CHAPTER 1

INTRODUCTION

1.1 Theoretical Background:

The cycle rickshaw is a small-scale local means of transport; it is also known by a variety of other

names such as velotaxi, pedicab, bikecab, cyclo, becak, or trishaw or, simply,rickshaw which also

refers to auto rickshaws, and the, now uncommon, rickshaws pulled by a person on foot. Cycle

rickshaws are human-powered, a type of tricycle designed to carry passengers in addition to the

driver. They are often used on a for hire basis. Cycle rickshaws are widely used in major cities

around the world, but most commonly in cities of South, Southeast and East Asia.

1.2 Configurations:

The vehicle is pedal-driven by a driver, though some configurations are equipped with an electric

motor to assist the driver. Electric-assist pedicabs were banned in New York City in January 2008,

along with all other forms of electric vehicles; the city council decided to allow pedicabs propelled

only by muscle power. The vehicle is usually a tricycle, though somequadra cycle models exist,

and some bicycles with trailers are configured as cycle rickshaws. The configuration of driver and

passenger seats vary by design, though passenger seats are usually located above the span of the

longest axle.

1.3 Nomenclature:

Table 1.1 : Nomenclature of Rickshaw

1

S.No Country Nomenclature

1. India And Bangladesh Cycle Rickshaw

2. Cambodia Cyclo

3 Mayanmar Saika

4. China and Malaysia Trishaw

5. Indonesia Becak

6. Philippines Padyak

7. Mexico Bicitaxi or Taxi Ecologico

The Cycle rickshaw is an important mode of transportation in many small cities and towns in

India. The traditional cycle rickshaw is seen in many shapes and sizes but there is a common

thread that makes most of them rather inefficient, uncomfortable and often, unsafe vehicles. This

is one of the prime reasons for the gradually diminishing clientele of the cycle rickshaws.

1.4 Economic and political aspects

In many Asian cities where they are widely used, cycle rickshaw driving provides essential

employment for recent immigrants from rural areas, generally impoverished men. One study in

Bangladesh showed that cycle rickshaw driving was connected with some increases in income for

poor agricultural laborers who moved to urban areas, but that the extreme physical demands of the

job meant that these benefits decreased for long-term drivers. In Jakarta, most cycle rickshaw

drivers in the 1980s were former landless agricultural laborers from rural areas of Java.

2

CHAPTER 2

LITERATURE REVIEW

2.1 Dead axles/lazy axles

A dead axle, also called lazy axle, is not part of the drive train but is instead free-rotating. The rear

axle of a front-wheel drive car may be considered a dead axle. Many trucks and trailers use dead

axles for strictly load-bearing purposes. A dead axle located immediately in front of a drive axle is

called a pusher axle. A tag axle is a dead axle situated behind a drive axle. On some vehicles (such

as motor coaches), the tag axle may be steerable.

Some dump trucks and trailers are configured with lift axles (also known as airlift axles or drop

axles), which may be mechanically raised or lowered. The axle is lowered to increase the weight

capacity, or to distribute the weight of the cargo over more wheels, for example to cross a weight

restricted bridge. When not needed, the axle is lifted off the ground to save wear on the tires and

axle and to increase traction in the remaining wheels. Lifting an axle also makes the vehicle

perform better on tighter turns.

2.1.1 Causes of failure of axle:

Presence of cyclic overloads

Stress concentration

Wrong adjustment of bearings, insufficient clearance.

2.1.2 Desirable properties for material of axle

Sufficient high strength.

A low sensitivity to stress concentration.

Ability to withstand heat and case hardening treatment.

Good machinability

2.2 Curved Beams

3

One of the assumptions of the development of the beam bending relations is that all longitudinal

elements of the bean have the same length, thus restricting the theory to initially straight beams of

constant cross section. Although considerable deviations from this restriction can be tolerated in

real problems, when the initial curvature of the beams becomes significant, the linear variations of

strain over the cross section are no longer valid, even though the assumption of plane cross

sections remaining plane is valid. A theory for a beam subjected to pure bending having a constant

cross section and a constant or slowly varying initial radius of curvature in the plane of bending is

developed as follows. Typical examples of curved beams include hooks and chain links. In these

cases the members are not slender but rather have a sharp curve and their cross sectional

dimensions are large compared with their radius of curvature.

2.2.1 Introduction

Machine frames having curved portions are frequently subjected to bending or axial loads or to a

combination of bending and axial loads. With the reduction in the radius of curved portion, the

stress due to curvature become greater and the results of the equations of straight beams when

used becomes less satisfactory. For relatively small radii of curvature, the actual stresses may be

several times greater than the value obtained for straight beams [2]. It has been found from the

results of Photoelastic experiments that in case of curved beams, the neutral surface does not

coincide with centroidal axis but instead shifted towards the centre of curvature. It has also been

found that the stresses in the fibres of a curved beam are not proportional to the distances of the

fibres from the neutral surfaces, as is assumed for a straight beam.

2.2.2 Bending in the Plane of the Curve

In a straight beam having either a constant cross section or a cross section which changes

gradually along the length of the beam, the neutral surface is defined as the longitudinal surface of

zero fiber stress when the member is subjected to pure bending [7]. It contains the neutral axis of

every section, and these neutral axes pass through the centroids of the respective sections. In this

section on bending in the plane of the curve, the use of the many formulas is restricted to those

members for which that axis passing through the centroid of a given section and directed normal to

the plane of bending of the member is a principal axis. The one exception to this requirement is for

a condition equivalent to the beam being constrained to remain in its original plane of curvature

such as by frictionless external guides. To determine the stresses and deformations in curved

4

beams satisfying the restrictions given above, one first identifies several cross sections and then

locates the centroids of each. From these centroidal locations the curved centroidal surface can be

defined. For bending in the plane of the curve there will be at each section (1) a force N normal to

the cross section and taken to act through the centroid, (2) a shear force V parallel to the cross

section in a radial direction, and (3) a bending couple M in the plane of the curve. In addition there

will be radial stresses σr in the curved beam to establish equilibrium. Circumferential normal

stresses due to pure bending. When a curved beam is bent in the plane of initial curvature, plane

sections remain plane, but because of the different lengths of fibers on the inner and outer portions

of the beam, the distribution of unit strain, and therefore stress, is not linear. The neutral axis does

not pass through the centroid of the section. The error involved in their use is slight as long as the

radius of curvature is more than about eight times the depth of the beam. At that curvature the

errors in the maximum stresses are in the range of 4 to 5%. In part the formulas and tabulated

coefficients are taken from the University of Illinois Circular by Wilson and Quereau [4]. For

determining circumferential stresses at locations other than the extreme fibers, one can find

formulas in texts on advanced mechanics of materials [6] [7]. The circumferential normal stress is

given as

σθ = My/Aer

Where M is the applied bending moment, A is the area of the cross section, e is the distance from

the centroidal axis to the neutral axis, and y and r locate the radial position of the desired stress

from the neutral axis and the center of the curvature, respectively.

2.3 Rickshaw chain

A chain bicycle is a roller chain that transfers power from the pedals to the drive-wheel of a

bicycle, thus propelling it.

5

Figure 1.1 Basic Chain Derive geometry

Most bicycle chains are made from plain carbon or alloy steel, but some are nickel-plated to

prevent rust, or simply for aesthetics. Nickel also confers a measure of self-lubrication to a chain's

moving parts. Nickel is a relatively non-galling metal.

2.3.1 Efficiency

A bicycle chain can be very efficient: one study reported efficiencies as high as 98.6%. The study,

performed in a clean laboratory environment, found that efficiency was not greatly affected by the

state of lubrication. Larger sprocket will give a more efficient drive, reducing the movement angle

of the links. Higher chain tension was found to be more efficient: "This is actually not in the

direction you'd expect, based simply on friction" [6].

2.3.2. Chain Drive Systems

Consists of two or more sprockets connected with chain

The sprockets are mounted on shafts that are supported by bearings

Purpose: to transmit power and motion between shafts

6

2.3.3. Advantages over belt drive systems:

Do not slip or creep (no power loss from slippage)

More compact for a given capacity

Lower loads on shafts (because high tension is not required as with belt drives)

Easy to install

Not affected by sun, heat, or fluids (such as oil and grease)

Do not deteriorate with age

More effective at lower speeds

Require little adjustment

2.3.4. Advantages over gear drive systems:

Flexible center distances

Less expensive

Simpler installation and assembly

Better shock absorption

2.3.5. Disadvantages:

Require lubrication (in most cases)

Noisier than belt drives

More expensive than belt drives

Impractical for extremely long center-to-center distances where flat belts could be used

Less efficient than flat belts at extremely high-speed ranges

Must be used on parallel shafts; cannot twist chain like belts

7

Chordal action- slight pulsation in the output sprocket –becomes less pronounced as the

number of sprocket teeth are increased

Transmission Roller Chain is the most widely chain used because of its versatility.

2.3.6. Roller chains are made up of the following:

Roller link: inside link made up of two roller (inside) link plates, two bushings and two

rollers

o Roller link plate: one of the plates forming the tension members of a roller link

o Roller: a ring or thimble which turns over the bushing

o Bushing: a cylindrical bearing in which the pin turns

Pin link: outside link made up of two pin link plates assembled with two pins

o Pin link plate: one of the plates forming the tension members of a pin link

Connecting link: a pin link having one side plate that is detachable (retained by cotter pins

or a spring clip)

Offset link: a link consisting of two offset plates assembled with a bushing and roller at

one end and an offset link pin at the other end; used when chain has an odd number of

links  

2.3.7 Roller Chain Sprockets

Types:

a) plate- flat hub less sprocket used for mounting on flanges, hubs or other devices,

b) Hub on one side- used for low-load applications and small diameter sprockets

c) Hub on both sides- used for large diameter sprockets and high-load applications

d) Detachable hub-plate sprocket mounted on hub

e) Shear pin and slip clutch sprockets- designed to prevent damage to the drive or other

equipment caused by overloads or stalls

8

Sprocket Classes

1) Commercial- used with slow to moderate speed drives; in general, drives requiring

Type A or Type B lubrication would use Commercial sprockets

2) Precision- used when extreme high speed in combination with high load is involved,

or where the drive involves fixed centers, critical timing, or close clearance with

outside interference; in general, drives requiring Type C lubrication may require

Precision sprockets (consult the manufacturer)

Sprocket Diameters

o Pitch diameter: diameter of the pitch circle that passes through the centers of the

link pins as the chain is wrapped on the sprocket

o Bottom diameter: diameter of a circle tangent to the curve (seating curve) at the

bottom of the tooth gap; equal to the pitch diameter minus the diameter of the roller

o Caliper Diameter: equal to the bottom diameter for a sprocket with even number of

teeth- for a sprocket with an odd number of teeth, it is the distance from the bottom

of one tooth gap to that of the nearest opposite tooth gap

o Outside Diameter: diameter of the circle at the tips of the teeth

Sprocket/Shaft mounting

o Both keys and set screws should be used to mount a sprocket to a shaft

o Key- used to prevent rotation

o Set screw- located over flat key to prevent longitudinal displacement

o American Chain Association recommendations.

Center distance between sprockets

o Minimum center distance: 1-1/2 times the diameter of the larger sprocket and a

minimum of 30 times the pitch (30 pitches)

9

o Optimum results: 30 to 50 pitches

o Maximum center distance: 80 pitches

o When necessary, drives may be operated with a small amount of clearance between

the sprockets; in these cases it follows that the center distance must be a little

greater than the sum of the half the diameter of the sprockets

o A longer chain is recommend in preference to the shortest allowed by the sprocket

diameters because the rate of chain elongation is inversely proportional to the

length

o Center distance, c = P/8 (2L – N2 – N1+ ((2L – N2 – N1)2 – 0.810(N2 – N1)2)1/2)

Where:

P = chain pitch

L = chain length in pitches

N2 = Number of teeth in large sprocket

N1= number of teeth in small sprocket

Size of sprockets

General practice to use minimum size sprocket of 17 teeth and maximum of 67 teeth in

order to obtain smooth operation and long life at high speeds

For greater life expectancy and smoother operation (because of the lessening of tooth

impact) use sprocket with 19-21 teeth

On low speed, special purpose, and/or space limiting operations, sprockets with fewer than

17 teeth can be used

Normal maximum number of teeth is 120

Chain wrap: minimum of 120 degrees on driver; will always be 120° with a two sprocket

drive with a ratio of 3.5:1 or less

Ratio of driver to driven sprocket should be no more than 6:1 10

rv = N1/N2 = n2/n1

Where:

N1 = Number of teeth of driver

N2 = Number of teeth of driven

n1 = angular velocity of driver (rev/min)

n2 = angular velocity of driven (rev/min)

2.3.8 Chain Length, Drive Arrangement, and Lubrication

Chain Tension

o Chain sag should be approximately 2 percent of the center distance

o An idler (when necessary) should be placed on the slack side of the drive

o When the idler is placed on the tight side of the chain to reduce vibration, it should

be on the lower side and located so the chain will run in a straight line between the

two main sprockets

Chain Length: function of the number of teeth in both sprockets and of the center distance

o Chain length is given in an integral number of pitches (with even number

preferable)

o Chain length L= 2C + (N2+ N1)/2 + (N2-N1)2/(4p 2C)

Where:

L= chain length (number of pitches)

C= center distance (pitches)

N2 = number of teeth in large sprocket

N1 = number of teeth in small sprocket

Lubrication

o Must be applied to minimize metal-to-metal contact

11

o If supplied in sufficient volume, it also provides effective cooling and impact

damping at higher speeds

Type A- Manual or Drip Lubrication: Manual-applied with a brush or spout can at least

once every eight hours; Drip-oil drops from a drip lubricator directed between link plates

Type B- Bath or Disc Lubrication: Bath- lower strand of the chain runs through a sump of

oil in the drive housing. The oil should reach the pitch line of the chain at its lowest point

while operating. Disc- chain operates above oil level; disc picks up oil and deposits it onto

the chain

Type C- Oil Stream Lubrication: oil applied continuously inside the chain loop evenly

across the chain width, and directed at the slack strand

2.4. Designing a Chain Drive System

Based on the following factors:

1. Average HP

2. RPM of driving and driven members

3. Shaft diameter

4. Permissible diameters of sprockets

5. Load characteristics (smooth and steady, pulsating, heavy-starting, or subject to peaks)

6. Lubrication

7. Life expectancy (total amount of service required, or total life)

2.4.1. Classification Of Chains :

Hoisting and hauling chains

Chain with oval links.

Chain with square links

Conveyor ( or tractive) chains

12

Detachable or hook joint type chain

Closed joint type chain

Power transmitting (or driving) chains

Block Chain

Bush Roller Chain

Inverted tooth or silent chain

2.4.2. Faliure Modes of Chain:

Fatigue of the link plate

Repeated loading/unloading from tight side to slack side.

Contact between roller and sprockets

Galling between the pain and bushing

2.5. Sprocket

The process designing and drawing a sprocket is an excellent way to incorporate algebra and

geometry skills and knowledge.

The following text offers the information and procedural steps necessary to generate the profile of

standard pitch sprockets. This process will yield an approximate tooth form that can be used to

generate solid models of the sprockets used in the GEARS-IDS kit of parts. The process of

producing and saving a solid model library of GEARS-IDS sprockets and parts, provides students

and instructors with the opportunity to combine algebra, geometry and trigonometry knowledge

with engineering drawing skills to produce the design elements necessary to fully visualize their

mechanical creations.

13

Figure 2.1 : Sprocket Tooth Geometry

2.5.1. Sprocket Tooth Design Formulas

Refer to above Sprocket Tooth Geometry figure.

The tooth form of a sprocket is derived from the geometric path described by the chain roller as it

moves through the pitch line, and pitch circle for a given sprocket and chain pitch. The shape of

the tooth form is mathematically related to the Chain Pitch (P), the Number of Teeth on the

Sprocket (N), and the Diameter of the Roller (Dr). The formulas for the seating curve, radius R

and the topping curve radius F include the clearances necessary to allow smooth engagement

between the chain rollers and sprocket teeth.

The following formulas are taken from the American Chain Association Chains for Power

Transmission and Material Handling handbook, and they represent the industry standards for the

development of sprocket tooth forms.

14

Table 2.1 Sprocket design formulae

P = Chain Pitch

N = Number of Teeth

Dr = Roller Diameter ( See Table)

Ds = (Seating curve diameter) = 1.0005 Dr +

0.003

R = Ds/2 = 0.5025 Dr + 0.0015

A = 35°+60°/N

B = 18°- 56°/N

ac = 0.8 x Dr

M = 0.8 x Dr Cos (35°+60°/N)

T = 0.8 x Dr Sin (35°+60°/N)

E = 1.3025 Dr + 0.0015

Chordal Length of Arc xy = (2.605 Dr +

0.003) sin (9°−28°/N)

yz = Dr [1.4 Sin (17° − 64/N) – 0.8 Sin (18° -

56°/N )]

ab = 1.4 Dr

W = 1.4 Dr Cos 180°/N

V = 1.4 Dr Sin 180°/N

F = Dr [ 0.8 Cos( 18° - 56° / N) + 1.4 Cos (17°

- 64°/ N]

H = √ F 2 - ( 14 Dr – P/2)2

S = P/2 Cos 180°/N + H Sin 180° / N

PD = P/ Sin [180°/ N]

2.5.2. Additional Sprocket Formulas:

Outside Diameter of a sprocket when j = 0.3P

OD = P (0.6 + Cot 180°/N)

Outside diameter of a sprocket when tooth is pointed

OD = P Cot 180° / N + Cos 180°/N (Ds – Dr) + 2H

 

CHAPTER 3

PRESENT WORK15

3.1. Problem formulation:

The rickshaw is made by an artisan. Every part of the body of rickshaw like its axle, its chain, its

curved plate etc are selected by artisan by his experience. We as a team were to study various

forces, acting points of various forces, the reaction of various forces etc and then to make

complete force analysis and hence to refine the existing design. It is an endeavor to improve upon

the existing design thereby making significant changes if necessary, to improve puller as well as

passenger comfort by reducing the overall weight of rickshaw without compromising the strength

and safety etc.

3.2 Objective:

The machine would be mechanically refined yet simple and easy to ride.

3.3 Experimental Work

In our experimental work, we firstly measure the weight of rickshaw. Then we consider the

problems of designing the axle for rickshaw, curved plate for rickshaw and chain for rickshaw.

3.3.1 Weight of Cycle Rickshaw

According to project point of view, firstly we measure the weight of cycle rickshaw.

Table 3.1 Weight of cycle rickshaw

S.No Parts Weights(In Kg)

1. Upper Parts (Body) 28.7

2. Lower Parts (Chaises) 50.3

3.4 Design of Curved Beams

Notations and Symbols Used

16

σ = Stress, MPa.

σd = Direct stress, tensile or compressive, MPa.

σi = Stress at inner fibre, MPa.

σo = Stress at outer fibre, MPa.

σbi = Normal stress due to bending at inner fibre, MPa.

σbo = Normal stress due to bending at outer fibre, MPa.

Mb = Bending moment for critical section, N-mm.

ci = Distance of neutral axis from inner fibre, mm.

co = Distance of neutral axis from outer fibre, mm.

e = Eccentricity, mm.

ri = Distance of inner fibre from centre of curvature, mm.

ro = Distance of outer fibre from centre of curvature, mm.

rc = Distance of centroidal axis from centre of curvature, mm.

rn = Distance of neutral axis from centre of curvature, mm.

d = Diameter of circular rod used in curved beam, mm.

h = Depth of curved beam [square, rectangular, trapezoidal or I-section], mm.

τmax = Maximum shear stress, MPa.

A = Area of cross-section of member, (curved beam), mm2.

P = Load on member, N.

3.4.1 Derivation of Expression to Determine Stress at any Point on the Fibres of a Curved

Beam

Consider a curved beam with rc, as the radius of centroidal axis, rn, the radius of neutral surface, ri,

the radius of inner fibre, ro, the radius of outer fibre having thickness ‘h’ subjected to bending

moment Mb.

Let AB and CD be the two adjacent cross-sections separated from each other by a small

angle dφ.

Because of Mb the section CD rotates through a small angle dα. The unit deformation of any fibre

at a distance y from neutral surface is:

17

Deformation, Є = δ/ l = yd α/(rn – y)dθ ………… (1.1)

The unit stress on this fibre is,

Stress = Strain × Young’s modulus of material of beam

σ = εE = Eyd α/(rn – y)dθ……………….(1.2)

For equilibrium, the summation of the forces acting on the cross sectional area must be zero.

i.e ∫ σdA = 0

or, ∫ Eyd αdA/(rn – y)dφ = 0

Ed α/dθ∫ydA/(rn-y) = 0 ……………..(1.3)

Also the external moment Mb applied is resisted by internal moment. From equation 1.2 we have,

∫ y(σdA) = M

i.e ∫ Ey2d αdA/(rn – y)dφ = M

Edα/ dφ ∫y2dA/(rn – y) = M ………………….. (1.4)

i.e M = Edα/ dφ∫(-y)dA + rn∫ ydA/(rn-y) ……………………(1.5)

Note: In equation 1.5, the first integral is the moment of cross sectional area with respect to

neutral surface and the second integral is zero from equation 1.3.

Therefore, M = [Edα/ dφ]Ae ………………. (1.6)

Here ‘e’ represents the distance between the centroidal axis and neutral axis.

i.e., e = rc − rn

Rearranging terms in equation 1.6, we get

dα/ dφ = M/AeE ………………….. (1.7)

Subsituting dα/ dφ = M/AeE in equation 1.2

We get,

Stress σ = Eydα/ dφ(rn – y) becomes,

= EyM/(rn – y)AeE

i.e σ = EyM/(rn – y)AeE ……………………(1.8)

18

But we know,

rn = v – y

y = rn – v

Therfore, from equation 1.3,

∫ ydA/(rn – y) = ∫ (rn – v)dA/(rn – y)

= rn∫ dA/v - ∫dA = 0

= rn∫ dA/V - A = 0

Or, rn = A/∫dA/v ……………… (1.9)

Note: Since e = rc – rn, equation 1.9 can be used to determine ‘e’. Knowing the value of ‘e’,

equation 1.8 is used to determine the stress σ .

3.5 Designing of curved beam in the rickshaw 1960N

52.5 mm 40 mm 95 mm

5 mm

4o mm

Figure 3.1 Side view and crossection of curved plate

Area of section, A = 40 x 5 = 200 mm2

= 200 x 10-6 m2

19

Bending moment due to load is =

M = 1960 x(40 + 52.5) x 10-3

= 181.3 Nm

Resultant stresses at inside and outside of curved section:

Direct stress, σd = P/A

= 1960/200 x 10-6

= 9.8 x 106 N/m2

= 9.8 Mn/m2 ------- (Compressive)

Now as the curved beam is of rectangular section, therefore:

h2 = R3/D Loge [(2R +D) / (2R-D)] - R2

Where:

R = radius of curvature of centroidal axis

D = depth of rectangular section plate curved beam

h2 = constant used in Winkler Bach Formula

In the rickshaw the values are:

R = 52.5 mm

= 0.0525 m

D = 5 mm

0.005 m

Put these values in given h2 formula, we get:

h2 = (0.0525)3 / (0.005) Loge [(2x 0.0525 + .005) / (2 x 0.0525 – 0.005)] – (0.0525)2

= 0.028940 Loge [1.1] – (.0525)2

= 0.00275827 – 0.0027562

= 2.0766 x 10-6 m2

20

Now bending stress due to M at inside point is:

σb = M/AR [1 – R2 / h (y / R - y)]

= 181.3/ (200 x 10-6 x 0.0525) [1 – (0.0525)2 / 2.0766 x 10-6 {0.0025/(0.0525 – 0.0025)}

= 17.26 x 106 [1- 0.0013315 x 106 (0.0025/0.05)]

= 17.26 x 106 [1- 0.0013315 x 106 (0.05)]

= 17.26 x 106 [1- 66.575]

= - 1131.82 x 106 N/m2

= - 1131.82 MN/m2------ (Compressive)

Now total stress at inside point is equal to direct stress at inside point + bending stress at inside point

= 9.8 MN/m2 + 1131.82 MN/m2

Total stress = 1141.62 MN/m2 (compressive)

For stress at outside point:

Now bending stress due to M at outside point is:

σb = M/AR [1 + R2/ h (y / R+ y)]

= 181.3/ (200 x 10-6 x 0.0525) [1 + (0.0525)2 / 2.0766 x 10-6 {0.0025 / (0.0525 + 0.0025)}

= 17.26 x 106 [1 + 0.0013315 x 106 (0.0025 / 0.0525 + 0.0025)]

= 17.26 x 106 [1 + 0.0013315 x 106 (0.04545)]

= 17.26 x 106 [1 + 60.5]

= 1061.49 x 106 N/m2

= 1061.49 MN/m2---------- (tensile)

Now total stress at point 1 is equal to direct stress at outside point + bending stress at outside point

= 9.8 MN/m2 (compressive) + 1061.49 MN/m2 (tensile)

Total stress = 1051.69MN/m2 (tensile)

21

3.6 Design of dead axle for the rickshaw:

In the rickshaw, the total length of the axle rod is 80 cm. The whole sitting arrangement (3920 N)

weight is placed on the axle rod at two points exactly 11 cm from the each end. So 58 cm is the

span of axle between these two points. From the given arrangement and for the analysis purpose

the axle is assumed to be a simply supported beam carrying two equal loads of 1960 N each acting

at two points 11 cm from each end. The total weight is shifted to the ground on two rim and tyre

pairs.

As the axle is not transmitting any torque, so there are not any external shear stresses set up

in the axle. Therefore the axle is designed for bending only. But as the lateral loading is there, on

the axle, so shear forces also develop in the axle along with the bending stresses. Since at every

point it is assumed that the particles of the material of axle is in equilibrium, the effect of shearing

forces and bending moments must be consistent. There is involvement of two factors. The applied

shearing forces will be distributed as a shearing stress across transverse sections of the axle. But at

each point on the section, the transverse shearing stress will produce a complimentary horizontally

shearing stress i.e there will be shearing stresses acting between successive layers of the beam,

tending to resist sliding between these layers. So we have to firstly calculate the bending stresses

by using bending moment equation and then shear stresses using necessary formulae:

Axle 1960 N 1960 N

AXLE LOADING DIAGRAM

11 cm 11 cm

80 cm

1960N 1960N

SF DIAGRAM

22

1960N 1960N

21560Ncm 21560Ncm

BM DIAGRAM

0 Ncm 0 Ncm

Figure 3.2 : Loading ,SF and BM diagram of axle

For bending stresses

The bending moment equation is used as follows:

M/I = σb/y = E/R

Where: M = maximum bending moment on the axle

I = moment of inertia of circular axle

y = distance of extreme fiber of axle rod from its neutral axis (=d/2)

E = young’s modulus of elasticity of the material of axle

R = radius of curvature of bending axle neutral axis

σb = bending stress in the axle rod

In the given rickshaw, the diameter of the axle rod is d = 2.54 cm

d = 2.54 cm

I = 3.14 d4/64

23

= 3.14 x (2.54)4/64

= 2.0421355 cm4

y = 1.27 cm

Now bending stress, σb = M * y/I

σb = (21560 * 1.27)/ 2.0421355

σb = 13408.121N/cm2

For shearing stresses

The equation for calculating maximum shear stress in the circular section of axe is

τ = 4S/3 π R2

Where :

S = maximum shear stress on the axle

R = radius of the axle rod

τ = shear stress developed due to shear force S

now in the present axle the maximum shear stress as is clear from the shearforce diagram is,

S = 1960 N

R = 1.27 cm

Therfor applying the above shearing equation:

τ = 4S/3 π R2

τ = (4 x 1960)/(3 x 3.14 x 1.27 x 1.27)

τ = 516 N/cm2

24

Now due to both bending and shear stress the net principle stresses developed in the axle. These

principal stresses are given by the following formula:

σp = σb/2 + √σb/2 + τ2

So, principle stresses are:

σp = 13408.121/2 + √(13408.121/2)2 + (516)2

σp = 6704.0605 + √44944427 + 266256

σp = 6704.0605 + √ 45210683

σp = 6704.0605 + 6723.889

σp1 = 13427.95 N/cm2

&

σp2 = -19.82 N/cm2

Now according to shear strain energy theory or distortion energy theory (Von-Mises Henky

Theory) the elastic failure occurs where the shear strain energy per unit volume in the stressed

material reaches a value equal to the shear strain energy per unit volume at the elastic limit

point in the simple tensile test.

Mathematically the equation of failure is written as:

σet2 = σp1

2 + σp2

2 – σp1 σp2

σet2 = (13427.95)2 + (-19.82)2 - (13427.95) (-19.82)

σet2 = (180309841.2) + (392.83) + 266141.97

σet2 = 180576375.999

σet = 13437.87 N/cm2

25

σet = 134.37 MN/m2

therefore the axle is safe in rickshaw because as per the given loading conditions or constraints the

maximum elastic limit stress needs to be equal to 134.37 MN/m2 which is far less than the elastic

limit stress of mild steel material.

3.7 Design Procedure for Chain:

Determine the velocity ratio of the chain drive

V.R = 3.142(DN)/60

 Where D = Diameter of the pitch circle

Select the minimum number of teeth on the smaller sprocket.

Find the number of teeth on the largest sprocket

T2 = T1 * N1/N2

Pitch line velocity of the smaller sprocket

V1 = 3.142d1 N1/60

Load on the chain

W=Load/Pitch line velocity

Centre distance b/w the sprockets = p(30-50)

Number of chain links

K = (T1 +T2)/2 + 2x/p + [{T2 + T1}/2*3.142] [{T2 + T1}/2*3.142] p/x

Length of the chain. L = K*p

3.8 Designing Chain Design for the Rickshaw:

The velocity ratio of chain drive

V.R.=3.142[D*N]/60

D=diameter of the pitch circle.

=3.142[10*18]/60

=9.56mm

Minimum number of teeth on the smaller sprocket

T(s) =16

26

The number of teeth on the larger sprocket

T(l)=T(s)*N1/N2

[NI/N2=Speed ratio]

=16*2

=32

Pitch line velocity of the smaller sprocket

V(s) = 3.142*d1*NI/60

Where d1=pitch dia. of driving sprocket.

=3.142*50*16/60

=0.40m/s

Load on the chain;

W=load (L)/pitch line velocity

400kg =L / 0.40

L =400/0.40

=398.52N

Center distance between the sprockets:

30<Cp<50

Cp=center distance in number of pitches.

Chain in even number of pitches

= P (30-50) = 15.875(20)

Cp=410mm

Number of chain links; K = (Ts+Tl)/2+2x/p+[{Tl+Ts}/2*3.14]*

*[(Tl+Ts)/2*3.14] p / x

= (16+32)/2+2*0.2/15.875 + [(16+32)/2*3.14]

*[(16+32)/2*3.14]15.875/0.2

=90

Length of the chain;

K*P=120/4*15.875

=04ft

27

CHAPTER 4

RESULTS AND DISSCUSSION

The principal idea was to develop a modern cycle rickshaw that could demonstrate the possibility

of growth of this traditional mode of transportation in India to counter the growing menace of

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motor vehicular pollution. It provides comfortable and safe seating. Following results are obtained

after analysis:

Design of axle is safe

Design of curved plate is safe

Chain is designed for the rickshaw

REFERENCES

[1] Shepard W.K., (1907), “Problems in strength of materials” Ginn and company,

New York

29

[2] Merriman M., (1910), “Mechanics of materials”, John Wilay and Sons, Chapman

and Hall Limited

[3] Timoshenko S., (1923), “Bending Stresses in Curved Tubes of Rectangular Cross-

section” ASME journal, Volume, 45, p. 135 - 143

[4] Wilson B. J. and J. F. Quereau (1927), “A Simple Method of Determining Stress in

Curved Flexural Members” ASME Journal, Volume 45, pp 64 – 73, 1927

[5] S P Timoshenko, S.P, (1953), “History of the Strength of Materials”, McGraw-Hill

[6] Cook R. D. and W. C. Young (1998), ‘‘Advanced Mechanics of Materials,’’ 2nd

edition, Prentice-Hall

[7] Budynas R. G. (1999), ‘‘Advanced Strength and Applied Analysis,’’ 2nd edition,

McGraw-Hill

[8] Sharma P.C., Aggarwal D.K., (1999), “Machine Design” 9th edition, S.K Kataria

and Sons, India

[9] Rajput R.K., (2006), “ Strength of Materials” 8th edition, S Chand and Company,

India

[10] Bansal R.K., (2007), “Strength of materials” 4th edition, Luxmi Publications, India

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