Determination of the comprehensive stiffness of the gear teeth of the thickened gear teeth The comprehensive stiffness of the gear teeth is the comprehensive effect of the pairs of gear teeth participating in the meshing zone, mainly with the elastic deformation of the single teeth and the comprehensive elastic deformation of the single pair of teeth. And the degree of gear coincidence. The elastic deformation of a single tooth is an elastic deformation of the meshing tooth surface of a single tooth under load, including bending deformation, shear deformation and contact deformation. Here, the material mechanics method is applied to simplify the tooth to a variable-section cantilever beam on the elastic foundation. It is considered that the comprehensive elastic deformation of the meshing tooth is caused by the bending deformation and shear deformation of the cantilever beam and the additional deformation caused by the elastic deformation of the foundation. The contact surface deformation of the upper tooth surface is composed of three parts. However, for a thickened gear, since the displacement coefficient is different in different sections, the tooth thickness varies along the axial direction (if the displacement coefficient changes linearly, the tooth thickness also changes linearly in the axial direction), therefore, When the gear teeth of the thickened gear are simplified into a cantilever beam, not only the radial direction is a variable cross section, but the cylindrical gear is also a variable cross section. In the determination of the elastic deformation of the thickened gear teeth, it is necessary to improve on the basis of calculating the elastic deformation formula of the cylindrical gear teeth. The bending deformation and shear deformation of the toothed portion of the thickened gear wheel are used to calculate the deformation of the tooth portion. First, the tooth is divided into several small segments within the contact range, and each small segment is regarded as a cantilever beam, and the total contact point at the load contact point is The deformation is obtained by summing the various segments. Additional deformation due to the root (basic) elasticity of the thickened gear. In the calculation of the elastic deformation, it is assumed that the tooth is a rigidly supported cantilever beam. However, in reality, the root of the tooth is an elastic rim, so additional deformation of the meshing point due to the elasticity of the root rim must be considered. By simplifying the thickening gear teeth into cantilever beams with variable cross-section in both radial and axial directions, the calculation formula of the deformation of the tooth meshing points is derived, and the calculation of the comprehensive stiffness of the gear teeth of the thickening gears is solved for the first time. Through the programming process, the meshing integrated stiffness of a pair of internally meshed thickened gear teeth is calculated.
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