A Contact Fatigue Assessment Model for Gears Considering Residual Stress and Inhomogeneities

doi:10.12141/j.issn.1000-565X.240278

Abstract

Abstract:

Gear surface treatment techniques such as gear grinding, shot peening and surface finishing may generate residual stress inside the material. Meanwhile, inhomogeneities are inevitably present in metal materials. Both residual stress and inhomogeneities have a significant impact on the contact fatigue life of gears. In order to effectively assess the contact fatigue risk of gears, this paper proposes a numerical model that comprehensively considers the combined effects of residual stress and inhomogeneities. This model uses the equivalent inclusion method to convert the inhomogeneities inside the gear into inclusions containing eigenstrains, and considers the coupling effect of inhomogeneities and residual stress in the displacement equation. During the research process, the stress distribution under the joint action of residual stress and inhomogeneities is computed, and the model is verified using the finite element method. The equivalent stress is calculated using Dang Van criterion, which is then incorporated into the Lundberg-Palmgren life model to find the minimum number of cycles, and the influence laws of residual stress and inhomogeneities on the gear’s contact fatigue life are analyzed. Analytical results show that inhomogeneities have a much greater influence on the contact fatigue life of gears than residual stress, and they predominantly determine the earliest meshing point of contact fatigue on the gear; and that, under the combined effects of residual tensile stress and inhomogeneities, the maximum stress in the sub-surface layer increases and shifts towards the material surface, making the gear more prone to contact fatigue.

Key words: gear, contact fatigue, residual stress, inhomogeneous material, risk assessment, Dang Van criterion

CLC Number:

TH117.1

LIU Yi, SUN Linlin, YANG Wenhan, GUO Hui, HOU Shengwen, LIU Geng. A Contact Fatigue Assessment Model for Gears Considering Residual Stress and Inhomogeneities[J]. Journal of South China University of Technology(Natural Science Edition), 2025, 53(7): 50-59.

Figures/Tables 12

Fig.1

Table 1

Basic parameters of gear"

参数名称	参数符号	参数值		参数符号	参数值
模数	m	3.2 mm	齿宽	b	35
压力角	$α$	25°	输入扭矩	T	540 N·m
大齿轮齿数	Z₁	41	齿面摩擦系数	$μ f$	0.15
小齿轮齿数	Z₂	40	杨氏模量	E	210 GPa
齿顶高系数	h $a *$	1	泊松比	$ν$	0.3
顶隙系数	c*	0.25

Table 1

Fig.2

Fig.3

Table 2

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Fig.9

Table 3

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点	等效半径/mm	最大法向载荷/N		等效半径/mm	最大法向载荷/N
1	12.11	101.4	6（节点）	12.23	139.8
2	12.16	113.6	7	12.22	139.4
3	12.21	128.0	8	12.19	139.3
4	12.22	132.8	9	12.16	139.0
5	12.22	140.4	10	12.12	120.7

残余应力情况	最小循环次数
残余应力情况	均质材料	非均质材料
有残余拉应力	5.45×10⁸	2.00×10⁸
有残余压应力	2.70×10⁹	4.03×10⁸
无残余应力	1.81×10⁹	3.30×10⁸