Influence of the Bearing Thermal Deformation on Nonlinear Dynamic Characteristics of an Electric Drive Helical Gear System.

Xianghuan Liu,Xiaolan Hu,Defu Liu

doi:10.3390/s21010309

Xianghuan Liu, Xiaolan Hu + Show 1 more

Open Access

https://doi.org/10.3390/s21010309

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Abstract

Based on the statics and quasi-statics analysis methods, the thermal deformation calculation model of a deep-groove ball bearing was constructed for the helical gear transmission system of a high speed electric drive, and the radial and axial bearing stiffness values of the bearing were calculated under the thermal deformation in this study. The obtained radial and axial stiffness values were introduced into the established dynamics model of helical gear system, and the influence of changed bearing stiffness, resulting from the thermal deformation, on the nonlinear dynamic characteristics of gear pair was analyzed using the Runge–Kutta method. The results show that the axial and radial deformations of bearing occur due to the increase of working speed and temperature, in which the axial stiffness of bearing is improved but the radial stiffness is reduced. The decreasing degree of axial stiffness and the increasing degree of radial stiffness decrease with the gradually increasing working rotational speed. When considering the influence of thermal deformation on the bearing stiffness, the helical gear system will have nonlinear behaviors, such as single periodic, double periodic, and chaotic motion with the change of working speed. Therefore, in order to improve the nonlinear dynamic characteristics of high speed electric drive gear systems, the influence of bearing stiffness change on the dynamic performance of a gear system should be considered in the industrial applications.

Highlights

The transmission system is a core unit of automobile and train power systems, and it plays a critical role in the dynamic performance of automobile and high speed trains [1,2]
In order to improve the NVH performance of a high speed electric drive transmission system [27], this paper studied the thermal deformation of bearing under the high speed working conditions and the influence of bearing stiffness, which was changed by the thermal deformation [28,29], on the nonlinear dynamic characteristics of an electric drive helical gear transmission system
The gear dynamic model established in this paper only considers the movement along x, y, and z directions and the rotation around z direction, according to the axial and radial stiffness calculated by Equations (39) and (41), the bearing stiffness in the dynamic model can be established as:

Summary

Introduction

The transmission system is a core unit of automobile and train power systems, and it plays a critical role in the dynamic performance of automobile and high speed trains [1,2]. When analyzing the dynamic characteristics of a high speed electric drive gear transmission system, the axial and radial loads create a contact stress between the ball and the inner ring, or the outer ring, changing its contact angle, resulting in the bearing wear failure [23], and the temperature rise of bearing can change the dynamic stiffness [24], the dynamic response of the gear and its amplitude [25,26], which may affect the whole transmission. The bearing stiffness values under different thermal deformation conditions were calculated and introduced into the nonlinear dynamic model of the high speed electric drive helical gear transmission system. Combining the above equations and the specific parameters of bearing, the calorific values can be obtained under different rotating speeds and preload values with no-load and load conditions, as shown in Figure 6a,b, respectively, ignoring the influence of time-varying meshing force of gear on the bearing characteristics. Temperature Rise and Thermal Deformation of the Bearing Based on the Thermal Resistance

Network Method

Calculation of Bearing Stiffness under the Thermal Deformation Condition

Conclusions

Jb K k kv