Paper:

# Statistics-Based Measuring Point Selection for Monitoring the Thermal Deformation of a Workpiece in End-Milling

## Mengmeng Yang^{*}, Feng Zhang^{**}, and Koji Teramoto^{*,†}

^{*}Division of Engineering, Muroran Institute of Technology

27-1 Mizumoto, Muroran, Hokkaido 050-8585, Japan

^{†}Corresponding author

^{**}Shenyang Agricultural University, Shenyang, China

The deformation of the thermal workpiece in the end-milling process has a significant effect on the accuracy of machining. In-process direct measurement of workpiece deformation is difficult because process disturbances occur during machining. On the other hand, local temperatures of the workpiece can be easily and accurately measured using common measuring methods. This study aims to develop a monitoring method for workpiece deformations. A sensor-configured thermal simulation is proposed by combining local temperature measurements with thermal simulations to estimate the thermal states of the workpiece in small-lot production. Furthermore, an empirical modeling method is introduced to estimate the workpiece deformation from measured temperatures, thereby accelerating process time. A reliable estimation requires the selection of appropriate measuring points. Using multiple linear regression (MLR), a statistics-based selection method is proposed to establish a relationship between thermal deformation and temperatures of measuring points in various machining situations. During the end-milling process, the predicted time-series of deformations at the machining point and temperatures of the measuring points are regarded as output variables and input variables, respectively, in the finite element method (FEM)-based thermal simulation. The number of measuring points is determined by evaluating Akaike information criterion (AIC), and effective measuring points are selected using the *p*-value index. The proposed systematic construction method is evaluated using simulation-based case studies. The constructed temperature-based model for measuring workpiece deformation corresponded well to the FEM simulation. Therefore, the constructed model can represent workpiece deformation with the minimum number of measuring points.

*Int. J. Automation Technol.*, Vol.16, No.5, pp. 562-571, 2022.

- [1] I. Lazoglu and B. Bugdayci, “Thermal modelling of end milling,” CIRP Annals – Manufacturing Technology, Vol.63, No.1, pp. 113-116, 2014.
- [2] Y. Sun, J. Sun, and J. Li, “Modeling and experimental study of temperature distributions in end milling Ti6Al4V with solid carbide tool,” Proc. of the Institution of Mechanical Engineers, Part B: J. of Engineering Manufacture, Vol.231, No.2, pp. 217-227, 2017.
- [3] C. Dinc, I. Lazoglu, and A. Serpenguzel, “Analysis of Thermal Fields in Orthogonal Machining with Infrared Imaging,” J. of Materials Processing Technology, Vol.198, Issues 1-3, pp. 147-154, 2008.
- [4] M. Sato, T. Ueda, and H. Tanaka, “An experimental technique for the measurement of temperature on CBN tool face in end milling,” Int. J. of Machine Tools and Manufacture, Vol.47, No.14, pp. 2071-2076, 2007.
- [5] S. Lin, F. Peng, J. Wen, Y. Liu, and R. Yan, “An investigation of workpiece temperature variation in end milling considering flank rubbing effect,” Int. J. of Machine Tools and Manufacture, Vol.73, pp. 71-86, 2013.
- [6] W. Baohai, C. Di, H. Xiaodong, Z. Dinghua, and T. Kai, “Cutting tool temperature prediction method using analytical model for end milling,” Chinese J. of Aeronautics, Vol.29, No.6, pp. 1788-1794, 2016.
- [7] Y. Xiong, W. Wang, R. Jiang, and K. Lin, “Analytical model of workpiece temperature in end milling in-situ TiB2/7050Al metal matrix composites,” Int. J. of Mechanical Sciences, Vol.149, pp. 285-297, 2018.
- [8] K. Teramoto and M. Onosato, “In-process visualization of machining state with sensor-based simulation to support the recognition ability of operators,” Human Friendly Mechatronics 2001, pp. 389-394, 2001.
- [9] Y. Huang and T. Hoshi, “Optimization of fixture design with consideration of thermal deformation in face milling,” J. of Manufacturing Systems, Vol.19, No.5, pp. 332-340, 2001.
- [10] K. Teramoto, R. Tanaka, T. Ishida, and Y. Takeuchi, “Thermal State Visualization of Machining Workpiece by Means of a Sensor-Configured Heat Conduction Simulation,” JSME Int. J. Series C Mechanical Systems, Machine Elements and Manufacturing, Vol.49, No.2, pp. 287-292, 2006.
- [11] D. Wu and K. Teramoto, “An evaluation criterion to select temperature measurement positions in end-milling,” Int. J. Automation Technol., Vol.12, No.1, pp. 105-112, 2018.
- [12] Y. Sasaki, H. Iwai, Y. Wakazono, Y. Sakurai, and Y. Oka, “Development of Real-Time Thermal Displacement Compensation System,” J. of JSPE, Vol.83, No.2, pp. 121-124, 2017 (in Japanese).
- [13] S. G. Makridakis, S. C. Wheelwright, and R. J. Hyndman, “Forecasting: Methods and Applications,” John Wiley and Sons, 1998.
- [14] H. Akaike, “A new look at the statistical model identification,” IEEE Trans. on Automatic Control, Vol.19, No.6, pp. 716-723, 1974.
- [15] S. Sahoo and M. K. Jha, “On the statistical forecasting of groundwater levels in unconfined aquifer systems,” Environmental Earth Sciences, Vol.73, No.7, pp. 3119-3136, 2015.
- [16] C. S. Ding and M. L. Davison, “Assessing Fit and Dimensionality in Least Squares Metric Multidimensional Scaling Using Akaike’s Information Criterion,” Educational and Psychological Measurement, Vol.70, No.2, pp. 199-214, 2010.
- [17] L. A. Barrientos, F. R. Zuniga, Q. R. Perez, and M. G. Speziale, “Variation of
*b*and*p*values from aftershocks sequences along the Mexican subduction zone and their relation to plate characteristics,” J. of South American Earth Sciences, Vol.63, pp. 162-171, 2015. - [18] C. K. Li, Y. C. Liu, Y. J. Shi, P. Yi, J. H. Xie, X. L. Ma, and L. F. Cui, “Modeling of High-Frequency Induction Heating Surface Cladding Process: Numerical Simulation, Experimental Measurement and Validation,” Proc. of the 6th Int. Asia Conf. on Industrial Engineering and Management Innovation (IEMI), pp. 747-759, 2015.
- [19] R. B. Dessau and C. B. Pipper, ““R”–project for statistical computing,” Ugeskrift for Laeger, Vol.170, No.5, pp. 328-330, 2008.
- [20] A. H. He, R. P. Singh, Z. Sun, Q. Ye, and G. Zhao, “Comparison of Regression Methods to Compute Atmospheric Pressure and Earth Tidal Coefficients in Water Level Associated with Wenchuan Earthquake of 12 May 2008,” Pure and Applied Geophysics, Vol.173, No.7, pp. 2277-2294, 2016.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.