Six-High Cold Rolling Mill Critical Vibration Speed Prediction
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Solution Overview
Problem
Existing methods for predicting critical vibration speed in six-high cold rolling mills are limited by simplifications, such as treating components as mass points and ignoring shear deformation, leading to inaccurate models and reduced precision.
Innovation Solution
A three-dimensional prediction method for critical vibration speed is developed, utilizing a finite element model and Timoshenko beams to account for shear deformation, along with a dynamic rolling force calculation and vertical vibration dynamic equation to predict the critical speed.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If components are simplified as mass points, then device complexity is reduced, but measurement precision and manufacturing precision deteriorate
Solution Approach 1:
The patent transitions from simplified mass point models to a three-dimensional finite element model, adding spatial dimensions to the analysis. This allows the model to capture complex structural behaviors including shear deformation and roll bending/shifting that cannot be represented in simplified models, thereby improving prediction accuracy while managing complexity through systematic discretization.
Solution Approach 2:
The patent applies segmentation by dividing the rolling mill components into discrete finite elements. This allows the complex continuous structure to be analyzed through manageable segments, where each element can be modeled with appropriate physics (including shear deformation), balancing computational complexity with prediction precision.
2Device complexity
If Euler-Bernoulli beam theory is used for rolls, then device complexity is reduced, but manufacturing precision deteriorates due to ignoring shear deformation
Solution Approach 1:
The patent changes the fundamental modeling parameter from Euler-Bernoulli beam theory (which neglects shear deformation) to Timoshenko beam theory (which includes shear deformation effects). This parameter change in the constitutive model allows accurate prediction of roll vibration and bending under high-speed rolling conditions where shear effects are significant, improving manufacturing precision without excessive complexity increase.
3Ease of operation
If vibration speed of rolls is not considered in rolling force calculation, then ease of operation is improved, but measurement precision deteriorates
Solution Approach 1:
The patent introduces dynamic considerations by incorporating roll vibration speed into the rolling force calculation. The model transitions from static force analysis to dynamic analysis, where the rolling force varies with vibration amplitude and frequency. This dynamic approach accurately captures the coupling between roll vibration and rolling force, improving measurement precision while maintaining computational tractability through systematic formulation.
Data Source
AI summary
The invention provides a prediction method for critical vibration speed of a six-high cold rolling mill based on a three-dimensional model. The critical vibration speed is predicted based on a three-dimensional six-high cold rolling mill model, under the consideration that the rolls shall be considered as short and thick beams and influence of shear deformation needs to be considered, Timoshenko beams are selected, and besides, Hermite interpolation is used for node displacement vectors; a vertical vibration dynamic equation of the mill-strip system can be established by stress analysis among the strip, rolls and mill housing; solving is performed by the Newmark-Beta method, a displacement response curve of the rolls at a specific speed can be obtained, and if the amplitude of displacement response curve is constant, the speed is the critical vibration speed of the six-high rolling mill.