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Technical Report on Vibration-Damping Materials and Their Performance Measurement 5

13. Selection of Cantilever Beam Method and Central Excitation Method

The cantilever beam method and the central vibration method have the following characteristics in use, so caution is necessary.

Product Information
cantilever beam
Central Vibration Enhancement
The simplicity of temperature testing

Available

△
Response during high temperatures.

×

Possible with a vibro chamber.
Problem with the clamp section.

exist

None
first mode measurement

not possible

can
Measurement of higher-order modes

difficult

easy
mass cancel

do not

to want
Measurement of soft material single item.

can

not possible
Measurement of the anti-resonance side

difficult

easy
Price

Available

×
SWIPE

14. Comparison of loss coefficients obtained from each testing method.

Using data from the cantilever beam method, the loss coefficient and Young's modulus of the damping material were derived in the form of a conversion frequency nomogram. This nomogram was then used to estimate the loss coefficients of test specimens using the impedance method, SAE method, and MIL method. The figure below plots the estimated loss coefficients on the vertical axis against the experimental values obtained from the impedance method, SAE method, and MIL method on the horizontal axis, showing the relationship between the two. From the figure, it can be seen that the correlation coefficient is 0.946, indicating that the loss coefficients obtained from the cantilever beam method align quite well with those obtained from the impedance method, SAE method, and MIL method.

15. Mass Cancel

When conducting tests using the central vibration method, it is common to use an impedance head to measure driving point impedance and mobility, among other parameters, to determine the loss factor. In this case, the impedance head itself has a mass for measuring acceleration, which means that even when the force is zero, the mass will still be measured by the force sensor. Therefore, the weight of the test specimen plus this mass will be measured, resulting in incorrect impedance readings. For this reason, it is necessary to correct for this added mass in advance when conducting tests. This operation is generally referred to as mass cancel.

The above figure shows an example of a mass cancellation method, and the below figure illustrates an example of a test system for actually performing mass cancellation.

The figure below shows an example of impedance measured using this system. It can be seen that the presence or absence of mass cancellation leads to differences, especially on the resonant frequency side.

Calculation formula for mass cancellation in FFT calculations.

Red: Green: Mobility without mass cancellation
Blue: Mobility after mass cancellation calculated by [ (V / F) - (V / F 0) ]
Red: Mobility after mass cancellation using a mass cancellation amplifier

Red: Green: Mobility without mass cancellation
Blue: Mobility after mass cancellation calculated by (V / F)(1 / H) − (V / F 0)(1 / H) (1 / H)
Red: Mobility after mass cancellation using a mass cancellation amplifier

The waveform of mechanical impedance will be omitted, but when performing mass cancellation using calculations such as FFT.

  1. The function of the molecule F (such as mechanical impedance) can be subtracted directly as (F / V) - (F 0 / V).

  2. When using a function with F as the denominator (such as mobility), it is necessary to first bring F to the numerator by calculating the inverse of the frequency response function (1 / H), then perform the inverse calculation for the added mass and subtract it, and finally calculate the inverse again to return to the original function with F as the denominator. If we denote the frequency response function without work as FRF1, the frequency response function without mass cancellation with work applied as FRF2, and the frequency response function after mass cancellation as FRF3;

    FRF3 = 1/((1/FRF2) - (1/FRF1))

    .

Furthermore, it shows the relationship between the presence or absence of mass cancellation and the loss coefficient in the case of the central vibration method. From the figure below, it can be seen that when the loss coefficient is less than 0.01, there is a slight difference in the loss coefficient depending on the presence of mass cancellation.