POWER SCREWS
APPLICATION OF POWER SCREWS
The function of a power screw is to provide a means for obtaining a large mechanical
advantage and at the same time transmitting power by converting angular, into linear motion.
Common applications include lifting jacks, presses, vices, and lead screws for lathe
machines. Figure 1.1 shows the application in a lifting jack, while Figure 1.2 shows the
same concept when used for a press.
SCREW JACK APPLICATION
SCREW PRESS APPLICATION
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Engineering Design
Power screws
THREAD FORMS FOR POWER SCREWS
Power screws use either square, or trapezoidal thread forms. Two types of trapezoidal thread
forms are the ACME thread standard, used widely in the English speaking countries, and
based on the inches units, and the Metric trapezoidal standard, originating in Europe, and
now adopted by the International Standards Organisation (ISO).
Figure 1.3 shows the three geometric profiles of the three thread forms used for power
screws.
The (ISO) Metric trapezoidal thread form standard includes specifications that relate screw
shaft diameter to pitch, as shown in Table 1.1. For the square and ACME thread form
standards, only the geometric profile of the thread form is specified, and the designer is left to
chose the size of thread for each screw shaft diameter. This does not pose any serious
problem because each power screw application is often a special case.
Table 1.1: (ISO) Metric Trapezoidal screw thread standards-Diameter and Pitch
specifications
Nominal
(Major
Exernal)
Diameter
d
8
10
12
16
20
24
28
32
36
40
44
48
52
60
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Coarse
Medium
Fine
Pitch
Diameter
d 2  D2
8
8
10
10
10
12
12
12
14
1.5
2
3
4
4
5
5
6
6
7
7
8
8
9
1.5
2
2
2
3
3
3
3
3
3
3
3
3
7.25
9.00
10.50
14.00
18.00
21.50
25.50
29.00
33.00
36.50
40.50
44.00
48.00
55.50
Pitch p
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Major
Internal
Diameter
D
Minor Diameter
External
d1
Internal
D1
8.30
10.50
12.50
16.50
20.50
24.50
28.50
33.00
37.00
41.00
45.00
49.00
53.00
61.00
6.20
7.50
8.50
11.50
15.50
18.50
22.50
25.00
29.00
32.00
36.00
39.00
43.00
50.00
6.50
8.00
9.00
12.00
16.00
19.00
23.00
26.00
30.00
33.00
37.00
40.00
44.00
51.00
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Figure 1.4 illustrates the dimensions of the (ISO) Metric Trapezoidal thread standard shown
in Table 1.1.
MECHANICS OF POWER SCREW (SQUARE THREADED)
Figure 1.5 shows the geometry and dimensions of a square threaded power screw, with a
single start thread.
The power screw carries an axial load F, and this is to be raised or lowered by applying a
turning moment or torque on the screw shaft. The screw and nut machine then coverts the
torque on the screw shaft, into the desired axial load. This is the typical situation in the screw
jack, and the screw press concepts shown at Figures 1.1 and 1.2.
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The axial load F applied on the screw shaft is resisted by an equal and opposite force acting
on the nut. The rest of the variables in Figure 1.5 are:
F  Axial Load to be raised or lowered
  Helix angle for thread
p  Pitch of thread
d m  Mean diameter of screw thread
dm 
D1  d
2
EXTERNAL LOAD ON SCREW SHAFT
TORQUE REQUIRED IN A SQUARE THREADED POWER SCREW
It is necessary to determine the torque required in a power screw, as a function of the axial
load to be raised or lowered, because this torque comprises one of the external loads that the
screw shaft and its threads must withstand. This torque load is found to be a function of the
axial load F, the geometry and dimensions of the screw shaft and its threads, and the coefficient of friction between screw and nut threads.
TORQUE TO RAISE AXIAL LOAD WITH SQUARE THREAD FORM
To determine the relationships between the torque required, and the axial load to be raised F,
the screw thread is simplified into an inclined plane. Figure 1.6 shows a single thread of the
screw, unrolled or developed, to show the forces operating on the thread surface when the
load F is being raised. The axial load F is then considered as representing the summation of
all the unit forces acting on the direction of the axial load to be raised.
In Figure 1.6, the horizontal force P is the resultant force arising out of the applied torque. It
operates to move the axial load F, along the inclined plane formed by the developed thread
surface.
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Although the unit forces, whose summation is F and P, act on the entire thread surface
between minor internal diameter D1 and the major external diameter d , the resultant forces
are simplified to be concentrated at the mean of the two diameters d m 
D1  d
. For single
2
start thread, the inclined plane, along which the load F is moved, is therefore a triangle whose
angle of inclination is the helix angle  of the screw thread defined by tan  
l
d m
The length of the side opposite to the lead angle is equal to the lead l of the screw thread. The
base of the triangle is equal to the circumference of the mean thread diameter, which equals
d m .
The triangle at Figure 1.6 applies to one turn of a thread, but is similar to the case of the
entire length of engaged threads. The forces F and P can therefore represent the summation of
forces on the entire surface of the engaged threads.
In reaction to the forces F and P, operating on the surface of the threads, there is a normal
force N, and a frictional resistance given by the expression  * N . The unknown forces in this
system of forces can be determined as shown below, by the requirements of equilibrium:
 Fh  P  N sin    N cos   0
 Fv  F  N sin   N cos   0
Where
Fh  Horizontal
;
forces
Fv  Vertical forces
Solving the two equations for F and P,
Solving the two equations for F and P
P  N sin   N cos 
F  N cos   N sin 
Substituting for tan  
l
d m
 l  d m 
and P  F 

 d m  l 
But the torque resulting from the force P, is the product of P and the mean radius
dm
at which the force P is presumed to act. Consequently, the torque T is given by the
2
expression:
T 
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F dm
2
 l  d m 


 d m  l 
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THE CASE OF ANGULAR THREAD FORM
The equation for the torque required on the screw shaft to raise an axial load F, has been
derived, and is therefore valid, for the square thread form, where the normal thread loads are
parallel to the axis of the screw shaft. In the case of an angular thread form, such as ACME,
(ISO) Metric Trapezoidal or other angular thread forms used in fasteners, the thread angle for
the various thread forms is as shown in the table below:
Thread Form
ACME
(ISO) Metric Trapezoidal
Metric Fasteners
Thread angle =2* in degrees
29
30
30
In these angular thread forms, the load normal to thread surface is inclined to the axis of the
screw shaft by an angle , or half the thread angle. This is illustrated at Figure 1.7.
The effect of this inclination to the axis of the screw shaft of the normal load on thread
surface is to increase the frictional force on the thread surface, by the wedging action of the
threads. The frictional force is increased by a factor equal to the reciprocal of cos .
To account for this increased frictional force, the frictional terms in the torque equation are
divided by cos . The equation for the torque required when raising an axial load F, where
the screw thread form has a thread angle of 2*, therefore becomes:
T
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Fd m
2
 l   d m sec  


 d m  l sec  
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TORQUE REQUIRED TO LOWER LOAD
From the force diagram in Figure 1.6, it is seen that when raising an axial load F, the force P
(and hence the torque T), has to overcome both the axial load F, as well as the friction on the
thread surface. However, when lowering the axial load F, the axial load F itself assists the
torque T to overcome the thread friction.
The torque required to lower load is therefore given by the expressions:
1. Square thread form -Torque to lower load
T
Fd m
2
 l   d m 


 d m  l 
2. Angular thread form -Torque to lower load
T
Fd m  l   d m sec  


2  d m  l sec  
TORQUE TO OVERCOME COLLAR FRICTION
In most applications, the axial load F must be transmitted through a thrust collar. This is
necessary so that when operating the screw shaft, the collar pad may remain stationary with
the load being lifted, or work to be pressed, while the screw shaft rotates, as shown in Figure
1.8.
For this reason, an additional friction force appears at the collar pad, and the external torque
applied to operate the power screw shaft must also overcome this extra force, which gives
rise to an extra friction torque.
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Figure 1.8 shows a typical thrust collar arrangement, with the thrust load assumed to be
concentrated at the mean collar diameter. The torque required to overcome collar friction is
then given approximately by the expression:
F c d c
, Where,
2
F  Axial load to be raised ,  c  Co  efficient of collar friction
Tc 
di  do
(approximately )
2
d i  Inner diameter of collar , d o  Outer diameter of collar
d c  Mean collar diameter, d c 
Tc  Torque to overcome collar friction
For large collars, the friction torque at collar bearing will be more accurately computed
as for a disc clutch.
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Power screws
THREAD STRESSES
These are given by the expressions:
s 
2F
,
d1 h
n 
2F
,
dh
b 
4 pF
h(d 2  d1 2 )
Where, h  Height of nut , and p  pitch of screw threads
 s  Average shear stress on screw threads
 n  Average shear stress on nut threads
  Bearing stress on thread surfaces
b
When these thread stresses are computed, they should not exceed the limiting values for the
chosen materials.
ALLOWABLE BEARING PRESSURES
Limiting values of bearing pressures on thread surfaces for various combination of screw and
nut material have been determined empirically and are found to be as shown in Table 1.2.
TABLE 1.2: SAFE BEARING PRESSURES FOR POWER SCREWS
Type
of
Power Screw
Screw
Material
Hand press
Jack-screw
Jack-screw
Hoisting screw
Hoisting screw
Lead screw
Steel
Steel
Steel
Steel
Steel
Steel
Nut
Bronze
Cast iron
Bronze
Cast iron
Bronze
Bronze
Safe Bearing
Pressure
N / mm 2
17.0-24.0
12.0-17.0
11.0-17.0
4.0-7.0
5.5-10.0
1.0-1.6
Rubbing speed in m / s
Low speed, well lubricated
Low speed <2.5
Low speed<3
Medium speed (6-12)
Medium speed (6-12)
High speed>15
DESIGN PROCEDURE FOR SCREW SHAFT AND NUT
After determining the torque required to raise axial load F, and the extra value required to
overcome collar friction, all the external loads on the screw element are known, and the
screw shaft can then be analysed for its ability to resist these forces. Similarly, the same
forces act on the nut, and this element can also therefore be analysed for strength.
In the examples of the lifting jack and screw press shown at Figures 1.1 and 1.2, the screw
and nut elements can be designed without considering the frame arrangements. In this case
therefore, the steps listed below are appropriate in the design of screw shaft and nut.
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(a) Select the material and thread form for the screw;
(b) Decide on the type and material for thrust bearing;
(c) If column failure is a possibility, determine required diameter of screw shaft based on this
requirement; otherwise select a trial screw shaft diameter with strength to withstand
stresses due to axial load only.
(d) Using the screw shaft diameter from ©, determine thread dimensions, and stresses on
screw shaft, (namely, axial, bending, and torsional.
(e) Compare stresses induced in screw shaft with strength of material selected;
(f) Select new screw shaft diameter, if factor of safety is inadequate;
(g) Determine thread stresses and confirm factor of safety adequate;
CONDITION FOR SELF LOCKING
For the square threaded screw, the torque required to lower load is seen to vary with the lead
of screw thread according to the expression:
Fd m
2
T
 l   d m 


 l  d m 
Ignoring collar friction and equating the torque to zero, gives the limiting conditions at which
the load F will cause the thread to operate and lower itself, without any external torque. The
limiting value of the lead at which the screw ceases to be self locking therefore becomes:
Fd m  l   d m 

  0, or  d m  l
2  l  d m 
l
and  
 tan 
d m
T
Thus the limiting condition for self-locking for a square threaded screw is when the coefficient of friction between thread and nut surfaces equals the tangent of the lead or helix
angle. Self-locking ceases when the tangent of the helix angle is greater than the co-efficient
of friction.
Self  locking
ceases when tan   
EFFICIENCY OF SCREW
This is given by the expression:
e
F *l
,
2T
Where
e  efficiency of screw
For a square threaded screw, without collar friction, the efficiency becomes:
e
l
d m
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 d m  l 


  d m  l 
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