Achieving high workpiece accuracy is the long-term goal of machine tool designers. There are many causes for workpiece inaccuracy, with thermal errors being the most common. Indirect compensation (using prediction models for thermal errors) is a promising strategy to reduce thermal errors without increasing machine tool costs. The modelling approach uses transfer functions to deal with this issue; it is an established dynamic method with a physical basis, and its modelling and calculation speed are suitable for real-time applications. This research presents compensation for the main internal and external heat sources affecting the 5-axis machine tool structure including spindle rotation, three linear axes movements, rotary C axis and time-varying environmental temperature influence, save for the cutting process. A mathematical model using transfer functions is implemented directly into the control system of a milling centre to compensate for thermal errors in real time using Python programming language. The inputs of the compensation algorithm are indigenous temperature sensors used primarily for diagnostic purposes in the machine. Therefore, no additional temperature sensors are necessary. This achieved a significant reduction in thermal errors in three machine directions X, Y and Z during verification testing lasting over 60 h. Moreover, a thermal test piece was machined to verify the industrial applicability of the introduced approach. The results of the transfer function model compared with the machine tool's multiple linear regression compensation model are discussed.

实现高工件精度是机床设计人员的长期目标。造成工件误差的原因有很多，最常见的是热误差。间接补偿（使用热误差预测模型）是一种在不增加机床成本的情况下减少热误差的有前途的策略。建模方法使用传递函数来解决此问题。它是一种已经建立的具有物理基础的动态方法，其建模和计算速度非常适合实时应用。这项研究提出了补偿影响5轴机床结构的主要内部和外部热源，包括主轴旋转，三个线性轴运动，C轴旋转和随时间变化的环境温度影响，但不包括切削过程。使用传递函数的数学模型直接在铣削中心的控制系统中实现，以使用Python编程语言实时补偿热误差。补偿算法的输入是本地温度传感器，主要用于机器中的诊断目的。因此，不需要额外的温度传感器。这样可以显着减少三个方向的热误差验证测试期间的X，Y和Z持续超过60小时。此外，对热测试件进行了加工以验证所引入方法的工业适用性。讨论了传递函数模型与机床多元线性回归补偿模型的结果。