LOVELY PROFESSI ONAL UNIVERSITY

PHAGWARA( PB.)

TERM PAPER

Sub. :- Mechanics of solids (MEC-201)

Topic :-SCREW JACK(strength and analysis)

Submitted to, Submitted by,

MR AJAY SIR, Omkar Kumar Jha

RH-4901-A12

10902923

MECHANICAL ENGG. (III rd TERM)

SCREW JACK

A screw jack is a portable device consisting of a screw mechanism used to

raise or lower the load.

There are two types of jack are named-hydraulic and mechanical. Hydraulic

jack consists of cylinder and piston mechanism. The movement of piston

rod is used to raise or lower the load.

Mechanical jacks can be either hand operated or power driven. Although a

jack is a simple and widely used device, the use of any lifting device is

subjected to certain hazards. In screw-jack application, hazards are

dropping, tipping or slipping of machines or their parts during the

operation. These hazards may result in serious accidents are as follows:

1. the load is improperly secured on the jack

2. The screw jack is overloaded.

3. The centre of gravity of the load is off centre with respect to the axis

of the jack.

4. The screw jack is not placed on hard and level surface.

5. The screw jack is used for a purpose, for which it is not designed.

Proper size, strength and stability are the essential requirements for the

design of the screw jack from safety consideration…

A screw jack consists of a screw and a nut. The nut is fixed in a cast iron

frame and remains stationary. The rotation of the nut inside the frame is

prevented by pressing a setscrew against it.The screw is rotated in the nut

by means of a handle that passes through a hole in the head of the screw.

The head carries a cup, which supports load and remains stationary, while

the screw is being rotated. There is a collar friction at the head of the

screw. A washer is fixed to the other end of the screw inside the frame that

prevents the screw to be completely turned out of the nut.

PROBLEM SPECIFICATIONS

It is required to design a screw jack supporting the machine parts during

their repair and maintenance on the shop floor. It should be a general

purpose jack with a load carrying capacity of 100KN and maximum lifting

height of 0.5 m. The jack is to be manually operated.

۞SELECTION OF MATERIALS:-

(i) The frame of the screw jack has complex shape. It is subjected to

compressive stress. Grey cast iron of grade FG200

( S ut = mmN2

) is selected as the material for the frame. Cast

iron is cheap and it can be given any complex shape without

involving costly machining operation. Cast iron has higher

compressive strength compared with steel. There fore, it is

technically and economically advantageous to use cast iron for the

frame.

(ii) The screw is subjected to torsional moment, compressive force and

bending moment, from strength consideration, plain carbon steel of

grade 30C8 ( s yt =400 mmN2

and E=207000 mmN2

) is

selected as martial for the screw.

(iii) There is relative motion between the screw and the nut that results

in friction. The friction causes wear at the contacting surfaces.

When some martial is used for these two components, the surfaces

of both components get worn out, requiring replacement. This is

undesirable. The size and shape of the screw make it costly

compared with the nut. Therefore, if at all a component is to be

replaced due to wear. It should be the nut, which is less costly

compared with the screw. The wear is always restricted to softer

surface. Therefore, the nut should be made of softer material. This

protects the screw against wear. Cast verity of phosphor bronze of

grade-1 ( S ut =190 mmN2

) is selected as the material for the

nut. Phosphor bronze is soft compared with hardened steel screw.

In addition to this consideration, phosphor, bronze has a low

coefficient of friction, which reduces the torque to overcome

friction at the thread surface. it has excellent conformability and

machine ability .conformability is the ability of the material to

yield and adopt its shape to that of the screw. Cost is the main

limitation of phosphor bronze. For steel screw and phosphor

bronze nut, the permissible bearing pressure ( sb ) and coefficient

of friction are taken as 10 mmN2

and0.1 respectively.

(iv) The handle is subjected to bending moment and yield strength is

the criterion for the selection of material .plain carbon steel of

grade 30C8 ( S ut =400 mmN2

) is selected as the material for

the handle.

(v) The shape and dimensions of the cup are such that it is easier and

economical to make it by casting process. Grey cast iron of grade

FG200 is used for the cup.

۞GENERAL CONSIDERATIONS :-

1) The screw jack is manually operated. According to ergonomists, hand

force should not exceed 130 N. however; this value is permitted in

prolonged work. Jack is never operated continuously and as such a

higher value of 400 N is assumed for hand force in this analysis. It is

further assumed that two workers are required to raise the load of 100

kN. When two workers are at work, there is inconvenience and the

resultant force is less than twice the individual force. A coefficient of

0.9 is assumed in the case to account for reduction in force due to

inconvenience. Therefore, total hand force exerted on the handle by

two worker( p ) is given by,

p = (0.92400) N

2) Screw jack is lifting device and subject to certain hazards. Breakdown

of the jack has serious consequences, such as injury to the operator

and damage to the machine parts. The jack should be robust and idiot

proof. To account for this safety aspect, a higher factor of safety of 5

is used for the component of the screw jack.

DESIGN

BILL OF MATERIAL:-

۞DESIGN OF SCREW:-

Screw jack is intermittently used device and wear of the threads is not an

important consideration. Therefore, instead if trapezoidal, threads, the screw

is provided with square threads. Square threads have higher efficiency and

provision can be made for self-locking arrangement. When the condition of

self-locking is fulfilled, the load itself will not turn the screw and descend

down, unless the handle is rotated in reverse direction with some effort.

SR.NO NAME OF

COMPONENT

QUANTITY MATERIAL

1 FRAME 1 GREW CAST IRON

FG200 (IS : 210-1993)

2 SCREW 1 STEEL

30C8 (IS : 1570-1978)

3 NUT 1 PHOSPHOR BROZE

GRADE-1

(IS : 28-1975)

4 HANDLE 1 STEEL

30C8 (IS : 1570-1978)

5 CUP 1 GREY CAST IRON

FG200 (IS : 210-1993)

6 SET SCREW 1 COMMERCIAL STEEL

7 WASHER 1 -- DO --

d c

W

2

4

d c

2

2

4

10100

The portion of the screw between the handle and the nut is subjected to

maximum stress, when the load is being raised. The screw is subjected to

torsional moment, compressive force and bending moment which is

illustrated in fig. the screw is made of plain carbon steel

( s yt =400 mmN2

) assuming,

ss ytyc =400 mmN

2

And the factor of safety of 5,

e = fs

s yc

=5

400=80 mmN

2

fig. no. 4,

e =

Where, d c is the core diameter of the screw. Substituting the values

80=

d c =39.89 or 40 mm.

There are additional stresses due to torsional and bending

moments. The diameter should be increased to account for these stresses. As a first trial, a square threaded screw with 60 mm

nominal diameter and 9 mm pitch (table) is selected.

LOAD IN RAISED POSITION TORQUE DIAGRAM

COMPRESSION OF SCREW BENDING MOMENT DIAGRAM

Trail no-1:-

d =60 mm and p =9 mm

From eqs.

d c = pd = 60-9 = 51 mm

d m = pd 5.0 =60- 0.5(9) = 55.5 mm

It is assumed that the screw has single-start threads.

pl =9 mm

d m

1tan = 5.55

9

or, 95.2

The coefficient of friction between steel screw and bronze nut is normally

taken as 0.1. the maximum possible value of the friction is maximum on

account of poor lubrication. we will consider the worse case where the

operator is careless about the lubrication of the screw.

18.0tan Or, 20.10

Since, . The screw is self locking. Now

)tan2

WdM

m

T

=

)95.220.10tan(2

5.55101003

=648316.3 N-mm

The torque diagram for the screw is shown in fig. it is important to note

following points with respect to this diagram .

(i) The portion of the screw between the nut and the axis of the handle

is subjected to torque M t only.

(ii) The portion of the screw between the cap and the axis of the

handle is subjected to torque cTm .

(iii) The external torque lnP exerted at the axis of the handle consists

of addition of M t + cTm .

(iv) No cross-section of the screw is subjected to addition of M t

+ cTm .

At section X-X,

d

M

c

t

3

16

=

513

)03.648316(16

=24.89 mmN2 ------ (i)

d c

c

W

2

4

= 2

3

514

10100 =48.95 mmN

2 ------ (ii)

The portion of the screw with the side view of the handle is shown in fig.

The hand force P acting on the handle cause a bending moment at

section X-X. The bending moment is given by,

lM Pb 1

The lifting height of the jack is 500mm and the distance 1l can be assumed

as,

1l =500 + 50 +20 =570 mm

lM Pb 1

=(0.92400)(570)

=410400 N-mm

Therefore,

b dM

c

b

3

32

3

51

)410400(32

31.51 mmN2 ------ (iii)

Stresses at section XX,

a) Direct compressive stresses

b) Bending stresses

c) Resultant stresses

Fig. shows the superimposition of direct compressive stress and bending

stress as determined by (ii) and (iii). In this fig., tensile and compressive

stresses are shown as positive and negative respectively. The resultant

stresses are compressive. Compressive stress closes the crack, while tensile

stress opens the crack. In general , failure is associates with tensile stress

rather than compressive stress. To be on the safe side, we will neglect the

compressive stress as determined by eq. (ii) and consider the effort of

combination of torsional shear and bending stresses as determined by eqs (i)

and (iii) respectively. The principle shear stress at section X-X, is given by,

22

max2

b

= 22

89.242

51.31

=29.46 mmN

2

The factor of safety is given by,

fsmax

xys

max

5.0

yts 79.6

46.29

)400(5.0

Since the factor of safety is more than 5, the design is safe. Therefore, the

screw with single start square threads of 60mm nominal diameter and 9mm

pitch is suitable for the screw jack.

BUCKLING CONSIDERATION

The buckling of columns is discussed in chapter 23; section 23.5 on buckling

of columns explains Johnson’s equation and Euler’s equation. When the load

is raised through a distance of 500 mm , the portion of the screw between the

nut and the handle acts as a column. For the purpose of buckling, the length

of the column ( l ) is taken as,

mml 55050500

For a circular cross-section of diameter cd ,

l =64

4

d c

and 4

2

d cA

A

lK

Substituting values of l and A ,

mmd

K c 75.124

51

4

Therefore, the slenderness ratio of the screw is given by,

mmk

l 14.43 -------- (i)

Since one end of the screw is fixed in the nut and the other end is free ,the

end fixity coefficient is 0.25. the borderline between the short and long

columns is given by,

22

2k

l

Ensyt

Substituting values,

22 )207000()25.0(

2

400

kl

Or, 53.50k

l --------- (ii)

The critical slenderness ratio is 50.53. The slenderness ratio of screw

(43.14) is less than critical slenderness ratio (50.53). Therefore, the screw

should be treated as short column and Johnson’s equation is applied.

2

241

k

l

En

sASp

yt

ytct

)207000()25.0(4

)14.43(400151

4400

2

22

=519386.04 N

The factor of safety from buckling consideration is given by,

19.510100

04.5193863

W

Pfs er

Therefore, the screw is safe against buckling.

NUT

The permissible bearing pressure between steel screw and bronze nut is

2/10 mmN . The number of threads required to support the load is Z .

75.12

)5160)(10(

)10100(4422

3

22

cb dds

WZ

Or, 13.

The axial length of nut (H) is given by,

H=ZP= (13) (9) =117 mm

The transverse shear stress at the root of the thread in the nut is given by,

23

/07.9)13)(5.4)(60(

)10100(mmN

dtz

Wn

47.1007.9

)190(5.05.0)(

n

ut

n

u SSfs

The dimensions of the nut are shown in fig. the outer diameter of the nut is

assumed to be twice of the nominal diameter of the thread.

CUP

As shown in fig. the annular area of collar friction has outer diameter of

1.6d. the inner diameter is assumed as 0.8d

mmdD 96)60(6.16.10

mmdDi 48)60(8.08.0

The collar friction torque ctM is given by,

)(4

ioc

ct DDW

M

mmN

720000)4896(4

)10100)(2.0( 3

The total torque ttM required to raise the load is given by,

mmNMMMctttt 03.136831672000003.648316

The external torque, which is exerted by two workers, is given by,

)40029.0( htt lM

mmlh 43.1900

The length of the handle hl is too large and impractical. It is, therefore,

necessary to change the design of the cup and replace the sliding friction

with rolling friction by using thrust ball bearing. In thrust ball bearing, the

friction torque ctM is so small, that it can be neglected.

Thrust ball bearing shown in figure is suitable for purely axial load. It is a

single-direction thrust ball bearing, because it can support axial load in one

direction only. i.e. vertically downward. This ball bearing should not be

subjected to the radial load. Single-direction thrust ball bearing are separable

and the mounting is simple as the components can be mounted individually.

There are three separable parts of this bearing known as a shaft washer, a

housing washer and the ball and cage assembly. The mounting of thrust

bearing is shown in fig. The inner diameter of the shaft washer is press fitted

in the screw body. The outer diameter of the housing washer is press fitted in

the cup. These two components are separable before final assembly.

The procedure for selection of the ball bearing from manufacture’s catalogue

is explained in section. The screw jack is intermittently used and as such the

life of the thrust bearing is assumed as 300hr. The handle is rotated manually

and it is not possible to find out the speed of rotation accurately For the

purpose of bearing selection, it is assumed that the handle rotates at 10 rpm.

Therefore, the life of the bearing in million revolutions is given by.

L = 610

60 bln

the dynamic load capacity of the bearing is given by, it is assumed that the

bore diameter of the bearing is 50mm. For this diameter, following four

bearing table are available. From above table, bearing no. 51410 with

dynamic load carrying capacity of 159000 N is selected for the jack. The

dimension of the bearing are follows:

The dimensions of the cup are shown in figure. The section thickness is kept

20 mm throughout as far as possible.

BEARING SELECTION

0c =static load capacity C=dynamic load capacity

Sr.

no.

d

(mm)

D

(mm)

H

(mm)

C

(N) 0c (N)

)(1 mmD Designation

1 50 70 14 25500 50000 52 51110

2 50 78 22 41600 73500 52 51210

3 50 95 31 97500 160000 52 51310

4 50 110 43 159000 250000 52 51410

HANDLE

The handle is subjected to bending moment. The force exerted by two

workers on the handle is given by,

NP )40029.0(

The handle is made of steel 30c8 ( S YT= 400 mmN

2

). There is no collar

friction torque. Therefore,

tthb MlpM

And,

3

32

h

bb

d

M

The handle is inserted through a hole in

the head of the screw as shown in figure.

Two holes are provided, at right angles to

each other, for changing the position of

the handle after a quarter revolutions.

The dimensions of the cast iron frame are

shown in figure.

.

SAFETY ASPECT

To guard against injury to the workers and prevent damage to the machine

parts, following safety measure should be taken:

1. After fabrication the mechanical jack should be proof tested. In proof

test, the jack is loaded to 150%of its rated load, with the lifting

member at approximately 90% of full extension. After this text, the

jack should be functional for full extensions under 100% of lifting

rated load.

2. The jack should be provided with a warning. a sample of warning is as

follows:

“WARNING; DOES NOT OVERLOAD JACK. PLACE LOAD ON

THE CENTER OF CUP ONLY. PLACE THE FRAME OF JACK ON

HARD LEVEL SURFACE. LOAD AND STAND SHALL BE STABLE,

STUDY,UNDERSTAN AND FOLLOW ALL INSTRUCTIONS.

FAILURE TO HEED THIS WARNING MAY RESULT IN

PERSONAL INJURY AND/OR PROPERTY DAMAGE.”

3. Following operational instructions should be given in the manual or

leaflet of the jack:

i) Jack shall be visually examined for general condition before

each shift or each use, which ever is less frequent.

ii) A determination of the load shall be made to assure that it is

within the load rating of the jack.

iii) The jack shall be firmly supported at the base such that it is

stable under load.

iv) Operators shall be instructed in proper use of the jack.

v) Remove the handle when not in use to avoid accidental

dislocation of the jack and reduce tripping hazard.

vi) Take precaution to ensure that all personnel are clear of the

load before lowered.

vii) Ensure that there is sufficient swing area for the handle.

viii) Off-centre loading of jacks should be avoided.

4. The rated load should be legibly and durably marked in a prominent

position on the jack.

5. The nut and the thrust ball bearing of the jack should be regularly

lubricated with grease.

The analysis of strength and stability considerations in design is no doubt

essential for safety. However, they are not enough to prevent an accident.

It is also essential to have personal involved in the use and operation of

jack to be careful, component, trained and qualified in safe operation of

the screw jack and in proper use…….

NOTE:-

ALL THE DATA AND CALCULATION MENTIONED HERE IS TAKEN

AS VARIABLE AND THE VALUE MAY DEPANDS UPON SIZE AND

WORKING CONDITION..BUT THE FORMULA WILL ALWAYS

CONSIDERD AS STANDERD….