Vulcanization Degree Estimation via Torque Curve Fitting
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Solution Overview
Problem
Existing methods for estimating the vulcanization degree of rubber compounds are inaccurate due to difficulties in determining the values of invariables in the vulcanization curve expression, leading to limited precision in controlling vulcanizing temperature and time.
Innovation Solution
A method involving the measurement of shearing resistance (torque) to obtain a measured vulcanization curve, followed by determining values of K1, K2, and m that minimize the error between the measured and estimated curves, using a process of variable calculation and curve fitting to achieve a precise estimation of vulcanization degree.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If fixed real numbers are assigned to invariables m, n and K1, and only K2 is determined to approximate the actual vulcanization curve, then the integration of the expression becomes feasible, but the vulcanization degree cannot be accurately estimated
Solution Approach 1:
The invention transforms the original expression with fixed parameters into a new expression where invariables m, n, and K1 are determined through systematic parameter optimization. By changing from fixed arbitrary values to optimized parameters derived from measured data, the accuracy of vulcanization degree estimation is significantly improved while maintaining integration feasibility.
Solution Approach 2:
The invention implements a feedback mechanism where the determined invariables are used to calculate the vulcanization degree, which is then compared with actual measured values. The expression is refined by minimizing the error between calculated and measured vulcanization degrees, creating a closed-loop optimization process that enhances estimation accuracy.
2Measurement precision
If the values of invariables m, n, K1 and K2 are determined to make the expression closer to the actual vulcanization curve, then the estimation accuracy improves, but the process becomes complex and difficult
Solution Approach 1:
The invention segments the determination process into distinct stages: first determining invariables m and n from the shape characteristics of the vulcanization curve, then determining K1 and K2 from the measured curve data. This segmentation simplifies the overall complex process by breaking it into manageable, systematic steps that reduce computational difficulty.
Solution Approach 2:
The invention performs preliminary determination of invariables m and n based on the general shape of the vulcanization curve before proceeding to determine K1 and K2. This preliminary action establishes a foundation that simplifies subsequent parameter determination, reducing the overall complexity of the process.
3Measurement precision
If more invariables are determined to improve accuracy, then the estimation becomes more precise, but the time and computational effort increase
Solution Approach 1:
The invention performs preliminary determination of invariables m and n from the shape characteristics of the vulcanization curve before determining K1 and K2. This preliminary action reduces the computational burden in later stages, minimizing total processing time while maintaining high accuracy through systematic parameter optimization.
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
This method allows for accurate estimation of the vulcanization degree of rubber compounds, reducing errors and improving the control of vulcanizing conditions, thereby enhancing the manufacturing process of rubber products like vehicle tires.
Implementation Method 1
a measured vulcanization curve which is a change curve of the vulcanization degree of the rubber compound with vulcanizing time is obtained by actually measuring the shearing resistance (or torque) of the rubber compound during vulcanization
Data Source
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AI summary
A method for estimating the vulcanization degree of a rubber compound is disclosed. The torque of the rubber compound during vulcanization is measured to obtain a vulcanization curve. values of invariables K1, K2 and m of a specific expression (1) which values minimize the error between the measured vulcanization curve and a (estimated cure) curve defined by the expression (1), are obtained. Each of different real numbers is assigned to the invariable K1 of the expression (1), and the expression (1) is approximated to the measured vulcanization curve, and then from the approximated expression (1), a set of values of the invariables K1, K2 and m are obtained. Such plural sets of the values are assigned to the expression (1) to obtain a plurality of the estimated vulcanization curves from which an estimated vulcanization curve whose error from the measured vulcanization curve is smallest, is found out.