Dynamic calibration of force transducers

The reliable measurement of dynamic forces plays an important role in industry. To provide the metrological infrastructure required, PTB has been pursuing an approach that describes the dynamic behavior of the force transducer by means of a mathematical model. The transducer and the calibration device are modeled as a series arrangement of mass-springdamper elements. The mass, the stiffness and the damping parameters of the force transducer are identified applying the model equation to dynamic measurement data. The goal is the general characterization of the dynamic behavior, irrespective of the particular measuring application or the type of force excitation. Calibrations with shock or sine excitations should provide consistent parameters.

Earlier tests using a high-bandwidth force transducer did not give consistent results. A new model offers a thorough explanation. The force transducer used as a case study (measuring range ±1 kN, force introduction via two threaded rods) was subjected to shock or sine forces. Intended variations of the dynamic behavior could be realized by using additional load masses. The pulse duration ranged from 0.1 ms to 1 ms. The maximum excitation frequency was 30 kHz.

The force transducer has two dominant resonances whose characteristics depend on the size of the coupled mass. In the case of a typical shock excitation without load masses, the lowest resonant frequency is caused by the vibrating transducer housing, whereas it is due to the elastically coupled mass itself in the case of a sinusoidal excitation with high mass values. The new model of three elastically coupled masses considers a two-sided elastic coupling of the transducer. The resonant frequencies measured with the different measurement setups were compared with those of the model, and the stiffness parameters of the transducer were thus identified.

The improved model-based dynamic calibration now provides consistent parameters from measurement data with sinusoidal and pulse-shaped force excitation. This proves the suitability of this new calibration methodology. Complementary investigations with finite-element methods have confirmed these results. The dynamic measurement behavior of the force transducer can therefore be transferred to a specific measurement application by extending the model correspondingly.