Screw Compressor Rotor Profile Quadratic Function Minimization
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Solution Overview
Problem
Screw compressor efficiency is hindered by slip phenomena at rotor contact points, increased leakage triangle volumes, and machining errors due to complex rotor profiles, leading to wear, noise, and reduced precision.
Innovation Solution
A rotor profile for screw compressors featuring a female rotor with a quadratic function curve at the operation contact point, minimizing slip ratio and leakage triangle volume, while maintaining a suitable tool pressure angle to enhance efficiency and reduce noise and vibration.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of energy
If the rotor profile is made asymmetric to minimize leakage triangle and enhance insulation performance, then compressor efficiency is improved, but the curve configuration becomes very complicated leading to increased machining errors
Solution Approach 1:
The patent changes the mathematical parameters of the rotor profile curve from complex higher-order functions to a quadratic function (second-order polynomial). This parameter simplification maintains the asymmetric shape needed for leakage reduction while enabling precise machining through simpler mathematical control and tool path generation.
Solution Approach 2:
The patent employs a quadratic function to define the rotor profile curve, which provides smooth curvature transitions. This curved mathematical formulation eliminates sharp corners and complex geometric features, making the profile easier to manufacture with standard machining tools while maintaining the asymmetric configuration for leakage control.
2Loss of energy
If the vacuum-forming space is made smaller and the following-side radius of the female rotor is reduced to decrease leakage triangle size, then compressor efficiency is improved, but the tool pressure angle decreases making precise machining difficult
Solution Approach 1:
The patent adjusts the parameters of the quadratic function (coefficients a, b, c) to optimize both the leakage triangle volume and the tool pressure angle. By carefully selecting these mathematical parameters, the profile achieves small leakage triangles while maintaining adequate tool pressure angles for precise machining with standard tools.
Solution Approach 2:
The patent reduces the following-side radius of the female rotor only to the extent necessary to minimize leakage triangle volume, rather than making it excessively small. This partial reduction approach maintains the tool pressure angle within acceptable ranges for machining while still achieving significant leakage reduction.
3Loss of energy
If the rotor profile geometry is optimized to minimize leakage triangle, then compressor efficiency is improved, but slip phenomenon occurs at contact points causing rotor wear and increased noise
Solution Approach 1:
The patent optimizes the quadratic function parameters to control the contact point geometry between rotors. By adjusting the curvature and slope parameters of the profile, the contact conditions are improved to minimize slip ratio, thereby reducing rotor wear and noise while maintaining the optimized leakage triangle configuration.
Data Source
AI summary
A rotor profile for a screw compressor includes a male rotor and a female rotor, which are operated in an operation space while being engaged with each other, wherein a rotor profile of the female rotor includes a curve having an operation contact point located around a pitch circle at a following-side of the female rotor, the operation contact point being contacted with the male rotor to operate the male rotor when the female rotor is operated, and the curve is configured with a quadratic function y=Lx2+Mx+N. Here, the constants L, M and N are values determined such that a slip ratio at the operation contact point is minimized. This rotor profile for a screw compressor minimizes a slip ratio at the operation contact point, thereby decreasing abrasion and reducing noise of the compressor.