B-spline Curve Fitting Method of the Formed Grinding Wheel Profile for Gears

Currently, straight lines or arcs are commonly used to approximate the profile of the formed grinding wheel for gears, resulting in discontinuity and fluctuations in the profile curve of the grinding wheel and even changing the concavity and convexity of the original profile curve, limiting the precision of the gears processed by the dressed formed grinding wheel. Besides, the dressing program is cumbersome and the amount of data is large. Aiming at this problem, a method of using B-spline curve to fit the profile of the formed grinding wheel is proposed, which is convenient for the numerical control system of the gear grinding machine to use the spline interpolation function to dress the formed grinding wheel. The method first calculates the profile of the involute helical gear formed grinding wheel. Feature points are then extracted from the data points of the grinding wheel profile and fitted with a B-spline curve. The fitting errors of the non-feature points are calculated using differential evolution algorithm. The data point with the maximum fitting error is added to the feature points. This process is iteratively repeated until the generated B-spline curve satisfies the fitting error requirement, fitting the profile of formed grinding wheel with fewer control points while meeting the specified error requirements. Simulation results show that the method can effectively fit the profile of the formed grinding wheel and the fitting error can meet the specified requirements.