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Technical Report: Vibration Damping Materials and Their Performance Measurement 5

13. Selection between cantilever beam method and central excitation method

The cantilever beam method and the central excitation method have the following characteristics in terms of their use, so caution is necessary.

Product Information
cantilever beam
Central vibration
Ease of temperature testing

○

△
Especially when dealing with high temperatures

×

Possible with a vibro chamber
Problems with the clamping mechanism

Yes

none
Measurement of primary mode

Not possible

Possible
Measurement of higher-order modes

difficult

easy
Mass Cancel

Unnecessary

Essential
Measurement of individual soft materials

Possible

Not possible
Measurement on the anti-resonance side

difficult

easy
price

○

×
SWIPE

14. Comparison of loss coefficients obtained from each test method

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

15. Mass Cancel

When conducting tests using the central excitation method, an impedance head is typically used to measure the drive point impedance and mobility, and then the loss coefficient is determined. In this case, the impedance head itself has a mass for measuring acceleration, and even if the force is zero, the force sensor will still measure the force due to this mass. Therefore, since the weight of the test specimen plus this mass is measured, the impedance will not be measured correctly. For this reason, it is necessary to correct for this added mass before conducting the test. This operation is generally called mass cancellation.

The upper figure shows an example of a mass cancellation method, and the lower figure shows 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 makes a difference, particularly on the resonant frequency side.

Formula for calculating mass cancellation using FFT

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

Red: Green: Mobility without mass cancellation
Blue: Calculation 2 [(V/F) (1/H) − (V/F 0 Mobility after mass cancellation calculated by (1/H) (1/H)
Red: Mobility after mass cancellation using a mass cancellation amplifier

The waveform of mechanical impedance is omitted, but when mass cancellation is performed in calculations such as FFT...

  1. Functions with a numerator F (such as mechanical impedance) can be subtracted directly as (F/V) - (F0 /V).

  2. When using a function with F in the denominator (such as mobility), it is necessary to first calculate the inverse of the frequency response function (1 / H) to bring F into the numerator, subtract the added mass by taking the reciprocal, and then take the reciprocal again to return to the original function with F in the denominator. The actual calculation formula is as follows, where FRF1 is the frequency response function without the workpiece, FRF2 is the frequency response function with the workpiece but without mass cancellation, and FRF3 is the frequency response function after mass cancellation:

    FRF3 = 1/((1/FRF2)−(1/FRF1))

    That is the case.

Furthermore, the relationship between the presence or absence of mass cancellation and the loss coefficient in the case of the central excitation method is shown. From the figure below, it can be seen that when the loss coefficient is less than 0.01, the loss coefficient differs slightly depending on whether or not mass cancellation is used.