2.3 Tire Mechanics

Question 1

What are the main features of pneumatic tires?

Answer 1

The main features of pneumatic tires are their flexibility and low mass, which allow contact with the road to be maintained even on uneven surfaces. Additionally, the rubber ensures high grip.

Question 2

What is the basic structure of a pneumatic tire?

Answer 2

A pneumatic tire consists of a carcass of flexible, yet almost inextensible cords encased in a matrix of soft rubber, all inflated with air.

Question 3

How does a tire roll on a rigid surface compared to a rigid wheel?

Answer 3

Unlike a rigid wheel, a deformable tire flattens at the contact area with the road surface, creating a contact patch that distributes forces and maintains better contact with the road.

Question 4

What type of material is rubber considered in tire mechanics?

Answer 4

Rubber is considered a visco-elastic material, showing behavior that lies between that of an elastic solid and a viscous liquid.

Question 5

How does a visco-elastic material behave under deformation?

Answer 5

A visco-elastic material reverts to its initial shape after deformation, but only after a certain time (hysteresis). The delay is accompanied by a dissipation of energy in the form of heat.

Question 6

How does an elastic solid respond to an applied force?

Answer 6

When pushing an elastic solid (like a spring), it compresses; when released, it returns to its initial length. The harder we push, the more it compresses, with a proportionality between force and displacement: F = kx.

Question 7

How does a viscous liquid respond to an applied force?

Answer 7

When pushing a viscous liquid (like in a damper), it does not move immediately - movement lags behind the application of force. There is a proportionality between force and speed: F = c·ẋ.

Question 8

What is hysteresis in the context of tire mechanics?

Answer 8

Hysteresis is the delay in a visco-elastic material returning to its original shape after deformation. It directly relates to the loss of energy and is at the origin of the tire grip mechanism.

Question 9

What are the two main types of friction generated by rubber tires?

Answer 9

Rubber tires generate two distinct kinds of friction: adhesive friction (adhesion) and hysteresis grip.

Question 10

How does adhesion grip work when braking?

Answer 10

Adhesion grip occurs when the tire’s rubber molecules temporarily bond with the road surface. As the tire rolls, these bonds are continuously formed and broken, providing grip.

Question 11

How does hysteresis grip work when braking?

Answer 11

Hysteresis grip occurs when the tire rubber is deformed by road irregularities. As the rubber returns to its original shape, it creates forces that contribute to grip, which is particularly important on wet or rough surfaces.

Question 12

What are the main components of a tire carcass?

Answer 12

The main components of a tire carcass are: tread, bead, sidewall, shoulder, and ply.

Question 13

What is the tread and what is its function?

Answer 13

The tread is the part of the tire that comes in contact with the road surface. The portion in contact with the road at a given instant is called the contact patch or footprint. The tread pattern is characterized by the geometrical shape of grooves, lugs, voids, and sipes.

Question 14

What is the tire bead and what is its function?

Answer 14

The bead is the part of the tire that contacts the rim. It is typically reinforced with steel wire and compounded of high strength, low flexibility rubber. It seats tightly against the rim to ensure that a tubeless tire holds air without leakage.

Question 15

What is the sidewall and what is its function?

Answer 15

The sidewall bridges between the tread and bead. It contains air pressure and transmits torque applied by the drive axle to the tread to create traction. It is reinforced with fabric or steel cords for tensile strength and flexibility.

Question 16

What are plies in a tire and what is their function?

Answer 16

Plies are layers of relatively inextensible cords embedded in the rubber to hold its shape by preventing the rubber from stretching in response to internal pressure. The orientation of the plies is fundamental for tire performance.

Question 17

What is the difference between radial and cross-ply tires?

Answer 17

A radial tire has cords running radially from bead to bead, with a belt running around the outside. A cross-ply tire has cords running diagonally across the tire. Radial tires have greater lateral stiffness and offer less rolling resistance.

Question 18

What advantages do radial tires have over cross-ply tires?

Answer 18

Radial tires separate the function of road-holding from that of providing a comfortable ride, have greater lateral stiffness, and offer less rolling resistance since the walls flex more readily.

Question 19

How does a properly inflated tire carry a vertical load?

Answer 19

In a properly inflated tire, the load path runs through the sidewalls. In the contact patch area, the radial cords in the sidewalls undergo a reduction of tension because they no longer have to balance the air pressure. The net result is that the total upward pull of the cords on the bead exceeds the downward pull by an amount equal to the vertical load.

Question 20

What is the contact patch and why is it important?

Answer 20

The contact patch or footprint is the area that transmits forces between the tire and the road via pressure and friction. It is crucial for understanding tire mechanics and vehicle handling, as it directly affects how forces are transferred from the vehicle to the road.

Question 21

What causes rolling resistance in tires?

Answer 21

Rolling resistance is caused by the fact that the resultant vertical force is applied to the frontal part of the contact patch, creating a moment that opposes motion. It’s also related to hysteresis losses as the tire deforms and rebounds.

Question 22

How is rolling resistance coefficient calculated?

Answer 22

The rolling resistance coefficient (f) is calculated as: f = f₀ + f₁V + f₂V², where V is speed. Typical values are: f₀ = 0.011, f₁ = 0, f₂ = 6.5×10⁻⁶ s²/m².

Question 23

What is the formula for rolling resistance force?

Answer 23

The rolling resistance force is calculated as: Fᵣₒₗₗ = f·Fz, where f is the rolling resistance coefficient and Fz is the vertical load on the tire.

Question 24

What is the effective rolling radius of a tire and how is it calculated?

Answer 24

The effective rolling radius (rₑ) is defined as the ratio between vehicle speed (V) and the angular rate of wheel rotation (Ω): rₑ = V/Ω. This is important for active systems and indirect tire pressure measurement.

Question 25

What is tire slip ratio and how is it defined?

Answer 25

**Slip ratio** (s) is defined as s = (V - ΩR)/V, where V is vehicle speed, Ω is wheel angular velocity, and R is wheel radius. It is positive during braking and negative during traction according to some conventions.

Question 26

What is slip angle and how does it affect lateral force?

Answer 26

**Slip angle** (α) is the angle between the direction the wheel is pointing and the direction it is actually traveling. As slip angle increases, lateral force increases up to a maximum value, after which it begins to decrease.

Question 27

What happens in the contact patch during braking?

Answer 27

During braking, the shear stress within any element of the tire tread rises as it moves along the contact patch. When braking effort increases, the shear stress at the trailing edge will eventually reach a limiting value. This creates "stick" and "slip" sectors in the contact patch, with the slip area growing as braking intensity increases.

Question 28

What are the main forces and moments acting on a tire?

Answer 28

The main forces and moments acting on a tire include: **longitudinal force** (Fx), **lateral force** (Fy), **vertical force** (Fz), **overturning moment** (Mx), **rolling resistance moment** (My), and **aligning moment** (Mz).

Question 29

What is the aligning moment (or self-aligning torque)?

Answer 29

The **aligning moment** (Mz) is the torque around the vertical axis that tends to align the wheel with the direction of travel. It results from the asymmetrical distribution of lateral forces in the contact patch.

Question 30

How does camber angle affect tire forces?

Answer 30

**Camber angle** produces a lateral force called **camber thrust**, although its effect is much less significant than the effect of slip angle. Positive camber generally reduces lateral force capacity while negative camber can increase it up to a point.

Question 31

What is combined slip in tire mechanics?

Answer 31

**Combined slip** occurs when a tire experiences both longitudinal slip (acceleration/braking) and lateral slip (cornering) simultaneously. This significantly affects the tire's ability to generate forces in both directions.

Question 32

How do longitudinal and lateral forces interact during combined slip?

Answer 32

During combined slip, the available friction force must be shared between longitudinal and lateral directions. This creates an **ellipse of friction** that shows the trade-off between these forces - increasing one force reduces the maximum available of the other.

Question 33

What is the Pacejka Magic Formula?

Answer 33

The **Pacejka Magic Formula** is a semi-empirical tire model that uses a mathematical formula to describe tire behavior. It relates tire forces and moments to slip parameters using curve-fitting techniques based on experimental data.

Question 34

What are the key parameters in the Pacejka tire model?

Answer 34

The key parameters in the **Pacejka model** include: longitudinal slip (κ), slip angle (α), vertical load (Fz), camber angle (γ), and friction coefficient (μ). These parameters are used to calculate tire forces and moments.

Question 35

What are longitudinal slip stiffness and cornering stiffness in the Pacejka model?

Answer 35

**Longitudinal slip stiffness** (Cx) and **cornering stiffness** (Cα) represent the slope of the force curves for small slip/slip angle. They are given by the product BCD in the Pacejka formula and are used for simplified (linearized) tire models.

Question 36

What is tire relaxation?

Answer 36

**Tire relaxation** refers to the delay between a change in slip or slip angle and the corresponding change in tire forces. It occurs because the tire carcass needs time to reach a new deformation state.

Question 37

How is tire relaxation modeled mathematically?

Answer 37

Tire relaxation is characterized by first-order dynamics. The key parameter is the **relaxation length** (Lrel), and the ratio between relaxation length and velocity determines the time constant of the system: τ = Lrel/V.

Question 38

How are tire forces integrated into vehicle longitudinal dynamics?

Answer 38

Tire forces are integrated into vehicle longitudinal dynamics through the equation: ẍ = V̇ = (Faero + Mg·sin(α) + ∑Fx,i)/m, where Fx,i depends on slip (σi), vertical load (Fz,i), and friction coefficient (μ).

Question 39

What are the rotational wheel dynamics equations?

Answer 39

The rotational wheel dynamics equation is: ω̇r = (Tm - TB - TR - Fx·R)/Ir, where Tm is motor torque, TB is brake torque, TR is rolling resistance torque, Fx is longitudinal force, R is tire radius, and Ir is wheel rotational inertia.

Question 40

What information is included on the EU tire label?

Answer 40

The EU tire label includes information on: 1) **Fuel Efficiency** (rated A to G based on rolling resistance), 2) **Wet Grip** (rated A to G based on braking performance on wet roads), and 3) **Noise** level (measured in decibels).

Question 41

How does fuel efficiency rating on the tire label relate to vehicle fuel consumption?

Answer 41

The fuel efficiency rating relates to the tire's rolling resistance. Tires account for 20-30% of a vehicle's fuel consumption, and switching from Class G tires to Class A tires can reduce fuel consumption by up to 9%.