Differential Gear Tooth Geometry for Pinion Root Stress Relief
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Differential gear mechanisms with reduced pinion gear diameter experience increased stress on tooth roots during high torque transmission, reducing durability due to the shape of the pinion tooth bottom surface.
Innovation Solution
Inclining the tooth tip surface of crown gear teeth and pinion tooth bottom surfaces to increase the thickness of pinion gears inward of the outer periphery, allowing the pinion tooth bottom surface to be parallel to the contact line with crown gear teeth, thereby reducing stress on the tooth roots.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Volume of moving object
If pinion gears are reduced in diameter to make the mechanism compact, then the axial length of crown gears is reduced, but stress on pinion tooth roots increases during high torque transmission
Solution Approach 1:
The pinion tooth bottom surface is designed with different geometries in different regions: an inclined portion in the outer peripheral region and a substantially flat portion in the inner peripheral region. This local differentiation allows the outer region to increase thickness and reduce stress while maintaining compact overall dimensions, resolving the contradiction between compact size and durability.
2Volume of moving object
If the thickness of pinion gear portion inward of pinion tooth bottom surface is increased, then the distance between pinion tooth bottom surface and inner peripheral surface is increased, but stress on tooth roots increases due to meshing with crown gear teeth
Solution Approach 1:
The pinion tooth bottom surface employs asymmetric geometry with an inclined portion on the outer side and a flat portion on the inner side. The inclined portion increases thickness at the outer periphery where stress concentration occurs, while the flat portion maintains appropriate thickness at the inner periphery, creating an asymmetric distribution that reduces stress without excessive material addition.
Data Source
AI summary
A differential gear mechanism in which when a plurality of contact lines between a gear tooth and a pinion tooth is defined on either a tooth surface of the gear tooth of a crown gear or a tooth surface of the pinion tooth of a pinion gear at a predetermined angle around an axis of the pinion gear, and the plurality of contact lines and a center line of a pinion tooth bottom surface of the pinion gear are projected onto a plane, including an axis of a pair of the crown gears, around the axis of the pinion gear, the center line of the pinion tooth bottom surface projected onto the plane includes an inclined line passing through a range between two of the contact lines which are selected from the plurality of contact lines projected onto the plane and by which a contact ratio is 1.0 or higher.