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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.

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S a lar ba lam l

OMÜ 325WEEK 4-L1Tires:

Fy, Fx & Mz

S.Çağlar Başlamışlı


Summary
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
TIRE FORCE GENERATION

SAE tire axis system


Tire force generation1
TIRE FORCE GENERATION

The Pneumatic tire is a complex system with

Multiples inputs and outputs!



Derivation of cornering force characteristics
DERIVATION OF CORNERING FORCE CHARACTERISTICS

Deflection:

Normal Force Distribution:

Max. Normal Force Distribution:



Derivation of cornering force characteristics1
DERIVATION OF CORNERING FORCE CHARACTERISTICS

Define:

Stiffness of a brush element

Transition to sliding (xt) found by equating :


Derivation of cornering force characteristics2
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!!!



Warning
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


Cornering force characteristics3
CORNERING FORCE CHARACTERISTICS

Will be explained later


Cornering force characteristics4
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.




CORNERING FORCE CHARACTERISTICS

Positive Camber

Negative Camber


Cornering force characteristics7
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.


Cornering force characteristics8
CORNERING FORCE CHARACTERISTICS

View from behind

Top view

View from behind

Top view

Influence of camber



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

Influence of inflation pressure


Sat characteristics
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.


Sat characteristics1
SAT CHARACTERISTICS

Caster trail


Sat characteristics2
SAT CHARACTERISTICS

Pneumatic trail




Fx characteristics
Fx CHARACTERISTICS

  • Slip Ratio

    • Slip ratio is defined as the slip velocity as a percentage of the free rolling velocity.

    • Since

    • then



Fx characteristics1
Fx CHARACTERISTICS

Slip Ratio definition (SAE J670)

re = effective rolling radius for free rolling @  = 0







Warning1
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.



Magic formula1
Magic Formula

  • Combined Slip Formulation:

  • Pure Slip Formulation:

  • Shaping Function:


Magic formula2
Magic Formula

Combined Slip Formulation:

Pure Slip Formulation:

Shaping Function:



S a lar ba lam l1

OMÜ 325END OF WEEK 4-L1Tires:

Fy, Fx & Mz

S.Çağlar Başlamışlı


S a lar ba lam l2

S.Çağlar Başlamışlı

OMÜ 325WEEK 4-L2Introduction to Vehicle Handling:

The Bicycle Vehicle Model


Summary1
SUMMARY

  • Assumptions

  • Bicycle Model

  • Handling Behavior





Assumptions3
ASSUMPTIONS

(constant u)











S a lar ba lam l3

S.Çağlar Başlamışlı

OMÜ 325END OF WEEK 4-L2Introduction to Vehicle Handling:

The Bicycle Vehicle Model


Gough s experiment
GOUGH’S EXPERIMENT

adhesion+sliding

adhesion

sliding