Frequency Analysis from the Basics (39) - "Torso Vibration Measurement"

This time, as a continuation of our previous discussion on "rotational fluctuation measurement," we will talk about "torsional vibration measurement."
​Torsional vibrations can cause various problems, such as shaft breakage and noise, in components like the crankshafts of gasoline and diesel engines, and the propeller shafts of rear-wheel-drive vehicles. Therefore, measuring torsional vibration and rotational fluctuations are important measurement items for rotating bodies.

Torsional vibration is a phenomenon in which a rotating body, at a certain rotational speed, experiences a large twist in its shaft due to rotational force (torque), causing torsional resonance at the torque frequency. Typically, the rotational speed is swept, the twist angle of the rotating body's shaft is measured, and tracking analysis of the angular displacement fluctuation component is performed. This time, we will introduce two methods for measuring torsional vibration.

As with the previous demonstration, we will use the rotating demonstration device shown in Figure 1. This device has a rotating shaft with a disc and three gears (60 P/R) attached, and a fluctuating load from a magnet attached to the tip of the shaft. MP-992 A type Electromagnetic Detector is attached to extract a sinusoidal rotation information signal, and a high-speed FV converter is used. FV-1500 Use this to convert it to an analog signal, and then DS-3000 Figure 2 shows the results of tracking analysis performed with a series FFT analyzer (with a rotational order component of 4th order amplitude and phase). From these results, it can be seen that there are torsional resonances at approximately 1650 r/min and approximately 3000 r/min. heyVibration mode It can be seen that it has the shape shown in Figure 3.

Next, we will use this rotating demonstration device to measure torsional vibration. Specifically, we will determine the angular displacement fluctuation of MP3 (torsional resonance at a rotational speed of approximately 1650 r/min in Figure 3) using MP1 as a reference.
There are two main methods for obtaining rotational speed (angular velocity) information from Electromagnetic Detector, such as the one shown in Figure 1, and calculating torsional angular displacement.

1. The rotational speed information from MP1 and MP3 is converted to angular velocity (frequency) information using F/V conversion.
   Convert and the difference Time integral Then, determine the angular displacement variation component.···············(1)
   The numerical value 360 on the right side of equation (1) is obtained when, after performing a single integral, the angular frequency is converted to angular displacement.
   This is to allow angles to be read directly in degrees (deg).
2. ​The instantaneous phase (angular displacement) is calculated from the time waveforms (sine waves) output from Electromagnetic Detector MP1 and MP3 using the Hilbert​ ​transform function, and the angular displacement fluctuation component is determined from the difference between them.
   ∆θ=θ(MP3) − θ(MP1) (2)

The two calculations described above were performed using Oscope, a time-series data analysis tool from Ono Sokki, as a secondary processing calculation.
Yes, there are. Below, I will explain the steps for the two methods.

1. How to use the F/V conversion function
   ① Use the F/V converter (signal processing menu) to convert the time waveforms of MP1 and MP3.
   Instantaneous frequency The time signal is determined. (Figure 4)
   (Note) The vertical axis represents the rotational frequency, and the unit is Hz.
   ② Using inter-channel operations (signal processing menu),
   The angular frequency variation component is calculated using (MP3-FV - MP1-FV) x 360.
   ③ Use single integral in time-axis calculus (signal processing menu) to convert the angular frequency variation component into phase difference angular variation component. (Note) The vertical axis is angles, and the unit is degrees (deg).
   ④ Stoichiometric tracking analysis Use the (Waveform Analysis menu) to determine the rotational speed and amplitude value (angular displacement fluctuation) of the torsional vibration.
   (Analysis conditions)
   Rotation speed: 1000~3500 r/min
   Number of analysis blocks: 400
   Maximum analysis order: 50
   The analysis results using the above procedure are shown in Figure 5, and it can be seen that the torsional resonance of the fourth-order component occurs at a rotational speed of 1658 r/min, and its angular displacement amplitude is approximately 0.564 degrees.Figure 4 shows the result of F/V conversion of the time signal from MP1.Figure 5 shows the torsional vibration results (4th order component) obtained using the "F/V conversion function".
2. How to use the Hilbert transform function
   ① The instantaneous phase (angular displacement) is determined from the time signals from MP1 and MP3 using the Hilbert transform. (Figure 6)
   (Note) Instantaneous phase refers to extracting the phase angle θ of a time signal (sine wave) Asinθ as a function of time (horizontal axis: time, vertical axis: phase angle).
   Figure 6 Phase of the time waveform of MP1
   The phase increases over time as it rotates around the circumference many times in a 360-degree cycle.
   The image is folded back by ±180 degrees for display.
   ② Use the inter-channel calculation (signal processing menu) to calculate the angle difference between MP1 and MP3 and find the phase difference angle variation component. (Note) The vertical axis is angle and the unit is degrees (deg). However, in this case the angle is a time signal of 60 teeth per rotation. Electric angle Quite reasonable, actual mechanical angle It needs to be divided by 60.
   ③ Use constant-ratio tracking analysis (waveform analysis menu) to determine the rotational speed and amplitude value (angular displacement fluctuation) of the torsional vibration.
   (Analysis conditions)
   Rotation speed: 1000 ~ 3500 r/min
   Number of analysis blocks: 400
   Maximum analysis order: 50
   The analysis results using the above procedure are shown in Figure 7, and it can be seen that the torsional resonance of the fourth component occurs at a rotational speed of 1658 r/min, and its angular displacement amplitude is approximately 33.988 degrees in electrical angle (approximately 0.566 degrees in mechanical angle).
   Figure 7 shows the torsional vibration results (4th order component) obtained using the "Hilbert transform function".

Note that Method 1 (using the FV conversion function) is a method that calculates from the instantaneous frequencies of MP1 and MP3. Therefore, as mentioned previously, there is also a method of measuring the tangential velocity v of the disk attached to the rotating demo device with a laser in-plane velocometer and determining the instantaneous frequency from the relationship V = rω (where r is the radius of the disk).

In conclusion, here's a summary.

1. Torsional resonance in the shaft can lead to shaft damage and noise problems, so measuring torsional vibration and rotational fluctuations is very important in vibration measurement of rotating bodies.
2. Torsional vibration is a phenomenon in which a rotating body, at a certain rotational speed, experiences a large twist in its shaft due to rotational force (torque), causing torsional resonance at the torque frequency at that time.
3. Torsional vibration measurement requires determining the difference in torsional angle between two channels, and there are two main methods for doing so.
4. Method 1 involves measuring the instantaneous frequency (angular velocity) of the axis using a rotation detector or laser in-plane velocometer, determining the difference between the two channels, and integrating the result over time to obtain the angular displacement fluctuation component.
5. Method 2 calculates the instantaneous phase (angular displacement) from the time signal detected by the rotation detector using the Hilbert transform function, and then determines the angular displacement fluctuation component from the difference.
6. By performing tracking analysis on the angular displacement fluctuation components obtained from (4) and (5) above, the amplitude value of the angular displacement fluctuation component of torsional resonance at a certain rotational speed is determined.

【keyword】
Torsional vibration, rotational fluctuation, rotational force, torque, torsional resonance, torsional angle, torsional vibration mode, time integration, Hilbert transform, instantaneous phase, instantaneous frequency, constant ratio tracking analysis, electrical angle, mechanical angle, laser in-plane velocometer

【reference】

1. Ono Sokki Webpage "3.5 Torsional Vibration Meter"
2. Measurement Column (emm No. 180) Frequency Analysis from the Basics (29) - "Hilbert Transform and Analyzed Signal" -

(Excerpt from the email newsletter issued on July 25, 2018)