Thermal error caused by the thermal deformation is one of the most significant factors influencing the accuracy of the machine tool. Among all the heat sources which lead to the thermal distortions, ...the spindle is the main one. This paper presents an overview of the research about the compensation of the spindle thermal error. Thermal error compensation is considered as a more convenient, effective and cost-efficient way to reduce the thermal error compared with other thermal error control and reduction methods. Based on the analytical calculation, numerical analysis and experimental tests of the spindle thermal error, the thermal error models are established and then applied for implementing the thermal error compensation. Different kinds of methods adopted in testing, modeling and compensating are listed and discussed. In addition, because the thermal key points are vital to the temperature testing, thermal error modeling, and even influence the effectiveness of compensation, various approaches of selecting thermal key points are introduced as well. This paper aims to give a basic introduction of the whole process of the spindle thermal error compensation and presents a summary of methods applied on different topics of it.
•Thermal error compensation is an effective and economical way to reduce the error.•Analyzing, testing, modeling and compensating are main aspects of the research.•Various devices and systems for temperature and thermal error testing are introduced.•Different kinds of methods used for thermal error modeling are studied.•Two commonly used mechanisms of thermal error compensation are explained.
•This paper first reviews different methods of designing thermal error models, before concentrating on employing ANFIS models.•The GM(1, N) model and fuzzy c-means clustering are used for variable ...selection, which is capable of simplifying the system prediction model.•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.
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.
Thermal error caused by thermal deformation is one of the most significant factors influencing the accuracy of the machine tool. Compensation is a practical and efficient method to reduce the thermal ...error. Among all the thermal error compensation processes, thermal error modeling is the premise and basis because the effectiveness of the compensation is directly determined by the accuracy and robustness of modeling. In this paper, an overview of the thermal error modeling methods that have been researched and applied in the past ten years is presented. First, the modeling principle and compensation methods of machine tools are introduced. Then, the methods are classified and summarized in detail. Finally, the future research trend of thermal error modeling is forecasted.
Thermally induced errors significantly affect the accuracy of the CNC machining process as they account for 40–70% of overall machining errors. The amount of thermal error is a function of the ...temperatures of the machine tool mixed with that of the environment, posing difficulty to accurately predict the thermal errors. To address this, this work compares prediction models under variations of cutting parameters and environmental temperatures and summarizes the strategy of manipulating the input data to attain a robust estimation of the thermal offset error. In particular, the accuracy of a prediction model can vary under varying ambient temperatures, and therefore, the robustness and generalizability are rather important in evaluating model’s efficacy. Here, four models, namely linear regression (LR), eXtreme gradient boosting (XGBoost), back propagation neural network (BPNN), and gated recurrent unit (GRU), are compared using the variance and average of the root mean square error (RMSE) for three spindle speed profiles. The averaged RMSEs fall into the range between 3.5 and 4.2 μm across all models and among them, the SFS–LR model yields the lowest variance. Finally, the estimated error is then being compensated using the zero-point shift function on the FANUC controller of the machine tool through the VMX platform developed by the Industrial Technology Research Institute (ITRI) in Taiwan. The resultant thermal error based on the SFS–LR model reduces 21.6 to 8.8 μm after compensation.
The axial thermal error of five-axis CNC machine tools is a significant factor affecting the machining accuracy. To predict the axial thermal error during the machining process, a method is proposed ...to model axial thermal error in the machining space of five-axis machine tools with a double swing table. The comprehensive thermal error model of the machining space is first established, which includes the axial thermal error of the spindle, worktable, and other components. The spindle is then simplified as a rod, and an analytical model for the axial thermal error of the spindle is developed based on the heat transfer governing equations. This model enables the determination of the time-varying behavior of the axial thermal error at different speeds. Furthermore, the worktable is simplified as a circular plate, and the analytical model for the axial thermal error of the worktable is established based on the thermal bending differential equation of the small deflection circular plate. This model allows for the determination of the time-space variation of the axial thermal error at different radii of the worktable. Finally, based on the axial comprehensive thermal error field of the five-axis CNC machine tool processing space, the distribution of the axial thermal error in the machine tool processing space under thermal equilibrium conditions is revealed. Experimental verification of the proposed model is conducted on the VMC-C50 double swing five-axis CNC machine tool. The experimental results show that the error between the measured axial thermal error value and the axial comprehensive thermal error model value is within 26.6%, thus confirming the accuracy of the proposed model.
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•Spindle thermal error modeling based on mayfly algorithm (MA) optimizing CNN for the complex working conditions with the training set of the constant speeds is proposed.•MA is used ...to optimize the number of convolutional kernels and the combination of convolutional kernel sizes in each convolutional layer.•Depth features of hidden layers of MA-CNN model are analyzed by comparing with the logarithm of the exponential thermal error mechanism model.•The turning point of the depth feature guides to establish a more accurate exponential thermal error mechanism model.•The model is verified by comparing with five other models and actual compensation experiment.
The dynamic changes in the temperature fields make it unavoidable for the spindle to undergo thermal deformation. Thermal error modelling is helpful in enhancing the accuracy of machine tools. This paper proposes a spindle thermal error modelling method based on the mayfly algorithm (MA) for complex working conditions. First, different working conditions are set to obtain thermal deformation and temperature data. A thermal error model is established using MA. MA is used to optimize the number and size of convolutional kernels. Next, the depth features of the model are compared with the exponential thermal error model in logarithmic space. The model is compared with five other models. The results indicate that the MA-CNN model has a higher accuracy. Finally, the compensation is conducted in three directions. The results show that the average thermal error in the Z direction is reduced by 63.75 %, which demonstrates the good performance of the model.
High-speed electric spindle is an important part of computer numerical control (CNC) machining equipment. The thermal displacement generated by the electric spindle during operation is the main ...reason that affects the machining stability and machining accuracy of the electric spindle. Compensating the thermal error of the high-speed electric spindle can effectively improve the CNC machining. Improve equipment processing performance. Therefore, it is particularly important to establish the accuracy of the thermal error prediction model. Taking the A02 high-speed electric spindle as the research object, ANSYS is used to analyze the thermal characteristics of the electric spindle, and the temperature and thermal displacement monitoring points of the electric spindle are arranged according to the simulation results, and the temperature and thermal displacement data of the monitoring points under different rotational speeds are collected; using K-means to classify temperature measurement points, uses the gray relation analysis degree to determine the correlation between the temperature measurement point and the thermal displacement data, and selects 4 temperature-sensitive points from 10 temperature measurement points. Finally, particle swarm optimization (PSO) is used to optimize the penalty factor and kernel function of support vector machine (SVM), and the PSO-SVM prediction model is established to compare with the neural network prediction model of SVM and genetic algorithm (GA) optimized SVM. The results show that PSO-SVM has better robustness, stability, and generalization ability.
Prediction and compensation of thermal position and orientation errors of a 5-axis machine tool by supervised online machine learning based on information from process-intermittent probing, used to ...identify and update a thermal autoregressive with exogenous input (ARX) model, is presented. The method of Weighted Least Squares (WLSQ) is introduced for adaptive parameter updates, to handle the diverse sample rates of the measured errors by on-machine probing. The down time for modelling is almost eliminated, by a continuous adaption of the model parameters. The compensation reduces more than 95% of the occurring errors during an experimental investigation of 88h.
In the Present machine tool industry, CNC machine tools are capable of meeting the demands like high productivity, high precision and reliability. But, accuracy of the machine tools is greatly ...affected by three types of errors, 1) geometric error, 2) thermal error and 3) cutting force induced error. Among these errors thermal error contributes more than 70% of total error. Thermal error management on machine tool is done through two approaches; they are 1) Thermal error reduction approach and 2) Thermal error compensation approach. This work deals with only thermal error compensation approach. Identification of thermal sensitive region on machine tool is the most challenging task of thermal error compensation. Thermal imaging is an experimental method which is currently being used to identify thermal sensitive region on machine tool. But this method is associated with more time, human efforts and high cost. Hence, in this work, two numerical methods such as thermal error sensitive method and thermal modal analysis method were used identify the thermal sensitive region. Here, cantilever beam was considered as a case study to illustrate the selection of thermal sensitive points.
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