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附 录AFormula SAE is a student competition sponsored by Society of Automotive Engineers (SAE), were students design, build, and compete with a small formula style race car. The basis of the competition is that a fictitious company has contracted a group of engineers to build a small formula car. Since the car is intended for the weekend autocross racer, the company has set a maximum price of $8,500. The race car is also limited to a single 610cc displacement engine with a single inlet restrictor. Other major rules require that the car must have a suspension system with a minimum wheel travel of 50mm and a wheelbase greater than 1524mm. The remainder of the rules define safety requirements such as side impact protection . The competition is separated into static and dynamic events. The static events include the cost nalysis, sales presentation, and engineering design. The dynamic portions of the competition are the 15.25 m diameter skid-pad, 91.44 m acceleration event, 0.8 km autocross, 44 km endurance race, and fuel economy.The FSAE competition has been established to provide an educational experience for college students that is analogous to the type of projects they will face in the work force. To participate in FSAE, student groups work with a project from the abstract design until it is completed. The aspects of engineering design, team work, project management, and finance have been incorporated into the basic rules of Formula SAE.This paper is intended to cover some of the basic concepts of suspension and frame design and also highlights the approach UM-Rolla used when designing their 1996 suspension and frame. The suspension section addresses the basic design parameters and presents specific examples. Next, the frame section discusses how to achieve a compromise with the FSAE design constraints. Finally, the design section gives a brief overview of the design methodology used by UM-Rolla for the 1996 race car.1.Suspension GeometryFSAE suspensions operate in a narrow realm of vehicle dynamics mainly due to the limited cornering speeds which are governed by the racetrack size. Therefore, FSAE suspension design should focus on the constraints of the competition. For example, vehicle track width and wheelbase are factors governing the success of the cars handling characteristics. These two dimensions not only influence weight transfer, but they also affect the turning radius.Not only do the kinematics have to be considered for FSAE suspension, but the components must also be reasonably priced for the cost analysis and marketable for the sales presentation. For example, inboard suspension could be a more marketable design, while outboard suspension might cost less and be easier to manufacture.The suspension geometry section concentrates on some of the basic areas of suspension design and highlights what the UM-Rolla design team selected for their 1996 race car suspension geometry. UM-Rolla chose to use a four wheel independent suspension system with push rod actuated inboard coil over shocks. This decision was mainly because of packaging constraints. Furthermore, the appearance of inboard suspension was considered important for both the design judging and the sales presentation because of its similarity to modern race cars.Also, this section of the paper was written with short-long arm suspension systems in mind. However, many of the concepts are valid for other suspension types.2.Track Width and WheelbaseThe definition of track width is the distance between the right and left wheel centerlines which is illustrated in Figure 1. This dimension is important for cornering since it resists the Upper Ball JointTrack WidthLow Ball JointUpper Control ArmUpper Control ArmFigure 1. Track Widthoverturning moment due to the inertia force at the center of gravity (CG) and the lateral force at the tires . For the designer, track width is important since it is one component that affects the amount of lateral weight transfer . Also, the designers must know the track width before kinematic analysis of the suspension geometry can begin.When selecting the track width, the front and rear track widths do not necessarily have to be the same. For example, track width is typically wider in the front for a rear wheel drive race car. This design concept is used to increase rear traction during corner exit by reducing the amount of body roll resisted by the rear tires relative to the front tires. Based on the corner speeds and horsepower to weight ratio of FSAE cars, this concept should be considered by the designer.The wheelbase also needs to be determined. Wheelbase is defined as the distance between the front and rear axle centerlines, and also influences weight transfer, but in the longitudinal direction. Except for anti-dive and anti-squat characteristics, the wheelbase relative to the CG location does not have a large effect on the kinematics of the suspension system. However, the wheelbase should be determined early in the design process since the wheelbase has a large influence on the packaging of components.For track width and wheelbase starting points, the designers should research the oppositions dimensions to serve as a baseline for their own calculations. FSAE car specifications for the competing teams, including track width and wheelbase, are available in the event program published by SAE.The 1996 design team selected a 1727 mm wheelbase, 1270 mm front track width, and a 1219 mm rear track width, which were based on previous UM-Rolla cars. Although this wheelbase was adequate for the FSAE competition size courses, the UM-Rolla design team has decided to increase the wheelbase for the next car to 1854.2 mm. This increase in wheelbase is an attempt to improve stability for high speed corner entry at the competition.3.Tire and WheelAfter track width and wheelbase considerations have been addressed, tire and wheel selection is the next step in the design process. Since the tire is important to the handling of the vehicle, the design team should thoroughly investigate the tire sizes and compounds available. The tire size is important at this stage of the design since the height of the tire must be known before the geometry can be determined. For example, the tire height for a given wheel diameter determines how close the lower ball joint can be to the ground if packaged inside the wheel.Tire Size - The designers should be aware that the number of tire sizes offered for a given wheel diameter is limited. Therefore, considering the importance of the tire to handling, the tire selection process should be a methodical process. Since the amount of tire on the ground has a large influence on grip, it is sometimes desirable to use wide tires for increased traction. However, it is important to remember that wide tires add rotating mass which must be accelerated by a restricted FSAE engine. This added mass might be more detrimental to the overall performance than the increase in traction from the wider tires. Not only does a wider tire add mass, but it also increases the amount of rubber that must be heated. Since racing tires are designed to operate most efficiently in a specific temperature range, this added material may prevent the tires from reaching the optimum temperature range . The UM-Rolla team used tires for the 1996 competition that were designed to work most efficiently at a minimum of 71.During the selection process the designers must consider how the tires will influence the performance of the entire package. For example, the weather conditions for the FSAE dynamic events might determine which tire compound and tire size should be used for the competition. Another important consideration is the price of the tires since the cost can be a large portion of a teams budget.For the 1996 competition, UM-Rolla selected a 20 by 6-13 racing tire for both the front and rear of the car. Because of the low vehicle mass, a narrow tire was selected so tire temperatures would be greater than previous UM-Rolla designs. This tire selection increased the operating temperature from 48o to 60oC. For the competition, the weather was predicted to be cool, so the team brought a set of hard and soft compound tires. The team chose to use the harder compound since the weather for the endurance was predicted to be clear and warm.Wheel Selection - Once a decision has been made as to which tire sizes to use, the wheel selection should be next. Usually, the wheel dimensions are fixed and allow for little modification. Therefore, it is important to have some design goals in mind before investing in wheels. Generally, the upright, brake caliper, and rotor are placed inside the wheel which requires wheel offset for clearance. It is usually easier to design the suspension geometry if the wheel profile is known. For example, the ball joint location is limited to the area defined by the wheel profile. Some packaging constraints are shown in Figure 2.Other considerations for wheel selection include: cost, availability, bolt circle, and weight. For example, three-piece rims, although expensive, have the distinct advantage of offering many offsets and profiles that can be changed during the design process .Figure 2. 1996 Front SuspensionUM-Rolla designed the 1996 suspension geometry around a wheel profile from a previous car and then acquired a set of three-piece rims to meet the design specifications. All four wheels selected for the 1996 competition were size 6 by 13. This wheel selection allowed for tire rotations, reduced cost, and a wide selection of tire sizes, compounds, and manufacturers.4.GeometryThe designer can now set some desired parameters for the suspension system. These usually include camber gain, roll center placement, and scrub radius. The choice of these parameters should be based on how the vehicle is expected to perform. By visualizing the attitude of the car in a corner, the suspension can be designed to keep as much tire on the ground as possible. For example, the body roll and suspension travel on the skid pad determines, to a certain extent, how much camber gain is required for optimum cornering. The amount of chassis roll can be determined from roll stiffness while the amount of suspension travel is a function of weight transfer and wheel rates.Once a decision has been made about these basic parameters, the suspension must be modeled to obtain the desired effects. Before the modeling can begin, the ball joint locations, inner control arm pivot points, and track width must be known.The easiest way to model the geometry is with a kinematics computer program since the point locations can be easily modified for immediate inspection of their influence on the geometry. Should a dedicated kinematics computer program not be available, then a CAD program can be used simply by redrawing the suspension as the points are moved.When designing the geometry, it is important to keep in mind that designing is an iterative process and that compromises will be inevitable. For instance, the desired scrub radius might not be possible because of packaging constraints. When modeling the suspension, the designers should not aimlessly modify points without first thinking through the results. For example, the designer should visualize how the wheel will camber relative to the chassis when making the lower A-arm four times longer than the upper A-arm. One method that can be used to visualize the results is the instant center location for the wheel relative to the chassis. Another method is to use the arcs that the ball joints circumscribe relative to the chassis. For a complete explanation for determining suspension point locations from instant center locations refer to Milliken .Scrub Radius, KPI, and Caster - The scrub radius, or kingpin offset, is the distance between the centerline of the wheel and the intersection of the line defined by the ball joints, or the steering axis, with the ground plane which is illustrated in Figure 2. Scrub radius is considered positive when the steering axis intersects the ground to the inside of the wheel centerline. The amount of scrub radius should be kept small since it can cause excessive steering forces . However, some positive scrub radius is desirable since it will provide feedback through the steering wheel for the driver .Kingpin inclination (KPI) is viewed from the front of the vehicle and is the angle between the steering axis and the wheel centerline . To reduce scrub radius, KPI can be incorporated into the suspension design if packaging of the ball joints near the centerline of the wheel is not feasible. Scrub radius can be reduced with KPI by designing the steering axis so that it will intersect the ground plane closer to the wheel centerline. The drawback of excessive KPI, however, is that the outside wheel, when turned, cambers positively thereby pulling part of the tire off of the ground. However, static camber or positive caster can be used to counteract the positive camber gain associated with KPI.Caster is the angle of the steering axis when viewed from the side of the car and is considered positive when the steering axis is tilted towards the rear of the vehicle . With positive caster, the outside wheel in a corner will camber negatively thereby helping to offset the positive camber associated with KPI and body roll. Caster also causes the wheels to rise or fall as the wheel rotates about the steering axis which transfers weight diagonally across the chassis . Caster angle is also beneficial since it will provide feedback to the driver about cornering forces .UM-Rollas suspension design team chose a scrub radius of 9.5 mm, zero degrees of KPI, and 4 degrees of caster. This design required the ball joints to be placed near the centerline of the wheel, which required numerous clearance checks in the solid modeling program.Roll Center - Once the basic parameters have been determined, the kinematics of the system can be resolved. Kinematic analysis includes instant center analysis for both sets of the wheels relative to the chassis and also for the chassis relative to the ground as shown in Figure 3. The points labeled IC are the instant centers for the wheels relative to the chassis. The other instant center in Figure 3, the roll center, is the point that the chassis pivots about relative to the ground . The front and rear roll centers define an axis that the chassis will pivot around during cornering. Since the CG is above the roll axis for most race cars, the inertia force associated with cornering creates a torque about the roll center. This torque causes the chassis to roll towards the outside of the corner. Ideally, the amount of chassis roll would be small so that the springs and anti-roll bars used could be a low rate for added tire compliance . However, for a small overturning moment, the CG must be close to the roll axis. This would indicate that the roll center would have to be relatively high to be near the CG. Unfortunately, if the roll center is anywhere above or below the ground plane, a jacking force will be applied to the chassis during cornering forces . For example, if the roll center is above ground, this jacking force causes the suspension to drop relative to the chassis. Suspension droop is usually undesirable since, depending on the suspension design, it can cause positive camber which can reduce the amount of tire on the ground. Conversely, if the roll center is below the ground plane, the suspension goes into bump, or raises relative to the chassis, when lateral forces are applied to the tires. Therefore, it is more desirable to have the roll center close to the ground plane to reduce the amount of chassis vertical movement due to lateral forces .Figure 3. Front Roll CenterSince the roll center is an instant center, it is important to remember that the roll center will move with suspension travel. Therefore, the design team must check the migration of the roll center to ensure that the jacking forces and overturning moments follow a relatively linear path for predictable handling . For example, if the roll center crosses the ground plane for any reason during cornering, then the wheels will raise or drop relative to the chassis which might cause inconstant handling.The roll center is 35.6 mm below ground in the front and 35.6 mm above ground in the rear for UM-Rollas 1996 car. Since none of the previous UM-Rolla cars had below ground roll centers, the selection of the 1996 points was basically a test to understand how the below ground roll center affected the handling. Because of the large roll moment, the team designed enough camber gain into the suspension to compensate for body roll associated with soft springs and no anti-roll bar. The team was very happy with the handling but decided, for the next car, to have both roll centers above ground for a direct comparison between both designs.Camber - Camber is the angle of the wheel plane from the vertical and is considered to be a negative angle when the top of the wheel is tilted towards the centerline of the vehicle. Camber is adjusted by tilting the steering axis from the vertical which is usually done by adjusting the ball joint locations. Because the amount of tire on the ground is affected by camber angle, camber should be easily adjustable so that the suspension can be tuned for maximum cornering. For example, the amount of camber needed for the small skid pad might not be the same for the sweeping corners in the endurance event.The maximum cornering force the tire can produce will occur at some negative camber angle . However, camber angle can change as the wheel moves through suspension travel and as the wheel turns about the steering axis. Because of this change, the suspension system must be designed to compensate or complement the camber angle change associated with chassis and wheel movements so that maximum cornering forces are produced.The amount of camber compensation or gain for vertical wheel movement is determined by the control arm configuration. Camber gain is usually obtained by having different length upper and lower control arms. By using different length control arms, the ball joints will move through different arcs relative to the chassis. The angle of the control arms relative to each other also influence the amount of camber gain. Because camber gain is a function of link geometry, the amount of gain does not have to be the same for both droop and bump. For example, the suspension design might require the wheels to camber one degree per 25mm of droop versus negative two degrees per 25mm of bump.Static camber can be added to compensate for body roll, however, the added camber might be detrimental to other aspects of handling. For example, too much static camber can reduce the amount of tire on the ground, thereby affecting straight line braking and accelerating. Similarly, too much camber gain during suspension travel can cause part of the tire to loose contact with the ground.Caster angle also adds to the overall camber gain when the wheels are turned. For positive caster, the outside wheel in a turn will camber negatively, while the inside wheel cambers positively. The amount of camber gain caused by caster is minimal if the wheels only turn a few degrees. However, FSAE cars can use caster angle to increase the camber gain for the tight corners at the FSAE competition.UM-Rolla designed for a relatively large amount of camber gain since anti roll bars were not used in the 1996 suspension design. The use of low wheel rates with a large roll moment required the suspension to compensate for the positive camber induced by chassis roll and suspension travel. The camber gain for UM-Rollas 1996 car was from both the caster angle and the control arm configuration.5.Steering SystemThe steering
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