Flat Wave Gear Tooth Profile Design for Continuous Meshing
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Solution Overview
Problem
Flat wave gear devices face challenges in maintaining continuous meshing and increasing ratcheting torque at low reduction ratios, particularly due to high flexural stress and tooth-jumping issues, which are not effectively addressed by existing tooth profile designs.
Innovation Solution
A method for setting a tooth profile in a flat wave gear device with a flexible externally toothed gear and two rigid internally toothed gears, where the flexible gear has a non-positive deflection coefficient, using a convex arc with a specific radius and movement locus to increase tooth depth and prevent tooth-jumping, ensuring continuous meshing and enhanced ratcheting torque.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Strength
If tooth depth is increased to prevent ratcheting under high load torque, then ratcheting torque is improved, but flexural stress increases at low reduction ratios
Solution Approach 1:
The patent applies parameter changes by modifying the tooth profile geometry parameters, specifically using a convex arc with radius ρ≦ρOPT and setting the flexing coefficient κ≦1. This changes the physical parameters of the tooth profile to achieve both increased tooth depth and controlled flexural stress, resolving the contradiction between strength and stress.
2Reliability
If tooth depth is increased to maximize meshing region, then continuous meshing is improved, but tooth profile interference occurs with conventional designs
Solution Approach 1:
The patent applies spheroidality by using a convex arc (curved profile) instead of straight or conventional tooth profiles. The convex arc with radius ρ≦ρOPT creates a curved geometry that enables continuous meshing across the entire movement locus while avoiding interference, as the curved shape adapts better to the elliptical deformation of the flexible gear.
3Stress or pressure
If flexing coefficient is reduced to prevent flexural stress increase, then stress is reduced, but tooth meshing continuity deteriorates
Solution Approach 1:
The patent simultaneously optimizes multiple parameters: setting the flexing coefficient κ≦1 while also defining the convex arc radius ρ≦ρOPT. This multi-parameter optimization ensures that the tooth profile maintains appropriate engagement depth and continuity even with reduced flexing, resolving the contradiction between stress reduction and meshing continuity.
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
The solution increases ratcheting torque and load capacity by maintaining continuous meshing over the entire range of movement, effectively addressing the limitations of existing designs at low reduction ratios.
Implementation Method 1
the degree of radial deflection κmn (κ being the flexing coefficient, and m being the module of both gears) must be reduced
Data Source
AI summary
In a flat wave gear device, there is determined a rack-approximated movement locus Lc1 of a flexible externally toothed gear with respect to an S-side rigid internally toothed gear accompanying rotation of a wave generator. ρOPT is a minimum value of the radius of curvature of the movement locus Lc1, and is determined from an evolute e of the movement locus Lc1. A convex arc having a radius ρ (ρ≦ρOPT) is used in a main part of a tooth profile of the flexible externally toothed gear. A parallel curve c that is set apart from a movement locus Lc2 by the arc radius ρ is used on a main part of a tooth profile to be generated on the S-side rigid internally toothed gear. The movement locus Lc2 accounts for the actual number of teeth, and is obtained from a center A of a convex arc of the flexible externally toothed gear being drawn with respect to the rigid internally toothed gear. In a flat wave gear device that is provided with a flexible externally toothed gear having a non-positive deflection (κ≦1) tooth profile, a tooth depth of the flexible externally toothed gear can be increased, whereby ratcheting torque is increased and meshing can occur continuously over an entire range of a movement locus; and a load capacity of the flat wave gear device is increased.