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Model parameter identification of torque transducers from measurement data


The dynamic calibration of torque transducers requires the modelling of the measuring device and of the transducer under test. The transducer’s dynamic properties are described by means of model parameters which are to be identified from measurement data. To be able to do so, two transfer functions are calculated. In this paper, the transfer functions and the procedure for the model parameter identification are presented. An example shows results of the parameter identification.

The model is a linear time-invariant (LTI) system and consists of a combination of mass moment of inertia elements in series, connected by a torsional spring and damper system.  The measuring device and the corresponding model are depicted in Fig. 1. The properties of the measuring device (in blue) were determined in advance by means of independent measurement procedures [1], [2]. The orange model parameters of the transducer under test are to be identified by means of the measurement data.

Figure 1: Dynamic torque measuring device (left) and the corresponding model components (right) of the measuring device (blue) and of the transducer (orange).

During measurement, the shaft assembly is excited by sinusoidal oscillations with different frequencies, and the angular acceleration at the bottom, the angle position at the top, and the output signal of the transducer are acquired.

For the parameter estimation, two transfer functions are calculated based on the measurement data, describing the dynamic behaviour of the top and of the bottom part of the measuring device’s shaft assembly. The unknown model parameters of the transducer are identified from measurement data. An estimator approximates the model function to the measurement data, minimising the residuals. For this purpose, different estimators can be used [3]. As the first step, a maximum likelihood estimator was implemented. This estimator is a good compromise between the uncertainty of the estimated parameters and the required knowledge about the system.

First results show a good agreement of the measurement data and the model function. The identified model parameters of the transducer are plausible.

Detailed information about the method can be found in [3].



[1] Leonard Klaus, Thomas Bruns and Michael Kobusch, “Modelling of a dynamic torque calibration device and determination of model parameters”, Acta IMEKO, vol. 3 (2), Seiten 14-18, Juni 2014, acta.imeko.org/index.php/acta-imeko/article/viewFile/IMEKO-ACTA-03%20%282014%29-02-05/253

[2] Leonard Klaus and Michael Kobusch, “Experimental Method for the Non-Contact Measurement of Rotational Damping”, Proc. of Joint IMEKO International TC3, TC5 and TC22 Conference 2014, Kapstadt, Südafrika, Februar 2014, http://www.imeko.org/publications/tc22-2014/IMEKO-TC3-TC22-2014-003.pdf

[3] Leonard Klaus, “Identification of Model Parameters of a Partially Unknown Linear Mechanical Systemfrom Measurement Data”, Proc. of XXI IMEKO World Congress 2015, Prag, Tschechische Republik, 2015, www.imeko.org/publications/wc-2015/IMEKO-WC-2015-TC3-050.pdf


Contact persons:

Leonard Klaus, FB 1. 7, AG 1. 73, E-Mail: leonard.klaus(at)ptb.de
Michael Kobusch, FB 1. 7, AG 1. 73, E-Mail: michael.kobusch(at)ptb.de