Heavy-mass Mechanical Systems

Bringing the real scheme of electric drive to mechanical part with computed one the rigidity of elements was neglected. Actually elements of mechanical part of electric drive have specified final rigidity (in the previous article the rigidity of elements was infinite), so that under definite loads they are deformed (in the limits of resilient deformations). Referring to above considered scheme of mechanical part for lifting pullies of electric drive, we mean cable K and shafts that connect drive with reduction gear and reduction gear with drum. For consideration of influence of such deformation the notion of rigidity factor for elastic elements is entered. At reciprocative motion the character of rigidity factor is linear C_l. At rotational motion the feature of torsion rigidity factor is C_t. One rigid element of real scheme is considered for two-mass scheme. For three-mass – two rigid elements of real scheme.

For rigid elements that moves reciprocally the rigidity factor C_l is a factor of proportionality between linear deformations of element and force that arise in it when stretching and pressing

, []

Where F – force that arises in the rigid element when its stretching or pressing, (N);

∆L – linear deformation of element when its stretching or pressing, (g).

For elastic element (shaft) at torsion the rigidity factor C_t is a factor of proportionality between angular deformation of shaft and moment that arises in it

, [N^.m]

Where M_n – moment that arises on a rigid element (shaft) at torsion, [N·m];

∆φ – angular deformation of shaft at torsion, [rad].

Two-mass computation mechanical system will be available in the case when one rigid element of real kinematic scheme is considered. Such computation system has the view

Figure 2.4 – Two-mass computation mechanical system

Frequently the first mass is formed with a mass of movable parts of electric drive (rotor) and a mass of other elements of mechanical part of electric drive between electric motor and rigid element G. Another mass II is formed with a mass of actuating mechanism and a rigid element G. Both inertia masses (I and II) are connected with a rigid element G with a rigidity factor C_i.

The motion of two-mass system is sufficiently complex and in most cases has oscillation character. This oscillations are determined with energy exchange between masses I and II through rigid element G. At that the phenomenon of mechanical resonance may occur.

Three-mass mechanical systems have more complicated motion, when the rigidity of two elements of mechanical part of electric drive is considered (not like in two-mass systems – only one element is considered).

Heavy-mass computed schemes may be obtained in many other cases, for example when δ spaces between elements of mechanical part of electric drive are considered. Availability of such spaces results in non-linear character of motion that significantly makes computation of such schemes difficult.

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