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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.




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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



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CORNERING FORCE CHARACTERISTICS

Positive Camber

Negative Camber

Center of turn


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CORNERING FORCE CHARACTERISTICS

Positive Camber

Negative Camber

Center of turn


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CORNERING FORCE CHARACTERISTICS

Positive Camber

Negative Camber

Center of turn



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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:



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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)











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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



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