Typically, the signals that can be input to analysis devices such as FFT analyzers are voltage signals.
When measuring physical quantities such as acceleration, velocity, force, and sound pressure, detectors (sensors) that convert these physical quantities into voltages are used. For example, if there is an acceleration detector that outputs a voltage signal proportional to the magnitude of acceleration (m/ s²), the measured voltage value can be converted to acceleration and displayed using its proportionality constant (sensitivity). When measuring the magnitude of vibration, the magnitude is sometimes expressed in terms of acceleration (m/ s²), but it can also be expressed in terms of decibels (dB).
This time, we'll show you how to set up a system to express the magnitude of vibration in decibels (dB).
Decibels of acceleration
The general formula for expressing acceleration values in decibels (L) is as follows:
a: acceleration (m/s 2), a0: reference acceleration (m/s 2)
The reference acceleration used when determining the vibration acceleration level as defined in JIS 1510 "Vibration Level Meter" is a0 = 1 × 10⁻⁵ (m/ s²), but other standards may use different reference acceleration values.
Furthermore, while it is ideal when the standard acceleration value is clearly stated in the specifications, it is often expressed as "10 m/ s² is set to 120 dB." In this case, the standard acceleration a0 can be calculated using equation (2), which is a modified version of equation (1).
（m/s2）
For example, substituting L = 120 dB and a = 10 m/ s² into equation (2), we obtain a0 = 1 × 10⁻⁵ m/ s².
Decibels are defined as 1 m/ s² = 0 dB.
When analyzing data using our FFT analyzer and displaying the power spectrum in decibels, unless otherwise specified (using the unit name m/ s²), the displayed decibel value will be set to 0 dB, with 1 m/s² being the unit value. Figures 1 and 2 show examples of settings in the DS-0221 FFT analysis software and DS-3000 real-time acoustic vibration analysis software when the accelerometer sensitivity is 1.02 mV/(m/ s²).
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Figure 1: Setting DS-0221 to 0 dB at 1 m/s² (Example setting)
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Figure 2: Setting 1 m/s² to 0 dB on the DS-3000 (Example setting)
JIS C1510 Vibration Acceleration Level in "Vibration Level Meter"
In JIS C1510 "Vibration Level Meters," the vibration acceleration level is defined as "20 times the common logarithm of the value obtained by dividing the effective value of vibration acceleration by the reference vibration acceleration (10⁻⁵ m/ s²)," which corresponds to the value calculated using equation (1) where a₀ = 1 × 10⁻⁵ m/ s².
The DS-0221 FFT analysis software and similar programs do not have a function to set the reference acceleration when displaying decibel values. Therefore, the physical quantity (EU value) is set to a value obtained by correcting the sensitivity of the acceleration detector with the reference acceleration. If the sensitivity of the acceleration detector is 1.02 mV / (m/ s²) = 1.02 × 10⁻³ V / (m/ s²), then the physical quantity (EU value) is set to 1.02 × 10⁻⁸, which is obtained by multiplying this by the reference acceleration of 1 × 10⁻⁵ (m/ s²). Leave the unit name blank.
Figure 3 shows an example of the settings on the DS-0221, and Figure 4 shows an example of the time-domain waveform and power spectrum when an acceleration signal with an effective value of approximately 10 m/ s² (single amplitude 14 m/ s²) is input. The power spectrum correctly shows 120 dB, but the peak value of the time-domain waveform is a very large value of 1,424,598. This does not mean that an acceleration of 1,420,000 m/s² is being generated. Multiplying this value by the reference acceleration of 1 × 10⁻⁵ (m/ s²), we get 1,424,598 × 10⁻⁵ = approximately 14.2 m/ s², which is the actual acceleration value being generated.
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Figure 3: Setting the reference acceleration to 1 × 10⁻⁵ (m/s²) in DS-0221 (Example setting)
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Figure 4 Power spectrum and time-domain waveform of DS-0221 (example display)
The DS-3000 real-time acoustic vibration analysis software allows you to set the reference acceleration for displaying decibel values as a 0 dB reference value. Set the unit name to m/ s², the EU value to set the sensitivity of the acceleration detector, and set the reference acceleration to 1 E-5 (1 × 10⁻⁵ m/ s²) as the 0 dB reference value. Note that some older versions of the DS-3000 software do not allow you to set a 0 dB reference value, so please upgrade to the latest version before use.
Figure 6 shows an example of the time-domain waveform and power spectrum when an acceleration signal with an effective value of approximately 10 m/ s² (single amplitude 14 m/ s²) is input. Both the power spectrum value of approximately 120 dB and the peak value of the time-domain waveform of approximately 14 m/s² are displayed as correct values.
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Figure 5: Setting the reference acceleration to 1 × 10⁻⁵ m/s² on the DS-3000 (Example setting)
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Figure 6 Power spectrum and time-domain waveform of DS-3000 (example display)
Decibels are expressed with 1 G equal to 60 dB.
When using the standard gravitational acceleration value as the unit of acceleration, it is defined as 1.0 G = 9.806 65 m/ s². G is not included in the SI units, and its use in commercial transactions is not permitted under Japanese measurement law, however, there are cases where the unit G is used for comparison with previously measured data.
Here, we will show an example of settings for displaying in decibels, with 1 G being 60 dB.
Substituting L = 60 dB and a = 1 G into equation (2), we find that the reference acceleration should be set to a0 = 1 × 10⁻³ G.
The DS-0221 FFT analysis software does not have a function to set the reference acceleration when displaying decibel values. Therefore, the physical quantity (EU value) is set to a value corrected for the sensitivity of the acceleration detector. If the sensitivity of the acceleration detector is 1.02 mV / (m/s2) = 10.0 mV / G = 10.0 × 10⁻³ V / G, then the physical quantity (EU value) is set to 1.0 × 10⁻⁵, which is obtained by multiplying this by the reference acceleration of 1 × 10⁻³ G. Leave the unit name blank. An example of the setting is shown in Figure 7.
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Figure 7: Setting 1 G to 60 dB on DS-0221 (Example setting)
The DS-3000 real-time acoustic vibration analysis software has a function to set a 0 dB reference value. Set the unit name to G, the EU value to the sensitivity of the acceleration detector converted to G (0.01, 10.0 mV/G), and the 0 dB reference value to the reference acceleration (0.001, 1 × 10⁻³ G). An example of the settings is shown in Figure 8.
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Figure 8: Setting 1 G to 60 dB on the DS-3000 (Example setting)
Decibels are calculated with 9.8 m/ s² equal to 60 dB.
In the method described above, the unit of the time-domain waveform becomes G. However, if the software has a 0 dB reference value function, the unit of the time-domain waveform remains m/ s², and 9.8 m/ s² (1 G) can be set to 60 dB. The standard gravitational acceleration is precisely 9.80665 m/ s², but since measurements using an acceleration detector do not have that level of precision, it is acceptable to use 9.8 m/ s².
Substituting L = 60 dB and a = 9.8 m/ s² into equation (2), we find that the reference acceleration should be set to a0 = 9.8 × 10⁻³ m/ s².
When setting the parameters using the DS-3000 real-time acoustic vibration analysis software, set the unit name to m/ s², the EU value to the sensitivity of the acceleration detector, and the 0 dB reference value to 9.8 E-3 (9.8 × 10⁻³ m/ s²). An example of the settings is shown in Figure 9.
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Figure 9: Setting DS-3000 to 60 dB at 9.8 m/s² (Example setting)
Calibration method using a calibration vibrator
Sensitivity calibrators and calibration exciters for acceleration detectors are exciters that vibrate at a predetermined magnitude (for example, 10 m/ s²). By placing the acceleration detector on top of this exciter, calibration can be performed using the output signal (calibration signal).
For example, if the reference acceleration a0 = 1.0 × 10⁻⁵ m/ s² and the effective value of acceleration a = 10 m/ s², substituting these into equation (1) gives a calibration value of L in decibels of 120 dB.
In the unit and calibration functions of each software, after setting all settings except for the physical quantity (EU value) using the procedure described in the previous section, calibrate using the signal calibration (EU/SP) function with a calibration value of L (120 dB). The calibration procedure is the same as that introduced in the previous article (Measurement Column No. 149), except that the Y-axis setting is set to LOG instead of LIN.
summary
In previous articles, we introduced how to set up an analysis system to express the magnitude of vibration in terms of acceleration (m/ s²). This time, we will introduce how to set up the system to express the magnitude of vibration in terms of decibels (dB).
Up until now, we've introduced units and calibration methods related to vibration measurement. In the next installment, we plan to introduce units and calibration methods related to sound measurement.
Please also refer to the following document for information on decibel values.
Ono Sokki Technical Report: "What is a Decibel?"
(Excerpt from the email newsletter issued on April 17, 2014)
