Swing Arms, Pushrods, Uprights and Bell Cranks

Abstract

Inspired by the FSAE Formula Student competition, a fully fledge working suspension system was designed for the race car in order to solve the issues that were detected early on in the troubleshooting stage. All parts except the engine and seat were designed from first principles.

By understanding the basic concepts of suspension systems and mechanical design, this project aims to give an insight in to re-designing the current car. To fully understand the chassis-suspension geometry model, a ground foundation in vector theory was established and specifically applied to the new design in order to determine the positions of all external components relative to the chassis.

Once the geometry and layout of the new chassis-suspension model was determined, the next stage of the process was to design all the external components and run each of the custom-made parts through a stress analysis. Ground knowledge of finite element analysis was required in order to understand the appropriate forces and constraints to apply to the new parts.

Knowledge of composites, metals and methods of manufacturing was also required for the design of the swing arms, pushrods, uprights and bell cranks.

FSAE Suspension Design Objectives

• Research the various types of suspension systems by giving a brief outline on suspension theory.
• Troubleshoot any potential design issues on the existing car by carrying out inspections and speaking to members of the Formula Student team.
• Design the suspension system and investigate the use of advanced materials without compromising structural integrity.
• Determine the most elegant user-friendly interface between the car and race team members.
• Determine the parameters that influence both static and dynamic motion in the chassis suspension system by carrying out sprung and unsprung mass calculations. Using these results, further determine an appropriate shock absorber to purchase ‘off the shelf’.
• Determine appropriate manufacturing methods for each of the individual custom components.
• Construct a fully-fledged working SolidWorks model demonstrating all the position geometry, linkages and joining of the components.

Introduction

The need for high performance suspension systems in race cars lies to do with optimizing vehicle performance when the vehicle is subjected to severe physical and dynamic conditions. This must be achieved while maintaining control and uncompromising vehicle and driver safety. From initial concept design to selecting appropriate materials that can withstand environmental and dynamic forces, there exist a series of technical challenges engineers must consider when designing a suspension system.

Types of Suspension Systems

Selecting a suspension system is dependent on the application and type of motor vehicle concerned. With current motorcar designs, engineers have to consider everything from chassis design to the amount of luggage space the car can facilitate. In terms of suspension, vehicle handling is the main area of focus for many car manufacturers. For high performance car manufacturers and even Formula 1 teams, it becomes the very heart and soul of vehicle design. There are various types of suspension systems and selecting one can be a challenge in itself. Designers are limited to various parameters from vehicle space to cost. As performance and optimization was the project’s main area of focus, cost was not considered.

Solid-axle

Arranging the wheels along a solid beam is referred to as a solid axle system. The motion of the wheels is constrained to allow only a translation in the vertical direction by mounting the springs and dampeners perpendicular to the axle. If one wheel were to experience bump however, the other wheel is usually affected. Conventional vehicle designs employed the solid axle due to its simplicity and ease of maintenance. Shown in Figure is an example of a solid axle beam with leaf springs and dampeners connected perpendicular to the direction of the beam.

Solid-axle suspensions are restricted to the level of adjustment and are therefore usually employed in conventional vehicles and in lorry trailers where adjustment is not necessary

Independent wheel suspension

Independent wheel suspension systems allow the motion where if one wheel where to experience bump the other wheels would not necessarily be directly affected. The wheels are connected to the chassis through a series of control arms that allow vertical motion through a spring-dampener connected to the arm. This method of connecting the wheels-brake assembly to the chassis is practiced in modern vehicle design to accompany for smoother ride comfort and adjustment. There are various types of independent suspensions, each displaying their own characteristics and benefits depending on their application.

Trailing arm (swing arm) independent suspension

Trailing end is characterized by having the wheel assembly connected by a control arm that connects through a rotational joint mounted to the chassis with the spring dampener mounted above the control arm.

MacPherson strut independent suspension

MacPherson Strut suspension systems are characterized by having the spring-dampener mounted directly to the wheel mount (upright)  Many modern vehicles employ this design for the ease of access, adjustment and space saving. Due to its geometry, the strut assembly can be mounted directly to the chassis therefore saving the number of parts and weight. Adjustment is restricted however so this system is usually employed in your average family car.

Double wishbone independent suspension

Double wishbone suspension systems are becoming more common in modern vehicle design due to its higher level of performance and stability. The wheel assembly is supported by a top and bottom swing arm. This gives the motion of the wheels more stability during bump or cornering. It also allows more room for adjustment depending on the application

STEERING OBJECTIVE

• To provide directional stability to the vehicle
• To facilitate straight ahead recovery after completing a turn
• To obtain a turning circle radius (T.C.R.) as minimum as possible
• To obtain perfect rolling of all the wheels about a single point

PERFECT STEERING CONDITION

cot φ – cot Θ = c/b

 Θ = angle turned by inner wheel

 φ = angle turned by outer wheel

  b = wheel base

  c = distance between pivot points 

STEERING MECHANISMS

We analyzed Davis and Ackermann steering mechanisms.

Davis steering mechanism obtains the required steering angle using sliding pairs. Due to the presence of such sliding pairs, mechanical wear and tear increases. This increases the possibility of failure. Also due to the increase in the number of links, it increases the weight making it bulky and inefficient.

Ackermann steering mechanism is basically 4 bar linkage mechanism. It consists of turning pairs and no sliding pairs. This helps to decrease the wear and tear of steering mechanism.

Thus, we prefer Ackermann steering mechanism over Davis steering mechanism

Ackermann steering mechanism is basically of 3 types –

• Ackermann steering mechanism-Angle turned by inner wheel is greater than that of outer wheel.
• Anti-Ackermann steering mechanism-Angle turned by inner wheel is less than that of outer wheel.
• Pro-Ackermann steering mechanism-Angle turned by outer wheel is equal to that of inner wheel.

In case of Anti-Ackermann, there was also a problem of interfering of tie-rod with the suspension strut. In Pro-Ackermann, wear of tires is more. Instead, Ackermann steering mechanism is used.

RACK AND PINION STEERING MECHANISM

Considering the following aspects this mechanism was opted

• It minimizes the steering effort.
• It occupies less space.
• It does not involve bulky linkages.
• Due to less linkages possibility of wearing out of joints is minimum.

Rotary motion of the steering wheel is transmitted to the pinion through universal joints. The circular motion of the pinion is converted into linear motion of the rack, which is further relayed through ball joints and tie-rods to the wheels to be steered.

Introduction to Suspension Kinematics and Kinetics

Vehicle dynamics is the study of all forms of transportation (trains, airplanes, boats, and automobiles). However vehicle dynamics as we know it is the study of the performance of the automobile in all of its motions (ride, acceleration, cornering, and baking). The vehicles suspension plays a key roll in each of these motions. The study of a vehicles suspension can be broken into two major categories: suspension kinetics and suspension kinematics. Suspension kinetics is a dynamic and a vibration analysis on the vehicle and suspension systems. Suspension kinematics involves analyzing the motion of the tires as the suspension compresses and extends. Each of these two divisions will be analyzed in depth in the following sections.

Suspension Kinetics

Suspension kinetics is an analysis that is important to the overall performance of the vehicle because it is what determines if the vehicle is capable of absorbing ground loads; it is what judges the comfort of the driver, it is what determines if the vehicle will roll or not; and it is what determines the resonant frequency of the chassis, the shock and the tire; it is what determines the handling performance of the vehicle. The vehicle will see a wide range of vibrations because of the speeds it travels and the boundaries it travels on, thus it is important to analyze the resonant frequency of the suspension components and the chassis. The ride quality (or vertical dynamics) of a vehicle can be analyzed using the half car model. The handling performance of the vehicle can be analyzed using the bicycle model. However before each of these models are considered

it is important to define the vehicle axis and the appropriate rotations about each of the axis. The conventional axis system is placed at the center of mass of the vehicle with the x axis pointing towards the front of the vehicle, the y axis pointing towards the right side of the vehicle, and the z axis pointing towards the bottom of the vehicle. The x axis is known as the longitudinal axis, the y axis is known as the lateral axis, and the z axis is known as the vertical axis. The rotation about the x axis is know as roll, the rotation about the y axis is known as pitch and the rotation about the z axis is known as yaw (Figure 1: Vehicle axis system). Vehicle ride modeling is the study of the motions transmitted to the vehicle chassis, and thus the motions felt by the passengers in the vehicle. The motions transmitted to the vehicle chassis come from the vibration of the suspension as it absorbs the motion coming from the disturbance at the ground. It is these vibrations that cause the passengers to feel uncomfortable when they are riding in a vehicle. Therefore, vehicle ride problems arise from the vibrations of the vehicle body (chassis). One of the main objectives of the suspension system is to control the vibrations of the vehicle body in order to provide a comfortable ride for the driver.

Fig-28 Suspension Kinetics

Vehicle axis system

Vehicle ride modeling (vertical dynamics)

Mechanical vibrations in a vehicle represent a very complex field, and usually require multiple degrees of freedom to accurately predict the vertical performance of the vehicle. However, there exist two simplified models which when combined give an accurate approximation as to the ride quality of the vehicle. These include the quarter car model (corner model) (used to predict the motion of a single suspension unit) and the bounce/pitch model (used to predict the motions of the sprung mass of the vehicle). These models combined produce the half car model (four degrees of freedom model). The vertical performance of the vehicle is directly linked to the sprung mass, the unsprung mass, the pitch inertia, the suspension stiffness, the tire stiffness, the damping in the tires, the damping in the suspension units, and the excitation frequency. Before the half car model is introduced, the quarter car model and the bounce/pitch models will be introduced.

The quarter car model is a model that models the motion of a single suspension system (it models one corner of the car) (Figure 2: The quarter car model). The sprung mass in this model represents some portion of the total sprung mass of the system. The tire is excited because of the shape of the path it is following (the shape is not flat, especially for an off road track). Applying Newton’s 2nd law of motion.

Fig- 28 The quarter car model 

The Suspension Stiffness and Damping

The suspension stiffness is one of the most important parameters when considering the vertical performance of the vehicle. It is generally best to have a moderate spring rates. This is because low spring rates reduce the tire deflection which increases the tire grip, however it also allows for increased body motions (in roll and in pitch) which are harmful to the overall handling performance of the vehicle. The opposite is true for high spring rates. Therefore, there should be a compromise between implementing high and low suspension stiffness’. Also, according to Maurrie Olley the following set of rules should be followed when designing a suspension system for the comfort of the passenger, and they are:

1. Front suspension should have a 30% lower ride rate than rear suspension

2. Pitch and bounce frequencies should be close together, bounce frequency should be 1.2 times the pitch frequency

3. Neither the bounce nor the roll frequency should be greater than 1.3Hz. The reason for this is that the front of the vehicle will ride over the bump (or disturbance) first creating an excitation in the front suspension, and then seconds later the rear suspension will ride over the bump creating an excitation in the rear suspension. If the two suspension rates are identical the phase lag between the front and the rear suspensions will create an undesirable motion in pitch. There have been studies that have shown that the driver/passenger is/are very uncomfortable in pitch motion, it tends to cause neck muscle strains. Therefore, by increasing the suspension rate in the rear suspension allows for the rear of the vehicle to “catch up” to the front of the vehicle

Figure 29 The front and the rear suspension amplitudes as a function of time

It can be seen from the figure above that there exists a phase lag between the front and the rear excitations, and that by having a rear suspension rate higher than the front suspension rate allows for the rear excitation to catch up to the front excitation.

The Tire Stiffness and Damping

The tires stiffness and the tires viscous damping coefficient are important to the ride quality of the vehicle, but more importantly to the handling performance of the vehicle. In typical passenger car vehicles the stiffness of the tires is of an order of magnitude greater than the suspension stiffness. It is typically the tire deflection that is important for the handling performance of the vehicle, because the tire deflection is one of the parameters in which decides the tires grip capabilities. As the deflection of the tire increases, the grip capabilities of the tire will decrease. It is very important to not allow the tire to lose contact with the ground, because if it does the car will not be controllable in handling. Typically, the damping coefficient of the tires is neglected because it is generally very low compared to the other parameters in the system, and neglecting it results in a small error in the analysis.

The Sprung and Unsprung Mass

The mass of the vehicle is an important parameter in the analysis of the vertical dynamics of the vehicle. The mass of the vehicle is one of the main parameters in which will decide the deflections of both the front and the rear tires, and the suspension units when they are excited. The mass of the vehicle is divided into two parts the sprung mass and the unsprung mass. The sprung mass consists of everything the suspension units have to support, and these include the chassis, and the engine. The unsprung mass consists of everything the tires have to support, and these include the front and rear axles. Typically the sprung mass is of an order of magnitude greater than the unsprung mass. Therefore the following formula can be used to calculate the sprung mass and the unsprung mass based on the mass of the vehicle

The tire cornering stiffness

The tire cornering stiffness is an important parameter in determining the handling performance of the vehicle. It is to some extent arbitrary; each tire has its own stiffness, and the tires on a vehicle can be changed. Therefore the cornering stiffness can be chosen by the user to precisely predict turning (cornering) characteristics of the vehicle. It is this parameter that will determine whether the car is an understeering (the actual cornering radius increases with vehicle speed) or an oversteering (the actual cornering radius decreases with vehicle speed) automobile because the center of mass of the vehicleis a fixed parameter (Figure 7: Oversteering and Understeering Vehicle). It is generally better to have an understeering vehicle, because the vehicle is normally more stable. In an oversteering case, the vehicle over steers the turn, and the driver will be forced to decrease the steering angle as he/she turns in order to stay on the desired path (the path the vehicle takes when there is no lateral slipping).

Figure 30 Over steering and Under steering Vehicle

There are also more chances that the vehicle spins on the spot (about its own z-axis). In an understeering case, the car understeers and the driver is forced to increase the steering angle in order to stay on the desired path. There are several ways to determine the tires cornering stiffness. Two of these ways are by using the magic tire model and second by using an estimation given the tires dimensions.

Suspension Kinematics

Suspension kinematics is the study of the motions of the tire. It describes the orientation of the tire as a function of wheel travel and steering angle. The motions of the tire are highly dependent on the type of suspension. In general there are two types of suspension systems; solid axles and independent suspensions. A solid axle suspension is a suspension where the movement of one wheel is transmitted to the other wheel causing them to move together. This type of suspension is essentially a dependent suspension, the motion of the two wheels are correlated to one another. The biggest advantage of this type is that the camber angle is not affected by vehicle body roll. The major disadvantage of this type of suspension is the vibrations which are induced into the system if the solid axle suspension also incorporates vehicle steering. Independent suspension systems allow the left and right wheels to move independently; the movement of one wheel will have no effect on the other wheel. The advantages of independent type of suspensions are: they provide better resistance to steering vibrations; they provide a high suspension roll stiffness; steering geometry is easily controlled; suspension geometry is easily controlled; and they allow for higher wheel travel. The major disadvantages are: the camber angle changes quite a bit over suspension travel; increased unsprung mass; and the high cost of the system. The study of suspension kinematics allows for several different suspension parameters to be determined throughout suspension travel and steering angle. Some of the most important parameters include: roll center position and instant center, camber angle, caster angle, toe angle, tire scrub, kingpin angle, scrub radius, caster trail, aligning moment, vehicle ride height, track width, wheel rates, roll stiffness, roll axis, understeer/oversteer characteristics, roll steer, bump steer, motion ratio, and anti dive/anti-squat. The following will be a discussion of each of these parameters.

WHEEL ALIGNMENT

Camber angle

The camber angle is defined as the inclination of the tire with respect to the road surface in the vertical plane (when looking at the vehicle from the front view). Negative camber occurs when the top of tire points in towards the vehicle, and positive camber occurs when the top of the tire points out away from the vehicle (chassis) (Figure 13: Definition of camber angle (note in the figure one is looking at the vehicle from the front)). Camber on a wheel will produce a lateral force which is known as camber thrust. A rolling tire that is cambered will produce a lateral force which is in the direction the tire is tilting in. When the camber angle is generating a lateral force with no slip angle present it is known as camber thrust. Camber force or camber thrust is a function of the following parameters: tire type, tire geometry, pressure, tread pattern, camber angle, slip angles, traction or braking force, and the tire dimensions.

Camber thrust is easily understood by examining the contact patch of a tire. If the contact patch of the tire is examined when the vehicle is not moving with no camber angle, it will be an oval shape which represents the area the tire is in contact with the ground. If he contact patch is examined when the vehicle is not moving with a camber angle the contact patch will be an oval shape but will be curved in the direction of the tilt of the tire.

 If the contact patch is examined when the vehicle is moving with no sideslip angle and with a camber angle the contact will be an oval shape that will not be distorted or curved (Figure 14: The effect camber has on the tire contact patch).

Figure : The effect camber has on the tire contact patch 

The camber thrust is the amount of force required to straighten out the contact patch so that it is perfectly oval. Therefore, there are two things which generate a lateral force; camber angle and slip angle. The lateral force generated by a slip angle will be greater than the lateral force generated by a camber angle; that is the lateral force generated from 1 degree of slip angle will be greater than the lateral force generated from 1 degree of camber angle. The cornering stiffness  is generally five to six times greater than the camber stiffness. Thus, the effective cornering stiffness of a tire is the addition of the cornering stiffness and the camber stiffness and it is this value that should be used to predict the handling dynamics of a vehicle. For a tire that has a positive camber angle the effect is to decrease the effective cornering stiffness, and for a tire that has a negative camber angle, the effect is to increase the effective cornering stiffness. Therefore, the peak lateral force is increased by adding negative camber to the tires which is a good thing; the lateral capabilities of the tire are increased (Figure 15: The effect of the camber angle on the cornering curve)

Figure 36: The effect of the camber angle on the cornering 

As can be seen in the figure above, the effective cornering stiffness of the tire does increase as the tire is cambered in the negative direction. The camber angle at which the maximum amount of lateral force will occur will change with the initial lateral load (lateral load at 0 degree camber). As the initial load increases the maximum load will occur at a later negative camber angle. Typically the maximum amount of lateral force or maximum  will occur at a camber angle between -2 and -7 degrees. When a vehicle corners it will roll and thus will force the tires to camber by the same amount on both sides; the tires will camber at the roll angle on both sides, one will camber out and one will camber in. However, as the vehicle rolls, there will be weight transfer from the left to the right and thus the suspension on one side of the vehicle will be in jounce while the suspension on the other side will be in rebound. Therefore there will be a change in the camber angle from the movement of the tire with respect to the frame. Thus, the total camber angle when the vehicle is cornering is the addition of the roll angle and the camber angle obtained from the kinematics of the suspension. The amount of lateral force generated during roll will depend on both the roll angle and the angle generated from the kinematics of the suspension; that is the amount of camber thrust generated will depend on the roll angle. In general, it is best to go with a static negative camber angle because it improves the effective cornering stiffness of the tire and it increase the maximum lateral force or the Fy/Fz ratio. However too much of a negative camber angle is undesirable because eventually it will start to decrease both the cornering stiffness and the Fy/Fz ratio. Also, a large camber angle (negative or positive) increases tire wear which is undesirable. For best performance the camber angle should remain between -2 and -7 degrees throughout the suspension travel. In this FSAE car we are taking -3 degree camber. It can be seen in the image below. Camber angle> 180-183= -3 degree.

Castor angle

The caster angle is defined as the angle between the steering axis and the vertical plane viewed from the side of the tire. The caster trail is defined as the distance at the ground between the center of the contact patch (also known as wheel contact point) the point at which the steering axis intersects the ground (Figure 16: Caster angle and caster trail).

Figure 37: Caster angle and caster trail 

The caster angle is positive when the steering axis (the steering axis is defined as a line that passes through the ball joints on the upper and lower control arms) is inclined in such a way as it points to the front of the vehicle; a good way to remember positive caster angle is from the forks of a motorcycle (they are always inclined to the front). The caster angle defined in the figure above is a positive caster angle. Positive caster trail occurs when the steering axis intersects the ground at a point that is in front of the center of the contact patch. The caster trail defined in the figure above is a positive caster trail. It is important that the caster angle and caster trail be positive because both of these quantities will affect the aligning moment. The aligning moment is the moment that will act against the driver as he/she is trying to steer the vehicle. It is important that this moment acts against the driver so that when the driver lets go of the steering wheel it will correct itself; the moment will force the tire to re straighten itself.

 Caster trail is important because it defines how much of a moment will be applied to the steering axis; as the caster trail increases, the moment arm increases and thus the moment acting on the steering axis will increase. It is this moment that is acting to self-center the tire if the caster trail is positive. However, if the caster trail is too large the driver will have a difficult time trying to turn the wheels about the steering axis. Caster angle will cause the wheel to rise or fall during steering. Caster angle causes the wheel to displace up or down as the wheel is turning about the steering axis. Therefore, if the caster geometry is the same on both sides the vehicle will roll as it is being steered; one side will toe out and one side will toe in, thus one side will lift and one side will fall causing the vehicle to roll. The caster angle also affects the camber angle as the wheel is turned about the steering axis. With the same positive caster angle on both wheels the outside tire in a turn will camber in a negative direction and the inside tire will camber in a positive direction. This effect is a bit desirable because it allows the vehicle to lean into the turn. Therefore, it is desirable to have a small positive caster angle and a small to moderate caster trail to produce desirable results. The caster angle should not be increased too much because it will cause too much camber angle change with steer and will cause to tire to raise or fall too much with steer. In our FSAE car castor angle is 0 deg. It can be seen in the image below.

Toe angle, roll steer and bump steer

 The toe angle is defined as the angle between the longitudinal axis of the vehicle and a line passing through the center of the tire when viewed from the top (Figure 39: Toe angle).

Figure 39: Toe angle (note the view in the figure is the top view)

 Toe in occurs when the front of the tire points in towards the vehicle, and tow out occurs when the front of the tire points away from the vehicle. The concept of toe in and toe out is outlined in the figure above. The toe angle is a measure of the initial steer of the vehicle. There will be usually some elastic deformation of the suspension under driving or braking that will cause changes in the toe angle. Therefore, it is common practice to put an initial toe angle on the suspension system so that the deformation in the system will force the tire to straighten when the vehicle is driving or braking. The tire is usually toed so that the tire will be straight when the vehicle is propelling forward. However, if the braking acceleration is much higher than the driving acceleration then the tire will be initially toed in so that it will straighten itself when the vehicle is braking. It is important to recognize that the suspension and steering systems are coupled. As the suspension goes through its travel, so does the tie rod and it is important that the tire does not toe with suspension travel. The inside point of the tie rod is fixed (the point at the steering rack) so that if the length of the tie rod is not at the correct length and the tie rod does not have the same instant center as the suspension system then as the suspension travels and thus the tie rod travels (but not at the appropriate path) it will force the tire to rotate about the steering axis. Bump steer by definition is toe angle change with suspension travel. If one tire goes over a bump and experiences a toe angle change the vehicle will steer. This condition is very troublesome for the driver because the driver will consistently have to correct the vehicle as the vehicle travels over changes in road conditions. Roll steer occurs when a vehicle rolls and there is weight transfer and thus the suspension on the inside compresses and the suspension on the outside goes into rebound. The net effect is that one side of the vehicle will toe in and one side of the vehicle will toe out, thus forcing the vehicle to steer as it rolls. The steering geometry can be chosen such that the more the vehicle rolls the more it will steer or the less it will steer. Therefore, the over steer/understeer characteristics can be controlled by the roll steer effect. However, most of the time the suspension geometry and tie rod position and length are chosen to minimize toe angle change with suspension travel, and thus minimizing the effects of roll steer and bump steer. The following is a discussion of how to choose the position and the length of the tie rod in order to have no change in toe angle with suspension travel. This is a very important concept and needs to be considered when designing the suspension and steering systems. The tie rod should lie on a line passing through the instant center of the suspension system, and on this line a proper length can be chosen. The following is a list of the proper steps to take in order to choose the proper tie rod position and length.

1. Draw a line that passes through the steering axis (this line will pass through the ball joints of the upper and lower control arms)
2. Draw a line that passes through the joints of the A-arms at the inside section of the A-arms
3. Extend the lines drawn in steps 1 and 2 until they intercept, denote the interception point as P2
4. Locate the instant center of the suspension system, and denote it as P1 or IC
5. Draw a line that goes from the outer tie rod point to the instant center, note the tie rod must lie on this line
6. Draw a line that passes through the outer tie rod point and the outer point of the upper control arm (the ball joint)
7. Calculate the angle between the line passing through the tie rod ends to the IC (the line from step 5) and the line passing through the lower control arm points to the IC, and denote this angle α.
8. Draw a line that connects the IC to P2
9. Draw a line that is at an angle of α from the line drawn in step 8 and that starts from the IC; draw this line until it intercepts the line drawn in step 6, denote the interception point as P3
10. Draw a line that passes through P3 and the inner point of the upper control arm and extend it until it intercepts the line from step 5
11. The interception point from step 10 locates the point where the inner tie rod point must lie to have no toe angle change with wheel travel.

Figure 40: The necessary steps to locate the tie rod position to have no toe angle change with suspension travel

There is essentially two things that can be changed in order to deviate from the ideal position and length. The first is to change the tie rod length and the second is to raise or lower the steering rack. If the tie rod is shortened the deflection of the suspension will cause toe out, and if it is lengthened the deflection of the suspension will cause toe in. If the steering rack is raised the tire will toe in when it is in compression and will toe out when it is in rebound (roll steer behavior). The opposite is true if the steering rack is lowered.

 In order for the wheels to roll without slip (especially at low speeds) there must be toe out with steer. Therefore the toe angle must change with the steering angle. This can be seen on most steering angle versus toe angle curves. It is not a linear relationship between the two. This effect is usually known as Ackermann steering; the effect that there must be some toe out with steer. For proper Ackermann steering to be designed into the suspension system.

If Ackermann geometry is introduced into the suspension system, then there will be an increase in the slip angles at the outer tires when the vehicle is turning. Therefore, using higher slip angles at the outer tire tends to generate more lateral forces with less steer angles and rolling losses. The location of the rack position in respect to the longitudinal position effects the amount of Ackermann steering generated. Therefore the height of the rack and the size of the rack will be chosen first in order to optimize the bump steer and roll steer characteristics of the suspension system. The longitudinal position of the rack will be chosen last in order to obtain the desired amount of Ackermann steering. Most of the time a little bit of Ackermann steering is designed into the suspension system. However, severe deviations from Ackermann steering lead to tire wear because deviations from Ackermann lead to tire scrub.

Scrub Radius

The scrub radius is the distance in front view between the steering axis and the center of the contact patch of the wheel, where both would theoretically touch the road. Scrub radius in our FSAE car is

Kingpin angle and scrub radius

The kingpin angle is the angle between the steering axis and the vertical plane when viewing the tire from the front. The scrub radius is the distance measured at the ground level between the center of the contact patch and the point where the steering axis intercepts the ground. The scrub radius is measured when looking at the wheel from the front plane (Figure 38: Kingpin angle (steering inclination angle) and scrub radius). A positive kingpin angle occurs when the steering axis points outward; note the kingpin angle defined in the figure is positive. A positive scrub radius occurs when the steering axis intercepts the ground at the inside of the tire; note the scrub radius shown in the figure is a positive scrub radius.

It is important that the kingpin angle and scrub radius are positive because both of these quantities will affect the aligning moment. The aligning moment is the moment that will act against the driver as he/she is trying to steer the vehicle. It is important that this moment acts against the driver so that when the driver lets go of the steering wheel it will correct itself; the moment will force the tire to re straighten itself. The effect of a positive kingpin angle is to raise the wheel as the wheel is turned about the kingpin axis. The greater the kingpin angle is the more the wheel will rise as it is being steered. Note, the wheel will rise regardless of the direction it is being turned. It is to be noted that the greater the distance between the ball joints for a given kingpin angle the greater the amount of lift that will occur. Essentially, the kingpin angle and the length between the ball joints is trying to raise the wheel so that it can center the steering axis to provide less scrub while steering.

Figure 38: Kingpin angle (steering inclination angle) and scrub radius

The kingpin angle affects the camber angle as the wheel is steered about the steering axis. With a positive kingpin angle, the tire will lean out as it is steered about the steering axis. Therefore, the greater the steering angle, the greater the amount of positive camber generated, and the greater the kingpin angle the greater the amount of change in the camber angle. When a wheel is rolling over a bump, the effective rolling radius of the tire will change, thus resulting in changes in the effective rolling speed of the tire. The change in the rolling speed of the tire will give rise to a longitudinal force acting at the wheel center, and this causes a kickback into the steering system. The reaction forces caused by the change in the rolling speed will try to force the wheel to toe, and thus cause a shock to the driver, and the driver will have to react quickly in order to correct this change in toe angle. The amount of kickback is proportional to the distance between the ball joints, the greater the distance, the greater the amount of kickback. Driving and braking forces will introduce a torque about the steering axis, and this torque will be proportional to the moment arm, the scrub radius. If the driving and braking forces are different on either side of the vehicle than the driver will feel a net steering torque acting to steer the vehicle. The amount the tire scrubs against the ground as the wheel turns is dependent on the scrub radius. If one the wheels losses traction when the vehicle is braking then the opposing wheel will toe an amount that is determined by the compliance in the steering system. This will tend to steer the car in a straight line even though the braking forces are the same on both sides. Note the last effect described will only occur when the scrub radius is negative. In general, a small negative scrub radius is desired, however if the scrub radius is negative than the kingpin angle will be have to be large in order to ensure the aligning torque is positive.

 Typically, a small positive scrub radius is used on vehicles with a small to moderate kingpin angle is used. If the distance between the ball joints is large then a smaller kingpin angle is used and if the distance is small then moderate kingpin angles are used.

In our FSAE car kingpin angle is 5.82 degree and scrub radius is 70.58mm. it can be seen from the image given below.

Anti-dive/anti-squat

There will be weight transfer from the back to the front when the vehicle is braking and from the front to the back when the vehicle is accelerating. The anitdive/ anti-squat properties of a suspension are similar to the roll center concept applied earlier (5.2.2). The anti-dive/anti-squat concept applies to the longitudinal force where as the roll center concept applies to the lateral force. A portion of the forces will pass through the suspension components and be transferred to the frame, and this amount is depicted by the amount of anti-dive or anti-squat present. In the study of anti-dive/antisquat the roll center is known as the pitch center. The definition of the pitch canter is the same as that of the roll center except it is the longitudinal force and not the lateral force that is applied at the pitch center. The pitch center is the location where the longitudinal forces can be applied without causing the vehicle to pitch.

The location of the pitch center is found in a similar way as that of the roll center except it is calculated by looking at the vehicle from the side. The following is the necessary steps to calculate the pitch center for double A-arm type of suspension only (note to calculate the pitch center for a different type of suspension it is advised to refer to a vehicle dynamics text). The first step is to locate the instant center of the front or rear suspension in the side plane of the vehicle. This is done by drawing a line that passes through both of the A-arms (the upper and the lower A-arm) and the interception of these lines represents the instant center. The next step is to draw a line which connects the point at the center of the contact patch of the tire to the instant center. If the previous steps were done for the front suspension, repeat the steps for the rear suspension. The location where the lines going from each of the center of the tire contact patch to the instant center of their appropriate suspension intercept one another represents the pitch center. The following drawing can be used for clarification (Figure 20: The pitch center).

Figure 41: The pitch center 

The pitch center can be used to indicate the amount of pitch generated. The distance between the height of the pitch center and the height of the center of mass of the vehicle gives an indication of the amount of pitch. The smaller this distance is the smaller the amount of pitch generated will be. However, just like with the roll center is the fact that the amount of jacking forces increases as the height of the pitch center is increased. Thus there should be a compromise in the height of the pitch center; it should not be too high because the jacking forces will be too high and it should not be too low because there will be too susceptible to pitch.

The path of the tire in the longitudinal direction as a function of suspension travel will determine whether the suspension is classified as anti-dive or anti-squat. If the suspension is classified as anti-dive the point of contact of the tire will move forward (towards the front of the vehicle) as the suspension compresses and with move rearward as the suspension extends (goes into rebound) (Figure 21: Anti-dive suspension geometry). If the suspension is classified as anti-squat the point of contact of the tire will move rearward as the suspension compresses and will move forward as the suspension extends (Figure 22: Anti-squat suspension geometry). Anti-dive designed into the suspension system leads to harsh response over bumps; the suspension will be trying to push into the bump instead of riding over it with ease. As the suspension goes over a bump it will compress, and when the anti-dive suspension compresses it moves forward and thus tries to push into the bump. This tends to cause a harsh response, and in some cases can induce vibrations in the system which can be felt by the driver. However, antisquat designed into the suspension improves the performance of the suspension. The suspension will ride over bumps with ease. As the suspension goes over a bump it compresses and moves rearward, thus it will follow the path of the bump with ease and give the indication of a smooth ride to the driver.

Figure 42: Anti-dive suspension geometry 

If anti-dive is designed into the suspension system it will prevent the vehicle from diving; the vehicle dives when it is braking. If anti-squat is designed into the suspension system it will prevent the vehicle from squatting. If anti-squat is designed into the suspension it will assist the vehicle at diving, and if anti-dive is designed into the suspension it will assist the vehicle at squatting. Therefore, it is common proactive to use a small percentage of anti-squat in the rear and a small percentage of anti-dive in the front.

Figure 43: Anti-squat suspension geometry 

The reason why anti-squat is designed in the rear is that when the vehicle is squatting weight is transferred to the rear. Therefore the effect of designing the suspension to prevent the vehicle from squatting will be greater by designing anti-squat into the rear suspension because the weight is being transferred to the rear. This is the same reason why anti-dive is designed into the front suspension; when the vehicle is diving weight is being transferred to the front. However, since anti-dive leads to a harsh response over bumps which are detrimental to the suspension system, therefore a small amount of anti-squat is typically designed into the suspension to optimize the performance of the suspension. It is important that the amount of anti-squat be kept to a small percentage in both the front and rear when they are both designed for anti-squat. This is what is typically done to suspensions today, a small amount of anti-squat is designed into both the front and rear in order to improve the response of the suspension to changes in road conditions.

Motion ratio and wheel rate

The motion ratio describes the amount of shock travel for a given wheel travel. The motion ratio is simply the shock travel divided by the wheel travel. A motion ratio of 0.6 implies that the shock will compress 0.6 inches when the wheel compresses 1 inch (Figure 44: Motion ratio). As the motion ratio decreases the control arms will have to be built stronger because the effective bending moment acting on them will increase. The effective bending moment will increase because the moment arm will increase; the moment arm is defined as (d2 – d1) from figure 44. Therefore it is more ideal to have a motion ratio as close to one as possible so that the load put on the control arms is kept to a minimum so that they can be designed as light as possible thus decreasing the unsprung mass.

Figure 44: Motion ratio 

The amount of force transmitted to the vehicle chassis is reduced when the motion ratio increases. This implies that the wheel rate will increase as the motion ratio increases. Since the motion ratio relates both the force and displacement of the spring to the wheel center, it must be squared to relate the wheel rate (also known as wheel center rate) to the spring rate (if the motion ratio is reduced then the amount of spring travel and the amount of force absorb by the spring will decrease).