Amperage v Speed on electric motors - exponential, linear or quadratic?

Question

Is it possilbe to work out the speed characteristics of a motor?
By using quadratic equations can the speed and amperage realtionship of motor be worked out.

For example if a lift is running at 1.0m/s at 50hz, 415v and 90 amps, then by turning the speed of the lift down to 0.75m/s, what would be relation between the other three electrical propertys.

Can this be done using quadratic equations or would other maths be required.

Iain T, quite right an AC invertor, DC lift are no longer in favour, too expensive and complicated

Answer 1

A motor with very small resistance(sa.01ohms) but which was mechanically prevented from rotating would carry a high current;as given by Ohms law (in the case of a DC motor).When such a motor is allowed to turn freely it will reach a speed so that the voltage given to it is very very nearly equal to that generated(induced into the coils) by the motors coil as they rotate.The point is this, induced voltage is of opposite sign to that provided to the motor,so oddly enough for a DC motor mechanical power output is nearly zero at zero speed and at Maximum speed.
IN THE CASE OF THE AC MOTOR YOU MENTION FOR THE LIFT, POWER INPUT(IN WATTS) IS APPROXIMATELY VOLTS times AMPS.
Obviously if the speed of the lift (with same mass) is reduced by 25% then power to the lift motor could be reduced by about the same %age.There are various ways this can be done but, simply,the frequency stays fixed and you reduce the voltage.In the end VoltsX amps for the reduced load situation will be 75% of the old(1.0m/s) situation.I would point out that AC circuits involve Power Factors and Phase Shifts;electrical engineers need some considerable grasp of maths not taught at O-level.

Answer 2

How have you reduced the speed of the lift?
I would expect a variable speed lift to have either a DC motor or an AC motor driven from an inverter.
Generally though, the power of a motor would vary with the square of the speed.
i.e. double the speed 4x the power or vice versa half the speed 1/4 the power. If the voltage is constant then it will be the current that varies with the power.

Answer 3

I think that the current is roughly proportional to the speed but you would need an electrical engineer to give you a definite answer. If I'm right then the current to run at 0.75m/s would be about 67.5A. Probably a little more as the motor needs some current just to keep itself running.

Answer 4

A quadratic has to have a squared variable in it, this would not. An exponential function has to have a variety or variable raised to a variable ability, this would not This one is linear - purely a variable that isn't raised to any ability (quadratic is raised to the flexibility 2.) answer: Linear

Answer 5

Depends on the flavour of the 3ph motor. Get a copy of Hughes Electrical Technology from the library or Amazon. It's the electrician's Bible.

Answer 6

You'd have to know the magnetic characteristics of the motor because as it spins, it acts as a generator and produces a voltage on the winding that opposes the applied voltage. You can't write a generalized equation.