Tyres – The Basics for Recent
Development
Prof. R. Krishna Kumar
Department of Engineering Design
Indian Institute of Technology Madras
Acknowledgement
JK Tyres for sponsoring the largest
project from a private company to
an educational Institution in India
Tyre as a Vehicle Component
• Support the load during dynamic and static
conditions – Filter vibrations in vertical
dynamics
• Traction and Braking support during
longitudinal dynamics
• Key role in Lateral Dynamics – Cornering force
and Moments
• Key gas guzzler and a fantastic replacement
market
Low Rolling Resistance Tyres Green Tyre
Run Flat Tyres Low Aspect Ratio - Radial Tubeless - Radial
Low Aspect Ratio - Bias Tubeless - Bias All Steel Radials
Radial Tyre – Aramid belt Radial Tyre – Steel belt Radial Tyre – Textile belt
Tyre with cotton reinforcement Rayon reinforcement Nylon reinforcement
Wheel Radius = Rim Radius + hT
+1 concept
Passenger Radial Tyre Layout
Inner Liner
Body Ply
Belt-1
Belt-2
Tread
Bead
Chaffer
Filler
Cap Strip
Sidewall
Rim Strip
Truck Radial Tyre
Radial Tyre
Bias Tyre
Radial vs Bias
• How does the tyre transmit load?
Tread Pattern
Tyre Terminologies
• Normal Stiffness
• Longitudinal stiffness
• Longitudinal Slip Stiffness
• Lateral Stiffness
• Cornering Stiffness
• Camber Stiffness
• Self Aligning Moment
• Twisting Moment
• Relaxation Length
• Rolling Resistance
What is Slip ?
Tyre during Braking
Slipping is not skidding
Slip is a micro movement and skid is a macro movement
Vx re
Longitudinal Slip,
Vx
Characterizing Longitudinal Force
Range of Operation
Longitudinal Force Coeff., = F / N
Longitudinal Force, F = (kκκ)N = Kκκ
Kκ is called the dimensional stiffness of longitudinal slip.
kκ is called the longitudinal slip stiffness.
These stiffness need not be the same in braking and driving
How does the friction develop
Elastic Visco-elastic
•The loading and the unloading path are not the same – hysteresis
•Hysteresis central to the grip mechanism or friction
Molecular Adhesion – The other
mechanism for grip
Note the decrease
Lateral Force Development
Combined Forces
Rolling Resistance
Fw= fwN = (d / R ) N
fw is called the rolling friction coefficient
0.018 1.59 106 2
f w 0.0085 V for V 165 kmph
p p
0.018 2.91106 2
fw V for V 165 kmph
p p
Axi Symmetric Model (24-35)
22 plies and
TYRE OD NSD Tread 2 Breakers
Width
OTR 2204 58 550
Full 3D-Model of the Tyre
CPRESS : Simulation vs. Experiment
Contact Pressure Distribution: Rolling
Temperature and Rolling Resistance
filler bead
7% 0%
ply
Contribution of dissipation at 18%
different tyre regions
belt
tread
4%
55%
rs
6%
sw
10%
Variation of tread material loss modulus
Temperature distribution contours
Tread with
Smooth tread
circumferential grooves
RR = 100.1267 RR = 106.3685
Temperatures and Rolling Resistance with Speed
TBR – Temperature Distribution
Mathematical Modelling
Vehicle Road
Data Parameters
Road
Vehicle Model
model
Tyre
Characteristics
Tyre Model
Vehicle Model
A set of degrees of freedom, represented as a vector
A set of location points called hard points
A set of properties, such as Mass and Moment of Inertia
A set of Input Forces from the Environment
Multibody Dynamics Equation
A set of Constraint Equations, Φ
Differential – Algebraic
Equations
Tyre Model Numerical Solution
Fx = F(σ, N, α, …)
Fy = F(σ, N, α,γ …)
M = F(σ, N, α,γ …)
Why does one want to do Vehicle
Dynamics Simulation
• Handling & Stability
• Ride Analysis
• Durability
• Roll Over Stability
• Suspension fine tuning
• Active Suspension Development
• NVH
Is the Tyre Model the Same for all these analysis?
NO !
Tyre Models in Vehicle Dynamics
Classification of Tyre Models
Simple Tyre Models: Fiala Model
•Tyre modelled as a linear springs.
•Longitudinal / Lateral forces defined by a linear relationship.
•No Combined Slip.
•Only Low Frequency Behaviour
Approximation / Empirical Models: “Magic Formula” Model
•Non Linear Approximation of Tyre Force
•Combined Slip
•Can be combined with vertical Stiffness
•Applications restricted by frequency
•Short Wave length Roads are not taken into account
Physical and Semiphysical Models: “Brush Models”
•Can be used for high Frequencies
•Takes into account tyre belt vibrations
•Road Envelopes are considered – A tyre road contact model
Tyre Models in the Market
• 20 different tyre models in the market
• MF group of tyre models, SWIFT model etc.
• RTire and FTire models etc.
• RMOD-K Model
• There are two issues: Measurements and
Representation – Includes tyre and Road
Measurement data
• For many models the procedure is established, but
mathematics is very complex
Magic Formula Tyre Model
y = D sin[C arctan{Bx – E(Bx – arctan Bx)}]
with Y(X) = y(x) + SV
x = X + SH
where Y : Fx or Fy or Mz
X : slip angle tan or slip
and B – Stiffness Factor
C – Shape Factor
D – Peak Value
E – Curvature Factor
SH – Horizontal Shift
SV – Vertical Shift
B, C, D, E, SH and SV are known as primary MF parameters.
Conicity and plysteer represent tyre cornering behaviour at diminishing slip angle.
These are represented through horizontal shift SH and vertical shift SV.
The primary Coeff., depend on normal load, camber etc.
Force and Moment Characteristics
FEA Experiments FEA
-6000 80
-5000 70
Lateral force (N)
Self-aligning torque
Experiments
60
-4000
50
-3000 40
(Nm)
30
-2000
20
-1000 10
0 2 4 6 8 10
0
0
Slip angle (Deg) -10 0 2 4 6 8 10
-20 Slip angle (Deg)
8000
Longitudinal Force (N)
7000
6000
5000
4000
3000 Experiments FEA
2000
1000
0
0 5 10 15 20 25 30
% Slip
Thank You for Your Attention