Equation for mechanical motion

As it was mentioned above, elements of mechanical part of ED electric motor either rotate or move translatory with different speed, having different stiffness at it different masses or inertia moments, and in most cases the connections between them have spaces.

The availability of such particulars of ED mechanical part introduces definite disturbances into the process of motion transfer from electric motor to actuator mechanism and requires respective control.

Mechanical motion of any ED elements (as powerful as well as control elements) is described with the help of electromechanical laws. Primarily, that is the second Newton’s law, that describes the motion of material body.

If rigid body moves translatory, the law is:

(2.1)

if it rotates around its axis:

. (2.2)

Here , - vectors sums of forces and moments respectively, that act on a body.

, - mass and inertia moment of a body respectively;

, - acceleration and angular acceleration of a body that moves translatory or rotates respectively.

As on body motion around stationary axis or on translational motion of a body along linear axis all vectors are directed along one axis, then scalar values can be used in places of vector values.

Equation (2.1) and (2.2) enables to define the character of ED mechanical motion.

drive operates with constant speed or it is in a rest state. (2.3)

drive operates with acceleration (2.4)

Determination of dependence of motion speed in time and is accomplished by integrating of equations (2.1) or (2.2), and with this are to be set:

- mass and inertia moment;

- character of pulling forces or moments action.

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