Podcast
Questions and Answers
What does the 'Friction Circle' or ellipse illustrate regarding tire forces?
What does the 'Friction Circle' or ellipse illustrate regarding tire forces?
- It represents the direct proportionality between longitudinal and lateral forces.
- It shows the trade-off between maximum longitudinal and lateral forces a tire can generate. (correct)
- It illustrates how a tire's rolling resistance increases linearly with applied force.
- It demonstrates that a tire's maximum force capability is independent of slip angle.
According to the provided material illustrating the 'friction circle', what happens as a vehicle increases its braking force?
According to the provided material illustrating the 'friction circle', what happens as a vehicle increases its braking force?
- Its maximum cornering force capability is unaffected.
- The relationship cannot be determined from the friction circle.
- Its maximum cornering force capability increases proportionally.
- Its maximum cornering force capability decreases. (correct)
In Pacejka's 'Magic Formula', what do the variables X and Y typically represent?
In Pacejka's 'Magic Formula', what do the variables X and Y typically represent?
- X represents the combined longitudinal and lateral forces and Y represents vehicle speed.
- X represents the tire load, and Y represents the inflation pressure.
- X represents lateral force, and Y represents longitudinal force.
- X represents the 'slip angle' or 'skid ratio', and Y represents lateral force, aligning moment, or braking force. (correct)
A vehicle is experiencing a slip angle of 4 degrees and a braking slip ratio of 0.036. Based on the 'Friction Circle Example', what is the approximate resultant force relative to the 800 lb lateral force and 500 lb braking force?
A vehicle is experiencing a slip angle of 4 degrees and a braking slip ratio of 0.036. Based on the 'Friction Circle Example', what is the approximate resultant force relative to the 800 lb lateral force and 500 lb braking force?
What is the primary purpose of Pacejka's 'Magic Formula' in the context of tire dynamics?
What is the primary purpose of Pacejka's 'Magic Formula' in the context of tire dynamics?
In the context of the provided image, what does the slip angle represent?
In the context of the provided image, what does the slip angle represent?
In the Tractive/Braking Force Variation graph, what does the x-axis represent?
In the Tractive/Braking Force Variation graph, what does the x-axis represent?
According to the figure illustrating the construction of a friction ellipse, what is being plotted on the vertical axis?
According to the figure illustrating the construction of a friction ellipse, what is being plotted on the vertical axis?
In the context of combined longitudinal and lateral tire forces, what does the term 'free-rolling' typically imply?
In the context of combined longitudinal and lateral tire forces, what does the term 'free-rolling' typically imply?
Referring to the TABLE 1.6 Values of the Coefficients in the Magic Formula for a Car Tire, as the load ($F_z$) increases, what generally happens to the value of coefficient D for $F_y$?
Referring to the TABLE 1.6 Values of the Coefficients in the Magic Formula for a Car Tire, as the load ($F_z$) increases, what generally happens to the value of coefficient D for $F_y$?
Flashcards
Combined Longitudinal & Lateral Force
Combined Longitudinal & Lateral Force
Combined forces acting on a tire in both the longitudinal (driving/braking) and lateral (cornering) directions.
Friction Circle (or Ellipse)
Friction Circle (or Ellipse)
Graphical representation of the maximum forces a tire can generate. It forms a circle or ellipse, showing the trade-off between longitudinal and lateral forces.
Pacejka's 'Magic Formula'
Pacejka's 'Magic Formula'
A semi-empirical formula that can represent lateral force, aligning moment, or braking force.
Traction vs. Braking (Sakai Definition)
Traction vs. Braking (Sakai Definition)
Graphical representation demonstrating that traction is defined as less than zero and braking is defined as greater than zero.
Signup and view all the flashcardsStudy Notes
Combined Longitudinal & Lateral Force
- Focus is on the effect of tractive/braking effort on cornering for radial tires
Friction Circle
- Friction circle or ellipse occurs if the maximum longitudinal force does not equal the maximum lateral force
Construction of Friction Ellipse
- Plot cornering force vs slip angle
- Copy cornering force to vertical axis of right half when longitudinal force is 0, free-rolling
- Plot variation of cornering force as longitudinal force increases as Fx increases for each value of alpha
Tractive/Braking Force Variation
- Variation occurs due to slip ratio and slip angle
- Sign conventions may differ based on the data source
Friction Circle Example
- Y-axis represents lateral force vs slip angle
- X-axis represents longitudinal force vs slip ratio
- Traction is defined as i0 by Sakai of the Japan Automobile Research Institute
Point A Example
- 4° slip angle, 0.036 braking slip ratio
- 800 lb lateral force, 500 lb braking force, which leads to a resultant force of about 950 lb
Point B At Limit
- 1100 lb lateral force; ~13° slip angle, there is no braking or tractive force
Pacejka's Magic Formula
- Semi-empirical model used to model tire behavior
- Y can represent lateral force, aligning moment, or braking force
- X represents sideslip angle or skid ratio
- Formula includes variables B, C, D, E, Sh, Sv, which vary with vertical load Fz.
- Provided in Wong, Table 1.6
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