1. OMÜ 325 WEEK 4-L1 Tires:
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 3

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

13. CORNERING FORCE CHARACTERISTICS
sliding
adhesion 13

14. DERIVATION OF CORNERING FORCE CHARACTERISTICS
Deflection:
Normal Force Distribution:
Max. Normal Force Distribution: 14

15. CORNERING FORCE CHARACTERISTICS15

16. DERIVATION OF CORNERING FORCE CHARACTERISTICS
Define:
Stiffness of a brush element
Transition to sliding (xt) found by equating : 16

17. 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!!! 17

18. CORNERING FORCE CHARACTERISTICS18

19. 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 19

20. CORNERING FORCE CHARACTERISTICS
Will be explained later 20

21. 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. 21

22. CORNERING FORCE CHARACTERISTICS
Influence of load 22

23. CORNERING FORCE CHARACTERISTICS23

24. CORNERING FORCE CHARACTERISTICS
Positive Camber
Negative Camber

25. 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. 25

26. CORNERING FORCE CHARACTERISTICS
View from behind
Top view
View from behind
Top view
Influence of camber 26

27. CORNERING FORCE CHARACTERISTICS27

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

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

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

31. CORNERING FORCE CHARACTERISTICS

32. CORNERING FORCE CHARACTERISTICS
Influence of inflation pressure

33. 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. 33

34. SAT CHARACTERISTICS
Caster trail 34

35. SAT CHARACTERISTICS
Pneumatic trail 35

36. SAT CHARACTERISTICS 36

37. SAT CHARACTERISTICS 37

38. Fx CHARACTERISTICS Slip Ratio
Slip ratio is defined as the slip velocity as a percentage of the free rolling velocity.
Since
then 38

39. Tire Rolling Radius 39

40. Slip Ratio definition (SAE J670)
Fx CHARACTERISTICS
Slip Ratio definition (SAE J670)
re = effective rolling radius for free rolling @  = 0 40

41. Fx CHARACTERISTICS 41

42. Fx CHARACTERISTICS 42

43. Influence of Fx on Fy
(braking) 43

44. Friction Circle 44

45. Influence of Fx on Fy & Mz45

46. 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. 46

47. Magic Formula

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

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

50. Magic Formula

51. OMÜ 325 END OF WEEK 4-L1 Tires:
Fy, Fx & Mz
S.Çağlar Başlamışlı

52. OMÜ 325 WEEK 4-L2 Introduction to Vehicle Handling:
The Bicycle Vehicle Model
S.Çağlar Başlamışlı 52

53. SUMMARY
Assumptions
Bicycle Model
Handling Behavior 53

54. ASSUMPTIONS 54

55. ASSUMPTIONS 55

56. ASSUMPTIONS 56

57. ASSUMPTIONS
(constant u) 57

58. ASSUMPTIONS 58

59. ASSUMPTIONS 59

60. BICYCLE MODEL 60

61. BICYCLE MODEL 61

62. BICYCLE MODEL 62

63. BICYCLE MODEL 63

64. BICYCLE MODEL 64

65. BICYCLE MODEL 65

66. HANDLING BEHAVIOR 66

67. OMÜ 325 END OF WEEK 4-L2 Introduction to Vehicle Handling:
The Bicycle Vehicle Model
S.Çağlar Başlamışlı 67

68. GOUGH’S EXPERIMENT
adhesion+sliding
adhesion
sliding

69. CORNERING FORCE CHARACTERISTICS69