DESIGN PROJECT

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 JhaDesign project guide: Prof. B . K Jha

Manvendra Singh Inaniya(08BME126)

9047288146

Ravi Shekhar (08BME181)

9566810725

INTRODUCTIONINTRODUCTION

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.

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.

Half - Shafts

• A half - shaft is an axle on a front wheel drive vehicle connecting the transmission to the driven wheels.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.

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 .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.

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.

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.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.

LITERATURE

REVIEWREVIEW

DESIGN CRITERIA AND DURABILITY

APPROVAL OF WHEEL HUBSAE 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 loadingcomponents 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.

FRACTURE ANALYSIS OF WHEEL HUB

FABRICATED FROM PRESSURE DIE

ALUMINIUM ASSEMBLYtheoretical 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. Ananalytical investigation was carried out using tool of linear elasticfracture mechanics to establish the cause of failure. The non – linearfracture mechanics to establish the cause of failure. The non – linearbehavior is due to the presence of material inhomogeneties anddiscontinuities.

An analytical estimation was carried out in order tocalculate the minimum no. of cycles carried by wheel hub in service.The initiation of crack growth is complex because the heterogeneityand morphology of fracture surface. Fractographic andmetallographic studies are carried out to assist the understanding ofcorner cracking problem.

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: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.

PRELIMINARY PRELIMINARY

PRODUCT DESIGN

Prototype CAD Model

Half - Shaft

Isometric View

Parameters for Half-shaft

• L – Length of shaft

• Do – Outer diameter of shaft

• Di – Internal diameter of shaft

• T – Maximum Torque applied by • 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

Wheel Hub

Parameters of Wheel Hub

• n - Number of Bolts

• b - Bolt Circle Diameter or

Pitch Circle Diameter

• d - Flange diameter is measured • 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

THEORETICAL

DESIGNDESIGN

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: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

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 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.

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

d = 28.39 mmdo = 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.

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 .

Brake Force Calculation

• Brake force is required to estimate the load on the

wheel hub.

• As almost all the design parameters of a wheel • 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.

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 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

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

F = m * aFtotal = 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

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:-

T = F *rTdisc = 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

SOFTWARE SOFTWARE

ANALYSIS

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..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

Finite Element Analysis

No external force External force applied

Factor of Safety = 2Factor of Safety = 2

Safe Design

DETAILED PRODUCT

DESIGNDESIGN

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.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

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.

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. 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.

GANTT CHART(Design Project)

"DESIGN OF HALF - SHAFT OF A PROTOTYPE RACE CAR"

Sl

No. CATEGORY

Time in Weeks

1 2 3 4 5 6 7 8 9 10 11 12

A

Topic and guide selection

for project

B Literature review

C

Develop preliminary

product design

D Theoretical DesignD Theoretical Design

E CAD modelling

F Software analysis

G Optimization of design

H

Develop detailed product

design

I

Final Presentation

Compilation

***Please note that the weeks mentioned above doesnot contain the CAT weeks.

THANK YOU