The document details the design project for the half-shaft and rear wheel hub assembly of a Formula 1 race car, aiming for stability and minimal weight to enhance performance. Key design considerations included material selection, stress analysis, and adherence to parameters for optimal functionality under racing conditions. The project culminated in using CAD modeling and finite element analysis to validate designs, with calculations supporting the specifications established for the components.

1. DESIGN PROJECT

2. DESIGN OF HALF – SHAFT AND REAR
WHEEL HUB ASSEMBLY OF A RACE CAR
Faculty co-ordinator: Prof. Gokul Kumar
Design project guide: Prof. B . K Jha
Manvendra Singh Inaniya(08BME126)
9047288146
Ravi Shekhar (08BME181)
9566810725

3. INTRODUCTION

4. Project Objective
• It was required to design a hub assembly and
half–shafts for the Formula 1 car of mass about
640 kg, maximum speed of 300 km/hr and
average speed of 150km/hr.
• The assembly must give stability during rotation
of the wheels. The weight and the dimension of
the hub must be as small as possible because of
the unsprung weight which further reduces the
rotational mass. The half-shafts should not fail
under stress.

5. Red Bull RB7 Formula 1 Car
RB7 F1 is the official car from World Champions Red Bull for the 2011 season of
Formula 1. We have considered this vehicle as a reference for this Design Project
as it is one of the fastest and most technologically matured vehicle in the racing
scenario.

6. Half - Shafts
• A half - shaft is an axle on a front wheel
drive vehicle connecting the transmission to
the driven wheels.
• The rear wheel driven Formula 1 vehicle
being observed for the project uses half shafts
in rear, as the differential is rigidly mounted
and an independent rear suspension is used.

7. Design Consideration
Half shafts are designed as
– a hollow metal tube to reduce weight.
– CV joint at either end, allowing the driven wheels
to maintain constant velocity .
– Splines to transmit power between differential, CV
joints, shaft and wheel hub.
– the suspension travels during driving.
– fatigues due to high speed rotation.

8. Wheel-Hub
• A hub assembly contains the wheel bearing,
and the hub to mount the wheel to vehicle.
• It is located between the brake rotors and axle.

9. Design Consideration
• The bolt pattern is determined by the number
of bolts on the wheel hub.
• Selection of material strong enough to take the
weight of the car.
• Wheel bearings in the hub depending on ID
and OD of spindle coming out of hub.
• Type of lug nuts or bolts.

10. LITERATURE
REVIEW

11. DESIGN CRITERIA AND DURABILITY
APPROVAL OF WHEEL HUB
SAE international,USA 11-16-1998 technical paper
authors : Gerhard fischer , Vatroslov V. grubisic
The author says that the design of wheel hub must be based on
stress generated under customer usage through operational
loads acting on wheels. Wheel hub are highly steered safety
components which must not fail under the applied loading
conditions.
The main parameters for design of wheel hub
assembly are loading conditions , manufacturing process and
material behavior. The influence of these parameters are
interactive so material fatigue behaviour will be changed
depending upon the wheel hub design and loading conditions.

12. FRACTURE ANALYSIS OF WHEEL HUB
FABRICATED FROM PRESSURE DIE
ALUMINIUM ASSEMBLY
theoretical and applied fracture mechanics ,vol 9 feb 1988
authors : S . Dhar
The author says that a catastrophic failure of wheel hub occurred
during service. The nature of crack was a corner crack. An
analytical investigation was carried out using tool of linear elastic
fracture mechanics to establish the cause of failure. The non – linear
behavior is due to the presence of material inhomogeneties and
discontinuities.
An analytical estimation was carried out in order to
calculate the minimum no. of cycles carried by wheel hub in service.
The initiation of crack growth is complex because the heterogeneity
and morphology of fracture surface. Fractographic and
metallographic studies are carried out to assist the understanding of
corner cracking problem.

13. Finite element modeling of dynamic impact and
cornering fatigue of cast aluminum and forged
magnesium road wheels.
Proquest dissertation and thesis 2006
authors : Shang, Shixian (Robert)
The author says that numerical investigation of wheel dynamics impact and
cornering fatigue performance is essential to shorten design time , enhance
mechanism performance and lower development costs. The desertion
focused on two objectives:
i) Finite element models of a dynamic impact test on wheel and tire
assembly were developed which considered the material in homogeneity
of wheels. Comparison of numerical predictions with experimental
measurements of wheel impact indicated 20% reduction of initial striker
kinetic energy provide an effective method for simplifying modeling.
ii) numerical prediction of wheel cornering fatigue testing was considered.
It proceeded in two methods, first was static stress analysis with bending
direction applied to the hub. Second was dynamic stress analysis with
application of a rotating bending moment applied to hub.

14. PRELIMINARY
PRODUCT DESIGN

15. Prototype CAD Model
Half - Shaft
Isometric View

16. Parameters for Half-shaft
• L – Length of shaft
• Do – Outer diameter of shaft
• Di – Internal diameter of shaft
• T – Maximum Torque applied by
differential on shaft
• σ – Maximum Normal Stress on shaft
• τ – Maximum Sheer Stress on shaft
• J – Polar Moment of Inertia of shaft
• G – Modulus of Rigidity

17. Wheel Hub

18. Parameters of Wheel Hub
• n - Number of Bolts
• b - Bolt Circle Diameter or
Pitch Circle Diameter
• d - Flange diameter is measured
between opposite holes
• S - Spoke hole diameter
• W - Width centre to flange
• P - Load capacity is the amount of
weight a wheel will carry

19. THEORETICAL
DESIGN

20. Half - Shaft
GIVEN :
• Maximum Torque of engine at 14000 rpm = 280 N-m
• Gear ratio for 1st gear = 1.833
• Final Drive ratio = 2.15
Material selection:
• The material chosen for the design of Half – shaft is ion nitrided titanium
alloy.
• The titanium and titanium alloys have unique corrosion, nonmagnetic and
strength – to-weight ratio properties.
• Mechanical properties of nitride titanium alloys are as follows:
Yield stress = 1.24105631 × 109 Pascal
Maximum Sheer Stress = 0.62052815 × 109 Pascal

21. Calculation of Torque at half-shafts:
Shock torque = factor of safety x first gear ratio x final drive x maximum engine torque
= 2.5 x 1.833 x 2.15 x 280
= 2758.665 N-m.
Internal to external diameter ratio, k = 5
As T = 6246.765 N-m , τ = 0.62052815 × 109 Pascal , k = 5
The Axial Force acting upon the half-shafts has been countered by adding plunge to the
C.V. joints at the end of the half-shafts
The Gyroscopic couple acting due to rotational masses likes tyres, camshafts and
crankshafts is negligible as the rims, camshafts and crankshafts are made of light weight
titanium alloys which contribute insignificantly to gyroscopic couple.
No bending moment is observed as no additional weight, except self-weight of half-
shafts, is loaded on the half-shafts. Thus our calculations would be based upon the
strength required from shaft under torsional loading only.

22. T = (π/16) x τ x (do)3 x [ 1 – (di / do)4]
We have, k = di / do = 5
So, 2758.665 = (3.14/16) x 0.62x 109 x (do)3 [ 1 – (1/5)4]
do3 = 22882.115
do = 28.39 mm
Or, do = 29 mm.
Therefore, di = 29/5
di = 5.66 mm.
From the design calculation we find that the required external and internal
diameter of the half – shaft as per the specified engine parameters and given
conditions is 29 mm and 5.6 mm.

23. Wheel-Hub Assembly
Tires and rims selection:
The tires selected were of 13” diameter. The diameter was selected as
such that floor of the formula car does not touch the ground. At the same
time a low ride height would give an aerodynamic as well as low Center-
of-gravity advantage.
Number of bolts is taken 4 as it is a standard for 13” wheels.
Pitch Circle Diameter(P.C.D.) is fixed at 100 mm as it is a standard for
13” wheels.
Spoke Hole Diameter(S) is taken as M12 as it is a standard for 13”
wheels.
Material : Ti6Al4V - titanium alloy is the most widely used .

24. Brake Force Calculation
• Brake force is required to estimate the load on the
wheel hub.
• As almost all the design parameters of a wheel
hub are fixed by the size of wheel, the thickness
of the wheel hub is the defining parameter.
• The thickness of wheel hub is determined by
maximum force acting on a wheel.

25. Brake Calculation :-
Velocity of Vehicle = vo
Frictional force will be acting on it = F
Stopping distance = d
Friction force of the road must do enough work on the car to reduce its kinetic
energy to zero .
To reduce the kinetic energy to zero
Workfriction = µmgd = 0.5mv02
d= vo2/2µg
Velocity of our vehicle = 150 km/hr
Friction of road = 0.90
d = 98.31 m

26. Acceleration of the vehicle:-
vo2 = u2 + 2ad
Where a is the acceleration of the vehicle
a = vo2/2d
a = 8.8m/s
Total force acting on the vehicle
Ftotal = mv* a
Where mv is the mass of the vehicle = 640kg
Ftotal = 640 * 8.8 = 5632N
Force on each wheel:-
F1 = Ftotal/4 = 3953.43/4 =1408 N
F1 = 1408 N

27. Torque on the tire:-
Tr = F1 * rtire
Rim is taken to be 13”
rtire = 20.43 * 0.0254/2 = 0.2595 m
Tr = 1408 * 0.2595 = 365.35 N-m
Torque on disc:-
Tdisc = Ffriction*reffective
disc is assumed to be 200mm , therefore reffective should be 9cm
we know that Tdisc = Ttire
Ffriction = 25647.012 / 9
Ffriction = 2849.67N
Force on the clamp:-
Fclamp = Ffriction/µ = 2849.67/0.5 = 5699.34 N

28. SOFTWARE
ANALYSIS

29. Wheel Hub Assembly
• In design stage, we estimated all the forces acting on hub and disc
• The wheel hub was modeled in CAD with given parameters
• The forces were applied on model using Finite Element Analysis in
..COSMOS
• The thickness of hub was varied in increments of 2 mm till a Factor
..of Safety value of 2 was attained
• Thus the final design of wheel hub is complete

30. Finite Element Analysis
No external force External force applied
Factor of Safety = 2

31. Safe Design

32. DETAILED PRODUCT
DESIGN

33. Half - Shaft
Material = ion nitride titanium alloy
Yield stress = 1.241 x 109 Pascal
Max. Shear stress = 0.62 x 109 Pascal
Engine characteristics
N = 1400 rpm
T = 280 N-m.
First gear ratio = 2.833
Final drive ratio = 2.15
Shock torque = 2758.665 N-m.
K, d0/di =5
External dia. = 29 mm.
Internal dia. = 5.6 mm

34. Wheel hub
Tyre dia. = 13”
No. of bolts =4
Pitch circle dia. = 100mm.
Spoke hole dia . = M12
Material = Ti6Al4V – titanium alloy
Stopping distance = 98.31 m.
Velocity of vehicle = 150 Km/hr.
Acceleration of vehicle = 8.8 m/s2.
Force on each wheel = 1408 N.
Torque on tyre (R-13) = 388.75 N-m.
Diameter of disc = 200 mm.
Effective radius = 90 mm.
Clamping force = 8638.86 N.
Width of flange = 10 mm.

35. conclusion
• Wheel Hub has been designed for a formula 1 car of mass about 640 kg,
maximum speed of 300 km/hr and average speed of 150 km/hr.
• The designed assembly gives stability during rotation of the wheels.
• The weight and dimension of the hub is such that it reduces the rotational
mass.
• The design project enabled us to understand the various forces that act on a
half – shaft and wheel hub, while the Formula 1 race car is in running
condition.
• The calculated parameters help us to design half - shaft and wheel hub
such.
• The design project helped to better under the uses of software in real
scenario.

36. GANTT CHART(Design Project)
"DESIGN OF HALF - SHAFT OF A PROTOTYPE RACE CAR"
Sl Time in Weeks
No. CATEGORY 1 2 3 4 5 6 7 8 9 10 11 12
Topic and guide selection
A for project
B Literature review
Develop preliminary
C product design
D Theoretical Design
E CAD modelling
F Software analysis
G Optimization of design
Develop detailed product
H design
Final Presentation
I Compilation
***Please note that the weeks mentioned above doesnot contain the CAT weeks.

37. THANK YOU