Gear Tooth Root Profile Design for Stress Reduction
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Solution Overview
Problem
Conventional gear designs concentrate stress at the tooth root during engagement, leading to potential damage due to the formation of a triangular-pointed recess hole at the tooth bottom, which compromises the strength and durability of the gear.
Innovation Solution
The gear features a tooth root profile with a first curved surface that smoothly connects to the involute curve and a second curved surface defined by a quadratic function, eliminating the triangular-pointed recess hole and distributing stress more evenly, thereby reducing stress concentration and enhancing strength.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If the tooth space between adjacent teeth is embodied in the form of a pointed arch at the tooth bottom, then the gear structure is simplified and manufacturing is easier, but stress concentrates at the triangular-pointed recess hole causing potential damage
Solution Approach 1:
The invention replaces the pointed arch (triangular) tooth space with a curved arc-shaped tooth space. The tooth bottom is formed with a rounded arc profile instead of a sharp triangular point, eliminating the stress concentration at the recess hole while maintaining structural integrity and ease of manufacturing through standard gear generation processes.
2Reliability
If the tooth flanks are made to approximate a trochoid curve, then the engagement performance is improved, but the tooth root stress concentration increases due to the pointed arch tooth space
Solution Approach 1:
The invention maintains the trochoid curve approximation for tooth flanks to ensure good engagement performance while simultaneously modifying the tooth bottom to have a curved arc profile instead of a pointed arch. This combination achieves both reliable tooth engagement and reduced stress concentration at the tooth root.
3Ease of manufacture
If standard tooth flanks are used, then manufacturing is simpler, but stress concentrates at the tooth root leading to reduced durability
Solution Approach 1:
The invention uses standard tooth flanks for simple manufacturing while modifying the tooth bottom profile to a curved arc shape. This eliminates the triangular-pointed recess hole that causes stress concentration, thereby improving gear durability and long-term performance without complicating the manufacturing process.
Data Source
AI summary
A gear includes teeth 3 to be engaged with teeth of a corresponding gear to transmit a rotational motion, in which a form (b) of a tooth root side of each tooth 3 includes: a first curved surface c which smoothly connects with a tooth surface a having an involute curve and has a profile represented by a curve which is convex in a direction opposite to the involute curve of the tooth surface a; and a second curved surface d which smoothly connects with the first curved surface c and has a profile defined by a quadratic function having a curve being convex in the same direction as that of the first curved surface c. Therefore, a stress generated on the tooth root side at the time of engagement with the teeth of the corresponding gear can be reduced, and the strength of the teeth can be increased.