Investigation on the influence of heat on the dynamic characteristics of a gear transmission system

Analytical calculation models for mesh stiffness and backlash of spur gears under temperature effects

“…The temperature effect on the mesh stiffness shown in Figure 7(a) illustrates that the thermal TMVS decreases compared with the traditionally elastic TMVS (red stippled line) both in the single-tooth region and the double-tooth region, which is the same result as the Reference 28. However, the simplified calculation model was used to calculate the elastic TVMS, which leads to a relatively larger stiffness value according to the Reference 28. In this paper, basically the same spur gear pair parameters are used but the stiffness value is smaller.…”

“…With the increases of tooth surface temperature, the mesh stiffness and the backlash variation decrease, the total deformation increases and the load sharing ratio remains unchanged. The temperature effect on the mesh stiffness shown in Figure 7(a) illustrates that the thermal TMVS decreases compared with the traditionally elastic TMVS (red stippled line) both in the single-tooth region and the double-tooth region, which is the same result as the Reference 28. However, the simplified calculation model was used to calculate the elastic TVMS, which leads to a relatively larger stiffness value according to the Reference 28.…”

“…However, the dynamic responses of the gear system under different temperature conditions can be obtained. Recently, Luo and Li 28,29 carried out the experiments based on the closed power flow gear testing machine and the temperature and vibration signals of the system at different times were recorded. The results are extracted out and displayed in Table 2.…”

“…Moreover, this thermal deflection and elastic deformation of gear pair in meshing are coupled rather than independent to each other and will further complicate the interaction among the gear teeth contact forces. As Luo and Li 28 defined in their paper, the thermal stiffness of the gear is the magnitude of the external load that can lead to unit amount of thermo-elastic coupling deformation, and the key is to find the method to calculate the thermo-elastic coupling deformation, which has not been analyzed in previous literatures. Considering that thermal deflection affects the gear geometric parameters, in this section, tooth profile thermal deflection amount is calculated and then the calculation method of elastic deformation of gear pair is proposed.…”

“…However, the fillet foundation stiffness was not considered in the above analytical expression and the critical angle affected by temperature was not correctly expressed. Luo and Li [28][29][30] proposed the meshing thermal stiffness of gear and introduced it into the system dynamics equation. However, the formula was based on a so-called "thermal load correction coefficient" which was obtained by FEM and the calculation method of the meshing elastic stiffness was also inaccurate.…”