Controlled relative radius of curvature forged bevel gears with involute section

A method of fabricating forging dies to forge mating bevel gears, the method comprising:

• cutting multiple surfaces of a first forging die, the multiple surfaces of the first forging die cooperating to define a first cavity that is configured to form a pinion gear having a plurality of pinion gear teeth that are formed with a curvature on each of the sides of the pinion gear teeth wherein the curvature on the pinion gear teeth is formed to include a first involute section contained within a first controlled relative radius of curvature section, wherein the first controlled relative radius of curvature section that is not included in the first involute section is defined by a first radius of curvature, wherein the first radius of curvature has a minimum value at a first location that is closest to a pitch line of the pinion gear teeth, wherein the first radius of curvature has a value that increases with increasing distance from the first location where the first radius of curvature has its minimum value, wherein the first radius of curvature provides gear teeth formed with a pinion dedendum below the pitch line of the pinion gear teeth and a pinion addendum above the pitch line of the pinion gear teeth, wherein an exterior surface of the pinion dedendum is convex in shape, wherein an exterior surface of the pinion addendum is convex in shape, and wherein the exterior surfaces of the pinion dedundum and addendum are separated by the first involute section, wherein the first involute section is defined by a second radius of curvature, wherein the second radius of curvature has a minimum value that is closest to a bottom land of the pinion gear teeth and wherein a value of the second radius of curvature increases with increasing distance away from the bottom land of the pinion gear teeth;
• and
• cutting multiple surfaces of a second forging die, the multiple surfaces of the second forging die cooperating to form a second cavity that is configured to form a side gear having a plurality of side gear teeth that are formed with a curvature on each of the sides of the side gear teeth, wherein the curvature on the side gear teeth is formed to include a second involute section contained within a second controlled relative radius of curvature section, wherein the second controlled relative radius of curvature section that is not included in the second involute section is defined by a third radius of curvature, wherein the third radius of curvature has a minimum value of radius of curvature at a second location that is closest to a pitch line of the side gear teeth, wherein the third radius of curvature has a value that increases from the minimum value at the second location with increasing distance away from the second location where the second radius of curvature has its minimum value, wherein the third radius of curvature provides gear teeth formed with a side gear dedendum below the pitch line of the side gear teeth and a side gear addendum above the pitch line of the side gear teeth, wherein an exterior surface of the side gear dedendum is convex in shape, wherein an exterior surface of the side gear addendum is convex in shape, and wherein the exterior surfaces of the side gear dedundum and addendum are separated by the second involute section, wherein the second involute section is defined by a fourth radius of curvature, wherein the fourth radius of curvature has a minimum value of radius of curvature at a location that is closest to a bottom land of the side gear teeth, and wherein a value of the fourth radius of curvature increases with increasing distance away from the bottom land of the side gear teeth.

Mating bevel gears comprising:

• a pinion gear having a body that rotates about an axis;
• a side gear having a body that rotates about an axis that intersects the axis of the pinion gear;
• the pinion gear having a plurality of pinion gear teeth, the pinion gear teeth having a side that defines a curvature with an involute section through which a pitch line extends and a parabolic shape between the pinion gear teeth;
• and
• side gear teeth of the side gear having a side defining a curvature with an involute section through which a pitch line extends and a parabolic shape between the side gear teeth,
• wherein the curvatures on the pinion and the side gear teeth cooperatively define a controlled relative radius of curvature section except where the involute sections are located, the controlled relative radius of curvature section defines a sum of values of radius of curvature at a point of contact between the curvatures of the pinion gear teeth and the side gear teeth, the sum having a constant or decreasing value.

A method of fabricating forging dies to forge mating bevel gears, the method comprising:

• programming a control system to establish a cutting program for a forging die configured to form a pinion gear of the mating bevel gears having pinion gear teeth;
• programming the control system to establish a cutting program for a forging die configured to form a side gear of the mating bevel gears having side gear teeth each;
• cutting multiple surfaces on the forging die for the pinion gear with the cutting program that are configured to form a curvature on each of the sides of the pinion gear teeth having a minimum value of radius of curvature closest to the pitch line and an increasing value of radius of curvature toward the top land and the bottom land of the pinion gear teeth that is interrupted by an involute section at the pitch line having a minimum value of radius of curvature closest to the bottom land and an increasing value of radius of curvature toward the top land;
• and
• cutting multiple surfaces on the forging die for the side gear with the cutting program that are configured to form a curvature on each of the sides of the side gear teeth having a minimum value of radius of curvature closest to the pitch line and an increasing value of radius of curvature toward the top land and the bottom land of the side gear teeth that is interrupted by an involute section at the pitch line having a minimum value of radius of curvature closest to the bottom land and an increasing value of radius of curvature toward the top land of the side gear teeth.