Abstract : Based on indexing theory, this paper analyzes the working principle of the indexing mechanism and the mechanism of indexing error generation during gear forming grinding. The main error sources affecting the transmission accuracy of the indexing mechanism are identified, a complete on-machine indexing error compensation scheme is established, the control system is designed and the control program is compiled. The correctness of the indexing error theoretical analysis and the practicality of the entire error compensation system are verified through experiments. Keywords : Gear, Indexing Mechanism, Error, Error Compensation [align=center]Research on Error Composition for Dividing Mechanism of the Gear from Grinding MA Yan1, LI Ju-bo2, ZHANG Luo-ping3, WU Yu-qing1 (1.Zhejiang Xinchang Peer Bearing Co.,Ltd; Xinchang; Zhejiang 312500; China; 2.School of Mechanical Engineering; Jiangsu University; Zhenjiang; Jiangsu212013;China; 3.Electromechanical Engineering College; Henan University of Science & Technology; Luoyang; Henan471003;China) Abstract : Based on the division theory, this paper studies the operation principle of the dividing mechanism and the reasons for generating error in the gear division process. Form grinding was deeply analyzed, the main errors which affected the accurate dividing were found, one integrated error compensation scheme was set up, the control system was explicated, and the error control system was programmed in this paper. Through the on-machine error compensation experiment, the correctness of the theoretical analysis and the feasibility of the compensation method were proved. Key Words : Gear, Dividing Mechanism, Error, Error Compensation 0 Introduction Gears, as the basic components for transmitting power and motion, have the characteristics of large power range, high transmission efficiency, long service life, and safety and reliability, and have become an indispensable transmission component for many mechanical products. The design and manufacturing level of gears will directly affect the performance and quality of mechanical products [1]. With the development of gear manufacturing technology, higher requirements have been put forward for gear indexing technology and error compensation technology of indexing mechanism. The key to achieving high-precision machining of parts on machine tools is to improve the machining positioning accuracy of machine tools. Error compensation technology can significantly improve the positioning accuracy of CNC machine tools. Without altering the machine tool structure or manufacturing precision, spatial position errors during machining can be detected in real time using a position detection device. Simultaneously, the detected error is fed back to the machine tool's control system, and the ideal CNC commands are corrected, thereby improving the machine tool's machining positioning accuracy and achieving effective error compensation. This paper mainly studies how to improve the positioning accuracy of the indexing mechanism by compensating for the transmission system error. 1. Measurement and Processing of Feed Error In the indexing process of gear machining, the error clearance of the transmission chain has a significant impact on gear machining, making transmission chain error clearance compensation particularly important. Considering actual manufacturing, assembly, and wear conditions, this paper pre-measures the error of the transmission feed system during the indexing process and uses the measured values ​​to determine the error compensation value during indexing. During error measurement, measurements are taken at the same interval increments. Through analysis and comparison of the measured values, outliers with large deviations are eliminated, and the fitted points of the measurement curve are used to replace them, making the indexing error value closer to the actual situation and achieving better error compensation results. The specific error measurement work can be completed in the following parts: 1.1 Determination of the mechanical origin. In the error measurement process, the mechanical origin must first be determined. Because the mechanical origin of the system is the reference of the entire measurement process, the accuracy of the determination of the mechanical origin will have an important impact on the measurement results. This system uses an inductive limit switch for coarse positioning. Once the indexing worm gear of the indexing mechanism reaches the sensing area of ​​the limit switch, the limit switch sends a signal, and the servo control system decelerates and continues to slowly rotate the worm gear until the first Index signal of the encoder disk measuring the rotation angle appears. This position is the precise positioning mechanical origin. All subsequent rotations or indexings use this position as the counting zero point and position it as the current zero point position of the indexing worm gear. The specific positioning principle of the mechanical origin is as follows: The computer first receives the signal from the limit switch, and then issues a capture Index signal command based on the switch signal and controls the motor to rotate forward or backward. The first Index signal encountered by the controller and the encoder is used as the trigger signal for position capture. The captured current position can be used as the mechanical origin of the system. The origin position captured by the controller is the actual position of the indexing worm wheel at the moment the trigger pulse arrives. The capture position accuracy can reach +/-1 pulse, which can make the origin positioning error within 5um. 1.2 Error measurement principle When performing error measurement, the error measurement and compensation must be aligned with the same reference point. Generally, the zero point of the machine tool is selected as the reference point for compensation and measurement. Since the same reference is used for each indexing error during the measurement process, this makes the reference of each measurement point uniform, eliminates the system error, and greatly improves the measurement and compensation accuracy [2]. The error measurement principle is shown in Figure 1. Assume that N measurement points (the size of N is determined by the measurement accuracy) are evenly distributed along the worm wheel rotation angle, 0 is the coordinate origin, and the distance between the points is . After each point is measured, it is necessary to return to the origin and start measuring the next point. The data of each measurement is automatically stored in the computer. After analysis and comparison, the most ideal error value is obtained. The error value is directly used for compensation. The error of the points in the middle of each measurement point can be determined by interpolation or linear fitting. [align=center] Figure 1 Error measurement principle diagram[/align] 1.3 Fitting of indexing error Since the indexing error has a clear linear relationship with the rotation angle of the indexing worm gear, we can perform real-time curve fitting on the indexing error in the indexing process, and then perform real-time feedback compensation on each indexing error in the indexing process. Among the various methods of linear interpolation and fitting of data, the least squares curve fitting method has the advantage of minimizing the sum of squares of errors at each measurement point, and does not require equal distance between nodes, and the expression is unique and easy to calculate. As a data processing method, the least squares method has been widely used in experimental curve fitting, combined measurement data processing, etc. [3]. This paper uses the least squares method to perform curve fitting on each point of the indexing error. First, read the corresponding indexing errors (φi, δi) for each worm gear rotation angle from the analyzed error data file, which are: Solve the above system of equations to obtain the values ​​of parameters a[sub]1[/sub], a[sub]2[/sub], a[sub]3[/sub], ..., a[sub]k[/sub], thus obtaining the equation of the fitting function and the complete compensation value of the indexing error. Based on the above discussion of relevant theoretical foundations, and due to the use of the least squares method, the influence of the error source on the angular accuracy is minimized, therefore the obtained result has high accuracy. 2. Control Strategy of Error Compensation System After measuring and analyzing the indexing error of the indexing mechanism in gear forming grinding, the indexing rotation error can be compensated. In the actual error compensation process, the ideal position compensation scheme must be processed into a feasible error compensation program through a specific compensation method in order to achieve effective compensation. During the indexing process, the position of the indexing worm gear is fed back to the position control system in real time using a position detection device. Combining the relationship between the drive gear and the indexing worm gear in the indexing mechanism, as well as the transmission ratio between each transmission chain and the corresponding pulse voltage, the error value of the transmission system is converted into a corresponding pulse voltage to adjust the speed of the servo motor, allowing the drive gear to run at an appropriate speed to compensate for possible indexing errors. This process is repeated to drive the indexing mechanism cyclically, ultimately achieving the compensation goal and obtaining a satisfactory indexing effect. The compensation algorithm flowchart is shown in Figure 2. Based on the modular design concept, this paper developed specific software to implement error compensation. The software consists of: an indexing display module, a parameter setting module, a compensation control calculation module, a servo control module, a diagnostic discrimination module, and a data communication module, etc. The software flowchart is shown in Figure 3. [align=center] Figure 2 Compensation Algorithm Flowchart Figure 3 Compensation Software Flowchart[/align] 3. Experimental Verification and Analysis 3.1 Experimental Apparatus To verify the correctness of the indexing error factor analysis and the feasibility of the compensation scheme in this paper, an error analysis experiment was conducted during the gear indexing process. The experimental setup primarily consisted of a large gear forming milling machine requiring CNC retrofitting. Its indexing mechanism's transmission chain comprised two stages of gear transmission and one stage of worm gear transmission, with a total transmission ratio of 648. The first-stage gear ratio was 2.25, the second-stage gear ratio was 1.8, and the worm gear ratio was 160. The control system of this experimental setup mainly utilized an Advantech industrial control motherboard, a Galil DMC-1842 four-axis motion control board (USA), a Yaskawa SGMGH-44ABA servo motor, and a Mel encoder AINH58 (Germany). The software was programmed using Visual C++. 3.2 Experimental Principle During the indexing mechanism operation experiment, the motor transmits power to the gear reducer via a 1:1 synchronous pulley. A position encoder is installed on the indexing worm gear shaft. The industrial control computer exchanges information with the DMC-1842 motion controller via a communication interface, including sending motion control commands to the motion controller and obtaining the current status and relevant control parameters of the motion controller through this interface. The motion controller receives the position and trajectory commands from the industrial control computer, completes real-time trajectory planning, closed-loop position servo control, host command processing, and controller management, converting them into a command format acceptable to the servo driver, which then processes and amplifies the commands before outputting them to the servo motor. The photoelectric encoder installed on the end of the indexing worm gear shaft acts as an angle sensor, used to measure the movement distance of the indexing worm gear, thus constructing a closed-loop control system through the motion controller. The motion controller can also obtain motion position feedback information through the encoder interface and control the servo motor through the analog voltage output interface to achieve the motion required by the host. The experimental principle of error compensation is shown in Figure 4: [align=center] Figure 4 Schematic diagram of error compensation experiment[/align] 3.3 Experimental Results During the experimental operation, after converting the transmission ratio relationship of the transmission system, the correspondence between the motor encoder and the position detection encoder can be obtained. Figure 5 shows the difference curve of the equivalent error of the two encoders detected in the experiment when the indexing error after error compensation is reflected on the circumferential arc length of the machined gear with a diameter of 1.6m during the operation of the indexing mechanism. [align=center] Figure 5 Relationship between equivalent indexing error and indexing worm gear rotation angle[/align] 4. Conclusion It can be seen from the curve that as the indexing angle changes, the equivalent indexing error on the circumferential arc length is a sine curve with an amplitude range of ±1mm and a period of 2. The error is compensated relatively ideally, achieving the compensation effect and meeting the accuracy requirements of the indexing mechanism. It also verifies the correctness of the indexing error analysis in this paper and the rationality of the error compensation scheme, and provides an effective way for the indexing error compensation of gear forming grinding. References [1] Shang Xiangdong, Jin Jiaqi et al. Gear Machining Accuracy [M]. Beijing: Machinery Industry Press, 2000: 152-153. [2] Liu Huanlao, Li Bin, Shi Hanmin et al. Position Accuracy Evaluation and Error Compensation System for Embedded CNC Machine Tools [J]. Journal of Huazhong University of Science and Technology (Natural Science Edition), 2004, 32 (10): 31-33. [3] Li Qingyang, Wang Nengchao, Yi Dayi. Numerical Analysis [M]. Wuhan: Huazhong University of Science and Technology Press, 2003, 68-74. About the author : Ma Yan (1979-), female, from Weinan, Shaanxi, assistant production scheduling manager and assistant engineer at Zhejiang Xinchang Pier Bearing Co., Ltd., mainly engaged in production management and advanced manufacturing technology research. Tel: 13967527729 E-mail: [email protected] Li Jubo (1979–), male, from Nanyang, Henan Province, is a doctoral candidate in the School of Mechanical Engineering, Jiangsu University, mainly engaged in research on intelligent control technology. Tel: 13598472389 E-mail: [email protected] Zhang Luoping (1955–), male, from Luoyang, Henan Province, is a professor and master's supervisor in the School of Mechanical and Electrical Engineering, Henan University of Science and Technology, mainly engaged in research on numerical control technology. E-mail: [email protected]