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S.Çağlar Başlamışlı

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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  1. OMÜ 325WEEK 4-L1Tires: Fy, Fx & Mz S.Çağlar Başlamışlı

  2. SUMMARY • Lateral Force Characteristics : Fy • Self Aligning Torque Characteristics : Mz • Longitudinal Force Characteristics : Fx • Influence of Fx on Fy & Mz • Magic Formula

  3. TIRE FORCE GENERATION SAE tire axis system

  4. TIRE FORCE GENERATION The Pneumatic tire is a complex system with Multiples inputs and outputs!

  5. CORNERING FORCE CHARACTERISTICS sliding adhesion

  6. DERIVATION OF CORNERING FORCE CHARACTERISTICS Deflection: Normal Force Distribution: Max. Normal Force Distribution:

  7. CORNERING FORCE CHARACTERISTICS

  8. DERIVATION OF CORNERING FORCE CHARACTERISTICS Define: Stiffness of a brush element Transition to sliding (xt) found by equating :

  9. 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!!!

  10. CORNERING FORCE CHARACTERISTICS

  11. 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

  12. CORNERING FORCE CHARACTERISTICS Will be explained later

  13. 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.

  14. CORNERING FORCE CHARACTERISTICS Influence of load

  15. CORNERING FORCE CHARACTERISTICS

  16. CORNERING FORCE CHARACTERISTICS Positive Camber Negative Camber

  17. 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.

  18. CORNERING FORCE CHARACTERISTICS View from behind Top view View from behind Top view Influence of camber

  19. CORNERING FORCE CHARACTERISTICS

  20. CORNERING FORCE CHARACTERISTICS Positive Camber Negative Camber Center of turn

  21. CORNERING FORCE CHARACTERISTICS Positive Camber Negative Camber Center of turn

  22. CORNERING FORCE CHARACTERISTICS Positive Camber Negative Camber Center of turn

  23. CORNERING FORCE CHARACTERISTICS

  24. CORNERING FORCE CHARACTERISTICS Influence of inflation pressure

  25. 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.

  26. SAT CHARACTERISTICS Caster trail

  27. SAT CHARACTERISTICS Pneumatic trail

  28. SAT CHARACTERISTICS

  29. SAT CHARACTERISTICS

  30. Fx CHARACTERISTICS • Slip Ratio • Slip ratio is defined as the slip velocity as a percentage of the free rolling velocity. • Since • then

  31. Tire Rolling Radius

  32. Fx CHARACTERISTICS Slip Ratio definition (SAE J670) re = effective rolling radius for free rolling @  = 0

  33. Fx CHARACTERISTICS

  34. Fx CHARACTERISTICS

  35. Influence of Fx on Fy (braking)

  36. Friction Circle

  37. Influence of Fx on Fy & Mz

  38. 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.

  39. Magic Formula

  40. Magic Formula • Combined Slip Formulation: • Pure Slip Formulation: • Shaping Function:

  41. Magic Formula Combined Slip Formulation: Pure Slip Formulation: Shaping Function:

  42. Magic Formula

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