7th Workshop on Analysis of Dynamic Measurements
October 15 – 16, 2012, Paris, France
Experimental Determination of Torsional Stiffness, Mass
Moment of Inertia and Damping of Components of the
Dynamic Torque Calibration Device
Leonard Klaus, Thomas Bruns, Michael Kobusch
Physikalisch-Technische Bundesanstalt
Division Mechanics and Acoustics
Department Acoustics and Dynamics
Measuring Device
air bearing
radial grating disk for angular
acceleration measurement
coupling
transducer
under test
coupling
rotational
exciter
Leonard Klaus, PTB Braunschweig, Germany
2/14
Model of Measuring Device
coupled mass
moment of inertia
JM2
cM
dM
JM1
angular acceleration
measurement
components
coupling
transducer under test
JH
dT
cT
JB
JE2
cE
dE
coupling
rotational exciter
JE1
Leonard Klaus, PTB Braunschweig, Germany
3/14
Determination of Torsional Stiffness
The torsional stiffness is defined as the torque to torsion ratio:
Measurement set-up utilising PTB's 20 N·m Torque
Calibration Machine:
M
mirror
autocollimator / Δφ2
DUT
Δφ1
reference torque
transducer
Leonard Klaus, PTB Braunschweig, Germany
-M
4/14
Measurement Procedure
●
●
Test procedure is based
on DIN 51309 standard
for static calibration of
torque transducers.
After pre-loading, load
increases in steps of 10%
to the nominal load.
Clockwise and counterclockwise load
Normalised load
●
Leonard Klaus, PTB Braunschweig, Germany
5/14
First Measurement Results
First results:
• Torsional angle values
show linear dependency
• First order regression line
fits measurement values
• Value for torsional
stiffness results from
gradient of regression
line
Leonard Klaus, PTB Braunschweig, Germany
6/14
Determination of Torsional Stiffness
Coupling:
• Four measurements
• 2x clockwise load,
2x counterclockwise load
HBM T5:
• 2x clockwise load and
1x counterclockwise load
HBM T10F:
• Torsional stiffness from
datasheet:
• Dismounting and
remounting after one
completed load cycle
• Reduced torque (6 N·m)
due to limited range of
• But due to shaft end
operation of autocollimators
adapters reduced torsional
stiffness
• No dismounting
•
•
Leonard Klaus, PTB Braunschweig, Germany
•
7/14
Determination of Mass Moment of Inertia
Measurement principle is based on a
compound pendulum:
For small angles of excitation,the
equation can be linearised:
Swing frequency of the pendulum is
dependent on the mass moment of
inertia J:
Leonard Klaus, PTB Braunschweig, Germany
8/14
Determination of Mass Moment of Inertia
scanning head
radial
grating
disk
●
air bearing
●
●
additional mass bodies, Ji
device under test
(DUT), JDUT
pendulum, J0
Measurement of pendulum frequency with
several mass bodies
Mass moment of inertia and distance from
axis of rotation of mass bodies is well
known.
Determination of mass moment of inertia of
all components of the pendulum but for the
mass bodies by extrapolation.
τ²
extrapolation
-(J0+JDUT)
Leonard Klaus, PTB Braunschweig, Germany
regression line
measurement
values
Jtotal
9/14
Determination of Mass Moment of Inertia
scanning head
radial
grating
disk
additional mass bodies, Ji
air bearing
device under test
(DUT), JDUT
pendulum, J0
additional
mass bodies
Leonard Klaus, PTB Braunschweig, Germany
10/14
Measurement of pendulum swing
TTL quadrature
signal
PXI DAQ
counter/timer
interpolation unit
25x
sin/cos
quadrature
signal
scanning head
air bearing
pendulum swing
predetermination of
magnitude, phase,
frequency, damping
Nonlinear Levenberg-Marquardt
four parameter fit
radial grating
disk
9000 lines/
circumference
device under test
(DUT), JDUT
Leonard Klaus, PTB Braunschweig, Germany
11/14
Influence of Damping
●
●
●
●
●
Assumption of undamped
oscillations of the pendulum for
determination of mass moment
of inertia
Determination of damping by
Levenberg-Marquardt-fit
Result of non-linear fit
268 swings
Relation of undamped (ω0) and
damped (ω1) pendulum frequency
Influence is very small, ca. 8·10-8.
range of fit
Leonard Klaus, PTB Braunschweig, Germany
12/14
Determination of Damping
linear guides
generation of torque
●
●
●
●
Generation of a negative step by
failure of a cylindric specimen with
predetermined breaking point
Determination of damping by means
of the decay of the oscillation
magnitude
Specimen made from machineable
engineering ceramics (Macor®)
Non-contact measurement of
vibrations by means of a rotational
vibrometer
Leonard Klaus, PTB Braunschweig, Germany
specimen to break
rotational vibrometer
device under test
13/14
Conclusions
●
●
●
Modeling of measuring device prerequisite for determination
of transducer's dynamic properties.
Described methods enable the determination of torsional
stiffness, mass moment of inertia and damping
Parameters of measurement device need to be known for
future identification of model parameters of torque
transducer under test from measurement data.
The research leading to these results has received funding from the
European Union on the basis of Decision No 912/2009/EC.
Leonard Klaus, PTB Braunschweig, Germany
14/14
7th Workshop on Analysis of Dynamic Measurements
October 15 – 16, 2012, Paris, France
Experimental Determination of Torsional Stiffness, Mass
Moment of Inertia and Damping of Components of the
Dynamic Torque Calibration Device
Leonard Klaus, Thomas Bruns, Michael Kobusch
Physikalisch-Technische Bundesanstalt
Division Mechanics and Acoustics
Department Acoustics and Dynamics
References
●
●
●
●
●
T. Bruns, “Sinusoidal Torque Calibration: A Design for Traceability in Dynamic
Torque Calibration” in Proc. of XVII IMEKO world congress; 2003, Dubrovnik,
Croatia, CD publication, online at www.imeko.org:
http://www.imeko.org/publications/wc-2003/PWC-2003-TC3-008.pdf
M. Kobusch, A. Link, A. Buss, T. Bruns, “Comparison of Shock and Sine Force
Calibration Methods” in Proc. of IMEKO TC3 & TC16 & TC22 International
Conference; 2007, Merida, Mexico, CD publication, online at www.imeko.org:
http://www.imeko.org/publications/tc3-2007/IMEKO-TC3-2007-007u.pdf
G. Baker, J. Blackburn, The pendulum: A case study in physics, Oxford University
Press, Chapter 3, pp. 30-31, 2005.
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, online at www.imeko.org:
http://www.imeko.org/publications/wc-2012/IMEKO-WC-2012-TC21-O7.pdf
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, online at www.imeko.org:
http://www.imeko.org/publications/wc-2012/IMEKO-WC-2012-TC3-O33.pdf