Targeted tooth surface predesign and machine-tool settings identification methodology of spiral bevel gear considering ease-off

Abstract

A novel approach has been proposed to predesign to-be-modified tooth surface of spiral bevel gear with face milling manufacturing method, based on the preset of deviation of discretized points along normal direction. Five typical target geometry topographies have been established to achieve modification of directions of tooth trace, tooth profile and bias. Three typical solving algorithms, including linear and nonlinear methods, have been applied to identify the machine-tool settings to achieve the modification of geometry topography. The instability of numerical values resulting from ill-conditioning problem of the Jacobian matrix using singular value decomposition (SVD) has been investigated. Truncated singular value decomposition (TSVD) has been applied to void the ill-conditioned problem. The Levenberg-Marquardt (LM) was used to solve the machine-tool settings with iteration steps by controlling descent direction and iteration step size. The residual root-mean-square error (RMSE) of the modified tooth surface was computed to evaluate the degree of closeness between the modified tooth surface and predesigned target tooth surface. The results indicate that the maximum residual RMSE with LM algorithm is smaller than 2 μm, also far smaller than machining error. The solved machine-tool settings can be used for practical machining of spiral bevel gear.

Keywords

• spiral bevel gear
• tooth surface modification
• target tooth surface predesign
• machine-tool settings identification
• ease-off