Research on Algorithms of Spiral Bevel Gear NC Machining and Tooth Surfaces Contacting Points Solution

Based on maintenance of the movement relationship between the cutter head and the work gear unchanged in the process of spiral bevel gear machining,the NC generation of gear cutting is realized by means of the matrix transformation.As sophisticated calculation of the transformation is hard to implement in each sampling time of NC machining,the coordinated motion of NC coordinate axes is expressed as quintic parametric spline functions,which use the rotation angle of the work gear as the parameter,and the real-time and accuracy of interpolation are guaranteed.The constrained optimization method of three design variables is established to obtain contacting points of gear tooth surfaces,which are acquired by solving nonlinear equations sets traditionally.The condition of normal coincidence is simplified and the object function of the equal position vectors of mating gears is established.An example is given to demonstrate and verify the methods.