THE GENERATING SPACE FOR PARABOLIC MOTION ERROR SPIRAL BEVEL GEARS CUT BY THE GLEASON METHOD

Because of their inherent pseudo-conjugate natures, spiral bevel gears cut by the Gleason method basically transmit motion in a nonuniform manner. This motion nonuniformity, or motion error, repeated at each tooth engagement and at high speeds and loads, can cause vibrations in transmissions and contact-entry impact loads on gear teeth which affect the life of a gearset. It is customary to make small changes to machine settings in order to produce gear pairs with vastly improved kinematics. Therefore, machine setting changes must be carefully chosen such as to produce appropriate unloaded kinematical motion error that will cancel tooth bending deflection and contact deformation at a given load, and thus reduce noise and vibrations due to motion nonuniformity. This paper presents a study on the effects of machine settings, such as cutter tilt, machine center to back and offset, on the unloaded kinematical motion error. Applying CAD Boolean operations on the results, it is found that, for a given speed ratio, an infinite number of cutter tilt, work offset and machine center to back combinations will produce gear sets with convex parabolic motion error curve of any desired amplitude. Moreover, the amplitude of motion error curves can be linked directly to contact bias on the tooth flank. Thus, gear sets with any parabolic motion error in the unloaded state can be produced, such as to cancel tooth bending deflection and contact deformation in the loaded state.