Statistical optimization and assessment of a thermal error model for CNC machine tools

Lee, Jinhyeon; Yang, Seung-Han

doi:10.1016/s0890-6955(01)00110-9

Cited by 89 publications

(40 citation statements)

References 9 publications

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“…The common advantages of the existing mathematic statistics method include the following: a large number * Chengxin Zhang qfzcx_sd@163.com Feng Gao gf2713@126.com of sensors can be arranged on a machine tool, and several optimal measurement points can then be selected from the arranged sensors through a statistical analysis [4][5][6][7][8][9][10][11][12]. However, there are certain disadvantages of this type of method:…”

Section: Mathematical Statistics Methodsmentioning

confidence: 99%

A novel linear virtual temperature constructing method for thermal error modeling of machine tools

Zhang

Gao

Zhenhua

et al. 2015

Int J Adv Manuf Technol

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When a thermal error model of a machine tool is established, selecting the appropriate temperature measurement point is a very difficult problem. This paper proposes a novel method for constructing a linear virtual temperature. The proposed method can overcome the problem of selecting the temperature measurement point. First, temperaturethermal expansion hysteresis characteristics are used to divide the temperature measurement points into two groups. Each temperature variable is then chosen through a principal component analysis (PCA). Finally, using two temperaturevariable weights and the correlative coefficient thermal displacement as the maximum optimal indexes, two temperatureweighted coefficients are calculated, and a linear virtualtemperature variable related to the thermal error linearity is then formed. In establishing the proposed thermal error model, the linear virtual temperature formed can serve as a system input variable. The proposed method was tested on a threeaxis milling machine to determine the spindle Z-axial thermal error, and the results show that the root mean square error (RMSE) is reduced by 11 % and the sum of the squares of the error (SSE) is reduced by 39 % in comparison with a direct application of a temperature variable when establishing such a model. In the proposed method, only two temperature measurement points are used to establish a model, through which the complexity in determining the optimal measurement points through a traditional method, along with the number of temperature measurement points required, is greatly reduced.

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Section: Mathematical Statistics Methodsmentioning

confidence: 99%

A novel linear virtual temperature constructing method for thermal error modeling of machine tools

Zhang

Gao

Zhenhua

et al. 2015

Int J Adv Manuf Technol

View full text Add to dashboard Cite

show abstract

“…An error prediction model was built on the premise of finding temperature-sensitive points most relevant to thermal errors through correlation analysis. Lee et al [7] organically combined linear regression with correlation analysis to optimize temperature-sensitive points and considered the minimum sum of residual squares as the basis for selecting temperaturesensitive points. Yang et al [8,9] screened five temperaturesensitive points with the highest grey correlation degree by computing the grey correlation between thermal errors and temperature sensors, thereby achieving the goal of optimization.…”

Section: Introductionmentioning

confidence: 99%

Thermal Errors Classification Compensation without Sensor for CNC Machine Tools

Wei

Gao

et al. 2018

Mathematical Problems in Engineering

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Both multicollinearity and utilization deficiency of temperature sensors affect the robustness and the prediction precision of traditional thermal error prediction models. To address the problem, a thermal error prediction model without temperature sensors is proposed. Firstly, the paper analyzes the temperature field and thermal deformation mechanisms of the spindle of a CNC gear grinding machine in accordance with the parameters, efficiencies, and structures of the machine spindle and bearing. A preliminary theoretical model is established on the basis of the mechanism analysis. Secondly, the theoretical model is corrected according to the actual operation parameters of the machine. Thirdly, verification experiments are carried out on machine tools of the same type. It is found that the corrected model has higher precision in predicting thermal errors at the same rotational velocity. The standard deviation and the maximum residual error are reduced by at least 39% and 48% separately. The prediction precision decreases with the increase in prediction range when predicting thermal errors at different rotational velocities. The model has high prediction precision and strong robustness in the case of reasonable prediction range and classified prediction. In a word, prediction precision and robustness of the model without temperature sensors can be effectively ensured by reasonably determining the prediction range and practicing classified prediction and compensation for thermal errors at different rotational velocities. The model established can be applied to machine tools that have difficulties in arranging sensors or those whose sensors are significantly disturbed.

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“…Lee of South Korea has been reduced temperature measurement point by using correlation coefficient and linear regression method. Some results have been obtained [15], but the nonlinear of temperature data is not considered adequately. Creighton et al established the model of temperature rise and thermal deformation by using finite element method [16].The temperature rise and thermal deformation of the key points were obtained by using thermocouple and capacitance meter.…”

Section: Introductionmentioning

confidence: 99%

A Hybrid Prediction Method of Thermal Extension Error for Boring Machine Based on PCA and LS-SVM

Cheng

et al. 2017

MATEC Web Conf.

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Thermal extension error of boring bar in z-axis is one of the key factors that have a bad influence on the machining accuracy of boring machine, so how to exactly establish the relationship between the thermal extension length and temperature and predict the changing rule of thermal error are the premise of thermal extension error compensation. In this paper, a prediction method of thermal extension length of boring bar in boring machine is proposed based on principal component analysis (PCA) and least squares support vector machine (LS-SVM) model. In order to avoid the multiple correlation and coupling among the great amount temperature input variables, firstly, PCA is introduced to extract the principal components of temperature data samples. Then, LS-SVM is used to predict the changing tendency of the thermally induced thermal extension error of boring bar. Finally, experiments are conducted on a boring machine, the application results show that Boring bar axial thermal elongation error residual value dropped below 5 μm and minimum residual error is only 0.5 μm. This method not only effectively improve the efficiency of the temperature data acquisition and analysis, and improve the modeling accuracy and robustness.

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Statistical optimization and assessment of a thermal error model for CNC machine tools

Cited by 89 publications

References 9 publications

A novel linear virtual temperature constructing method for thermal error modeling of machine tools

A novel linear virtual temperature constructing method for thermal error modeling of machine tools

Thermal Errors Classification Compensation without Sensor for CNC Machine Tools

A Hybrid Prediction Method of Thermal Extension Error for Boring Machine Based on PCA and LS-SVM

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