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
**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.
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