# Determination of main parameters in bevel gear dynamic system model

The dynamic model of bevel gear transmission contains various geometric parameters, physical parameters and load parameters. The geometric parameters include the number of teeth of the bevel gear, the radius of the base circle and the length of the transmission shaft. These parameters have been determined at the beginning of the design of the bevel gear transmission system. The physical parameters include mass, stiffness and damping, which are calculated by relevant formulas after the geometric parameters of bevel gear transmission system are determined. The following is a detailed introduction to the determination of physical parameters in bevel gear transmission system.

1) Moment of inertia of bevel gear

The structure of aeroengine bevel gear is complex, which is difficult to be determined by the basic calculation formula of moment of inertia. Considering that the modeling of bevel gear structure is generally completed through three-dimensional drawing software (such as UG, Solidworks, etc.), the moment of inertia of aeroengine bevel gear can be obtained through the volume analysis function of three-dimensional drawing software.

2) Moment of inertia of shaft

When considering the moment of inertia of the bevel gear shaft itself, in the dynamic analysis model, in order to facilitate calculation, the moment of inertia of the shaft is superimposed on the bevel gear under the condition that the total kinetic energy and total center of mass remain unchanged. As shown in Figure 2, the moment of inertia of the two gears on the bevel gear shaft is I1 and I2. The distance from the center of mass to the left end of the bevel gear shaft is. According to the above conditions, the moment of inertia of the shaft can be equivalently distributed as follows.

Suppose the moment of inertia equivalent to bevel gear 1 is Ι 01, the moment of inertia assigned to bevel gear 2 is Ι 02, then: