This month, as an example of measuring everyday objects, we will introduce a case study in which we measured the natural frequency and damping factor of a coffee can.
Vibration is an unavoidable phenomenon when machinery is in operation, but since vibration is not only unpleasant but can also cause malfunctions, it is important to conduct thorough prior consideration and implement measures to prevent or reduce vibration. In particular, the phenomenon of resonance can cause large vibrations even with small external forces, so it is necessary to understand the natural frequencies and damping ratios of machinery, structures, and their components, and to design in a way that suppresses vibration to below acceptable levels by incorporating appropriate damping.
Measuring the natural frequency and damping ratio of products and parts by impact is a simple method, but accurate measurement requires know-how and practice. Coffee cans (with and without contents) have several natural frequencies, and measurement is relatively easy. This time, we will introduce the example of coffee cans as a subject for practice and education in natural frequency and damping ratio measurement.
Example of a measurement system
- ONO SOKKI NP-3211 Accelerometer with Built-in Preamplifier
- ONO SOKKI GK-3100 Impulse Hammer
- ONO SOKKI DS-3000 Series Data Station
- ONO SOKKI DS-0321 FFT Analysis Function (Software)
- PC
There are several methods for measuring natural frequencies and damping ratios, including (1) measuring the damping ratio using the half-width method from the frequency response function, and (2) measuring the damping ratio using the Hilbert transform. Method (1) requires an impulse hammer, but method (2) can be done with a wooden mallet, a metal ball, or even a fingernail or pencil for practice.
FFT analyzer settings (example)
- Connect the impulse hammer to CH.1 and the accelerometer to CH.2. If you are not using the impulse hammer, connect the accelerometer to CH.1.
- The sample conditions will be internal sampling, and the number of sample points will be set to 2048.
- The frequency range should be set to a relatively high value, approximately 2 to 10 times the expected natural frequency.
- If the impulse hammer and acceleration detector are of the CCLD (constant current source) type, turn on the CCLD setting.
- Initially, set the voltage range to a low value, and if input overload occurs during actual operation, increase it one step at a time. If you used the auto-ranging function to adjust the voltage range, turn it off once you have determined the voltage range to be used (to prevent the voltage range from dropping during periods of no signal).
- Set the trigger source to CH.1, the trigger position to-128 (pre-trigger), and the trigger level to around 10%, adjusting as needed to match the signal.
- For units and calibration, you set the sensitivity of the impulse hammer and acceleration detector.
- The window function should be set to rectangular. The averaging mode should be power spectrum averaging. 4 to 10 averaging iterations should suffice.
- When using an impulse hammer, six graphs will be displayed: time-domain waveform (CH.1, CH.2), power spectrum (CH.1, CH.2), frequency response function (CH.1-2), and coherence function (CH.1-2). When not using an impulse hammer, three graphs will be displayed: time-domain waveform, power spectrum, and Hilbert transform.
- The Y-axis scale of the time-domain waveform will be left at its default setting. This is to understand the margin of safety relative to the voltage range and to make it easier to adjust the trigger level.
The frequency range and sample count are adjusted by actually striking the circuit and observing the time waveform and power spectrum. If there are clearly no high-frequency components, the frequency range is reduced. Also, if the attenuation waveform does not fit within the FFT time window length, either reduce the frequency range or increase the sample count.
Lowering the frequency range increases the FFT time window length. For example, with a 200 Hz range and 2048 points, the FFT time window length is 4 seconds, meaning you need to wait at least 4 seconds after each trigger. Also, the lower the frequency range, the more difficult it becomes to adjust the trigger level, so avoid lowering the frequency range more than necessary.
Selection of Impulse Hammer Tips
The excitation frequency characteristics of an impulse hammer can be changed by replacing the tip at its end. The frequency characteristics need to extend to the range of the natural frequency to be measured, but if a tip that is too hard is used, unwanted high-frequency components will be generated, making it difficult to adjust the voltage range and trigger level, and also worsening the signal-to-noise ratio.
The time-domain waveforms and power spectra when the impulse hammer tip is changed to a soft tip (green), a plastic tip (blue), and a hard tip (orange) are shown in the figure below.
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Figure 1-1 Time-domain waveform of impulse hammer (soft/plastic/hard tip)
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Figure 1-2 Power spectrum of impulse hammer (soft/plastic/hard tip)
Measurement results
1. Measurement of damping rate using Hilbert transform, Part 1 (Empty coffee can)
An accelerometer was attached to the side of an empty coffee can (185g steel can), suspended by a string attached to the pull tab, and the rim of the bottom of the coffee can was struck with an impulse hammer (plastic tip). The peaks at 850 Hz and 1400 Hz were considered to be natural frequencies, and the natural frequencies and damping ratio (damping factor) were measured using the Hilbert transform. The results are shown in Figure 2.
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Figure 2. Measurement results of natural frequency and damping ratio (coffee can).
2. Measurement of damping rate using Hilbert transform, Part 2 (Coffee can with contents)
An accelerometer was attached to the side of a coffee can (190g steel can) containing coffee, and it was suspended by a string attached to the pull tab. The rim of the bottom of the coffee can was struck with an impulse hammer (plastic tip), and the peaks at 556 Hz and 1188 Hz were considered to be natural frequencies. The natural frequencies and damping ratio (damping factor) were measured using the Hilbert transform, and the results are shown in Figure 3.
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Figure 3: Measurement results of natural frequency and damping ratio (coffee can with contents inside)
3. Measurement of attenuation rate using frequency response function (coffee can with contents)
Under the same conditions as in Section 2 above, the results of measuring the natural frequency and damping ratio (damping factor) using the frequency response function are shown below. Note that the number of sample points was changed to 8192 for the measurement.
- Natural frequency: 548 Hz, Damping ratio: 0.887%, Loss factor: 1.774%
- Natural frequency: 1195 Hz, Damping ratio: 0.741%, Loss factor: 1.481%
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Figure 4. Measurement results of natural frequency and damping ratio (coffee can with contents).
Using the method described above, we were able to measure the natural frequency and damping factor of the coffee can. We hope that these measurements will be useful for practicing and teaching vibration measurement, as well as for verifying the operation of measuring equipment.
For more information on coefficients such as damping ratios and their measurement methods, please refer to the following document.
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The following link will take you to our company's website.
[Reference materials]
Ono Ono Sokki Technical Report: Coefficients Representing Vibration Damping
Ono Sokki Technical Report: Vibration Damping Materials and Their Performance Measurement
CF-7200 "Measurement of Damping Ratio ζ (Damping Factor) using Hilbert Transform"
CF-7200 "Procedure for measuring frequency response function in impact testing"
Ono Sokki Simple Operation Manual
(Excerpt from the email newsletter issuedonApril19,2012)
