Hi Mick,
I don't understand why we are getting 4397w when the motor is rated at 3000w
Nor do I but you provided the torque and speed figures. The shaft output is just that, it has no bearing on the electrical
means by which it was generated and the calculation is exactly as Isaac Newton proposed.
My guess is that the torque figure supplied was somewhat higher than its 'rated torque' The motor does not just stop when its gets
to its rated torque, if the drive produces yet more current the motor will produce yet more torque and therefore power to the load. Over a period
of time you might expect it to overheat. The 'rated' output is more about a thermal condition rather than an absolute limit.
There are two figures of merit that apply to servos which can be relied on to produce accurate numbers. The first, called the torque constant or Ka
is in so many 'Nm per Amp' Thus if a motor is supplied 10A and its Ka is 0.95 Nm/a then its torque at that operating condition is 9.5Nm.
The second is called the back EMF constant or Kv in so many 'Volts per 1000 rpm' or some other equivalent units. Thus a motor spinning at 2000 rpm
with a Kv of 100 V/1000rpm will have a back emf of 200V. If our supply is 230V, the motor cannot run much faster as the back emf is close to defeating
the applied voltage.
The two numbers relate very much to the design and construction of the motor. In general we want Ka to be high, that is a motor than can produce
a lot of torque from a small current. For instance you might decide to have a high number of turns in the stator so that it produces a strong magnetic
flux for a given current and choose high strength rare earth permanent magnets for the armature.
Both of these however increase Kv also, and as we have seen its the back emf that determines the motors top speed for a given input voltage.
You came across an example yesterday where a servo produced high torque up to 2600rmp and then seemed to die. The Kv figure is such that the servos top
speed with 230V input is 2600 rpm. To get it to go faster you have to artificially manipulate its Kv, which can be done, within limits, with field oriented control
with a technique called field weakening.
Craig