Dynamics of Electromechanical Systems Containing Long Elastic Couplings and Safety of Their Operation

The electromechanical systems under analysis include electric drives, working machines that perform specific tasks in the technological process, and working mechanisms that transmit mechanical power between the electric drive and the working machine. The vast majority of electric motors included in drive systems require rotational speed control. This task is most often performed with the use of closed-loop control structures based on speed controllers. A step or overly rapid change in the speed reference causes a temporary lock of the speed controller due to the applied limitations at its output. Particularly, unfavorable effects of such a lock can be observed in drive systems in which there is a long elastic coupling (transmission shaft) between the electric motor and the working machine. As a consequence, shaft torsion and accompanying twisting moments of considerable amplitudes appear. This article proposes an uncomplicated active torque limiter structure, which enables the uninterrupted operation of the speed controller thanks to the automatic adaptation of the rate of the speed reference change to any moment of inertia of the rotor and attached rotating masses. The results of the investigations confirm the effectiveness of the proposed structure.

Free vibration analysis of nonsymmetrically laminated cross-ply L-shaped frames

Fiber-reinforced composite laminates can be tailored to produce structural elastic couplings that optimize their response in dynamic environments. It is therefore essential that the free vibration characteristics of structural elements fabricated from fiber-reinforced composites be accurately modeled and investigated. In this work, an analytical wave-based approach is extended to study the in-plane vibrations of nonsymmetrically laminated cross-ply L-shaped frames. The proposed theory accounts for the effects of shear deformation, rotary inertia, and the elastic coupling between in-plane bending and longitudinal deformations. The reflection matrices at the boundaries, together with the reflection and transmission matrices at the corner joint of the L-shaped frame are derived. A traveling wave approach is then used to systematically assemble the small-order matrices into a single expression that can be used to efficiently calculate the exact natural frequencies. An expression for evaluating the mode shapes of the frame for general boundary conditions is also given. The application of the wave-based method is illustrated through several numerical examples and the results are validated using independent finite element models. As part of the numerical analysis, the influence of the number of cross-ply layers on the natural frequencies is investigated.

Actively Driven Fluctuations in a Fibrin Network

Understanding force propagation through the fibrous extracellular matrix can elucidate how cells interact mechanically with their surrounding tissue. Presumably, due to elastic nonlinearities of the constituent filaments and their random connection topology, force propagation in fiber networks is quite complex, and the basic problem of force propagation in structurally heterogeneous networks remains unsolved. We report on a new technique to detect displacements through such networks in response to a localized force, using a fibrin hydrogel as an example. By studying the displacements of fibers surrounding a two-micron bead that is driven sinusoidally by optical tweezers, we develop maps of displacements in the network. Fiber movement is measured by fluorescence intensity fluctuations recorded by a laser scanning confocal microscope. We find that the Fourier magnitude of these intensity fluctuations at the drive frequency identifies fibers that are mechanically coupled to the driven bead. By examining the phase relation between the drive and the displacements, we show that the fiber displacements are, indeed, due to elastic couplings within the network. Both the Fourier magnitude and phase depend on the direction of the drive force, such that displacements typically propagate farther, but not exclusively, along the drive direction. This technique may be used to characterize the local mechanical response in 3-D tissue cultures, and to address fundamental questions about force propagation within fiber networks.

DIFFERENTIAL EQUATIONS FOR TRAIN STARTING WITH ELASTIC CONNECTIONS

The starting mode for the train is the most difficult. An effective method of pulling is the selection of coupling clearances. In this case, the cars are set in motion sequentially and the inert mass, as well as the static friction force immediately at the moment of starting, are minimal. This method has two significant drawbacks - a small fixed value of the gaps in the couplings and the shock nature of the impulse transfer. These disadvantages can be avoided by using elastically deformable couplings. The aim of this work is to construct a mathematical model of "easy" starting of a train with elastic couplings. The softening of the train start-off mode is essentially due to the replacement of the simultaneous start-off of the sections with alternate ones. To exclude longitudinal vibrations of the composition, after reaching the maximum tension of the coupling, the possibility of its harmonic compression should be mechanically blocked.