# Positioning Errors Measurement of CNC Machine Tools Based on J-DBB Method
## 1 Introduction  
Machining parts with high accuracy is a key issue in the field of precision manufacturing. The emergence of CNC machine tools provides the possibility to process high-accuracy parts [1, 2]. Due to the increasingly high precision requirements of parts in modern processing and manufacturing industries, CNC machine tools are facing the challenge of achieving high-precision machining on complex parts [3]. The factors that affect the accuracy of CNC machine tools can be broadly divided into geometric errors, thermal induction errors, and positioning errors [4, 5]. Double ball bar (DBB) has been widely used in the error measurement of NC machine tools since it was proposed [6, 7]. DBB measures the movement errors of the machine tool through a displacement sensor. Compared with other measurement methods, DBB has higher measurement accuracy, easier operation, and is more convenient [8], so scholars have done a lot of research on the use of DBB to measure machine tool errors. The volume error of the vertical machining center was analyzed using DBB [9]. The errors of the rotary axis of a five-axis CNC machine tool were measured using a fixed-length DBB [10, 11]. The accuracy of the machine tool was evaluated using DBB under no-load conditions [12, 13]. A measurement technique based on telescopic DBB is proposed to measure the thermal error of CNC machine tools [14]. A kinematic calibration method for fiveDOF and six DOF in-parallel actuated mechanisms was proposed based on DBB [15]. The volume error model of the coordinate measuring machine based on DBB was established, and the validity was verified by the compensation experiment [16]. However, DBB is a single degree of freedom measuring instrument; in the above studies, data collection can be completed only through multiple measurements in different positions or directions, which cannot meet the needs of efficient measurement. Many new devices based on the DBB method were designed to better measure the error of machine tools. The telescoping magnetic ball bar (TMBB) has been provided to detect the motion errors of the machine tool [17], but due to the limitation of the structure, the measurement accuracy is not high enough. An instrument that utilizes three rotary encoders and link mechanisms (RELM) has been developed to measure the motion accuracy of the CNC machine tools [18]. Its measurement radius is constant, and the measurement efficiency is low. The double rings string (DRS) method was studied to estimate the error of large-scale machine tools. However, the accuracy of DRS was slightly lower [19]. A linkage bar mechanism composed of rotary encoder was proposed to improve the measurement accuracy of machine tool motion error [20; 21]. This new device with a variably measuring radius can largely extend the measurement ranges. Nevertheless, the measuring capability of the device is limited to a plane in a fixed direction. The linked ball bar (LBB) is developed to measure machine tool motion errors in a plane [22]. The device using two link bars solved the problem of the short measurement range of DBB and has high measurement accuracy. The double ball bar with a spherical joint (J-DBB) was developed to measure machine tool motion errors of the arbitrary space path [23]. Compared with the DBB that only measures on the plane, the J-DBB method reflects the spatial error of the machine tool through the space angle between the two bars, which is more in line with the real error measurement requirements of the machine tool. However, there is currently no comprehensive method for measuring spatial angles, so this paper decouples the spatial angles into two plane angles to verify the feasibility of the J-DBB method. The J-DBB device has a flexible measuring range and was used to measure five geometric errors of the machine tools. These five geometric errors are related to the shape errors of the machine tool guide rail.