Fundamental Research On Multi-degree-of-freedom Magnetic Levitation Fine Stage

Multi-degree-of-freedom(Multi-DOF) magnetic levitation fine stages have advantages of high positioning accuracy, fast response, no friction and vacuum compatibility. They have broad application prospects in modern precision, ultra-precision equipment domains such as semiconductor photolithography processing, ultra precise measurement, and biological chip technology. In recent years, magnetic levitation fine stages have attracted widespread attention in academic research and industrial applications. Based on the summary of the existing configurations of fine stages, a new integrated scheme for magnetic levitation fine stage is presented in this thesis, which combines the Lorentz planar motor and the magnetic levitation gravity compensator. The novel fine stage has some advantages such as compact structure, high force linearity, low vertical stiffness, low surface temperature rise, and so on. Taking the multi-DOF fine stage as the research object, the modeling of accurate analytical model, suppression of force ripple, optimization of vertical stiffness, study of electromagnetic design method and suppression of surface temperature rise are researched in this thesis. The research method is based on the combination of theoretical analysis, numerical calculation and experimental verification.The basic configuration and six-DOF driving unit of the magnetic levitation fine stage is introduced. Based on the equivalent charge model and image method, the accurate analytical expression of the 3D air-gap magnetic field for Lorentz planar motor is derived. The position relationship and the contribution to force of each driving unit is discussed. The complete force expressions for the Lorentz planar motor that considers the coil end force are established. Based on the equivalent current model, the mathematical model of the proposed cylindrical magnetic levitation gravity compensator with Halbach secondary structure is built, which include the expressions of air-gap magnetic field, static levitation force, dynamic levitation force and vertical stiffness. The above analysis lays a theoretical foundation for the force characteristic optimization and design method research of the fine stage.To achieve high-precision positioning, the magnetic levitation fine stage should have low force ripple and good vibration isolation performance. Therefore, the force characteristic of the Lorentz planar motor and the vertical stiffness of the magnetic levitation gravity compensator are further studied. The leading cause of the force ripple in Lorentz driving unit is described, and the influence of horizontal displacement, vertical displacement and pitching/deflection angle on the force are summarized. To enhance the end magnetic field and reduce the force ripple, a new Halbach magnet with unequal thickness is presented. The levitation force and stiffness from two types of passive magnetic levitation units which includes conventional secondary and Halbach secondary, respectively, are analyzed and compared. The variation rules of the levitation force and stiffness with radial air-gap length, magnet thickness, magnet height and height ratio of Halbach array are summarized. It can be found that the zero-stiffness point will shift when the stiffness is low enough. In this thesis, the "magnetization increasing and demagnetization effect" of permanent magnets is adopted to theoretically explain the phenomenon and put forward several means to adjust the zero-stiffness point.The electromagnetic design method for Lorentz planar motor and magnetic levitation gravity compensator are researched respectively on account of the independentability of the magnetic circuit. The design principles for the Lorentz planar motor are first given. The main dimensions’ equation of the driving unit is derived, and the three main dimensions are determined. According to the established mathematical model, the influence of parameters on the motor performance is studied, which provides an important reference for the design of primary and secondary of Lorentz planar motor. A prototype of Lorentz planar motor is manufactured and the static force/torque testing platform is set up. The force/torque linearity and force ripple of the prototype are tested. Based on the specifications and features of the magnetic levitation gravity compensator, the related design principles and flow chart are given. To solve the problem that classical analytical model is not valid in the low stiffness applications, a semi-analytical model for the magnetic levitation gravity compensator is proposed. A prototype of magnetic levitation gravity compensator is manufactured and the levitation force testing platform is set up. The levitation forces characteristics of the prototype as a function of axial displacement, radial displacement and coil current are are tested, respectively. Finally, the vertical stiffness within the effective motion range is calculated.In high-precision positioning systems, the surface temperature rise of the fine stage is strictly restricted to reduce its influence on the measuring system. The 3D temperature field finite element models for the Lorentz planar motor and the magnetic levitation gravity compensator are built, and the specific cooling systems are designed. For the Lorentz planar motor, the temperature rise and cooling experiments of the coil cooling unit are completed to evaluate the cooling capacity of the water-jaclet type cooling structure first. The cooling structure of the Lorentz planar motor is then proposed, and the separation plate is presented to achieve equal distribution for the three cooling branches. Finally, the influence of structural material on the temperature rise of coil part is analyzed using finite element method, and the analysis results are verified by the experiment. For the magnetic levitation gravity compensator, the cooling mode setting water channel slots near four coils is proposed. In addition, the temperature field simulation model is built and the relevant experiments are completed, which lays a technology foundation for the use of magnetic levitation gravity compensator in the high-precision positioning applications.