Codemo Alessandro – alessandro.codemo@studenti.unipd.it
Updated on July the 8th, 2020

## Introduction

It is well known that the road vehicles need to constantly maintain contact with the ground in order to not losing grip and thus have good performances in track. But in the other hand, suspensions are also used to ensure the best level of comfort for driver and passengers. Hence, year after year these mechanisms are improved to find the best compromise, finally leading the suspension to have good control of the wheels’ trajectory during the compression stroke.

That is why recently numerical analysis on a multibody environment are carried out to study the suspension kinematics and optimize the dimension and orientation of each component of the mechanism. Nowadays, a good design model is the multilink, which works as an independent suspension: in fact, the wheel can move freely and unhindered by the one in the opposite side [1].

A multilink suspension is composed by three or more lateral arms which allow a specific trajectory, controlling the camber and the vertical movement, and by one or more longitudinal arm which control toe, steer and lateral compliance. These arms do not have to be of equal length and may be angled away from their obvious direction. Typically, each arm has a spherical joint, or rubber bushing at each end: thus, they react to loads along their own length, in tension and compression, but not bending [2].

Moreover, they have different degrees of freedom depending on the number of rods that are connecting the wheel to the vehicle. For example, a 3-link model allows vertical, longitudinal and rotational movements; with a 4-link layout there are only two free movements, vertical and rotational [1,4].

The 5-link suspensions are mechanisms with one d.o.f., constituted by five rods, which in fact eliminate five d.o.f., connecting the wheel carrier to the car body, through joints that, in the most general case, can be considered as spherical [3,5].

Objectives – Kinematic analysis

Considering the hypothesis of rigid bodies and ideal joints, this mechanism has only one degree of freedom: the vertical movement. It is therefore possible to assume the spring extension as the independent coordinate, and the frame Oxyz attached to the car body as the main fixed frame.

Using ADAMS multibody environment, an MSC software, the kinematical simulation will be performed controlling the typical parameters of a vehicle suspension: the camber and the toe, the track and the wheelbase, everything as a function of the bounce. In order to measure the angles and the displacements of the wheel, the movable frame will be focused on the wheel centre of mass and then the plots per steering rotation will be inspected, every time changing one rod length.

Controlling the upward movement as the independent coordinate with an actuator, the code does not see any degree of freedom. Thus, the kinematic analysis will be focusing on the components’ position, solving a vectorial problem. The input data that the code is taking in account initially are the standard coordinates of the points that were chosen and therefore the length of each rod. Controlling the length of the links, all the code equations change.

3.1 Variation of the rod lengths

In order to study the performances of the system while varying the lengths of the suspension rods, the numerical procedure is based on the following hypotheses: no compliances in the joints and rigid rods. All the links were changed one per time in a specific way, modifying the coordinates of the points in correspondence of the chassis, but keeping constant the orientation of the respective rods.

First thing first, the upper and the lower arms interchange their lengths, so that it is possible to observe the camber behaviour under different design. As a second step, the trailing arm is aligned with the lower arm instead of the upper, and the leading arm in the opposite way. Last change was in the length of the control arm.

Hence, four kinematic simulation were carried out in total: the “Standard” one, with no changes; the “UpLow”, the “LeadTrail” and the “Steer” ones, with their respective changes. For all the simulations was also studied the effect of different steering rotation.

In these analyses the geometrical parameters related to the attachment points of the links on the chassis have been modified, without modifying the direction of the links themselves, and the characteristic curves have been obtained. Each modified configuration of the suspension represents a mechanism kinematically and geometrically different from the previous one, therefore it can be possible to notice the difference in the suspension behaviour between the various configurations.

## The modelling problem

This paper is focused on a 5-link suspension (fig.1), designed from the beginning, following some observations taken from Honda’s history [4].

Fig.1 – The multi-link suspension scheme.

The model has two mainly rods, the upper and the lower arms, which control the camber angle and the vertical movement (fig.2). They are not the same length: indeed, imposing the upper arm to be shorter, it is possible to have negative camber both for compression and extension of the suspension stroke.

There are other two links, the trailing and the leading arms, which prevent the wheel to move freely forward and backward (fig.3): thus, they are controlling the vertical and the lateral displacements.

Finally, the model provides for a presence of the fifth rod, the controlling arm, used to prevent free steer rotation (fig.2): in this case it is also used to control the steering rotation with a steer bar, which links the two opposite front wheels.

For better stability the suspension is linked directly to the wheel carrier, near the control arm attachment. In this paper however the dynamic simulation is not carried out.

Fig.2 – Rear view: upper/lower arms (green); control arm (orange).

Fig.3 – Top & lateral views: trailing/leading arms (red).

The position of the ends of each link was chosen in order to recreate the double-wishbone suspension with the upper and the lower arms and the Watt’s linkage suspension with the trailing and leading arms (tab.1). Moreover, the vehicle attached point of the trailing arm is aligned with the upper arm end in the top view, and the same consideration is taken for the leading and the lower arms [4].

 Points’ Position (x, y, z) [mm] Fixed to wheel Car body Upper arm (100, 100, -25) (275, 100, -25) Lower arm (100, -100, -25) (300, -100, -25) Trailing arm (50, -86.67, -75) (275, -26.67, -300) Leading arm (50, 86.67, 25) (300, 20, 275) Control arm (125, -50, 50) (350, -50, 50)

Tab.1 – Points’ coordinates w.r.t. the wheel centre of mass.

All the joint between the components, near their standard position and orientation, can provide the maximum value of d.o.f. to the respective links: it means that spherical joints can be assumed for an appropriate kinematics. However, within the numerical simulation, an isostatic mechanism is required, so that there are not redundant constraints. For that reason, the joints attached to the car body won’t be spherical, but universal joints instead.

Simulations and analysis of results

In the following figures the various characteristics in terms of toe angle, camber angle, wheelbase and wheel track have been reported as a function of the wheel bounce, assuming that 0 is the standard starting vertical position of the wheel.

In relation to the “Standard” simulation, the following characteristic curves were found (fig.4):

Fig.4 – Characteristic curves of the standard configuration.

The design of the multilink suspension provides a centre of steering rotation not perfectly aligned with the centre of mass of the wheel. This means that, as the graphs are showing, the wheel moves horizontally and laterally during the suspension stroke. Moreover, having the upper arm shorter than the lower one, for the most part the camber value is negative. The result is that also the toe value is negative for each steering rotation: this can slightly ensure a better grip of the tire with the ground, while the suspension is working [4].

In the following figure (fig.5), the characteristic curves of the multilink are reported, referring to the “UpLow” simulation. The configuration has been indeed modified interchanging the lengths of upper and the lower arms.

Fig.5 – Characteristic curves of the first new configuration.

How it can be noticed, with this little change the wheel track and the steering are not that much different. Nevertheless, the camber assumes increasingly positive values, and in addition the lateral movement tends to go out of control for highly negative steering values.

Regarding the second changed configuration, studied in the “LeadTrail” simulation, the characteristic curves are as follows (fig.6).

Fig.6 – Characteristic curves of the second configuration.

Changing the lengths of the trailing and the leading arms, keeping constant their orientation, apparently did not bring a noticeable difference w.r.t. the standard configuration, or even, it seems a slightly better configuration. Considering that this project involves a re-design from scratch of a given multilink suspension, controversial results are plausible. It should be evident anyway that modifying these two arms the toe and the track are changing too. In the case of changing also their orientation, the wheelbase should change too.

For completeness, the fourth “Steer” simulation was carried out: the results are as follows in (fig7).

Fig.7 – Characteristic curves of the third configuration.

As it was expected, nothing changed deeply: indeed, the control arm serves the purpose to maintain a certain value of the steering rotation. If it had been increased even more, it would have eventually ruined the controlled trend of the toe angle.

Conclusion

With a kinematical analysis of a brand new project such this, it is shown that it is possible to understand the importance of each component of the suspension by studying its characteristic curve, and so the performances in terms of handling, and by modifying the length of the various rods, eventually combining their effects.

The behaviour of a multilink suspension has been analysed. Four simulations have been carried out in a way that it can be possible to find in which cases some particular changes of the kinematics would affect the suspension behaviour. Thus, in order to change the length of the links, the joints’ coordinates on the chassis were varied one per time, and within each simulation the plots per steering rotation were inspected.

In general, it is already known that modifying the morphology of one component of the mechanism, one or two characteristic curves should change. The upper and the lower arms are acting principally along the rear-view plane: thus, increasing or decreasing their lengths relative to each other, even if the orientation is kept constant, the camber angle value changes. Following the tips of Honda’s double wishbone suspension history, it seems that during the wheel bounce negative camber has better performances, so the upper arm should be shorter than the lower one [4].

The trailing and the leading arms are pointing towards the centre of rotation of the wheel, which is not aligned with the its centre of mass, especially for rear suspension. They must be angled away so that they can act better along the rolling direction, keeping the tire centred, but they also need to ensure a correct vertical translation in relation on the previous two links. Modifying the position and the length of the trailing and the leading arms should mainly change the wheel track.

Finally, the control arm is used to prevent any free steering rotation: in fact, changing the position, orientation and length will eventually change the toe angle during the compression stroke.

The technique of changing just one time the rods’ length is not sufficient itself to optimize the suspension performances, but it can be repeated multiple times to eventually combine all the considerations in once during the design stage of the new mechanism. When starting from a desired configuration, this procedure permits to identify the correct length of each single rod of the suspension itself.

## References

[3]    Knapczyk, J., Dzierzek, S. – Displacement and force analysis of fiverod suspension with flexible joints – ASME, Journal of Mechanical Design, vol. 117, pp.532-538, 1995.

[5]    Knapczyk, J., Dzierzek, S. – Displacement analysis of five-rod wheel guiding mechanism by using Vector Method – Proc. Of 25th ISATA, Florence, v. Mechatronics, p. 920893, pp. 687-695.