SYMBOLIC EQUATIONS FOR A FULL-CAR MODEL

2000 ◽  
Vol 24 (3-4) ◽  
pp. 493-514
Author(s):  
Natalie Baddour ◽  
K. A. Morris
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
A Priori ◽  
Active Suspension ◽  
Lagrangian Mechanics ◽  
Full Generality ◽  
Active Suspensions ◽  
Car Model ◽  
Simplifying Assumptions ◽  
Improved Performance

Active suspensions provide improved performance over conventional, passive suspensions. In this paper, modelling issues for an active suspension are considered. Symbolic equations for a full car model are derived using Lagrangian mechanics. The model has ten degrees of freedom instead of the usual seven. Furthermore, many of the usual simplifying assumptions are not made a priori so that the model retains its full generality. The model is developed so that modifications to any of the assumptions might easily be made and so that the equations of motion can be easily altered to satisfy more restrictive assumptions.

The Influence of Loading Position in A Priori High Stress Detection using Mode Superposition

2020 ◽  
Vol 1 (1) ◽  
pp. 93-102
Author(s):  
Carsten Strzalka ◽  
◽  
Manfred Zehn ◽  
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
A Priori ◽  
High Stress ◽  
Von Mises Stress ◽  
Detailed Knowledge ◽  
Variable Loading ◽  
Numerical Effort ◽  
Von Mises

For the analysis of structural components, the finite element method (FEM) has become the most widely applied tool for numerical stress- and subsequent durability analyses. In industrial application advanced FE-models result in high numbers of degrees of freedom, making dynamic analyses time-consuming and expensive. As detailed finite element models are necessary for accurate stress results, the resulting data and connected numerical effort from dynamic stress analysis can be high. For the reduction of that effort, sophisticated methods have been developed to limit numerical calculations and processing of data to only small fractions of the global model. Therefore, detailed knowledge of the position of a component’s highly stressed areas is of great advantage for any present or subsequent analysis steps. In this paper an efficient method for the a priori detection of highly stressed areas of force-excited components is presented, based on modal stress superposition. As the component’s dynamic response and corresponding stress is always a function of its excitation, special attention is paid to the influence of the loading position. Based on the frequency domain solution of the modally decoupled equations of motion, a coefficient for a priori weighted superposition of modal von Mises stress fields is developed and validated on a simply supported cantilever beam structure with variable loading positions. The proposed approach is then applied to a simplified industrial model of a twist beam rear axle.

scholarly journals On the Benefits of Semi-Active Suspensions with Inerters

2012 ◽  
Vol 19 (3) ◽  
pp. 257-272 ◽  
Author(s):  
Xin-Jie Zhang ◽  
Mehdi Ahmadian ◽  
Kong-Hui Guo
Keyword(s):  
High Performance ◽  
Control Method ◽  
Hybrid Control ◽  
Active Suspension ◽  
Vertical Acceleration ◽  
Active Suspensions ◽  
Quarter Car Model ◽  
Suspension Systems ◽  
Car Model ◽  
Quarter Car

Inerters have become a hot topic in recent years especially in vehicle, train, building suspension systems, etc. Eight different layouts of suspensions were analyzed with a quarter-car model in this paper. Dimensionless root mean square (RMS) responses of the sprung mass vertical acceleration, the suspension travel, and the tire deflection are derived which were used to evaluate the performance of the quarter-car model. The behaviour of semi-active suspensions with inerters using Groundhook, Skyhook, and Hybrid control has been evaluated and compared to the performance of passive suspensions with inerters. Sensitivity analysis was applied to the development of a high performance semi-active suspension with an inerter. Numerical simulations indicate that a semi-active suspension with an inerter has much better performance than the passive suspension with an inerter, especially with the Hybrid control method, which has the best compromise between comfort and road holding quality.

Integral and State Variable Feedback Controllers for Improved Performance in Automotive Vehicles

1991 ◽  
Author(s):  
Mohamed M. ElMadany
Keyword(s):  
Attitude Control ◽  
Body Force ◽  
Analytical Investigation ◽  
Feedback Controller ◽  
Feedback Controllers ◽  
Active Suspensions ◽  
State Variable ◽  
Car Model ◽  
Potential Benefits ◽  
Improved Performance

Abstract An analytical investigation of a half-car model using an integral plus state variable feedback controller for tracking and regulation is performed. The potential benefits of incorporating, actively or semi-actively, such controller to remedy the inherent problems associated with conventional passive suspensions and active suspensions based on state variable feedback controllers are examined. Both random and deterministic roadway inputs as well as deterministic body force and moment disturbances are used. The results demonstrate that an optimal suspension using an integral plus state variable feedback controller retains both excellent ride and attitude control characteristics.

Design of Non-Fragile H∞ Controller for Active Vehicle Suspensions

2005 ◽  
Vol 11 (2) ◽  
pp. 225-243 ◽  
Author(s):  
Haiping Du ◽  
James Lam ◽  
Kam Yim Sze
Keyword(s):  
State Feedback ◽  
Closed Loop ◽  
A Priori ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Active Suspensions ◽  
Vehicle Suspensions ◽  
Quarter Car Model ◽  
Car Model ◽  
Controller Gain

In this paper we present an approach to design the non-fragile H ∞ controller for active vehicle suspensions. A quarter-car model with active suspension system is considered in this paper. By suitably formulating the sprung mass acceleration, suspension deflection and tire deflection as the optimization object and considering a priori norm-bounded controller gain variations, the non-fragile state-feedback H ∞ controller can be obtained by solving a linear matrix inequality. The designed controller not only can achieve the optimal performance for active suspensions but also preserves the closed-loop stability in spite of the controller gain variations.

The Equations of Motion for the Torsional and Bending Vibrations of a Stranded Cable

1992 ◽  
Vol 59 (2S) ◽  
pp. S224-S229 ◽  
Author(s):  
Warren N. White ◽  
Srinivasan Venkatasubramanian ◽  
P. Michael Lynch ◽  
Chi-Lung D. Huang
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Hamilton’S Principle ◽  
Attached Mass ◽  
Hamilton's Principle ◽  
Bending Vibrations ◽  
Aerodynamic Loading ◽  
Simplifying Assumptions ◽  
Rotational Degrees Of Freedom

Equations of motion of a thin, stranded elastic cable with an eccentric, attached mass and subject to aerodynamic loading are derived using Hamilton’s principle. Coupling between the translational and rotational degrees of freedom owing to inertia, elasticity, and stranded geometry are considered. By invoking simplifying assumptions, the equations of motion are reduced to those obtained previously by other researchers.

DISCRETE TIME ADAPTIVE ACTIVE SUSPENSION FOR A HALF-CAR MODEL

1997 ◽  
Vol 21 (3) ◽  
pp. 221-272 ◽  
Author(s):  
R.V. Dukkipati ◽  
S.S. Vallurupalli ◽  
M.O.M. Osman
Keyword(s):  
Discrete Time ◽  
Degrees Of Freedom ◽  
Vibration Isolation ◽  
Reference Model ◽  
Moving Average ◽  
Active Suspension ◽  
Parameters Estimation ◽  
Degree Of Freedom ◽  
Computational Time ◽  
Car Model

This paper presents a discrete time adaptive active suspension for a multi-degree of freedom (MDOF) half-car model. The study involves formulation of a pitch plane half-car model involving four degrees of freedom and various nonlinear time varying (NTV) parameters. A multi-degree of freedom skyhook reference model has been described in this paper. Discrete auto regressive moving average (DARMA) models for the NTV-MDOF and the reference model have been developed. A modified version of the least squares estimation in which the controller parameters are updated as a matrix rather than as a vector has been derived in this paper. This approach reduces the computational time required for an adaptive controller parameters estimation and enhances the hardware implementation process. Computer simulation results indicate good adaptation to the reference model and maintenance of static equilibrium conditions for large squat and nose diving longitudinal manoeuvres. The responses also indicate an optimal vibration isolation and suspension travel performance by adapting to the reference model.

Designing Efficient Trajectories for Underwater Vehicles Using Geometric Control Theory

2005 ◽  
Author(s):  
M. Chyba ◽  
T. Haberkorn
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Underwater Vehicles ◽  
Lagrangian Mechanics ◽  
The Maximum Principle ◽  
Marine Vehicles ◽  
Time Problem ◽  
Time Optimal ◽  
6 Degrees Of Freedom ◽  
Minimum Time Problem

In this paper, we consider the minimum time problem for underwater vehicles. Using Lagrangian mechanics, we write the equations of motion for marine vehicles with 6 degrees of freedom as a controlled mechanical system. We then apply the necessary conditions from the maximum principle for a trajectory to be time optimal. Using techniques from differential geometry we analyze the resuls. Finally we supplement the theoretical study with numerical simulations.

Online Adaptive Neuro-Fuzzy Based Full Car Suspension Control Strategy

2015 ◽  
pp. 992-1039
Author(s):  
Laiq Khan ◽  
Shahid Qamar
Keyword(s):  
Degrees Of Freedom ◽  
Ride Comfort ◽  
Sliding Mode ◽  
Active Suspension ◽  
Suspension System ◽  
Car Model ◽  
Car Suspension ◽  
Neuro Fuzzy ◽  
Suspension Control ◽  
Soft Computing Technique

Suspension system of a vehicle is used to minimize the effect of different road disturbances for ride comfort and improvement of vehicle control. A passive suspension system responds only to the deflection of the strut. The main objective of this work is to design an efficient active suspension control for a full car model with 8-Degrees Of Freedom (DOF) using adaptive soft-computing technique. So, in this study, an Adaptive Neuro-Fuzzy based Sliding Mode Control (ANFSMC) strategy is used for full car active suspension control to improve the ride comfort and vehicle stability. The detailed mathematical model of ANFSMC has been developed and successfully applied to a full car model. The robustness of the presented ANFSMC has been proved on the basis of different performance indices. The analysis of MATLAB/SMULINK based simulation results reveals that the proposed ANFSMC has better ride comfort and vehicle handling as compared to Adaptive PID (APID), Adaptive Mamdani Fuzzy Logic (AMFL), passive, and semi-active suspension systems. The performance of the active suspension has been optimized in terms of displacement of seat, heave, pitch, and roll.

scholarly journals Dynamic Bridge Response for a Bridge-friendly Truck

10.14311/646 ◽  
2004 ◽  
Vol 44 (5-6) ◽  
Author(s):  
V. Šmilauer ◽  
J. Máca ◽  
M. Valášek
Keyword(s):  
Rear Axle ◽  
Bridge Deck ◽  
Equations Of Motion ◽  
Surface Profile ◽  
Bridge Structure ◽  
Active Suspensions ◽  
Simply Supported ◽  
Car Model ◽  
Tire Forces ◽  
Original Concept

A truck with controlled semi-active suspensions traversing a bridge is examined for benefits to the bridge structure. The original concept of a road-friendly truck was extended to a bridge-friendly vehicle, using the same optimization tools. A half-car model with two independently driven axles is coupled with simply supported bridges (beam, slab model) with the span range from 5 m to 50 m. Surface profile of the bridge deck is either stochastic or in the shape of a bump or a pot in the mid-span. Numerical integration in the MATLAB/SIMULINK environment solves coupled dynamic equations of motion with optimized truck suspensions. The rear axle generates the prevailing load and to a great extent determines the bridge response. A significant decrease in contact road-tire forces is observed and the mid-span bridge deflections are on average smaller, when compared to commercial passive suspensions. 

Optimal Semi-Active Suspension with Preview Based on a Quarter Car Model

1992 ◽  
Vol 114 (1) ◽  
pp. 84-92 ◽  
Author(s):  
A. Hac´ ◽  
I. Youn
Keyword(s):  
Frequency Domain ◽  
Piecewise Linear ◽  
A Priori ◽  
Bilinear System ◽  
Active Suspension ◽  
Problem Formulation ◽  
System Response ◽  
Quarter Car Model ◽  
Car Model ◽  
Quarter Car

This paper deals with the synthesis of an optimal yet practical finite preview controller for a semi-active dissipative suspension system based on a two-degree-of-freedom (2-DOF) vehicle model. The proposed controller utilizes knowledge about approaching road disturbances obtained from preview sensors to minimize the effect of these disturbances. A truly optimal control law, which minimizes a quadratic performance index under passivity constraints, is derived using a variational approach. The optimal closed loop system becomes piecewise linear varying between two passive systems and a fully active one. It is shown that the steady state system response to a periodic input is also periodic and its amplitude is proportional to the amplitude of the input. Therefore, frequency domain characteristics in a classical sense can be generated. The problem formulation and the analytical solution are given in a general form and hence they apply to any bilinear system with system disturbances that are a priori unknown but some preview information is possible. The results of this analysis are applied to a quarter car model with semi-active suspension whose frequency domain and time domain performances are evaluated and compared to those of fully active and passive models. The effect of preview time on the system performance is also examined.

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