Rolling resistance and energy loss in tyres Mohammad Mehdi Davari [email protected] KTH Vehicle Dynamics Department of Aeronautical and Vehicle Engineering
SVEA seminar May 20, 2015 Contents
• Background and challenges • Research objectives • Rolling loss • Tyre models • Modelling process • Results • Summary and conclusions
MOHAMMAD MEHDI DAVARI 2015-05-19 2 Vehicle energy usage
8
100 100 0,38 6 4,14 Inertial forces 1,33 0,78 4,93 km 4 0,76 Aerodynamic forces 0,97 2,24 2,19 Internal frictional forces 2 0,55 0,59 Rolling resistance forces 2,57 0,5
Contributionliters/ in 1,47 1,56 1,38 0 Urban Extraurban Major and minor Motorway roads
Every day 2 millions tonnes of fuel burns up to overcome rolling resistance! Source: Michelin
MOHAMMAD MEHDI DAVARI 2015-05-19 3 Reducing rolling resistance and consequently the fuel consumption is a major development goal for vehicle and tyre manufactures.
MOHAMMAD MEHDI DAVARI 2015-05-19 4 What does the vehicle industry do?
Narrower
Larger
VW XL1: 115/80 R15 Michelin BMW i3: 155/70 R19 Bridgestone
MOHAMMAD MEHDI DAVARI 2015-05-19 5 What about the tyre industry?
Source: Michelin
MOHAMMAD MEHDI DAVARI 2015-05-19 6 …but, there are challenges!
Green tyres
Source: Michelin
MOHAMMAD MEHDI DAVARI 2015-05-19 7 What we as vehicle dynamicists can do to affect the rolling resistance?
MOHAMMAD MEHDI DAVARI 2015-05-19 8 Research goal…
… presenting an idea, apart from the state-of-the-art methods, to reduce the resistance originated from the tyre.
MOHAMMAD MEHDI DAVARI 2015-05-19 9 Research questions
• What is an appropriate model to characterise the rolling loss in the tyre during a vehicle manoeuvre?
• Is it reasonable to believe that there is any potential to reduce the rolling loss and thereby fuel consumption by using active chassis solutions?
MOHAMMAD MEHDI DAVARI 2015-05-19 10 Rolling resistance
Main contributors associated with tyre rolling resistance; • Hysteretic losses in the sidewall and the tread • Tyre aerodynamic drag and air circulations • Tyre-road interaction and surface losses
Rubber deformation 80 – 95 %
Aerodynamic resistance 0 – 15 %
Tyre-road interaction <5 %
MOHAMMAD MEHDI DAVARI 2015-05-19 11 Rolling resistance
In-door measurement Out-door measurement
Rolling direction
[Source: Technical University of Gdansk]
퐹푟 푓푟 = 퐹푧 푀푦 푀푦 = 퐹푧 ∙ 푒 푓푟 = 퐹푧 ∙ 푧푡 ISO 18164:2005 measuring rolling resistance, under controlled laboratory conditions (free rolling, straight ahead driving, specific load and speed)
MOHAMMAD MEHDI DAVARI 2015-05-19 12 A global definition
Pressure distribution and shape of the contact patch depend on driving conditions and wheel alignments, thus this coefficient will be a variable dependent to other parameters;
푠푖푑푒 푠푙푖푝 푎푛푔푙푒
푐푎푚푏푒푟 푎푛푔푙푒 푠푙푖푝 푟푎푡푖표
푅표푙푙푖푛푔 푟푒푠푖푠푡푎푛푐푒 푐표푒푓푓푖푐푖푒푛푡 = 푓 푣푒푟푡푖푐푎푙 푙표푎푑 푠푝푒푒푑 푡푒푚푝푒푟푎푡푢푟푒 푚푎푡푒푟푖푎푙 …
Therefore, for free-rolling, straight ahead driving and neutral wheel alignment in-plane rolling resistance coefficient (푓푟) will be used instead and in general the term rolling resistance coefficient (푓푅).
MOHAMMAD MEHDI DAVARI 2015-05-19 13 Rolling loss
“Rolling loss" refers to the energy dissipation in the tyre due to deflections as well the losses in the sliding region.
Dissipation sources
Adhesion force limit Sliding force limit
Adhesion region
-a 0 a SlidingSliding region region Contact patch length
Internal losses External losses
MOHAMMAD MEHDI DAVARI 2015-05-19 14 Tyre models
Empirical models Similarity based models Simple physical models Complex physical models
Degree of fit
Low dependency Independency on number of from number of experiments full scale tests
Insight in tyre Simplicity of behaviour formulation
Less computational effort
MOHAMMAD MEHDI DAVARI 2015-05-19 15 Initialisation Rolling loss Expectations from the model... Tyre Rubber Time Energy observer
Inputs Internal loss Bristle External loss • Be applicable within vehicle deflection δ Bristle force Longitudinal speed Vx dynamics simulations. Vertical force F x x
level z
Vehicle Slip ratio y Rubber model y Total rolling resistance • Considering the rolling loss Side slip angle z z Camber angle Friction observer In-plane rolling resistance
in tyre from a holistic level Chassis Chassis approch. Pressure distribution
Pressure K
Tyre z • Be able to simulate the level (vertical stiffness) Updating Time Quarter car internal and external losses. And model
Road roughness Bristle deflection level
Road
MOHAMMAD MEHDI DAVARI 2015-05-19 16 Modelling process: Dissipation modelling
Loss angle Rate Viscoelastic modules dependent Rate Friction modules independent
Force Displacement
Phase
20
15
10
5
0
Force [N] Force -5 1 Hz -10 10 Hz Friction -15
-20 -0,01 -0,005 0 0,005 0,01 Displacement [m] Rubber model
MOHAMMAD MEHDI DAVARI 2015-05-19 17 Modelling process: Tyre modelling Extended Brush tyre Model (EBM)
Finite number of Flexible carcass 0.05
lines and bristles 0
-0.05
-0.1
-0.15 Brush tyre Z [m] State observer theory -0.2 -0.25 Lateral force -0.3 Friction ellipse -0.1 -0.05 0 0.05 0.1 Y [m] Maximum Dissipation Rate Mode (MDRM)
- Think about animtion - Use bigger fonts
MOHAMMAD MEHDI DAVARI 2015-05-19 18 Model algorithm
MOHAMMAD MEHDI DAVARI 2015-05-19 19
Results
MOHAMMAD MEHDI DAVARI 2015-05-19 20 Global forces
Longitudinal slip 6000
5000
The structural behaviour of the 4000
Magic Formula 3000
tyre model represented by the [N] EBM x global forces shows good fit F 2000 with measured data and Magic Formula. 1000
0 0 10 20 30 40 50 60 70 80 90 100 [-] x Combined slip Lateral slip 500 3000 Measured data at = 0 0 EBM at = 0 Measured data at = 6 2000 = -2 -500 EBM at = 6
1000 -1000 Measurement 0 EBM -1500
Measurement [N]
[N] y
y -1000 EBM -2000 F
F
-2000 = 4 -2500
-3000 -3000
-3500 -4000
-4000
-4000 -3000 -2000 -1000 0 1000 2000 3000 4000 5000 0 5 10 15 20 25 30 F [N] [deg] x
MOHAMMAD MEHDI DAVARI 2015-05-19 21 Detailed study of contact patch
= 0 , = 0
4 0.15 Inner edge x 10 0 0.1
0.05 5
[Pa]
z 0 p 10
-0.05
Contact width [m] width Contact 15 -0.1 = 0 -0.1 -0.05 0.1 = -2 0 0.05 -0.15 Outer edge 0.05 0 = -3 -0.05 0.1 -0.1
-0.1 -0.05 0 0.05 0.1 0.15 y[m] x[m] Contact length [m]
Make another movie to prevent flickering
MOHAMMAD MEHDI DAVARI 2015-05-19 22 Influence of vehicle level parameters: speed
0.025 0.02
EBM FEM 0.02 0.015
0.015
0.01
0.01
0.005
0.005 Rollingresistance coefficient [-] Rollingresistance coefficient [-] Rubber A Rubber a Rubber B Rubber b Rubber C Rubber c 0 0 0 10 20 30 40 50 5 10 15 20 25 30 35 40 Velocity [m/s] Velocity[ m/s]
MOHAMMAD MEHDI DAVARI 2015-05-19 23 Influence of vehicle level parameters: load and torque
0.019
0.0185
0.018
0.0175
0.017
0.0165
Rollingresistance coefficient [-] 0.016
0.0155 2000 3000 4000 5000 6000 7000 8000 Vertical force [N]
4000
3500
3000
2500
2000
1500
1000
500
Energy loss per unit distance travelled [J/m] travelleddistance unit lossper Energy 0 -6000 -4000 -2000 0 2000 4000 6000 Fx [N] Braking Driving
MOHAMMAD MEHDI DAVARI 2015-05-19 24 Influence of chassis and tyre level parameters
0.0146 0.16
0.0145 0.14
0.0145 0.12
0.0144 0.1
0.0144 0.08
0.0143 0.06
0.0143 0.04
0.0142 0.02 Rollingresistance coefficient [-]
Rollingresistance coefficient [-]
0.0142 0 -6 -4 -2 0 2 4 6 -6 -4 -2 0 2 4 6 Camber angle [deg] Side slip angle [deg] 0.035
0.03
0.025 Tyre pressure and 0.02 vertical stiffness are linearly dependent 0.015 푃 ∝ 푘푧 0.01
Rollingresistance coefficient [-] 0.005 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Relative vertical stiffness [-]
MOHAMMAD MEHDI DAVARI 2015-05-19 25 Energy studies
1800 Longitudinal dissipation =0 [deg] 1600 Lateral dissipation =0 [deg] 훼 1400 Vertical dissipation =0 [deg] Longitudinal dissipation =2 [deg] 1200 Lateral dissipation =2 [deg] 1000 Vertical dissipation =2 [deg]
800
600
Total dissipated energy Total [J]dissipated energy 400
200
0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Time [s]
MOHAMMAD MEHDI DAVARI 2015-05-19 26 2000 0.04 Dynamic maneouvres 1000 =0 0.03 0 =-2
[N] 0.02 y Steering angle F -1000 0.01 -2000 0 1 1.5 2 2.5 [rad] angle Steering 56 =0 54 5 N 10,0% =-2
[N]
r
F 52
50 1 1.5 2 2.5
2000 =0 -19,0% =-2 435 N [N] R 1000
F
0 1 1.5 2 2.5
1000 =0 30 W -2,5% =-2 900
800
Internal lossInternal [W] rate 1 1.5 2 2.5
1000 =0 -11,5% 72 W 500 =-2
0
External loss [W] rate 1 1.5 2 2.5 훾 = 0° Time [s]
MOHAMMAD MEHDI DAVARI 2015-05-19 27 Internal Loss (E) Internal Loss Rate (dE/dt) 1 1 = 0 = 0 = -2 = -2
[J] 0 0
x
/dt [W]
x
E
dE
-1 -1 0 0.5 1 1.5 2 2.5 3 3.5 1 1.5 2 2.5
40 100
[J] 20
y /dt [W] 50
y
E
dE 0 0 0 0.5 1 1.5 2 2.5 3 3.5 1 1.5 2 2.5
3000 950
1421
2000 1420.5
[J]
z 900 1420 /dt [W]
z E 1000
1419.5 dE
1.6119 1.612 1.6121 0 850 0 0.5 1 1.5 2 2.5 3 3.5 1 1.5 2 2.5
3000 1000
2000 1620 1615 950 E [J] 1000 1610
dE/dt [W] 900
1.802 1.804 1.806 0 0 0.5 1 1.5 2 2.5 3 3.5 1 1.5 2 2.5 time time
MOHAMMAD MEHDI DAVARI 2015-05-19 28 Summary and future work
Internal losses
Parametrising the Implementation rolling resistance
External losses
Tyre modelling Control strategies
Rolling losses
Rolling loss Rolling loss studies in full modelling vehicle
MOHAMMAD MEHDI DAVARI 2015-05-19 29 Conclusion
• A tyre model to investigate the rolling loss is presented.
• The presented model kept simple but is still applicable to analyse the tyre behavior, in terms of global forces and moments.
• The model provides a detail understanding of rolling loss under different driving conditions.
• Dependency of the in-plane rolling resistance on vehicle inputs, wheel alignment and tyre parameters is investigated.
• The model can be used for a detailed study of contact patch.
• A holistic approach to study the tyre rolling loss is presented.
• A platform for investigating the effect of road roughness on rolling loss.
• Facilitating the tyre wear studies using the presented model.
MOHAMMAD MEHDI DAVARI 2015-05-19 30 Thank you for your attention!
MOHAMMAD MEHDI DAVARI 2015-05-19 31