Thermal error modelling of NC machine tools based on impulse response model

In CNC machine tools, transient temperature variation in the headstock assembly is the major contributors for spindle thermal error. The compensation of thermal error is critical for ensuring the accuracy of machine tool. The performance of an error compensation system depends largely on the accuracy and robustness of the thermal error model. In the present work, a robust thermal error model is developed for minimizing the error in lateral direction of the spindle which significantly influences the geometrical accuracy of the workpiece. Analysis-of-variance (ANOVA) is applied to the results of the experiments in determining the percentage contribution of each individual temperature key point against a stated level of confidence. Based on the analysis of existing approaches for thermal error modeling of machine tools, an approach of LASSO (least absolute shrinkage and selection operator) is proposed in order to avoid the multi collinearity problem. The proposed method is an innovative variable selection method to remove redundant or unimportant temperature key points in the linear thermal error model and minimize the residual sum of squares. The predictive error model is found to have better robustness and accuracy in comparison to the combination of grey correlation and step wise linear regression for error compensation of CNC lathe. Keywords: Analysis Of Variance (ANOVA), CNC Machine Tool, Grey Correlation Analysis (GCA), Headstock Assembly, LASSO Regression, Mean Absolute Deviation (MAD), Mean Square Error (MSE), Robustness, Standard Deviation (SD), Thermal Error.

Thermal errors are major contributor to dimensional errors of a part during precision machining. Error compensation is an effective method to reduce thermal errors. Accurate modeling of thermal errors is a prerequisite for thermal error compensation. In this paper, five key temperature points of a computer numerical control (CNC) machine tool were selected based on grey relational analysis method (GRAM). One thermal error model based on the five key temperature points was proposed using artificial fish swarm and ant colony algorithm-based back-propagation neural network (AFSACA-BPN). AFS is applied to generate initial pheromone value of ACA, which improves the computational efficiency of BPNs and prediction accuracy of thermal error modeling. One thermal error real-time compensation system was developed based on the proposed model. An experiment was carried out to verify the performance of the compensation system. Experiment results show that the diameter error of the workpiece reduced from 23 to 10 μm after compensation.

With the structure design and manufacture of CNC machine tool becoming more and more perfect, its geometry errors have been controlled, thermal error generated by thermal deformation of CNC machine tool is the main error, which has strongly influence on the CNC machine tool's process precision. Thermal error compensation is an important method for increasing the process precision of CNC machine tool, and the neural networks technology is the major tool in thermal error modeling and compensation. In this paper, some applications of neural networks in thermal error modeling and compensation are introduced, and they are demonstrated by examples, the results prove that researches on artificial neural networks and relative algorithms have good effects on CNC machine tool's thermal error modeling and compensation.

Having great impacts on machining precision, thermal error is one of the main error sources for heavy-duty computer numerical control machine tools. Thermal error compensation using prediction models with temperature field is an effective way to improve machining precision of computer numerical control machine tools. The accuracy and robustness of thermal error prediction models depend considerably on the selection of temperature measurement points. Too many temperature measurement points will increase the complexity of thermal error prediction models and incur over-fitting problems. To improve the complexity and performances of prediction models, a selection method of key temperature measurement points based on density peaks clustering is presented in this article. This method is able to cluster massive temperature measurement points quickly and select the key temperature measurement point which characterizes the common feature of each cluster automatically. It is verified on the ZK5540A heavy-duty computer numerical control gantry drilling machine tool. Six key temperature measurement points are selected from the total 222 temperature measurement points with this method. Then, the back propagation neural network optimized by genetic algorithm thermal error model with the six key temperature measurement points is built and the accuracy and robustness of the model are analyzed. The results show that the model has high prediction accuracy and strong robustness.

Thermal errors can have significant effects on CNC machine tool accuracy. The errors come from thermal deformations of the machine elements caused by heat sources within the machine structure or from ambient temperature change. The effect of temperature can be reduced by error avoidance or numerical compensation. The performance of a thermal error compensation system essentially depends upon the accuracy and robustness of the thermal error model and its input measurements. This paper first reviews different methods of designing thermal error models, before concentrating on employing an adaptive neuro fuzzy inference system (ANFIS) to design two thermal prediction models: ANFIS by dividing the data space into rectangular sub-spaces (ANFIS-Grid model) and ANFIS by using the fuzzy c-means clustering method (ANFIS-FCM model). Grey system theory is used to obtain the influence ranking of all possible temperature sensors on the thermal response of the machine structure. All the influence weightings of the thermal sensors are clustered into groups using the fuzzy c-means (FCM) clustering method, the groups then being further reduced by correlation analysis.A study of a small CNC milling machine is used to provide training data for the proposed models and then to provide independent testing data sets. The results of the study show that the ANFIS-FCM model is superior in terms of the accuracy of its predictive ability with the benefit of fewer rules. The residual value of the proposed model is smaller than ±4μm. This combined methodology can provide improved accuracy and robustness of a thermal error compensation system.

The thermal distortion of YK3610 hobbing machine is analyzed. The concept of clustering analysis is proposed and implemented on the gear hobbing machine. The model was used in the experimental of thermal error compensation. The results show that the thermal error compensation control system can reduce thermal errors significantly and the prediction accuracy of the thermal error model is high enough.

High-speed motorized spindle heating will produce thermal error, which is an important factor affecting the machining accuracy of machine tools. The thermal error model of high-speed motorized spindles can compensate for thermal error and improve machining accuracy effectively. In order to confirm the high precision thermal error model, Beetle antennae search algorithm (BAS) is proposed to optimize the thermal error prediction model of motorized spindle based on BP neural network. Through the thermal characteristic experiment, the A02 motorized spindle is used as the research object to obtain the temperature and axial thermal drift data of the motorized spindle at different speeds. Using fuzzy clustering and grey relational analysis to screen temperature-sensitive points. Beetle antennae search algorithm (BAS) is used to optimize the weights and thresholds of the BP neural network. Finally, the BAS-BP thermal error prediction model is established. Compared with BP and GA-BP models, the results show that BAS-BP has higher prediction accuracy than BP and GA-BP models at different speeds. Therefore, the BAS-BP model is suitable for prediction and compensation of spindle thermal error.

The thermal error model of the 5-axis grinding machine tool was acquired by the homogeneous coordinate transformation, including 17 thermal error components. The thermal volumetric error real time compensation model was built by using the multiple regression analysis. The thermal error compensation control system and the temperature sensing system were developed and used as real-time compensation for the 5-axis grinding machine tool.

Thermal error caused by the thermal deformation of computer numerical control (CNC) machine tools is one of the main factors to affect the machining accuracy. With monitoring data of the temperature field, establishing data-driven thermal error model is considered as a more convenient, effective and cost-efficient way to reduce the thermal error. As a matter of fact, it is very difficult to develop a thermal error model with perfect generalization adapting to different working conditions of machining tools. In this paper, a method of an ensemble modeling (EM) based on Convolution Neural Network (CNN) and Back Propagation (BP) Neural Network for modeling thermal error is presented. This ensemble model takes full advantages of two different neural networks, namely CNN having self-extracting feature to solve collinear problem in temperature field and BP can process heat source to thermal error by mapping nonlinear function, then combined into a EM. To demonstrate the effectiveness of the proposed model, an experiment platform was set up based on a heavy-duty CNC machine tool. The results show that the proposed model achieves better accuracy and strong robustness in comparison with only with BP network and CNN network respectively.

Revolutionizing gear hobbing machine precision: Innovative thermal error compensation and intelligent error control with enhanced crystal structure algorithm and self-attention bidirectional minimal gated unit network

Thermal error is the major factor in restricting the accuracy of CNC machining. The modeling accuracy is the key of thermal error compensation which can achieve precision machining of CNC machine tool. The traditional thermal error compensation models mostly focus on the fitting accuracy without considering the robustness of the models, it makes the research results into practice is difficult. In this paper, the experiment of model robustness is done in different spinde speeds of leaderway V-450 machine tool. Combining fuzzy clustering and grey relevance selects temperature-sensitive points of thermal error. Using multiple linear regression model (MLR) and distributed lag model (DL) establishes model of the multi-batch experimental data and then gives robustness analysis, demonstrates the difference between fitting precision and prediction precision in engineering application, and provides a reference method to choose thermal error compensation model of CNC machine tool in the practical engineering application.

An approach to identify and select optimal temperature-sensitive measuring points for thermal error compensation modeling in CNC machines: A case study using cantilever beam

The modeling and compensation method is a common method for reducing the influence of thermal error on the accuracy of machine tools. The prediction accuracy and robustness of the thermal error model are two key performance measures for evaluating the compensation effect. However, it is difficult to maintain the prediction accuracy and robustness at the desired level when the ambient temperature exhibits strong seasonal variations. Therefore, a year-round thermal error modeling and compensation method for the spindle of machine tools based on ambient temperature intervals (ATIs) is proposed in this paper. First, the ATIs applicable to the thermal error prediction models (TEPMs) under different ambient temperatures are investigated, where the C-Means clustering algorithm is utilized to determine ATIs. Furthermore, the prediction effect of different numbers of ATIs is analyzed to obtain the optimal number of ATIs. Then, the TEPMs corresponding to different ATIs in the annual ambient temperature range are established. Finally, the established TEPMs of ATIs are used to predict the experimental data of the entire year, and the prediction accuracy and robustness of the proposed ATI model are analyzed and compared with those of the low and high ambient temperature models. The prediction accuracies of the ATI model are 20.6% and 41.7% higher than those of the low and high ambient temperature models, respectively, and the robustness is improved by 48.8% and 62.0%, respectively. This indicates that the proposed ATI method can achieve high prediction accuracy and robustness regardless of the seasonal temperature variations throughout the year.

In the process of thermal error modeling of machine tools, the error information is not transparent and the data characteristics are not comprehensive. The Dijkstra algorithm provides an optimization for the classical algorithm, and improving the accuracy of machine tools is an important issue in advanced manufacturing technologies. In this paper we study two methods of error avoidance and error compensation. For CNC machine tools, computer real-time error compensation technology is an economical and effective basic approach. The application of the folded Dijkstra algorithm to realize the compensation technology of the full error model of geometrical machine tool including geometric error and thermal error is put forward. The practical results show the geometric error and thermal error are compensated on 3-axis and 4-axis CNC machine tools, and the accuracy of the error model and the practicality of the compensation method.

Thermal error significantly influences the accuracy of CNC machine tool. A high-performance compensation system depends upon the accuracy and robustness of the model and appropriate model inputs of temperatures. In this paper, fuzzy clustering is conducted in temperature classification. Based upon an evaluation model, an optimal temperature classification can be found. The representative temperatures from each group construct temperature candidates. Then, a sliced inverse regression (SIR) model is introduced in thermal error modeling, which can change the problem of high-dimensional forward regression into several one-dimensional regression and meanwhile further eliminate the coupling among temperatures candidates. To evaluate the performance of SIR model, measuring experiment was carried out on a horizontal machining center for temperature and thermal error information under two experimental conditions. The proposed classification method was used to classify 29 temperature variables into five groups. A SIR model was built upon the five temperature candidates. Meanwhile, stepwise regression (SR) theory is also conducted for temperature variable selection and thermal error modeling. Comparison shows that both of the two models have high fitting accuracy, while the SIR model is more excellent in robustness than the SR model. Finally, a compensation system was developed. Compensation experiment shows that the SIR model is practical and effective, which can reduce the axial thermal error from 43 to 7 μm.