In automotive engineering a multitude of different wheel suspensions is used.
Independent from the type of the respective wheel suspension it is intended that the wheels are lead at the vehicle body in a way in which the potential of the wheels is used optimally in all driving situations. Next to functionality, other aspects such as weight, space requirements as well as cost play an important role in the design of the chassis. Therefore, depending on the car classification and consequentially the requirements regarding comfort, driver safety and cost as well as constructive aspects, propelled, or not propelled, guided or unguided axes are used.
Over the course of decades, the composition of wheel suspensions has devel- oped into three fundamentally different concepts:
• beam axle, the oldest known form of wheel suspension,
• twist-beam rear suspension, that are especially used as rear axles without drive shaft,
• independent suspension in which the following two forms are distinguished:
– independent suspension with one pivot axis and – independent suspension with more than one pivot axis.
Typical independent suspensions with one rotation axis are trailing-arm, wishbone and semi trailing-arm axles. Typical independent suspensions with more than one rotation axis are double wishbone axles as well as suspension struts under the MacPherson principle. Multilink axles for which single rotation axes are not clearly distinguishable are counted towards the group of the independent sus- pensions with more than one rotation axis.
The following section presents a few practical implementations of the previ- ously named concepts. Attached one can find a short kinematic description with the main characteristics such as the number of kinematic loops, the number of bodies and joints as well as the consequential degree of freedom. Furthermore the advantages and disadvantages of the practical features of the respective concepts are illustrated.
6.2.1 Beam Axles
The solid connection of two wheels via a lateral axle is called a beam axle (Figs.6.2and6.3). Here, the two opposing wheels can influence each other. This concept originates from horse-drawn carriages. Today, beam axles are only very rarely used as the front axles of automobiles. It’s only in all-terrain vehicles that the beam axle has proven itself thanks to its good off-road characteristics. This kind of axle is used more frequently as power-driven rear axle in utility cars (Table6.1).
Fig. 6.2 Power-driven rigid front axle with Panhard bar of the Mercedes G-Class (courtesy of Daimler AG 2009)
Fig. 6.3 Rigid body model of the front axle of the Mercedes G-Class (without steering mechanism)
6.2.2 Twist-Beam Suspension
Twist-beam axles are a form of semi-rigid axle that, unlike rigid axles, allow relative movement between the wheel carriers as a result of the torsion of the axle beam. The axle beam is intentionally given elastic properties to combine the characteristics of beam axles and independent rear suspension. Both wheel carriers are attached to the torsional stiff and deflection-resistant trailing arms, which in turn are transversally connected via a deflection-resistant profile (cross member) with low torsional stiffness (Figs.6.4and6.5), (Table6.2).
Table 6.1 Model characteristics and features of the beam axle
Model Advantages Disadvantages
4 bodies Simple structure High space requirements 6 spherical
joints
Inexpensive Heavy
No change in track width high off-road articulation possible
Kinematic coupling of right and left side and therefore large camber variation for unilateral deflection high unsprung mass
496=24 Equations of motion 693=18 Constraints
6 DoF of the axles (vertical deflectionf1, rollf2, 4 isolated rotational DoFf3,f4,f5,f6) 2 Kinematic loops L1and L2
rigid axle trailing arm
trailing arm
Fig. 6.4 Twist-beam suspension of the Golf IV (courtesy of Volkswagen AG 1997)
6.2.3 Trailing-Arm Axle
Trailing-arm axles are a form of independent suspension with a single link (or arm) between the wheel carrier and body. The link is rigidly connected to the wheel carrier and via a revolute joint to the chassis. Depending on the alignment of the link’s axis of rotation, they are classified as trailing-arm or semi-trailing-arm (Sect.6.2.4) and trailing-arm suspension (Figs.6.6and6.7).
Trailing-arm axles have only one trailing link per wheel, which absorbs the longitudinal and lateral forces allowing the wheel to swing around a rotational axis perpendicular to the longitudinal axis of the vehicle. The links are usually elas- tically mounted to the body in a way that allows them to move longitudinally for improved comfort (Table6.3).
length compensation required!
symmetric:
Fig. 6.5 Rigid body model of a twist-beam suspension
Table 6.2 Model characteristics and features of the twist-beam suspension
Model Advantages Disadvantages
4 bodies Low space requirements Drive difficult to implement 1 revolute joint with torsion
spring
Stabilizing effect through cross member
Steering difficult to implement 2 spherical joints Low weight Limited potential for optimizing
driving dynamics 1 prismatic joint Good roll compensation
1 cylindrical joint
496=24 Equations of motion
195+293+195+ 194=20
Constraints
4 DoF: 2 DoF of the axle (bilateral vertical deflectionf1, unilateral vertical deflectionf2), isolated rotationf3 and compensation for longitudinal movements1;s2
1 Kinematic loop L1
Fig. 6.6 Trailing-arm rear axle of the Mercedes A-Class (Mửdinger et al.1997)
Fig. 6.7 Rigid body model of a trailing-arm wheel suspension
Table 6.3 Model characteristics and features of the trailing-arm wheel suspension
Model Advantages Disadvantages
1 body Little space requirements Restricted design for axle kinematics 1 revolute joint Simple construction No roll compensation
Small unsprung masses Low instant center of rotation, therefore strong rolling tendency Track width, toe in and camber
constant with unilateral suspension (not relative to road surface)
Poor longitudinal elasticity
196=6 Equations of motion 195=5 Constraints
1 DoF per wheel suspension (f1)
0 Kinematic loops
6.2.4 Trailer Arm Axle
The skewed assembly of a single rod enables a good absorption of longitudinal and transverse forces if it is connected to the chassis by means of two axes of rotation set out in the longitudinal direction of the car (Figs.6.8and6.9). Through this the advantages of trailing-arm wheel and wishbone wheel suspension can be combined without encompassing large disadvantages (Table6.4).
6.2.5 Double Wishbone Axles
If a wheel suspension is only guided with laterally placed rods, there needs to be one rod above and one below the center of the wheel. Additionally there needs to be a steering rod in order to prohibit steering or to allow for defined steering Fig. 6.8 Trailer arm axle of the Volkswagen Sharan (Schuster et al.1995)
Fig. 6.9 Rigid body model of a trailer arm wheel suspension
(Fig.6.10). Such an assembly is called a double wishbone axle wheel suspension.
In Fig.6.11 the tie rod, which is mounted via spherical joints, undertakes the transmission of the steering forces towards the wheel carrier. Hence the rigid body model’s isolated DoFf3(Table6.5).
Table 6.4 Model characteristics and features of the trailer arm wheel suspension
Model Advantages Disadvantages
1 body Relatively simple structure Restricted possibilities of elasto- kinematic set-up
1 revolute joint
Good applicability for powering Roll compensation possible 196=6 Equations of motion 195=5 Constraints
1 DoF per wheel suspension (f1)
0 Kinematic loops
Fig. 6.10 Steered double wishbone axle front wheel suspension of the VW Tuareg (courtesy of Volkswagen AG 2002)
6.2.6 Wheel Suspension Derived from the MacPherson Principle
In wheel suspensions derived from the MacPherson Principle one differentiates fundamentally between the two designs of spring struts and damper struts. If the damper uses the clearance in the helical spring and at the same time supports both ends of the spring, it is called a spring strut (see Fig.6.12). If the spring on the other hand is not mounted on the damper but separately, it is called a damper strut.
Essential features of the damper strut and spring strut axles are that a standing damper is connected with the wheel carrier tightly and the piston rod of the damper is mounted at the chassis hinged. Thus a cylindrical joint is created which enables the steering and spring displacement of the wheel carrier. For completion of the wheel suspension two further rods are needed. One serves as a steering rod and is connected to the steering. The other works in the lower tier, usually in the form of a triangular wishbone, for the guidance of the wheel (Fig.6.13), (Table6.6).
isolated DoF Fig. 6.11 Rigid body model
of a double wishbone axle wheel suspension
Table 6.5 Model characteristics and features of the double wishbone axle wheel suspension
Model Advantages Disadvantages
5 bodies Spatial wheel kinematics (track width, toe in, camber) largely freely designable
Large space requirements
2 revolute joints Very well suitable for powering Complex structure
1 prismatic joint Complex longitudinal
suspension and elasto- kinematic set-up 4 spherical joints
25ỵ15ỵ43ẳ27 Constraints
56ẳ30 Equations of motion
3 DoF per wheel suspension (springf1, steerf2, isolated DoFf3)
2 Kinematic loops L1 and L2
6.2.7 Multi-Link Axles
The use of four or more links for the suspension of a wheel is only possible if none of them is connected rigidly to the wheel carrier. Therefore every rod needs to be fixed to the wheel carrier by means of a movable joint. In order to exploit all of the kinematic potential of the layout, five independent links have to be used. The Fig. 6.12 MacPherson spring strut axle of the BMW Mini with steering system (courtesy of BMW Group 2001)
isolated DoF Fig. 6.13 Rigid body model
of a MacPherson spring strut wheel suspension
installation of a trapezoidal link instead of two lower two-pivot-links leads to a so- called integral-link-suspension (Fig.6.14). Here, the absorption of the torque created by longitudinal forces is realized through a perpendicular additional link (integral-link) which supports the wheel carrier on the trapezoidal link (Fig.6.15), (Table6.7).
Table 6.6 Model characteristics and features of the MacPherson wheel suspension
Model Advantages Disadvantages
5 bodies Low building effort Bending torque in damper
impairs responding qualities.
1 revolute joint Low space requirements
2 prismatic joints Few unsprung masses Large design height 4 spherical joints Well suitable for drive
56ẳ30 Equations of motion
15ỵ25ỵ43ẳ27 Constraints
3 DoF per wheel suspension (spring
f1, steerf2, isolated DoFf3)
2 Kinematic loops L1and L2
Fig. 6.14 Integral-IV wheel suspension of the BMW 5 Series (courtesy of BMW Group 2003)