Sensitivity of system parameters to gear vibration amplitude

The sensitivity of parameters is very important to the dynamic design and optimization of gear system. There are three commonly used sensitivity analysis methods: adjoint matrix variable method, differential method and disturbance method. Each of the three methods has its own advantages and disadvantages. The model of adjoint matrix variable method is more complex, and it is suitable for sensitivity analysis when there are few variables.

Differential method has the characteristics of clear concept, which is especially suitable for sensitivity analysis when there are not many factors of system variables to be investigated. When there are too many factors to be investigated, the workload of derivative operation will become particularly heavy. Therefore, considering that there are many design parameters in non-circular gear, the perturbation method with simple concept and no complicated derivative operation is used to analyze the sensitivity of parameters. For each parameter in the system, the sensitivity calculation method is as follows:

Considering that each parameter in the gear system has different dimensions, for example, the order of magnitude of stiffness coefficient is usually about 10000000-100000000, while the dynamic response can only reach micron level sometimes. The difference of order of magnitude between various physical quantities will seriously affect the difficulty of calculation, which makes it impossible to directly carry out the lateral comparison of sensitivity.

Therefore, it is necessary to modify the sensitivity and introduce the relative sensitivity sR = s · Xi / F (x1, X2 Xn), which means the ratio of the change rate of the system performance index to the disturbance rate. Relative sensitivity refers to the sensitivity of all system parameters as the denominator and the sensitivity of each system parameter to be investigated as the numerator. The proportion of each variable to be investigated in the overall sensitivity is compared by solving the ratio of numerator and denominator. The sensitivity in the following paper refers to relative sensitivity.