Highly sensitive,precise, and traceable measurement of force

Force in the micronewton range may be traced to the International System of Units by an electrostatic force balance weight system. However, there is a conflict between range and sensitivity. To solve this problem, a lever-type force metrology system based on the null-balance method is reported. The force is loaded on one end of the lever, causing elastic torsion of the central rod, and an electrostatic force is applied to the other end. With a variety of mass loading positions and standard weights, a wide range of moments may be produced to calibrate the system. The electrostatic force was generated by a pair of coaxial cylindrical capacitors where the applied voltage was converted into electrode displacement. The design of the inner and outer cylindrical capacitors was deduced considering the material and miniaturization requirements, and concentric alignment was ensured by a vision system. The null balance was achieved by a proportion-integration-differentiation control system, so that the external force was compensated by the electrostatic force. A method to increase the center of gravity was used to improve the resolution. The mechanism was analyzed based on stiffness, strength, stability, and frequency. Furthermore, the impact on the capacitance gradient due to the capacitor tilt caused by the applied force was estimated. Standard weights were utilized to evaluate the system performance. The results showed that a stiffness of 0.8 N/m and a force resolution of 10^?8 N were achieved.