Rolling Load Distribution With Friction-Inclusive Contact Arc Calculation
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Solution Overview
Problem
Existing methods for calculating rolling load distribution in rolling mills neglect the influence of frictional stress, leading to increased approximation errors under conditions where frictional stress is high, such as rolling with dull rolls or high-strength steel, and require complex numerical solutions unsuitable for online calculations.
Innovation Solution
A method that calculates rolling load distribution and contact arc length in the elastic region using Hooke's law and plane-strain conditions, considering frictional stress, with equations to determine rolling load distribution and contact arc length in both elastic recovery and reduction regions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If frictional stress is neglected in the elastic region, then the calculation is simplified, but the approximation error increases under conditions where frictional stress is high
Solution Approach 1:
The patent changes the parameter consideration by explicitly including frictional stress in the elastic region calculations, transitioning from a frictionless approximation to a friction-inclusive model. This is achieved by modifying the stress distribution equations to account for frictional effects while maintaining analytical solvability through careful formulation of the differential equations.
Solution Approach 2:
The patent replaces the need for complex numerical solution methods with an analytical approach by formulating the problem in terms of differential equations that can be solved explicitly. This substitution of solution methodology maintains accuracy while improving computational efficiency for online applications.
2Measurement precision
If a rigorous theoretical equation based on Airy's stress function is used, then the rolling load prediction accuracy is improved, but the calculation requires numerical solutions of differential equations which are not suitable for online calculation
Solution Approach 1:
The patent substitutes numerical solution methods with an analytical solution approach by formulating the stress distribution in terms of solvable differential equations. The key innovation is deriving closed-form or efficiently computable analytical expressions for the rolling load that maintain rigor while enabling fast online calculation.
Solution Approach 2:
The patent transforms the rigid theoretical framework into a more flexible formulation that allows for analytical treatment. By carefully selecting the form of the stress function and boundary conditions, the patent enables solutions that are both accurate and computationally efficient for real-time applications.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
Enables high-speed and accurate calculation of rolling load distribution and contact arc length even under conditions of increased frictional stress, suitable for online use in rolling mills.
Implementation Method 1
calculating a contact arc length of either or both of an elastic recovery region and an elastic reduction region based on Hooke's law under a plane-strain condition of a rolled material
Data Source
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AI summary
A method of calculating the rolling load distribution of a rolling mill 10, the method comprising: calculating the contact arc length of at least one of the elastic recovery region and the elastic reduction region based on Hooke's law under the plane-strain condition of a rolled material 1, the force balance within the roll bite of the rolling mill 10, and the rolling-direction stress distribution approximated by a function dependent on the position coordinate in the rolling direction of the rolling mill 10; and calculating the rolling load distribution of at least one of the elastic recovery region and the elastic reduction region based on the contact arc length.