Logarithmic Milling Head Tooth Pitch for Speed and Surface Quality
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Solution Overview
Problem
Existing form milling heads face challenges in achieving high processing speeds while maintaining surface quality, due to limitations in the number of milling teeth and the resulting mechanical overload and surface roughness.
Innovation Solution
A form milling head with a profile-constant or logarithmic surface, featuring a larger number of milling teeth arranged along the circumferential area, where the tooth spacing is determined by a specific polynomial relationship, optimizing the tooth width-to-gap ratio and tooth height.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If the number of milling teeth is increased to achieve higher processing speeds, then productivity improves, but mechanical overload and surface roughness increase
Solution Approach 1:
The patent applies parameter changes by optimizing the tooth pitch according to a specific polynomial formula y = a·x^5 + c·x^3 + d·x^2 + e·x + f, where x is the diameter and y is the tooth pitch. This mathematical relationship allows precise control of tooth spacing to maximize the number of teeth while avoiding mechanical overload and surface roughness issues.
2Productivity
If the number of milling teeth is increased to achieve higher processing speeds, then productivity improves, but surface quality deteriorates
Solution Approach 1:
The patent uses parameter changes by implementing a optimized tooth pitch formula that balances tooth density with surface quality. The polynomial relationship y = a·x^5 + c·x^3 + d·x^2 + e·x + f precisely controls tooth spacing to achieve high processing speeds while maintaining acceptable surface finish by preventing excessive tooth interaction and material disruption.
Data Source
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AI summary
It is proposed to provide a milling head (1) having a plurality of cutting milling teeth (2) and intervening tooth gaps (3), wherein the milling teeth (2) and the tooth gaps (3) are arranged along a circumferential surface of the milling head (1), with a number of milling teeth (2) that is greater than and/or substantially equal to the number of milling teeth (2) determined using the relationship y = a·x⁵ + b·x⁴ + c·x + d·x + e·x + f, where x is the diameter of the milling head (1) in millimeters and y is the tooth pitch, i.e., the distance between two adjacent milling teeth (2) in millimeters, and where essentially a = 2·10⁻⁹, b = -8·10⁻⁷, c = 1·10⁻⁴, d = 9.1·10⁻³, e = 3.145·10-1 and f = -2.062·10-1 applies.