Use of multiple linear regression to compensate for diametrical deviations in machined components due to thermal errors. (2022) - Gowda, Chethana R.; Dutta, Rahul; Pasha, Aslam Taj; Ravi, L.
Abstract: Computer Numeric Control (CNC) machine tools such as CNC milling machines and CNC turning centers produce components with a higher dimensional precision and accuracy when compared to traditional machine tools. The precision, accuracy of the dimensions are still governed by factors such as geometric errors, cutting forces induced errors and thermal errors. Thermal errors are a major contributing factor to dimensional deviations of the machined component. The heat generating sources of the machine tool which include spindle ball bearings, spindle motor, the axes motors, transformer pack, coolant pump, lubricant pump among others. The ambient temperature and weather also play a role in inducing thermal errors in a machine tool. The heat generated at these sources gets transferred to the adjacent elements of the machine tool causing them to distort or deform. These distortions or deformations of the various machine tool elements produce a cumulative effect which leads to the increase or decrease of the gap between the tool and work piece resulting in dimensional deviation in the final machined component. In the current work an attempt has been made to compensate for these thermal errors by building a prediction model based on experimentally measured diametrical and temperature data. Multiple linear regression has been used to create the prediction model, where the diametrical deviations were considered as dependent variables and temperature data was considered as independent variables. Least squares method is employed in multiple linear regression to obtain regression coefficients which would then be used in a mathematical equation to determine the deviation between tool point and work piece, which can be compensated to maintain the dimensions of the machined components. Four case studies were carried out in this work. Logarithmic transformation was used in the final case study to transform non-linear data into linear data which lead to consistent model behaviour when applied to several hours of test data.