Ball End Mill Arcuate Cutting Edge Rake Angle Distribution
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Solution Overview
Problem
Conventional ball-end mills face challenges in achieving high accuracy and effective chip removal when finishing works with vertical walls and high-hardness materials, due to issues with rake angle distribution and vibration, leading to poor surface roughness and increased cutting resistance.
Innovation Solution
The ball-end mill design features arcuate cutting edges with a radial rake angle that increases from the tip end to the rotationally most projecting point and then decreases to the peripherally outermost point, with a positive radial rake angle at the most projecting point, and a spirally-shaped peripheral cutting edge to reduce cutting resistance and enhance chip removal.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Strength
If the rake angle of the cutting edge at the most projecting position is negative to strengthen the cutting edge, then the cutting edge strength is improved, but the capability of finishing works with high accuracy deteriorates
Solution Approach 1:
The patent applies different rake angles to different locations of the cutting edge. The tip end portion has a positive rake angle (5-15 degrees) for high accuracy finishing, while the peripheral portion has a negative rake angle (-5 to -15 degrees) for cutting edge strength. This local differentiation resolves the contradiction by optimizing each region for its specific function.
Solution Approach 2:
The cutting edge is segmented into distinct regions with different rake angle characteristics. The tip end portion (radial angle 0-45 degrees) is separated from the peripheral portion (radial angle 60-90 degrees), with an intermediate portion connecting them. This segmentation allows independent optimization of finishing accuracy and cutting edge strength.
2Productivity
If the rake angle is increased in the peripheral portion to improve chip removal, then chip removal capability is improved, but the cutting edge strength deteriorates
Solution Approach 1:
The patent assigns a negative rake angle (-5 to -15 degrees) to the peripheral portion where cutting edge strength is critical, while maintaining a positive rake angle in the tip end portion for effective chip removal. This local quality differentiation resolves the contradiction by placing each rake angle configuration in the region where it provides the greatest benefit.
3Strength
If the rake angle is made largely negative at the center to improve cutting edge strength, then the cutting edge strength is improved, but the capability of finishing works with high accuracy deteriorates
Solution Approach 1:
The patent maintains a positive rake angle (5-15 degrees) at the tip end portion (radial angle 0-45 degrees) where high accuracy finishing occurs, while applying a negative rake angle to the peripheral portion. This resolves the contradiction by ensuring the center region has the geometry needed for precision work while the periphery provides structural strength.
4Productivity
If the rake angle gradually increases from the tip end to the periphery to improve chip removal, then chip removal is improved, but the capability of finishing works with high accuracy deteriorates
Solution Approach 1:
The patent maintains a positive rake angle in the tip end portion (radial angle 0-45 degrees) where high accuracy finishing is performed, ensuring finishing precision is not compromised. The intermediate portion (radial angle 45-60 degrees) shows gradual change, and the peripheral portion has a negative rake angle for strength. This resolves the contradiction by protecting the accuracy-critical region while still providing chip removal capability.
Data Source
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Figure 3~5
Figure 6(a)~6(c)
AI summary
A ball-end mill comprising, in a tip end portion of an end mill body, arcuate cutting edges each extending from a tip end to a peripherally outermost point along a curve in an S shape when viewed from the front side, spirally-shaped, peripheral cutting edges each smoothly connected to each arcuate cutting edge, and a convex rake face of each arcuate cutting edge protruding forward in a rotation direction; each arcuate cutting edge having a radial rake angle meeting the condition of β < α ≤ γ, wherein α is a radial rake angle at a radial angle of 5°, β is a radial rake angle at a radial angle of 90°, and γ is a radial rake angle at a rotationally most projecting point of the arcuate cutting edge; the radial rake angle of the arcuate cutting edge having the maximum value at a radial angle in a range of 12-40°; and the radial rake angle continuously decreasing in a range from the rotationally most projecting point to the peripherally outermost point.