Explicit error modeling of dynamic thermal errors of heavy machine tool frames caused by ambient temperature fluctuations

The frames of heavy machine tools generate considerable dynamic and position-dependent thermal errors due to their large scale and irregular temperature distribution caused by ambient temperature fluctuations. They are difficult to predict by conventional experimental data-based thermal error modeling methods. In this paper, a typical gantry frame of a heavy gantry type machine tool is taken as a vehicle to present a thermal error modeling methodology. The frame was firstly divided into several parts (elements). Then, an element simplification method was put forward to approximate it by simplified square tube shapes that retain most of the information from the original element. Based on this simplification, the temperature distribution and the equivalent load of the element were explicitly derived at selected key points on the frame. The static thermal error of the frame was obtained by the matrix displacement method, where a C¹ continuity stiffness matrix, including the shear deformation, was used to improve calculation accuracy. According to the formulated calculation method of the static thermal error and of the temperature impact convolution, the dynamic thermal error was derived utilizing the historical temperature sequence at the key points. Finally, the proposed thermal error model was verified by comparing it with FEM results in the static-state and by experimental results in the dynamic-state. The proposed method allows the formulation of an explicit dynamic thermal error model with a simple expression, which can be easily embedded in the PLC of a machine tool for compensation purposes. The method has the potential to be used for structural thermal error compensation in a wide range of heavy machine tools.