## 1 Introduction  
With the development of the manufacturing industry, computer numerical control (CNC) machine tools are also toward the goal of high reliability and high precision, and for industry, such as aviation, aerospace, shipping, and energy, higher requirements are put forward for the manufacturing precision of related parts, especially the super large parts. The processing of super-large parts is mainly completed on the ultra-heavy duty machine tool [1], and the indexing ability of the rotary table determines the precision level of the workpiece [2]. In a vertical machine tool, the C-axis is the axis rotating around the spindle of the table. The rotary feed movement of the spindle can be driven by a servo motor or a spindle motor combined with an encoder. C-axis indexing positioning and other feed axis linkage can achieve arbitrary trajectory processing [3]. The development of the C-axis indexing feed system of CNC machine tools is mainly divided into the following stages [4]. The traditional C-axis positioning is driven by a single motor drive mechanism and with the damping clamping device. The transmission gear meshes with the large gear ring on the spindle of the table, which drives the table to rotate. At the same time, the detection element detects the speed and feeds back to the control system. By correcting the motor parameters, the speed and angle are controlled to form a closed-loop control. The transmission precision of the mechanism is improved, and the indexing and positioning function of the feed system is realized [5; 6; 7]. Because of the use of a single servo motor with a single drive chain, the damping clamp device is usually only relied on to eliminate the tooth clearance. Its driving accuracy is low and positioning accuracy is poor. Under the condition of higher demand for C-axis indexing feed accuracy, how to effectively reduce or eliminate the clearance error through the design of the driving system is the main problem for improving the positioning accuracy of the C-axis. At present, the general method is to use a double drive chain to eliminate the clearance. The drive system consists of two identical gear mechanisms that are driven by a servo motor. After reducing the speed of the reduction mechanism, one of the independent shafts is selected and a constant pressure oil cylinder and a spring set are installed at both ends of the shaft. Through the helical gear axial movement, the end gears of the two gear mechanisms are meshed with the positive and negative meshing surfaces of the main shaft's large gear ring, respectively, so as to eliminate the blank path error of the whole transmission chain [8; 9; 10]. Although this transmission mechanism can effectively eliminate the blank path error that is generated by the side clearance of the end gear, it cannot eliminate the gear side clearance of the front part of the transmission chain, which will still have a great impact on the indexing and feeding accuracy of the whole system. The requirements for dynamic performance and tracking accuracy of the system in practical applications cannot be met due to the presence of tooth clearance, friction dead zone, and other non-linear links in the mechanical drive mechanism of the above two C-axis servo control systems. In addition, due to the limited motor capacity, it is difficult to realize the high-power output in the practical application of ultra-heavy machine tools only by the transmission mechanism driven by a single motor. In view of the above problems, the current ultra-heavy machine tools mainly adopt the dual servo motor to achieve the C-axis rotation and indexing feed function. The dual servo motor adopts the master-slave control function, with the independent drive chain to eliminate the tooth side clearance [11; 12; 13; 14]. This kind of transmission structure can not only meet the power demand of the ultra-heavy machine tool, but also use the control means to eliminate the lateral clearance of gear teeth of the transmission mechanism and improve the positioning accuracy.