A flank correction face-milling method for bevel gears using a five-axis CNC machine

Face milling is extremely popular in industrial mass production of spiral bevel and hypoid gears because of its high productivity and the superior contact performance of the gear pairs it produces. This method, however, includes many cutting systems that must be implemented on numerous dedicated traditional machines with differently designed mechanisms. The five-axis CNC machine, in contrast, has enough degrees of freedom to handle all these cutting systems. As a result, the use of a general five-axis machine to produce face-milled bevel gears is attracting growing attention because it is so much more flexible than dedicated machines in small-scale diverse production. This paper therefore proposes a face-milling system with flank correction for bevel gears on a five-axis CNC machine. First, a mathematical model of the tooth surface is established based on a trunnion table type machine, after which the five coordinates of the five-axis machine are derived using the machine settings of a virtual cradle type bevel gear cutting machine. These five coordinates are degenerated to a function of the generating angle, and each coordinate is approximated as a polynomial in a Maclaurin series. Because flank topographic errors can be systematically reduced by adjusting the polynomial coefficients, a flank correction technology is developed based on a sensitivity analysis that investigates flank topographic deviations in terms of changes in coefficients. Based on this sensitivity matrix and the tooth surface errors measured, corrections are made to the five-axis coefficients using the least squares method. Finally, following a program accuracy check using NC verification software, several cutting experiments are performed to verify the correctness of the mathematical models.