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 引用本文: 余远锋, 李泽卫, 郑晓亚. 粗糙表面之间接触热阻反问题研究[J]. 力学学报, 2018, 50(3): 479-486.
Yu Yuanfeng, Li Zewei, Zheng Xiaoya. THE INVERSE PROBLEM OF THERMAL CONTACT RESISTANCE BETWEEN ROUGH SURFACES[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(3): 479-486.
 Citation: Yu Yuanfeng, Li Zewei, Zheng Xiaoya. THE INVERSE PROBLEM OF THERMAL CONTACT RESISTANCE BETWEEN ROUGH SURFACES[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(3): 479-486.

THE INVERSE PROBLEM OF THERMAL CONTACT RESISTANCE BETWEEN ROUGH SURFACES

• 摘要: 当两个固体表面相互接触时,由于接触面粗糙度的影响,界面间就形成了非一致接触,这种接触导致热流收缩,进而产生接触热阻. 目前的理论研究主要集中在正问题研究,对反问题的研究相对较少. 接触热阻反问题研究是通过研究部分边界温度、热流和部分测量点的温度来反演得到界面上的接触热阻. 反问题研究在很多工程领域都有应用,如航空航天、机械制造、微电子等,是工程中确定接触热阻一种快速有效的方法. 本文采用边界元法和共轭梯度法研究了二维空间随坐标变化的接触热阻反问题. 为了验证方法的准确性和可行性,假定在已知部分测量点温度和真实接触热阻的情况下,反演计算得到界面的温度和热流,进而得到接触热阻,并与真实接触热阻进行比较. 结果表明采用边界元法和共轭梯度法在无测量误差的情况下,可以准确反演获得界面的真实接触热阻. 若存在测量误差,反演计算结果对测量误差极其敏感,反演结果误差会由于测量误差的引入而被放大. 为处理这种不适定性, 采用最小二乘法对反演计算结果进行校正,结果表明采用最小二乘法能够避开反问题中一些偏离实际值较大的测量点,显著提高反演计算结果的准确性.

Abstract: When two solid surfaces are in contact, it leads to non-uniform contact because of surfaces roughness. This causes constriction of heat flux and forms thermal contact resistance. The theoretical research is mainly focused on the positive problem, but there are few studies on the inverse problem. The inverse problem of thermal contact resistance is to obtain thermal contact resistance by a part of the boundary temperature, heat flux and some of the measured point temperature. The research has been applied in many fields, such as aerospace, mechanical manufacturing, microelectronics and other fields. It is a fast and effective method to determine thermal contact resistance in engineering field. In this paper, the inverse problem of thermal contact resistance with 2-D coordinate variation was solved by the boundary element method (BEM) and the conjugate gradient method (CGM). In order to verify the accuracy and feasibility of the method, according to the measured point temperature and the assumed thermal contact resistance, the temperature and the heat flux of the interface could be obtained, and then calculated and compared with the value of actual thermal contact resistance. The results show that the actual thermal contact resistance can be accurately obtained by using the BEM and CGM without the measurement error. But there exists the measurement error, the calculated result will be extremely sensitive to the measurement error, and the error of inversion result will be amplified due to the measurement error. In order to deal with this ill-posed problem, the least-squares method (LSM) was used to correct the calculated results. The results show that it can avoid some points deviating from the actual value in the inverse problem, and obviously improve the accuracy of calculations.

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