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

• A nonlinear dynamic model is proposed to describe the gear tooth crack growth.
• The dynamics of crack growth is modeled as a modified Paris equation.
• The dynamics of crack opening stresses is modeled as a nonlinear AR equation.
• The model parameters are estimated by means of a two-step estimation method.
• The effectiveness of the model is validated with the G6 gear tooth crack data.

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.