by Robert Q. Riley
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 ride and handling characteristics of an automobile center on the characteristics of the tires. Tires are the vehicle’s reaction point with the roadway. They manage the input of forces and disturbances from the road, and they are the final link in the driver’s chain of output commands. Tire characteristics are therefore a key factor in the effect the road has on the vehicle, and in the effectiveness of the output forces that control vehicle stability and cornering characteristics. The tire’s basic characteristics are managed by the system of springs, dampers, and linkages that control the way in which tires move and react to disturbances and control inputs.
The bounce and steering movements of the wheels provide for a variety of simultaneous needs. They provide steering input for directional control, they compensate for (or utilize) body roll to improve cornering ability, and they move vertically in response to roadway irregularities in order to smooth out the ride and maintain adhesion. Wheels are connected to the sprung mass through linkages and are therefore affected by the rolling and pitching movements that occur about the suspensions system’s reaction centers. The mechanical requirements for directional control, cornering forces, and ride comfort are continuously changing according to roadway and driving conditions. The suspension and steering linkages are designed to allow the wheels to move as needed to meet the dynamic requirements of various combinations of events. However, the designer is normally constrained by mechanical conflicts between structural members, the engine and drivetrain, and other components that also must fit into the vehicle. Consequently, errors in geometry are common, and the actual suspension system often falls short of the ideal in a variety of ways.
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 “uncomfortable ride.”
The ride quality normally associated with the vehicle’s response to bumps is a factor of the relatively low frequency bounce and rebound movements of the suspension system. Following a bump, the undamped suspension (without shocks) of a vehicle will experience a series of oscillations that will cycle according to the natural frequency of the system. Ride is perceived as most comfortable when the natural frequency is in the range of 60 to 90 cycles per minute (CPM), or about 1 Hz to 1.5 Hz. When the frequency approaches 120 CPM (2 Hz), occupants perceive the ride as harsh. Consequently, the suspension of the average family sedan will have a natural frequency of about 60 to 90 CPM. A high-performance sports car will have a stiffer suspension with a natural frequency of about 120 to 150 CPM (2 to 2.5 Hz).
Originally, human sensitivity to ride frequency was believed to be associated with the natural oscillations of an adult human body during a walking gait. An adult walks at the rate of about 70 to 90 steps per minute (frequency), and the torso moves up and down about 2 inches (amplitude) with each step. Early designers therefore attempted to constrain vehicle oscillations to those limits, the ride was indeed comfortable, and the theory was therefore believed to be correct. Today, our information about human sensitivity to vibrations is more sophisticated. We know that amplitude affects human sensitivity to frequency, and that there are some frequencies that are especially uncomfortable. For example, a frequency in the range of 30 to 50 CPM will produce motion sickness. The visceral region of the body objects to frequencies between 300 and 400 CPM. The head and neck regions are especially sensitive to vibrations of 1,000 to 1,200 CPM (18 to 20 Hz). These are the types of vibrations that are likely to emanate from the tires or from axle hop. Longitudinal oscillations are sensed primarily in the torso. Surprisingly, humans are most uncomfortable with longitudinal vibrations in the 60 to 120 CPM range (the region of greatest comfort for vertical vibrations). Discomfort from longitudinal disturbances occur when the vehicle pitches or when the seats lean rearward at a higher-than-normal angle.
The perception of ride quality is degraded by virtually any disturbance experienced by the occupant. Human sensitivity varies according to the nature of the disturbance. Consequently, a “good ride” depends on the overall design of the vehicle, rather than just the design of the suspension system. To produce a comfortable ride, the high-frequency vibrations of wind and drivetrain noise must be minimized and properly isolated, and the suspension must be set in appropriate rubber mountings to isolate high-frequency roadway-induced vibrations. However, the natural frequency of the suspension system is still considered the cornerstone of a comfortable ride.
The static deflection rate of the suspension determines its natural frequency. Static deflection is the rate at which the suspension compresses in response to weight. Other factors, such as the effects of damping (shocks) and system friction, alter the natural frequency of the suspension system. However, the primary determinate is the undamped static deflection rate. If this rate is used in calculations, results will likely be very close to the actual value needed for a smooth ride.
The static deflection rate of the suspension is not the same as the spring rate. Springs are located inboard of the wheels where they are normally subjected to the mechanical advantage of the suspension linkages. Static deflection is related to the distance the sprung mass (essentially the body) moves downward in response to weight. A static deflection of 10 inches in response to a weight equal to that of the sprung mass will produce a natural frequency of 1 Hz. A 5 inch deflection produces a 1.4 Hz frequency, and a 1 inch deflection results in a 3.13 Hz frequency. The natural frequency of a suspension can be determined by a simple formula expressed as follows:
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.
Variations in payload affect the natural frequency of the suspension. The critical damping force also varies with load. Over-damping (above 100 percent) dramatically reduces ride quality. In order to avoid over-damping at light loads, some degree of under damping is usually accepted at the fully-laden weight. Also, a passive suspension in combination with a high payload-to-vehicle weight ratio require a relatively high static deflection rate (a stiff suspension) in order to avoid undesirable effects on vehicle ride height. Ride height refers to the height of the body at a given load. It is important to keep ride height variations within predetermined limits in order to maintain headlight dip angle, provide adequate suspension stroke, and to provide an appropriate ground clearance. Load naturally affects the standing height of the vehicle. As load increases, the vehicle rests lower on its suspension, and at lighter loads it rests higher. Heavy loads in the luggage compartment can affect the pitch of the vehicle.
The importance of a high payload-to-vehicle weight ratio becomes more apparent when the effect of payload on a standard sedan is compared to the effect of the same payload on a hypothetical ultralight vehicle. For example, a standard sedan of 3,500 pounds curb weight and a natural frequency of 1.2 Hz will rest 0.7 inch lower with the weight of two, 175 pound occupants aboard. The same static deflection rate in a 1,000-pound vehicle will cause the body to rest 2.45 inches lower with an equal, two-occupant load. A deflection of this magnitude will cause significant changes in the geometric relationship of suspension components. With a single occupant load, such a suspension would also allow the body to list to one side. In order to equal the payload-induced deflection of the large car, the 1,000 pound vehicle must have a static deflection rate of 2 inches, which will result in a relatively stiff, sports-car-like ride of 2.2 Hz natural frequency. Consequently, an ultralight vehicle with a relatively high ratio of payload to vehicle weight will also have a relatively stiff ride. A self-leveling suspension and active damping could improve the suspension characteristics, but at higher cost and increased mass.
Payload variations can also have a much greater effect on the center of gravity of a low mass vehicle. Payload typically comes in human packages ranging from about 125 to 200 pounds each. A two-occupant load would therefore represent roughly one-third of the curb weight of a 1,000-pound vehicle. The same load amounts to only 10 percent of the curb weight of a 3,500 pound automobile. The effect of payload variations on center of gravity therefore becomes increasingly more significant as vehicle weight is reduced. Target handling characteristics of an extremely low mass vehicle should be based on the fully-laden weight.
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.
Vehicle “feel” and handling characteristics have to do with the way in which the vehicle’s inertial forces and the cornering forces of the tires act against each other. The magnitude and vector of the inertial forces are established by the vehicle’s weight and balance. In a turn, angular acceleration results in a force that is centered at the vehicle center of gravity and acts in a direction away from the turn center. The ability to overcome these forces and produce a controlled, stable turn depends upon the combined characteristics of the suspension and tires. The job of the suspension system is to support, turn, tilt and otherwise manage the tires and their relationship to the vehicle and the ground in a way that will maximize their capabilities.
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.
Vertical load on the tires has an effect on the lateral cornering force generated at a given slip angle. In general, cornering force increases as the vertical load increases, but the increase is not proportional to the load. The tire’s ability to develop cornering force, in relation to its vertical load, is known as its “cornering coefficient”. Tire cornering coefficient declines as vertical load increases. However, the inertial forces of a vehicle in a turn increase in proportion to the increase in weight. Consequently, tires that are more lightly loaded can handle greater g-loads during turns, which is a feature that is especially relevant to the handling characteristics of low mass vehicles. The graph in Figure 2 shows the relationship between vertical load and cornering coefficient (click on the link to retrieve the image). The coefficient is determined by the percentage of rated load that is represented by the actual vertical load imposed on the tire. The graph in Figure 3 provides another way to view the relationship between slip angle, vertical load, and lateral cornering force.
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.
Understeer results when the slip angle of the front tires is greater than the slip angle of the rear tires. A greater steering angle is then required in order to maintain the turn. When the steering angle reaches full lock and the turn cannot be maintained, the vehicle drifts to the outside. In an understeer condition, the driver is attempting to negotiate a turn, but the vehicle mushes ahead refusing to cooperate. Oversteer produces just the opposite condition.
During oversteer, the slip angle of the rear tires is greater than the front. Consequently, the turn-rate increases on its own and the driver therefore reduces the steering angle to compensate. During severe oversteer, the steering angle may reach full lock in the opposite direction while the vehicle continues on into the turn. The vehicle is then said to “spin out.” A vehicle that understeers is considered safer in the hands of the average driver.
An obvious solution to the negative effects of understeer and oversteer would seem to be that cars ought to be designed for neutral steer. Neutral steer is the theoretical ideal in which the slip angle of front and rear tires increase in unison throughout the range of steering angles. Unfortunately, the factors that influence vehicle dynamics are not so precisely manageable. With the slightest encouragement, a car with neutral steer characteristics can easily cross over into an oversteering condition. Consequently, designers prefer to create some degree of understeer in order to avoid oversteer.
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 anti-roll bar is essentially a transverse-mounted torsion bar designed to reduce body-roll during turns. It exerts no influence on the suspension when wheels bounce in unison. If vertical movement on one side exceeds the vertical movement on the other, the anti-roll bar exerts an opposing force. Along with its primary function of reducing body-roll, the anti-roll bar will also reduce the combined cornering force and the adhesion limits of the side-by-side tires that are being acted upon. Consequently, the location and stiffness of the bar can be modified to influence the oversteering or understeering characteristics of the vehicle.
An oversteering tendency will be reduced by locating the anti-roll bar at the front where it will reduce the cornering force and adhesion of the front tires. If the vehicle understeers, the anti-roll bar should be located at the rear. If an anti-roll bar is already required at both ends of the vehicle to achieve adequate roll stiffness, use an anti-roll bar of greater stiffness/diameter at the end of the vehicle where reduced cornering force is desired, and use a less-stiff/smaller-diameter bar at the other end.
Changing the tire’s inflation pressure has a more limited effect on handling characteristics. Inflation pressure influences the slip angle of the tire. A softer tire will require a greater slip angle in order to achieve equal cornering forces. Also a lower inflation pressure will cause the tire to reach its limit of adhesion at lower g-loads. Consequently, increase the inflation pressure at the end of the vehicle requiring greater cornering forces (greater adhesion). Reduce the inflation pressure for reduced adhesion and cornering forces.
Tire/wheel size is another important variable. Larger diameter tires tend to ride more smoothly, and they also develop greater cornering forces. However, installing larger tire to improve cornering is not always practical. Larger tires can cause clearance problems if the vehicle was not design for them, and they also affect suspension geometry. An alternative approach would be to install the same tires on wider rims. This provides a wider cross-sectional base for the tires and thereby improves cornering. Wider tires also aid in cornering, but at the expense of a rougher ride. Tires with a lower aspect ratio (low profile tires) develop significantly greater cornering forces and therefore can be used to improve the handling of a vehicle with marginal handling characteristics. Within limits, varying tire-size, rim-width and inflation-pressure can adjust cornering forces to achieve the desired overall performance.
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.
A low polar moment of inertia results in a vehicle with more responsive handling, but it also produces a more choppy ride. A vehicle with high polar mass is less nimble, but it offers a smoother ride. Sports cars tend to have a low polar moment of inertia for nimble handling, and they also tend to ride more roughly than passenger cars. Normally, a good balance between ride and handling can be achieved. The designer does not have to decide between one or the other extreme.
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
|Vehicle Type||cg Height (inches)||Tread (inches)||Rollover Threshold (lateral g-load)|
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.
Overshooting the steady-state roll angle can lift the inside wheels off the ground, even though the vehicle has a high static margin of safety against rollover. Once lift-off occurs, the vehicle’s resistance to rollover rapidly diminishes, which results in a condition that quickly becomes irretrievable. The roll moment of inertia reaches much greater values during slalom turns wherein the forces of suspension rebound and the opposing turn combine to throw the body through its roll limits from one extreme to the other. The inertial forces involved in overshooting the steady-state roll angle can exceed those produced by the turn-rate itself.
Tripping is another cause of rollover in an otherwise rollover-resistant vehicle. Tripping occurs when a vehicle skids against an obstacle, such as a curb. In this case, the lateral speed of the vehicle is suddenly arrested and extremely high momentary loads are imposed across the vehicle’s center of gravity. If the load spike exceeds the vehicle’s rollover threshold, rollover will occur.
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.
The distance the steering axis is offset from the tire centerline is called the “pivot radius”. Cars are normally designed with a positive pivot radius (the tire centerline is outboard of the swivel-line at ground level) in order to provide a feel of the road. However, if the pivot radius is too great, obstacles can then produce uncomfortable steering inputs that, in the extreme, can cause loss of control.
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.
Steering axis inclination is responsible for most of the self-centering force of the steering system. The steering axis of passengers cars normally leans inboard 10 to 15 degrees. The incline places the swivel-line the wheels off-plane with the ground. As a result, a steering movement in either direction moves the wheels downward and lifts the vehicle upward. The weight of the vehicle therefore produces a resultant that keeps wheels aligned to the vehicle heading.
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.
When wheels move through the arc prescribed by the suspension linkages, they may be dragged laterally inboard and outboard as they move up and down. Lateral movement causes a scrubbing action at the contact patch, which reduces adhesion and shortens tire life. Severe lateral scrubbing can also cause a condition known as “bump-steer.” A suspension system with a large scrubbing action will cause the vehicle to veer to one side when adhesion or vertical wheel movement is not equal at both side-by-side wheels. Ideally, the camber angle will change during jounce enough to compensate for the suspension-induced lateral movement at the hub. Camber change should also compensate for body roll to keep the outside wheel from lean away from the turn. Tire scrubbing (changes in the tread) should be minimized by good suspension design, and camber changes should be minimal as well.
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 “Ackerman Steering.”
An important requirement for wheels steered around separate axes is that the inside front wheel must turn at a sharper angle than the outside wheel. This is due to the fact that the inside wheel moves through a smaller arc. The difference between the inside and outside steering angles progressively increases as the wheels are turned more sharply (higher lock angles). At the low steering angles typical of highway speeds, differential steering is relatively unimportant. Figure 10 illustrates the geometry of Ackerman Steering.
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
(Retrieve Figure 10 for Angle X illustration)
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 suspension system.
The unequal length, non-parallel A-arm system allows the designer to place the reaction point of the wheel at virtually any point in space. The actual position of that point (virtual reaction point) is controlled simply by moving the inboard connection of the upper and lower A-arms up or down, or closer together or farther apart. For example, moving the inboard connection points farther apart moves the reaction point farther way until it reaches infinity when the arms are parallel. If the inboard connection points are moved still farther apart, the reaction point then flips to the other side and assumes a position in space some distant to the outside of the wheel.
A line projected from the bottom of the wheel to the virtual reaction point establishes the vehicle roll center at the point of intersection with the vertical centerline of the vehicle. The height of the roll center is therefore controlled by varying the inboard connection points of the upper and lower A-arms as needed to vary the height of the virtual reaction point (see Figure 12).
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.
The advantages of the MacPherson strut include its simple design of fewer components, widely spaced anchor points that reduce loads, and efficient packaging. From a designer’s viewpoint, its disadvantages include a relatively high overall height which tends encourage a higher hood and fender line, and its relatively limited camber change during jounce. A disadvantage on the consumer level is the comparatively high cost of servicing the shock absorber.
A small camber change during jounce and rebound is characteristic of the strut design. The vehicle roll center is controlled by raising or lowering the inboard anchor point of the transverse link, and by varying the steering axis inclination.
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 Axles, such as the one-piece beams at the rear of front-wheel-drive vehicles
Live axles with the final drive incorporated.
Independent suspension systems.
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.
The traditional live axle of older American cars is the Hotchkiss drive. The Hotchkiss drive is distinguished by its semi-elliptical leaf springs that also serve as the suspension links. Difficulties with the Hotchkiss drive have to do with its limited ability to transfer torque, its high interleaf friction and high unsprung weight, and the imprecise location of the rear axle assembly. Consequently, it is difficult to achieve a good ride and to appropriately manage the torsional loads of braking and power transfer. Braking and acceleration transfer high torsional loads to the axle, which can rotate off plane due to the flexibility of the springs.
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 cars.
Swing-axles produce large changes in camber and tread during bounce, and the design can become unstable in turns due to the “jacking” effect. Setting the wheels at a negative camber can reduce the tendency to jack. However, too much negative camber can also produce a vehicle with a vague, mushy feel of directional instability. Slings under the axles or zee brackets can be designed to limit downward travel and thereby avoid wheel tuck-under. A correctly designed swing axle suspension works reasonably well, but its undesirable characteristics can never be fully overcome.
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.
If the rear wheels are powered, the final drive is mounted in a fixed location and each wheel is driven by an axle half-shaft. Each half-shaft is equipped with an outboard and inboard universal joint to accommodate angular variations during bounce. Half-shafts also have a telescopic action to accommodate the variation in final drive-to-wheel distance as wheels move up and down. Rear end lift during braking is countered by the downward component at the leading end of the arms.
Body roll produces camber and toe changes in the semi-trailing arm design. Consequently, camber thrust and modest slip-angle forces can combine to produce steering inputs as the body rolls to the outside of the turn. Roll-steer effects are at a minimum when the arm axis is parallel to the ground and increase when the inboard end is raised or the outboard end is lowered. The degree of camber change depend primarily on the distance to the instantaneous center. The instantaneous center is normally located no closer than the centerline of the opposite wheel. A closer location will produce wheel movements that emulate the swing-axle, along with the negative attributes of tuck-under and unfavorably large camber change.
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.
Use the fully-laden weight for performance and handling calculations.
Keep unsprung weight to a minimum. Consider a simplified suspension design, and use lightweight alloys or plastic composites for springs and structural members.
Keep the center of gravity as low as possible. Correct cg location is especially important in low mass vehicles, and even more so in three wheel designs.
The center of gravity should be ahead of the wheelbase mid-point of a four wheel platform, and no farther than 35 percent of the wheelbase from the side-by-side wheels of a three wheeler.
The tread should be as wide as possible and the wheelbase as long as possible within the constraints of the vehicle package. Locate wheels at each of the extreme corners of the vehicle.
Use a fully independent suspension, and keep the contact patch location stable (minimal lateral movement).
Eliminate suspension and steering geometry errors. Go the extra mile for precession.
Establish the roll center according to the vehicle cg. If the cg is extremely low, the roll center may be at, or near ground level. The roll moment should be lower for extremely low mass vehicles.
Roll stiffness is essential for a low mass vehicles. If the vehicle understeers, place the anti-roll bar at the rear. If it oversteers, place the anti-roll bar at the front.
For increased traction, use wider rims and/or wider tires.
A torsionally rigid platform (frame) is essential for precise handling characteristics.
At freeway speeds, aerodynamic effects will be an important consideration, and aerodynamic effects increase as weight decreases. Consequently, the aerodynamic center of pressure should be as close as possible to the vehicle center of gravity. Eliminate lift, keep ground clearance minimal, angle the body slightly downward at the front.