Testing Stockbridge dampers on a shaker by D.G.Havard

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TESTING STOCKBRIDGE DAMPERS ON A SHAKER:

A VECTOR BASED ANALYSISAND COMMENT ON PRESENT

STANDARDSBy D.G. Havard

Presentation to CIGRE WG11July 2007

Testing Stockbridge dampers on a shaker by D.G.Havard

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Standards frequently used:● IEEE Standard 664-1993“IEEE Guide for laboratory measurements of the power dissipation characteristics of aeolian vibration dampers for single conductors”● IEC Specification EN 61897 1999 “Requirements and tests of Stockbridge type aeolian vibration dampers”

The need is for better guidance on performing reference tests with no damper installed and how to interpret the resulting data

Testing Stockbridge dampers on a shaker by D.G.Havard

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The test is called the “Forced Response Method” and is carried out with the damper attached directly to a shaker

Typical mounting arrangement for a damper on a shaker

Testing Stockbridge dampers on a shaker by D.G.Havard

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Note that the fixture has significant mass.

● The IEEE Standard identifies the need to correct for the additional force required to oscillate the fixture supporting the damper and for some of the possible instrumentation effects.

● The descriptions are not detailed enough to guide actual practice and that may need to be addressed in a future revision of that IEEE Standard.

● The IEC specification is less informative about testing techniques.

Testing Stockbridge dampers on a shaker by D.G.Havard

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Recent tests included a calibration test in which the fixture used to support the damper was driven through the same amplitude and frequency spectrum as that specified for the damper.

The product of zero to peak amplitude, Y0, and frequency, f, was chosen to be a constant value of 0.1 m/s.

At all frequencies there is a force required to drive the mass of the fixture without the damper attached.

At some higher frequencies there is also a small component of damping.

Testing of Stockbridge dampers on a shaker D.G.Havard

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Figure 1 Energy dissipation of fixture aloneThis shows that these forces are smaller than those due to the damper, but not negligible.

Testing Stockbridge dampers on a shaker by D.G.Havard

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Figure 2: Representation of a Stockbridge damper and fixture:

Mf = Fixture mass Cf = Fixture damping Md = Stockbridge damper mass Kd = Stockbridge damper stiffness Cd = Stockbridge damper damping

Figure 2 shows the assumed relationships and transfer of forces between the mass, Mf, and viscous damping, Cf, of the fixture, and mass, Md, viscous damping, Cd, and elastic stiffness, Kd, of the damper.(Upside down relative to test arrangement)

With these assumed components, the damper and fixture behave in a linear relation to the displacement and its derivatives.

θsin2

Fkydtdyc

dtydm =++

Testing Stockbridge dampers on a shaker by D.G.Havard

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Figure 2: Two modes of vibration of a symmetrical Stockbridge damperThe linear model is a

simplification because the messenger wire, which serves as the damping element, has a complex non-linear damping mechanism.

Also there are four resonant frequencies of many types of Stockbridge dampers, and the Figure 2 is simplified to a system with only one natural frequency.

Testing Stockbridge dampers on a shaker by D.G.Havard

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Figure 3 Amplitude magnification factor versus ration of frequency to natural

frequency and damping for a single degree of freedom spring, mass and damper system

θsin2

Fkydtdyc

dtydm =++

Figure 3 represents the ratio of the motion of each

damper mass to the shaker motion.

Figure 3 applies for each resonance of

the Stockbridge damper.

.

Testing Stockbridge dampers on a shaker by D.G.Havard

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Figure 4 Schematic vector diagram representing

forces due to the mass and damping of the fixture and

mass, stiffness and damping of the damper

during a test of a Stockbridge damper by the

Forced Response Method

Figure 4 shows the vectors of force due to mass and damping due to the fixture, Ff and Df, and the vectors of force due to mass, damping, and stiffness of the Stockbridge damper, Fdm , Dd and Fdk, in a polar diagram.

This diagram applies at each test condition of amplitude of motion and frequency.

Testing of Stockbridge dampers on a shaker D.G.Havard

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The vectors representing forces due to the mass, Fdm, and stiffness, Fdk, are in the direction of the acceleration and those representing force due to damping, Dd, are in the direction of the velocity.

20ωYMF ff =

The measured forces, Fcal and Ftest, are the vector sums of inertia and damping force as shown, and they have angles to the acceleration, θf and θtest, as indicated in the figure.

Figure 4 is based on measuring the fixture response, but the vector of fixture force, Ff, can also be determined mathematically from its mass and acceleration, as follows:

Testing Stockbridge dampers on a shaker by D.G.Havard

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If the fixture damping is neglected, as it is normally very small, the calculations that follow can be applied after setting the force due to damping Df equal to zero.

When the test of the damper is performed, the shaker provides energy to drive both fixture and damper.

The motion applied to the damper is assumed to be the same as that applied to the fixture, and that the fixture damping is thesame with and without the damper at each frequency.

Testing Stockbridge dampers on a shaker by D.G.Havard

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fcalf FF θcos= fcalf FD θsin=

testtestdkdmf FFFF θcos=−+ testtestdf FDD θsin=+

From the calibration test of the fixture alone the forces due to the mass and damping are, referring to Figure 4:

From the test with the damper mounted on the fixture the forces due to the mass, stiffness and damping are:

and

and

Testing Stockbridge dampers on a shaker by D.G.Havard

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fcaltesttestdkdm FFFF θθ coscos −=−

fcaltesttestd FFD θθ sinsin −=

22)( ddkdmres DFFF +−=

)(tan 1

dkdm

dd FF

D−

= −θ

Forces due to the mass, stiffness and damping of the damper alone are:

and

The resultant damper force is given by:

and the angle between force and acceleration by:

These equations are sufficient to determine the corrected damperforce and phase angle from the calibration and test data. Theseequations can be solved using standard procedures built into an Excel spread sheet.

Testing of Stockbridge dampers on a shaker D.G.Havard

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Power dissipation P is given by:

= frequencyF = rms force applied to the damper A = peak acceleration

= phase angle between force and acceleration

Using uncorrected damper force and phase angle gives uncorrected damper powerSubtracting power to drive the fixture gives partial correctionUsing corrected force and phase angle gives the most correct damper power Figure 5 shows the different power curves for a sample damper

φπ

sin41 FAf

P =

f

φ

Testing of Stockbridge dampers on a shaker D.G.Havard

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Energy dissipation of fixture aloneIncluded in IEEE Standard 664

Figure 5 Damper power dissipation measurements: uncorrected, by power correction and by force correction (current method)

Testing of Stockbridge dampers on a shaker D.G.Havard

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CONCLUSIONS

• Present Specifications and Standards for damper testing need revision

• Specifications and Standards need to clarify sources of error in the measurements and how to avoid them

• Effect of fixture mass is not properly described in specifications

• A vector based description clarifies the forces during the shaker test

• A method of making more correct adjustments for fixture effects is presented

Testing Stockbridge dampers on a shaker by D.G.Havard

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AUTHOR: DR. DAVID G. HAVARD

PRESIDENT, HAVARD ENGINEERING INC.TEL: 1-905-273-3076 FAX: 1-905-273-5402

E-MAIL: dhavard@rogers.comWEB PAGE: www.havardengineering.com

ADDRESS: 3142 LINDENLEA DRIVE,

MISSISSAUGA, ONTARIO, CANADA, L5C 2C2