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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.Çağlar Başlamışlı

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OMÜ 325WEEK 4-L1Tires:

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

TIRE FORCE GENERATION

The Pneumatic tire is a complex system with

Multiples inputs and outputs!

sliding

DERIVATION OF CORNERING FORCE CHARACTERISTICS

Deflection:

Normal Force Distribution:

Max. Normal Force Distribution:

DERIVATION OF CORNERING FORCE CHARACTERISTICS

Define:

Stiffness of a brush element

Transition to sliding (xt) found by equating :

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

• 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 CHARACTERISTICS

Will be explained later

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

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.

CORNERING FORCE CHARACTERISTICS

View from behind

Top view

View from behind

Top view

Influence of camber

CORNERING FORCE CHARACTERISTICS

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.

Caster trail

Pneumatic trail

Fx CHARACTERISTICS

• Slip Ratio

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

• Since

• then

Fx CHARACTERISTICS

Slip Ratio definition (SAE J670)

(braking)

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

• Combined Slip Formulation:

• Pure Slip Formulation:

• Shaping Function:

Magic Formula

Combined Slip Formulation:

Pure Slip Formulation:

Shaping Function:

Magic Formula

OMÜ 325END OF WEEK 4-L1Tires:

Fy, Fx & Mz

S.Çağlar Başlamışlı

S.Çağlar Başlamışlı

OMÜ 325WEEK 4-L2Introduction to Vehicle Handling:

The Bicycle Vehicle Model

SUMMARY

• Assumptions

• Bicycle Model

• Handling Behavior

(constant u)

BICYCLE MODEL

BICYCLE MODEL

BICYCLE MODEL

BICYCLE MODEL

BICYCLE MODEL

BICYCLE MODEL

HANDLING BEHAVIOR

S.Çağlar Başlamışlı

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

The Bicycle Vehicle Model