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Introduction
High machining precision is critically important and has increased demand in recent years in aerospace, military, ships, cars, and other industries. Fabrication of high precision parts is heavily dependent of machining capabilities and capacity of the used tool. A variety of error sources related to the machine tool are responsible for machining errors. Therefore, to alleviate this problem, it is important to establish a mapping relationship between machine tool errors and machining errors. This would allow tracing machining errors caused by machine tool errors.
Geometric errors in machine tool parts contribute to spatial errors, which are a major factor affecting machining accuracy.[1] Considerable effort has been made by researchers to identify each geometric error by direct measurements on the machine. In 1982, Bryan[2] first reported the use of magnetic ball bars for measuring linear axis motion errors. Since then, various groups have applied this method to measure geometric errors of machines. Knapp and Matthias[3] proposed a circular test for identifying machine errors by measuring circular contour along different flat of machining space. This allowed identification of the main source of errors due to uncertainty of machine in three-dimensional space. Kakino et al.[4] carried out an in-depth study using the circular test with the aid of magnetic ball bars to obtain a relationship between machine motion errors and radial errors in polar plots. Tsutsumi and Saito[5] proposed an algorithm to identify eight specific geometric errors for a five-axis machine tool using the ball bar. Lei et al.[6] proposed a double ball bar test to measure rotary axes motion errors by simultaneously moving only two rotary axes while keeping all linear axes stationary. Ziegert and Mize[7] employed laser ball bars for measuring volumetric errors in a lathe. Mize and Ziegert[8] used the laser ball bar to measure all geometric errors for a three-axis machine in less than 30 min. Weikert[9] proposed a R-test measuring device for a five-axis machine tool, which has also been adopted by ISO 10791-6:2014.[10] This device can simultaneously detect displacement in three directions. As a result, this device provides more information in a single measurement. Ibaraki et al.[11] presented an efficient calibration method to identify location errors and position-dependent geometric...