Strain Wave Gear Tooth Profile Design for Stress Separation
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Solution Overview
Problem
Strain wave gearings face challenges in reducing superimposed bending and tensile stresses at the major axis of the external gear, which limits their transmission torque capacity, and existing solutions either reduce flexing amount or require negative deflection flexing.
Innovation Solution
The solution involves defining specific tooth profiles for the internal and external gears to separate the positions where bending and tensile stresses are generated, allowing for complete avoidance of stress superimposition without reducing the flexing amount, by using formulas to specify the addendum profiles of the gears and shifting tooth profiles in axis-perpendicular cross-sections.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Power
If the external gear is ellipsoidally flexed by a wave generator to mesh with the internal gear, then gear meshing function is achieved, but bending stress and tensile stress are superimposed in sections at either end of the major axis, reducing transmission torque capacity
Solution Approach 1:
The patent divides the stress analysis into two separate components: bending stress from flexion and tensile stress from meshing load. By segmenting the stress sources, the invention identifies that they occur at different locations when proper tooth profiles are used, allowing the superimposed stress problem to be resolved by spatial separation of these stress zones.
Solution Approach 2:
The invention applies different tooth profile characteristics at different locations. Specifically, the tooth profiles are designed so that bending stress concentrates at one location while tensile stress concentrates at another location along the major axis, creating local quality differentiation that prevents stress superimposition and maximizes transmission torque capacity.
2Stress or pressure
If the flexing amount of the external gear is reduced to reduce bending stress, then bending stress is reduced, but the transmission torque capacity is limited
Solution Approach 1:
The invention extracts the tensile stress component from the bending stress location by designing tooth profiles that shift the meshing contact point. This extraction separates the two stress types spatially, allowing the external gear to maintain normal flexing amounts for high torque capacity while avoiding superimposed stress that would limit transmission capability.
3Stress or pressure
If negative deflection flexing is applied to reduce bending stress, then bending stress is reduced and stress superimposition is avoided, but the device complexity increases
Solution Approach 1:
Instead of using negative deflection flexing to move the neutral axis outward, the invention inverts the approach by designing tooth profiles that naturally position the meshing contact point away from the major axis sections. This profile-based solution achieves stress separation without requiring complex negative deflection control mechanisms.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach effectively separates bending and tensile stresses, enhancing the transmission torque capacity of strain wave gearings without requiring negative deflection flexing, and enables continuous meshing between the gears, thereby improving performance.
Implementation Method 1
a flexible external gear is flexed from a true circular state to an ellipsoidal shape by a wave generator, and therefore bending stress due to flexing is produced in sections at either end of the major axis of the ellipsoidal shape
Implementation Method 2
Once ellipsoidally flexed, an extrnal gear will mesh with the internal gear in these sections at either end of the major axis, thereby giving rise to tensile stress caused by load torque transmitted via the meshing sections
Data Source
Figure 1
Figure 2(a)~2(c)
Figure 3A
AI summary
In a strain wave gearing, the addendum tooth profile of an internal gear is defied by the formula a and that of an external gear is by the formula b at a principal cross-section located at a tooth-trace-direction center of the external gear, on the basis of a movement locus (Mc) of κ = 1 by the teeth of the external gear with respect to those of the internal gear. It is possible to avoid superimposition of flexion-induced bending stresses and tensile stresses caused by load torque at the major-axis locations of the external gear, and the transmission torque capacity of a strain wave gearing can be improved. xCal=0.25mnπ+θ−sin θyCal=0.5mn−1+cos θ where 0 ≤ θ ≤ π xFal=0.25mnπ−θ+sinθ−εcosθ/2−sinθ/22yFal=mn0.51−cosθ−ε/4sinθ/2−cosθ/22 where 0 ≤ ε ≤ 0.1 and 0 ≤ θ ≤ π