Article citation information:
Wheatley G.,
Zaeimi M. Anti-roll bar design for a Formula SAE vehicle
suspension. Scientific Journal of
Silesian University of Technology. Series Transport. 2022, 116, 257-270. ISSN: 0209-3324. DOI: https://doi.org/10.20858/sjsutst.2022.116.17.
Greg WHEATLEY[1], Mohammad ZAEIMI[2]
ANTI-ROLL BAR DESIGN FOR A FORMULA SAE VEHICLE SUSPENSION
Summary. This work
outlines the development and analysis of an anti-roll bar system vehicle
carried out by James Cook University. A detailed design phase was completed,
clearly showing all stages of the design approach from the initial proposed
design to the final design. Several analysis strategies are used throughout the
report including weld calculations and FEA modelling. These calculations led to
design changes impacting the final recommended system. This report demonstrates
compliance with all Formula SAE rules regarding anti-roll bar systems.
Keywords: anti-roll
bar system, finite element analysis, Formula SAE, suspension system
1. INTRODUCTION
Although anti-roll bar (ARB) systems
have a simple function, their design is influenced by many factors which are
not often precisely known including available space, materials, vehicle weight
transfer, roll resistance, vehicle and suspension and geometry. Therefore, some
assumptions should be made during the design process. Calculations assume a
totally rigid chassis, friction-free mountings, geometric perfection, symmetric
weight distribution on a stationary car, no flexing of ARB levers and
steady-state cornering conditions [1]. The impossibility of obtaining
and designing for all of these parameters necessitates the use of track testing
to finalize the design and emphasizes the difficulty of obtaining an accurate
design based on purely theoretical calculations [2]. Materials have also been developed
significantly to optimize the strength to weight ratio. Originating from a
steel tube or rod bent between 50 and 90 degrees [1], ARBs have
been developed into multi-component devices with materials such as Teflon,
aluminium, high strength steels and composites such as carbon fibre.
University Racing Eindhoven (URE) [3], proposed a
design involving a solid ARB with splined ends and carbon fibre drop rods with
aluminium inserts. The levers were welded to a splined bushing, which slid over
the ends of the bar and was axially fixed by a c-clip. URE’s method
highlights the important parameters in the ARB system design. Their results are
used for comparison in this study. This project aims to develop a front and
rear ARB system with mechanically adjustable system settings. Adjustment
settings must be easily accessible for fast changes without the removal of
other major components. The recommended design must also comply with all
relevant rules and regulations of the FSAE competition [4].
2. DESIGN APPROACH
ARBs
are characterized by their torsional resistance. If the stiffness is too soft,
the ARB provides limited roll resistance and the vehicle has a greater tendency
to oversteer or understeer. Conversely, if the ARB is too hard, it reduces
vehicle turnability and may cause the tyre to skip along the road surface.
Excessive oversteer or a need to increase understeer can be achieved by
slackening the rear ARB or increasing the stiffness of the front ARB [5]. The opposite
configuration is used to address excessive understeer.
2.1. Preliminary
considerations
Rules and regulations from the
Australian Formula SAE [4] are considered in the design of the ARB.
The geometry of the ARB is dependent on the location of the mounting points and
the range of movements of the suspension system. First, the ARB is to be
located in an area with sufficient space, both for the rotation of the lever
arms and easy access to the adjustment settings. Second, it has to be mounted
to a solid bar that is not subject to flexing during vehicle cornering. This
will most likely be a member of the frame that is parallel to the axis of
suspension. Next, the position of the ARBs must be close to the suspension
system. A remote linkage connecting the ARBs to the suspension may prove
unreliable, and therefore, will not be considered. Finally, the front and rear
ARBs must be positioned such that the stiffness settings can be easily adjusted
without the removal of other major vehicle components. Furthermore, the
geometry of the rockers is highly influential on the function of the bar, where
the rotation of the rockers determines the displacement of the end of the ARB
lever arms. Heim joints are placed between the two parallel faces of each
rocker and threaded into the drop link rods. The distance between the parallel
faces determines the size of the spacers to be used on either side of the heim
joint head but do not present significant constraints regarding the heim joint
size.
Due to the varying load application,
the material is required to provide sufficient fatigue life. Sharp geometric
discontinuities are to be avoided, if possible, to reduce areas of high stress
concentration. The chosen material must also satisfy the manufacturing
criteria. Aluminium has the high strength-to-weight ratio desired in the
motorsports industry but is expensive and has low weldability. Aluminium
welding operations require a tungsten inert gas welder, and due to the melting
properties of aluminium, it can be very difficult to work with if not properly
experienced. Unlike aluminium, steel has good strength properties and is easily
welded; however, it is heavier. Furthermore, Chromoly (4130 Steel–Chrome
Molybdenum) was an option which was considered the possibility of its use. The
high strength-to-weight ratio makes Chromoly desirable for different
applications.
2.2. Initial design
The first
concept of the ARB is shown in Figure 1. There are two options available for
the bar, tubular or solid rod. Tubular ARBs have a weight/stiffness ratio
advantage over solid metal but can cause welding difficulties if chosen as the
lever arm connection choice. Solid bars are stronger and have greater torsional
stiffness compared to tubes; however, they have a greater sensitivity to
outside diameter alterations than tubes [1]. The initial
design was on a tube due to its strength-to-weight ratio advantage.
Fig. 1. First
design of the anti-roll bar
One considerable concern is with the
connection between the lever arms and the bar. The connection between the
lever arms and the main bar can be a keyway that drives torsion to the bar, and
a clip to prevent sliding, as shown in Figure 2a. Keyways are often used to
transfer torque through components such as is used in the rear hub shaft of the
current FSAE vehicle. The main disadvantage of using keyways in ARBs is that a
precision machining is required to ensure that the fitting clearance is below
the required tolerance, which can be both complex and costly. Although it is
not anticipated that the bar will be subjected to significant longitudinal
loads, the clip may not provide sufficient security and may fall off or loosen
during racing conditions.
Another option is to minimize the
clearance in the joint between the lever arms and the bar. For this purpose, a
hexagon shaped end of the bar was suggested. This end slot in a hexagonal hole
through the lever arms is shown in Figure 2b. In this way, the force would be divided
up consistently on any edge of the hexagon instead of just on the keyway. The
assembly could be locked with a special retaining ring fitted in a rut on the
hexagonal end. These rings are cheap and are specially made for such a purpose.
The chance of losing this retaining ring is greatly reduced as opposed to the
simple clip used in the previous design. However, the major flaw of this design
is the manufacturing difficulty to produce the complex shape hole and bar end.
Manufacturing process would require CNC machining, which is costly. In
addition, this option also requires a solid bar, which has a weight/stiffness
ratio disadvantage compared to tubes. In consideration of this, the design
progressed to welded joints.
|
(a) |
(b) |
Fig. 2. Lever
arm connection by; (a) keyway, (b) minimizing the clearance in the joint
Another
concern was related to the material and geometry of the lever arms. They can be
made of steel and thick enough to encompass the rod. As shown in Figure 3a,
there are 3 adjustment slots that can apply the most torque to the ARB through
a greater moment arm. To simplify the entire design and reduce manufacturing
costs, the lever arms were divided up into flat sheets instead of one thick
block (Figure 3b). An advantage of this solution is the weight reduction and
stiffer arms. This results in less bending in the arms and almost all of the
height difference between the arms while cornering is caused by the torsion of
the bar. These sheets will be fixed in parallel planes at specific distance
apart and welded to the round bar. For optimized force translation and weight
reduction, the height of the sheet decreases over its length.
|
(a) |
(b) |
Fig. 3. Lever
arm; (a) thick block, (b) flat sheets
Since
the method for joining the lever arms to the bar is welding, this allows the
lever arms to be set at any
angle and is easier and cheaper to manufacture. A problem with interfacing the
tube design decision with the welding proposal is depending on the wall
thickness of the tube, as it could be difficult to weld the arms on the tube if
there is not enough material. For this situation, some solid steel will be
welded into the tube at the sections where the arms will be welded (Figure 4a). The vertical rods used in the design
consist of three components; two heim joints threaded into a solid bar that was
drilled at tapped either end, as presented in Figure 4b. This design would
provide strength and resilience against bending stress. The heim joints were fixed
to the lever arms and rockers via hex bolts. The heim joints ensured that the
rod could be arranged at different angles to vary the lever arm length and
apply different torsions to the ARB.
|
(a) |
(b) |
Fig. 4. (a) Welded-in
material, (b) Vertical rod with heim joints
Fig. 5. Connection
Rocker
Common hexagon bolts and matching nuts
fix the rod ends to the arms and the rockers. The ARB rod ends will be
connected to the same location on the rockers as the pushrod. The rod ends
will be mounted on the outer side of the rocker and spacers will be placed on
either side of the heim joints to ensure that sufficient clearance is
available. The spacers could be manufactured out of a matching tube (Figure 5). The above designs recommend bolting
the entire ARB system to the frame, which makes it removable. Making the
roll bar removable simplifies servicing and allows for easy adjustments. Due to
the stability of the frame, it is not recommended to bolt the ARB directly on
the frame tubing. Therefore, additional saddles or metal sheets will have to be
welded to the frame. This removes the chances of damaging the frame from
the tension of the mounting bolts.
The most convenient and practical
mounting point of the ARB system is underneath the frame and the floor
closeout. This location ensures that functional components will not be
interfered with, and the closeout works as a secure barrier for the driver. The
distance between the lowest point of the ARB system and the ground is large
enough to ensure that there will be no contact. This satisfies the FSAE rules
for ground clearance. Another advantage of the above configuration is that as
the front ARB is not located in the driver’s cell, it does not require a cover
(Driver’s leg protection regulation).
2.3. Numerical analysis
2.3.1. Force and endurance limit
calculation
To perform FEA on the anti-roll model, the applied force acting on the ARB and its
endurance limit should be determined. From the free body diagram of the rocker
shown in Figure 6, which is obtained from a maximum cornering load case, the
applied force acting on the ARB can be identified. It should be noted that the
suspension rocker and spring had a direct influence on the anti-roll design.
First, the geometry of the rockers determined the displacement of the ARB lever
arms during suspension spring compression. Vertical displacement influenced the
torsion in the bar while horizontal displacement (that is, in the plane of the
rocker faces) influenced the stress experienced at the lower heim joints.
Second, the suspension spring stiffness affects the degree of vehicle roll,
which will be resisted by the springs through a parameter known as spring
rate. The spring rate is the relationship between load and deflection. When
used in conjunction with the ratio of wheel movement to spring movement, the
total portion of vehicle roll that is resisted by springs can be calculated.
Fig. 6. Free
body diagram of the rocker
Tab.
1
Endurance limit factors for the fatigue stress
concentration
|
Factors |
Description |
Value |
Reasoning or
formula |
|
|
Load factor |
1.0 |
Using von
Mises equivalent |
|
|
Size factor |
0.91 |
For rotating
circular shaft: |
|
|
Surface factor |
0.78 |
For
machined-cold drawn 4130 Chrome-Moly |
|
|
Temperature
factor |
1.0 |
Assuming
operating temperature |
|
|
Reliability
factor |
0.814 |
Assuming 99%
reliability |
|
|
Stress
concentration factor |
0.868 |
Taking into consideration the added fillets on the
moment arms to represent welds: |
|
|
Miscellaneous
effects factor |
1.0 |
Assuming no
other significant factors |
The spring stiffness (K), maximum
rotation (R), and F1 are 44 N/mm, 24°, and 2500 N. F2 is the unknown force
acting on the ARB moment arm from the rocker mounting point. Breaking the load
of 2500 N into X and Y components gives forces of 1767.76 N acting in both
directions. Inputting the rotation and spring properties, an estimated
worst-case value for F2 of approximately 400 N was obtained using the force
probe tool in ANSYS. F2 will apply an upward force on the ARB, causing a
reaction force of 400 N to act on the opposite side of the ARB in a downward
direction, creating torsion in the ARB. This loading will occur during
cornering when the ARB acts to equalize loads between the left and right
suspension systems. The loading will be fully reversed.
From Table 1 and Eq. 1, the fatigue stress concentration for fatigue analysis (Kf) is 0.5015; the
fillet weld stress concentration was also accounted for through the endurance
limit factors:
|
|
(1) |
2.3.2.
Results and design development
Static structural analysis was set up
and the geometry of the proposed ARB was imported directly from the SolidWorks
model. The 4130 Chrome-Moly was chosen as the material of the ARB based on its
availability, ease of manufacturing and desirable mechanical properties [6].
The initial model for FEA consisted of nine bonded
bodies including four moment arm sheets, 16 mm diameter and 3 mm thick hollow
torsion bar, two inserts and two bolts. However, to improve the model, the
initial assembly was combined into one body to eliminate issues with the bonded
contacts; the bolt was removed and replaced by a distributed load on the holes
of either moment arm. To further increase the accuracy of the model in ANSYS
and represent the welds that will be used to bond the lever arms to the
shaft, 5 mm fillet welds were considered and added on either side of the lever
arm plates. This is a conservative and practical value for the given
application (Appendix A has details of the weld analysis). A solid fillet is
stronger than an actual weld; however, this should help improve the accuracy of
the model and can be considered in the endurance limit.
Fig.
7. Stress distribution from the first FEA
The first FEA result of the model is
shown in Figure 7 above. The distribution of the stress throughout the shaft
was evenly distributed; however, there is a relatively large maximum stress of
162.8 MPa occurring on the inside of the moment arms. In addition, Figure 8
shows the safety factor of 0.74185, which
indicates failure. Therefore, to increase the factor of safety to above 1,
design changes will be made to improve the strength of the ARB model.
Two changes were made, the length of
the moment arms was shortened, reducing torsion on the bar and the torsion bar
was changed from a hollow 3 mm tube to a solid bar. These changes, however,
have some negative effects, as changing the length of the moment arms reduces
the amount of adjustability available to the vehicle. Likewise, changing
the torsion bar from tubular to solid will increase the cost and overall weight
of the ARB. However, both of these changes will increase the overall stiffness
and strength of the ARB. Note that the adjustment of the outside diameter of
the ARB tube was also a possible option. However, an increase in the outer
diameter would have the effect of increasing the torsional stiffness and,
subsequently, the shear stress. Greater torsional stiffness decreases angular
deflection, meaning that a larger portion of one lever arm displacement is
transferred to the opposite lever arm. This has the effect of increasing
vehicle roll resistance.
Fig. 8. Initial
model for FEA analysis
The moment arms were reduced to a
length of 65 mm centre to centre rather than 80 mm. This reduces the moment
acting on the bar. Along with the solid Chrome-Moly bar, this reduced the
maximum stress to 81.55 Mpa. The maximum and minimum stresses obtained from the second
FEA are shown in Figure 9. Similarly, the minimum and maximum strain occur in
the same locations of the maximum and minimum stress; the maximum value for
strain is 0.00039821 m/m. From Figure 10, the maximum
deformation in the ARB is 0.0013871 m. This occurs
between the ends of the two moment arm sheets as expected, as the moment
rotates around the ARB from this point. The safety
factor obtained, as shown in Figure 11, had a value of 1.057 minimum, which
gives infinite life to the entire ARB. Therefore, the recommended solutions are
altering the ARB to a solid Chrome-Moly bar and shortening the moment arms from
80 to 65 mm. In addition, the previously used inserts, which supported the
welding of the arm plates to the torsion bar, are now unnecessary. The final anti-roll design is shown in
Figure 12.
Fig.
9. Stress distribution from the second FEA
Fig.
10. Deformation from the second FEA
Fig.
11. Safety factor from the second FEA
Fig. 12. Final
design
2.4. Design assessment
While
the FEA analysis determined the required dimensions to avoid failure, the
following section partially assesses the effectiveness of the ARB design in
providing roll resistance. For a solid rod subject to torsion, the following
equations from reference [7]
are used to calculate the angular deflection, spring rate and factor of safety
of the bar. These parameters are typically used in the calculations for the
required diameter of ARBs to achieve a specified roll resistance.
2.4.1. Angular deflection
The bar is assumed to be constructed
from 4130 Chrome-Moly, which has a yield strength Sy of 435 MPa, modulus of elasticity E of 205 GPa and a Poisson’s ratio
|
|
(2) |
The above analysis resulted in an
angular deflection of 34.31 and 27.97° for the front
and rear, respectively. The angular deflection is the amount of twist over the
length of the bar and was used in ref [3] to determine the roll motion ratio of
the vehicle. The roll motion ratio was then used in combination with the body
roll angle and the vehicle roll resistance to determine the required diameter
of the bar. This parameter is used as an indication of the effectiveness of the
current design. Using the maximum target body roll angle (
The estimated roll motion ratios for
the front and rear are 19.06 and 15.4 compared with
the result of ref [3] with a roll motion ratio of 10.7, meaning that the current design has a ‘softer’
ARB and provides less roll resistance to the vehicle. The spring rate or the
torsional resistance of the bar may also be compared using the following
equation [7]:
|
|
(3) |
2.4.2. Spring rate
The
amount of the vehicle roll that is resisted by the suspension system is
calculated using the spring rate. The spring rate is the ratio of wheel
movement to spring movement. The spring rate K was found to be 852.05 Nm/rad, which is
comparable to the results of ref [3] 1000 Nm/rad.
URE’s ARB system is more ‘hard’ as it has greater torsional
resistance and translates more of the force between the left and right
suspension systems.
2.4.3. Safety factor
Safety factor
is determined using the following equation [7]:
|
|
(4) |
The
factor of safety for the front and rear solid ARB rods using static loading
conditions was found to be 7.768. This indicates that the bar is highly
unlikely to fail. Under fatigue loading, the factor of safety would be reduced;
however, given the safety margin, it is not expected to fail. In ref [3],
was reported a static safety factor of 1.4 for the front ARB. As they completed
a full analysis with measured data and vehicle dynamics simulations, their
need to be conservative was significantly less, so the safety factors are
comparatively different.
3. CONCLUSION
This
paper provides key considerations for designing and analysing the ARB system of
a Formula SAE vehicle produced by James Cook University students. There
are several recommendations and outcomes for the design of an actual ARB. The connection between the lever arms and
the bar, the geometry of the lever arms and the connection of the entire ARB
system to the frame are clearly discussed. Furthermore, the geometry of the
rockers is shown as the proper option to determine the displacement of the
lever arms during suspension spring compression and related forces. By considering welding requirements, weight and strength, the Chromoly
was an appropriate option for the design. Thus, it is
proposed that the geometry of rockers is highly influential on the function of
the bar. To ensure the quality, the proposed system is designed based on the
FSAE rules, and the justification is achieved through finite element analysis
by investigating the stress and strain of each part of the system and the
safety factor using SolidWorks and ANSYS. The design assessment is performed by
comparing some important parameters including the angular deflection, spring
rate and factor of safety of the bar with the corresponding values taken
from the literature.
APPENDIX A
This analysis was used to
determine the size of the fillet welds located on either side of the four lever arm plates.
Figure 13 shows the force F applied by the drop link connection and
the reaction force V and moment T about the torsion bar axis. The external
force used in the FEA
analysis was 400 N. The applied force will therefore be 200 N for a single
lever arm plate. The furthest
adjustment setting L imposes maximum stress, so is used as a critical load
case. The external force is applied in-plane and offset from the centroid of
the weld group G, subjecting it to direct shear stress (primary τ') and superimposed
torsional stress (secondary τ"). The force vectors of the primary and secondary
shear are also shown in Figure 13. The dimensions
of the bar used in the analyses are L=65 mm and r=8 mm.
Fig. 13. Lever
arm free body diagram and weld group
From Figure 13, the maximum stress
will be on the inner side of the ARB if the external force is down (shown), and
on the outside, if the external force is up. As the throat length t of the
fillet weld is unknown, the unit polar moment of inertia J is used in the calculations.
The weld group will be subject to
fully reversed cyclic loading, approximated using a sine curve and analyzed on
an SN diagram. The endurance limit, Se assumes the weld rod is ER80-D2, which
has an ultimate tensile strength of 80 ksi, reliability of 99% and the weld
‘reinforcement’ is present. The welds are compared to the Goodman
failure criteria for infinite life (SFN=Se) with a safety factor N of 1.5. The following analysis uses
equations from ref [7]. Total
torsional stress:
|
|
(5) |
Where
From the above analysis, the
recommended leg size of the weld is 0.02 mm. This
small value indicates that the estimated maximum loading conditions will not
damage the integrity of
a 5 mm weld (Table 3).
Tab. 2
Endurance limit factors for the fatigue stress
concentration
|
Factors |
Description |
Value |
Reasoning |
|
|
load factor |
1.0 |
Using von Mises equivalent |
|
|
Size factor |
0.8 |
Convention |
|
|
Surface factor |
0.47 |
Weld
with reinforcement attached, assume equivalent to ‘As forged’ |
|
|
Temperature factor |
1.0 |
Assuming
operating temperature |
|
|
Reliability factor |
0.814 |
Assuming 99% reliability |
|
|
Stress concentration factor |
0.37 |
|
|
|
Miscellaneous effects factor |
1.0 |
Assuming
no other significant factors |
Tab.
3
Endurance limit factors for the fatigue stress
concentration
|
Variable |
Description |
value |
|
V |
Shear force |
200 N |
|
A |
Cross-sectional
area of the rod |
0.0335 h |
|
T |
Twisting moment |
13 Nm |
|
|
Primary shear stress |
5627.826 h-1 |
|
|
Secondary shear stress |
45726 h-1 |
|
|
Mean stress |
392.507 h-1 |
|
Se |
Endurance limit |
31.231 MPa |
Reference
1.
Staniforth Allan. 2006. Competition Car
Suspension. Haynes Publishing.
ISBN: 978-1844253289.
2.
Milliken William,
Milliken Douglas. 1995. Race Car Vehicle Dynamics.
SAE International.
3.
Bos Van Den. 2010. „Design of a Formula
Student Race Car Spring-Damper System”. PhD thesis. Eindhoven University of Technology. Department of
Mechanical Engineering.
4.
Formula SAE Rules.
2015. SAE International.
5.
Gould Daniel. 2006. “Lateral weight
transfer and roll resistance”. In: Competition Car suspension.
Haynes Publishing.
6.
MatWeb. “AISI 4130 Steel Normalised at 870
deg”. Available at:
http://www.matweb.com/search/DataSheet.aspx?MatGUID=e1ccebe90cf94502b35c2a4745f63593&ckck=1.
7.
Juvinall Robert C.,
Kurt M. Marshek. 2006. Fundementals of Machine Component Design.
Technology & Engineering.
Received 10.04.2022; accepted in
revised form 02.06.2022
Scientific Journal of Silesian University of Technology. Series
Transport is licensed under a Creative Commons Attribution 4.0
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[1] College of Science and Engineering, James Cook University, Townsville, Australia. Email: greg.wheatley@jcu.edu.au. ORCID: https://orcid.org/0000-0001-9416-3908
[2] Mechanical Engineering Department, University of Guilan, Rasht, Iran. Email: mohammad.zaeimi@gmail.com. ORCID: https://orcid.org/0000-0003-0987-9253