THE INVERSE PROBLEM OF THERMAL CONTACT RESISTANCE BETWEEN ROUGH SURFACES
YuYuanfeng1, LiZewei2, ZhengXiaoya1,*, 1 School of Astronautics, Northwestern Polytechnical University, Xi’an 710072, China;2 The 43st Institute of the Forth Academy of CASC,Xi’an 710025, China; 中图分类号:TU311 文献标识码:A
关键词:接触热阻;反问题;边界元法;共轭梯度法;最小二乘法 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.
Keywords:thermal contact resistance;inverse problem;boundary element method;conjugate gradient method;least square method -->0 PDF (1346KB)元数据多维度评价相关文章收藏文章 本文引用格式导出EndNoteRisBibtex收藏本文--> 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 https://doi.org/10.6052/0459-1879-18-076 YuYuanfeng, LiZewei, ZhengXiaoya. THE INVERSE PROBLEM OF THERMAL CONTACT RESISTANCE BETWEEN ROUGH SURFACES[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(3): 479-486 https://doi.org/10.6052/0459-1879-18-076
由图3和图4可以看出,正问题的测量误差会随着反问题的求解而被放大. 在 m,相对误差最大量值为20.23%;在 m,相对误差最小为0.43%,平均的相对误差 ,标准差为 K m /W,其结果的相对误差的最大值和最小值与测量误差相比,分别被放大了约225倍和5倍. 本节算例说明本文所采用的边界元法和共轭梯度法可以解决接触热阻反问题,但反问题的求解对测量误差比较敏感,结果会因测量输入误差而产生较大偏差.
新窗口打开 显示原图|下载原图ZIP|生成PPT 图7相对误差曲线 -->Fig. 7Relative error curve --> 从表1可以看出,在一些位置上,经过最小二乘法优化后,其计算结果的相对误差下降明显,与真实值更接近. 由图7可以看出,采 用最小二乘法优化后,整体的相对误差有所下降. 在处理之前平均相对误差为 , K m /W,处理后平均相对误差为 , K m /W,经过最小二乘法处理后,平均相对误差减小41.5%,标准差减小2.45%. 最小二乘法拟合的曲线既反映接触热阻的变化趋势,还消除了其局部波动,避开了计算结果中偏离真实值较大的测量点,使其总体误差进一步减小,计算结果更准确. 本节算例说明了最小二乘法可以作为处理不适定性问题的一种有效方法,最小二乘法优化算法可以使误差减小,使计算结果较不适定处理前的计算值更接近真实值,显著提高了计算结果的准确性.
4 结 论
本文将边界元法和共轭梯度法结合起来,研究了二维空间随坐标变化的接触热阻反问题,具有一定的实际参考价值,所得结论如下: (1)在接触热阻的反问题识别中,采用边界元法和共轭梯度法可求解反问题. 由于边界元法不需要知道和计算内部区域的温度和热流,因而大大减少了计算量. (2)在无测量误差的情况下,本文采用的方法准确可行,可以真实地反演计算得到接触面上的接触热阻值. (3)反问题对测量误差较敏感,存在误差的情况下,计算结果会偏离真实值. 且正问题的误差会随反问题的求解而被放大,使得反问题求解的数值结果误差较大. (4)在正问题中的误差在反问题中被放大的情况下,为处理不适定性问题,采用了最小二乘法,使曲线避开反问题计算结果中一些偏离实际值较大的点,显著提高了反演计算结果的准确性. The authors have declared that no competing interests exist.
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