experimental determination of torsional stiffness, mass moment of
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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
7th Workshop on Analysis of Dynamic MeasurementsOctober 15 – 16, 2012, Paris, France
Physikalisch-Technische BundesanstaltDivision Mechanics and AcousticsDepartment Acoustics and Dynamics
2/14Leonard Klaus, PTB Braunschweig, Germany
Measuring Deviceair bearingradial grating disk for angular acceleration measurement
coupling
transducer under test
coupling
rotationalexciter
3/14Leonard Klaus, PTB Braunschweig, Germany
couplingrotational exciter
coupled mass moment of inertiaangular acceleration measurement componentscoupling
transducer under test
cM dM
JM2
JM1
dT
JH
cT
JB
JE2
cE dE
JE1
Model of Measuring Device
4/14Leonard Klaus, PTB Braunschweig, Germany
M
-M
autocollimator / Δφ2
mirror
DUT
reference torque transducer
Determination of Torsional Stiffness
Δφ1
The torsional stiffness is defined as the torque to torsion ratio:
Measurement set-up utilising PTB's 20 N·m Torque Calibration Machine:
5/14Leonard Klaus, PTB Braunschweig, Germany
Measurement Procedure
Norm
alise
d loa
d
● 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 counter-clockwise load
6/14Leonard Klaus, PTB Braunschweig, Germany
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
7/14Leonard Klaus, PTB Braunschweig, Germany
Determination of Torsional StiffnessCoupling:• Four measurements• 2x clockwise load,
2x counterclockwise load• Dismounting and
remounting after one completed load cycle
•
HBM T5:• 2x clockwise load and
1x counterclockwise load• Reduced torque (6 N·m)
due to limited range of operation of autocollimators
• No dismounting•
HBM T10F:• Torsional stiffness from
datasheet:
• But due to shaft end adapters reduced torsional stiffness
•
8/14Leonard Klaus, PTB Braunschweig, Germany
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:
9/14Leonard Klaus, PTB Braunschweig, Germany
-(J0+JDUT) Jtotal
τ² measurement values
regression line
extrapolation
Determination of Mass Moment of Inertia
pendulum, J0
additional mass bodies, Ji
air bearingscanning head
radial grating disk
device under test (DUT), JDUT
● 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.
10/14Leonard Klaus, PTB Braunschweig, Germany
Determination of Mass Moment of Inertia
pendulum, J0
additional mass bodies, Ji
air bearingscanning head
radial grating disk
device under test (DUT), JDUT
additional mass bodies
11/14Leonard Klaus, PTB Braunschweig, Germany
Measurement of pendulum swing
air bearingscanning head
radial grating disk
9000 lines/ circumference
device under test (DUT), JDUT
25xinterpolation unit
sin/cos quadrature signal
PXI DAQcounter/timer
pendulum swing
predetermination of magnitude, phase, frequency, damping
Nonlinear Levenberg-Marquardt four parameter fit
TTL quadrature signal
12/14Leonard Klaus, PTB Braunschweig, Germany
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
● Relation of undamped (ω0) and damped (ω1) pendulum frequency
● Influence is very small, ca. 8·10-8.
268 swings
range of fit
13/14Leonard Klaus, PTB Braunschweig, Germany
Determination of Damping
● 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
rotational vibrometerdevice under test
linear guidesgeneration of torque
specimen to break
14/14Leonard Klaus, PTB Braunschweig, Germany
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.
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
7th Workshop on Analysis of Dynamic MeasurementsOctober 15 – 16, 2012, Paris, France
Physikalisch-Technische BundesanstaltDivision Mechanics and AcousticsDepartment 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
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