Based on the nominal stress method for fatigue life prediction, the model for predicting the fatigue life of mechanical structures under random cyclic load is developed in this paper. The uncertainty of the cyclic loads applied on the mechanical structures is analyzed. With the number of load application as the life index, the fatigue life prediction models of mechanical structures under random cyclic load are developed with the probability weighted method and the Miner linear cumulated damage rule, when the relationships between fatigue life and stress can be expressed as the exponential function and the power function, respectively. Finally, the models proposed are used to predict the fatigue life of train axis.

For the over-speed failure mode, the method for determining the reliable life parameter of turbine wheel of turbocharger is proposed in this paper. The shortage of design criteria based on conventional safety factor for turbine wheel with over-speed failure mode is analyzed. In order to embody the characteristics of structure and over-speed failure mode, the turbine wheel is taken as a series system consisting of several blade symmetrical components in the reliability modeling process. The time-reliability models of turbine wheel are derived and the relationship between the reliability and failure rate of turbine wheel and life parameter is studied. Then, the method for determining the reliable life parameter of turbine wheel of turbocharger with over-speed failure mode is proposed based on the reliability model and reliability curve. As long as the design parameters including the number of blades, speed, stress, and strength are given, the reliable life of turbine wheel of turbocharger with over-speed failure mode can be determined with the method proposed.