Calibration of Some Willmore Seismometers

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Publisher’s version / Version de l'éditeur:

Technical Note (National Research Council of Canada. Division of Building Research), 1965-09-01

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Calibration of Some Willmore Seismometers

Ward, H. S.

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453

DIVISION OF BUILDING RESEARCH

NOTlE

No.

'f

E

_C

_{1HIN ][ CAlL}

NATIONAL RESEARCH COUNCIL OF CANADA

PREPARED BY

H. S. Ward CHECKED BYTDN APPROVED ay NBH

DATE September 1965

PREPARED FOR

Inquiry and record purposes

SUBJECT

CALIBRATION OF SOME WILLMORE SEISMOMETERS

The six Willmore seismometers used for the measurement of wind-induced vibrations of buildings have been calibrated in the

past by an electrical method. It was decided to perform a calibration

of the same instruments through the use of a shaking table. The

Inspection Services Branch of the Department of National Defence very kindly offered the use of their equipment for the purpose of the calibration tests.

METHOD OF CALIBRATION

The shaking table was manufactured by the All American Co.

of Skokie, Illinois, U. S. A. The maximum possible motion of the

table was O. 150 in. peak to peak, and the lowest reproducible frequency

was around 2.5 cps. The 3 ft of the cradle of the seismometer were

centred on the shaking table by 3 locating marks, and the seismometers were securely locked to the shaking table and the cradle by a canvas belt (Figure 1).

The motion of the shaking table was monitored by fixing a previously calibrated.:!: 0.25 g Statham accelerometer (#10181) to the

table. As another check of the motion at the higher frequencies, sight

marks were placed on the shaking table and the seismometers, and a

telescope that could measure displacements within ｾ 0.001 in. was

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2

-The seismometers were damped to approximately 0.6 of the critical value by placing a load impedance in parallel with the

seismometers, and the voltage output was measured across this load

impedance. The voltage outputs of the accelerometer and the

seismometer were recorded on a Sanborn recorder. A certain amount

of 60 cps noise was present in the output of the seismometers, and this was eliminated by passing the signal through a Kronhite band-pass filter with the low cut-off at 0.2 cps and the high cut-off at

approximately 35 cps. The frequency setting at the high end was

determined by finding the setting that did not attenuate the output of the seismometer when it was excited at 15 cps (the highest test frequency) .

Each seismometer was calibrated for three different values

of its natural period. For a given setting of the natural period the

seismometer was excited at frequencies lying in the range of 2.5 cps

to 15 cps. The first seismometer to be calibrated (#171766) was

te sted to 19. 2 cps, but the tele scope information showed that the mounting arrangement was beginning to show a resonance effect. Thus, for the remaining te sts the highe st frequency was 15 cps.

Upon completion of the shaking-table calibration, the relation between the number on the dial of the seismometer and its

natural period of vibration was investigated. This was achieved by

applying a dc voltage across the coil of the seismometer; the voltage was then removed and the re suIting undamped vibrations of the

seismometers were recorded. RESULTS

The results of the shaking-table tests are given in Table I.

The frequency of excitation was determined from the recording paper

which provided a timing line every 0.1 sec. With this value of the

frequency, the velocity recorded by the Willmore was estimated from the acceleration measurements of the Statham and the displacement

measurements of the telescope. For all but the highest test frequency,

the two values of the velocity at a given frequency agreed within 5 per

cent. In these cases, the average value of the two velocities was used

in the calculation of the calibration constants of the seismometer. In

the case of the frequencies above 15 cps, the accelerations were

greater than the design range of the accelerometer (0. 5 g peak to peak); the velocity obtained from the telescope was used for the calculation of the calibration constants.

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3

-Figure 2 shows a plot of the theoretical frequency response of a 60 per cent critically-damped Willmore seismometer. The frequency response is plotted in terms of two non-dimensional parameters; one is the sensitivity at a given frequency divided by the maximum sensitivity of the seismometer, and the second is the ratio of the exciting frequency to the natural frequency of the

seismometer. Some of the results in Table I are plotted on Figure 2,

and they indicate that the actual frequency response of the seismometers is close to the theoretical one except in one instance.

The resonance condition of the seismometer mounting arrangement is shown in Figure 3. This was determined by comparing the motion of the shaki.ng table and the seismometer,

obtained from observations made with the telescope. It was observed by means of the telescope that the mass in the seismometer tended to move at the low frequencies rather than remain stationary. This is consistent with the decrease in sensitivity of the seismometers at the lowest test frequencies for the lower period adjustments.

Figure 4 shows some of the results obtained with Willmore #171589 when its natural period was 2.2 sec. The records were examined to investigate the phase response of the seismometers. This was achieved by assuming that the output of the Statham accelerometer represented the true phase of the shaking-table motion. If the seismometers do not affect the phase of the motion, their outputs should lag that of the accelerometer by 900

• As

indicated by Figure 3, the phase response of the Willmores appears to be very satisfactory within the frequency range of 2 cps to 15 cps.

Figures 5 to 10 show the relation between the number on the dial governing the natural period of the seismometers and the actual measured period.

CONCLUSIONS

Within the frequency range of the tests (2 to 15 cps), the Willmore seismometers have a reasonably flat frequency response, although it is beginning to fall off at 2 cps. The phase response of the seismometers also appears to be satisfactory in this same frequency range.

It would be of interest to continue the calibration of the Willmores on a shaking table for the frequency range of O. 1 cps to 2 cps, as it is in this area that the sensitivity of the seismometer is

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4

-decreasing.

ACKNOWLEDGEMENTS

The Division of Building Research would like to express its thanks to the Inspection Services Branch of the Department of National Defence and, in particular, to Mr. Dan Slade and Mr. Edward Jordan for their as sistance during this project.

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TABLE I

CALIBRATION CONSTANTS OF THE WILLMORE SEISMOMETERS

Willmore Period, Damping

Number sec Resistor

10 30hms 3.2 4.8 6.7 9.7 9.8 12.5 14.5 19.2 Frequency (cps) 0.76 4 7.9 8.6 8.4 8.7 8.5 9.7 8.8 8.9 ｶｯｬｴｳＯｩｮｾ sec -1 171766 0.92 8 2.7 5.0 8.4 9.7 14.7 Frequency (cps) 10.0 9.7 9.5 9.2 9.2 Calibration Constant

volts/ in. sec -1

2.5 5.0 8. 1 9.8 14.5 Frequency (cps) 1. 10 15 10.7 10.8 10.7 10.5 11.2 Calibration Constant volts/in. sec -1 2.8 4.8 8.3 9.8 14.5 0.85 4 7.0 7.5 7.8 7.6 8.0 171588 1. 29 8 2.8 5.0 8.4 9.8 14.5 8.8 9.2 9.3 9. 1 9.8 2:

6

5.2 8.3 9.8 14.5 2.04 15 10. 1 10.5 10.7 10.5 11. 1 2.2 2.6 5.0 7.7 9.7 14.7 0.88 4 6.8 7.4 8.2 8.2 8. 1 8.3 3.2 5. 1 7.7 9.6 14.7 171586 1. 05 8 8.6 9.2 9.0 9.6 9.2 2.7 5. 1 8. 1 9.8 14.7 \ 1. 15 15 10.5 10.4 10. 1 9.9 10. 1

_.

3.4 5.2 8.4 9.8 14.5 0.82 4 4.7 7.5 6.6 7.3 7.8 3.1 5.0 8.2 9.9 14.5 171770 1. 29 8

I

9.2 9.2 9.4 8.7 8.9 3.4 4.9 7.9 9.8 14.5 2.14 15 9.9 10. 3 10. 1 10.0 10. 1 3. 1 5.0 8. 1 9.6 14.3 0.88 4 6.7 7.0 7.2 7.2 7.0 2.8 5. 1 8.3 9.6 14.5 171589 1.34 8 9:0 9.0 9.7 9.5 9.0

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TABLE I {continued}

CALIBRATION CONSTANTS OF THE WILLMORE SEISMOMETERS

Willmore Period, Damping

Number sec Resistor,

10 30hrns 3.2 5.2 8.5 10.0 14.7 2.20 15 11.5 10.6 11.5 10.4 10.6 2.7 5. 1 8.0 9.8 14.7 0.85 4 7.2 7.8 7.7 7.4 7.7 2.4 5.0 7.9 9.7 14.5 171592 1. 19 8 8.9 9.4 9.4 9.3 9.6 3.0 5.2 8.3 9.6 14.5 Frequency (cps) 1. 73 15 10.2 10.5 10.2 10.4 12.2 Calibration Constant volts/in. sec- l

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