scholarly journals АНАЛІТИЧНЕ ДОСЛІДЖЕННЯ ДИНАМІКИ ТИПОВИХ КУЛІСНИХ МЕХАНІЗМІВ ТЕХНОЛОГІЧНИХ МАШИН ЛЕГКОЇ ПРОМИСЛОВОСТІ

2018 ◽  
Vol 122 (3) ◽  
pp. 9-18
Author(s):  
В. М. Дворжак
Keyword(s):  
Differential Equation ◽  
Computer Simulation ◽  
Angular Velocity ◽  
Equation Of Motion ◽  
Analytical Investigation ◽  
Light Industry ◽  
Sewing Machine ◽  
Characteristic Points ◽  
Crank Mechanism ◽  
Angle Of Rotation

Improving methods of designing technological machines mechanisms of light industry in CAD-programs. The analytical method of vector transformation of coordinates for calculation of typical mechanisms of technological machines and a numerical method for solving differential equations are used. Mathematical models describing the functions of the position of the moving links and the characteristic points of the multi-link mechanism of the thread take-up mechanism for the sewing machine and the dynamics of its operation are obtained. Schematic modeling of the mechanism in the Mathcad program was performed. The graphs of the dependence of the angular velocity and acceleration on time and on the angle of rotation of the crank mechanism. The algorithm of numerical and analytical investigation of the dynamics of the flat six-link articulated mechanism of the thread take-up of the sewing machine is proposed on the basis of the numerical solution of the differential equation of motion of the mechanism and a computer simulation of the mechanism in the program Mathcad. Practical Value is to use the results of research in kinematic and dynamic study of the target sewing machine mechanisms.

scholarly journals Impact of cranks displacement angle on the motion non-uniformity of roller forming unit with energy-balanced drive

2021 ◽  
pp. 141-155
Author(s):  
Viacheslav Loveikin ◽  
Kostiantyn Pochka ◽  
Mykola Prystailo ◽  
Maksym Balaka ◽  
Olha Pochka
Keyword(s):  
Differential Equation ◽  
Angular Velocity ◽  
Electric Motor ◽  
Steady Motion ◽  
Equation Of Motion ◽  
Start Up ◽  
Change Function ◽  
Displacement Angle ◽  
The Impact ◽  
Motion Mode

The impact of the cranks displacement angle on the motion non-uniformity is determined for three forming trolleys of a roller forming unit with an energy-balanced drive mechanism. At the same time, the specified unit is presented by a dynamic model with one freedom degree, where the extended coordinate is taken as the angular coordinate of the crank rotation. For such a model, a differential equation of motion is written, for solved which a numerical method was used. The inertia reduced moment of the whole unit, and the resistance forces moment, reduced to the crank rotation axis, to move of forming trolleys during the formation of products from building mixtures are determined, and also the nominal rated power of the electric motor was calculated, when solved a differential equation of motion. According to these data, asynchronous electric motor with a short-circuited rotor was chosen, for which a mechanical characteristic is constructed by the Kloss formula. Having solved the differential equation of motion with all defined characteristics, we obtain the change function of the crank angular velocity from start-up moment and during steady motion mode. After that, we calculated the time corresponding to the angular velocity value, and obtained the change function of the crank angular acceleration from start-up moment and during steady motion mode. The motion non-uniformity of the roller forming unit has been determined by the motion non-uniformity factor, the motion dynamism factor and the extended factor of motion assessment during steady motion mode. The impact of drive cranks displacement angle on the motion non-uniformity has been traced, as a result, the specified factors have the minimum values at cranks displacement on the angle Δφ=60°. The results may in the future are used to refine and improve the existing engineering methods for estimating the drive mechanisms of roller forming machines, both at design stages and in practical use.

Finite difference code for velocity and surface traction of a Fluid between Two Eccentric Spheres

2015 ◽  
Vol 11 (1) ◽  
pp. 2960-2971
Author(s):  
M.Abdel Wahab
Keyword(s):  
Velocity Field ◽  
Angular Velocity ◽  
Finite Difference ◽  
Numerical Study ◽  
Outer Sphere ◽  
Equation Of Motion ◽  
Annular Region ◽  
Surface Traction ◽  
Angular Velocities ◽  
Axis Passing

The Numerical study of the flow of a fluid in the annular region between two eccentric sphere susing PHP Code isinvestigated. This flow is created by considering the inner sphere to rotate with angular velocity 1  and the outer sphererotate with angular velocity 2  about the axis passing through their centers, the z-axis, using the three dimensionalBispherical coordinates (, ,) .The velocity field of fluid is determined by solving equation of motion using PHP Codeat different cases of angular velocities of inner and outer sphere. Also Finite difference code is used to calculate surfacetractions at outer sphere.

The Numerical Methods of Peridynamics Theory Used in Failure Analysis of Materials

2014 ◽  
Vol 1030-1032 ◽  
pp. 223-227
Author(s):  
Lin Fan ◽  
Song Rong Qian ◽  
Teng Fei Ma
Keyword(s):  
Differential Equation ◽  
Integral Equation ◽  
Numerical Integration ◽  
Integration Method ◽  
Equation Of Motion ◽  
Numerical Integration Method ◽  
Volume Integral ◽  
Volume Integral Equation ◽  
Method Of Molecular Dynamics ◽  
Classic Theory

In order to analysis the force situation of the material which is discontinuity,we can used the new theory called peridynamics to slove it.Peridynamics theory is a new method of molecular dynamics that develops very quickly.Peridynamics theory used the volume integral equation to constructed the model,used the volume integral equation to calculated the PD force in the horizon.So It doesn’t need to assumed the material’s continuity which must assumed that use partial differential equation to formulates the equation of motion. Destruction and the expend of crack which have been included in the peridynamics’ equation of motion.Do not need other additional conditions.In this paper,we introduce the peridynamics theory modeling method and introduce the relations between peridynamics and classic theory of mechanics.We also introduce the numerical integration method of peridynamics.Finally implementation the numerical integration in prototype microelastic brittle material.Through these work to show the advantage of peridynamics to analysis the force situation of the material.

scholarly journals About a Partial Differential Equation-Based Interpolator for Signal Envelope Computing: Existence Results and Applications

2013 ◽  
Vol 2013 ◽  
pp. 1-18 ◽  
Author(s):  
Oumar Niang ◽  
Abdoulaye Thioune ◽  
Éric Deléchelle ◽  
Mary Teuw Niane ◽  
Jacques Lemoine
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Mathematical Problem ◽  
Existence Results ◽  
Test Results ◽  
Partial Differential ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Mode Decomposition ◽  
Characteristic Points

This paper models and solves the mathematical problem of interpolating characteristic points of signals by a partial differential Equation-(PDE-) based approach. The existence and uniqueness results are established in an appropriate space whose regularity is similar to cubic spline one. We show how this space is suitable for the empirical mode decomposition (EMD) sifting process. Numerical schemes and computing applications are also presented for signal envelopes calculation. The test results show the usefulness of the new PDE interpolator in some pathological cases like input class functions that are not so regular as in the cubic splines case. Some image filtering tests strengthen the demonstration of PDE interpolator performance.

scholarly journals ON OSCILLATIONS DESCRIBING A GENERALIZED DIFFERENTIAL RELAY EQUATION

2020 ◽  
pp. 53-60
Author(s):  
Vasiliy Olshansky ◽  
Stanislav Olshansky ◽  
Oleksіі Tokarchuk
Keyword(s):  
Differential Equation ◽  
Initial Conditions ◽  
Oscillatory System ◽  
Equation Of Motion ◽  
Resistance Force ◽  
Oscillatory Process ◽  
Initial Deviation ◽  
Approximate Analytical Solutions ◽  
Positive Exponent ◽  
Generalized Differential

The motion of an oscillatory system with one degree of freedom, described by the generalized Rayleigh differential equation, is considered. The generalization is achieved by replacing the cubic term, which expresses the dissipative strength of the equation of motion, by a power term with an arbitrary positive exponent. To study the oscillatory process involved the method of energy balance. Using it, an approximate differential equation of the envelope of the graph of the oscillatory process is compiled and its analytical solution is constructed from which it follows that quasilinear frictional self-oscillations are possible only when the exponent is greater than unity. The value of the amplitude of the self-oscillations in the steady state also depends on the value of the indicator. A compact formula for calculating this amplitude is derived. In the general case, the calculation involves the use of a gamma function table. In the case when the exponent is three, the amplitude turned out to be the same as in the asymptotic solution of the Rayleigh equation that Stoker constructed. The amplitude is independent of the initial conditions. Self-oscillations are impossible if the exponent is less than or equal to unity, since depending on the initial deviation of the system, oscillations either sway (instability of the movement is manifested) or the range decreases to zero with a limited number of cycles, which is usually observed with free oscillations of the oscillator with dry friction. These properties of the oscillatory system are also confirmed by numerical computer integration of the differential equation of motion for specific initial data. In the Maple environment, the oscillator trajectories are constructed for various values of the nonlinearity index in the expression of the viscous resistance force and a corresponding comparative analysis is carried out, which confirms the adequacy of approximate analytical solutions.

Analytical investigation of nonlinear heave-coupled response of tension leg platform

2018 ◽  
Vol 233 (3) ◽  
pp. 699-713
Author(s):  
Mohammad Reza Tabeshpour ◽  
Reza Hedayatpour
Keyword(s):  
Degrees Of Freedom ◽  
Structural Response ◽  
Wave Theory ◽  
Equation Of Motion ◽  
Analytical Investigation ◽  
Response Analysis ◽  
Wave Forces ◽  
Tension Leg Platform ◽  
Heave Motion ◽  
Diffraction Effects

Having deep view in structural response of tension leg platform is important issue not only for response analysis but also for engineering design. Coupling between surge and heave motions of tension leg platform is such a problem. Here, tension leg platform motions are considered only in surge and heave degrees of freedom without pitch effect. The coupled term of heave is a nonlinear differential equation. Because the focus of this article is on this term, therefore, Duffing equation of motion in the surge direction is linearized. The wave forces are calculated using Airy’s wave theory and Morison’s equation, ignoring the diffraction effects. Current force also can be very important in dynamic analysis of tension leg platform. Because it affects the term of heave that is coupled with surge. It is shown that the effect of surge motion coupling on heave motion is very important in large displacement of surge motion in many sea states. The main result is that the coupling effects appeared in some frequencies such as heave and surge frequency, twice the frequency of wave, twice the natural surge frequency, and summation and difference of frequency of wave and surge frequency.

A Semi-Discrete Approach for the Numerical Simulation of Freestanding Blocks

2016 ◽  
pp. 416-439
Author(s):  
Fernando Peña
Keyword(s):  
Differential Equation ◽  
Numerical Simulation ◽  
Numerical Modeling ◽  
Discrete Model ◽  
Mathematical Formulation ◽  
Equation Of Motion ◽  
Rigid Bodies ◽  
The Body ◽  
Discrete Approach ◽  
Rocking Motion

This chapter addresses the numerical modeling of freestanding rigid blocks by means of a semi-discrete approach. The pure rocking motion of single rigid bodies can be easily studied with the differential equation of motion, which can be solved by numerical integration or by linearization. However, when we deal with sliding and jumping motion of rigid bodies, the mathematical formulation becomes quite complex. In order to overcome this complexity, a Semi-Discrete Model (SMD) is proposed for the study of rocking motion of rigid bodies, in which the rigid body is considered as a mass element supported by springs and dashpots, in the spirit of deformable contacts between rigid blocks. The SMD can detect separation and sliding of the body; however, initial base contacts do not change, keeping a relative continuity between the body and its base. Extensive numerical simulations have been carried out in order to validate the proposed approach.

Inverse Wheel Dynamics

2006 ◽  
Author(s):  
V. V. Vantsevich
Keyword(s):  
Angular Velocity ◽  
Power Distribution ◽  
Vehicle Dynamics ◽  
Inverse Dynamics ◽  
Equation Of Motion ◽  
Torque Control ◽  
Vehicle Performance ◽  
Performance Control ◽  
Wheel Torque ◽  
And Performance

Wheel dynamics is a significant component of vehicle dynamics and performance analysis. This paper presents an innovative method of studying wheel dynamics and wheel performance control based on the inverse dynamics formulation of the problem. Such an approach opens up a new way to the optimization and control of both vehicle dynamics and vehicle performance by optimizing and controlling power distribution to the drive wheels. An equation of motion of a wheel is derived first from the wheel power balance equation that makes the equation more general. This equation of motion is considered the basis for studying both direct and inverse wheel dynamics. The development of a control strategy on the basis of the inverse wheel dynamics approach includes wheel torque control that provides a wheel with both the referred angular velocity and rolling radius and also with the required functionals of quality. An algorithm for controlling the angular velocity is presented as the first part in the implementation of the developed strategy of the inverse wheel dynamics/performance control.

Casimir Effect on Voltage Response of Superharmonic Resonance of NEMS Resonators

2017 ◽  
Author(s):  
Martin Botello ◽  
Christian Reyes ◽  
Julio Beatriz ◽  
Dumitru I. Caruntu
Keyword(s):  
Differential Equation ◽  
Multiple Scales ◽  
Nonlinear Partial Differential Equation ◽  
Equation Of Motion ◽  
Second Order ◽  
Mode Shapes ◽  
Voltage Response ◽  
Casimir Forces ◽  
Superharmonic Resonance ◽  
Reference Length

This paper investigates the voltage response of superharmonic resonance of the second order of electrostatically actuated nano-electro-mechanical system (NEMS) resonator sensor. The structure of the NEMS device is a resonator cantilever over a ground plate under Alternating Current (AC) voltage. Superharmonic resonance of second order occurs when the AC voltage is operating in a frequency near-quarter the natural frequency of the resonator. The forces acting on the system are electrostatic, damping and Casimir. To induce a bifurcation phenomenon in superharmonic resonance, the AC voltage is in the category of hard excitation. The gap distance between the cantilever resonator and base plate is in the range of 20 nm to 1 μm for Casimir forces to be present. The differential equation of motion is converted to dimensionless by choosing the gap as reference length for deflections, the length of the resonator for the axial coordinate, and reference time based on the characteristics of the structure. The Method of Multiple Scales (MMS) and Reduced Order Model (ROM) are used to model the characteristic of the system. MMS transforms the nonlinear partial differential equation of motion into two simpler problems, namely zero-order and first-order. ROM, based on the Galerkin procedure, uses the undamped linear mode shapes of the undamped cantilever beam as the basis functions. The influences of parameters (i.e. Casimir, damping, fringe, and detuning parameter) were also investigated.

scholarly journals Effective Approaches to Control the Epidemic Based on the Improved SIR Model

2016 ◽  
Vol 6 (2) ◽  
pp. 154
Author(s):  
Shuai Shao ◽  
Hao Li ◽  
Yuanbiao Zhang ◽  
Kailong Li
Keyword(s):  
Differential Equation ◽  
Computer Simulation ◽  
Quantitative Method ◽  
Sir Model ◽  
Equation Model ◽  
Control Measures ◽  
Uncertain Parameters ◽  
Differential Equation Model ◽  
Qualitative And Quantitative ◽  
Epidemic Area

<p class="zhengwen">In this paper, we have established a SECADI model on the basis of the traditional epidemic model and under the consideration of factors such as the spread of the disease, the quantity of the medicine in need, the medicine production speedetc. We have improved the crowd classification standard and the spread styledifferential equation model in classical SIR model. We distinguished the crowd into six categories, including the susceptible, the exposed, the curable, the advanced, the dead and the immune, and we established integrated transformation relationships between them after taking control measures through qualitative and quantitative method, and then derive the adequate epidemic differential equation model before taking controls. We applied the method of computer simulation to solve the model, worked out uncertain parameters with the method of parameter identification, and we verified the validity and accuracy of the SECADI model. Meanwhile, we calculated with the actual data of Ebola in the epidemic area in WesternAfrica, simulated the evolution of the epidemic, analyze and offered effective approaches to control the epidemic situation. We further discussed development directions of this model in the end.</p>

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