OMÜ 325 WEEK 4-L1 Tires: Fy, Fx & Mz S.Çağlar Başlamışlı

SUMMARY Lateral Force Characteristics : Fy Self Aligning Torque Characteristics : Mz Longitudinal Force Characteristics : Fx Influence of Fx on Fy & Mz Magic Formula

TIRE FORCE GENERATION SAE tire axis system 3

TIRE FORCE GENERATION The Pneumatic tire is a complex system with Multiples inputs and outputs! 4

CORNERING FORCE CHARACTERISTICS sliding adhesion 13

DERIVATION OF CORNERING FORCE CHARACTERISTICS Deflection: Normal Force Distribution: Max. Normal Force Distribution: 14

CORNERING FORCE CHARACTERISTICS 15

DERIVATION OF CORNERING FORCE CHARACTERISTICS Define: Stiffness of a brush element Transition to sliding (xt) found by equating : 16

DERIVATION OF CORNERING FORCE CHARACTERISTICS Now, find Fy by integrations: From –a to –xt for the sliding part From –xt to a for the adhesion part Hw: Derive the above equation and show that Fy=mu*Fz for large alpha!!! 17

CORNERING FORCE CHARACTERISTICS 18

WARNING Up to now we tried to understand what to expect from cornering force generation based on theoretical modeling and (simple) assumptions. Starting from this point on, we will analyze experimental results. You will observe that while our theoretical prediction seems to be quite good, it is in general not accurate enough to model the complex behavior of the tire. You will investigate more complex analytical & empirical tire models in your HW: Dugoff, Allen, STI, etc 19

CORNERING FORCE CHARACTERISTICS Will be explained later 20

CORNERING FORCE CHARACTERISTICS Cornering stiffness is the change in lateral force per unit slip angle change at a specified normal load in the linear range of the tire. 21

CORNERING FORCE CHARACTERISTICS Influence of load 22

CORNERING FORCE CHARACTERISTICS 23

CORNERING FORCE CHARACTERISTICS Positive Camber Negative Camber

CORNERING FORCE CHARACTERISTICS Camber stiffness is the change in lateral force per unit camber angle change at a specified normal load in the linear range of the tire. 25

CORNERING FORCE CHARACTERISTICS View from behind Top view View from behind Top view Influence of camber 26

CORNERING FORCE CHARACTERISTICS 27

CORNERING FORCE CHARACTERISTICS Positive Camber Negative Camber Center of turn

CORNERING FORCE CHARACTERISTICS Positive Camber Negative Camber Center of turn

CORNERING FORCE CHARACTERISTICS Positive Camber Negative Camber Center of turn

CORNERING FORCE CHARACTERISTICS

CORNERING FORCE CHARACTERISTICS Influence of inflation pressure

SAT CHARACTERISTICS Self-Aligning Torque is derived from a combination of caster trail and the tires own pneumatic trail. If the mechanical (caster) trail is small the tires aligning torque (Pneumatic Trail) will dominate the steering effect. Pneumatic trail is derived from the shear force distribution in the tire footprint. 33

SAT CHARACTERISTICS Caster trail 34

SAT CHARACTERISTICS Pneumatic trail 35

SAT CHARACTERISTICS 36

SAT CHARACTERISTICS 37

Fx CHARACTERISTICS Slip Ratio Slip ratio is defined as the slip velocity as a percentage of the free rolling velocity. Since then 38

Tire Rolling Radius 39

Slip Ratio definition (SAE J670) Fx CHARACTERISTICS Slip Ratio definition (SAE J670) re = effective rolling radius for free rolling @  = 0 40

Fx CHARACTERISTICS 41

Fx CHARACTERISTICS 42

Influence of Fx on Fy (braking) 43

Friction Circle 44

Influence of Fx on Fy & Mz 45

WARNING Up to here, we saw a simple analytical tire model and provided a lot of experimental findings. We saw that our simple analytical tire model is not accurate enough as it does not accurately model at least the peaking behavior, The dependence on longitudinal slip Etc... Complex analytical models are hard to derive and are out of the scope of this course But we can at this point introduce a simple empirical tire model : the Magic Formula, which has become a standard in vehicle dynamics simulation. 46

Magic Formula

Magic Formula Combined Slip Formulation: Pure Slip Formulation: Shaping Function:

Magic Formula Combined Slip Formulation: Pure Slip Formulation: Shaping Function:

Magic Formula

OMÜ 325 END OF WEEK 4-L1 Tires: Fy, Fx & Mz S.Çağlar Başlamışlı

OMÜ 325 WEEK 4-L2 Introduction to Vehicle Handling: The Bicycle Vehicle Model S.Çağlar Başlamışlı 52

SUMMARY Assumptions Bicycle Model Handling Behavior 53

ASSUMPTIONS 54

ASSUMPTIONS 55

ASSUMPTIONS 56

ASSUMPTIONS (constant u) 57

ASSUMPTIONS 58

ASSUMPTIONS 59

BICYCLE MODEL 60

BICYCLE MODEL 61

BICYCLE MODEL 62

BICYCLE MODEL 63

BICYCLE MODEL 64

BICYCLE MODEL 65

HANDLING BEHAVIOR 66

OMÜ 325 END OF WEEK 4-L2 Introduction to Vehicle Handling: The Bicycle Vehicle Model S.Çağlar Başlamışlı 67

GOUGH’S EXPERIMENT adhesion+sliding adhesion sliding

CORNERING FORCE CHARACTERISTICS 69