Dynamic Enthalpy Model for Steel Sheet Cooling Control
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Solution Overview
Problem
Current methods for controlling the temperature of steel sheets during cooling processes, particularly from the Ae3 temperature onwards, face challenges in precision due to inadequate consideration of dynamic specific heat and transformation delays, leading to inaccuracies in temperature prediction and control.
Innovation Solution
The method involves calculating dynamic enthalpy using the enthalpies of the austenite and ferrite phases and their untransformed fractions, with a dynamic specific heat gradient to improve temperature prediction and control, especially at high cooling rates, and applying this in the temperature prediction model to achieve precise temperature control.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional cooling control methods using basic heat transfer equations are used, then the cooling process can be implemented, but the temperature prediction precision deteriorates due to inadequate consideration of dynamic specific heat and transformation delays
Solution Approach 1:
The patent applies parameter changes by transitioning from static specific heat values to dynamic specific heat values that vary with temperature and transformation fraction. The specific heat is calculated as a function of transformation fraction using the formula Cp = Cpγ·Xγ + Cpα·(1-Xγ), where Cpγ and Cpα are the specific heats of austenite and ferrite phases respectively, and Xγ is the transformation fraction. This dynamic parameter adjustment significantly improves temperature prediction precision during the cooling process.
Solution Approach 2:
The patent implements feedback mechanisms by continuously monitoring the transformation fraction during cooling and using this information to adjust the specific heat calculations in real-time. The transformation fraction is determined based on temperature and cooling rate, and this feedback loop allows the system to account for transformation delays and dynamic changes in material properties, thereby improving temperature control accuracy.
2Productivity
If high cooling rates are applied to improve productivity, then the cooling efficiency increases, but the temperature control precision deteriorates due to transformation delays
Solution Approach 1:
The patent applies dynamics by considering the transient nature of phase transformation during high-rate cooling. Instead of assuming equilibrium conditions, the model accounts for transformation delays by using dynamic specific heat values that reflect the actual non-equilibrium state of the material. The transformation fraction is calculated based on the cooling rate and temperature history, allowing the system to accurately predict temperatures even at high cooling rates where transformation lags behind equilibrium predictions.
Solution Approach 2:
The patent explicitly models phase transitions from austenite to ferrite during cooling by incorporating transformation fraction calculations. The specific heat is expressed as a weighted average of the specific heats of the two phases based on their respective fractions. This approach captures the thermal effects of phase transformation, including latent heat release, and allows accurate temperature prediction during the transition region even at high cooling rates.
3Measurement precision
If conventional specific heat models are used, then the calculation is simple, but the temperature prediction accuracy deteriorates at high cooling rates and during transformation
Solution Approach 1:
The patent changes the specific heat parameter from a constant or simple temperature-dependent value to a dynamic value that depends on both temperature and transformation fraction. The specific heat is calculated as Cp(T, Xγ) = Cpγ(T)·Xγ + Cpα(T)·(1-Xγ), where the specific heats of individual phases are functions of temperature and the transformation fraction Xγ is determined from the cooling history. This parameter transformation maintains computational feasibility while dramatically improving prediction accuracy.
Solution Approach 2:
The patent treats the transforming steel as a composite material system consisting of two phases (austenite and ferrite) with different thermal properties. The overall specific heat is calculated as a composite of the individual phase specific heats weighted by their respective fractions. This composite approach allows the model to capture the complex thermal behavior during transformation while maintaining a relatively simple calculation framework based on additive contributions from each phase.
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 approach significantly enhances the precision of temperature prediction and control, allowing for the production of steel sheets with targeted properties by accurately managing the end-of-cooling temperature, improving cooling process efficiency and product quality.
Implementation Method 1
the basic heat transfer equation based on the coefficient of heat transfer and specific heat is used
Implementation Method 2
the specific heat of the ferrite phase divided into the specific heat of magnetic transformation and the specific heat without magnetic transformation
Implementation Method 3
the specific heat of the ferrite phase divided into the specific heat of magnetic transformation and the specific heat without magnetic transformation
Data Source
AI summary
A method for controlling the cooling of a steel sheet characterized by controlling the end-of-cooling temperature in a cooling process from the Ae3 or above temperature of the steel sheet, during which; preliminarily obtaining enthalpies (Hγ and Hα) of an austenite phase and ferrite phase respectively at some temperature, obtaining a gynamic enthalpy (Hsys) defined by formula (1) with an untransformed fraction (Xγ) of austenite in accordance with a target temperature pattern, predicting the temperature by using a gradient of this dynamic enthalpy with respect to temperature as a dynamic specific heat and controlling the cooling of the steel sheet:Hsys=Hγ(Xγ)+Hα(1−Xγ). formula (1)