Thermal network-based compensation model for a vertical machining center subjected to ambient temperature fluctuations

Thermal influences, on and by the machine tool are one of the main reasons for the machining error. Although both the internal and the external heat sources lead to the thermal error, their relative proportion is typically dependent on the operating conditions such as machining parameters, the duration of machining and availability of temperature-controlled space to name a few. Literature survey reveals that a significant portion of the research either addresses the effects of internal heat sources or a combination of internal and external heat sources since the de-facto standard is to commission the machine tool in a temperature-controlled space. However, in this work, only the influence of external heat sources, predominantly caused by ambient temperature variations onto the distortions observed at the Tool Center Point (TCP) is considered. Smart sensory device such as Resistance Temperature Detector (RTD) sensor data is used for the modelling of thermal distortion due to external heat sources. The model is inherently based on the development of a thermal network using a lumped system approach for the estimation of temperatures of machine tool components and then the TCP distortion using the construction relation. Further, the model is modified through the introduction of two aspects: first is the addition of thermal contact conductance as the machine tool components are practically connected; and the second is the parameterization of free convection heat coefficient from being a stationary value to a function of the ambient temperature. The proposed method is then applied to predict the thermal error on a vertical machining center subjected to environmental temperature variation. The results show that the model considering a combination of the thermal contact conductance and parameterized free convection coefficient leads to a closer agreement with the experimental data. The strategy along with a thermal compensation technique presented in this research successfully lead to the improved machining precision (approximately 70% of the original thermal error is addressed across the combinations) without a need of a conditioned environment for C-frame type vertical machining centers.