Abstract: An approach based on CNC grinding machine for diagonal modified helical gear is proposed to reduce vibration and grinding errors. The deviations curve is designed and deviations surface of diagonal modified helical gear is fitted by 3 B-Spline based on tooth surface grid data established by the deviation curve. A Free-Form flank topographic correction method based on a six-axis CNC gear profile grinding machine with flat wheel is established according to principle of rack-cutter generated involutes gear and the kinematic relationships of the axes are derived based on equivalence of rack and flat wheel. An error correction model based on a sensitivity analysis is determined. Besides, each axis of the grinding machine are formulated as a six-degree polynomial and a disturbed polynomial coefficients on the topographic flank errors is developed by estimating whether the wheel contacts with the pinion. Using minimum squared error as the objective function, the particle swarm optimization algorithm are introduced to solve equations of the corrections , and the polynomial coefficients are ascertained, and this method of calculating results are stable and high precision. The result shows that slight variations in pressure angle, helix angle and generating angle along longitudinal tooth can get some specific diagonal modified tooth respectively, besides, diagonal modified tooth can then be efficiently ground by slightly adjusting six-axis movement according to the solved corrections and the validity of this method is numerically demonstrated using the six-axis CNC gear profile grinding machine, which effectively reduces grinding errors. The correctness of the theory and algorithm are supported by the sensitivity analysis of machine tool motion.

Key words: helical gear;diagram modified;computer numerical control grinding;free-form machining;flat wheel