# Research on tooth profile modification of multistage gears

Profile modification is to modify the helical angle or axial profile of the gear according to the predetermined law according to the elastic deformation of the gear system after the force is applied. Its purpose is to ensure the uniform distribution of the load in the direction of tooth width. One of the key technical points of tooth profile modification is to calculate the elastic deformation of the system after the force is applied. Simplified empirical formula or theoretical analysis method can be used. Gonzalez Perez et al. Established the model of gear shaft with beam element, and considered the influence of gear shaft bending deformation on the meshing error of gear pair. Kim et al. Calculated the meshing tooth direction error caused by the comprehensive deformation of gear shaft, bearing and housing in Masta. Another key point of tooth profile modification is to calculate the load distribution on the tooth surface after the deformation of the support system. Slice method, influence (flexibility) coefficient method or contact finite element method can be used. Fang Zongde put forward a set of finite element program for helical gear. By automatically generating the finite element mesh and contact line of tooth surface, the flexibility matrix of the nodes on the contact line was calculated, and then considering the deformation of support system, the optimal tooth surface modification was obtained by mathematical programming method. Changshan et al. Considered the influence of matrix in the flexibility coefficient matrix and compiled a set of shape modification program combined with penalty function method. Mao established the meshing model of gear pair with fine contact element in the general finite element software, and solved the tooth surface stress under different modification parameters. Li used a commercial finite element software to calculate the stress distribution of the tooth surface with meshing error and modification. Xu et al. Calculated the tooth surface stress of spur gear pair in the general finite element software, and confirmed that there is still stress concentration at the edge of the tooth even if there is no meshing tooth alignment error.

There are some problems in the optimization of dynamic performance of gear system

① The optimization of the box structure mainly aims at improving the dynamic performance of the box itself. As the basis of supporting transmission system, the influence of the structure optimization on gear meshing and dynamic load has not been studied.

② Gear modification mainly takes the static deformation of the gear system as the input condition, but it is not consistent with the actual deformation of the gear system; the stress concentration effect at the edge of the tooth is generally ignored in the tooth profile modification, which leads to underestimation of the actual eccentric load of the gear pair; the Research of multi-stage gear system modification is only limited to the tooth profile modification, and does not involve three-dimensional topological modification.

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