Influences of gear design parameters on dynamic tooth loads and time-varying mesh stiffness of involute spur gears
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Sådhanå (2020)45:258 https://doi.org/10.1007/s12046-020-01488-x
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Influences of gear design parameters on dynamic tooth loads and time-varying mesh stiffness of involute spur gears ˘ UZ DOG ˘ AN1, FATIH KARPAT1,* , OSMAN KOPMAZ1 and STEPHEN EKWARO-OSIRE2 OG 1
Department of Mechanical Engineering, Bursa Uludag University, 16059 Gorukle, Bursa, Turkey Department of Mechanical Engineering, Texas Tech University, Lubbock, TX 79409, USA e-mail: [email protected]; [email protected]; [email protected]; [email protected]
2
MS received 21 April 2019; revised 4 July 2020; accepted 13 July 2020 Abstract. Gears are one of the most significant machine elements in power transmission due to the many advantages such as high load capacity, long life, and reliability. Due to the increasing power and speed values, the characteristics expected from the transmission elements are also increasing. Significant changes occur in the dynamic behavior of the gears at high speed due to the resonance. For this reason, determining the resonance frequencies is becoming an important issue for designers. This paper presents a method for determining the resonance regions of the gear system under different design parameters. The main purpose of this study is to examine the effects of different gear design parameters on spur gear dynamics. For this aim, the effects of these parameters on the mesh stiffness and contact ratio are examined, and the interaction of mesh stiffness, contact ratio, and dynamic response is presented. Different mesh stiffness calculation methods used to calculate timevarying mesh stiffness and a parametric gear dynamic model are proposed. To solve the equations of motions, a computer program is developed in MATLAB software. Five different design parameters, which are teeth number, pressure angle, reduction ratio, profile shifting factor, addendum factor, and damping ratio, are taken into consideration. The dynamic factor variation is calculated for 1600 rpm a constant pinion speed for each parameter for a single mesh period. Furthermore, the dynamic factor is calculated for the pinion speed between 400–30000 rpm and the frequency response and the resonance regions of the gear system are defined. As a result of the study, the profile shifting and the addendum factor are the most effective two parameters on the gear dynamics. Also, the contact ratio and mesh stiffness have a great effect on the dynamic response of the system. The methods decreasing dynamic load factors are also discussed at the end of the study. Keywords.
Dynamic analysis; spur gear; dynamic tooth loads; mesh stiffness.
1. Introduction Gears are the most common transmission elements in the industry. They are used from small watches to huge wind turbines. Nowadays, due to the increase in power and speed in the machines, the performances expected from the transmission organs are increasing too. For this reason, the issue of gear dynamics is gaining special importance. Designers must
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