Research Of Charge Distribution Characteristics And Displacement Sensing Characteristics In Spherical Scattering Electric Field

Nowadsys high-precision measurement of structures like small holes with high aspect ratio challenges the current sensing technology, and the capacitive sensor based on spherical capacitive plate can meet this chanllenge due to its characteristics of noncontact measurement and there-dimensional isotropic sensing which can eliminate the influence of deformation and attitude error of the stylus. The contradiction between the measurable aspect ratio and aiming accuracy of sensor can be resolved effectively, and therefore the capacitive sensor based on spherical capacitive plate is of great significance to the research of high-precision measurement of structures with high aspect ratio.The solution of spherical surface charge density in spherical scattering electric field formed by spherical capacitive plate aiming conductor surface is the analytic basis of sensing characteristics of spherical capacitive plate sensor, however, because of the complexity of the model’s boundary conditions and the combination of the macro scale and the micro scale in the electric field, there has been no appropriate solution by now. This subject accordingly aimed at exploring a kind of applicable solution to spherical scattering electric field based on existing solving methods of the electrostatic field and by using the method,analyze the sensing properties of spherical capacitive plate sensor, providing a theoretical support for the design and application of the sensor. The main contents of the research are as follows:First, Laplace equation expressing space potential distribution of spherical capacitive plate aiming measured surface needs to be derived, so are spherical surface charge density and the calculation formula of the aiming capacitance and the displacement sensitivity. After analyzing and comparing the commonly used method of electrostatic field, finite difference method, based on the non-uniform mesh division of finite difference method, has been identified to solve this topic model, deducing 3D 7-points finite difference stencil of non-uniform grid under rectangular coordinate system and spherical coordinates, and determining the judgment conditions of the iterative procedure.Second, 3-d non-uniform grid under spherical coordinates is selected after comparing with the rectangular coordinate system. The scale of grids on r axis, a nonuniform grid based on index growth, theta and phi coordinates is proposed and analyze the potential electric distribution of spherical capacitive plate aiming plane surface of conductor with it. Then comparing the result with the analytical solution obtained by electrical images method, the accuracy is tested.In this research, the distribution characteristics of spherical plate surface charge density and the changing rule of the aiming capacitance have been analyzed. In addition, it has verified the accuracy of the finite difference method changing with aiming gap and the diameter of the spherical capacitive plate by comparing them with computed value of electric method.Thirdly, the model of spherical capacitive plate aiming cylndrical surface of conductor was analyzed based on finite difference method with the non-uniform grid proposed in chapter 3, and the space electric potential distribution in solution domain was obtained and cpmpared with the analytical solution obtained by electrical images method. In this way the accuracy and applicability of the analytical approach based on finite difference method with non-uniform gird was validated. For the model of spherical capacitive plate aiming spherical surface of conductor, the chatacteristics of space electric potential distribution and the surface charge density on the spherical surface of the spherical capacitive plate was analyzed, and the aiming capacitance and the displacement sensitivity for different radius of spherical capacitive plate and the spherical surface aimd was studied.Finaly, to research the measurement of the bore diameter of holes with high aspect ratio, the model of spherical capacitive plate aiming cylndrical surface of conductor was analyzed. The chatacteristics of space electric potential distribution and the surface charge density on the spherical surface of the spherical capacitive plate was analyzed, and the aiming capacitance and the displacement sensitivity for different radius of spherical capacitive plate and cylinder was studied.