29.09.2014
For the dynamic calibration of force transducers, the approach of the model-based calibration is followed. The model parameters of the force transducer which characterize the dynamic behaviour are to be determined from dynamic measurement data. To excite the transducer’s resonance frequencies sufficiently strong by using shock excitation, a pendulum shock with smaller impact masses was experimentally tested at PTB’s 20 kN force shock calibration device.
The 20 kN shock force calibration device at PTB employs two airborne impact masses of approx. 10 kg that are brought to collision with the force transducer mounted in-between. The typical duration of a shock pulse for a hard, metallic shock – i.e. without additionally introduced elastic intermediate layers – is about one millisecond. The inertial forces generated during the shock process are measured by means of laser interferometry and provide the traceability of the dynamic force calibration.
In the case of the model-based calibration, the observed dynamic behaviour is determined by means of a model where the force transducer and the calibration device are described by a series arrangement of spring-mass-damper elements. Thereby, the sought model parameters of the force transducer, its masses, stiffnesses and dampings, are to be identified from the measurement data.
Experimental investigations of force transducers of different design, size and mechanical coupling have shown that shock pulses with a duration of 1 ms excite the resonance frequencies of small force transducers to only a very limited extent [1]. First results of the parameter identification with smooth shock pulses (see Figure 1, left) indicate that the parameter identification process requires shock responses with excited natural frequencies as these probably carry the key information for a clear identification of the model parameters if the considered model exhibits several degrees of freedom. To be able to excite the resonance frequencies by shock excitation to a greater extent, two different methods have been tested.
Figure 1: Measured shock forces obtained with different impact masses.
The first method utilizes a much smaller pendulum impact mass that replaces the original airborne 10 kg impact mass of the calibration device. As an example, Figure 1 shows the shock responses which have been obtained with the different impact masses. Whereas the 10 kg impact mass provides a smooth pulse of approx. 1.3 ms without ringing, the smaller pendulum masses generate pulses which are much shorter (up to 0.1 ms for a pendulum mass of 7 g), and the shock-excited force transducer reacts with a pronounced ringing.
In the case of the second method, additional load masses were mounted to the head section of the force transducer in order to reduce the resonance frequency of the force transducer. Differently large masses then provide different shock responses which are used for model validation and parameter identification. It turned out that the investigated force transducer has two dominating resonances which determine the dynamic measurement behaviour. The system responses obtained with different load masses (analysis of the ringing signal in the frequency domain) are shown in Figure 2.
Figure 2: DFT analysis of the ringing in the force transducer signal for different load masses.
The presented investigations have been carried out within the scope of the European research project EMRP IND09 "Traceable Dynamic Measurements of Mechanical Quantities". The activities for modelling, data analysis and parameter identification were carried out in close cooperation with Working Group 8.42 "Data Analysis and Measurement Uncertainty" of PTB. Further information can be found in [2].
Literature:
[1] M. Kobusch, S. Eichstädt, L. Klaus, T. Bruns, "Investigations for the model-based dynamic calibration of force transducer by using shock forces", Proc. of Joint IMEKO International TC3, TC5 and TC22 Conference, Cape Town, South Africa, 2014. online at: www.imeko.org/publications/tc22-2014/IMEKO-TC3-TC22-2014-005.pdf
[2] M. Kobusch, S. Eichstädt, L. Klaus, T. Bruns, "Analysis of shock force measurements for the model-based dynamic calibration”, 8th Workshop on Analysis of Dynamic Measurements, Turin, Italy, 2014, online at: www.inrim.it/ADM2014/slides/M.Kobusch.pdf
Contact persons:
Michael Kobusch, Department 1.7, WG 1.73, e-mail: michael.kobusch(at)ptb.de
Sascha Eichstädt, Department 8.4, WG 8.42, e-mail: sascha.eichstaedt(at)ptb.de