Generation of a double-crowned involute helical gear with twist-free tooth flanks by a CNC hobbing machine with three synchronous axes

Abstract

In the conventional hobbing process, a double-crowned involute helical gear is generated by the hob cutter with parabolic-curve tooth profiles for the cross-profile crowning and varied the center distance between the hob and work gear for the longitudinal crowning. Therefore, to cut a double-crowned helical gear not only requires at least four synchronous axes and hob cutter regrinding (which increases production costs) but also induces twisted tooth flanks on the generated work gear. In this paper, I propose a hobbing method by applying a modified work gear rotation angle that enables double-crowning of involute helical gear's tooth flanks using a standard hob cutter and a computer numerical control (CNC) hobbing machine with only three synchronous axes. The proposed method has also verified by using two computer simulation examples to compare the meshing-conditions, contact ellipses, and transmission errors of the double-crowned gear pairs with that produced by applying the conventional hobbing method. Computer simulation results reveal the advantages of the proposed novel hobbing method.

Double modification of a rack cutter using a variable pressure angle and modulus

“…Vectors n g f and n p f are, respectively, the unit normal vector for the unmodified gear and the modified pinion in the fixed coordinate system S f . equation (19) and equation (20) give a system of five independent equations, because jn g f j À jn p f j ¼ 0. Parameter ˘g is given a specific value.…”

“…Parameter ˘g is given a specific value. Using the five independent equations that are generated using equation (19) and equation (20), five unknowns t g , t p , ˘p, θ p , and θ g are be solved simultaneously. The calculation of transmission error of the gear pair can be expressed as…”

“…Wu et al 18 determined the intersection angle of a gear hobbing tool and a gear as a linear function of the movement of the gear hobbing cutter to modify the gear flank. Tran 19 used a non-linear function to move the hobbing tool to modify the tooth flank of the gear. Tran et al 20 used a non-linear function and a rotation angle as the variables for the machining of gears for the hobbing process and used these for the longitudinal modification of the flank of helical gears.…”