A Low Computational Cost Nonlinear Formulation for Multibody Railroad Vehicle Systems

2007 ◽  
Author(s):  
Graham G. Sanborn ◽  
Jason R. Heineman ◽  
Ahmed A. Shabana
Keyword(s):  
Coordinate System ◽  
Degrees Of Freedom ◽  
Dynamic Models ◽  
Computational Cost ◽  
Space Curve ◽  
The Body ◽  
Degree Of Freedom ◽  
Arbitrary Body ◽  
Resistance Forces ◽  
Low Computational Cost

In this investigation, a multibody system formulation for the nonlinear dynamics of railroad vehicles is developed. This formulation, which permits developing simplified models for the forces acting on rail cars, allows the analysis of long trains at a low computational cost. In the dynamic models developed using the formulation proposed in this investigation, each rail car can be represented as a single rigid body. The configurations of the bodies in a train model are defined with respect to trajectory coordinate systems which follow a space curve whose geometry is defined at a preprocessing stage. In the formulation presented in this study, the number of degrees of freedom of an arbitrary body can be varied from one to six degrees of freedom. The principal degree of freedom of an arbitrary body is the arc length along the space curve. This degree of freedom defines the location of the origin and the orientation of the body trajectory coordinate system. The other five degrees of freedom define the location and orientation of the body with respect to the body trajectory coordinate system. The nonlinear equations of motion of the bodies in a train model are developed using the three-dimensional Newton-Euler equations. These equations are then expressed in terms of the trajectory coordinates and their derivatives. To this end, a velocity transformation is obtained by expressing the Cartesian and angular velocities of the bodies in terms of the time derivatives of the trajectory coordinates. Various force element models particular to rail cars are developed in this study. These forces include tractive effort, and air brake and dynamic brake forces, as well as a model of available wheel-rail adhesion. Additionally, various types of couplers are formulated as force elements, allowing the modeling of connections between cars. Resistance forces are also modeled in order to be able to simulate rolling, curve, and air resistance forces that may act on the cars during the train operations.

Rolling Condition and Gyroscopic Moments in Curve Negotiations

2012 ◽  
Author(s):  
Ahmed A. Shabana ◽  
Martin B. Hamper ◽  
James J. O’Shea
Keyword(s):  
Coordinate System ◽  
Degrees Of Freedom ◽  
The Body ◽  
Contact Forces ◽  
Body Motion ◽  
Global Coordinate System ◽  
Gyroscopic Moment ◽  
Absolute Angular Velocity ◽  
Pure Rolling ◽  
The Stability

In vehicle system dynamics, the effect of the gyroscopic moments can be significant during curve negotiations. The absolute angular velocity of the body can be expressed as the sum of two vectors; one vector is due to the curvature of the curve, while the second vector is due to the rate of changes of the angles that define the orientation of the body with respect to a coordinate system that follows the body motion. In this paper, the configuration of the body in the global coordinate system is defined using the trajectory coordinates in order to examine the effect of the gyroscopic moments in the case of curve negotiations. These coordinates consist of arc length, two relative translations and three relative angles. The relative translations and relative angles are defined with respect to a trajectory coordinate system that follows the motion of the body on the curve. It is shown that when the yaw and roll angles relative to the trajectory coordinate system are constrained and the motion is predominantly rolling, the effect of the gyroscopic moment on the motion becomes negligible, and in the case of pure rolling and zero yaw and roll angles, the generalized gyroscopic moment associated with the system degrees of freedom becomes identically zero. The analysis presented in this investigation sheds light on the danger of using derailment criteria that are not obtained using laws of motion, and therefore, such criteria should not be used in judging the stability of railroad vehicle systems. Furthermore, The analysis presented in this paper shows that the roll moment which can have a significant effect on the wheel/rail contact forces depends on the forward velocity in the case of curve negotiations. For this reason, roller rigs that do not allow for the wheelset forward velocity cannot capture these moment components, and therefore, cannot be used in the analysis of curve negotiations. A model of a suspended railroad wheelset is used in this investigation to study the gyroscopic effect during curve negotiations.

Regulating a Formation of a Large Number of Vehicles

2005 ◽  
Author(s):  
Akira Okamoto ◽  
Dean B. Edwards
Keyword(s):  
Control Problem ◽  
Coordinate System ◽  
Formation Control ◽  
Control Algorithm ◽  
Degrees Of Freedom ◽  
Degree Of Freedom ◽  
Relative Distance ◽  
Control Algorithms ◽  
Distance Measurements ◽  
Six Degree Of Freedom

Various control algorithms have been developed for fleets of autonomous vehicles. Many of the successful control algorithms in practice are behavior-based control or nonlinear control algorithms, which makes analyzing their stability difficult. At the same time, many system theoretic approaches for controlling a fleet of vehicles have also been developed. These approaches usually use very simple vehicle models such as particles or point-mass systems and have only one coordinate system which allows stability to be proven. Since most of the practical vehicle models are six-degree-of-freedom systems defined relative to a body-fixed coordinate system, it is difficult to apply these algorithms in practice. In this paper, we consider a formation regulation problem as opposed to a formation control problem. In a formation control problem, convergence of a formation from random positions and orientations is considered, and it may need a scheme to integrate multiple moving coordinates. On the contrary, in a formation regulation problem, it is not necessary since small perturbations from the nominal condition, in which the vehicles are in formation, are considered. A common origin is also not necessary if the relative distance to neighbors or a leader is used for regulation. Under these circumstances, the system theoretic control algorithms are applicable to a formation regulation problem where the vehicle models have six degrees of freedom. We will use a realistic six-degree-of-freedom model and investigate stability of a fleet using results from decentralized control theory. We will show that the leader-follower control algorithm does not have any unstable fixed modes if the followers are able to measure distance to the leader. We also show that the leader-follower control algorithm has fixed modes at the origin, indicating that the formation is marginally stable, when the relative distance measurements are not available. Multi-vehicle simulations are performed using a hybrid leader-follower control algorithm where each vehicle is given a desired trajectory to follow and adjusts its velocity to maintain a prescribed distance to the leader. Each vehicle is modeled as a three-degree-of-freedom system to investigate the vehicle’s motion in a horizontal plane. The examples show efficacy of the analysis.

Implementation of Low Computational Cost Nonlinear Formulation for Multibody Railroad Vehicle Systems

2007 ◽  
Author(s):  
Graham G. Sanborn ◽  
Jason R. Heineman ◽  
Ahmed A. Shabana
Keyword(s):  
Degrees Of Freedom ◽  
Computational Cost ◽  
Companion Paper ◽  
Computer Interface ◽  
Model Parameters ◽  
Nonlinear Formulation ◽  
Vehicle Systems ◽  
Railroad Applications ◽  
Railroad Vehicle ◽  
Low Computational Cost

In a companion paper [1], a low computational cost nonlinear formulation was presented to for the analysis of the forces of long trains. The formulation allows systematically changing the number of degrees of freedom of each rail car and includes the force inputs that are typically found in railroad applications. In this paper, the implementation of this nonlinear formulation is described. A computer interface is also developed in order to allow the user to operate a virtual train model in real time and also change the model parameters and car connectivity conditions. Numerical results are presented in order to demonstrate the use of the formulation proposed and its computer implementation.

Modeling and Experimental Evaluation of Asymmetric Pantograph Dynamics

1988 ◽  
Vol 110 (2) ◽  
pp. 168-174 ◽  
Author(s):  
S. D. Eppinger ◽  
D. N. O’Connor ◽  
W. P. Seering ◽  
D. N. Wormley
Keyword(s):  
High Performance ◽  
Degrees Of Freedom ◽  
Dynamic Models ◽  
Dynamic Testing ◽  
Dynamic Performance ◽  
Performance Model ◽  
Degree Of Freedom ◽  
Additional Degree ◽  
Three Degree Of Freedom ◽  
Two Degree Of Freedom

High-performance pantograph design requires control of pantograph dynamic performance. Many pantograph dynamic models developed to aid in the design process have employed two degrees of freedom, one for the head mass and one for the frame. In this paper, the applicability of these models to symmetric and asymmetric pantograph designs is reviewed. Two degree-of-freedom models have been shown to be appropriate to represent a number of symmetric pantograph designs. To represent the asymmetric designs considered in this paper, an additional degree of freedom representing frame dynamics has been introduced to yield a three degree-of-freedom nonlinear dynamic performance model. The model has been evaluated with experimental data obtained from laboratory dynamic testing of an asymmetric pantograph.

Flight performance and visual control of flight of the free-flying housefly ( Musca domestica L.) I. Organization of the flight motor

1986 ◽  
Vol 312 (1158) ◽  
pp. 527-551 ◽  
Keyword(s):  
Coordinate System ◽  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Rigid Bodies ◽  
The Body ◽  
Midsagittal Plane ◽  
Torque Vector ◽  
Translation Velocity ◽  
Flight Motor

Free-flying houseflies have been filmed simultaneously from two sides. The orientation of the flies’ body axes in three-dimensional space can be seen on the films. A method is presented for the reconstruction of the flies’ movements in a fly-centred coordinate system, relative to an external coordinate system and relative to the airstream. The flies are regarded as three-dimensionally rigid bodies. They move with respect to the six degrees of freedom they thus possess. The analysis of the organization of the flight motor from the kinematic data leads to the following conclusions: the sideways movements can, at least qualitatively, be explained by taking into account the sideways forces resulting from rolling the body about the long axis and the influence of inertia. Thus, the force vector generated by the flight motor is most probably located in the fly’s midsagittal plane. The direction of this vector can be varied by the fly in a restricted range only. In contrast, the direction of the torque vector can be freely adjusted by the fly. No coupling between the motor force and the torques is indicated. Changes of flight direction may be explained by changes in the orientation of the body axes: straight flight at an angle of sideslip differing from zero is due to rolling. Sideways motion during the banked turns as well as the decrease of translation velocity observed in curves are a consequence of the inertial forces and rolling. The results are discussed with reference to studies about the aerodynamic performance of insects and the constraints for aerial pursuit.

scholarly journals Design and Analysis of Steering and Lifting Mechanisms for Forestry Vehicle Chassis

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Wenhao Li ◽  
Feng Kang
Keyword(s):  
Complex Terrain ◽  
Degrees Of Freedom ◽  
The Body ◽  
Degree Of Freedom ◽  
Working Environment ◽  
Steering Mechanism ◽  
Working Principle ◽  
Turning Radius ◽  
And Function ◽  
Vehicle Chassis

Due to its special topographical structure, the forest working environment requires a vehicle chassis that can adapt well to complex terrain conditions. This article describes the key components of a chassis that was designed to adapt to complex terrain. The working principle and structural design of the steering structure and the lifting structure are analyzed in detail, and function verification is carried out. The steering mechanism has three degrees of freedom, and the first degree of freedom reduces the body’s inclination by 30°. The second degree of freedom can increase the steering angle of the chassis to 47°, decreasing the turning radius of the chassis. The third degree of freedom reduces the body rollover inclination by 30°. The entire steering mechanism enhances the ride and stability of the chassis. With the lifting mechanism, the wheel-legs are lifted so that the chassis can pass a limit height of 187 mm, and the wheel-legs are lowered to raise the center of gravity of the vehicle chassis by 244 mm. The entire lifting mechanism greatly improves the vehicle's ability to cross forest terrain. The size is reduced by 10% compared to other structures, and the lifting height and obstacle resistance are improved by 12.7%.

Time Domain Method for Parameter System Identification

1990 ◽  
Vol 112 (3) ◽  
pp. 281-287 ◽  
Author(s):  
A. Hac ◽  
P. D. Spanos
Keyword(s):  
Least Squares ◽  
Computational Cost ◽  
Degree Of Freedom ◽  
Parameter Estimates ◽  
Noisy Environment ◽  
Adaptive Kalman Filter ◽  
System Parameters ◽  
System Equation ◽  
Two Degree Of Freedom ◽  
Low Computational Cost

In this paper a method of parameter identification for a multi-degree-of-freedom structural system in a noisy environment is presented. The method involves an iterative procedure in which initial parameter estimates are obtained by relying on a least squares kind of approximation. This estimate is used in an adaptive Kalman filter to obtain an improved estimate of the system state. The improved estimate is then utilized in the least squares approximation to produce refined estimates of the system parameters. The iteration is repeated until it converges within an acceptable margin. The parameter errors are compensated during filtering by adding pseudonoise to the system equation; the noise itensity is updated in each iteration. Results of a simulation study conducted for a two-degree-of-freedom system indicate that the method can yield, for a relatively low computational cost, reliable estimates of system parameters, even when the data record is short.

Design and Evaluation of a Passive Ankle Prosthesis With Rotational Power Generation by a Compliant Coupling Between Leg Deflection and Ankle Rotation

2014 ◽  
Author(s):  
Jacob J. Rice ◽  
Joseph M. Schimmels
Keyword(s):  
Degrees Of Freedom ◽  
Gait Cycle ◽  
The Body ◽  
Degree Of Freedom ◽  
Rotational Degree ◽  
Kinematic Data ◽  
Active Behavior ◽  
Ankle Prosthesis ◽  
Compression Spring ◽  
Translational Degree

This paper presents the design and simulation results of a passive prosthetic ankle prosthesis that has mechanical behavior similar to a natural ankle. The presented design achieves active behavior with powered push-off to propel the body forward. The design contains a conventional compression spring network that allows coupling between two degrees of freedom. There is a translational degree of freedom along the leg and a rotational degree of freedom about the ankle joint. During a standard gait cycle, potential energy from the person’s weight is stored in the spring network from deflection along the leg. The energy is released by the spring network as rotation of the foot. With this design, capping the allowable leg deflection at 15 millimeters produces 45% of the rotational work that a natural ankle will produce. This is based on simulation using published average kinetic and kinematic data from gait analyses.

scholarly journals Aerial Manipulator Control Method Based on Generalized Jacobian

2021 ◽  
Vol 33 (2) ◽  
pp. 231-241
Author(s):  
Takahiro Ikeda ◽  
Kenichi Ohara ◽  
Akihiko Ichikawa ◽  
Satoshi Ashizawa ◽  
Takeo Oomichi ◽  
...  
Keyword(s):  
Coordinate System ◽  
Unmanned Aerial Vehicle ◽  
Control Method ◽  
The Body ◽  
Degree Of Freedom ◽  
Bridge Inspection ◽  
Generalized Jacobian ◽  
Aerial Manipulator ◽  
Aerial Vehicle ◽  
Manipulator Control

This paper describes a control method for an aerial manipulator on an unmanned aerial vehicle (UAV) by using a generalized Jacobian (GJ). Our task is to realize visual check of bridge inspection by employing a UAV with a multi-degree-of-freedom (DoF) manipulator on its top. The manipulator is controlled by using the GJ. Subsequently, by comparing the aerial manipulator control with a conventional Jacobian experimentally, we discovered that the accuracy of the control improved by applying the GJ. The manipulator has three DoFs in the X-Z plane of the UAV coordinate system. The experiment shows that the manipulator controlled with the GJ can compensate for the pose error of the body by 54.5% and 47.7% in the X- and Z-axes, respectively.

WAVELET ADAPTIVE MULTIRESOLUTION REPRESENTATION: APPLICATIONS TO VISCOUS MULTISCALE FLOW SIMULATIONS

2006 ◽  
Vol 04 (02) ◽  
pp. 333-343 ◽  
Author(s):  
YEVGENII A. RASTIGEJEV ◽  
SAMUEL PAOLUCCI
Keyword(s):  
Degrees Of Freedom ◽  
Computational Cost ◽  
Reynolds Numbers ◽  
Great Ability ◽  
Driven Cavity ◽  
Multiresolution Representation ◽  
Order Of Magnitude ◽  
Comparable Accuracy ◽  
Solution Accuracy ◽  
Low Computational Cost

We present a new wavelet-based adaptive multiresolution representation (WAMR) algorithm for the numerical solution of multiscale evolution problems. Key features of the algorithm are fast procedures for grid rearrangement, computation of derivatives, as well as the ability to minimize the degrees-of-freedom for a prescribed solution accuracy. To demonstrate the efficiency and accuracy of the algorithm, we use it to solve the two-dimensional benchmark problem of incompressible fluid-flow in a lid-driven cavity at large Reynolds numbers. The numerical experiments demonstrate the great ability of the algorithm to adapt to different scales at different locations and at different times so as to produce accurate solutions at low computational cost. Specifically, we show that solutions of comparable accuracy as the benchmarks are obtained with more than an order of magnitude reduction in degrees-of-freedom.

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