# Sensitivity of system parameters to gear vibration amplitude

When calculating the sensitivity of each parameter, other parameters remain unchanged. According to the data of noncircular gears in table 3-1, the input speed, eccentricity, static transmission error, average meshing stiffness, amplitude ratio of meshing stiffness and sensitivity of load torque to peak to peak value of dynamic response of gears are calculated. The positive and negative values of SR respectively represent that the performance index increases or decreases with the increase of parameters

(1) In Figures 1, 3 and 5, the sensitivity increases with the increase of parameters ω 1, EI and α 1. In Figure 2, the sensitivity of ε to PPV increases first and then decreases with the increase of ε. In Fig. 5, the sensitivity of T2 to PPV increases rapidly when it is less than 7n · m, and then tends to a constant value. Among the six parameters, the sensitivity of kk0k0k0ppv in Fig. 3 is negative The absolute value of sensitivity first decreases and then tends to be constant, and the sensitivity changes gently in the whole process.

(2) When calculating the sensitivity of a parameter in the system, the value of other parameters will have a certain influence on the sensitivity of the parameter. For example, when the input speed ω 1 is increased, the sensitivity value of static transmission error will be greatly increased. In addition, the torque sensitivity curve will change from the fast rising trend from 0 to 1 in Fig. 5 to slow rise, so the analysis results of gear sensitivity have certain limitations, but this method has good guiding significance for vibration suppression of gear system with parameters determined.

For the reducer variable speed integrated gear, the sensitivity of the six parameters to vibration is shown in Fig. 6, in which the abscissa number represents the parameter ω 1, ε, EI, K0, α 1 and T2 respectively, and the ordinate represents the sensitivity of the six parameters to PPV. It can be seen that at this time, the influence of ε, K0, α 1 and T2 on the vibration is greater. Reducing the value of ε, α 1 and T2 or increasing K0 is an effective method to suppress the vibration of the gear, while increasing the accuracy of the gear or reducing the rotational speed has no obvious effect on the vibration suppression.

in summary,

(1) The time-varying transient center excitation in the reducer variable speed integrated gear transmission is a kind of low-frequency excitation, which belongs to the parametric excitation type. It is combined with high frequency meshing stiffness excitation, which makes the gear produce nonlinear vibration with complex frequency components. The frequency components include fundamental frequency, double frequency and combined frequency.

(2) With the increase of input speed, gear eccentricity, error amplitude, meshing stiffness amplitude ratio and torque, the vibration of non-circular gear will be intensified, while with the increase of average meshing stiffness, the vibration of gear will be reduced; under high-speed condition, the dynamic performance of gear will deteriorate rapidly; the dynamic performance of the gear can be improved by tooth modification.

(3) The sensitivity of each parameter to the vibration response changes with its own value. The increase of input speed, error amplitude and meshing stiffness amplitude will increase the corresponding sensitivity; the sensitivity of eccentricity will first increase and then decrease with the increase of input speed; under light load, the sensitivity of load torque will increase rapidly with the increase of load, while under heavy load, the sensitivity of load torque will remain constant; the mean value of meshing stiffness will be increased With the increase of the sensitivity, the absolute value of sensitivity first decreases and then tends to be constant.

(4) Therefore, the sensitivity analysis results are very suitable for dynamic performance optimization of gear system with parameters determined.

The effects of system parameters, such as input speed, eccentricity, static transmission error, average meshing stiffness, amplitude ratio of meshing stiffness and load torque, on the vibration characteristics of reducer variable speed integrated gear are analyzed. On this basis, the sensitivity of system parameters to gear vibration amplitude is studied. The results show that there are complex multi frequency responses of gears under the excitation of compound parameters. The response amplitude increases with the increase of rotating speed, eccentricity, error amplitude, meshing stiffness amplitude ratio and load torque. The parameter values of gear system have great influence on the sensitivity values of itself and other parameters. 