Symmetry in Mechanical Engineering Printed Edition of the Special Issue Published in Symmetry www.mdpi.com/journal/symmetry Adam Glowacz, Grzegorz Królczyk and Jose A. Antonino-Daviu Edited by Symmetry in Mechanical Engineering Symmetry in Mechanical Engineering Special Issue Editors Adam Glowacz Grzegorz Kr ́ olczyk Jose A. Antonino-Daviu MDPI • Basel • Beijing • Wuhan • Barcelona • Belgrade • Manchester • Tokyo • Cluj • Tianjin Special Issue Editors Adam Glowacz AGH University of Science and Technology Poland Grzegorz Kr ́ olczyk Opole University of Technology Poland Jose A. Antonino-Daviu Universitat Politecnica de Val` encia Spain Editorial Office MDPI St. Alban-Anlage 66 4052 Basel, Switzerland This is a reprint of articles from the Special Issue published online in the open access journal Symmetry (ISSN 2073-8994) (available at: https://www.mdpi.com/journal/symmetry/special issues/Symmetry Mechanical Engineering). For citation purposes, cite each article independently as indicated on the article page online and as indicated below: LastName, A.A.; LastName, B.B.; LastName, C.C. Article Title. Journal Name Year , Article Number , Page Range. ISBN 978-3-03936-214-1 (Pbk) ISBN 978-3-03936-215-8 (PDF) c © 2020 by the authors. Articles in this book are Open Access and distributed under the Creative Commons Attribution (CC BY) license, which allows users to download, copy and build upon published articles, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications. The book as a whole is distributed by MDPI under the terms and conditions of the Creative Commons license CC BY-NC-ND. Contents About the Special Issue Editors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Grzegorz Krolczyk, Stanislaw Legutko, Zhixiong Li and Jose Alfonso Antonino Daviu Introduction to Special Issue on Symmetry in Mechanical Engineering Reprinted from: Symmetry 2020 , 12 , 245, doi:10.3390/sym12020245 . . . . . . . . . . . . . . . . . 1 Baojun Qu, Qingxin Yang, Yongjian Li, Miguel Angel Sotelo, Shilun Ma and Zhixiong Li A Novel Surface Inset Permanent Magnet Synchronous Motor for Electric Vehicles Reprinted from: Symmetry 2020 , 12 , 179, doi:10.3390/sym12010179 . . . . . . . . . . . . . . . . . 5 Vigneashwara Pandiyan, Wahyu Caesarendra, Adam Glowacz and Tegoeh Tjahjowidodo Modelling of Material Removal in Abrasive Belt Grinding Process: A Regression Approach Reprinted from: Symmetry 2020 , 12 , 99, doi:10.3390/sym12010099 . . . . . . . . . . . . . . . . . . 19 Kevin Kuan-Shun Chiu, Jeou-Long Lee, Ming-Lang Tseng, Rosslyn Hsiu-Ling Hsu and Yen-Jen Chen A Hybrid Mechanism for Helicopters Reprinted from: Symmetry 2020 , 12 , 33, doi:10.3390/sym12010033 . . . . . . . . . . . . . . . . . . 47 Ondiz Zarraga, Imanol Sarr ́ ıa, Jon Garc ́ ıa-Barruetabe ̃ na and Fernando Cort ́ es An Analysis of the Dynamical Behaviour of Systems with Fractional Damping for Mechanical Engineering Applications Reprinted from: Symmetry 2019 , 11 , 1499, doi:10.3390/sym11121499 . . . . . . . . . . . . . . . . . 55 Iosif Birlescu, Manfred Husty, Calin Vaida, Nicolae Plitea, Abhilash Nayak and Doina Pisla Complete Geometric Analysis Using the Study SE(3) Parameters for a Novel, Minimally Invasive Robot Used in Liver Cancer Treatment Reprinted from: Symmetry 2019 , 11 , 1491, doi:10.3390/sym11121491 . . . . . . . . . . . . . . . . . 71 Darius Andriukaitis, Andrius Laucka, Algimantas Valinevicius, Mindaugas Zilys, Vytautas Markevicius, Dangirutis Navikas, Roman Sotner, Jiri Petrzela, Jan Jerabek, Norbert Herencsar and Dardan Klimenta Research of the Operator’s Advisory System Based on Fuzzy Logic for Pelletizing Equipment Reprinted from: Symmetry 2019 , 11 , 1396, doi:10.3390/sym11111396 . . . . . . . . . . . . . . . . . 89 Mircea Mih ̆ alcic ̆ a, Sorin Vlase and Marius P ̆ aun The Use of Structural Symmetries of a U12 Engine in the Vibration Analysis of a Transmission Reprinted from: Symmetry 2020 , 12 , 1296, doi:10.3390/sym11101296 . . . . . . . . . . . . . . . . . 107 Qipeng Chen, Qingsheng Xie, Qingni Yuan, Haisong Huang and Yiting Li Research on a Real-Time Monitoring Method for the Wear State of a Tool Based on a Convolutional Bidirectional LSTM Model Reprinted from: Symmetry 2019 , 11 , 1233, doi:10.3390/sym11101233 . . . . . . . . . . . . . . . . . 121 Adriana M. Osorio, Mois ́ es O. Bustamante, Gloria M. Restrepo, Manuel M. M. L ́ opez and Juan M. Men ́ endez-Aguado A Study of the Effect of Medium Viscosity on Breakage Parameters for Wet Grinding Reprinted from: Symmetry 2019 , 11 , 1202, doi:10.3390/sym11101202 . . . . . . . . . . . . . . . . . 139 v Guocheng Li, Fei Shuang, Pan Zhao and Chengyi Le An Improved Butterfly Optimization Algorithm for Engineering Design Problems Using the Cross-Entropy Method Reprinted from: Symmetry 2019 , 11 , 1049, doi:10.3390/sym11081049 . . . . . . . . . . . . . . . . . 151 Lu Lu, Yu Yuan, Heng Wang, Xing Zhao and Jianjie Zheng A New Second-Order Tristable Stochastic Resonance Method for Fault Diagnosis Reprinted from: Symmetry 2019 , 11 , 965, doi:10.3390/sym11080965 . . . . . . . . . . . . . . . . . 171 Andrius Laucka, Vaida Adaskeviciute and Darius Andriukaitis Research of the Equipment Self-Calibration Methods for Different Shape Fertilizers Particles Distribution by Size Using Image Processing Measurement Method Reprinted from: Symmetry 2019 , 11 , 838, doi:10.3390/sym11070838 . . . . . . . . . . . . . . . . . 187 Liang Bai, Yun-Wen Feng, Ning Li, Xiao-Feng Xue and Yong Cao Data-Driven Adaptive Iterative Learning Method for Active Vibration Control Based on Imprecise Probability Reprinted from: Symmetry 2019 , 11 , 746, doi:10.3390/sym11060746 . . . . . . . . . . . . . . . . . 203 Yuanming Xie, Wenqiang Li, Yin Luo, Yan Li and Song Li A Method to Determine Core Design Problems and a Corresponding Solution Strategy Reprinted from: Symmetry 2019 , 11 , 576, doi:10.3390/sym11040576 . . . . . . . . . . . . . . . . . 225 Jia Li, Xiumin Chu, Wei He, Feng Ma, Reza Malekian and Zhixiong Li A Generalised Bayesian Inference Method for Maritime Surveillance Using Historical Data Reprinted from: Symmetry 2019 , 11 , 188, doi:10.3390/sym11020188 . . . . . . . . . . . . . . . . . 243 Lei Chen, Xiao Zhang, Zhengfeng Yan and Rong Zeng Matching Model of Dual Mass Flywheel and Power Transmission Based on the Structural Sensitivity Analysis Method Reprinted from: Symmetry 2019 , 11 , 187, doi:10.3390/sym11020187 . . . . . . . . . . . . . . . . . 255 Lei Zhang, Aimin Ji, Weidong Zhu and Liping Peng On the Identification of Sectional Deformation Modes of Thin-Walled Structures with Doubly Symmetric Cross-Sections Based on the Shell-Like Deformation Reprinted from: Symmetry 2018 , 10 , 759, doi:10.3390/sym10120759 . . . . . . . . . . . . . . . . . 285 Qianlei Cao, Chongzhen Cao, Fengqin Wang, Dan Liu and Hui Sun Robust Adaptive Full-Order TSM Control Based on Neural Network Reprinted from: Symmetry 2018 , 10 , 726, doi:10.3390/sym10120726 . . . . . . . . . . . . . . . . . 307 Wu Deng, Hailong Liu, Shengjie Zhang, Haodong Liu, Huimin Zhao and Jinzhao Wu Research on an Adaptive Variational Mode Decomposition with Double Thresholds for Feature Extraction Reprinted from: Symmetry 2018 , 10 , 684, doi:10.3390/sym10120684 . . . . . . . . . . . . . . . . . 323 Yanrong Wang, Hang Ye, Long Yang and Aimei Tian On the Existence of Self-Excited Vibration in Thin Spur Gears: A Theoretical Model for the Estimation of Damping by the Energy Method Reprinted from: Symmetry 2019 , 10 , 664, doi:10.3390/sym10120664 . . . . . . . . . . . . . . . . . 347 vi About the Special Issue Editors Adam Glowacz received his Ph.D. in Computer Science from the AGH University of Science and Technology, Cracow, Poland, in 2013. Adam Glowacz is the author/coauthor of 106 scientific papers (58 papers indexed by Web of Science) that correspond to a h-index of 21 and 1026 citations in Web of Science and a h-index of 23 and 1407 citations in Google Scholar. He has supervised 30 B.Sc. and 12 M.Sc. theses. Adam Glowacz is an Associate Editor of Symmetry, Electronics, Measurement, and Advances in Mechanical Engineering, and has also authored 300 scientific reviews. Grzegorz Krolczyk is Professor and Vice-Rector for Research and Development at Opole University of Technology and author and coauthor of 200 scientific publications (110 JCR papers), as well as around 30 studies and industrial applications. His main scientific activities are in the analysis and improvement of manufacturing processes, surface metrology, and surface engineering. His research focuses on sustainable manufacturing as a tool for the practical implementation of the concept of social responsibility in the area of machining. Grzegorz Krolczykis is a member of several scientific organizations, including an expert in the Section of Technology of the Committee on Machine Building of the Polish Academy of Sciences. In addition, he is a member of several editorial committees of scientific journals. He has participated in advisory and opinion-forming bodies, including the advisory team of the Minister of Science and Higher Education. The coauthor of two patent applications, Grzegorz Krolczyk has been awarded on numerous occasions for his scientific activities in Poland and around the world. Jose A. Antonino-Daviu received his M.Sc. and Ph.D. degrees in Electrical Engineering, both from the Universitat Polit‘ecnica de Val‘encia, Valencia, Spain, in 2000 and 2006, respectively. He has worked for IBM, where he was involved in several international projects. He is currently Full Professor in the Department of Electrical Engineering, Universitat Polit‘ecnica de Val‘encia. He was an Invited Professor at Helsinki University of Technology, Finland, in 2005 and 2007; Michigan State University, USA, in 2010; Korea University, South Korea, in 2014; Universit ́ e Claude Bernard Lyon 1, France; and Coventry University, U.K., in 2016. He is a coauthor of more than 200 papers published in technical journals and conference proceedings and one international patent. Dr. Antonino-Daviu is Associate Editor of IEEE Transactions on Industrial Informatics, IEEE Industrial Electronics Magazine, and IEEE Journal of Emerging and Selected Topics in Industrial Electronics. He received the IEEE Second Prize Paper Award fromthe Electric Machines Committee of the IEEE Industry Applications Society (2013). He also received the Best Paper Award in the conferences IEEE ICEM 2012, IEEE SDEMPED 2011, and IEEE SDEMPED 2019 and “Highly Commended Recognition” of the IET Innovation Awards in 2014 and in 2016. He was the General Co-Chair of SDEMPED 2013 and is a member of the Steering Committee of IEEE SDEMPED. In 2016, he received the Medal of the Spanish Royal Academy of Engineering (Madrid, Spain) for his contributions in new techniques for predictive maintenance of electric motors. In 2018, he was awarded the prestigious “Nagamori Award” from the Nagamori Foundation (Kyoto, Japan). In 2019, he received the SDEMPED Diagnostic Achievement Award (Toulouse, France) for his contributions to the advanced diagnosis of electric motors. vii symmetry S S Editorial Introduction to Special Issue on Symmetry in Mechanical Engineering Grzegorz Krolczyk 1, * , Stanislaw Legutko 2 , Zhixiong Li 3 and Jose Alfonso Antonino Daviu 4 1 Faculty of Mechanical Engineering, Opole University of Technology, 76 Proszkowska St., 45-758 Opole, Poland 2 Faculty of Mechanical Engineering and Management, Poznan University of Technology, 3 Piotrowo Street, 60-965 Poznan, Poland; stanislaw.legutko@put.poznan.pl 3 School of Mechanical, Materials, Mechatronic and Biomedical Engineering, University of Wollongong, Wollongong, NSW 2522, Australia; zhixiong.li@ieee.org 4 Instituto Tecnol ó gico de la Energ í a, Universitat Polit è cnica de Val è ncia (UPV), Camino de Vera s / n, 46022 Valencia, Spain; joanda@die.upv.es * Correspondence: g.krolczyk@po.opole.pl Received: 22 January 2020; Accepted: 22 January 2020; Published: 5 February 2020 1. Introduction Recent advancements in mechanical engineering are an essential topic for discussion. The topics relating to mechanical engineering include the following: measurements of signals of shafts, springs, belts, bearings, gears, rotors, machine elements, vibration analysis, acoustic analysis, fault diagnosis, construction, analysis of machine operation, analysis of smart-material systems, integrated systems, stresses, analysis of deformations, analysis of mechanical properties, signal processing of mechanical systems, and rotor dynamics. Mechanical engineering deals with solid and fluid mechanics, rotation, movements, materials, and thermodynamics. 2. The Content This Special Issue, with 15 published articles, presents the topic “Symmetry in Mechanical Engineering”. The presented topic is interesting. It is categorized into eight di ff erent sections: • deformation; • stresses; • mechanical properties; • tribology; • thermodynamic; • measurement; • fault diagnosis; • machine; The authors of the first paper analysed the self-excited vibration of a thin spur gear caused by the initial transverse vibration [ 1 ]. The article [ 2 ] described a new technique to identify sectional deformation modes of the doubly symmetric thin-walled cross-section. The matching model of the dual mass flywheel and the power transmission by integration of the sensitivity analysis method was presented in the paper [ 3 ]. In the paper [ 4 ], the authors presented an approach for the active control of structural vibration. The authors of the paper [ 5 ] presented an approach to the correction of optical measurement results of fertilizer particles. Fault diagnosis of the rolling bearing using vibration signals was presented in [ 6 ]. A study of the e ff ect of medium viscosity on breakage parameters for wet Symmetry 2020 , 12 , 245; doi:10.3390 / sym12020245 www.mdpi.com / journal / symmetry 1 Symmetry 2020 , 12 , 245 grinding was presented in [ 7 ]. The monitoring method for the wear state of a tool using a convolutional bidirectional LSTM model was shown in the article [ 8 ]. The use of structural symmetries of a U12 engine using vibration analysis was presented in [9]. The Special Issue contains other interesting papers about mechanical engineering. The presented solutions, methods, and approaches can be improved and used in the future. Moreover, mechanical engineering is essential for fault diagnosis of machines [ 10 – 22 ] and the analysis of temperature [ 23 – 25 ]. The mechanical properties of materials are also investigated in the literature [ 26 – 28 ]. Acoustic analysis is also profitable for the analysis of the power transformer and detection of defects in on-load tap-changers [ 29 , 30 ]. Acoustically induced cavitation bubbles in insulating oil are also presented in the literature [31]. 3. Summary The development of techniques and methods related to mechanical engineering is growing every month. The described articles have contribution to mechanical engineering. The proposed research can find applications in factories, oil refineries, and mines. It is essential to develop new improved methods, techniques and devices related to mechanical engineering. Author Contributions: All the authors contributed equally to the conception of the idea, implementing and analyzing the experimental results, and writing the manuscript. All authors have read and agreed to the published version of the manuscript. Acknowledgments: The Guest Editors would like to thank all authors, reviewers and the editorial board of the MDPI Symmetry journal for their valuable contributions to this Special Issue. Conflicts of Interest: The author declares no conflict of interest. References 1. Wang, Y.; Ye, H.; Yang, L.; Tian, A. On the Existence of Self-Excited Vibration in Thin Spur Gears: A Theoretical Model for the Estimation of Damping by the Energy Method. Symmetry 2018 , 10 , 664. [CrossRef] 2. Zhang, L.; Ji, A.; Zhu, W.; Peng, L. On the Identification of Sectional Deformation Modes of Thin-Walled Structures with Doubly Symmetric Cross-Sections Based on the Shell-Like Deformation. Symmetry 2018 , 10 , 759. [CrossRef] 3. Chen, L.; Zhang, X.; Yan, Z.; Zeng, R. Matching Model of Dual Mass Flywheel and Power Transmission Based on the Structural Sensitivity Analysis Method. Symmetry 2019 , 11 , 187. [CrossRef] 4. Bai, L.; Feng, Y.-W.; Li, N.; Xue, X.-F.; Cao, Y. Data-Driven Adaptive Iterative Learning Method for Active Vibration Control Based on Imprecise Probability. Symmetry 2019 , 11 , 746. [CrossRef] 5. Laucka, A.; Adaskeviciute, V.; Andriukaitis, D. Research of the Equipment Self-Calibration Methods for Di ff erent Shape Fertilizers Particles Distribution by Size Using Image Processing Measurement Method. Symmetry 2019 , 11 , 838. [CrossRef] 6. Lu, L.; Yuan, Y.; Wang, H.; Zhao, X.; Zheng, J. A New Second-Order Tristable Stochastic Resonance Method for Fault Diagnosis. Symmetry 2019 , 11 , 965. [CrossRef] 7. Osorio, A.M.; Bustamante, M.O.; Restrepo, G.M.; Lopez, M.M.M.; Menendez-Aguado, J.M. A Study of the E ff ect of Medium Viscosity on Breakage Parameters for Wet Grinding. Symmetry 2019 , 11 , 1202. [CrossRef] 8. Chen, Q.; Xie, Q.; Yuan, Q.; Huang, H.; Li, Y. Research on a Real-Time Monitoring Method for the Wear State of a Tool Based on a Convolutional Bidirectional LSTM Model. Symmetry 2019 , 11 , 1233. [CrossRef] 9. Mihalcica, M.; Vlase, S.; Paun, M. The Use of Structural Symmetries of a U12 Engine in the Vibration Analysis of a Transmission. Symmetry 2019 , 11 , 1296. [CrossRef] 10. Irfan, M. A Novel Non-intrusive Method to Diagnose Bearings Surface Roughness Faults in Induction Motors. J. Fail. Anal. Prev. 2018 , 18 , 145–152. [CrossRef] 11. Caesarendra, W.; Tjahjowidodo, T.; Kosasih, B.; Tieu, A.K. Integrated Condition Monitoring and Prognosis Method for Incipient Defect Detection and Remaining Life Prediction of Low Speed Slew Bearings. Machines 2017 , 5 , 11. [CrossRef] 12. Glowacz, A. Recognition of acoustic signals of induction motor using FFT, SMOFS-10 and LSVM. Eksploat. I Niezawodn. Maint. Reliab. 2015 , 17 , 569–574. [CrossRef] 2 Symmetry 2020 , 12 , 245 13. Glowacz, A. Recognition of Acoustic Signals of Loaded Synchronous Motor Using FFT, MSAF-5 and LSVM. Arch. Acoust. 2015 , 40 , 197–203. [CrossRef] 14. Sikora, M.; Szczyrba, K.; Wrobel, L.; Michalak, M. Monitoring and maintenance of a gantry based on a wireless system for measurement and analysis of the vibration level. Eksploat. I Niezawodn. Maint. Reliab. 2019 , 21 , 341–350. [CrossRef] 15. Glowacz, A.; Glowacz, Z. Recognition of rotor damages in a DC motor using acoustic signals. Bull. Pol. Acad. Sci. Tech. Sci. 2017 , 65 , 187–194. [CrossRef] 16. Caesarendra, W.; Wijaya, T.; Tjahjowidodo, T.; Pappachan, B.K.; Wee, A.; Roslan, M.I. Adaptive neuro-fuzzy inference system for deburring stage classification and prediction for indirect quality monitoring. Appl. Soft Comput. 2018 , 72 , 565–578. [CrossRef] 17. Irfan, M.; Saad, N.; Ibrahim, R.; Asirvadam, V.S.; Alwadie, A. Analysis of distributed faults in inner and outer race of bearing via Park vector analysis method. Neural Comput. Appl. 2019 , 31 , 683–691. [CrossRef] 18. Glowacz, A.; Glowacz, W.; Kozik, J.; Piech, K.; Gutten, M.; Caesarendra, W.; Liu, H.; Brumercik, F.; Irfan, M.; Khan, Z.F. Detection of Deterioration of Three-phase Induction Motor using Vibration Signals. Meas. Sci. Rev. 2019 , 19 , 241–249. [CrossRef] 19. Glowacz, A. Acoustic fault analysis of three commutator motors. Mech. Syst. Signal Process. 2019 , 133 , 106226. [CrossRef] 20. Stief, A.; Ottewill, J.R.; Baranowski, J.; Orkisz, M. A PCA and Two-Stage Bayesian Sensor Fusion Approach for Diagnosing Electrical and Mechanical Faults in Induction Motors. IEEE Trans. Ind. Electron. 2019 , 66 , 9510–9520. [CrossRef] 21. Xi, W.K.; Li, Z.X.; Tian, Z.; Duan, Z.H. A feature extraction and visualization method for fault detection of marine diesel engines. Measurement 2018 , 116 , 429–437. [CrossRef] 22. Li, Z.X.; Wu, D.Z.; Hu, C.; Terpenny, J. An ensemble learning-based prognostic approach with degradation-dependent weights for remaining useful life prediction. Reliab. Eng. Syst. Saf. 2019 , 184 , 110–122. [CrossRef] 23. Chen, J.L.; Su, J.; Kochan, O.; Levkiv, M. Metrological Software Test for Simulating the Method of Determining the Thermocouple Error in Situ during Operation. Meas. Sci. Rev. 2018 , 18 , 52–58. [CrossRef] 24. Wang, J.F.; Kochan, O.; Przystupa, K.; Su, J. Information-measuring System to Study the Thermocouple with Controlled Temperature Field. Meas. Sci. Rev. 2019 , 19 , 161–169. [CrossRef] 25. Maruda, R.W.; Feldshtein, E.; Legutko, S.; Krolczyk, G.M. Analysis of Contact Phenomena and Heat Exchange in the Cutting Zone Under Minimum Quantity Cooling Lubrication conditions. Arab. J. Sci. Eng. 2016 , 41 , 661–668. [CrossRef] 26. Krolczyk, G.; Legutko, S.; Stoic, A. Influence of cutting parameters and conditions onto surface hardness of Duplex Stainless Steel after turning process. Teh. Vjesn. Tech. Gaz. 2013 , 20 , 1077–1080. 27. Kumar, R.; Chattopadhyaya, S.; Hloch, S.; Krolczyk, G.; Legutko, S. Wear characteristics and defects analysis of friction stir welded joint of aluminium alloy 6061-t6. Eksploat. I Niezawodn. Maint. Reliab. 2016 , 18 , 128–135. [CrossRef] 28. Krolczyk, J.B.; Krolczyk, G.M.; Legutko, S.; Napiorkowski, J.; Hloch, S.; Foltys, J.; Tama, E. Material flow optimization—A case study in automotive industry. Teh. Vjesn. Tech. Gaz. 2015 , 22 , 1447–1456. 29. Borucki, S.; Cichon, A.; Boczar, T.; Fracz, P. The Analysis of the Impact Point of the Power Transformer Core of Torsional Load on the Measured Parameters of the Vibroacoustics Signals. In Proceedings of the 2012 IEEE International Symposium on Electrical Insulation (ISEI), San Juan, PR, USA, 10–13 June 2012; pp. 175–178. 30. Cichon, A.; Fracz, P.; Boczar, T.; Zmarzly, D. Detection of Defects in On-Load Tap-Changers Using Acoustic Emission Method. In Proceedings of the 2012 IEEE International Symposium on Electrical Insulation (ISEI), San Juan, PR, USA, 10–13 June 2012; pp. 184–188. 31. Szmechta, M.; Zmarzly, D.; Boczar, T.; Lorenc, M. Acoustic Spectra of Ultrasound Induced Cavitations in Insulating Oils. Acta Phys. Pol. A 2008 , 114 , A231–A238. [CrossRef] © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http: // creativecommons.org / licenses / by / 4.0 / ). 3 symmetry S S Article A Novel Surface Inset Permanent Magnet Synchronous Motor for Electric Vehicles Baojun Qu 1,2 , Qingxin Yang 1 , Yongjian Li 1, *, Miguel Angel Sotelo 3 , Shilun Ma 4, * and Zhixiong Li 5,6 1 State Key Laboratory of Reliability and Intelligence of Electrical Equipment, Hebei University of Technology, Tianjin 300130, China; qbj22@sina.com (B.Q.); qxyang@tjpu.edu.cn (Q.Y.) 2 School of Mechanical Engineering, Shandong University of Technology, Zibo 255049, China 3 Department of Computer Engineering, University of Alcal á , 28801 Alcal á de Henares, Madrid, Spain; miguel.sotelo@uah.es 4 School of Transportation and Vehicle Engineering, Shandong University of Technology, Zibo 255049, China 5 Suzhou Automotive Research Institute, Tsinghua University, Suzhou 215134 China; zhixiong_li@uow.edu.au 6 School of Mechanical, Materials, Mechatronic and Biomedical Engineering, University of Wollongong, Wollongong, NSW 2522, Australia * Correspondence: liyongjian@hebut.edu.cn (Y.L.); msl@sdut.edu.cn (S.M.); Tel.: + 86-022-6043-5928 (Y.L.) Received: 17 December 2019; Accepted: 14 January 2020; Published: 19 January 2020 Abstract: Aiming to successfully meet the requirements of a large output torque and a wide range of flux weakening speed expansion in permanent magnet synchronous motors (PMSM) for electric vehicles, a novel surface insert permanent magnet synchronous motor (SIPMSM) is developed. The method of notching auxiliary slots between the magnetic poles in the rotor and unequal thickness magnetic poles is proposed to improve the performance of the motor. By analyzing the magnetic circuit characteristics of the novel SIPMSM, the notching auxiliary slots between the adjacent magnetic poles can a ff ect the q -axis inductance, and the shape of magnetic pole e ff ects the d-axis inductance of the motor. The combined action of the two factors not only weakens the cogging torque, but also improves the flux weakening capability of the motor. In this paper, the response surface methodology (RSM) is used to establish a mathematical model of the relationship between the structural parameters of the motor and the optimization objectives, and the optimal design of the motor is completed by solving the mathematical model. Experimental validation has been conducted to show the correctness and e ff ectiveness of the proposed SIPMSM. Keywords: electric vehicles; PMSM; auxiliary slot; response surface methodology 1. Introduction With the rapid development of the automobile industry, the two global problems of environmental pollution and energy shortage are becoming more and more serious. Under such a severe situation, many countries have begun to formulate plans to ban the sale of fuel vehicles. Electric vehicles are powered by electricity and have the advantages of zero emission, low noise and energy saving. Therefore, the development and promotion of electric vehicles is highly valued by governments all over the world [1]. As the core component of electric vehicle, the performance of the driving motor directly a ff ects the performance of electric vehicles. The research and development of high-performance electric vehicle drive motors has become one of the important factors restricting the development of electric vehicles [ 2 ]. The main types of drive motors for electric vehicles are brushless DC motors, induction motors, switched reluctance motors and permanent magnet synchronous motors (PMSM). The PMSM has a series of advantages, such as a simple structure, high e ffi ciency and excellent performance of Symmetry 2020 , 12 , 179; doi:10.3390 / sym12010179 www.mdpi.com / journal / symmetry 5 Symmetry 2020 , 12 , 179 flux-weakening speed expansion—making it more and more widely used as an electric vehicle drive motor in recent years [ 3 ]. However, for PMSM, the magnetic energy generated by the permanent magnet will interact with the stator slot, which will produce the slot e ff ect, increase the harmonic content in the air gap, and reduce the control accuracy of the drive system. Therefore, reducing the cogging torque and improving the performance of flux-weakening speed expansion are the important research contents of PMSM for electric vehicles. The cogging torque is reduced by changing the size and shape of the magnetic barrier of PMSM [ 4 ]. The auxiliary slot in the stator of the surface mounted PMSM is designed, and the mathematical model of the size of the auxiliary slot is established [ 5 , 6 ]. Through the analytical mathematical model, the cogging torque of the motor is optimized. A method of the axial combination of di ff erent permanent magnets in a rotor is proposed to reduce harmonic content in airgap and torque ripple [ 7 ]. Stator tooth modification is used to reduce the harmonic content of the teeth, thereby reducing the eddy current loss and vibration noise, and improving the e ffi ciency of the motor [ 8 – 10 ]. In summary, most of the structure optimization methods of PMSM are based on a single parameter or index. The optimization values are determined by the parameters, then the other structure parameters are optimized one by one, and, finally, the optimized parameters are combined. However, PMSM is di ffi cult to obtain the optimal results by optimizing a single index or parameter. The Taguchi method is used to optimize the shape of permanent magnet, which improves the e ffi ciency and reduces the torque ripple of the motor [ 11 ]. However, the optimal value obtained by this method can only be a combination of the levels used in the experiment, and the optimal result has certain limitations. A genetic algorithm is used to optimize the structural parameters of the interior asymmetric V type magnetic pole, which reduces the torque ripple of the motor [ 12 ]. However, the genetic algorithm can easily fall into the extreme point near the optimal solution in the later stage of calculation, so the results obtained by this method tend to approach the optimal solution rather than the optimal value. A particle swarm optimization algorithm is used to optimize the piecewise width and pole arc coe ffi cient of the permanent magnet of the surface mounted PMSM, which improves the output characteristics of the motor [ 13 ]. However, the disadvantage of the particle swarm optimization algorithm is that the optimal results can easily fall into the problem of local optimum [ 14 ]. The structure optimization of flexible rotor of hollow traveling wave ultrasonic motor is carried out based on response surface methodology (RSM), and the experiment results verify the correctness of the optimization method. The correctness of the optimization method is verified by the experiment. RSM is used to optimize the design of slotless permanent magnet linear synchronous motor to increase the average reasoning and reduce the torque ripple [ 15 ]. The accuracy of RSM design method is verified by experiments. The emergence of RSM is the result of the close connection of statistics, mathematics and computer science. Owing to this optimization method takes many factors into account and it establishes complex multi-dimensional surface which is closer to the actual situation than other optimization methods, response surface method is widely used, so RSM is widely used in practical engineering. In this paper, a novel surface insert permanent magnet synchronous motor (SIPMSM) is proposed, and the primary design parameters of the motor are determined by empirical formulas. By establishing the mathematical model of the cogging torque and inductance of the magnetic circuit of the SIPMSM, the influence factors of the cogging torque and flux-weakening speed expansion of the developed SIPMSM are deduced. Then the multi-objective mathematical model of the relationship between the structural parameters and the influencing factors of the motor is established by RSM. Optimal structural parameters are obtained by solving the mathematical model. Lastly, the traditional SIPMSM and the novel SIPMSM are trial-manufactured and compared. The reminders of this study are organized as follows. Section 2 describes the mathematical model of the proposed SIPMSM. Section 3 performs the parameter optimization for the SIPMSM. Experimental validation is carried out in Section 4 and conclusions are drawn in Section 5. 6 Symmetry 2020 , 12 , 179 2. The Proposed SIPMSM 2.1. Structure Design The shape of magnetic pole e ff ects the output characteristics of PMSM directly. The permanent magnet of typical SIPMSM is a tile shape with inner and outer arc centers at the same point—as shown in Figure 1. A PMSM with this kind of magnetic pole usually has the disadvantages of large cogging torque, large leakage and poor flux weakening capability [ 16 ]. Therefore, a novel SIPMSM is developed, as shown in Figure 2. The permanent magnet in the novel SIPMSM is an unequal thickness magnetic pole with di ff erent inner and outer radians, which results in the uneven distribution of the radial air-gap flux density and remarkable magnetic congregate e ff ect. In order to reduce the leakage flux and the high harmonic content in the air-gap, an auxiliary slot is notched in the rotor, as shown in Figure 3. ( a ) ( b ) Figure 1. Schematic diagram of typical SIPMSM and tile shape magnetic poles. ( a ) Schematic diagram of traditional SIPMSM; ( b ) Schematic diagram of tile shape magnetic poles. ( a ) E Figure 2. Schematic diagram of the novel SIPMSM and unequal thickness magnetic poles. ( a ) Schematic diagram of the novel SIPMSM; ( b ) Schematic diagram of unequal thickness magnetic poles. 7 Symmetry 2020 , 12 , 179 Figure 3. Schematic diagram of auxiliary slot in rotor. According to the performance requirements of PMSM for electric vehicles, the structure parameters of the novel SIPMSM are determined by using the empirical formula (see Table 1). Table 1. Initial Design Parameters of the novel SIPMSM. Parameters Numberical Value Parameters Numberical Value Rated voltage (V) 60 Rated speed (r / min) 3000 Rated power (kW) 3 Rated torque (N · m) 89 Number of pole pairs 4 Rotor outer diameter (mm) 30 Number of slots 24 Rator inner diameter (mm) 70 Stator inner diameter (mm) 90 Number of turns per slot 12 Stator outer diameter (mm) 145 Magnet width 29 Maximun magnet thickness (mm) 6 Slot width of rotor / mm 7 Minimum magnet thickness(mm) 4 Slot depth of rotor / mm 5 2.2. Infulence on Cogging Torque Compared with the traditional SIPMSM, the shape of the auxiliary slot and the unequal thickness of the permanent magnet between magnetic poles changes the harmonic content in the air gap flux density, which inevitably a ff ects the cogging torque. In this paper, a mathematical model of the cogging torque of the novel SIPMSM is established based on the energy method, and the influence of auxiliary slot in the rotor on the cogging torque is analyzed. The cogging torque is defined as the negative derivative of the magnetic field energy, relative to the position angle when the armature winding does not turn on the current [ 17 ]. The cogging torque of the permanent magnet motor can be expressed as T cog = − ∂ E ∂ α (1) where E is the energy of the magnetic field in the air-gap; B is the air-gap flux density; V is the volume of air-gap between stator and rotor; α is the relative position angle between stator and rotor. The energy of the air-gap magnetic field can be expressed as E = 1 2 μ 0 ∫ V B 2 ( θ , α ) dV (2) 8 Symmetry 2020 , 12 , 179 where θ is the angle between the air-gap magnetic density and the central line of the magnetic pole; μ 0 is vacuum permeability. The mathematical model of air-gap density distribution along the rotor surface with the unequal thickness magnetic pole is expressed as B ( θ , α ) = B r ( θ ) h m ′ ( θ ) h m ′ ( θ ) + δ ( θ , α ) (3) where, B r ( θ ) is the distribution of the remanence of permanent magnet along the circumferential direction; δ ( θ , α ) is the distribution of e ff ective air-gap length along the circumferential direction; h m ′ ( θ ) is the distribution of the direction of magnetization along the circumferential direction at the minimum thickness of permanent magnet. Substituting (2) into the E , we obtain E = 1 2 μ 0 ∫ V B 2 r ( θ )[ h m ′ ( θ ) h m ′ ( θ ) + δ ( θ , α ) ] 2 dV (4) Perform Fourier decomposition of B 2 r ( θ ) without considering the influence of the relative position of stator and rotor. B 2 r ( θ ) = B r 0 + ∞ ∑ n = 1 B rn cos 2 np θ = α p B 2 r + ∞ ∑ n = 1 2 n π B 2 r sin n α p π (5) where, p is the number of pole pairs and α p is polar arc coe ffi cient. By Fourier transform formula [ h ′ m ( θ ) h ′ m ( θ )+ δ ( θ , α ) ] , we can get [ h m ′ ( θ ) h m ′ ( θ ) + δ ( θ , α ) ] = G 0 + ∞ ∑ n = 1 G n cos nz θ (6) Substituted (2), (3), (4) and (5) into (1) and the expression of cogging torque is obtained by integrating the trigonometric functions within [0, 2 π ]. T cog ( α ) = π L a 4 μ 0 ( R 2 1 − h 2 ) ∞ ∑ n = 1 nG n B r nz 2 p sin nz (7) where L a is the axial length of the motor; R 1 is the outer arc radius of unequal thickness magnetic poles; h is the vertical distance from the center of the outer arc to the permanent magnet; n is an integer that makes ( nz / 2 p ) an integer. According to the triangle similarity theorem, one can get h 2 = R 2 1 − h 2 max d 2 4 h ′ 2 m (8) where h max is the maximum thickness of permanent magnet; h ′ m is the minimum thickness of permanent magnet; d is the width of permanent magnet. Substitute (8) into (7), then the cogging torque expression of the SIPMSM with unequal thickness magnetic poles can be described as T cog ( α ) = π L a h 2 max d 2 16 μ 0 h ′ 2 m ∞ ∑ n = 1 nG n B r nz 2 p sin nz (9) 9 Symmetry 2020 , 12 , 179 When the auxiliary slot is notched between the magnetic poles, the back EMF and magnetic field distribution of the motor will be greatly a ff ected, and the high-order harmonic content in the air-gap flux density will be reduced, so the cogging torque of the motor will be weakened [18]. When the number of auxiliary slots is k, the Fourier decomposition coe ffi cients of [ h ′ m h ′ m + δ ( θ , α ) ] in the [ − π z , π z ] can be expressed as: G n = 2 n π ( h ′ m h ′ m + X d ) 2 [ 2 cos n π 2 sin ( n π 2 − nz θ s 0 2 ) − 2 sin nz θ s 0 2 ∑ i = 1 cos 2 in π k + 1 ] (10) where θ s 0 is the width of auxiliary slot in the rotor, X d is auxiliary slot in rotor, and k = 1. By substituting (10) into (9), the expression of cogging torque with slots between magnetic poles of unequal thickness can be obtained as T cog ( α ) = π L a h 2 max d 2 4 μ 0 ( h ′ m + X d ) 2 ∞ ∑ n = 1 [ cos n π 2 sin ( n π 2 − nz θ s 0 2 ) − sin nz θ s 0 2 ∑ i = 1 cos in π ] B r nz 2 p sin nz (11) From (11), it can be seen that the structural parameters a ff ecting the cogging torque include the axial length of the motor, the number of pole pairs, the maximum thickness of permanent magnet, the minimum thickness of permanent magnet, the width of permanent magnet, the width of slotting, the depth of the auxiliary slot and the number of stator slots. This paper mainly studies the influence of the notching auxiliary slot between adjacent magnetic poles. 2.3. Influence of Notching Auxiliary Slots The auxiliary slots will increase the magnetic reluctance of the q axis magnetic circuit of SIPMSM. On the one hand, the di ff erence of inductance between the d and q axis will produce reluctance torque. On the other hand, increasing the d axis inductance or reducing the q axis inductance can improve the flux weakening capability of the motor [ 19 , 20 ]. This section mainly studies the influence of the shape of unequal thickness magnetic poles and size of auxiliary slots on the flux weakening capability of the motor. When the speed of PMSM exceeds the base speed, the phase current and phase voltage will reach the maximum value. In order to ensure that the limiting voltage does not exceed the limit voltage of the controller, the flux weakening control of PMSM is needed [ 21 , 22 ]. When the motor reaches the maximum speed, the stator current is used to weaken the magnetic field. The voltage amplitude is equal to the voltage limit of the controller. It can be seen that the d and q axis voltage in the rotating coordinate system can be expressed as: ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ u d = R s i d + d ψ d d t − ωψ q u q = R s i q + d ψ q d t + ωψ d (12) where u d is the voltage of d axis; u q is the voltage of q axis; R s is the resistance of armature winding; i d is the current of d axis; i q is the current of q axis; Ψ d is the flux linkage of d axis; Ψ q is the flux linkage of q axis; ω is the angular speed of rotor rotation. The change of current and flux linkage is zero when the motor is in steady state, so the steady state d and q axis voltage equation of the motor is obtained as: { u d = R s i d − ω L q i q u q = R s i q + ω ( L d i d + ψ PM ) (13) 10 Symmetry 2020 , 12 , 179 When the motor is controlled by flux weakening control, the base speed of the motor can be expressed as: ω 0 = u lim p √ ( ψ PM + L d i d ) 2 + ( L q i q ) 2 (14) where u lim is the limit voltage; ψ PM is the flux linkage of permanent magnet; L d is the d axis inductance of motor; L q is the q axis inductance of motor. When the output current of the inverter is all d axis demagnetizing current, that is i q = 0. The ideal maximum speed of the motor can be expressed as ω max = u lim ∣ ∣ ∣ ψ PM − L