Spherical joints have attracted increasing interest in the engineering applications of machine tools, industrial robots, medical equipment, and so on. As one of the promising methods of detecting the micro-clearance in spherical joints, the measurement accuracy of a spherical capacitive sensor could be affected by imperfectness during the manufacturing and installation of the sensor. This work presents error analysis of a spherical capacitive sensor with a differential structure and explores the dependence of the differential capacitance on manufacturing and the installation imperfectness. Five error sources are examined: the shape of the ball and the capacitive plate, the axial and radial offset of the plate, and the inclined installation of the plate. The mathematical models for calculating the capacitance errors of the spherical capacitive sensor are deduced and validated through a simulation using Ansoft Maxwell. The results show that the measurement accuracy of the spherical capacitive sensor is significantly affected by the shape of plates and ball, the axial offset, and the inclined angle of the plate. In contrast, the effect of the radial offset of the plate is quite small.

中文翻译：

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用于球形接头微间隙检测的球形电容传感器的误差分析。

球形接头在机床，工业机器人，医疗设备等的工程应用中引起了越来越多的兴趣。作为检测球形接缝中微间隙的一种有前途的方法，球形电容式传感器的测量精度可能会受到传感器制造和安装过程中不完善的影响。这项工作提出了具有差分结构的球形电容传感器的误差分析，并探讨了差分电容对制造和安装不完善的依赖性。检查了五个误差源：球和电容板的形状，板的轴向和径向偏移以及板的倾斜安装。通过使用Ansoft Maxwell进行的仿真推导并验证了用于计算球形电容传感器的电容误差的数学模型。结果表明，球形电容传感器的测量精度受板和球的形状，轴向偏移和板的倾斜角度的影响很大。相反，板的径向偏移的影响很小。