Automobile Ride, Handling, and Suspension Design
With Implications for Low-Mass Vehicles
When carried to the extreme, today's emphasis
on automobile mass reduction has significant implications for vehicle ride and suspension
design. We therefore review traditional automobile suspension systems and offer comments
on the special considerations of suspension systems of extremely low-mass passenger cars.
The quality referred to as "ride comfort" is affected by a variety of
factors, including high frequency vibrations, body booming, body roll and pitch, as well
as the vertical spring action normally associated with a smooth ride. If the vehicle is
noisy, if it rolls excessively in turns, or lurches and pitches during acceleration and
braking, or if the body produces a booming resonance, occupants will experience an
NF = Natural Frequency in Cycles Per Minute (divided by 60=Hz).
SD = Static Deflection in Inches.
Implications of High Payload-to-Vehicle Weight Ratio
As vehicle mass is reduced, the payload-to-vehicle weight ratio naturally increases,
which has trickle-down effects throughout the vehicle. An extremely low mass automobile,
in the order of 1,000 pounds or less, for example, will have an unusually high
payload-to-vehicle weight ratio.
The Ratio of Sprung to Unsprung Weight
Unsprung weight includes the mass of the tires, brakes, suspension linkages and other components that move in unison with the wheels. These components are on the roadway side of the springs and therefore react to roadway irregularities with no damping, other than the pneumatic resilience of the tires. The rest of the mass is on the vehicle side of the springs and therefore comprises the sprung weight. Disturbances from the road are filtered by the suspension system and as a result are not fully experienced by the sprung weight. The ratio between sprung and unsprung weight is one of the most important components of vehicle ride and handling characteristics.
Unsprung weight represents a significant portion of the total weight of the vehicle. In today's standard-size automobile, the weight of unsprung components is normally in the range of 13 to 15 percent of the vehicle curb weight. In the case of a 3,500 pound vehicle, unsprung weight may be as high as 500 pounds. A 500 pound mass reacting directly to roadway irregularities at highway speeds can generate significant vertical acceleration forces. These forces degrade the ride, and they also have a detrimental effect on handling.
Early pioneers believed that the primary job of the suspension system was to absorb bumps and smooth out the ride. Today we understand that an equally important function of the suspension is to keep the tires in contact with the road. This is not as easy as it might appear to be. When a tire encounters an irregularity the resulting forces tend to reduce contact pressure and therefore degrade adhesion. Obstacles impart a vertical acceleration to tires that increases in proportion to the forward speed of the vehicle and the size of the obstacle. The greater the accelerated mass (unsprung weight) the greater the kinetic energy. In a sense, a raised obstacle throws tires away from the roadway. A depression causes the surface to rapidly drop away leaving the tire to follow along when inertia can be overcome by the downward pressure of the springs. Both occurrences reduce the tire's contact-pressure and tires can actually become airborne if the forces are great enough.
The forces generated by roadway irregularities (bumps) must be overcome by the springs in order to keep tires in contact with the road. The force of the springs comes from the compressive load imposed by the weight of the vehicle. The lighter the vehicle, the less compressive force is available, and the easier it is for the vertical motion of the wheels to overcome the inertia of the sprung mass and transfer motion to it as well. The ideal combination occurs when the ground pressure is maximized and inertial forces are minimized by a high sprung-to-unsprung weight ratio. A high ratio keeps the tires more firmly in contact with the road, and it also produces the best ride.
The sprung-to-unsprung weight ratio is particularly important to the design of extremely low mass vehicles. The necessarily higher suspension frequency produces a rougher ride, which can be accentuated by smaller tires typical of smaller cars. Smaller diameter tires react more violently to bumps and potholes. Their reduced radius causes them to move deeper into depressions and climb more quickly over obstacles. The higher acceleration rates are offset to a large degree by the reduced mass of the smaller tires. Tests have shown, however, that smaller tires do in fact produce a rougher ride, even though they are lighter. With smaller, lighter vehicles, it is even more important to keep the ratio of sprung to unsprung weight as high as possible in order to reduce the undesirable effects of smaller tires.
When the ratio of payload to vehicle weight is exceptionally high, the fully laden weight provides the most valid basis for comparison. For example, the curb weight of Urbacar was only 650 pounds, which at the typical large-car ratio would have provided for a total unsprung mass of less than 100 pounds. At 23 pounds each just for the tire/wheel assemblies (exclusive of brakes, axles and suspension linkages), it is easy to see that Urbacar was far off the mark. However, the two-up weight of Urbacar was approximately 1,000 pounds. Using the two-up weight of both vehicles, the 500 pound unsprung mass of the 3,500 pound car (3,850 lb with two occupants) equates to a 130 pound unsprung mass for Urbacar, which is more in line with the actual weight of the components.
Regardless of the perspective, every component of the unsprung mass must be more closely scrutinized in low mass vehicles in order to keep unsprung weight to an absolute minimum. The advantages for the designer in this regard are that a low mass vehicle will impose significantly lower structural demands on components, and the lower operating speeds result in greatly reduced unsprung acceleration forces.
According to Newton's First Law, a moving body will continue moving in a straight line
until it is acted upon by a disturbing force. Newton's Second Law refers to the balance
that exists between the disturbing force and the reaction of the moving body. In the case
of the automobile, whether the disturbing force is in the form of a wind-gust, an incline
in the roadway, or the cornering forces produced by tires, the force causing the turn and
the force resisting the turn will always be in balance.
The Tires In A Turn
At relatively low speeds (parking lot maneuvers) the vehicle turns according to the geometric alignment of the wheels. The wheels roll in the direction they are heading, and the vehicle turns about the point established by a projection of the front axles intersecting a projection of the rear axle. As speed increases, the actual turn center moves forward due to the slip angle of the tires. Click on Figure 1 below to retrieve a drawing that illustrates the location of the turn center.
Slip angle is related to the lateral load or cornering force of the tire. As lateral
loads increase due to higher cornering speeds, tires creep to the outside of the turn and
therefore move in a direction that is different from their heading. The difference between
the tire's heading and the direction of travel is called the slip angle.
Another cornering force comes from the tire's camber angle. When a tire rolls at a camber angle it generates a lateral force in the direction in which it is leaning. The lateral force is known as "camber thrust". The thrust produced by camber angle is much less than the force produced by slip angle. However, it can be a significant component of the total forces that contribute to vehicle handling characteristics.
Oversteer and Understeer
The weight bias of the vehicle determines its inherent oversteer/understeer
characteristics. A vehicle that is heavier at the front will tend to understeer and one
that is heavier at the rear will oversteer. A vehicle in which the weight is equally
distributed between the front and rear axles tends to exhibit neutral steer
characteristics. Although the inherent understeer/oversteer characteristics of a vehicle
are determined by its weight distribution, the design of the suspension and the selection
of wheel and tire size can enhance or moderate those characteristics.
Tuning the Suspension of a Completed Vehicle
When the suspension is designed, certain handling characteristics are targeted.
However, mechanical compromises, errors, or limitations of the art may result in a vehicle
that does not handle precisely as intended. Even after the vehicle is finished, the
suspension can be tuned for different cornering characteristics. The variables available
for tuning the suspension include changes in tire and rim size, tire inflation pressure,
and the stiffness and location of the anti-roll bar.
The Effect of Polar Moment of Inertia
The moment of inertia has to do with a body's resistance to angular acceleration. Polar
refers to the ends. Consequently, the polar moment of inertia of a vehicle is related to
the mass that is located near the front and rear. The effect of polar mass can be
experienced by rotating a dumbbell back-and-forth around a central axis. The weight
concentrated at the ends makes the barbell resist changes in direction. A ball of equal
weight will reverse directions with little effort because the mass is concentrated at the
center. Most passenger cars are designed with a relatively high polar moment of inertia.
The engine is located over the front or rear axle and the fuel and luggage are located at
the opposite end. The center of the vehicle is hollow to provide room for the occupants.
At the most fundamental level, a vehicle's rollover threshold is established by the simple relationship between the height of the center of gravity and the maximum lateral forces capable of being transferred by the tires. Modern tires can develop a friction coefficient as high as 0.8, which means that the vehicle can negotiate turns that produce lateral forces equal to 80 percent of its own weight (0.8 g) before the tires loose adhesion. The cg height in relation to the effective half-tread of the vehicle determines the L/H ratio which establishes the lateral force required to overturn the vehicle. As long as the side-force capability of the tires is less than the side-force required for overturn, the vehicle will slide before it overturns. This analysis is useful for comparing the rollover propensity of various vehicles, as shown in Table T-1. Under dynamic conditions, however, a vehicle's rollover threshold is a more complicated issue.
ROLLOVER THRESHOLD COMPARISON
Rapid onset turns impart a roll acceleration to the body that can cause the body to
overshoot its steady-state roll angle. This happens with sudden steering inputs, it occurs
when a skidding vehicle suddenly regains traction and begins to turn again, and it occurs
when a hard turn in one direction is followed by an equally hard turn in the opposite
direction (slalom turns). The vehicle's roll moment depends on the vertical displacement
of the center of gravity above its roll center. The degree of roll overshoot depends upon
the balance between the roll moment of inertia and the roll damping characteristics of the
suspension. An automobile with 50 percent (of critical) damping has a rollover threshold
that is nearly one third greater than the same vehicle with zero damping.
The nature of these conditions and the resulting forces are difficult to predict in real-world conditions. Consequently, the best design for rollover protection will include adequate roll damping and the greatest possible static margin of safety against rollover.
The Relationships of Steering Axis Inclination, Caster, Camber, and Pivot Radius In Front Suspension Systems
The geometric relationships of the front wheels would be relatively simple if it were not for the fact that they also steer the vehicle. Once the wheels take on the job of steering, the dynamic requirements and the angular relationships become much more complicated. With early beam axles, the steering movements were provided by the kingpin. The first kingpins were aligned perpendicular to the ground and as a result, steering movements were very simple; a wheel steered around its axis just like a door swings on a hinge. However, a suspension with a perpendicular kingpin has no self-aligning characteristics, and the slightest bump at one wheel can impart significant steering inputs. Consequently, the perpendicular kingpin was discarded very early on. Thereafter, the kingpin was attached to the axle at an angle so the swivel line projected outboard and forward toward the ground plane. The lateral tilt is known as the steering axis inclination and the longitudinal tilt is called the caster angle.
Steering Axis Inclination
Steering axis inclination refers to the lateral tilt of the axis around which the wheel
rotates when it is steered. By leaning the steering axis inboard at the top (or outboard
at the bottom) the swivel-line is projected much nearer the tire centerline at ground
level. That reduces directional disturbances caused when the tire encounters an obstacle.
If the steering axis meets the ground inboard of the tire centerline, an obstacle will
cause the wheel to steer outboard. If the steering axis projects outboard past the tire
centerline, an obstacle will create a steering input toward the inside. A steering axis
that meets the ground at the tire centerline eliminates the steering inputs of obstacles,
but it also eliminates the "feel" of the road.
Other requirements of the suspension system, as well as mechanical conflicts between
components, may prevent the designer from locating the steering axis projection
appropriately close to the tire centerline. Wheels can then be set at a slight positive
camber angle to move the contact patch inboard toward the swivel line.
Caster angle introduces a new element. The caster angle refers to the longitudinal inclination of the steering axis. It creates a self-centering force that is somewhat different from the one created by the lateral steering axis inclination. A positive caster is established when the steering axis meets the ground ahead of the center point of the contact patch (a point directly under the axle). Most passenger cars have a positive caster on the order of 0 to 5 degrees. A positive caster causes the wheel to trail behind the steering axis. When the vehicle is steered, the caster angle develops an opposing force that tends to steer the vehicle out of the turn. Click on Figure 7 to retrieve a drawing of caster angle.
Another effect of caster angle is that it causes the camber angle to change when the wheels are steered. When the vehicle is steered, the inside wheel progresses into a positive camber and the outside wheel progresses into a negative camber. Considered independently of steering axis inclination, the effect of caster in a turn is to drop the side of the vehicle on the outside of the turn and to raise it on the inside of the turn.
Camber is the lateral inclination of the wheel. If the wheel leans out at the top, away from the vehicle, it has a positive camber angle. With a negative camber angle, the wheel leans inward at the top. Camber-changes occur when the body leans during a turn and when the wheels move vertically through jounce and rebound. A wheel set at a camber angle produces "camber thrust," which is a lateral force generated in the direction of the lean. The magnitude of camber thrust is substantially less than the forces generated by slip angle (direction in which the tire is rolling). Bias ply tires produce significantly greater camber thrust than do radial tires.
As a general rule, the vehicle will handle well if the camber angle meets certain
criteria. At the fully laden ride height, the front wheels should assume a zero or
slightly positive camber angle. During jounce, as the wheel moves upward through its arc,
camber should progress to a negative angle in relation to the vehicle. The purpose of the
negative camber angle is to maximize cornering forces by keeping the outside tire upright
or at a slightly negative camber angle as the body leans to the outside of the turn. The
second purpose of negative camber is to minimize lateral movement, or tire scrubbing, at
the contact patch.
Consideration of camber angle has traditionally emphasized the front wheels. With the proliferation of independent rear suspension systems, the effects of camber angle have become just as important at the rear of the vehicle. Rear wheel camber changes can augment cornering forces, and they can influence the balance between oversteer and understeer.
The idea of steering the front wheels around separate axes was invented in 1817 by a
Munich carriage builder named Lankensperger. His agent, a fellow by the name of Rudolph
Ackerman, took out an English patent on the invention. Later in 1878, a French carriage
builder, Charles Jeantaud, introduced a refinement known as the "Jeantaud
Diagram" which provided a more precise prediction of the correct geometry. Today,
Lankensperger's invention, along with Jeantaud's refinements, is usually referred to as
Books on chassis design explore the subject in great detail and provide the graphical and analytical data required to determine length and inclination of steering knuckles, both ahead of and behind the wheels. Calculations can be quite involved and must take into account a host of variables in linkage and suspension system layouts. Several years ago, Walter Korff worked out a table that applies to simple beam axles with the steering knuckles behind the kingpin axes. Since the results of most calculations must be graphically verified, one could use Mr. Korff's table as a starting point, then adjust the angles to remove real-world errors.
STEERING KNUCKLE ANGLE
With independent suspension systems, each front wheel is steered individually by a separate link. This arrangement introduces important new geometric relationships. The links of a simple rack and pinion steering assembly must be of the correct length and correctly located. If the geometric relationships are not correct, bumps can produce steering inputs. In general, the steering linkage should be located near, and parallel with, the lower suspension link, as shown in Figure 11. The rate of differential steering is affected by the for-to-aft location of the steering box in relation to the steering knuckles, as well as by the steering knuckle angular offset.
Front Suspension Systems
The two types of front suspension systems that account for nearly all vehicles in production today are the double A-arm and the MacPherson strut. There are also a few variations that have not worked well in large-car applications, but may offer new possibilities with low mass vehicles.
The beam axle is a familiar design but it is no longer considered appropriate for automobile application. It is strong and inexpensive, and as a result, it is ideally suited to heavy trucks and smaller utility vehicles. The advantages of the design include its simplicity, low cost, and rugged layout, as well as a naturally high roll center which reduces body roll in turns. The disadvantages have to do with its performance. A bump at one wheel is transferred across to the other wheel. In addition, the gyroscopic forces of both wheels work together to induce shimmy, and the design results in greater unsprung weight and a rough ride.
The Double A-Arm Suspension System
The upper and lower A-arm suspension has been the predominate system of U.S. cars for
nearly half a century. Early versions had two parallel A-arms of equal length which
resulted in wheels that leaned outboard in turns. The design also caused excessive tire
scrubbing because of the large variation in tread-width as the wheel moved off the neural
position. When the concept of unequal length A-arms was developed, designers were given a
new design tool that provided almost infinite control over the movements of the wheels.
Today, handling characteristics are limited only by the limits of tire performance and the
basic weight and balance of the vehicle, not by the mechanical limitations of the
Anti-dive is another feature that is easily designed into the double A-arm suspension. Vehicles with a soft ride tend to dive when braking. This is due to the weight transfer toward the front of the vehicle. The tendency to dive on braking can be partially alleviated by tilting the upper A-arm as shown in the drawing in Figure 13.
The MacPherson Strut
The MacPherson strut front suspension system was invented in the 1940's by Earl S.
MacPherson of the Ford Motor Company. It was introduced on the 1950 English Ford and has
since become one of the predominate suspensions systems of the world. This simple system
utilizes the piston rod of the built-in telescopic shock absorber to also serve as the
kingpin axis. Normally, a coil spring is mounted over the strut assembly, in which case, a
thrust bearing at the top of the spring prevents spring wind-up during turns. The lower
link may be in the form of an ordinary A-arm. More commonly, a narrow transverse link
(sometimes called a track rod) locates the lower end of the strut in the transverse
direction and a separate member called a radius rod locates the assembly in the
longitudinal direction. However, the anti-roll bar can serve as the longitudinal link and
thereby eliminate the separate radius rod.
Both Urbacar and Urba Electric utilized a specially designed miniature MacPherson that did not suffer as badly from the tall shock-tower syndrome of existing designs. Another interesting concept utilizes a flat spring as the transverse link. The idea of replacing a suspension link with a leaf spring has been tried in a variety of configurations. Difficulties have centered on the high longitudinal loads imposed caused by braking, and the limited deflection characteristics typical of leaf springs. However, the lower loads typical of low mass vehicles, along with the greater control over spring characteristics provided by composite spring designs, offer an opportunity for a new look at unconventional suspension systems.
Rear Suspension Systems
Designers have traditionally invested a great deal of effort in front suspension design. Often, the rear axle was simply hung in place and the driving was left to the front. Things have changed in the last couple of decades. Rear suspension design has become just as sophisticated as the front. In fact, the design variations are probably greater at the rear. Rear suspension systems can be divided into three basic categories:
Dead Rear Axle
The dead rear axle comes in a variety of configurations. Every layout of the powered rear suspension system becomes a dead axle layout when power is not transferred to the wheels. The rear wheels are not considered as steering wheels. As a result, even the beam axle is a more docile layout when the axle is used at the rear in an unpowered configuration. The most popular dead rear axles include the beam axle and the trailing arm and semi-trailing arm suspensions.
One-Piece Live Axle
The live rear axle is similar to the beam front axle or the dead rear axle, except that
it is subjected to the torsional loads involved in transmitting power to the road. The
design is rugged, simple, and relatively inexpensive, but its high unsprung weight results
in a poor ride. The rear axle is not involved in steering so the disadvantages are
somewhat less troublesome than those experienced with the beam front axle. However,
unsprung weight is very high and as a result the design produces a rougher ride and is
very susceptible to wheel hop and tramp.
Designers have attempted to overcome the limitations of the live axle by replacing the leaf springs with coil springs and locating the axle with linkages of various configurations. Such systems do improve cornering performance, as well as smooth out the ride. When linkages are introduced, control is also gained over the dive and squat characteristics associated with acceleration and braking.
The Swing Axle
Ride and handling are greatly improved when the wheels can respond independently to
disturbances. The swing axle design is the most simple way of achieving an independent
rear suspension. Its simple design utilizing the drive axle as the transverse link and the
inboard universal joints as the suspension axis was responsible for its early
attractiveness. With swing axles a disturbance on one side is not transferred to the
opposite wheel as it is with a solid axle. Ride and handling are therefore improved. The
first swing-axle design to gain wide popularity in the U.S. was the immortal VW Beetle.
When the Beetle was introduced into the U.S., its fully independent suspension system
represented a significant step forward in suspension design. However, swing axles do
suffer from characteristic limitations and as a result the design is rarely used on modern
Trailing Arm and Semi-Trailing Arm Suspensions
With trailing arm and semi-trailing arm suspensions the wheels are free to bounce
independently. Each wheel moves up and down around the axis of a trailing or semi-trailing
arm. The difference between the two designs is that the axis of the trailing arm is at
right angles to the vehicle centerline whereas the semi-trailing arm axis angle inboard
and toward the rear. Both configurations are popular for either powered or non-powered
rear suspension systems.
Strut and A-arm Rear Suspensions
The rear suspension system can emulate the design of the MacPherson strut or the upper and lower A-arm front suspension system. At the rear, a MacPherson style suspension is referred to as a "Chapman strut", or simply a "strut" suspension. The geometry, mechanical layout, and wheel travel characteristics are essentially the same, except the strut rear suspension does not steer (at least in the traditional sense). Upper and lower A-arm systems come in a variety of unique configurations. Designs sometimes utilize the drive axles as suspension links, such as with the Jaguar and Corvette rear suspension systems.
Suspension Guidelines for Extremely Low Mass Vehicles
Extremely low mass vehicles are often penalized by poor suspension design. Just the opposite approach is necessary in order to bring out the natural handling capabilities of a low mass vehicle. Whereas a high mass vehicle has greater inherent stability, a low mass vehicle has greater inherent agility and handling precision. These natural characteristics can be degraded by poor design, or they can be enhanced by good design. Use the following general guidelines with low mass vehicles.
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