Page 88 - Robotics Designing the Mechanisms for Automated Machinery

3.3 Electric Drives 77

FIGURE 3.14 Characteristic of an AC
induction motor: torc^ue versus speed of
the rotor.

s m = the slip value at the point of maximal torque, and
0) = speed of the rotor.
For example, we consider an electromotor with parameters:

The characteristics of this motor will have the form shown in Figure 3.14a). (We
created the figure using the MATHEMATICA language as follows:

zO=Plot[471 (314-w)/(2218+(314-w)A2),{w,0,314},AxesLabel->{"w","T"}]).
Then we can answer the natural question: how will the process of acceleration of
a system driven by such a motor develop?
2
Assuming the moment of inertia of the system I - 0.075 kg m and neglecting, for
this example, the resistance, we formulate the equation of motion in terms of MATH-
EMATICA as:
f20=.075 w'[t]- 471 (314- w[t])/(2218+(314-w[t])A2)
j20=NDSolve [|f20==0,w[0]==0}, {w[t] },{t,0,10},MaxSteps-> 1500]
y20=Plot[Evaluate[w[t]/.j20],{t,0,10}^xesLabel->{"t"/'w"},
Frame->True,GridLines->Automatic]

One can see in Figure 3.14b) that in 10 seconds the system reaches the maximal
rotation speed of about 300 rad/sec.

FIGURE 3.!4a) Characteristics of an
asynchronous motor.