Modeling and analysis of gear tooth crack growth under variable-amplitude loading

Abstract The purpose of this paper is to reveal the pattern of gear tooth crack growth under variable-amplitude loading. To this end, a nonlinear dynamic model is proposed to describe the gear tooth crack growth. The state variables of the model are crack length and crack opening stress. The dynamics of crack growth is modeled as a modified Paris equation based on the concept of crack closure. A nonlinear second-order autoregressive equation is developed to model the dynamic behavior of the crack opening stresses. The model parameters are estimated by means of a two-step estimation method because of relatively small sample size of crack length data for G6 gear tests. The model is also validated with the crack growth data of the G6 gear.

[1]  Zhihong Man,et al.  Optimal sinusoidal modelling of gear mesh vibration signals for gear diagnosis and prognosis , 2012 .

[2]  M. Shiratori,et al.  Analysis of stress intensity factors for surface cracks subject to arbitrarily distributed surface stresses. , 1985 .

[3]  Asok Ray,et al.  Fatigue crack growth under variable-amplitude loading: Part I – Model formulation in state-space setting , 2001 .

[4]  J. Schijve.  Fatigue Crack Growth under Variable Amplitude Loading , 1974 .

[5]  P. C. Paris,et al.  A Critical Analysis of Crack Propagation Laws , 1963 .

[6]  Asok Ray,et al.  State-space modeling of fatigue crack growth in ductile alloys☆ , 2000 .

[7]  E. Wolf.  Fatigue crack closure under cyclic tension , 1970 .

[8]  Ne Dowling.  Fatigue Life Prediction for Complex Load Versus Time Histories , 1983 .

[9]  Igor Rychlik,et al.  NOTE ON CYCLE COUNTS IN IRREGULAR LOADS , 1993 .

[10]  Zhihong Man,et al.  Statistical modeling of gear vibration signals and its application to detecting and diagnosing gear faults , 2014, Inf. Sci..

[11]  J. Newman.  A crack opening stress equation for fatigue crack growth , 1984 .

[12]  Weiping Hu,et al.  A Crack Growth Rate Conversion Module: Theory, Development, User Guide and Examples , 2007 .

[13]  俊郎 三好,et al.  任意分布力を受ける表面き裂の応力拡大係数の解析 : 第3報, 丸棒中の半だ円表面き裂に対する影響係数の解析とその応用 , 1987 .

[14]  J. Schijve,et al.  FATIGUE CRACK CLOSURE MEASUREMENT OF 2024-T3 SHEET SPECIMEN , 1994 .

[15]  C. Vavlitis.  Crack Growth Behaviour of Spur Gears: A Fractographic Analysis. , 1998 .

[16]  M. Ciavarella,et al.  A generalized Paris' law for fatigue crack growth , 2006 .

[17]  Robert L. Norton,et al.  Machine Design: An Integrated Approach , 1996 .

[18]  Asok Ray,et al.  Fatigue crack growth under variable-amplitude loading: Part II – Code development and model validation , 2001 .