28. Application of evolution-based uncertainty design on gear
Boqiang Shi1, Yanhua Shen2, Guoqing Yu3, Guochen Duan4, Ruiyue Liu5
School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China
E-mail: firstname.lastname@example.org, email@example.com, firstname.lastname@example.org, email@example.com, firstname.lastname@example.org
Received 13 November 2016; accepted 14 November 2016
Abstract. The evolution of mechanical parameters, a factor affecting the mechanical reliability, has gathered more attention nowadays. However, studies on time varying uncertainty can hardly be found. A new method based on evolution-based uncertainty design (EBUD) is applied to the design of gear in this paper. Considering the wear evolution over the lifetime, a tooth wear’s time‑varying uncertainty model based on the continuous-time model and Ito lemma is established. Drift and volatility functions dependent on the drift rate and volatility rate of rotational speed and torque are used to express the time-varying uncertainty of tooth thickness. The method can predict the reliability and provide an instruction in reliability improving, maintenance and repair of the gear system.
Keywords: evolution-based uncertainty design, tooth wear, reliability.
 Ryazantsev A. A. Analysis of means of reliability and service life growth for open gear drive of ore‑pulverizing mills. Metallurgical and Mining Industry, Vol. 6, Issue 4, 2014, p. 6‑22.
 Starzhinsky Victor E., Soliterman Yuri L., Goman Arcadi M. Reliability prediction of gear transmissions. Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, American Society of Mechanical Engineers, New York, 2008, p. 165‑172.
 Netpu S., Srichandr P. Failure of a helical gear in a power plant. Engineering Failure Analysis, Vol. 32, Issue 9, 2013, p. 81‑90.
 Alemayehu F. M., Ekwaro-Osire S. Uncertainty considerations in the dynamic loading and failure of spur gear pairs. Journal of Mechanical Design, Transactions of the ASME, Vol. 135, Issue 8, 2013, p. 084501.
 Shi B. Q., Duan G. C., Shen Y. H., et al. Evolution-based uncertainty design for complex mechanical systems. Journal of Xi’an Jiaotong University, Vol. 49, Issue 3, 2015, p. 80‑86.
 Shi B. Q., Yan Y. Y., Fan H. F., et al. Mechanical design method with uncertain evolution. Journal of University of Science and Technology Beijing, Vol. 30, Issue 9, 2008, p. 1050‑1054.
 Yan Y. Y., Shi B. Q. Time dependent reliability analysis under uncertainty. Journal of Xi’an Jiao Tong University, Vol. 41, Issue 11, 2007, p. 1303‑1306.
 Li S. Lubrication and contact fatigue models for roller and gear contacts. The Ohio State University, 2009.
 Miryam B. S., Miguel P., Jose I. P. Calculation of tooth bending strength and surface durability of internal spur gear drives. Mechanism and Machine Theory, Vol. 95, 2016, p. 102‑113.
 Ruey S. Tsay Analysis of Financial Time Series. Posts and Telecom Press, Beijing, 2010.
 Cramer H. Mathematical Methods of Statistics. Princeton University Press, New Jersey, 1964.
Cite this article
Shi Boqiang, Shen Yanhua, Yu Guoqing, Duan Guochen, Liu Ruiyue Application of evolution‑based uncertainty design on gear. Mathematical Models in Engineering, Vol. 2, Issue 2, 2016, p. 143‑150.
Mathematical Models in Engineering. December 2016, Volume 2, Issue 2
© JVE International Ltd. ISSN Print 2351-5279, ISSN Online 2424-4627, Kaunas, Lithuania