Article citation information:
Marciano, P.,
Wheatley, G., Ali, A. Differential designing for FSAE motor sports vehicle JCU.
Scientific Journal of Silesian University
of Technology. Series Transport. 2022, 114,
67-78. ISSN: 0209-3324. DOI: https://doi.org/10.20858/sjsutst.2022.114.6.
Pieta MARCIANO[1],
Greg WHEATLEY[2],
Ahmed ALI[3]
DIFFERENTIAL DESIGNING FOR FSAE MOTOR SPORTS
VEHICLE JCU
Summary. The objective
of this work was to design a differential assembly for an FSAE motor sports
vehicle. The designed differential system consists of 3 braces made of AISI
1045 steel. The output shafts were made of AISI 4140 steel with hardened
splines. These shafts were initially going to drive 94 mm constant velocity
shafts. A 75 mm tripod joint was used to minimize the weight and cost of the
system. The housing was held together with grade 12.8 hex head bolts, and the
shafts were bolted onto the tri-pod joints using bolts of grade 8.8 which
complies with FSAE rules. The input shaft which acts on the differential itself
is made of EN36A steel and is where the drive sprocket is bolted to. All
components were modeled using Finite Element Analysis to determine stresses and
displacements under operating conditions.
Keywords: torque
transition, shaft system, FEA
The objective of this work is to develop and
improve the existing design for the differential of a 600 cc formula car.
Differential devices are an integral component of any motor vehicle that allows
the driving wheels (either front or rear) to rotate at different speeds when
turning. When a vehicle is rounding a corner or traveling in any direction
other than exactly straight, the outer wheel of the vehicle is required to
travel a larger distance than the inner wheel. To compensate for this
difference in distance traveled, a differential allows the outer wheel to
travel faster to counteract the disparity in the distance, while in most cases,
supplying both wheels with equal torque.
When designing a differential system, the main
concerns are cost, weight, and reliability. In addition, the developed
differential must comply with all the relevant 2010 FSAE competition
guidelines, which are:
(1)
The drive train
must not leak.
(2)
If a chain is used
it must have a guard following the appropriate FSAE rules.
(3)
All bolts used
must have a grade of M8.8 or greater.
(4)
The design must be
compatible with the purchase parts.
(5)
The differential
must be compatible with a CBR 600 cc motor.
(6)
The driveline must
not exceed 15 kg.
(7)
The driveline must
not exceed an allocated budget of $5,000.
(8)
The driveline must
complete all of the competition without fail.
There are many different types of differential
devices such as:
(1) Locking Differential: the main feature of this
differential is the ability for it to be “locked” to give the
effect of a common shaft between the wheels. This allows both wheels to turn in
unison, and thus, rotate at the same speed, irrespective of the amount of
traction identified at each wheel. The benefit of the locking design
differential becomes apparent when the surface traction experienced by each
wheel differs significantly [1].
(2) Spool Differential: consists of only a pinion and ring
gear with a solid center. The solid axle arrangement permits both wheels to
travel at the same speed and allows for greater torque where needed at each
wheel. A disadvantage of a spool differential is that each wheel travels at the
same speed. It is highly economical and is usually employed on vehicles that
spend most of their life driving off-road where high traction is essential [2].
(3) Limited slip differential (LSD): works like basic
differentials under normal driving conditions, while under abnormal conditions,
where one wheel experiences a higher resistance than the other, the torque is
appropriately divided between the wheels (with a greater amount of torque
applied to the wheel of higher resistance). The most common types of LSD are
torque-sensitive differentials (geared, clutch, and cone-based differentials)
and speed-sensitive differentials (viscous and clutch pack). A high friction
Automatic Torque Biasing (ATB) differential, such as the Torsen differential,
provides the same function as a basic limited slip differential, but uses added
gear teeth as opposed to added clutches. The disadvantage of a LSD is that if
no load is applied at one wheel, then no torque multiplying can occur, thus no
extra torque can be applied to the other wheel. This disadvantage can be
overcome in some cases through the application of the rear brakes and precision
driving [3].
The type of differential arrangement employed
in any vehicle is dependent upon the driving conditions it is anticipated to
experience. For a predominately off-road vehicle, a spool differential or
locking differential may be the most appropriate system as it provides
increased traction where it is needed most, while a LSD would be more favorable
in high performance vehicles, like ours, in anticipation of the event that one
wheel suffers traction loss.
Gears are used in a rear axle design as one
method of transmitting torque from the motor to the drive shafts. Tooth shaped
gears provide a greater area of tooth contact along with greater strength
allowing a high amount of torque to be transmitted. Although the downside with
this configuration is that the correct adjustment is needed to prevent gear
noise, the design is heavy and a custom gear would have to be made to fit.
An alternative method to using gears is using a
chain to transmit torque to the different parts that make up the drive train
system. This method involves using two sprockets and a bike chain to transmit
torque. A greater amount of weight is saved when using this method compared to
gears. The disadvantage of this method is the possibility of the chain snapping
if too much load is applied.
This method is not often incorporated into
formula style race car designs because of the high possibility of slip
occurring and breakage/snapping of the belt. This occurs when too much load is
applied to the two pulleys and belt that transmit torque from the engine to the
drive shafts. The only advantage is the amount of weight that is saved.
In differential systems involving a rotating
housing, the differential is bolted to the housing so that it rotates as the
housing does. Connected to the housing is the sprocket which connects to two
shafts, the shafts lead from the differential out to the CV joints. Using this
method allows each wheel to rotate at different speeds, which reduces tire wear
and increases traction. The mass moment of inertia of this system is ideal
along with the weight. However, when excessive conditions are applied to this
design, the housing could allow for leakage.
Differential and Non-Rotating Housing: This
system requires the case to be locked while the differential rotates inside; an
output shaft then connects to the sprocket which is required to transmit the
torque to the differential. Two hollow shafts are required to complete the
drive process and transmit the torque to the two wheels. The ability of the
differential to rotate freely reduces the mass moment of inertia; this also
reduces the risk of leakage due to the fixed nature of the housing allowing a
vent to be incorporated.
CBR 600 cc: The FSAE guidelines and rules
request that an engine no larger than 600 cc be used in supplying the power
needed to drive the car. This implies that two 300 cc engines could be
incorporated into the design of the car or even more simply one 600 cc engine
could be used. The maximum torque the 600 cc engine produced at the wheels of
the car was calculated, using the engine specifications, as 1,180 Nm, which is
equivalent to a total engine capacity of 50 Nm.
The differential was a Torsen differential. To
comply with the rules of FSAE, the differential must be encased in oil and the
unit must not leak. The original unit was designed so that the differential
housing rotated with the differential itself. Another problem that comes with
having a rotating housing is that the oil plug becomes a rotating unbalanced
mass, meaning that it will contribute to vibration in the rear section of the
vehicle, which can add stress and limit the life of components such as
bearings.
The CV joints assigned to the current design
were supplied by Brett Ellacott. These are a bolt-on variety of unknown
manufacture. In addition, the condition of the joints is questionable, as one
or more of the CV boots are cracked, which means debris may have entered the
joint and caused some damage. Ideally, a CV shaft from a road-going vehicle
would enable the university to save costs in making custom CV shafts as these
are expensive to fabricate at a custom length. Furthermore, it would also be
beneficial to eliminate bolting the CV shafts to intermediate plates with
splines; this should reduce weight and eliminate weak areas, and the necessity
to balance the extra components to eliminate vibration. The issue with using a
predetermined length CV is that the driveline group will have to work carefully
with the suspension group and the group in charge of designing the uprights.
The differential housing itself will be the most affected in using a
predetermined length CV.
Currently, a 42 teeth chain ring is available
for the driveline; however, this is not ideal, as a large top speed is not
required for FSAE events. Therefore, a 52 teeth chain ring or greater would be
ideal and with the current setup should still be able to reach a speed of up to
200 km/hr depending on the gear ratios within the CBR600 gearbox. The chain
ring should be easily sourced from a wrecker or motorbike shop. The chain ring
was designed to be bolted to the differential housing, rather than using a
spline. This must be applied carefully as the shearing of bolts can be an
issue. The grade of the bolt must be carefully chosen, grade 8.8 or greater
should be used. This will be verified using calculations. Further, as this is
mounted to the differential itself, FEA calculations will have to be conducted
to verify if the case can handle the loads applied.
For the final mounting location for the
differential housing, it is essential to have good communication with the
suspension group and the uprights group. Moreover, the final mounting location
may be limited by the frame as the size of the chain ring and the size of the
rear section of the frame may be an issue as seen below in Figure 6. Similarly,
the angle at which the chain can exit the driving sprocket is an issue due to
the design of the gearbox. Normally on a motorbike, the chain ring/sprocket is
situated a much further distance away from the driving cog allowing a smaller
exit angle for the chain. Due to the design limitations, this has to be
carefully considered when choosing the size of the chain ring and the location
of the differential mount.
(1)
The output torque
from the 600 cc CBR motor will be transferred from a 14-tooth sprocket to a
49-tooth sprocket bolted to the housing of the differential using a chain.
(2)
The housing of the
differential will be stationary and should not leak in accordance with the
rules. It will incorporate a vent in which the oil cannot escape as the
temperature increases and the oil expands.
(3)
The shaft that
transmits from the sprocket will have to be hollow to allow the torque to be
transmitted back out of the wheels. This shaft will also need to have a spline
connecting it to the differential as well as a connection to the sprocket.
(4)
The shafts that
connect the differential to the wheels will need splines to fit the differential
and connections to the CV joints.
(5)
The housing will
require 3 seals to contain any oil leaking.
(6)
The differential
unit will be mounted inside the housing in 2 ball bearings (single row deep
groove ball bearings).
(7)
The chain will be
tensioned using an adjustable mounting system.
(8)
The oil used to
fill the housing will be a 75 W-90 gear oil.
(9)
The CV joints will
be a tripod format from Taylor Racing.
The tripod assembly was selected for the design
due to its low cost and weight. The tripod assembly consists of a tripod joint,
housing, and boot. Two of these assemblies are required for the attachment to
the output shafts. A further two assemblies are required by the rear uprights
team which would connect via a half shaft.
A sprocket is similar to a gear in that it has
teeth that mesh with a chain, track or other perforated or indented material. A
sprocket is more commonly referred to as a profiled wheel and differs from both
a gear in that sprockets are never meshed together directly, and from a pulley
in that sprockets have teeth and pulleys are smooth. From basic calculations
and solid works drawings, the most appropriate sprocket for the differential,
when keeping the engine sprocket was a 50-tooth gear. This is a standard gear
sizing which means it is easily sourced from companies. A 50-tooth sprocket
specified for the rear gives a final drive ratio of 3.2:1. To attach this
sprocket to the differential, a flange with 6 x M8.8 bolts with a pitch circle
diameter of 80 mm will be used. To ensure the sprocket can take the loadings
and forces applied to it by the various driving conditions of the FSAE
competition, it is necessary to look at options to increase the fatigue life of
the material used. Flame hardening is widely used in deep hardening for large
substrates and is only applicable to steels that have sufficient carbon and
alloy content to allow quench hardening. This hardening treatment does not
significantly change the dimensions. Flame hardening uses a high intensity
oxy-acetylene flame that is applied to the selected region. The temperature is
raised high enough to be in the region of Austenite transformation.
The chains function in the driveline system is
to transfer power from the engine to the sprocket on the differential. If a
maximum load was to occur, to save the engine and the differential unit from
unnecessary damage, the chain is required to snap before any of the car’s
essential components. This would be an important consideration when choosing a
relevant chain design. For future design considerations, a new 520 chain should
be purchased. The chain has two options, O-ring or non-O-ring. The cost and friction
benefits of the non-O-ring chain make the choice easy. The most appropriate
chain was sourced to be the D.I.D. 520-ERT due to its strength price and
availability. This is a lightweight chain, but its breaking strength of 8470
pounds compares well to a standard 520 pitch O-ring chain with an approximate
breaking strength of 9000 lbs.
Current differential style was a LSD
manufactured by Torsen. This type of differential is simply a torque multiplier
that works through the use of friction generated by thrust forces from the
internal gearing. It multiplies the torque available from the wheel that is
starting to spin-up or lose traction and sends that available torque,
multiplied by the TBR, to the slower turning wheel with the better traction.
The differential itself weighs about 3 kg and can transmit anywhere up to 5200
Nm of torque. The differential has a torque bias ratio of 3.2:1, however, as
the gears wear, this ratio can drop anywhere within 2.6:1. This means that the
output of any of the two shafts singularly can never reach 100% torque. Thus,
allowing the torque to be transmitted to the wheels even if one is not in
contact with the ground.
A bearing is a device that allows constrained
relative motion between two or more parts, typically rotation or linear
movement, while a seal prevents leakage or the addition of unwanted material.
Bearings may be broadly classified according to the motions they allow and
their principle of operation as well as by the directions of applied loads they
can handle. Seals simply come in kits that relate to their required task.
Bolted joints are one of the most common
elements in construction and machine design. They consist of fasteners that
capture and join other parts and are secured with the mating of screw threads.
There are two main types of bolted joint designs. In one method, the bolt is
tightened to a calculated clamp load, usually by applying a measured torque
load. The joint is designed such that the clamp load is never overcome by the
forces acting on the joint (and therefore, the joined parts see no relative
motion). The bolts used in the differential design must follow the FSAE rules.
This infers that a M8 bolt of grade 8.8 or higher must be used to comply with
the rules. Presently, M8 bolts are used to mount the differential housing into
the car and seal the differential housing.
Venting and Sealing: When designing the
differential, it must not leak, as this would fail according to the FSAE rules.
To avoid this, a stationary housing with the differential rotating inside was
used. It was assumed that if the housing was still the oil would not have a
chance to slosh around as much and pool in places where its expanding could
cause a leak. With the housing stationary, a breather is allowed to be
positioned on top, allowing increased pressure from the oil expanding to be
dispersed. Sealing is also an important consideration when trying to avoid oil
leaking. The seals are added to the joining of the housing and between the
joining to stop the oil from working its way into places like the flange.
When designing the input shaft, it was
necessary to consider factors such as friction, acceleration and torque. These
factors are important when considering the calculation of forces as if the
maximum amount of torque the engine can supply was transmitted to the tires,
they would slip or skid. It can be seen that when a car is accelerating, there
is a transfer of weight to the rear wheels of the car, this increases the
torque required to skid the tires. Currently, the car is estimated to weigh
around 400 kg, with 200 kg of this lying at the rear axle. Considering these
weights, the center of gravity is noted to be halfway between the centers of
the wheels. The height of the center of gravity is to be 300 mm and the length
from the centers of the tires is to be 1.72 m. The force acting due to
acceleration through the center of gravity could be calculated as:
|
|
|
(1) |
|
Drag force |
|
(2) |
|
Moment |
|
(3) |
|
Accelerating torque |
|
(4) |
|
Maximum normal stress |
|
(5) |
|
Maximum shear stress |
|
(6) |
|
Fatigue life |
|
(7) |
|
Fatigue constants |
|
(8) |
Where:
|
μ = |
Coefficient of friction of
the tires = 0.9 [2] |
|
r = |
Radius of the tires = 250
mm [4] |
|
K = |
Shock loading factor = 1.4
[5] |
Using equations (1)-(8), the drag force, maximum weight
acting on the rear wheels due to acceleration, accelerating torque, maximum
normal and shear stresses, and fatigue life were calculated, both for the input
and output shafts, and tabulated in Błąd! Nie można
odnaleźć źródła odwołania..
Tab. 1.
Summary of the design loading
|
Parameter |
Input shaft |
Output shaft |
|
Drag force, N |
360 |
- |
|
Max. weight on the rear wheels, N |
262.79 |
- |
|
Accelerating torque, Nm |
85 |
540 |
|
Maximum normal stress, MPa |
294 |
225 |
|
Maximum shear stress, MPa |
257 |
225 |
|
Selected material |
EN36A |
AISI 4140 |
|
Fatigue life, cycles |
1,362,200 |
34,648,000,000 |
Finite Element Analysis was conducted for all
major components of the differential assembly. This was done to identify areas
of stress concentration and determine if the design will fail. Below is the
FEA, conducted in SolidWorks, of the left and right output shafts. The torques
applied to the left and right output shafts were 540 Nm and 85 Nm, respectively
(Błąd! Nie można
odnaleźć źródła odwołania.). A very fine mesh was applied in
areas of high stress concentration.
Fig. 1. Mesh of the left output shaft
Fig. 2. Mesh of
the right output shaft
Fig. 3. von Mises
stress distribution for the left output shaft
Fig. 4. von Mises
stress distribution for the right output shaft
Fig. 5. Displacement distribution for the left (on the left) and
right (on the right) output shaft
From Fig. 3 and Fig.
4 above, it is seen that yielding
occurs in localized areas, which means failure of the overall model should not
occur. Under operation, these areas of yielding will work harden (strain
harden). In addition, the largest von Mises Stresses that occurred were below
the yield strength of the AISI 4140 strain hardened material of 900 MPa.
The input shaft is made of EN36A. The maximum
stress, Fig. 6(a), occurs at the stress
concentration areas below the yield strength.
The results of the left, middle, and right
braces assembly showed that the design will not yield Fig. 7).
A summary of the results of the FEA analysis is
tabulated in Tab. 2. All the components showed a good
failure resistance.
Fig. 6. (a) von
Mises stress and (b) displacement distribution for the input shaft
Fig. 7. von Mises
stress distribution for (a) left, (b) middle, and (c) right braces
Tab. 2.
Summary of FEA results
|
Part |
Material |
Yield strength, MPa |
Displacement, mm |
von Mises stress, MPa |
|
Right output shaft |
AISI 4140 Mild Steel |
900 |
0.3129 |
|
|
Left output shaft |
0.1135 |
728.1 |
||
|
Input Shaft |
EN36A Hardened Steel |
540 |
0.1616 |
326.7 |
|
Left brace |
AISI 1045 Mild Steel |
560 |
- |
113 |
|
Middle brace |
- |
72 |
||
|
Right brace |
- |
47 |
In designing the differential, we aimed to
incorporate low cost, lightweight and reliability while adhering to all the
physical constraints and regulations defined by the Formula SAE governing body.
However, these factors were achieved without compromising concepts like speed,
braking and acceleration.
The design of the differential was analyzed
with the available tools (FEA). It was found that the Formula SAE differential appears
to meet the stated goals of reduced weight, better integration with the car,
and increased robustness over previous designs.
A lot of work was conducted to ensure the
reliability of the project and its findings; however, there is room for
improvement. Improvement is possible in areas such as the Finite Element
Analysis section where it is admittedly not very thorough as certain loads were
ignored or roughly estimated. Along with this, further analysis such as fatigue
and motion analysis would be beneficial. Limitations aside, it is hoped that
this design will serve as a starting point for further optimization of the
differential. Determining the "best" design solution is always a
compromise of strength, functionality, manufacturability, cost, and other
factors. While this differential offers much strength in these areas, it is
important to note that a racecar is never complete and better alternatives or
improvements always exist.
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Wikipedia.
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Received 19.10.2021; accepted in
revised form 09.12.2021
Scientific Journal of Silesian University of Technology. Series
Transport is licensed under a Creative Commons Attribution 4.0 International
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[1] College of Science and Engineering, James Cook
University, Townsville QLD 4811.
Australia. Email: pieta.marciano@my.jcu.edu.au.
ORCID: https://orcid.org/0000-0002-9115-9695
[2] College of
Science and Engineering, James Cook University, Townsville QLD 4811. Australia.
Email: greg.wheatley@jcu.edu.au.
ORCID: https://orcid.org/0000-0001-9416-3908
[3] College of
Engineering, King Saud University, Riyadh, Saudi Arabia. Email: jubara66@hotmail.com. ORCID: https://orcid.org/0000-0001-7490-4545