Manufacturing industries demand machine tools (MT) that are precise throughout their life cycle to address the ever-increasing market demands on quality and productivity. Thermal deformation of MT structure results in tool center point (TCP) drift which is one of the issues contributing to the part geometry deviations. Various approaches are employed to deal with it. Thermally stable design of the MT enables the distribution of heat uniformly in the MT structure to reduce the drift; however, it involves MT redesign. On the other hand, the data-driven models capture the MT thermal characteristics; however, they require tedious experimentations to measure temperature and TCP drift that is not cost-effective and increases downtime. To overcome this FE-based simulations paved a path to understanding the problem economically. The FE simulations reported in the literature employ the formula method for TCP drift prediction, which inherits prediction error due to its inability to capture the MT condition in real-time. On the other hand, employing a large number of temperature sensors requires regular monitoring, and in case of sensor failure, real-time modelling and visualization would be adversely affected. On the other hand, the setup and sensors needed for TCP drift measurement are complex and expensive. Hence, there is a need to develop an approach that can predict the TCP’s drift with a minimum number of temperature sensors and avoid the physical measurement of the TCP drift.

In the present work, the limitations of the formula-based approach are eliminated by the energy balance-based FEA simulation that considers the experimentally obtained data on heat flux to predict the TCP’s thermal drift. The resistance temperature detector sensors are mounted on the thermal hotspots, which are identified using infrared imaging during sensitivity analysis of the MT, to supply the heat flux as input to the FE model. The sensitivity analysis reveals that the MT spindle and Z-axis drive are critical in heat generation. To understand the detailed thermal response of the MT, the FE simulation is conducted by considering: (i) only the MT spindle and (ii) the whole milling MT. The simulations on the MT spindle reveal that the TCP drift in the Z-axis direction is very high compared to the other two axes. Based on the above analysis, the whole MT TCP drift is simulated along the Z-axis. The accuracy of the simulated TCP drift is validated against the experimental results, obtained under different process conditions, with an accuracy of 88.80%. A neural network (NN) model is developed to capture the relation between temperature measurements and thermal drift. A large data set obtained from the FE model by providing the heat flux at various spindle speeds was used to train the NN without performing expensive and tedious experimentation for TCP drift measurements. The number of temperature sensors is reduced to reduce the cost and complexity of the model considering the Pearson correlation coefficient, from eight to three. The NN model was validated on a different data set obtained at 8000 rpm spindle speed and achieved an accuracy of 91.12 % (eight sensors) and 89.83 % (three sensors).

Keywords: Machine tool, Thermal error, Finite element analysis, Machine learning models