# Reverse engineering solution of machining parameters of spiral bevel gear machine tool

Spiral bevel gear is widely used in power transmission of aviation, vehicles and machine tools because of its stable transmission and strong bearing capacity. In the design and machining stage of spiral bevel gear tooth surface, the expected topological geometry of spiral bevel gear tooth surface is often obtained through the reverse engineering technology of machine tool machining parameters. The influence of machining parameters of machine tool on the machining error of spiral bevel gear is analyzed; Wang Xiaochun described the deviation between the theoretical tooth surface and the actual tooth surface through the difference surface, and proposed a method to modify the adjustment parameters of the machine tool by using the characteristic parameters of the difference surface; Lin, a Taiwanese scholar, takes the actual adjustment range of machine tool processing parameters as the constraint condition of the equation group, and uses the optimization method to correct the deviation of the tooth surface of spiral bevel gear; Based on the error sensitive coefficient matrix, the generalized inverse matrix method is used to solve the overdetermined equations. Due to the singularity of the coefficient matrix, the machining parameters of the machine tool are easy to exceed the actual adjustment range of the machine tool; Chen Shuhan proposed to solve the deviation equations by truncated singular value decomposition and L-curve method, which improved the accuracy of reverse solution to a certain extent.

(1) Aiming at the traditional spiral bevel gear milling machine with shaking table structure, the least square mathematical model of spiral bevel gear tooth surface approximation is established, and a Levenberg Marquardt iterative algorithm based on confidence region strategy is used to reverse the machining parameters of the machine tool.

(2) Compared with the generalized inverse matrix method and truncated singular value decomposition method, the L-M iterative algorithm can achieve high-precision approximation to the tooth surface of the target spiral bevel gear, and the machining parameters of the machine tool are in a reasonable range.

(3) The L-M iterative algorithm has high practical value for the accurate control of the tooth surface geometry of spiral bevel gear.

The inverse algorithm is the key factor to realize the reverse engineering solution of machine tool machining parameters. We study an iterative algorithm to deduce the theoretical spiral bevel gear tooth surface equation of small wheel based on differential geometry and spatial meshing theory; By comparing the deviation between the target tooth surface and the initial value tooth surface, the least square optimization model is established, and the Levenberg Mar quartt iterative algorithm based on the confidence region strategy (i.e. L-M algorithm) is used to inverse calculate the machining parameters of the small wheel machine tool approximated with the target spiral bevel gear tooth surface.

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