Three new models for evaluation of standard involute spur gear mesh stiffness


To transfer torque and speed from a rotating power source to another device, a transmission system is usually required. The most common and widely used transmission system is the gearbox. Various types of gearboxes have been designed so as to meet various application demands. The need to minimize failure rates of gears during operation and further improve on the quality during the design process, gear dynamics have been established. Existing literature has already established that the main internal excitation source of gear dynamics relates to time-varying mesh stiffness. Therefore, accurate evaluation of gear mesh stiffness has been deemed crucial for gear dynamic analysis. Presently, experimental approaches for analyzing gear dynamics have show auspicious attributes. Unfortunately, no published experimental plan is easy to implement as they demand intricate measurement devices or complex mathematical derivations.

Dr. Xihui Liang (currently at University of Manitoba) and Prof. Ming J. Zuo at University of Alberta in collaboration with Dr. Hongsheng Zhang at Harbin Institute of Technology and Prof. Yong Qin at Beijing Jiaotong University developed three new models for spur gear mesh stiffness evaluation. They anticipated that the proposed models would be effective in dealing with involute spur gears with tooth profile modification in the absence of tooth damage. They used the finite element analysis to evaluate the mesh stiffness of standard involute spur gears. Their work is currently published in the research journal, Mechanical Systems and Signal Processing.

The research technique used by the scientist commenced with a thorough description of the proposed model 1 for gear mesh stiffness evaluation. Next, the researchers presented the proposed model 2 which was used to evaluate the gear mesh stiffness by using angular deflections at different circumferential angles of an end surface circle of the gear bore. They then proceeded to the proposed model 3 which required the angular deflection at an arbitrary circumferential angle of an end surface circle of the gear bore but could only be used for gears with the same tooth profile among all teeth of a gear. Lastly, the accuracy of the proposed models was evaluated using finite element analysis.

The authors observed that the proposed model 1 could cope with involute spur gears with tooth damage, like tooth crack and pitting. Additionally, they noted that the proposed model 3 could not deal with involute gears having tooth damage. Lastly, the researchers realized that the proposed model 2 had an unknown capability of dealing with tooth damage.

In summary, the study presented three novel models for evaluating time-varying gear mesh stiffness. Their main observation was that the proposed model 1 gave a very accurate mesh stiffness result when compared with other existing models, but with an underlying assumption of the gear bore surface being rigid. Furthermore, finite element analysis and comparisons demonstrated that proposed models 2 and 3 had potential to yield accurate result in gear mesh stiffness evaluation and that they were insensitive to gear bore size. Altogether, a comparison with the proposed model 1, the maximum error caused by the proposed models 2 or 3 was seen to be 3.3%, which was quite small.

Three new models for evaluation of standard involute spur gear mesh stiffness - Advanced Engineering

About the author

Dr. Xihui Liang is an Assistant Professor in the Department of Mechanical Engineering, University of Manitoba, Canada. He received his BSc and MSc degrees in Mechanical Engineering from Shandong University, China, in 2007 and 2009, respectively, and the PhD degree in mechanical engineering from University of Alberta in early 2016. After that, he worked as a Postdoc Research Fellow at the University of Alberta for about two years. He has authored/coauthored about 30 articles in prestigious journals, such as IEEE Transactions on Industrial Electronics, Mechanical Systems and Signal Processing, and Reliability Engineering & System Safety.

His research interests include dynamic modeling of mechanical systems, condition monitoring, fault diagnostics and prognostics, reliability analysis, intelligent manufacturing and maintenance. More information can be found at Here

About the author

Dr. Hongsheng Zhang is an Assistant Professor with tenure in the School of Mechatronics Engineering, Harbin Institute of Technology, China. He received his BSc, MSc and PhD degrees in Mechanical Engineering from Harbin Institute of Technology, China, in 2003, 2005 and early 2010, respectively. After that, he worked as an Assistant Professor at the Harbin Institute of Technology. He has authored/coauthored about 10 articles in prestigious journals, such as Mechanical Systems and Signal Processing, Mechanism and Machine Theory, and Engineering Mechanics.

His research interests include Dynamics of Cranes and Mechanical System, Stability and Nonlinearity of Steel Structure, Nonlinear Structural Control and Health Monitoring.

About the author

Dr. Ming J Zuo received the Bachelor of Science degree in Agricultural Engineering in 1982 from Shandong Institute of Technology, China, and the Master of Science degree in 1986 and the Ph.D. degree in 1989 both in Industrial Engineering from Iowa State University, Ames, Iowa, U.S.A. He is currently Full Professor in the Department of Mechanical Engineering at the University of Alberta, Canada.

Department Editor of IIE Transactions, Regional Editor of International Journal of Strategic Engineering Asset Management, Regional Editor of Chinese Journal of Mechanical Engineering, and Editorial Board Member of Reliability Engineering and System Safety, Journal of Traffic and Transportation Engineering, International Journal of Quality, Reliability and Safety Engineering, and International Journal of Performability Engineering. He is Fellow of the Institute of Industrial and Systems Engineers (IISE), Fellow of the Engineering Institute of Canada (EIC), Founding Fellow of the International Society of Engineering Asset Management (ISEAM), and Senior Member of IEEE.

His research interests include system reliability analysis, maintenance modeling and optimization, signal processing, and fault diagnosis.

About the author

Dr. Yong Qin is Professor and Vice Dean of the State Key laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University. He received his BSc and MSc degrees in Transportation Automation and Control Engineering from Shanghai Railway University, China, in 1993 and 1996, respectively, and the Ph.D. degree from China Academy of Railway Sciences in Information Engineering and Control in 1999. He is a member of IEEE ITS and RS and senior member of IET. He has authored or coauthored more than 100 papers (SCI/EI), 1 ESI highly cited paper and 5 books, has 23 patents granted including 2 USA patents, also won 11 science and technology progress awards.

His research areas mainly focus on Prognostics and Health Management for railway transportation systems, transportation network safety and reliability, and rail operation planning and optimization.


Xihui Liang, Hongsheng Zhang, Ming J. Zuo, Yong Qin. Three new models for evaluation of standard involute spur gear mesh stiffness. Mechanical Systems and Signal Processing 101 (2018) page 424–434.

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