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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!


Cornering force characteristics

CORNERING FORCE CHARACTERISTICS

sliding

adhesion


Derivation of cornering force characteristics

DERIVATION OF CORNERING FORCE CHARACTERISTICS

Deflection:

Normal Force Distribution:

Max. Normal Force Distribution:


Cornering force characteristics1

CORNERING FORCE CHARACTERISTICS


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!!!


Cornering force characteristics2

CORNERING FORCE CHARACTERISTICS


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 characteristics5

CORNERING FORCE CHARACTERISTICS

Influence of load


Cornering force characteristics6

CORNERING FORCE CHARACTERISTICS


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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


Cornering force characteristics9

CORNERING FORCE CHARACTERISTICS


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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


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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


Sat characteristics3

SAT CHARACTERISTICS


Sat characteristics4

SAT CHARACTERISTICS


Fx characteristics

Fx CHARACTERISTICS

  • Slip Ratio

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

    • Since

    • then


Tire rolling radius

Tire Rolling Radius


Fx characteristics1

Fx CHARACTERISTICS

Slip Ratio definition (SAE J670)

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


Fx characteristics2

Fx CHARACTERISTICS


Fx characteristics3

Fx CHARACTERISTICS


Influence of fx on fy

Influence of Fx on Fy

(braking)


Friction circle

Friction Circle


Influence of fx on fy mz

Influence of Fx on Fy & Mz


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 formula

Magic Formula


Magic formula1

Magic Formula

  • Combined Slip Formulation:

  • Pure Slip Formulation:

  • Shaping Function:


Magic formula2

Magic Formula

Combined Slip Formulation:

Pure Slip Formulation:

Shaping Function:


Magic formula3

Magic Formula


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OMÜ 325END OF WEEK 4-L1Tires:

Fy, Fx & Mz

S.Çağlar Başlamışlı


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S.Çağlar Başlamışlı

OMÜ 325WEEK 4-L2Introduction to Vehicle Handling:

The Bicycle Vehicle Model


Summary1

SUMMARY

  • Assumptions

  • Bicycle Model

  • Handling Behavior


Assumptions

ASSUMPTIONS


Assumptions1

ASSUMPTIONS


Assumptions2

ASSUMPTIONS


Assumptions3

ASSUMPTIONS

(constant u)


Assumptions4

ASSUMPTIONS


Assumptions5

ASSUMPTIONS


Bicycle model

BICYCLE MODEL


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BICYCLE MODEL


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BICYCLE MODEL


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BICYCLE MODEL


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BICYCLE MODEL


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BICYCLE MODEL


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HANDLING BEHAVIOR


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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


Cornering force characteristics10

CORNERING FORCE CHARACTERISTICS


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