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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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OMÜ 325WEEK 4-L1Tires:

Fy, Fx & Mz

S.Çağlar Başlamışlı

• Lateral Force Characteristics : Fy

• Self Aligning Torque Characteristics : Mz

• Longitudinal Force Characteristics : Fx

• Influence of Fx on Fy & Mz

• Magic Formula

SAE tire axis system

The Pneumatic tire is a complex system with

Multiples inputs and outputs!

sliding

Deflection:

Normal Force Distribution:

Max. Normal Force Distribution:

Define:

Stiffness of a brush element

Transition to sliding (xt) found by equating :

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!!!

• 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

Will be explained later

• 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.

Positive Camber

Negative Camber

• 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.

View from behind

Top view

View from behind

Top view

Influence of camber

Positive Camber

Negative Camber

Center of turn

Positive Camber

Negative Camber

Center of turn

Positive Camber

Negative Camber

Center of turn

Influence of inflation pressure

• 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

• Slip Ratio

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

• Since

• then

Slip Ratio definition (SAE J670)

(braking)

• 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.

• Combined Slip Formulation:

• Pure Slip Formulation:

• Shaping Function:

Combined Slip Formulation:

Pure Slip Formulation:

Shaping Function:

OMÜ 325END OF WEEK 4-L1Tires:

Fy, Fx & Mz

S.Çağlar Başlamışlı

OMÜ 325WEEK 4-L2Introduction to Vehicle Handling:

The Bicycle Vehicle Model

• Assumptions

• Bicycle Model

• Handling Behavior

(constant u)

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

The Bicycle Vehicle Model