7_power screw.pdf
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Power Screw Threads
Square thread
Acme thread
Lead screws of lathes and other machine tools, automotive jacks,
vises, linear actuators, adjustable floor posts and micrometers etc
ButtressThreads
Multi-start
Screw Jack
Lead Screw
Lathe
DVD drive
The Mechanics of Power Screws
Square-threaded power screw
single thread
Mean diameter ‘dm’
pitch ‘p’
lead angle ‘λ’
helix angle ‘ψ’
loaded by the axial compressive force ‘F’
Helix angle: Angle that thread makes with plane perpendicular to thread axis
Lead angle : Angle between the helix and a plane of rotation
FBD of one thread, (a) raising and (b) lowering
0cossin fNNPF RH
0cossin NfNFFV
0cossin fNNPF LH
0cossin NfNFFV
Raising load: Lowering Load:
A single thread of the screw is unrolled or developed for exactly a single turn. Then one edge
of the thread will form the hypotenuse of a right triangle whose base is the circumference of
the mean-thread-diameter circle and whose height is the lead
tan=(l / dm)
sincos
cossin
f
fFPR
sincos
sincos
f
fFPL
m
m
R
dlf
fd
lF
P
.1
m
m
L
dlf
dlfF
P
.1
fld
fdlFdT
m
mmR
2
fld
lfdFdT
m
mmL
2
Raising:
Lowering:
Torque, (a) raising and (b) lowering
Self locking of power screws
• TL gives the torque required to overcome the
friction in order to lower the load
• In certain instances, the load may itself lower by
causing the screw to spin
• In such cases, TL is either zero or negative.
• Whenever, the load does NOT lower by itself
unless a positive TL is applied, the screw is said to
be self-locking
fld
lfdFdT
m
mmL
2
lfdT mL 0 tanf
Self-locking of Screw jack
A screw is self locking whenever the coefficient
of friction is greater than the tangent of the lead
angle.
tanf
Collar friction
• Normally a collar is employed to enable the power screw system to have sufficient bearing area hold the component being raised
• Since the collar slides against the component being raised, additional torque needs to be applied to raise the load, this is called as collar friction torque Tc
• To estimate the Tc, whenever the collar is not too big, it is enough to use a mean diameter, dc, at which the collar friction force is concentrated
2
ccc
dFfT
Total torque required to rise the load; TR’ = TR + Tc
Total torque required to rise the load; TL’= TL + Tc
Power screw’s raising efficiency
• It is the ratio of raising torque without friction to the raising torque with friction
• Can be defined both with and without collar friction
2
FlTo
RR
o
T
Fl
T
T
2
fld
fdlFdT
m
mmR
2
Coefficient of friction (f)
Use Tables 8-5 and 8-6 for values of coefficient of f and fc.
Table 8–5 Coefficients of Friction ‘f’ for Threaded Pairs
Table 8–6 Thrust-Collar Friction Coefficients
Raising torque for ACME screws
• A simple approximate equation is
The effect of the thread angle in ACME thread is to increase the
friction force between the screw and the nut due to the wedging
action of the thread.
For power screw application, though the ACME thread is not
suitable due to higher frictional force resulting from wedging action,
is commonly used because it is easier to manufacture than the
square threads.
sec
sec
2 fld
fdlFdT
m
mmR
fld
fdlFdT
m
mmR
2
Critical element at which the
von-Mises stress is evaluated
Bearing
pressure
T
F
Body stresses in power screws
0
4
6
2
z
r
y
tr
x
d
F
pnd
F
n=Number of engaged threads
Body stresses in power screws
• Bending stress, x
• Torsional shear stress, xy
• Axial compressive stress, y
• Transverse shear (no contribution to von-Mises stress because it is maximum where bending stress is zero and is zero where bending stress is maximum; hence needs to be only independently checked for)
• Bearing pressure (no contribution to von-Mises stress because it is distributed over the thread and is maximum at the middle of thread and is zero at the root of the thread)
resultant is von-mises
stress at top of the root
plane
Body stresses in the screw threads: von-
Mises stress at the critical element
3
16
r
Rxy
d
T
3
16
r
Lxy
d
T
or 2
4
r
yd
F
A
F
pd
F
pnd
F
cI
M
rtr
x
28.26
Power screws are operated normally at low speeds and
hence static design is enough.
42)(
12
1;
4
3p
candp
ndIp
FM tr
The engaged threads cannot share the load equally. Some experiments show that the first
engaged thread carries a maximum of 38% of the load. In estimating thread stresses by
the equations above, substituting 0.38F for F and setting nt to 1 will give the largest level of
stresses in the thread-nut combination.
21
2222226
2
1' zxyzxyxzzyyx
Resultant von-Mises stress
Body stresses in the screw threads:
von-Mises stress at the critical element
21
22226
2
1' xyxyyx
Body stresses: Transverse shear and bearing
pnd
F
pnd
F
tmtm
B
2
2
pd
F
pnd
F
pnd
F
A
V
rtrtr
14.13
22
3
2
3
Must be less than the safe bearing pressure
given in Table 8-4. Causes too much wear
and sometimes crushing.
It is at the centre of the root
area. Must be less than the shear
yield strength of material.
substituting 0.38F for F and setting nt to 1
will give the largest level of stresses in the
thread-nut combination.
pd
F
pnd
F
mtm
B
76.02
Table 8–4
Screw Bearing Pressure
need to be independently checked (no need to consider in von-Mises stress)
Problem
A power screw has triple thread of major diameter 25 mm,
minor diameter 21.5 mm and pitch of 3 mm. A vertical load
on the screw reaches a maximum of 6 kN. The coefficient
of friction is 0.06 for threads and 0.03 for collar. The
friction diameter of the collar is 30 mm. Find the following:
(a) total torque required to raise the load, (b) total torque
required to lower the load, (c) efficiency, (d) bending stress,
axial normal stress, torsional shear stress and the resultant
von-Mises at the root for one thread (by assuming the first
engaged thread carries a maximum of 0.38 of the load). (e)
bearing and transverse shear stress
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