Research on Real Tooth Surface Deviation Correction of Spiral Bevel Gear Based on Truncated Singular Value Decomposition

Abstract

According to structure of traditional milling machine, the tooth surface error identification model of forming processing spiral bevel gear is established by the 4×4 Denavit-Hartenberg homogeneous transformation matrix, the gear meshing theory and so on. In view of the present commonly used least squares method’s solution defects, the truncated singular value decomposition (TSVD) and the L curve method are proposed to solve the identification model and the solution method accuracy was verified by the example and experiment. The results show that the gear concave average error is at 0.01498mm before correction, and the average error will drop down to 0.00084mm after using this method correction, and the error corrects 94.4%. The gear convex average error is at 0.00846mm before correction and the average error will drop down to 0.00176mm after using this method correction and the error corrects 79.2%.

Compensation Method for Inclination Errors in Measurement Results of Tooth Surface of Spiral Bevel Gear

“…Peng et al researched the effects of eccentricity error on the gear dynamic responses and proposed a simple method using translational kinematic transmission error modification to reduce the computational time [24]. Using the truncated singular value decomposition and the L curve method, Chen and Yan solved the identification equation of the tooth surface deviation and compared it with the least square method to verify the validation of this method [25]. Xie et al presented a coordinate measuring method for the variable ratio noncircular bevel gear by coordinate measuring machine [26].…”