Crash testing: a dynamic force application (MIRA)
Dynamic force measurements are widely used in many industrial areas, and the increasing demands on measurement accuracy have set new metrological challenges.
For example, dynamic measurements play an important role in the following areas:
Depending on the application, the nature of the time-dependent force is very different. For example, in the case of fatigue tests, periodic forces are applied; in machining processes, step-like and continuous force changes; and in the case of crash tests, shock forces.
In case of dynamic force loads, the transducer’s internal structural distribution of mass and elasticity generates frequency-dependent inertia forces that are superimposed on the input force to be measured so as to disturb the measurement [1]. Additional influences may come from the coupled mechanical components, e.g., from the force introduction and the adaptation parts. Moreover, the dynamic properties of the electrical signal processing chain must also be taken into account. Therefore, a frequency-dependent measurement behaviour will generally arise.
Given the range of dynamic applications with very different force signals, the question arises under which conditions dynamic effects must be taken into account. The most interesting aspect here is whether a dynamic force measurement can still be performed with statically calibrated characteristics or whether the required measurement uncertainty is exceeded by disturbing inertia forces. A realistic indication of the acting dynamic forces and of the measurement uncertainties is not easy and requires knowledge of the dynamic properties of the transducer and of the measuring set-up.
A first step towards the selection and assessment of a force transducer to be used dynamically is often the knowledge of its fundamental resonance frequency. Additional information about the dynamic suitability of a force transducer is offered by data on stiffness and mass.
To understand fully a dynamic measurement in a given application, the approach of a model-based calibration is followed. The force transducer is dynamically characterized by model parameters, and the dynamic behaviour in the considered mechanical set-up is described by an appropriately expanded model.
Documentary standards or commonly accepted guidelines and procedures for dynamic force measurements are still lacking today, but the need for dynamic calibrations is widely known. For example, current standards on instrumentations for crash tests in the automotive industry (ISO 6487 [2], SAE J211/1 [3]) specify error limits for the amplitude response of measurement transducers which must generally be met, pointing out that satisfying methods for the dynamic calibration of force transducers are not yet known.
Whereas the static calibration of force transducers is specified by international standards (DIN EN ISO 376, [4]), corresponding standards for the calibration of dynamically loaded transducers are still missing. It is, therefore, common practice to calibrate statically force transducers that are to be used dynamically.
At best, some dynamic force measurements on a suitable testing device are performed in addition. Such tests are well suited for comparison tests and are, therefore, widely used in industry, as they provide information about whether ‒ and to what extent ‒ the dynamic measuring behaviour of a force transducer has changed in the course of time and if the transducer must be replaced.
The dynamic suitability of a force transducer is often judged by its fundamental resonance frequency. This characteristic parameter which is relevant to dynamics is mentioned in the German Directive VDI/VDE 2638 [5].
Force transducers are electromechanical transducers with a sensor element that is introduced into the force flow. In general, the output signal of the force transducer is assumed to be proportional to elastic deformation, which depends on the acting input quantity force.
Two types of force transducers with different measurement principles are most commonly found in industrial applications:
The applied force elastically deforms the mechanical structure of a strain gage transducer, and the deformations are sensed by several strain gauges bonded onto the surfaces at specific locations with strong and uniform strain. For this reason, the mechanical design of such a transducer often features a structural part of higher compliance, which is considered as the measuring spring.
The electrical resistance of a strain gauge changes proportionally with its mechanical elongation. In order to compensate parasitic components, temperature effects and to achieve a large signal, usually four strain gauges are electrically connected to a Wheatstone bridge circuit. A bridge amplifier feeds this circuit with a supply voltage and amplifies the small force-proportional output signal (bridge signal) of the transducer.
Piezoelectric force transducers use a piezoelectric sensor element which is pre-stressed between two force introduction components. The force-proportional output signal is either an electrical charge (charge type), or an electrical voltage for transducers with integrated electronics (IEPE type).
Compared to strain gauge transducers, piezoelectric transducers are more compact (smaller) and have higher stiffness, as they do not need an elastic spring element, which results in higher resonant frequencies which makes them better suited to dynamic application.
General criteria and recommendations to select a suitable force transducer for a given dynamic measurement application are difficult to make, as the coupled mechanical environment and parasitic loads may have great influence on the dynamic measurement results.
First of all, the user has to be aware of the fact that the high precision of static force measurements might be substantially compromised for dynamic measurements, depending on the application. Therefore, good static performance might not automatically imply a good dynamic performance and vice versa. In general, the structural design of the transducer is of great importance as internal inertia forces have influence on the dynamic measurement signal. Some criteria for dynamic force applications are given in the following.
The fundamental resonance frequency, the vibration along the measuring axis for a transducer rigidly mounted at its base, gives a first hint on the usable frequency range, but one have to take into account that high resonance frequencies are associated with high stiffness and/or low head mass and vice versa. In a given dynamic application, the force transducer is coupled to its mechanical environment, i.e. the dynamic behaviour of this mechanical system may change substantially.
Low sensitivity against parasitic forces and moments is an important criterion if bending modes might be excited. Depending on the structural design of the transducer and the coupling to its mechanical environment, low-frequent bending modes might occur that limit the usable dynamic measurement range.
To estimate the dynamic behaviour of the force transducer and / or the mechanical system, a finite element modelling would give a great benefit.
It is recommended to fasten screw connections with defined torque in order to achieve good reproducibility of the elasticity of the mechanical coupling. For high stiffness, the pretension force should be large, the contacting surfaces should be flat and slightly lubricated and the setting should be kept small.
Special care might be taken to guarantee that the force transducer and its electrical measuring chain are not susceptible to electromagnetic noise, as such parasitic components could be in-phase with the dynamic input signal. The susceptibility might be experimentally estimated by probing the environment with an unmounted transducer.
See also the presentation made at the BIPM dynamic measurements workshop here.
For dynamic calibration, sinusoidal and shock-shaped forces have the greatest practical importance. These two types of excitation which are, however, rather different in the time and frequency domain, allow the variety of dynamic force measuring tasks to be covered with relatively good practical orientation. A comprehensive overview about the dynamic calibrations devices is given in [6]. Dynamic calibration devices have been developed at three National Measaurement Institutes, providing both sinusoidal (PTB, CEM, LNE) and shock force excitation (PTB). In each case, primary traceability is achieved by the measurement of inertia forces using laser interferometers. The measurement principle is based on Newton's second law; the acting dynamic force 
is determined by the product of mass 
and linear acceleration 
as 
.
In the case of sinusoidal calibration, sinusoidal forces of varying frequency are applied, and the amplitude and phase responses related to a reference signal are evaluated as a dynamic calibration result. The German metrology institute PTB offers a calibration service up to 2 kN force amplitude and 2 kHz excitation frequency.
In the case of shock calibration, force pulses of defined amplitude, shape and duration are applied. Here, the ratio between the pulse height of output signal and input force is often the typical measurement result. On closer examination, however, this result turns out to be insufficient for calibration purposes owing to dependencies associated with the signal shape or spectral content.
A model-based calibration approach allows a linking between different calibration results obtained with different methods (sine, shock) and calibration devices. The force transducer is dynamically characterised by model parameters, and the dynamic behaviour in a considered mechanical set-up is described by an appropriately expanded model.
The model parameters of a force transducer under test identified from measurements by fitting modelled and measured data (in the time or frequency domain).
Having identified the model parameters of the force transducer from dynamic calibration measurements, its dynamic measurement behaviour in a given mechanical set-up can be derived by applying an appropriately extended model that includes the transducer and the coupled environment. Here, the corresponding model parameters (mass, stiffness, damping) of the coupled components have to be known, e.g. by dedicated measurements. The dynamic force input signal, or the signal at a specific location in the force chain, can then be derived from the measured force output by a deconvolution process.
With identified model parameters of the force transducer, it is possible to predict the dynamic behaviour of the force transducer in a given application with sufficient knowledge about the coupled mechanical environment (measurement system / set-up) using a properly expanded model.
[1] R. Kumme: The main influences on the dynamic properties of force measuring devices, Proc. of XiV IMEKO World Congree, pp. 102-107, Tampere, Finland, 1997
[2] International Standard ISO 6487: Road vehicles – Measurement techniques in impact tests – Instrumentation, International Organization for Standardization, Geneva, Switzerland, 2002
[3] American Standard SAE J211-1 (R) Instrumentation for impact test ‒ Part 1 ‒ Electronic instrumentation, SAE International, Warrendale, USA, 2007
[4] DIN EN ISO 376: Metallische Werkstoffe –Kalibrierung der Kraftmessgeräte für die Prüfung von Prüfmaschinen mit einachsiger Beanspruchung, Beuth Verlag Berlin, 2005
[5] VDI-Richtlinie VDI/VDE/DKD 2638, Kenngrößen für Kraftaufnehmer ‒ Begriffe und Definitionen, Beuth, 2006
[6] M. Kobusch, T. Bruns, R. Kumme: Dynamic calibration of force transducers, Special Issue PTB-Mitteilungen, 118, No. 2 and No. 3, pp. 42-47, 2008
International Standard ISO 16063-13: Methods for the calibration of vibration and shock transducers – part 13: Primary shock calibration by laser interferometry, International Organization for Standardization, Geneva, Switzerland, 2001
M. Kobusch, O. Mack, T. Bruns: Experimentelle und theoretische Untersuchungen zum Resonanzverhalten piezoelektrischer Kraftaufnehmer, Technisches Messen 73 (2006) 12, pp. 655‒663, Oldenbourg Verlag, München
A. Link, M. Kobusch, T. Bruns, C. Elster: Modellierung von Kraft- und Beschleunigungsaufnehmern für die Stoßkalibrierung, Technisches Messen 73 (2006) 12, pp. 675‒683, Oldenbourg Verlag, München
A. Link, A. Täubner, W. Wabinski, T. Bruns, C. Elster: Calibration of accelerometers: Determination of amplitude and phase response upon shock excitation, Measurement Science and Technology, 17 (2006), pp. 1888‒1894
C. Bartoli et al.: Traceable dynamic measurement of mechanical quantities: objectives and first results of this European project, International Journal of Metrology and Quality Engineering: 3 (2012), 3, 127 – 135
M. Kobusch, T. Bruns, L. Klaus, M. Müller: The 250 kN primary shock force calibration device at PTB, Measurement: 46 (2012), 5, 1757 – 1761
C. Schlegel, G. Kiekenap, B. Glöckner, R. Kumme: Dynamic calibration of force sensors using sinusoidal excitations, Sensordevices 2011, Nice, France
C. Schlegel, G. Kieckenap, B. Glöckner, A. Buß, R. Kumme: Traceable periodic force measurement, Metrologia, 49 (212), 224–235, 2012