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Technical Paper

Using Digital Image Correlation to Measure Dynamics of Rolling Tires

Vehicles are in contact with the road surface through tires, and the interaction at the tire-road interface is usually the major source of vibrations that is experienced by the passengers in the vehicle. Thus, it is critical to measure the vibrational characteristics of the tires in order to improve the safety and comfort of the passengers and also to make the vehicle quieter. The measurement results can also be used to validate numerical models. In this paper, Digital Image Correlation (DIC) as a non-contact technique is used to measure the dynamics of a racing tire in static and rolling conditions. The Kettering University FSAE car is placed on the dynamometer machine for this experiment. A pair of high-speed cameras is used to capture high-resolution images of the tire in a close-up view. The images are processed using DIC to obtain strain and displacement of the sidewall of the tire during rolling. The experiment is performed for various testing speeds.
Technical Paper

Traction and Clutch Effects on the Natural Frequency and Vibration Stability of Limited Slip Differential Axles

The torsional natural frequencies of axles equipped with limited slip differential clutches depend on whether or not the tires and clutches are slipping since the effective inertia at each end of the axle is different for slipping and non-slipping conditions. Limited slip axle vibrations are typically analyzed for one tire slipping and the other not since that is the case for which the limited slip clutches are used. Vibrations often arise, however, during normal turning when both drive tires have good traction.
Technical Paper

State Space Formulation by Bond Graph Models for Vehicle System Dynamics

Modeling and simulation of dynamic systems is not always a simple task. In this paper, the mathematical model of a 4 Degree Of Freedom (DOF) ride model is presented using a bond-graph technique with state energy variables. We believe that for the physical model as described in this research, the use of a bond-graph approach is the only feasible solution. Any attempt to use classical methods such as Lagrange equations or Newton's second law, will create tremendous difficulties in the transformation of a set of second order linear differential equations to a set of first order differential equations without violating the existence and the uniqueness of the solution of the differential equations, the only approach is the elimination of the damping of the tires, which makes the model unrealistic. The bond-graph model is transformed to a mathematical model. Matlab is used for writing a computer script that solves the engineering problem.
Technical Paper

Physical Validation Testing of a Smart Tire Prototype for Estimation of Tire Forces

The safety of ground vehicles is a matter of critical importance. Vehicle safety is enhanced with the use of control systems that mitigate the effect of unachievable demands from the driver, especially demands for tire forces that cannot be developed. This paper presents the results of a smart tire prototyping and validation study, which is an investigation of a smart tire system that can be used as part of these mitigation efforts. The smart tire can monitor itself using in-tire sensors and provide information regarding its own tire forces and moments, which can be transmitted to a vehicle control system for improved safety. The smart tire is designed to estimate the three orthogonal tire forces and the tire aligning moment at least once per wheel revolution during all modes of vehicle operation, with high accuracy. The prototype includes two in-tire piezoelectric deformation sensors and a rotary encoder.
Technical Paper

Investigation and Development of a Slip Model for a Basic Rigid Ring Ride Model

With the recent advances in rapid modeling and rapid prototyping, accurate simulation models for tires are very desirable. Selection of a tire slip model depends on the required frequency range and nonlinearity associated with the dynamics of the vehicle. This paper presents a brief overview of three major slip concepts including “Stationary slip”, “Physical transient slip”, and “Pragmatic transient slip”; tire models use these slip concepts to incorporate tire slip behavior. The review illustrates that there can be no single accurate slip model which could be ideally used for all modes of vehicle dynamics simulations. For this study, a rigid ring based semi-analytical tire model for intermediate frequency (up to 100 Hz) is used.
Technical Paper

Feasibility Study Using FE Model for Tire Load Estimation

For virtual simulation of the vehicle attributes such as handling, durability, and ride, an accurate representation of pneumatic tire behavior is very crucial. With the advancement in autonomous vehicles as well as the development of Driver Assisted Systems (DAS), the need for an Intelligent Tire Model is even more on the increase. Integrating sensors into the inner liner of a tire has proved to be the most promising way in extracting the real-time tire patch-road interface data which serves as a crucial zone in developing control algorithms for an automobile. The model under development in Kettering University (KU-iTire), can predict the subsequent braking-traction requirement to avoid slip condition at the interface by implementing new algorithms to process the acceleration signals perceived from an accelerometer installed in the inner liner on the tire.
Journal Article

Effect of Limited Slip Clutch Friction on the Driveline Dynamics of a Rear Wheel Drive Vehicle Coasting in a Turn

A model and simulation results are presented for the torsional dynamics of a rear wheel driveline while the vehicle is coasting in a turn. The model includes the effects of road load and powertrain drag, limited slip differential clutch friction, the inertias of the vehicle, wheels, axles, differential carrier, and driveshaft, the final drive ratio, torsional stiffnesses of the axles and driveshaft, vehicle track width, and radius of the turn. The dynamics of coasting in a turn differ from powered driving due to changes in the inertia loading the driveshaft, the damping effect of the disengaged transmission, and nonlinearities in the clutch friction. Specific focus is given to vibration in the axles and driveshaft due to variations in the torque-speed slope of the clutches, which is determined by the slope of the friction coefficient ‘μ’ versus sliding speed ‘v’ in the limited slip clutches.
Technical Paper

Effect of Chassis Design Factors (CDF) on the Ride Quality Using a Seven Degree of Freedom Vehicle Model

The kinematics and kinetics of a seven degree of freedom vehicle ride model with independent front and rear suspension are developed. Lagrange's equation is used to obtain the mathematical model of the vehicle. The equations of motion are transformed to state space equations in Linear Time Invariant (LTI) form. The effect of Chassis Design Factors (CDF) such as stabilizer bars, stiffness', Dynamic Index in Pitch (DIP) and mass ratio on the vehicle ride quality are investigated. The ride quality of the 3 dimensional vehicle that includes bounce, pitch, roll and unsprung masses motion is demonstrated in time domain response. The vehicle is considered as a Multi-Input-Multi-Output System (MIMO) subjected to deterministic ground inputs. Outputs of interest for the ride quality investigation are vertical and angular displacement and vertical accelerations. Numerical computer simulation analysis is performed using MATLAB® software.
Technical Paper

Application of Bond Graph Technique and Computer Simulation to the Design of Passenger Car Steering System

Vehicle Dynamics play an important role in responsiveness of a vehicle. The performance of a vehicle depends on its ride and handling characteristics [1]. Handling is a measure of the directional response of a vehicle and one of the important characteristics from the vehicle dynamics point of view. The directional response of a vehicle depends on the dynamics of the steering system. A good steering control provides an accurate feedback about how the vehicle reacts to the road. In this paper, the powerful techniques of Bond graphs and state equations [2] are used to design and analyze the dynamics of a manual rack and pinion steering system. The author obtains the transfer function between the Angle of rotation of front tire and the Angle of rotation of steering wheel. The overall steering ratio of the bond graph modeled steering system is compared with the overall ratio of a similar vehicle to validate the model.
Technical Paper

Analysis of a 4-DOF Vehicle Model Using Bond Graph and Lagrangian Technique

Bond graph modeling is a powerful technique to study the complex interactions occurring between various components in a system. A few investigations were carried out to study vehicle dynamics using Bondgraphs, but are limited to 2 degree of freedom systems [1,2&3]. In this work, a 4-DOF-vehicle model was developed using bond graphs. A frequency response analysis was also carried out to study the natural frequencies. This model was later validated using Lagrangian principles. The results correlated well for a typical passenger car using the manufacturer supplied information available in the public domain.