I have to start by saying that my strategy here would be what several others of my cohort have suggested: keep the car until you get old enough you can't hear the noise. I estimate, from the spectrum posted in the linked article in the OP, that the whine is 44 dB down on the road noise. I wouldn't be able to hear that and can't on the recording. But if you hear it and it annoys you then it annoys you.
More to the point: what is it? I don't know, of course, but here's my guess. The cars contain 3 phase motors which work by chopping up the battery DC and sending the chopped DC to the stator coils in the motors (this is the case in both the synchronous and PM motors) such that a rotating magnetic field of desired phase, frequency and amplitude is produced. The chopping is done at a fixed rate and the frequency phase and amplitude are done by controlling the chopping duty cycle. To produce a low voltage, low frequency waveform one would start at a very low duty cycle and gradually increase it to a moderate duty cycle and then gradually lower it. This would produce a half sine wave of long period and moderate amplitude. Varying the duty cycle from low to high and then back to low again more rapidly would produce a higher voltage, higher frequency wave.
It's probably already obvious that I think the 4 kHz is the chopping rate. It is, in the linked spectrogram, really, really pure and nothing from the suspension or magnetic field harmonics would be so pure not to mention that there would be appreciable variation with speed which, if I have read the previous posts correctly, isn't there.
Thus it appears that stator current is being turned on and off at a 4 kHz rate. Leakage inductance would smooth that somewhat but every effort is made to keep leakage inductance down. Magnetostriction will thus cause the stator to vibrate at a 4 kHz rate with the intensity of the vibration varying as the duty cycle changes. Thus I would expect the loudness of the tone to vary with load more than speed. Under heavy load the magnitude of the currents produced will be higher and the sound, presumably, higher.
Now I would have thought the chopping rate would be higher but if I assume a maximum rotor speed of 10,000 rpm and a 4 pole motor that gives me at least 12 chopping interval per cycle (if I did the math right) and while that's sufficient I would have expected more.
There is nothing fundamentally different in the design of a SR as opposed to an IM motor that would make it more or less susceptible to this because the stators of each will be presented with sinusoidal wave forms synthesized by PWM (Puls Width Modulation is the name given to this technique). However some secondary aspect of the SR stator, such as its saliency, may make it more susceptible to the induced magnetostrictive vibrations.
Bottom line is that this is result of the design. I won't say it's a flaw because I don't hear it. But it is not something that can be fixed except by redesign. It's inherent in the way these cars work.
If anyone thinks that I wrote this based on an autopsy of a Tesla motor or a sit-down with one of their engineers, please disabuse yourself of that notion. It is pure speculation based on my limited understanding of the general practices in the EV industry today.
More to the point: what is it? I don't know, of course, but here's my guess. The cars contain 3 phase motors which work by chopping up the battery DC and sending the chopped DC to the stator coils in the motors (this is the case in both the synchronous and PM motors) such that a rotating magnetic field of desired phase, frequency and amplitude is produced. The chopping is done at a fixed rate and the frequency phase and amplitude are done by controlling the chopping duty cycle. To produce a low voltage, low frequency waveform one would start at a very low duty cycle and gradually increase it to a moderate duty cycle and then gradually lower it. This would produce a half sine wave of long period and moderate amplitude. Varying the duty cycle from low to high and then back to low again more rapidly would produce a higher voltage, higher frequency wave.
It's probably already obvious that I think the 4 kHz is the chopping rate. It is, in the linked spectrogram, really, really pure and nothing from the suspension or magnetic field harmonics would be so pure not to mention that there would be appreciable variation with speed which, if I have read the previous posts correctly, isn't there.
Thus it appears that stator current is being turned on and off at a 4 kHz rate. Leakage inductance would smooth that somewhat but every effort is made to keep leakage inductance down. Magnetostriction will thus cause the stator to vibrate at a 4 kHz rate with the intensity of the vibration varying as the duty cycle changes. Thus I would expect the loudness of the tone to vary with load more than speed. Under heavy load the magnitude of the currents produced will be higher and the sound, presumably, higher.
Now I would have thought the chopping rate would be higher but if I assume a maximum rotor speed of 10,000 rpm and a 4 pole motor that gives me at least 12 chopping interval per cycle (if I did the math right) and while that's sufficient I would have expected more.
There is nothing fundamentally different in the design of a SR as opposed to an IM motor that would make it more or less susceptible to this because the stators of each will be presented with sinusoidal wave forms synthesized by PWM (Puls Width Modulation is the name given to this technique). However some secondary aspect of the SR stator, such as its saliency, may make it more susceptible to the induced magnetostrictive vibrations.
Bottom line is that this is result of the design. I won't say it's a flaw because I don't hear it. But it is not something that can be fixed except by redesign. It's inherent in the way these cars work.
If anyone thinks that I wrote this based on an autopsy of a Tesla motor or a sit-down with one of their engineers, please disabuse yourself of that notion. It is pure speculation based on my limited understanding of the general practices in the EV industry today.
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