Application of Optimized GM (1,1) in the Machine Tool Thermal Error Modeling

Yu, Bo

doi:10.4028/www.scientific.net/amr.443-444.813

Cited by 2 publications

(3 citation statements)

References 5 publications

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“…= (G + I) −1 z, (12) where G = VV or G = ⟨k , k ⟩. Combining (12) with 7, can be obtained and w can be calculated by (10).…”

Section: Building the Anfis Model As Can Be Seen Frommentioning

confidence: 99%

“…Indirect compensation procedures based on auxiliary values such as temperature measurements build physical or mathematical models that reveal the relationship between temperature variables and thermal deformation. Various methods, such as finite element analysis [4,5], regression analysis [6,7], 2 Mathematical Problems in Engineering neural networks [8,9], and grey system theory [10,11], or the combination of two or three of these methods [12,13], have been applied to build error compensation models. Thermal deformations are calculated using representative temperature measurement points in the machine structure.…”

Section: Introductionmentioning

confidence: 99%

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Thermal Error Modelling of the Spindle Using Data Transformation and Adaptive Neurofuzzy Inference System

et al. 2015

Mathematical Problems in Engineering

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This paper proposes a new method for predicting spindle deformation based on temperature data. The method introduces the adaptive neurofuzzy inference system (ANFIS), which is a neurofuzzy modeling approach that integrates the kernel and geometrical transformations. By utilizing data transformation, the number of ANFIS rules can be effectively reduced and the predictive model structure can be simplified. To build the predictive model, we first map the original temperature data to a feature space with Gaussian kernels. We then process the mapped data with the geometrical transformation and make the data gather in the square region. Finally, the transformed data are used as input to train the ANFIS. A verification experiment is conducted to evaluate the performance of the proposed method. Six Pt100 thermal resistances are used to monitor the spindle temperature, and a laser displacement sensor is used to detect the spindle deformation. Experimental results show that the proposed method can precisely predict the spindle deformation and greatly improve the thermal performance of the spindle. Compared with back propagation (BP) networks, the proposed method is more suitable for complex working conditions in practical applications.

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“…= (G + I) −1 z, (12) where G = VV or G = ⟨k , k ⟩. Combining (12) with 7, can be obtained and w can be calculated by (10).…”

Section: Building the Anfis Model As Can Be Seen Frommentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Thermal Error Modelling of the Spindle Using Data Transformation and Adaptive Neurofuzzy Inference System

et al. 2015

Mathematical Problems in Engineering

View full text Add to dashboard Cite

show abstract

“…By using physical or mathematical methods, researchers build relationship models between temperature data and thermal deformation. Various techniques, such as finite element analysis, 9,10 grey system theory, 11,12 regression analysis, 13,14 neural networks, 15,16 and combinations of two or three methods, 17,18 have been developed.…”

Section: Introductionmentioning

confidence: 99%

Thermal error prediction of the spindle using improved fuzzy-filtered neural networks

Wang

et al. 2015

Proceedings of the Institution of Mechanical Engineers, Part B:

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An improved fuzzy-filtered neural network model is utilized to predict spindle deformation based on temperature data. The improved fuzzy-filtered neural network model combines the fuzzy logic qualitative approach and neural network adaptive capabilities, and it is composed of fuzzy filtering and adaptive layers. A verification experiment is conducted to evaluate the performance of the improved fuzzy-filtered neural network model. Nine Pt100 thermal resistances are employed to monitor spindle temperature. An inductive current sensor is utilized to detect spindle deformation. Experimental results show that the improved fuzzy-filtered neural network model can better predict spindle deformation than back propagation network, and it can significantly improve the performance of the spindle. Under the new cutting condition, the residual error of spindle deformation along the z-axis can be reduced to less than 6 µm.

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Application of Optimized GM (1,1) in the Machine Tool Thermal Error Modeling

Cited by 2 publications

References 5 publications

Thermal Error Modelling of the Spindle Using Data Transformation and Adaptive Neurofuzzy Inference System

Thermal Error Modelling of the Spindle Using Data Transformation and Adaptive Neurofuzzy Inference System

Thermal error prediction of the spindle using improved fuzzy-filtered neural networks

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