# Laser R-Test for Angular Positioning Calibration and Compensation of the Five-Axis Machine Tools
## 1 Introduction  
The five-axis machine tool is composed of three translational axes, (T), and any two rotary axes, (R) (3T2R). The definition of a rotary axis is based on ISO 230-2 [1], as shown in Figure 1. The machine tool used in this paper is a B-Type five-axis machine tool (UX300, Quaser Machine Tools, Taiwan) with a HEIDENHAIN controller iTNC530. In recent years, the use of five-axis machine tools has been adapted more and widely. With the increasing number of rotary components, the accuracy of the machine tools is more important. The wear of the machine tools during the long processing time impacts the machine's accuracy. The measurement and machine calibration must be carried out  
Figure 1: The schematic illustration of the translational axis and the rotary axis. regularly to ensure the accuracy of the machine tools. Additionally, the error of the five-axis machine tool includes translational axis error and a rotary axis error total of 43 items. Translational axis errors have 21 items on three axes (X, Y, and Z), and rotary axis errors have 22 items on two rotary axes (AC). Each rotary axis has 11 errors, including 6 component errors and 5 location errors. The six component errors of the rotary axes change with the C-axis motion, as shown in Figure 2. Figure 2A shows the six component errors of the rotary axis, which are as follows:  
E\({}_{\text{XC}}\), radial error motion of C in X-direction;  
E\({}_{\text{YC}}\), radial error motion of C in Y-direction;  
E\({}_{\text{ZC}}\), radial error motion of C in Z-direction;  
E\({}_{\text{AC}}\), tilt error motion of C around X-axis;  
E\({}_{\text{BC}}\), tilt error motion of C around Y-axis;  
E\({}_{\text{CC}}\), angular positioning error motion of C.  
Figure 2B shows the five location errors of the rotary-axis, which are as follows:  
XOC, error of the location of C in the X-axis direction;  
YOC, error of the location of C in the Y-axis direction;  
AOC, error of the orientation of C in the A-axis direction;  
BOC, error of the orientation of C in the B-axis direction;  
CCC, error of the orientation of C in the C-axis direction. If the NON-BAR [2] instrument developed in the previous studies for ISO-10792-2 [3] referred to measuring location errors on five-axis machine tools, this paper proposes a system named Laser R-test for angular positioning calibration (component error) and compensation of the five-axis machine tools, provides a simple measurement and calibration method, and maintains high precision for machine tools as a research target. Because the Laser R-test was designed based on the NON-BAR system, the Laser R-test could meet both ISO regulations ISO-10792-2 and ISO-230-2. In angular positioning, previous studies were developed with a laser diode, reflective grating, position-sensitive device, encoder, motor rotary table, or CCD [4,5]. The commercial instrument for machine tools angular positioning mostly uses a high-accuracy rotary table with an encoder and a laser interferometer, but the optical measurement path of these methods is easily affected by the concentric nature of the machine tool rotary table, and the correction of concentricity between the instrument and machine tools rotary table is time consuming. In 2007, [PERSON] [6] used the constant relative position between the standard ball and the probe, so the geometric errors were measured in the standard ball of the device and showed X-, Y-, and Z-direction errors. In 2008, [PERSON] [7] derived a model for eight motion errors of the rotary axis and three vertical errors of the translational axis by using a double ball bar (DBB), which improved on the machining accuracy. In 2013, [PERSON] [8] measured the volumetric error of machine tools' workspace by three CCD cameras. In 2014, [PERSON] [9] used DBB to measure the relative distance between the spindle and the work table and calculated the geometric error of the machine tools through the homogeneous transformation model.