Abstract
In this paper, the mathematical modeling of spiral bevel gear is built using gear meshing theory, differential geometry theory and principle of virtual conjugate base surface, and software package is also developed accordingly. The mesh point coordinates of convex and concave surfaces of spiral bevel gear are determined by the parameters of machine tool adjustment, gear cutter and spiral bevel gear, the strategies of measurement control and the corresponding solving algorithm are determined accordingly. 3D scanning probe system is calibrated using a new method. With 3D scanning probe system, the scanning path of tooth surface is planned. The method of following-motion continuous scanning of tooth surface is proposed based on constant force measurement through parametric spline surfaces and the corresponding fitting algorithm. In virtue of this method, the offsets of 3D scanning probe in three directions are controlled through the interpolation points generated by measurement data, which can avoid interruption in the scanning process and the problem of probe accidental collision. The practicability and effectiveness of the above proposed methods, which lays a foundation for measuring spiral bevel gear highly effectivity and highly precision.
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