Unit 4 Design of Power Screw and Screw Jack

Unit 4
Power Screws
Prepared By
Prof. M.C. Shinde
[9970160753]
Mech. Engg. Dept., JSCOE, Hadapsar

Unit 4
Power Screws
Session 4.1 Introduction to Power Screws , Terminology,
Forms of Thread
Prepared By
Prof. M.C. Shinde

SPPU Syllabus Content: (06 hrs)
Forms of threads, multiple start screws, Torque analysis
and Design of power screws with square and trapezoidal
threads, Self locking screw, Collar friction torque,
Stresses in power screws, design of a C-Clamp. Design of
screw jack, Differential and Compound Screw and Re-
circulating Ball Screw (Theoretical treatment only).

Power Screw
•A power screw is a mechanical device used for
converting rotary motion into linear motion and
transmitting power.
•A power screw is also called a translation screw. It uses
helical translatory motion of the screw thread in
transmitting power rather than clamping the machine
components.

Power Screw
•There are three essential parts of the power screw, viz., screw,
nut and a part to hold either the screw or the nut in its place.
•Depending upon the holding arrangement, power screws
operate in two different ways.
•In some cases, the screw rotates in its bearing, while the nut
has axial motion. The lead screw of the lathe is an example of
this category.
•In other applications, the nut is kept stationary and the screw
moves in an axial direction. A screw jack and machine vice are
the examples of this category.

The main applications of power screws are as follows:
(i) To raise the load, e.g., screw-jack;
(ii) To obtain accurate motion in machining operations, e.g., lead-screw of lathe;

The main applications of power screws are as follows:
(iii) To clamp a work piece, e.g., a vice;
(iv) To load a specimen, e.g., universal testing machine.

Advantages of Power Screw
• A power screw has large load carrying capacity.
• The overall dimensions of the power screw are small, resulting in
compact construction.
• A power screw is simple to design.
• The manufacturing of a power screw is easy without requiring
specialised machinery. Square threads are turned on the lathe.
Trapezoidal threads are manufactured on a thread milling machine.
• A power screw provides large mechanical advantage. A load of 15 kN
can be raised by applying an effort as small as 400 N. Therefore, most
of the power screws used in various applications like screw-jacks,
clamps, valves and vices are manually operated.

Advantages of Power Screw
•A power screw provides precisely controlled and highly
accurate linear motion required in machine tool
applications.
•A power screw gives smooth and noiseless service without
any maintenance.
•There are few parts in a power screw. This reduces cost and
increases reliability.
•A power screw can be designed with self locking property. In
screw-jack application, self-locking characteristic is required
to prevent the load from descending on its own.

Disadvantages of Power Screw
•A power screw has very poor efficiency, as low as 40%.
Therefore, it is not used in continuous power transmission in
machine tools, with the exception of the lead screw.
•High friction in threads causes rapid wear of the screw or
the nut. Therefore, wear is a serious problem in power
screws.

Terminology of Power Screw
•Nominal diameter(d)
•Core diameter(dc)
•Mean diameter(dm)
•Pitch (p)
•Lead (l)
•Lead angle(ƛ)
•Hand of threads

Nominal diameter(d)
•It is the largest diameter of an
external or internal thread.
•The screw is specified by this
diameter.

Core diameter(dc)
•It is the smallest diameter of an
external or internal thread.

Pitch (p)
•It is the distance from any point on
the thread to the corresponding
point on the adjacent thread
measured parallel to the axis.

Lead (l)
“It is the distance which a screw
advances axially in one rotation of
the nut”. OR “distance between two
corresponding points on the same
helix.
Lead=number of starts*pitch
L=N*p
For single start screw pitch is equal
to lead……so on.

Lead angle(ƛ)
“It is an angle made by a helix or
thread with plane perpendicular to
an axis of screw.”

Hand of threads
When the axis of screw is vertical if the thread slope
upward from left to right, it is Right Hand Threads.
Right Hand Threads. Left Hand Threads.

1.Square Threads
• Advantages
1. Square threads have maximum efficiency of all thread forms.
2. They exert minimum radial pressure on nut.
3. They can transmit power in either direction.
• Disadvantages
1. Strength of the square threads is lowest of all the thread forms.
2. Theses threads cannot be used conveniently with split nut because:
engagement and disengagement is difficult
• Applications:
Used in Screw jacks, presses & clamping devices

2.ACME/Trapezoidal Threads
• Advantages
1. Acme threads permit the use of split nut which can compensate the wear.
2. Acme threads are stronger than the square threads in shear because of the
larger cross-section at the root.
3. Acme threads can transmit power in either direction.
• Disadvantages
1. Because of slope given to the sides the efficiency of acme threads is lower
than that of square threads.
2. Slope on the sides introduces some bursting pressure on the nut.
• Applications:
Used for lead screws of machine tools, bench
vices

3. Buttress Threads
• Advantages
1. Buttress threads are stronger in shear than any other power threads
because of the largest cross section at the root.
2. Buttress threads combine the high efficiency of square threads and high
strength of V- threads.
• Disadvantages
1. Buttress threads are used to transmit power in only one direction.
2. Theses threads are difficult to manufacture.
• Applications:
Used in screw jacks & vices where force is to be
applied in only one direction.

1.Write short note on Power Screws.
2.Explain in brief terminology used in Power Screws.
3.Explain Different types of threads.
Assignment 4.1

Unit 4
Power Screws
Session 4.2 Torque Analysis, Self Locking &Overhauling
of Screw
Prepared By
Prof. M.C. Shinde

Torque required to raise the load against thread friction
• The advancement (motion) of the screw or nut in the direction of load is
equivalent to raising the load, as shown in fig.1 the force diagram of an
equivalent inclined plane for raising the load is shown in fig.2

Torque required to raise the load against thread friction

Torque required to lower the load against thread friction
• The advancement (motion) of the screw or nut in the direction of load is
equivalent to lowering the load, as shown in fig.1 the force diagram of an
equivalent inclined plane for raising the load is shown in fig.2

Torque required to lower the load against thread friction

Self locking Screws
Torque required to lower the load against thread friction is given by
In this equation if the torque required to lower the load Tt will be
positive. Such screw is known as self-locking screw.
For self-locking screw, friction angle is greater than lead angle and
torque required to lower the load Tt will be always positive.
Applications:
Self locking screw is used in screw-jack & C-Clamps.

Over hauling Screws
Torque required to lower the load against thread friction is given by
In this equation if the torque required to lower the load Tt will be
negative. i.e. load will start moving downward without the application of any
torque causing the screw to rotate. Such screw is known as over hauling
screw.
For over hauling screw, friction angle is less than or equal to lead angle
and torque required to lower the load Tt will be zero or negative.

1.Write short note on Self locking of screw
2.Write short note on Over hauling of screw
3. Derive expression for torque required to raise the
load.
Assignment 4.2

Unit 4
Power Screws
Session 4.3 Screw Efficiency, Collar Friction Torque
Prepared By
Prof. M.C. Shinde

Screw efficiency of square threads
Screw efficiency: it is the ratio of zero friction input torque to the actual
input torque
Expression for Screw efficiency:
zero friction input torque to the actual input torque is given by,

Collar friction Torque
•In many applications, load does not rotate
with screw, and hence some additional
torque must be applied to overcome the
friction at collar.
•Fig. shows the power screw with the collar
and cup. The collar of the power rotates
with screw while cup remains stationary due
to load W. this results in friction at the
annular surface between the collar and the
cup.

Expression for collar friction Torque
•The torque required to overcome the collar friction is given by,
According to uniform pressure theory
According to uniform wear theory
In general can be written in this form

Overall efficiency of Power screw- Method 1
•Overall efficiency :- ratio of total zero friction input torque to total
actual input torque.
Expression for overall efficiency
Total actual input torque is given by
Total zero friction input torque is given by
overall efficiency

Overall efficiency of Power screw- Method 2
•When torque T completes one rotation(i.e. rotates through radians)
load W moves through a distance l.
Expression for overall efficiency
Work output =
Work input =
overall efficiency is given by

Ex.4.1 The following data refers to a screw jack:
• Nominal diameter of screw=40mm
• Pitch of threads=7mm
• Type of screw=single start square threaded
• Coefficient of thread friction=0.15
• Coefficient of collar friction=0.1
• Effective mean diameter of collar=70m, if operator can comfortably
exert a force of 150N at a radius of 1.2m to raise the load, calculate
i) The maximum load that can be lifted
ii) The efficiency of the screw
iii) The overall efficiency.

Torque required to raise the load

Torque applied by the operator

Maximum load that can be lifted
Torque reqd to raise the load=torque applied by operator

Ex.4.2 in a machine tool application, the tool holder is pulled by means
of an operating nut mounted on a screw. the tool holder travels at a
speed of 5m/min. the screw has a single start square threads of 48mm
nominal diameter and 8 mm pitch. The operating nut exerts a force of
500N to drive the tool holder. The mean radius of friction collar is 40
mm. if the coefficient of friction for thread and collar surfaces is 0.15
calculate:
i) The power required to drive the screw
ii) The efficiency of the mechanism

Torque required to drive the screw

Power required to drive the screw

Ex.4.3 a two start, trapezoidal screw is used in a screw jack to raise a
load of 300 N. the screw has a nominal diameter of 100mm and a pitch
of 12mm. The coefficient of screw friction is 0.15. neglecting the collar
friction, determine :
i) The torque required to raise the load;
ii) The torque required to lower the load;
iii) Screw efficiency

Torque required to lower the load

Ex.4.4 a machine vice has a single start square threaded screw with a
nominal diameter of 22 mm and pitch of 5 mm. a clamping collar has
inner and outer diameter as 45 mm and 55mm respectively. The
coefficient of friction for threads as well as collar is 0.15. the operator
can apply a force of 100 N on which is 150 mm long. Assuming uniform
wear condition for collar, determine ;
i) Clamping force developed
ii) Overall efficiency

Torque required to overcome thread friction

Torque required to overcome the collar friction

Maximum load that can be lifted
Torque reqd to overcome friction=torque applied by operator

Ex.4.5 the lead screw of a lathe has a single start I.S.O. metric
trapezoidal threads of 52mm nominal diameter and 8 mm pitch. The
screw is required to exert on axial force of 2kN in order to drive the tool
carriage during the turning operation. The thrust is carried on collar
of100mm outer diameter and 60 mm inner diameter. The values of
coefficient of friction at the screw threads and collars are 0.15 and 0.12
respectively. If the load screw rotates at 30 rpm. Calculate
i) The power required to drive the lead screw
ii) The efficiency of screw.
Evaluate the results using uniform wear theory and uniform pressure
theory.

Note:- Consider Uniform wear theory

Screw efficiency

Overall efficiency

Case II Uniform Pressure theory

Note:- Consider Uniform Pressure theory

Screw efficiency

Overall efficiency

Stresses in Power Screw
1. Stresses in Screw Body
2. Stresses in Screw Threads

Direct compressive or tensile stress
Direct compressive or tensile stress in a screw body due to an axial force
W is given by

Torsional shear stress
Torsional shear stress in a screw body due to twisting moment (or Torque)
T is given by

Maximum shear stress
According to maximum shear stress theory, the maximum shear stress
induced in the screw body is given by

Buckling of screw
When an axial load on the screw is compressive and the
unsupported length of screw between the load and nut is too long, screw
body must be checked for the buckling failure.
According to J.B. Johnson formula critical or buckling load for the
screw is given by
Syc - yield strength in compression for screw material N/mm2
E - modulus of elasticity for screw material, N/mm2
C - end fixity coefficient
L - Unsupported length of the screw between load & nut
K - least radius of gyration of screw cross section

Bearing Pressure
As there is relative motion between screw and nut ,there exist bearing
pressure between contacting surfaces of screw and nut threads.
Bearing pressure between threads is given by,
Where
d-nominal diameter of screw
Z-number of threads in engagement
h-height of nut h=Z*p

Direct shear stress in screw threads
Direct shear stress induced in the screw threads is given by
Where
dc-core diameter of screw
t-thickness or width of thread at the root

Direct shear stress in nut threads
Direct shear stress induced in the nut threads is given by
Where
t-thickness or width of thread at the root

Ex.4.6 The construction of a gate valve used in high pressure pipeline is
shown in fig. the screw is rotated by means of the handle. The nut is
fixed to the gate. When the screw rotates the nut along with gate
moves downward or upward depending upon the direction of rotation
of the screw. The screw has single start square threads of 40mm outer
diameter and 7mm pitch. The weight of the gate is resistance between
the gate and its seat. The resultant frictional resistance in axial direction
is 2kN. The inner and outer diameters of thrust washer are 40mm and
80mm respectively. The coefficient of friction at the threads and at the
washer are 0.15 and 0.12 respectively. If the handle is rotated by two
arms, each exerting equal force at radius of 500mm from the axis of the
screw,

calculate:
i. The maximum force exerted by each arm
when the gate is being raised;
ii. The maximum force exerted by each arm
when the gate is being lowered;
iii. The efficiency of the gate mechanism
iv. The number of threads in engagement ,if
the permissible bearing pressure is 5
N/mm2
v. Length of nut

Torque required to raise the gate

Force to be exerted by each arm to raise the gate(FR)

Torque required to lower the gate(TL)
When the gate is lowered frictional resistance due to water pressure,
which always opposes the motion, acts upward.
Total force acting in downward direction which is to be lowered is

Force to be exerted by each arm to lower the gate(FL)

Number of threads in engagement(Z)

Ex.4.7 A power screw having double start square threads of 30mm
nominal diameter and 6mm pitch is acted upon by an axial load of
10kN. The outer and inner diameters of screw collar are 50mm and
30mm respectively. The coefficient of thread friction and collar friction
may be assumed as 0.25 and 0.18 respectively. The screw rotates at 12
rpm. Assuming uniform wear condition at the collar and allowable
thread bearing pressure of 6.3N/mm2,find;
1. The power required to rotate the screw;
2. The stresses in screw;
3. The height of nut.

Power required to rotate the screw

Direct compressive stress in body

Torsional shear stress in body

Direct shear stress in screw threads

Ex.4.8 A square threaded, triple start power screw, used in a screw jack
has a nominal diameter of 50mm and a pitch of 8mm. The screw jack is
used to lift load of 8kN. The coefficient of thread friction is 0.12 and
collar friction is negligible. If the length of nut is 48mm, calculate;
i. The maximum shear stress in the screw body;
ii. The direct shear stress in the screw and nut;
iii. The bearing pressure
State the conditions of the screw.

Direct compressive stress in screw body

Torsional shear stress in screw body

Maximum shear stress in a screw body

Direct shear stress in a screw threads

Direct shear stress in nut threads

Condition of screw
In this case, =9.429 and =6.8428
As screw is over hauling

Permissible compressive stress

Shear stress induced in Nut threads

Shear stress induced in Screw threads

Ex.4.9 Design a bottle type screw jack for a load capacity of 65kN and a
lifting height of 2.5m, with the following data;
• Tensile yield strength of screw material(alloy steel 40CrL)=
460 N/mm2
• Compressive yield strength of screw material(alloy steel 40CrL)=550
N/mm2
• Tensile yield strength of nut material(phosphor bronze)=110N/mm2
• Compressive yield strength of nut material(phosphor
bronze)=130N/mm2
• Yield strength of nut material in shear(phosphor bronze)=90N/mm2
• Tensile yield strength of handle material (plain carbon
steel,55C8)=400N/mm2

• Permissible bearing pressure between the screw and
nut =18N/mm2
• Coefficient of friction between the screw and nut=0.14
• Coefficient of collar friction=0.16
• Factor of safety=3

To find core diameter dc of screw

Select standard square thread for screw

Check maximum torsional shear stress < Permissible
Design of screw body is safe hence

Check Shear stress induced in Nut threads<Permissible
Hence nut threads are safe against shear failure

Check Shear stress induced in Screw threads<Permissible
Hence screw threads are safe against shear failure

Diameter of handle
To find dh, H1=2*dh

Ex.4.10 design a nut of screw jack using following data;
• Load to be lifted =50kN
• Lift of screw jack=500mm
• Pitch of threads=12mm
• Tensile yield strength for nut=300MPa
• Permissible bearing pressure=12MPa

Allowable tensile stress for nut

Allowable shear stress for nut

Bearing pressure between nut and screw thread

Dimensions for Nut let us consider Z=4 threads

Check direct shear stress in Nut< Permissible
Hence nut threads are safe against shear failure

Bearing Pressure
Height of Nut(h) =Z*p

Ex.4.11 The following data refers to C-clamp;
• Maximum clamping force required=4kN
• Tensile yield strength of screw material(Plain Carbon Steel,35C8)=320N/mm2
• Compressive yield strength of screw material(Plain Carbon
Steel,35C8)=390N/mm2
• Shear strength of the nut and body material(FG200)=230N/mm2
• Coefficient of the screw friction=0.14
• Coefficient of the collar friction=0.16
• Mean collar radius=8mm
• Permissible bearing pressure between nut & screw=12N/mm2
• Distance between the axis of the handle and nut surface, in clamped
condition=150mm
• Force applied by an operator=100N
• Distance between the axis of the screw and centroidal axis of vertical column of
the C-clamp body=100mm

Design the screw and nut for C-clamp and determine the following
parameters:
i. The standard dimensions of screw body;
ii. The height of nut;
iii. Length of handle;
iv. The dimensions of I-Section of the C-clamp body.

Check maximum torsional shear stress < Permissible
Design of screw body is safe

Permissible tensile stress along Y-Y

Maximum tensile stress along Y-Y

Ex.4.12 The following data refers to C-clamp;
• Maximum force exerted by C-Clamp=4kN
• Nominal diameter=12mm
• Pitch =2mm,
• Nut height=25mm
• Type of screw=single start square thread
• Mean collar radius=6mm
condition=150mm
• Force applied by an operator=80N
• Distance between the axis of the screw and centroidal axis of vertical column of
the C-clamp body=100mm

Determine;
i) The length of handle, if additional length provided for gripping is
50mm;
ii) The maximum shear stress in the screw body and its location;
iii) The bearing pressure on the threads

Differential screw
It consists of two screws in series having same
Hands, arranged such that the resultant
motion is the difference of individual motions
of the two screws.
Differential screw, shown in fig. consist of
lower screw with pitch p1(LH) and the upper
screw with pitch p2(LH)
When the nut is turned through one revolution
in clockwise direction viewed from top, the top
screw advances by a distance (p1-p2) in

Compound screw
It consists of two screws in series having
opposite hands, arranged such that the
resultant motion is the sum of individual
motions of the two screws.
compound screw, shown in fig. consist of
lower screw with pitch p1(LH) and the upper
screw with pitch p2(LH)
When the nut is turned through one revolution
in clockwise direction viewed from top, the top
screw advances by a distance (p1+p2) in

Recirculating Ball screw
• In a power screw, if the sliding friction at the threads is replaced by
rolling friction efficiency of screw can be improved substantially.
This is achieved by screw known as recirculating ball screw.
• Typical recirculating ball screw shown in fig consist of three
components i.e. Screw, nut and steel balls
• A screw and a nut have a semi-circular thread profile. the contact
between the screw and nut threads is through the steel balls.
• As the nut or screw rotates, rolling balls move along the circular
grooved helical path.

Advantages of Recirculating Ball screw
• In recirculating ball screw, as the sliding friction is replaced by
rolling friction, efficiency is very high.
• As the nut or screw is preloaded in one direction to reduce the
backlash, high positional accuracy is obtained.
• Because of low coefficient of friction, conversion of rotary to linear
motion can be reversible.
• As the nut or screw rotates, rolling balls move along the circular
grooved helical path.

Applications of Recirculating Ball screw
• Ball screws are used in aircraft and missiles to move control
surfaces, especially for electric fly by wire.
• Used in automobile power steering to translate rotary motion from
an electric motor to axial motion of the steering rack.
• They are also used in machine tools, robots and precision assembly
equipment.
• High precision ball screws are used in steppers for semiconductor
manufacturing.
• They are also incorporated into the actuator mechanisms of
computer controlled self-pleasure devices.

Theory Questions for Practice
i. Explain different types of threads used for power screws. Give
advantages and limitations of each type.
ii. Derive an equation for the efficiency of square threaded screw.
iii. Show that efficiency of self-locking square threaded power screw
is less than 50%
iv. Explain with neat sketch differential screw
v. Explain with neat sketch re-circulating ball screw

Ex.01 The following data refers to C-clamp;
• Maximum clamping force =4000N
• Nominal diameter=12mm
• Pitch =2mm,
• Nut height=25mm
• Type of screw=single start trapezoidal thread
• Mean collar diameter=12mm
condition=150mm
• Operator Force at the end of handle=80N
Numerical for Practice

Determine;
i) The length of handle, if 50mm additional length for gripping ;
ii) stresses in the screw body at two critical sections;
iii) The bearing pressure on the screw threads

Ex.02 A C-clamp as shown in fig. below is used on
the shop floor has single-start square thread of
22mm nominal diameter and 5mm pitch. The
coefficient of friction at the threads and the collar is
0.15. the mean radius of friction collar is 15mm. The
capacity of the clamp is 750N. The handle is made
of steel 30C8 (Syt=400MPa) it can be assumed that
the operator exerts force of 20N on the handle.
i. Evaluate the torque required to tighten the
clamp to its full capacity.
ii. Determine the length and diameter of the
handle such that it will bend with a permanent
set when the rated capacity of the clamp is
exceeded.

Ex.03 A power screw having double start square threads nominal diameter 25mm and pitch
5mm subjected to axial load of 1000N. The outer and inner diameter of the screw collar is 50
and 20mm respectively. The coefficient of friction for collar thread and screw thread are 0.15
& 0.20 respectively. The screw rotates at 12rpm. Assume uniform wear condition, and
allowable bearing pressure is 5.77N/mm2.determine,
i) Power required to rotate the screw.
ii) Stresses in screw body and threads
iii) No. of threads of nut in engage with screw.
Ex.04 A load of 600kN is to be raised and lowered by means of two square threaded screws. If
the coefficient of friction between the screw and nut is 0.048, determine the size of screw and
nut. Take ,P=15MPa,pitch=10mm. Find also the torque required to raise and lower the
load.
Ex.05 The lead screw of lathe has single start ISO metric trapezoidal threads of 52mm nominal diameter
and 8mm pitch. The screw is required to exert an axial force of 2kN in order to drive the tool carriage
during turning operation. The thrust is carried on a collar of 100mm outer diameter and 60mm inner
diameter. The value of coefficient of friction at the screw threads and the collar are 0.15 and 0.12
respectively. The lead screw rotates at 30r.p.m evaluate
i) The power required to drive the lead screw.

Ex.06 A nut and screw combination having double start square threads nominal diameter
25mm and pitch 5mm subjected to axial load of 1000N. The outer and inner diameter of the
screw collar is 50mm and 20mm respectively. The coefficient of friction for collar thread and
screw thread are 0.15 and 0.2 respectively. The screw rotates at 12rpm. Assume uniform wear
condition and allowable bearing pressure is 5.77N/mm2 determine
i) Power required to rotate the screw.
ii) Stresses in screw body and threads
iii) no. of threads of nut in engage with screw.
Ex.07 a triple threaded power screw used in screw jack has nominal diameter of 50mm and
pitch of 8mm. The threads are square and length of nut 48mm. The screw jack is used to lift
load of 8kN. The coefficient of friction at the threads is 0.12. calculate
i) The principal shear stress in the screw body
ii) The transverse shear stresses in the screw and nut
iii) The unit bearing pressure. State the condition of screw with statement.

……………..Any Questions??

Unit 4 Design of Power Screw and Screw Jack

Recommended

Recommended

More Related Content

What's hot

What's hot (20)

Similar to Unit 4 Design of Power Screw and Screw Jack

Similar to Unit 4 Design of Power Screw and Screw Jack (20)

Recently uploaded

Recently uploaded (20)

Unit 4 Design of Power Screw and Screw Jack