Enhanced stiffness characterization of load cells by relative change of the natural frequency forced by a defined mass shift

Abstract High-precision force measurement systems such as mass comparators, balances, or tactile force sensors usually feature kinematic structures designed as compliant mechanisms. The applications require precise knowledge of the properties of the mechanism. Stiffness is critical here, as it has a major influence on measurement resolution and uncertainty. When implementing the manufactured mechanisms, it is necessary to consider that even small variations in the geometric and material properties result in significant deviations from the pre-calculated properties. An experimental characterization is therefore essential. However, the stiffness determination methods described by the state-of-the-art are either time-consuming or have a high uncertainty. For this reason, a time-saving, low-uncertainty method was developed. The approach is based on the determination of the natural frequency. To significantly reduce the measurement uncertainty compared to the existing natural frequency method, the absolute elastic stiffness value is characterized by the relative change in natural frequency when attaching a well-known mass. This reduces the uncertainty of the stiffness value by at least 75 %. This work includes the derivation of the method, the consideration of analytical and numerical models, and the experimental verification using two applications.