Thermal Error Modeling Research Articles

Improved exponential model for thermal error modeling of machine-tool spindle based on fruit fly optimization algorithm

Establishing a robust thermal error model is crucial for thermal error compensation of machine tools. In this paper, an improved exponential model for thermal error modeling was proposed. First, the improved exponential model is established by combining the exponential model and the temperature-dependent model. Second, the improved fruit fly optimization algorithm is used to determine the parameters. Finally, two strategies are used to select the optimal sensor location from six potential ambient temperature sensors. The ambient temperature data is proved to be effective in improving the robustness of the model. The average root mean square error of the proposed model, the exponential model without ambient temperature, and the linear model are 1.18 μm, 1.79 μm, and 2.70 μm, respectively. The modeling results show that the proposed model has high accuracy and strong robustness, which is suitable for workshop environment and variable conditions in thermal error modeling of machine tools.

Analysis of thermal error model of ball screw feed system based on experimental data

In order to investigate the effect of thermal expansion on the ball screw feed system (BSFS) of a precision machine tool, theoretical modeling of and experimental study on thermally induced error are focused in this paper. A series of thermal experiments are conducted on the machine tool to measure the temperature of the main heat source and measuring points of BSFS. This study is to classify the main heat sources and discuss the impact on the ball screw feed system separately. By the experimental data of ball screw system, the thermal model of screw shaft in the axial direction is analyzed and verified. Based on the heat generation and transfer analysis of ball screw system, thermal expansion of screw shaft in the axial direction is modeled mathematically. In addition, by analyzing the effects of machining parameters such as rotational speed, preloads, and lead, we get the parameter influence of BSFS’s temperature rising and thermal deformation. This work can help us reduce thermal deformation effectively and improve the precision of CNC machining.

Thermal error modeling of spindle and dynamic machining accuracy reliability analysis of CNC machine tools based on IA and LHSMC

Machining accuracy reliability as a key index of CNC machine tools is seriously influenced by the geometric and thermal errors. In the paper, a spindle unit thermal error modeling and machining accuracy reliability analysis method is proposed. By analyzing the heat generation mechanism, a thermal error model was developed to describe the thermal deformation of the electric spindle. Based on the immune algorithm (IA), the heat generation power and the heat transfer coefficient were optimized, and the thermal error was obtained by finite element thermal-mechanical coupling. By adopting the multi-body system theory (MBS), a dynamic machining accuracy model was put forward including the geometric and thermal errors. Based on the Latin hypercube sampling Monte Carlo method (LHSMC), a machining accuracy reliability analysis method was proposed to characterize the machining accuracy reliability considering the geometric and thermal errors. The method was employed to a machine tool, and the experimental results indicate the verification and superiority of the method.

A Novel Two-Mode Integral Approach for Thermal Error Modeling in CNC Milling-Turning Machining Center

Thermal errors have the largest contribution, as much as about 70%, to the machining inaccuracy of computer-numerical-controlled (CNC) machining centers. The error compensation method so far plays the most popular and effective way to minimize the thermal error. How to accurately and quickly build an applicable thermal error model (TEM) is the kernel work of thermal error compensation. On the basis of some comprehensive machine-learning schemes, past proposed TEMs had impressive merits for dealing with the thermal error modeling of single-function (milling or turning cutting) machine tools with only considering one set of thermal key points. These proposed modelling methodologies become worse when applied to CNC compound milling-turning machining centers in actual cutting applications. This paper proposes a two-mode integral TEM based on the Lasso and the random forest regression schemes to quickly and accurately predict the thermal deformations of such a machine. The first mode is the thermal error modeling for milling cutting conditions, and the second mode is that for turning cutting conditions. For data reduction, two different sets of temperature key points, one for milling and the other for turning, are obtained. Then, on the basis of the random forest regression scheme, we separately establish two TEMs but concurrently use them to predict the tool-center-point deformations of both milling as well as turning spindles. Further, we compare our proposed TEM with several frequently-used machine-learning-based TEMs and the results show that our proposed TEM are the best among all, no matter in the modelling experiment or in the test experiment. The proposed TEM has a maximum prediction error of 6.08 &#x03BC;<i>m</i> for milling cutting and that of 1.455&#x03BC;<i>m</i> for turning cutting in the modeling experiment. By our proposed two-mode integral TEM, the thermal error of a multi-function milling-turning machining center can be accurately predicted and quickly compensated.

Simultaneous geometric and thermal error control of gear profile grinder based on analytical correlation between tooth surface error and position error of grinding wheel/workpiece

The gear profile grinder is important to ensure the geometric accuracy of tooth surfaces. However, its machining accuracy is significantly reduced by the geometric and thermal errors. So the geometric and thermal errors should be controlled simultaneously. The geometric error modeling and decoupling of the gear profile grinder are studied, and the mapping relationship between the geometric accuracy of tooth surfaces and machine errors is constructed. To establish a robust thermal error model, a physically-based model is established to prove the feasibility of using the bidirectional long short term memory network (Bi-LSTMN) to establish a self-learning error model. The high-frequency noises are filtered and singular values are reduced by the Savitzky–Golay (SG) filtering algorithm. An attention-gate-based Bi-LSTMN (AGBi-LSTMN) is proposed to reduce the time complexity. Then the mixed-variants whale optimization algorithm (MVWOA) is proposed to optimize the hyper-parameters, and SG-MVWOA-AGBi-LSTMN is proposed for the thermal error prediction. Finally, the simultaneous geometric and thermal error control is implemented. The results show that the total tooth profile precision is increased by ISO level 3, and the tooth profile tilt precision is increased by ISO level 5 with the simultaneous geometric and thermal error control.

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 IMPACT OF KEY TEMPERATURE MEASURING POINTS ON THERMAL ERROR COMPENSATION MODEL TRANSFER BETWEEN MILLING CENTERS OF THE SAME PRODUCT LINE

Machine tool thermal errors are an important element in machined workpiece inaccuracies. In the past few decades, thermal errors have been successfully reduced by software compensation techniques such as multiple linear regression analysis, finite element method, neural network and transfer function (TF). A phenomenological approach based on TFs is used for thermal error compensation in this research. This approach respects basic heat transfer mechanisms in the MT structure and requires a minimum of additional gauges. Every MT is unique due to manufacturing inaccuracies in components, assembly processes (different preloads in bolts, deviations in the assembly and seating of components, etc.) or working environment (air-conditioned room or ordinary production hall). The aim of this paper is to investigate thermal error compensation model transfer between machines of the same product line to improve thermal error model prediction. Several milling centers of the same product line were tested with varying non-stationary activities of heat sources from linear axis movements and in varying working environments. The issue of key temperature point selection is considered.

Research on Thermal Characteristics of Ball Screw Feed System Considering Nut Movement

The heat generated by the ball screw feed system will produce thermal errors, which will cause the positioning accuracy to decrease. The thermal simulation modeling of the ball screw feed system is the basis for compensating thermal errors. The current thermal characteristic modeling method simplifies the reciprocating movement of the nut pair on the screw shaft to varying degrees, which leads to a decrease in simulation accuracy. In this paper, the nut is regarded as a moving heat source, and a novel method is adopted to make the moving process of the heat source closer to the actual nut movement process. The finite difference method is used to simulate the temperature field and thermal error of the ball screw feed system under different working conditions. Firstly, based on the heat transfer theory, the heat conduction differential equation of the feed system is established and discretized. The thermal error model of the ball screw feed system is established. Then, the relationship between nut heat source position and operating time is established to simulate nut reciprocating motion. Finally, the temperature and thermal error experiments of the ball screw feed system were carried out, and the temperature experiment results were compared with the simulation results of the finite difference method. The results show that the maximum simulation error of the average temperature in the operating interval is 11.4%, and the maximum simulation error of thermal error is 16.4%, which verifies the validity and correctness of the method. The thermal characteristic modeling method of the ball screw feed system proposed in this paper has a substantial application value for accurately obtaining the temperature field of the feed system.

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.

The Thermal Error Estimation of the Machine Tool Spindle Based on Machine Learning

Thermal error is one of the main sources of machining error of machine tools. Being a key component of the machine tool, the spindle will generate a lot of heat in the machining process and thereby result in a thermal error of itself. Real-time measurement of thermal error will interrupt the machining process. Therefore, this paper presents a machine learning model to estimate the thermal error of the spindle from its feature temperature points. The authors adopt random forests and Gaussian process regression to model the thermal error of the spindle and Pearson correlation coefficients to select the feature temperature points. The result shows that random forests collocating with Pearson correlation coefficients is an efficient and accurate method for the thermal error modeling of the spindle. Its accuracy reaches to 90.49% based on only four feature temperature points—two points at the bearings and two points at the inner housing—and the spindle speed. If the accuracy requirement is not very onerous, one can select just the temperature points of the bearings, because the installation of temperature sensors at these positions is acceptable for the spindle or machine tool manufacture, while the other positions may interfere with the cooling pipeline of the spindle.

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.

A data-driven model for thermal error prediction considering thermoelasticity with gated recurrent unit attention

It is of great significance to reduce the thermal error of machine tools. However, there is a time lag between different temperature measurement points due to the thermoelastic effect, which causes inaccurate prediction when using only the current temperature. In this paper, the GRU time series neural network with an attention mechanism is employed to establish the thermal error model of the screw, which uses historical data and sets different weights for them. In addition, since the thermal error is closely related to the working condition, the electronic control data that reflect the working condition in the CNC system are considered. Compared with several state-of-art methods, such as RNN and LSTM, the prediction results demonstrate the superiority of the proposed method. The actual machining indicates that the compensation rate exceeds 75% and can reduce the thermal error from 20 µm to 5 µm.

Thermal error prediction of ball screws based on PSO-LSTM

Thermal error of ball screws seriously affects the machining precision of computerized numerical control (CNC) machine tools especially in high speed and precision machining. Compensation technology is one of the most effective methods to address the thermal issue, and the effect of compensation depends on the accuracy and robustness of the thermal error model. Traditional modeling approaches have major challenges in time series thermal error prediction. In this paper, a novel thermal error model based on long short-term memory (LSTM) neural network and particle swarm optimization (PSO) algorithm is proposed. A data-driven model based on LSTM neural network is established according to the time series collected data. The hyperparameters of LSTM neural network are optimized by PSO, and then a PSO-LSTM model is established to precisely predict the thermal error of ball screws. In order to verify the effectiveness and robustness of the proposed model, two thermal characteristic experiments based on step and random speed are conducted on a self-designed test bench. The results show that the PSO-LSTM model has higher accuracy compared with the radial basis function (RBF) model and back propagation (BP) model with high robustness. The proposed method can be implemented to predict the thermal error of ball screws and provide a foundation for thermal error compensation.

Numerical and Experimental Investigation of the Temperature Rise of Cutting Tools Caused by the Tool Deflection Energy

Tool temperature variation in flank milling usually causes excessive tool wear, shortens tool life, and reduces machining accuracy. The heat source is the primary factor of the machine thermal error in the process of cutting components. Moreover, the accuracy of the thermal error modeling is greatly influenced by the formation mechanism of the heat source. However, the tool heat caused by the potential energy of the tool bending and twisting has essentially not been taken into consideration in previous research. In this paper, a new heat source that causes the thermal error of the cutting tools is proposed. The potential energy of the tools’ bending and twisting is calculated using experimental data, and how tool potential energy is transformed into heat via friction is explored based on the energy conservation. The temperature rise of the cutting tool is simulated by a lattice-centered finite volume method. To verify the model, the temperature separation of a tool edge is measured experimentally under the given cutting load. The results of the numerical analysis show that the rise in tool temperature caused by the tool’s potential energy is related to the time and position of the cutting edge involved in milling. For the same conditions, the predicted results are consistent with the experimental results. The proportion of temperature rise due to tool potential energy is up to 6.57% of the total tool temperature rise. The results obtained lay the foundation for accurate thermal error modeling, and also provide a theoretical basis for the force–thermal coupling process.

A Review of Thermal Error Modeling Methods for Machine Tools

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.

Thermal error compensation method for CNC machine tools based on deep convolution neural network

To avoid the resetting of temperature-sensitive points caused by seasonal and weather changes and the influence on the accuracy of the thermal error model, a thermal error prediction and compensation method for CNC machine tools without preselected temperature-sensitive points was proposed based on deep learning method. The original temperature data of the CNC machine tool were converted into thermal images and directly serve as the input of the deep learning network. To improve the prediction accuracy of the thermal error model, a thermal error model of CNC machine tool with 10 hidden layers was constructed by using the powerful image feature learning ability of deep convolution network. The nonlinear mapping relationship between temperature image and thermal error without pre-selection of temperature key points was established, and more relationships between thermal error and temperature feature of a machine tool were retained. STM32F4 microprocessor was used as thermal error compensation controller to develop software and hardware system. The application experiment of the thermal error compensation system is carried out on the CNC grinder, and the effectiveness of the thermal error compensation system is verified.

Thermal error prediction of machine tool spindle using segment fusion LSSVM

The key temperature points are the input variables of the thermal error model for prediction and compensation of thermal errors for precision CNC machine tools. However, the revealed time-varying characteristics of the key temperature points may jeopardize the robust prediction. To this end, the segment fusion least squares support vector machine (SF-LSSVM) thermal error modeling method is proposed. Firstly, the temperature data and thermal error data are divided into different segments according to time. Then, using the LSSVM with excellent nonlinear mapping capabilities as the basic model, the sub LSSVM thermal error model building and the corresponding key temperature points selection in each segment are fulfilled with genetic algorithm (GA) in a wrapper manner to preserve the corresponding local prediction characteristics. Finally, pick some of or all the sub LSSVM thermal error models to fuse together as the final thermal error model which may incorporate both the local and global prediction characteristics. The modeling and prediction experiment results on the spindle thermal error of a horizontal machining center demonstrate that the mean root-mean-square error (RMSE) on 5 spindle speeds after compensation is only 3.1 μm. Comparing with two traditional thermal error models, the prediction performance of the present model is improved by up to 51%. This research casts new light on both the mechanism of key temperature points and the prediction method of thermal errors.

Synthetic positioning error modelling of a feed axis for a precision CNC machine tool

The linear feed system is a kernel movement component in a CNC machine tool. Because of thermal generation principally caused by motor and frictional action between motion pairs, such as cutter-workpiece and ball-raceway pairs, positioning errors have not only geometrical errors but also thermal errors, which plays an important role on the machining accuracy of parts. Geometrical errors solely related to position can be extracted through coordinate rotation transformation and expressed in the form of a polynomial. Many temperature sensors are allocated at different places to acquire the overall temperature changes in the feed system. To eliminate the correlation between some temperatures, the K-means clustering algorithm is employed to categorize the temperature measurement points, and key points are selected based on grey correlation analysis to achieve representative measurements. Consequently, a thermal error model is implemented by a BP neural network to establish the relationship between temperature and thermal deformation. A synthetic model is obtained through superposition of the above two error models to predict the positioning error. A thermal characteristic experiment of the linear feed axis carried out on a precision CNC machine verifies the effectiveness of the positioning error modelling method and provides a feasible and reliable reference to compensate for feed axis positioning errors in CNC machine tools.

Thermal Error Modeling of Rotary Axis Based on Convolutional Neural Network

Abstract Rotary axes are the key components for five-axis computerized numerical control machines, while their motions are dramatically influenced by thermal issues. To precisely model the thermal error of rotary axis, a convolutional neural network (CNN) model is developed. To form data sets for the CNN, a laser interferometer is used to measure the angular positioning error at different temperatures and a thermal imager is taken to obtain thermal images of the rotary axis. The measured thermal error is fitted to a sine curve so that training parameters are reduced. And the thermal pixel values of the initial thermal image are subtracted from all the thermal images to consider the incremental thermal effect, so the influence of the initial temperature is negligible. Finally, a deep CNN model with multiple output classifications is designed to complete the data training, verifying and testing. The experimental results show that the prediction accuracy for the parameters is higher than 90%, and the percentage reduction in error is higher than 80%.

Thermal error modeling based on BiLSTM deep learning for CNC machine tool

The machining accuracy of computer numerical control machine tools has always been a focus of the manufacturing industry. Among all errors, thermal error affects the machining accuracy considerably. Because of the significant impact of Industry 4.0 on machine tools, existing thermal error modeling methods have encountered unprecedented challenges in terms of model complexity and capability of dealing with a large number of time series data. A thermal error modeling method is proposed based on bidirectional long short-term memory (BiLSTM) deep learning, which has good learning ability and a strong capability to handle a large group of dynamic data. A four-layer model framework that includes BiLSTM, a feedforward neural network, and the max pooling is constructed. An elaborately designed algorithm is proposed for better and faster model training. The window length of the input sequence is selected based on the phase space reconstruction of the time series. The model prediction accuracy and model robustness were verified experimentally by three validation tests in which thermal errors predicted by the proposed model were compensated for real workpiece cutting. The average depth variation of the workpiece was reduced from approximately 50 µm to less than 2 µm after compensation. The reduction in maximum depth variation was more than 85%. The proposed model was proved to be feasible and effective for improving machining accuracy significantly.