Modeling and design of an overlapped-flexure hinge for joule balance

In the joule balance experiment, the electromagnetic force and the gravity of the test mass should be aligned along the vertical direction precisely; otherwise, an alignment error will be introduced into the redefinition of the kilogram and the realization of the standard mass. In order to decouple and align those forces, a flexure hinge with an overlapped structure is proposed. The proposed overlapped-flexure hinge contains two flexure hinges, namely, the outer flexure hinge and the inner flexure hinge. The outer flexure hinge is connected to the suspension coil to bear the electromagnetic force, while the inner flexure hinge is connected to the test pan to bear the gravity of the test mass. As the mechanical structure ensures the above hinges coaxial and identical, this hinge can decouple the above-mentioned forces adequately and align these forces along the same vertical line. In this paper, a theoretical compliance model is first established based on Castigliano's second theorem to precisely design the flexure hinge. Second, the key dimension parameters of the overlapped-flexure hinge are designed to satisfy the requirements of the joule balance. Third, finite element analysis simulations and experiments are carried out to validate the performances of the hinge. Finally, in the joule balance experiment, the alignment uncertainty between the electromagnetic force and the gravity of the test mass is proved to be less than 50 ppb by using this overlapped-flexure hinge.