MATHEMATICAL JUSTIFICATION OF STABILITY OF STEERING BRIDGE OF WHEELED TRACTOR

The article deals with the influence of wheel oscillation and the micro-profile of the road surface on the stability of the wheel tractor axle movement. The reasons for the oscillations of the steered wheels, the design diagram of the controlled axle of the tractor and the sequence for determining the oscillation frequency of the axle of the tractor are presented. The reasons for the oscillation of the steered wheels are collisions with bumps, imbalance of the wheels and a double connection with the tractor frame through the steering system and the fastening of the steering axle beam. The most common functions for describing road irregularities that affect the movement of a tractor are the mathematical expectation and the average value of the ordinates of the micro-profile, the variance or standard deviation of the ordinates, the correlation function characterizing the relationship of various implementations of the micro-profile functions along the length of the road section and spectral density. Oscillations of the steered wheels have a side effect on the stability of the tractor, which leads to oscillations of the steered axle due to the presence of an additional degree of freedom (turning around the pivot) in comparison with uncontrolled ones. In addition, the steered wheels are interconnected by a steering linkage, which is damped due to clearances. Oscillations of the wheels can also occur due to the fact that the radial (normal) stiffness of the tires around the circumference is not the same. When such a tire rolls, the wheel begins to oscillate in a vertical plane. Such oscillations, performed due to changes in the parameters of the oscillatory system, are called parametric. Self-oscillations of the steered wheels cause significant dynamic loads on the steering parts, intense tire wear and lead to a loss of tractor controllability and driving stability. One of the main reasons for the occurrence of oscillations of the steered wheels is the presence of a gyroscopic relationship between the angular oscillations of the beam of the steered bridge in the transverse plane and the rotation of the wheels of this bridge relative to the pins. The article also discusses the physical essence of the processes occurring during self-oscillations of the tractor's controlled wheels.

Numerical Simulation of Interaction Between Kr+ Ion and Rotating C60 Fullerene Towards for Nanoarchitectonics of Fullerene Materials

Dynamics of charged fullerene in a surface layer of fullerite is studied under the influence of neutral or charged particles of the gas phase surrounding the fullerite material. The translational displacements of the nodes of the crystal lattice structure are determined by the equations of motion of the centers of mass of fullerenes. Central fullerene, which is described as a discrete set of sixty carbon atoms, plays a special role in the presented mathematical model. Angular oscillations and rotations of the central fullerene are described by the dynamic Euler equations. All other fullerenes have a centrally symmetric field of the potential of interaction with the surrounding atoms and molecules. In this regard, we use the hybrid discrete–continuous mathematical model with four potentials that describe the interactions between the surrounding fullerenes, smoothed fullerene and an atom, a pair of atoms, and electric charges. The results of a numerical study of influence of the Coulomb interaction on the rotational and translational motion of the C60 fullerene are presented.

Dynamics of a DC Motor-Driving Arm with a Circular Periodic Potential and DC/AC Voltage Input

In this paper, we investigate the dynamics of an electromechanical system consisting of a DC motor-driving arm within a circular periodic potential created by three permanent magnets. Two configurations of the circular potential appear when one varies the positions of the magnets and the length of the DC motor, respectively. Two different forms of input signal are used: DC and AC voltage sources. For each case, conditions under which the mechanical arm can perform a complete rotation are obtained. Under the DC voltage excitation, the arm oscillates and then is stabilized at an equilibrium position for a DC voltage lower than a critical value [Formula: see text]. When the DC voltage is higher than the critical value [Formula: see text], the arm performs large amplitude motions (complete rotation). Submitted to an AC voltage with amplitude lower than a critical value, the mechanical arm exhibits sinusoidal oscillations around the equilibrium position [Formula: see text] with amplitudes less than one turn. Angular oscillations with amplitudes greater than one turn are observed when the voltage amplitude is higher than the critical value. Bifurcation diagrams show that the simple system can enter chaotic regime with the amplitudes of angular oscillations varying erratically from small to high values.

Issues of Synthesis and Practical Evaluation of the Compensation Mode Error of a Two-Component Gyroscope

The paper introduces the results of studying the characteristics of various dynamically tuned gyroscopes operating in the mode of a variable rate sensor. Within the study, we determined the dependence of the dynamic error of the rate sensor on the amplitude and frequency of angular oscillations of the gyroscope body. We analyzed the methodological and hardware support for evaluating the dynamic error of a dynamically tuned gyroscope — the rate sensor in order to reduce its influence on the operational characteristics of the device. To experimentally research and practically evaluate the dynamic error of the dynamically tuned gyroscope — the rate sensor, we proposed a design of the rotary vibration test bench, developed requirements for it, and calculated its elastic-mass characteristics.

Nonlinear oscillations of the interface of two liquids at the angular oscillations of the tank

The development of rocket and space technology in recent years has led to the widespread use of various cryogenic liquids. To increase the shelf life of cryo-products on board spacecraft or in tankers of future space filling stations, it is proposed to create a certain stock of cryo-product, which is simultaneously in a two-phase or three-phase state and forms layers of liquid. The paper considers the problem in a nonlinear formulation about the oscillations of the interface of a two-layer liquid in an arbitrary axisymmetric cavity of a solid body performing angular oscillations around a horizontal axis. For the considered class of cavities with an arbitrary bottom and a lid, the nonlinear problem is reduced to the sequential solution of linear boundary value problems. Nonlinear differential equations describing the oscillations of the interface between two liquids in the vicinity of the main resonance are obtained. In the case of a circular cylindrical cavity with flat bottoms, solutions of boundary value problems in the form of cylindrical functions were used to calculate linear and nonlinear hydrodynamic coefficients depending on the depth and density of the upper liquid.

Mathematical modeling of centrifugal machines rotors seals for the purpose of assessing their influence on dynamic characteristics

With an increase of equipment parameters, such as the pressure of the sealing medium and the speed of shaft rotation, the problems ensuring its hermetization efficiency are rising up. In addition to hermetization itself, the sealing system affect the overall operational safety of the equipment, especially vibratory. Groove seals are considered as hydrostatodynamic supports capable of effectively damping rotor oscillations. To determine the dynamic characteristics, models of grooved seals and single-disc rotors with grooved seals are examined. The obtained analytical dependences for computation of dynamic characteristics for the hydromechanical rotor-seals system, describing radial-angular oscillations of the centrifugal machine rotor in groove seals are presented as well as the formulas for computation of amplitude frequency characteristics. An example for the computation dynamic characteristics of one of the centrifugal machine rotor models is drawn.

A Model for Performance Estimation of Flapping Foil Operating as Biomimetic Stream Energy Device

During the recent period intensive research has focused on the advancement of engineering and technology aspects concerning the development and optimization of wave and current energy converters driven by the need to increase the percentage of marine renewable sources in the energy-production mix, particularly from offshore installations. Most stream energy-harvesting devices are based on hydro-turbines, and their performance is dependent on the ratio of the blade-tip speed to incident-flow speed. As the oncoming speed of natural-occurring currents varies randomly, there is a penalty for the latter device’s performance when operating at non-constant tip-speed ratio away from the design value. Unlike conventional turbines that are characterized by a single degree of freedom rotating around an axis, a novel concept is examined concerning hydrokinetic energy converters based on oscillating hydrofoils. The biomimetic device includes a rotating, vertically mounted, biomimetic wing, supported by an arm linked at a pivot point on the mid-chord. Activated by a controllable self-pitching motion the system performs angular oscillations around the vertical axis in incoming flow. In this work, the performance of the above flapping-foil, biomimetic flow energy harvester is investigated by application of a semi-3D model based on unsteady hydrofoil theory and the results are verified by comparison to experimental data and a 3D boundary element method based on vortex rings. By systematical application of the model the power extraction and efficiency of the system is presented for various cases including different geometric, mechanical, and kinematic parameters, and the optimal performance of the system is determined.

Assessment of a Hydrokinetic Energy Converter Based on Vortex-Induced Angular Oscillations of a Cylinder

Vortex-induced oscillations offer a potential means to harness hydrokinetic energy even at low current speeds. In this study, we consider a novel converter where a cylinder undergoes angular oscillations with respect to a pivot point, in contrast to most previous configurations, where the cylinder undergoes flow-induced oscillations transversely to the incident free stream. We formulate a theoretical model to deal with the coupling of the hydrodynamics and the structural dynamics, and we numerically solve the resulting nonlinear equation of cylinder motion in order to assess the performance of the energy converter. The hydrodynamical model utilizes a novel approach where the fluid forces acting on the oscillating cylinder are split into components acting along and normal to the instantaneous relative velocity between the moving cylinder and the free stream. Contour plots illustrate the effects of the main design parameters (in dimensionless form) on the angular response of the cylinder and the energy efficiency of the converter. Peak efficiencies of approximately 20% can be attained by optimal selection of the main design parameters. Guidelines on the sizing of actual converters are discussed.