For many years flared or dish-shaped grinding wheels have been utilized on gear grinding machines for finish grinding spiral bevel and hypoid gears. The grinding process comprises rotating a flared or dish-shaped grinding wheel about its axis while simultaneously oscillating the grinding wheel through an arc corresponding to the curvature of the desired longitudinal shape of the bevel or hypoid gear tooth. The primary advantage of this process is that sufficient clearance is provided to promote access of coolant between the grinding wheel and gear tooth resulting in the substantial elimination of overheating and damage to the tooth surfaces Detailed descriptions of this process can be found in the disclosures of U.S. Pat. No. 1,815,336 to Shlesinger et al. and U.S. Pat. No. 1,830,971 to Taylor.
According to known methods for grinding bevel or hypoid gear teeth, machines with flared or dish-shaped grinding wheels are used to simultaneously form-grind adjacent tooth sides of one member of a work gear pair, but the adjacent tooth sides of the other gear member are generated separately with a conventional cup-shaped grinding wheel. The separate treatment of the gear tooth sides in one member of a work gear pair has been required to appropriately mismatch the longitudinal tooth curvature of the form-ground member. Typically, a small amount of mismatch between mating tooth curves is desirable to permit some adjustment in the operating positions of the mating gears, however, the amount of mismatch associated with an attempt to simultaneously form adjacent gear teeth in both members of a mating gear by known methods, may greatly exceed desirable mismatch between mating tooth curves. Likewise, the formation of adjacent gear tooth sides of at least one member of a mating work gear pair in separate working steps or operations, as an alternative to simultaneously forming adjacent gear teeth in both members, is time consuming and may add considerable cost to the manufacture of the work gear pair.
Also according to known methods, longitudinal mismatch is provided between mating bevel and hypoid gear teeth by adjusting the radius of a cup-shaped grinding wheel, used to grind a tooth side in one member of a gear set, with respect to the radius of oscillation of a dish-shaped grinding wheel used to grind a mating tooth side of the other member of the pair. Longitudinal mismatch between mating tooth sides is determined by the difference between the respective radii of the cup-shaped grinding wheel and the arcuate path of oscillation of the dish-shaped grinding wheel. Thus, known mismatch between mating bevel and hypoid gear teeth may be represented as the separation between two arcs of different radii that are theoretically coincident at a single point. Under load, however, mating gear teeth tend to deform slightly and contact between the two surfaces spreads out over a portion of the tooth length.
One method of controlling the contact pattern between mating gear teeth is addressed in U.S. Pat. No. 1,982,050 to Gleason et al. wherein the grinding wheel follows a helical path as it moves across the face of a work gear. This helical motion is introduced by orienting the cup-shaped cutter axis perpendicular to the pitch line of the teeth and then adding motion along the cup-shaped cutter axis as the grinding wheel is oscillated through the curvature of a tooth. The helical motion maintains uniform inclinations between the active surfaces of the grinding wheel and the pitch surface of the gear and produces tooth profiles which control contact bias with mating gear tooth surfaces.
A method of controlling longitudinal mismatch is disclosed in U.S. Pat. No. 4,780,990 to Cody, Jr. et al. whereby motion along the cradle axis is added along with the oscillation of the grinding wheel about the cradle axis. The grinding wheel is reciprocated with respect to the work gear support along the cradle axis in a timed relationship with the oscillation of the grinding wheel and this timed relationship is controlled so that the rate of displacement of the work gear support changes with respect to the angular displacement of the grinding wheel about the cradle axis. This process, for example, enables the grinding wheel to be withdrawn at the ends of a tooth of a work gear to effectively control the radii of longitudinal tooth curvature of the work gear to appropriately mismatch the teeth of the work gear with the teeth of a mating member.
The above-described timed relationship may be further defined by a power series equation in which the displacement of the work gear is determined as a function of the angular displacement of the dish-shaped grinding wheel. Specific terms of the power series equation may be used to control relative machine motions to produce an improved form of mismatch between mating gear teeth. By controlling mismatch in such a manner, desirable contact characteristics are preserved between mating gear teeth over a wider range of loads and mounting adjustments.
However, there remains a need for motions in addition to the above-described motions along the cradle axis in order to more completely and precisely control the profile of gear teeth to thereby yield more accurate amounts and locations of desired mismatch and to enhance contact patterns between mating gear teeth.