Gear Tooth Profile Uniformizes Stress Variation
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Solution Overview
Problem
Existing gear designs in power transmission mechanisms fail to adequately address stress variation widths at the tooth bottom side, leading to insufficient durability due to maximum stress amplitude generation at the center of the tooth.
Innovation Solution
The gear features a tooth shape with a right-angled cross-sectional design, comprising first, second, and third involute portions, and a connecting curved portion, optimized through structural analysis to uniformize stress variation, reducing tensile stress and preventing maximum stress amplitude at the tooth bottom center.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional tooth shapes are used, then the gear structure is simple, but the stress variation width is not uniformized and maximum stress amplitude generates at the tooth bottom center, reducing durability
Solution Approach 1:
The invention applies curvature by forming an arcuate portion at the tooth bottom side area with a specific radius of curvature. This curved design replaces the conventional straight or simple filleted tooth bottom, creating a smooth transition that uniformizes stress distribution. The arcuate shape eliminates stress concentration at the tooth bottom center while maintaining structural integrity, directly resolving the contradiction between durability improvement and shape complexity.
Solution Approach 2:
The invention changes geometric parameters of the tooth shape, specifically introducing a radius of curvature for the arcuate portion and optimizing the dimensions of the first and second involute portions. By adjusting these parameters through structural analysis, the stress variation width is uniformized across the tooth bottom side area, preventing maximum stress amplitude generation and improving durability without excessive complexity.
2Strength
If the tooth bottom side area is strengthened, then local strength improves, but stress variation width is not considered and maximum stress amplitude still generates at the center, insufficiently improving durability
Solution Approach 1:
The invention applies local quality by creating different geometric characteristics in different regions of the tooth. The arcuate portion at the tooth bottom side area has a specific radius of curvature optimized for stress uniformization, while the first and second involute portions have different dimensional characteristics. This localized optimization ensures that each region contributes to overall durability by addressing the specific stress conditions in that area, rather than applying a uniform strengthening approach.
Data Source
Figure 1A~1B
Figure 2~3
Figure 4A~4B
AI summary
A half of a tooth right-angled cross-sectional shape in a tooth bottom side area (10) of a tooth (7) divided at a tooth bottom center (P0) as a boundary is defined by a first involute portion (13) extending from the tooth bottom center (P0) toward a tooth surface (8), an arcuate portion (14) connected smoothly to an end portion of the first involute portion (13), a second involute portion (15) connected smoothly to an end portion of the arcuate portion (14), a third involute portion (16) connected smoothly to an end portion of the second involute portion (15), and a tooth surface connecting curved portion (17) connecting an end portion of the third involute portion (16) and the tooth surface (8) smoothly. Radii of curvature of the first involute portion (13), the arcuate portion (14), the second involute portion (15) and the third involute portion (16) are determined so that a stress variation width in a stress state of a so-called partly reverse state caused by a tensile stress and a compression stress generated in the tooth bottom side area of the tooth before and after the meshing of the tooth can be uniformized.