MODELING , ANALYSIS AND VERIFICATION OF OPTIMAL FIXTURE DESIGN ERNEST TAN YEE TIT B Eng (Mech.), NUS A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF ENGINEERING DEPARTMENT OF MECHANICAL ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2003 ACKNOWLEDGEMENTS I am very grateful to the following from whom I received help and guidance for this research: A/Prof A Senthil kumar for his valuable direction, insight and giving me the opportunity to complete my research under him A/Prof Jerry Y H Fuh for his precious time, concern and valuable guidance Mr Vincent Ling Yun and Mr Kevin Lim Heng Tong, final-year students, for their contribution in this research Without them this research would not have been successful Dr Lim Han Seok for his expertise and help in developing the experimental force sensor system Mr Lim Soon Cheong who helped me arrange for the experiments Staff at Workshop who helped produce the fixtures and sensor bodies i TABLE OF CONTENTS Acknowledgements .i Table of Contents .ii Summary v List of Figures vi List of Tables viii List of Symbols ix Chapter Introduction 1.1 Background 1.2 Literature survey 1.3 Objectives .6 1.4 Organization of the Thesis Chapter Automatic Selection of Clamping Surfaces and Positions using the Force Closure Method .7 2.1 Theory of Force Closure .7 2.1.1 2.1.2 2.2 Stages of implementation .12 2.2.1 2.2.2 2.2.3 2.2.4 2.2.5 2.2.6 2.3 Force model .7 Convex hull algorithm .9 Inputs 13 Marking off unavailable grid points on the base plate 13 Identify candidate clamping surfaces 13 Generate spiral mesh 14 Visualization 16 Clamp Sequencing 17 Summary .18 Chapter Modeling of Minimum Clamping Force 19 ii 3.1 Introduction 19 3.2 Optimization Equations 19 3.3 Example 21 3.4 Summary .22 Chapter Experimental Force Sensor 23 4.1 Working Principle of the Sensor 24 4.2 Visual Basic Data Acquisition Program .27 4.3 Software Requirements .29 4.4 Calibration of Sensors 29 4.5 Evaluation of Sensor Performance .30 4.6 Summary .31 Chapter Finite Element Modeling of the Workpiece-Fixture Setup 32 5.1 Description of the Developed FEM model 32 5.2 Comparison Study 33 5.2.1 5.2.2 5.3 Model - Mittal’s FEM Model .34 Model - Tao’s FEM Model 38 Summary .43 Chapter Experimental Verification of the Finite Element Model 44 6.1 Instrumentation 44 6.2 Stiffness Test 45 6.3 Description of Case Study 47 6.4 Results & Discussions of Case Study 51 6.5 Description of Case Study 55 6.6 Results & Discussion of Case Study 58 Chapter Conclusions and Recommendations .63 iii 7.1 Conclusions 63 7.2 Recommendations 64 References .66 Appendix A1 iv SUMMARY Fixture design is an important manufacturing activity which affects the quality of parts produced In order to develop a viable computer aided fixturing tool, the fixture-workpiece system has to be accurately modeled and analysed This thesis describes the modeling, analysis and verification of optimal fixturing configurations by the methods of force closure, optimization, and finite element modeling (FEM) Force closure has been employed to find optimal clamping positions and sequencing, while optimization is used for determining the minimum clamping forces required to balance the cutting forces The developed FEM is able to determine in detail what are the reaction forces, workpiece displacement, deformation in the workpiece and fixtures In order to produce a more accurate model for predicting the behaviour of the fixture–workpiece system, the developed FEM includes fixture stiffness, while past models have assumed as rigid bodies The reaction forces on the locators are experimentally verified A sensor-embedded experimental fixturing setup was developed to verify the modeling and the data was used to compare with the FEM Two case studies were conducted and compared in the experiment and in FEM As a secondary objective, a prototype fixture-integrated force sensor was developed for use in the experiment But it was insufficiently reliable at this stage and the measurement of reaction force fell back upon the existing Kistler slimline force sensor It was found that the FEM-predicted reaction forces trends match well with the experimental data Therefore this improved finite element model allowing room for slight error could be used to simulate the behaviour of an actual fixture-workpiece system during machining v LIST OF FIGURES Figure 1.1 Framework of Computer-Aided Fixture Design .2 Figure 2.1 Approximation of Friction Cone for Contact Ci .9 Figure 2.2 Spiral Mesh of clamping surface to find candidate clamping points 15 Figure 2.3 Colour Map of Side Clamping Surfaces based on rmax (Blue is the optimal area and red is the infeasible area.) 16 Figure 2.4 Colour Map of Top Clamping Surfaces based on rmax (Blue is the optimal area and red is the infeasible area.) 17 Figure 3.1 Minimum clamping force required vs time predicted by optimization algorithm 22 Figure 4.1 Sensor integrated fixture-workpiece system 23 Figure 4.2 The structure of the sensor 24 Figure 4.3 Uniform load over a small central area of radius r0, edge simply supported .25 Figure 4.4 Side view of the sensor showing the air gap between the cap and brass plate 26 Figure 4.5 Circuit and output connection of the sensor 26 Figure 4.6 Frequency output of the sensor 27 Figure 4.7 Instrumentation Layout 29 Figure 5.1 Model after meshing (With reference to Mittal’s model) .34 Figure 5.2 Fixturing layout for model 35 Figure 5.3 Machining profile for model 35 Figure 5.4 Reaction force vs time chart obtained by Mittal 37 Figure 5.5 Results from finite element analysis 37 Figure 5.6 Model after meshing (With reference to Tao’s Model) 39 Figure 5.7 Fixture layout and location for model 40 vi Figure 5.8 Reaction force vs time obtained in Tao’s experiment 41 Figure 5.9 Finite element results for Tao’s model (without fixture element stiffness) .42 Figure 5.10 FEM results from developed model (with fixture element stiffness) 42 Figure 6.1 Schematic of the Fixture Stiffness Test 45 Figure 6.2 Relationship of force applied vs deflection on supporting element 46 Figure 6.3 Relationship of force applied vs deflection on locating elements 47 Figure 6.4 Modeling of the workpiece and locations of clamps/locators for Case Study 48 Figure 6.5 Experimental Setup for Case Study 49 Figure 6.6 Typical dynamic force obtained from experiment Reaction force is shown at locator .50 Figure 6.7 A graph of reaction forces of supports and locators vs time of Case Study 53 Figure 6.8 A graph of reaction forces of clamps vs time of Case Study 54 Figure 6.9 Experimental Setup for Case Study 55 Figure 6.10 Dimension of workpiece and locations of clamps/locators of Case Study 2.57 Figure 6.11 A graph of reaction forces of locators and supports vs time of Case Study 61 Figure 6.12 A graph of reaction forces of clamps vs time of Case Study 62 vii LIST OF TABLES Table 5.1 Comparison of FEM models 32 Table 5.2 Modeling Data 33 Table 5.3 Comparison of features between Mittal’s model and the proposed model .34 Table 5.4 Modeling data for model 36 Table 5.5 Comparison of features between Tao’s model and the proposed model .38 Table 5.6 Modeling data for model 40 Table 6.1 Fixture element stiffness 46 Table 6.2 Clamping forces applied in sequence of Case Study 49 Table 6.3 Cutting data of Case Study .50 Table 6.4 Clamping forces applied in sequence of Case Study 56 Table 6.5 Cutting data of Case Study 56 viii LIST OF SYMBOLS fik unit generator of polyhedral friction cone αik positive factor for the linear combination of unit generators unit normal of clamping face µi coefficient of static friction between contact i and workpiece n number of contacts A matrix of facet normals x six-dimensional point in the convex hull space b vector of facet offsets bi w six dimensional wrench fikx, fiky, fikz force components of six dimensional wrench (ri × fik)x , (ri × fik)y , (ri × fik)z moment components of six dimensional wrench rmax radius of maximally inscribed hypersphere S, T unit direction vectors of clamping surface ix X L7 (14,34,0) L6 (172,34,0) S3 (171,0,10) S5 (10, 0, 10) L0 (184,50,62) 114 Z C4 (0, 50, 62) C8 (102,92,25) Cutter direction S1 ( 92,0,106) mm C2 (92,34,114) 69 69 Legend L locator S support C clamp 184 TOP VIEW Slope of height mm Fixture contact surface C8 X C4 L6 L7 L0 Y 92 90 C2 S5 S1 FRONT VIEW S3 Spring attached to ground represents fixture stiffness * All units in mm Figure 6.10 Dimension of workpiece and locations of clamps/locators of Case Study 57 6.6 Results & Discussion of Case Study A comparison of the actual reaction force and FEM-predicted reaction force with respect to time is shown in the two graphs in Figure 6.11 and Figure 6.12 and will be referred to in this discussion All force profiles consist of three distinct linear segments; before 19s, between 19s and 38s and after 38s The first segment and third segment exhibit the same increasing or decreasing behaviour, depending on the fixture element This is linked by a second segment with a steeper gradient, but not necessarily of the same sign as the gradient of the first and third segments The reason for this is the linearly increasing depth of cut from mm to mm as the end mill passes the sloped region of the workpiece Locator L0 produces an almost constant reaction force of 815N before 19s, which linearly increases to about 830N between 19 s and 38s and gradually rises to 840N at 60s.The increase in reaction force was significant between 19 s and 38 s because the end mill was traversing across a slope of increasing gradient and thus produced the increase Reaction force after 38s was higher because the cutting force in the x direction (towards L0) increased when the depth of cut increased to mm It is observed that the general trend of the FEM prediction makes a good comparison with that of the experimental trend, but in overall the FEM profile predicted reaction forces lower than that of the experiment as shown in Fig 6.11 The range of variation in force between the FEM profile and the experimental profile is in a close agreement 58 For Locator L6, reaction force is initially at 270N and increases until 19s where the reaction force decreases a little until 38s, and after 38s, reaction force increases gradually Reaction force for locator L7 starts at 500N, and decreases linearly As the end mill moves away from L7 and towards L6, the reaction force decreases for L7 and increases for L6 It can be observed that reaction forces for locators L6 and L7 have the opposing trends The FEM profiles of L6 and L7 both have similar trends with that of the experimental data and the range of variation is also correspondingly small For clamp C2, reaction force is initially at 760N before 19s and increases slightly to 800N until 38s and remains at 800N to the end of the cut This is due to the increase in the depth of cut across the slope causing the end mill to exert increasing force in the z-direction (towards C2) For the FEM prediction, it seems to project a rather conservative increase, from around 750N to 765N For locator C4, the reaction force decreases very minimally in the experimental data, about 840N from the start to about 830N till the end The FEM projects a more generous decrease in the reaction C4 is the clamp opposite that of L0, and as the cutter moves towards L0, and away from C4, the cutter exerts increasing force in the x-direction (towards L0) Thus the reaction forces decreases for C4 and increases for L0, reflecting a mirror image of each other Reaction forces at clamp C8 remains almost constant throughout the milling process The FEM data compares well with the experimental data Although the FEM profiles shows similarity to those of the actual reaction forces at the 59 locators and clamps, there are errors present that can be positive or negative The magnitudes in variations for the finite element modeling are also noticeable The uncertainty in chosen values of fixture stiffness and friction coefficient could be reasons for the discrepancy Since the general trends compares well with the experimental data, this improved finite element model allowing room for a slight error could be used to simulate the behaviour of an actual fixture-workpiece system during machining 60 Reaction Forces at Fixture Contacts vs Time FEM simulation and experimental results (Locators and supports) 1000.00 L0 EXPT 900.00 S3-FEM L0-FEM 800.00 700.00 Reaction Force /N S1-FEM 600.00 S5-FEM 500.00 L7-FEM L7 EXPT 400.00 300.00 L6 EXPT L6-FEM 200.00 100.00 0.00 10 20 30 40 50 60 70 Time /s L0 EXPT L6 EXPT L0-FEM L6-FEM S1-FEM L7 EXPT S3-FEM L7-FEM S5-FEM Figure 6.11 A graph of reaction forces of locators and supports vs time of Case Study 61 Reaction Forces at Fixture Contacts vs Time FEM simulation and experimental results (Clamps) 2.30E+03 C8 EXPT 2.10E+03 C8-FEM 1.90E+03 Reaction Force /N 1.70E+03 1.50E+03 1.30E+03 1.10E+03 C2 EXPT C4 EXPT 9.00E+02 C4-FEM C2-FEM 7.00E+02 10 20 30 40 50 60 70 Time /s C2 EXPT C2-FEM C4 EXPT C4-FEM C8 EXPT C8-FEM Figure 6.12 A graph of reaction forces of clamps vs time of Case Study 62 Chapter CONCLUSIONS AND RECOMMENDATIONS 7.1 Conclusions The developed FEM model is able to provide a realistic simulation of the fixture-workpiece interaction during machining than Mittal’s[2] and Tao’s[6] models as it takes into account fixture stiffness, contact friction and elasticity of the workpiece With this increased complexity, greater accuracy can be obtained from the model Inputs such as the fixture stiffness and friction coefficient are not easily determined Presence of coolant and surface profile are some factors that may affect the friction coefficient at the fixture contacts This work has presented three techniques of fixture analysis which may be used by a fixture designer in a complementary manner The initial stages of choosing clamping positions and surfaces and clamping sequence are handled well by the force closure method Then for fixture analysis, one can use either the optimization method or FEM, depending on the level of accuracy required The optimization method is very fast but gives only information about minimum clamping forces FEM allows for analyzing workpiece deformation, location error and fixture deformation The main drawbacks of FEM are: the need to determine accurate inputs and longer time for constructing the model and running the simulation 63 7.2 Recommendations In research there is always room for investigation and improvement The following research directions are recommended: • Dynamic modeling of the workpiece-fixture system in FEM Further research can be pursued in the investigation of dynamic effects Abaqus/Explicit is a software module that supports the FEM modeling of dynamic interactions Focus should be on the dampening effect of the fixture and predicting and avoiding the natural frequency of the system Experimental work can be conducted to analyse the spectral distribution of vibrations in the workpiece and the effect on the workpiece quality • Integrated Capacitance Force Sensor System This experimental sensor system has many benefits, most significant of which is robustness and cost-effectiveness It is much more durable than Kistler’s slimline piezoelectric force sensors, which often receive damage in the cable leads Further work needs to be done on the microprocessor circuit to account for the drift in readings because of changes in temperature Sampling rate has to be raised to an acceptable level of at least 100Hz if it is to measure the dynamic effects • Prediction of Fixture Stiffness A FEM model of the fixture assembly can be formulated, with the representation of fastener joints as simplified finite elements By applying varying loads and checking the deflection in the same direction, a load-deflection graph can be plotted From this graph, the fixture stiffness value for the SPRING element can be 64 determined If this can be proven to be reasonably accurate, then there is no need for stiffness tests A second use for this fixture stiffness model would be to warn the fixture designer if a fixture assembly is not sufficiently stiff 65 REFERENCES [1] S H Lee, M R Cutkosky, “Fixture Planning with Friction”, Transactions of the ASME, Vol 13, August 1991 [2] R O Mittal, Paul H Cohen, B J Gilmore, “Dynamic Modeling of the Fixture-Workpiece System”, Robotics and Computer-Integrated Manufacturing, Vol No 4, pp 201-217, 1991 [3] De Meter E.C., Min-max load model for optimizing machining fixture performance, Journal of Engineering for Industry, 117, pp 186-193, 1995 [4] B Li and S N Melkote, Optimal Fixture Design Accounting for the Effect of Workpiece Dynamics, International Journal of Advanced Manufacturing Technology (2001) 18:701–707 [5] J D Lee, L S Haynes, “Finite Element Analysis of Flexible Fixturing System”, Transactions of the ASME, Vol 109, May 1987 [6] Tao, Z J., A Senthil, Kumar, Nee A.Y.C., Automatic Generation Of Dynamic Clamping Forces For Machining Fixtures, International Journal of Production Research, 37(12), pp 2755-2776, 1999 [7] Kevin Rong, Stephens Zhu, “Computer-Aided Fixture Design”, Marcel Dekker, Inc., 1999 [8] IMAO Venlic Block Jig System (BJS) Catalog, IMAO Corporation, Japan, 1990 [9] Quick Hull Library, The Geometry Center, http://www.geom.umn.edu/software/qhull/, 2001 66 [10]A Senthil, Kumar, Fuh, Y H., Kow, T S., An Automated Design And Assembly of Interference-free Modular Fixture Setup, Computer-Aided Design, 32(2000), pp 583-596, 1999 [11]Tao, Z J., A Senthil, Kumar, Nee A.Y.C., A Computational Geometry Approach to Optimum Clamping Synthesis of Machining Fixtures, International Journal of Production Research, 1998 [12]Kerr, J., B Beth, Analysis of Multi-fingered hands, International Journal of Robotics Research, 4(4) pp 3-17, 1986 [13]Mishra B , N Silver, Some discussion of static gripping and its stability, IEEE Sys Man Cybernet, 19(4), pp 783-796, 1989 [14]Quick Hull Library, The Geometry Center, http://www.geom.umn.edu/software/qhull/, 2001 [15]Raymond J Roak & Warren C Young, “Formulas for Stress and Strain”, McGraw-Hill International Book Company, 1984 [16]Hibbit, Karlsson & Sorensen, Inc., ABAQUS/Standard 6.2 User Manual, 2001 [17]DeMeter, E.C., Sayeed Q., R.E DeVor, R.E and S.G Kapoor, S.G “An internet-based model for technology integration and access, Part 2: Application to process modeling and fixture design” Symposium on Agile Manufacturing, ASME International Mechanical Engineering Congress & Exposition, 1995 67 APPENDIX A-1 Data acquisition during experiment Edit the calibration file data Setup the workpiece and start the NC program Read Tm, from all eight sensors, continuously before commencing cutting Actual time, t, is recorded for each reading Start cutting Stop reading sensors when cutting is finished Repeat from step for all runs Data processing A-2 Program Functions in Pseudocode A-2.1 Reading a single sensor 100 times Single read button is pressed Case { Case “0”: Loop 100 times { Send “A” to tell the microprocessor to read sensors Wait a fixed time for the reply Store time, t and Tm for sensor } Case “7”: A-1 Loop 100 times { Send “H” to tell the microprocessor to read sensors Wait a fixed time for the reply Store time, t and Tm for sensor } } Plot results using Microsoft Chart object A-2.2 Recording all sensors for 100 times Loop for 100 times { Send “AB” to tell the microprocessor to read sensors and Wait a fixed time for the reply Store time, t and Tm for sensors and Send “CD” to tell the microprocessor to read sensors and Wait a fixed time for the reply Store time, t and Tm for sensors and Send “EF” to tell the microprocessor to read sensors and Wait a fixed time for the reply Store time t and Tm for sensors and Send “GH” to tell the microprocessor to read sensor and Store time t and Tm for sensors and } Save results file Plot results using Microsoft Chart object A-2 A-2.3 Continuous recording function Do Loop { Send “AB” to tell the microprocessor to read sensors and Wait a fixed time for the reply Store time, t and Tm for sensors and Send “CD” to tell the microprocessor to read sensors and Wait a fixed time for the reply Store time, t and Tm for sensors and Send “EF” to tell the microprocessor to read sensors and Wait a fixed time for the reply Store time t and Tm for sensors and Send “GH” to tell the microprocessor to read sensor and Store time t and Tm for sensors and } Loop until stopped by user Save results file Plot results using Microsoft Chart object A-3 Publication Resulting from this Thesis Modeling, analysis and verification of optimal fixturing design, Ernest Y T Tan, A Senthil Kumar*, J Y H Fuh, A Y C Nee, submitted to IEEE Journal of Automation Science and Engineering, Special Issue on Fixturing, March 2003 A-4 [...]... from an expert designer In designing a fixture, there are two necessary steps, viz., fixture synthesis and fixture analysis (see Figure 1.1) Fixture synthesis is supported by a CAD representation system which has access to a parametric fixture element database Issues such as the setup and machining operation, fixture element connectivity, selection of fixturing surfaces and points are considered in... interference between fixture, workpiece and cutting tool Kinematic analysis checks for correct location with respect to datum surfaces (to avoid any over-constrained location) 1 and whether the fixture contacts are positioned adequately to oppose the cutting forces The most commonly adopted method of kinematic analysis is force closure Framework of Computer-Aided Fixture Design Fixture Design Synthesis... contact pair Fixture stiffness has been studied by Rong & Zhu [7] The deformation of fixture components and their connections may significantly contribute to machining inaccuracy of parts and dynamic instability during the machining process Some factors that affect fixture stiffness are: fastening force magnitude and the orientation of the fixture components The most direct way of determining fixture stiffness... (1) the use of the force closure method to predict optimal clamping positions and clamping sequence, (2) using an optimization algorithm to predict the reaction forces at the fixture contacts, and (3) development of an FEM model of the fixture- workpiece system that includes fixture stiffness The force closure method generates a set of optimal clamping positions based on pre-selected locating and supporting... Computer-Aided Fixture Design Force analysis checks that the reaction forces at the fixture contacts are sufficient to maintain static equilibrium in the presence of cutting forces Cutting force profiles need to 2 be known for this level of analysis Lastly, especially important for flexible parts, deformation analysis that determines the elastic or plastic deformation of the part under the clamping and cutting... parts and change programs on the fly, move parts between machines automatically, but when it comes to fixturing, a human machinist is required to accurately locate and clamp the parts and in some cases design the fixture setup Surely this is a bottleneck because of the possibility of human error and long lead time for fixture design, which is a complex task requiring heuristic knowledge from an expert designer... Representation Analysis Geometric Analysis Machining Interference Parametric Fixture Database Assembly Interference Fixture Element Connectivity Kinematic Analysis Setup Information Machining Operation Force Closure Force Analysis Minimum Clamping Force Selection of Fixturing Surface and points Bill of Materials AFD / SFD / IFD FEM Deformation Analysis FEM Included in thesis Figure 1.1 Framework of Computer-Aided... originating from the centre of the face for containment computations instead of starting from the corners Figure 2.2 illustrates the increasing size of the spiral and shows when the iteration stops Variables used are mesh size D = 20 mm, number of loops N, centre point of face and surface unit vectors of the clamp face S and T 14 S T Figure 2.2 Spiral Mesh of clamping surface to find candidate clamping points... friction coefficient, cutting force as a function of time, workpiece weight and centre of gravity of the workpiece The optimization algorithm minimizes the friction capacity ratio of the fixture- workpiece system, subject to the constraints of static equilibrium, positive location and Coulomb friction This generates a minimum reaction force profile of all the fixture contacts with respect to time It is the... fixture- workpiece system and comparison with two FEM models by Mittal and Tao Chapter 6 is an experimental verification of the FEM model with two case studies Chapter 7 concludes the thesis 6 Chapter 2 AUTOMATIC SELECTION OF CLAMPING SURFACES AND POSITIONS USING THE FORCE CLOSURE METHOD This section focuses on the selection of optimal clamping points and formulates an acceptable clamping sequence Locating and supporting ... method of kinematic analysis is force closure Framework of Computer-Aided Fixture Design Fixture Design Synthesis CAD Representation Analysis Geometric Analysis Machining Interference Parametric Fixture. .. accurately modeled and analysed This thesis describes the modeling, analysis and verification of optimal fixturing configurations by the methods of force closure, optimization, and finite element... heuristic knowledge from an expert designer In designing a fixture, there are two necessary steps, viz., fixture synthesis and fixture analysis (see Figure 1.1) Fixture synthesis is supported by