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Home , Chapman strut, Roll center, Swing axle, Torque tube

SUSPENSION SYSTEM Suspension - set of elements connecting with vehicles’ body

• A vehicle suspension is required to perform effectively under a range of operating conditions including high levels of braking and accelerating, cornering at speed and traversing rough terrain – manoeuvres which are required to be done in comfort and with safety. • Suspension system connects vehicles body with wheel and its and allow vertical movement of the wheel in relation to body. • The , through the suspension linkage, must propel, steer, and stop the vehicle, and support the associated forces. Suspension system

1. To provide good ride and handling performance – this requires the suspension to have vertical compliance providing isolation and ensuring that the wheels follow the road profile with very little tire load fluctuation; 2. To ensure that control is maintained during maneuvering – this requires the wheels to be maintained in the proper positional attitude with respect to the road surface; 3. To ensure that the vehicle responds favorably to control forces produced by the as a result of longitudinal braking and accelerating forces, lateral cornering forces and braking and accelerating torques – this requires the suspension geometry to be designed to resist squat, dive and roll of the vehicle body; 4. To provide isolation from high frequency vibration arising from tire excitation – this requires appropriate isolation in the suspension joints to prevent the of ‘road noise’ to the vehicle body.

Types of suspension system

• Each spatial body with six degrees of freedom can be constrained with suitable elements – like rod links – to reduce the number of DoF • A suspension system should provide one degree of freedom for the wheel. This can be done in different ways for example by adding 5 rod link – each of which would “fix” one degree of freedom. • In real suspension systems links constrain wheel carriers – which can be “carry” one or more wheels. Types of suspension system Factors which primarily affect the choice of suspension type at the front or rear of a vehicle are engine location and whether the wheels are driven/undriven and /or steered /unsteered. In general, suspensions can be broadly classified as dependent or independent types. Dependant suspension system (rigid). Both wheels are mounted to jointed, rigid which is fixed with frame or body by means of elements. Independant suspension system. Each wheel is fixed to the body (or frame) individually. Dependant suspension system is used in majority of trucks, and in some passenger as a suspension of rear driving axle

The advantage of a dependant suspension system is its simplicity, which is especially important in vehicles with significant load on axles Independant suspension system has more advantages comparing with dependent suspension systems, and therefore their more frequent usage, especially in trucks, can be observed in recent years. Most significant advantages are: • Reduction of of the vehicle. • Favourable suspension kinematics in terms of driving stability. • Possibility of very soft spring elements application Dependent suspension Solid-axle, leaf-spring • A solid axle is one in which wheels are mounted at either end of a rigid beam so that any movement of one wheel is transmitted to the opposite wheel causing them to steer and camber together • Solid beam axles are commonly used on the front of heavy trucks where high load-carrying capacity is required • is readily maintained, minimizing tire wear • The major disadvantage of solid steerable axles is their susceptibility to tramp-shimmy steering vibrations • When a live solid axle is connected to the body with nothing but two leaf springs, it is called the , • Leaf springs are not suited for taking up the driving and braking traction forces. • These forces tend to push the springs into an S-shaped profile • The driving and braking flexibility of leaf springs, generates a negative caster and increases instability

JAZAR, R. N. 2008. : Theory and Application, Springer US. Dependent suspension Solid-axle, leaf-spring • To reduce the effect of a horizontal force and S- shaped profile appearance in a solid axle with leaf springs, the axle may be attached to the chassis by a longitudinal bar - anti-tramp • Although an anti-tramp bar may control the shape of the , it introduces a twisting angle problem when the axle is moving up and down, • Twisting the axle and the wheel about the axle is called caster • If the right wheel goes over a bump, the axle is raised at its right end, and that tilts the left wheel hub, putting the left wheel at a for the duration of deflection.

JAZAR, R. N. 2008. Vehicle Dynamics: Theory and Application, Springer US. Rigid Axles with Longitudinal and Lateral Links • The elements which control the motion of a rigid rear axle must allow translation in the vertical direction as well as rotation about the vehicle’s longitudinal axis. To enable these motions, the axle must be connected to the vehicle’s body with at least one ball joint and one link element. • The lightweight, frictionless coil springs which provide the springing function for these designs do not play a role in controlling the axle’s motion in the lateral or longitudinal directions. • Lateral forces are transmitted between the axle and the vehicle’s body by a or one of the other types of linkages. The motion of a Panhard rod causes the vehicle’s body to shift laterally during compression and rebound. This lateral motion can be eliminated by using a Watt’s linkage for lateral control.

HEIßING, B. & ERSOY, M. 2010. Chassis Handbook: Fundamentals, JAZAR, R. N. 2008. Vehicle Dynamics: Theory and Driving Dynamics, Components, Mechatronics, Perspectives, Application, Springer US. Vieweg+Teubner Verlag. Dependent suspension Solid-axle • In other cases, there have been problems, such as axle tramp, particularly when high tractive force is used. To locate the axle more precisely, or more firmly, sometimes additional links are used, such as the longitudinal traction bars above the axle, opposing pitch rotation • In other cases, the leaf springs have been retained as the sole locating members but with the springing action assisted by coils, giving good load spreading into the body. • with the readier availability of coil springs, in due course the rear leaf-spring axle finally disappeared from passenger cars, typically being replaced by the common with four locating links, this system being used by several manufacturers. • In response to the shortcomings of leaf spring suspensions, the four-link rear suspension • The lower control arms provide longitudinal control of the axle while the upper arms absorb braking/driving torques and lateral forces. • Occasionally, the two upper arms will be replaced by a single, triangular arm, but it remains functionally similar to the four-link. • The ability to use coil springs (or air springs) in lieu of leaf springs provides better ride and NVH by the elimination of the coulomb friction characteristic of leaf DIXON, J. 2009. Suspension Analysis and Computational springs. Geometry, Wiley. Dependent suspension Solid-axle

• The basic geometry of the four-link system is retained in the T-bar system with the cross- arm of the T located between longitudinal ribs on the body, allowing pivoting with the tail of the T, connected to the axle, able to move up and down in an arc in side view. • The rigid axle is sometimes fitted with a rigid tube going forward to a cross member in which it can rotate as in a ball joint. This, perhaps confusingly, is called a ‘torque tube’, presumably because it reacts to the pitch effect of torque in the driveshafts acting on the wheels. It does give very good location of the axle in pitch. Additional lateral location is required at the rear, such as by a Panhard rod

DIXON, J. 2009. Suspension Analysis and Computational Geometry, Wiley. Undriven Rigid Axles • Undriven rigid axles, used at the rear of front-drive vehicles, have the same geometric location requirements as live rigid axles, but are not subject to the additional forces and moments of the driveaction, and can be made lower in mass. • lateral location can be optained by the long diagonal member. This form eliminates the lateral displacements in bumpof the Panhard rod. If the longitudinal links are fixed rigidly to the axle then the axle acts in torsion as an anti-roll bar, the system then being a limiting case of a trailing-twist axle.

DIXON, J. 2009. Suspension Analysis and Computational Geometry, Wiley. Semi-dependent systems

• In this form of suspension, the rigid connection between pairs of wheels is replaced by a compliant link. This usually takes the form of a beam which can bend and flex providing both positional control of the wheels as well as compliance. Such systems tend to be very simple in construction but lack scope for design flexibility. Independant suspension:

A broad term for any automobile suspension system that allows each wheel on the same axle to move vertically (i.e. reacting to a bump in the road) independently of each other. Note that “independent” refers to the motion or path of movement of the wheels. It is common for the left and right sides of the suspension to be connected with anti-roll bars or other such mechanisms. The anti-roll bar ties the left and right suspension spring rates together but does not tie their motion together. Disadvantages: • Occurrence of the moment increasing side roll • Inclination of wheels along with the body while cornering • Different values of side forces on right and left wheels

 - angle of body inclination while cornering;  -

angle of wheel lean; FY,W,f,i lub O – side forces; mBo,f - the part of mass applied on front axle; Fc,Bo,f - centrifugal force Independent Suspension

Independent suspensions is introduced to let a wheel to move up and down without affecting the opposite wheel Their main advantages are: little space requirement; • a kinematic and/or elastokinematic -in change, tending towards understeering • is possible • easier steerability with existing drive; • low weight; • no mutual wheel influence.

REIMPELL, J., STOLL, H. & BETZLER, J. 2001. The Automotive Chassis: Engineering Principles, Elsevier Science. Independent Suspension

JAZAR, R. N. 2008. Vehicle Dynamics: Theory and Application, Springer US.

The may be between the lower arm The McPherson is a further development of double wishbone suspension. The upper transverse and the chassis,. It is also possible to install the link is replaced by a pivot point on the wheel house spring between the upper arm and the chassis, panel, which takes the end of the piston rod and the or between the upper and lower arms. In coil spring. Forces from all directions are either case, the lower or the upper arm, which concentrated at this point and these cause bending supports the spring, is made stronger and the stress in the piston rod. other arm acts as a connecting arm. Independent Suspension When the two side bars of an A-arm are attached to each other with a joint, then the double A-arm is called a multi-link mechanism. A multi-link mechanism is a six-bar mechanism that may have a better coupler motion than a double A-arm mechanism. However, multi link suspensions are more expensive, less reliable, and more Complicated compare to a double A-arm four-bar linkage. There are vehicles with more than six-link suspension with possibly better kinematic performance. JAZAR, R. N. 2008. Vehicle Dynamics: Theory and Application, The main advantages of the double wishbone Springer US. suspension are its kinematics

HEIßING, B. & ERSOY, M. 2010. Chassis Handbook: Fundamentals, Driving REIMPELL, J., STOLL, H. & BETZLER, J. 2001. The Dynamics, Components, Mechatronics, Perspectives, Vieweg+Teubner Verlag. Automotive Chassis: Engineering Principles, Elsevier Science. Independent Suspension

Modern McPherson-type suspension systems feature a coil spring inclined in three dimensions located above the wheel. The spring is oriented such that its central axis is offset from the axis of the damper’s piston rod . The forward end of JAZAR, R. N. 2008. Vehicle Dynamics: Theory and Application, the crescent-shaped lower three-point Springer US. is connected to the wheel carrier via a ball joint. This allows the wheel carrier to rotate freely with respect to the control arm

HEIßING, B. & ERSOY, M. 2010. Chassis Handbook: Fundamentals, Driving Dynamics, Components, Mechatronics, Perspectives, Vieweg+Teubner Verlag. Independent Rear Driven

• The most common early independent driven suspension was the simple , which has the advantage of constant driveshaft lengths, and low unsprung mass

DIXON, J. 2009. Suspension Analysis and Computational Geometry, Wiley. Independent Driven

The Chapman strut is a strut suspension in which the lower lateral location is provided by a fixed-length driveshaft.

DIXON, J. 2009. Suspension Analysis and Computational Geometry, Wiley. Independent Driven multilink relatively recent extension of the wishbone concept is to separate each wishbone into two separate simple links. There are then five links in total, two for each wishbone and one steer angle link. This system has been used at the front and the rear, and, with careful design, makes possible better control of the geometric and compliance properties. The advantages seem real for driven rear axles, but undriven ones have not adopted this scheme. The concept has also been used at the front for steered wheels

DIXON, J. 2009. Suspension Analysis and Computational Geometry, Wiley. Multi-arm suspension • Advantages : • Obtaining arbitrary offset radius and arm of the disturbing force, • compensation of longitudinal, pitching while braking and accelerating , • Favourable wheel inclination in terms of toe-in, tire wear etc., • Appropriate longitudinal susceptibility obtained without loss of vehicle steering precision, • Disadvantages: • More complicated design, • Higher cost of production, • Possible occurrence of kinetic incompatibility, • Sensitive on joint wear, • Greater requirements for of defamations and durability maintenance, Independent Undriven

DIXON, J. 2009. Suspension Analysis and Computational Geometry, Wiley. Trailing-Twist Axles

• This design is a logical development of the fully- independent trailing-arm system. Beginning with a simple pair of trailing arms, it is often desired to add an anti-roll bar. Originally, this was done by a standard U-shaped bar with two mountings on the body locating the bar, but allowing it to twist. Drop links connected the bar to the trailing arms. • A disadvantage of this basic system was that the anti-roll bar transmitted extra noise into the passenger compartment, despite being fitted with rubber bushes. This problem was reduced by deleting the connections to the body, instead using two rubber-bushed connections on each trailing arm, so that the bar was still constrained in torsion DIXON, J. 2009. Suspension Analysis and Computational Geometry, Wiley.

REIMPELL, J., STOLL, H. & BETZLER, J. 2001. The Automotive Chassis: Engineering Principles, Elsevier Science. • Some manufactures describes rear suspension systems by their own definition, which only sometimes correctly defines the original designs, nevertheless it is common that typical systems are only different by its name. • Double wishbone (Honda Accord, Jaguar S Type) independent suspension with double lateral arm; this solution has sport origin • Delta Link (Volvo), Multilink (Mercedes) both are names of multi-arm suspension system where the only difference is various number and configuration of the control arms. • Scott-Russell rod (Nissan Primera) - a kind of sectional lateral arm with two internal joints, that cooperates with torsion axle which connects the trailing arms; this system is similar to historical suspension of rigid axle laterally fixed by means of Watt rod. Roll Center and Roll Axis

Roll centre and roll axis concepts are important aids in studying vehicle handling, enabling simplifications to be made in load transfer calculations for cornering operations.

There are two definitions of roll center, one HAPPIAN-SMITH, J. 2001. An Introduction to Modern Vehicle based on forces and the other on kinematics. Design, Butterworth-Heinemann. 1. point in the transverse plane through any pair of wheels at which a transverse force may be applied to the sprung mass without causing it to roll. 2. the roll center is the point about which the body can roll without any lateral movement at either of the wheel contact areas

• In general each roll center lies on the line produced by the intersection of the longitudinal center plane of the vehicle and the vertical transverse plane through a pair of wheel centers. • The line joining the centers is called the roll axis, with the implication that a transverse force applied to the sprung mass at any point on this axis will not cause Roll Center and Roll Axis • The position of the roll centers at the front and back and the course of the direction line joining these – the roll axis C is of decisive importance for the handling properties: the height of the roll centers determines both the wheel load differences of an axle and hence the self-steering properties of the vehicle through the tire properties, as well as the necessary roll suspension, which is again crucial to comfort in the case of unilateral deflection where a high level of roll rigidity is required and a stabilizer is used. • The position of the roll center also depends on the instantaneous position of the wheel links • The height of the roll center and the change in the roll center with wheel travel is consequently a compromise between the following requirements • defined changes in wheel load during cornering to achieve the required (understeering) self- steering properties; • track changes with wheel travel which are not critical for the dynamics of vehicle movement; • roll spring stiffness which is not crucial to comfort; • desired – or permissible – camber change; • as small as possible reaction forces acting on the body; • the position of the roll axis.

The roll axis should rise slightly towards the rear in order to make use of fractions of the body damping to damp the yawing movements of the vehicle.

REIMPELL, J., STOLL, H. & BETZLER, J. 2001. The Automotive Chassis: Engineering Principles, Elsevier Science. Roll Center and Roll Axis

• The design of a chassis firstly requires the determination of the height hRo,f of the front body roll center (dependent on the track alteration) so that, in a second step, an appropriate rear axle can be provided; in the case of independent wheel suspensions with a slightly higher • If the vehicle is fitted with a rigid axle, the body enjoys less anti-roll support on bends as a result of the shorter effective distance of the springs relative to the track • To balance this out, it is recommended that the body roll center be designed slightly higher at the rear

REIMPELL, J., STOLL, H. & BETZLER, J. 2001. The Automotive Chassis: Engineering Principles, Elsevier Science. Roll Center and Roll Axis • The roll axis is the instantaneous line about which the body of a vehicle rolls. Roll axis is found by connecting the roll center of the front and rear suspensions of the vehicle. Assume we cut a vehicle laterally to disconnect the front and rear half of the vehicle. Then, the roll center of the front or rear suspension is the instantaneous center of rotation of the body with respect to the ground. • To find the roll center of the body with respect to the ground, we analyze the two-dimensional kinematically equivalent mechanism • The center of tireprint is the instant center of rotation of the wheel with respect to the ground, so the wheels are jointed links to the ground at their center of tireprints. • The instant center 퐼18 is the roll center of the body with respect to the ground. • To find 푰ퟏퟖ, we apply the Kennedy theorem and find the intersection of the line 퐼12퐼28 and 퐼13퐼38 • The point 퐼28 and 퐼38 are the instant center of rotation for the wheels with respect to the body. The instant center of rotation of a wheel with respect to the body is called suspension roll center • So, to find the roll center of the front or rear half of a , we should determine the suspension roll centers, and find the intersection of the lines connecting the suspension roll centers to the center of their associated tireprints.

The Kennedy theorem states that the instant center

of every three relatively moving objects are colinear. JAZAR, R. N. 2008. Vehicle Dynamics: Theory and Application, Springer US. Roll Center internal or external

• Roll center of an independent suspension can be internal or external. • An internal suspension roll center is toward the vehicle body, while an external suspension roll center goes away from the vehicle body. • A suspension roll center may be on, above, or below the road surface,

JAZAR, R. N. 2008. Vehicle Dynamics: Theory and Application, Springer US. Roll Center and Roll Axis McPherson • A McPherson suspension is an inverted slider crank mechanism. • The point 퐼12 is the suspension roll center, which is the instant center of rotation for the wheel link number 2 with respect to the chassis link number 1. The more vertical the McPherson and dampers and the more horizontal the lower control arm GD1, the closer the body roll center Ro is to the ground. This results in an adverse camber alteration when the wheels are in bump travel. Lengthening the lower suspension control arm (point

D1 to D2) improves the kinematic properties.

JAZAR, R. N. 2008. Vehicle Dynamics: Theory and Application, Springer US.

REIMPELL, J., STOLL, H. & BETZLER, J. 2001. The Automotive Chassis: Engineering Principles, Elsevier Science. Roll Center

• The height of the (instantaneous center of rotation) P determines the position of the body roll center Ro • If P is above ground level, Ro will also be above ground. • The virtual center of rotation distance q from virtual center of rotation to tire contact-patch center can be measured or calculated simply

REIMPELL, J., STOLL, H. & BETZLER, J. 2001. The Automotive Chassis: Engineering Principles, Elsevier Science. Suspension relative angles Vehicle geometry

HAPPIAN-SMITH, J. 2001. An Introduction to Modern Vehicle Design, Butterworth-Heinemann. Suspension relative angles Camber • Camber is the angle of the wheel relative to vertical line to the road, as viewed from the front or the rear of the car. If the wheel leans in toward the chassis, it is called negative camber and if it leans away from the car, it is called positive camber. • A tire develops its maximum lateral force at a small camber angle. This fact is due to the contribution of camber thrust, which is an additional lateral force generated by elastic deformation as the tread rubber pulls through the tire/road interface. • To optimize a tire’s performance in a turn, the suspension should provide a slight camber angle in the direction of rotation. • The more the wheel must deflect from its static position, the more difficult it is to maintain an ideal camber angle. • When a vehicle is loaded with two or three persons a slightly positive camber would be useful on passenger cars to make the tires roll as upright as possible on the slightly transverse-curved road surface and give more even wear and lower rolling resistance.

JAZAR, R. N. 2008. Vehicle Dynamics: Theory and Application, Springer US. Suspension relative angles Swivel pin offset • Swivel pin or kingpin inclination is the lateral inward tilt (inclination) from the top between the upper and lower swivel ball joints or the kingpin to the vertical • If the swivel ball or pin axis is vertical (perpendicular) to the ground, its contact center on the ground would be offset to the center of the tire contact patch • If the swivel ball or pin axis is vertical (perpendicular) to the ground, its contact center on the ground would be offset to the center of the tire contact patch. The offset between the pivot center and contact patch center is equal to the radius (known as the scrub radius) of a semicircular path followed by the rolling wheels when being turned about their pivots. • No offset (zero offset radius) prevents the tread rolling and instead causes it to scrub as the wheel is steered so that at low speed the steering also has a heavy response • A compromise is usually made by offsetting the pivot and contact wheel centers to roughly 10-25% of the tread width for a standard sized tire.

Pivot inclination produces a self-centring action which is independent of vehicle speed or traction but is dependent upon the weight concentration on the swivel joints and their inclin-ation. A typical and popular value would be 8 or 12°.

HEISLER, H. 2002. Advanced Vehicle Technology, Butterworth- Heinemann Suspension relative angles Caster • Caster is the angle to which the steering pivot axis is tilted forward or rearward from vertical, as viewed from the side. • If the steering axis is turned about the wheel yw-axis then the wheel has positive caster • If the steering axis is turned about the wheel −yw-axis, then the wheel has negative caster. • Negative caster aids in centering the after a turn and makes the front tires straighten quicker thus is used to enhance straight-line stability. • Most street cars are made with 4−6deg negative caster • Zero castor provides: easy steering into the corner, low steering out of the corner, low straight-line stability. • Negative caster provides: low steering into the corner, easy steering out of the corner, more straight- line stability, high tireprint area during turn, good turn-in response, good , good steering feel. • When a castered wheel rotates about the steering axis, the wheel gains camber. This camber is generally favorable for cornering

HEISLER, H. 2002. Advanced Vehicle Technology, Butterworth- JAZAR, R. N. 2008. Vehicle Dynamics: Theory and Application, Springer US. Heinemann Suspension relative angles Toe • The amount of toe can be expressed in degrees of the angle to which the wheels are not parallel. • Toe settings affect three major performances: tire wear, straight-line stability, and corner entry handling • For minimum tire wear and power loss, the wheels on a given axle of a car should point directly ahead when the car is running in a straight line • Excessive toe-in causes accelerated wear at

the outboard edges of the tires, JAZAR, R. N. 2008. Vehicle Dynamics: Theory and Application, Springer US. • too much toe-out causes wear at the inboard edges • Toe-in increases the directional stability of When driving torque is applied to the wheels, the vehicle (makes the steering function they pull themselves forward and try to lazy) create toe-in. Furthermore, when pushed • toe-out increases the steering response down the road, a non-driven wheel or a (makes the vehicle unstable) braking wheel will tend to toe-out. Suspension relative angles Toe

• Front toe-in: slower steering response, more straight-line stability, greater wear at the outboard edges of the tires.

• Front toe-zero: medium steering response, minimum power loss, minimum tire wear.

• Front toe-out: quicker steering response, less straight-line stability, greater wear at the inboard edges of the tires. JAZAR, R. N. 2008. Vehicle Dynamics: Theory and Application, Springer US.

• Rear toe-in: straight-line stability, traction out of the corner, more steerability, higher top speed. Suspension relative angles Trust angle

• The trust angle υ is the angle between vehicle’s centerline and perpendicular to the rear axle. It compares the direction that the rear axle is aimed with the centerline of the vehicle. • Zero angle confirms that the rear axle is parallel to the front axle, and the on both sides of the vehicle are the same.

JAZAR, R. N. 2008. Vehicle Dynamics: Theory and Application, Springer US. Literature

1. CROLLA, D. 2009. Automotive Engineering e-Mega Reference, Elsevier Science. 2. GARRETT, T. K., NEWTON, K. & STEEDS, W. 2000. Motor Vehicle, Elsevier Science. 3. GILLESPIE, T. D. 1992. Fundamentals of Vehicle Dynamics, Society of Automotive Engineers. 4. HAPPIAN-SMITH, J. 2001. An Introduction to Modern Vehicle Design, Butterworth- Heinemann. 5. HEISLER, H. 2002. Advanced Vehicle Technology, Butterworth-Heinemann. 6. HEIßING, B. & ERSOY, M. 2010. Chassis Handbook: Fundamentals, Driving Dynamics, Components, Mechatronics, Perspectives, Vieweg+Teubner Verlag. 7. JAZAR, R. N. 2008. Vehicle Dynamics: Theory and Application, Springer US. 8. KARNOPP, D. 2004. Vehicle Stability, CRC Press. 9. LEON, P. 2008. Mechanika ruchu, Warszawa, WKŁ. 10. NUNNEY, M. 2015. Light and Heavy Vehicle Technology, Routledge. 11. RAJAMANI, R. 2011. Vehicle Dynamics and Control, Springer US. 12. REIMPELL, J., STOLL, H. & BETZLER, J. 2001. The Automotive Chassis: Engineering Principles, Elsevier Science. 13. WONG, J. Y. 2001. Theory of Ground Vehicles, Wiley.