experimental determination of torsional stiffness, mass moment of

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