The efforts directed toward ensuring long trouble-free operation of rotating machinery are in the focus of many scientific investigations. Electric power rotors and turbines, aircraft engines, automotive drive trains, kinetic energy storage systems are only few examples of machines that are to operate efficiently and safely. Very often they are imposed on external excitations, which are characterized by time-dependent characteristics and causing nonstationary random oscillations. In this paper, the dynamics of high-speed rotating rotor is analytically and numerically analyzed. The analytical investigations studied the steady-state vibrations in the neighborhood of resonance conditions of a rotor with 6 degrees of freedom in linear homogeneous elastoviscous field. Unstable frequencies zones are determined by “limited” power of an electric motor with linear characteristic and only one time constant. The analytical solution of the differential equations is implemented applying Bogoliubov–Mitropolski's asymptotical method in neighborhood of resonances. The analytical solution verifies the numerical dynamic model derived using a general purpose program system for computer code generation of the dynamic equation and simulation of motion of multibody systems of rigid and flexible bodies. It is regarded an unbalanced rotor attached to a flexible shaft and operating in elastoviscous field. Examples of the rotor in elastoviscous field with clearances in the bearings are presented.

A city bus with hybrid drive system was studied for its performance. The driveline under consideration consists of two alternative energy sources—an internal combustion engine (ICE) and kinetic energy storage (KES)—a hydrostatic transmission (HST), a drive axle and corresponding gears. A generalized law for HST control is obtained that satisfies kinematic and torque requirements for the alternative energy sources and the different modes of operation of the bus. A test stand was developed for validation of the chosen control strategy and for the energy flow simulations through the HST. The estimated maximum energy recovery potential is around 20–25%.

This paper examined the spectral properties of quadruple symmetric real functions. Theorem is formulated, under which the complex spectra of such symmetric functions are conjugated. The properties of the trigonometric functions are used in the proof of the theorem. Numerical results are presented for illustrating of the proven theorem.

The spectral properties of quadruple symmetric real signals are analyzed in the study. Six number theorems are formulated and proofed analytically in a capacity of central results of the research. Lasted theorem could be used to construct complex Fourier spectrum for arbitrary real function by even - odd decomposition. The theorem is illustrated numerically. The initial signal with length N (analogous values length interval or number of discrete samples) in the time domain is Fourier transformed through two spectral - real and imaginary parts with length N in the frequency domain. The real and imaginary parts of the complex Fourier spectrum of the initial signal, could be obtained by procedure, described in the paper. Spectral parts could be calculated by equivalent functions-signals. Even left and odd right equivalent functions-signals contain N/2 nonzero analogous values or discrete samples. This strategy allows constructing complex Fourier spectrum of the initial signal with length N in the time domain based on equivalent real and imaginary spectral parts with the length N/2 in the frequency domain. The study is an extension and resume of AMC 221(2013) pp. 344-350.

The chapter proposes and analyzes a differential variable transmission (DVT) with a wide range of regulation satisfying, relatively small part of the input power to be transmitted by the friction joints, and a high mechanical efficiency and lack of “circulating” power are determined. To meet these requirements, it is to connect a classic variable transmission (CVT) as a closing unit in a differential gear mechanism with externally-internally engaging wheels and guide (AI—planetary gear) has been proposed. The transmission, as well as the conditions for the lack of “circulating” power, is determined. The synthesis of a friction variator with theoretically zero geometric sliding between the working surfaces when changing the transmission ratio is introduced, that is, the adjustment takes place with centroid rolling. The working surfaces are obtained by rotating the centroid pairs around their axes, provided that their point of intersection always lies on the common tangent of the two contours. With the help of elements of differential geometry, the first order system equations have been derived and solved in an analytical form, whose integrals uniquely define the centroid pairs.