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本文从三维热传导的基本微分方程出发,利用格林等式,建立了三维热传导问题的边界积分方程;通过对此问题的边界积分方程及三维调和算子基本解进行处理,得出了轴对称热传导问题的边界积分方程及基本解,然后利用所得基本解及边界元计算公式,对K48E 型柴油机活塞顶温度场进行分析。计算结果同实际柴油机活塞的测量结果和轴对称有限元计算结果颇为一致。实际计算表明,用边界元法分析活塞顶温度场,计算精度高,同实测值相比,误差在2%左右,而且计算前的数据准备工作量仅为有限元的1/5～1/10。
Based on the basic differential equations of three-dimensional heat conduction, the boundary integral equation of three-dimensional heat conduction problem is established by using Green’s equation. By solving the boundary integral equation and the basic solution of the three-dimensional harmonic operator, the axisymmetric heat conduction problem Boundary integral equations and basic solutions, and then use the basic solution and the boundary element formula to calculate the K48E diesel piston top temperature field analysis. The calculation results are in good agreement with the actual diesel piston measurement results and the axial symmetry finite element calculation results. The actual calculation shows that the boundary element method is used to analyze the top temperature field of the piston and the calculation accuracy is high. Compared with the measured value, the error is about 2%, and the data preparation before calculation is only 1/5 ~ 1/10 of the finite element .