1 Introduction In the modern machinery manufacturing industry, the CNC machine tool known as the 'work mother machine' occupies an irreplaceable position in the development of the manufacturing industry, and its research and development level symbolizes the comprehensive strength of the manufacturing industry to a certain extent. With the rapid development of the manufacturing industry, the requirements for the accuracy of machine tool parts are increasing day by day, and the research on machine tool accuracy has received extensive attention. The machining error is the most direct manifestation of the machining accuracy of the machine tool on the workpiece. Machining error refers to the deviation between the actual machining path of the tool and the theoretical contour of the workpiece. The geometric error is the most direct and critical factor affecting the machining accuracy of the machine tool. As shown in Figure 1, a CNC machine tool is mainly composed of a translation axis and a rotary axis. Taking the CNC cylindrical grinder as an example, the motion errors of each axis interact and jointly affect the machining accuracy of the CNC machine tool. The precision research of CNC machine tools mainly includes two aspects: precision design and error compensation. Accuracy design refers to finding the key error sources that affect the accuracy of the machine tool according to the error sensitivity analysis results of key components in the early stage of machine tool design, and improving the original accuracy of the machine tool by improving the manufacturing accuracy of key components and a reasonable tolerance allocation method. Error compensation is to adjust the tool pose, modify the machine tool control parameters, and adjust the G code through hardware or software to compensate for the errors generated during the machine tool movement. This paper discusses the research status and urgent problems of precision optimization design of CNC machine tools through four aspects: error modeling, sensitivity analysis of key components, precision optimization allocation and error compensation. Fig. 1 Error factors of CNC cylindrical grinder 2 Error modeling method of CNC machine tools error etc. According to the mechanical and dynamic characteristics of the error, the machine tool error is usually divided into static error and dynamic error. Static errors include dimensional errors of key components and pose errors between assemblies. The dynamic error mainly includes the deformation vibration and thermal error generated by each axis during the movement process. In order to reflect the mapping relationship between the machine tool error source and the tool pose error, the spatial pose error of each motion axis of the machine tool is expressed through error modeling. The commonly used mathematical tools mainly include screw theory, exponential product formula and quaternary method, etc. Among them, the homogeneous coordinate transformation method is the most widely used, and its clear mathematical expression is widely used in the error modeling of machine tools. In the aspect of error modeling, a lot of research work has been carried out. At present, a variety of different mathematical model modeling methods for motion errors have been developed, such as geometric modeling method, error matrix method, mechanism modeling method, rigid body kinematics method and Many-body systems theory, etc. Based on multi-body system kinematics, Fan J.W. et al. proposed a general machine tool geometric error model by constructing the machine tool topology structure (where the relative motion of adjacent bodies is shown in Figure 2). Ding G. et al. established a spatial positioning accuracy model of a five-axis cylindrical milling machine based on multi-body system theory and homogeneous coordinate transformation. Wu C. et al. established a tool pose prediction model for five-axis non-orthogonal CNC machine tools based on multi-body system theory and relative motion constraint equations. Fig. 2 Schematic diagram of relative motion of adjacent bodies At present, the research on error modeling is relatively mature, and it is particularly important to study the influence of machine tool dynamic factors on machine tool accuracy under precision and ultra-precision machining conditions. There are relatively few studies on thermal errors. 3 Sensitivity analysis of key parts Sensitivity analysis of machine tool error is to study the sensitivity of the uncertainty source of the geometric error of the parts to the machining accuracy of the machine tool, sort the parts according to their sensitivity, and find out the items that have a higher impact on the machine tool accuracy. Allocate tolerances to improve the spatial positioning accuracy of the machine tool. Sensitivity analysis is often regarded as a prerequisite for error modeling and analysis, and is an important theoretical basis for machine tool precision design. At present, sensitivity analysis methods are mainly divided into local sensitivity analysis method and global sensitivity analysis method. Relative local sensitivity analysis and global sensitivity analysis comprehensively consider the influence of the distribution and shape of the probability density function of each factor, and each factor can change continuously during the analysis process. Based on the global sensitivity analysis method, Cheng Q. et al. proposed a method for identifying key geometric errors of multi-axis machine tools. By identifying key errors, the machining accuracy of machine tools can be improved. Taking a five-axis machine tool as an example, Li J. et al. proposed a generalized local sensitivity index, a generalized global sensitivity index and a general global sensitivity fluctuation index on the basis of the traditional sensitivity index definition. This method not only reduces the error component of the machine tool, but also improves the cutting tool. cutting accuracy. Fang J. et al. proposed a global sensitivity analysis method for five-axis machining errors based on quasi-Monte Carlo algorithm. Using the machine tool space motion error model, certain mathematical operations are performed on the parameters of each error source, and the obtained results are normalized and sorted from large to small.In this way, the components that have a greater influence on the spatial motion error of the machine tool can be judged.