Strain Wave Gear Tooth Profile Design for Continuous Meshing
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Solution Overview
Problem
Current strain wave gearings face challenges in achieving continuous meshing over a wide range, particularly from the major axis to the minor axis of the ellipsoidal rim-neutral curve of the flexible externally toothed gear, which limits their load torque performance.
Innovation Solution
The tooth profiles of the strain wave gearing are designed using first and second homothetic curves derived from movement loci, ensuring continuous meshing by prescribing addendum and dedendum profiles for both the internal and external gears, with profile shifts to accommodate coning, allowing for non-deflected, positive-deflection, and negative-deflection states, thereby increasing the meshing range and torque transmission.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional tooth profiles are used in strain wave gearings, then the structure is simple to manufacture, but continuous meshing cannot be achieved over a wide range from major axis to minor axis of the ellipsoidal rim-neutral curve
Solution Approach 1:
The patent applies parameter changes by modifying the tooth profile geometry based on the deflection coefficient κ. Different tooth profiles are designed for different κ values (non-deflected κ=1, positive-deflection κ>1, negative-deflection κ<1), allowing the gearing to maintain continuous meshing across various operational states and positions of the ellipsoidal rim-neutral curve.
Solution Approach 2:
The invention incorporates dynamic adaptation by designing tooth profiles that accommodate the dynamic flexing behavior of the external gear. The tooth profiles are specifically engineered to work with the wave generator-induced flexing, ensuring continuous meshing as the gear transitions between different deflection states during operation.
2Power
If the flexible externally toothed gear is made to flex into an ellipsoidal shape, then torque transmission is enabled, but the tooth surfaces do not maintain congruity across the entire tooth trace
Solution Approach 1:
The patent applies local quality by designing different tooth profile characteristics for different locations along the tooth trace. The tooth profiles are specifically tailored to maintain congruity at critical locations (major axis positions) while accommodating the varying flexure amounts (w = 2κmn) at different positions, ensuring both torque transmission and surface congruity.
Solution Approach 2:
The invention utilizes curvature principles by designing tooth profiles that conform to the ellipsoidal shape created by the wave generator. The tooth surfaces are shaped to maintain congruity despite the varying curvature along the ellipsoidal rim-neutral curve, allowing continuous contact and effective torque transmission.
3Power
If conventional tooth profiles are used, then manufacturing is easier, but the meshing range is limited and torque transmission is reduced
Solution Approach 1:
The patent achieves enhanced torque transmission through parameter changes in the tooth profile design. By incorporating specific geometric parameters derived from the movement locus and applying profile shifts based on the deflection coefficient, the meshing range is extended across the entire tooth trace, enabling higher torque transmission capability.
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 design ensures continuous meshing across the entire tooth trace, enhancing torque transmission and extending the life of the strain wave gearing by maintaining congruent tooth surfaces throughout the meshing process.
Implementation Method 1
the flexible externally toothed gear is made to flex into an ellipsoidal shape by the wave generator
Implementation Method 2
Such a flexing action of the flexible externally toothed gear caused by the wave generator is referred to as 'coning'
Data Source
AI summary
The dedendum tooth profiles of the internal teeth and external teeth of a strain wave gearing are prescribed by a first homothetic curve BC and a second homothetic curve AC obtained from a curve segment from a point A, at which the angle formed by the tangent to a movement locus Mc when meshing is approximated by rack meshing and the major axis is ΘA, to a low point B. The dedendum tooth profile of the internal teeth is prescribed by a curve formed on the internal teeth in the course of the addendum tooth profile of the external teeth moving from an apex of the movement locus to point A. The dedendum tooth profile of the external teeth is prescribed by a curve formed on the external teeth when the addendum tooth profile of the internal teeth moves from the apex to arrive at point A.