Firstly, the reliability of gear nonlinear vibration is defined as the probability that the vibration displacement, vibration velocity and vibration acceleration response of gear nonlinear vibration exceed the specified threshold number of times within a specified time and under specified conditions.
According to the different task conditions of gears, the specified threshold in the above definition can be regarded as random variables. For example, for the gear mechanism in machine tool, when the machine tool processes different types of workpieces (especially single piece and small batch condition), due to the randomness of precision requirements, the requirements for various vibration indexes of gears are also different. In this case, when analyzing the reliability of nonlinear vibration within the service life of gears, the threshold value of nonlinear vibration response can be regarded as random variable.
According to the above definition, a reliability analysis framework of gear nonlinear vibration based on series system model is proposed.