中文摘要：

温度变化会引起机械零件几何尺寸的变化，传统热变形量计算公式是近似和线性的，在精度要求较低时适用，在高精度领域具有很大的局限性。经过多年的研究发现，温度变化时，零件任一尺寸的热变形不遵循传统的线性公式，而与零件形体其他几何尺寸有关，可表示为其他几何尺寸的非线性函数。利用晶体材料线膨胀系数与体积膨胀系数之间的关系，利用该关系建立圆柱轴类零件和孔型零件在稳态均匀温度场中的受热变形的数学模型，模型考虑形状因素对轴类零件和孔型零件热变形的影响。利用测量精度为±0．4μm热变形测量装置对不同圆柱轴类零件和孔型零件进行测量，试验结果显示，考虑形状因素的计算结果比传统公式计算结果更加接近试验值。

英文摘要：

Variation in temperature leads to corresponding variation in physical dimension of mechanical parts. The conventional calculation of thermal deformation is approximate and linear, which can be applied in normal or low precision field, but has great limitation in high precision field. After years of research, it is found that when temperature changes, thermal deformation of mechanical part does not follow the conventional linear formula, but relates to the physical dimension of the form of mechanical part, which can be indicated by a nonlinear formula. Mathematical models based on the relationship between volume expansion coefficient and linear expansion coefficient of crystal materials are established to calculate thermal deformations of cylindrical shaft parts and hollow parts in steady uniform temperature field, and the effect of form factors on thermal deformation of parts is considered. Thermal deformations of different cylindrical shaft parts and hollow parts are measured by using a thermal deformation measuring device with a measurement accuracy of 4-0.4~tm. Experimental results show that the calculation results with the form factors considered are closer to the experimental values than those of conventional formulas.