25.10.2012
In the context of the European Metrology Research Programme (EMRP), the Joint Research Project IND09 focuses on the dynamic measurement of mechanical quantities (force, pressure, torque). For the determination of model parameters of a dynamic torque measuring device, the mass moment of inertia and torsional stiffness properties are to be determined. For this purpose two measurement set-ups were developed.
1) Determination of torsional stiffness
Torsional stiffness is defined as the ratio of the torque M applied to the device under test and the resulting torsion Δφ
c = M / Δφ .
A well known torque is generated in the measurement set-up and the resulting torsional angles at the top and at the bottom of the device under test are measured. For the determination of the torsional stiffness, several torque levels are applied and the resulting torsion is calculated as the difference of the two angles. Therefore, it is possible to find out about the linearity of the device under test. A reversion of the direction of torque enables the identification of hysteresis effects and of influences due to the direction of torque.
Fig. 1: Measurement set-up for the determination of torsional stiffness
2) Determination of mass moment of inertia
The measurement set-up for the determination of the mass moment of inertia is based on the principle of a compound pendulum. The equation of motion of a pendulum can be linearised for small angles of excitation. In this case, there is a direct relationship between the mass moment of inertia J and the squared pendulum swing time τ
J = m g l τ² / ( 4 π²) .
The pendulum’s design is based on an air bearing to achieve a low damping of the swing. The measurement of the pendulum excitation is carried out as a non-contact measurement by means of an optical incremental angle encoder.
Additional mass bodies can be mounted in the pendulum lever. These mass bodies have a known mass moment of inertia. If mounted at a known distance from the axis of rotation, the acting mass moment of inertia is given by the Huygens-Steiner theorem.
By adding known mass moment of inertia elements, the mass moment of inertia of the pendulum itself and the device under test can be determined.
References:
[1] L. Klaus, T. Bruns, M. Kobusch, “Determination of Model Parameters of a Dynamic Torque Calibration Device” in Proc. of XX IMEKO World Congress; 2012, Busan, Republic of Korea, 
Link
[2] C. Bartoli et al., “Traceable Dynamic Measurement of Mechanical Quantities: Objectives and First Results of this European Project” in Proc. of XX IMEKO World Congress; 2012, Busan, Republic of Korea, Link
[3] Homepage of the Joint Research Project “Dynamic Measurement of Mechanical Quantities” EMRP IND09: Link
Contact person:
Leonard Klaus, Dept. 1.7, WG 1.73, e-mail: leonard.klaus@ptb.de