Influence of Nonlinear Wheel/Rail Contact Geometry on Stability of Rail Vehicles

1977 ◽  
Vol 99 (1) ◽  
pp. 172-185 ◽  
Author(s):  
R. Hull ◽  
N. K. Cooperrider
Keyword(s):  
Dry Friction ◽  
Numerical Technique ◽  
Equations Of Motion ◽  
Nonlinear Behavior ◽  
Rail Vehicles ◽  
Freight Car ◽  
The Stability ◽  
Nonlinear Equations Of Motion ◽  
Lateral Behavior ◽  
Hunting Stability

Nonlinear behavior caused by wheel flanges, worn wheel treads, and dry friction can have an important effect on rail-vehicle stability. In this paper the influence of such nonlinearities on the stability of rail freight vehicles is investigated using quasi-linearization techniques. Nonlinear equations of motion are presented that describe the lateral behavior of a 9-degree-of-freedom representation of a complete freight car with three-piece trucks. The nonlinear wheel/rail geometric constraint functions for the rolling radii, angle of wheel/rail contact, and wheelset roll angle are found by a numerical technique. The suspension description includes dry friction where appropriate. The hunting stability of the freight car is studied by employing describing-function techniques. Results are presented for a typical freight car with three different wheel profiles. The stability results illustrate the dependence of behavior on the amplitudes of vehicle motions. Application of the results in realistic situations and suggestions for future quasi-linear studies are discussed.

Analysis of the Nonlinear Dynamics of a Railway Vehicle Wheelset

1973 ◽  
Vol 95 (1) ◽  
pp. 28-35 ◽  
Author(s):  
E. Harry Law ◽  
R. S. Brand
Keyword(s):  
Lateral Displacement ◽  
Equations Of Motion ◽  
Vertical Displacement ◽  
Linear Analysis ◽  
Design Parameters ◽  
Railway Vehicle ◽  
Nonlinear Variation ◽  
Constraint Equations ◽  
The Stability ◽  
Nonlinear Equations Of Motion

The nonlinear equations of motion for a railway vehicle wheelset having curved wheel profiles and wheel-flange/rail contact are presented. The dependence of axle roll and vertical displacement on lateral displacement and yaw is formulated by two holonomic constraint equations. The method of Krylov-Bogoliubov is used to derive expressions for the amplitudes of stationary oscillations. A perturbation analysis is then used to derive conditions for the stability characteristics of the stationary oscillations. The expressions for the amplitude and the stability conditions are shown to have a simple geometrical interpretation which facilitates the evaluation of the effects of design parameters on the motion. It is shown that flange clearance and the nonlinear variation of axle roll with lateral displacement significantly influence the motion of the wheelset. Stationary oscillations may occur at forward speeds both below and above the critical speed at which a linear analysis predicts the onset of instability.

On The Steady State and Dynamic Performance Characteristics of Floating Ring Bearings

1981 ◽  
Vol 103 (3) ◽  
pp. 389-397 ◽  
Author(s):  
Chin-Hsiu Li ◽  
S. M. Rohde
Keyword(s):  
Steady State ◽  
Linear Theory ◽  
High Speed ◽  
Dynamic Performance ◽  
Equations Of Motion ◽  
Nonlinear Behavior ◽  
Journal Bearings ◽  
Transient Problem ◽  
The Stability ◽  
Bearing System

An analysis of the steady state and dynamic characteristics of floating ring journal bearings has been performed. The stability characteristics of the bearing, based on linear theory, are given. The transient problem, in which the equations of motion for the bearing system are integrated in real time was studied. The effect of using finite bearing theory rather than the short bearing assumption was examined. Among the significant findings of this study is the existence of limit cycles in the regions of instability predicted by linear theory. Such results explain the superior stability characteristics of the floating ring bearing in high speed applications. An understanding of this nonlinear behavior, serves as the basis for new and rational criteria for the design of floating ring bearings.

ON MODELLING THE TRANSITION TO TURBULENCE IN PIPE FLOW

2017 ◽  
Vol 59 (1) ◽  
pp. 1-34 ◽  
Author(s):  
LAWRENCE K. FORBES ◽  
MICHAEL A. BRIDESON
Keyword(s):  
Numerical Technique ◽  
Equations Of Motion ◽  
Type Equation ◽  
Transition To Turbulence ◽  
Eigenvalue Approach ◽  
Cylindrical Pipe ◽  
Full Generality ◽  
Fluid Turbulence ◽  
Linearized Problem ◽  
The Stability

As a possible model for fluid turbulence, a Reiner–Rivlin-type equation is used to study Poiseuille–Couette flow of a viscous fluid in a rotating cylindrical pipe. The equations of motion are derived in cylindrical coordinates, and small-amplitude perturbations are considered in full generality, involving all three velocity components. A new matrix-based numerical technique is proposed for the linearized problem, from which the stability is determined using a generalized eigenvalue approach. New results are obtained in this cylindrical geometry, which confirm and generalize the predictions of previous recent studies. A possible mechanism for the transition to turbulent flow is discussed.

Nonlinear Truck Ride Analysis

1974 ◽  
Vol 96 (2) ◽  
pp. 597-602 ◽  
Author(s):  
G. R. Potts ◽  
H. S. Walker
Keyword(s):  
Numerical Integration ◽  
Nonlinear Equations ◽  
Digital Computer ◽  
Dry Friction ◽  
Shock Absorber ◽  
Equations Of Motion ◽  
Deflection Curve ◽  
Force Velocity ◽  
Nonlinear Equations Of Motion ◽  
Dry Friction Damping

The nonlinear vibratory motions of a three-axle semitrailer truck were investigated via the use of a digital computer. The nonlinear equations of motion are presented and a method of numerical integration is discussed. The analysis allows any shape of suspension force-deflection curve (including wheel hop, suspension stops, and dry friction damping) and a similar liberality of shock absorber force-velocity characteristics. An experimental vibration study, performed on a model truck, is described and the results compare favorably with the calculated results of the numerical integration.

Linear Stability Analysis of a Waveboard Multibody Model With a Minimal Set of Equations

2021 ◽  
Author(s):  
A. G. Agúndez ◽  
D. García-Vallejo ◽  
E. Freire ◽  
A. M. Mikkola
Keyword(s):  
Stability Analysis ◽  
Multibody System ◽  
Equations Of Motion ◽  
Nonholonomic Constraints ◽  
Design Parameters ◽  
Multibody Model ◽  
Aspect Ratios ◽  
Holonomic And Nonholonomic Constraints ◽  
The Stability ◽  
Nonlinear Equations Of Motion

Abstract In this paper, the stability of a waveboard, the skateboard consisting in two articulated platforms, coupled by a torsion bar and supported of two caster wheels, is analysed. The waveboard presents an interesting propelling mechanism, since the rider can achieve a forward motion by means of an oscillatory lateral motion of the platforms. The system is described using a multibody model with holonomic and nonholonomic constraints. To perform the stability analysis, the nonlinear equations of motion are linearized with respect to the forward upright motion with constant speed. The linearization is carried out resorting to a novel numerical linearization procedure, recently validated with a well-acknowledged bicycle benchmark, which allows the maximum possible reduction of the linearized equations of motion of multibody systems with holonomic and nonholonomic constraints. The approach allows the expression of the Jacobian matrix in terms of the main design parameters of the multibody system under study. This paper illustrates the use of this linearization approach with a complex multibody system as the waveboard. Furthermore, a sensitivity analysis of the eigenvalues considering different scenarios is performed, and the influence of the forward speed, the casters’ inclination angle and the tori aspect ratios of the toroidal wheels on the stability of the system is analysed.

Parametric Stability of a Two-Degree-of-Freedom Machine System: Part I—Equations of Motion and Stability

1987 ◽  
Vol 109 (2) ◽  
pp. 210-215 ◽  
Author(s):  
R. I. Zadoks ◽  
A. Midha
Keyword(s):  
Equations Of Motion ◽  
Monodromy Matrix ◽  
Degree Of Freedom ◽  
Computationally Efficient ◽  
Machine System ◽  
Stable Operating ◽  
System Part ◽  
The Stability ◽  
Nonlinear Equations Of Motion ◽  
Two Degree Of Freedom

An important question facing a designer is whether a certain machine system will have a stable operating condition. To date, the investigations which deal with this question have been scarce. This study treats an elastic two-degree-of-freedom system with position-dependent inertia and external forcing. In Part I, the nonlinear equations of motion are derived and linearized about the system’s steady-state rigid-body response. The stability of the linearized equations is examined using Floquet theory, and a computationally efficient method for approximating the monodromy matrix is presented. A specific example is proposed and the results are presented in Part II of this paper.

Stability of Liquid-Filled Spinning Spheroids Via Liapunov’s Second Method

1979 ◽  
Vol 46 (2) ◽  
pp. 259-262 ◽  
Author(s):  
P. C. Parks
Keyword(s):  
Stability Analysis ◽  
Nonlinear Equations ◽  
Stability Theory ◽  
Equations Of Motion ◽  
Spin Axis ◽  
Liapunov Functions ◽  
The Stability ◽  
Nonlinear Equations Of Motion

In this paper the stability theory of Poincare´ and others, expounded in the last few pages of Sir Horace Lamb’s textbook Hydrodynamics, is extended by a stability analysis using Liapunov functions to cover the full nonlinear equations of motion of spinning liquid-filled spheroids. The linearized criterion is confirmed, that is for stability c/a < 1 or c/a > 3 where the semiaxes of the spheroid are a, a, c, the c-axis being also the spin axis. The unstable motion for 1 < c/a < 3 is examined, and a conjecture that viscosity will destabilize spinning spheroids with c/a > 3 is proposed.

Investigation of Turbulence Effects on the Nonlinear Vibration of a Rigid Rotor Supported by Finite Length 2-Lobe and Circular Bearings

2019 ◽  
Vol 14 (12) ◽  
Author(s):  
Nuntaphong Koondilogpiboon ◽  
Tsuyoshi Inoue
Keyword(s):  
Nonlinear Vibration ◽  
Limit Cycles ◽  
Reynolds Equation ◽  
Equations Of Motion ◽  
Rigid Rotor ◽  
Reynolds Equations ◽  
Multiplier Analysis ◽  
Turbulence Effects ◽  
The Stability ◽  
Nonlinear Equations Of Motion

Abstract This study investigated the effect of turbulence on the nonlinear vibration of a symmetrical rigid rotor supported by two identical journal bearings. The bearings consisted of various length to diameter (L/D) ratio circular and 2-lobe bearings with differing pad preloads. Two turbulent (Ng–Pan–Elrod and Constantinescu model) and one laminar Reynolds equations were selected for comparison, and they were solved using a finite difference method to obtain nonlinear bearing forces. The nonlinear equations of motion for the rotor-bearing system were solved using a shooting method and arclength continuation to obtain limit cycles for each bearing configuration. Floquet multiplier analysis was then utilized to identify the stability of the obtained limit cycles. For the cases of the circular and 2-lobe bearing without pad preload, the turbulent Reynolds equations yielded a lower onset speed of instability and L/D ratio at which the bifurcation type changed from supercritical to subcritical than the laminar Reynolds equation. However, at higher pad preloads (preloads of 0.25 or 0.5), the turbulence effects increased the onset speed of instability, especially for L/D ratios > 0.7, and only supercritical bifurcation was observed. For all bearing configurations, the ratio of the limit cycle whirl frequency to shaft rotational speed for both turbulence bearing models was higher than that of the laminar bearing model, and the Ng–Pan–Elrod turbulence model always generated lower onset speed of instability than the Constantinescu model.

scholarly journals Motion of a Rigid Body Supported at One Point by a Rotating Arm

1993 ◽  
Vol 1 (2) ◽  
pp. 121-134
Author(s):  
Jeffrey D. Stoen ◽  
Thomas R. Kane
Keyword(s):  
Energy Dissipation ◽  
Rigid Body ◽  
Exact Solutions ◽  
Equations Of Motion ◽  
Stability Diagrams ◽  
Mass Properties ◽  
State Of Rest ◽  
The Stability ◽  
Nonlinear Equations Of Motion ◽  
System Geometry

This article details a scheme for evaluating the stability of motions of a system consisting of a rigid body connected at one point to a rotating arm. The nonlinear equations of motion for the system are formulated, and a method for finding exact solutions representing motions that resemble a state of rest is presented. The equations are then linearized and roots of the eigensystem are classified and used to construct stability diagrams that facilitate the assessment of effects of varying the body's mass properties and system geometry, changing the position of the attachment joint, and adding energy dissipation in the joint.

Multibody Dynamics of a Floating Wind Turbine Considering the Flexibility Between Nacelle and Tower

2018 ◽  
Vol 18 (06) ◽  
pp. 1850085 ◽  
Author(s):  
Vahid Jahangiri ◽  
Mir Mohammad Ettefagh
Keyword(s):  
Wind Turbine ◽  
Degrees Of Freedom ◽  
Multibody System ◽  
Equations Of Motion ◽  
System Response ◽  
Floating Wind Turbine ◽  
Conservation Of Momentum ◽  
The Stability ◽  
Nonlinear Equations Of Motion ◽  
6 Degrees Of Freedom

Stability and dynamic modeling of the floating wind turbine (FWT) is a crucial challenge in designing of the type of structures. In this paper, the tension leg platform (TLP) type FWT is modeled as a multibody system considering the flexibility between the nacelle and tower. The flexibility of the FWT is modeled as a torsional spring and damper. It has 6 degrees of freedom (DOFs) related to the large-amplitude translation and rotation of the tower and 4 DOFs related to the relative rotation between the rotor-nacelle assembly and the tower. First, the nonlinear equations of motion are derived by the theory of momentum cloud based on the conservation of momentum. Then, the equations of motion are solved and the system is simulated in MATLAB. Moreover, the effect of flexibility between the nacelle and tower is investigated via the dynamic response. The stability of the system in three different environmental conditions is studied. Finally, the spring and damping coefficients for the system response to get near to instability are determined, by which the critical region is defined. The simulation results demonstrate the importance of the flexibility between the nacelle and tower on the overall behavior of the system and its stability.

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