电磁感应淬火温度场的非Fourier效应研究

发布时间：2018-04-27 17:35

本文选题：非Fourier效应 + 温度场　；参考：《北京理工大学》2015年硕士论文

【摘要】：电磁感应淬火是曲轴广泛采用的表面强化技术之一。本文在深入理解电磁感应淬火原理和实际淬火工艺的基础上，开展了电磁感应淬火非Fourier效应温度场的理论及数值分析。主要内容包括：根据电磁感应淬火过程这一工程背景，在分析电磁感应加热过程分布内热源的基础上，推导得到了直角坐标系下一维含内热源非Fourier效应温度场的数学模型。采用格林函数，拉氏变换及其逆变换得到了直角坐标系下含矩形分布内热源和线性分布内热源的非Fourier温度场解析解。由此分析对比了Fourier效应温度场与非Fourier效应温度场，结果表明，考虑热传播非Fourier效应时，由于热传播速度有限，在温度稳定之前，温度变化有明显的震荡，需要经过相对于Fourier导热更长的时间，才能达到稳定温度。同时，分析了内热源脉冲宽度对非Fourier效应的影响，结果表明，非Fourier效应与加热脉冲宽度有关，宽度越大，非Fourier效应越不明显。同时，对比分析了线性分布内热源与矩形分布内热源对应的温度场，结果表明，这两种内热源形式对应的温度场基本一致，，因此，在研究线性分布内热源时，可以简化为对应的矩形分布内热源问题以简化计算。针对柱坐标系及球坐标系下的一维含内热源非Fourier强瞬态导热问题，根据转轴公式，由直角坐标系分别推导出柱坐标系及球坐标系下的温度场控制方程。运用格林函数法对其进行求解，采用无量纲法和离散化积分法，获得了柱坐标系及球坐标系下一维含内热源的非Fourier效应温度场。结果表明，由于其形状的特点，柱坐标系及球坐标系下的热量传播与直角坐标系下不同，不再是以矩形方波的形式传播，而是出现尖峰，因此，其震荡会相对于直角坐标时更剧烈。由此可以预测，在同样的热扰动下，柱坐标系及球坐标系下温度波动性更明显，出现的最大温度更高，由此导致的工程问题会更显著。采用数值差分方法，针对二维非Fourier效应的导热温度场进行了研究，得到了其显式差分格式，分析了其稳定性。结果表明，二维非Fourier效应温度场的显式差分格式不符合稳定性要求。
[Abstract]:Electromagnetic induction quenching is one of the widely used surface strengthening techniques for crankshaft. Based on the deep understanding of the principle of electromagnetic induction quenching and the actual quenching process, the theory and numerical analysis of the temperature field of non- effect of electromagnetic induction quenching have been carried out in this paper. The main elements include: According to the engineering background of electromagnetic induction quenching process, based on the analysis of the distribution of internal heat source in electromagnetic induction heating process, the mathematical model of non- effect temperature field of one-dimensional internal heat source in right-angle coordinate system is derived. By using Green's function, Laplace transform and inverse transformation, the analytical solutions of non- temperature field with rectangular and linear internal heat sources are obtained in rectangular coordinate system. The temperature field of Fourier effect and that of non- effect are analyzed and compared. The results show that, considering the non- effect of heat propagation, the temperature change has obvious oscillation before the temperature is stabilized because of the limited heat propagation velocity. It takes longer than the Fourier heat conduction to achieve a stable temperature. At the same time, the influence of the pulse width of the internal heat source on the non- effect is analyzed. The results show that the non- effect is related to the width of the heating pulse, and the larger the width, the less obvious the non- effect is. At the same time, the temperature field corresponding to the internal heat source in the linear distribution is compared with that in the rectangular distribution. The results show that the temperature field corresponding to the two internal heat sources is basically the same. Therefore, in the study of the internal heat source in the linear distribution, It can be simplified to the corresponding internal heat source problem of rectangular distribution to simplify the calculation. In view of the non- strong transient heat conduction problem in cylindrical and spherical coordinates, the governing equations of temperature field in cylindrical coordinate system and spherical coordinate system are derived according to the formula of rotation axis. The Green's function method is used to solve the problem and the dimensionless method and discrete integral method are used to obtain the non- effect temperature field in the cylindrical coordinate system and the spherical coordinate system. The results show that the heat propagation in cylindrical coordinate system and spherical coordinate system is different from that in rectangular coordinate system because of its shape characteristics. The shock will be more intense than the rectangular coordinates. It can be predicted that under the same thermal disturbance, the temperature fluctuation in cylindrical coordinate system and spherical coordinate system is more obvious, the maximum temperature is higher, and the engineering problem will be more obvious. The numerical difference method is used to study the thermal conduction temperature field of two-dimensional non- effect. The explicit difference scheme is obtained and its stability is analyzed. The results show that the explicit difference scheme of two-dimensional non- effect temperature field does not meet the requirements of stability.
【学位授予单位】：北京理工大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TG156.3

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