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Bergamo Lecture 5 - Tyre Modelling Simulation

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Tyre Modelling Simulation

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Lecture 5- Tyre Modelling Professor Mike Blundell Phd, MSc, BSc (Hons), FIMechE, CEng Bergamo University Italy 12th -14th June 2012
Contents • History and Tyre Construction • Tyre Force and Moment Generation • Tyre Models for Handling and Durability (MF Tyre Model, Finite Element models, Ftire) • Aircraft Tyre Modelling • New Developments
History of Tyres The first pneumatic tyre, 1845 by Robert William Thomson. A number of air filled tube inside a leather case. Resistant to punctures but old solid rubber remained in favour with the public. http://www.blackcircles.com/general/history 3 Boyd Dunlop reinvented the pneumatic tyre whilst trying to improve his sons bike in1888 http://www.blackcircles.com/gener al/history In 1895 the pneumatic tyre was first used on automobiles, by Andre and Edouard Michelin. http://www.blackcircles.com/general/history http://polymerprojecttopics.blogspot.com/ 2010/08/radial-tyre-vs-bias-tyre.html Michelin first introduced steel-belted radial tires in Europe in 1948 http://polymerprojecttopics.blogspot.com/2010/08/radial-tyre-vs-bias- Michelin first announced the Tweel in 2005, a non-pneumatic tyre, removing the necessity checking tyre pressures http://auto.howstuffworks.com/tweel- airless-tire.htm
Tyre Sidewall Information 205/55 R15 87V 205 Nominal Section-width in mm TUBELESS Tubeless / Tube Type E4 All passenger car tyres from current production comply with ECE Standard 30 026504 Approval number acc. To ECE regulation 30 4008 Production code (40th week, 2008 DOT Department of Transportation, USA TWI Tread Wear Indicator (1.6mm) 4 Continental Technical Data Book. Car Tyres 1999
Tyres for All Seasons • Motorsport -Slicks -Intermidiates -Full Wets • Passenger Cars -Summer Tyres -All Season Tyres -Winter Tyres -Mud and Snow Tyres
Radial Tyre Structure 6 http://www.dunlopatl.co.uk/tech_support/aircraft-tyre- technology.aspx http://www.hankooktire-eu.com/technology/types-of-tires/ according-to-structure.html
Rubber Compound Formulation • Two Major Ingredients – the rubber and the filler (carbon black and silica) • Combined to achieve different objectives – maximise wet and dry traction/ achieve superior rolling resistance • Four major types of rubber o natural rubber o styrene-butadiene rubber (SBR) o polybutadiene rubber (BR) o butyl rubber (along with halogenated butyl rubber) • The first three are primarily used as tread and sidewall compounds, while butyl rubber and halogenated butyl rubber are primarily used for the inner liner • Other ingredients also come into play to aid in the processing of the tire or to function as anti-oxidants, anti-ozonants, and anti-aging agents. In addition, the “cure package”—a combination of curatives and accelerators—is used to form the tire and give it its elasticity.
Tyre Thread Design http://www.checkthatcar.com/tyre%20anatomy.asp 8 Groove http://www.ctyres.co.uk/tyre_info/tyre_type.html Rib Shape Lug Shape Rib-Lug Shape Block Shape Asymmetric pattern Directional pattern Sipe: Fine groove in the tread pattern to improve grip in icy conditions Studs: Further improvement of grip in icy conditions http://www.hankooktire-eu.com/technology/types- of-tires/according-to-season.html
FEA Tyre Models 9 http://www.cosin.eu/
Automotive Applications 10 Main applications are in the automotive industry for: – Simulation of vehicle handling – Prediction of vehicle ride quality – Determination of component loads from systems model
Aerospace Applications 11 There is a growing need in the aerospace industry for: – Prediction of shimmy – Rough field performance – Ride & controllability – Ground loads – Landing, Takeoff, Taxiing
SAE Tyre Axis System 12 {Ysae }1 {Zsae }1 {Xsae }1 P γ α Spin Axis {V}1 Angular Velocity (ω) Wheel Torque (T) WC Direction of Wheel Heading Direction of Wheel Travel Lateral Force (Fy ) Normal Force (Fz ) Tractive Force (Fx )
Frictional Force Component due to Adhesion 13 Direction of Sliding Tyre Material Road Surface Adhesive Forces due to Molecular Bonding
Tyre Testing • Lateral force with slip/camber angle • Aligning moment with slip/camber angle • Longitudinal force with slip ratio Courtesy of Dunlop TYRES Ltd. Slip Angle Fy
Lateral Force Fy with Slip Angle α 15 Courtesy of Dunlop Tyres Ltd.
Tyre Modelling Prediction of Vehicle Ride Quality -Simple Physical Models (Stiffness/Damping) -More Advanced Physical Models (FTire) Simulation of Vehicle Handling -Interpolation models (Lookup Tables) -Simple Equation based representations (Fiala) -Complex Mathematical Fits to Test Data (Magic Formula) -Pure and Combined Slip Models Determination of Component Loading -Simple Physical Models (Equivalent Volume) -More Advanced Physical Models (FTire) -Full Non-Linear Finite Element Models
Vehicle/Tyre Model Interaction VEHICLE MODEL Wheel centre - Position, Orientation and Velocities  Mathematical Solution at Integration Time Steps  TYRE MODEL Fx - longitudinal tractive or braking force Fy - lateral cornering force Fz - vertical normal force Mz - aligning moment Mx - overturning moment My - rolling resistance moment Tyre Model Fy Fx Fz Mz Tyre Model Fy Fx Fz Mz
Tyre Model/Data Assessment Fy Slip Angle  Check plots in ADAMS tyre rig model FIALA MODEL MAGIC FORMULA MODELS INTERPOLATION MODELS Vehicle Model
Tyre Model/Data Assessment
20 Tyre Model Summary
21 Tyre Model Summary Interpolation Model • It uses tyre test data to interpolate results for a particular scenario Empirical Model • Empirical models use test data to determine equations and parameters to replicate the tyre data Physical Model • These use physical representations of tyre to generate results (e.g. radial belts with spring elements)
The Fiala Tyre Model • Input Parameters 2 R2 R1 R1 R2 Tyre Dimensions Model Geometry 22
The Fiala Tyre Model Input Parameters R1 The unloaded tyre radius R2 The tyre carcass radius kz The tyre radial stiffness Cs The longitudinal tyre stiffness Ca Lateral tyre stiffness due to slip angle Cg Lateral tyre stiffness due to camber angle (Not Used) Cr The rolling resistant moment coefficient ζ The radial damping ratio m0 The tyre to road coefficient of “static” friction m1 The tyre to road coefficient of “sliding” friction 23
The Fiala Tyre Model (Lateral Force and Aligning Moment) • Example of the Lateral Force Generation 24 α z 1 C F μ 3 tan α*                   z α 3 z y F μ 3 tanα C - 1 H where , α sgn H 1 F μ F   α sgn F μ F z y   And so if |α|<α* then: The critical slip angle is: Else if |α|>α* then: • Example of the Aligning Moment Generation And so if |α|<α* then: Else if |α|>α* then:     α sgn H H 1 R F μ 2 M 3 2 z z   0 . 0 Mz 
The Fiala Tyre Model • Limitations • No camber thrust • Not suitable for combined slip • Constant cornering stiffness with load • Zero aligning moment at high slip angles 25
The “Magic Formula” Tyre Model The basis of this established model is that tyre force and moment curves look like sine functions which have been modified by introducing an arctangent function to “stretch” the slip values on the x-axis. Fx Mz Slip Angle  Slip Ratio  (1) Bakker E., Nyborg L. & Pacejka, H.B., Tyre modelling for use in vehicle dynamics studies, SAE paper 870421. (2) Bakker E., Pacejka H.B. & Linder L., A new tyre model with application in vehicle dynamics studies", SAE paper 800087, 4th Auto Technologies Conference, Monte Carlo, 1989. 26 Fy
The “Magic Formula” Tyre Model The general form of the model (version 3) is: y(x) = D sin [ C arctan{ Bx - E ( Bx - arctan ( Bx ))}] where Y(X) = y(x) + Sv Y = Fx, Fy, or Mz x = X + Sh X =  or  Sh = horizontal shift Sv = vertical shift D ys arctan (BCD) Sh X x y Y Sv 27
The “Magic Formula” Tyre Model The Main Parameters in the General Equation are D - is the peak value. C - is a shape factor that controls the “stretching” in the x direction. 1.30 - lateral force curve. 1.65 - longitudinal braking force curve. 2.40 - aligning moment curve. B - is referred to as a “stiffness” factor. BCD is the slope at zero slip. E - is a “curvature” factor which effects the transition in the curve and the position xm at which the peak value if present occurs. E is calculated using: Bxm - tan ( p / 2C) E = Bxm - arctan ( Bxm ) ys - is the asymptotic value at large slip values and is found using: ys = D sin ( p C / 2) 28
The “Magic Formula” Tyre Model At zero camber the cornering stiffness BCDy reaches a maximum value defined by the coefficient a3 at a given value of vertical load Fz which equates to the coefficient a4. The slope at zero vertical load is taken as 2a3/a4. arctan (2a3/a4) 0 Fz (N) BCDy (N/rad) a4 a3 29
The “Magic Formula” Tyre Model • General Formula (Version 3) • y(x)=Dsin[Carctan{Bx-E(Bx-arctan(Bx))] • Y(X) = y(x) + Sv • x = X + Sh • B = stiffness factor • C = shape factor • D = peak factor • Sh = horizontal shift • Sh = vertical shift • B= dy/dx(x=0) / CD • C = (2/p) arcsin (ys/D) • D = ymax • E = (Bxm-tan(p/2C))/(Bxm - arctan (Bxm)) • Lateral Force • Xy = a • Yy = Fy • Dy = my Fz • my = (a1Fz + a2) (1 - a15 g2) • BCDy = a3 sin(2 arctan(Fz/a4)) (1 - a15| g |) • Cy = a0 • Ey = (a6Fz+a7) (1-(a16g + a17)sgn(a + Shy)) • By = BCDy / CyDy • Shy = a8Fz + a9 + a10g • Svy = a11Fz + a12 + (a13Fz2 + a14Fz)g 30
The “Magic Formula” Tyre Model • Longitudinal Force • Xx = k • Yx = Fx • Dx = mx Fz • mx = b1Fz + b2 • BCDx = (b3 Fz2 + b4Fz) exp(-b5Fz) • Cx = b0 • Ex = (b6Fz2 + b7Fz + b8)(1- b13sgn(k + Shx)) • Bx = BCDx / CxDx • Shx = b9Fz + b10 • Svy = b11Fz + b12 • Brake force only (b11 = b12 = b13 = 0) • Aligning Moment • Xz = a • Yz = Mz • Dz = (c1Fz2 + c2Fz) (1 - c18g2) • BCDz = (c3Fz2+c4Fz)(1- c6 | g |)exp (-c5Fz) • Cz = c0 • Ez = (czFz2 + c8Fz + c0) (1 - (c19g + c20)* • *sgn(a + Shz)) / (1 - c10 | g | ) • Bz = BCDz / CzDz • Shz = c11Fz + c12 + c13g • Svz = c14Fz + c15 + (c16Fz2 + c17Fz)g 31
Laboratory Simulation - Shaker Rig RIDE AND VIBRATION Simple Spring Damper Model Flexible Ring Method Modal FE Model in MBS
Ride Simulation (Comfort) X Z m k c z Zg Vehicle Body or Sprung Mass Suspension Spring and Damper Ground Input Body Response Time (s) Also important in Motorsport Vehicles Also important in Military Vehicles
Component Load Prediction Fy Lateral loads Fx Longitudinal loads Fz Vertical loads FINITE ELEMENT MODEL ADAMS MODEL Tyre Modelling Radial Spring Models Equivalent Plane Method Equivalent Volume Method Flexible Ring Method Coupled Explicit FE and MBS Methods
Tyre Modelling FINITE ELEMENT MODELS A Physical Tyre Model is required Finite Element Modelling is an example Can model deformable terrain as well Not practical in terms of modelling time Excessive computational effort Mainly a tool for Tyre Manufacturers
Contact Forces • Used on Helisafe EU project and for tracked vehicles • Modelled hard non-destructive landings • Bi-linear model with tyre and wheel stiffness • Contact function based on stiffness and damping • Includes friction Eurocopter Model 5m/s ground impact Tracked Vehicle operating in deep snow
Examples of Tyre Interactions 37
Durability Tyre Models • Early durability tyre models were 2D • Radial Spring or Equivalent Plane • Capture deformed shape of tyre enveloping terrain • Resultant force towards wheel centre Radial Spring Model Equivalent Plane
Durability Tyre Model • Originally developed in Finland for logging vehicles • Captured tyre interaction with sawn tree trunks on rough terrain • 3d Model - Discritization into cross-sectional elements Definition of tyre carcass shape for a durability tyre model      Input points to define shape Tyre centre line Tyre centre line Tyre cross-sectional elements
Early Road/Terrain Model Road modelled using triangular planar elements Friction can vary on element by element basis 1 2 3 4 5 6 Intersection of tyre sectional elements with road elements
A Tyre Model for Ride & Durability Simulations A Flexible ring tyre model Tire phenomena based on a mechanical model Developed by Cosin (www.cosin.eu) Developed by Cosin (www.cosin.eu) The FTIRE Model FTire on Belgian Pave FTire on Belgian Pave
• Structural dynamics based, full 3D nonlinear in-plane and out-of-plane tire model for simulation of belt dynamics, local pressure distribution in the contact patch, rolling resistance, side-wall contact, large camber angles and misuse scenarios. • Suitable for a frequency range up to 200Hz, excited by short surface wavelength, mass imbalance, non-uniformity or irregular tread patterns. • Very fast and flexible. Orders of magnitude faster than explicit FE models. • Simulation of imbalances by inhomogeneous mass distribution and local wear. • Belt temperature distribution model. The FTIRE Model
cbend. ctang. crad. cbelt bending stiffness both in-plane and out-of-plane (simplified) Tyre structure described with distributed mass, connected to rim by distributed stiffness & damping elements The FTIRE Model
3D Road/Terrain Model Regular Grid Road Data Files (RGR Files) Open Source software developed by Daimler AG VIRES GmbH 3D Road Data Curved regular Grid (CRG) Representation Data Files can be generated from laser scans along a road Belgian Block XYZ map Open CRG Visualisation
FTire Animations Detailed Tread Pattern Detailed Tread Pattern Truck Tire Passing a big bump Truck Tire Passing a big bump
FTire Animations Rolling over a high kerb Rolling over a high kerb Local Belt Deformation Local Belt Deformation
FTire Animations Sine wave with Sine wave with decreasing wave length decreasing wave length FTire on RGR Road Surface FTire on RGR Road Surface
200 mm 10 mm v = 80 km/h wheel load [N] longitudinal force [N] 0 0.02 0.04 0.06 0.08 0.1 1000 2000 3000 4000 5000 0 0.02 0.04 0.06 0.08 0.1 -2000 -1000 0 1000 2000 FTire: Running over an Obstacle
side-slip angle [deg] M [Nm] z 0 5 10 15 20 25 30 35 40 45 -100 -50 0 50 100 150 200 aligning torque F [N] y side-slip angle [deg] 0 5 10 15 20 25 30 35 40 45 0 1000 2000 3000 4000 5000 6000 7000 8000 side force Fz = 2, 4, 6, 8 kN FTire: Handling Characteristics
Aircraft Tyre Modelling •EPSRC Project with AIRBUS UK •Simulate landing, takeoff, taxiing •Tyre Testing by Airbus in Toulouse •Developed model in a MATLAB/SIMULINK Environment with export to ADAMS • Low Parameter Model based on Harty Approach with extended Load/Speed dependence • Shimmy Modelling (Early NASA work) remains elusive
Aircraft Tyres • Aircraft tyres are pushed to the extremes of operational envelopes compared to other forms of ground vehicles • Typical automotive applications would see tyres experiencing slip angles of around 10o however aircraft tyres can go up to 90o • Typically speeds of up to 200mph will be experienced (225-235mph being the speed ratings typically seen (from Bridgestone (2011)))
Extreme Operating Conditions • Because of the operational loads of the aircraft the vertical loads experienced by the tyre’s are also magnified • The rated load of a nose wheel can be approx. 40 kN; an automotive tyre of similar size can be seen to have a load of approx 6 kN • Large landing gear tyres can have rated loads in excess of 300 kN Daugherty (2003)
Tyre Costs (All figures are based upon Michelin prices (from Air Michelin (2007))) • The costs involved with aircraft tyres can best be seen when comparing them against an automotive example • An average automotive tyre can cost around £60-70 (using an example tyre size of 205/55 R16) • An aircraft tyre of similar size can cost £1,708 (based upon a 27x7.7in (686x196mm) tyre) • Then comparing this to a large aircraft tyre of size 1,400 x 530mmwhich costs £4,154 (this is the size of tyre on the main landing gear for an Airbus A380)
How Fast They Wear • The rate at which a tyre will wear is highly dependent on the operational life of the tyre • A tyre can last for days or months depending upon the scenarios it is put through • If the aircraft lasts for 30 years that can mean an average tyre change of around 500 or more • Bias ply tyres can be retreaded more than radial (bias ply on average about seven and radials about three retreads) • This has obvious impacts on the market trends of using radial tyres for weight saving purposes (Information from an Interview with Dunlop Aircraft Tyres Chairman and Managing Director (from TyrePress (2011)))
Aircraft Tyre Testing • To test aircraft tyres to the extremes highlighted through the operational characteristics means a specialised array of test facilities is required • Different facilities have different capacities to explore the responses of the tyres • These tend to fall into three main brackets: 1. High straight-line speed (with limited slip angle) 2. Vertical load (with limited slip angle) 3. High slip angle (with limited speed)
An example of a dynamometer from MTS working with Boeing These facilities can apply vertical loads to the tyre as required operationally and can evaluate slip angles to 20-30o (Data from MTS (2006)) NASA’s test facility has the capacity to test tyres up to 253mph and slip angles of 15o (Data from Daugherty (2003)) Airbus’s TERATYRE facility is able to examine high slip angles and loads but has speed limitations (Data from Ding (2006))
The Current Market Trends to 2030 • Between 2000 and 2010 air travel has seen an increase of around 45% despite the numerous events which have affected the market • Two of the biggest manufactures have clear views on where the market is heading over the next twenty years to 2030 and they see the same kind of growth again • Boeing and Airbus both predicted significant rises in the number of airliners that will be required for the 2030 market • Airbus estimates around 29,000 new airliners will be required with Boeing supporting the figures predicting 33,000 Data in this slide has come from Airbus (2011a) and Boeing (2011a)
Sustainable mobility Fuel economy improvement by low rolling resistance and constant tyre pressure monitoring 58 http://www.dunlop.eu/ dunlop_uk/ what_sets_dunlop_apart/ future_eu_tyre_label Constant tyre pressure monitor using pressure sensors or comparing wheel speeds using ESP http://www.mysheriff.co.uk http://www.tirepressuremonitoring.com/ Intelligent tyres / Cyber tyre Wireless Monitoring of Automobile Tires for Intelligent Tires, R. Matsuzaki, 2008 Fuel efficiency labels
Conclusions • A single tyre model for all applications does not currently exist (Ftire?) • Tyre models are developed to address specific analyses • Tyre dynamics are complex and highly non-linear • Tyre models are only as good as the data supplied • What does the future hold – Rolling Resistance, Tyre Data Monitoring Systems, ... 59

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Bergamo Lecture 5 - Tyre Modelling Simulation

  • 1. Lecture 5- Tyre Modelling Professor Mike Blundell Phd, MSc, BSc (Hons), FIMechE, CEng Bergamo University Italy 12th -14th June 2012
  • 2. Contents • History and Tyre Construction • Tyre Force and Moment Generation • Tyre Models for Handling and Durability (MF Tyre Model, Finite Element models, Ftire) • Aircraft Tyre Modelling • New Developments
  • 3. History of Tyres The first pneumatic tyre, 1845 by Robert William Thomson. A number of air filled tube inside a leather case. Resistant to punctures but old solid rubber remained in favour with the public. http://www.blackcircles.com/general/history 3 Boyd Dunlop reinvented the pneumatic tyre whilst trying to improve his sons bike in1888 http://www.blackcircles.com/gener al/history In 1895 the pneumatic tyre was first used on automobiles, by Andre and Edouard Michelin. http://www.blackcircles.com/general/history http://polymerprojecttopics.blogspot.com/ 2010/08/radial-tyre-vs-bias-tyre.html Michelin first introduced steel-belted radial tires in Europe in 1948 http://polymerprojecttopics.blogspot.com/2010/08/radial-tyre-vs-bias- Michelin first announced the Tweel in 2005, a non-pneumatic tyre, removing the necessity checking tyre pressures http://auto.howstuffworks.com/tweel- airless-tire.htm
  • 4. Tyre Sidewall Information 205/55 R15 87V 205 Nominal Section-width in mm TUBELESS Tubeless / Tube Type E4 All passenger car tyres from current production comply with ECE Standard 30 026504 Approval number acc. To ECE regulation 30 4008 Production code (40th week, 2008 DOT Department of Transportation, USA TWI Tread Wear Indicator (1.6mm) 4 Continental Technical Data Book. Car Tyres 1999
  • 5. Tyres for All Seasons • Motorsport -Slicks -Intermidiates -Full Wets • Passenger Cars -Summer Tyres -All Season Tyres -Winter Tyres -Mud and Snow Tyres
  • 7. Rubber Compound Formulation • Two Major Ingredients – the rubber and the filler (carbon black and silica) • Combined to achieve different objectives – maximise wet and dry traction/ achieve superior rolling resistance • Four major types of rubber o natural rubber o styrene-butadiene rubber (SBR) o polybutadiene rubber (BR) o butyl rubber (along with halogenated butyl rubber) • The first three are primarily used as tread and sidewall compounds, while butyl rubber and halogenated butyl rubber are primarily used for the inner liner • Other ingredients also come into play to aid in the processing of the tire or to function as anti-oxidants, anti-ozonants, and anti-aging agents. In addition, the “cure package”—a combination of curatives and accelerators—is used to form the tire and give it its elasticity.
  • 8. Tyre Thread Design http://www.checkthatcar.com/tyre%20anatomy.asp 8 Groove http://www.ctyres.co.uk/tyre_info/tyre_type.html Rib Shape Lug Shape Rib-Lug Shape Block Shape Asymmetric pattern Directional pattern Sipe: Fine groove in the tread pattern to improve grip in icy conditions Studs: Further improvement of grip in icy conditions http://www.hankooktire-eu.com/technology/types- of-tires/according-to-season.html
  • 10. Automotive Applications 10 Main applications are in the automotive industry for: – Simulation of vehicle handling – Prediction of vehicle ride quality – Determination of component loads from systems model
  • 11. Aerospace Applications 11 There is a growing need in the aerospace industry for: – Prediction of shimmy – Rough field performance – Ride & controllability – Ground loads – Landing, Takeoff, Taxiing
  • 12. SAE Tyre Axis System 12 {Ysae }1 {Zsae }1 {Xsae }1 P γ α Spin Axis {V}1 Angular Velocity (ω) Wheel Torque (T) WC Direction of Wheel Heading Direction of Wheel Travel Lateral Force (Fy ) Normal Force (Fz ) Tractive Force (Fx )
  • 13. Frictional Force Component due to Adhesion 13 Direction of Sliding Tyre Material Road Surface Adhesive Forces due to Molecular Bonding
  • 14. Tyre Testing • Lateral force with slip/camber angle • Aligning moment with slip/camber angle • Longitudinal force with slip ratio Courtesy of Dunlop TYRES Ltd. Slip Angle Fy
  • 15. Lateral Force Fy with Slip Angle α 15 Courtesy of Dunlop Tyres Ltd.
  • 16. Tyre Modelling Prediction of Vehicle Ride Quality -Simple Physical Models (Stiffness/Damping) -More Advanced Physical Models (FTire) Simulation of Vehicle Handling -Interpolation models (Lookup Tables) -Simple Equation based representations (Fiala) -Complex Mathematical Fits to Test Data (Magic Formula) -Pure and Combined Slip Models Determination of Component Loading -Simple Physical Models (Equivalent Volume) -More Advanced Physical Models (FTire) -Full Non-Linear Finite Element Models
  • 17. Vehicle/Tyre Model Interaction VEHICLE MODEL Wheel centre - Position, Orientation and Velocities  Mathematical Solution at Integration Time Steps  TYRE MODEL Fx - longitudinal tractive or braking force Fy - lateral cornering force Fz - vertical normal force Mz - aligning moment Mx - overturning moment My - rolling resistance moment Tyre Model Fy Fx Fz Mz Tyre Model Fy Fx Fz Mz
  • 18. Tyre Model/Data Assessment Fy Slip Angle  Check plots in ADAMS tyre rig model FIALA MODEL MAGIC FORMULA MODELS INTERPOLATION MODELS Vehicle Model
  • 21. 21 Tyre Model Summary Interpolation Model • It uses tyre test data to interpolate results for a particular scenario Empirical Model • Empirical models use test data to determine equations and parameters to replicate the tyre data Physical Model • These use physical representations of tyre to generate results (e.g. radial belts with spring elements)
  • 22. The Fiala Tyre Model • Input Parameters 2 R2 R1 R1 R2 Tyre Dimensions Model Geometry 22
  • 23. The Fiala Tyre Model Input Parameters R1 The unloaded tyre radius R2 The tyre carcass radius kz The tyre radial stiffness Cs The longitudinal tyre stiffness Ca Lateral tyre stiffness due to slip angle Cg Lateral tyre stiffness due to camber angle (Not Used) Cr The rolling resistant moment coefficient ζ The radial damping ratio m0 The tyre to road coefficient of “static” friction m1 The tyre to road coefficient of “sliding” friction 23
  • 24. The Fiala Tyre Model (Lateral Force and Aligning Moment) • Example of the Lateral Force Generation 24 α z 1 C F μ 3 tan α*                   z α 3 z y F μ 3 tanα C - 1 H where , α sgn H 1 F μ F   α sgn F μ F z y   And so if |α|<α* then: The critical slip angle is: Else if |α|>α* then: • Example of the Aligning Moment Generation And so if |α|<α* then: Else if |α|>α* then:     α sgn H H 1 R F μ 2 M 3 2 z z   0 . 0 Mz 
  • 25. The Fiala Tyre Model • Limitations • No camber thrust • Not suitable for combined slip • Constant cornering stiffness with load • Zero aligning moment at high slip angles 25
  • 26. The “Magic Formula” Tyre Model The basis of this established model is that tyre force and moment curves look like sine functions which have been modified by introducing an arctangent function to “stretch” the slip values on the x-axis. Fx Mz Slip Angle  Slip Ratio  (1) Bakker E., Nyborg L. & Pacejka, H.B., Tyre modelling for use in vehicle dynamics studies, SAE paper 870421. (2) Bakker E., Pacejka H.B. & Linder L., A new tyre model with application in vehicle dynamics studies", SAE paper 800087, 4th Auto Technologies Conference, Monte Carlo, 1989. 26 Fy
  • 27. The “Magic Formula” Tyre Model The general form of the model (version 3) is: y(x) = D sin [ C arctan{ Bx - E ( Bx - arctan ( Bx ))}] where Y(X) = y(x) + Sv Y = Fx, Fy, or Mz x = X + Sh X =  or  Sh = horizontal shift Sv = vertical shift D ys arctan (BCD) Sh X x y Y Sv 27
  • 28. The “Magic Formula” Tyre Model The Main Parameters in the General Equation are D - is the peak value. C - is a shape factor that controls the “stretching” in the x direction. 1.30 - lateral force curve. 1.65 - longitudinal braking force curve. 2.40 - aligning moment curve. B - is referred to as a “stiffness” factor. BCD is the slope at zero slip. E - is a “curvature” factor which effects the transition in the curve and the position xm at which the peak value if present occurs. E is calculated using: Bxm - tan ( p / 2C) E = Bxm - arctan ( Bxm ) ys - is the asymptotic value at large slip values and is found using: ys = D sin ( p C / 2) 28
  • 29. The “Magic Formula” Tyre Model At zero camber the cornering stiffness BCDy reaches a maximum value defined by the coefficient a3 at a given value of vertical load Fz which equates to the coefficient a4. The slope at zero vertical load is taken as 2a3/a4. arctan (2a3/a4) 0 Fz (N) BCDy (N/rad) a4 a3 29
  • 30. The “Magic Formula” Tyre Model • General Formula (Version 3) • y(x)=Dsin[Carctan{Bx-E(Bx-arctan(Bx))] • Y(X) = y(x) + Sv • x = X + Sh • B = stiffness factor • C = shape factor • D = peak factor • Sh = horizontal shift • Sh = vertical shift • B= dy/dx(x=0) / CD • C = (2/p) arcsin (ys/D) • D = ymax • E = (Bxm-tan(p/2C))/(Bxm - arctan (Bxm)) • Lateral Force • Xy = a • Yy = Fy • Dy = my Fz • my = (a1Fz + a2) (1 - a15 g2) • BCDy = a3 sin(2 arctan(Fz/a4)) (1 - a15| g |) • Cy = a0 • Ey = (a6Fz+a7) (1-(a16g + a17)sgn(a + Shy)) • By = BCDy / CyDy • Shy = a8Fz + a9 + a10g • Svy = a11Fz + a12 + (a13Fz2 + a14Fz)g 30
  • 31. The “Magic Formula” Tyre Model • Longitudinal Force • Xx = k • Yx = Fx • Dx = mx Fz • mx = b1Fz + b2 • BCDx = (b3 Fz2 + b4Fz) exp(-b5Fz) • Cx = b0 • Ex = (b6Fz2 + b7Fz + b8)(1- b13sgn(k + Shx)) • Bx = BCDx / CxDx • Shx = b9Fz + b10 • Svy = b11Fz + b12 • Brake force only (b11 = b12 = b13 = 0) • Aligning Moment • Xz = a • Yz = Mz • Dz = (c1Fz2 + c2Fz) (1 - c18g2) • BCDz = (c3Fz2+c4Fz)(1- c6 | g |)exp (-c5Fz) • Cz = c0 • Ez = (czFz2 + c8Fz + c0) (1 - (c19g + c20)* • *sgn(a + Shz)) / (1 - c10 | g | ) • Bz = BCDz / CzDz • Shz = c11Fz + c12 + c13g • Svz = c14Fz + c15 + (c16Fz2 + c17Fz)g 31
  • 32. Laboratory Simulation - Shaker Rig RIDE AND VIBRATION Simple Spring Damper Model Flexible Ring Method Modal FE Model in MBS
  • 33. Ride Simulation (Comfort) X Z m k c z Zg Vehicle Body or Sprung Mass Suspension Spring and Damper Ground Input Body Response Time (s) Also important in Motorsport Vehicles Also important in Military Vehicles
  • 34. Component Load Prediction Fy Lateral loads Fx Longitudinal loads Fz Vertical loads FINITE ELEMENT MODEL ADAMS MODEL Tyre Modelling Radial Spring Models Equivalent Plane Method Equivalent Volume Method Flexible Ring Method Coupled Explicit FE and MBS Methods
  • 35. Tyre Modelling FINITE ELEMENT MODELS A Physical Tyre Model is required Finite Element Modelling is an example Can model deformable terrain as well Not practical in terms of modelling time Excessive computational effort Mainly a tool for Tyre Manufacturers
  • 36. Contact Forces • Used on Helisafe EU project and for tracked vehicles • Modelled hard non-destructive landings • Bi-linear model with tyre and wheel stiffness • Contact function based on stiffness and damping • Includes friction Eurocopter Model 5m/s ground impact Tracked Vehicle operating in deep snow
  • 37. Examples of Tyre Interactions 37
  • 38. Durability Tyre Models • Early durability tyre models were 2D • Radial Spring or Equivalent Plane • Capture deformed shape of tyre enveloping terrain • Resultant force towards wheel centre Radial Spring Model Equivalent Plane
  • 39. Durability Tyre Model • Originally developed in Finland for logging vehicles • Captured tyre interaction with sawn tree trunks on rough terrain • 3d Model - Discritization into cross-sectional elements Definition of tyre carcass shape for a durability tyre model      Input points to define shape Tyre centre line Tyre centre line Tyre cross-sectional elements
  • 40. Early Road/Terrain Model Road modelled using triangular planar elements Friction can vary on element by element basis 1 2 3 4 5 6 Intersection of tyre sectional elements with road elements
  • 41. A Tyre Model for Ride & Durability Simulations A Flexible ring tyre model Tire phenomena based on a mechanical model Developed by Cosin (www.cosin.eu) Developed by Cosin (www.cosin.eu) The FTIRE Model FTire on Belgian Pave FTire on Belgian Pave
  • 42. • Structural dynamics based, full 3D nonlinear in-plane and out-of-plane tire model for simulation of belt dynamics, local pressure distribution in the contact patch, rolling resistance, side-wall contact, large camber angles and misuse scenarios. • Suitable for a frequency range up to 200Hz, excited by short surface wavelength, mass imbalance, non-uniformity or irregular tread patterns. • Very fast and flexible. Orders of magnitude faster than explicit FE models. • Simulation of imbalances by inhomogeneous mass distribution and local wear. • Belt temperature distribution model. The FTIRE Model
  • 43. cbend. ctang. crad. cbelt bending stiffness both in-plane and out-of-plane (simplified) Tyre structure described with distributed mass, connected to rim by distributed stiffness & damping elements The FTIRE Model
  • 44. 3D Road/Terrain Model Regular Grid Road Data Files (RGR Files) Open Source software developed by Daimler AG VIRES GmbH 3D Road Data Curved regular Grid (CRG) Representation Data Files can be generated from laser scans along a road Belgian Block XYZ map Open CRG Visualisation
  • 45. FTire Animations Detailed Tread Pattern Detailed Tread Pattern Truck Tire Passing a big bump Truck Tire Passing a big bump
  • 46. FTire Animations Rolling over a high kerb Rolling over a high kerb Local Belt Deformation Local Belt Deformation
  • 47. FTire Animations Sine wave with Sine wave with decreasing wave length decreasing wave length FTire on RGR Road Surface FTire on RGR Road Surface
  • 48. 200 mm 10 mm v = 80 km/h wheel load [N] longitudinal force [N] 0 0.02 0.04 0.06 0.08 0.1 1000 2000 3000 4000 5000 0 0.02 0.04 0.06 0.08 0.1 -2000 -1000 0 1000 2000 FTire: Running over an Obstacle
  • 49. side-slip angle [deg] M [Nm] z 0 5 10 15 20 25 30 35 40 45 -100 -50 0 50 100 150 200 aligning torque F [N] y side-slip angle [deg] 0 5 10 15 20 25 30 35 40 45 0 1000 2000 3000 4000 5000 6000 7000 8000 side force Fz = 2, 4, 6, 8 kN FTire: Handling Characteristics
  • 50. Aircraft Tyre Modelling •EPSRC Project with AIRBUS UK •Simulate landing, takeoff, taxiing •Tyre Testing by Airbus in Toulouse •Developed model in a MATLAB/SIMULINK Environment with export to ADAMS • Low Parameter Model based on Harty Approach with extended Load/Speed dependence • Shimmy Modelling (Early NASA work) remains elusive
  • 51. Aircraft Tyres • Aircraft tyres are pushed to the extremes of operational envelopes compared to other forms of ground vehicles • Typical automotive applications would see tyres experiencing slip angles of around 10o however aircraft tyres can go up to 90o • Typically speeds of up to 200mph will be experienced (225-235mph being the speed ratings typically seen (from Bridgestone (2011)))
  • 52. Extreme Operating Conditions • Because of the operational loads of the aircraft the vertical loads experienced by the tyre’s are also magnified • The rated load of a nose wheel can be approx. 40 kN; an automotive tyre of similar size can be seen to have a load of approx 6 kN • Large landing gear tyres can have rated loads in excess of 300 kN Daugherty (2003)
  • 53. Tyre Costs (All figures are based upon Michelin prices (from Air Michelin (2007))) • The costs involved with aircraft tyres can best be seen when comparing them against an automotive example • An average automotive tyre can cost around £60-70 (using an example tyre size of 205/55 R16) • An aircraft tyre of similar size can cost £1,708 (based upon a 27x7.7in (686x196mm) tyre) • Then comparing this to a large aircraft tyre of size 1,400 x 530mmwhich costs £4,154 (this is the size of tyre on the main landing gear for an Airbus A380)
  • 54. How Fast They Wear • The rate at which a tyre will wear is highly dependent on the operational life of the tyre • A tyre can last for days or months depending upon the scenarios it is put through • If the aircraft lasts for 30 years that can mean an average tyre change of around 500 or more • Bias ply tyres can be retreaded more than radial (bias ply on average about seven and radials about three retreads) • This has obvious impacts on the market trends of using radial tyres for weight saving purposes (Information from an Interview with Dunlop Aircraft Tyres Chairman and Managing Director (from TyrePress (2011)))
  • 55. Aircraft Tyre Testing • To test aircraft tyres to the extremes highlighted through the operational characteristics means a specialised array of test facilities is required • Different facilities have different capacities to explore the responses of the tyres • These tend to fall into three main brackets: 1. High straight-line speed (with limited slip angle) 2. Vertical load (with limited slip angle) 3. High slip angle (with limited speed)
  • 56. An example of a dynamometer from MTS working with Boeing These facilities can apply vertical loads to the tyre as required operationally and can evaluate slip angles to 20-30o (Data from MTS (2006)) NASA’s test facility has the capacity to test tyres up to 253mph and slip angles of 15o (Data from Daugherty (2003)) Airbus’s TERATYRE facility is able to examine high slip angles and loads but has speed limitations (Data from Ding (2006))
  • 57. The Current Market Trends to 2030 • Between 2000 and 2010 air travel has seen an increase of around 45% despite the numerous events which have affected the market • Two of the biggest manufactures have clear views on where the market is heading over the next twenty years to 2030 and they see the same kind of growth again • Boeing and Airbus both predicted significant rises in the number of airliners that will be required for the 2030 market • Airbus estimates around 29,000 new airliners will be required with Boeing supporting the figures predicting 33,000 Data in this slide has come from Airbus (2011a) and Boeing (2011a)
  • 58. Sustainable mobility Fuel economy improvement by low rolling resistance and constant tyre pressure monitoring 58 http://www.dunlop.eu/ dunlop_uk/ what_sets_dunlop_apart/ future_eu_tyre_label Constant tyre pressure monitor using pressure sensors or comparing wheel speeds using ESP http://www.mysheriff.co.uk http://www.tirepressuremonitoring.com/ Intelligent tyres / Cyber tyre Wireless Monitoring of Automobile Tires for Intelligent Tires, R. Matsuzaki, 2008 Fuel efficiency labels
  • 59. Conclusions • A single tyre model for all applications does not currently exist (Ftire?) • Tyre models are developed to address specific analyses • Tyre dynamics are complex and highly non-linear • Tyre models are only as good as the data supplied • What does the future hold – Rolling Resistance, Tyre Data Monitoring Systems, ... 59

Editor's Notes

  • #2: First, let’s define what we mean when we say Virtual Prototyping. We’re talking about functional simulation of real-world systems in order to: -Reduce time-intensive, costly, hardware build-test-refine cycles -Improve quality (cut warranty and repair/maintenance costs) -Address bottlenecks in strategic industries: auto, aero/defense, and rail
  • #41: This presentation introduces a new tire model that will be available in ADAMS Version 11. The new model is called FTire, which stands for “Flexible Ring Tire Model”. The new tire model will close the gap between pure handling models like Fiala’s model and several versions of Pacejkas Magic Formula, and Finite-Element-based flexible body tire models. Steady state handling models are very fast, but not appropriate for ride comfort and durability simulations, whereas flexible body descriptions reflect very accurately the linear modal properties of the tire, but are very time-consuming and do not reflect the handling properties at all.
  • #42: FTire reflects the relevant nonlinear tire properties. This is indispensable to ride comfort and durability simulations, where extremely large deflections might occur. FTire is designed to be valid for excitation frequencies up to 120 Hertz. It shows the resulting oscillatory behavior both for vibrations in the rim mid-plane, as well as perpendicular to that plane. As this is very important for ride comfort on extremely uneven roads, FTire resolves wave-lengths far below 5 cm. In fact , the resolution reaches the range of few millimeters only. By that, FTire recognizes extremely sharp edges of single obstacles, like curb-stones and so on. The present version of FTire, however, allows only for sharp edges in the rolling direction. In transverse direction, FTire recognizes long-waved road inclination only. Recently, a downward compatible true 3D extension of FTire is under development, that will overcome this restriction. Further objectives had been: the ease of data supply, by using easy-to-get static and modal tire properties, computing time as short as possible, valid also for steady-state and dynamic handling properties, ease of implementation into MBS code like ADAMS, and preparation of downward compatible, even more detailed versions.
  • #43: FTire describes the tire belt as an extensible and flexible ring. This ring consists of some 50 to 100 nodes. Every node has all three translatoric degrees of freedom. The nodes are connected to the rim by nonlinear springs in all three directions. In addition, every node is linked to the rim by a spring-damper series connection. This reflects the radial stiffening at higher speeds. Furthermore, the belt nodes are coupled with their direct neighbors by stiff springs and by bending stiffnesses both in-plane and out-of-plane. All discrete stiffness and damping values mentioned so far are calculated during pre-processing. This is done by automatically fitting measured or calculated static and modal tire properties. I will give further details on data supply later. Tire forces and moments acting on the rim are determined by summing up all spring and damper forces that act on the rim.