Abstract: It is very important for the development of machinery industry to investigate the dynamic and gradual coupling reliability. This reason is that the part of mechanical equipment bears a dynamic load generally, has the random size, form and relative position of its geometrical elements due to the stochastic propriety of manufacturing process and more than 80% of the parts are subjected to gradual failure because of the deterioration of some parameters. The reliability problem of the linear and continuous system which bears dynamic load, is subjected to gradual failure due to strength deterioration and has several random parameters would be studied in this paper. According to the random dynamics theory of the linear and continuous system, the stochastic response is formulated and the stochastic alternating stress model is given. The uncertainty of the original strength and the evolution process of the strength deterioration are described by a random variable and a non-stationary Gamma process respectively. Then, the dynamic and gradual coupling state function and reliability of the linear and continuous system are modeled. The proposed reliability analysis method is employed to analyze the dynamic and gradual coupling reliability of the shaft torsional vibration system. The equivalent normalization and design checking point method are jointed to estimate the dynamic and gradual coupling reliability and the central difference method is used to analyze the reliability sensitivity. The practicality and validity of the proposed method are demonstrated by a numerical example. The results show that the presented dynamic and gradual coupling reliability analysis method could solve the reliability problem of t the linear and continuous system which bears dynamic load, is subjected to gradual failure due to strength deterioration and has several random parameters.

Key words: Strength deterioration, Continuous system, Dynamic reliability, Gradual reliability