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Technical Report: Vibration Damping Materials and Their Performance Measurement 4

12. Central vibration method

This test method is also commonly known as the mechanical impedance method in Japan and is adopted in the JIS standard for vibration-damping steel plates mentioned above, but it is not common in Europe or the United States. The figure below shows the loss coefficient measurement system for the central vibration method, which is common in Japan, similar to the cantilever beam method.

In the United States, the term "impedance method" refers to a method of determining the loss factor by measuring impedance using block-shaped damping materials, as shown in the following diagram.

Recently, the central excitation method has been introduced in SAE 920406.

1. Characteristics of the central vibration method

Strong Points

  • It can measure up to high frequency ranges.

  • Compared to the cantilever beam method, it offers greater flexibility in the dimensions of the test specimen.

Cons

  • The testing equipment is complex.

  • The effect of the support structure is unknown.

Test specimen

  • Strip-shaped, block-shaped.

Test Procedure

  • Sine or random excitation; the sweep for sine excitation is slow.

  • The response was recorded using a frequency response analyzer, FFT analyzer, and level recorder. Attention was paid to frequency resolution, truncation, and reading errors.

Assumptions and precautions during the exam

  • The dimensions of the test specimen should preferably have an aspect ratio of 20:1 or greater.

  • The test should be conducted within the linear range. Pay attention to the excitation amplitude. It is desirable that the vibration is not visible to the naked eye.

  • The excitation force is always constant.

  • Care must be taken to ensure that bending excitation does not turn into torsional excitation.

  • Measurements should be limited to the vicinity of the resonant frequency. → Range of fc / 10
    It is desirable to have 20 or more measurement points within the half-width.

  • Ideally, the bonding width of the knife edge should be "zero," but it is desirable to have a width of 1/200 or less of the sample length (0.5 mm or less for a 100 mm test piece).

  • Mass cancellation of load cells.
    When the loss factor of the test specimen falls below 0.03, the effect of the presence or absence of mass cancellation becomes significant.

  • Zoom analysis must be performed.
    When the loss factor of the test specimen falls below 0.03, the effect of whether or not zoom analysis is performed becomes extremely large.

2. Impedance head

Structurally, it can be considered as a single unit incorporating two sets of sensors: a load sensor and an acceleration sensor. It is an indispensable detector for the central excitation method. It is fixed on top of the exciter, and the sample to be measured is excited via the impedance head, and the excitation point impedance is measured. Considering that the impedance head will be placed in a constant temperature bath, a charge-sensitive type is preferable. The sensitivity of the force sensor and Accelerometer should preferably be 100 pC/N or higher and 1 pC/ms-2 or higher, respectively, considering that the weight of the material under test is at most about 100 g and the excitation force is at most about 10 N. When using a voltage-sensitive type, attention should be paid to the upper limit of the operating temperature, and the sensitivity of the force sensor and Accelerometer should preferably be 100 mV/N or higher and 1 mV/ms-2 or higher, respectively. Also, since tilting mode may occur, the height of the impedance head should be as low as possible, and considering the balance between front, back, left, and right, the lead wires should be routed symmetrically, and short connectors are preferable.

3. Resonance and anti-resonance in the central excitation method

In the central excitation method, when the impedance (F [force] / V [velocity]) is measured, resonant and anti-resonant frequencies appear alternately, as shown in the figure below. At the resonant frequency, the excitation force is very small, and the specimen vibrates greatly. On the other hand, at the anti-resonant frequency, the excitation force is large, but the specimen hardly vibrates at all.

The vibration modes are as shown in the following figure. As you can see, the vibration modes are completely different at the resonant frequency and the anti-resonant frequency.

Furthermore, the central position of the second-order anti-resonance mode in central excitation is different from the second-order resonance mode in a two-point suspension system, even though they may seem similar. The boundary conditions are the same as those for the resonance mode with twice the length of a cantilever suspension.

The figure below shows the measurement results of the loss coefficient of vibration-damping steel plates, illustrating the cases where the length of the test specimen and the test temperature differ. As can be seen in the figure, there is a difference between the resonant frequency and the anti-resonant frequency.

As shown in the figure, for frequency dependences that are upward sloping, the anti-resonance side is larger, while for those that are downward sloping, the resonance side is larger. This phenomenon is not observed in two-layer (overst beam) designs.

4. Error factors of the central excitation method

  1. Problems in test specimen preparation → Inconsistent physical properties, dimensional errors, and poor adhesion.

  2. Types of adhesives → Pay attention to the thickness of the adhesive; some are insensitive to temperature changes.

  3. Temperature control → Pay attention to the uniformity of the temperature distribution within the test specimen.

  4. Analysis error → Noise reduction in the response signal, sweep speed, etc.

  5. The energy loss in the support structure needs to be minimized.