Contents lists available at ScienceDirect Applied Acoustics journal homepage: www.elsevier.com/locate/apacoust Transmission error model-based optimisation of the geometric design parameters of an automotive transmission gearbox to reduce gear-rattle noise Mehmet Bozca Yıldız Technical University, Mechanical Engineering Faculty, 34349 Yildiz, Istanbul, Turkey ARTICLE INFO Keywords: Optimisation Gear rattle Torsional vibration Transmission error ABSTRACT The optimisation of gearbox geometric design parameters to reduce gear-rattle noise in an automotive trans- mission based on a transmission error model is presented. Towards this aim, a four-degree-of-freedom torsional vibration model for the geared system is obtained. Differential equations of the pinion gear-wheel gear system are obtained. The state-space forms of the differential equations are obtained. The transmission error of the gear system is calculated via a state-space model. An empirical model is used for rattle noise calculation for the five- speed gearbox. The transmission error is considered as the objective function, and bending stress, contact stress and the constant distance between gear centres are considered as constraint functions. By optimising the geo- metric parameters of the gearbox, such as the module, number of teeth, axial clearance, and backlash, it is possible to obtain a gear structure with high bending and contact strength and to minimise the torsional vi- bration, transmission error and gear-rattling noise. It is concluded through optimisation that minimising the transmission errors of the gearbox leads to reduced vibration and noise levels of the gearbox. It is determined that the optimised geometric design parameters reduce the calculated rattle noise level by 10% [dB] compared with the sample five-speed gearbox. Furthermore, a 95% reduction in transmission error results in a 12% de- crease in rattle noise. All optimised geometric design parameters are significant for the required constraints. 1. Introduction The optimisation of gearbox geometric design parameters to reduce gear-rattle noise in automotive transmissions based on a transmission error model is presented. The purpose of this study is to reduce gear- rattle noise by minimising the transmission error. Transmission errors are calculated based on torsional vibration equations via state-space equations. Transmission error results both from manufacturing inaccuracies and from design inaccuracies. Therefore, transmission error is an im- portant parameter during significant gear design. Gear motion causes gear-rattling noise and gear-clattering noise, and a low noise level is required for high comfort in the automotive design. Hence, reducing gear-rattling noise and gear-clattering noise in the automotive transmission is necessary to increase the comfort level in car design. The following results on rattling noise are presented in the litera- ture: The main transmission noises are rolling contact noises of gear pairs under load, which can be described as whining noises. Tooth rigidity changing with the meshing position causes the whining noises. A second kind of noise is gear-rattle noise, which may occur with auto- motive transmissions if unloaded gear wheels are excited by torsional vibration [1]. The maximum rotation between the two gear wheels indicates the beginning of the gear-rattle limit and the beginning of double-sided impacts. Gear rattle starts at the point where the rotation becomes greater than zero [1]. Gear-rattling noise in change-over gears of automobiles is an un- wanted phenomenon and causes comfort problems. The torsional vi- brations of the transmission system cause excitation at the entrance of the gearbox [2]. Gear-rattling and gear-clattering noises are caused by torsional vi- bration. The internal combustion engine causes this torsional vibration. If the transmission is in neutral, it is called gear-rattling noise. If the gear is under power, it is called clattering noise, which was concluded in [3]. Gear rattling and gear clattering are caused by the torsional vibra- tion of loose parts. Idler gears and synchroniser rings are loose parts in the neutral position, which was concluded in [3]. http://dx.doi.org/10.1016/j.apacoust.2017.10.005 Received 28 March 2017; Received in revised form 22 September 2017; Accepted 2 October 2017 E-mail address: mbozca@yildiz.edu.tr. Applied Acoustics 130 (2018) 247–259 0003-682X/ © 2017 Published by Elsevier Ltd. MARK