Nonlinear Modeling and Experimental Validation of Tire Nonuniformity Induced Tangential Steering Wheel Vibrations

2006 ◽  
Author(s):  
Virgile Ayglon ◽  
Nader Jalili ◽  
Imtiaz Haque
Keyword(s):  
Degrees Of Freedom ◽  
Nonlinear Modeling ◽  
Equations Of Motion ◽  
Quantitative Measure ◽  
Steering System ◽  
Steering Wheel ◽  
Vehicle Speed ◽  
Pinion Gear ◽  
Stiffness And Damping ◽  
Vehicle Chassis

This paper describes the model integration and validation that followed the development of nonlinear models of a tire with non-uniformities, a double wishbone suspension and rack-and-pinion power steering. These submodels are integrated to investigate the effects of variation of tire, suspension and steering parameters on the transmission of tire forces acting on the wheel spindle to the steering system and vehicle chassis. The tire model is based on a rigid ring model which includes mass imbalance and balancing mass. The suspension is idealized as rigid links with seven degrees-of-freedom and the bushings are represented by spring-damper elements. The equations of motion are derived using the Lagrange multiplier method in Maple, and solved numerically using Matlab DAE solver. The steering system is idealized as a four degree-of-freedom system and considers motion of the rack, rack housing, pinion gear and steering wheel. Nonlinear compliant friction is considered between the pinion gear / rack, and the steering column / chassis interfaces. The analytical model is used to develop a quantitative measure of the relative importance of the parameters such as mass/inertia, suspension bushing stiffness and damping, torsion bar stiffness and damping, rack friction and damping, to the force transmissibility to the vehicle chassis and the steering system. Experimental results include a modal analysis, a shop-testing and road testing, which are used to cross verify the numerical simulations. The testing shows the variation of forces in the steering system due to tire imbalances, emphasizing the nonlinear variation of the nibble phenomenon with vehicle speed and tire imbalance. Results obtained from simulation matches well with the experimental measurements.

Development of a Non-Linear Model of a Double Wishbone Suspension for the Characterization of Force Transmission to the Steering Column and Chassis

2004 ◽  
Author(s):  
Vinod Cherian ◽  
Nader Jalili ◽  
Imtiaz Haque
Keyword(s):  
Numerical Simulation ◽  
Linear Model ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Quantitative Measure ◽  
Steering System ◽  
Force Transmission ◽  
Non Linear ◽  
Tire Forces ◽  
Vehicle Chassis

A non-linear model of a double wishbone suspension is developed to investigate the effects of variation of suspension parameters on the transmission and distribution of tire forces acting on the wheel spindle to the steering system and the vehicle chassis. The suspension is idealized as a four degree-of-freedom model, with suspension members considered as rigid links and the bushings idealized as linear spring-damper elements. Degrees-of-freedom representing the longitudinal compliance of the suspension mounting bushings, steering and the rotation of the control arms are considered. The equations of motion are derived using the Lagrange multiplier method, and solved numerically using MATLAB. A system of relative co-ordinates is used to reduce the number of equations due to the large number of geometric and kinematic constraints for an efficient numerical simulation. The equations retain all the non-linearity’s associated with large changes in the geometric configuration of the suspension system. The analytical model can be used to develop a quantitative measure of the importance of the parameters such as mass, inertia of the control arms, suspension bushing stiffness and damping and spatial geometry of installation to the force distribution and force transmissibility to the vehicle chassis and the steering system. The results of numerical simulation are compared with simulation data obtained from ADAMS.

Nonlinear Modeling and Theoretical Development of Tire Nonuniformity Induced Tangential Steering Wheel Vibrations

2005 ◽  
Author(s):  
Vinod Cherian ◽  
Nader Jalili ◽  
Imtiaz Haque
Keyword(s):  
Nonlinear Modeling ◽  
Equations Of Motion ◽  
Kinematic Chain ◽  
Steering System ◽  
Theoretical Development ◽  
Analytical Models ◽  
Steering Wheel ◽  
Virtual Test ◽  
Relative Coordinates ◽  
Linear Spring

This paper describes a nonlinear modeling approach for a double wishbone suspension developed to investigate the nonlinear kinematics and dynamics in the closed, spatial kinematic chain configuration of the suspension. This model is linked to a nonlinear rack and pinion steering subsystem model in order to study the steering nibble (steering wheel rotational vibrations). The suspension mechanism is idealized as a four degree-of-freedom model for a power assisted rack and pinion steering system, with suspension members considered as rigid links and the bushings idealized as linear spring-damper elements. A system of relative coordinates is used in the suspension subsystem model to minimize the number of equations that would be necessary due to the large number of geometrical and kinematic constraints. The equations of motion for the analytical subsystem models are derived symbolically using Maple and solved numerically using Matlab. The results of simulation of the model subjected to a virtual Kinematics and Compliance (K&C) test are compared with the results generated by the developed ADAMS model based on the parameters obtained from a vehicle manufacturer subjected to the same virtual test. Based on the results of the virtual K&C tests and quasi static simulation of the ADAMS model and the analytical models of the vehicle suspension subsystem, the kinematics results match ADAMS model very closely.

Ride Dynamics of a Flexible Multibody Model of an Urban Bus

2007 ◽  
Author(s):  
G. Georgiou ◽  
A. Badarlis ◽  
S. Natsiavas
Keyword(s):  
Degrees Of Freedom ◽  
Ride Comfort ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Accurate Information ◽  
Algebraic Equations ◽  
Multibody Model ◽  
Road Excitation ◽  
Urban Bus ◽  
Stiffness And Damping

Dynamic response of a large order mechanical model of an urban bus is investigated. The emphasis is first put on developing a quite complete model, which can be utilized in order to extract sufficiently reliable and accurate information related to its dynamics in a fast way. Since some of the components of the bus undergo large rigid body rotation, in addition to motion resulting from their deformability, a multibody dynamics framework is adopted. This implies that the resulting equations of motion appear in the form of a strongly nonlinear set of differential-algebraic equations, which are difficult to handle even numerically. In fact, the modeling becomes more involved because all the significant nonlinearities appearing in the interconnections of the structural components and especially in the front and rear suspension subsystems of the bus are taken into account. In order to alleviate some of these complexities, the number of degrees of freedom of each component, associated with its deformability, is reduced drastically by applying an appropriate coordinate condensation methodology. Finally, this model is employed and numerical results are obtained for motions resulting from typical road excitation. In particular, selected response quantities related to ride comfort are examined for characteristic combinations of the bus suspension stiffness and damping parameters.

Comparative Study of the Linear and Non-Linear Locomotive Response

1979 ◽  
Vol 101 (3) ◽  
pp. 263-271 ◽  
Author(s):  
E. H. Chang ◽  
V. K. Garg ◽  
C. H. Goodspeed ◽  
S. P. Singh
Keyword(s):  
Dynamic Response ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Design Parameters ◽  
Suspension Systems ◽  
Damping Characteristics ◽  
Time Histories ◽  
Steady State Responses ◽  
Stiffness And Damping ◽  
State Responses

A mathematical model for a six-axle locomotive is developed to investigate its dynamic response on tangent track due to vertical and/or lateral track irregularities. The model represents the locomotive as a system of thirty-nine degrees of freedom. The nonlinearities considered in the model are primarily associated with stiffness and damping characteristics of the primary suspension system. The transient and steady-state responses of the locomotive are obtained for the linear and nonlinear primary suspension systems. The response time-histories of the locomotive obtained by integrating the generalized equations of motion are presented. The potential uses of the model are indicated for studying the influence of different design parameters and predicting subsequent dynamic response.

On the Lateral Stability and Control of the Automobile as Influenced by the Dynamics of the Steering System

1966 ◽  
Vol 88 (3) ◽  
pp. 283-294 ◽  
Author(s):  
Leonard Segel
Keyword(s):  
Degrees Of Freedom ◽  
Steering System ◽  
Degree Of Freedom ◽  
Design Parameters ◽  
Steering Wheel ◽  
Directional Control ◽  
Natural Modes Of Motion ◽  
Three Degree Of Freedom ◽  
And Control ◽  
Automobile Use

Measurements of the directional response of an automobile to torque inputs applied at the steering wheel are compared with predictions yielded by a five-degree-of-freedom model of a four-wheeled, pneumatic-tired vehicle. This comparison demonstrates that the directional control and stability of the “free-control” automobile is satisfactorily characterized by the addition of a quasilinear representation of a steering system (i.e., a mechanism having two degrees of freedom with Coulomb friction introduced as the single nonlinear element) to a linear three-degree-of-freedom representation of the “fixed-control” automobile. Use is made of the experimentally substantiated five-degree-of-freedom mathematical model to study the relationship between automotive design parameters and the response and stability in each of the four natural modes of motion that exist for the free-control vehicle.

Modeling and Simulation of Electric Power Steering System Based on Multi-Body Dynamics

2011 ◽  
Vol 121-126 ◽  
pp. 2091-2097
Author(s):  
Jian Jun Hu ◽  
Zheng Bin He ◽  
Peng Ge ◽  
Guo Yun Li
Keyword(s):  
Electric Power ◽  
Dynamic Characteristic ◽  
Degrees Of Freedom ◽  
Steering System ◽  
Network Control ◽  
Steering Wheel ◽  
Electric Power Steering ◽  
Power Steering System ◽  
Power Steering ◽  
Electric Power Steering System

In order to analyze dynamic characteristic accurately during steering, electric power steering system is selected as research object and dynamic equation of steering system is established. Combined with eleven degrees of freedom vehicle model and tire model at combined conditions of longitudinal slip and side slip, the integral-simulation model of electric power steering system is established. The dynamic response of steering system at different steering wheel angle, control methods, front wheel steering angle and braking force is analyzed. The simulation results show that electric power steering system with neural network control has good stability, tracking performance, assist characteristic and anti-interference ability. The established model can reflect the dynamic characteristic correctly and effectively during steering.

The Research of Steer by Wire System Based on Fuzzy Logic Control

2011 ◽  
Vol 55-57 ◽  
pp. 780-784
Author(s):  
Shu Fang Geng ◽  
Qing Feng Peng ◽  
Li Fang Wang
Keyword(s):  
Fuzzy Logic ◽  
Fuzzy Logic Control ◽  
Control Method ◽  
Steering System ◽  
System Structure ◽  
Steering Wheel ◽  
System Control ◽  
Vehicle Speed ◽  
Response Characteristics ◽  
Logic Control

This paper describes SBW system structure and principle, for different vehicle speed inputs and steering wheel angle step inputs, the simulation model run in Simulink, and obtain yaw rate response characteristics, so the steering system control requirements is proposed, establishes fuzzy logic control system. This control strategy can improve vehicle’s stability and fast respond characteristics. Simulations are carried out to gain a series of transmission ratio curves, show the validity of the proposed fuzzy logic control method.

Experimental Testing and Validation of Tangential Steering Wheel Vibrations Due to Tire Nonuniformity

2005 ◽  
Author(s):  
Virgile Ayglon ◽  
Vinod Cherian ◽  
Nader Jalili
Keyword(s):  
Dynamic Testing ◽  
Experimental Testing ◽  
System Modeling ◽  
Companion Paper ◽  
Steering System ◽  
Analytical Models ◽  
Shop Floor ◽  
Steering Wheel ◽  
Vehicle Speed ◽  
Road Testing

This paper describes the experimental testing and validation of the analytical models developed in our companion paper (IMECE2005-81581) for the nonlinear kinematics and dynamics of the suspension linked to a nonlinear rack and pinion steering system model. More specifically, the experimental results are used to cross verify the numerical simulations of the nibble using custom built analytical and ADAMS models, described in the companion paper. For this, shop floor based quasi-static Kinematic and Compliance (K&C) and dynamic testing results along with track testing on special purpose track at Michelin are presented. Other results include impulse testing of the steering system, as mounted on the vehicle, as well as shaker testing to verify the results. Road testing is also carried out at speeds close to the vehicle critical speed in order to compare and validate the suspension models using the quasi-static K&C testing. The road testing results demonstrate the variation of forces in the steering system due to tire imbalances, emphasizing the nonlinear effects in the vehicle system modeling as well as the variation of the shimmy phenomenon with vehicle speed and tire imbalance.

High-Speed Vehicle Models Based on a New Concept of Vehicle/Structure Interaction Component: Part II—Algorithmic Treatment and Results for Multispan Guideways

1993 ◽  
Vol 115 (1) ◽  
pp. 148-155 ◽  
Author(s):  
L. Vu-Quoc ◽  
M. Olsson
Keyword(s):  
High Speed ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Structural Equations ◽  
Component Part ◽  
Vehicle Speed ◽  
Vehicle Structure ◽  
Algorithmic Treatment ◽  
Nonlinear Equations Of Motion ◽  
High Speed Vehicle

The predictor structural equations for the vehicle models developed in Part I are derived here for use with a new class of predictor/corrector algorithms to solve the mildly nonlinear equations of motion of the vehicle/structure models. Having all accelerations of the vehicle component eliminated, and with the aid of further simplifying approximations, the predictor structural equations are linear with respect to the structural degrees of freedom. In the algorithms, the predictor structural equations are different from the corrector structural equations; the proposed algorithmic treatment has been proved (elsewhere) to yield accurate energy balance. Results obtained for both continuous and discontinuous guideways are discussed, and optimal guideway configurations suggested. Effects of high-speed vehicle braking on a flexible guideway are analyzed using the vehicle models and the proposed algorithmic treatment. The influence of the guideway flexibility on the vehicle speed, an important feature of the present formulation, is clearly demonstrated.

A Prototype Steering Weave Stabilizer for Automobiles

1991 ◽  
Vol 113 (1) ◽  
pp. 138-142 ◽  
Author(s):  
J. C. Whitehead
Keyword(s):  
High Speed ◽  
Steering System ◽  
Lateral Acceleration ◽  
Steering Wheel ◽  
Phase Lag ◽  
Vehicle Speed ◽  
Control Torque ◽  
Concentrated Mass ◽  
Wheel Rim ◽  
The Difference

A prototype high-speed steering stabilizer for automobiles applies transient steering torques so that the sum of natural steering restoring torque and the control torque is more nearly in phase with steer angle than the natural restoring torque alone. The resulting reduction in the phase lag from steer angle to restoring torque mitigates the steering weave mode. Since steering restoring torque is nearly proportional to vehicle lateral acceleration, weave controller circuitry could subtract instantaneous lateral acceleration from expected steady-state lateral acceleration calculated from steer angle and vehicle speed, and thence command a steering torque actuator depending on the difference signal. The prototype performs the same function using a concentrated mass on the lower steering wheel rim which is passively sensitive to both steer angle and lateral acceleration, thereby applying only transient steering torques in the desired manner at a vehicle speed of 30 m/s. The additional steering system inertia alone affects the weave mode, so a non-stabilizing configuration with the same mass distributed around the steering wheel rim is tested for direct comparison. The experimental data show a dramatic stabilization of weave for the configuration which applies control torque.

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