According to the above-mentioned time-varying meshing stiffness equation of helical gear, the contact line of helical gear pair is used to replace the tooth width of helical gear into the equation. According to the boundary conditions, the time-varying meshing stiffness of sliced spur gear is offset and superimposed according to the helix angle. The total time-varying meshing stiffness of helical gear without fault can be solved as shown in Fig. 1 It can be seen that the gear teeth are meshed alternately by two and three teeth.
It can be seen that the variable cross-section cantilever beam model takes into account the base circle and the root circle of the gear. The gear meshing schematic diagram is shown in Fig. 2, and RF, Rb and RA are the radii of the tooth root circle, base circle and tooth top circle respectively It can be seen that there is a big difference between the radii of the base circle and the root circle of the sun gear. Therefore, when the base circle and the tooth root circle are not considered, the time-varying meshing stiffness curve obtained is 1.2 times of the time-varying meshing stiffness obtained by considering the part of the base circle and the tooth root circle.
At present, in many studies using potential energy method to solve time-varying meshing stiffness of gears, tooth width B is included in the five part stiffness expression, as shown in Figure 4 below In order to obtain the comprehensive meshing stiffness curve of meshing gear by using tooth width, the contact line expression is used to replace the tooth width to solve the time-varying meshing stiffness. The total time-varying meshing stiffness curve of helical gear obtained by solving the two different contact line expressions established in this paper is shown in Fig. 5.
It can be seen from Fig. 4 that the total time-varying meshing stiffness obtained by using the bending stiffness, radial compressive stiffness, shear stiffness, Hertz contact stiffness and matrix stiffness established by tooth width increases slightly compared with the total time-varying meshing stiffness when the contact line is considered It can be concluded that: the change trend of the total time-varying meshing stiffness obtained by using the contact line expression established by the contact degree is the same, but the total time-varying meshing stiffness value obtained by solving the contact line expression established by the contact degree is too large, and the meshing time in the three tooth meshing area is longer.
