Flexures for Kibble balances: Minimizing the effects of anelastic relaxation

Modern weighing cells would not be possible without flexure technology. Flexures are created by thinning metal in a specific shape so that it bends as desired when an external torque is applied. In contrast to other pivots, such as knife edges and different types of bearings, flexures provide rotary motion without stick-slip friction. Flexures, however, suffer from anelastic effects, most importantly a time-dependent torque that slowly decays after a large excursion. This effect is known as anelastic relaxation. In traditional servo-controlled mass comparators, the range of motion is minimal, and, hence, anelastic relaxation is negligible. Employing the same technology in Kibble balances challenges that assumption because the necessary velocity mode requires a relatively large excursion of the balance. Here, we present measurements of the anelastic relaxation that would occur after excursions held for tens of minutes of time in a balance beam in closed-loop operation. Procedures to mitigate the effect of spurious torque from anelastic effects are discussed. We found a static shift of the flexure's internal equilibrium after a change in the stress and strain state. These static shifts, although measurable, are small, and are uncritical in the Kibble balance application at present.