# Design of Optical Free-Form Surface Milling Machine Based on Mechanical Shunt and Dynamic Analysis
## 1 Introduction  
In the whole process chain of optical free-form surface machining, precision milling has a great influence on the surface and sub-surface quality of optical free-form surfaces, and its machining effect will directly determine the efficiency and feasibility of subsequent machining such as grinding and polishing. Therefore, the development of an optical free-form surface milling machine has become one of the key factors to improve the manufacturing ability of an optical free-form surface, and the coupling of high stiffness, large damping and long-term stability in the design of an optical free-form surface milling machine have also made it one of the most complex and risky engineering problems. The structural dynamic performance of machine tools is a key factor that affects the machining precision and productivity. Structural design optimization is a type of crucial approach to improve the dynamic performance of machine tool structures and maximize the utilization ratio of materials [1; 2; 3]. [PERSON] et al. [4] analyzed the influence of machining process parameters on milling dynamics. [PERSON] et al. [5; 6] presented a methodology of a thermal distortion compensation system for the large machine tools design; this method can greatly compensate the thermal deformation error of the machine tool. [PERSON] et al. [7] evaluated the surface roughness during precise ball end milling of low hardened alloy steel. The traditional mode of production for machine tools (for example, the cycle of design, manufacture, experiment, and adjustment) cannot meet the requirements. Fortunately, the development of computer simulation technology and virtual machine tools provides a possible solution to this problem. The virtual machine tool is a simulation of the entire machine tool. It involves the structure of the machine tool and a computer numerical control system. Research into the virtualmachine tools has attracted more and more attention at research institutes [8; 9]. Using the virtual machine tool model, we can obtain the kinematics and structural dynamics, which notably influence the performance of machine tools. To meet all the requirements of the virtual machine tool in the best possible way, an accurate physical prototype must be established first. In the past decades, many studies have been performed on the issue. These studies are generally based on one of the following three models: finite element method (FEM) [10; 11; 12; 13; 14], multibody simulation [15; 16; 17], and discrete mass-spring-damper models [18; 19; 20]. In addition, [PERSON] and [PERSON] [21] presented a method for modeling machine tools by integrating the finite element method with multibody simulations. Because of the complexity of the machine tool's structure, a hybrid theoretical-experimental modeling method has been proposed in previous studies [22]. Dynamic design combined with static design has become an inevitable trend in the development of modern machine tool design. Because the characteristic parameters of the joint surface have a significant impact on the performance of the machine tool, the research on the identification technology of the joint surface parameters has become very important. This includes the input of the joint surface parameters to the virtual prototype for performance information, and comparison with the data obtained from the physical prototype experiment to determine the accuracy of the virtual prototype model. There are few reports on the impact of gravity balance device on machine tool dynamics. So, this paper establishes a virtual prototype of the optical free-form surface milling machine, based on the model, the influence of the gravity balance device on the \(Z\)-axis dynamics of the milling machine was studied from a quantitative and qualitative perspective. The optical free-form surface in the paper is a kind of precise optical component used in the optical system.