3D Tooth Profiles in Harmonic Gearing for Easier Tooth Cutting
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Solution Overview
Problem
Existing cup-shaped or top-hat-shaped strain wave gearings face challenges in achieving three-dimensional meshing across the entire tooth trace direction due to restrictions in tooth cutting processes, which make it difficult to cut tooth profiles with varying thickness, pressure angle, and tooth depth.
Innovation Solution
Both the internal and external teeth of the strain wave gearing are set to three-dimensional tooth profiles, where the internal teeth have a proportionally reduced profile and the external teeth have a proportionally increased profile along the tooth trace direction, facilitating easier tooth cutting and achieving three-dimensional meshing.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If a three-dimensional tooth profile with varying thickness, pressure angle, and tooth depth is used to achieve three-dimensional meshing, then meshing performance is improved, but tooth cutting process difficulty increases
Solution Approach 1:
The patent applies parameter changes by systematically varying tooth profile parameters (thickness, pressure angle, tooth depth) along the tooth trace direction. The tooth thickness varies from a first value at the start to a second value at the end, the pressure angle varies from a first angle to a second angle, and the tooth depth varies from a first depth to a second depth. This controlled parameter variation enables three-dimensional meshing while maintaining manufacturability through predictable geometric progressions.
Solution Approach 2:
The patent transitions from traditional two-dimensional tooth profiles to three-dimensional tooth profiles by adding variation along the tooth trace direction (z-axis). This dimensional extension creates a volumetric tooth geometry where parameters change along the length of the tooth, enabling three-dimensional meshing contact between gear teeth rather than simple line contact.
2Ease of manufacture
If the tooth profile is simplified for easier cutting, then manufacturing ease is improved, but three-dimensional meshing capability deteriorates
Solution Approach 1:
The patent maintains manufacturability by using systematic parameter variations rather than arbitrary complex geometries. The tooth thickness, pressure angle, and tooth depth follow controlled variation patterns along the tooth trace direction, which can be achieved through modified conventional cutting processes. This approach balances manufacturing simplicity with three-dimensional meshing 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 approach alleviates restrictions on tooth cutting processes, making it easier to realize three-dimensional meshing across the entire tooth trace direction, and allows for the manufacture of strain wave gearings with improved meshing performance.
Implementation Method 1
The externally toothed gear is ellipsoidally flexed by the wave generator and meshes with the internally toothed gear at both ends of the long axis of the ellipsoidal shape
Data Source
Figure 1(a)~1(b)
Figure 2(a)~2(c)
Figure 3
AI summary
A three-dimensional tooth profile of internal teeth (20) in a strain wave gearing (1) is a basic internal-teeth tooth profile (20(0)) at an internal-teeth outer end (20a), and is a reduced tooth profile, in which the basic internal-teeth tooth profile (20(0)) is proportionally reduced only in the lateral direction, at other tooth-trace-direction positions. A three-dimensional tooth profile of external teeth (3) is a basic external-teeth tooth profile (30(0)) at an external-teeth outer end (30a), and is an increased tooth profile, in which the basic external-teeth tooth profile (30(0)) is proportionally increased only in the lateral direction, at other tooth-trace-direction positions. Tooth cutting process becomes easier than when only the external teeth (30) employ a three-dimensional tooth profile. Since the tooth profiles, which are proportionally reduced and increased only in the lateral direction along the tooth trace direction, are employed, it is further easier in tooth cutting process.