chapter 6 tire behavior

8/3/2019 Chapter 6 Tire Behavior

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Chapter 6: Tire Behavior

After chapters on rubber, friction, and tire design and manufacture, here's what we

know so far:

A tire, one of the most useful and complicated devices made, is a gas-pressurized,

textile/rubber composite with a rubber traction coating. Rubber is a mixture of

polymers, reinforcing fillers, and other chemicals that, after vulcanization, have

viscoelastic characteristics that are not fully understood. Tires are difficult to

manufacture consistently, but current technology and manufacturing facilities produce

an extremely reliable, durable, and inexpensive product. A finished tire is a bonded

unit, so failed tires are difficult to analyze post-failure. Rubber friction, mainly due to

adhesion and deformation, exhibits viscoelastic effects and is sensitive to

compounding variations, vertical loading, sliding speed, and temperature.

Now let's look at some of the details of how tires behave during use.

How a Car Turns a Corner: Revisited

Fig. 6.1


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At any moment in time a car turning a corner is accelerating toward the center of an

instantaneous circular arc as in Fig. 6.1. The radius of that arc might be changing, butat any instant the path is a specific arc. The car's tires supply the force to turn the car.

That force is called lateral force or side force or just grip. In this schematic we

combine the lateral forces of the four tires and have it acting on the center of gravity

(CG) of the car.

Slip Angle

A tire produces lateral force with a slip angle, shown in Fig. 6.2. Slip angle happens

when the steering wheel is turned from straight ahead and it's the angle, "a" in the

schematic, between where the tire is pointed and where the car is actually going.


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Fig. 6.2

The elastic nature of a tire makes a slip angle possible. The tire grips the road but also

yields to external force, resists movement with an opposing force, and recovers whenthe external force is removed. This elastic characteristic of a tire allows the tire to be

pointed in a direction different from the direction the car is headed.

It's important that we understand what's going on in the contact patch between road

and tire that creates a slip angle. The tire is rolling, so any one point on the tread

rotates into and out of the contact patch with every revolution. When the tire is rolling


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in a straight line that point on the tread sees a regularly repeating thump of vertical

force as it rotates into the contact patch and momentarily bears this tire's share of the

vehicle weight.

As soon as the driver turns the steering wheel, conditions change at the contact patch.

Steering input causes the tire to turn, and now the leading edge of the tread rotates onto the road slightly to one side of the rest of the contact patch. As the tire rolls, eachsmall increment of tread rubber coming onto the road sits down another small distance

toward the direction the tire is pointed.

As the car's weight comes onto these small increments, they stick to the road. The

tread is now pulling the rest of the tire and generating forces that go through the wheeland the suspension to turn the car. The force needed to change the car's path is

generated by the tire. This is called lateral force or side force.

As in Chapter 1, we can use the analogy shown in Fig. 6.3 of a person walking tofurther explain slip angle. A person walking on a circular path changes direction in

small increments. At each step a foot is turned in a small angle toward the path of thearc. The heel contacts the ground and the rest of the shoe comes down in this new

direction. As weight comes onto the shoe sole, the shoe is pointed in the new

direction. The next step also changes the walker's path a small amount. These small

changes continue to build up and the direction the walker is headed changes also.


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Fig. 6.3

That's exactly what happens when a tire is given some steering input. Each small

increment of tread rubber rotating into contact with the road surface latches onto theroad surface a small increment toward a new heading. As long as the steering input

remains the same, each increment of the tread contacts the road the same amounttoward the new direction. The rest of the contact patch thinks it's headed in the olddirection, but the old contact patch continually rotates out of road contact. The next

time that part of the tire touches down, the heading of the tire and car will have

changed.

The tire tread actually deforms as it rotates through the contact patch area and thenrecovers as the car's weight comes off the contact patch. The force needed to deform

the tire is what produces the lateral force needed to change the path of the car.

When the front tires respond to steering input with a slip angle and begin to developlateral forces, the front of the car turns to a new heading and the entire car rotates in

yaw. If the rear wheels were mounted like casters they would swivel and the rear ofthe car would spin outward, away from the turn. But the rear tires are fixed in

direction and they resist yawing with their own slip angles and lateral forces.

Lateral Force vs. Slip Angle

Fig. 6.4 shows the general relationship between the lateral force a tire generates and

the slip angle of the tire. A tire does not generate side force until it is steered away

from its current course and it assumes a slip angle. The shape of this curve is not thesame for all tires. A graph like this is a specific characteristic of a tire design-the

result of the cord angles and rubbers used in the tire structure and the rubber

compounds in the tire tread.


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Fig. 6.4

Notice that this curve has three distinct shapes. First there's an almost straight section

at small slip angles where an increase in slip angle gives a proportional increase inlateral force. The slope of this section of the curve is the "stiffness" of the tire. In this

region of the curve the tread is not sliding on the road at any point in its contact patch.

A tire designed to have more stiffness in the tread and sidewalls will have a steeper

slope in this area of the curve.

At higher slip angles portions of the tire patch are sliding, and you get less increase inlateral force with an increase of slip angle. This is called the transition region. As the

curve tops out, more of the contact patch is sliding and the tire produces less lateral

force. After the peak of the curve, lateral force can fall off 30% within a few degreesof extra slip angle. At these high slip angles most of the contact patch is sliding,

producing a lot of heat and wear.

Figure 6.5


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The schematics in Fig. 6.5 came from visual observation of contact patch shapes at

varying slip angles. The tire is rolling in the direction of the top of the page and isturning left. This contact patch is much more narrow than that of a current tire, but

that helps us see the changes more easily. Notice how the leading edge of the contact

patch curves toward the turn. This is the result of slip angle; the tire is pointed in the

direction forced by steering input. The leading edge of the contact patch is pointing inthe steering direction while the rearward portion of the contact patch lags behind on

the old heading.

Longitudinal Forces

The forces on a tire during acceleration and braking deform the sidewall enough thatthe contact patch moves a noticeable amount. The three schematics in Fig. 6.6 show

how braking and driving forces can move the contact patch compared to static

conditions.


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Fig. 6.6

During braking and acceleration tires generate longitudinal force, and there is some

longitudinal slip between the tread and the road. This shows up as a differencebetween the actual rotation of the tire and the rotation needed if there were no slip.

Under hard acceleration the tire turns a little faster, and during hard braking the tire

rotates less than it would if there were no slip. These two graphs show driving (Fig.

6.7) and braking forces (Fig. 6.8) vs. percent slip.


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Fig. 6.7 Fig. 6.8

The shape of these two curves suggest the tire reacts to braking and driving forces in

different ways. As soon as driving slip approaches 50%, driving force falls off rapidly.

Braking slip falls off at only 25% slip, but the force reduction is more gradual. I don't

know the source of the data for these graphs but they might look more alike if thepercent-slip scale were the same.

Another possibility is that the driving-force curve drops off and flattens out because

the tire is still spinning and the tread surface has a chance to cool, where the braking

tire is locked at 100% slip and slides on the same contact patch. This heats up therubber, lowering its friction capability. I'll bet the braking curve continues to fall off

after 100% slip, off the scale of this graph.

Of course these curves represent generic data from passenger-car tires. Testing at high

slip is difficult due to the forces involved. Probably the only valid test vehicle forracetires is a competitive, fully-instrumented racecar driven by a world-class driver.

Even then the tire/road/driver system varies continuously creating noise in the data.

Combined Forces

Fig. 6.9 Fig. 6.10


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Data showing tire behavior under a combination of both lateral and longitudinal slip is

almost nonexistent outside of the tire companies' test facilities. Graphs similar to Fig.6.9 and 6.10 appear in various books and are very general. The main point made is

that lateral force falls off rapidly with any additional slip due to acceleration or

braking.

Friction Circle

The graphs above show that tires produce maximum lateral force when there are no

driving or braking forces. The friction circle graphic in Fig. 6.11, actually a half-circle

because the other half would look roughly the same, illustrates how lateral force falls

off in the presence of braking or acceleration. The concept is equally applicable to a

single tire or a vehicle.

Fig. 6.11

The three thick arrows show maximum driving, braking, and lateral forces when those

are the only forces present. When the tire sees a combination of forces, driving forceand lateral force are shown here, maximum lateral force is not available. In this

example, adding driving power to the tire reduces the available lateral force. Ofcourse this is what we feel powering out of a slow corner-power oversteer-one of the

most fun things you can do with a car.

Lateral Deformation of the Tread


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It bears repeating that it is the elastic characteristic of the pneumatic tire that allows

the generation of a slip angle, and it is the forces resisting the deformation of the tirestructure combined with the tread's grip on the road that allows a car to turn a corner

at speed. The schematic in Fig. 6.12 represents tread deformation in the contact patch

of a tire rolling to the left with some right-hand steering angle and a resulting slip

angle. The dotted line with an arrowhead represents the direction the vehicle isheaded. The angle between the vehicle heading and the wheel heading is the slip

angle.

Fig. 6.12

The curved solid red line represents tire lateral deformation from its unstressedposition. Once again, it is the tire's resistance to this deflection that creates the lateral

force that turns the car. The curved line tracks the lateral deformation of a single pointon the surface of the tread rubber as it travels through the contact patch and isdeformed by the road acting on the tire. The solid line with a left-pointing arrow is the

zero-deflection line. The difference between those two lines is the distance the tire

deflects.

The tread rotates into the contact patch at point A, and the lateral deflection at point A

is called the initial deflection. Point A marks the leading edge of the contact patch, butdeflection starts prior to that. The tire carcass has some stiffness and the tread is even

more stiff, so there has to be some deflection starting well before the tire rotates into

the contact patch.

From point A to point B, somewhere near the midline of the contact patch, the tread

stays stuck to the road (at this slip angle anyway) and lateral deflection in the carcass

and in the tread rubber increases linearly. But at some point the force required to

deflect the tread exceeds the local friction coefficient times the local load, and the


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tread begins to slide on the road. At higher slip angles sliding starts farther forward, as

we saw in the drawings in Fig. 6.5.

At point B the tread begins to recover from maximum lateral deflection and at point Cthe tread rotates out of the contact patch. Notice that there is still some lateral

deflection at C. The tire has to rotate farther before the lateral deflection fullyrecovers. Once again it is the remarkably strong but elastic nature of a tire that enables

it to deform, assume a slip angle, and generate turning forces.

In the book I follow up this section with explanations of why wide tires generate more

grip and why tires are load sensitive.

chapter 6 tire behavior

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