Resonance Zone Research Articles

Diagnostic of spindle units on rolling bearings based on measuring of the housing vibrations

The analysis of modern methods of accuracy and technical condition evaluation of spindle units on rolling bearings has been performed. The prospectivity of measurements in the resonant vibrations zones is assessed. To evaluate the accuracy and technical condition of spindle units on rolling bearings at the stages of manufacturing and maintenance, it is proposed to use the previously developed method for indirect measurement of resonance vibrations of the spindle, based on spindle quill vibration measurement of the spindle units with subsequent calculation of spindle vibrations (mandrel installed in the spindle) using theoretical compliance function. Usage of this method in accuracy and diagnosing defects identification in manufacturing and assembly of the spindle units, a theoretical justification of the measurement schemes is given, the dynamic model of the test rig is adapted, and the corresponding research methods are developed. The general experimental part of research methods provides for: determining the first natural frequency of the test rig frame; determination of spindle speeds corresponding to frame resonant vibrations as a result of manifestation of manufacturing and assembling defects of the spindle unit; spindle quill vibrations measurement at these rotational speeds. The general theoretical part of the methods assumes: the calculation of dynamic compliance and the compliance function which connects mandrel and spindle quill subsystems vibrations; mandrel vibration spectra calculation from the experimental vibration spectra of the spindle quill and determination of the relative vibrations amplitudes of the mandrel at the forced vibrations characteristic frequencies. Based on the results, depending on the task, a 3D spectrum of vibrations or a spindle rotation error diagram in a given range of rotation frequencies is calculated. The results of evaluating the accuracy and technical condition of the grinding head at idle and under load are presented.

Slow oscillations in systems with inertial vibration exciters

The problem of the occurrence of semi-slow speed oscillations of an unbalanced rotor during its passage through the resonance zone has been solved using the method of direct separation of motions. It has been proved that when a stationary regime is established, semi-slow damping oscillations of the rotor speed arise in the region of the Sommerfeld effect, they are the result of the superimposement of free accompanying oscillations with a relatively low frequency on forced fast oscillations. In this respect, the initial amplitudes of such oscillations are quite large, and oscillations damping is relatively slow.

On the divergence of first-order resonance widths at low eccentricities

ABSTRACT Orbital resonances play an important role in the dynamics of planetary systems. Classical theoretical analyses found in textbooks report that libration widths of first-order mean motion resonances diverge for nearly circular orbits. Here, we examine the nature of this divergence with a non-perturbative analysis of a few first-order resonances interior to a Jupiter-mass planet. We show that a first-order resonance has two branches, the pericentric and the apocentric resonance zone. As the eccentricity approaches zero, the centres of these zones diverge away from the nominal resonance location but their widths shrink. We also report a novel finding of ‘bridges’ between adjacent first-order resonances: at low eccentricities, the apocentric libration zone of a first-order resonance smoothly connects with the pericentric libration zone of the neighbouring first-order resonance. These bridges may facilitate resonant migration across large radial distances in planetary systems, entirely in the low-eccentricity regime.

Experimental research of vertical movements and accelerations of the drum vibrations of the DM-617 vibratory roller during soil compaction

Rheological modeling of how the elements of a vibratory roller during soil compaction interact with each other allows the optimization of parameters of the roller and soil compaction modes based on the study of the obtained model, as well as the improvement of the soil compaction continuous control system, and the solution of other practically important tasks. To verify the models, it is required to compare the calculation results for the models with experimental data. The paper includes the results of experimental studies of the acceleration range for the vibratory drum of the DM-617 vibratory roller during soil compaction in the steady vibration mode, when the vibration is turned on, and when it is turned off. It is established that during the compaction of the soil in question in the range Evd = 14…25 MPa, the range of vertical movements and accelerations of the vibratory drum in the steady vibration mode does not depend on the soil density. When the vibration is turned on, the vertical movements and accelerations of the drum is 1.5…2 times higher than those of the steady mode. When the vibration is turned off, the vertical movements are increased by 1.5…2 times when passing the resonance zone, and the drum accelerations do not exceed the range of those in the steady vibration mode. The obtained results allow the mathematical models of vibratory rollers during soil compaction to be verified not only in the steady vibration modes, but also in transient modes, including passing the resonance areas when switching the vibration on and off.

Selected Tribological Properties and Vibrations in the Base Resonance Zone of the Polymer Composite Used in the Aviation Industry.

The revolution in the global market of composite materials is evidenced by their increasing use in such segments as the transport, aviation, and wind industries. The innovative aspect of this research is the methodology approach, based on the simultaneous analysis of mechanical and tribological loads of composite materials, which are intended for practical use in the construction of aviation parts. Simultaneously, the methodology allows the composition of the composites used in aviation to be optimized. Therefore, the presented tests show the undefined properties of the new material, which are necessary for verification at the application stage. They are also a starting point for further research planned by the authors related to the improvement of the tribological properties of this material. In this article, the selected mechanical and tribological properties of an aviation polymer composite are investigated with the matrix of L285-cured hardener H286 and six reinforcement layers of carbon fabric GG 280P/T. The structure of a polymer composite has a significant influence on its mechanical properties; thus, a tribological analysis in the context of abrasive wear in reciprocating the movement for the specified polymer composite was performed. Moreover, the research was expanded to dynamic analysis for the discussed composite. This is crucial knowledge of material dynamics in the context of aviation design for the conditions of resonance vibrations. For this reason, experimental dynamical investigations were performed to determine the basic resonance of the material and its dynamics behavior response. The research confirmed the assumed hypotheses related to the abrasive wear process for the newly developed material, as well as reporting an empirical evaluation of the dependencies of the resonance zone from the fabric orientation sets.

Linear stability analysis of a liquid film down on an inclined plane under oscillation with normal and lateral components in the presence and absence of surfactant

In this work, we first study the interface instability of a fluid layer flowing down on an inclined plane under periodic oscillation having both normal and lateral components. After that, we examine the effect of an insoluble surfactant covering the free surface under normal oscillation, lateral oscillation, and both normal and lateral oscillations. The time periodic linear system, corresponding to the governing equations, is treated using the Chebyshev spectral collocation method for spatial resolution, and for temporal resolution, we use the Floquet theory. We show that the stabilizing effect of normal oscillation amplitude on the gravitational instability, reported by Woods and Lin [J. Fluid Mech. 294, 391 (1995)], is strengthened by introducing lateral oscillation, and this contributes to the complete suppression of this instability. The harmonic and subharmonic zones, initially stable in the work of Woods and Lin [J. Fluid Mech. 294, 391 (1995)], are destabilized by the lateral oscillation, and the first unstable parametric resonance becomes without threshold. Conversely, the unstable domain of the gravitational instability and the second resonance zone reported by Lin, Chen, and Woods [Phys. Fluids 8, 3247 (1996)] can be reduced by introducing normal oscillation. Finally, we show that the surfactant has a stabilizing effect that contributes to accelerate the suppression of the gravitational instability and opposes the destabilizing effect of the lateral oscillation on the first subharmonic resonance to give rise to a competition between the two effects.

Sommerfeld effect in a single-DOF system with base excitation from motor driven mechanism

Sommerfeld effect is a nonlinear phenomenon observed in rotating machinery driven by a non-ideal source. It is characterised by capture at resonance for a finite range of drive power followed by a sudden release. This paper investigates the dynamics of a direct current (DC) motor driven mechanism which excites the base of a vibrating structure. A slotted cam follower mechanism and a scotch yoke mechanism are chosen for the base excitations of a single degree of freedom oscillator. It is shown that the Sommerfeld effect leads to capture-and-escape (jump) through multiple resonance zones, and as a result, some intermediate speed ranges are missed. The critical power/voltage input to escape through all the resonances may exceed that required to escape the primary resonance. Moreover, while increased structural damping makes it easier to escape resonance capture, it reduces the system efficiency at super-critical operating speeds. These are important design considerations for sizing the motor drives of these mechanisms. Analytical predictions for jumps are obtained from a steady-state power balance whereas the transient analysis is performed with the help of Bond Graph (BG) models and MSC-ADAMS software. The transient responses from the numerical models are used to verify the analytical results.

Propagation of Overvoltages in the Form of Impulse, Chopped and Oscillating Waveforms in Transformer Windings—Time and Frequency Domain Approach

This paper describes a comparison of overvoltage propagation in transformer windings. Expanding and evolving electrical networks comprise various classes of transient waveforms, related to network reconfigurations, failure stages and switching phenomena, including new sources based on power electronics devices. In particular, the integration of renewable energy sources—mainly solar and wind—as well as expanding charging and energy storage infrastructure for electric cars in smart cities results in network flexibility manifested by switching phenomena and transients propagation, both impulse and oscillating. Those external transients, having a magnitude below the applied protection level may have still a considerable effect on winding electrical insulation in transformers, mainly due to internal resonance phenomena, which have been the root cause of many transformer failures. Such cases might occur if the frequency content of the incoming waveform matches the resonance zones of the winding frequency characteristic. Due to this coincidence, the measurements were performed both in time and frequency domain, applying various classes of transients, representing impulse, chopped (time to chopping from 1 µs to 50 µs) and oscillating overvoltages. An additional novelty was a superposition of a full lighting impulse with an oscillating component in the form of a modulated wavelet. The comparison of propagation of those waveforms along the winding length as well as a transfer case between high and low voltage windings were analyzed. The presented mapping of overvoltage prone zones along the winding length can contribute to transformer design optimization, development of novel diagnostic methodology, improved protection concepts and the proper design of modern networks.

ОЦІНЮВАННЯ СТІЙКОСТІ РОБОТИ АВТОМОБІЛЬНОГО ДВИГУНА ЗА УМОВИ ПОСТІЙНОЇ КУТОВОЇ ШВИДКОСТІ КОЛІНЧАСТОГО ВАЛА

The operation of the automobile engine at a constant angular speed of the crankshaft at an unsteady mode of movement of the car allows increasing its energy and fuel efficiency. It is necessary to use a continuously variable transmission, which allows you to change the speed of the vehicle with infinitely variable gear ratio change transmission without acceleration of the rotating masses of the engine. With a continuously variable automatic change gear ratio of the transmission, it is possible to realize engine operating modes that provide maximum effective engine power, maximum effective engine torque, and also minimum effective specific fuel consumption. It should be noted, that even with perfect management continuously variable transmission fails to obtain the constant value of the angular velocity of the crankshaft, as the internal combustion engine generates oscillations of the indicator torque. As a result of the study, an assessment of the possibility of maintaining a constant angular velocity of the crankshaft at steady and unsteady vehicle motion modes was made. The possibility of transmission operation in the pre-resonance and non-resonance frequency regions has been taken into account. A method has been developed for assessing the stability of an automobile engine with uneven effective torque of an internal combustion engine and a continuously variable transmission. The calculated dependencies are obtained, taking into account the elastic-inertial properties of the transmission and the coefficient of unevenness of the engine's torque, allowing determining the maximum deviations of the angular velocity of the crankshaft in the considered vehicle motion modes. It is shown, that the operation of the transmission in the near- resonance zone not only leads to additional cyclic loads on the parts and components of the transmission itself, but also reduces the energy efficiency of the vehicle power plant. Recommendations to improve the performance of motor-transmission units are formulated.

Design features of hybrid bearings with adjustable stiffness

The article considers a mathematical model of a combined bearing assembly, operating on the principle of separation of speeds. The features of the influence of the switching mechanism on the dynamic stiffness coefficients of the bearing assembly are established, the effect of the appearance of resonance on transient conditions is revealed, recommendations are made on the detuning of the rotor-support system from the resonance zone.

ПОПЕРЕЧНЫЕ КОЛЕБАНИЯ БАЛКИ СО СВОБОДНЫМИ КРАЯМИ НА УПРУГОМ ОСНОВАНИИ ПРИ ДЕЙСТВИИ ДИНАМИЧЕСКОЙ НАГРУЗКИ

It is known that in the case of dynamic influences, the important dynamic characteristics of the structures of a structure are the frequencies and forms of natural vibrations, with which its response to dynamic effects is associated. These structures include structures lying on the ground, which can be considered when calculating them as beams on an elastic foundation. Using the method of initial parameters for a beam with free edges located on an elastic base, the problem of determining the influence of the attached mass m1 on the circular frequency of natural transverse vibrations (without taking into account the resistance forces) is solved, the first three frequencies and forms of natural transverse vibrations of the beam are determined. The problem of determining the efforts in the beam, taking into account its own weight and dynamic load (perturbing force) F (t), with the frequency of forced vibrations corresponding to the resonance and interresonance zones applied at an arbitrary point d, was solved. The conditions are formulated that must be taken into account when analyzing the dynamic behavior of a structure under the action of variable loads in various design situations.

Key-Component Force and Modal Analysis of Chamfering Machine for Curved Side-Shaped Ice Spoon

The edge-curved ice spoon is a wooden tool to eat ice cream, and the machine tool adopted to chamfer and deburr the unformed curved edge ice spoon is called surface-taking machine (chamfering machine). In the course of cutting, the results are primarily dependent on the speed of cutter shaft. In order to guarantee the quality of the spoon, scraping-edge device of the surface-taking machine is anatomized and designed, and the working principle of the surface picking machine is introduced. The cutting force is analyzed from theoretical and experiential perspectives. The device is modeled in the SolidWorks and simulated by ADAMS to attain time-varying curves of scraping-edge device displacement and contact force of the cam and wheel. The modal analysis of the cutter shaft is carried out on ANSYS Workbench, the vibration frequency and vibration mode of the former six steps are attained, and the critical speed of the cutter shaft is calculated to determine the rotational speed of the cutter shaft, which effectively avoids the resonance zone and ensures the effective operation of device. Additionally, the actual production and processing are able to lay a theoretical basis.

Engine-and-transmission installation frequency analysis of a wheeled forestry tractor

The article provides a frequency analysis of an engine-and-transmission installation of a wheeled forestry tractor. It can be used for machine-building enterprises of the forest complex. During the wheeled forestry tractors operation in the engine-and-transmission installation, resonance phenomena may occur when the internal frequencies of the system coincide with the external disturbance. The solution of the problem was carried out on the basis of the developed equivalent dynamic circuit, which was described by the differential equations of torsional vibration. As a result of solving these equations, the values of the engine-and-transmission installation natural frequencies were obtained. A comparative analysis of the frequencies obtained with regard to the damping properties of the system has been made, and possible resonance zones have been identified. The information obtained allows selecting the optimal damping indicators for the wheeled forestry tractor engine-and- transmission installation operation in a resonant-free mode.

PUMP PIPING VIBRATIONS REDUCTION BY VIBRATION ISOLATORS FORMING SPECIFIED FORCE CHARACTERISTICS

A significant part of the stock of pumping equipment of pumping stations is age-related. A common occurrence is the failure of equipment or its individual parts due to vibration overload. The source of increased vibration of pumping units in some cases are vibrations of pump piping. A high level of vibration leads to fatigue breakdowns of equipment at oil pumping stations. Each case of pipeline vibration occurrence requires a thorough and qualified analysis, since there are no universal methods for reducing the vibration of technological pipelines. For vibration isolation, it is proposed to use vibration isolators with negative stiffness on the basis of a special form shapes. The pipeline in this case acts as a stabilizer for a vibration isolator with negative stiffness. The force characteristic of the «pipeline - vibration isolator» system at the same time in a certain range becomes flat, which reduces its stiffness and, consequently, its natural frequencies. Using these systems, it is possible to shift the resonant zone of vibration-proof systems to the area of low frequencies, which leads to an increase in the coefficient of vibration isolation. Analytical calculations were performed to confirm the effectiveness of the proposed solution. A passive vibration isolator based on an elastic element moving along the guides of a special form perpendicular to their axis, allows to create the power characteristics of a given shape, which are necessary to protect against vibration in each case.

Secondary resonances due to solar radiation pressure in the vicinity of Glonass and GPS regions

The secondary resonances due to solar radiation pressure are investigated in the vicinity of orbits of the global navigation systems GLONASS (main resonance is 8:17) and GPS (main resonance is 1:2). The secondary resonances were considered for both the main resonances and the sub-resonances i- and e-types. The secondary resonances locations were estimated analytically and were improved by numerically. The secondary resonance zones were found for both low (0.02, 0.2, and 1 m2/kg) and high (10 m2/kg and more) area-to-mass ratios. The secondary resonances have a significant effect on the dynamical evolution of objects with area-to-mass ratio 10 m2/kg and more. This result is very important when describing the long-term orbital evolution of space debris.

Ultra-High Refractive Index Sensing Structure Based on a Metal-Insulator-Metal Waveguide-Coupled T-Shape Cavity with Metal Nanorod Defects.

An ultra-high plasmonic refractive index sensing structure composed of a metal–insulator–metal (MIM) waveguide coupled to a T-shape cavity and several metal nanorod defects is proposed and investigated by using finite element method. The designed plasmonic MIM waveguide can constitute a cavity resonance zone and the metal nanorod defects can effectively trap the light in the T-shape cavity. The results reveal that both the size of defects in wider rectangular cavity and the length of narrower rectangular cavity are primary factors increasing the sensitivity performance. The sensitivity can achieve as high as 8280 nm/RIU (RIU denotes the refractive index unit), which is the highest sensitivity reported in plasmonic MIM waveguide-based sensors to our knowledge. In addition, the proposed structure can also serve as a temperature sensor with temperature sensitivity as high as 3.30 nm/°C. The designed structure with simplicity and ease of fabrication can be applied in sensitivity nanometer scale refractive index sensor and may potentially be used in optical on-chip nanosensor.

New results on orbital resonances.

Perturbative analyses of planetary resonances commonly predict singularities and/or divergences of resonance widths at very low and very high eccentricities. We have recently reexamined the nature of these divergences using non-perturbative numerical analyses, making use of Poincaré sections but from a different perspective relative to previous implementations of this method. This perspective reveals fine structure of resonances which otherwise remains hidden in conventional approaches, including analytical, semi-analytical and numerical-averaging approaches based on the critical resonant angle. At low eccentricity, first order resonances do not have diverging widths but have two asymmetric branches leading away from the nominal resonance location. A sequence of structures called "low-eccentricity resonant bridges" connecting neighboring resonances is revealed. At planet-grazing eccentricity, the true resonance width is non-divergent. At higher eccentricities, the new results reveal hitherto unknown resonant structures and show that these parameter regions have a loss of some - though not necessarily entire - resonance libration zones to chaos. The chaos at high eccentricities was previously attributed to the overlap of neighboring resonances. The new results reveal the additional role of bifurcations and co-existence of phase-shifted resonance zones at higher eccentricities. By employing a geometric point of view, we relate the high eccentricity phase space structures and their transitions to the shapes of resonant orbits in the rotating frame. We outline some directions for future research to advance understanding of the dynamics of mean motion resonances.

Vibrations of the nonlinear system in which stationary harmonic excited multivalued regimes in the vicinities of resonances do not exist

A nonlinear dynamical system is investigated which consists from a mass between two linear elastic connecting elements with different coefficients of stiffness. Laws of vibrations and characteristics of eigenvibrations of the system as well as of self-decaying vibrations of the system with damping and of the system with harmonic excitation are determined. Dynamical qualities of the system are revealed. It is shown that the system has infinite number of eigenfrequencies and that in the resonance zones multivalued stable and unstable motions do not exist in the system.

Super and sub-harmonic synchronization in generalized van der Pol oscillator

Effects of quasiperiodic beatings and sub- and super-harmonic synchronization reveal in plasma physics, optics, acoustics, neurophysiology, etc., but also very often in aero-elasticity of large slender engineering structures, e.g., bridge decks, towers, masts, high rise buildings, ropes, where these phenomena emerge in relation with vortex shedding effects. This applies mainly to quasiperiodic beatings that can be encountered especially in the lock-in regimes, when the vortex frequency becomes close to the structure eigenfrequency ω0 with a small positive or negative detuning. This phenomenon has been thoroughly investigated for the van der Pol system in the previous study by the authors of this paper. However, experimental testing in a wind tunnel showed also other phenomena that can occur in the system resonance zone due to excitations with a multiple or rational fraction frequency leading to sub- or super-harmonic synchronization. All these effects are very dangerous from the viewpoint of reliability and safety of respective systems and hence, a robust theoretical background for design of adequate countermeasures are worthwhile to be developed. In this subsequent study the original sub- and super-synchronization effects are identified and quantified including assessment of their dynamic stability.

Neptune’s resonances in the scattered disk

The Scattered Disk Objects (SDOs) are thought to be a small fraction of the ancient population of leftover planetesimals in the outer solar system that were gravitationally scattered by the giant planets and have managed to survive primarily by capture and sticking in Neptune's exterior mean motion resonances (MMRs). In order to advance understanding of the role of MMRs in the dynamics of the SDOs, we investigate the phase space structure of a large number of Neptune's MMRs in the semi-major axis range 33--140~au by use of Poincar\'e sections of the circular planar restricted three body model for the full range of particle eccentricity pertinent to SDOs. We find that, for eccentricities corresponding to perihelion distances near Neptune's orbit, distant MMRs have stable regions with widths that are surprisingly large and of similar size to those of the closer-in MMRs. We identify a phase-shifted second resonance zone that exists in the phase space at planet-crossing eccentricities but not at lower eccentricities; this second resonance zone plays an important role in the dynamics of SDOs in lengthening their dynamical lifetimes. Our non-perturbative measurements of the sizes of the stable resonance zones confirm previous results and provide an additional explanation for the prominence of the $N$:1 sequence of MMRs over the $N$:2, $N$:3 sequences and other MMRs in the population statistics of SDOs; our results also provide a tool to more easily identify resonant objects.