Methods for generating gear teeth of a double involute pinion-face gear drive system

1. A method of generating teeth of a double involute pinion on a conventional hobbing machine that mesh with face gear teeth of a double involute pinion-face gear drive system, comprising the steps of:

providing a double involute pinion blank, of cylindrical shape, having a blank face width center plane and a blank axis perpendicular to said blank face width center plane, that rotates continuously about said blank axis,

providing a face hob tool having a tool axis and a tool pitch plane perpendicular to said tool axis within which a tool base circle identical to the teeth base circle of radius rb of said face gear is defined, including a plurality of equi-spaced rack cutters, with cutting teeth of symmetrical or asymmetrical type projecting from one plane face of said face hob tool body in a direction of said tool axis and arranged such that lines of intersection between said tool pitch plane and rake surfaces of said cutting teeth are tangent to a tool circle concentric to said tool base circle,

positioning said face hob tool offset from and perpendicular to said blank axis at a predetermined center distance of said double involute pinion-face gear drive system, such that a teeth width middle section plane of said double involute pinion blank is tangent to said tool base circle and, at a start machining position, said face hob tool is adjacent but not in generating engagement with said double involute pinion blank,

rotating said face hob tool continuously about said tool axis in timed relation with said continuous rotation of said double involute pinion blank about said blank axis, while simultaneously and continuously radially feeding said face hob tool toward an outer peripheral cylindrical surface of said double involute pinion blank along the direction of said tool axis and into generating engagement with said double involute pinion blank,

whereby said face hob tool, of modified involute type, is specifically designed such that a concentric circle of said face hob tool has its radius equal to either (rb+p) or (rb−p) where p is the amount of involute modification of said face gear teeth, generates double involute external teeth of constant height and circular pitch, of symmetrical or asymmetrical type, on an outer cylindrical surface of said double involute pinion blank, shaped in form of a normal involute in their profile direction and curved in their longitudinal direction in form of an either shortened or an extended involute curve of said face gear base circle, respectively.

2. The method of generating a double involute pinion of claim 1 wherein said face hob tool, of normal involute type, having said cutting teeth of symmetrical type, is specifically designed such that said concentric circle of said face hob tool has its radius equal to face gear circle radius rb, generates double involute teeth of symmetrical type on said double involute pinion blank, shaped in form of a normal involute in a profile direction and curved in a longitudinal direction in form of a normal involute curve of said face gear base circle.

3. The method of generating a double involute pinion of claim 1 wherein said face hob tool, of normal involute type, having said cutting teeth of asymmetrical type, is specifically designed such that said face hob tool concentric circle has its radius equal to face gear circle radius rb, generates double involute teeth of asymmetrical type on said double involute pinion blank, shaped in a form of a normal involute in a profile direction and curved in a longitudinal direction in form of a normal involute curve of said face gear base circle.

4. A method of generating teeth with a hobbing machine on a double involute pinion that mesh with face gear teeth of a double involute pinion-face gear drive system, comprising the steps of:

providing a double involute cylindrical pinion blank having an outer surface, a blank face width center plane and a blank axis perpendicular to said blank face width center plane,

rotating said double involute cylindrical pinion blank continuously about said blank axis,

providing a face hob tool having a tool axis and a tool pitch plane perpendicular to said tool axis within which a tool base circle identical to a teeth base circle of radius rb of said face gear is defined, including a plurality of equally spaced rack cutters, with cutting teeth of symmetrical or asymmetrical type projecting from one plane face of said face hob tool in a direction of said tool axis and arranged such that lines of intersection between said tool pitch plane and rake surfaces of said cutting teeth are tangent to a tool circle concentric to said tool base circle,

positioning said face hob tool offset from and perpendicular to said blank axis at a predetermined center distance of said double involute pinion-face gear drive system, such that a teeth width middle section plane of said double involute pinion blank is tangent to said tool base circle and, at an initial machining position, said face hob tool is adjacent but not in engagement with said double involute pinion blank,

rotating said face hob tool continuously about said tool axis in timed relation with said continuous rotation of said double involute pinion blank while simultaneously and continuously radially feeding said face hob tool toward said outer surface of said double involute pinion blank along the direction of said tool axis and into engagement with said double involute pinion blank,

whereby said face hob tool is configured so that a concentric circle of said face hob tool has its radius equal to either (rb+p) or (rb−p) where p is the amount of involute modification of said face gear teeth which generates double involute external teeth of constant height and circular pitch on said outer surface of said double involute pinion blank which are shaped in a normal involute in a profile direction and curved in a longitudinal direction.

5. The method of generating a double involute pinion of claim 4 wherein said face hob tool is of normal involute type and has cutting teeth of symmetrical type which are configured so that said concentric circle of said face hob tool has its radius equal to face gear circle radius rb, generates double involute teeth of symmetrical type on said double involute pinion blank, are shaped in a normal involute in a profile direction and curved in a longitudinal direction.

6. The method of generating a double involute pinion of claim 4 wherein said face hob tool of normal involute type has cutting teeth of asymmetrical type, configured such that said face hob tool concentric circle has its radius equal to face gear circle radius rb, generates double involute teeth of asymmetrical type on said double involute pinion blank, shaped in a normal involute in their profile direction and curved in a longitudinal direction.

7. A method of generating teeth with a hobbing machine on a double involute pinion that mesh with face gear teeth of a double involute pinion-face gear drive system, comprising the steps of:

providing a double involute cylindrical pinion blank having an outer surface, a blank face width center plane and a blank axis perpendicular to said blank face width center plane,

rotating said double involute cylindrical pinion blank continuously about said blank axis,

providing a face hob tool having a tool axis and a tool pitch plane perpendicular to said tool axis within which a tool base circle identical to a teeth base circle of radius rb of said face gear is defined, including a plurality of equally spaced rack cutters, with cutting teeth projecting from one plane face of said face hob tool in a direction of said tool axis and arranged such that lines of intersection between said tool pitch plane and rake surfaces of said cutting teeth are tangent to a tool circle concentric to said tool base circle,

positioning said face hob tool offset from and perpendicular to said blank axis at a predetermined center distance of said double involute pinion-face gear drive system, such that a teeth width middle section plane of said double involute pinion blank is tangent to said tool base circle and, at an initial machining position, said face hob tool is adjacent but not in engagement with said double involute pinion blank,

rotating said face hob tool continuously about said tool axis in timed relation with said continuous rotation of said double involute pinion blank while simultaneously and continuously radially feeding said face hob tool toward said outer surface of said double involute pinion blank along the direction of said tool axis and into engagement with said double involute pinion blank,

whereby said face hob tool is configured so that a concentric circle of said face hob tool has its radius equal to either (rb+p) or (rb−p) where p is the amount of involute modification of said face gear teeth which generates double involute external teeth of constant height and circular pitch on said outer surface of said double involute pinion blank which are shaped in a normal involute in a profile direction and curved in a longitudinal direction.

8. The method of generating a double involute pinion of claim 7 wherein said face hob tool is of normal involute type and has cutting teeth of symmetrical type which are configured so that said concentric circle of said face hob tool has its radius equal to face gear circle radius rb, generates double involute teeth of symmetrical type on said double involute pinion blank, are shaped in a normal involute in a profile direction and curved in a longitudinal direction.

9. The method of generating a double involute pinion of claim 7 wherein said face hob tool of normal involute type has cutting teeth of asymmetrical type, configured such that said face hob tool concentric circle has its radius equal to face gear circle radius rb, generates double involute teeth of asymmetrical type on said double involute pinion blank, shaped in a normal involute in their profile direction and curved in a longitudinal direction.