The equation of mechanical motion
According to Newton's second law (1687), transformed for bodies of revolution:
where M is the moment of motion, N • m; - the moment of resistance, N • m; - the dynamic moment, N • m.
Equation (2.1) in the electric drive has also been called the "equation of motion". According to the equation of motion, if , and the drive is in a state of acceleration. If , then - the electric drive decelerates or decelerates. And, finally, if , then - the drive is at rest or steady steady motion.
Thus, the dynamic moment is manifested and operates only in transient modes during acceleration and deceleration of the electric drive. That is, when the kinetic energy of the electric drive changes. The expression for determining the dynamic moment is found from the equation determining the kinetic energy reserve in the rotating body:
where is the moment of inertia of a body having mass m, kg · m2;
r - the radius of a rotating body of a regular cylindrical shape, m.
The power that rotating masses receive during acceleration of the electric drive or give at braking:
Then the dynamic moment can be found from the expression
The equation for determining the dynamic moment consists of two components: the first of them determines the change in the dynamic moment with the angular velocity m of the electric drive, the second - with the change of its moment of inertia J
In the electric drive, the change in the moment of inertia is observed in the mechanisms of robots or manipulators, in the event that during their rotation around the central axis the outstretch of the hand changes. An example showing the change of the moment of inertia during the rotation can be observed in skaters performing the "rotation" element. Holding the hands to the body during rotation, the skater reduces his own moment of inertia. Since the kinetic energy does not change in this case, its rotational speed increases sharply. When designing electric drives, it must be remembered that the same processes occur in the kinematics of some types of electric drives.
In those cases when the moment of inertia of the drive J does not change with time, the second term on the right-hand side of equation (2.4) is neglected and the dynamic moment is determined from the expression
Thus, the dynamic moment in an electric drive is manifested in most practical cases only when accelerating or decelerating.
The moment of motion in an electric drive usually provides an electric motor and only in some cases - the working mechanism of the production mechanism, and the electric machine brakes it, ensuring the uniform motion.
The moment of motion of the M electric machine is a function of its speed ω. The relationship between the speed ω of an electric machine and its moment is called a mechanical characteristic.
The mechanical characteristics of electrical machines are depicted in the form of graphs in the right Cartesian coordinate system (Figure 2.1).
Fig. 2.1 . Mechanical specifications
For convenience of considering the processes occurring in the electric drive, one of the two possible directions of engine rotation is considered positive. As a rule, for a positive direction of rotation of the engine, a rotation coincides with the direction of rotation of the clockwise arrow. Take the moment of the electric motor with the same sign as the angular velocity, if their directions coincide. In electric drive systems, the main mode of operation of an electric machine is the motor mode. The motor operating mode of the electric machine is located in the first and third quadrants. Generator operating modes of the electric machine are located in the second and fourth quadrants.
In steady state operation, the moment of resistance has a retarding character and acts towards the engine torque. For the sake of simplicity of finding the steady-state operating mode of the electric drive, assume for positive direction of the moment of resistance , opposite to the positive direction of the motor torque. In Fig. 2.1 the steady-state value of the speed is determined in accordance with formula (2.1) with the absolute value of the moment of motion M and the moment of resistance
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