Dynamics of Gas-Lubricated Slider Bearings in Magnetic Recording Disk Files—Part II: Numerical Simulation

1986 ◽  
Vol 108 (4) ◽  
pp. 589-593 ◽  
Author(s):  
D. K. Miu ◽  
D. B. Bogy
Keyword(s):  
Numerical Simulation ◽  
Magnetic Recording ◽  
Dynamic Performance ◽  
Equations Of Motion ◽  
Disk Surface ◽  
Surface Velocity ◽  
Rotating Disks ◽  
Step Size ◽  
Slider Bearings ◽  
Lubrication Equation

This two part paper presents the experimental observation and numerical simulation of the dynamic response of self-acting gas-lubricated slider bearings used to maintain the sub-micron spacings between the Read/Write transducers and the rotating disks in magnetic recording disk files. In this Part II, a factored implicit finite difference scheme is used to integrate the Reynolds lubrication equation, which describes the isothermal compressible fluid flow within the bearing region, and a fourth order Runge-Kutta method is used to solve the equations of motion, which describe the slider dynamics. Using this numerical model, the theoretical slider response due to a rectangular step in the disk surface is obtained. Excellent correlation is observed between theory and experiment. Results are presented to illustrate the effects of step size, step location, and surface velocity on the dynamic performance of slider bearings.

Dynamics of Gas-Lubricated Slider Bearings in Magnetic Recording Disk Files—Part I: Experimental Observation

1986 ◽  
Vol 108 (4) ◽  
pp. 584-588 ◽  
Author(s):  
D. K. Miu ◽  
D. B. Bogy
Keyword(s):  
Numerical Simulation ◽  
Dynamic Response ◽  
Experimental Observation ◽  
Magnetic Recording ◽  
Laser Doppler ◽  
Rotating Disks ◽  
Interferometric Technique ◽  
Slider Bearings

This two part paper presents the experimental observation and numerical simulation of the dynamic response of self-acting gas-lubricated slider bearings used to maintain the sub-micron spacings between the Read/Write transducers and the rotating disks in magnetic recording disk files. In this Part I, a novel laser Doppler interferometric technique is used to measure the transient motions of the R/W head as it encounters an artificially introduced crater-like surface imperfection and a sputtered rectangular step.

Geometric Elimination of Constraint Violations in Numerical Simulation of Lagrangian Equations

1994 ◽  
Vol 116 (4) ◽  
pp. 1058-1064 ◽  
Author(s):  
S. Yoon ◽  
R. M. Howe ◽  
D. T. Greenwood
Keyword(s):  
Numerical Simulation ◽  
Equations Of Motion ◽  
Nonholonomic Constraints ◽  
Geometric Constraints ◽  
State Variables ◽  
Step Size ◽  
Constraint Equations ◽  
Lagrangian Equations ◽  
Small Step Size ◽  
Gradient Based

Conventional holonomic or nonholonomic constraints are defined as geometric constraints. The total enregy of a dynamic system can be treated as a constrained quantity for the purpose of accurate numerical simulation. In the simulation of Lagrangian equations of motion with constraint equations, the Geometric Elimination Method turns out to be more effective in controlling constraint violations than any conventional methods, including Baumgarte’s Constraint Violation Stabilization Method (CVSM). At each step, this method first goes through the numerical integration process without correction to obtain updated values of the state variables. These values are then used in a gradient-based procedure to eliminate the geometric and energy errors simultaneously before processing to the next step. For small step size, this procedure is stable and very accurate.

Mulit-Pulse Orbits and Chaotic Motion of Composite Laminated Plates

2008 ◽  
Author(s):  
Xiangying Guo ◽  
Wei Zhang ◽  
Ming-Hui Yao
Keyword(s):  
Numerical Simulation ◽  
Normal Form ◽  
Differential Equations ◽  
Thin Plate ◽  
Equations Of Motion ◽  
Laminated Plates ◽  
Phase Method ◽  
Rectangular Thin Plate ◽  
Partial Differential ◽  
Chaotic Motions

This paper presents an analysis on the nonlinear dynamics and multi-pulse chaotic motions of a simply-supported symmetric cross-ply composite laminated rectangular thin plate with the parametric and forcing excitations. Firstly, based on the Reddy’s three-order shear deformation plate theory and the model of the von Karman type geometric nonlinearity, the nonlinear governing partial differential equations of motion for the composite laminated rectangular thin plate are derived by using the Hamilton’s principle. Then, using the second-order Galerkin discretization approach, the partial differential governing equations of motion are transformed to nonlinear ordinary differential equations. The case of the primary parametric resonance and 1:1 internal resonance is considered. Four-dimensional averaged equation is obtained by using the method of multiple scales. From the averaged equation obtained here, the theory of normal form is used to give the explicit expressions of normal form. Based on normal form, the energy phase method is utilized to analyze the global bifurcations and multi-pulse chaotic dynamics of the composite laminated rectangular thin plate. The results obtained above illustrate the existence of the chaos for the Smale horseshoe sense in a parametrical and forcing excited composite laminated thin plate. The chaotic motions of the composite laminated rectangular thin plate are also found by using numerical simulation. The results of numerical simulation also indicate that there exist different shapes of the multi-pulse chaotic motions for the composite laminated rectangular thin plate.

A Strategy to Accelerate the Numerical Integration in the Dynamic Simulation of Multibody Systems

1997 ◽  
Author(s):  
Jesús Cardenal ◽  
Javier Cuadrado ◽  
Eduardo Bayo
Keyword(s):  
Multibody Systems ◽  
Equations Of Motion ◽  
Stiff Systems ◽  
Step Size ◽  
Step Method ◽  
Integral Of Motion ◽  
Time Step ◽  
Time Step Size ◽  
Variable Time ◽  
Numerical Integrator

Abstract This paper presents a multi-index variable time step method for the integration of the equations of motion of constrained multibody systems in descriptor form. The basis of the method is the augmented Lagrangian formulation with projections in index-3 and index-1. The method takes advantage of the better performance of the index-3 formulation for large time steps and of the stability of the index-1 for low time steps, and automatically switches from one method to the other depending on the required accuracy and values of the time step. The variable time stepping is accomplished through the use of an integral of motion, which in the case of conservative systems becomes the total energy. The error introduced by the numerical integrator in the integral of motion during consecutive time steps provides a good measure of the local integration error, and permits a simple and reliable strategy for varying the time step. Overall, the method is efficient and powerful; it is suitable for stiff and non-stiff systems, robust for all time step sizes, and it works for singular configurations, redundant constraints and topology changes. Also, the constraints in positions, velocities and accelerations are satisfied during the simulation process. The method is robust in the sense that becomes more accurate as the time step size decreases.

Numerical modelling of swirling momentumless turbulent wake dynamics

2018 ◽  
pp. 37-48
Author(s):  
Андрей Геннадьевич Деменков ◽  
Геннадий Георгиевич Черных
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Mathematical Models ◽  
Equations Of Motion ◽  
Turbulent Wake ◽  
The Body ◽  
Jet Flows ◽  
Reynolds Stresses ◽  
Bodies Of Revolution ◽  
Averaged Equations

С применением математической модели, включающей осредненные уравнения движения и дифференциальные уравнения переноса нормальных рейнольдсовых напряжений и скорости диссипации, выполнено численное моделирование эволюции безымпульсного закрученного турбулентного следа с ненулевым моментом количества движения за телом вращения. Получено, что начиная с расстояний порядка 1000 диаметров от тела течение становится автомодельным. На основе анализа результатов численных экспериментов построены упрощенные математические модели дальнего следа. Swirling turbulent jet flows are of interest in connection with the design and development of various energy and chemical-technological devices as well as both study of flow around bodies and solving problems of environmental hydrodynamics, etc. An interesting example of such a flow is a swirling turbulent wake behind bodies of revolution. Analysis of the known works on the numerical simulation of swirling turbulent wakes behind bodies of revolution indicates lack of knowledge on the dynamics of the momentumless swirling turbulent wake. A special case of the motion of a body with a propulsor whose thrust compensates the swirl is studied, but there is a nonzero integral swirl in the flow. In previous works with the participation of the authors, a numerical simulation of the initial stage of the evolution of a swirling momentumless turbulent wake based on a hierarchy of second-order mathematical models was performed. It is shown that a satisfactory agreement of the results of calculations with the available experimental data is possible only with the use of a mathematical model that includes the averaged equations of motion and differential equations for the transfer of normal Reynolds stresses along the rate of dissipation. In the present work, based on the above mentioned mathematical model, a numerical simulation of the evolution of a far momentumless swirling turbulent wake with a nonzero angular momentum behind the body of revolution is performed. It is shown that starting from distances of the order of 1000 diameters from the body the flow becomes self-similar. Based on the analysis of the results of numerical experiments, simplified mathematical models of the far wake are constructed. The authors dedicate this work to the blessed memory of Vladimir Alekseevich Kostomakha.

Influence of Material Damping on In-Plane Modal Parameters for Rotating Disks

2012 ◽  
Author(s):  
Hamid R. Hamidzadeh ◽  
Ehsan Sarfaraz
Keyword(s):  
Elastic Moduli ◽  
Damping Ratio ◽  
Equations Of Motion ◽  
Elastic Stability ◽  
Rotating Disks ◽  
Governing Equations ◽  
Annular Disk ◽  
Stress Theory ◽  
Hysteretic Damping ◽  
Circumferential Wave

The linear in-plane free vibration of a thin, homogeneous, viscoelastic, rotating annular disk is investigated. In the development of an analytical solution, two dimensional elastodynamic theory is employed and the viscoelastic material for the medium is allowed by assuming complex elastic moduli. The general governing equations of motion are derived by implementing plane stress theory. Natural frequencies are computed for several modes at specific radius ratios with fixed-free boundary conditions and modal loss factors for different damping ratios are determined. The computed results were compared to previously established results. It was observed that the effects of rotational speed and hysteretic damping ratio on natural frequency and elastic stability of the rotating disks were related to the mode of vibration and type of circumferential wave occurring.

A novel model-based robust control design for collaborative robot joint module

2022 ◽  
pp. 095440622110547
Author(s):  
ShengChao Zhen ◽  
WangXu Cui ◽  
XiaoLi Liu ◽  
GuanJun Meng ◽  
Ye-Hwa Chen
Keyword(s):  
Numerical Simulation ◽  
Robust Control ◽  
Trajectory Tracking ◽  
Dynamic Performance ◽  
Dynamic Control ◽  
Robot System ◽  
Excellent Control ◽  
Robust Control Design ◽  
The Impact ◽  
Collaborative Robot

In order to reduce the impact of load and system parameter changes on the dynamic performance of collaborative robot joint module, a novel robust control algorithm is proposed in this paper to solve the problem of dynamic control of collaborative robot joint module trajectory tracking. The controller is composed of two parts: one is a nominal control term designed based on the dynamical model, aiming to stabilize the nominal robot system; the other is a robust control term based on the Lyapunov method, aiming to eliminate the influence of uncertainty on tracking performance, where the uncertainties include nonlinear friction, parameter uncertainty, and external disturbances. The Lyapunov minimax method is adopted to prove that the system is uniformly bounded and uniformly ultimately bounded. We performed numerical simulation and experimental validation based on an actual collaborative robot joint module experimental platform and the rapid controller prototype cSPACE. The numerical simulation and experimental results show that the controller has excellent control performance for the collaborative robot joint module and provides more accurate trajectory tracking under the influence of uncertainties.

scholarly journals Optimization on Reducing Slag Entrapment in 150 × 1270 mm Slab Continuous Casting Mold

Materials ◽  
2019 ◽  
Vol 12 (11) ◽  
pp. 1774 ◽  
Author(s):  
Yang Wang ◽  
Shufeng Yang ◽  
Feng Wang ◽  
Jingshe Li
Keyword(s):  
Numerical Simulation ◽  
Continuous Casting ◽  
Casting Speed ◽  
Surface Velocity ◽  
Continuous Casting Mold ◽  
Slab Continuous Casting ◽  
Eddy Simulation ◽  
Submerged Entrance Nozzle ◽  
Dynamics Simulations ◽  
Slag Entrapment

To reduce slag entrapment in 150 × 1270 mm slab continuous casting molds at the Tang Steel Company, the effect of submerged entrance nozzle (SEN) depth and casting speed on the phenomenon was studied by computational fluid dynamics simulations. Then, the slag entrapment behavior in continuous casting molds, utilizing Large Eddy Simulation (LES) by coupling the volume of fluid (VOF) method, was also used. Finally, the effect of several common oils usually used to simulate slag in water modelling on slag entrapment was discussed and the water modelling results were used to validate the numerical simulation findings. The results showed that the optimum scheme is a submerged depth of SEN 90 mm and a casting speed of 1.6 m/min. Under optimal conditions, the maximum surface velocity is smallest (0.335 m/s) and the maximum slag entrapment ratio (0.44%) appears in the position of 0.1 m below the meniscus after 15 s. The water modelling results were in good agreement with the numerical simulation results.

Stability and Accuracy Analysis of Baumgarte’s Constraint Violation Stabilization Method

1995 ◽  
Vol 117 (3) ◽  
pp. 446-453 ◽  
Author(s):  
S. Yoon ◽  
R. M. Howe ◽  
D. T. Greenwood
Keyword(s):  
Equations Of Motion ◽  
Integration Step ◽  
State Variables ◽  
Stabilization Method ◽  
Lagrange Equations ◽  
Step Size ◽  
Constraint Violation ◽  
Truncation Errors ◽  
Numerical Stability Analysis ◽  
Stability And Accuracy

When Baumgarte’s Constraint Violation Stabilization Method (CVSM) is used in the simulation of Lagrange equations of motion with holonomic constraints, it is shown that, with suitable assumptions on the integration step size h and the eigenvalues (λ’s) of the linearized system, the constraint variables are effectively integrated by the same algorithm as that used for the state variables. A numerical stability analysis of the constraint violations can be performed using this so-called pseudo-integration equation. A study is also made of truncation errors and their modeling in the continuous time domain. This model can be used to determine the effectiveness of various constraint controls and integration methods in reducing the errors in the solution due to truncation errors. Examples are presented to illustrate the use of a higher-order truncation error model which leads to an accurate quantitative steady-state analysis of the constraint violations.

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