Sinusoidal Law Research Articles

ОПРЕДЕЛЕНИЕ КИНЕМАТИЧЕСКИХ И ДИНАМИЧЕСКИХ ХАРАКТЕРИСТИК ТЕХНОЛОШИЧЕСКИХ МАШИН ПЛАНЕТАРНОГО ТИПА

The article deals with issues related to the study of planetary machines. It is demonstrated that they are able to significantly intensify most of the processes applicable to them. This is due to the complication of the trajectory of the movement of the working body and the increase in inertial forces. In addition, planetary units are energy efficient. The influence of the mutual action of grinding bodies on their power characteristics in a planetary mill with external and internal running of the drums is presented. The dependence of destructive forces on the angular velocity, the degree of filling of the grinding drums, the geometric ratios of the mill itself is shown. Sufficiently simple dependences have been obtained for calculating the total speed at any point of the planetary working body of the smoothing machine. Their use makes it possible to analyze the change in speed over a wide range, depending on a number of design and technological parameters. The proposed method allows to calculate the speeds of the working bodies that make planetary motion. Using the methods of classical mechanics, using the instantaneous center of velocities, a formula is obtained for calculating the speed at any point of the mixing blade. It is established that the speed of the blade changes in time according to a sinusoidal law. The total power gradually increases with increasing angular velocity. The results obtained in this article can be applied in the design and operation of planetary units.

Characteristic Analysis of the Dynamics of Shock Wave Propagation in a Medium with a Nonuniform Density Distribution

This paper is devoted to the numerical study of shock wave (SW) propagation in a medium with a nonuniform density distribution. The mathematical model is based on the Euler equations, which are solved in the shock-attached frame. This approach makes it possible to carry out an accurate characteristic analysis of the problem. First, the problems of SW propagation in a medium with finite-length segments with linearly increasing and decreasing density are considered. The obtained results are compared with the known analytical solutions. Then the case of a continuous change in the density of the medium in front of the SW according to the sinusoidal law is considered. The resulting flow is described and explained using the results for the case of a linear density gradient.

Dynamics of phase inclusion during rotational oscillations of simply connected annulus

The dynamics of a phase inclusion in a coaxial liquid layer divided with a radial partition is studied experimentally. The working volume of the container is filled with a viscous liquid, inside which an air bubble, immiscible with the main phase, is injected. This inclusion has a lower density than the surrounding liquid does. The container performs rotational oscillations as a whole with the zero average rotation. Such a motion brings to the generation of a harmonically oscillating azimuthal shear flow, which, as a consequence, excites the oscillations of the phase inclusion. During the bubble’s oscillations, the displacement of its geometric center follows the sinusoidal law. On the background of such a motion a periodic deformation of the bubble is observed, i.e. the phase boundary starts oscillating. A new and surprising result of the experiments is found, when the light bubble sinks and takes a quasi-steady position near the inner wall of the layer.

Kinematic characteristics of ultrasonic surface treatment

We investigate the kinematic characteristics of ultrasonic surface-plastic deformation when the oscillations are introduced in the direction tangential to the treated surface in order to assess the potential of this method for treating parts made of metals and alloys of various hardness. The kinematic parameters (trajectory, velocity, acceleration) of ultrasonic surface-plastic deformation were calculated in a rectangular coordinate system. Analytical dependencies were obtained for the trajectory length, resulting velocity, and acceleration as functions of the constituent types of motion (rotational, translational, oscillatory). The obtained equations and their graphical solutions allowed us to establish that, under ultrasonic surface-plastic deformation, the indenter moves along a complex trajectory with a variable velocity and acceleration. It is shown that the translation of ultrasonic oscillations to the indenter determines the complex nature of its movement, which differs significantly from that in the diamond burnishing method. In this case, the process parameters (velocity and acceleration) change according to a cyclic (sinusoidal) law, the periodicity of which depends on the frequency of ultrasonic oscillations and determines the final state of the treated surface. According the obtained results, the change in the input direction of ultrasonic oscillations (from normal to tangential) ensures the possibility of changing the contact condition from cyclic to constant, thereby affecting the deforming force during processing. It was found that the angle of oscillation input relative to the main velocity vector is a technological parameter significantly affecting the kinematic characteristics. An assumption is made about the possibility of using the tangential pattern of ultrasonic surfaceplastic deformation for parts made of metals and alloys of various hardness.

Modern Developments in Catalysis, Volume 2

A new construction of the pulsator for generating sinusoidal pulsating flows of a continuous medium in the channels of experimental setups have been performed. The pulsator is based on operating experience of existing types of latter used for the frequency range 0.03 < f < 0.8 Hz and is differed from them due to the use of a profiled flap. The flow structure using the pulsator is studied based on the theoretical analysis and experimental verification via the hot-wire anemometry and SIV method. It is shown that the profiled flap allows more than an order increase in the frequency of the flap rotation f ˜ 25 Hz, which maintains an almost sinusoidal law of flow rate. A criterion for estimating the efficiency of pulsator has been presented and an analytical expression has been obtained for estimating the impact of inertial forces on the law of variation of average velocity over the phase angle. The deviation from the harmonic law realized by the submitted pulsator at f = 25 Hz is 3 times smaller than the deviation characteristic for a pulsator with a ball flap and 6 times smaller for one with a butterfly flap at f = 0.04 Hz.

Dynamic responses of pitching hydrofoil in laminar–turbulent transition regime

Recently, the problem of a transitional boundary layer around a pitching foil has been attracting increasing attention. To determine the underlying physical mechanisms, in this study, a pitching hydrofoil is numerically investigated using the shear stress transport (SST) k–ω turbulence model coupled with the γ–Re˜θt transition model. First, the prediction of the static performance is compared with the experimental measurements and XFOIL data to validate and verify the numerical accuracy of the proposed method. Subsequently, the flow morphologies induced by sinusoidal and non-sinusoidal pitching laws are analyzed and compared in different reduced frequencies. The results indicate that reducing the empirical coefficient, A1, in the SST k–ω turbulence model can generate the flow separation in advance, thus improving the prediction of the hydraulic performance at a high angle of attack. The dynamic behavior of the laminar separation bubble is strongly associated with the pitching method and velocity. The collapse of the laminar separation bubble can destabilize the local boundary layer, generating multi-laminar separation bubbles. When new separation bubbles form and shed, a turbulent boundary layer moves downstream and is adsorbed on the surface simultaneously. The turbulence flow passes through the trailing edge, destroying the local vortex, contributing to a transiently elevated hydrodynamic lift. During a rapid pitching down, a counterclockwise trailing edge vortex becomes increasingly unstable, repeating the processes of inception, development, and shedding. The Theodorsen model fails to produce a reasonable hysteresis loop owing to the assumption of a fully attached flow. The results of a hybrid of the Theodorsen and Øye models show noticeable improvement in the dynamic lift prediction. The empirical coefficient, ks, of the Snel model is optimized, improving the predictions of low-frequency pitching significantly. All dynamic stall models present the same trend: low-frequency motions show better agreement than high-frequency ones. In the former, modeling of a non-sinusoidal pitching is closer to the transient numerical results than that of a sinusoidal motion.

Research and simulation of the sheet leveling machine manufacturing capabilities

One of the main tasks to determine the technological settings of the sheet leveling machine (leveler) is to identify the maximum roll overlap. In the well-known works on the study of sheet metal-roll leveling, the overlaps are set on the basis of experimental data, which is applicable for the leveling sheets from material with the 800-MPa yield strength. But for materials with a higher yield strength, additional research is required. The purpose of this work is to establish criteria affecting the maximum allowable overlap for the working rolls by the leveler and to determine the dependencies for the most rational working roll adjustment. When solving the set tasks, developed by the authors, an analytical mathematical model of the leveling process was used as an objective function that allows to determine the energy-power characteristics and the sheet curvature after leveling, depending on the individual settings of the leveler rolls. Within the framework of studies, an algorithm of a mathematical model was developed that allows to determine the leveler technological settings necessary for correcting the longitudinal curvature and comes down to determining the aligning coordinates for each of the movable rolls depending on the known characteristics of the metal being processed, the leveler geometric parameters, and the permissible value of the sheet residual curvature after leveling. In consequence of studying the influence of the working roll setup on the sheet metal-roll quality during leveling on a multi-roll leveling machine, the laws for the rational rolls positioning were established. The linear and sinusoidal laws were identified as optimal ones. Boundary factors were also established as affecting the maximum overlap of the rolls. These factors included the condition of the pickup and the condition of the roll strength. Using the example of implementing the developed finite element model of the sheet leveling process at the leveler of NKMZ (Ukraine), it was found that the pickup condition has a dominant influence when leveling sheets with a thickness of less than 6 mm, and with larger thicknesses the condition of the roll strength is prevailing. With a decrease in the yield strength of the material or the width of the sheets, this ratio will be redistributed toward the pickup condition.

Numerical investigations into supercavitating flows and hydrodynamic characteristics of a heaving hydrofoil

This paper presents the effects of heaving motions on the hydrodynamic characteristics, supercavitating flow regimes and vortex structures for a two-dimensional (2D) supercavitating hydrofoil. The sinusoidal heaving motion of the supercavitating hydrofoil is realized by overset grid technology. The lift coefficient, drag coefficient, supercavitating flow regime and vortex structures around the supercavitating hydrofoil are analyzed and compared among different amplitudes of the heaving motion. The predicted cavities and the hydrodynamic characteristics are in good accordance with the experiments at a stationary state. The lift coefficient and drag coefficient of the heaving hydrofoil present a sinusoidal law, which is related to the effective angle of attack. The heaving motion would affect the cavity length and its thickness. The greater the heaving amplitude, the greater the difference in cavity pattern at different heaving positions. The cavity variation would affect the shear layer and thus change the vortex shedding characteristics, which are different from those at a stationary state.

Study on the mechanical-electric effect law of dynamic output voltage of board level mounted BaTiO3-MLCC under high impact

BaTiO3-MLCC has the characteristics of unstable output voltage under high impact, which may lead to signal distortion and even failure of the electronic system. In this study, we aim to explore the dynamic output voltage characteristics of board level mounted BaTiO3-MLCC under high impact. A mechanical-electric effect modeling method of BaTiO3-MLCC dynamic output voltage based on dynamic model and piezoelectric effect is proposed. The high impact experimental study has been carried out, the results show that the dynamic output voltage curve of BaTiO3-MLCC and the dynamic strain curve of PCB at the installation position accord with the sinusoidal oscillation law of exponential attenuation. The characteristic frequencies of dynamic voltage curve completely include that of dynamic strain curve, and their fundamental frequencies are the same. These laws are the same as those characterized by the mechanical-electric effect model, which proves the feasibility and correctness of the proposed mechanical-electric effect modeling method.

Математическое моделирование движения зерноочистительной машины с приводом от линейного электродвигателя

An experimental mechanism for cleaning grain mixtures with a drive from a linear asynchronous electric motor has been developed and manufactured in the Bashkir State Agrarian University. More favorable conditions for sifting the grain mixture are created as a result of the use of an asynchronous linear electric motor for its drives in comparison with traditionally used machines driven by rotation motors. Based on the Lagrange equations, a mathematical description of the movement of the links of the mechanism is carried out and the electromagnetic force required in accordance with the cleaning technology is found. It is created in the windings of a linear electric motor by an electronic switch. It is found that the shape of the pulse of the required electromagnetic force is close to sinusoidal. However, it is possible to replace the electromotive force varying according to the sinusoidal law by a force constant in modulus and equal in impulse. Contribution of the authors: the authors contributed equally to this article. The authors declare no conflicts of interests.

Порівняльна характеристика кінематичних параметрів плоско штанцювального преса

Aim. Carrying out a comparative characterization of the kinematic parameters of the developed flat die-cutting press, the drive mechanism of the movable pressure plate of which includes a cam, rollers, spring and levers, with two laws of periodic movement of the executive link (roller). Method. A flat die-cutting press was chosen as the research material, for which a new design of the drive mechanism of the movable pressure plate was developed, for which a Ukrainian patent for the invention was obtained. Analytical studies of the kinematic parameters of the flat die-cutting press, followed by their comparison, were carried out for two traditional laws of periodic movement of the executive link (roller) for packaging engineering. The geometric dimensions of the flat die-cutting press are chosen taking into account material saving and ensuring compactness. Results. The work established that in the researched flat die-cutting press with given geometric dimensions, the sinusoidal law of periodic movement of the executive link is characterized by the following parameters: maximum speed of the roller Vr = 0,498 m/s, maximum acceleration of the roller Wr = 1,446 m/s2, maximum speed of the pressure plate Vп = 0,193 m/s, maximum acceleration of the pressure plate Wп = 0,588 m/s2. Whereas for the cosinusoidal law of periodic motion, the following indicators are valid: maximum speed of the roller Vr = 0,391 m/s, maximum acceleration of the roller Wr = 1,194 m/s2, maximum speed of the pressure plate Vп = 0,160 m/s, maximum acceleration of the pressure plate Wп = 0,826 m/s2. As a result of the comparative characteristics of the kinematic parameters of the flat die-cutting press, it became obvious that with sinusoidal law of periodic motion, the maximum roller speed is 1.27 times higher, maximum roller acceleration is 1.21 times higher, maximum pressure plate speed is 1.21 times higher, but maximum pressure plate acceleration in 1.40 times lower. Scientific novelty. Analytical studies and comparative characteristics of the developed flat die-cutting press for two laws of periodic movement of the executive link, the drive mechanism of the movable pressure plate consisting of levers, rollers, a cam and a spring, were carried out. It has been demonstrated that the law of periodic movement of the executive link significantly affects the kinematic parameters of the flat die-cutting press with similar geometric dimensions. Practical significance. The obtained results of studies of the kinematic parameters of the flat die-cutting press can be used for further research, in particular for: efforts synthesis of the flat die-cutting press; preparation for refusal; magnitudes of elastic deformations and thicknesses of activation of parts that are in constant contact (a cam and roller).

Synthesis of precision dosing system for liquid products based on electropneumatic complexes

This paper reports the construction of a mathematical model for the process of dosing liquid foods (non-carbonated drinking water). The model takes into consideration the differential equations of changes in the kinematic parameters of the liquid in a dosing device's channels and the corresponding accepted initial and boundary conditions of the process. The boundary conditions account for the influence of software-defined airlift dosing modes using the driver and the geometry of the product pipeline. The current's value measured in mA (with an accuracy of 0.001 mA) relative to the standard scale Imin is Imax=4...20 mA. Individual stages of the dosing process were analytically described, followed by the analysis of separate stages and accepted assumptions. The accuracy achieved when testing the experimental sample of the dispenser, with the repetition of the dose displacement process, ranged between 0.35 % and 0.8 %. The reported results are related to the established dosage weight of 50 ml when changing the initial level of liquid in the tank of the dosing feeder by 10 mm. An experimental bench has been proposed for investigating the functional mechatronic dosing module under the software-defined modes to form and discharge a dose of the product. The bench operates based on proportional feedback elements (4–20 mA) for step and sinusoidal pressure control laws in the dosing device. The control model with working dosing modes has been substantiated. The control models built are based on proportional elements and feedback. During the physical and mathematical modeling, the influence of individual parameters on the accuracy of the product dose formation was determined; ways to ensure the necessary distribution of compressed air pressure, subject to the specified productivity of the dosing feeder, were defined. The study results make it possible to improve the operation of precision dosing systems for liquid products based on electro-pneumatic complexes

Anisotropic constitutive model coupled with damage for Sn-rich solder: Application to SnAgCuSb solder under tensile conditions

With the rapid development of microelectronics and nanoelectronics, Moore law has significantly slowed down and More than Moore based system in packaging (SiP) is expected to be more and more important, at least for next one to two decades. Mechanical behaviors of interconnect materials such as solders are critical for yield in processes and reliability in testing and operation. Based on the framework of crystal plastic theory and continuum damage mechanics, an anisotropic constitutive model coupled with damage was developed to describe the deformation behaviors of Sn-rich solder. In the proposed model, the inelastic shear rate function was presented by hyperbolic sinusoidal form and power law form. For the damage evolution law, the total shear strain was chosen as the damage function variable. The proposed model was implemented into the general finite element software ABAQUS by forward Euler integration procedure. Some simulation examples were performed to verify the proposed model by comparing the simulation results with the experiments at uniaxial tensile conditions with SnAgCuSb solder chosen as the Sn-rich solder. The tensile stress-strain curves of the simulation results agreed well with the experiments at small strain under different temperatures and strain rates. The simulated stress-rupture stages showed reasonable accuracy with the experiments under four representative tensile conditions. Different tensile stress-strain curves of single grains with orientation of (0-0-0)°, (0-45-0)°, and (0-90-0)° were obtained under the same loading conditions, with an inverse relationship between the tensile strength and elongation. This relationship was in accordance with a referable literature. All these results indicate that the proposed model can describe the deformation behaviors of SnAgCuSb solder well under the tensile conditions in consideration of the mechanical anisotropy and the damage evolution.

Effect of Heat Exchange Transient Conditions With Moving Water-Air Interface on Space Charge Accumulation in Undersea HVdc Cables

The accumulation of space charge inside the dielectric layer of an HVdc cable is one of the most important issue to be considered in the design stage and during the operating conditions. The separation of space charge is due to several factors including the dependence on temperature of the electrical conductivity of the insulation and the establishment of a thermal gradient under load conditions. This article is focused on the investigation of the effect of an axial heat transmission on the space charge and electric field distributions in an HVdc cable. In order to assess the impact of this phenomenon, a case study involving a cable immersed partly in water and partly in air has been simulated by means of a 2-D thermal and electrical model in time domain. The electric field calculation is based on the quasi-static Maxwell model and the current continuity equation. To simulate the effect of waves, a moving water-air interface is considered, with time varying sinusoidal law. The results show the establishment of an electrical field peak near the water-air interface due to an increased temperature drop over the insulation in this area. The approach and the findings described in this article attempt to improve the knowledge in the relationship between thermal and electrical phenomena in HVdc cables. Moreover, this article focuses on the advisability of appropriately considering the impact of the axial heat transfer in the standards on the thermal rating of HVdc cables.

Experimental investigation of the flow behind a circular cylinder controlled by combination of a rotary oscillation and a radial deformation

This paper describes an experimental work which consists of a structural analysis of the flow around a circular cylinder subjected to a radial deformation of the cross section, according to a sinusoidal law, combined to a rotary oscillation. Experiments were performed for a Reynolds number of Re = 2700. The control parameters are the amplitude of the rotary oscillation; 30, 60 and $$80^{\circ }$$ are considered, the relative rotary oscillation frequency ranging from 0 to 4.5, and the amplitude of the radial deformation, 5% and 7%. The qualitative and quantitative analysis of the near wake snapshots revealed that the structure of the wake depends strongly on the control parameters. Compared to the simple rotary oscillation control, it is established that the combination of the aforementioned technique and the radial deformation of the cylinder cross-section allows reduction of the formation zone length with a rate of 37% and its width by 35%, anticipating the closure of the wake around the cylinder and increasing the emission frequency with a rate of 30%. Addition of radial deformation induces apparition of a new vortices emission mode, consisting of shed small vortices instead of big coherent structures in absence of the radial deformation, the defragmentation of big vortices and the dislocation of the wake. These results suggest a substantial reduction in additional drag.

Bubbles injection effect on Taylor–Couette flow controlled by deformations of inner cylinder cross-section

A numerical simulation is carried out to make investigation of bubbles interactions when injected in Taylor–Couette system. This process can affect the flow patterns, especially when it is combined with inner cylinder cross-section oscillations. The included phase is modeled by the Lagrangian approach. The flow regime range is considered until the onset of the wavy Taylor vortex flow (low regime). We attempt to characterize bubbles dispersion effects on the drag force near the inner-cylinder while it is executing radial sinusoidal deformations. It is assumed that the obtained configurations of air-bubbles accumulations are compared for validation with experimental and numerical studies from the literature. The bubbles have uniform spherical shape with a diameter Db = 0.06d, where d is the system gap width. The inner cylinder oscillation is imposed using a sinusoidal law with a fixed deforming frequency and different amplitude ratios of the initial radius R1. Overall, without reaching a fully developed regime, the obtained results for a low Taylor number showed that the drag reduction ratio could be decreased when the inner cylinder is deformed.

SELECTION OF BASIC PARAMETERS OF HYDRAULIC SYSTEM OF STAND FOR FULL-SCALE TESTS OF PIPES FOR DURABILITY BY INTERNAL PRESSURE

A complex of formulas is presented, the consistent application of which allows, based on the given characteristics of the sinusoidal law of variation of the internal pressure in the test pipe, to calculate and select the main parameters of the hydraulic system of the test bench. An example is given of using a simple method for checking the correctness of the choice made.

Sinusoidal FM patterns of fault-related vibration signals for planetary gearbox fault detection under non-stationary conditions

Vibration signals related to planetary gearbox faults under non-stationary conditions will be equipped with sinusoidal modulation laws in their amplitude modulation (AM) and frequency modulation (FM) modes. Extracting fault features implied in the AM and FM modes is the key issue to detect inner gear faults occurring in planetary gearboxes. However, there exist few signal analysis approaches that are able to track the fast oscillating nature implied in the fault-induced sinusoidal FM patterns. To address such a challenging issue, this paper conducts a detailed study on sinusoidal FM patterns of the fault-related vibration signal model and proposes a novel method to extract them successfully. To be specific, the proposed method firstly separates the AM and FM modes via Hilbert transform to avoid their mutual interference. The intrinsic modulation features implied in the AM and FM modes can then be separately extracted by a developed signal decomposition method named iterative-joint chirp mode decomposition (I-JCMD) with a composite mode optimization scheme. Compared with the existing fault detection techniques, the proposed method is not only able to avoid the complicated sideband analysis but also identify the fast and time-varying oscillating nature of the FM mode with a high accuracy. The performance of our method is finally verified by three simulated cases and four groups of real vibration signals related to four types of sun gear faults occurring in a planetary gearbox test-rig, which also reveals a potential scaling relation between load strength and the oscillating coefficient of the FM mode.

Numerical method for solving the problem of the gas-dynamic state of a main gas pipeline section relief of a variable cross-sectional area

The paper proposes a numerical method for solving the problem of the gas-dynamic state of a main gas pipeline linear section, which is characterized by a path change in the diameter and leveling height of the pipeline axis. The quasi-one-dimensional equations of gas pipeline transport are derived with account for the local and convective components of the inertia force, the quadratic law of resistance and the force of gravity at a variable cross-sectional area of the pipeline. At the inlet to the section, a time change in hydrostatic pressure is set, and at the outlet from the section a mass rate of gas flow is set. The initial distribution of gas-dynamic indices was taken for a stationary mode of operation. The equations were transformed to the equations of direct and reverse traveling waves presented in dimensionless variables, and approximated by an implicit scheme, taking into account the direction of excitation propagation. The iterative processes were formed by virtue of the nonlinearity of equations and boundary conditions, A calculation program was developed that allowed studying the process dynamics depending on the time change in the inlet pressure and the outlet mass flow rate under a path change in the diameter and leveling height of the pipeline axis. The results of separate calculations on transient processes were presented, when, at the section outlet the mass flow rate increases abruptly, and the pipe diameter has a local increase according to a sinusoidal law.

Calculation on seismic resistance of box-shaped structures of large-panel buildings

The article is devoted to the theoretical calculation of the box-shaped structure of large-panel buildings on dynamic effects, taking into account the spatial work of transverse and longitudinal walls under dynamic effects, set by the base displacement according to a sinusoidal law. The problem is solved using the finite difference method.