Everyone is familiar with the population mobility and the increasing severity of driving conditions: freeways turnpikes tremendous horsepower power steering power brakes revised driving habits faster breaking and cornering greater accelerations high-speed car-to-car proximity. All this automobile torque is transmitted through the tires. In addition to providing propulsion and directional forces tires must insulate against road disturbances.
In many ways a tire is an engineering marvel. This can be better understood from a discussion of the following tire engineering subjects: tire application tire behavior tread pattern performance analysis and tire construction.
Tire Application
A great number of tire species can be identified. It is convenient to group them according to the type of vehicle on which they are applied. The major classifications are passenger truck off the road farm and aircraft. Others are racing motorcycle industrial bicycle and moon tire. Within each classification it is important to determine the type of service conditions that will be encountered. More than 3000 different sizes and types of tires are produced in the USA.
Passenger: Nearly 200 million passenger tires are manufactured yearly. About three-fourths of these are replacement tires and one-fourth is original equipment. Most passenger tires today are tubeless. Passenger tires are produced in a considerable variety of sizes types and construction.
For example 10 basic sizes are produced (A B C D E F G H J L). These letters represent approximate tire width and load capacity with ‘A’ denoting small size and ‘L’ large size.
Tires are made in three basic rim diameters (13 14 15 inches).
Basic Passenger Tires
ITEM | CHARACTERISTIC |
SIZES | A B C D E F. G H J L |
RIM DIAMETERS (IN.) | 13 14 15 |
ASPECT RATIOS | .83 .78 .70 .60 .50 |
TYPES | BIAS BIAS/BELTED RADIAL |
SIDEWALLS | BLACK WHITE RING WHITE LETTERS |
TREAD DESIGNS | RIB SNOW ASYMMETRIC |
LOAD RANGES | B C D |
Not inclusive; others available.
Tires are available in five basic aspect ratios (.83 .78 .70 .60 .50). Aspect ratio is tire section height divided by section width. A low aspect ratio indicates a wider tire with a flatter profile. The original aspect ratio was 1.00 but the ratio has been decreasing over the years.
Tires come in three basic types (bias bias/belted radial). Tires have three basic sidewalls (black white ring white letters).
In addition tires are produced in three basic tread designs (rib snow asymmetric).
Finally tires are available in three basic load ranges (B C D). The load range identifies the tire inflation and load limits.
Tires come in various combinations of the above. Thus a tire marked HR78-15/B 2W would be an H-size radial of .78 aspects made to fit a 15-inch rim. In addition the tire would be load range B white ring rib design.
In addition to the basic categories other sizes and types as well as older sizes and types are produced. Several manufacturers, such as Falken, are developing different types of tires for both racing and regular passenger cars.
Each of these sizes and types is engineered for specific vehicles and/or service conditions. Passenger tire loads range up to 2230 pounds and deflections range from 18 to 24 percent. Passenger tires carry about 50 times their weight.
Truck: There are about 17 million trucks in the USA today from pickups to tractor-trailer rigs. These trucks travel 217 billion miles annually. There are approximately 80 million truck tires on these vehicles. Truck tires can be conveniently classified into light and heavy and they divide the market about 50/50.
Light truck tires generally are single bead. Heavy truck tires usually are dual bead. The smallest truck tire made is the 7.00-13 with a diameter of 26 inches. The largest is the 14.00-24 with a diameter of nearly 53 inches. The most popular is the 10.00-20 with a diameter of nearly 42 inches. Truck tire loads can go up to 10000 pounds. Deflections range from 10 to 18 percent.
Truck tires carry about 50 times their weight. Off-The-Road – Off-the-road tires operate on uneven terrain.
This often demands flotation characteristics for soft ground as well as special resistance to bruises and rock cutting. Off the road tires can be divided into four categories: compactor dozer/loader truck grader and earthmover. The smallest tire in the group is the 7.00-10 with a diameter of 24 inches. The most popular is the 23.5-25 which has a diameter exceeding five feet.
The most fascinating types are the giant earthmover tires which can be nearly 12 feet in diameter and carry loads of more than 1000 pounds. The largest the 40.00-57 weighs nearly four tons and contains 860 pounds of tire cord. This rugged tire contains more than 200000 cords which poses a complex engineering problem in optimizing the composite configuration.
Earthmover tires are rated for ton-mile-per-hour (TMPH) or ability to carry a given load at a given speed. The rating is calculated by multiplying the average load per tire by the average speed of the machine per hour (Equation 3):
™ M T E + L M x N
TMPH =:~—x—77— (->)
Z 11
Where
E = “empty” tire load
L = “loaded” tire load
M = round trip distance (miles)
N = number of trips
H = total hours of operation
The concept of large cords and reduced plies has found application here. This concept is based on the principle of taking the required fabric for a tire and redesigning it into less plies of greater strength. For example the number of plies in a 32PR earthmover tire could range from 26 to 2 depending on the cord size used.
Reduced Ply Earthmover Tires
CORD | NUMBER |
CONSTRUCTION | OF PLIES |
840/2 | 26 |
1260/2 | 22 |
1260/3 | 16 |
3360/2 | 12 |
6720/3 | 6 |
15120/3 | 4 |
37800/3 | 2 |
Farm: Prior to 1930 practically all farm tractors were on steel wheels. By the end of World War II most had been converted to pneumatic tires. Basic types of farm tires include rear tractor front tractor garden tractor and implement. The smallest farm tire is the 3.00-7. The largest is the 30.5-32 which is six feet in diameter. Tractor tires operate at about a 20 percent deflection. Farm tires remain in service for many years.
Aircraft: Aircraft tires can be grouped into three basic divisions: general aviation commercial and military. The smallest aircraft tire made is the 5.00-4; the largest is the 56 x 20.00-20. The most popular commercial tire is the 40 x 14. The most used military size is the 30 x 8.8. Aircraft tire loads can go as high as 750 pounds. Speeds can reach 320 mph. Deflections can go as high as 35 percent. Aircraft tires carry several hundred times their weight.
Racing: Racing tires are perhaps the most specialized tires made. Racing includes several major categories: Championship: Includes races such as the Indianapolis 500. Speeds up to 220 mph
Stock car: Heavy passenger-type cars on tracks such as Daytona. Speeds up to 220 mph
Sports car: These courses include left and right turns, grand Prix races and Trans-Am/Can-Am races fall into this category. Speeds up to 220 mph
Drag: This is a 1/4-mile race from a standing start. Speeds to nearly 250 mph in 6.1 seconds have been reached Land speed – All-out attempts to travel as fast as possible. For these races, special drag racing tires are needed to ensure good grip on the surface. Record is 622.4 mph set on the salt flats of Utah.
Racing tires generally operate at low deflections (7 to 8 percent).
Moon Tire: The first vehicle to operate on the moon the modular equipment transporter (MET) of Apollo 14 was equipped with 4.00-8 pneumatic tires. These specially engineered tires are 16 inches in diameter and weigh 4.1 pounds.
Application Range: Each of these tires is approximately equal in size (about 30 inches in diameter). However the potential load requirements range from 1200 to 210 pounds; the potential speed requirements range from 10 to 250 mph; and the potential time in service ranges from hours to years.
Tire Applications
TIRE | SERVICE REQUIREMENTS | ||||
Diameter | Load | Speed | |||
Type | Size | (in.) | (lb) | (i’mph) | Time |
PASSENGER | LR78-15 | 29.1 | 1680 | 100 | 40000 Ml |
TRUCK | 7.00-15 | 29.6 | 1720 | 70 | 50000 Ml |
OFF-THE-ROAD | 7.50-15 | 29.8 | 4200 | 10 | YEARS |
FARM | 7.5L-15 | 29.4 | 1590 | 10 | YEARS |
AIRCRAFT | 30 x 8.8 | 30.4 | 21000 | 250 | INTERMITTENT |
RACE | 8.20-15 | 29 | 1200 | 220 | HOURS |
Thus tire applications are a load-speed-time function and the tire must be engineered for specific vehicles and/or applications.
Tire Behavior
Dynamic behavior of a tire in service is quite complex. As previously described a tire is a modified torus. A torus can be visualized as the volume of space that a sphere occupies while orbiting some center. For simplicity the tire toroidal shell is often treated two-dimensionally as a circular and as a meridian shape.
Bias Tire: If a tire behaved like a steel wheel the inflated radius R| would be the effective radius of the tire. However, one of the basic characteristics of a pneumatic tire is its ability to act like a spring when in contact with the road. It deflects under load. This flattening of the contact surface is known as the pneumatic resilience effect. Therefore the effective radius is not R| but a shorter distance R->. This loaded radius R-> is determined by equilibrium between the tire geometry inflation pressure and load. Consequently the footprint or contact area is in compression. This action is called pantographing which causes the tread to squirm as it goes through the footprint. This scrubs the tread against the road thus wearing off the rubber. As the tire deflects under load and the cord changes a compression-tension flex cycle occurs. The magnitude of the stress cycle is controlled by the deflection CR i Ro)-
Belted Tire: The operation of a belted tire can be represented as a fixed circumference hoop the tire can be visualized as a steel band rolling on the pavement, its circumference would be the same whether it is circular elliptical or semi-elliptical in shape. Due to its high planar rigidity the belt provides a virtually inextensible and incompressible hoop structure that stabilizes or stiffens the tread by minimizing pantographing in the footprint.
The result is less-tendency to squirm and scuff. Note the presence of the standing wave and the opening and closing of the tread grooves. On the left is a belted tire. Note the reduction in tread squirming. Belts tend to hold the tread surface flat against the road.
Belts are an efficient way to engineer improved tread-wear traction crown bruise resistance rolling resistance fuel economy cornering and handling and road holding properties. In addition belts reduce tire running temperature groove cracking and noise. The disadvantage is a somewhat firmer ride.
Footprint: When a tire is deflected by load it flattens until the ground contact area multiplied by the inflation pressure equals the load. The tire footprint or contact patch on the road is remarkable in its behavior. The area of a tire footprint is about equal to the human foot yet it controls a heavy vehicle at high speeds. The tire footprint grips the road steers the vehicle and provides a comfortable and quiet ride. Tire engineering requires an extensive knowledge of the behavior of the contact patch.
The tire experiences a fluctuating load cycle as it passes through the footprint. The initial cord tension results from tire inflation. The tension then increases as the tire rolls. Cord tension drops and reaches a minimum in the footprint. Load again increases as the cord leaves the footprint and the cycle repeats itself. Each time a segment of the tire comes into contact with the road the cords undergo a cycle of compression and tension and the rubber around them goes through a cycle of shear stress. The amplitude of the cycle depends on the deflection.
The average tire will rotate about 800 times in a mile. This means that at 60 mph each point on the tire will be flexed 800 times per minute. A passenger tire will be subjected to as many as 35 million flex cycles during its lifetime.
Techniques have been developed to determine experimentally the stresses and strains in a tire. Strain gauges and photo-elastic films are two of these methods.
Strain gauges are devices built into a tire to quantitatively measure cord tensions through displacement. Strain gauges can be mechanical optical or electrical. They generally operate as follows. Dynamic behavior of a tire changes the tire geometry which in turn changes the resistance of the strain gauge. The cord tensions are proportional to this change in resistance.
Photo-elastic films have found application in experimental stress analysis. This technique is based on the phenomena of polarized light and crystallization of polymers under stress. In this system a transparent photo-elastic coating is applied to the tire. While the tire is stressed polarized light is reflected off the tire and is observed through a Polaroid filter oriented 90 degrees to the polarized light source. The result is a pattern of colors.
From this photo-elastogram the magnitude (Isochromatics) and direction (isoclinics) of stress at any point on the tire can be quantitatively determined. It is possible to build the whole tire from the transparent polymer and to incorporate a polarizing filter thereby enlarging the scope of analysis.
The goal of tire scientists is to predict tire behavior theoretically. The mathematics of tire behavior is quite complex and has been extensively treated in the literature.
Tread Pattern
The tread pattern or tread design is a specialized area of tire engineering. The pattern usually consists of circumferential grooves and zigzag ribs. The ribs also normally contain sipes or blades. Other tires may contain cross ribs or lugs.
The tread pattern on any tire provides adhesion (or grip) to the road especially when wet. This is accomplished by wiping the road with the discrete design elements and channeling the water through the grooves and voids. This squeegee action permits the tread rubber to grip the road surface. If there is no pattern water accumulates between the tread and the road and traction and skid resistance are greatly reduced. This can sometimes lead to zero contact area at which point the tire is completely supported on a film of water. Under these conditions known as hydroplaning the vehicle is difficult to control. This is the danger when operating on “bald” tires. For this reason wear indicators are incorporated into the tread design. These are a series of radial bars that appear on the surface of the tire when the nonskid has been worn to 1/16 of an inch deep. Their appearance indicates that the tire should be replaced. The tread pattern also mechanically softens the tread which permits better enveloping of small irregularities in the road surface.
As the tire rolls however the many tread elements necessary for traction and skid resistance impact the road creating tire noise. The number size spacing and angles of the various elements in the pattern determine the intensity and tonality of noise generated. Noise level also increases with speed load and degree of wear. By sequencing the pitch lengths of the tread around the circumference of the tire the result is a multiple-pitch tread design to minimize noise. This is accomplished by use of computers.
Another audible characteristic is tire squeal caused by vibration of the shoulder rib of the tire as it begins to slide in cornering. The geometry of the outer rib and groove can be modified to minimize squeal.
Tires come in a multiplicity of patterns depending on types of service conditions. Some designs are highly complex and contain as many as 9000 gripping edges. Tire patterns are optimized for maximum traction tread-wear quiet ride stability and resistance to chunking at high speeds.
Performance Analysis
Nearly 100 tire performance parameters must be considered in engineering a tire. Each of these requirements in turn depends upon many factors.
Tread-wear: Each tire requirement can be analyzed thoroughly through techniques of technological forecasting such as relevance trees. Tread-wear is the useful life of a tire as determined by its wearing off due to abrasion on the road surface and depends on a multitude of factors. Tread-wear is a function of tread compound including type and percentage of elastomer type and percentage of carbon black type and percentage of oils degree of dispersion and type and state of cure.
Tread-wear is a function of the tire design factors of construction tread pattern mold shape and tire dimensions. Each of these in turn is subdivided into additional features. Similarly tread-wear is a function of fabric type (in the carcass and belt) and fabric stiffness. All these tread-wear features are under the jurisdiction of the tire engineer.
Other factors affecting tread-wear however include the road conditions and the driver. Tire tread-wear is dependent on the type of road traveled. The surface rugosity and profile of the road have a definite effect on tread-wear. Each of these factors also can be subdivided. As can be seen new roads result in poorer tread-wear performance. Tread-wear performance improves as the road is “broken in.” Road temperature and weather conditions also affect tread-wear.
Finally the driver and service conditions determine the degree of tread-wear. Such factors as speed rate of acceleration and braking and amount of cornering and lane changing have a significant effect. Tread-wear rating of 100 at 50 mph decreases about 20 percent for each 10-mile increment in speed. The tread-wear rating at 80 mph is only 43 percent of 50 mph. stopping starting and curves also are major causes of tire wear. A simple test can be used to illustrate this.
The effect of frequent braking and acceleration may reduce tread-wear to one-half the rating for continuous driving as shown below:
Tread-wear Item | rating | |
Continuous driving at | 50 mph | 100 |
Driving at 50 mph with stops every five miles | 50 |
Inflation and load also are important. The type of vehicle alignment maintenance and tire rotation also is factors in tread-wear performance.
More detailed analyses of tread-wear and all other tire requirements (including mathematical analyses) are beyond the scope of this book but have been described in the literature.
Maintenance: A tire is subjected to a cyclic effect as it passes through the footprint. The load and inflation pressure control tire deflection (i.e. the cycle amplitude). Speed controls the cycle frequency. Tire abuse generally involves improper load inflation pressure and speed. If the load is too high for a tire or if the inflation pressure is too low tire deflection will be excessive and will result in premature failure. This can show up as uneven tread-wear sidewall cracking fatigue breaks or composite separations depending on the degree of heat buildup. Heat buildup is a major factor in tire durability. Excessive speed coupled with the above will hasten the process.
Proper inflation pressure is especially important since the compressed air supports the vehicle. One hypothesis of how this takes place is as follows: As the cord tension is reduced in the footprint it results in an upward pull on the rim thus supporting the load. It has been estimated that approximately 10 percent of the load is supported by the tire structure; the other 90 percent is supported by the compressed air. This is why tire engineers constantly stress the importance of proper tire care and maintenance. Inflation pressure should be checked when the tire is “cold” i.e. less than one mile of travel. Tires build up heat (and pressure) in service which is normal. For example a tire with 24-psi inflation cold will measure about 26 psi in around the town service and can build up as high as 30 psi after a day of travel on the interstate. Tires should not be “bled” if the original pressure is correct.
Many attempts have been made to replace the compressed air in the tire with some other substances including water alcohol and carbon dioxide oats rice ping pong balls latex graphite spring coils lead shot polystyrene and colloidal lead. None have been successful. One recent innovation on a commercial basis utilizes sponge-like foam for filling a tire in place of air. Foam-filled tires significantly reduce downtime in seiyice where punctures cannot be tolerated. At the present time foam-filled tires are restricted in operating speed and have a large weight penalty.
Finally as discussed previously proper tire and vehicle maintenance is fundamental to good tire performance.
Tire Construction
As described previously a tire is subjected to complex stresses and strains in service. These originate from deflection (pneumatic resilience) compression and tension (from the contact patch) inflation pressure centrifugal force and external forces.
Tire Mechanics: In developing a tire the tire engineer must analyze the intended tire application. From this analysis the basic dimensions of the tire for the specific vehicle and service conditions can be determined. The relationship between tire dimensions inflation pressures and load capabilities is given by the Tire & Rim Association basic formula in Equation (4):
L = k x .425 x P’585 x S62 139 x (DR + S62 $) (4)
Where
L = load of tire in pounds
k = load service factor
P = inflation pressure (psi)
S^2 ^ = section width on 62.5 percent rim
DR = nominal rim diameter
This is the basic formula and modifications are specified for certain tires.
After dimensions are established the meridian shape envelope of the tire (cross section) is defined utilizing the tire geometry. This example is for a bias tire.
Where
y ^{—} axial dimension normal to the tire centerline from any point on the tire contour
ym = maximum axial tire dimension
a = acute angle formed by the cord and a circumferential line at any point on the tire contour
aQ = acute angle at pQ with respect to the circumferential centerline
p = radius from axis of rotation to any point on the tire contour
PQ = radius distance from the axis of rotation to the neutral contour at the centerline
= radhis distance from the axis of rotation to point on the tire contour where y is maximum
The path of a cord from bead to bead in a bias tire is a cosine path and can be described by Equation (5):
Cos |S cos aQ
All terms have been previously defined except R which is the radius of the tire building drum and (3 which is the bias angle in the layers of flat cord material. The law of cosines is a basic formula in tire engineering.
The cord angle in a tire changes from the crown of the tire to the bead. The cord angle at any point in a tire is given by Equation (6):
J pcosaQ
aN = cos: ~r
The cord angle affects many tire calculations including strength shear stresses and cord tensions.
In general high cord angles result in tires with higher section height narrower section width and rounder tread radius. Conversely low cord angles give lower wider tires with flatter tread radius. High cord angles tend to be better for tire strength fatigue resistance rolling resistance ride performance road contact length and developing ability. Low cord angles are better for high-speed performance low heat generation lateral stability and tread-wear. High cord angles generally result in lower cord tensions and conversely low angles give higher cord tensions.
Thus-the cord angle must be optimized depending on the type of tire and service conditions.
Another expression of importance is the cord tension at the centerline described in Equation (7): p0sin2a0*? 0w
Where
T = cord tension
P = inflation pressure
17 = cord count
w = number of plies
As can be seen cord tension is a function of the curvature of the cord path and inflation pressure. In designing a tire to withstand this tension cord properties become an important factor in belted tires the belts restrict the tire circumferentially and laterally and act as a constraint on the natural shape of the carcass envelope. The degree of restriction r determines the effectiveness to the belt and is a ratio of the inflated belted section height SH^ to the natural section height SH by the relationship shown in Equation (8):
SH SHb
r= SH
The tension in the carcass cords is progressively reduced as the degree of restriction is increased. The desired restriction generally ranges from .01 to 0.1 in terms of section height changes. Another relationship of interest is the final tire profile or aspect ratio defined in Equation (9):
Where
A = aspect ratio
SH = section height
SD = section width
The Tire Composite: A composite must meet the following criteria. It must be man-made; it must be a combination of at least two chemically distinct materials; the materials must have a distinct interface; the materials must be combined three dimensionally; and the composite must result in properties that could not be achieved by any of the components acting alone. The pneumatic tire is the most widely used high performance composite of commercial importance. As described previously a tire is a cord/rubber composite.
The stress-strain characteristics of cord and rubber are more dissimilar than most composite components. The cord component is high in strength with relatively low elongation; the rubber matrix is relatively low in strength with high elongation. The ratio of ultimate cord stress to ultimate rubber (matrix) stress is approximately 50. This ratio is high in comparison with dispersion-strengthened or particle strengthened composites and is even higher than most fiber-strengthened composites.
Thus in the case of the tire composite the reinforcing cords carry the major share of the structural load. The rubber matrix transmits the load to the reinforcing cords through shear action. This can be shown theoretically and empirically. Mathematically it can be shown that as the length of the cord increases (as in tires) or when the ratio of composite-to-matrix modulus is large then the composite strength and modulus become less dependent on the matrix. Therefore the performance of the composite will be highly dependent on the properties of the reinforcing cords and their arrangement in the tire. Each basic tire type requires specific cord physical properties.
The desired properties for the cord in a tire carcass are high strength high fatigue and durability dimensional stability high dynamic modulus low heat generation low stress decay low growth and creep high resonance frequency high specific gravity and no flat-spotting. Cords for tire belt applications require the following different balance of properties: ultrahigh modulus (dynamic and compression) high stiffness high strength low growth and creep and minimal fatigue requirements. Composite configuration must be optimized for each type tire.
Composite strength is plotted as VF or pounds of fabric per tire. Cord spacing is shown as ends per inch. A maximum and minimum number of ends per inch is specific for each cord size. Outside these limits the fabric rivets (distance between cords) will be too high or too low. The cord spacing (or ends per inch) is affected by the cord angle. An increase in cord angle lowers the cord count; a decrease increases the cord count. The cord count at any point in the tire can be calculated from Equation (10):
Aliai- (10)
‘ psina
Where
17 = cord count in the tire
7} 1 = cord count in the layers of flat cord material
Usually the cord count in the cured tire is lower than the starting cord count due to the expansion of the tire during assembly.
The total quantity of reinforcing material in a tire is a function of cord count cord angle cord length and number of plies. This can be determined mathematically by Equation (11) where the only new expression introduced is/ the length of each cord:
Q = 2-n pit] sin a (11)
The calculated carcass strength of a tire is a function of the cord strength cord count cord angle and number of plies. Often the cord angle is disregarded and the following equation is used to express carcass inch-strength:
Sj = Sc x r? X w (12)
Where Sc = cord strength
Several other relationships are important. The gauge of rubber between cords or rivet is given by Equation (13):
r = i-d (13)
V
Where
T7 = cord count in the tire
d = cord diameter
Where 7 equals gauge of the rubber-coated cord fabric
Since the reinforcing cord carries the major share of the structural load the total volume of cord material in a tire composite is important. In general the VT factors used (disregarding tread rubber) are 30 to 50 percent for the bias tire and 20 to 40 percent for the belted tire.
The degrees of freedom available to the tire engineer in designing a tire composite include a choice of several basic cord materials (rayon nylon polyester fiberglass wire etc.); an array of cord constructions (cord size); many cord twists; a range of surface areas; a variety of gauges (cord and ply); a selection of rivets and cord spacing’s (ends per inch); and a choice of number of plies.
Each of these constructions however will behave differently in the tire. In general three-ply cords have better durability. High end count fabrics result in greater tire plunger strength. Low end count fabrics have more rivets and give better separation resistance. Computer programs generally are used to optimize the tire composite.