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

Year: 2025

Type: article

Abstract: Joule Balance is a kilogram realization method based on Planck constant. According to the kilogram realization key comparison in 2021, The relative measurement uncertainty of the joule balance is 4E-8. The measurement uncertainty induced by misalignment is 1.7E-8; which is one of the largest errors in joule balance. Thus, to solve the problem, a new mechanism based on reciprocal principle is designed. In this research, the reciprocal principle and dual-mode measurement principle of joule balance are combined. In joule balance, the gravitational work of mass in the force measurement mode is equal to the change in electromagnetic energy in the flux difference measurement mode. However, the parasitic forces outside the direction of gravity in force measurement mode do not equate to the electromagnetic energy changes in the parasitic displacements in flux difference measurement mode. Therefore, alignment errors are generated. According to the principle of mechanical reciprocity, for an elastic structure under two different load conditions, the forces and displacements interacting in these conditions exhibit reciprocity. If the force measurement and guidance mechanisms are unified into a single mechanism, the mechanical reciprocity theorem ensures that the forces and displacements interacting in both modes exhibit reciprocity in the same range of motion. Consequently, the parasitic force work and the energy changes in the parasitic displacements become consistent, thereby eliminating alignment errors. To achieve the mechanical reciprocity principle and eliminate alignment errors in the joule balance, we designed an integrated force-measuring and guiding mechanism. To apply this principle, the integrated mechanism of force measurement and guidance is designed. The integrated mechanism is composed of three parallelogram hinges, which are based on elliptical hinges. The deformation of the parallelogram hinge is used to achieve a small axial stiffness, and the mutual pulling effect of the three parallelograms is used to achieve a larger off-axial stiffness. Thus, the structure can achieve high sensitivity and straightness. Meanwhile, a multi-axis grating interferometer with separated beams is designed to measure deformation of the mechanism. Therefore, the force can be easily measured. Theoretical and finite element analysis are applied to verify the stiffness. Experiment setups are built for force measurement sensitivity and straightness. The force measurement sensitivity of the mechanism is 7.2 N/m; The stroke is 17.2 mm and the straightness is 4.32 μm. The integrated mechanism can be used for force measurement and guidance simultaneously. And the dual-mode reciprocal measurement can be achieved in joule balance. With this structure, the uncertainty induced by alignment error can be reduced from 1.7E-8 to 1.0E-8.

Source: IEEE Transactions on Instrumentation and Measurement

DOI: 10.1109/tim.2025.3552451

Authors: Yue Wang, Yang Bai, Zhengkun Li, Zhonghua Zhang

Institutions: National Institute of Metrology, State Administration for Market Regulation

Language: English

Topic: Scientific Measurement and Uncertainty Evaluation

Subfield: Statistics, Probability and Uncertainty

Field: Decision Sciences

Domain: Social Sciences

Open Access status: gold

Estimated APC paid: $2,645

Funders: National Natural Science Foundation of China, National Key Research and Development Program of China