Double Cogged V-Belt Root Geometry for Crack Resistance
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Solution Overview
Problem
Conventional double-cogged V-belts for variable speed transmissions face challenges in achieving high longitudinal flexibility and transverse stiffness while maintaining proper side contact, often resulting in root cracking and early failure due to stress concentration and alignment issues with the upper and lower cogs.
Innovation Solution
A double-cogged V-belt design with symmetric upper and lower cog profiles featuring a sequence of lines and arcs connected from the center of a root to the center of an adjacent cog, where the sum of the length of a line plus the radius of an arc is within 20% of the sum of the length of a corresponding line plus the radius of an arc in the lower profile, with at least one upper root aligned with a lower root, and the ratio of upper to lower cogs up to 1.3, enhancing flexibility and crack resistance.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If alternating thick and thin sections (cogs and roots) are formed on the belt to provide transverse stiffness and longitudinal flexibility, then the belt achieves the needed mechanical properties, but stress concentration occurs at the root areas leading to cracking and early failure
Solution Approach 1:
The patent applies different geometric characteristics to different parts of the cog profile. The cog sections have increased thickness for transverse stiffness, while the root areas are designed with optimized curvature and transition zones to reduce stress concentration. This local differentiation allows each region to perform its specific function without compromising overall reliability.
Solution Approach 2:
The patent employs curved transitions at the root areas instead of sharp corners. The rounded root geometry distributes bending stresses more evenly and prevents stress concentration that would lead to cracking. The curved profile maintains structural integrity while enabling the necessary flexibility in the longitudinal direction.
2Adaptability or versatility
If the belt is made relatively wider and thinner to accommodate radial movement in variable sheaves, then the belt can move in and out for speed variation, but transverse stiffness becomes more difficult to achieve
Solution Approach 1:
The patent divides the belt cross-section into alternating cog and root sections. The cog sections act as structural ribs that provide transverse stiffness, while the root sections provide flexibility. This segmentation allows the belt to maintain stiffness in the transverse direction even with a wider, thinner overall geometry needed for radial movement.
Solution Approach 2:
The cog sections are designed with increased local thickness at strategic positions to provide transverse stiffness where needed, while the overall belt remains thin enough to accommodate radial movement. This localized thickening at cog sections without increasing overall belt thickness resolves the contradiction between stiffness and adaptability.
3Ease of manufacture
If conventional double-cogged V-belt designs are used with aligned upper and lower cogs, then manufacturing is simplified, but bending stresses become highly concentrated at the root areas where web sections are very thin
Solution Approach 1:
The patent designs the root areas with optimized curvature and transition zones that maintain reasonable web thickness even when upper and lower cogs are aligned. The curved geometry at the roots prevents sharp thin sections, distributing bending stresses more evenly while preserving manufacturing simplicity.
4Strength
If cogs are made thicker to increase transverse stiffness, then the belt maintains proper side contact, but longitudinal flexibility is reduced
Solution Approach 1:
The patent segments the belt into alternating thick cog sections and thin root sections. The thick cogs provide transverse stiffness for side contact, while the thin roots provide longitudinal flexibility for bending. This segmentation allows the belt to exhibit both stiffness and flexibility characteristics simultaneously in different directions.
Solution Approach 2:
The cog sections are locally thickened to provide transverse stiffness where needed for side contact with sheaves, while the root sections maintain thin geometry for longitudinal flexibility. This localized differentiation of thickness allows the belt to satisfy contradictory requirements in different spatial directions.
Data Source
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AI summary
A double-cogged V-belt with the upper and lower cog profiles symmetric and having lines ("L") and arcs ("A") connected according to a sequence from the center of a root to the center of an adjacent cog of Ll-Al -L2-A2-L3 for the upper profile and L4-A3-L5-A4-L6, and with at least one upper root and one lower root substantially aligned with each other, and with the sum of the length of Ll plus the radius of Al equal to or within 20% of the sum of the length of L4 plus the radius of A3. The upper and lower pitches may be equal and all the roots aligned, or there may be more upper cogs than lower cogs. Some or all arcs and lines may be connected tangentially.