ROBUST DESIGN OF MINIATURISED SPINDLE MOTORS FOR HARD DISK DRIVE GAO XIAN KE NATIONAL UNIVERSITY OF SINGAPORE 2002 ROBUST DESIGN OF MINIATURISED SPINDLE MOTORS FOR HARD DISK DRIVE GAO XIAN KE (M.Eng, B.Eng) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2002 Acknowledgements Acknowledgements The road to this Ph.D. degree has been frustrating and fulfilling at all times. There has been long up hill stretches as well as exhilarating downhill sprints. Without the dear affection of people I have met along, it would not have been possible to reach this destination. First of all, I am greatly indebted to Professor Low Teck Seng, for giving me the opportunity to complete my academic journey under his supervision. He has been a constant source of encouragement and has provided valuable insight toward solving the problems addressed in this work. I would like to express my genuine gratitude to him for his excellent guidance and advice during the research work. I also wish to express my sincere appreciation to Dr. Chen Shixin for his guidance with high experienced perspective. Some parts of this work would not have been possible without his guidance, encouragement and support. Unfortunately, he passed away when I almost finished my thesis. I would like to dedicate this thesis to the memory of Dr. Chen Shixin. I am also deeply thankful to Dr. Liu Zhejie, Dr. Bi Chao and Dr. Guo Guoxiao for their valuable time, support and recommendations. I would like to thank Prof. Loh Han Tong and Prof. M. A. Jabbar for agreeing to serve as committee members. I am very grateful to Dr. Zhang Qide, Dr. Yang Jiaping, Mr. Wang Hongtao, Mr. Li Xinping and Mr. Shen Zhenqun, all members in MCAD & EDM groups, for their ideas and help throughout the project. I would also like to thank Mr. Lim Thiam Soh and Ms. Cynthia with their support and help. Special note of appreciation to my friends’ kind and selfless support and help. i Acknowledgements Words are inadequate to express my gratitude to my wife and family, for their patience, selfless and immense support. True love and encouragement was provided by my parents and parents-in-law which kept me through thick and thin. Especially, I would like to dedicate this work to my lovely son, Wenqi, who always gives me heartwarming encouragement throughout my research and study. ii Table of Contents Table of Contents Acknowledge i Table of Contents iii List of Tables viii List of Figures xiii List of Symbols xvi Summary xxi Chapter Introduction 1.1 Introduction 1.2 Research Objectives 1.3 Literature Survey 1.3.1 Survey of Robust Design Methodology 1.3.2 Survey of the Grey System Method and the Monte Carlo Method 12 1.4 Hard Disk Drive Technology 13 1.5 Scope of Work 17 1.6 Organization of Thesis 18 Chapter Numerical Calculation of HDD Spindle Motor 2.1 Introduction 22 2.2 Original Design and Finite Element Analysis 23 iii Table of Contents 2.2.1 Torque Calculation 25 2.2.2 UMP Calculation 28 2.2.3 30 Power Loss Calculation 2.3 Parameter Analysis 32 2.4 Conclusions 37 Chapter Robust Design of Torque Optimization for HDD Spindle Motors Using Taguchi Method 3.1 Introduction 39 3.2 Review of Taguchi Method 41 3.3 Taguchi’s System Design and Parameter Design for Torque Optimization 47 3.3.1 Background 47 3.3.2 Objective Definition 49 3.3.3 Experimental Design 49 3.3.4 Prediction, Verification and Analysis 53 3.4 Conclusions 61 Chapter Robust Parameter Design and Tolerance Design for UMP Optimization 4.1 Introduction 64 4.2 Review of Taguchi’s Parameter and Tolerance Design 65 4.3 Objectives and Screening Experiment 68 4.4 Taguchi’s Parameter Design for UMP Optimization 72 4.5 Taguchi’s Tolerance Design for UMP Optimization 76 iv Table of Contents 4.6 Conclusions 78 Chapter Robust Torque Optimization of HDD Spindle Motors Using Response Surface Methodology 5.1 Introduction 81 5.2 Response Surface Methodology 82 5.2.1 Analysis Techniques 84 5.2.2 87 Conceptualization of the Central Composite Design 5.3 Torque Optimization Using Mixed Resolution Central Composite Design 90 5.3.1 Mixed Resolution Central Composite Design 91 5.3.2 Torque Optimization 94 5.3.3 Zoom-In MR-CCD Design 98 5.4 Torque Optimization Using Higher Degree Model Technique 102 5.5 Conclusions 105 Chapter Hybrid Robust Design of Torque Optimization for HDD Spindle Motors 6.1 Introduction 108 6.2 Proposed Methodology 111 6.2.1 Step One: Identifying Variables 113 6.2.2 Step Two: Determining Order 114 6.2.3 Step Three: Constructing Experiment 114 6.2.4 Step Four: Fitting Model 114 6.2.5 Step Five: Optimizing Variables 115 v Table of Contents 6.2.6 Step Six: Analyzing Performance 6.3 Hybrid Design for Torque Optimization 116 116 6.3.1 Spindle Motor Torque Optimization 117 6.3.2 Zoom-In Hybrid Design 121 6.4 Conclusions 123 Chapter Robust Design Using Grey Relational Analysis Based on Orthogonal Array 7.1 Introduction 126 7.2 Grey Relational Analysis 127 7.3 Torque Optimization Using Grey Relational Analysis 131 7.3.1 Grey Relational Analysis Based on Orthogonal Array Experiment 131 7.3.2 Grey Relational Analysis Based on Reduced OA Experiment 7.4 Improved Grey Relational Analysis 136 140 7.4.1 Original Grey Relational Analysis 140 7.4.2 New Grey Relational Analysis 142 7.4.3 Analysis and Assessment 145 7.4.4 Concluding Remarks 147 7.5 Conclusions 148 Chapter Robust Design Incorporated with Monte Carlo Method 8.1 Introduction 150 8.2 Review of Monte Carlo Method 151 vi Table of Contents 8.3 Torque Optimization Using RSM with Monte Carlo Simulation 155 8.3.1 Proposed Approach Using TEE and MCS 156 8.3.2 159 Torque Optimization Using MCS 8.4 Results and Discussion 164 8.5 Conclusions 165 Chapter Conclusions and Future Research 9.1 Summary of Research Results 168 9.2 Summary of Conclusions 170 9.3 Original Contributions 173 9.4 Future Work 175 References 178 Publications 199 Appendix A 203 Appendix B 233 vii List of Tables List of Tables Page Table 1.1 Comparison of Taguchi Method and RSM Table 2.1 Iron Loss Calculation 32 Table 2.2 Levels of Design Parameters 33 Table 2.3 Experiments Using FEA 34 Table 3.1 Design Parameters 52 Table 3.2 Effect of Various Factors on the Performance Indices 56 Table 3.3 Prediction and Verification for Robust Design Using Taguchi Method 57 Table 3.4 Verification Using Original Design With Noise Effect 59 Table 3.5 Verification Using Traditional Optimization With Noise Effect 59 Table 3.6 Verification Using Taguchi’s Parameter Design With Noise Effect 59 Table 4.1 Confounding Effects Caused by a Wrong Layout 70 Table 4.2 Experiments Using Screening Method 71 Table 4.3 Analysis of Variance for S/N Ratio 74 Table 4.4 Comparison between Original Design and Taguchi’s Parameter Design 74 Table 4.5 Analysis of Variance for Standard Deviation 77 Table 4.6 Performance Comparison Using Parameter Design and Tolerance Design 78 Table 5.1 The Analysis of Variance 85 Table 5.2 Different α Values for the Rotatable CCD 88 Table 5.3 Standard CCD with Three Variables 88 viii Appendix B 237 Appendix B Figure B-2. Predicted response surfaces of UMP vs. different parameters combination 238 Appendix B 239 Appendix B 240 Appendix B Figure B-3. Predicted response surfaces of the fitted model for the 6-pole 9-slot spindle motor 241 Appendix B 242 Appendix B 243 Appendix B Figure B-4. Predicted contours of the fitted model for the 6-pole 9-slot spindle motor 244 Appendix B 245 Appendix B 246 Appendix B Figure B-5. Predicted response surfaces of the fitted response model for the 6-pole 9slot spindle motor (zoom-in) Figure B-6. Predicted contours of the fitted response model for the 6-pole 9-slot spindle motor (zoom-in) 247 Appendix B Figure B-7. Second-degree fitted response surfaces (crossed-experiment) 248 Appendix B (a) (b) (c) (d) (e) (f) Figure B-8. Third-degree fitted response surfaces (crossed-experiment) 249 Appendix B Figure B-9. Second-degree fitted response surfaces using pareto-optimal design 250 Appendix B Figure B-10. Visualization of the fitted response model for the 8-pole 6-slot spindle motor 251 Appendix B Figure B-11. Visualization of the fitted response model for the 8-pole 6-slot spindle motor (zoom-in) 252 [...]... robust design for electromechanical components in hard disk drive, tailored for spindle motors in this research This is a significant issue since the choice of the design parameter values could affect all aspects of the product/process specification This is the leading work in systematical research and application of robust design in hard disk drive industry As the objective of the research is to formulate... existing problems in hard disk drive (HDD), and proposes solutions and ways to optimize the performance characteristics for HDD Finally, the scope of work, and the organization of this thesis are concisely described The goal of this research is to realize the robust design of spindle motors in hard disk drives to achieve the miniaturization, which is a key trend today This novel design applied in HDDs... and S/N Ratios for Reduced Experiments (II) 231 Noise Effect on Cogging Torque for a 6-pole 9-slot Spindle Motor Using Grey Optimal Design 232 Table A-37 xii List of Figures List of Figures Page Figure 1.1 Conceptual framework of experimental design 5 Figure 1.2 Overview of hard disk drive 14 Figure 2.1 Geometry modeling of an 8-pole 9-slot BLDC spindle motor 24 Figure 2.2 Cross section of one slot and... Using Taguchi’s Parameter Design for an 8p9s Spindle Motor – UMP Analysis 213 ANOM in Parameter Design for an 8-pole 9-slot Spindle Motor – UMP Analysis 214 ANOVA in Parameter Design for an 8-pole 9-slot Spindle Motor – UMP Analysis 214 Tolerance Design I: Experiment for an 8-pole 9-slot Spindle Motor – UMP Analysis 215 Tolerance Design II: Experiment for an 8-pole 9-slot Spindle Motor – UMP Analysis... and effectiveness of Taguchi’s robust design approach and RSM for optimization in HDD spindle motors design Several effective alternatives are proposed in this research to deal with the weaknesses of Taguchi’s design and RSM approach in torque optimization for HDD spindle motors The hybrid design, which is an integration of regression model and orthogonal array approach, is proposed for multiple-response... The Ratio of Tc/Tr Simulation and Analysis for a 6-pole 9-slot Spindle Motor Using Pareto-Optimal Design 224 Experiment of Noise Effect for a 6-pole 9-slot Spindle Motor (Tc) 225 Table A-28 Experiment of Noise Effect for a 6-pole 9-slot Spindle Motor (Tr) 225 Table A-29 Experiment of Noise Effect for a 6-pole 9-slot Spindle Motor (Tc/Tr) 226 Table A-30 Crossed Experiment for an 8-pole 6-slot Spindle. .. Chapter 1: Introduction of this study is to formulate the effective robust design approaches systematically and generally for design and optimization of electromechanical systems in hard disk drive The design using Taguchi’s orthogonal array, signal-to-noise ratio, analysis of mean and analysis of variance in miniaturized HDD electromechanical systems, is one idea for the approach The design using mathematical... After Taguchi’s Parameter Design 207 Screening Experiment for UMP Optimization of an 8p9s Spindle Motor 208 ANOM in Screening Experiment for an 8p9s Spindle Motor – UMP Analysis 209 ANOVA in Screening Experiment for an 8p9s Spindle Motor – UMP Analysis 210 Inner Array (L9) for an 8p9s Spindle Motor – UMP Analysis 211 Outer Array (L9) for an 8p9s Spindle Motor – UMP Analysis 212 Performances in Crossed Experiment... edge length of square m = the overall mean of performance statistics mxi = the mean of performance statistics of x control factor at i level xvi List of Symbols n = number of experiment runs n0 = the equivalent sample size nr = the number of repetition of the verification P = pole-arc/pole-pitch ratio Q() = quality loss R = an appropriate experimental region R2 = a measure of the proportion of total variation... regression of the fitted model SSSFx = the sum of squares due to each factor SST = total sum of squares ti = tolerance of ith variable Tc = cogging torque Tr = running torque Tc/Tr = ratio of cogging torque to running torque Tµ = mean torque performance Tσ = variance of torque performance xvii List of Symbols X = matrix (n×k) of the levels of the independent variables Xi = Xi* = the mean of the Xij . ROBUST DESIGN OF MINIATURISED SPINDLE MOTORS FOR HARD DISK DRIVE GAO XIAN KE NATIONAL UNIVERSITY OF SINGAPORE 2002 ROBUST DESIGN OF MINIATURISED SPINDLE MOTORS. 3 Robust Design of Torque Optimization for HDD Spindle Motors Using Taguchi Method 3.1 Introduction 39 3.2 Review of Taguchi Method 41 3.3 Taguchi’s System Design and Parameter Design for. Survey of Robust Design Methodology 4 1.3.2 Survey of the Grey System Method and the Monte Carlo Method 12 1.4 Hard Disk Drive Technology 13 1.5 Scope of Work 17 1.6 Organization of Thesis