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Approximate analytical solution for induction heating of solid cylinders

机译:实心圆筒感应加热的近似分析解决方案

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摘要

An approximate solution to the mathematical model for induction heating of a solid cylinder in a cylindrical induction coil is presented here. The coupled multiphysics model includes equations describing the electromagnetic field in the heated object, a heat transfer simulation to determine temperature of the heated object, and an AC circuit simulation of the induction heating power supply. A multiple-scale perturbation method is used to solve the multiphysics model. The approximate analytical solution yields simple closed-form expressions for the electromagnetic field and heat generation rate in the solid cylinder, for the equivalent impedance of the associated tank circuit and for the frequency response of a variable frequency power supply driving the tank circuit The solution developed here is validated by comparing predicted power supply frequency to both experimental measurements and calculated values from finite element analysis for heating of graphite cylinders in an induction furnace. The simple expressions from the analytical solution clearly show the functional dependence of the power supply frequency on the material properties of the load and the geometrical characteristics of the furnace installation. The expressions developed here provide physical insight into observations made during load signature analysis of induction heating.
机译:此处介绍了圆柱感应线圈中实心圆柱感应加热的数学模型的近似解。耦合多物理场模型包括描述加热对象中电磁场的方程式,确定加热对象温度的传热模拟以及感应加热电源的AC电路模拟。使用多尺度摄动法求解多物理场模型。近似分析解决方案针对固体圆柱体中的电磁场和热量产生率,相关储能电路的等效阻抗以及驱动储能电路的变频电源的频率响应得出简单的闭式表达式。通过将预测的电源频率与实验测量值以及感应炉中加热石墨缸的有限元分析计算出的值进行比较,可以验证这一点。分析解决方案中的简单表达式清楚地表明了电源频率对负载的材料特性和炉具几何特性的功能依赖性。此处开发的表达式提供了对感应加热负载特征分析期间所做观察的物理洞察力。

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