2. Power Screws:
A power screw is a mechanical device used for
converting rotary motion into linear motion and transmitting
power. Its also called as translation screw.
Power screw has three essential parts screw ,nut
and part to hold either the screw or the nut in its place.
Depending upon the holding arrangement power screw operate
in two different ways. In first case the screw rotates in its
bearing, while the nut has axial motion eg. Lead screw. In
second case the nut is kept stationary and the screw moves in
axial direction eg. Screw jack, machine vice.
2
5. Advantages of power screws:
• It has large load carrying capacity.
• Overall dimensions are small hence compact
construction.
• It is simple to design.
• The manufacturing of power screw is easy.
• It provides large mechanical advantage.
• It gives smooth and noiseless service without any
maintenance.
• It has few parts hence reduces cost and increases
reliability.
• A power screw can be designed with self locking
property.
5
6. Disadvantages of power screws:
• It has very poor effciency as low as 40%.
• High friction in threads causes rapid wear of the screw or the
nut.
Applications of power screws:
• To raise the load eg. Screw jack
• To obtain accurate motion in machining operations eg. Lead
screw of lathe.
• To clamp a work piece eg. Vice.
• To load a specimen eg. Universal testing machine.
6
7. Forms of threads:
There are two popular types of threads used for power screw.
• Square thread.
• ISO metric trapezoidal thread.
𝟏.Square thread
7
8. Advantages of square threads:
• Square threads has high effciency.
• There is no radial pressure or side thrust on the nut.
Disadvantages of square threads:
• Square threads are difficult to manufacture.
• Square threads have less thickness at the core diameter hence
this reduces the load carrying capacity.
• If thread surface is weared it is not possible compensate for
wear in square threads, therefore when worn out, the nut or the
screw requires replacement.
Square threads are used for screw jack, presses and
clamping devices.
8
9. 𝟐.Trapezoidal threads:
Advantages of trapezoidal threads:
• Trapezoidal threads are economical to manufacturing.
• It has more thickness at the core diameter hence it has large
load carrying capacity.
• The axial wear on the surface of trapezoidal threads can be
compensated by means of a spilt-type of nut.
9
10. Disadvantage of trapezoidal threads:
• It has less efficiency.
• There is radial pressure or side thrust on the nut.
There is special type of trapezoidal thread called acme thread.
Trapezoidal and acme threads are identical in all respects expect
the thread angle. In acme thread the thread angle is 290 instead
of 300.
10
11. Trapezoidal and acme threads are used for lead-screw and
other power transmission devices in machine tools.
Buttress thread:
It combines the advantages of square and trapezoidal
threads. Buttress threads are used where a heavy axial force acts
along the screw axis in one direction only.
11
12. Advantages of buttress thread:
• It has higher efficiency as compared with trapezoidal
threads.
• It can be economically manufactured.
• The axial wear at the thread surface can be compensated by
means of a spilt type nut.
• A screw with buttress thread is stronger the an equivalent
screw with either square or trapezoidal threads.
Buttress threads have one disadvantage it can
transmit power and motion only in one direction.
Buttress threads are used in vices, where force is
applied in one direction only.
12
13. Terminology of Power Screw
Pitch:
The pitch is defined as the distance measured
parallel to the axis of the screw from a point on
one thread to the corresponding point on the
adjacent thread.
It is denoted by the letter p.
Lead:
It is defined as the distance measured parallel to
the axis of the screw which the nut will advance in
one revolution of the screw.
It is denoted by the letter l.
For a single-threaded screw, the lead is same as
the pitch. For double-threaded screw, the lead is
twice of the pitch, and so on.
13
14. Nominal Diameter:
Nominal diameter is the largest diameter of the screw. It is also
called major diameter.
It is denoted by the letter d.
Core Diameter:
The core diameter is the smallest diameter of the screw thread. It
is also called minor diameter.
It is denoted by the letter dc.
Helix Angle:
The helix angle is defined as the angle made by the helix of the
thread with a plane perpendicular to the axis of the screw. It is also
called lead angle.
It is denoted by α.
14
15. Helix Angle continued...
From fig.
And , dm is the mean diameter of the screw.
It is given by,
15
16. Considering the right angle triangle, the relationship between the
helix angle, mean diameter and lead can be expressed in the
following form:
16
17. 17
Force analysis of square thread:
𝟏.Lifting load:
The screw is considered as an inclined plane with inclination α
as shown in fig.
Forces act at a point on inclined plane
• Load W
• Normal reaction N
• Frictional force µN
• Effort P
P
N
µN
W
l
π𝑑𝑚
𝐹𝑜𝑟𝑐𝑒 𝑑𝑖𝑎𝑔𝑟𝑎𝑚 𝑓𝑜𝑟 𝑙𝑖𝑓𝑡𝑖𝑛𝑔 𝑙𝑜𝑎𝑑
α
18. P =
𝑊(𝜇 cos 𝛼 +sin 𝛼)
(cos 𝛼 − 𝜇 sin 𝛼)
Dividing right hand side by cos α
P =
𝑊( µ + tan α )
(1 − µ tan α )
(c)
The coefficient of friction
µ = tan ϕ ϕ = friction angle
18
19. 19
Substituting µ = tan ϕ in eq. (c)
𝑃 =
𝑊( tan ϕ + tan α )
( 1 − tan ϕ tan α )
or
𝑃 = 𝑊 tan(ϕ + α)
The torque required to raise the load is given by
𝑀𝑡 =
𝑃𝑑𝑚
2
𝑀𝑡 =
𝑊𝑑𝑚
2
tan(ϕ + α)
20. 20
𝟐.Lowering load:
The forces acting at a point on the inclined plane as shown
in fig.
µN
N
P
W
l
π𝑑𝑚
𝐹𝑜𝑟𝑐𝑒 𝑑𝑖𝑎𝑔𝑟𝑎𝑚 𝑓𝑜𝑟 𝑙𝑜𝑤𝑒𝑟𝑖𝑛𝑔 𝑙𝑜𝑎𝑑
α
Considering the equilibrium of horizontal & vertical forces
𝑃 = µ𝑁 cos α − 𝑁 sin α (a)
𝑊 = 𝑁 cos α + µ𝑁 sin α (b)
21. 21
Dividing (a) by (b)
𝑃 =
𝑊(𝜇 cos 𝛼 − sin 𝛼)
(cos 𝛼 + 𝜇 sin 𝛼)
Dividing right hand side by cos α
𝑃=
𝑊( µ − tan α )
(1+ µ tan α )
(c)
Substituting µ = tan ϕ in eq. (c)
𝑃 =
𝑊( tan ϕ − tan α )
( 1 + tan ϕ tan α )
𝑃 = 𝑊 tan(ϕ − α) 𝑀𝑡 =
𝑊𝑑𝑚
2
tan(ϕ − α)
22. 22
Force analysis of trapezoidal thread:
2Ѳ
W 𝑊
cos Ѳ
For trapezoidal thrread2Ѳ = 300
For acme thread 2Ѳ = 290
W is the axial force on the screw (load)
𝑊
cos Ѳ
or (𝑊 sec Ѳ) is the normal force
on the thread surface.
The frictional force depends upon the
normal force therefore the effect of
thread angle is to increase the
frictional force by a term sec Ѳ.
To account for this effect the
coefficient of friction is taken as
µ 𝑠𝑒𝑐Ѳ
Ѳ
23. 23
Case 1. Lifting load
Modifying eq. (c) in case of square thread lifting load.
𝑃 =
𝑊( µ sec Ѳ + tan α )
(1 − µ sec Ѳ tan α )
𝑀𝑡 = 𝑃
𝑑𝑚
2
=
𝑊𝑑𝑚
2
( µ sec Ѳ + 𝑡𝑎𝑛 α )
( 1 − µ sec Ѳ tan α)
Case 2. Lowering load
Modifying eq. (c) in case of square thread lowering load
𝑃 =
𝑊( µ sec Ѳ − tan α )
(1 + µ sec Ѳ tan α )
𝑀 = 𝑃
𝑑𝑚
=
𝑊𝑑𝑚 ( µ sec Ѳ + 𝑡𝑎𝑛 α )
24. 24
Self-locking Screw:
The torque required to lower the load 𝑀𝑡 =
𝑊𝑑𝑚
2
tan(ϕ − α)
Case 𝟏.
when ϕ < αthe torque required to lower the load is negative. It
indicates no force is required to lower the load. The load itself
will begin to turn the screw and descend down, unless a
restraining torque is applied. This condition is called as
overhauling of screw or back driving of screw. This property not
used in screw jack application. It is used in Yankee screwdriver.
Case 𝟐.
when ϕ ≥ α positive torque is required to lower the load. In this
condition the load will not return the screw and will not descend
on its own unless an effort P is applied. In this case the screw is
said to be self-locking. A self-locking screw will hold the load in
place without a brake. This property is used in screw jack
application.
25. 25
A screw will be self-locking if the coefficient of friction is
equal to or greater than the tangent of the helix angle.
For a self-locking screw,
ϕ > α
tan ϕ > tan α
µ >
1
π 𝑑𝑚
Self-locking of screw is not possible when the coefficient of
friction is low.
Self-locking property of the screw is lost when the lead is
large.
26. 26
Collar friction:
In many applications of the power screw there is
collar friction in addition to the friction at the thread surface.
The principle of collar friction explained with help of fig.
The cup remains stationary under the action
of load W, while the collar that is integral with
the screw rotates when the load is being raised
or lowered. Therefore, there is relative motion
between the cup and the collar at the annular
interface from diameter 𝐷𝑖 to 𝐷𝑜. This relative
motion results in friction called collar friction.
The torque required to overcome this friction
is collar friction torque. Collar friction torque
can be determined by using uniform pressure
theory or uniform wear theory.
27. Overall Efficiency
The total external torque required to raise the load consists of two factors- the torque
required to overcome friction at the thread surface and the collar friction torque.
Therefore,
(Mt)t = Mt + (Mt)c
Where,
(Mt)t= external torque required to raise the load (N-mm);
Mt = torque required to overcome friction at the thread surface (N-mm); and
(Mt)c = collar friction torque (N-mm)
Work output = fore * distance travelled in the direction of force = (Wl)
The input consists of torque applied to the screw (Mt)t,
Work input = torque * angle turned through = [(Mt)t * (2π)]
The overall efficiency ηo of the power screw is given by,
27
28. 28
Stresses in screw:
The body of the screw is subjected to
an axial force W and torsional
moment 𝑀𝑡 as shown in fig.
The direct compressive stress σ𝑐
σ𝑐 =
𝑊
(
π
4
𝑑𝑐
2
)
The torsional shear stres
τ =
16 (𝑀𝑡)𝑡
π𝑑𝑐
3
The principal shear stress
τ𝑚𝑎𝑥 = (
σ𝑐
2
)2+τ2
29. 29
The threads of the screw is subjected to transverse shear stress
τ𝑠 =
𝑊
π 𝑑𝑐 𝑡 𝑧
τ𝑠= transverse shear stress at the root of the screw (𝑁 𝑚𝑚2)
𝑡 = thread thickness at the core diameter (mm)
z = number of threads in engagement with the nut.
π 𝑑𝑐 𝑡= shear area of one thread
The threads of the nut is subjected to transverse shear stress
τ𝑛 =
𝑊
π 𝑑 𝑡 𝑧
τ𝑛= transverse shear stress at the root of the nut (𝑁 𝑚𝑚2
)
𝑡 = thread thickness at the core diameter (mm)
π 𝑑 𝑡= shear area of one thread
The bearing pressure between the contacting surfaces of
the screw and the nut.
31. 31
Differential & Compound Screws:
• Differential Screw:
A differential screw is defined as a mechanical
device consist of two screws in series, which are arranged in
such way that the resultant motion is the difference of
individual motions of the two screws.
The composite screw consist of
larger part 𝑆1 (pitch=4𝑚𝑚) &
smaller part 𝑆2 (pitch=3𝑚𝑚).
The hand of helix for both the
screw is right-handed. The 𝑆1
moves through frame F. There
is square nut N on 𝑆2.
The rotation of nut is prevented is shown in fig (c) it can only
slide in axial direction w.r.t. frame.
32. 32
The handle turned through one revolution in clockwise direction
when viewed from right hand side. The direction of movement of
the nut is opposite to that of the screw. The 𝑆1 will move through
4𝑚𝑚 to the left w.r.t. frame & nut 3𝑚𝑚 to the right w.r.t. frame.
The resultant motion of the nut w.r.t. frame will be 4 − 3 𝑚𝑚 to
the left. In general if 𝑝1 &𝑝2 are the pitches of the screws the
resultant motion is equal to (𝑝1 - 𝑝2 )or the difference of the
individual motion of the two screws.
• Compound Screws:
A compound screw isdefined as a mechanical device consist of
two screws in series, which are arranged in such way that the
resultant motion is the sum of individual motions of the two
screws. The arrangement is same as differential screw, except
hand of helix for two screws are different.
33. 33
The threads on 𝑆1 are
right handed while those on 𝑆2
left handed. The resultant
motion of the nut w.r.t. frame
will be 4 + 3 𝑚𝑚 to the left.
In general if 𝑝1 & 𝑝2 are the
pitches of the screws the
resultant motion is equal to
(𝑝1 + 𝑝2 ) or the sum of the
individual motion of the two
screws.
34. 34
Recirculating Ball Screw:
It consist of screw & nut, the
surfaces of which separated by a
series of balls. The screw & nut have
semi-circular thread profiles. As the
screw rotated, the balls advance in
the grooves in nut & screw. They are
collected at the end of the nut &
returned back. It is also called as
ball bearing screw or ball screw.
Such screws are preloaded and give accurate motion due
elimination of backlash. There is no heat generation due to
negligible friction. These screw can be used for high speed even
upto10 𝑚 𝑚𝑖𝑛. The balls, nut, screw are subjected to contact
stresses.
35. 35
Advantages:
• Due to rolling friction efficiency is high as 90%.
• It is wear-free due to presence of lubricating film between
contacting surfaces & protection from contamination by dirt
particles.
• It has large load carrying capacity.
• Operation of RBS is smooth.
Disadvantages:
• RBSis more costly.
• They are usually overhauling due to low friction.
• In RBS buckling of screw & critical speed are serious problem.
• RBS requires a high degree of cleanliness.
Applications:
Automobile steering gear, power actuators, X-Y recorders of CNC
machines, aircraft landing gear retractors, hospital bed adjustors,
machine tool control.
