Thermal error modeling of spindle based on the principal component analysis considering temperature-changing process

Li, Yang; Wei, Wenming; Su, Dongxu; Zhao, Wanhua; Jun, Zhang; Wu, Wenwu

doi:10.1007/s00170-018-2482-z

Cited by 18 publications

(7 citation statements)

References 14 publications

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“…Relative to the multivariate linear regression algorithm model coefficient estimation formula shown in equation (2)(3)(4)(5), the ridge regression algorithm proposed by Hoerl and Kennard [44] estimates the model coefficients as follows:…”

Section: ) Ridge Regression Modeling Algorithmmentioning

confidence: 99%

“…where k is the ridge parameter, k ≥ 0, and I is the identity matrix. From equation (2)(3)(4)(5)(6)(7)(8), it can be seen that the ridge regression algorithm adds a normal number matrix kI to X T X.…”

Section: ) Ridge Regression Modeling Algorithmmentioning

confidence: 99%

“…Then, the variance of the model coefficients can be given as shown in equation (2)(3)(4)(5)(6)(7)(8)(9).…”

Section: ) Ridge Regression Modeling Algorithmmentioning

confidence: 99%

“…Then, x * and y * are n-dimensional vectors in space. Bringing equation (4-1) into equation (2)(3)(4)(5)(6) to obtain the new calculation formula (4-2) for the correlation coefficient, ρ xy reflects the cosine of the angle between vectors x * and y * .…”

Section: Mechanism Analysis Of the Pseudocorrelation Problem Of Tmentioning

confidence: 99%

“…∂x * (1) 2 = 0 is essentially a quadratic equation having one unknown; therefore, according to the root-seeking formula, the solution is (4)(5)(6)(7)(8)(9)(10)(11)(12)(13), as shown at the bottom of this page. According to equation (4)(5)(6)(7)(8)(9)(10)(11)(12)(13), the terms under the root consist of the multiplication and addition of the sum of squares, indicating that there must be two real solutions, that is,…”

Section: Mechanism Analysis Of the Pseudocorrelation Problem Of Tmentioning

confidence: 99%

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Thermal Error Modeling for Machine Tools: Mechanistic Analysis and Solution for the Pseudocorrelation of Temperature-Sensitive Points

et al. 2020

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The temperature-sensitive point is the input variable of the thermal error compensation model of computer numerical control (CNC) machine tools. At present, the most commonly used selection method is to measure the multipoint temperature and thermal error of the machine tool synchronously and select several temperature measurement points with the highest thermal error correlation as temperature-sensitive points according to the measurement data. This study reveals that this method sometimes has obvious mis-selection and causes the model to fail. The reason is that the weak correlation temperature measurement point away from the machine tool heat source amplifies the volatility of the correlation evaluation result, owing to the small overall change. If the calculated result exceeds the true strong correlation temperature measurement point, it will be incorrectly selected as the temperature-sensitive point. This scenario has been termed herein as the pseudocorrelation problem. With the gradual popularization of thermal error compensation technology for CNC machine tools, pseudocorrelation will seriously affect the mass production pass rate. Therefore, the study analyzes and rigorously proves the mathematical mechanism of this problem, and the temperature measurement point preselection algorithm based on the correlation coefficient volatility determination factor (CCVDF) is proposed to eliminate potential pseudocorrelation temperature points before selecting temperature-sensitive points. After 1000 random simulation experiments, the failure rate of Z-direction thermal error modeling after preselection decreased from 5.1% to 0.5%, and the Y-direction error decreased from 33.7% to 1.5%. This algorithm can greatly improve the qualification rate of large-scale equipment of thermal error compensation technology. INDEX TERMS CNC machine tool, thermal error modeling, temperature-sensitive point, correlation, mathematical mechanism.

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