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Note: No, there are no inverters involved in this question here.

I've perceived that most, if not all induction motors make a "howling" sound in their coils that is different from the constant 60 Hz tone they produce due to the working frequency.

This howl has pitch shifts depending on the rotor speed. In very low speeds it is low-pitched and blends with the 60 Hz hum, but as it speeds up the sound evolves into higher pitches. When accelerating I can hear it standing out when it gets around ~100 Hz and then it starts getting quieter after reaching ~400 Hz. When decelerating it does the opposite (I start hearing at ~400 Hz and then it goes down until it blends with the 60 Hz hum).

I have the impression that in motors with more poles this sound is much more audible, like my 16-pole ceiling fan motor. In it the howling is very audible when its spinning at low speeds, like 60 RPM.

And the more "effort" the motor is doing the louder the howl, reversing the fan during operation makes a much louder howl just before reversing (while it's at a low speed and decelerating, nearly stopping) than just after reversing.

I've also heard that howl in several other induction motors, most of them being 4-pole motors. The motors in vertical washing machines, for example, make a quite audible howl when accelerating (in the centrifugation step).

I know that this is probably the result of the interaction between the applied Electromotive Force and the Back Electromotive Force induced on the stator windings, as they're not in-phase and the speed of the rotor modulates the back-EMF on the stator windings.

The resultant between the EMF and the back-EMF (and the successive iterations of inductions between the stator and the rotor) might produce a higher frequency signal on the windings.

However, I can't figure out exactly how this happens.

Does anyone know how can I model the process making that sound?

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    \$\begingroup\$ You seem to believe that the source of that sound is electrical. Are you sure it is not the airflow between stator and rotor that causes it? Many "howling" sounds produced by rotating machines are due either to mechanical friction in the bearings or from the cooling airflow. \$\endgroup\$ – Lorenzo Donati -- Codidact.com Aug 4 '19 at 12:00
  • \$\begingroup\$ are you talking about a whining sound that is associated with servos and stepping motors? ... "howling" usually refers to loud sounds .... stepping motors make a whining sound when stalled \$\endgroup\$ – jsotola Aug 5 '19 at 4:15
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The major sources of acoustic noise in induction motors are magnetostrictive effects, torque ripple effects and aerodynamic effects. There may also be some effects due to magnetic forces that are orthogonal to torque. As mentioned by @Lorenzo Donati, Rotor imbalance and bearing noise may also contribute even if the motor is properly balanced and in good condition.

The magnetostrictive effects are driven by the power frequency in the stator and by the frequency of the rotor current which varies with slip.

Torque ripple is caused by reluctance variation with rotor angle in the stator-rotor flux path due to the way in which the stator slots align with the rotor slots. There is also torque variation in single-phase motors due to the inherent variation of power transfer.

Aerodynamic effects are due to the rotor fins and other motor cooling fans attached to the rotor.

There are also a secondary effects due to mechanical resonance of the motor parts.

Noise may also be produced in the motor by load variations and in the load by motor torque ripple. Noise produced in the load may be difficult to distinguish from noise produced in the motor.

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  • \$\begingroup\$ I forgot to mention: I discarded all solely mechanical sources, as I tested in several machines with lots of inertia (like the ceiling fan and the washing machine) and the howling instantaneously disappears when the motor is powered off, even though the motor is still spinning at nearly the same speed. Also, the howling is usually louder in very low speeds, when the cooling fins wouldn't produce this sound (even at full speed they're very silent and the timbre of the sound is totally different). \$\endgroup\$ – user2934303 Aug 4 '19 at 18:59
  • \$\begingroup\$ But the magnetic reluctance is a very promising candidate. The problem in considering harmonics caused solely by magnetostrictive effects (and their modulation by slip) is that those will produce frequencies around or lower than the network frequency, there was no reason for higher frequencies to appear. But the magnetic reluctance variation seems like a better candidate, as the frequency of its variation depends only on rotor speed, the amount of stator slots and rotor slots. I know the rotor slots are skewed exactly to avoid vibration by that cause, but it probably can't eliminate it totally \$\endgroup\$ – user2934303 Aug 4 '19 at 19:06
  • \$\begingroup\$ Or, to be more precise, the forces caused by magnetic reluctance will vary due to both the variations in magnetic flux (which depends on the working frequency and also on the back-EMF) and variations in the magnetic reluctance as the rotor moves. Might be kind of hard to model that, but I see how higher frequencies might appear in this process \$\endgroup\$ – user2934303 Aug 4 '19 at 19:22
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An induction motor's stator creates a rotating magnetic field ; say a 4-pole 3-phase motor running on 50 Hz will have a magnetic field rotating at 1500 rpm or 25 Hz. This emits audible noise at 25 Hz, 50 Hz and harmonics. That's why the first thing you hear when starting one of these (or when it gets stuck) is a buzz. Once it rotates the noise of spinning things becomes louder than the buzz.

In an induction motor, the rotor does NOT rotate at the same frequency as the magnetic field. Difference in rotation speed is called "slip" and this increases with load torque. When the motor is unloaded, slip is very low, but it is never zero as there is always some friction torque from air resistance, bearings etc.

So, if the magnetic field rotates at 25Hz (1500 rpm) and the rotor turns at 24.9 Hz (1494 rpm) your slip is 0.1Hz or 6 rpm. Noise from the rotor vibrations is at 24.9Hz and harmonics, while noise from the magnetic field is at 25Hz and harmonics. This creates a beat frequency and constructive/destructive interference, which can result in a sound like "vvvooOOoooommm... vvvooOOoooommm..." repeating on a period equal to the slip (10 seconds in this example case). At high torque, slip increases and so does the beat frequency, which produces all sorts of sound effects.

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  • \$\begingroup\$ I know all of that, but those produces low frequencies, my question was how the higher frequencies appear from that. \$\endgroup\$ – user2934303 Aug 4 '19 at 18:56
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From your answer you seem to believe that the sounds you hear are electrical in nature. You seem to have neglected completely the mechanical origin of sounds in rotating machines.

This article on noise sources in industrial environments has a section about that (emphasis mine):

5.3.4. Electric Motors

Noise from electrical equipment such as motors and generators is generally a discrete low frequency, superimposed on a broadband cooling system noise. The electric motor converts electrical energy to magnetic and then mechanical energy with the output of a useful torque at the motor shaft. Part of the energy transformation is converted to heat, causing a rise in rotor, stator and casing temperature; therefore an electric motor must be supplied with a cooling fan system. The cooling fan can be incorporated inside as in the case of an "OPEN" motor or outside as in the case of a "Totally Enclosed Fan Cooled (TEFC)" motor. TEFC motors are more widely used, due to their robust construction which can withstand a dirty environment. OPEN motors are less used due to possible contamination by the environment. An OPEN motor is sometimes (but not always) less noisy than a TEFC motor since the noisy fans are incorporated inside.

There are three basic sources involved in the noise generated by electric motors:

  1. Broad-band aerodynamic noise generated from the end flow at the inlet/outlet of the cooling fan. The cooling fan is usually the dominant noise source.
  2. Discrete frequency components caused by the blade passing frequencies of the fan.
  3. Mechanical noise caused by bearing, casing vibration, motor balancing shaft misalignment, and/or motor mounting. Thus careful attention should be given to the vibration isolation, mounting and maintenance.

Noise generated by the motor fan is the dominant motor noise source, especially for TEFC motors. A sharp increase in noise occurs as the shaft rotational speed increases from 1800 to 3600 RPM. For large motors in the range of 1000 kW, 3600 RPM, a sound pressure level of as high as 106 dB(A) occurs. Measurements carried out in the laboratory for a range of TEFC motors from 25 to 2500 HP, no load, with and without the straight blade motor fan, show a difference of up to 50 dB(A) in the total sound pressure level. This large distribution of the fan noise is due to the fan shape. Motor fan blades are usually straight, so that the motor cooling is independent of rotation direction. Straight blade fans are very noisy, due to the large aerodynamic turbulent sound generated. Noise reduction in electric motors can be achieved by the use of an absorptive silencer (Gerges, 1992) or by redesign of the cooling fan, e.g. with irregular spacing of straight blades as in chapter10 (see Figure 10.17.).

This other article (sorry, it is a scanned document, so no time to copy the relevant text manually). is also relevant. In section 4.3 cites induction motor cooling fans as a major noise source. It also cites magnetostrictive effects, as already mentioned in @Charles Cowie's answer.

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  • \$\begingroup\$ Sorry, I forgot to mention: I did consider and discarded all solely mechanical sources, as I tested in several machines with lots of inertia (like the ceiling fan and the washing machine) and the howling instantaneously disappears when the motors is powered off and instantaneously reappear when powered on again, and with nearly the same pitch (as the rotation speed didn't change). Also, in both cases, the speeds are too low to cause noise by the rotor ventilation, and I've also heard this sound in a motor that doesn't have inner ventilation (it needed a external fan attached to it). \$\endgroup\$ – user2934303 Aug 4 '19 at 18:54

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