DEGREE PROJECT IN ELECTRICAL ENGINEERING, SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2019 3D Finite Element Analysis of a Hybrid Stepper Motor YUANYI FAN KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE 3D Finite Element Analysis of a Hybrid Stepper Motor YUANYI FAN Degree Project in Electrical Energy Conversion Date: September 25, 2019 Supervisor: Dr. Bin Liu Examiner: Dr. Oskar Wallmark School of Electrical Engineering and Computer Science Host company: ABB Swedish title: 3D FEM-analys av en hybrid stegmotor iii Abstract Hybrid stepper motors are being applied to more and more industrial regions due to their low cost compared with servo motors and prominent performance. Many industrial applications require accurate and effective methods for pre- dicting a motor’s performance at the design stage. The geometry of the motors is complicated and the magnetic saturation effect is also serious, giving rise to the difficulty of understanding the transient behavior of the motors. Fur- thermore, the drive circuit and control algorithm are more sophisticated than those of traditional AC or DC motors. Lastly, the losses of the motors create the rising of temperature, while the thermal effect and dynamic performance affect each other. All these factors can be solved by simulating a hybrid stepper motor with a model combining the effect of electromagnetic field, control algorithm, and motor loss together. In this thesis, a three-dimension (3D) finite element model is developed in the software Maxwell for studying motor character- istics. The electromagnetic field is analyzed in a static state. The simulated back electromagnetic force is verified by experiments. The feasibility of full- step control algorithm is analyzed. The vector control algorithm is applied to the model through co-simulation of Simulink and Maxwell in Simplorer. The 3D model is proved to be unrealistic for co-simulation. In the end, this the- sis summarizes the modeling experience and gives recommendations on the transient simulation of the motor. iv Sammanfattning Hybridstegsmotorer appliceras i fler ochfler industriapplikationer tack vare deras låga kostnad och förbättrad prestanda jämfört med servomotorer. Många branschapplikationer kräver exakta och effektiva metoder för att förutsäga motorns prestanda redan i konstruktionsstadiet. Motorns geometri är kompli- cerad och den magnetiska mättnadseffekten är också betydande, vilket försvå- rar modelleringen. Dessutom är drivkretsen och styralgoritmen mer sofistike- rad än den för traditionella växel- eller likströmsmotorer. Vidare så resulterar motorns förluster i temperaturökningar vilka påverkar dynamiska. Alla dessa faktorer kan studeras genom att simulera hybrida stegmotorer med en modell som kombinerar effekten av elektromagnetiskt fält, kontrol- lalgoritm och motorförluster tillsammans. I detta examensarbete utvecklas en tredimensionell finit elementmodell i programvaran Maxwell för att studera motorns elektromagnetiska egenskaper. Det elektromagnetiska fältet analy- seras i ett statiskt tillstånd. Den beräknade mot-EMK:n har verifieras genom experiment. Vektorkontrollalgoritmen tillämpas på modellen genom samsi- mulering i Simulink och Maxwell i Simplorer. Den tredimensionella model- len visade sig vara orealistisk för samsimulering. Till sist summeras uppnåda erfarenheter och rekommendationer för fortsatt arbete ges. v Acknowledgement I want to express my sincere gratitude to my knowledgeable and experienced supervisor, Dr. Bin Liu. He leads me in the right direction and helps me a lot in modifying my experiments and thesis. His positive working attitude and optimistic attitude are what I should learn in my life. Also, I want to thank my examiner associate professor, Oskar Wallmark, for his precious recom- mendation and continuous guidance. Then, I want to thank my colleagues for helping me a lot in my daily life during my stay in ABB Sweden Research Center. Having Fika and lunch together with them is really happy. In the end, I would like to offer my thanks to my family, giving me a warm back up; To my beloved girlfriend, Mengyao Jiang, giving me support every day; And to my friends, Helin Zhou, Feifan Liu, etc, always encouraging me and providing a lot of help. Contents 1 Introduction 1 1.1 Purpose . .1 1.2 Scope and Challenge . .1 1.3 Background . .2 1.4 Previous Work/Literature Review . .3 1.5 Contribution . .7 1.6 Thesis Outline . .7 2 Hybrid Stepper Motor 9 2.1 Stepper Motor . .9 2.2 Basic Structure and Working Principle . 10 2.3 Detent Torque and Holding Torque . 12 2.4 Motor Loss . 13 2.4.1 Copper Loss . 14 2.4.2 Iron Loss . 14 3 FEM Modeling of Motors 17 3.1 Theory of Electromagnetic Field . 17 3.2 Introduction to Maxwell . 19 3.3 Co-simulation of Maxwell and Simulink . 24 4 Simulation 29 4.1 3D Model . 29 4.2 Static State . 30 4.3 Back EMF . 33 4.4 Full-Step Control . 35 4.5 Vector Control . 40 vii viii CONTENTS 5 Conclusions and Future Work 45 5.1 Conclusion . 45 5.2 Future Work . 46 5.2.1 2D Model . 46 5.2.2 Verification of FEM Model . 46 5.2.3 Thermal Simulation . 47 Bibliography 49 Chapter 1 Introduction 1.1 Purpose This thesis work aims to investigate the feasibility of simulating the transient behavior of hybrid stepper motors by a universal three-dimension (3D) Finite Element Method (FEM) commercial software. The method proposed in this thesis is beneficial for predicting characteristics of this kind of motor in prac- tical industrial applications. The research provides motor designers and users with reference to apply the motor in multiple working circumstances. 1.2 Scope and Challenge The work is a continuation of previous master thesis projects and some re- sults are directly used in this thesis. In order to analyze the complex tran- sient behavior of hybrid stepper motors, a precise model should be built and verified using existing instruments. The thesis intends to find an effective modeling method for this kind of motor and operate corresponding simula- tions properly for representative working conditions. Restricted by time and instruments, this work only does a limited number of simulations. The elec- tromagnetic field is analyzed in a static state. The back electromotive force is simulated and the result is verified by experimental results. The simple open- loop control algorithm is applied to the numerical model. Also, the relatively complicated vector control algorithm is tried to apply on the model through co-simulation of Simulink and Maxwell. Although there are many kinds of hybrid stepper motors on the market, this thesis work only studies a specific motor. That is to say, the effect of motor dimension is not studied in this thesis. 1 2 CHAPTER 1. INTRODUCTION The challenge of this project is mainly on establishing an FEM model. The model needs to be verified with the motor by trial and error: a model is built and simulated, and then the model is changed to get a better simula- tion result which is closer to the experimental result. However, the simulation of 3D FEM is very time-consuming and heavily relies on experience. Thus, another challenge lies in shortening the simulation time, which is realized through model reduction. As previous studies simulated the motor only in static solvers, the biggest challenge of this project is thinking out how to sim- ulate the motor in a transient solver and how to verify the effectiveness of the simulation. That will be detailedly discussed in Section 1.4. 1.3 Background A stepper motor is an electromechanical component that produces a corre- sponding angular displacement or line displacement when it is applied with an electrical pulse signal. It is widely used as an actuator in various modern industrial products, such as reversing radar, printers, and lighting system of automobile [1]. In comparison with servo motors, the most outstanding merit of stepper motors is being cheap. Therefore, researchers and engineers have tried to replace servo motors in some applications with stepper motors, which could yield huge economic benefits. The use of stepper motors is growing rapidly that the market share of stepper motors currently accounts for about 17% of the global drive motor market [2]. In the case of low control accuracy requirements, stepper motors can be open-loop controlled by digital signals, making them easy to construct a sim- ple, inexpensive but reliable control system. However, under open-loop con- trol, stepper motors have poor control accuracy, which limits their range of application. Therefore, in the past three years, three projects have been con- ducted to explore the control strategy of stepper motors with higher posi- tional accuracy on the premise of reducing hardware cost. In these projects, microstepping and vector control strategy were applied to an inexpensive po- sition sensor and a hybrid stepper motor. The control strategy satisfied the demand for position accuracy and the achievement was published in three master thesis [3, 4, 5]. However, when the hybrid stepper motor is attempted to provide power to an automation machine, the power density is too small to meet industrial de- mand. That is to say, under normal load, the operation speed of that machine is too slow, thereby reducing the production efficiency. It is obliged to enlarge the power of the hybrid stepper motor. Greater power means a larger current CHAPTER 1. INTRODUCTION 3 is supplied to the motor. However, for one thing, a large current may cause the motor to heat up too much and the temperature is too high, which may damage the motor. It is well known that the temperature and dynamic charac- teristics influence each other, especially in over-heated condition. For another thing, the heating energy comes from the losses of motor, meaning that the large excitation current would alter the motor efficiency, i.e. the economic value. Therefore, a relative precise model combined the dynamic and thermal features of a hybrid stepper motor should be developed so as to help re- searchers investigating the performance limit and understanding the transient behavior.