view, the glide ratio effectively describes the efficiency of the sailplane.

A modern sailplane has the best glide ratio up to 75.

An albatross, known as one of the best gliders among birds, has the glide ratio 20. This is a rare example of where mankind has defeated nature.

0.2 Radio Controlled Glider The object of the research is a radio controlled glider, Longshot 2, produced by Horejsi [2]. It is a competition model in group F3K, where the main objective is to maximize flight time. The model is also known as a Disc Launch Glider (DLG). DLG models are launched similarly to an athlete launching a disc. We have measured the launch speed and we can easily reach 100 km/h. The reader is kindly asked to type “DLG launch” on the YouTube page to see it for themselves. The model data is: wingspan 1.499 m, length 1.14 m, weight 320 g, wing area 22.5 dm2, wing load 14 g/dm2, airfoil profile 4xxct, see Figs. 8 and 12.

effectiveness of the sailplane. However, direct angle measurement using some kind of sensor mounted on the plane is another difficult task. We found that the use of photogrammetry is an ideal solution for our task.

Photogrammetry is the first remote sensing technology ever developed in which geometric properties about objects are determined from photographic images. Historically, photogrammetry is as old as modern photography itself, and can be dated to mid-nineteenth century [3]. In the simplest example, the distance between two points which lay on a plane parallel to the photographic image plane can be determined by measuring their distance on the image if the scale of the image is known. In our case, the scale is computed using the length of the sailplane. Two images are extracted out of a video movie in a known time interval. In Fig. 2 the principle of the measurement is shown. The movie is captured by a simple video camera, making the measurement extremely cheap. The resultant processing is simple using basic trigonometry functions easily understandable by every secondary school student.

1 THE MEASURMENT OF SPEED END GLIDE ANGLE USING PHOTOGRAMMETRY The main object of the experimental part of work is to measure the glide ratio. From Eq. (3) it can be established that this could be done in two ways. The first way is with the aerodynamic force measurement which is suitable for a wind tunnel experiment. The second way is by measuring the glide angle directly.

This cannot be done in the wind tunnel but has to be done in real flight. Since the glide angle varies with the speed of the flight, the velocity also has to be measured. This could be done using a Pitot tube and pressure sensors. The small weight of our sailplane, (320 g), prevents any mount of experimental facilities since increasing the weight dramatically changes the 148

Fig. 2. The principle of the measurement and typical sequence of two images overlapped; the perspective angles of the wing are indicating that the camera centre line is between the sailplane figures

1.1 The Experimental Procedure Some assumptions have to be set. As mentioned above, the first assumption is a steady flight. In the experiment this was achieved by minimizing the movement of the sailplane control surfaces in order to make thesailplane angle and speed steady. The second

Ramšak, M.

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)3, 147-155

assumption is that the flight is a parallel to the video image. This was achieved by flying the sailplane over a straight line path on the ground over the pilot`s head.

The third assumption is that the two images from the film are chosen in such a manner that the midline is aligned with the camera centre line as shown in Fig. 2. In order to have a minimal influence of air thermal soaring the experiment was done in the morning on a cloudy, windless day.

Fig. 3. Scale error for all measurement images, see Eq. (4)

In order to check the assumptions the following result processing is done, see Fig. 2. In each image the beginning and ending point of the sailplane image coordinates are picked up using Corel Photo-Paint, namely {x1, y1} and {x2, y2} in the first image and {x3, y3} and {x4, y4} in the second image. The unit used is a pixel. Using the overall length of the sailplane Lref the scale in the first image is computed as:

Scale1 =

Lref

( x2 − x1 )2 + ( y2 − y1 )2

.

(4)

In the same manner, the Scale2 is computed from the second image. By comparing both of them the Scale error is computed. The average Scale is used in further computations. The fulfilling of the second and third assumptions can be checked using the Scale error, see Fig. 3. It is clearly shown that the obtained Scale error was below 1 mm/pixel.

Next, the travel path of the sailplane nose could be computed as:

Pathnose = Scale *

Velocity =

Path (6) , ∆t

where Δt is the time interval between images. The accuracy of the time interval was checked by shooting a digital stopwatch from the computer monitor.

Comparing our video processing time interval and reference Δt captured from the digital stopwatch, the error obtained was lower than 0.01 second. The error of Path determination is estimated on ±2 pixels. One pixel at each pick. Using a typical scale value 20 mm/ pixel and typical Δt 0.4 s results in a velocity error of ±0.1 m/s. Typical velocity was 10 m/s, resulting in a 1% error.

The error of measured velocity can be also estimated using a measured scale error Eq. (4) plotted in Fig. 3. All values are below 1 mm/pixel. The typical path length Eq. (5) was 200 pixels, where the video resolution is 720x576 pixels. Using a scale error and typical path length the path error is 0.2 m. Dividing this by 0.4 s results in a maximal error of 0.5 m/s.

Using a typical velocity value of 10 m/s, the maximal relative error is 5%. Repeating the procedure several times, the obtained standard deviation value is 0.26 mm/pixel of measured scale error, the velocity error is 1.3%. This means that the 68% of all the measured values have an error lower than 1.3%, which is almost exactly in line with the estimated velocity error value of 1% in the previous paragraph.

The measurement calibration was done by shooting a bicycle on the move. The length of a bicycle is approximately the same as the sailplane length, the speed is in the same range and other video parameters are the same. The reference velocity was measured using a bicycle velocity meter. The error obtained was far below 1% which is almost exactly in line with the computed error estimation, see Fig. 4.

( x3 − x1 )2 + ( y3 − y1 )2 . (5)

Similarly, the path of the tail using points 4 and 2.

Again, the second and third assumptions are checked by comparing the error between both computed paths.

The average path is used for computation of the sailplane velocity:

Fig. 4. The velocity calibration using a bicycle velocity meter

Radio Controlled Sailplane Flight: Experimental and Numerical Analysis

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We shall proceed with the angle measurement procedure. First, the nose glide angle is computed using sailplane nose path Eq. (5) as: tan GAnose =

tan AoA'1 =

2 NUMERICAL MODELLING USING COMPUTATIONAL FLUID DYNAMICS (CFD)

y1 − y3 . (7) x1 − x3

Similarly, the tail glide angle is computed using points 2 an 4. Both angle values are corrected using an angle of spirit level indicating the exact angle of the horizontal line, see Fig. 2. As we have did before with scale and path comparison, both angles are compared to check assumptions one to three. The difference between both angles, called Glide angle error, is plotted in Fig. 5. It is shown that glide angle error is less than 3 degrees in all measurements. An overall GA error is the standard deviation value 1.1 degrees using 68% probability.

Next, the Angle of Attack (AoA) is computed using the angle of sailplane longitudinal axis:

that controlling a steady Glide angle is more difficult than constant speed between two photo shots.

y2 − y1 , (8) x2 − x1

and computed as a difference AoA1=AoA1’ ‒ GA. Similarly, as before, the AoA on both acquired figures are compared in order to check steady flight assumptions. The AoA measurement is found to be the most unreliable, as expected. The source of the error is the picking error of ±2 pixels. Comparing this to the typical difference y2‒y1 value of 20 pixels, the relative error is of the order of 10%. However, the AoA results are scattered between 0 and 5 degrees, where the majority is in the interval between 1 and 3 degrees.

CFD is one of the branches of fluid mechanics that uses numerical methods and algorithms to solve and analyse problems that involve fluid flows [4]. We have used the ANSYS CFX software for solving Navier-Stokes equations.

2.1 Computational Domain and Boundary Conditions The main aim is to compute the glide ratio at various speeds using a steady flight assumption. The plan is to compute drag and lift forces at a prescribed velocity and angle of attack (AoA). The weight is computed by the Pythagorean theorem using drag and lift force, see Fig. 1. Glide ratio is then determined from the AoA – weight relation at the actual sailplane weight 3.2 N at the prescribed velocity. Modelling interpretation is as though somebody was holding the sailplane in the wind tunnel changing the AoA until the sailplane would hover. There is more adequate interpretation using a motor cargo airplane: changing the AoA until lift equals weight and thrust equals drag.

Fig. 6. Forces and angles in real flight and simulated flight

Fig. 5. Glide Angle error for all measurement images, see Eq. (7)

The measured results are shown and discussed in the last section, where they are compared with the numerical simulation. The reader should keep in mind 150

In reality the airplane moves in the air. As is common in these kinds of simulations, the simulated airplane is still and the air moves with the prescribed velocity. Next, varying the AoA is much more easily accomplished by altering the velocity angle as the inlet boundary condition in comparison with physically altering the airplane angle which would require new meshing, see Fig. 7.

Ramšak, M.

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)3, 147-155

Fig. 7. Computational domain and boundary conditions

the recommended value 10-4 to 10-5 significantly improves the picture, see Fig. 10. The mesh sensitivity for lift force drops from 2 to 0.04 %, which can be neglected.

The decision of choosing the right mesh density and convergence criteria is a compromise between result accuracy and CPU consumption. Since, in our case, the maximal CPU consumption is approx.

1 hour, the highest mesh density is used in all other computations, see Fig 10.

The assumption of the flow symmetry is set, resulting in decreasing the size of the computational domain by half, see Fig. 7. The symmetry boundary condition is prescribed at a cutting surface. There are 2 inlet boundaries; upstream on the left and downward for a positive AoA. They both have the same velocity and AoA boundary conditions. The sailplane surface is treated as a wall using nonslip boundary condition.

All other boundaries are openings with the prescribed static pressure 0.

Fig. 9. Computed drag force as a function of mesh density and convergence criteria Fig. 8. Surface mesh over the sailplane surface for middle mesh density

The flow regime has to be set. The Reynolds number value, based on the airfoil chord length 0.2 m and velocity 10 m/s, is of order 105, clearly indicating turbulent flow. We have used SST k-omega turbulent model [5] since it has become very popular in aerodynamic computations. The basic idea is to use a combination of two two-equation eddy viscosity models. Each model is applied in a region where it is better. The k-omega model is applied in a boundary layer and k-epsilon model to a free stream region.

2.2 Mesh Sensitivity and Convergence Three mesh densities have been used to obtain a mesh sensitivity analysis. As a result, an indicator and integral value of lift and drag forces has been computed, see Figs. 9 and 10. The drag force changed only 0.5% between 270,000 and 414,000 mesh nodes, while the lift changed by 2%.

Based on the large deviations of the lift force we obtained, we suspected that the convergence criteria have been too weak. Increasing it from

Fig. 10. Computed drag force as a function of mesh density and convergence criteria

An explanation of what happened with the computed aerodynamic forces in relation to the convergence criteria follows. In our application the drag force is mainly a consequence of shear stresses, while lift is mainly a result of the pressure difference between the upper and lower wing sections. During an iterative procedure of solving Navier-Stokes equations the pressure field is much more sensitive and oscillating than shear stresses on airplane walls.

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That is why the lift force is more sensitive to mesh density and convergence criteria in comparison to the drag force sensitivity.

value would be the optimal for a cargo airplane with a weight of 7 N and thrust 0.6 N, flying at 10 m/s. Using the actual sailplane weight, the computed glide angle is 9.2 degrees and the glide ratio 6.3. These figures are only valid for a velocity of 10 m/s.

Fig. 12. Streamlines at high angle of attack 15 deg and 10 m/s

Fig. 11. CPU consumption as a function of mesh density and convergence criteria

2.3 Numerical Results and Discussion As mentioned before, at each prescribed velocity, a series of results are computed using different AoA. In Figs. 13 and 14 the computed drag and lift forces are plotted as a function of AoA in the interval ‒5 to a huge 50 degrees for velocity 10 m/s. As expected, the drag force has a minimum of 0.4 N at zero AoA and it increases monotonically after that, while lift has a maximum at the approx value of AoA of 15 degrees. This maximum is a consequence of a recirculation vortex on the upper side of a wing, see Fig. 12. A practical consequence of these results is that the maximal weight of our sailplane could be approximately 15 N. Bearing in mind the steady flight assumption, such aircraft would need a thrust of 4 N to fly horizontally. If not, it would sail with a glide ratio of approx. 4 (this value is coincidentally the same as the drag force value), see Figs. 13 and 14. While the drag is always positive, the lift sign changes at an AoA value of –2 degrees. The resulting interpretation is: having a zero weight airplane, it would fly horizontally even at an AoA of ‒2 degrees having a thrust of 0.5 N. For lower AoA values, there is no airplane and horizontal oriented thrust to fly horizontally. The actual value of the AoA for our sailplane model is 0.3 degrees, where the lift force is approx. 3.2 N and the drag is 0.4 N. A more practical value is shown in the next graph in Figs. 15 and 16, where both glide angle and glide ratio are plotted as a function of the AoA. The best computed glide ratio is 11.6, obtained at an AoA of 3 degrees. This AoA 152

In the following Figs. 17 and 18 the drag and lift forces are plotted in a velocity range from 5 to 20 m/s as a function of the AoA, similar to Figs. 13 and 14. Using higher velocities, the aerodynamic forces are increasing, while the glide angle and glide ratio are approximately the same as a function of the AoA for all computed velocities, see Figs. 19 and 20. The minimal sailplane velocity could be determined using the lift diagram in Fig. 17 and sailplane weight 3.2 N. It is approx. 5 m/s. The actual sailplane characteristics are determined using its weight, 3.2 N. They are shown and discussed in the next section.

Fig. 13. Computed drag force as a function of the angle of attack at a velocity of 10 m/s

The comparison of computed lift force between the upper and lower sides of the wing results in a higher lift on the upper side. The reason is a higher average pressure difference on the upper side than on the lower side. At an AoA of 0 degrees the average pressure on the lower side of the wing is lower than 0, which means that the resulting lift force is downward.

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Fig. 14. Computed lift force as a function of the angle of attack at a velocity of 10 m/s

Fig. 17. Computed lift force as a function of the angle of attack and velocity

Fig. 15. Computed glide angle as a function of the angle of attack at a velocity of 10 m/s

Fig. 18. Computed drag force as a function of the angle of attack and velocity

Fig. 16. Computed Lift/Drag ratio as a function of the angle of attack at a velocity of 10 m/s

Fig. 19. Computed glide angle as a function of the angle of attack and velocity

At higher AoA values this force turns upward as

lower side even at high values of AoA. The typical lift difference is 3 times higher on the upper side.

The highest possible sailplane speed is obtained using numerical results, which could not be measured

expected. To conclude, the vacuum on the upper side of the wing is higher than the over pressure on the

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easily. The terminal speed is achieved by flying straight vertical. The AoA is zero. The drag equals weight. For our sailplane data this occurs at 30 m/s. If the desired velocity would be 100 m/s, the weight of the sailplane must be 32 N at the same geometry.

3 COMPARISONS OF COMPUTATION AND MEASUREMENT In the following section the measured and computed drag, angle of attack, glide angle and glide ratio are compared as a function of velocity, see Figs.

21 to 24.

we did not measure lower velocities, and this is the reason why the measured points are more scattered at lower velocities in comparison to high velocities in general. There is another reason for this involvement of the air movement and thermal soaring, which is more notable at lower velocities. And finally, flying fast is more fun.

The most significant variable is the AoA, see Fig. 22. The computed range of the AoA is from 2.2 to ‒1.4 deg for velocity 7.5 and 20 m/s respectively. The measured range is from 5 to ‒1 deg, scattered almost randomly. This was expected since the estimated measurement error of the AoA is the highest, as mentioned in the experimental section. However, the majority of the measurement points are between 2 and 3 deg, which is completely in line with the computed results.

Fig. 20. Computed lift drag ratio as a function of the angle of attack and velocity

Fig. 22. Comparison of computed and measured Angle of Attack as a function of velocity

Fig. 21. Comparison of computed and measured drag force as a function of velocity

All the measured velocities are in the range between 10 and 20 m/s. As mentioned above, the minimal computed velocity is 5 m/s for our sailplane model. After a short consideration we consider this to be a good result. It is very difficult to control straight and steady flight at low velocity taking into account the steady flight assumption. This is the reason why 154

Fig. 23. Comparison of computed and measured glide angle as a function of velocity

Next, the drag force comparison is discussed, see Fig. 21. The computed drag force increases from 0.4

Ramšak, M.

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to 2.0 N for 7.5 to 20 m/s, which is in accord with the measurements. If the result for a minimal velocity of 5 m/s is added to the discussion, then the drag force has a minimum at 7.5 m/s. This is only to be expected, since the AoA at low velocity should drastically increase changing the flow pattern at the suction side of the wing, including a recirculation vortex. In contrast to the AoA measured points, the drag points show a correct tendency to increase in line with increasing velocity. The quantitative agreement is excellent at 15 m/s. At lower velocities the computed drag is overestimated by approx 0.2 N, while it is underestimated for higher velocities.

Fig. 24. Comparison of computed and measured glide ratio as a function of velocity

The most interesting point is the comparison of flying performance expressed using glide angle and glide ratio, see Fig. 24. Since they are the result of the drag force, the discussion in the previous paragraph is also relevant here. The agreement is excellent at 15 m/s. Even at higher velocities the agreement is very good. There are two highly questionable measured points at 10 m/s having an excellent glide ratio of 30.

Obviously, these two flights were almost horizontal with decreasing velocity and obviously violating the steady flight assumption. As mentioned at the beginning of this section, the measured values at low velocities are questionable. Interestingly, the measured glide ratio clearly indicates a local maximum of 20 between 10 and 15 m/s, while the computed glide ratio has a maximum of 10 at 7.5 m/s. We are confident at least of one reason for the quantitative disagreement,

that is the accuracy of the sailplane model geometry. It is roughly estimated at ±2 mm, which is good enough for sailplane trunk estimation but definitely poor for a wing approximation. There is another important geometry parameter e.g. the inclination angle between the front and back wings. In the real sailplane it is optimized for the best performance and stability, while in the numerical model it is zero. This could explain the better glide ratio when measured rather than computed.

5 CONCLUSIONS The aerodynamic forces and flying performance of the radio controlled sailplane model were measured using a video camera and numerically modelled using computational fluid dynamics.

The comparison of flying performance is good at higher velocities, while it is relatively poor at lower velocities, where the assumption of steady flight was questionable. The main reason is human factor as the pilot was controlling a very unstable flight. This is indicated by the highly scattered measured points. The source of large deviations is definitely not the velocity measuring error, which was computed and calibrated as ±1%. We believe that the second source of partial disagreement between the measured and computed results is poor geometry approximation. In the future a more accurate geometry acquiring procedure should be implemented.

6 REFERENCES [1] Stefanović, Z., Kostić, I. (2010). Analysis of the sailplane final approaches performed by cosinelaw speed variations. Strojniški vestnik - Journal of Mechanical Engineering, vol. 56, no. 7-8, p. 436-446.

[2] Radio controlled glider, Longshot 2 (2009), from: http://www.horejsi.cz/, accessed at 2009-11-01.

[3] Gruner, H. (1977). Photogrammetry: 1776-1976.

Photogrammetric Engineering and Remote Sensing, vol. 43, no. 5, p. 569-574.

[4] Anderson, D.A., Tannehill, J.C., Pletcher, R.H. (1984), Computational Fluid Mechanics and Heat Transfer, Hemisphere Publishing Co., New York.

[5] Menter, F.R. (1994). Two-equation eddy-viscosity turbulence models for engineering applications, The American Institute of Aeronautics and Astronautics (AIAA) Journal, vol. 32, no. 8, p. 1598-1605.

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Strojniški vestnik - Journal of Mechanical Engineering 58(2012)3, 156-164 DOI:10.5545/sv-jme.2011.097

Paper received: 2011-05-04, paper accepted: 2012-01-24 © 2012 Journal of Mechanical Engineering. All rights reserved.

Use of Genetic Algorithms for Optimal Design of Sandwich Panels Subjected to Underwater Shock Loading Salimi, H. – Saranjam, B. – Hoseini, A. – Ahmadzadeh, M. Hamidreza Salimi1,* – Bahador Saranjam2 – Ahmad Hoseini Fard1 – Mohsen Ahmadzadeh1 1 Shiraz Branch, Islamic Azad University, Shiraz, Iran 2 Department of Marine Structures, Air Naval Research Center, Shiraz, Iran

Sandwich composite panels are increasingly used in the construction of marine vehicles because of their outstanding strength, stiffness and light weight properties. However, the use of composite panels comes with difficulties in the design process as a result of the large number of design variables involved, including composite material design, topologies and laminate schemes. Hence, this work deals with the presentation of an optimal design of laminated composite sandwich marine structures subjected to underwater explosion. The optimization process is performed using a genetic algorithm (GA), associated with the finite element method (FEM) for the structural analysis. In this optimization procedure, sandwich composite panel finite element model is built up, then the coupled acoustic–structural arithmetic from the widely used calculation program of the finite element “ABAQUS” is used to simulate and analyze the transient dynamic response of a sandwich composite panel that experiences loading by an acoustic pressure shock wave resulting from an underwater explosion “UNDEX”.

This approach is well suited for enhancing the response of orthotropic and/or laminated composites which involve many design variables. In GA method, a new approach is considered to improve this evolutionary algorithm for laminated stacking sequence and material selection of face layer and cores. Simple crossover, modified ply mutation, and a new operator called “ply swap” are applied to achieve these goals.

Keywords: optimization, genetic algorithm, finite element method, sandwich panel, underwater explosion, cavitation

0 INTRODUCTION Sandwich structures by definition are made of two thin faces with high stiffness and high strength and a core with low density and low stiffness. As an effective weight saving structure, sandwich structures were first applied in small airplanes during World War I. Development of core materials has continued from the 1940's through today in an effort to reduce the weight. Nowadays, sandwich structures are used in almost every industrial sector ranging from buildings to aerospace applications because of the drive for lightweight structures with high stiffness to weight ratio, high bending strength to weight ratio, and good acoustical insulation [1]. Due to their high specific strength and high shock resistance signatures, composites are widely used as face materials in sandwich structures especially for large ship hulls.

High stiffness combined with high energy absorption capability makes FGRP (Fiber Glass Reinforced Plastics) and CRP (Carbon Reinforced Plastics)faced sandwich structures ideal as the hull of marine vehicles. End-grain balsa wood and the closed-cell polymer foams such as polyvinyl chloride (PVC) or polyurethane are commonly used today as core materials in ship industry.

However, a large number of design variables and complex mechanical behavior associated with such materials turn the structural design into much more difficult and laborious than those involving conventional materials [2].

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The earlier works in the field of composite structures optimization employed the same methods already used to optimize conventional material structures. These methods are based on gradients of the objective and constraints functions with respect to the design variables, which are considered to be continuous in the design space. Such works resulted in limited success because composite laminate design falls on a discrete optimization problem, since in practice the variables are restricted to few values imposed by the manufacturing process. Moreover, the composite optimization problems typically involve multimodal search spaces which may lead gradient based methods to converge to locally optimal regions in the design space [3]. Many other optimization techniques have been tested as an alternative to the gradient based methods, having the genetic algorithm (GA) stand out the others because it perfectly adjusts to the characteristics of the composite optimization problem. GAs are probabilistic search methods mimicking the biological reproduction and natural selection process through random but structured operators. The design variables usually restricted to discrete values are coded as genes using binary or integer numbers and grouped together in chromosomes strings that represent an organism (a possible solution in the design space). Instead of working with just one search point in the design space, GA uses a population of designs that by reproduction and selection operators evolve through successive generations. Many search points dispersed in the design space prevent the GA to get stuck in locally optimal regions, avoiding a

*Corr. Author’s Address: Air Naval Research Center, 7194915685, Shiraz, Iran, hr.salimi@gmail.com

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premature convergence of the process. New designs are generated by the reproduction process that consists of the application of the genetic operators to parents selected from the existing population. These genetic operators are counterparts of the natural genetic mechanisms acting over the chromosomal strings of the organisms [4]. The selection of parents for the reproduction process and the selection of organisms to fill each new generation are both probabilistic.

However, the chances of selection of each organism is proportional to its fitness, as it happens in the nature where fittest organisms have more chances to reproduce and to continue in the next generation.

The organism fitness is obtained directly from an objective function using simple structure information and gradient evaluations are not required. Various researchers have studied the problem of sandwich panels optimization, but the use of GA and FEM together has not been widely explored, especially when the structure is subjected to underwater shock loading. In real designs cases, when the structural geometry is usually complex and the prediction of the structural behavior must be accurate, it is necessary to use numerical tools, such as the FEM, for the structural analysis.

In the present study, the optimal design of sandwich panels subjected to underwater shock loading is treated. The effect of cavitation on the structure is also considered. Cavitation is mentioned to a phenomenon which occurs in water, caused by the reflection of a shock wave at a free surface.

For large structures, such as the design of a hull or superstructure, the optimization is divided into smaller, tractable, subproblems using predefined local loads to constrain the optimization [5]. The mass of the sandwich plates with orthotropic facesheets and core is minimized, considering deflection and certain failure loads as constraints. The design process requires the specification of the stacking sequence, which is defined by the orientation and material type of each ply layer, creating a discrete optimization problem.

Many researchers have proposed modifications to the classical GA structure to take advantage of composite laminate characteristics and minimize the computational cost. Some of these new strategies are applied in this work, consisting essentially of a GA restructuring of the variable codification and the genetic operators.

Given the superior strength-to-weight ratio, sandwich composite panels have been used extensively in the main structure of ships and underwater vehicles. In the present work an example

of optimization of sandwich composite panels using parallel computing between the FEA and a developed genetic algorithm are studied. This approach is well suited for enhancing the response of orthotropic and/ or laminated composites which involve many design variables.

It is assumed that a sandwich panel consists of various facing lamination and different core thickness (Fig. 1). This plate structure is typical for the deck, side, and bottom of a ship hull girder. The loads acting on a panel in a ship is in-plane compression or tension, resulting from the overall hull-girder bending moment or torsion, shear force resulting from the hull-girder shear force, and lateral pressure resulting from the external wave or shock loading. Most studies of such structures generally consider shock loads in air.

Fig. 1. Typical sandwich panel structure

This study attempts to utilize the finite element code “ABAQUS” [6] to examine the dynamic reaction of a sandwich panel to underwater shock loads. Underwater explosion pressure in that study is analyzed using Cole’s formula [7]. Finally, the optimized stacking sequence of facesheets, the number of plies, fiber orientations and core thickness are determined by varying the ply angles and core thickness in order to achieve the minimum weight.

1 APPROXIMATION OF SHOCK LOADING During an underwater explosion, the charge instantly converts the explosive energy into hot gas of approximately 3000 °C and induces a shock pressure of up to 5000 MPa [7]. This investigation only considers the effects of the shockwaves. This shockwave propagates into the water medium with a spherical shape. The shock energy deliver to the structure produced by the underwater explosion is a function of the charge weight and the standoff distance.

The shock pressure at a given point has a sharp peak in time, followed by a decaying exponential function, which is given by:

P ( t ) = Pmax ⋅ e

Use of Genetic Algorithms for Optimal Design of Sandwich Panels Subjected to Underwater Shock Loading

t −  λ,

(1)

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where Pmax is the peak pressure of the shock wave; λ is the time decay constant, and t is the time since the shock wave front arrived at the target point. For trinitrotoluene (TNT) or Pentolite, the peak pressure Pmax and the time decay constant λ are [7]: A  W 1/ 3  1

Pmax = K1  , (2)  R    θ = K 2 ⋅W

1/ 3

 W 1/ 3 ⋅  R 

  

A2

, (3)

where W is the explosive weight, R is the standoff distance, and K1, K2, A1 and A2 are the shock parameters of the explosive as defined in Table 1.

Table 1. Shock wave parameters [8] Constants TNT

A1 1.18

A2 -0.185

K1 52.12

K2 0.092

2 SIMULATION AND ANALYSIS OF DYNAMIC RESPONSES OF A SANDWICH COMPOSITE PANELS In this work, the finite element code, “ABAQUS” [6], was applied to analyze the dynamic responses of sandwich composite panel subjected to an underwater explosion. ABAQUS consists of two main analysis products: ABAQUS/Standard and ABAQUS/ Explicit. ABAQUS/Standard is a general purpose analysis product that can solve linear and nonlinear problems involving the static, dynamic, thermal and electrical response of components. It solves a system of equations implicitly at each increment whereas ABAQUS/Explicit finds a solution forward through time in small time increments without solving a coupled system of equations at each increment [6].

ABAQUS/Explicit is a special purpose analysis product that uses an explicit dynamic finite element formulation. It is convenient for modeling transient dynamic events, such as blast, acoustic and shock problems. In ABAQUS, the shock analysis of a structure includes acoustic finite elements to model the effects of the mass of the fluid and incident wave loading to model UNDEX effects on the structure interacting with fluid. The explosive load is defined with an incident wave load. The load is applied on both the structure and the fluid at the common interface and is similar to a distributed load. These loads are supported only on transient dynamic procedures.

In Fig. 2, the shock loads acting on a sandwich panel in a ship arrangement is shown. The structural part is simulated by S4R four-node doubly curved 158

shell element, shown in Fig. 3; and the infinite fluid domain was modeled and meshed using fluid 4-node AC3D4 acoustic tetrahedral elements in ABAQUS. The whole structural model surrounded by the fluid, as a FEM model, is depicted in Fig. 4. The fluid elements were given the properties of water. The bulk modulus of water was specified using the formula ρc2, where ρ is the density of water and c is the speed of sound in water.

The explicit time integration method is employed for computing time integration. Since the explicit time integration method is a conditional stable integration, the magnitude of the time step of the stable integration is a function of the element characteristic length.

Therefore, when the mesh is divided into too small units, computational time is extended. In addition to considering integration stability, the division of the fluid element must account for the frequency of the shockwave, primarily because during transmission of the shockwave in the medium, the shockwave will be refracted and reflected when it runs into a gap or boundary, cause the shockwave to undergo superposition on or cancellation by the incident wave.

To avoid this phenomenon in the computational process, which can result in significant errors, one must ensure that when analyzing a shockwave, each time step must not exceed that of two elements.

Since the wavelength of a shockwave decreases as the frequency of a shockwave increases, this work can determine the minimum element length by calculating the upper range of shockwave frequency.

The general principle is Lmax < c/(n·fmax), where Lmax is the maximum permitted element length of the fluid element, fmax is the upper frequency range of the shockwave, c is the acoustic speed of the fluid, and n is the wavelength of the shockwave within the element, so the recommended value is n ≥ 6 [6].

Fig. 2. Attack geometry of an underwater explosion

The distance between the explosion point and target panel is 7.62 m, and the wavelength of the underwater shockwave is 6.7 to 10 λ, as recommended

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by Keil [9]. Thus, the upper frequency range is 2665 Hz. To ensure analytical accuracy, this study uses n = 9; the length of the fluid element along the shockwave transmission direction is 60 mm.

However, contrary to classical optimization methods, GA does not provide an absolute optimum solution and the final result has to be obtained by inspection.

The major strength of the GA method is multi-point discrete search technique ability, so it is possible to reach the global optimum.

3.1 GA Details

Fig. 3. The 4-node thin-shell element

Fig. 4. Finite element models

The boundaries of the fluid may cause shockwave refraction or reflection, resulting in its superposition on or cancellation by the incident wave. To prevent this phenomenon, the boundary condition of the fluid element is set as a non-reflective boundary during the analysis. Restated, all pressure flows out of this boundary and will not cause reflection which typically affects the outcome of the analytical range.

Between the sandwich panel and fluid, the nodal motion between the fluid and solid is connected by establishing the restraining condition of the interactive surface.

3 OPTIMIZATION APPLICATION As discussed previously, the genetic algorithm is applied here to optimize a laminated composite sandwich panel which could not be performed appropriately by the gradient concept. GA is an optimization method that appeared in the early 70s. It is based on a simulation of Darwin’s theory of species evolution. As such, GAs combine both exploration of the search space and exploitation of visited points.

Typical GA elements include the encoding structure of the individual, operators to affect individuals (mutation, crossover and ply swap), a fitness criterion to determine the goodness of each individual and a selection function (selection). From one population GA then builds a new population with better global fitness to the criterion. Constraints in GA are handled in three ways: data structuring control repair operator and penalty functions. Data structuring control refers to defining the design variables, so that the optimizer always produces feasible designs. Since only the fittest individuals survive and reproduce, the genes of weaker individuals disappear gradually. Therefore, it follows if the environment (fitness law) does not change during the process, then finally the population will converge to a state where every individual has the fittest genes [10].

3.1.1 Population There seems to be no novel idea by which to exactly decide the size of the population. This is especially true for complex problems. However, Goldberg et al. proposed an approximate population scaling law [11].

Biologically, individuals of the population make up a set of chromosomes which consist of combined genes and represent a solution set. In the present case, each ply must be encoded for the use in the GA. The values of plies are recorded in chromosomes as integer number encoding [3], For example, integer values from 0 to 2 represent the orientation of each ply. The positive integers map to orientation angles 0 to 90 and ±45 degrees from 1 to 2, respectively, with the zero encoding representing an empty ply. In the present work chromosomes are composed of four parts (refer to Fig. 5).

Fig. 5. Chromosome structure

The distance between the explosion point and target panel is 7.62 m, and the wavelength of the

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underwater shockwave is 6.7–10 λ, as recommended

by Keil [9]. Thus, the upper frequency range is 2665 Hz. To ensure analytical accuracy, this study uses n = 9; the length of the fluid element along the shockwave transmission direction is 60 mm.

3.1.2 Fitness Before making the random selection, each chromosome string is evaluated in the objective function relative to the chromosome’s fitness. Stresses and deflections in each element are first calculated by FEA. Values of the safety factor for material failure is delivered from the FEA process to the GA process of Fig. 9 and used for fitness evaluation. The goal of the first step of the optimization is to find the lightest design for each panel that does not violate any of the imposed constraints. The problem is formulated as: Minimize W( τ ) such that Gj( τ ) ≥ 0, j = 1, ..., ng, where W( τ ) is the panel weight as a function of the design variables τ , and ng is the number of constraints. The constraints are normalized, so that a constraint value of –0.1 corresponds to 10% constraint violation, while a constraint value of 0.1 corresponds to a 10% constraint margin. The design margin of safety is then defined by the most critical constraint Gmin = min(Gj). If Gmin is negative, the design is infeasible, and a penalty is added to the objective function to help the search move into the feasible area of the design space. If Gmin is positive, we have a feasible design with a positive margin, and we want to introduce a slight reduction to the objective function that will be a bonus for that margin.

3.1.3 Selection Selection methods include roulette, ranking, tournament and elitist preserving [12]. The tournament selection approach is used here, with an elite’s preservation. A random number generator in the GA plays an important role in the selection process of the various selection methods just cited. the tournament technique transfers the best fitness individuals among a certain number of selected individuals into the next generation by means of the random number. The process is repeated until the size of the population reaches the quorum. The elite preservation strategy prevents the best individual in a generation from being destroyed by mutation, crossover, and ply swap. The elite concept enables the best individual to always progress to the next generation [13].

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3.1.4 Crossover Crossover is an essential GA operator, having the fundamental task of creating new organisms (children) in a reproduction process. It acts by combining genetic information taken from a pair of organisms (parents) selected from the current population. The created children will hopefully be better than, or at least equivalent, in fitness to its parents. The crossover operator is applied by first generating a random number to define the crossover point. Then, the gene strings of both material and orientation chromosomes are split at the same point in both parents. For example, by splicing together the left part of the string of one parent with the right part of the string of the other parent, two child strings are generated (Fig. 6).

The crossover operator is usually applied with some probability [14].

Fig. 6. Crossover operator 3.1.5 Mutation After a child is created, the operators of adding, deleting, or mutating genes occur with small probabilities. These operators make up genetic mutation, and are illustrated in Fig. 7.

Fig. 7. Mutation

In order to avoid too rapid convergence of the population to a local optimum, the mutation function

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is used. For example, if the value of the first gene for all designs in the population achieved the same value, the mutation operator would be the primary means of introducing a different value to that bit; thus, mutation can help the crossover operator remain effective if the characteristics of all the designs in the population become uniform. When adding a ply stack, a uniform random number is chosen to the genes of the chromosomes. For the design problems considered in this work, outer plies in the laminate will get set up faster because they have a greater influence on the objective function, see Fig. 7a. To delete a ply stack, a random number is chosen and the corresponding stack is removed from the stacking sequence by replacing it with a 0 gene. The laminate is then re-stacked so that all empty plies are pushed to the outer edge of the laminate, see Fig. 7b. Gene alteration is shown in Fig. 7c. Each gene in the string switches with a small probability to any other permissible integer value.

3.1.6 Ply Swap The ply swap operator is implemented by randomly selecting two genes in the string and switching their positions, see Fig. 8. The main characteristic of the ply swap operator is the ability to modify laminate stack sequence without changes of the total number of plies with fibers oriented on each permissible direction. Ply swap can be effective for problems where certain parts of the laminate stacking sequence get set up faster than others. For example, if the optimized stacking sequence for the outer section of the laminate has been determined first (as is the case for laminate design problems which involve bending), the ply swap operator may help the GA determine the optimized orientations for the inner part of the laminate by swapping plies from each section.

Fig. 8. Ply Swap operator

3.1.6 Convergence Criteria It is known that GA does not lead to a unique solution and this is one of the major drawbacks of this technique. However, convergence does occur as fitness becomes better and this makes it possible to identify an appropriate time to terminate the GA. After the computation of several populations, the last one is then composed of several very good individuals

according to the fitness criterion. Three convergence criteria are used in this work. If any of them is reached, then the optimization process terminates.

These criteria are: 1. When the percentage difference between the average value of all the designs and the best design in a population reaches a very small specified value c1, Wa − W * × 100 ≤ c1 , (4)

Wa where W* is the fittest design in a population, Wa is the average objective value in a generation defined by: 1 µ Wa = ∑ W j , (5)

µ j =1 and μ is the population size, 2. If the fittest design has not changed for 50 successive generations, or the difference of the fittest design of the current generation, Wc*, and that of 50 generations before, Wb* , is less than a small amount c2, i.e., Wc* − Wb* × 100 ≤ c2 . (6)

Wc* 3. If the maximum number of generations is reached.

3.2 Parallel Computing Technique Genetic Algorithm is very suitable for the parallel computing scheme because multiple design points should be evaluated in a calculation step. In other words, the algorithm can be programmed so that multiple design points in a generation may be divided into some sub-populations and the corresponding calculation of each sub-population is allocated to one processor in a parallel computer. The programming was coded with MPI (Message Passing Interface) library in this study. Its schematic diagram is shown in Fig. 9. The computing system used was CRAY-T3E and a PC cluster with 16 Pentium-4 processors. The total CPU run time was approximately 3 days.

4 OPTIMAL DESIGN OF COMPOSITE PLATES 4.1 Problem Definition The optimization problem can be formulated as finding the face sheet parameters (the number of

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layers, their materials, and ply angles) and the core thickness that satisfy strength and deflection constraints while minimizing the weight of the panel.

Constraints considered include face sheets strength constraint, core transverse shear strength constraint, panel deflection constraint, and the symmetric layup constraint, but this is satisfied automatically by the coding rule that only half of the laminates are represented in a chromosome.

as min W ( τ ) , such that; τ Gc ( τ ) ≥ 0 (Compressive strength constraint), Gt ( τ ) ≥ 0 (Tensile strength constraint), Gc ( τ ) ≥ 0 (Shear strength constraint), Gu ( τ ) ≥ 0 (Displacement constraint), tc ∈ {8, 10, 12} (Core thickness in mm), θi ∈ {0°, ‒90°, ±45°}, i = 1, ..., n (ply angles), mi ∈ {Carbon/Polyester, Glass/Polyester} n ∈ [nmin, nmax].

The critical constraint is defined as: Ga ( τ ) = min {Gc, Gt, Gs, Gu}, (8)

and the constrained optimization problem is transformed into an unconstrained maximization problem for the GA. This is done by using penalty parameters. The fitness function to be maximized is defined as:  −W ( τ ) + Gcr δ , Gcr ≥ 0 ,

(9) F ( τ ) =  p −W ( τ ) (1 − Gcr ) , Gcr < 0 , where δ and p are bonus and penalty parameters, respectively.

Table 2. Material properties of the laminated facesheets Property

Fig. 9. Schematic diagram of Genetic Algorithm with parallel computing

The set of discrete (and commercially available) values of design variables is expressed as a vector τ = {θ1, ..., θn, m1, ..., mn, tc, n}, where n is an implicit design variable dictated by the number of layers in the face sheet stacking sequence; θi and mi are the orientation and material of the ith ply, respectively; tc is the core thickness. Material properties for the ply and the foam are provided in Table 2 and Table 3, respectively. The design problem is typically formulated to provide a minimum mass structure:

n   W = tc ρc + 2∑i =21 t if ρif  ( ab ) , (7)  

where ρc and ρf are material densities of the core and face ply, respectively; n is the total number of plies; ab is the panel area. The optimization problem with displacement and strength constraints can be expressed 162

Longitudinal modulus (E11) [GPa] Transverse modulus (E12) [GPa] In-plane shear modulus (G12) [GPa] Poisson’s ratio (ν12) Density (ρ) [kg/m3] Longitudinal tensile Strength (XT) [MPa] Longitudinal compressive Strength (XC) [MPa] Transverse tensile Strength (YT) [MPa] Transverse compressive Strength (YC) [MPa] In-plane shear strength (S) [MPa] Thickness (tf) [mm]

Glass Carbon Polyester Polyester 19.2 55 19.2 55 3.2 7.1 0.32 0.3 1619 1500 227 350 150 280 227 350 150 280 35 70 0.7 0.5

5 RESULTS AND DISCUSSION The optimum weight of the laminate is obtained in terms of thickness of plies, stacking sequence, number of plies etc., for a given underwater explosion induced by 18.3 kg TNT fired 7.62 m away from the bow of the hull. Therefore, the spherical incident wave is applied as a transient load active on both the acoustic and structural meshes at their common surfaces (the wetted interface). The geometric shape of the sandwich panel in a ship arrangement is shown in Fig. 10.

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Table 3. Material properties of the core Material properties In-plane tensile modulus [GPa] Transverse tensile modulus [GPa] In-plane tensile strength [MPa] Transverse tensile strength [MPa] In-plane compressive modulus [GPa] Transverse compressive modulus [GPa] In-plane compressive modulus [MPa] Transverse compressive strength [MPa] Transverse shear modulus [GPa] Transverse shear strength [MPa] Density [kg/m3] Poisson’s ratio

H-250 PVC 0.2898 0.2898 6.1824 8.5008 0.1449 0.3864 5.1198 5.6028 0.104328 4.347 252.8842 0.32

When the pressure is lower than the fluid vapor pressure, local cavitation effects appear between the fluid and structure which causes the target to separate from the fluid. This local cavitation is depicted in Fig. 12; blue colors specify the zone and distribution of local cavitation formed on the fluid-solid interface after the shockwave hit the structure.

The parameters used for the GA are shown in Table 4. By parametric study, the probabilities of mutation, crossover and ply swap were selected as 0.1, 0.75 and 0.05, respectively. With a population size of 30, iterations more than 50 were sufficient for convergence.

Table 4. Parameters of GA Parameters Chromosome length Upper limit of generation Population size Probability of mutation Probability of crossover Probability of ply swap

Fig. 10. Sandwich panel in this study

Value 18 100 30 0.1 0.75 0.05

Table 5. Optimized materials and core thickness Facesheets materials 1st Best 2nd Best 3rd Best

[C/G/C/C/G/G]S [G/C/G/C/G/G]S [G/C/C/G/C/G/G]S

tc [mm]

W [kg]

12 12 10

113.18 118.93 120.65

Table 6. Optimized facesheets orientations 1st Best 2nd Best 3rd Best

Fig. 11. Shock wave propagation

Fig. 12. Cavitation zone

The shock wave propagation is shown in Fig. 11. The maximum shock wave was calculated as 1.491×107 Pa which is close to the theoretical value of 1.488×107 Pa based in Eq. (2).

Facesheets orientations [0-90/0-90/±45/0-90/±45/±45]S [0-90/0-90/±45/±45/0-90/±45]S [±45/0-90/0-90/±45/0-90/±45/±45]S

W [kg] 113.18 118.93 120.65

The possible maximum number of plies was set as 16 and only 8 plies were used as the design variables because all laminates were assumed to be symmetric.

The symmetric laminate may have any number of plies and each ply may be made of either Glass/Polyester or Carbon/ Polyester (refer to Table 2 to compare the properties). The usable ply angles were limited to 0 to 90° and ±45° for the practical application. The allowed thickness of the core is 8, 10 or 12 mm and made of Divinycell HD-250. Material properties for the core are provided in Table 3. To start the optimization, the base model is built in “ABAQUS” version 6.10.

Then, the “ABAQUS” Input File (.inp) is generated.

This .inp file is modified with design variables of each chromosome string. To calculate the fitness value of each member of the population, “ABAQUS” runs the input file. Fig. 13 shows the convergence of fitness

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with the number of generations for four different initial populations. It could be observed that about 50 generations are required for convergence. Also, all of the four diagrams converge to the unique value. The GA stopping condition is either a limit on the total number of function evaluations or when there is no change in the fitness function between generations, whichever occurs first. Results for three best stacking sequences are shown in Tables 5 and 6.

Fig. 13. Convergence plot for weight minimization with four different initial populations

6 CONCLUSIONS A technique for combining genetic algorithms with the finite element method to minimize the weight of sandwich panel with laminated composite facesheets with several design variables is described in this paper.

The GA was successfully applied to obtain the optimal design of sandwich panels. It has been shown that the number of plies, stacking sequence of facesheets, fiber orientations and core thickness could be improved considerably by optimization process, which was demonstrated by a comparison of the design constraints between initial and optimized designs. The performance of the GA in optimized design of sandwich panels was studied, showing that the method is very efficient in finding near optimal solutions, and an important saving in computer time can be obtained by using of suitable values for the GA parameters and when results of different analyses are stored.

The resultant design with reasonable values of design variables proves that the optimized values

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of the design variables are even difficult to guess for a skillful engineer with exceptional experience.

The results demonstrated that when relatively small populations associated with a large limit of the number of generations are used, better performances of the GA are obtained.

7 REFERENCES [1] Zenkert, D. (1997). The Handbook of Sandwich Construction. Chameleon Press, London.

[2] Goubalt, P., Mayes, S. (1996). Comparative analysis of metal and composite materials for the primary structures of a patrol craft. Naval Engineers Journal, vol. 108, no. 3, p. 387-394, DOI:10.1111/j.1559-3584.1996. tb01575.x.

[3] Soremekun, G.A.E., Gürdal, Z., Haftka, R.T., Watson, L.T. (2001). Composite laminate design optimization by genetic algorithm with generalized elitist selection.

Computers and Structures, vol. 79, p. 131-143, DOI:10.1016/S0045-7949(00)00125-5.

[4] Goldberg, D.E. (1989). Genetic algorithms in search, optimization, and machine learning. Addison-Wesley Publishing Company, Boston.

[5] McMahon, M.T. Watson, L.T. (2000). A distributed genetic algorithm with migration for the design of composite laminate structures.

Parallel Algorithms and Applications, vol. 14, p. 329-362, DOI:10.1080/10637199808947394.

[6] ABAQUS User’s Manual, Version 6.10 (2010). Hibbitt, Karlsson & Sorensen, Inc., Michigan.

[7] Cole, R.H. (1965). Underwater explosions. Dover Pub. Inc., New York.

[8] Rajendran, R. (2009). Numerical simulation of response of plane plates subjected to uniform primary shock loading of non-contact underwater explosion.

Materials and Design, vol. 30, no. 4, p. 1000-1007, DOI:10.1016/j.matdes.2008.06.054.

[9] Keil, A.H. (1961). The response of ships to underwater explosions. Transaction of Society of Naval Architecture and Marine Engineering, vol. 69, p. 366-410.

[10] Eiben, A.E., Smith, J.E. (2007). Introduction to Evolutionary Computing, 2nd ed. Springer, Berlin.

[11] Goldberg, D.E., Deb, K., Clark, J.H. (1992). Genetic algorithms, noise, and the sizing of populations.

Complex Systems, vol. 6, no. 4, p. 333-362.

[12] Gen, M., Cheng, R. (2000). Genetic algorithms and engineering optimization. Wiley-Interscience, New York.

[13] Michalewicz, Z. (1996). Genetic algorithms + data structures = evolution. Springer, New York.

[14] Gürdal, Z., Haftksa, R.T., Hajela, P. (1998). Design and optimization of laminated composite materials. WileyInterscience, New York.

Salimi, H. – Saranjam, B. – Hoseini, A. – Ahmadzadeh, M.

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)3, 165-174 DOI:10.5545/sv-jme.2011.167

Paper received: 2011-09-06, paper accepted: 2012-01-27 © 2012 Journal of Mechanical Engineering. All rights reserved.

Application of Taguchi Method for Surface Roughness and Roundness Error in Drilling of AISI 316 Stainless Steel

Çiçek, A. - Kıvak, T. - Samtaş, G. Adem Çiçek1 -Turgay Kıvak2,*- Gürcan Samtaş2 1 Düzce University, Faculty of Technology, Department of Manufacturing Engineering, Düzce, Turkey 2 Düzce University, Cumayeri Vocational School of Higher Education, Düzce, Turkey In this study, the effects of deep cryogenic treatment and drilling parameters on surface roughness and roundness error were investigated in drilling of AISI 316 austenitic stainless steel with M35 HSS twist drills. In addition, optimal control factors for the hole quality were determined by using Taguchi technique. Two cutting tools, cutting speeds and feed rates were considered as control factors, and L8(23) orthogonal array was determined for experimental trials. Multiple regression analysis was employed to derive the predictive equations of the surface roughness and roundness error achieved via experimental design. Minimum surface roughness and roundness error were obtained with treated drills at 14 m/min cutting speed and 0.08 mm/rev feed rate. Confirmation experiments showed that Taguchi method precisely optimized the drilling parameters in drilling of stainless steel.

Keywords: cryogenic treatment, drilling, surface roughness, roundness error, Taguchi method

0 INTRODUCTION To provide cost effectiveness in manufacturing and especially machining operations, there is a continuous need to reduce tooling costs. The most well-known methods used to reduce tooling costs are various applications of more resistant tool materials, heat treatments, cutting fluids, speed and feed rates, and the development of coated cutting tool [1]. One of these methods is the application of cryogenic treatment used in recent years. Over the past few years, there has been an increasing interest in the application of cryogenic treatment [2]. Cryogenic treatment has been an effective method in improving the tool life of different cutting tools (in particular HSS and cemented carbide) used in machining processes. There are many studies, which have proven significant increases in tool life after deep cryogenic treatment (from –125 to –196°C) in the literature. It was reported that deep cryogenic treatment increased tool life by 90 to 400% [3]. In addition, lower cutting forces and surface roughness were obtained with treated cutting tools. Cryogenic treatment not only improves the tool life, but also provides significant benefits for machining conditions [4].

The surface quality is an important parameter to evaluate the productivity of machine tools as well as machined components. Hence, achieving the desired surface quality is of great importance for the functional behavior of the mechanical parts [5]. A reasonably good surface finish is desired for improving the tribological properties, fatigue strength, corrosion resistance and aesthetic appeal of the product. Excessively better surface finish may involve more cost of manufacturing. The surface

roughness and roundness error are affected by several factors including cutting tool geometry, cutting speed, feed rate, the microstructure of the workpiece and the rigidity of the machine tool [6] and [7]. These parameters affecting the surface roughness and drilled hole qualities (roundness, cylindricality and hole diameter) can be optimized in various ways such as Taguchi method and multiple regression models.

Therefore, a number of researchers have been focused on an appropriate prediction of surface roughness and roundness error [8] and [9].

The Taguchi method has been widely used in engineering analysis and is a powerful tool to design a high quality system. Moreover, the Taguchi method employs a special design of orthogonal array to investigate the effects of the entire machining parameters through the small number of experiments. Recently, the Taguchi method has been widely employed in several industrial fields, and research works [10] and [11]. By applying the Taguchi technique, the time required for experimental investigations can be significantly reduced, as it is effective in the investigation of the effects of multiple factors on performance as well as to study the influence of individual factors to determine which factor has more influence, which one less [12] and [13]. Yang and Chen [14] used the Taguchi parameter design in order to identify optimum surface roughness performance on an aluminium material with cutting parameters of depth of cut, cutting speed, feed rate and tool diameter. It was found that tool diameter is not a significant cutting factor affecting the surface roughness. Bagci and Ozcelik [15] used the Taguchi method to explore the effects of drilling parameters on the twist drill bit temperature for a design optimization

*Corr. Author’s Address: Düzce University, Cumayeri Vocational School of Higher Education, 81700, Cumayeri, Düzce, Turkey, turgaykivak@duzce.edu.tr

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of cutting parameters. Their works revealed that the Taguchi method was a powerful approach used in design of experiment. Davim and Reis [16] presented an approach using the Taguchi method and ANOVA to establish a correlation between cutting speed and feed rate with the delamination in a composite laminate. A statistical analysis of hole quality was performed by Furness et al. They found that feed rate and cutting speed have a relatively small effect on the measured hole quality features. With the expectation of hole location error, the hole quality was not predictably or significantly affected by the cutting conditions [17].

Tsao and Hocheng [18] performed the prediction and evaluation of thrust force and surface roughness in drilling of composite material. The approach used Taguchi and the artificial neural network methods. The experimental results show that the feed rate and the drill diameter are the most significant factors affecting the thrust force, while the feed rate and spindle speed contribute the most to the surface roughness. Zhang et al. [19] performed a study of the Taguchi design application to optimize surface quality in a CNC face milling operation. Taguchi design was successful in optimizing milling parameters for surface roughness.

Nalbant et al. [20] utilized the Taguchi technique to determine the optimal cutting parameters for surface roughness in turning of AISI 1030 steel with TiN coated inserts. Three cutting parameters such as insert radius, feed rate, and depth of cut, are optimized for minimum surface roughness. Kurt et al. [21] employed the Taguchi method in the optimization of cutting parameters for surface finish and hole diameter accuracy in dry drilling processes. The validity of the Taguchi approach to process optimization was well established.

The objective of this study is to investigate the effects of different heat treatments applied to M35 HSS drills and the drilling parameters on surface roughness and roundness error, and is to determine the optimal drilling parameters using the Taguchi technique and multiple regression analysis in drilling of AISI 316 stainless steel.

1 EXPERIMENTAL METHODS

Table 1. Chemical composition of AISI 316 austenitic stainless steel C 0.05

Si

Mn

P

S

Cr

0.380 0.971 0.039 0.006 16.58

Ni 9.94

Mo

Cu

2.156 0.321

Distance to drill tip from the tool holder was determined as 30 mm for eliminating of the twisting effect. The surface roughness of the machined holes was measured using a Mitutoyo Surftest SJ-301 portable surface roughness tester, and the average roughness values (Ra) were evaluated. In order to measure the surface roughness, austenitic stainless steel blocks were sliced with wire EDM as parallel to hole axes. The roundness error measurements were performed using a Mitutoyo CRT-A C544 three dimensional coordinate measuring machine (CMM) device. Minimum 10 points were measured to obtain the ideal roundness error at a certain depth of the hole.

1.2 Cryogenic Treatment A number of uncoated M35 HSS twist drills (Guhring) with a diameter of 6 mm were cryogenically treated in order to observe the effects of deep cryogenic treatment on surface roughness and roundness error.

Chemical composition and properties of M35 HSS twist drills used in the experiments are given in Tables 2 and 3, respectively.

Table 2. Chemical composition of M35 drills

1.1 Drilling Experiments In the present study, AISI 316 austenitic stainless steel blocks were used as workpiece material. The dimensions of a work piece were 100×170×15 mm.

Chemical composition of AISI 316 stainless steel is shown in Table 1. Blind holes were drilled on stainless steel blocks. Before the drilling experiments, 166

the stainless steel blocks were ground to eliminate the adverse effects of any surface defect on the work piece. Three holes were drilled to compare the surface roughness (Ra) and roundness error (Re) measurements in each machining condition.

The average of these measurements was used for evaluation. To provide the initial conditions of each experiment, a new drill was used. The drilling tests were performed using Johnford VMC 850 model three axes CNC vertical machine center equipped with a maximum spindle speed of 6.000 rpm and a 7.5 kW drive motor. They were performed at two different cutting speeds (12 and 14 m/min) and feed rates (0.08 and 0.1 mm/rev) while hole depth was kept constant at 13 mm.

C 0.9

Cr 4.2

Co 4.8

Mo 5.0

W 6.5

V 2.0

The cryogenic treatment for M35 HSS drills was performed by gradually lowering temperature from room temperature to -196 °C at the cooling rate of about 1.5 °C/min and holding at this cryogenic

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temperature for 24 h, then raising the temperature back to room temperature at the heating rate of 1.5 °C/ min to avoid thermal cracks.

Table 3. Properties of M35 drills Tool material Tool reference Coating Diameter Point angle Helix angle

M35 DIN 1897 Uncoated 6 mm 118° 35°

2 EVALUATIONS OF EXPERIMENTAL RESULTS During cryogenic treatment, the secondary carbides precipitate in the austenite matrix, promote the transformation of the retained austenite to martensite and consequently enhance hardness and wear resistance of the alloy [22]. In addition, it is reported in the literature that the cryogenic treatment relieves the residual stresses [23]. The main reasons affecting hole quality (surface roughness and roundness) in drilling process are the tool wear and cutting forces.

With increasing tool wear and cutting forces, product quality is negatively affected. In this study, the hole quality significantly improved due to tool wear and cutting forces decreased after cryogenic treatment.

Surface roughness decreased with increasing cutting speed [24] and [25]. This event can be explained with the decreased built up edge (BUE) formation due to higher temperatures generated in the cutting zone depending on increasing cutting speed [26]. BUE which has unstable structure significantly influences the surface roughness. When BUE is large and unstable, the surface roughness increases and the surface quality of workpiece is deteriorated. In addition, with increasing cutting speed, the surface quality improves due to the decreasing tool-chip contact area [27]. In this study, hole quality decreased with increasing cutting speed due to decreasing BUE and tool-chip contact area. In addition, the hole quality significatnly deteriorated with feed rate due to the increasing cutting forces [28].

3 TAGUCHI EXPERIMENTAL DESIGN APPROACH The Taguchi method developed by Genuchi Taguchi is a statistical method used to improve the product quality. It is commonly used in improving industrial product quality due to the proven success [29] and [30]. With the Taguchi method, it is possible to significantly reduce the number of experiments. The

Taguchi method is not only an experimental design technique, but also a beneficial technique for highquality system design [31] and [32].

The Taguchi technique includes the following steps: • determine the control factors, • determine the levels belonging to each control factor and select the appropriate orthogonal array, • assign the control factors to the selected orthogonal matrix and conduct the experiments, • analyze data and determine the optimal levels of control factors, • perform the confirmation experiments and obtain the confidence interval, • improve the quality characteristics.

The Taguchi method uses a loss function to determine the quality characteristics. Loss function values are also converted to a signal-to-noise (S/N) ratio (η). In general, there are three different quality characteristics (Eqs. (1) to (3)) in S/N ratio analysis, namely “Nominal is the best”, “Larger is the better” and “Smaller is the better”. For each level of process parameters, signal-to-noise ratio is calculated based on S/N analysis.

Nominal is the best;

 y η = S / NT = 10 log  2  sy 

  ,  

(1)

larger is better;

1 n 1  η = S / N L = −10 log  ∑ 2  ,  n i =1 y 

(2)

smaller is better;

1 n  η = S / N S = −10 log  ∑ yi 2  ,  n i =1 

(3)

where y is the mean of observed data, s 2y is the variance of y, n is the number of observations and y is the observed data [20].

3.1 Selection of Control Factors and Orthogonal Array In this study, cutting tools (CHT – Conventionally Heat Treated, CT – Cryogenically Treated), cutting speed (V) and feed rate (f) were selected as control factors and their levels were determined as shown in Table 4.

The first step of the Taguchi method is to select an appropriate orthogonal array. The most appropriate orthogonal array (L823) was selected to determine [33]

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the optimal drilling parameters and to analyze the effects of these parameters. The drilling parameters were assigned to each column and eight combinations of drilling parameters were formed as shown in Table 5.

Table 4. Cutting parameters and their levels Symbol

Levels

Cutting Parameter

A B C

Cutting Tools (Ct) Cutting Speed (V) [m/min] Feed Rate (f) [mm/rev]

1 CHT 12 0.08

2 CT 14 0.1

Table 5. Orthogonal array of Taguchi L8(23) Trial no. L8 1

A 1

B 1

C 1

2 3 4 5 6 7 8

1 1 1 2 2 2 2

1 2 2 1 1 2 2

2 1 2 1 2 1 2

In the Taguchi method, orthogonal array can provide an effective experimental performance with a minimum number of experimental trials. The

configuration of orthogonal arrays is determined with respect to total degrees of freedom of the targeted function. The degree of freedom (degree of freedom 8–1 = 7) for L8 orthogonal array can be more than or at least equal to the determined process parameters. The surface roughness and roundness error values were measured via the experimental design for the each combination of the control factors. The determination of the quality characteristics of the measured control factors was provided by signal-to-noise (S/N) ratios.

3.2 Analysis of the Signal-to-Noise (S/N) Ratio The Taguchi method uses S/N ratio to measure the variations of the experimental design. The equation of “smaller is the better” (Eq. (3)) was selected for the calculation of S/N ratio since the lowest values of surface roughness and roundness error were the desired results in terms of good product quality. S/N ratios of surface roughness and roundness error are shown in Table 6. As shown in Table 6, the drilling parameters were discriminated by considering different levels and possible effects according to the selected orthogonal array. As results from the eight experimental trials, the mean value of surface roughness was calculated as 2.08 µm and mean S/N ratio for surface roughness value were –6.29 dB. The

Table 6. S/N ratios of experimental results for surface roughness and roundness error Cutting parameter level Trial no.

A Cutting tool B Cutting speed C Feed rate (Ct) (V) (f) 1 CHT 12 0.08 2 CHT 12 0.1 3 CHT 14 0.08 4 CHT 14 0.1 5 CT 12 0.08 6 CT 12 0.1 7 CT 14 0.08 8 CT 14 0.1 TRa (Surface roughness total mean value)= 2.08 µm TRa–S/N (Surface roughness S/N ratio total mean value)= –6.29 dB TRe (Roundness error total mean value)= 6.36 µm TRe-S/N (Roundness error S/N ratio total mean value)= –16.03

Measured surface roughness

S/N (ηi i = 1−8)

Measured roundness error

S/N (ηi i = 1−8)

Ra [µm]

[dB]

Re [µm]

[dB]

2.35 2.47 1.9 1.95 2.1 2.22 1.82 1.81

-7.42 -7.85 -5.57 -5.80 -6.44 -6.92 -5.20 -5.15

6.3 7.5 6.1 6.4 6.1 7.1 5.4 6

-15.99 -17.50 -15.71 -16.12 -15.71 -17.03 -14.65 -15.56

Table 7. Mean S/N ratios [dB] of control factors Control Factors A B C

168

Surface Roughness (Ra) Level 1 -6.66 -7.16 -6.16

Level 2 -5.93 -5.43 -6.43

Roundness Error (Re) Max–Min 0.73 1.73 0.27 Çiçek, A. - Kıvak, T. - Samtaş, G.

Level 1 -16.33 -16.55 -15.51

Level 2 -15.74 -15.51 -16.55

Max–Min 0.59 1.04 1.04

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Fig. 1. Effects of control factors on surface roughness and roundness error; A: Cutting tool, B: Cutting speed [m/min], C: Feed rate [mm/rev], TRa-S/N: Surface roughness S/N ratio total mean value line, TRe-S/N : Roundness error S/N ratio total mean value line

mean value of roundness error and mean S/N ratio for roundness error value were also calculated as 6.36 µm and -16.03 dB respectively. Mean S/N ratios for each level of drilling parameters and level differences of parameters are shown in Table 7.

The effects of the level of each factor on the quality characteristics can be analyzed using S/N ratios. These effects are defined and evaluated according to total mean values of experimental trial results or S/N ratios. The optimum surface roughness and roundness error values can be calculated by means of total mean values of experimental trial results. Another requirement in the calculation of optimum values is to determine the optimum levels.

The optimum levels can be determined by evaluating two different levels of the control factors according to the results from the combinations generated by the orthogonal array. The levels of control factors were determined for both surface roughness and roundness error represented in Table 7, and S/N graphics of these levels were used for the evaluation (Fig. 1).

Distribution of the means of S/N ratios for surface roughness and roundness error are shown in Fig. 1. Since “smaller is the better” was selected for surface roughness and roundness error, the lowest values at first level and second level were eliminated to determine the optimal combination of cutting tool, cutting speed and feed rate. Therefore, the optimum combination of surface roughness and roundness error were determined as A2B2C1 (A2 = CT, B2 = 14 m/min, C1 = 0.08 mm/rev) and A2B2C1 (A2 = CT, B2 = 14 m/ min, C1 = 0.08 mm/rev), respectively. The calculated optimal values were proposed for eight trials and their eight possible combinations (8 from 23 = 8).

3.3 ANOVA and the Equations of Surface Roughness and Roundness Error In this study, ANOVA was used to analyze the effects of cutting tools, cutting speed and feed rate on surface roughness and roundness error. In addition, multiple regression analysis was used to derive the mathematical models of the control factors and their interactions. ANOVA is a statistical method used for determining individual interactions of all control factors. In the analysis, the percentage distributions of each control factor were used to measure the corresponding effects on the quality characteristics.

The performed experimental plan was evaluated at a confidence level of 95%. ANOVA values belonging to experimental results for the surface roughness and roundness error and S/N ratios are shown in Tables 8 and 9, respectively. The significance of control factors in ANOVA is determined by comparing F value of each control factor and F0.05 value from table.

In consequence of the conducted assessments, the factor C (feed rate) and error value for surface roughness were removed from Table 8. The error term (e) and total error variance (et) which includes this error were combined by the pooling method.

These terms removed from the table were marked with sign “*”. According to pooling results, factor B (cutting speed) had a dominant effect (78.11%) on the surface roughness. This factor was followed by factor A (cutting tool) with a ratio of 13.594%. Combined error ratio (8.296%) was found small according to the other ratios. The terms removed from table were marked with sign “*” by considering the results of ANOVA performed for S/N ratio in Table 9. When the remaining factors were evaluated according to

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the pooling results, it was observed that factor B was found to be the major factor (80.086%). This factor is followed by factor A with a ratio of 13.573%. The combined error ratio (6.341%) obtained according to S/N ratios is smaller than other ratios. ANOVA analyses of the experimental trials and the S/N ratios of surface roughness were parallel.

As a result of the evaluations, factor A (cutting tool) and error value for roundness error were removed from Table 8. It was found that factors B and C had significant effects (35.352%) on the roundness error, when the remaining factors were evaluated according to the pooling the results. Combined error (pooled error) was calculated as 29.296%. As shown from S/N ratios of the roundness error in Table 9, factor B has the most significant effect (35.489%). Factor C has also as more important effect (35.235%) as factor

B. Combined error ratio became 29.276%. ANOVA analyses of the experimental trials and the S/N ratios of roundness error were parallel.

Multiple regression analysis was employed to derive the predictive equations of the surface roughness and roundness error. The equations of surface roughness and roundness error were generated based on the control factors and their interactions. The predictive equations generated for surface roughness (Ra1) and roundness error (Re1) are given in Eqs. (4) and (5), respectively.

Ra1 = 4.73 – 0.18 Ct + 0.2075 V + 3.5 f ,

(4)

Re1 = 8.55 – 425 Ct + 0.3875 V + 38.75 f ,

(5)

where R2 (coefficient of determination) values for the surface roughness and roundness error were calculated as 0.963 and 0.909 respectively. On the other hand, the

Table 8. Results of ANOVA for surface roughness and roundness error Variance Source Surface roughness (Ra) A B C Error (e) Pooled Error (et) Total Roundness error (Re) A B C Error (e) Pooled Error (et) Total

Sum of squares (SS)

Degree of freedom (DF)

Mean square (MS)

F ratio

Contribution [%]

0.064 0.344 0.01* 0.016* (0.026) 0.434

1 1 1 4 (5) 7

0.064 0.344 (0.005) -

16.51 87.76 -

13.594 78.11 8.296 100

0.361* 1.201 1.201 0.275* (0.636) 3.038

1 1 1 4 (5) 7

1.201 1.201 (0.127) -

17.47 17.47 -

35.352 35.352 29.296 100

Sum of squares (SS)

Degree of freedom (DF)

Mean square (MS)

F ratio

Contribution [%]

1.069 5.979 0.149* 0.185* (0.334) 7.382

1 1 1 4 (5) 7

1.069 5.979 (0.067)

23.14 129.42 -

13.573 80.086 6.341 100

0.705* 2.183 2.169 0.446* (1.151) 5.503

1 1 1 4 (5) 7

2.183 2.169 (0.23) -

19.56 19.44 -

35.489 35.235 29.276 100

Table 9. Results of ANOVA for S/N ratio Variance Source Surface roughness (Ra) A B C Error (e) Pooled error (et) Total Roundness error (Re) A B C Error (e) Pooled error (et) Total

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predictive equations which contain the control factors and their interactions for surface roughness (Ra2) and roundness error (Re2) are shown in Eqs. (6) and (7), respectively.

Ra2 = 2.968 – 0.955 Ct + 0.0875 V + + 38.25 f + 0.07 CtV + 1.5 Ctf – 2.5 Vf ,

(6)

Re2 = 12.563 – 0.975 Ct + 1.263 V + + 246.25 f – 0.125 CtV + 2.5 Ctf – 16.25 Vf . (7)

In interactive model, R2 values of the equations were calculated as 0.998 and 0.990, respectively. The coefficient of determination of surface roughness became 99.8% in interactive factor model, while it was calculated as 96% in factor model. Similarly, the coefficient of determination of roundness error became 99% in interactive factor model, while it was calculated as 91% in factor model. Thus, the interactive regression models for both surface roughness and roundness error (Ra2 and Re2) are suggested.

3.4 Confirmation Experiments The final step of the Taguchi method is the confirmation experiments conducted for examining the quality characteristics. The model used in the confirmation tests is defined with the total effect generated by the control factors. The factors are equals to the sum of each individual effect. The optimum levels are evaluated by considering the pooled error losses. The optimal surface roughness and roundness error were obtained by taking into account the influential factors within the evaluated optimum combination. Therefore, the predicted optimum surface roughness (Eq. (8)) was calculated by considering individual effects of the factors A2, B2 and C1, and their levels.

RaP = TRa + ( A2 – TRa ) + ( B2 – TRa ),

(8)

where TRa is the surface roughness total mean value. A2 and B2 are the means (1.98 µm, 1.87 µm) of experimental trials at the second level of both factors. According to these values, the optimal surface roughness (RaP) was computed as 1.77 µm.

The factors B2 and C1 and their levels were used in the calculation of the predicted optimal roundness error (Eq. (9)) by considering individual effects of the factors A2, B2 and C1 and their levels.

ReP = TRe + ( B2 – TRe ) + ( C1 – TRe ),

(9)

where TRe is the roundness error total mean value.

B2 is the mean (5.98 µm) of experimental trials

at the second level of factor B2, and C1 is the mean (5.98 µm) of experimental trials at the first level of factor C1. According to these values, the optimal roundness error (ReP) was calculated as 5.60 µm. The confidence interval was employed to verify the quality characteristics of the confirmation experiments. The confidence interval for the predicted optimal values is calculated as follows [34];

 1 1 CI = Fα:1,V2 xVe x  + ,  neff r   

(10)

where, Fα:1,v2, F-ratio of significant level α, α: significant level, 1-α: confidence level, V2: degreeof-freedom of pooled error variance, Ve: pooled error variance, r: number of repeated trials, neff: number of effective measured results defined as; neff =

total exp erimental trials . (11)  total deg ree of freedom  1+    of factors used for prediction 

In this study, three confirmation experiments (r = 3) were carried out to evaluate the performance of experimental trials for surface roughness under optimal conditions (A = CT, B = 14 m/min and C = 0.08 mm/rev). The value of Fα:1,v2 = 6.61 which has a 95% confidence level was found with respect to α = 0.05 and V2 = 5 by considering the lookup table. The confidence interval was calculated as 0.209 µm using Eqs. (10) and (11). With a 95% confidence level, the confirmation test results for the surface roughness was expected to be in the confidence interval of 1.77±0.153 µm or 1.617 to 1.923 µm. The measurements in three confirmation tests conducted with regard to the optimal levels (A2B2C1) were 1.82, 1.71 and 1.83 µm. As depicted in Table 10, the mean of the measurements was 1.79 µm. This mean falls within the determined confidence interval (1.617<1.79<1.923). Therefore, the system optimization for surface roughness was achieved using the Taguchi method at a significance level of 0.05.

On the other hand, three confirmation experiments for roundness error were performed under optimal conditions (A = CT, B = 14 m/min and C = 0.08 mm/ rev). The value of Fα:1,V2 = 6.61 which has a 95% confidence level for roundness error, was found with respect to α = 0.05 and V2 = 5, by considering the look-up table. The confidence interval was calculated as 0.106 µm by use of Eqs. (10) and (11). With a 95% confidence level, the result values of the confirmation

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Table 10. Comparisons of surface roughness and roundness error Surface Roughness Ra [µm] S/N [dB] 2.47 –7.85 1.79 –5.05 1.77 –4.95

Level Initial combination Optimal combination (Experiment) Optimal combination (Prediction)

A 1B 1 C 2 A 2B 2 C 1 A 2B 2 C 1

tests conducted for the roundness error were expected to be in the confidence interval of 5.60±0.771 µm or 4.829 to 6.371 µm. The measurements in three confirmation tests conducted with regard to the optimal levels (A2B2C1) were 5.40, 5.44 and 5.38 µm.

As shown in Table 10, the mean of the measurements was calculated as 5.40 µm. This mean falls within the determined confidence interval (4.829<5.40<6.371).

Hence, the system optimization for roundness error was successfully carried out by using the Taguchi method at a significance level of 0.05.

The comparisons of the surface roughness and roundness error values according to optimal test and the predicted combination A2B2C1, and the combination A1B1C2 selected from eight initial trials are given in Table 10. According to these comparisons, the surface roughness and roundness error values were reduced from 2.47 µm to 1.79 µm and from 7.5 µm to 5.40 µm, respectively. The improved accuracy efficiency because of the optimal combination was increased up to 27.53% ((2.47–1.79)/2.47) for surface roughness and to 28% ((7.5-5.40)/7.5) for roundness error. To compare the quality characteristics of the initial and optimal conditions, S/N ratios in Table 10 were used. The quality losses are given in Table 11.

Table 11. Comparisons of experimental trials Initial combination Level Ra (µ) Quality loss [%] Level Re (µ) Quality loss [%]

A 1B 1C 2 2.47 A1B1C2 7.5 -

Optimal combination Prediction Confirmation A 2B 2C 1 A 2B 2C 1 1.77±0.153 1.79 52.36 A 2B 2C 1 A 2B 2C 1 5.60±0.771 5.40 51.76%

In practice, the quality losses between initial and optimal combinations for both surface roughness and roundness error are calculated as follows [34]:

Lopt ( y )

1 ≈ Lini ( y )  2 

∆η / 3

,

(12)

where, Lopt(y) and Lini(y) are optimal and initial combinations respectively. ∆η is the difference 172

Re [µm] 7.5 5.40 5.60

Roundness Error S/N [dB] –17.50 –14.65 –14.96

between S/N ratios of optimal and initial combinations.

The differences of S/N ratios that can be used to evaluate the quality loss (Eq. (12)) of the optimal combination for surface roughness and roundness error were found as 2.80 (∆η = 2.80 (= 7.85 – 5.05)) and 2.85 (∆η = 2.85 (= 17.50 – 14.65)), respectively.

The quality loss of surface roughness was calculated as 0.5236 using Eq. (11). Thereby, the quality loss at the optimal combination became only 52.36% of the initial combination. When these results were evaluated, the quality losses for the surface roughness were reduced to 47.64% by using the Taguchi method. The quality loss for roundness error was calculated as 0.5176. Thereby, the quality loss in the optimal combination was only 51.76% of the initial combination. The quality losses for the roundness error were reduced to 48.24% by using these results.

Based on the confirmation experiment results, the surface roughness and roundness error decreased 1.38 times and 1.39 times, respectively.

4 CONCLUSIONS In this study, the optimization of drilling parameters were carried out by the Taguchi method to obtain optimum surface roughness and roundness error values in the drilling of AISI 316 austenitic stainless steel with untreated and treated drills. In the performed experimental trials using Taguchi orthogonal arrays, it was found that the cutting speed (78.11%) had a significant effect on the surface roughness and that the cutting speed (35.352%) and feed rate (35.352%) had significant effects on the roundness error. The quality losses (52.36%) of the surface roughness obtained at optimal combinations (Ct = CT, V = 14 m/min, f = 0.08 mm/rev) were nearly equal to half of the ones obtained from experimental combinations. Similarly, the quality losses of the roundness error obtained at optimal combinations became 51.76%. Optimal surface roughness and roundness error values were calculated as 1.77 µm and 5.60 µm using optimal parameters, respectively.

The Taguchi method was successfully applied to determine the optimal combinations of drilling parameters and to minimize machining costs and

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Strojniški vestnik - Journal of Mechanical Engineering 58(2012)3, 165-174

time in drilling of AISI 316 stainless steel. Further research works could consider more factors such as drilling depth, lubricant, tip and helix angle and cryogenic treatments at different soaking time (i.e. 4, 8, 12, 36, 48 h, and so on) and at different cryogenic temperatures (–70, –125, –150 °C and so on) affecting surface roughness and roundness error.

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[18] Tsao, C.C., Hocheng, H. (2008). Evaluation of thrust force and surface roughness in drilling composite material using Taguchi analysis and neural network.

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[33] Ranjit, K.R. (1990). A primer on the Taguchi method, competitive manufacturing series. Van Nostrand Reinhold, New York.

[34] Liu, Y.T., Chang, W.C., Yamagata, Y.A. (2010). A Study on optimal compensation cutting for an aspheric surface using the taguchi method. CIRP Journal of Manufacturing Science and Technology, vol. 3, no. 1, p.

40-48, DOI:10.1016/j.cirpj.2010.03.001.

Çiçek, A. - Kıvak, T. - Samtaş, G.

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)3, 175-182 DOI:10.5545/sv-jme.2011.135

Paper received: 2011-07-12, paper accepted: 2012-01-27 © 2012 Journal of Mechanical Engineering. All rights reserved.

Theoretical and Experimental Study of Fatigue Strength of Plain Woven Glass/Epoxy Composite Movaghghar, A. – Lvov, G.I. Ali Movaghghar* – Gennady Ivanovich Lvov Kharkov State Polytechnic University, Faculty of Mechanical Engineering, Ukraine

In this paper an energy-based model for predicting fatigue life and evaluation of progressive damage in composite materials is proposed. The damage model is based on the concepts of continuum damage mechanics. The applicability of the proposed energy model was studied in fatigue experiments on 10-layer composite laminates made of glass fabric impregnated with epoxy-phenolic resin. Experimental results were processed by the method of least squares to determine the unknown parameters of the model. Theoretical fatigue strength curves are in good agreement with experimental data.

Keywords: composite materials, fatigue, damage mechanics, fracture, finite element modelling, mechanical properties

0 INTRODUCTION With the increasing use of composite materials comes an increasing need to understand their fatigue behavior.

They exhibit very complex failure mechanisms under fatigue loading because of anisotropic characteristics in their strength and stiffness. Cyclic loading causes extensive damage throughout the composite volume, leading to failure from general degradation of the material instead of a predominant single crack. A predominant single crack is the most common failure mechanism in static loading of isotropic, brittle materials such as metals. There are four basic failure mechanisms in composite materials as a result of fatigue: matrix cracking, delamination, fiber breakage and interfacial debonding [1]. The different failure modes combined with the inherent anisotropies, complex stress fields, and overall non-linear behavior of composites severely limit our ability to understand the true nature of fatigue.

Different fatigue models have been established during the last decades, which are based on the wellknown S-N curves. They usually require extensive experimental work and do not take into account the actual damage mechanisms, such as matrix cracking and fiber breakage. These models make up the first class of the so-called ‘fatigue life models’ [2]. The second class comprises the phenomenological models for residual stiffness and strength. The reliability of a composite component can change over time because of the strength and stiffness loss the material exhibit.

These models propose an evolution law which can describe the gradual deterioration of the stiffness or strength of the composite specimens in terms of macroscopically observable properties. The third class of models introduces one or more properly chosen damage variables which describe the deterioration of the composite component. These models are based on

a physically sound modeling of the underlying damage mechanisms, which lead to the macroscopically observable degradation of the mechanical properties.

They can predict the damage growth in composite component, such as the number of transverse matrix cracks per unit length and the size of the delamination area. One of the important outcomes of all established fatigue models is the prediction of fatigue life and each of these three categories uses its own criterion for determination of fatigue life [2].

In this paper a model for predicting fatigue life and evaluation of progressive damage is proposed.

The unknkown parameters of this model were estimated using experimental results of fatigue tests on glass fiber/epoxy composite mark STEF-1.

1 EFFECTIVE STRESS CONCEPT In contrast to fracture mechanics which considers the process of an equilibrium condition or initiation and growth of microcracks as a discontinuous phenomenon, continuum damage mechanics uses a continuous internal variable, which is related to the density of these microdefects. The damage variable, based on the effective stress concept, represents average material degradation, which reflects the various types of damage at the micro-scale level like nucleation and growth of voids, cavities, micro-cracks, and other microscopic defects. In the literature various forms of damage have been proposed in recent years, for example, scalars, vectors, second and forth order tensors. The complexity and variety of mechanisms of accumulation of fatigue damage and degradation of strength properties of the composite component make reasonable use of an internal scalar variable for the quantitative description of damage. For the case of isotropic damage, the damage variable is scalar and associated with a decrease in the effective area of any

*Corr. Author’s Address: National Technical University «KhPI », 61002, Kharkov, Frunze St. 21, Ukraine, alinetscope@yahoo.com

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cross-section in the vicinity of this point of the body and is defined using the concept of effective stress in the following manner [3]: A − A

D= , (1) A where A is the effective resisting area corresponding ~ to the damaged area A. The effective area A is obtained from A by removing the surface intersections of the micro-cracks and cavities and correcting for the micro-stress concentrations in the vicinity of discontinuities and for the interactions between closed defects. By definition, theoretical value of D should be within 0 ≤ D ≤ 1. In the multiaxial case of isotropic damage, all the stress components act on the same effective area, so the effective stress tensor is:

σ ij =

σij 1− D

. (2)

In the case of anisotropic damage, the damage variable has been shown to be tensorial in nature. The case of anisotropic damage is much more complicated to ensure a good representation of the physics as well as compatibility with thermodynamics. In a general state of deformation and damage, the effective stress tensor σ is related to the stress tensor σ by the following linear equation:

σ ij = M ijkl ⋅ σkl , (3)

but this lead to a nonsymmetric tensor and a complicated theory. As only the symmetric part accounts for the constitutive equations of elasticity, a symmetrical form for σij can be obtained through the transformation [4]:  ij = 1 σ ( δ − D )−1 + ( δ − D )−1 σ  , σ ik kj kj il il lj  (4)

2 where δij is the Kronecker delta and Dij is a second order damage tensor. Firs must use the second principle of thermodynamics to derive the proposed energy model mut be used, because accumulation of damage is a dissipative process that is governed by the laws of thermodynamics. The second principle of thermodynamics, also referred to as the ClausiusDuhem inequality, can be written as [5]:

T σij ε ij − ρ( ψ + sT ) − qi ,i ≥ 0 , (5) T

 where q is the heat flux vector associated with the temperature gradient for the non isothermal processes, ψ Helmholtz free energy and s entropy density. The Helmholtz free energy is a function of all the 176

state variables. If it is assumed that no plastic deformation occurs in ccan write its rate can be written as: ψ =

∂ψ ∂εije

ε ije +

∂ψ  ∂ψ  T+ D, (6) ∂T ∂D

together with the definition of the associated variables, Eq. (5) becomes:  ∂ψ  σij − ρ  ∂εije 

 T ∂ψ   ∂ψ    ε ije − ρ  s + T −ρ D − qi ,i ≥ 0.. (7)   T ∂T  ∂D  

On the other hand, the analytical expression for the Helmholtz free energy together with the principle of strain equivalence and the concept of effective stress for isothermal processes can be written as [4]: ψ=

1 aijkl εije εekl (1 − D ) , (8) 2ρ

where aijkl is the elastic stiffness tensor. The state laws are derived from the state potential so the law of elasticity coupled with damage will have the form: σij = ρ

∂ψ ∂εije

= aijkl εekl (1 − D ) . (9)

The thermodynamics of irreversible processes defines its associated variable Y, (a positive quadratic function) called the “energy density release rate” for scala damage D, that can be defined as [5]: Y = −ρ

∂ψ 1 = aijkl εije εekl , (10) ∂D 2

this means that to always satisfy inequality of positive dissipation Eq. (7), the damage rate D must be a nonnegative function, so: Y ⋅ D ≥ 0. (11)

2 DEFINING RELATIONS FOR THE DEVELOPMENT OF DAMAGE IN COMPOSITE The direct measurement of damage as the surface density of microdefects (cracks, pores or inclusions) is difficult to perform and is used only in laboratories well equiped for micrography. It is easier to take advantage of the coupling between damage and elasticity to evaluate the damage by inverse methods [6]. Throughout the composite’s life, growth of damage can be monitored nondestructively by measuring one of the properties of the material: the moduli, for instance, or the electrical conductivity, or

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light scattering, or the x-ray absorption, or ultrasonic attenuation, or the damping coefficient, or by acoustic emission detection [7]. In general, the damage variable D is described as a function of cyclic stress range Δσ, number of loading cycles N, stress ratio R, environmental conditions such as temperature T, and material properties such as stiffness E, as given below:

(

)

D = D ∆σ, N , Eijkl , R ,T ,... . (12)

In the make the further assumption is made that the damage accumulation rate depends on the maximum value of specific elastic strain energy We per cycle, the load ratio R and on the current level of scalar isotropic damage D, then:

dD = f ( R , D ,We ) . (13) dN

If it is assumed that a power relation exists between the maximum value of specific elastic strain energy per cycle and damage growth rate, kinetic equation for the damage parameter can be written in the form [8]:

dD n = m ⋅ k ( R ) ⋅ (We )max , (14) dN

where We is the elastic strain energy per unit volume of the body which is computed from the individual stress components and elastic strains, k(R) function which depends on the stress ratio, m, n constants which define the rate of damage accumulation.

According to the principle of strain equivalence, with the definition of the effective stress expressecan write Eq. (14) can be written in the form:

n

dD 1  = m ⋅ k ( R ) ⋅  σ ij εij  , (15) dN 2  max

or:

  1 dD = m ⋅ k ( R) ⋅  ⋅ Cijkl σij σkl  dN  2 (1 − D ) 

n

, (16) max

where Cijkl is the tensor of elastic constants of undamaged composite. It is also possible to replace stresses by strains: n

dD 1  = m ⋅ k ( R ) ⋅  aijkl εije εekl ( 1 − D ) . (17) dN 2   max

The fatigue life-time, meaning the number of cycles to increase damage parameter from D1 to D2 is found by integrating Eq. (13) to give N:

D2

N= ∫

D1

dD . (18) f ( R , D ,We )

In the case of uniaxial loading, the dependence of scalar damage parameter on the number of cycles will have the following form calculated by means of this model: 1  ( n + 1) ⋅ m ⋅ k ( R ) ⋅ σ2 n  n +1 D = 1−  − ⋅ N + 1 , (19)

  2n ⋅ E n   where E is the modulus of elasticity of the corresponding direction. Because of considerable nonlinearity dependence of the damage parameter on the number of cycles, at the stage preceding failure, the growth rate increases and tends to infinity, material becomes unstable and ruptures. Therefore, integration of Eq. (13) over the interval 0 to 1 gives the number of cycles to rupture corresponding to the critical value of the damage:

 2n ⋅ E n 1 σ= ⋅  ( n + 1) ⋅ m ⋅ k ( R ) N f 

1

 2n  , (20)  

where Nf is the number of cycles to failure and E is the modulus of elasticity of the corresponding direction.

For investigating the validity of this presented energy model assumptions series of fatigue experiments were performed on plain woven glass/epoxy composite laminates.

3 EXPERIMENTAL PROCEDURES 3.1 Description of Material and Experimental Determination of the Elastic Moduli The material used in this study is a plain woven glass/ epoxy composite. The plain woven glass fabric was stacked in 10 layers impregnated with epoxy-phenolic resin. Material manufactured in sheets with the dimensions of 890×1020 mm and nominal thickness of 2 mm. It is macroscopically orthotropic, having two orthogonal axes of symmetry of mechanical properties, coinciding with the directions of warp and weft threads (Fig. 1).

For fatigue experiments 30 identical specimens were cut in the warp and 30 specimens in weft directions of the fabric. Specimens had rectangular cross-section 2×15 mm with length of 175 mm. A resonance frequency technique was first applied to determine the Young’s modulus of specimens.

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The test method is nondestructive in nature and can be used for specimens prepared for other tests. One end of the composite test specimen was fixed to an electrodynamic shaker (vibration exciter) and the frequency was slowly increased. At a particular instance of time, the input frequency becomes equal to the first natural frequency of the system and the amplitude level increases significantly. This is the resonance peak and can be clearly distinguished in the response curve.

where L = 147 mm is the working length of specimen in vibration tests. A series of vibration tets were performed on 30 specimens that were cut in warp direction and the mean value of their first natural resonance frequencies was determined: 30

f1 = ∑

fi

i =1 30

=26 Hz. (23)

Once resonance frequency is determined we can define Young's modulus in the warp direction using Eq. (22): E11 =

4π2 f1

2

ρFL4 2

( 3.515 ) I z

= 5.62 ⋅109 Pa. (24)

The same tests were carried out on specimens that were cut in weft direction and the mean value of their first natural frequencies was determined: Fig. 1. Structure of material (plain-woven fabric, 1-warp; 2-weft threads)

fi

30

f2 = ∑

i =1 30

=23.5 Hz. (25)

The value of Young's modulus of corresponding specimens can be defined as: E22 =

4π 2 f 2

2

ρFl 4 2

( 3.515 ) I z

= 4.59 ⋅109 Pa. (26)

Other physical and mechanical properties like Poisson's ratio and density of this composite material were taken from literature [10]. They are given in Table 1.

Table 1. Physical and mechanical properties of the composite laminates Density, [kg/m3]

Fig. 2. The fixing scheme of test specimen on the shaker platform: 1-test specimen; 2-vibration platform

For a uniform clamped-free beam the differential equation of motion can be written as [9]:

EI

∂ 4Y ( x ,t ) ∂x 4

+ ρF

∂ 2Y ( x ,t ) ∂t 2

= 0 , (21)

where E is Young's modulus of the corresponding direction, I the moment of interia, F the cross-section area, ρ density. Using boundary conditions and general solution of Eq. (21) we can determine the first natural resonance frequency of the composite beam:

178

T=

ρFL4 1 2π = , (22) f 3.515 EI

Young’s modulus, [MPa] Poisson’s ratio

Warp direction Weft direction Warp direction Weft direction

1860 5620 4590 0.22 0.18

3.2 Fatigue Tests Tests were performed on a special machine type DP-5/3 which is used to determine the bending fatigue resistance of sheet fibrous woven specimens.

Machine imposes an alternating bending angle on the upper clamp (point B). At the down end the specimen is clamped (point A). Machine allows simultaneous testing of three specimens at the same angle of bending with or without the preliminary tension of specimens with removable weights. Testing machine DP5/3 is shown in Fig. 3.

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Fig. 3. Machine type DP-5/3 used for fatigue tests

The value of the imposed bending angle is a controllable parameter over a wide range of 20 to 180°. Working length of specimens in fatigue tests was L = 92 mm (Fig. 4).

in room temperature. After the automatic shutdown of the machine due to the destruction of specimens the number of cycles at failure established by the counters was recorded.

The constitutive equations for evaluation of stresses and bending moments are based on the classical beam theory. A composite test specimen cannot experience any deflection at points A and B. A derivative of the deflection function is zero at the point A. Because the other end is free to rotate about the Z axis, a derivative of deflection function is equal to θ at point B. The point of maximal deflection C occurs between points A and B. This deflection is a function of x and bending angle θ: Y = Y ( x ,θ ) . (27)

In the linear formulation we can determine the value of the deflections, using differential equation: EI

d 4Y dx 4

= 0 , (28)

where E is the Young’s modulus of the corresponding direction. Eq. (28) has a solution of the form:

Y ( x ) = c1 + c2 x + c3 x 2 + c4 x3 , (29)

where c1, c2, c3 and c4 constants that can be defined from boundary conditions. The boundary conditions at points A and B are:

Y = 0, dY/dx = 0, x = 0,

Y = 0, dY/dx = θ, x = L. (31)

(30)

Once deflections are determined, we can define the values of bending moment and normal stress: Fig. 4. Schematic drawing of the bending fatigue setup

The desired frequency of fully-reversed bending can be installed on 100 or 300 bending cycles in a minute. Two sets of fatigue experiments were carried out with no preliminary tension. In the first set, experiments were performed to examine the fatigue bending resistance of 30 specimens that were cut in the warp direction with different values of the imposed bending angle of 60, 50, 45, 40, 35 and 30°. A total of five specimens were tested at each bending angle. In the second set, the same tests were carried out on 30 specimens that were cut in the weft direction. Specimens were all tested at the same frequency of 100 fully-reversed bending cycles in a minute. Tests were continued until a complete failure

σ x= −y⋅ E

d 2Y

 2θ 6θ = − y ⋅ E − + 2 dx l  l 2

 x  . (32) 

In the tests when deflection is greater than the thickness of specimen a non-linear analysis and formulation is required to determine the deflection [11]: 2 2 d 4Y  3  dY   d Y  

EI 4 −  EF  ⋅  2   = 0. (33)  dx  dx   dx    2 A finite element analysis (FEA) was carried out using Ansys 11 software to assess the validity of the calculated values of stresses. The element used for the analysis was 8-node structural Shell93 which has six degrees of freedom at each node. This element is particularly well suited to model curved orthotropic

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shells in case of large deflections [12]. A boundary condition of fixing all displacements and rotations on the upper line (point A), fixing all displacements with a given rotation about the Z axis Rot z = θ on the lower line (point B) was applied (Fig. 5).

By taking logarithms of both sides of the Eq. (35) and introducing new variable t = ln N there is a new function Q': 2

1 30  1 2n 1  − ti1   + Q ′ = ∑  ln σi1 −  ln E11 + ln  2n m ⋅ ( n + 1 ) 2n   i =1  2  2

30 

1  1 2n 1 + ∑  ln σi 2 −  ln E22 + ln − ti 2   . 2  n m ⋅ ( n + ) n 2 1 2 i =1    

If a = Fig. 5. Shell element for modeling the composite specimen

It should be noted that the difference between the stress values obtained from Eqs. (32) and (33) and values calculated by Ansys software do not exceed 5%.

j

2

Q ( m , n , E11 , E22 ) = ∑ σi1 ( Ni1 ) − F ( Ni , E11 , m , n )  + i =1 j

2

+ ∑ σi 2 ( Ni 2 ) − F ( Ni , E22 , m , n )  .

(34)

i =1

Function F has the form of a power law Eq. (20), if it is assumed that the function of cycle parameter has the constant value of k(R) = 1 under stationary loading conditions, then function Q will take the form: 

2

30  1  Q ′ = ∑  ln σ i1 −  ln E11 + a + bti1   + 2 i =1    (37) 2 30   1   + ∑  ln σi 2 −  ln E22 + a + bti 2   . i =1  2 

Taking the derivative of Q' with respect to a and b, setting them to zero gives the following set of equations: ∂Q ′ ( a ,b , E11 , E22 ) ∂a

180

∂Q ′ ( a ,b , E11 , E22 ) ∂b

= 0. (38)

m = 1.034 ·10–27 [Pa], n = 3.521 .

(39)

These values are substituted into Eq. (20) to obtain two theoretical S-N curves for fatigue study of specimens cut in different directions:

 2n ⋅ E n 1 11 σ1 ( N1 ) =  ⋅  ( n + 1) ⋅ m N f 1   2n ⋅ E n 1 22 σ2 ( N 2 ) =  ⋅  ( n + 1) ⋅ m N f 2 

30 

= 0,

Solving these equations gives the following least square estimates of m and n as:

2

1 −1   2n E11n  2 n  Q = ∑  σi1 −  ⋅ N i21 n  +  ( n + 1 ) ⋅ m  i =1       (35) 2 1  −1  n n 2 n  2 E22  30   + ∑  σi 2 −   ⋅ N i22n  .  i =1  ( n +1)⋅ m     

 1 1  2n ln  , leads to  and b = −  2n 2n  m ⋅ ( n + 1 ) 

the following:

4 PROCESSING THE RESULTS OF FATIGUE EXPERIMENTS For practical application of the proposed model it is necessary to identify the unknown functional dependency parameters Eq. (14) on the basis of experimental results. Therefore, the results of fatigue tests were processed by the method of least squares to determine constants m and n in such way that the sum of the squared errors over all the observations is minimized. i.e., the quantity Q we are interested in minimizing is:

(36)

1

 2n  ,   (40) 1

 2n  .  

The theoretical S-N curve and fatigue test results in warp direction obtained at different stress levels are plotted in Fig. 6, as the number of cycles to failure, Nf, against the applied stress, σ.

In the same way for test specimens that were cut in weft direction in Fig. 7 shown theoretical S-N curve and fatigue tests results.

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Strojniški vestnik - Journal of Mechanical Engineering 58(2012)3, 175-182

as a function of number of fatigue cycles for two types of specimens cut in different directions using Eq. (19), as it is shown in Fig. 8.

Note that graphs were constructed at the same given value of stress amplitude, for example σ = 1.5·108 Pa and k(R) = 1. It is possible to observe that the damage parameter consistently increases until the end of the test when it increases very fast until rupture.

5 CONCLUSIONS

Fig. 6. Theoretical fatigue curve and experimental results from tests in warp direction

Fig. 7. Theoretical fatigue curve and experimental results from tests in weft direction

In the present work an energy-based model for predicting fatigue life and quantitative evaluation of progressive damage using Lemaitre’s concept of equivalent stress hypothesis was proposed. The model allows the prediction of fatigue durability by taking into account the principal directions of the stress tensor relative to the planes of elastic symmetry of material. The unknkown parameters of this model defining the fatigue damage accumulation rate, were identified using experimental results from fatigue tests of glass fiber/epoxy composite specimens that were cut in both the warp and weft directions. Then, the model has been applied to study the evolution of damage in specimens cut in different directions under fatigue tests. It has been shown that the theoretical fatigue strength curves obtained by means of this model were in good agreement with experimental data.

6 REFERENCES

Fig. 8. Evolution of damage parameter in specimens cut; 1-in warp 2- in weft directions.

After identifying the damage model parameters, it can be applied to predict quantitatively the damage evolution of structural elements. It is possible to draw the graphs of the evolution of scalar damage variable

[1] Harris, B. (2003). Fatigue in composites. CRC Press, Woodhead Publishing Ltd., Cambridge.

[2] Van Paepegem, W., Degrieck, J. (2000). Fatigue Damage Modelling of Fiber-reinforced Composite Materials: Review. Applied Mechanics Reviews, vol.

54, no. 4, p. 279-300.

[3] Kachanov, L.M. (1986). Introduction to Continuum Damage Mechanics. M. Nijhoff Publ., Dordrecht.

[4] Voyiadjis, G.Z., Kattan, P.I. (2005). Damage mechanics. CRC Press, A Taylor & Francis Company, Florida, DOI:10.1201/9781420027839.

[5] Lemaitre, J. (1996). A course on damage mechanics (2nd Edition). Springer-Verlag Berlin, DOI:10.1007/978-3642-18255-6.

[6] Lemaitre, J., Desmorat, R. (2005). Engineering damage mechanics: ductile, creep, fatigue and brittle failure.

Springer, New York.

[7] Seruga, D., Fajdiga, M., Nagode, M. (2011). Creep damage calculation for thermo mechanical fatigue.

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vol. 57, no. 5, p. 371-378, DOI:10.5545/svjme.2010.108.

[8] Movaghghar, A., Lvov, G.I. (2010). An energy model for fatigue life prediction of composite materials using continuum damage mechanics. ICMAE 2010 proceedings, p. 275-279.

182

[9] Meirovitch, L. (2001). Fundamentals of vibration.

MacGraw-Hill Companies, Inc. [10] Handbook of composites (1982), (ed. Lubin, G.), Van Nostrand Reinhold, New York.

[11] Reddy, J.N. (2007). Nonlinear finite element analysis.

Oxford University Press.

[12] Ansys V.11 Help Reference (2011).

Movaghghar, A. – Lvov, G.I.

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)3, 183-190 DOI:10.5545/sv-jme.2009.091

Paper received: 2009-07-21, paper accepted: 2010-12-03 © 2012 Journal of Mechanical Engineering. All rights reserved.

CFD-Based Investigation of the Response of Mechanical Ventilation in the Case of Tunnel-Fire Muhasilovic, M. – Duhovnik, J. Mezid Muhasilovic* – Jožef Duhovnik

University of Ljubljana, Faculty of Mechanical Engineering, Slovenia The fact that many underground facilities, as large-scale spaces, differ in their geometric characteristics, continually sets new tasks for the researcher investigating the fluid phenomena. In this manner, we performed a computationally aided investigation of the new covered traffic road-communication that goes under a part of the Slovenian capital of Ljubljana. Although not yet finished – we were in position with the employed RANS transient approach (interpreting turbulence by k-ε model) using the technical drawings of the road-tunnel for the design of the computational domain, to give a CFD-forecast of the effectiveness of ventilation in the event of both, 40 and 80 MW fires.

Keywords: CFD, large-scale combustion, tunnel-fire, critical velocity

0 APPLIED CFD-BASED APPROACHES THUS FAR Due to an increasing number of accidental fires in enclosed spaces, especially in the area of modern society where our freedom is mostly expressed – traffic and tourism – there is an on-going need to undertake scientific research, aiming at better understanding these reactive flow phenomena. One of the direct benefits of such research is a suggestion for the implementation of the most effective fire suppression methods that should follow world-wide statistical data of one traffic accident occurring every 107 kilometres of covered (tunnel) road [1] and [2].

The field models for numerical research of fires in enclosed spaces (which was our applied mode as well) are established in the CFD-community over the zone-model-approach [3] and [4]. Such codes (field model based) do not divide the area of interest into very few smaller control volumes only, but are based on the full solution of the fundamental physical laws of conservation. Here, the computational domain is divided into thousands of much smaller control volumes ‘cells’, where, after their discretisation mathematical models are “translated” into a programme code for combustion, radiation, turbulence etc. Therefore, between the mid 1980s and mid 1990s, hardware sources supported computational domains with few thousands cells [5] and [6]. However, in spite of these limiting conditions highly satisfying results were accomplished in attempts of both, the validation [7] to [11] of software tools and aimed CFD-prognoses for particular explored cases of confined fluid phenomena [1] and [12].

Modern field-model codes that have been engaged in CFD-research within the last decade supported by powerful hardware can cope with the domains made out of several hundred thousands cells. All of these research works attempts that have

been brought up into the CFD-community, report on good capability of the numerical approaches used in handling the reactive flows in straight enclosed traffic objects that were validated against some distinguished experiments [13].

However, in addition to the slight denivelation of a few percent, the geometry of the arbitrary tunnels was relatively a simple one [14]. Therefore, in our research, we explored the “Sentvid” tunnel that goes under the city of Ljubljana and is being changed in its cross-section surface (from three-lane down to twolane road) [15]. At about half of its length of 1470 m it has the bifurcation zone, where one-lane road (tunnelpart) climbs up to the local road.

1 TREATMENT OF THE TURBULENCE - APPLIED MATHEMATICAL MODEL IN THIS STUDY In this study the flow phenomena are computed by the Reynolds Averaged Navier-Stokes (RANS) equations, with the turbulence k-ε model [16], representing the major characteristic of the applied CFD-investigationtool of the FLUENT; and handling the buoyancy by applying the Boussinesq approximation. This approach is not affected by the fluctuation of the initial conditions, offering a more accurate presentation of the time dependent flow – particularly the distribution of the gaseous combustion products [17]. Since the investigations have shown that the maximum value for the Mach Number is of the order of 0.035, such a flow can be assumed as incompressible [18].

Therefore, while crossing the reaction front, the fluid does not undergo thermal-caused expansion and the reaction makes no impact onto flow-velocity.

A further assumption, to have a planar propagation front of combustion in a motionless fluid, leads to the application of the Boussinesq approximation [19] without external forces [20]. Here, the flow velocity

*Corr. Author’s Address: University of Ljubljana, Faculty of Mechanical Engineering, Aškerčeva 6, 1000 Ljubljana, Slovenia, muhasilovic@gmail.com

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obeys the incompressible Navier-Stokes equation with a temperature-dependent force term [20].

The change of temperature is described by an advection-reaction-diffusion equation. For this incompressible gaseous reactive flow at low velocity, the governing equations of the combustion-induced flow read: ∂v j = 0,

(1) ∂x j

∂vi ∂ ( vi v j ) 1 ∂p 1 ∂τ ij + =− + − giα∆T , (2) ∂t ∂x j ρ ∂xi ρ ∂x j

∂T ∂ (Tv j ) ∂ = + ∂x j ∂t ∂x j

 λ ∂T  1   + R (T ) .  ρ c p ∂x j  z

(3)

Here vi denotes the average velocity component, T the mean local temperature, p the pressure, ρ the density, t the time and xi the space coordinates.

The R(T) = ¼·T·(1 – T) stands for reaction rate [20] where the reciprocal value of reaction time-scale is represented by z, λ is the thermal conductivity, cp is the heat capacity at the constant pressure. Temperature T will also be used as the expression for reactionprogress-variable whose purpose is to distinguish the burned, the unburned and the partially burned state, providing an easy interpretation of flame propagation.

The term –giαΔT denotes buoyancy treated according to the Boussinesq approximation, where ΔT shows the difference between local and reference temperature.

The symbol g denotes the gravity and α is the coefficient of thermal expansion. The model for the stress tensor [21], τ ij is related to the local strain rate:

τij = (τij)N + (τij)T ,

(4)

where we distinguish between the Newtonian stress (τij)N = 2μSij featuring molecular viscosity; and the turbulent Reynolds stress (τij)T = 2μT Sij, since the stress rate tensor Sij is defined as:

Sij ≡

1  ∂vi ∂v j +  2  ∂x j ∂xi

and the turbulent viscosity:

µT = Cµ

k2 , ε

  , 

(5)

(6)

with k the turbulent kinetic energy and ε the dissipation rate of turbulent energy.

The applied k-ε model [22] is a two-equation eddy viscosity model [23] and [24] that uses transport 184

equations for these two variables [25]. One of these equations governs the distribution through the field of k, the local kinetic energy of the fluctuating motion.

The other one yields the energy dissipation rate ε [26].

 k2  ∂k k2 Pd − ε − Gb , − ∇ ⋅  Cµ ∇k  = C µ ∂t ε ε  

 k2  ∂ε ε − ∇ ⋅  Cε ∇ε  = C1kPd − ( C3 λv N 2 + C2ε ) . (8) ∂t ε k  

(7)

µt ∇T models the Pr t buoyancy effects, where Prt denotes turbulent Prandtl Number (which is of the order of unity). The constants are given: C1 = 0.126, C2 = 1.92, Cµ = 0.09, Ce = 0.07.

The energy term Gb = α gi

2 BOUNDARY CONDITIONS AND MESHING IN COMPUTATIONAL DOMAIN – A NUMERICAL APPROACH For transient simulations (a CFD-mode that was applied in this study) the governing equations must be discretised in both space and time [24] and [27]. In choosing the numerical method we rely on the standard of the finite volumes [18], [27] and [28]. The spatial discretisation of time-dependent equations employed a segregated solution method.

The linearised equations result in a system of linear equations for each cell in the computational domain, containing the unknown variable at the cell centre as well as the unknown values in the surrounding neighbour cells.

This mechanism for a scalar transport equation is also used to discretise the momentum equations; in the same mode for the pressure field (if face mass fluxes were known) and the velocity field will also be obtained in the same way. In case the pressure field and face mass fluxes are not known, FLUENT [24] uses a co-located scheme, whereby pressure and velocity are both stored at cell centres. The need for interfacial values includes an application of an interpolation scheme to compute pressure and velocity from cell values. The integration over the arbitrary volume (a cell in a computational domain) can be performed yielding the discretised equation for the mass flux through an arbitrary surface of a face.

In the sequential procedure of the segregated solver, the continuity equation is used as an equation for pressure as well [24]. However, the pressure does not appear explicitly for incompressible flows since the density is not directly related to pressure.

Therefore, the SIMPLE-family [27] of algorithms is used for introducing pressure into the continuity

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equation. In this way, it supports the pressure-velocity coupling though the algorithm for the unsteady flows as for the fluid mechanics phenomenon, explored in this study. The SIMPLE uses a relationship between velocity and pressure corrections to enforce mass conservation and to obtain the pressure field.

Since in our CFD-approach, the longitudinal artificial ventilation was employed immediately, the tunnel-entrance and exits (both towards the main tunnel-line and towards the local road) characterised as open (pressure) boundaries with pressure increase due to the ventilation-caused velocity (of 4 m/s).

The fuel “pool” – the simulated fire-place, has been determined by the constant max flux rate of heptane of the order 0.4545 kg/m²s [29] for simulating the fire thermal power of 40 MW over the surface of 2 m²; and for the 80 MW fire [30] the double mentioned value for the mass flux. Heptane was taken as an inflammable good as one of the most commonly used fuels in experiments and fire-tests.

The tunnel itself (the left tube), with the slope of 2.2%, has two major main-curves with a Radius of 4000 and 1500 m with both “horse-shoe” crosssection and rectangular cross-section, where the first one determines the first 1080 m of the tunnel. Starting as a three-lane tunnel, after the bifurcation (on the 720th meter of its length) the “main stream” of the “horse-shoe-shaped” tunnel “continues” as a twolane traffic communication; the “horse-shoe-shaped” tunnel line exites and elevates to the point of about 12 m above the road-level of the main tunnel-stream, with the length of a further 400 m and a change from a one-lane to the two-lane “horse-shoe-shaped” cross-section. Therefore, the Aspect-Ratio changed in this tunnel: for three-lanes part Ap = 1.707 to the rectangular and other horse-shoe-shaped part with two lanes with Ap = 1.32.

Tunnel-entrance as open (pressure) boundary was used for initializing computational values for the velocity and pressure in the domain since the global temperature was set to the 293 K. The tunnel housing, tunnel road and tunnel walls, were presumed to be heat transparent. This decision was based on previous research [31] and [32], using the particular thermal conductivity of a rock, where a tunnel was built through [33], the reality-oriented investigation on tunnel-construction was conducted.

Particularly for the Sentvid tunnel that was built in the Karst area, the specific thermal conductivity of such limestone (λ = 2.3 W/mK)[33] and [34] was integrated in the boundary conditions.

Fig. 1. Left tube of “Sentvid” as computational domain the 1470 m long left tube with exit to the local road that runs above the tunnel; on the upper side there is the entrance from Ljubljana (from the south)

Fig. 2. Road-junction within the tunnel with the continuing tunneldirection (right) and the beginning of the exit line towards local road (left); different characteristics of the single-cells were applied in order to achieve mesh-independency and save computing-time in one stroke

3 FIRST STEP IN INVESTIGATION – THE SIMULATION OF 40 MW-FIRE WITH NATURAL VENTILATION After the explained computational approach was validated [35], a CFD-investigation of the 40 MW fire accident in tunnel natural air-movement only was performed. This numerical experiment ran for 120 s, which is the time of real-case physical experiments [35]. The findings of this investigative step assured us that after accidental fire is established (7th second) – there is a strongly expressed propagation (113th second) of the hot gaseous combustion products towards the actual traffic-entrance (higher geodetic position). The accompanied occurrences are thermal damaging, not only to the re-enforced concrete (concrete spalling) of the tunnel cavity, but the

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also destruction of the asphalt road-layer. Those results point to the extremely important task for the longitudinal (forced) ventilation that should not only induce evacuation of the smoke towards the positive tunnel direction (in the sense of traffic) but should protect the tunnel body and road-elements from thermal damages before a fire-event is localised and finally extinguished.

Fig. 3. The 7th second of the 40 MW fire - velocity fields point at not established propagation of the gases

to stop the propagation of the smoke in unwanted direction.

We estimated that for this covered road facility the value of the critical velocity is 4 m/s. Indeed, in the area of the fire-accident, the overall velocity gains value due to the constructive interference of buoyant forces in fluid (caused by the combustion process) and the longitudinal air movement (caused by forced ventilation).

Fig. 5. In 113th second fire is “leaving” the actual source and temperature is pointing to the inflaming of the road-asphalt; concrete spalling is inevitable; the smoke is moving towards the entrance

However, the applied ventilation-velocity (due to the 16 Pa pressure-difference) in the 22nd second of the fire-accident shows the characteristics of “backlayering” – the smoke movement along the tunnelceiling against the applied ventilation. The temperature profiles pass the concrete spalling-temperature, which might start in about the 10th minute of a thermal load [36].

Fig. 4. The view to the fire-place in the part with rectangular crosssection in 7th second

4 SIMULATION OF 40 MW-FIRE AND 80 MW-FIRE WITH ARTIFFICIAL LONGITUDINAL VENTILATION We started this numerical experiment with an assumption that the accidental fire (both of 40 and of 80 MW) was already established and the longitudinal ventilation in the left-tube (composed out of 7 ventilator-pairs) was set to meet the criteria of the “critical velocity” – the velocity in the ventilating process of a tunnel-fire-event that is just enough 186

Fig. 6. The view of the 40 MW- fire-place towards the tunnel bifurcation-zone (deep in the sketch); upper left, is the planned exit to the local road

A little further from the fire place is the connection of the two kinds of tunnel cross-section-

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parts (rectangular and “horse-shoe-shaped”). The temperature iso-surfaces showing destructible thermal load in the vicinity of the tunnel-ceiling (above the fire-place).

Fig. 7. A side view of the 22nd second of the longitudinal ventilation in case of 40 MW fire event; on the iso-surfaces that represent ventilation velocity of 4 m/s the temperature images are drown

second of the same fire-event. This implies that artificial longitudinal ventilation adjusted for 16 Pa of pressure difference can cope with the fire event up to 40 MW of the fire´s thermal-power – and this already after a minute-and-the-half. With this engagement, the possible RC-spalling is inhibited. However, the thermal impact (due to the developed temperature fields and due to the heat irradiance) destroys the asphalt road-layer that is, in this case, a cheaper part of this underground space facility, in terms of reconstruction.

The additional size of the temperature impact offers a view in 112 s, at the tunnel-ceiling and tunnelwalls next to the 80 MW fire-place (Fig. 9). The zones with the developed temperature of 500 K (the begin of the RC-spalling) “resist” the longitudinal ventilation, that in the 40 MW fire event was able to cope the accident. In this stage of the fire-development these occurrences present a dangerous part in the construction of the tunnel body (Fig. 9).

Fig. 9. The additional size of the temperature impact offers a view in 112 s, at the tunnel-ceiling and tunnel-walls next to the 80 MW fire-place

Fig. 8: Distinguishing two major groups of the flame-shapes in enclosure: a) the ones that impinge on the tunnel roof and the others that; b) influenced by the longitudinal (air)stream, do not; during the CFD-investigations, we recognised the latter ones [37]; here, the 4 m/s ventilation-velocity in the 88th second of the 40 MW fire provides protection for the walls of the tunnel cavity; still, there is a minor “back-layering” to be seen on the ceiling, above the fire-place only

In a further extraction of the results of our numerical experiment, we noticed that in the 88th second during the 40 MW fire, the longitudinal ventilation was as capable (in providing the lower temperatures on the tunnel cavity) as in the 120th

Fig. 10: 126th second of the 80 MW-fire; the central tunnel line is presented partly by the “neutral” grid and partly by the temperature´s central-plane

And not even in the 126th second, during the developing of the 80 MW fire-consequences, the applied longitudinal artificial ventilation with the velocity of 4 m/s was not able to perform a

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completely successful protection of the tunnel-walls and the tunnel-ceiling (Fig. 10); but the areas with the temperature of 500K that stand for the beginning of the RC thermal destruction can still be seen (Fig. 10).

The result we gained on the effectiveness of the proposed ventilation magnitude in case of 80 MW fire, encourages a further numerical experiment in order to estimate the optimal velocity of the ventilation (in case of 80 MW fire). It will offer appropriate thermal protection until accidental fire is fully under control.

However, the chosen velocity of the ventilation was able to suppress propagation of the hot gaseous combustion products in unwanted direction in both accidental cases.

By performing this study on only one object of interest of the given geometric characteristics, the CFD-based investigation on the accidental fire in the artificially ventilated tunnel “Sentvid” was conducted according to both standards and novel experimental [38] to [41] and computer aided [42] to [44] research [45] and [46].

With the results of this research-attempt, we intend to also address the civil-engineering sector [46] and [48] and enlarge data-base for the medical healthprotection [49].

The specific geometry of the object of interest – this traffic road-object built in Slovenia – was a “fine provocation” to conduct this research, expecting new answers due to the possible impact of a realityoriented enclosure (computational domain) onto large-scale fire and escorting occurrences.

The “chimney effect” of the exit up to the local road was not “strong enough” and its possible influence was inhibited due to applied longitudinal ventilation that forced gaseous combustion products towards traffic-positive direction, already after the first minute-and-a-half of numerical investigations.

Therefore, the propagation of the gaseous products “followed” the tunnel line (towards a lower geodetic position) and in the cases of 40 and 80 MW-fire, the expected major influence of the tunnel-road exit was not noticed.

5 ACKNOWLEDGEMENT Authors do thank to Mr. Marko Zibert, Dipl. Ing. and to Ass. Prof. Jurij Kazimir Modic, PhD. for decisive support in performing this study. Special gratitude goes to Prof. Karel Ciahotny, PhD. as well as to Prof.

Vazlav Koza, PhD. from the Institute of Chemical Technology, Prague for immense software-support during this CFD-based research.

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Paper received: 2011-02-17, paper accepted: 2012-01-11 © 2012 Journal of Mechanical Engineering. All rights reserved.

Tool-Edge Wear and Wavelet Packet Transform Analysis in High-Speed Machining of Inconel 718 Fang, N. – Pai, P. S. – Edwards, N. Ning Fang* - P Srinivasa Pai - Nathan Edwards

College of Engineering, Utah State University, U.S.A. Tool-edge wear (i.e., the wear of a tool cutting edge before it is fully worn away) is among significant concerns in high-speed machining because it can result in early tool failure and deteriorated quality of machined parts. Based on extensive experimental results, this paper shows how tool-edge wear is correlated with the cutting forces and vibrations in high-speed turning of Inconel 718. The following research findings are made from the present study: 1) The development of tool-edge wear depends on the initial tool-edge geometry and the cutting conditions employed. 2) The amount of tool-edge wear varies at different measurement points along the tool cutting edge, and increases as the feed rate increases. 3) The effect of tool-edge wear on the cutting forces depends on the initial tool-edge geometry and the cutting conditions employed.

4) The traditional time-domain analysis based on the vibration amplitude is not helpful in explaining and showing the dynamic development of tool-edge wear, and wavelet packet transform helps in identifying the changes in the vibration signals in different frequency bands.

Keywords: tool-edge wear, cutting forces, cutting vibrations, wavelet packet transform, Inconel 718, high-speed machining

0 INTRODUCTION Tool wear in high-speed machining (HSM) has long been a significant concern because it shortens tool life, increases cutting forces, temperatures, and vibrations, and deteriorates the quality of machined parts or components [1] to [3]. Tool wear can be classified into different types according to its mechanisms (i.e., the reasons that cause tool wear) or its forms (i.e., the locations on a cutting tool) [4] and [5]. By mechanisms, there are adhesive wear, abrasive wear, diffusion wear, delamination wear, attrition wear, fatigue, etc. By locations, there are crater wear, flank wear, notch wear, chip-groove wear, and so on.

Extensive literature review shows that the forms of tool wear that have been widely studied are crater wear [6] and [7] and flank wear [8] and [9]. In contrast, there is little research on another important form of tool wear called tool-edge wear [10]. Tool-edge wear is defined as “the wear of a tool cutting edge before it is fully worn away [11].” Fig. 1 shows the location of tool-edge wear on a cutting tool, including a 3D view and a 2D cross-sectional view of the tool cutting edge.

As seen from Fig. 1, the location of tool-edge wear is different from those of crater wear and flank wear. Tool-edge wear is also different from tool notch wear (also called tool nose-radius wear or depth-of-cut notching in some literature). Tool notch wear occurs in the tool nose radius area and is typically measured on the tool rake face. Tool-edge wear can occur not only in the tool nose radius area, but can also occur at any other locations along the tool cutting edge. Typically, tool-edge wear is measured at a selected point on the tool cutting edge by using a fine contour measuring instrument [11]. The change in the area of the cross

section of the tool cutting edge at the selected point (as shown in Fig. 1b) before and after cutting can be taken as the amount of tool-edge wear [in mm2] at that selected point.

a)

b) Fig. 1. Location of tool-edge wear on a cutting tool; a) 3D view and b) 2D cross-sectional view

*Corr. Author’s Address: Utah State University, 4160 Old Main Hill, Logan, UT 84322, U.S.A., ning.fang@usu.edu

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Tool-edge wear can lead to early failure of the tool cutting edge, such as severe plastic deformation and catastrophic breakage. In their 2D orthogonal high-speed machining experiments, Wu and Fang [11] have shown that tool-edge wear constantly changes the tool-edge geometry and dimensions before the tool edge is fully worn away.

The overall goal of the present study is to correlate tool-edge wear with the cutting forces and vibrations through a carefully designed set of CNC highspeed machining (in specific, turning) experiments that cover a wide range of cutting conditions. The present study applies an advanced signal-processing technique, called wavelet packet transform (WPT) [12] to [15], to establish the co-relationship between tool-edge wear and its associated cutting vibrations.

Nickel-based superalloy Inconel 718 was selected as the work material in cutting experiments in the present study. Research by others [16] to [18] has shown that the machining of Inconel 718 often results in significant tool wear, short tool life, high cutting forces and temperature, strong vibrations, and poor quality of the machined surface.

The logic structure of this paper is as follows.

Section 1 describes in detail the experimental set-up (including work material, tool material and geometry, and the cutting conditions) and the methods of measuring the tool-edge profile, the cutting forces and vibrations. Section 2 presents the experimental results of dynamic tool-edge wear and its effects on the cutting forces and vibrations. Representative examples of the tool-edge profiles and the variations of the cutting forces and vibration amplitudes at different cutting time intervals are provided. Section 3 performs time-frequency domain analysis of the vibration signals via wavelet packet transform.

Representative examples of the third-level wavelet packet decomposition of vibration signals at different cutting time intervals are also provided. The major research findings are summarized at the end of this paper.

1 EXPERIMENTAL PROCEDURE

conventional machining of Inconel 718. The feed rate [0.01 to 0.10 mm/rev] was the same magnitude as the tool edge radius [0.04 to 0.07 mm] of the cutting tools to magnify the effect of tool-edge wear. The depth of cut [0.8 mm] was the same as the tool nose radius.

The tool nose radius and the tool edge radius are two different concepts, and they are measured in different geometrical planes in 3D space. No coolants were employed in the cutting experiments to facilitate the collection of the cutting force and vibration signals.

Table 1. The major experimental set-up Variables Work material Workpiece dimension

Specifications Inconel 718 Solid cylindrical bar with the diameter of 45 mm Tool insert Flat-faced TPG 432 (made by Kennametal Inc.) Tool material Cemented carbide (KC 8050) with TiC/TiN/ TiCN coating Tool working rake angle 5° Tool working side cutting edge angle 0° Tool working flank angle 6° Tool nose radius 0.8 mm Tool edge radius Varied from 40 to 70 mm Cutting speed 125, 225, 275 m/min Feed rate 0.01, 0.04, 0.10 mm/rev Depth of cut 0.8 mm Coolants None

In order to study the dynamical development of tool-edge wear and its effects on the cutting forces and vibrations, each cutting experiment was carried out for one second and then repeated nine times with the same cutting conditions. The results of the cutting tests showed that tool wear developed very rapidly due to the use of high cutting speeds. The tool cutting edge was initially fresh in the first cut and was then worn out in the subsequent second, third, forth, …, ninth cuts. For each cut, the tool-edge profile was measured offline, and the cutting forces and vibrations were measured online.

1.1 Experimental Set-Up

1.2 Work Material

A CNC turning center (HAAS SL10) was employed in high-speed finish turning. Table 1 summarizes the major experimental set-up. To meet the cutting speed requirement in high-speed machining and to accelerate the tool-edge wear process, the cutting speed [125 to 275 m/min] was four to nine times higher than that typically employed [30 m/min] in

The work material employed in the present study was commercially available, nickel-based superalloy Inconel 718. The work material has the following chemical compositions in percentage of weight: Ni (+Co): 50 to 55%; Cr: 17 to 21%; Nb (+Ta): 4.75 to 5.5%; Mo: 2.8 to 3.3%; Ti: 0.65 to 1.15%; Co: 1.0%; Mg: 0.35%; Cu: 0.3%; Si: 0.35%; Al: 0.2 to 0.8%; C:

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0.08%; Fe: Balance. The heat treatment conditions were as follows: one hour at 954 to 982 °C, air cool, eight hours at 718 °C, cool 56 °C/h to 621 °C, hold eight hours, and finally air cool.

1.3 Tool Inserts and the Measurement of the Tool-Edge Profile A Mitutoyo type-SV602 fine contour measuring instrument was employed to measure (off-line) the profile of fresh or worn tool cutting edges for each cut. Due to manufacturing errors in the commercial tool inserts, the tool-edge profile of a fresh tool insert was not uniform along the tool cutting edge. The tooledge profile was measured at three locations along the cutting edge, as shown in Fig. 2. The center point was at the middle position of the curved tool cutting edge.

The inner point was close to the machined surface.

The outer point was close to the workpiece shoulder.

In machining, the actual tool edge engagement with the work material occurred from the outer point to the inner point.

mm and were used to study the effect of tool-edge wear under varying feed rate conditions. After cutting, the machine tool was stopped every one second (i.e., the cutting time interval was one second) in order to measure (offline) the profile of worn tool edges at each of the three measurement points on each tool insert.

Table 2. Six tool inserts employed in the cutting experiments Tool #1 #2 #3 #4 #5 #6

Cutting conditions Vc f ap 125 0.10 0.80 225 0.10 0.80 275 0.10 0.80 225 0.01 0.80 225 0.04 0.80 225 0.10 0.80

Tool edge radius [mm] Inner Center Outer Aver.

60.5 63.8 67.8 64.0 60.8 65.3 69.8 65.3 59.2 60.1 64.1 61.1 42.7 45.4 48.8 46.6 43.8 43.7 48.1 45.2 43.2 47.3 48.9 46.5

1.4 Measurement of the Cutting Forces For each cutting time interval, the cutting forces were measured online using a system that consisted of a Kistler 9257B, quartz three-component dynamometer; a Kistler 5010 B multi-channel, dual-mode charge amplifier; and a computer data acquisition system (Labview). A MATLAB code was written to filter the high-frequency noise from the collected force signals and determine the three components of the cutting forces, namely the cutting force Fc, the feed force Ff, and the passive force Fp. These three forces are in the tangential [x- or the cutting speed], axial [y- or the feed rate], and radial [z- or the depth of cut] direction, respectively.

1.5 Measurement of the Cutting Vibrations

Fig. 2. Location of the three measurement points along the tool cutting edge

More than 20 tool inserts were measured, and six tool inserts with the most uniform distribution of the tool edge radius along the tool cutting edge were finally selected for use in the cutting experiments.

The edge radii of these six “fresh” tool inserts at each measurement points are listed in Table 2, where Vc is the cutting speed [m/min], f is the feed rate [mm/rev], and ap is the depth of cut [mm]. Tool inserts #1 to #3 had the tool edge radius between 61.1 to 65.3 mm and were employed to study the effect of tool-edge wear under varying cutting speed conditions. Tool inserts #4 to #6 had the tool edge radius between 45.2 to 46.6

While the cutting forces were measured online by the Kistler 9257B dynamometer, the cutting vibration signals were simultaneously measured online for each cutting time interval via a 356A63 Triaxial ICP accelerometer that was fixed onto the tool holder through an insulation screw hole. The collected vibration signals were subjected to post-processing in both the time domain and the time-frequency domain.

In the time domain, the root mean square (RMS), which is the average of the squared values of the vibration amplitude, was calculated. The RMS gives positive values that can be used for vibration analysis. In the time-frequency domain, wavelet packet transform analysis was performed and will be described in detail in a subsequent section of this paper.

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2 Dynamic variation of tool-edge wear and its effects

which results in highest tool-chip friction at the outer point.

2.1 Profile and Development of Dynamic Tool-Edge Wear Figs. 3 and 4 show two representative examples of the 2D tool-edge profile measured at different cutting time intervals for tool inserts #3 and #4, respectively.

In Figs. 3 and 4, the first row is the tool-edge profile of a fresh tool, the second row is the tool-edge profile after cutting for 2 seconds, and the third row is the tool-edge profile after cutting for 9 seconds. The tooledge profile includes the tool rake face on the left side and the tool flank face on the right side of the profile.

Fig. 4. Representative examples of the 2D tool-edge profile measured at different cutting time intervals; tool insert #4 under the cutting conditions of Vc= 225 m/min, f = 0.01 mm/rev, ap = 0.80 mm

Fig. 3. Representative examples of the 2D tool-edge profile measured at different cutting time intervals; tool insert #3 under the cutting conditions of Vc= 275 m/min, f = 0.1 mm/rev, ap = 0.80 mm

Note that tool insert #3 was employed at the relatively larger feed rate of 0.10 mm/rev. Tool insert #4 was employed at the small feed rate of 0.01 mm/ rev, in which case the undeformed chip thickness was much smaller than the initial tool-edge radius. The following observations are made: 1) As the cutting continues, tool-edge wear develops either rapidly or slowly, depending on the initial tool-edge geometry and initial cutting conditions employed. At all measurement points, tool-edge wear are severer and more visible at 9 seconds than that at 2 seconds, as can be seen clearly from both Figs. 3 and 4.

2) The profile of tool-edge wear dynamically varies and often has irregular shape. This can be clearly seen from the profile measurements at the center and outer points in Fig. 3.

3) Tool-edge wear increases from the outer point, through the center point, to the inner point. This is because the outer point corresponds to the shear zone with the largest undeformed chip thickness, 194

4) Tool-edge wear increases as the feed rate increases. In Fig. 3, the work material undergoes more significant shear deformation and the tool-chip contact length is larger due to the relatively larger feed rate of 0.10 mm/rev. In Fig. 4, the “plowing” action (rather than the shear deformation) dominates and the tool-chip contact length is limited due to the use of small feed rate of 0.01 mm/rev. Less tool-edge wear can be observed in Fig. 4 when compared to Fig. 3.

2.2 Effect of Dynamic Tool-Edge Wear on the Cutting Forces Because tool-edge wear varies from point to point on the tool cutting edge, the best way to represent overall tool-edge wear is using the cutting time interval.

Figs. 5 and 6 quantitatively show how dynamic tool-edge wear – represented by the cutting time interval – affects the three components of the cutting forces under varying cutting speeds and feed rates, respectively. For comparison purposes, the scales of the vertical axes in these figures are made the same.

Fig. 5 shows that all three components of the cutting forces increase with increasing tool-edge wear at the cutting speed of 125 m/min. However, the increasing trend of the cutting forces is not significant at the relatively higher cutting speeds of 225 and 275 m/min. In all three sub-figures in Fig. 5, the cutting force Fc is higher than the feed force Ff, and the passive force Fp is the smallest among the three force components.

Fig. 6 shows that all three components of the cutting forces increase with increasing tool-edge wear

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at the feed rates of 0.01 and 0.10 mm/rev. However, the increasing trend of the cutting forces is not significant at the feed rate of 0.04 mm/rev. Under the feed rate of 0.04 and 0.10 mm/rev (see Figs. 6b and 6c), the cutting force Fc is higher than the feed force Ff. Under the small feed rate of 0.01 mm/rev (see Fig. 6a), the feed force Ff is higher than the cutting force Fc. This latter phenomenon is directly associated with the

tool-edge effect. A significant amount of theoretical and experimental studies in 2D machining [17] to [19] have shown that the thrust force (corresponding to the feed force in 3D machining) can be higher than the cutting force if the undeformed chip thickness is greatly lower than the tool edge radius.

The above experimental results reveal that the effect of dynamic tool-edge wear on the cutting

a)

a)

b)

b)

c) Fig. 5. The cutting forces vs. the cutting time at the feed rate of 0.10 mm/rev and the cutting speed of a) 125 m/min, b) 225 m/ min, and c) 275 m/min; tool inserts #1 to #3 were employed

c) Fig. 6. The cutting forces vs. the cutting time at the cutting speed of 225 m/min at the feed rate of a) 0.01 mm/rev, b) 0.04 mm/rev, and c) 0.10 mm/rev; tool inserts #4 to #6 were employed

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forces highly depends on particular cutting conditions employed as well as the initial tool-edge geometry. In the final analysis, the cutting forces are the results of interactions among tool-edge wear, cutting conditions, tool geometry, and so on.

2.3 Effect of Dynamic Tool-Edge Wear on the RMS Vibration Amplitude The RMS vibration amplitude is the square root of the average of the squared values of the vibration

a)

a)

b)

b)

c) Fig. 7. The vibration amplitude vs. the cutting time at the feed rate of 0.10 mm/rev and the cutting speed of a) 125 m/min, b) 225 m/ min, and c) 275 m/min; tool inserts #1 to #3 were employed

196

c) Fig. 8. The vibration amplitude vs. the cutting time at the cutting speed of 225 m/min at the feed rate of a) 0.01 mm/rev, b) 0.04 mm/rev, and c) 0.10 mm/rev; tool inserts #4 to #6 were employed

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amplitude. Figs. 7 and 8 show, respectively, the effect of dynamic tool-edge wear on the cutting vibrations under varying cutting speed [125, 225, and 275 m/ min] and varying feed rate [0.01, 0.04, and 0.1 mm/ rev] conditions. Except for Fig. 8b, two vibration components [Vx in the cutting speed direction and Vz in the depth of cut direction] exhibit higher values and have values very close to each other. The observation on all the six sub-figures in these two figures leads to a same conclusion: There is no obvious varying trend for the RMS vibration amplitude as tool-edge wear dynamically develops. The “ups and downs” of the vibration amplitude are found all over the map in the six sub-figures. In contrast, the cutting forces vary in a certain pattern as shown in previous Figs. 5 and 6.

Based on the results shown in Figs. 5 to 8, two important conclusions are drawn. 1) Compared to the cutting forces, the cutting vibrations are more sensitive to dynamic tool-edge wear. Because tool-edge wear is complex, the vibration signals are also complex.

2) The traditional time domain analysis based on the RMS vibration amplitude is not helpful in explaining and showing the dynamic development of tool-edge wear. No distinct features from the time domain vibration signals can be extracted to effectively corelate the cutting vibrations with dynamic tool-edge wear. Wavelet packet transform (WPT), a modern advanced signal-processing technique, was thus employed and is described as follows.

3 Time-frequency analysis via wavelet packet transform Compared to other signal processing techniques (such as fast Fourier transform, FFT) that relate tool wear (primarily crater and flank wear) and the cutting vibrations [20] to [23], wavelet packet transform not only helps in identifying the changes in the vibration signals in different frequency bands that are associated with dynamic tool-edge wear, but also helps in identifying the most important features of vibration signals that are most sensitive to dynamic tool-edge wear. A brief introduction to wavelet packet transform is first provided to better understand the wavelet packet algorithm employed in the present study.

3.1 Wavelet Packet Transform Wavelet transform (WT) is a mathematical function that multiplies the signal during all its length, with elongated and compressed versions of a mother wavelet. A signal is decomposed into a low

frequency component (called approximation) and a high-frequency component (called detail). The approximation in turn is then decomposed into a second level of approximation and detail and this process is repeated. WT can extract signal information in the time domain at different frequency bands and provides flexible time-frequency resolution properties [14]. However, WT has one drawback that the frequency resolution is rather poor in the high-frequency region. Thus, it faces difficulties in discriminating between signals having close highfrequency components [15].

To overcome the drawback of wavelet transform, wavelet packet transform is used as one of the most generalized signal decomposition methods. Wavelet packets are alternative wavelet bases formed by taking linear combination of the usual wavelet functions.

These bases inherit properties, e.g., orthonormality and time-frequency localization, from their wavelet functions [24]. In wavelet packet transform, both the approximation and detail parts are decomposed.

A wavelet packet function is a function with three indices (i, j, k) satisfying:

W jn,k (t ) = 2 j / 2 W n (2 j t − k ), (1)

where j and k are index of scale and translation operations, respectively; the index n is called the modulation parameter or the oscillation parameter and n = 0, 1, 2, ..., 2j-1.

Wavelet packet functions are defined by:

W2n ( x) = 2 ∑ k h(k )Wn (2 x − k ), (2)

W2n +1 ( x) = 2 ∑ k g (k )Wn (2 x − k ), (3)

where h(k) and g(k) are the low-pass and high-pass filters; W0(x) = ϕ(x) is the scaling function; and W1(x) = ψ(x) is the wavelet function.

The discrete filters h(k) and g(k) are quadrature mirror filters associated with scaling function and wavelet function [25]. To measure specific timefrequency information in a signal, the inner product of the signal and a particular basis function is taken.

The wavelet packet coefficients of a function f(x) is computed as:

W j ,n,k =< f , W jn,k >= ∫ f ( x)W jn,k ( x)dx. (4)

The whole set of the orthonormal bases is called a wavelet packet library. The discrete wavelet packet transform is then expressed as:

W j +1,2n = H W j ,n , (5)

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where H = {hl }

l∈Z

and G = { gl }

l∈Z

are the low-

pass and high-pass filter matrices; W0,0 represents the

measured signal; Wj,n is the wavelet packet where j and n indicate the level of the decomposition and the position at that level, respectively.

Finally, the reconstruction of the wavelet packets can be represented as:

W j ,n = H * W j +1,2n + G* W j +1,2n +1 , (7)

Fig. 9. Representative examples of the third-level wavelet packet decomposition of vibration signals during the cutting time of 1 to 2 seconds

198

where H* and G* represent the conjugate matrix of H and G, respectively [14].

3.2. Results and Analysis via Wavelet Packet Transform Figs. 9 and 10 provide two representative examples of the third-level wavelet packet decomposition of vibration signals acquired at a sampling frequency of 10 KHz using Daubechies 8 wavelet function. The

Fig. 10. Representative examples of the third-level wavelet packet decomposition of vibration signals during the cutting time of 8 to 9 seconds

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figures contain 8 frequency bands (8 wavelet packets W30 through W37) generated at the cutting time of 2 seconds and 9 seconds. The tool insert #3 was employed at the cutting speed of 275 m/min, the feed rate of 0.10 mm/rev, and the depth of cut of 0.80 mm.

A comparison between Figs. 9 and 10 shows that the energy in different frequency bands during the cutting time of 1 to 2 seconds is less than that during the cutting time of 8 to 9 seconds. This means that the energy in different frequency bands increases as tool-edge wear increases. As shown in the tool-edge wear profile in Fig. 3, tool-edge wear is less during 1 to 2 seconds (the tool edge is relatively fresh) and becomes severer during 8 to 9 seconds (the initiallyround tool edge becomes “flat” at the center and outer measurement points). In addition, when the tool is sharp (fresh), lower frequency vibration is mainly excited. As tool-edge wear progresses, it excites different frequencies of vibrations of the cutting tool, tool holder, and machine structure, resulting in the higher frequency components becoming dominant in the signal.

To further extract from wavelet packets for different tool-edge wear conditions, the RMS value of wavelet coefficients in each frequency band was calculated using :

RMSW(3, p ) = ∑ m k =1

(W(3, p ) (k ) − W(3, p ) )2 m

, (8)

where 3 stands for the third-level decomposition; p is the number of wavelet packets (8 in this case); W(3,p)(k) is the values of the individual wavelet packet coefficients; W(3, p ) is the mean value of the wavelet packet coefficient; and m is the number of coefficients in each wavelet packet.

The RMS of wavelet packet coefficients was calculated for different cutting conditions for each experiment. It has been found that compared to other wavelet packet coefficients, coefficients W(3,2) and W(3,3) [simply written as W32 and W33] are more sensitive to dynamic tool-edge wear. As an example, Figs. 11 and 12 show the RMS W33 wavelet coefficient [corresponding to a frequency band of 1,875 to 2,500 Hz] and the corresponding RMS vibration amplitude [in the cutting speed, x-direction] under varying cutting speed and feed rate conditions. The W33 wavelet packet coefficient (in the time-frequency domain) shows an exact replication of the trend of the variation of RMS values of cutting vibrations (in the time domain) with time under various cutting conditions in both Figs. 11 and 12.

a)

b)

Fig. 11. a) RMS W33 coefficient and b) the RMS vibration amplitude at varying cutting speeds

The W33 wavelet packet coefficient is the most sensitive coefficient that can be employed as an important input for pattern recognition techniques, e.g., artificial neural networks, in a future tool-edge wear monitoring system. A detailed discussion on how to incorporate the W33 coefficient into a tool wear monitoring system [26] and [27] that includes tool-edge wear monitoring is beyond the scope of this paper.

Finally, to demonstrate the advantage of wavelet packet transform over the conventional FFT analysis, Fig. 13 shows two FFT frequency spectra of vibration signals during the cutting time of 8 to 9 seconds and 1 to 2 seconds. Although FFT analysis can identify the variation of vibration amplitude at different frequencies in light and severe tool-edge wear, FFT analysis fails to reveal which particular frequency band (over a wide range of frequencies) directly corresponds to tool-edge wear. In other words, FFT analysis fails to identify the particular frequency band

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that can be employed to monitor and detect tool-edge wear.

2)

3) 4) a)

5)

b)

tool-edge geometry and the cutting conditions employed.

The amount of tool-edge wear varies at different measurement points that correspond to different undeformed chip thicknesses and tool-chip friction conditions at particular measurement points. In general, tool-edge wear increases from the outer point, through the center point, to the inner point. Tool-edge wear also increases as the feed rate increases.

The tool-edge wear profile dynamically varies and is often in irregular shape, adding to the complexity of dynamic tool-edge wear.

The effect of dynamic tool-edge wear on the cutting forces highly depends on particular cutting conditions employed as well as the initial tool-edge geometry. All three components of the cutting forces increase with increasing tool-edge wear at the feed rates of 0.01 and 0.10 mm/rev.

The increasing trend of the cutting forces is not significant at the feed rate of 0.04 mm/rev.

No obvious varying trend was observed for the RMS vibration amplitude as tool-edge wear develops. The traditional time domain analysis based on the RMS vibration amplitude is not helpful in explaining and showing the dynamic development of tool-edge wear.

Fig. 12. a) RMS W33 coefficient and b) the RMS vibration amplitude at varying feed rates

4 Conclusions As tool-edge geometry plays a significant role in machining at small feed rates [28] and [29], tool-edge wear significantly contributes to early tool failure and deteriorated quality of machined components and parts. Compared to tool crater wear and flank wear that have been well studied for decades, there has been little study on tool-edge wear. This paper has performed a fundamental study of tool-edge wear in high-speed finish machining of nickel-based superalloy Inconel 718. The emphasis of the present study is on the correlation among tool-edge wear, the cutting forces and vibrations. The major research findings are summarized in the following paragraphs.

1) As the cutting continues, tool-edge wear develops either rapidly or slowly, depending on the initial 200

a)

b) Fig. 13. FFT frequency spectrum of the vibration signals during the cutting time of a) 8 to 9 seconds and b) 1 to 2 seconds

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6) As one of the most generalized signal decomposition methods used in the timefrequency domain analysis, the wavelet packet transform helps in identifying the changes in the vibration signals in different frequency bands.

Under the initial tool geometry and cutting conditions employed in the present study, the W33 wavelet packet coefficient is identified as the most sensitive to dynamic tool-edge wear, and it can be employed as an important input for pattern recognition techniques in a future tooledge wear monitoring system.

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[26] Rehorn, A.G., Jiang, J., Orban, P.E. (2005). Stateof-the-art methods and results in tool condition monitoring: a review. International Journal of Advanced Manufacturing Technology, vol. 26, no. 7-8, p. 693-710, DOI:10.1007/s00170-004-2443-6.

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[27] Sick, B. (2002). On-line and indirect tool wear monitoring in turning with artificial neural networks: A review of more than a decade of research. Mechanical Systems and Signal Processing, vol. 16, no. 4, p. 487546, DOI:10.1006/mssp.2001.1460.

[28] Liu, K., Li, X.P., Rahman, M., Neo, K.S., Liu, X.D. (2007). A study of the effect of tool cutting edge radius on ductile cutting of silicon wafers. International Journal of Advanced Manufacturing Technology, vol.

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[29] Pušavec, F., Govekar, E., Kopač, J., Jawahir, I.S. (2011). The influence of cryogenic cooling on process stability in turning operations. CIRP Annals Manufacturing Technology, vol. 60, p. 101-104.

Fang, N. – Pai, P. S. – Edwards, N.

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)3, 203-212 DOI:10.5545/sv-jme.2011.042

Paper received: 23.2.2011, paper accepted: 12.1.2012 © 2012 Journal of Mechanical Engineering. All rights reserved.

Synthesis of Truss Structure Designs by NSGA-II and NodeSort Algorithm Stanković, T. – Štorga, M. – Marjanović, D. Tino Stanković* – Mario Štorga – Dorian Marjanović

University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture, Croatia This paper presents a genetic algorithm based approach for synthesis of truss structure designs. Genotype represented as a collection of binary encoded nodes is decoded into the phenotype by applying the NodeSort algorithm. A genotype extension to consider a cross-section as variable and variable length chromosomes to produce designs to successfully meet the boundary conditions are all being incorporated into the NodeSort to provide an efficient truss structures synthesis framework. The introduction of multi-objective optimisation using NSGA-II will help to address more real life engineering problems.

Keywords: truss structure design synthesis, genetic algorithms, NodeSort, NSGA-II

0 INTRODUCTION The work presented in this paper proposes a genetic algorithm based approach for synthesis of truss structure designs. It builds on the NodeSort [1] algorithm, which takes a collection of binary encoded nodes from a 2D domain and decodes these into a truss structure in a process similar to FEM meshing. In our previous work it was shown that the NodeSort is well suited for the generation of optimal truss structure designs [1]. To continue the development of a truss structures synthesis framework, within this paper the following points are set as the research goals: • To account for the multiple search objectives a non-dominated sorting genetic algorithm II (NSGA-II) [2] and [3] will be applied.

• Rather than being just a parameter, the crosssection area of trusses is defined as a variable what should improve the quality of produced solutions. Thus, the genotype is extended with one more binary encoded gene.

• To avoid the formation of node clusters occurring in near-optimal designs that had excessive number of predefined nodes, or in the opposite, to provide nodes to resolve a design solution when the course of evolution demands more trusses, a variable length chromosomes are introduced.

• To facilitate versatility and user-centricity, an arbitrary number of nodes with imposed loads are allowed to be specified.

The next section will address the applicability of evolutionary algorithms as powerful and apt optimizers. Then, the related work section will provide an overview of truss structures optimization approaches and drawn from these will justify the motivation for the NodeSort. To be able to accomplish the genotype extension and the introduction of variable length chromosomes, the adjustments need to be performed at the evolutionary operators’ level.

How are the crossover and mutation resolved to accommodate these changes, as well as the NodeSort algorithm, is presented in the third section. Section 4 gives FEM model of truss girder system and Section 5 formulates the objectives and constraints of multiobjective optimisation problem. Modifications of the search process parameters and penalty functions with the search algorithm given in pseudo-code are presented in Section 6. Case study and results discussion are presented afterwards. Conclusions and the future work notice close this paper.

1 EVOLUTIONARY ALGORITHMS Evolutionary algorithms (EA) are population based stochastic optimisers that are built on mimicking the notions from the natural evolution. Charles Darwin stated that evolution begins with the inheritance of good gene variations and that basically defines what the evolutionary algorithms are all about. Enforcing the survival of the fittest principle is managed by allowing higher ranked solutions to participate in an evolution process by the most. In a random process of mixing together the building-blocks taken from two parent solutions an offspring is produced. Presumably, if building blocks originate from a higher fitness individuals than there is a chance that newly generated individual might get a bit closer to a solution optimum.

With the whole process iterated over population generations to produce offspring which replace their parents at least to an extent, the emergence of solution occurs as a consequence of the most fit building-block combinations being frequently utilised in a solution construction. For such behaviour, it can be said that algorithm exhibited a learning process in identification of which building blocks to use and how [4] and [5].

The key issue of computational modelling [5] is to find out suitable problem representation acceptable both to the computational environment and to the

*Corr. Author’s Address: Faculty of Mechanical Engineering and Naval Architecture, I. Lučića 5, Zagreb, Croatia, tino.stankovic@fsb.hr

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task at hand. Thus, the problem representation has to concur to the algorithm’s requirements and it should be devised in a fashion that captures the most of the form and attributes of the design search space.

With EA’s, the problem representation is most often brought down to finding out the appropriate genotype encoding and its counterpart, decoding into a phenotype, thus representing a key point in designing an evolutionary computation based optimization method [4] and [5]. The extension of the genotype to include truss thicknesses, the utilization of variable length chromosomes, as well as the NodeSort dependent decoding are viewed as part of an effort to provide a good material for the truss design evolution process. In that way by expanding the set of means to realize the required behaviour, the navigation to more applicable design solutions is made possible.

design variables, such as the cross-sectional area, remain predefined and out of reach.

A more subtle approach using the simulated annealing (SA) method together with shape grammars for the structural optimization purposes was developed by Shea and Cagan (1998) [11].

Shape grammars provide a formal language, a design language for the structure shape manipulation.

Grammars are driven by a set of production rules, or simply productions, by which the solution is obtained from a series of transformations according to possible rules implementation sequences. However, for the description of all the possible truss structures, the set of rules must be equally large. Therefore, for a generic approach, to evolve the structures, the rules should be evolvable as well [12].

From the literature review, it can be found that the methods for the truss structure optimization are specialized either for the structure properties optimization [6] and [7] or the structure topology optimization [8] to [10]. By all means not diminishing the complexity of the problem, still the parametric optimisation genotypes are easily encoded because the layout of trusses is known and remains unchanged during the optimisation. As the initial variability of the shape is not being accounted for; instead the optimisation is carried over the usual truss design related variables, i.e. cross-sectional area, length, etc. By contrast, a different type of encoding is applied in the topological optimum design (TOD) cases [8] to [10]. The structure is represented in a discrete domain, most often in the form of material distribution, which is a straightforward approach in shape optimization. The genotype encodings may be accomplished in many ways, for example as matrices, Voronoi representations [9], or even by using 3-D FEM building blocks. The phenotype representation then visually depicts the resulting structure. An interesting cantilever optimization problem has been researched by Kim and de Weck [10], who addressed the quality of search with the domain resolution and chromosomal length [5]. They increased domain resolution gradually throughout the evolution to simulate the concretization process starting up from a vague concept as a small sized matrix to end up with a refined and concrete solution. TOD is computationally very demanding, it optimizes the structure in the form of the in-domain material distribution, but the other 204

?

Domain

2 RELATED WORK AND PROBLEM FORMULATION

y

x

F

Fig. 1. 2-D continuous search domain [1]

The problem of truss structure design in the 2-D continuous domain as seen within this work is pictured in Fig. 1. Assuming a random distribution of nodes and a number of predefined fixed nodes (supports and load nodes) all of which are contained within a chromosome, the topology of truss girder design emerges after the application of the NodeSort decoding algorithm [1] (Section 3.3 of this paper).

The genotype encoding and decoding applied in the NodeSort enable the search space to be as large and unconstrained as possible. It goes beyond parametric optimisation by allowing the optimisation of topology, it surpasses TOD approaches since it is much less computationally demandable with girder FEM’s being parametric and optimised in a continuous domain. The phenotype represented as a truss structure emerging out of inter-nodal arrangement is an algorithmically driven approach. It offers an alternative to shape grammars which being knowledge-driven achieve the increase in the performance by addition of new rules, thus retaining the same rule transformation principles. Usually, there is a trade-off between the

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algorithmic and the knowledge-driven approaches since the former requires code interventions for the performance increase and the latter requires the shared understanding about the domain and objective rule definitions, otherwise formalized knowledge becomes inconsistent and biased. Extensions to our previous work reflecting the new encoding/decoding scheme are presented within the next section.

3 EXTENDED ENCODING/DECODING SCHEME FOR 2D CONTINUOUS DOMAINS The model of truss structure is defined as the system comprised of a number of trusses and nodes. Boundary conditions specify the load cases, thus taking into account the amount of the loads being applied, as well as the type and the location of truss girder’s supports. The load is modelled as a distribution of nodal forces. Within each of the evolution turns for every candidate solution the FEM system stiffness matrix is re-calculated. The position and length of the truss elements are defined as a consequence of the nodal arrangements within the 2-D domain. Assuming circular cross-section, an extension of previous work is the introduction of a truss cross-section diameter as a variable. Hence, a new structural model that is established with the addition of the cross-section diameter enables refinement in the search thus, allowing getting closer to the optimal system topology.

Not being explicitly written in the chromosomal genes, the trusses emerge as a consequence of in-plane nodal positions. Thus, in order to be able to introduce a truss cross-section dependant attributes it has been decided to extend the length of the binary encoded node by one gene to contain a gamete of a truss crosssection. The diameter of each truss is then obtained as an average calculated over two gametes belonging to the nodes which define the span of a truss.

According to [1], both fixed nodes and free nodes where predetermined in numbers. To clarify a distinction, in contrast to free nodes, the fixed nodes have a static position in the 2-D search domain thus not being subjected to a position change during the course of the evolution. However, because of the way the cross-section area is calculated, the new thickness gamete addition has to be taken into account even with the fixed nodes. The number of fixed nodes is denoted as NoNx. The improvement introduced within this work enables an increase or decrease of free nodes to occur as demanded by the course of evolution. For example, by prescribing the boundary conditions including the maximal allowed crosssection thickness, the search might be put in a dead

end situation with no feasible results being generated unless it is allowed to increase the number NoN of free nodes. Hence, the increase in node numbers creates the possibility to generate more trusses since they appear as the result of nodal arrangements within the 2-D search domain. Consequently, a more stiffened and load capable structure will be designed. In contrast, by allowing the number of free nodes to be decreased is required in the case where the search has strayed in producing too complex solutions in respect to the defined loads. Then, it is necessary to reduce the number of trusses in order to obtain a best-fit solution.

3.1 Genotype Encoding The genotype is assembled two folded; on the primary level each of the nodes is represented as a bit string, and the secondary level comprises of a collection of decoded nodes from which truss structure will be determined. For free nodes, three binary encoded genes are required, two to represent in-plain positioning of the node and one for the determination of the cross-section diameter (Table 1). Fixed nodes only comprise one gene to participate in the crosssection diameter calculation. Genotype encoding with chromosome represented as a collection of nodes is shown in Table 2. Parameter nmax represents the allowed number of nodes per chromosome.

Table 1. Binary encoding of nodes Nodei yi coordinate, binary string li2

xi coordinate, binary string li1

di diameter gamete, binary string li3

Table 2. Chromosome structure Chromosomej Noden nj = NoNx + NoNj ≤ nmax

Node1, ..., Nodei, ...,

Decoding is performed using standard decoding function γ [5]. Decoding per gene i for desired interval uk , vk  ∈  is defined by the following expression:

l

γ k : {0 ,1} ik → uk , vk .

(1)

The complete decoding of each gene within a single free node i produces a vector of real numbers:

γi = γ1 × γ2 × γ3 .

(2)

3.2 Evolutionary Operators The mutation is performed simply, in a bit-flip manner, thus directly altering the nodal position

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or changing the cross-section diameter gamete in a random fashion. In order to improve the search process in the early stages of the solution evolution it was necessary to introduce scaling of the mutation rate. In the literature, there are a number of such mutation approaches [4] and [5]. They are driven by the notions from the natural evolution, justifying the initial mutation rate levels by the harsh environmental conditions. A bit-flip mutation rate is defined as a function of its initial rate p′m = 0.1 and the number of evolution iterations N. The static mutation rate is being set to p′′m = 0.02. The bit-flip mutation probability is calculated by a linear scaling formula defined over a desired number of iterations:

 p''m − p'm N + p'm  pm =  1000  p''m 

N < 1000,

(3)

otherwise.

Random addition or subtraction of nodes is performed by a node mutation procedure with the mutation probability taken the same as defined in Eq. (3). A simple random coin toss trial is performed to determine whether a point will be added or subtracted from the chromosome. Currently, only the free nodes are considered as legible for addition or subtraction.

The following formalism defines the procedure for the node mutation of chromosome providing the maximal length nmax and the mutation triggering condition p ≤ pm: add new randomly   initilzed free node randomly delete  a sinngle free node

if head ∧ n j < nmax ,

(4)

if tails ∧ NoN j − NoNx > 1.

Chromosome transcription during crossover acts to copy sequences of genetic material belonging to both parents in order to produce an offspring.

However, to be able to perform the crossover on the chromosomal structure as shown in Tables 1 and 2, a slight adaption of the usual operator is required; namely to address all of the genetic material, a crossover has to be performed on both levels of the genotype. The crossover procedure is defined with the following: • firstly, by randomly selecting one crossover point per each parent on the nodal levels, then, • corresponding to selected nodes, the crossover points are randomly chosen again but on the bitstring level.

206

After the crossover it may turn out that the length of an offspring violates the condition nk > nmax, as the result of an arbitrary nodal level crossover point selection. The formalism in Eq. (5) presents a way how to keep the size of the offspring k within the preset boundaries as defined by nmax :

Turn wise crossover point reposition :  parent towards begining, if nk >nmax , 1   parent2 towards end.

(5)  One point crossover :   on free nodes, if nk ≤ nmax .   on fixed nodes.

For the condition nk > nmax, both chromosome segments are being shortened for one node in a turn wise manner until the condition nk = nmax has been met. The turn wise relocation of the crossover point tries to average the loss in diversity of genetic material to both parents. Afterwards, the standard one point crossover is performed separately on the collections of free nodes and fixed nodes. At the end, the nodes are unified into a single collection to form new offspring individual.

3.3 Phenotype Generation with the NodeSort Algorithm Performing an automated search for the optimal system topology which employs the FEM methods for the system behaviour evaluation requires a creation of structural stiffness matrices absent of any singularities. Although the singular solutions can be ranked as infeasible by the constraint handling, their frequent occurrences will slow down and complicate the search process. To overcome the latter, drawn up on the engineering practice it is known that arranging trusses to form triangular substructures is the least requirement for the avoidance of mechanical joints formation in truss structures. Thus, if all of the substructures are triangular, the search space is narrowed down only to computable non-singular solutions, which helps to boost the efficiency of the search.

Therefore, the NodeSort employs a mapping to create phenotype out of the encoded chromosome resulting in a mesh composed of triangular schemes to satisfy topological stiffness requirement. This mapping is similar to the meshing techniques applied within various FEM methods. The NodeSort algorithm for generating a phenotype based on the nodal positions and truss thickness gametes is presented with the following pseudo-code:

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1. sort and collect nodes ascending over x, if equal compare over y, 2. point to first node in chromosome i ← 0, 3. while i < (ni – 2) do

A. if nodei.y ≥ nodei+1.y

foreach truss definition collect nodei+1, nodei+2 ,..., nodei+k which are ordered

ascending over y do

break the search if nodei+k+1 satisfies any

of the following:

a. is not ordered ascending over y,

b. is the second node in ascending order

satisfying nodei+k+1.y > nodei.y ,

c. i+k+1 > ni. od

B. else: similar as in A but collecting nodes in descending ordering over y with two break criteria redefinitions: (a) is not ordered descending over y, and (b) is the second node in descending order satisfying node.y < nodei.y.

C. define trusses between nodei and all nodes identified in A and B.

D. move to next node i ← i + 1 4. od.

The NodeSort algorithm starts with all of the nodes being sorted ascending based on their x coordinate. The first node from chromosome is taken into consideration by setting the counter i to zero (see pseudo-code line 2). In the following whiledo loop which is marked with 3, the algorithm will search for possible ways to define truss elements between the considered node i and all of the nodes with greater x coordinate. The resulting structure must be composed of triangular schemes with no trusses creating intersections. Inside the while-do loop two possibilities which are marked with letters A and B can appear: based on its position the first following node i + 1 can either be below or on equal height (A) or above the considered node i (B). Inside A all of the nodes will be ranked legible for truss definition if they do not violate the conditions a, b and c. The first condition (a), makes sure whether all of the following i+k+1 nodes are in an ascending order over y, the following (b) stops the search if the node is the second one above the node i and in the end (c) it is prevented for the counter to be larger the number of nodes ni.

The condition B takes into account situations opposite of A - the first following node being above node i thus collecting truss definition nodes in a descending order.

Except for the step (c) which considers the counter exceeding the number of nodes, the break criteria (a) and (b) are redefined for B to consider descending

order of nodes as shown in pseudo-code. Afterwards, the trusses are defined (C) over all possible attributes including truss cross-section diameter and the whole procedure is repeated for the following node (D). Fig. 2 pictures a truss structure phenotype generated by the NodeSort algorithm which corresponds to the nodal arrangement which has already been shown in Fig. 1:

Fig. 2. Truss structure obtained from nodal positions shown in Fig. 1 [1]

The singular condition that may occur when two or more nodes are very close to each other or when they overlap is regulated with a constraint that proscribes the minimal allowed length of trusses: l ≥ lmin .

(6)

4 STRUCTURAL FEM MODEL The structure is modelled using FEM planar trusses with possessing in total 6 degrees of freedom each.

It was necessary to introduce bending to trusses and implicitly convert them into beams. Otherwise, the result of the evolution taking the infinite stiffness to bending of truss FEM element will always converge to a single horizontal truss. Such structure would have zero displacement since it cannot bend, it would be minimal in mass since it is just a horizontal line.

Normal forces would also be equal to zero for the force vector put vertically as in Fig. 1. The relation between load F and the system’s nodal displacement u is given here by with the following expression:

{F}=[K]{u}.

(7)

The [K] is a standard stiffness matrix defined for planar girder elements. The load vector considering the start and end points of each of the trusses is given in its transposed form as: {FT}={N1, Q1, M1, N2, Q2, M2}.

(8) The vector of displacements per truss element is given with the following expression:

{uT}={u1, w1, φ1, u2, w2, φ2}.

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5 MULTI-OBJECTIVE OPTIMIZATION MODEL The search goal is to find an optimal distribution of trusses that comprise topology of the structure in respect to minimal mass m and minimal deflection δ.

The results will be obtained as a Pareto optimal front of truss structure designs. The optimisation problem is formulated with the following expression:

( (

) )

 min  m F , d max , E , nmax , NoNx , m' , BC      min δ F , d max , E , nmax , NoNx , m' , BC       subject to:   δ ≤ δmax  l ≥ lmin  . (10)  t −1 nt ≤ nmin   σ ≤ σ σ ≥ 0  T    | σ |< σ B σ < 0  x ∈ xmin , xmax  = xD   y ∈ ymin , ymax  = yD 

The overall mass of individual solutions m′ is also being accounted for as an increase to the imposed loads. Empirically within this research it was determined that an addition of m′ to the imposed loads pushes the search towards the optimum much earlier in the course of evolution.

The optimization parameters, variables and constraints are given as follows: • F – load vector – fixed node/nodes only, • dmax – allowed truss cross-section diameter, • E – Young’s modulus, • nmax – allowed number of nodes, • NoNx – predefined number of fixed nodes, • BC – boundary conditions – type of supports at particular fixed nodes, load distribution.

Problem variables: • x and y coordinates of each node considered, • d – truss cross-section diameter, • l – length of respective truss, • m′ – mass of individual truss design added to the overall loads.

Constraints within the search domain are defined as follows: • δmax – allowable nodal deflection, • lmin – minimally allowable truss length, • nt – dynamical and recursive constraint which proscribes that each population at step t is allowed to have the number of trusses less than or equal 208

to the least number of trusses found in feasible solutions of the previous t – 1 step, • σT – allowable tensile stress in trusses, and • σB – the Euler buckling stress for trusses.

It is assumed that compression stress state is calculated less than zero, and that the buckling strength will be entered as a parameter in its absolute value. Design search space is defined within 2-D bounding box.

6 CONTROL PARAMETERS, CONSTRAINT HANDLING AND ALGORITHM Control parameters of the search algorithm for the evolution of truss girder designs are given as follows: • population size: μ = 60, • offspring population size: μ = λ, • crossover probability for both genotype levels: pc = 1.0, • static mutation probability: p′′m = 0.02, • search halt criteria: either user defined or predefined by N≤ 5000, • bit-strings lengths in genotype (Table 1): li1 = li2 = li3 = 9.

Both feasible and unfeasible solutions enter a constrain-domination [2] and [3] process meaning that Pareto ranking is performed over all solutions to maintain diversity within the population. The feasible solutions are Pareto ranked over objective functions and the unfeasible ones are ranked according to their constraint violations. When comparing feasible and unfeasible solutions, the feasible always dominate the unfeasible ones. Constraint violation measure Ωi(ai) of ith solution ai ∈ P(t) from population P at iteration step t is derived as the summation of product between normalized violations ωj(ai) and the corresponding weighting factor Rj (Rj is normalized over the summation of all weighting factors). The expression for Ωi(ai) is given as follows: Ωi ( ai ) =

∑5j =1R j ω j (ai ) ∑5k =1Rk

.

(11)

Normalizations and weights per constrain violation of ith solution are defined as follows:

 R1 = 100.0  R = 1000.0  2   R3 = 1.0  R = 1.0  4  R5 = 1.0

Stanković, T. – Štorga, M. – Marjanović, D.

ω1 = 1.0 ω2 = 1.0

δi > δmax li < lmin

ω3 = nit - nmt -1in ω4 = σi / σT ω5 = σi / σ B

t -1 . (12) nit > nmin σi > σT σi > σ B

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Violation of minimal length is regarded as a severe constraint violation since it may lead to overlapping of the nodes in the search domain thus resulting in the systems singular stiffens matrix.

Secondly the violation of allowed deflection is also significant. These two constraints influence the initial search stages the most thus requiring the formation of so severe weighting factors. The other two constraints begin to significantly influence the search only in the later stages when most of the solutions being generated are meaningful solutions. Therefore, the weighting factor is set to 1.0 for the last three constraint violations. For the recursive constraint the normalized violations are calculated by subtracting the number of trusses of the considered solution and the least number of trusses found in feasible solutions of the previous iteration step. For the last two constraints the normalized violations are calculated by a division of current stresses found in trusses with the corresponding allowed stresses for tension and buckling.

6.1 The Search Algorithm The pseudo-code of the search algorithm is given in concordance with the general model of evolutionary algorithm [5]: 1. t ← 0; 2. P(t) ← init(μ, nmax, NoNx, BC); 3. F(t) ← eval(P(t), μ, F, dmax, E, m', xD, yD, θc) do;

A. decoding_γ(dmax, xD, yD);

B. check_points(P(t));

C. NodeSort((P(t));

D. [K] ← create_[K](P(t), E)

E. {F} ← create_{F}(P(t), F, m′);

F. {u} ← calculate_{u}((P(t), [K], {F});

G. {σ} ← calculate_{σ}((P(t), {u});

H. apply_Ω((P(t), θc); od

values (as given by Eq. (1)), displacing overlapping nodes (B), applying NodeSort (see Section 3.3), calculating displacements and stresses in trusses (steps D-G) as explained in Section 4. Step H concludes the evaluation by applying a constraint check using the Eqs. (11) and (12) to obtain constraint violation measure. For the sake of convenience all the relevant constraint parameters are denoted as θc. Step 4 onwards denotes the iterative while-do loop which lasts until the halting condition is satisfied. The crossover in step a. which produces offspring population of size λ is defined as given by the Eq. (5). To stress out the difference in respect to the parent population, the offspring population generated at step a is denoted with P′(t). The mutation of offspring’s involving steps b and c is defined by expressions for mutation probability calculation (Eq. (3)) for bit-flip mutation to form P′′(t) and nodal mutation (Eq. (4)) to form P′′′(t), respectively. The evaluation procedure at step d is comprised of the same subroutines as in the initial in steps D-G. The difference is that the evaluation is being applied to offspring population P′′′(t). Finally, the NSGA-II (e) creates a new population of size μ involving the Pareto based ranking.

7 TEST EXAMPLE Test example involves a multi-objective optimisation case with the boundary conditions selected as shown in Fig. 1. The input parameters are: load F = 2 t (~20 kN), maximal truss thickness dmax = 50 mm, Young’s modulus of elasticity for steel E = 210 MPa, maximal number of nodes involved nmax = 13, number of fixed nodes NoNx = 3. In respect to formalism in Eq. (11) the optimisation problem is given by the following Eq. 13:

( (

4. while (t < n) do

a. P'(t) ← cross(P(t), F, λ, pc, nmax, NoNx, BC);

od

b. P′′(t) ← bit-flip(P′(t), λ, pm); c. P′′′(t) ← node_mut(P′′(t), λ, pm, nmax, NoNx); d. F(t) ← eval(P′′′(t), λ, F, dmax, E, m′, xD, yD, θc) do... od e. P(t+1) ← NSGA_II(P(t) + P′′′(t), μ); f. t ← t + 1;

A random creation of the initial population composed of μ chromosomes refers to step 2 of the pseudo-code. Populations of free and fixed nodes are created separately and then joined together. The evaluation considers decoding (A) form integer to real

) )

min  m F , d max , E , nmax , NoNx , m' , BC      min δ F , d max , E , nmax , NoNx , m' , BC     subject to :   δ ≤ 0.015 m   . (13) l ≥ 0.250 m  t −1  nt ≤ nmin  2  σ ≤ 100.0 N / mm σ ≥ 0   σ<0   σ < σ B  x ∈ [ 0 ,15.0 m ]   y ∈ [ 0 , 7.5 m ] 

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8 DISCUSSION OF RESULTS

Table 3. Truss cross-section diameters

The scatter plot m ‒ δ (Fig. 3) shows the the Pareto optimal front formation during 5000 iterations recorded for every 100th step of truss design evolution.

The distinctive points on the Pareto curve which define the span (designs 1 and 3) are shown in Figs. 4 and 5, and the knee solution (design 2) is shown in Fig. 6. Crossed-out points within the scatter plot denote the infeasible solutions which violate the constraints according to Eqs. (11) to (13) taken without nt‒1 ≤ nt.

Corresponding to labelling defined in the scatter plot m ‒ δ (Fig. 3) and Figs. 4 to 6 the truss cross-section diameters and positions of nodes for designs 1, 2 and 3 of non-dominated set are shown in Tables 3 and 4.

The optimisation of the averages of objectives with standard deviation calculated at generation 5,000 during 10,000 evolution runs for distinctive points on the Pareto curve are shown in Table 5.

The algorithm score presented in Table 5 states high repeatability of the results in respect to the overall objectives. The only significant dispersions are noted over δ for Design@1 and Design@3. However, a 1/10 and 3/10 of a millimetre are more than acceptable for the proposed search domain as defined in Eq. (13).

The repeatability achieved over the design topology is shown in Fig. 7. The picture shows the spread of free nodes in knee solutions recorded for 5,000th iteration through 10,000 evolution runs.

Compression Design@ 1 2 3 Tension Design@ 1 2 3

d [mm] 2 3 43.5 42.0 47.5 46.7 50.0 49.9

1 45.4 45.0 50.0 5 22.4 29.1 49.9

6 24.2 33.9 49.9

d [mm] 7 20.3 31.6 49.9

9 22.5 28.9 49.5

Table 4. Nodal positions Free nodes starting with top left node [m] Design@ x y x y x 1 3.4 4.2 7.8 5.2 12.0 2 2.4 4.9 7.5 6.6 12.6 3 2.6 5.6 7.6 7.5 12.4 Fixed nodes starting with bottom left node [m] 1, 2, 3 0.0 0.0 7.5 0.0 15.0

y 4.0 4.6 5.6 0.0

Table 5. Averages of objectives with standard deviations Design@ 1 2 3

δ [mm]

m [t] m 0.33 0.48 0.88

SN 0.01 0.03 0.04

δ 2.33 1.26 0.83

Fig. 3. Scatter plot m – δ showing the Pareto optimal front formation recorded during 5000 iterations

210

8 22.7 33.1 49.9

4 44.0 44.0 50.0

Stanković, T. – Štorga, M. – Marjanović, D.

SN 0.34 0.11 0.05

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Fig. 4. Design@1 (lightweight design), m = 0.33 t, δ = 2.15 mm

Fig. 5. Design@3 (heaviest design), m = 0.92 t, δ = 0.78 mm

Fig. 6. Design@2 (knee solution), m = 0.49 t, δ = 1.19 mm

Fig. 7. Spread of free nodes recorded for the knee solution(Design@2 type)

9 CONCLUSION AND FURTHER WORK

for multi-objective optimization: NSGA-II. Parallel Problem Solving from Nature VI Conference.

[4] Goldberg, D.E. (2002). Design of Innovatinon. Kluwer Academic Publishers, Norwell.

[5] Bäck, T., Fogel, D.B., Michalewicz, Z. (2000).

Evolutionary Computation, Advanced Algorithms and Operators. Institute of Physics Publishing, Bristol.

[6] Hasançeb, Q. (2007). Optimization of truss bridges within a specified design domain using evolution strategies. Engineering Optimization, vol. 39, no. 6, p.

737-756, DOI:10.1080/03052150701335071.

[7] Coello, C.A.C., Christiansen, A.D. (2000).

Multiobjective optimization of trusses using genetic algorithms. Computers and Structures, vol. 75, no. 6, p.

647-660, DOI:10.1016/S0045-7949(99)00110-8.

[8] Jakiela, M.J., Chapman, C., Duda, J., Adewuya, A., Saitou, K. (2000). Continuum structural topology design with genetic algorithms. Computational Methods in Applied Mechanical Engineering, vol. 186, no. 2, p. 339-356, DOI:10.1016/S0045-7825(99)003904.

[9] Hamda, H., Schoenauer, M. (2002). Topological optimum design with evolutionary algorithms. Journal of Convex Analysis, vol. 9, no. 2, p. 503-517.

[10] Kim, Y.I., De Weck, O. (2004). Progressive structural topology optimization by variable chromosome length genetic algorithm. China-Japan-Korea Joint Symposium on Optimization of Structural and Mechanical Systems, M3, Kanazawa.

The test example verified that it is possible to utilize the NodeSort phenotype based decoding together with the proposed genotype extensions to include thickness gamete and variable length chromosomes to achieve a multi-objective NSGA-II backed optimisation. By supporting a complete topological search which maintains high results repeatability, an edge over presented methods has been achieved. Further work will address the influences on the optimal solution t −1 and search in respect to recursive constrain nt ≤ nmin the order of node sorting.

10 REFERENCES [1] Stanković, T., Marjanović, D., Bojčetić, N., Ščap, D. (2009). Enhancing Evolution of truss structures by using genetic algorithms. Transactions of FAMENA, vol. 33, no. 11, p. 1-10.

[2] Deb, K., Agrawal, S., Pratap, A., Meyarivan, T. (2002). A fast and elitist multiobjective genetic algorithm NSGA-II. IEEE Transactions on Evolutionary Computation, vol. 6, no. 2, p. 182-197, DOI:10.1109/4235.996017.

[3] Deb, K., Agrawal, S., Pratap, A., Meyarivan, T. (2000).

A fast elitist non-dominated sorting genetic algorithm

Synthesis of Truss Structure Designs by NSGA-II and NodeSort Algorithm

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[11] Shea, K., Cagan, J. (1998). Generating Structural Essays from Languages of Discrete Structures. Hero, j.s., Sudweeks, F. (Eds.) Artificial Intelligence in Design, Klower Academic Publishers, Dordrecht, p.

365-384.

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[12] Gero, J.S., Louis, S.L. (1995). Improving pareto optimal designs using genetic algorithms, Microcomputers in Civil Engineering, vol. 10, no. 4, p. 241-249, DOI:10.1111/j.1467-8667.1995.tb00286.x.

Stanković, T. – Štorga, M. – Marjanović, D.

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)3, 213-220 DOI:10.5545/sv-jme.2011.073

Paper received: 2011-04-04, paper accepted: 2011-11-18 © 2012 Journal of Mechanical Engineering. All rights reserved.

Numerical Analyses to Investigate the Feasibility and Effectiveness in Using Heat Pipe Embedded End Mills Liu, Y.-B. – Zhu, L. Jen, T.-C. – Zhao, J.-W. – Yen, Y.-H. Yong-Bin Liu1,3 – Lin Zhu1,2* – Tien-Chien Jen2 – Ji-Wen Zhao1 – Yi-Hsin Yen2 1 School

of Electrical Engineering and Automation, Anhui University, China Engineering Department, University of Wisconsin, USA 3 Department of Precision Machinery and Precision Instrumentation, University of Science and Technology of China, China 2 Mechanical

In this paper, the feasibility and effectiveness of heat pipe cooling in end milling operations are investigated. A new embedded heat pipe technology was utilized to remove the heat generated at the tool-interface in end milling processes. Numerical studies involved four cases, including dry milling, fluid cooling, heat-pipe cooling and heat-pipe cooling with cutting fluid supplied. The thermal, structural static and dynamic characteristics of the end-mill were investigated using a numerical calculation with Fast Finite Element (FFE) plus solvers based on explicit finite element analysis software. The results demonstrate that the heat pipe end-mill is most feasible and effective in the actual end milling processes.

Keywords: heat pipe cooling, feasibility and effectiveness, end-mill, thermal and structural analyses

0 INTRODUCTION The thermal aspect that occurs on the cutting tool during the material removal processes is a traditional concern because cutting temperatures strongly influence tool wear, tool life, workpiece surface integrity, chip formation mechanism and contribute to the thermal deformation of the cutting tool.

In end milling operations, tool temperatures become even more important due to the fact that the tool used in the milling operation undergoes thermal shock in each revolution. The fast heating and cooling of the tool at work may result in considerable temperature variations in cutting edge, and furthermore, the heat generated during chip formation does not flow easily through the workpiece and chip. Consequently, this increases the percentage of heat going to the tool, makes the temperature variation even higher than before, and causes cracking perpendicular to the cutting edge [1] to [3]. These increased cracks result either in chipping or, occasionally, in breakage of the cutting edge. To extend tool life, the most common approach is the use of cutting fluids flooding through the cutting zone.

However, cutting fluids often induce significantly negative impacts on environment, safety, operators’ health and operating cost and especially the use of water-based cutting fluids in end milling operations usually increases temperature variation and, hence, thermal cracks [2] and [4].

Heat pipe cooling is considered to be an effective alternative to conventional methods for removing heat from a tool tip, which allows machining operations to be implemented in a dry and “green” fashion [5] and [6]. A heat pipe is composed of a sealed container

(pipe wall and end caps), a wick structure, and a small amount of working fluid in equilibrium with its own vapor. The heat pipe is generally divided into three sections: evaporator section, adiabatic (transport) section and condenser section, as illustrated in Fig. 1 [5]. First, the working fluid is vaporized by the external heat load on the evaporator section. Then, the resulting vapor pressure drives the vapor from the evaporator section to the condenser section, at which the vapor condenses and releases its latent heat of vaporization to the low temperature environment.

Finally, the condensed working fluid is pumped back by capillary pressure from the meniscus in the wick structure. Note that heat transport can be continuous if there is sufficient capillary pressure generated to drive the condensed liquid back to the evaporator.

Using heat pipes for heat removal in machining has been occasionally reported. Judd et al. [7] investigated turning of steel with a heat pipe embedded in a tool holder and reported that the heat pipe is found effective in reducing the tool-holder temperature by 30%. Chiou et al. [8] and [9] conducted a finite element analysis and an experimental study of heatpipe cooling in steel machining using carbide tools.

The authors concluded that the heat pipe, embedded in a cutting insert, is able to alleviate the cutting tool temperatures, reduce tool wear, and prolong the tool life. For drilling, Jen, et al. [2] compared heat-pipe cooling with dry drilling in the actual machining operations numerically and experimentally and claimed that the heat pipe in the drill can reduce the drill temperature by 30 to 50%. To the best of our knowledge, however, there is a lack of additional published research on all of various cooling conditions in the practical drilling processes.

*Corr. Author’s Address: Mechanical Engineering Department, AnHui University, China, zl009@mail.ustc.edu.cn

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In this paper, the feasibility and effectiveness of heat-pipe cooling in end milling operations are investigated. Numerical studies focus on four different kinds of cooling cases: (1) dry milling, (2) fluid cooling, (3) heat-pipe cooling, and (4) heatpipe cooling with cutting fluid supplied. The thermal, structural static and dynamic characteristics of the end-mill are predicted using a numerical calculation with Fast Finite Element (FFE) plus solvers based on explicit finite element analysis software.

1.2 FEA Modeling For the purpose of obtaining accurate numerical simulation results, the strategy in this study is based on high-density mesh, in which each solid element has 10 nodes for regions requiring high resolution (Fig. 4). Four points Jacobian Check method for the distortion level of tetrahedral elements was used to mesh the entire tool and especially fine meshing at the tool tip. Fig. 5 shows the mesh distribution in the end-mill using COSMOS\works. It is worth pointing out 8123 elements and 13822 nodes were used for the end-mill, while 8812 elements and 14307 nodes for the heat pipe end-mill.

Fig. 1. A conventional Heat Pipe [5]

1 FEA MODEL Fig. 4. Parabolic solid element

1.1 Model Geometry The model geometries of end-mills with and without a heat-pipe were constructed in SolidWorks by means of feature-based modeling method. In terms of the real tool profile as shown in Fig. 2, the specifications of the tool are presented as follows (Fig. 3a):

Fig. 5. Meshes of a) solid end-mill geometry and b) heat pipe endmill geometry

2 RESULTS AND DISCUSSION 2.1 Parameters and Computing Time Fig. 2. Three-flute end mill

Fig. 3. Three-flute end-mill; a) without and b) with a heat pipe

• • • •

214

Three-flute tool, 20 mm ϕhead, 18 mm ϕend, 125 mm long.

Rake angle γ = 0°, clearance angle α = 12°, helix angle β = 30°.

Hard alloy material.

Based on [6] to [10], the dimensions of the heat pipe embedded in the end-mill are 5.5 mm ϕheatpipe, 110 mm lheatpipe (Fig. 3b).

Only one of the three cutting edges needs to be numerically simulated in this study due to the endmill being symmetrical and the cutting process being interrupted. Stainless steel was chosen for the workpiece material. Down-milling with passes in the longitudinal direction of the workpiece was used as a result of the fact that the thermal impact to the cutting tool during heating is larger in down milling than in up milling [11] to [13]. The associated parameters in the foregoing end milling process are presented as follows: • Spindle speed n = 5,000 rpm, depth of cut t = 5 mm, width of cut B = 20 mm, feed per tooth Sz = 0.1 mm /tooth.

Liu, Y.-B. – Zhu, L. Jen, T.-C. – Zhao, J.-W. – Yen, Y.-H.

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)3, 213-220

•

Based on [10], the loads acting on the cutting edge are presented below (Fig. 6): Ft = 1,377 N, Fa = 689 N, Fr = 565 N. • The thermal and physical properties of the tool material are:

E = 6×1011 Pa, μ = 0.33,

ρ = 14.7×103 kg/m3, σbb = 1,470 MPa, Cp = 50 J/(kg·k), λ = 5×10-6 / K, K = 35 W/(m·k).

cylinder due to the fact that non-cutting period is very short in high-speed end milling operations (Fig. 8), although end milling is an interrupted cutting process. According to [6], the heat input at the tool tip is included in the banded heat input zone, the heat input in the z-direction through the top cap is assumed to be negligible, the heat pipe in the center of the cylinder tool is modeled as a small hollow cylinder with the pipe wall maintained at a fixed temperature, and the temperature dependence in this direction can be neglected due to the symmetry in the angular direction.

Fig. 6. The loaded end mill

For end milling, an intermittent calculation was conducted in this study. Htooth of the end mill is equal to 3.06 mm (Fig. 7), so Tcutting for one cutting edge was calculated as 0.0006 s in each tool revolution dependent on the geometric parameters of the standard 3-flute end-mill and the prescribed operation conditions. This time actually represents the milling period from the cutting start point A to the cutting end point B, as illustrated in Fig. 7. A total calculation time of 0.0239 s elapsed for all simulations in this paper.

Fig. 8. Physical configuration of an idealized end mill with a heatpipe [6]

Thus, the following thermal boundary conditions are applied [6] and [7]: • At the end caps of the tool, an insulated boundary condition and a constant temperature are imposed, respectively:

•

•

Fig . 7. Three-flute tool tip

2.2 Thermal Analysis

2.2.1 Thermal Boundary Conditions for a Heat Pipe in an End-Mill

•

Based on [6], the heat pipe and the end mill in this study, for simplicity, are modeled as concentric cylinders due to their similar configurations as shown in Fig. 8. Heat generation, for simplicity, is modeled as a cylindrical band heat source surrounding the

•

∂T ∂z

T

= 0, z =0

z=L

= To . (2)

In the cutting zone area of heat pipe tool, a constant heat flux q''c is applied: kT

∂T ∂r

r =a

= q"C

for 0 ≤ z ≤  z . (3)

On the surface area outside the heat input zone, an adiabatic condition is exerted: ∂T ∂r

r =a

= 0 for z ≥  z . (4)

The temperature on the inner cylinder surface is fixed: T r = r = Thp for z ≥ . (5) o

The following boundary condition is applied for the end cap of the heat pipe: T z = = Thp for 0 ≤ r ≤ ro , (6)

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and the initial condition is: T τ=0 = To ,

(7)

where To is the ambient temperature, Thp is the heat pipe surface temperature (boiling temperature of the working fluid).

2.2.2 Temperature Distribution and Thermal Stress The ambient temperature was set to be constant at 25 °C, and 100 °C for the heat pipe under full operation condition with water as the working fluid. In view of the foregoing operation parameters, a calculated heat input of 8287 W was applied at the tip of the tool (Fig. 6), and with about 14.5% heat that enters the tool [14] to [15]. In addition, on all other surfaces imposed were the thermal boundary conditions seen above.

Seen from Fig. 9, for all the numerical simulation cases in this study, the peak temperatures occur at the end-mill tips, and the temperature at the outer tip is much higher than that at the inner tip.

The calculated results agree well with the actual milling operations. It is basically due to the facts as follows: new surface in end milling operations is generated as each tooth cuts away an arc-shaped segment. The undeformed chip thickness in the foregoing process is not constant but varies with tool rotation. The tool-chip constant length on the rake face varies with time (Fig. 10). According to Stephenson et al. [16], an end mill is modeled as a semi-infinite rectangular corner, x ≥ 0, y ≥ 0, z ≥ 0, heated by a heat flux as shown in Fig. 11. Thus, the heat source dimension in the x-axis direction is a function of cutting time. For down milling processes, the depth of cut is the largest at the beginning of the cutting, and approximates 0 at the end, as shown in Fig. 12.

°C (1010 K) for heat-pipe cooling, and 637 °C (910 K) for heat-pipe cooling with coolant, respectively.

Compared 13b) with 13c), it could be inferred that the temperature using heat pipe does reduce faster than that using coolant (see the black arrows). This is because most of heat generated on the end-mill tip is quickly removed dependent on convection heat transfer by means of heat pipe. From the effect of the peak temperature viewpoint, the heat pipe cooling therefore outperforms the cases with dry milling, even with effective coolant, respectively.

Fig. 10. Variation in tool-chip contact length in down milling

Fig. 11. Tool insert model

Fig. 12. Variation of heat source area in down milling

Fig. 9. a) Temperature distribution on the tool tip; b) detailed C of a); magnified view of the temperature distribution on the tool tip

Fig. 13 shows the temperature variations at the outer tip with time. As observed, the maximum temperatures are approximate 1027 °C (1300 K) for dry milling, 767 °C (1040 K) for fluid cooling, 737 216

Fig. 14 shows schematic for the variations of the thermal stress distributions at the end-mill tips under various cooling conditions. All of the maximum thermal stresses also occur at the tool tips within the equivalent time as above and especially the thermal stress at the outer tip is larger than that at the inner tip. As observed, the thermal stresses at the outer tip are approximately 650, 500, 480 and 340 MPa for dry milling, fluid cooling, heat-pipe cooling, and heatpipe cooling with coolant, respectively.

From Figs. 13 and 14, it can be seen that the peak temperature on the tool tip decreases from 1027 °C in dry milling to 737 °C in heat-pipe cooling by about 29% based on the equivalent amount of heat input,

Liu, Y.-B. – Zhu, L. Jen, T.-C. – Zhao, J.-W. – Yen, Y.-H.

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)3, 213-220

Fig. 14. The maximum thermal stresses in the cutting time: a) dry milling; b) fluid cooling; c) heat-pipe cooling; and d) heat- pipe cooling with coolant

Fig. 13. Plots between the maximum temperatures on the tool tip vs. time; a) dry milling,; b) fluid cooling; c) heat pipe cooling, and d) heat pipe cooling with coolant

and that the maximum thermal stress also reduces from 650 MPa for dry milling to 480 MPa for the heat-pipe cooling by an approximate factor of 1.4 under the same cooling conditions. Therefore, it can be concluded that with the aid of a heat pipe in the end milling operations, the probability of tool failure

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can be significantly reduced due to lower maximum temperature and thermal stress.

2.3 Structural Static and Dynamic Analysis In end milling operations, the undeformed chip thickness varies with tool rotation, and tool-chip constant length on the rake faces also varies with time.

Thus, the cutting edges must undergo much greater mechanical load due to their more numerous entrances and exits in the work-piece. This may generate cracks, chipping, and cutting edge breakage. Consequently, it is critical to choose a cutting tool with sufficient toughness and a rigid cutting edge in order to make the impacts less harmful to the tool. To verify the feasibility and effectiveness of the heat pipe end-mill, it is very essential to investigate its structural static and dynamic characteristics under the actual working conditions.

As depicted above, only one of the three cutting edges is considered in this study thanks to the symmetric structure and the interrupted cutting process of the end-mill. The loads exerted on the tool are normally resolved into the three following directions: the Ft in the circumferential direction, Fa in the axial direction and Fr in the radial direction, as illustrated in Fig. 15. Generally, Ft, Fa and Fr can result in the torsional deformation, the compressive deformation and the bending deflection of the endmill, respectively [3] and [14]. Consequently, this causes the various locations of the tip in the x-, y-, and z directions, thereby resulting in poor machining accuracy and surface quality of the workpiece.

Fig. 15. Correlation of the cutting force components in end milling operations

2.3.1 Static Stress & Strain Distributions In view of the above-mentioned operation conditions, a clamp length, e.g. 9.29 mm was selected along the axis of the end mill (the red arrow in Fig. 16). The calculated results are presented in Figs. 16 to 18.

218

Fig. 16. a) Static stress distribution on the solid end-mill, b) detailed C of a); magnified view of the static stress on the tool

Fig. 17. a) Static stress distribution on the heat pipe end-mill; b) detailed C of a); magnified view of the static stress on the tool

Fig. 18. Static strain distribution of the a) solid end-mill; and (b) heat pipe end-mill

For end milling, the pink static stresses, for the tool with or without heat-pipe cooling, both occur at the tool tip (Figs. 16 and 17). The maximum static stresses for heat-pipe tool and solid tool are 454.1 and 409.4 MPa, respectively. With heat pipe embedded in the tool, a roughly 10% increase in static stress compared with the solid tool.

Liu, Y.-B. – Zhu, L. Jen, T.-C. – Zhao, J.-W. – Yen, Y.-H.

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)3, 213-220

As illustrated in Fig. 18, the maximum strain for the solid tool only appears at the cutter tip (see the red ellipse); its value is 8.539×10–4, while on the heat pipe cutter there exist two locations with the maximum strain, which is 8.555×10–4. One also exists at the cutter tip, and the other appears at the clamp section (see the pink arrowhead).

As can be inferred from the above, the static stress and strain increase when the heat pipe end-mill is used.

This is basically due to the fact that embedding a heat pipe in the solid tool decreases the inertia moment of the heat-pipe tool and, therefore, increases the related bending deformation and bending stress. Note that for hard alloy material used for the end-mill; however, its maximum bending strength is 1470 MPa, so the heatpipe tool in this study can satisfy the requirements of the milling operations. For the higher static stress and strain in the heat-pipe tool, the strength and stiffness of the main cutting zone, especially of the tool tip, could be improved by optimizing the geometric shape and configuration of the end-mill [3] and [14]. And also, it is found in the actual applications that optimizing the clamp length of the tool can lower the probability of the cutter resonating, especially of chattering and, consequently, decrease the bending deformation and bending stress [3] and [14]. This plays a critical role in extending the end-mill’s lifetime.

2.3.2 Structural Dynamic Analysis Mechanical impacts are also frequent in end milling operations due to the interrupted cutting inherent to it. The shocks and load variation on the tool gain importance and cause the chipping in the end of depth of cut area, which has deleterious effects on either the dimensional accuracies of the workpiece or the lifetime of the end milling operation system.

Therefore, it is very essential to perform a structural dynamic analysis on the heat pipe end-mill.

In view of the actual vibrating state of the endmill, fifteen modes shapes are presented in this study dependent on the loads illustrated in Fig. 6. Fig. 19 shows vibration states of the solid end-mill. The frequencies are shown in Table. 1

Fig. 19. Mode shapes of a tool without a heat pipe

Compared the vibration modes of the solid endmill with those of the heat pipe end-mill, it could be seen from Fig. 20 that the vibration modes of the solid tool are a little higher than those of the heat pipe tool, which indicates that the solid end-mill deforms smaller than the heat pipe end-mill in the actual applications. This basically contributes to the fact that the higher frequency, for an end-mill in machining operations, leads to the larger rigidity. Significant vibration of the heat pipe tool may have deleterious effects on both the dimensional accuracy of a workpiece and the stability of the end milling operation system. All these could be improved by optimizing the milling speed. Furthermore, it is found in the industry applications that optimizing the clamp length of the end-mill does reduce the number of strong vibration modes in the end milling operations, thereby lowering the probability of the cutter resonating, especially of chattering [3] and [14].

Table 1. Frequencies of a tool without / with a heat pipe Frequency 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Solid tool [Hz] 1804.3 1806.2 7268.9 7273.4 10325 16115 16910 16916 20616 30031 30049 37398 41311 44032 44065

Heat-pipe tool [Hz] 1855.7 1856.4 7234.9 7235.8 10319 16146 16894 16906 20413 29785 29791 36228 41241 43268 43279

Fig. 20. Comparative vibration modes between a solid end-mill and a heat pipe end-mill under theclamp length 9.29 mm

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3 CONCLUSION From thermal, structural static, and dynamic analyses points of view, the feasibility and effectiveness of the heat pipe end-mill were investigated. The numerical simulation results indicate that the peak temperature on the tool tip decreases from 1027 °C for the solid end-mill to 737 °C for the heat pipe end-mill by about 29% based on the equivalent amount of heat input, and that the maximum thermal stress also reduces from 650 MPa for dry milling to 480 MPa for the heat pipe cooling by an approximate factor of 1.4 under the same cooling conditions. This implies that the use of a heat pipe in the end milling processes can effectively perform thermal management comparable to the flooding coolant cooling used pervasively in the machining industry.

The use of a heat pipe embedded the solid end-mill may increase the static stress and strain at the cutter tip and enhance the vibration frequency/magnitude due to its hollow center. However, for end milling, the foregoing negative effects could be improved by optimizing the geometric shape, configuration and the clamp length of the heat pipe tool [3] and [11].

The numerical simulation evidences in this study therefore demonstrate that the use of heat pipe embedded in an end-mill is most feasible and effective and that the dry end milling can be achievable in the actual machining operations. Based on the results obtained in this work, several end mills with/without heat pipes have been manufactured and the results from testing are forthcoming in a future paper.

4 ACKNOWLEDGEMENTS The authors would like to thank the financial support for the project from EPA-STAR grant through RD833357.

5 REFERENCES [1] Braghini, A.Jr., Diniz, A.E., Filho, F.T. (2009). Tool wear and tool life in end milling of 15-5 PH stainless steel under different cooling and lubrication conditions.

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43, p. 756-764, DOI:10.1007/s00170-008-1744-6.

[2] Johnson, D. (1996). Why cutting tools fail. Tooling & Production. Huebcore Communications Inc., Ohio.

[3] Trent, E., Wright, P. (2000). Metal Cutting. Butterworth/ Heinemann, Oxford.

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[4] Ding, Y., Hong, S.Y. (1998). Improvement of chip breaking in machining low carbon steel by cryogenically pre-cooling the workpiece. ASME Journal of Manufacturing Science and Engineering, vol. 120, p. 76-83, DOI:10.1115/1.2830113.

[5] Peterson, G.P. (1994). An introduction to Heat Pipes: Modeling, Testing, and Applications, Wiley, New York.

[6] Jen, T.C., Chen, Y.M., Gutierrez, G. (2002).

Investigation of heat pipe cooling in drilling applications. Part Ⅰ: preliminary numerical analysis and verification. International Journal of Machine Tools & Manufacture, vol. 42, p. 643-652, DOI:10.1016/S0890-6955(01)00155-9.

[7] Harley, C., Faghri, A. (1995). Two-Dimensional Rotating Heat Pipe Analysis. ASME Journal of Heat Transfer, vol. 117, no. 1, p. 202-208, DOI:10.1115/1.2822304.

[8] Ritcher, R., Gottschlich, J.M. (1994). Thermodynamics aspects of heat pipe operation. Journal of Thermodynamics and Heat Transfer, vol. 8, no. 2, p.

334-340, DOI:10.2514/3.543.

[9] Judd, R.L., MacKenzie, H.S., Elbestawi, M.A. (1995).

An investigation of a heat pipe cooling system for use turning on a lathe. International Journal of Advanced Manufacturing Technology, vol. 10, no. 6, p. 357-366, DOI:10.1007/BF01179398.

[10] Lin, Z., Tien-Chien, J., Chen-Long, Y. (2009).

Investigation of heat pipe cooling in drilling applications, part Ⅱ: Thermal, structural static, and dynamic analyses. Proceedings of the ASME International Mechanical Engineering Congress & Exposition, p. 1-8.

[11] Palmai, Z. (1987). Cutting temperature in intermittent cutting. International Journal of Machine Tool & Manufacture, vol. 6, no. 2, p. 261-274, DOI:10.1016/ S0890-6955(87)80055-X. [12] Tadic, B., Vukelic, D., Hodolic, J. (2011). Conservativeforce-controlled feed drive system for down milling. Strojniški vestnik – Journal of Mechanical Engineering, vol. 57, no. 5, p. 425-439, DOI:10.5545/ sv-jme.2009.055.

[13] Toh, C.K. (2005). Comparison of chip surface temperature between up and down milling orientations in high speed rough milling of hardened steel. Journal of Materials process Technology, vol. 167, p. 110-118.

[14] Shaw, M.C. (2005). Metal cutting principles. Oxford University Press, New York.

[15] Jen, T.C, Lavine, A.S. (1994). Prediction of tool temperature in interrupted metal cutting. Proceedings of the 7th International Symposium on Transport Phenomena in Manufacturing Processes, p. 211-216.

[16] Stephenson, D.A., Ali, A. (1992). Tool temperatures in interrupted metal cutting. ASME Journal of Engineering for Industry, p. 127-136.

Liu, Y.-B. – Zhu, L. Jen, T.-C. – Zhao, J.-W. – Yen, Y.-H.

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Vsebina Strojniški vestnik - Journal of Mechanical Engineering letnik 58, (2012), številka 3 Ljubljana, marec 2012 ISSN 0039-2480 Izhaja mesečno

Razširjeni povzetki člankov Matjaž Ramšak: Daljinsko voden let jadralnega letala: eksperimentalna in numerična analiza Hamidreza Salimi, Bahador Saranjam, Ahmad Hoseini, Mohsen Ahmadzadeh: Uporaba genetskih algoritmov za optimalno zasnovo sendvič panelov, izpostavljenih udarnim podvodnim obremenitvam Adem Çiçek, Turgay Kıvak, Gürcan Samtaş: Uporaba metode Taguchi pri površinski hrapavosti in napaki okroglosti po vrtanju v nerjavno jeklo AISI 316 Ali Movaghghar, Gennady Ivanovich Lvov: Teoretična in eksperimentalna študija trajne dinamične trdnosti kompozitnega materiala steklo/epoksi v platnovi vezavi Mezid Muhasilovic, Jožef Duhovnik: Raziskava odziva mehanskega prezračevanja na požar v predoru s pomočjo CFD Ning Fang, P Srinivasa Pai, Nathan Edwards: Obraba rezalnega roba orodja in analiza z valčno transformacijo pri visokohitrostni obdelavi Inconela 718 Tino Stanković, Mario Štorga, Dorian Marjanović: Sinteza palične konstrukcije z algoritmoma NSGA-II in NodeSort Yong-Bin Liu, Lin Zhu, Tien-Chien Jen, Ji-Wen Zhao, Yi-Hsin Yen: Numerična analiza izvedljivosti in učinkovitosti uporabe toplotnih cevi pri steblastih rezkarjih

SI 33 SI 34 SI 35 SI 36 SI 37 SI 38 SI 39 SI 40

Osebne vesti Magistrsko delo in diplome

SI 41

Prof. dr. Viktorju Prosencu - v spomin

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Prejeto 2009-11-05, Sprejeto: 2012-02-07 © 2012 Strojniški vestnik. Vse pravice pridržane.

Daljinsko voden let jadralnega letala: eksperimentalna in numerična analiza Ramšak, M. Matjaž Ramšak* Univerza v Mariboru, Fakulteta za strojništvo, Slovenia

Cilj prispevka je primerjati izmerjeno in izračunano razmerje sile vzgona in upora oziroma fineso daljinsko vodenega jadralnega letala Longshot pri različnih hitrostih.

Glavna predpostavka je ustaljen let jadralnega letala. Ta vključuje konstantno hitrost in konstanten kot leta.

Meritev finese je opravljena z metodo fotogrametrije s pomočjo poceni video kamere. Glavni razlog je v cenenosti meritve, dodaten razlog pa je tudi ta, da masa letala 320 gramov ne dopušča vgradnje merilnika hitrosti in zapisovalnika višine leta, prav tako pa zanju ni prostora v trupu letala. Numerična simulacija letala je opravljena s programskim paketom za računalniško dinamiko tekočin Ansys CFX. Za vsako računano hitrost je bila opravljena vrsta simulacij pri različnih vpadnih kotih na krilo (ang. Angle of Attack). Iz te vrste smo določili ustrezni vpadni kot, pri katerem je izračunana sila vzgona enaka resnični teži letala.

Merilno metodo smo umerili za merjenje hitrosti kolesarja. Izmerjena natančnost v umerjevalnem območju od 4 do 11 m/s je manjša od ±1 %. Ocenjena natančnost kota leta je manjša od 3 stopinj.

Izmerjena in izračunana finesa se pri hitrosti 15 m/s odlično ujemata, pri nižjih hitrostih pa je ujemanje slabše. Vzrok je velik raztros izmerjene finese, kar ni napaka meritve, ampak je posledica človeškega faktorja pri radijskem vodenju počasnega in nestabilnega leta. Posledično je predpostavka ustaljenega leta pri nizkih hitrostih zelo vprašljiva. Izračunana maksimalna finesa je 10 pri optimalni hitrosti 7,5 m/s. Izmerjena maksimalna finesa je reda velikosti 20 pri hitrosti 12 m/s, vendar obstajajo dvomi o resničnosti izmerjenega podatka zaradi omenjenih težav s kontroliranjem leta. Razen finese je izmerjen in izračunan tudi kot natekanja na krilo. Numerični rezultati vsebujejo tudi minimalno, optimalno in terminalno hitrost. Prav tako je določena maksimalna nosilnost letala pri različnih hitrostih. Določen je tudi kritični kot natekanja, kjer se pojavi recirkulacijski vrtinec na sesalni strani krila. Izmerjena in izračunana sila upora se lepo ujemata. Največja napaka in raztros sta pri primerjavi vpadnega kota na krilo. Vsi izmerjeni koti so v območju od 1 do 4 stopinj. Rezultat simulacije pa se giba od 2 stopinj pri 7,5 m/s do -1 stopinje pri 20 m/s.

Izmerjena minimalna hitrost je približno 10 m/s. Izračunana minimalna hitrost je po pričakovanjih manjša, in sicer 7,5 m/s. Le-to je v resničnem letu težko doseči, saj bi moral biti vpadni kot konstantno približno 3 stopinje, tak kot pa je pri daljinsko vodenem jadralnem letalu praktično nemogoče vzdrževati.

Kot zanimivost navajamo še izračunano terminalno hitrost 30 m/s. Pri diskastem izmetu iz roke (DLG kot Discus Launch Glider) je izmerjena hitrost meta v območju med 22 in 25 m/s. Izkušeni metalci lahko dosežejo izmetne hitrosti do 40 m/s.

Pri velikih letalih so meritve praviloma drage, ni pa razloga, da se prikazana merilna metoda ne bi uporabila tudi za velika letala. Numerična simulacija velikih letal je praktično identična malim.

Nadaljnje raziskovanje na področju meritev je možno v smeri obdelave več zaporednih fotografij leta. Na ta način bi lahko natančneje določili parametre leta kot povprečni rezultat. Dodatno bi bilo mogoče izračunati tudi spreminjanje hitrosti med posameznimi posnetki in izločiti tiste lete, ki ne bi ustrezali predpostavki ustaljenega leta.

Na področju računalniških simulacij je možno nadaljnje raziskovanje v smeri preizkusa različnih turbulentnih modelov in natančnejšega posnetka geometrije letala. Posebno poglavje se odpira z vključitvijo nagiba krmilnih površin.

Izvirnost prispevka se kaže v uporabi fotogrametrije za merjenje aerodinamičnih sil na letalo. Prikazana metoda je cenena in dostopna širokemu krogu modelarjev. Prav tako ni razloga, da se merilna metoda ne bi uporabila tudi za velika letala. Avtor na področju numerične simulacije ni zasledil podobnega primera, ki bi določal fineso jadralnega letala po opisanem postopku spreminjanja vpadnega kota.

Ključne besede: Računalniška dinamika tekočin, fotogrametrija, aerodinamika, finesa jadralnega letala, daljinsko vodeno letalo, letalne karakteristike

*Naslov avtorja za dopisovanje: Univerza v Mariboru, Fakulteta za strojništvo, Smetanova 17, 2000 Maribor, Slovenija, matjaz.ramsak@uni-mb.si

SI 33

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)3, SI 34

Prejeto: 2011-05-04, sprejeto: 2012-01-24 © 2012 Strojniški vestnik. Vse pravice pridržane.

Uporaba genetskih algoritmov za optimalno zasnovo sendvič panelov, izpostavljenih udarnim podvodnim obremenitvam Salimi, H. – Saranjam, B. – Hoseini, A. – Ahmadzadeh, M. Hamidreza Salimi1,* – Bahador Saranjam2 – Ahmad Hoseini Fard1 – Mohsen Ahmadzadeh1 1 Shiraz Branch, Islamic Azad University, Iran 2 Oddelek za pomorske konstrukcije, Zračno pomorski raziskovalni center, Iran

Kompozitni sendvič paneli se zaradi svoje izjemne trdnosti, togosti in majhne mase vse pogosteje uporabljajo pri gradnji plovil. Uporaba kompozitnih panelov pa prinaša tudi težave v procesu snovanja zaradi velikega števila konstrukcijskih spremenljivk, vključno z zgradbo kompozitnega materiala, topologijami in izvedbami laminatov, ki so izpostavljeni kompleksnim obremenitvam, zlasti kavitaciji pri podvodnih eksplozijah. Delo zato obravnava optimalno zasnovo laminiranih kompozitnih sendvič struktur za uporabo na morju, ki so izpostavljene podvodnim eksplozijam. Postopek optimizacije je bil izveden z genetskim algoritmom (GA) v povezavi z metodo končnih elementov (MKE) za analizo konstrukcij.

Dosedanje raziskave na področju optimizacije kompozitnih konstrukcij so bile zasnovane na uveljavljenih metodah za optimizacijo konvencionalnih materialov. Te metode so zasnovane na gradientih ciljnih in omejitvenih funkcij z ozirom na konstrukcijske spremenljivke, ki so zvezne v konstrukcijskem prostoru. Takšen pristop daje omejene rezultate, ker je snovanje kompozitnih laminatov diskreten optimizacijski problem – spremenljivke so v praksi omejene le na nekaj vrednosti, ki jih določa proizvodni proces. Problemi optimizacije kompozitov poleg tega vključujejo tudi multimodalne prostore iskanj, kjer metode na osnovi gradientov konvergirajo v območja lokalnih optimumov v konstrukcijskem prostoru. Pri iskanju alternative za metode na osnovi gradientov je bila prav zato preizkušena cela vrsta drugih optimizacijskih tehnik, med katerimi se izpostavljajo genetski algoritmi (GA) kot popolna rešitev za značilnosti problema optimizacije kompozitov. Študija obravnava optimalno zasnovo sendvič panelov, ki so izpostavljeni udarnim podvodnim obremenitvam.

Upoštevan je tudi vpliv kavitacije na konstrukcijo. Kavitacija je pojav v vodi, do katerega pride zaradi odboja udarnega vala na prosti površini. Sendvič paneli so sestavljeni iz laminata različnih usmeritev in jedra različnih debelin. Problem optimizacije je mogoče formulirati kot iskanje parametrov pločevine za oblogo in debeline jedra, ki izpolnjuje pogoje glede trdnosti in deformacij ob minimalni teži panela. Omejitve vključujejo trdnost pločevine za oblogo, prečno strižno trdnost jedra, deformacije panela in simetrično polaganje. Zadnji pogoj je izpolnjen že s tem, da je v kromosomu po pravilu kodiranja zastopana samo polovica laminata.

Osnovni model za optimizacijo je bil postavljen v paketu ABAQUS različice 6.10. Nato je bila ustvarjena vhodna datoteka ABAQUS (.inp). Datoteka .inp je bila prilagojena s konstrukcijskimi spremenljivkami vsakega kromosoma. ABAQUS obdela vhodno datoteko za izračun primernosti vsakega pripadnika populacije. Sl. 13 prikazuje konvergenco primernosti s številom generacij za štiri različne začetne populacije. Za konvergenco je potrebnih približno 50 generacij. Vsi štirje diagrami konvergirajo v edinstveno vrednost. Pogoj za končanje GA je bodisi omejitev skupnega števila ovrednotenj funkcij ali pa da se funkcija primernosti med generacijami ne spreminja več, kar pride prej.

Rezultati kažejo, da je z genetskim algoritmom mogoče uspešno poiskati optimalno zasnovo sendvič panelov.

Primerjava konstrukcijskih omejitev začetne in optimizirane zasnove kaže, da je s postopkom optimizacije mogoče občutno izboljšati število slojev, zaporedje zlaganja pločevin, orientacijo vlaken in debelino jedra.

Analiza zmogljivosti GA pri iskanju optimalne zasnove sendvič panelov kaže, da je metoda zelo učinkovita pri iskanju skoraj optimalnih rešitev, z uporabo primernih vrednosti parametrov GA in shranjevanjem rezultatov različnih analiz pa je mogoče prihraniti tudi precej računskega časa. Končna zasnova z vrednostmi konstrukcijskih spremenljivk dokazuje, da bi optimalne vrednosti konstrukcijskih spremenljivk težko dognal tudi dober in zelo izkušen inženir. Rezultati kažejo, da daje GA boljše rezultate z razmeroma majhnimi populacijami in večjim številom generacij.

Ključne besede: optimizacija, genetski algoritem, metoda končnih elementov, sendvič panel, podvodna eksplozija, kavitacija

SI 34

*Naslov avtorja za dopisovanje: Oddelek za pomorske konstrukcije, Zračno pomorski raziskovalni center, 7194915685, Shiraz, Iran, hr.salimi@gmail.com

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)3, SI 35

Prejeto: 2011-09-06, sprejeto: 2012-01-27 © 2012 Strojniški vestnik. Vse pravice pridržane.

Uporaba metode Taguchi pri površinski hrapavosti in napaki okroglosti po vrtanju v nerjavno jeklo AISI 316 Çiçek, A. - Kıvak, T. - Samtaş, G. Adem Çiçek1 -Turgay Kıvak2,*- Gürcan Samtaş2 1 Univerza Düzce, Tehnična fakulteta, Oddelek za proizvodno strojništvo, Turčija 2 Univerza Düzce, Visoka poklicna šola Cumayeri, Turčija

Cilj študije je raziskava vpliva različnih toplotnih obdelav svedrov iz hitroreznega jekla M35 in parametrov vrtanja na površinsko hrapavost in napako okroglosti, ter določitev optimalnih parametrov vrtanja v nerjavno jeklo AISI 316 po metodi Taguchi in z multiplo regresijsko analizo. Članek obravnava optimizacijo parametrov vrtanja v nerjavno jeklo AISI 316 s kriogensko obdelanimi in neobdelanimi vijačnimi svedri pri različnih rezalnih hitrostih (12, 14 m/min) in podajanjih (0,08 in 0,1 vrt/min) po metodi Taguchi. Ti parametri vrtanja so bili izbrani za kontrolne faktorje, eksperimentom pa je bilo dodeljeno ortogonalno polje L8(23). Opravljenih je bilo osem eksperimentov z določenimi kombinacijami parametrov.

Matematični modeli za površinsko hrapavost in napako okroglosti so bili pridobljeni z multiplo regresijsko analizo na osnovi rezultatov eksperimentov.

Optimizacija parametrov za optimalno površinsko hrapavost in napako okroglosti pri vrtanju v avstenitno nerjavno jeklo AISI 316 z neobdelanimi in obdelanimi svedri je bila izvedena po metodi Taguchi. Minimalna površinska hrapavost in napaka okroglosti je bila ugotovljena pri obdelavi z obdelanimi svedri z rezalno hitrostjo 14 m/min in podajanjem 0,08 mm/vrt. Rezultati eksperimentov kažejo, da ima rezalna hitrost (78,11 %) signifikanten vpliv na površinsko hrapavost, rezalna hitrost (35,352 %) in podajanje (35,352 %) pa imata signifikanten vpliv na napako okroglosti. Izguba kakovosti (52,36 %) pri površinski hrapavosti, dobljeni z optimalno kombinacijo parametrov (Ct = CT, V = 14 m/min, f = 0,08 mm/vrt) dosega skoraj polovico izgube kakovosti pri eksperimentalnih kombinacijah. Izguba kakovosti pri napaki okroglosti, dobljeni pri optimalnih kombinacijah, je 51,76 %.

Izračunani optimalni vrednosti površinske hrapavosti in napake okroglosti pri optimalnih parametrih sta 1,77 in 5,60 µm.

Vrednosti površinske hrapavosti in napake okroglosti so bile pridobljene po metodi Taguchi pri optimalnih parametrih s 95 % intervalom zaupanja. Rezultati potrditvenih preizkusov kažejo, da so vrednosti znotraj izračunanega intervala zaupanja in da je sistem zadovoljivo optimiziran po metodi Taguchi. Novost je v tem, da je bila metoda uporabljena za optimizacijo parametrov vrtanja v nerjavno jeklo s kriogensko obdelanimi svedri. V literaturi sicer ni najti optimizacijskih študij, ki bi obravnavale kriogensko obdelana orodja.

Uporaba nerjavnih jekel in kriogenske obdelave v industriji postaja vse pomembnejša. Tipična področja uporabe nerjavnih jekel so kemična in procesna industrija (npr. črpalke, armature itd.), prehrambena industrija, medicinski izdelki, dejavnosti na morju in pohištvena industrija. Za proizvodno industrijo je zelo pomembno tudi določanje optimalne kombinacije parametrov vrtanja, zmanjševanje stroškov in skrajšanje časa obdelave. V članku je opisana optimizacija parametrov vrtanja za zmanjšanje proizvodnih stroškov po metodi Taguchi.

Nadaljnje raziskovalno delo bo usmerjeno v dejavnike, ki vplivajo na površinsko hrapavost in napako okroglosti, kot so globina vrtanja, hladilna tekočina, kot konice in vijačnice ter čas (4, 8, 12, 36, 48 ur itn.) in temperatura kriogenske obdelave (-70, -125, -150 °C itn.).

Ključne besede: kriogenska obdelava, vrtanje, površinska hrapavost, napaka okroglosti, optimizacija, metoda Taguchi, multipla regresijska analiza

*Naslov avtorja za dopisovanje: Univerza Düzce, Tehnična fakulteta, Oddelek za proizvodno strojništvo, 81700, Cumayeri, Düzce, Turčija. turgaykivak@duzce.edu.tr

SI 35

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)3, SI 36

Prejeto: 2011-07-12, sprejeto: 2012-01-27 © 2012 Strojniški vestnik. Vse pravice pridržane.

Teoretična in eksperimentalna študija trajne dinamične trdnosti kompozitnega materiala steklo/epoksi v platnovi vezavi Movaghghar, A. – Lvov, G.I. Ali Movaghghar* – Gennady Ivanovich Lvov Državna politehnika v Harkovu, Fakulteta za strojništvo, Ukrajina

Z naraščajočo uporabo kompozitnih materialov je vse večja tudi potreba po poznavanju njihovega obnašanja pri utrujanju. Namen tega članka je predstavitev energijskega modela za napovedovanje trajne dinamične trdnosti in vrednotenje poškodb kompozitnih materialov. Izvedena je bila tudi eksperimentalna študija za razvoj in preverjanje teoretičnega modela napredovanja poškodb.

Energijski model na osnovi konceptov mehanike poškodb v kontinuumu (CDM) in principov termodinamike omogoča napovedovanje trajne dinamične trdnosti z upoštevanjem glavnih smeri napetostnega tenzorja glede na ravnine elastične simetrije materiala. Pri materialih s šibko odvisnostjo utrujenostnih lastnosti od smeri napetosti se vedno uporablja izotropni poškodbeni model. V tem delu je uporabljena predpostavka, da je hitrost akumulacije poškodb pri izotropnih poškodbah kompozitnega materiala odvisna od maksimalne vrednosti specifične energije elastičnih deformacij na cikel We, parametra cikla R in ravni poškodb D. Naslednja predpostavka je bila, da obstaja povezava med maksimalno vrednostjo specifične energije elastičnih deformacij na obremenitveni cikel in hitrostjo rasti poškodb.

Za praktično uporabo predlaganega modela je bilo treba identificirati neznane parametre modela. Zato je bila opravljena vrsta preizkusov utrujanja na 10-plastnem kompozitnem laminatu iz steklene tkanine, impregnirane z epoksi-fenolno smolo. Vzorci za preizkuse utrujanja so bili odrezani v smeri osnovne in votkovne niti. Za določitev ravninskega vzdolžnega elastičnega modula različnih preizkušancev je bila uporabljena tehnika resonančne frekvence. Vsi preizkusi utrujanja so bili opravljeni pri različnih konstantnih amplitudah deformacij pri sobni temperaturi, razmerje med spodnjo in zgornjo mejo obremenitve je bilo R = -1. Za vrednotenje in ocenjevanje napetosti je bila uporabljena analiza po metodi končnih elementov s programskim paketom ANSYS 11.

Eksperimentalni rezultati utrujenostnih preizkusov so bili obdelani po metodi najmanjših kvadratov za določitev neznanih parametrov predlaganega modela. Po določitvi neznanih parametrov modela je bila izrisana krivulja teoretične trajne dinamične trdnosti v smeri osnovne in votkovne niti. Izkazalo se je, da se teoretične krivulje trajne dinamične trdnosti dobro ujemajo z eksperimentalnimi podatki. Možno je modeliranje razvoja skalarnega parametra poškodbe v ustreznih smereh.

V članku je prikazana metoda praktičnega reševanja pomembnega problema določanja trajne dinamične trdnosti kompozitnih materialov. Predlagan je teoretični model razvoja poškodb v kompozitnih materialih.

Teoretične odvisnosti, pridobljene s pomočjo modela in rezultatov eksperimentov, so uporabne za analizo utrujanja tehničnih konstrukcij.

Ključne besede: kompozitni materiali, utrujanje, mehanika poškodb, lom, modeliranje po metodi končnih elementov, mehanske lastnosti, razvoj poškodb

SI 36

*Naslov avtorja za dopisovanje: Državna politehnika v Harkovu, Fakulteta za strojništvo, 61002, Kharkov, Frunze St. 21, Ukrajina, alinetscope@yahoo.com

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)3, SI 37 DOI:10.5545/sv-jme.2009.091

Prejeto: 2009-07-21, sprejeto: 2010-12-03 ©2012 Strojniški vestnik. Vse pravice pridržane.

Raziskava odziva mehanskega prezračevanja na požar v predoru s pomočjo CFD Muhasilovic, M. – Duhovnik, J. Mezid Muhasilovic* – Jožef Duhovnik

Univerza v Ljubljani, Fakulteta za strojništvo, Slovenija

Dejstvo, da se mnogi podzemni objekti, kot veliki prazni, prostori razlikujejo po svojih geometrijskih značilnostih, postavlja vedno nove naloge raziskovalcem, ki se ukvarjajo s pojavi v fluidih. V sodobnem prometu se pojavljajo omejena in velika območja, bodisi kot aktivni objekti (npr. predori) bodisi kot prometno statični objekti, kot so večetažne garažne hiše in podzemne garaže. Raziskava, upošteva statistično dejstvo, da se zgodi po en požar na vsakih 107 kilometrov ceste v predoru, pokritem vkopu ali podobno.

Pri snovanju takšnih sistemov velja, da je najboljša preventiva, zato je raziskovanje varnosti omenjenih prometnih sistemov eden od pomembnejših ciljev pri sodobnih gradbenih projektih. Fizikalne in matematične metode računalniške dinamike fluidov (CFD), na osnovi katerih je v šestdesetih in sedemdesetih letih prejšnjega stoletja nastala cela vrsta programskih rešitev, so postale običajen del vsakdanjih znanstveno-tehničnih raziskav, zlasti od devetdesetih let, ko se je izboljšala tudi zmogljivost strojne opreme. Pri interpretaciji fizikalnih procesov (zlasti termodinamičnih procesov in procesov dinamike fluidov) prevladuje model, ki obravnava celotno področje, ne pa samo njegove posamične dele. Pri tej raziskavi je bil model uporabljen komercialni programski opremi FLUENT. Programska oprema, ki uporablja model polja, razdeli obravnavani prostor (običajno 3D-prostor) v več sto tisoč ali celo več milijonov celic. Sofisticirana programska oprema v vsaki od teh celic preračunava značilne fizikalne veličine hitrosti, gibalne količine, ohranitve energije, temperature in kemične sestave.

Na ta način je bila izvedena računalniško podprta raziskava nove prekrite cestno-prometne povezave: prometni objekt se nahaja v Ljubljani, ter z vidika dinamike fluidov predstavlja zanimiv primer.

Tripasovna cesta vstopa v predor na južni strani in se po 720 m razcepi: ena veja (dvopasovna cesta) poteka proti severu, druga veja pa po približno 400 metrih izstopi iz hriba in je priključena na ljubljansko mestno omrežje.

Pri geometriji tega predora je (razen razcepa in možnega delovanja vzgona) zanimivo tudi dejstvo, da je južni vstop v predor nameščen višje od severnega izstopa. Naravni zračni tok (od nižje do višje geodetske kote) je zato trajno usmerjen nasproti pozitivnemu prometnemu toku.

To so pomembni argumenti za izvedbo te raziskave. Čeprav predor med raziskavo še ni bil dokončan, smo uporabili preventivni pristop na osnovi CFD. Optimalna programska rešitev za dani problem je bila uporaba pristopa RANS (Reynoldsove povprečene Navier-Stokesove enačbe) v časovno odvisnem načinu. Pri raziskavi se nismo odločili, da zanemarimo računsko napoved toplotnega sevanja. Turbulence pri simuliranem požaruv predoru smo prikazali kot k-ε model, funkcija PDF pa vključuje samo 21 kemičnih spojin. Po pravilih Družbe za avtoceste v Republiki Sloveniji je računski eksperiment obsegal čas dveh minut. Računska domena za CFDsimulacije je bila modelirana na osnovi tehničnih podatkov za cestni predor (zahodna cev predora Šentvid).

Požar je bil umeščen približno na četrtino dolžine tunela (od severnega izhoda). Dimenzije preizkusne posode za gorivo so bile povzete iz resničnega požarnega preizkusa, kjer je požar razvil moč največ 3,5 MW. Pri računanju pretoka goriva so bile upoštevane dimenzije preizkusne posode 1×2 m in gorivo heptan. V raziskavi smo preverili ali mehansko vzdolžno prezračevanje dosega po predpisih predvidene hitrostne razmere v odvisnosti od časa, in njegove posledicam pri požaru toplotnih moči 40 in 80 MW (resnični eksperiment s takšno toplotno močjo bi uničil konstrukcijo predora). Toplotno moč 40 MW smo pri numeričnem eksperimentu dosegli s pretokom goriva 0,454 kg/m²s, toplotno moč 80 MW pa z dvakrat tolikšnim pretokom. S CFD simulacijo smo preverili učinkovitosti prezračevanja ter porazdelitve temperatur za primer požarov moči 40 in 80 MW. Z modeliranimi toplotnimi obremenitvami smo se izognili nevarnim posledicam resničnega preizkusa.

Rezultati so predstavljeni v članku.

Ključne besede: računalniške dinamike fluidov (CFD), veliko toplotno sevanje, požar v predoru, tična hitrost

*Naslov avtorja za dopisovanje: Univerza v Ljubljani, Fakulteta za strojništvo, Aškerčeva 6, 1000 Ljubljana, Slovenija, muhasilovic@gmail.com

SI 37

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)3, SI 38

Prejeto: 2011-02-17, sprejeto: 2012-01-11 ©2012 Strojniški vestnik. Vse pravice pridržane.

Obraba rezalnega roba orodja in analiza z valčno transformacijo pri visokohitrostni obdelavi Inconela 718 Fang, N. – Pai, P. S. – Edwards, N. Ning Fang* - P Srinivasa Pai - Nathan Edwards

Tehnična fakulteta, Državna univerza v Utahu, ZDA

Cilji raziskave so bili poiskati korelacijo med obrabo rezalnega roba orodja ter rezalnimi silami in vibracijami pri visokohitrostni obdelavi.

Cilji raziskave so bili doseženi z izvedbo vrste eksperimentov visokohitrostnega struženja, s katerimi je bil pokrit širok razpon pogojev odrezavanja. Za določitev povezave med obrabo orodja in vibracijami med odrezavanjem je bila uporabljena valčna transformacija kot napredna tehnika obdelave signalov.

Za preučitev razvoja obrabe rezalnega roba orodja med procesom odrezavanja ter vpliva obrabe rezalnega roba orodja na rezalne sile in vibracije so bili opravljeni eksperimenti visokohitrostne obdelave. Rezalne sile v različnih obdobjih procesa odrezavanja so bile merjene s sistemom za merjenje sile, istočasno pa so bile merjene tudi vibracije med odrezavanjem s pospeškomerom, pritrjenim na držalo orodja skozi luknjo izolacijskega vijaka. Nato je bila izračunana povprečna vrednost kvadratov amplitude vibracij, oziroma vrednost RMS. Valčna transformacija (WPT) je sodobna napredna tehnika za obdelavo signalov in je bila uporabljena za iskanje najobčutljivejšega valčnega koeficienta, ki bo uporaben kot vhodni parameter za nadzor obrabe rezalnega roba. Članek se omejuje na visokohitrostno končno obdelavo nikljeve superzlitine Inconel 718.

1) Obraba rezalnega roba orodja med odrezavanjem se razvija hitro ali počasi, odvisno od začetne geometrije rezalnega roba in uporabljenih pogojev odrezavanja.

2) Obraba rezalnega roba orodja na različnih merilnih mestih je različna in ustreza različnim debelinam nedeformiranega odrezka in pogojem trenja med orodjem in odrezkom na posameznih merilnih mestih. Obraba rezalnega roba se v splošnem povečuje od zunanje točke prek srednje točke proti notranji točki. Obraba rezalnega roba se povečuje tudi s podajanjem.

3) Profil obrabe rezalnega roba se dinamično spreminja in je pogosto nepravilne oblike, kar povečuje zahtevnost dinamične obrabe rezalnega roba orodja.

4) Vpliv dinamične obrabe rezalnega roba orodja na rezalne sile je v veliki meri odvisen tako od vsakokratnih pogojev odrezavanja kakor tudi od začetne geometrije rezalnega roba orodja. Vse tri komponente rezalnih sil se povečujejo z naraščajočo obrabo rezalnega roba pri vrednostih podajanja 0,01 in 0,10 mm/vrt. Povečevanje rezalnih sil ni signifikantno pri podajanju 0,04 mm/vrt.

5) Z naraščanjem obrabe rezalnega orodja ni mogoče opaziti signifikantnega trenda pri vrednosti RMS amplitude vibracij. Tradicionalna analiza v časovni domeni na osnovi vrednosti RMS amplitude vibracij ni koristna za pojasnjevanje in prikazovanje dinamičnega razvoja obrabe rezalnega roba orodja.

6) Valčna transformacija kot ena najbolj splošnih metod za dekompozicijo signala v časovno-frekvenčni domeni pomaga pri identifikaciji sprememb signala vibracij v različnih frekvenčnih pasovih. Ugotovljeno je bilo, da je valčni koeficient W33 pri začetni geometriji orodja in rezalnih pogojih te študije najbolj občutljiv na dinamično obrabo rezalnega roba orodja in ima lahko pomembno vlogo pri prepoznavanju vzorcev v okviru prihodnjega sistema za nadzor obrabe rezalnega roba orodja.

Izsledki raziskave veljajo samo za visokohitrostno obdelavo nikljeve superzlitine Inconel 718. Prihodnje raziskave bodo vključile tudi druge materiale, kot so titanove zlitine in kaljena jekla.

Obraba rezalnega roba orodja je razmeroma slabo raziskana v primerjavi z luknjičasto obrabo in obrabo bokov orodja, ki jima je bilo v preteklih desetletjih posvečeno veliko pozornosti. Članek predstavlja fundamentalno študijo obrabe rezalnega roba orodja pri visokohitrostni končni obdelavi nikljeve superlitine Inconel 718. Ugotovitve te raziskave pomagajo pri razumevanju vpliva obrabe rezalnega roba orodja na dinamične spremembe sil in vibracij pri odrezavanju.

Ključne besede: obraba rezalnega roba, rezalne sile, vibracije pri odrezavanju, valčna transformacija, Inconel 718, visokohitrostna obdelava

SI 38

*Naslov avtorja za dopisovanje: Tehnična fakulteta, Državna univerza v Utahu, 6000 Old Main Hill, Logan, UT 84322, Združene države Amerike, ning.fang@usu.edu

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)3, SI 39 DOI:10.5545/sv-jme.2011.042

Prejeto: 23.2.2011 sprejeto: 12.1.2012 ©2012 Strojniški vestnik. Vse pravice pridržane.

Sinteza palične konstrukcije z algoritmoma NSGA-II in NodeSort Stanković, T. – Štorga, M. – Marjanović, D. Tino Stanković – Mario Štorga – Dorian Marjanović

Univerza v Zagrebu, Fakulteta za strojništvo in ladjedelništvo, Hrvaška

V članku je predstavljen predlog pristopa k sintezi paličnih konstrukcij na osnovi genetskega algoritma. Uporabljen je bil algoritem NodeSort, ki vzame zbirko binarno šifriranih vozlišč iz 2D-domene in jih dešifrira v palično konstrukcijo po postopku, ki je podoben mreženju pri metodi končnih elementov (MKE). Problem zasnove palične konstrukcije v zvezni 2D-domeni vključuje naključno porazdelitev prostih vozlišč in vnaprej določena fiksna vozlišča (podpore in točke obremenitev), pri čemer so vsa vozlišča vsebovana v kromosomu. Delo je nadaljevanje naših dosedanjih raziskav in v okviru sinteze paličnih konstrukcij so bili postavljeni naslednji raziskovalni cilji: • Za vključitev večkriterijskega iskanja bo uporabljen genetski algoritem z nedominiranim razvrščanjem (NSGA-II).

• Prerez palic je namesto kot parameter opredeljen kot spremenljivka, s čimer je izboljšana kakovost rešitev.

Genotip je zato razširjen z dodatnim binarno šifriranim genom.

• Da bi se izognili nastanku gruč vozlišč pri skoraj optimalnih zasnovah s čezmernim številom vnaprej določenih vozlišč, oziroma da bi nasprotno pridobili vozlišča za razrešitev zasnove, ko evolucija zahteva več palic, so bili uvedeni kromosomi spremenljive dolžine.

• Za univerzalnost in transparentnost je mogoče določiti poljubno število vozlišč z obremenitvami.

Model palične konstrukcije je opredeljen kot sistem, sestavljen iz določenega števila palic in vozlišč. Robni pogoji določajo obremenitvene primere, s čimer je v modelu upoštevano število obremenitev ter vrste in mesta podpor nosilcev paličja. V vsaki iteraciji evolucije se za vsako kandidatno rešitev izračuna matrika togosti sistema MKE. Model po MKE obravnava ravninsko paličje, pri čemer ima vsak element 6 prostostnih stopenj. Uvesti je bilo treba tudi upogibanje palic in jih implicitno pretvoriti v nosilce. Rezultat evolucije z neskončno upogibno togostjo paličnih elementov bi sicer vedno konvergiral v eno samo horizontalno palico. Takšna konstrukcija bi imela ničelne deformacije, ker se ne more upogibati, kot vodoravna linija pa bi imela tudi minimalno maso.

Preizkus realnega primera večkriterijske optimizacije zasnove palične konstrukcije z dvema podporama je pokazal, da je dešifriranje na osnovi fenotipa NodeSort mogoče uporabiti skupaj s predlaganimi razširitvami genotipa za vključitev gamete za debelino in kromosomov spremenljive dolžine pri večkriterijski optimizaciji NSGA-II. Šifriranje in dešifriranje genotipa v algoritmu NodeSort skrbi za to, da je prostor iskanja kar se da velik in neomejen. Pristop gre korak dlje od parametrične optimizacije, saj omogoča optimizacijo topologije, presega pa tudi topološke pristope optimalne zasnove (TOD), saj je računsko bistveno manj zahteven. Modeli nosilcev so namreč parametrični in optimizirani v zvezni domeni. Fenotip kot palična konstrukcija, ki izhaja iz razporeda vozlišč, je pristop na osnovi algoritma.

Pristop je alternativa za slovnice oblik, ki so zasnovane na znanju in dosegajo povečanje zmogljivosti z dodajanjem novih pravil, in tako ohranja enake principe pretvorbe pravil. Običajno je potreben kompromis med algoritmičnimi pristopi in pristopi na osnovi znanja, saj prvi zahtevajo posege v kodo za izboljšanje zmogljivosti, slednji pa zahtevajo deljeno razumevanje domene in objektivne definicije pravil, sicer postane formalizirano znanje nedosledno in pristransko. S podporo popolnemu topološkemu iskanju, ki zagotavlja visoko ponovljivost rezultatov, je bila dosežena prednost pred predstavljenimi metodami.

Prihodnje delo bo usmerjeno na vplive pri iskanju optimalne rešitve z ozirom na rekurzivne omejitve in vrstni red razvrščanja vozlišč.

Ključne besede: sinteza paličnih konstrukcij, genetski algoritmi, NodeSort, NSGA-II

*Naslov avtorja za dopisovanje: Fakulteta za strojništvo in ladjedelništvo, I. Lučića 5, Zagreb, Hrvaška, tino.stankovic@fsb.hr

SI 39

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)3, SI 40

Prejeto: 2011-04-04, Sprejeto: 2011-11-18 ©2012 Strojniški vestnik. Vse pravice pridržane.

Numerična analiza izvedljivosti in učinkovitosti uporabe toplotnih cevi pri steblastih rezkarjih Liu, Y.B. – Zhu, L. Jen, T.C. – Zhao, J.W. – Yen, Y.H. Yong-Bin Liu1,3 – Lin Zhu1, 2* – Tien-Chien Jen2 – Ji-Wen Zhao1 – Yi-Hsin Yen2 1 Šola

za elektrotehniko in avtomatizacijo, Univerza Anhui, Kitajska 2 Oddelek za strojništvo, Univerza v Wisconsinu, ZDA 3 Oddelek za natančne stroje in instrumente, Znanstveno-tehnična univerza, Kitajska

Za odvajanje toplote, ki nastaja med procesom steblastega rezkanja na stiku orodja in obdelovanca, je uporabljena nova tehnologija vdelane toplotne cevi. Občasno se pojavljajo tudi poročila o uporabi toplotnih cevi za odvod toplote pri obdelavi z odrezavanjem. Judd et al. so raziskovali struženje jekla z orodjem s toplotno cevjo, vdelano v držalu. Ugotovili so, da lahko toplotna cev zmanjša temperaturo orodnega držala za 30 %. Chiou et al. so opravili analizo po metodi končnih elementov in eksperimentalno študijo hlajenja s toplotno cevjo pri obdelavi jekla s trdokovinskimi orodji. Avtorji so zaključili, da lahko toplotna cev v rezalni ploščici zmanjša temperaturo in obrabo rezalnega orodja ter podaljša življenjsko dobo orodja. Jen et al. so opravili numerično in eksperimentalno primerjavo hlajenja s toplotno cevjo pri operacijah suhega vrtanja in poročajo, da lahko toplotna cev zmanjša temperaturo svedra za 30 do 50 %. Kolikor je znano avtorjem tega prispevka, pa je le malo objavljenih raziskav o različnih pogojih hlajenja pri praktičnih procesih vrtanja.

Predmet tega članka je izvedljivost in učinkovitost hlajenja s toplotno cevjo pri operacijah steblastega rezkanja. Numerične študije vključujejo štiri primere, vključno s suhim rezkanjem, dovodom hladilne tekočine, hlajenjem s toplotno cevjo, ter hlajenjem s toplotno cevjo in dovodom hladilne tekočine. Raziskava termičnih, statičnih in dinamičnih strukturnih značilnosti steblastega rezkarja je bila opravljena z numeričnimi izračuni po hitri metodi končnih elementov (FFE) s programsko opremo za eksplicitno analizo po MKE. V tej študiji je bila za doseganje natančnih rezultatov numerične simulacije uporabljena strategija mreže visoke gostote, kjer ima v območjih, kjer je potrebna visoka ločljivost, vsak element po 10 vozlišč. Za mrežo celotnega orodja in še zlasti za fino mrežo na konici orodja je bila uporabljena štiritočkovna Jacobijeva kontrola za stopnjo deformiranosti tetraedričnih elementov. Rezultati numeričnih simulacij kažejo, da se največja temperatura na konici orodja pri enakem vnosu toplotne energije zmanjša za 29 %, oz. s 1027 °C pri polnem steblastem rezkarju na 737 °C pri steblastem rezkarju s toplotno cevjo. Prav tako se zmanjšajo največje toplotne napetosti, s 650 MPa pri suhem rezkanju na 480 MPa pri hlajenju s toplotno cevjo, oziroma za 1,4-krat pri enakih pogojih hlajenja.

Hlajenje s toplotno cevjo je zato lahko učinkovit pristop za upravljanje s toploto pri procesih steblastega rezkanja, primerljivo s sicer prevladujočim tekočinskim hlajenjem.

Uporaba toplotne cevi, vdelane v polni steblasti rezkar, pa lahko zaradi votle sredice poveča statične napetosti in deformacije pri vrhu rezkarja. Vgradnja toplotne cevi v polno orodje namreč zmanjša vztrajnostni moment orodja, s tem pa se povečajo upogibne deformacije in upogibne napetosti. Največja upogibna trdnost trde zlitine, iz katere je izdelan steblasti rezkar, je 1470 MPa, zato orodje s toplotno cevjo izpolnjuje zahteve operacij rezkanja.

Zaradi večjih statičnih napetosti in deformacij orodja s toplotno cevjo bi bilo trdnost in togost v glavni rezalni coni, zlasti pri vrhu orodja, mogoče izboljšati z optimizacijo geometrijske oblike in konfiguracije steblastega rezkarja.

Pri realnih aplikacijah je tveganje resonance oz. drdranja rezkarja mogoče zmanjšati z optimizacijo vpenjalne dolžine orodja, s tem pa se zmanjšajo tudi upogibne deformacije in upogibne napetosti.

Primerjava zvrsti vibracij polnih steblastih rezkarjev in steblastih rezkarjev s toplotno cevjo vodi do sklepa, da so vibracijske zvrsti polnih orodij nekoliko višje kot zvrsti orodij s toplotno cevjo. Razlog je v deformacijah polnega steblastega rezkarja, ki so pri dejanskih aplikacijah manjše kot pri steblastih rezkarjih s toplotno cevjo.

Višja frekvenca steblastega rezkarja pri operacijah obdelave torej vodi do večje togosti. Signifikantne vibracije orodja s toplotno cevjo imajo lahko škodljiv vpliv na dimenzijsko natančnost izdelka in na stabilnost sistema za obdelavo s steblastim rezkanjem. Vse to je mogoče izboljšati z optimizacijo hitrosti rezkanja. Z optimizacijo vpenjalne dolžine steblastega rezkarja pri industrijskih aplikacijah se zmanjša število močnih vibracijskih zvrsti v operacijah steblastega rezkanja, s čimer se zmanjša verjetnost resonance rezkarja, predvsem drdranja. Rezultati numerične simulacije v tej študiji kažejo, da je uporaba vdelane toplotne cevi v končnem rezkarju izvedljiva in učinkovita, ter da je suho steblasto rezkanje dosegljivo tudi pri realnih operacijah obdelave.

Ključne besede: hlajenje s toplotno cevjo, izvedljivost in učinkovitost, steblasti rezkar, termična in strukturna analiza SI 40

*Naslov avtorja za dopisovanje: Šola za elektrotehniko in avtomatizacijo, Univerza Anhui, zl009@mail.ustc.edu.cn

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)3 SI 41-44 Osebne objave

Magistrsko delo in diplome

MAGISTRSKO DELO Na Fakulteti za strojništvo Univerze v Ljubljani je z uspehom zagovarjal svoje magistrsko delo: dne 4. januarja 2012 Lenart MARĐETKO z naslovom: »Termoenergetski preizkusi termoelektrarn« (mentor: izr. prof. dr. Mihael Sekavčnik).

DIPLOMIRALI SO Na Fakulteti za strojništvo Univerze v Ljubljani so pridobili naziv univerzitetni diplomirani inženir strojništva: dne 24. februarja 2012: Slobodan DJORDJEVIĆ z naslovom: »Razvoj inteligentne omare za hranjenje kemikalij« (mentor: izr. prof. dr. Jože Tavčar, somentor: prof. dr. Jožef Duhovnik); Gregor HUDOKLIN z naslovom: »Nosilec membrane zaznavala dinamičnega tlaka« (mentor: prof. dr. Franc Kosel, somentor: doc. dr. Viktor Šajn); Urban SAJOVIC z naslovom: »Analiza aerodinamičnih lastnosti letalskega krila v bližini tal« (mentor: prof. dr. Franc Kosel, somentor: doc. dr.

Viktor Šajn); Luka TRKULJA z naslovom: »Metoda za nadzorovanje kakovosti duroplastov BMC« (mentor: prof. dr. Igor Emri); Tadej ŽNIDERIČ z naslovom: »Uporaba vzvratnega inženirstva (RE) za izdelavo orodja za krivljenje cevi« (mentor: prof. dr. Janez Kopač, somentor: doc. dr. Franci Pušavec); * Na Fakulteti za strojništvo Univerze v Mariboru so pridobili naziv univerzitetni diplomirani inženir strojništva: dne 23. februarja 2012: Denis TRSTENJAK z naslovom: »Razvoj mikromontažnega sistema za sestavo očal« (mentor: red. prof. dr. Miran Brezočnik, somentor: red. prof. dr.

Jože Balič); * Na Fakulteti za strojništvo Univerze v Mariboru so pridobili naziv diplomirani inženir strojništva (UN): dne 23. februarja 2012:

Špela BRGLEZ z naslovom: »Parametrična analiza sevanja v avtomobilski meglenki z uporabo numeričnih simulacij« (mentor: red. prof. dr. Leopold Škerget, somentor: doc. dr. Jure Ravnik). * Na Fakulteti za strojništvo Univerze v Mariboru so pridobili naziv diplomirani gospodarski inženir (UN): dne 23. februarja 2012: Jure PLAZNIK z naslovom: »Izdelava programa za terminiranje naročil s prednostnimi pravili« (mentor: doc. dr. Iztok Palčič, somentor: red. prof. dr.

Anton Hauc); * Na Fakulteti za strojništvo Univerze v Ljubljani so pridobili naziv diplomirani inženir strojništva: dne 9. febrauarja 2012: Jure BADOVINAC z naslovom: »Vrednotenje razreza debelih nerjavnih pločevin« (mentor: prof. dr.

Mihael Junkar); Matic ČAH z naslovom: »Fiziologija pilota med opravljanjem dela, po njem in med počitkom (spanje)« (mentor: prof. dr. Rastko Golouh, somentor: izr. prof. dr. Tadej Kosel); Bogoslav FERLIN z naslovom: »Vpliv polnil na mehanske lastnosti poliestrskih kompozitov« (mentor: izr. prof. dr. Roman Šturm, somentor: prof. dr. Janez Grum); Andrej KOBE z naslovom: »Izdelava preizkuševališča in rezanje kamnitih plošč z diamantno žico« (mentor: prof. dr. Janez Kopač, somentor: doc. dr. Franci Pušavec); Janez STRMŠEK z naslovom: »Reševalno padalo za brezpilotno letalo« (mentor: izr. prof. dr.

Tadej Kosel); Gregor TIMPRAN z naslovom: »Ornitološka zaščita letališča« (mentor: pred. mag. Andrej Grebenšek, somentor: izr. prof. dr. Tadej Kosel); dne 10. febrauarja 2012: Andrej ČERMELJ z naslovom: »Priprava tehnologije varjenja posod iz nerjavnega jekla« (mentor: prof. dr. Janez Tušek); Luka KASTELEC z naslovom: »Razvoj pogonskega sistema za transportni trak v tunelski kalilni peči« (mentor: doc. dr. Jernej Klemenc, somentor: prof. dr. Matija Fajdiga); SI 41

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)3 SI 41-44

Matej KOLENC z naslovom: »Merjenje momenta zaradi obremenitve propelerja ventilatorja« (mentor: izr. prof. dr. Ivan Bajsić); Uroš PEKOLJ z naslovom: »Primerjalna analiza različnih sistemov ogrevanja enodružinske hiše« (mentor: prof. dr. Alojz Poredoš). * Na Fakulteti za strojništvo Univerze v Mariboru so pridobili naziv diplomirani inženir strojništva: dne 23. februarja 2012: Milena ČAS z naslovom: »Uvajanje nove tehnologije montaže bančnih vsebnikov« (mentor: red. prof. dr. Jože Balič);

SI 42

Simon ČASAR z naslovom: »Transporter s pomičnimi valji« (mentor: red. prof. dr. Iztok Potrč, somentor: izr. prof. dr. Tone Lerher); Timi FAZLIU z naslovom: »Varnostne zračne blazine v sodobnih vozilih« (mentor: red. prof. dr.

Miran Brezočnik, somentor: izr. prof. dr. Karl Gotlih); Primož LESJAK z naslovom: »Tehnološke izboljšave pri proizvodnji darilne embalaže« (mentor: red. prof. dr. Miran Brezočnik); Maksimiljan ZUPANIČ z naslovom: »Optimiranje ventilatorskega kolesa s spremembo geometrije in eksperimentalno verifikacijo« (mentor: red. prof. dr. Andrej Predin).

Strojniški vestnik - Journal of Mechanical Engineering 58(2012)3 SI 41-44

Prof. dr. Viktorju Prosencu – v spomin V 92. letu življenja je smrt iztrgala iz naših vrst upokojenega rednega profesorja dr. Viktorja Prosenca, priznanega in visoko cenjenega učitelja in znanstvenika varilske stroke v Sloveniji in nekdanji Jugoslaviji. Ob tem, da je bil dve mandatni obdobji dekan na Fakulteti za strojništvo Univerze v Ljubljani (FS UL), je bil mentor in vzornik mnogim študentom in več mlajšim sodelavcem, nosilec priznanja TZ Litostroj za inovacije, zaslužni član Zveze geoloških, rudarskih in metalurških inženirjev in tehnikov, častni član Društva za varilno tehniko Ljubljana in tudi nosilec odlikovanja Jugoslovanski red dela.

Rodil se je 12. decembra 1920, v Zagorju ob Savi, od koder ga je življenjska pot vodila na državno gimnazijo v Ljubljano. Zaradi vojne se je vrnil v domači kraj in se zaposlil v rudniku Zagorje, od tu pa je bil prisilno mobiliziran v nemško vojsko. Po vrnitvi v domovino je nadaljeval s študijem na Tehniški fakulteti Univerze v Ljubljani, kjer je leta 1951 diplomiral na oddelku Montanistike. Potem, ko se je posvetil proučevanju tehnologij varilskih procesov, je opravil tri mesečno specializacijo na Institutu za varjenje v Parizu (Institute de la soudure).

Doktoriral je leta 1975 na Tehniški Univerzi v Hannovru (TU Hannover, Institut für Metallkunde), pri mednarodno uveljavljenem strokovnjaku za varilstvo prof. dr. Friedrich Erdmann-Jesnitzer-ju; in sicer iz področja nukleacije in kristalizacije kovin.

Po diplomi ga je Fakulteta za rudarstvo in metalurgijo Tehniške visoke šole v Ljubljani, povabila za rednega asistenta na Katedro za metalurško strojništvo; in na tem mestu je ostal do leta 1958. Njegova naslednja zaposlitev je bila na novoustanovljenem (1956) Zavodu za varjenje SRS v Ljubljani, kjer je vodil Tehnološki oddelek. in se tako zapisal varilski stroki. V šolskem letu 1962/63 je bil na Fakulteti za naravoslovje in tehnologijo Univerze v Ljubljani, na Odseku za montanistiko izvoljen za predavatelja za področje Varjenje. Po zaposlitvi na Fakulteti za strojništvo Univerze v Ljubljani (FS UL), je delal na Institutu za strojništvo, kot predstojnik Tehnološkega odseka. Že naslednje leto je bil izvoljen za predavatelja za področje Varjenje in Preizkušanje kovin. Leta 1972 je tu osnoval Laboratorij za varjenje in izdelal program vaj za predmeta Varjenje in Tehnika spajanja ter pridobil tudi potrebno varilno opremo. Med pedagoškim in raziskovalnim delom se je izposojeno opremo v Laboratoriju za varjenje testiralo in posodabljalo, obenem pa se je prav s to opremo reševalo številne tehnološke in varivostne probleme za potrebe domačega gospodarstva. Leta 1976 je bil na FS UL izvoljen za izrednega in leta 1981 za rednega profesorja, obakrat za področji Varjenje in Gradiva.

V šolskem letu 1974/75 je na FS UL prvič uvedel t.i. višješolsko varilsko usmeritev študija strojništva in izdelal program predavanj in vaj za predmet Varilska tehnologija. V šolskem letu 1985/86 pa je, skupaj s prof. dr. Viljemom Kraljem, uvedel še univerzitetno varilsko usmeritev študija strojništva na FS UL ter nov predmet Fizikalno-kemijske osnove varilskih procesov. Vrsto let je bil nosilec predmeta Varilni procesi, na podiplomskem študiju za področje Avtomatizacija in proizvodna kibernetika. Opazen je tudi njegov prispevek na področju priprave učnega gradiva. Že leta 1959 je pripravil tri poglavja za prva skripta o varilskih tehnologijah, ki jih je izdal Zavod za varjenje. Je avtor samostojnih poglavij; Varjenje v Strojno-tehnološkem priročniku in Varilni preizkusi v Metalurškem priročniku, izdanih pri Tehniški založbi Slovenije. Na FS UL je pripravil zapiske iz predmetov: Varjenje in Tehnika spajanja ter skripta Varilska tehnologija, ki so bila natisnjena za interno uporabo.

Predaval je tudi na drugih fakultetah: na Fakulteti za strojništvo Univerze v Mariboru, Univerze v Mostarju, Novem Sadu in v Sarajevu ter na Fakulteti strojarstva in brodogradnje Univerze v Zagrebu.

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Strojniški vestnik - Journal of Mechanical Engineering 58(2012)3 SI 41-44

Izjemno bogato je zlasti njegovo strokovno in znanstveno-raziskovalno delovanje. Že kot mlad asistent je sodeloval pri projektiranju metalurških obratov v Železarni Sisak, Tovarni ferozlitin Šibenik in Livarni STT. Na koncu 70-tih let in na začetku 80-tih let prejšnjega stoletja je v TZ Litostroj vodil poglobljene raziskave varivosti martenzitne jeklene litine. Prav na osnovi rezultatov teh raziskav, v katerih je ob vodji Pločevinarne, Jakovu Klariću, uni. dipl. inž., sodeloval tudi spodaj prvopodpisani, je bil takrat izveden prehod izdelave hidromehanske opreme iz litih na varjene konstrukcije. Velik del prof. Prosenčevega ustvarjalnega opusa je razviden tudi iz številnih prispevkov, ki jih je predstavil na domačih in mednarodnih posvetovanjih ter iz objavljenih člankov v domačih in tujih strokovnih revijah.

Izredno dejaven je bil v številnih družbenih in strokovnih organizacijah. Bil je član Jugoslovanskega društva inženirjev in tehnikov, Nemškega društva inženirjev, Društva varilnih inženirjev Francije. Njegove izjemne strokovne, družbene in človeške vrline so visoko cenili številni starejši kolegi varilske stroke na celotnem prostoru nekdanje Jugoslavije. Ne nazadnje, ob njegovi smrti, so to tudi izrazili, z elektronsko poslanimi sožalji njegovi družini in Zvezi društev za varilno tehniko Slovenije, ki so jih izrekli kot predstavniki Društev za varilno tehniko iz Beograda, Sarajeva, Tuzle in Zagreba. Če strnemo spomine na profesor Prosenca, lahko zapišemo: Bil je ugleden strokovnjak in odličen pedagog.

Svojim študentom, kolegom in sodelavcem pa bo ostal v zavesti predvsem kot izjemen Človek.

Zato se mu ob tej priložnosti priklanjamo še z mislijo iz Naše besede, Otona Župančiča:

»Bil je med nami mož kot zrno klen in zdrav; ta, kakor knjige mi, ljudi je brati znal, ...« izr. prof. dr. Ivan Polajnar, prof. dr. Viljem Kralj

SI 44

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 Co-Editor Borut Buchmeister University of Maribor 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 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: Top figure presents a geometrical model of Disk Launch Glider made by Catia. The background is the photograph of Ribniško Pohorje which is perfect for thermal soaring in spring time. Middle figures are results of numerical simulations made by Computational Fluid Dynamic.

The streamlines at different angle of attack are plotted. At right figures the recirculation zone is clearly visible. At bottom photograph the real radio controlled DLG is in author’s hand.

Image courtesy: Institute for Power, process and environmental enginerring, Faculty of Mechanical Engineering, University of Maribor, Slovenia

ISSN 0039-2480 © 2011 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.

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, Bay Zoltan Inst. for Mater. Sci. and Techn., 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 Print Tiskarna Knjigoveznica Radovljica, printed in 480 copies General information Strojniški vestnik – Journal of Mechanical Engineering is published in 11 issues per year (July and August is a double issue).

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[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.

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422-427.

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[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.

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58 (2012) 3

http://www.sv-jme.eu

Strojniški vestnik Journal of Mechanical Engineering

Since 1955

Papers

147

Matjaž Ramšak: Radio Controlled Sailplane Flight: Experimental and Numerical Analysis

156

Hamidreza Salimi, Bahador Saranjam, Ahmad Hoseini, Mohsen Ahmadzadeh: Use of Genetic Algorithms for Optimal Design of Sandwich Panels Subjected to Underwater Shock Loading

165

Adem Çiçek, Turgay Kıvak, Gürcan Samtaş: Application of Taguchi Method for Surface Roughness and Roundness Error in Drilling of AISI 316 Stainless Steel

175

Ali Movaghghar, Gennady Ivanovich Lvov: Theoretical and Experimental Study of Fatigue Strength of Plain Woven Glass/Epoxy Composite

183

Mezid Muhasilovic, Jožef Duhovnik: Cfd-Based Investigation of the Response of Artificial Ventilation in the Case of Tunnel-Fire

191

Ning Fang, P Srinivasa Pai, Nathan Edwards: Tool-Edge Wear and Wavelet Packet Transform Analysis in High-Speed Machining of Inconel 718

203

Tino Stanković, Mario Štorga, Dorian Marjanović: Synthesis of Truss Structure Designs by NSGA-II and NodeSort Algorithm

213

Yong-Bin Liu, Lin Zhu, Tien-Chien Jen, Ji-Wen Zhao, Yi-Hsin Yen: Numerical Analyses to Investigate the Feasibility and Effectiveness in Using Heat Pipe Embedded End Mills

Journal of Mechanical Engineering - Strojniški vestnik

Contents

3 year 2012 volume 58 no.