# Mechanical part of the electric drive as an object of control...

## Mechanical part of the drive as control object

The resulting equations of motion allow us to analyze the dynamic features of the mechanical part of the electric drive as an object of control. The basis for the analysis are structural diagrams, the form of which is determined by the accepted design scheme of the mechanical part. For example, we obtain a block diagram for a two-mass system.

To obtain the structural scheme of a two-mass elastic mechanical system, we differentiate the third equation of the system (2.24)

(2.26)

Next we put d/dt = p in equations (2.24) describing the two-mass elastic mechanical system, then

(2.27)

This system of equations corresponds to the structural scheme presented below.

Fig. 2.9. Structural diagram of a two-mass elastic mechanical system

The structural scheme shown in Fig. 2.9, gives an idea of ​​the mechanical part of the electric drive in the form of a two-mass elastic system as a control object. The driving force here is the electromagnetic moment of the engine M, and the perturbations are the moments of the load M, and M ". The adjustable variables can be the velocities & lt; y, and d) 2, the displacements & lt; p, and & lt; p2, and also the elastic bond loads M12. A detailed analysis of the properties of a two-mass mechanical elastic system as a control object is performed by the transfer function of the system, for example, by the frequency method of the theory of automatic control.

## Properties of forces and moments. Mechanical characteristics

Let us consider in more detail the properties of forces and moments acting on moving elements. By the nature of the action, forces and moments are divided into active and reactive [7].

Active forces are called forces or moments caused by external sources of mechanical energy external to the element and acting regardless of the direction of motion of the element. So, the forces or moments created in the engine and applied to its movable element entering the mechanical part of the drive will be active. In the future, we will allocate this group of active forces or moments, since their formation is an important function of the electric drive. The forces and moments of static loads due to the potential energy of the goods can be active, if there is a vertical component, with the energy of compressed springs, wind, water flow, etc., when moving them. A characteristic feature of active forces and moments is the independence of the direction of their action from the direction of motion. Thus, the static moment (N/c), due to the weight of the load, is always directed in one direction, both during ascent and descent (characteristic 1 'in Figure 2.10).

Reactive are the forces and moments that arise as a reaction to movement and are always directed against movement. A characteristic example is the forces and moments of friction (characteristic in the form of a broken line 1 in Figure 2.10): they always accompany the movement and always counteract it. Characteristic 1 refers to the executive organ of the production mechanism, the resistance at the motion of which is created, mainly, by friction forces. Therefore, this characteristic is also called the dry friction characteristic.

Fig. 2.10. Mechanical characteristics of production mechanisms

Reactive forces and moments are caused by inelastic deformation or any destruction of materials: cutting of metal, deformation of the ingot by rolling mill rolls, destruction of the rock by the bucket of an excavator, etc.

The forces and moments applied to the elements under consideration can depend on the time, spatial coordinate, and its derivatives. When considering the operation of the electric motor that drives the production mechanism, it is first of all necessary to determine the correspondence of the mechanical characteristics of the engine to the characteristic of the production mechanism. Therefore, for correct design and economical operation of the electric drive, it is necessary to study these characteristics.

The relationship between the angular velocity of rotation applied to the motor shaft and the moment of resistance of the mechanism is called the mechanical characteristic of the production mechanism co = f (M c ). Working machines and production mechanisms have different mechanical characteristics. The analytical expression establishing the change in the static moment of resistance from the angular velocity can be represented for the majority of working machines and mechanisms by the following empirical relationship:

(2.28)

where N/s - the moment of resistance of the production mechanism at a speed со; M " - moment of frictional resistance in moving parts of the mechanism; M cm is the moment of resistance at the nominal angular velocity of rotation x - an indicator characterizing the change in the moment of resistance when the speed changes.

The above expression allows us to classify the mechanical characteristics of production mechanisms in roughly the following main categories [7]:

1. The speed-independent mechanical characteristic is straight (characteristics 1 and 1 'of Figure 2.10). In this case x = 0 and the moment of resistance does not depend on the speed. Such characteristics are, for example, hoisting cranes, winches, feed mechanisms for metal cutting machines, piston pumps with constant feed heights, conveyors with a constant mass of transported cargo, and mechanisms with a moment of resistance as the main moment of resistance, as usually within the operating speeds The frictional moment changes little.

2. A linearly increasing mechanical characteristic (straight line 2 in Figure 2.10). In this case, when x = 1, the moment of resistance varies in direct proportion to the angular velocity. Such characteristics are, for example, the following mechanisms: pasto-producers, root cutters, various grain cleaning machines, direct-current generator drive with independent excitation, etc.

3. Nonlinearly increasing (parabolic) mechanical characteristic (curve 3 in Figure 2.10). When x = 2, the mechanical characteristic is parabolic, and the moment of resistance depends on the square of the velocity. Mechanisms with this characteristic are sometimes referred to as mechanisms with a fan torque, since in fans the moment of resistance depends on the square of the velocity. Mechanisms with parabolic mechanical characteristics also include centrifugal pumps, propellers, separators, threshing drums when they are idle.

4. A nonlinearly decreasing mechanical characteristic (curve 4 in Fig. 2.10). In this case, x = - 1 and the moment of resistance M s varies inversely with speed, and the power consumed by the mechanism, remains constant. Such characteristics are, for example, some turning, boring, milling and other metal-cutting machines, coilers in metallurgical production, etc.

These characteristics do not exhaust all practically possible cases, but give an idea of ​​the characteristics of some typical production mechanisms.

The mechanical characteristic of an electric motor is the dependence of its rotational speed or angular velocity on the torque n = DM) or co = f (M).

The degree of change in the speed of rotation with varying torque for different types of electric motors is not the same. The magnitude characterizing this change is called the stiffness of the mechanical characteristic (R)

The concept of rigidity can be applied to the mechanical characteristics of production mechanisms. These characteristics can be evaluated by rigidity

(2.30)

In the case of a nonlinear motor characteristic, the stiffness value is variable and is defined at each point as the derivative of the angular velocity. Linear mechanical characteristics have a constant stiffness.

Typically, in working areas, the mechanical characteristics of the engines have a negative stiffness p 0.

The mechanical characteristics of electric motors can be divided into three main categories depending on the rigidity (/ 3).

1. Absolutely rigid characteristic (characteristic, in which the angular velocity with the change of the moment remains unchanged). For example, the one shown in Fig. 2.11, the mechanical characteristic of 1 synchronous motor.

2. Rigid mechanical characteristic (characteristic, in which the angular velocity with the change of the moment, although it falls, but to a small extent). For example, shown in Fig. 2.11, the natural characteristic 2 of the DC motor of independent excitation and the working part of the natural mechanical characteristic 3 of the induction motor.

Fig. 2.11. The natural mechanical characteristics of the engines

3. A soft mechanical characteristic (a characteristic in which, with a change in angular momentum, the angular velocity changes significantly). For example, shown in Fig. 2.11, characteristic 4 of the DC motor of the series and the characteristic 5 of the DC motor of mixed excitation.

The mechanical characteristics considered in the aggregate determine the dynamic force or moment at any speed, i.e. acceleration. Due to this, it is easy to find the time dependence of the velocity in dynamic regimes. An important property of mechanical characteristics is that they bind variables whose product determines the power: P = Fv or P = We.

Each point of the mechanical characteristic uniquely determines both the intensity and direction of energy transfer. From all the above examples it follows that a positive sign of power characterizes the flow into an element of energy from an external source, and the negative sign indicates that it is spent by an element on the performance of work due to the influence of external forces.

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