Vehicle dynamics

THANKS

Any question?

Contacts:

alessandro.tasora@unipr.it

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TIRES

Alessandro Tasora

Name Surname

1.

INTRODUCTION

Basic concepts of tires

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Why tire models?

• Vehicle dynamics: needs loads on vehicle body to write an ODE/DAE

• Tire forces are the most important loads

• We need a way to compute F (normal, lateral, longitudinal) from tire state (slip

angle? Longitudinal slippage? Temperature? …)

= { , , } =

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Tire footprint forces

• The contact is not a point – it is a patch.

• In most models, simplified to a point.

• Experimental devices can measure pressure, forces, deformation, etc.

Image credits: Goodyear Wrangler

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SAE tire reference

• Most general case: a “wrench”, 6 scalars:

•

three forces ,

• Longitudinal

• Lateral

• Vertical (normal)

•

three torques

• Overturning moment

• Rolling resistance

• Aligning torque

• ,

Note the slip angle

inclination angle, radius {, } = { , , , , , } =

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Simplified disk model

• Assume no thickness

• Assume local lateral elastic deformation

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Simplified disk model

• Enough for studying lateral forces and slip angle

• Elastic lateral deformation

• Slip angle > 0 even if local contact ≤

satisfies static Coulomb friction condition

• The “softer” the rubber, the lower the

cornering stiffness, even if good adhesion

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Simplified disk model

• Experimental results

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Tire lateral forces

•

Effect of slip angle

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Tire lateral forces

• Effect of normal force ( right: normalized )

• Note! If it was basic Coulomb friction, all curves in the plot at the right should be the same

• Instead, too high normal force usually leads to (a bit) lower lateral G forces, for same tire

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Tire lateral forces

• Effect of normal force

• Note! If it was basic Coulomb friction, all curves in the plot at the right should be the same

• Instead, too high normal force usually leads to (a bit) lower lateral G forces, for same tire

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Tire lateral forces

• Effect of inclination angle (camber)

• From rear:

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Longitudinal force

• Tractive / breaking force

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Longitudinal force

• Effect of Slip Ratio SR

• SAE definition:

• Free rolling: SR = 0

• Locked braking: SR=-1

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Longitudinal force

• Alternative definitions of Slip Ratio SR, for generic 3D case

• SAE :

• Calspan TIRF

• Goodyear

• Pacejka

• Sakai

• Note: all have singularities! Divisions by zero…

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Combined longitudinal-lateral

• Sakai plots:

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Combined longitudinal-lateral

• Increasing slip ratios will decrease

the ability of generating high

lateral corces

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Combined longitudinal-lateral

• In a single plot!

The friction circle diagram:

• For a fixed vertical load – if different

loads, one needs a family of plots

• Similar to the friction disc of

the Coulomb friction model

• Not perfectly circular (oblated)

• Tells easily which is the max force

that a tire can transmit to the

ground (see perimeter)

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Aligning torque

• Effect of slip angle and load:

• 

Practical result: “trail” torque on



steering wheel driver feedback:

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Rolling resistance torque

• Caused by

• Hystheresis

• Dirt road

• Brushing effects in tire threads

• Other

• Macroscopic effect: the tire contact

point, w.resultant of normal pressures,

is moved ahead by a rolling parameter

•

Rolling coefficient , for

=

• Rolling resistance torque, linearizing:

=

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1.

TIRE MODELS

Introduction to numerical modeling of tires

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Classification

• Which is the goal? Implement an algorithm to compute:

{, } = { , , , , , } =

• Empirical models (LUT)

• Only experimental data, stored in Look-up table (LUT) to be interpolated at run time.

• Very fast, but need to repeat experiments if tire parameters change

• Semi-Empirical models

• Based on fitting experimental data with some parameters (ex. Pacejka “magic formulas”)

• Very fast, often used in real-time simulators

• Physical models

• Can capture deformation, high frequency vibrations, 3D contact effects, etc.

• Based on Finite Elements or similar tech with many degrees of freedom, slow to

compute, for tire design rather than vehicle dynamics

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Coulomb

• The simplest semi empirical model.

• Only friction coefficient is needed.

• Unrealistic because assumes perfectly rigid tires.

• Can be used to study AGV robots, etc.

• Could work with obstacles (curbs, etc.), multiple contact points

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FTIRE

• One of the oldest tire models

• Pros:

• Simple formulas

• fast to compute

• Only 9 parameters

• Limitations:

• No camber effect

• Constant cornering stiffness with

changing load

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Pacejka

• Based on “magic formulas” that approximate the empirical plots, ex.

• Parameters adjusted by fitting experimental data

• Very fast to compute, quite realistic Image credits: www:racer.nl

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MF-Tire

• Based on Pacejka formulas

• Licensed by Delft as ready-to-use code

• Magic Formula slip characteristics

• Advanced non-linear relaxation effects

• Single point tyre-road contact

• Combined slip estimation possibilities

• Inflation pressure effects

• OpenCRG road modelling

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MF-Swift

• Extends MF-Tire

• Licensed by Delft as ready-to-use code

• Adds generic 3D obstacle enveloping and tyre belt dynamics

• Highlights:

• Magic Formula slip characteristics

• Unique advanced contact model for uneven roads

• Rigid ring model for representing tyre dynamics

• Parking and turnslip

• Inflation pressure effects

• OpenCRG road modelling

• Usable up to 100Hz effects

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TMeasy

• Semi-empirical

• Fast to compute

• Allows 3D terrain

• Allows parking, stand still

• First 2 eigenmodes are simulated

• See Prof. Georg Rill book and website

Image credits: www.tmeasy.de

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FTire

• Licensed ready-to-use code

• Physically-based model

• Very advanced, up to 250Hz effects, 1mm resol.

• Different degrees of fidelity, up to 3D deformations,

thermal effects, etc.

• Runs in hard-real-time

Image credits: www.cosin.eu

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CDTire

• Licensed code, from Fraunhofer

• CDTire/RT real time version:

• flexible belt model

• scalable belt discretization

• local brush type contact model

• real-time capable

• accurate in frequency range up to 150Hz Image credits: https://www.itwm.fraunhofer.de

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CDTire

• Licensed code, from Fraunhofer

• CDTire/3D physically based version:

• complete 3D shell based model

• separate modeling and parameterization

of all functional layers of a modern tire

• includes dedicated models for belt,

carcass, cap plies and tread

• capturing of belt/rim contact (ground out)

• flexible rim support

• dedicated local brush type contact model

• handle inflation pressure variations

• temperature model and cavity model

• applicable on arbitrary 3D road surfaces

• can be adapted to a motorcycle tire Image credits: https://www.itwm.fraunhofer.de

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THANKS

Any question?

Contacts:

alessandro.tasora@unipr.it

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AERODYNAMICS

Alessandro Tasora

Name Surname

1.

INTRODUCTION

Basic concepts of aerodynamics for vehicle dynamics

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Why aerodynamics?

• Negligible at low speeds

• Relevant loads on vehicle at high speeds

• 

Negative: drag less autonomy

• 

Negative: noise less comfort

• 

Positive: airfoils downforce higher performance in lateral dynamics

• Highly nonlinear effects

• How to estimate aero effects?

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Approaches

• Analytical (only for simple shapes)

• 

Experimental wind tunnels

• Expensive

• If scaling, must conserve at least

Reynolds number:

see also Strouhal number etc. Credits: Daimler, DE

• 

Numerical CFD software

• CPU intensive

• As for all software:

“garbage in – garbage out” rule. Do not

misuse them. Credits: OpenFOAM software, at https://sourceforge.net

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Concepts

• Static pressure p

• Dynamic pressure q

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Concepts

• Total pressure H

• Pitot tube

• To compute airspeed V

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Pressure distribution

• Design airfoils so that speed is different on the upper/lower side

• Integrate pressures over surfaces, obtain aerodynamic forces

• Exploit this to generate

• 

Lift airplanes

• 

Downforce racing cars

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Separation, turbulence

• Ops! Sharp corners cause separation and turbulence

• Turbulence and vortexes not always a bad thing…

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Drag coefficient

• Drag coefficient, a macroscopic measure of “ho