Models of the mechanical part of the electric drive
In the design and engineering calculations, the mechanical part of the drive is replaced by a model that, on the one hand, should be fairly simple, and on the other hand - reflect the basic physical processes of the real object. It should be borne in mind that one object corresponds to arbitrarily many models. All of them reflect different aspects of it, different properties, features. Models can be very good when they are exhaustively complete, laconically, convincingly reflect exactly those properties of the object that the engineer needs in this task; can be just good, when they have everything you need, but there is something superfluous; and can be bad - inadequate, reflecting not everything or not. A very important task of the engineer, the researcher is to prove the adequacy of the adopted model.
The choice or development of a model, first of all, depends on the specific purpose, the problem being solved. In practice, as a rule, we have to solve the following problems.
The first task : the mechanical part of the drive and the installation as a whole exist, and it is required to find the best in some sense means and algorithms for controlling the movement of the working body (technological process) or supplement existing in connection with the new working conditions.
It's easy to see that this type of tasks is a huge amount, and they often have to be solved not by electric professionals, but by engineers of related specialties. The solution can be based on simplified models of the mechanical part, built on the basis of available information about a specific installation.
The second task: The mechanical part of the drive is not completely defined, some of its elements are supposed to be replaced, providing the specified requirements for the movement of the working element and, possibly, some new useful properties.
The third task: creates a new installation and, accordingly, its electric drive. It must provide all the requirements for the movement of the working organ, and, obviously, it must be better than some analogues (sometimes in many ways): it is more reliable, economical, has better design, etc. It is already a difficult task, and its solution is the work of a team of specialists of various profiles. It will require a whole system of models, it is clear that some of them will concern the provision of the required quality of motion.
So, in all the above problems, both simple and very complex, one can easily see the general: the required quality of the movement of the working element must be guaranteed.
Thus, the models of the mechanical part should be used, which establish in an extremely simple form the relationships between the parameters of the elements connected in a certain way, the acting forces and moments, and the signs of motion-position, speed, acceleration. Such models should allow us, on the basis of known or given parameters and variables, to confidently find unknowns.
The resulted mechanical link of the electric drive
The mechanical part of the electric drive, as noted earlier, consists of several links and can be a complex kinematic chain with a large number of moving elements.
Assume that the mechanical part consists of absolutely rigid, undeformable elements and does not contain any gaps. In this case, the motion of one element gives complete information about the motion of all the other elements, that is, the functional dependencies that correspond to the laws of motion of all links in the kinematic chain of the drive are proportional to each other, and from the motion of one element one can go over the previously known relationship between the coordinates to the motion of any another element. Thus, the motion of the electric drive can be viewed on any one mechanical element to which all external moments or forces are listed, as well as all inertial masses of the mechanical links. Usually an engine shaft is taken for such an element.
Bringing the moment of resistance from one axis of rotation to another can be made based on the energy balance of the system. At the same time, the power losses in the intermediate gears are taken into account by the introduction of the corresponding efficiency factor into the calculations (). We denote by the angular velocity of the motor shaft, and - the angular velocity of the shaft of the production mechanism. On the basis of power equality we obtain:
where - the moment of resistance of the production mechanism, N m; - the same moment of resistance, reduced to the speed of the motor shaft, N m; - gear ratio.
Bringing the forces of resistance is done similarly to the reduction of the moments. If the translational velocity v, and the angular velocity of the motor shaft , then
where - the resistance force of the production mechanism, N.
Hence the moment of resistance reduced to the speed of the motor shaft is:
In the case of bringing the rotary motion to translational, the reduced force to the working member of the mechanism is determined as
The reduction of inertial masses and moments of inertia of the mechanical links to the motor shaft is that these masses and moments of inertia are replaced by one equivalent moment of inertia () on the motor shaft. The reduction condition is the equality of the kinetic energy determined by the equivalent moment of inertia, the sum of the kinetic energies of all the moving elements of the mechanical part of the drive, i.e.
where - moment of inertia of the motor rotor, kgm2; - moment of inertia i of the rotating element, kgm2; - the mass of its progressive element, kg; - gear ratio of the blade reducer of the engine to the i-th rotating element; - the radius of reduction of the progressive moving element to the motor shaft, m.
Equivalent moment of inertia () is called the resulting or total reduced moment of inertia of the drive. To calculate the given moment of inertia of the system, the moments of inertia of the rotating elements are divided by the square of the gear ratio of the kinematic scheme between these elements and the motor shaft, and the masses of the translational masses are multiplied by the square of the reduction radius and the resulting calculation results are added together with the moments of inertia of the engine and the elements rotating from it speed.
Examples of rotating elements in the mechanical part of the drive are, in addition to the motor rotors, couplings, brake pulleys, drums, swivel platforms of excavators and cranes. Progressive elements include bridges, trolleys and lifting cranes; stands, ski lifts; conveyor belts; the slider of the crank mechanism, etc.
It follows from formula (2.4) that in general the mechanically complicated kinematic part of the electric drive can be replaced by some equivalent or reduced mechanical link shown in Fig. 2.3. This link is a solid body rotating around its centerline at the speed of the engine, which has a moment of inertia () and is affected by the moment of the engine (M) and the moment of resistance ().
The obtained simple model of the mechanical part of the electric drive in the form of a single-mass system is valid, as noted earlier, for ideal mechanical links without elasticity and gaps. However, it can be retained in most practical cases and for real mechanical links that have small gaps and little mechanical elasticity.
In some cases it is of interest to find the laws of motion directly on the working part of the production machine. Such tasks often arise for hoisting-and-transport machines with a progressive moving body. In this case, the reduction is carried out to the working body with the same conditions. Inertial masses in this case are replaced by one resulting mass () on the working part of the mechanical part of the drive:
Fig. 2.3. The resulted mechanical link of the electric drive
where is the radius of the cast.
Thus, the reduced mechanical link in the considered case is a translationally moving mass (), defined by the formula (2.5), to which two forces are applied:/and
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