Thermal errors affect the machining quality to a great extent. The basis for error compensation and thermal structure optimization is thermal error modeling. However, existing analytical models encounter challenges in dealing with complex structures, determining boundary conditions and solving the temperature and deformation fields. In this paper, a thermal error analytical model of full-closed-loop feed systems based on equivalent temperature fields (ETF) is established. Firstly, the structural simplification and thermal parameter equivalence method is proposed. The machine components are equivalent to equivalent solid cuboid (ESC) with anisotropy so that the actual complex unsolvable problems are transformed into three-dimensional analytically solvable problems. Considering the ambient temperature variation and other nonhomogeneous influences, the transient ETF model is obtained based on Green’s function method. Secondly, the complex structure problems are separated into simple solvable one-dimensional problems. The functional relationship between measurable temperature and key thermal parameters is established. And the optimal key thermal parameters are solved inversely. Thirdly, the equivalent thermal deformation fields (ETDFs) are calculated by the Rayleigh-Ritz method combined with the obtained ETFs and subsequently corrected with the Gamma Distribution. The thermal positioning error model of the full-closed-loop feed system is established by combining the ETDF of each component with the gear grinding machine structure. Finally, the experiments and simulations are carried out to verify the proposed method. The results show that the proposed method can accurately describe the temperature field, deformation field, and thermal error of machine tools. Compared with the classical data-driven method, it is superior in prediction accuracy and robustness.

中文翻译：

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基于等效温度场的磨齿机全闭环进给系统热误差分析建模


热误差在很大程度上影响加工质量。误差补偿和热结构优化的基础是热误差建模。然而，现有的分析模型在处理复杂结构、确定边界条件以及求解温度和变形场方面遇到了挑战。本文建立了基于等效温度场 （ETF） 的全闭环馈电系统热误差分析模型。首先，提出了结构简化和热参数等效方法;机器组件等效于具有各向异性的等效固体长方体 （ESC），因此实际的复杂无法解决的问题被转化为三维分析可解决的问题。考虑环境温度变化和其他非均匀影响，基于 Green 函数法得到瞬态 ETF 模型。其次，将复杂的结构问题分解为简单可解的一维问题。建立了可测量温度和关键热参数之间的函数关系。并且对最优的关键热参数进行逆求解。然后，通过 Rayleigh-Ritz 方法结合获得的 ETF 计算等效热变形场 （ETDF），然后用 Gamma 分布进行校正。通过将各部件的ETDF与磨齿机结构相结合，建立了全闭环进给系统的热定位误差模型。最后，通过实验和仿真对所提方法进行了验证。结果表明，所提方法能够准确描述机床的温度场、变形场和热误差。 与传统的数据驱动方法相比，它在预测准确性和鲁棒性方面更胜一筹。