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Vibration spectrum analysis

If the iPhone is placed on the table and the application is turned on, countless peaks that move chaotically from place to place will gradually appear. As a matter of fact, the accelerometer oscillates even without external forces (we will call this "background oscillation") However, these movements are dry weak, which is why they practically do not affect stronger measurements.

Now we come to measuring the vibration of fans and a motor. We will start with the simplest example. We will measure the vibrations of a 6x6 cm DC fan, with rolling-element bearings. Giving the fan 4 volts and placing it on the iPhone, we get a single expressed peak at a frequency of 2103 rpm.

Everything is self-evident here. The frequency of vibration coincides with the rotational speed of the fan, and it can be determined that the fan turns at 2103 rpm. Notice that the force of the vibration (0.006387 g) is 30 times greater than the height of the peaks shown in the above graph.

Now we will raise the voltage a bit. This increases the speed of the fan, and the vibrational frequency increases accordingly. The figures below show how a second peak gradually emerges (corresponding to the new frequency of 2181 rpm), while the first peak disappears.

Continuing the gradual increase in voltage, we bring the peak to the rightmost bound of the rotational speed (frequency) graph.

Now we need to introduce the concepts of "sampling period" ("sampling frequency") and "false (lower) frequencies". The sampling period is the amount of time between two data measurements.

The iPhone 5S accelerometer can accomplish a sampling period of 0.0098 seconds. This equates to a sampling frequency of 102 Hz (1/0.0098). This sampling frequency allows for detecting frequencies up to 51 Hz (102/2; 51 Hz is 3060 rpm). With frequencies over 51 Hz, lower-frequency signals will appear (giving a false lower frequency).

More information on this can be found here.

Going back to the experiment, we will continue to increase the fan’s voltage and frequency of rotation. This causes the peak to move left.

As a result, we get false lower frequencies (rotations), but they can be used to determine the positions of the true frequency. This is because the true frequency determines the position of the false lower frequency. Upon further increasing the fan’s speed, the peak will return to the graph’s leftmost bound. This will occur at a frequency of 102 Hz (6120 rpm).

Moving on to the next experiment, we will investigate the vibration of a DC fan with plain bearings. We apply 9 volts to the fan.

The graph shows two peaks next to each other. It is too early to determine which one corresponds to the fan’s speed. Now, we will gradually reduce the voltage and speed of the fan.

The leftmost peak moves to the left, and the rightmost to the right. This means that the speed of the fan corresponds to the leftmost peak. If the rotational speed were grater than 3060 rpm, reducing the speed of rotation would cause the rightmost (false) peak to move right, in accord with the frequency. For the given fan, however, it is known beforehand that the speed must be below 3000 rpm.

We will continue to gradually reduce the fan’s speed.

Not only does the peak corresponding to the rotational speed move left, it also shrinks in size, to the point where it is practically indistinguishable from background oscillation. The peak of the bearing’s rotation, however, moves very little and remained significantly higher than the other peaks. This peak shows a false lower frequency; the true frequency is most likely much greater than 50 Hz, and even 100 Hz.

The next experiment will be even more complicated. We will be measuring the vibration of a DC motor, connected to an autotransformer through a rectifier. The motor’s vibration is too strong, which is why a foam rubber pad is placed between the motor and the iPhone.

The spectral graph shows a high peak at 126 rpm. Now, we will increase the voltage from 3.4 V to 4 V.

Now, we increase the voltage to 5 V.

And to 6 V.

The motor’s speed is definitely increasing. The tallest peak visibly remains at 126 rpm, which is why it cannot possibly correspond to the motor’s rotational speed, or any other vibrations dependent on the motor’s speed. The reason for this vibration is the voltage. After the transformer, the alternating voltage is rectified using the rectifier. It looks like this:

The result is waves that have twice the frequency of that in the electrical outlet. If the outlet has a frequency of 50 Hz, the frequency of the waves will be 100 Hz. The spectral graph, meanwhile, shows a false lower frequency. It reaffirms that, as stated earlier, a frequency of 102 Hz creates a false lower peak at 0 Hz.

This theory as to the reason for the vibration can be confirmed by smoothing the voltage with a capacitor. After connecting the capacitor, the height of the peak decreases from 0.008879 g to 0.002935 g (by a factor of 3).

The second peak at 1700 rpm is now more visible. To verify if this peak actually corresponds to the motor’s rotation, we attach a pulley, which creates a rotor imbalance.

As a result of the imbalance, a new peak appears at 800 rpm. This means that that peak was, in fact, the motor’s rotational speed. For further analysis, we will get rid of the voltage-induced vibration. To do this, we will connect the motor to a good power source, which will give a constant voltage (fans in the previous experiments were also connected to a good power supply unit).

The vibration from voltage is gone, but there remains a second, tall peak. The frequency of the second peak is exactly two times that of the rotational frequency. We will raise the voltage from 6 V to 7.5 V.

The motor’s rotation speed has increased to 1037 rpm. The second peak has also moved, and continues to have a frequency twice that of the motor’s rotation. Reasons for this vibration can be either the rotor brushes or changes in the direction of the rotor’s magnetic field during its rotation.

Now we take off the pulley to make sure that the peak at 1037 rpm is the motor’s actual rotation speed.

The peak became much smaller, which means that the supposition was correct.

The next experiment uses an AC fan.

Just like in the experiment where the motor was connected to a transformer through a rectifier, the tallest peak is at 2.1 Hz (126/60), corresponding to 126 rpm. We has already found out that this is a false lower frequency, and the peak is really at about 100 Hz—twice the frequency in the electrical outlet. The means by which this vibration is created can be found in the construction of this AC fan. Using the fan’s serial number, the Internet tell us that this is a shaded-pole motor.

Changing the voltage phase changes the magnetic field, which leads to a vibration that is twice the frequency of that in the power grid.

We have looked at only a few situations; to get more detailed information about the reasons behind this vibration, and vibrational spectrum analysis in general, it is better to read specialized articles on this subject matter.

Accelerometer connects to the headphone jack

• Measurement range from 5 Hz to 21000 Hz.
• Step 1 Hz (0.2 Hz).

ADXL335 accelerometer module with ANALOG (NOT digital) output:

MMA7361 accelerometer module with ANALOG (NOT digital) output:

If anything is unclear, be sure to drop me an email.

A stroboscope for an external accelerometer

(the feature was proposed by Todd French from Los Angeles, California)

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An attached flashlight can indicate the position (phase) of the rotating part, when there is maximum acceleration at the accelerometer axle (DIRECTED AWAY FROM THE CENTER OF ROTATION). For proper use of this feature, the following should be taken into account:

• Vibration due to the centre-of-gravity displacement of the rotating part must expressly predominate and a clear sine curve must be seen. This may require the use of springs.

• The acceleration reaches its maximum at zero speed with maximum displacement.

• System oscillations do not always match the part’s rotation, i.e. the displacement and the disturbing force may be not in phase. Tests with a flyweight under different speeds are definitely required.

Privacy policy

1. This application requires access to the microphone (accelerometer connects to the headphone jack). The data obtained through the microphone can be saved (and used) only by the user.

2. Spectrum and vibration wave images can be saved as a screenshot (taking a screenshot by lightly touching the screen). This requires permission to save images in "Photos". The application does not have access to the photos stored in the "Photos" folder.

3. The app DOES NOT collect any data at all, and especially confidential ones. The app doesn't send messages even if the app crashes. Therefore, if you do not inform me about frequent app crashes by email, I won't know about it and I won't fix the bug. The app may only need an Internet connection when making in-app purchases to unlock locked features.



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