Thermal Error Modeling Research Articles

Thermal error modeling of machine tool based on dimensional error of machined parts in automatic production line

Thermally induced error has proven to be the major source of machining error for the machine tool working in a non-temperature-controlled workshop. Current research on thermal error modeling and compensation is implemented based on the measured thermal deformation of machine tool, and the data is obtained referring to spindle idling rather than metal cutting condition, resulting in the disadvantages of the established model with low adaptability to varying conditions. In this paper, a modeling and compensation method based on the dimensional error of the machined parts is proposed to address the issue and verified through machine tools in an automatic production line. Compared with the modeling based on thermal deformation, the method formulates a more direct relations between temperature rise and machining error. The thermal error modeling is carried out by measuring the dimension deviation of the inner hole diameter of the motor end cover and the screened representative temperature variables. Meantime, considering the temperature coefficient in model is difficult to converge when modeling with the single-day data, the unified modeling with the multi-day data is realized by improving the conventional multiple linear regression model. Finally, the generalized model used for thermal error compensation in x direction of the machine tool is obtained. The real-time compensation of the thermal error based on the established model is realized with the machine tool machining in mass production. The verification results show that this error modeling and compensation method can reduce the machining error of the end cover by more than 52%, irrespective of experiencing various complicated working conditions. Stability and robustness of the modeling are also validated through application on the other machine tool with the same configuration and real machining over seven days.

Thermal error modeling of electrical spindle based on optimized ELM with marine predator algorithm

High-speed electric spindle is an important part of computer numerical control (CNC) machining equipment, and the thermal displacement generated by the electric spindle during operation affects the electric spindle machining stability and machining accuracy. Error compensation for the high-speed motorized spindle can well compensate for the influence of thermal displacement on machine tool processing. Therefore, the prediction of thermal displacement of electric spindle is particularly important. In this paper, firstly, the temperature field information is obtained by simulating and analyzing the calculation of the heat generation and heat exchange inside the electric spindle. Set up the experimental platform with reasonable temperature measurement points according to the simulation results; secondly, the temperature sensitive points are screened by fuzzy C-mean clustering algorithm and Pearson correlation coefficient, which can effectively improve the covariance and correlation between temperature variables; finally, based on the screened data for thermal error modeling, an optimized extreme learning machine based on marine predator algorithm (MPA-ELM) is provided to predict the thermal displacement of electric spindles model. And comparing the model accuracy of extreme learning machine (ELM), MPA-ELM and extreme learning machine optimized by genetic algorithm (GA-ELM), the experimental data show that MPA-ELM has better prediction accuracy.

Thermal error modeling of high-speed electric spindle based on Aquila Optimizer optimized least squares support vector machine

The thermal error of electric spindle is an important factor affecting the machining accuracy of machine tools. To establish the thermal error prediction model, the thermal characteristics of A02 electric spindle were simulated and analyzed by ANSYS, to determine the best temperature measuring point. The temperature and thermal error of A02 electric spindle at different rotational speeds were obtained by thermal characteristics experiment. Through the combination of systematic clustering and grey relational analysis, four best temperature measuring points were selected from ten temperature measuring points. A prediction model of least squares support vector machine (LSSVM) optimized by Aquila Optimizer (AO) is established and compared with the model optimized by Particle Swarm Optimization (PSO), it is superior to the latter in prediction accuracy (η), goodness of fit (R2), root mean square error (RMSE) and mean absolute error (MAE). The AO-LSSVM prediction model based on experimental data has a prediction accuracy of more than 94% for the thermal error of motorized spindle and has good stability and generalization ability.

Mist-edge-fog-cloud computing system for geometric and thermal error prediction and compensation of worm gear machine tools based on ONT-GCN spatial–temporal model

The geometric precision of worm gears (WGs) determines the service performance and life of precision machine tools, indexing turntables and other equipment. The machining accuracy of worm gear machine tools (WGMTs) is the core to guarantee the geometric precision of WGs, and is greatly affected by the thermal and geometric errors. To improve the machining accuracy of WGMTs, the thermal and geometric errors should be controlled and compensated. But the control system has a poor real-time performance, and the synchronous control of the geometric and thermal errors cannot be currently achieved, and the thermal error model has a low prediction accuracy and low robustness. To make up for the above gap, a mist-edge-fog-cloud computing system is designed for the error prediction and compensation to relieve the bandwidth pressure of the industrial Internet. Moreover, a sensor network composed of multiple sensors is constructed to obtain the thermal information, and then the ordered neuron temporal-graph convolutional network (ONT-GCN) is proposed based on the ordered neuron-long short term memory network (ON-LSTMN) and graph convolutional network (GCN) for the first time to conduct the spatial and temporal modeling of the thermal error data. The interaction among multiple sensors is explicitly considered, and the dependence of the temporal information of the thermal error data on and spatial information of sensors is taken into account. Besides, to realize the error control, the mapping relationship between the tooth surface error and geometric-thermal errors is established. The error mapping model converts 51 geometric errors and 4 thermal errors into the spatial errors of the hob. Moreover, the sensitivity of errors is analyzed, and then the key error items that affect the geometric precision of the tooth surface are identified and compensated. The results show that the ONT-GCN is superior to traditional time-series modeling methods and that the mist-edge-fog-cloud computing system can effectively shorten the executing time compared with other system frameworks, and can improve the machining accuracy of WGMTs.

Compensation of Thermally Induced Errors in Five-Axis Computer Numerical Control Machining Centers Equipped With Different Spindles

Abstract Thermally induced errors are the dominant source of inaccuracy in machine tools today and are often the most difficult type of error to reduce. Software compensation of thermally induced displacements at the tool center point (TCP) is a widely employed error reduction technique due to its cost-effectiveness and ease of implementation. Transfer function (TF)-based compensation methods lead to promising results, as has been shown in previous studies. Furthermore, machine tool manufacturers frequently offer the same type of machine tool equipped with different spindle units. This leads to different thermal deformation behavior depending on the specific spindle unit mounted in the machine tool. To demonstrate this difference, experimental research is carried out on three five-axis computer numerical control (CNC) machining centers of the same type equipped with three different spindle units. The experimentally obtained thermal errors at the TCP of three machine tools with different mounted spindle units are compared, showing a significant variation in thermal errors in the Z-direction depending on the spindle unit. The research presented in this paper shows a dynamic approach to thermal error compensation of five-axis CNC machining centers considering different spindle units. System identification theory is applied to build dynamic thermal error models for three different spindle units based on calibration experiments. Subsequently, the evaluation of model performance through spindle spectrum tests shows that a reduction in thermal error of up to 85% was achieved in the Z-direction after compensation.

Thermal error modeling of electric spindle based on particle swarm optimization-SVM neural network

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.

Ambient temperature-induced thermal error modelling for a special CMM at the workshop level based on the integrated temperature regression method

Ambient temperature-induced thermal error modelling for a special CMM at the workshop level based on the integrated temperature regression method

Year-Round Thermal Error Modeling and Compensation for the Spindle of Machine Tools Based on Ambient Temperature Intervals.

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.

Review on Thermal Error Suppression and Modeling Compensation Methods of High-Speed Motorized Spindle

Abstract: The internal structure of a high-speed motorized spindle is compact, and a large amount of heat is generated in the process of high-speed operation, which causes thermal deformation of the parts. The thermal characteristics of the motorized spindle become worse when the temperature increases, which seriously affects its machining accuracy. It is difficult to avoid the thermal error of motorized spindle and it accounts for a large proportion of the total error. How to restrain the thermal elongation of motorized spindle and establish an accurate thermal error model is particularly important. This paper reviews the methods of thermal error prevention and thermal error modeling compensation for the motorized spindle. By introducing several methods of thermal error suppression, optimization of temperature measurement points, and thermal error modeling theory, analyzes and discusses the advantages and disadvantages of various methods. Finally, prospects the future development of thermal error research of motorized spindle.

Thermal error analysis and modeling for high-speed motorized spindles based on LSTM-CNN

Thermal error analysis and modeling for high-speed motorized spindles based on LSTM-CNN

Thermal Error Analysis of Five-Axis Machine Tools Based on Five-Point Test Method

The accuracy of five-axis machine tools is a key performance indicator. Among the various error sources of high precision five-axis machine tools, thermal and geometric errors occupy the majority. Thermal errors have become the largest error source of high precision five-axis machine tools, accounting for about 45% of the total errors. Accurate measurement of thermal errors plays a vital role in improving the accuracy of five-axis machine tools. Taking the Shenyang HTM50100 turning and milling machine tool as an example, this paper proposes a method to measure the thermal error of the machine tool spindle using the five-point test method. In the process of thermal error modeling, we select the temperature key point and analyze the collected data. Finally, we evaluate thermal error model. The method is verified by an experiment. The experiment results show that the method is highly accurate, fast, and easy to use. It provides a theoretical basis and practical method for the measurement of thermal errors on five-axis machine tools. By evaluating the method based on multiple linear regression, the predictive ability of the model is about 77%. Compared with LSTM, the prediction accuracy is improved by 5.08%.

Feedback control–based active cooling with pre-estimated reliability for stabilizing the thermal error of a precision mechanical spindle

The thermal error stability (STE) of the spindle determines the machining accuracy of a precision machine tool. The “active cooling-spindle” system is regarded as a feedback control system, and the data-driven thermal error model is utilized to output feedback. In this way, the spindle thermal error can be stabilized by the homeostasis ability of the feedback control system under disturbance. Structural temperature measurements are considerably interfered by the active cooling, so the regression models trained with experimental data might output inaccurate feedback in unseen work conditions. Such inaccurate feedbacks are the primary cause for excessive fluctuations and failures of the thermal error control processes. The independence of the thermal data is analyzed, and a V-C (Vapnik–Chervonenkis) dimension–based approach is presented to estimate the generalization error bound of the regression models. Then, the model which is most likely to give acceptable performance can be selected, the reliability of the feedback can be pre-estimated, and the risk of unsatisfactory control effect will be largely reduced. Experiments under different work conditions are conducted to verify the proposed strategy. The thermal error is stabilized to be within a range smaller than 1.637 μm, and thermal equilibrium time is advanced by more than 78.3%.

Temperature-Sensitive Point Selection and Thermal Error Model Adaptive Update Method of CNC Machine Tools

The thermal error of CNC machine tools can be reduced by compensation, where a thermal error model is required to provide compensation values. The thermal error model adaptive update method can correct the thermal error model by supplementing new data, which fundamentally solves the problem of model robustness. Certain problems associated with this method in temperature-sensitive point (TSP) selection and model update algorithms are investigated in this study. It was found that when the TSPs were selected frequently, the selection results may be different, that is, there was a variability problem in TSPs. Further, it was found that the variability of TSPs is mainly due to some problems with the TSP selection method, (1) the conflict between the collinearity among TSPs and the correlation of TSPs with thermal error is ignored, (2) the stability of the correlation is not considered. Then, a stable TSP selection method that can choose more stable TSPs with less variability was proposed. For the model update algorithm, this study proposed a novel regression algorithm which could effectively combine the new data with the old model. It has advantages for a model update, (1) fewer data are needed for the model update, (2) the model accuracy is greatly improved. The effectiveness of the proposed method was verified by 20 batches of thermal error measurement experiments in the real cutting state of the machine tool.

Thermal error modeling and compensation based on Gaussian process regression for CNC machine tools

Thermal errors are one of the main factors affecting the accuracy of high-precision computer numerical control machine tools. Modeling and compensation are the most common approaches for reducing the influence of thermal error on machine tool accuracy. Accuracy and robustness are the key indicators of machine tool thermal error prediction models, especially under different working conditions. Existing thermal error modeling algorithms provide only point predictions of the thermal error; however, interval predictions of the thermal error are important for understanding the stochastic nature of the thermal error prediction and analysis of reliable risk. To address these challenges, this study proposes a novel thermal error modeling method based on Gaussian process regression (GPR) that provides interval predictions of thermal error and achieves high prediction accuracy and robustness. First, multiple batches of experimental data are used to establish the GPR thermal error model to ensure sufficient modeling information. Second, while existing methods select temperature-sensitive points (TSPs) before modeling, the GPR algorithm can adaptively select TSPs during training of the thermal error GPR prediction model. Third, the proposed model provides interval predictions of thermal errors for evaluating the thermal error prediction reliability. The prediction effects of the GPR model are compared with those of existing thermal error models. The experimental results indicate that the proposed model has the highest prediction accuracy and robustness under different working conditions of the tested compensation models. Furthermore, thermal error compensation experiments are conducted to verify the effectiveness of the proposed model.

Thermal error modeling of motorized spindle based on Elman neural network optimized by sparrow search algorithm

The thermal error of the motorized spindle is an essential factor affecting the machining accuracy of high-speed numerically controlled machines. The establishment of a high-speed motorized spindle thermal error model for thermal error compensation can effectively improve the impact of thermal errors on the machining accuracy of the machine tool. This paper proposes a sparrow search algorithm to optimize the Elman neural network to predict thermal errors in motorized spindles. First is the simulation analysis on thermal characteristics of A02 high-speed motorized spindle. Based on the simulation results, the position of the temperature measuring points is arranged in the temperature and thermal error experiment of the motorized spindle. The temperature and thermal displacement data of high-speed motorized spindle at different rotational speeds were collected; secondly, the method of combining pedigree clustering and k-means clustering is used to perform cluster analysis on each temperature measurement point, and the grey correlation degree is used to determine the correlation between temperature measurement points and thermal error. Three temperature-sensitive points were screened from ten temperature measurement points, which reduced the collinearity between temperature measurement points and the number of independent variables of the model. Finally, the weights and thresholds of the Elman neural network are optimized by the sparrow search algorithm, and the thermal error prediction model of motorized spindle based on SSA-Elman neural network is established and compared with Elman neural network and Particle Swarm Optimized Elman Neural Network prediction model. The results show that the SSA-Elman neural network model has the highest prediction accuracy and exhibits good stability and generalization ability.

Improved unscented Kalman filter algorithm-based rapid identification of thermal errors of machine tool spindle for shortening thermal equilibrium time

Thermal equilibrium of machine tools is needed before machining to ensure the accuracy. To shorten the warm-up time and improve the machining efficiency, a rapid identification of thermal errors is proposed. It can predict the thermal errors in the shortest identification time so that the thermal error compensation can be started in advance to shorten the thermal equilibrium time. A Singular Value Decomposition-Adaptive Unscented Kalman Filter algorithm (SVD-AUKF) is proposed with singular value decomposition and adaptive rule for the fast identification. A general exponential thermal error model is established and applied into the SVD-AUKF. RMSE of the thermal error data within each time is calculated for the evaluation to obtain the shortest identification time. K hysteresis rule, Δt judgment rule and maximum time rule are proposed for the prediction accuracy. Different experiments are proposed with two machine tools to testify the effectiveness of the shortest identification time.

Geometric-thermal error control system for gear profile grinding machine

Geometric and thermal errors, which are the main error factors for reducing the machining accuracy, should be controlled. But the control effect is poor, which is a stumbling block to limit the wide application of the error control. In this study, a geometric-thermal error control system (GTECS) is designed for gear profile grinding machines. For the mist layer of GTECS, the wireless sensor network is designed to realize the data collection and transfer. For the edge layer of GTECS, the edge controller is designed to conduct the sensitive error analysis. For the fog layer, the control module is designed to conduct the geometric and thermal error prediction. In this layer, the analytical model of the rolling guide/slider system is proposed to calculate geometric errors of X- and Z- axes, and the thermal boundary conditions are calculated, and the thermal error models of the spindle and C-axis are proposed based on transfer learning model (TLM) of the sooty tern optimization (STO)-bilinear temporal convolutional network (BTCN). For the cloud layer, the data computation and management are realized by Hadoop and Yet Another Resource Negotiator (YARN), respectively. The geometric and thermal error models of X- and Z-axes, thermal errors models of the spindle and C-axis, and multi-source error model are embedded into it. With the execution of GTECS, the geometric precision for the total tooth profile deviation and tooth profile deviation are increased from ISO level 8 to ISO level 5 and from ISO level 5 to ISO level 3, respectively.

Obtaining more appropriate temperature sensor locations for thermal error modeling: reduction, classification, and selection

Obtaining more appropriate temperature sensor locations for thermal error modeling: reduction, classification, and selection

A study on thermal displacement of CNC horizontal lathe based on movable component temperatures

ABSTRACT This paper presents a thermal error model for a lathe CNC machine using temperature on moving parts, which is usually a difficult measurement. Different working conditions are performed to obtain temperature and thermal displacement of the machine. A multi-linear regression model is applied for modelling relationship between temperatures and thermal errors. Data of two constant working conditions are implemented to find out the fitting function. Through analysis, it shows that thermal errors for X- and Z-axes can be estimated based on only four temperature points (T2, T3, T10 and T12 for the X-axis and T4, T6, T7 and T11 for the Z-axis). Results reveal that using movable part temperature data (T12), the average and maximum error in the predicted thermal displacement of the X-axis can be reduced about 1/3 and 2/5 compared to without using T12, while the movable temperature point on Z-Screw (T8) has a tiny effect on the average and maximum error of predicted thermal displacement of the Z-axis. Results herein can provide useful information to develop a thermal compensation for the CNC lathe machine.

An accurate thermoelastic model and thermal output error analysis of a hemispherical resonator gyroscope under varying temperatures

This paper proposes an accurate thermoelastic model of a hemispherical shell resonator (TM-HSR) taking into consideration thermal stress and reveals the effect of its thermal deformation on the hemispherical resonator gyroscope (HRG) output error for the first time. First, a set of thermoelastic dynamic equations of the TM-HSR are derived by leveraging the thermoelastic shell theory, and the relationship between temperature and the equivalent thermal load is determined. Next, an approximate analytical solution of thermal deformation of HSRs is derived using Bubnov-Galerkin method and its accuracy is evaluated by comparing its result with ANSYS simulation results of HSRs with different structures. The approximate analytical solution is found to be very accurate, which is important for temperature testing of HRGs and application to various vibratory sensors with hemispherical shell structures. Subsequently, the effects of thermal deformations under uniform and nonuniform temperature distributions on the HRG output error are revealed by using a thermal output error model. Comparative simulation and experimental results demonstrate the effectiveness and practicability of the proposed model. The proposed model can be used for accurate error analysis and developing a compensation scheme for the thermal output error of HRGs.