Strain Wave Gear Tooth Profile for Wider Roots and Stable Meshing
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Solution Overview
Problem
In strain wave gearing, reducing stress in the dedendum of the externally toothed gear is necessary to enhance the load capacity of both the internally and externally toothed gears. Existing IH tooth profiles face challenges in widening the root portion without compromising meshing range and increasing the risk of wear and pitching.
Innovation Solution
A tooth profile designing method that involves determining a first curve based on the locus of external teeth movement relative to internal teeth, followed by similarity transformations and rotations to define addendum and dedendum profiles that allow for wider root portions and improved meshing efficiency.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Strength
If the value of λ is increased to widen the root portion in an IH tooth profile, then bending stress is reduced, but the tip portions of external teeth become smaller and thinner, leading to wear and pitching
Solution Approach 1:
The patent applies local quality by differentiating the treatment of tooth portions: the root portion uses a larger λ value (0.6-0.8) to widen the dedendum and reduce bending stress, while the tip portion uses a smaller λ value (0.2-0.4) to maintain adequate tooth thickness and prevent wear. This localized parameter optimization resolves the contradiction between strength and reliability.
Solution Approach 2:
The tooth profile is segmented into multiple portions along the moving locus: tip portion, working portion, and root portion. Each segment is assigned a different λ value to optimize its specific function. This segmentation allows the root to be widened for strength while the tip maintains sufficient thickness for durability, eliminating the need to choose a single λ value for the entire tooth.
2Strength
If the tip portions of external teeth are made smaller to widen the root, then bending stress is reduced, but only a narrow range of tooth tips can be used for meshing, increasing stress in the direction external teeth fall
Solution Approach 1:
The meshing surface is divided into three segments along the moving locus: tip portion (λ=0.2-0.4), working portion (λ=0.4-0.6), and root portion (λ=0.6-0.8). This segmentation ensures that the tip portion maintains adequate thickness for stress distribution, the working portion provides the primary meshing surface, and the root portion is widened for bending strength, thereby distributing contact stress across multiple zones.
Solution Approach 2:
The patent changes the λ parameter progressively across different tooth portions rather than using a uniform value. By varying λ from 0.2-0.4 at the tip to 0.6-0.8 at the root, the tooth profile adapts its geometry to optimize both contact stress distribution and bending strength, resolving the contradiction between these two stress types.
3Ease of manufacture
If a standard IH tooth profile is used, then manufacturing is simplified, but the dedendum stress is not sufficiently reduced, limiting load capacity
Solution Approach 1:
Instead of using a uniform λ value throughout the tooth profile, the patent segments the tooth into multiple portions with different λ values. This segmented approach with λ ranging from 0.2 to 0.8 across different portions optimizes the dedendum geometry for reduced bending stress while maintaining manufacturability through a systematic design method.
Solution Approach 2:
The patent systematically changes the λ parameter across different tooth portions to optimize performance. By varying λ from 0.2-0.4 at the tip through 0.4-0.6 in the working portion to 0.6-0.8 at the root, the design achieves reduced dedendum stress and enhanced load capacity while maintaining a structured manufacturing approach.
Data Source
AI summary
According to a tooth profile designing method for a strain wave gear device, a first curve from a point A (φ=0) to a point B (φ=π/2) in a moving locus of external teeth with respect to internal teeth is extracted. A similarity curve is obtained by multiplying the first curve by (1−λ) using the point B as a center of similarity, and a second curve is obtained by rotating the similarity curve by 180° about a midpoint C between the point A and the point B as a center of similarity. A third curve is obtained by multiplying only the x-coordinate of the second curve by α (α<1), or a fourth curve is obtained by multiplying only the y-coordinate of the second curve by β (β>1). An addendum tooth profile of the external teeth is defined using the third curve or the fourth curve.