Free-Form Flank Correction in Helical Gear Grinding Using a Five-Axis Computer Numerical Control Gear Profile Grinding Machine

Abstract

To reduce form grinding errors, this paper proposes a free-form flank topographic correction method based on a five-axis computer numerical control (CNC) gear profile grinding machine. This correction method is applied not only to the five-axis machine settings (during grinding) but also to the wheel profile (during wheel truing). To achieve free-form modification of the wheel profile, the wheel is formulated as B-spline curves using a curve fitting technique and then normal correction functions made up of four-degree polynomials are added into its working curves. Additionally, each axis of the grinding machine is formulated as a six-degree polynomial. Based on a sensitivity analysis of the polynomial coefficients (normal correction functions and CNC machine settings) on the ground tooth flank and the topographic flank errors, the corrections are solved using the least squares method. The ground tooth flank errors can then be efficiently reduced by slightly adjusting the wheel profile and five-axis movement according to the solved corrections. The validity of this flank correction method for helical gears is numerically demonstrated using the five-axis CNC gear profile grinding machine.