scholarly journals Numerical simulation of rigid particles in Stokes flow: lubrication correction for general shape of particles

2021 ◽  
Author(s):  
Aline Lefebvre-Lepot ◽  
Flore Nabet
Keyword(s):  
Numerical Simulation ◽  
Asymptotic Expansion ◽  
Stokes Flow ◽  
Degrees Of Freedom ◽  
Contact Point ◽  
Singular Part ◽  
Range Interaction ◽  
Rigid Particles ◽  
Pressure Flows ◽  
Shape Of Particles

We address the problem of numerical simulation of suspensions of rigid particles in a Stokes flow. We focus on the inclusion of the singular short range interaction effects (lubrication effects) in the simulations when the particles come close one to another. As in LefebvreMerletNguyen2015, the key idea is to decompose the velocity and pressure flows in a sum of a singular and a regular part. In this article, the singular part is computed using an explicit asymptotic expansion of the solution when the distance goes to zero. This expansion is similar to the asymptotic expansion proposed in HillairetKelai2015 but is more appropriate for numerical simulations of suspensions. It can be computed for any locally convex (particles convex close to the contact point) and regular shape of particles. Using HillairetKelai2015 as an intermediate result, we prove that the remaining part is regular in the sense that it is bounded independently of the distance. As a consequence, only a small number of degrees of freedom are necessary to obtain accurate results. The method is tested in dimension 2 for clusters of two or three aligned particles with general rigid velocities. We show that, as expected, the convergence is independent of the distance.

Robustness Analysis of a Simple and Augmented Proportional Plus Derivative Controller in Trajectory Following Robots Using the Floquet Theory

2018 ◽  
Vol 13 (7) ◽  
Author(s):  
B. Sandeep Reddy ◽  
Ashitava Ghosal
Keyword(s):  
Numerical Simulation ◽  
Degrees Of Freedom ◽  
Floquet Theory ◽  
Robustness Analysis ◽  
Periodic Trajectory ◽  
Model Parameters ◽  
Asymptotically Stable ◽  
Pd Controller ◽  
Simulation Results ◽  
Trajectory Following

This paper deals with the issue of robustness in control of robots using the proportional plus derivative (PD) controller and the augmented PD controller. In the literature, a variety of PD and model-based controllers for multilink serial manipulator have been claimed to be asymptotically stable for trajectory tracking, in the sense of Lyapunov, as long as the controller gains are positive. In this paper, we first establish that for simple PD controllers, the criteria of positive controller gains are insufficient to establish asymptotic stability, and second that for the augmented PD controller the criteria of positive controller gains are valid only when there is no uncertainty in the model parameters. We show both these results for a simple planar two-degrees-of-freedom (2DOFs) robot with two rotary (R) joints, following a desired periodic trajectory, using the Floquet theory. We provide numerical simulation results which conclusively demonstrate the same.

scholarly journals 3DOF Ultrasonic Motor with Two Piezoelectric Rings

Sensors ◽  
2020 ◽  
Vol 20 (3) ◽  
pp. 834 ◽  
Author(s):  
Vytautas Jūrėnas ◽  
Gražvydas Kazokaitis ◽  
Dalius Mažeika
Keyword(s):  
Numerical Simulation ◽  
Magnetic Dipole ◽  
Attitude Control ◽  
Degrees Of Freedom ◽  
High Reliability ◽  
Experimental Studies ◽  
Main Idea ◽  
Ultrasonic Motor ◽  
Response Analysis ◽  
Magnetic Sphere

A novel design of a multiple degrees of freedom (multi-DOF) piezoelectric ultrasonic motor (USM) is presented in the paper. The main idea of the motor design is to combine the magnetic sphere type rotor and two oppositely placed ring-shaped piezoelectric actuators into one mechanism. Such a structure increases impact force and allows rotation of the sphere with higher torque. The main purpose of USM development was to design a motor for attitude control systems used in small satellites. A permanent magnetic sphere with a magnetic dipole is used for orientation and positioning when the sphere is rotated to the desired position and the magnetic field synchronizes with the Earth’s magnetic dipole. Also, the proposed motor can be installed and used for robotic systems, laser beam manipulation, etc. The system has a minimal number of components, small weight, and high reliability. Numerical simulation and experimental studies were used to verify the operating principles of the USM. Numerical simulation of a piezoelectric actuator was used to perform modal frequency and harmonic response analysis. Experimental studies were performed to measure both mechanical and electrical characteristics of the piezoelectric motor.

Numerical simulation of incompressible flows within simple boundaries: accuracy

1971 ◽  
Vol 49 (1) ◽  
pp. 75-112 ◽  
Author(s):  
Steven A. Orszag
Keyword(s):  
Numerical Simulation ◽  
Finite Difference ◽  
Spectral Methods ◽  
Degrees Of Freedom ◽  
Incompressible Flows ◽  
Finite Difference Methods ◽  
Fourier Method ◽  
Passive Scalar ◽  
Mathematical Basis ◽  
Improved Accuracy

Galerkin (spectral) methods for numerical simulation of incompressible flows within simple boundaries are shown to possess many advantages over existing finite-difference methods. In this paper, the accuracy of Galerkin approximations obtained from truncated Fourier expansions is explored. Accuracy of simulation is tested empirically using a simple scalar-convection test problem and the Taylor–Green vortex-decay problem. It is demonstrated empirically that the Galerkin (Fourier) equations involving Np degrees of freedom, where p is the number of space dimensions, give simulations at least as accurate as finite-difference simulations involving (2N)p degrees of freedom. The theoretical basis for the improved accuracy of the Galerkin (Fourier) method is explained. In particular, the nature of aliasing errors is examined in detail. It is shown that ‘aliasing’ errors need not be errors at all, but that aliasing should be avoided in flow simulations. An eigenvalue analysis of schemes for simulation of passive scalar convection supplies the mathematical basis for the improved accuracy of the Galerkin (Fourier) method. A comparison is made of the computational efficiency of Galerkin and finite-difference simulations, and a survey is given of those problems where Galerkin methods are likely to be applied most usefully. We conclude that numerical simulation of many of the flows of current interest is done most efficiently and accurately using the spectral methods advocated here.

Effects of Flexibility and Damping on Momentum Transfer During Locking of Two Moving Links, Part I: Numerical Simulation

1998 ◽  
Vol 65 (2) ◽  
pp. 479-484 ◽  
Author(s):  
W. Szyszkowski ◽  
K. Fielden
Keyword(s):  
Numerical Simulation ◽  
Momentum Transfer ◽  
Degrees Of Freedom ◽  
Large Scale ◽  
Slow Motion ◽  
Critical Values ◽  
Governing Equations ◽  
Two Degrees Of Freedom

The system consisting of two links and two joints is examined. The joints are idealy frictionless when unlocked. Due to flexibility of the links, the locking generates some damped vibrations. It is demonstrated that the presence of these vibrations, even of very small and seemingly neglegible amplitudes, have dramatic effects on the after-locking motion of the links. Depending on the level of flexibility and damping involved, the locking triggers a large-scale “slow” motion that may have either oscillatory or circular (clockwise or counterclockwise) characters. The links will stop at some resting configuration only at certain “critical” values of damping. The set of “critical dampings” seems to be infinite, though only two degrees-of-freedom are used to model the system. Governing equations for these phenomena are derived and discussed in Part II of this paper.

Elastically Mounted Double Aerodynamic Pendulum

2019 ◽  
Vol 19 (05) ◽  
pp. 1941007 ◽  
Author(s):  
Yury D. Selyutskiy ◽  
Andrei P. Holub ◽  
Marat Z. Dosaev
Keyword(s):  
Experimental Data ◽  
Numerical Simulation ◽  
Degrees Of Freedom ◽  
State University ◽  
Periodic Motions ◽  
Aeroelastic System ◽  
Subsonic Wind Tunnel ◽  
Trivial Equilibrium ◽  
Rotational Degrees Of Freedom ◽  
Moscow State University

Elastically mounted double aerodynamic pendulum is an aeroelastic system with two rotational degrees of freedom. A wing is attached to the second link of the pendulum. It is shown that it is possible to select values of parameters in such a way as to make the trivial equilibrium (where both links of the pendulum are stretched along the flow) unstable. Numerical simulation of behavior of the system in such situations is performed, and arising limit cycles are studied. Experimental investigation of such aerodynamic pendulum is performed in the subsonic wind tunnel of the Institute of Mechanics of Lomonosov Moscow State University. Characteristics of periodic motions are registered for different values of parameters of the system. It is shown that experimental data are in qualitative agreement with results of numerical simulation.

A multi-configuration kinematic model for active drive/steer four-wheel robot structures

Robotica ◽  
2015 ◽  
Vol 34 (10) ◽  
pp. 2309-2329 ◽  
Author(s):  
Edgar A. Martínez-García ◽  
Erik Lerín-García ◽  
Rafael Torres-Córdoba
Keyword(s):  
Degrees Of Freedom ◽  
Rotation Axis ◽  
Contact Point ◽  
Linear Equations ◽  
Kinematic Model ◽  
Robotic Systems ◽  
Control Law ◽  
Special Design ◽  
Wheel Drive ◽  
Four Wheel Drive

SUMMARYIn this study, a general kinematic control law for automatic multi-configuration of four-wheel active drive/steer robots is proposed. This work presents models of four-wheel drive and steer (4WD4S) robotic systems with all-wheel active drive and steer simultaneously. This kinematic model comprises 12 degrees of freedom (DOFs) in a special design of a mechanical structure for each wheel. The control variables are wheel yaw, wheel roll, and suspension pitch by active/passive damper systems. The pitch angle implies that a wheel's contact point translates its position over time collinear with the robot's lateral sides. The formulation proposed involves the inference of the virtual z-turn axis (robot's body rotation axis) to be used in the control of the robot's posture by at least two acceleration measurements local to the robot's body. The z-turn axis is deduced through a set of linear equations in which the number of equations is equal to the number of acceleration measurements. This research provides two main models for stability conditions. Finally, the results are sustained by different numerical simulations that validate the system with different locomotion configurations.

Analysis of generalized force and its influence on ride and stability of railway vehicle

2020 ◽  
Vol 51 (6) ◽  
pp. 95-109
Author(s):  
Rakesh Chandmal Sharma ◽  
Sakshi Sharma ◽  
Sunil Kumar Sharma ◽  
Neeraj Sharma
Keyword(s):  
Potential Energy ◽  
Degrees Of Freedom ◽  
Ride Comfort ◽  
Contact Point ◽  
Railway Vehicle ◽  
Energy Potential ◽  
Dissipation Energy ◽  
Rail Vehicle ◽  
Random Track Irregularities ◽  
Lagrange’S Method

Formulation of a rail vehicle model using Lagrange’s method requires the system’s kinetic energy, potential energy, spring potential energy, Rayleigh’s dissipation energy and generalized forces to be determined. This article presents a detailed analysis of generalized forces developed at wheel–rail contact point for 27 degrees of freedom–coupled vertical–lateral model of a rail vehicle formulated using Lagrange’s method and subjected to random track irregularities. The vertical–lateral ride comfort of the vehicle and the ride index of the vehicle are evaluated based on ISO 2631-1 comfort specifications and stability is determined using eigenvalue analysis. The parameters that constitute the generalized forces and critically influence ride and stability have been identified and their influences on the same have been analysed in this work.

scholarly journals The Extended Symmetry Lie Algebra and the Asymptotic Expansion of the Transversal Correlation Function for the Isotropic Turbulence

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
V. N. Grebenev ◽  
A. N. Grishkov ◽  
M. Oberlack
Keyword(s):  
Correlation Function ◽  
Asymptotic Expansion ◽  
Lie Algebra ◽  
Degrees Of Freedom ◽  
Isotropic Turbulence ◽  
Central Charge ◽  
Riemannian Metrics ◽  
Equivalence Transformation ◽  
Velocity Correlation ◽  
Correlation Tensor

The extended symmetry of the functional of length determined in an affine spaceK3of the correlation vectors for homogeneous isotropic turbulence is studied. The two-point velocity-correlation tensor field (parametrized by the time variablet) of the velocity fluctuations is used to equip this space by a family of the pseudo-Riemannian metricsdl2(t)(Grebenev and Oberlack (2011)). First, we observe the results obtained by Grebenev and Oberlack (2011) and Grebenev et al. (2012) about a geometry of the correlation spaceK3and expose the Lie algebra associated with the equivalence transformation of the above-mentioned functional for the quadratic formdlD22(t)generated bydl2(t)which is similar to the Lie algebra constructed by Grebenev et al. (2012). Then, using the properties of this Lie algebra, we show that there exists a nontrivial central extension wherein the central charge is defined by the same bilinear skew-symmetric formcas for the Witt algebra which measures the number of internal degrees of freedom of the system. For the applications in turbulence, as the main result, we establish the asymptotic expansion of the transversal correlation function for large correlation distances in the frame ofdlD22(t).

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