Magnetic Field Analysis And Stage Design For Long-stroke Electromagnetic Direct-drive Nanopositioning

Long-stroke nanopositioning technique is the key point to nanopositioning and nanomanufacture,which is widely applied in semi-conductor manufacturing and component-testing apparatus and factory automation.To overcome the drawbacks of the piezoelectric-driven and macro/micro nanopositioning stages,in this thesis,a long-stroke electromagnetic direct-drive nanopositioning stage is studied,as well as its magnetic field,design and control model.First,considering the deteriorating and decreasing magnetic field of the permanent magnet(PM)array,numerical and semi-analytic methods are respectively applied to solve the magnetic field of the finite-long irregular-shaped PM array.In the numerical aspect,an open-domain differential quadrature finite element method(DQFEM)is proposed to resolve the magnetic open-domain problem.According to this method,by the scaling function as well as the generalized blending functions,the infinite irregular-shaped computational domain is finally mapped into a rectangular shape.As a result,the solution to the magnetic field is obtained by the differential quadrature rule and the boundary conditions.In the semi-analytical aspect,based on the long-period Fourier series expansion,a general expression of the magnetic field of the PM array is obtained considering the end effect.Both methods are validated to be accurate and effective.Second,an appropriate-shaped PM array can help improve the magnetic field distribution and thrust performance,and thus is of significance for the positioning stage.In this thesis,three new-shaped PM arrays are designed,namely,the lateral sinusoidal,the bottom-curved and the curve-edged trapezoidal Halbach array.Then by applying the aforementioned two methods,their magnetic fields are resolved and optimized.The optimization results show that the magnetic harmonics and the thrust ripples are largely reduced,compared with the traditional rectangular or trapezoidal Halbach PM array.Thus the novel Halbach PM arrays are meaningful for engineering applications.Then,the long-stroke nanopositioning electromagnetic direct-drive stage is designed,and the related parameters are calculated,simulated and validated,including the thrust,the flux linkage,the back-EMF and the inductance matrix.The computational results show that the mutual inductances are not totally equal in the linear three-phase winding,and therefore the circuit model of the actuator is asymmetric,namely,there are still non-diagonal elements of coupling terms in the inductance matrix after dq transformation.Consequently,according to the classic vector control theory,real-time decoupled components are designed in terms of the phase angle,thus effect of the coupled terms can be eliminated and the dq axes are decoupled completely.Experiments show that the utilization of the asymmetric model eliminates the high-order currents,which is present while applying the symmetric model.Finally,experiments are implemented on the stage in the step response,positioning resolution,repeatability,long stroke and noise decreasing by dampers.The experimental results show that the expected performance of the positioning stage is achieved,and a positioning resolution of 20 nm within the travel range of 50 mm are realized.Therefore,it supplies theoretical support and technical foundation for the design and research of the next-generation long-stroke planar nanopositioning stage,and shows the potential utility in deep sub-micro semi-conductor manufacturing,component testing and factory automation.