Temperature variations in the machine tool structural components may lead to relative pose variations between the tool tip and the workpiece. Different thermal layouts may lead to various temperature distributions and generate various thermal deformations. Thermal symmetric design is often used to complete thermal balancing of machine tools. Studies on theoretical methods to guide the layout design of the heat sources (HS) and cooling sources (CS) in machine tools are insufficient. To address this problem, a novel analytical approach for characterising the equivalent cuboid thermal response of machine tool structural components is presented in this paper. The proposed analytical modelling method can realise analytical temperature field modelling with Green's function, calculating the equivalent thermal moment with Reissner's theory, and matching the thermal power-deformation mapping coefficient (TPDMC) using the finite element method (FEM). The explicit and correlative formulation between the thermal power of the HSs and CSs and the guideway thermal deviations is deduced. Furthermore, the layout principles of the CSs are presented according to the maximum efficiency of the thermal moment and the characterisation matching of the TPDMC curves. Afterwards, power matching of the CS is obtained with the aid of the minimum deformation principles of the key positions. Simulated and experimental results illustrated that the proposed method can be used to rapidly and accurately analyse the temperature and thermal deformation responses of the machine tool, as well as to provide a thermal balancing strategy according to specific thermal conditions. The analytical approach proposed in this paper is a general method suitable for the thermal balancing design of machine tools, and it is of great value for improving the thermally induced accuracy stability of machine tools.

机床结构部件中的温度变化可能导致刀头和工件之间的相对姿势变化。不同的热布局可能导致各种温度分布并产生各种热变形。热对称设计通常用于完成机床的热平衡。指导机床热源（HS）和冷却源（CS）布局设计的理论方法研究不足。为了解决这个问题，本文提出了一种新颖的分析方法，用于表征机床结构部件的等效长方体热响应。所提出的解析建模方法可以实现格林函数的解析温度场建模，并根据Reissner的理论计算等效热矩，使用有限元方法（FEM）匹配热功率变形映射系数（TPDMC）。推导了HS和CS的热功率与导轨热偏差之间的显式和相关公式。此外，根据热矩的最大效率和TPDMC曲线的特性匹配，提出了CS的布局原理。然后，借助关键位置的最小变形原理获得CS的功率匹配。仿真和实验结果表明，该方法可用于快速，准确地分析机床的温度和热变形响应，并根据具体的热工况提供一种热平衡策略。