Modeling and Validation of a Roll Simulator for Recreational Off-Highway Vehicles

2011 ◽  
Author(s):  
Scott B. Zagorski ◽  
Dennis A. Guenther ◽  
Gary J. Heydinger ◽  
Anmol S. Sidhu ◽  
Dale A. Andreatta
Keyword(s):  
Experimental Data ◽  
Degrees Of Freedom ◽  
Close Agreement ◽  
Energy Equation ◽  
Equations Of Motion ◽  
Excellent Correlation ◽  
Motor Systems ◽  
Non Linear ◽  
Entrapped Air ◽  
Three Degrees Of Freedom

A model of a roll simulator for recreational off-highway vehicles (ROV) is presented. Models of each sub-system are described including the equations of motion, the braking, hydraulic and roll motor systems. Derivation of the equations of motion, obtained using Lagrange’s energy equation, demonstrates that they have three degrees-of-freedom (two dynamic, one static) and are coupled and highly non-linear. Results from the hydraulic sub-system illustrated that the amount of entrapped air in the system can significantly influence the response. Comparisons of the model with experimental data from the actual roll simulator showed close agreement. The greatest difference was with motor pressure. The acceleration levels and roll motions for both the model and experimental data showed excellent correlation.

Modeling of Multibody Flexible Articulated Structures With Mutually Coupled Motions: Part II — Application and Results

1992 ◽  
Author(s):  
Jiechi Xu ◽  
Joseph R. Baumgarten
Keyword(s):  
Experimental Data ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Open Loop ◽  
Body Motion ◽  
Universal Joint ◽  
Open Loop System ◽  
Numerical Examples ◽  
Kinematic Properties ◽  
Good Agreement

Abstract The application of the systematic procedures in the derivation of the equations of motion proposed in Part I of this work is demonstrated and implemented in detail. The equations of motion for each subsystem are derived individually and are assembled under the concept of compatibility between the local kinematic properties of the elastic degrees of freedom of those connected elastic members. The specific structure under consideration is characterized as an open loop system with spherical unconstrained chains being capable of rotating about a Hooke’s or universal joint. The rigid body motion, due to two unknown rotations, and the elastic degrees of freedom are mutually coupled and influence each other. The traditional motion superposition approach is no longer applicable herein. Numerical examples for several cases are presented. These simulations are compared with the experimental data and good agreement is indicated.

The Vibrations of the Engine with Neo-Hookean Suspension

2013 ◽  
Vol 430 ◽  
pp. 53-59 ◽  
Author(s):  
Nicolae Doru Stanescu ◽  
Dinel Popa
Keyword(s):  
Degrees Of Freedom ◽  
Stable Equilibrium ◽  
Numerical Study ◽  
Equations Of Motion ◽  
Harmonic Force ◽  
Small Oscillations ◽  
Excited System ◽  
Beat Phenomenon ◽  
Three Degrees Of Freedom

Our paper realizes a study of the vibrations of an engine excited by a harmonic force and sustained by four identical neo-Hookean springs of negligible masses. The considered model is one with three degrees of freedom (one translation and two rotations) and we obtain for it the equations of motion. Using these equations, we determine for the unexcited system the equilibrium positions and their stability. We also study the small oscillations about the stable equilibrium positions and we find the fundamental eigenpulsations of the system. For the case of the excited system we perform a numerical study considering the situation when the pulsation of the excitation is far away from the eigenpulsations and the situation when the pulsation of the excitation is closed to one eigenpulsation, highlighting the beat phenomenon.

The Transverse Shear Effect of a New Plate Bending Finite Element Based on the Strain Approach

2018 ◽  
Vol 35 ◽  
pp. 1-10
Author(s):  
Sifeddine Abderrahmani ◽  
Toufik Maalem ◽  
Djamal Hamadi
Keyword(s):  
Finite Element ◽  
Numerical Analysis ◽  
Transverse Shear ◽  
Degrees Of Freedom ◽  
Close Agreement ◽  
Plate Bending ◽  
Shear Effect ◽  
Thin Plate Bending ◽  
Kirchhoff Theory ◽  
Three Degrees Of Freedom

In this paper, we present a comparative study of the transverse shear effect on the plate bending. The element used is a rectangular finite element called SBRPK (Strain Based Rectangular Plate-Kirchhoff Theory-), it used for the numerical analysis of thin plate bending, and it based on the strain approach. This element has four nodes and three degrees of freedom per node (w, θx, θy). Through the numerical applications with different loading cases and boundary conditions; the numerical results obtained are in close agreement with the analytical solution.

Contributions to the Determination of the Equations of Motion for Multidegree of Freedom Systems

1971 ◽  
Vol 93 (1) ◽  
pp. 191-195 ◽  
Author(s):  
Desideriu Maros ◽  
Nicolae Orlandea
Keyword(s):  
Differential Equations ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
System Of Differential Equations ◽  
Original Contribution ◽  
Deductive Method ◽  
Method Of Solution ◽  
Further Development ◽  
Three Degrees Of Freedom

This paper is a further development of the kinematic problem presented in our 1967 paper [1] in which we have obtained the transmission functions for different orders of plane systems with many degrees of freedom. This paper establishes the corresponding system of differential equations of motion beginning with these functions. The purpose of this paper is to facilitate computer programming. Our study is based on the work of R. Beyer [2, 3] and is the first original addition to his papers. A second original contribution to Beyer’s theories is the deductive method of solution, from general to particular, which we have, incorporated in our work. Beyer concluded that the cases having two or three degrees of freedom can be considered as particular solutions to the results obtained.

scholarly journals Decomposition of the Equations of Motion in the Analysis of Dynamics of a 3-DOF Nonideal System

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Jan Awrejcewicz ◽  
Roman Starosta ◽  
Grażyna Sypniewska-Kamińska
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Dynamical Behaviour ◽  
Engineering Systems ◽  
System Operation ◽  
Unbalanced Rotor ◽  
Nonideal System ◽  
Analysis Of Dynamics ◽  
Three Degrees Of Freedom

The dynamic response of a nonlinear system with three degrees of freedom, which is excited by nonideal excitation, is investigated. In the considered system the role of a nonideal source is played by a direct current motor, where the central axis of the rotor is not coincident with the axis of rotation. This translation generates a torque whose magnitude depends on the angular velocity. During the system operation a general coordinate assigned to the nonideal source grows rapidly as a result of rotation. We propose the decomposition of the equations of motion in such a way to extract the solution which is directly related to the rotation of an unbalanced rotor. The remaining part of the solution describes pure oscillation depending on the dynamical behaviour of the whole system. The decomposed equations are solved numerically. The influence of selected system parameters on the rotor vibration is examined. The presented approach can be applied to separate vibration and rotation of motions in many other engineering systems.

Dynamic Characteristics of an In-Contact Headslider Considering Meniscus Force: Part 1—Formulation and Application to the Disk With Sinusoidal Undulation

1999 ◽  
Vol 122 (3) ◽  
pp. 633-638 ◽  
Author(s):  
Takahisa Kato ◽  
Souta Watanabe ◽  
Hiroshige Matsuoka
Keyword(s):  
Dynamic Characteristics ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Disk Surface ◽  
Disk Interface ◽  
Meniscus Force ◽  
Calculation Results ◽  
Three Degrees Of Freedom

The authors present a three-degrees-of-freedom (3-DOF) model of an in-contact headslider/disk interface (HDI) system by which the dynamic characteristics of the in-contact headslider-suspension assembly can be obtained. Four regimes with respect to the interface of headslider and disk surface are shown to take the meniscus force of lubricant on the disk surface into account. The equations of motion of the in-contact headslider considering the meniscus force at each regime and the calculation results for the disk with sinusoidal undulation are described. [S0742-4787(00)01802-6]

scholarly journals Effect of Pulse Shape and Duration on Dynamic Response of a Forging System

2019 ◽  
Vol 13 (4) ◽  
pp. 226-232
Author(s):  
Arkadiusz Trąbka
Keyword(s):  
Dynamic Response ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Time History ◽  
Pulse Load ◽  
Negative Effects ◽  
Maximum Displacement ◽  
Soil Settlement ◽  
History Of ◽  
Three Degrees Of Freedom

Abstract Forging hammers are machines whose operation causes negative effects both at the place of their foundation (the soil settlement) and in their surroundings (e.g., vibrations propagating to the other devices, noise, etc.). Knowledge of the parameters characterizing the time history of the force that arises as a result of impact of a ram on a shaped material is of fundamental importance for the correct analysis of both the structure of the hammer and its impact on the surroundings. In the paper, the effect of the shape and duration of a pulse load on the dynamic response of a hammer-foundation forging system was assessed. An analytical method of description of the forces that arise as a result of impact of the ram on the forged material, using different forms of pulses was presented. The forces defined in this way as loads in a mathematical model of three degrees of freedom forging system were used. The equations of motion derived from d’Alembert’s principle were solved numerically in the Matlab program. The analyses for eight forms of the pulse loads with the same pulse sizes but different durations were performed. The results in the graphs were presented. It was found, among other things, that a greater impact on the maximum displacement, velocity and acceleration of each component of the hammer-foundation system as well as on the maximum forces transmitted to the soil has the duration of a pulse than its shape.

scholarly journals Non-Linear Response of Light Equipment System in a Torsional Building to Bi-Directional Ground Excitation

1999 ◽  
Vol 6 (5-6) ◽  
pp. 223-235 ◽  
Author(s):  
Abhijit K. Agrawal
Keyword(s):  
Degrees Of Freedom ◽  
Damping Ratio ◽  
Relative Displacement ◽  
Primary System ◽  
Time Domain Simulation ◽  
Earthquake Excitation ◽  
Non Linear ◽  
Torsional Coupling ◽  
Three Degrees Of Freedom ◽  
Equipment System

Dynamic response of a light equipment item attached to a non-linear and torsionally coupled main system is evaluated under bi-directional earthquake excitation. To account for the effect of translations and torsion, each story of the building is modelled as three degrees-of-freedom (DOFs), with two DOFs for translation in two orthogonal directions and third DOF for torsion. The responses (relative displacement between the equipment system and the floor of the primary system on which the equipment system is mounted and absolute acceleration of the equipment system itself), are determined under random ground motion in two orthogonal directions, which is idealized as a stationary random process represented by a white noise excitation. The responses are obtained by time domain simulation procedure. The response behavior of the light equipment is examined under a set of parametric variations. These parameters include the uncoupled lateral frequency of the primary and the equipment systems, the ratio of uncoupled lateral to rotational frequencies of the primary system, eccentricity ratios of the primary and the equipment systems in X and Y directions, damping ratio of the primary and the equipment systems and the mass ratio of the two systems. Results of the study indicate that under some parametric conditions the responses of the equipment system are significantly affected by torsional coupling and non-linearity of the primary system. It is also observed that the responses of the equipment system can be alleviated by increasing the damping ratio of the equipment system.

Countersteering to Recover Straight Ahead Running After a Disturbance

2016 ◽  
Author(s):  
Fabio della Rossa ◽  
Massimiliano Gobbi ◽  
Giampiero Mastinu ◽  
Giorgio Previati
Keyword(s):  
Degrees Of Freedom ◽  
Rear Axle ◽  
External Disturbance ◽  
Equations Of Motion ◽  
Driver Model ◽  
Steering Wheel ◽  
Non Linear ◽  
Oscillating Motion ◽  
Straight Ahead ◽  
Lateral Excitation

The paper deals with the analysis of a manoeuvre occurring frequently before crashes. Due to an external disturbance the straight ahead running of a vehicle is degradated into an oscillating motion. The driver is required to countersteer to recover the straight ahead motion. The bifurcation analysis of a simple model describing a vehicle+driver running straight ahead is performed. The mechanical model of the car has two degrees of freedom and the related equations of motion contain the non linear tyre characteristics. The driver is described by a non linear model defined by three parameters, namely the gain (steering wheel angle per lateral deviation from desired path), the prevision distance, the reaction time delay. Unreferenced bifurcations are discovered for the understeering vehicle. A supercritical Hopf bifurcation may occur as forward speed is increased. Also tangent (fold) bifurcations occur as the speed (or disturbance) are further increased. The vehicle+driver model is validated by means of a number of tests performed in a track. The validation relies on the identification of driver’s parameters. The track is equipped with a plank sliding laterally when the vehicle rear axle passes on it. Such a lateral excitation applies a disturbance to the vehicle which initiates a spin to be counteracted by the driver. An analysis is performed on driver’s parameters identification. Such parameter identification seems a possible way to assess single driver’s ability to perform recovery manoeuvres.

Influence of Geometry on the Non-Linear Vibrations of Cylindrical Shells With Internal Flowing Fluid

2010 ◽  
Author(s):  
Zenon J. del Prado ◽  
Paulo B. Gonc¸alves ◽  
Michael P. Pai¨doussis
Keyword(s):  
Cylindrical Shell ◽  
Degrees Of Freedom ◽  
Lateral Displacement ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Dynamic Environment ◽  
Geometric Parameters ◽  
Flowing Fluid ◽  
Non Linear ◽  
Linear Vibrations

In this work, the influence of the characteristic geometric parameters of a cylindrical shell, such as radius-to-thickness and radius-to-length ratios, on both the linear and non-linear vibrations of a fluid-filled cylindrical shell with internal flowing fluid is studied. The Donnell non-linear shallow shell equations are used to study a simply supported cylindrical shell subjected to both lateral and axial time-dependent loads with internal flowing fluid. The fluid is assumed to be inviscid and incompressible and the flow isentropic and irrotational. An expansion with eight degrees of freedom, containing the fundamental, companion, gyroscopic and five axisymmetric modes is used to describe the lateral displacement of the shell. The Galerkin method is used to obtain the nonlinear equations of motion which are, in turn, solved by the Runge-Kutta method. First, the parametric linear equations are used to study the influence of geometry and physical properties on the natural frequencies, critical flow and critical circumferential wavenumber. Secondly, numerical methods are used to describe the influence of geometric characteristics on the non-linear frequency-amplitude relations of the shell. The results obtained show the influence of the geometric parameters on the vibration characteristics of the shell and can be used as a basic tool for design of cylindrical shells in a dynamic environment.

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