Page 96 - Robotics Designing the Mechanisms for Automated Machinery

3.3 Electric Drives 85

When the drive is supplied by an asynchronous induction motor, we substitute Equa-
tion (3.48) into Equation (3.41). Here again, we will discuss the simplest case when
T r = 0. Thus, we rewrite Equation (3.41) in the form

Remembering the definition of slip given above, we obtain, instead of Equation (3.79),
the expression

Denoting (2T ms mco^ jl=A and s^cvo =B,we rewrite Equation (3.80) in the form

After obvious transformation, the final result can be obtained in the form:

For a synchronous motor the driving speed (as was explained above) remains coi
slant over a certain range of torques until the motor stops. Thus,

Q) = a> 0 - constant.
To reach the speed a> 0 from a state of rest when CD = 0, an infinitely large acceleratic
must be developed. To overcome this difficulty, synchronous motors are started in tf
same way as are asynchronous motors. Therefore, the calculations are of the same soi
and they may be described by Equations (3.79-3.82), which were previously applic
to asynchronous drives.
For the drive means of stepper motors, we must make two levels of assumptio
First, we assume that the stepper motor develops a constant driving torqu
Td=T 0 = constant (the higher the pulse rate, the more valid the assumption), which
the average value of the torque for the "saw"-like form of the characteristic. Then, fro]
the basic Equations (3.41) and (3.49), we obtain for the given torque characteristic tr
following equation of the movement of the machine:

Rewriting this expression, we obtain

The solution consists of two components, co = co l + (O 2. For the solution of the homo-
geneous equation we have