In the previous section, we found that if there is an imbalance, the excitation force F is derived from the unbalanced mass m, the distance r from the center, and the rotational angular velocity ω.
F＝mrω^2 ・・・・（1）
It was discovered that a certain force occurs, and this force generates vibrations.
Mass imbalance correction is performed not only on large rotating machinery such as fans and rotors, but also on more familiar items like car tires. Apparent imbalances caused by factors other than mass, such as alignment work, heat, and fluids, also occur, and field balancing is performed on-site to reduce vibrations.
This time, I'll talk about the concept of correcting this imbalance.
The imbalance
- The frequency of vibration due to imbalance is equal to the rotational speed, and the frequency component of the first rotation is measured.
- When the rotational speed is constant, the vibration is proportional to the magnitude of the imbalance (g-mm).
- The vibration phase from an arbitrary reference position defined for the rotating body corresponds to the position of the rotating body's imbalance.
We know that.
To correct the imbalance, reflective marks are placed on the axis, and a photoelectric detector, amplitude sensor, and FFT analyzer are used to detect them. Non-contact gap sensors or Accelerometer are used as amplitude sensors.
Figure 1 shows an example of a measurement system.
Figure 1: Field Balancing Analysis System
The basic concept of correcting imbalances is shown in Figure 2.
Figure 2: Relationship between unbalance and vibration of a rotating body
In Figure 2, let's assume there is an imbalance of F at point A on the rotating plane. The correction point is point C, which is 180 degrees opposite A, and we should attach a correction weight of the same amount as F to it.
To measure points A and F, the shaft is operated at a constant rotational speed, and the angle θ between the reference position and the position of maximum vibration is measured as shown in Figure 3. When the rotation is stopped and the reflective mark is aligned with the position of the photoelectric detector, the position at an angle θ in the opposite direction of rotation from the mounting position of the vibration sensor becomes the unbalanced position.
Figure 3. Rotational pulse and unbalanced signal
In fact, when using Accelerometer as a vibration sensor, the pickup is attached to the bearing, but due to the effects of rigidity and damping, the unbalanced position may not occur at position θ from the position of the pickup.
Therefore, we attach a test weight and create a vector diagram as shown in Figure 4 to determine point C, the position where the balance needs to be corrected.
Figure 4. Field balancing (one condition per surface)
First, measure the angle α1 and magnitude F of point A, which represents the initial imbalance.
Next, a test weight Mt(g) is placed at point B, and the unbalance angle α2 and magnitude T are measured in the same way. The initial unbalance will shift to F+T.
The correction point C is the point shifted by θ from point B where the test weight was attached.
When drawing the graph, pay attention to the relationship between the axis rotation direction and the polarity of the phase display on the FFT analyzer. Also, there may be a difference between the angular position drawn on the axis and the measured phase.
Point B, to which the test weight is attached, is used to determine the angular position of the axis, and by shifting it by θ from there, the axial position of point C is determined.
Also, the corrective weight Mu(g) is
Mu＝Mt×F/T ・・・・（2）
It can be calculated as follows:
First, measure the angle α1 and magnitude F of point A, which represents the initial imbalance.
Next, a test weight Mt(g) is placed at point B, and the unbalance angle α2 and magnitude T are measured in the same way. The initial unbalance will shift to F+T.
The correction point C is the point shifted by θ from point B where the test weight was attached.
When drawing the graph, pay attention to the relationship between the axis rotation direction and the polarity of the phase display on the FFT analyzer. Also, there may be a difference between the angular position drawn on the axis and the measured phase.
Point B, to which the test weight is attached, is used to determine the angular position of the axis, and by shifting it by θ from there, the axial position of point C is determined.
Also, the corrective weight Mu(g) is
Mu＝Mt×F/T ・・・・（2）
It can be calculated as follows:
The weights used to correct imbalances should be attached so that their distance from the center is the same as the radius at which the test weights were attached.
The operating speed should be set to the actual operating speed of the machine or a speed at which unbalance can be easily measured. In machines with variable rotation speeds, the rotation speed may be changed after unbalance correction to check the results.
While some rotors have a length that is larger than their diameter, if the length is more than half the diameter, it may be necessary to repair both sides (both surfaces) rather than just one side (one surface).
The advantages of being able to use an FFT analyzer are
- By attaching reflective marks to a rotating body and measuring the detection signal as a synchronization signal, the vibration amplitude and phase of the rotational speed component can be measured simultaneously using only an FFT analyzer.
- Because the data can be averaged, the vibration amplitude of the rotational speed component can be separated and measured accurately even if it fluctuates due to other disturbances.
These can be listed.
The method described above, which involves one measurement point, one correction point, and one rotation speed point, is known as one-face-one-correction and is commonly used.
The DS227 balancing software has functions such as single-plane correction, single-plane 1-correction 2-rotation speed measurement, and double-plane 2-correction.
References: FFT Analyzer User Manual, edited by Kenichi Kido
(Excerpt from the email newsletter issued on November 17, 2005)
