Spindle Thermal Error Research Articles

Multi-verse optimizer for thermal error modeling approach of spindle system based on thermal image

Since the spindle thermal error of CNC machine tools has a significant impact on machining precision, this paper introduces a unique approach for modeling spindle thermal error. Several key steps are involved in the proposed approach. First, the Fluke thermal imaging camera is employed for acquiring thermal image information of the spindle system. Second, the Gaussian filter is employed to denoise the thermal image sequence. Next, the temperature values at the measurement points are extracted from the thermal image sequence according to the mapping relationship between the grayscale value and the temperature value. Subsequently, critical temperature points are identified from thermal images using the density-based spatial clustering of applications with noise (DBSCAN) algorithm and the correlation coefficient method. Finally, the multi-verse optimized NARX neural network is employed to investigate the nonlinear prediction of thermal deformation. The research is conducted on the VMC-850E vertical machining center as the subject of study. The performance of the model is validated under conditions of idle spindle and 5000 r/min, comparing prediction results against traditional algorithms. The findings demonstrate that the non-contact measurement method based on thermal imaging successfully establishes the thermal error model, achieving a prediction accuracy of 0.1517 μm for the MVO-NARX model.

Intermittent multivariate time series spindle thermal error prediction under wide environmental temperature ranges and diverse scenario conditions

Intermittent multivariate time series spindle thermal error prediction under wide environmental temperature ranges and diverse scenario conditions

Research on electric spindle thermal error prediction model based on DBO-SVM

Research on electric spindle thermal error prediction model based on DBO-SVM

Adaptive thermal error prediction for CNC machine tool spindle using online measurement and an improved recursive least square algorithm

Establishing models for predicting and compensating for spindle thermal errors is cost-effective and necessary to improve the accuracy of machine tools for smart manufacturing. However, the prediction performance of existing methods deteriorates significantly with dynamic working conditions of machine tools because training from static conditions leads to the inability to adapt to dynamic conditions. Therefore, an adaptive thermal error modeling method using online measurement and an improved recursive least square algorithm is proposed to fill this research gap, which updates the thermal error model adaptively to ensure that dynamic working conditions are learned in real time. Particularly, Spearman's rank correlation coefficient method is first adopted for temperature-sensitive point selection to capture the nonlinear relationship between temperature and thermal error variables. Furthermore, a variable-forgetting factor-based recursive least square (VFF-RLS) algorithm is proposed to improve the prediction performance, in which the proposed variable forgetting factor is adaptively updated according to real-time thermal error data collected by online measurement. The experimental results showed that the proposed VFF-RLS method can maintain a high prediction accuracy of 1.75 μm and robustness of 0.16 μm on both constant and dynamic working conditions. The effectiveness of the VFF-RLS method is validated by verification experiments.

MA-CNN based spindle thermal error modeling using the depth feature analysis with thermal error mechanism

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.

A review on transfer learning in spindle thermal error compensation of spindle

A review on transfer learning in spindle thermal error compensation of spindle

Subspace Metric-Based Transfer Learning for Spindle Thermal Error Prediction Under Time-Varying Conditions

Subspace Metric-Based Transfer Learning for Spindle Thermal Error Prediction Under Time-Varying Conditions

A Thermal Error Prediction Method of High-Speed Motorized Spindle Based on Pelican Optimization Algorithm and CNN-LSTM

Given motorized spindles’ extensive periods of prolonged high-velocity operation, they are prone to temperature changes, which leads to the problem of thermal error, leading to diminished precision in machining operations. To address the thermal error issue in motorized spindles of computer numerical control (CNC) machine tools, this study proposes a pelican optimization algorithm (POA)-optimized convolutional neural network (CNN)–long short-term memory (LSTM) hybrid neural network model (POA-CNN-LSTMNN). Initially, the identification of temperature-sensitive locations in the spindle system is performed using a combination of hierarchical clustering, the K-medoids algorithm, and Pearson’s coefficient calculation. Subsequently, the temperature data from these identified points, along with real-time collected spindle thermal error data, are employed to construct the model. The Pelican optimization algorithm is used to enhance the model parameters to achieve the best performance. Finally, the proposed model is subjected to a comparative analysis with other thermal error prediction models. Drawing from the experimental findings, it is evident that the POA-CNN-LSTMNN model exhibits superior prediction performance.

Spindle Thermal Error Prediction Based on Back Propagation Neural Network and Hybrid Taguchi Genetic Algorithm for a Computer Numerical Control Machine Tool

Spindle Thermal Error Prediction Based on Back Propagation Neural Network and Hybrid Taguchi Genetic Algorithm for a Computer Numerical Control Machine Tool

An axial attention-BiLSTM-based method for predicting the migration of CNC machine tool spindle thermal error under varying working conditions

An axial attention-BiLSTM-based method for predicting the migration of CNC machine tool spindle thermal error under varying working conditions

Robust modeling for thermal error of spindle of slant bed lathe based on error decomposition

Thermal error of spindle is critical to the slant bed CNC lathe towards high machining precision. The heat generated by the spindle itself contributes to the thermal error indeed. However, the thermal error is also influenced by the thermal deformation of other components such as the turret and lathe bed, especially in complex structured slant-bed CNC lathes where error coupling commonly exists. In order to achieve robust modeling of thermal error, a decomposition method was proposed in this paper to separate the contributions of spindle, turret and lathe bed from the overall measured thermal deformation. The thermal error coupling relationship was established from the perspective of machine tool construction. A specific testing scheme was designed to determine the parameters of decoupling model. Additionally, a comparative experiment was carried out by placing the sensor support horizontally and vertically to verify the effectiveness of thermal error decoupling. Taking T65-750 high-precision CNC lathe as the object, the relationship between thermal error and tilt angle in the X-direction of the headstock, bed, and other components was revealed, achieving robust prediction of thermal error irrespective of the ambient temperature subject to change. Finally, the thermal error model built based on error decomposition was applied to improve the machining accuracy of cylindrical parts dramatically in practice.

A spindle thermal error modeling based on 1DCNN-GRU-Attention architecture under controlled ambient temperature and active cooling

A spindle thermal error modeling based on 1DCNN-GRU-Attention architecture under controlled ambient temperature and active cooling

Feedback control of the mechanical spindle thermal error based on thermal simulation with bearing heat sources analysis

The thermal error stability (STE) of the spindle seriously affects the machining accuracy of a machine tool, however existing empirical heating model-based active cooling strategies mainly focus on suppressing the spindle’s overall thermal deformation and cannot effectively stabilize the thermal error. This study regards the “active cooling-spindle” system as a feedback control system and employs a data-driven thermal error model to provide feedback. Thus, the spindle thermal error can be stabilized for a long time owing to the homeostasis of the feedback control system under disturbance. A mechanical spindle with an external cooling scheme is taken as the study object. Bearings are the primary heat sources of the mechanical spindle; thus, the angular contact ball-bearing heat generation is precisely modeled based on local heat sources analysis of bearing components, elastohydrodynamic lubrication, and micro-contact theory. Thermal simulation of the spindle under varying-coolant temperature cooling is conducted to pre-validate the thermal error suppression and variation trend influencing effect, and obtain the Reference Input of Thermal Error (RITE) for the feedback control under different work conditions. Subsequently, a spindle thermal error feedback control system is developed, including computation, cooling, and real-time monitoring modules with inter-communication. Finally, the thermal error feedback control strategy is applied on the mechanical spindle, and experimental comparisons with constant coolant temperature cooling show that the thermal equilibrium time is advanced by 61.46%, 59.16%, 40.51%, and 58.08%. The thermal error variation range (TEVR) after the preheating stage is reduced to1.92, 1.52, 1.91, and 1.69 μm, respectively. The significant reduction in TEVR validated the effectiveness of the proposed strategy for spindle thermal error stabilization.

Look-ahead prediction of spindle thermal errors with on-machine measurement and the cubic exponential smoothing-unscented Kalman filtering-based temperature prediction model of the machine tools

Reducing the thermal equilibrium time is one effective way to improving the efficiency and utilization and ensuring the accuracy of machine tools. This paper proposed the look-ahead prediction of spindle thermal errors based on CES-UKF temperature prediction model using on-machine measurement. It can predict the thermal errors during the warm-up stage just with the measured temperature data in the required on-machine measurement time (ROMT). With the thermal error compensation function, the machine tool only needs warm-up for ROMT to improve the efficiency and ensuring the accuracy of machine tools. The look-ahead temperature prediction is realized combining UKF and CES including real-time adjustment of exponential smoothing coefficients and ROMT calculation. Temperature-sensitive point selection based on self-attention mechanism is established. Gate recurrent unit (GRU)-based thermal error model is proposed considering the thermal hysteresis effects. Verifications and cutting experiments are carried out to testify the effectiveness and robustness of the method.

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%.

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.

Research on Thermal Error Modeling of Motorized Spindle Based on BP Neural Network Optimized by Beetle Antennae Search Algorithm

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 temperature-sensitive point screening for spindle thermal error modeling based on IBGOA-feature selection

Thermal error compensation is a simple and efficient method to reduce thermal errors of machine tools, and the compensation effect largely depends on the temperature-sensitive points screened for the thermal error modeling. In this paper, 5 spindle heating experiments are carried out, and a new temperature-sensitive point screening method based on the Improved Binary Grasshopper Optimization Algorithm (IBGOA) feature selection is proposed. Firstly, an optimal approximation criterion is added to the Binary Grasshopper Optimization Algorithm (BGOA) for ensuring the convergence of the algorithm. And the temperature measuring points are regarded as the feature of the thermal error. Then these feature temperature point subsets are generated by IBGOA. Next, the stepwise regression analysis is carried out to remove non-significant temperature points from these subsets. And each subset is evaluated to search the temperature-sensitive points based on the cross-validation result of the multiple linear regression (MLR). Finally, for further testing the applicability of the proposed temperature-sensitive points screening method, 3 common thermal error models are established with MLR, support vector regression, and back propagation neural network respectively. Compared with the traditional fuzzy C-means clustering (FCM) temperature-sensitive points screening method, the RMSE of these models could decrease by 30–50% in the thermal drift error of X-direction, 10%–30% in the thermal tilt error of Y-direction, generally 40%–60% in the thermal elongation of Z-direction and the thermal drift error of Y-direction. The results show the superiority of the proposed IBGOA-feature selection method.

Spindle thermal error modeling method considering the operating condition based on Long Short-Term Memory

Thermal error has a significant effect on machine tools’ precision. Traditional methods usually establish the thermal error model by temperature. As the temperature only describes the instant state of the machine tool, it is inadequate to clarify the generation process of thermal error. To improve the description completeness of thermal error generation process, the operating condition data such as spindle speed, rotational number and power are employed besides the temperature. Furthermore, Long Short-Term Memory (LSTM) based thermal error model was proposed which combined the operating condition with temperature. This model not only considers the dynamic characteristics of the thermal error, but also selects and remembers the previous thermal error data information. To improve the accuracy for the whole speed range, the K-Means clustering analysis was adopted to obtain the optimal speed categorization, then different LSTM sub-models were established separately. Experiments demonstrated that the predicting accuracy of the proposed K-Means segmental LSTM method (K-S-LSTM) is over 85.0% under different operating conditions. Moreover, comparison experiments indicated that the predicting performance of K-S-LSTM is better than Elman and IRNN models. Finally, the compensation experiment showed that the thermal error can decrease from 49 μm to 12 μm after compensation in actual numerical control system.

Spindle Thermal Error Prediction Based on LSTM Deep Learning for a CNC Machine Tool

In the precision processing industry, maintaining the accuracy of machine tools for an extensive period is crucial. Machining accuracy is affected by numerous factors, among which spindle thermal elongation caused by an increase in machine temperature is the most common. This paper proposed a key temperature point selection algorithm and thermal error estimation method for spindle displacement in a machine tool. First, highly correlated temperature points were clustered into groups, and the characteristics of small differences within groups and large differences between groups were realized. The optimal number of key temperature points was then determined using the elbow method. Meanwhile, the long short-term memory (LSTM) modeling method was proposed to establish the relationship between the spindle thermal error and changes of the key temperature points. The results show the largest root mean square errors (RMSEs) of the proposed LSTM model and the key temperature point selection algorithm were within 0.6 µm in the spindle thermal displacement experiments with different temperature changes. The results demonstrated that the combined methodology can provide improved accuracy and robustness in predicting the spindle thermal displacement.