The Mechanism for Force Measurement and Guidance Based on Reciprocal Measurement in Joule Balance

The Joule balance is a kilogram realization method based on Planck’s constant. In Joule balance, alignment error is the main uncertainty component. In order to solve the problem, the dual-mode reciprocal measurement method of Joule balance is analyzed in this article. We establish the reciprocal relationship between the parasitic generalized force in the weighing phase and the parasitic displacement in flux difference measurement mode. In addition, it is concluded that the integrated mechanism with force measurement and guidance is the base of reciprocal measurement. Then, an integrated mechanism of force measurement and guidance is designed with three parallelogram flexible hinges. The small axial stiffness and large off-axial stiffness are achieved to ensure force measurement and guidance. Theoretical and finite element analysis are applied to the mechanism. Experiment setups are built for force-measurement sensitivity and straightness. The force-measurement sensitivity of the mechanism is 7.2 mN/mm; within the guiding displacement of 17.2 mm, the straightness is $4.32~\mu $ m. The integrated mechanism can be used for force measurement and guidance simultaneously. In conclusion, the dual-mode reciprocal measurement can be achieved in Joule balance.

I. Introduction

The Joule balance, derived from the Kibble balance [1], [2], is a kilogram realization method based on Planck’s constant proposed in China [3], [4]. There are two measurement phases: the weighing phase and the flux linkage difference measurement phase. In the weighing phase, a current is applied to the suspended coil immersed in a radial magnetic field, which will produce an electromagnetic force. The electromagnetic force balances the gravity of the mass, establishing a force balance. By measuring the force at multiple points in the measurement interval , mechanical energy can be obtained. In the flux difference measurement phase, the radial magnetic field moves with respect to the suspended coil along the vertical direction. Meanwhile, the induced voltage across the suspended coil is integrated with respect to time t in the same interval . Thus, the flux linkage difference of the coil can be obtained, reflecting the change in the electromagnetic energy of the coil. The balance of mechanical energy in the weighing phase and electromagnetic energy in the flux linkage difference measurement phase achieves the kilogram realization based on Planck’s constant.