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# Can someone walk me through the math of not exploding a 12V rated motor with a 48V battery? Answered

I have a machine with a 12V motor. I have a battery that supplies 48V. I want to run the machine with the battery and NOT have the machine explode.

If I get a speed control that can handle 48V, is it a simple as making sure I don't run it higher than 25%?

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Thank you all for the responses.

Yes, I meant a PWM module, something "cheap and simple" like what you would find on Amazon by typing "DC speed control". Usually it is an H-bridge chip with a frequency generator onboard.

In reality, I have a 24-36V 600W Scooter motor and I have a 54V Lithium Ion Battery from the Ego Lawnmower (math was simpler with 12 and 48). What is the cheapest way to run A with B? .Then, if I plug it in and it overheats, etc. How much do I turn it down and more importantly, Why will turning it to X% duty cycle work?

I didn't want to use a DC-DC converter to convert from 48V to 12V, then use PWM to chop up that 12V to whatever the coil voltage should be. I haven't found any constant voltage speed controls though, I'll look that up. All I found usually put out what they are input...

The promise of PWM is that a PWM signal is almost the same thing as its average value.

Moreover the average value of a PWM signal is easy to calculate. If the signal only has two possible instantaneous voltages, Von, or Voff=0, then the average value works out to:

Vavg = (Von*Ton + Voff*Toff)/(Ton+Toff)

= (Von*Ton + 0)/(Ton+Toff) = Von*Ton/(Ton+Toff)

= Von*D

where D=Ton/(Ton+Toff) is a unitless quantity called, "duty cycle". Basically D is the fraction of the time that signal is on.

By the way, the average value of a signal is the same thing as its "DC part", or the "zero frequency" part.

So if you believe in low-pass filters,

https://en.wikipedia.org/wiki/Low-pass_filter

there exists the possibility you could use one of those to filter a PWM signal, and the only thing that would emerge from the output of this filter, is just the DC part, just the average value.

Often the low-pass filter, is there naturally, or maybe by design.

As an example I am going to point to the Wikipedia article for "Buck converter", in particular the circuit shown in figure 2.

https://en.wikipedia.org/wiki/Buck_converter

The inductor and capacitor on the right side of the circuit, those kind of look like a low-pass filter, and I am going to just claim that is what they're doing.

Also if you look at the equations in the text, there is one that is kind of familiar, namely,

Vout = Vin*D

where D is duty cycle.

That is the best, brief explanation, I can come up with for why PWM works.

I mean that is the theory.

There is also something I wanted to mention about power converters in practice.

The most important thing, is the cost, also size and weight, of a power converter tends to scale with the amount of power (in watts) that it throughputs.

Also for electricity, power is the product of two numbers. It is voltage (in volts) multiplied by current (in amperes).

I mean it will probably be easy to find an inexpensive PWM module, or buck converter, capapable of 60V input, at 2 or 3A.

But if you want the same thing at 20 or 30A, the amount of money they want for it, is going to get big quickly.

I forgot to mention: PWM is not the only thing under the sun.

There also exist switching power converters that use feedback to give constant output voltage, and using something like that would certainly give you a stiff (meaning low internal series resistance) 12 volt supply.

Also it is possible to sense the motors speed, with a speed sensor, and feedback from that signal, for an application that truly requires constant speed.

You speak of this thing called, "a speed control", but what is that really? Does it truly control speed, or something else, like voltage, or PWM duty cycle?

For example, I think most people call the trigger on a cordless drill, "a speed control", but in truth that is just a PWM kind of scheme; i.e the amount of duty cycle (from 0 to 100%) is proportional to the distance the trigger is depressed.

I think it is almost as simple as you suggest, assuming the thing you call a, "speed control" is some kind of PWM (pulse width modulation) switcher, and your words, "don't run it higher than 25%", refer to the duty cycle of that PWM waveform; i.e. on 25% of the time, and off 75% of the time.

The only other complication I can think of, is the internal series resistance of the battery. You know, the output voltage from your 48 volt battery, when it is supplying current, will be lower than 48 volts, by the voltage drop across that internal series resistance.

In a previous answer, Toga_Dan suggests actually putting a voltmeter across the motor, for to monitor the voltage across it, to see if the, what you call, "speed control", is doing you what you expect it to do; i.e. limiting the average voltage across the motor to a value less than 12 volts, and this is good advice. It is always good to measure, and confirm your devices are doing what you expect them to do.

I don't think it'll be that simple.
Some speed ctrls change the frequency.
If it were mine, I would put a meter on the ctrl with no load. gradually adjust from 0 to 100% while watching the V. A
Assuming that V is controlled, hook up the motor, and again gradually ramp it up from zero while watching the meter. Even then im not 100% sure your motor and ctrl are safe. Also look at amp ratings.