Thermal error modelling of machine tools based on ANFIS with fuzzy c-means clustering using a thermal imaging camera

Thermal errors are often quoted as being the largest contributor to CNC machine tool errors, but they can be effectively reduced using error compensation. The performance of a thermal error compensation system depends on the accuracy and robustness of the thermal error model and the quality of the inputs to the model. The location of temperature measurement must provide a representative measurement of the change in temperature that will affect the machine structure. The number of sensors and their locations are not always intuitive and the time required to identify the optimal locations is often prohibitive, resulting in compromise and poor results. In this paper, a new intelligent compensation system for reducing thermal errors of machine tools using data obtained from a thermal imaging camera is introduced. Different groups of key temperature points were identified from thermal images using a novel schema based on a Grey model GM (0, N) and Fuzzy c-means (FCM) clustering method. An Adaptive Neuro-Fuzzy Inference System with Fuzzy c-means clustering (FCM-ANFIS) was employed to design the thermal prediction model. In order to optimise the approach, a parametric study was carried out by changing the number of inputs and number of membership functions to the FCM-ANFIS model, and comparing the relative robustness of the designs. According to the results, the FCM-ANFIS model with four inputs and six membership functions achieves the best performance in terms of the accuracy of its predictive ability. The residual value of the model is smaller than ± 2 μm, which represents a 95% reduction in the thermally-induced error on the machine. Finally, the proposed method is shown to compare favourably against an Artificial Neural Network (ANN) model

Thermal error modelling of a gantry-type 5-axis machine tool using a Grey Neural Network Model

This paper presents a new modelling methodology for compensation of the thermal errors on a gantry-type 5-axis CNC machine tool. The method uses a “Grey Neural Network Model with Convolution Integral” (GNNMCI(1, N)), which makes full use of the similarities and complementarity between Grey system models and artificial neural networks (ANNs) to overcome the disadvantage of applying either model in isolation. A Particle Swarm Optimisation (PSO) algorithm is also employed to optimise the proposed Grey neural network. The size of the data pairs is crucial when the generation of data is a costly affair, since the machine downtime necessary to acquire the data is often considered prohibitive. Under such circumstances, optimisation of the number of data pairs used for training is of prime concern for calibrating a physical model or training a black-box model. A Grey Accumulated Generating Operation (AGO), which is a basis of the Grey system theory, is used to transform the original data to a monotonic series of data, which has less randomness than the original series of data. The choice of inputs to the thermal model is a non-trivial decision which is ultimately a compromise between the ability to obtain data that sufficiently correlates with the thermal distortion and the cost of implementation of the necessary feedback sensors. In this study, temperature measurement at key locations was supplemented by direct distortion measurement at accessible locations. This form of data fusion simplifies the modelling process, enhances the accuracy of the system and reduces the overall number of inputs to the model, since otherwise a much larger number of thermal sensors would be required to cover the entire structure. The Z-axis heating test, C-axis heating test, and the combined (helical) movement are considered in this work. The compensation values, calculated by the GNNMCI(1, N) model were sent to the controller for live error compensation. Test results show that a 85% reduction in thermal errors was achieved after compensation

Thermomechanical modeling of motorized spindle systems for high-speed milling

Motorized high speed spindles with angular contact ball bearings and minimum oil lubrication may suddenly fail due to thermal problems, for which the exact reason is unknown. Currently, internal temperatures, internal heat flow, thermal preload and stiffness changes in this type of spindle cannot be predicted with sufficient accuracy, and there are observations that cannot be fully explained by previous models. It is believed that the understanding of thermal and mechanical interactions between different spindle components in a practical spindle system is the key to improving spindle performance and reliability. This research proposes to develop an integrated thermo-mechanical model to account for all heat sources, heat transfer paths, heat sinks, and relative thermal expansions of the spindle system. The temperature field of the entire spindle is predicted by an axisymmetric finite difference model. The model includes linear heat conduction and nonlinear convection and can efficiently solve for the temperature growth of each element. The model accuracy is then validated by comprehensive experiments through accurate temperature and heat flux measurements. Finally, the predicted temperature field is used to determine the mechanical behavior changes in component fit conditions, stiffness, bearing preload, natural frequency, etc. Quantitative relations for temperatures, internal heat flow, thermal preload and spindle stiffness as functions of spindle speed, set cooling conditions and the rigidity of the preloading mechanism have been established. Sensitivity to changes of speed and cooling conditions was also investigated. These results reveal some new observations of spindle behavior that were not reported before. Temperatures of the spindle shaft at high speed are strongly dependent on convective heat flow to surrounding fluids. Also, it was possible to identify temperature oscillations of the bearings under certain operating conditions. The model can be used for diagnosis or design and aims at helping to reduce premature spindle failure and to avoid changing bearing stiffness during machining