jj309 fluid mechanics unit 5
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7/30/2019 JJ309 Fluid Mechanics Unit 5
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SCREW J1
UNIT 5
SCREW
OBJECTIVES
General Objective : To understand the concept of the wor k ing of a screw.
Specific Objectives : At the en d of thi s u n ityou should be able to :
state the terms that are im portan t for the study of screw.
match the pr in c ip leof screw work ing to that of f r iction o n an in c li n e d plane.
use these s u itable concepts to solve pro blem in v olve.
calculate the answer u s i n gthese concepts correctly.
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SCREW J3
Fig. 5.1 Fig. 5.2
The angle α,
Tan α = p
π D
(b) A Two-Start Thread
For a two-start thread the distance mov es axi a lly by the screw i n its nu t i n one
revoluti o nis the lead £ , which i s twice the p itch .
Tan α =£
π D
Tan α =2 p
π D
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5.2 THE VEE-THREADED SCREW
For a V-thread, the n or mal force between the nutand the screw i s increased s ince the
axi a lcomponent of t his force must equal W. Thus, i f the semi-angle of the thread i sφ,
Fig. 5.3., then nor mal force = W sec φ .
The f r ictio n force i s therefore i n creased i n the ratio sec φ : 1, so that the V-thread i s
equivalen t to a square thread hav ing a coef f ici e n tof f r ictio n ιv sec φ
Fig. 5.3
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INPUT
Tur n i n gthe screw i sequivalen t to moving a mass of weight W along the inclined p la ne by aho rizon talforce P.
5.3 RAISING LOAD
When the load i s raised by the force P the motion i sup the plane.(Fig.5.4).
Motion
RR
ξ ξ χ
Pξ + χ
W
P
W
Fig. 5.4
From the triangle of forces:
Tan (ξ + χ) = P
w
P = W tan (ξ + χ)
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Torque
The torque T required to rotate the screw agai n s tthe load i s :
T = P (1 D )2
0
T =1 PD
+
2
T =1
WD tan (Λ + χ)2 1
P
D2
Fig. 5.5: Cross-sectio n of Screw
Efficiency
The eff ici e ncy of the screw i sequal to:
Forward eff i c iency :
1 forward = force P req uired withoutf r iction (χ = 0)force P requi red w ithfr ic t io n
1 =w tanΛ
w tan(Λ + χ)
1 =tanΛ
tan(Λ + χ )
or,
1 = wo r k d o n e o n load W i n1 r e volu ti on
work doneby P i n1 revoluti o n
1 =we
P (π D)
1 =w
xe
P π D
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But,
w=
1
P tan(Λ + χ )
and tanΛ = £
τ D
1 =tanΛ
tan(Λ + χ )
Maximum Efficiency
1mak =1 −sin χ
1 + sin χ
Example 5.1
The helix angle of a screw tread is 100. If the coefficient of friction is 0.3 and the meandiameter of the square thread i s72.5mm,
calculate: (a) the p itc hof the tread,
(b) the eff i ciency when rai sin g a load of 1 kN, (c)the torque req u ir ed.
Solution 5.1
G iven :
α = 100 μ = 0.3 Dmean = 72.5mm
(a) tan α = p
τ D p = tan 100 (3.14)(72.5)
= 40.1
mm
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0
(b) μ = tan α
α = tan-1
0.3
α = 16.70
Ef f ici e ncy for raise load, 1
=
tanΛ
tan(Λ + χ )
1 =tan10
tan(100 + 16.7
0)
1 =
0.17630.5027
1 = 0.35 x 100%
1 =
35%
(c) Torque, T =
T =
T =
1WD tan (Λ + χ)
21
(1000)(72.5) tan (100 + 16.70)21
(1000)(72.5)(0.5027)2
T = 18.22 x 103
kNmm
T = 18.22 Nm
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5.4 LOAD BEING LOWERED
(i) When χ > Ι
P i sapplied to res ist the downward mov emen tof the load. Under
this cond iti o nthe load would just about to move downwards. If P
were no t appliedi n t his di rectio n the load would overhaul , that i smove down o n its own weight.
R
P
Motionχ χ
P
Rχ - Ι W
W
Fig. 5.6
From the tr i angle of forces:
Tan (χ - Ι) = P
w
P = W tan (χ - Ι)
Efficiency
Downward eff ici e ncy :
1downward = wo r k doneb y P i n1 r e volu ti o n work doneon load W i n1 revoluti o n
1 = P (τ D)
w£
1 =tan(χ Ι
)
tanχ
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SCREW J1
Example 5.2
Calculate the p itc hof a single-start square threaded screw of a jack w h ich wil l justallow the load to fall un i f or mly under i t s ownweight. The me an diameter of the
threads is 8 cm and μ= 0.08. If the p itch i s 15mm, what is the torque
required to lower a load of 3 kN?
Solution 5.2
If the load i s to fall u n if or mly under i t s ownweight, α = Ι
G iven :
μ = 0.08 μ = tan Ι Ι = 4.57°
Tan α = p
τ Dthen, α = Ι
Tan 4.57° = p
(3.14)(8)
p = 20mm
If the p i t c hi s15mm, Tan α = p
τ D
Tan α =15
(3.14)(8)
Tan α = 5.97
Torque, T =
T =
T =
α = 80.49°
1WD tan (α - Ι)
21
(3000)(8)tan (80.49°- 4.57°)2
1(3000)(8)(tan 75° 92’)
2
T = 2.4
Nm
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(ii) When − > ξ
If the angle of f r ictio n i sgreater than the angle of the p lane , then i t c an be seenf rom the tr i angle of force, that force P must be applied to help lower the load.
Motion
P
R
ξ −c ξ
R −c ξ W
ξ ξP
W
Fig. 5.7
From the tr i angle of forces:
Tan (−c ξ ) = P
w
P = W ta n ( −c ξ )
Efficiency
1 terbalik =tan(− ξ )
tanξ
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Example 5.3
The me an diameter of a squarecthreaded screw jack i s5 cm. The p itch of the thread i s1 cm. The coef f icie n tof fr ic t io nis 0.15. What force
must be applied at the end of a 70 cm long lever, which i s
perpendicular to the long itu d i n a laxi s of the screw to lower a load of 2to nnes?
Solution 5.3
G iven:
Mean diameter, d = 5 cm Pitch, p = 1 cm
Coefficient of friction, μ = 0.15 = tan 4 Then , 4 = 8.32°
Length of lever, L = 70 cm Load W = 2 t = 2000 kg
Force required to lower the load,
P = W tan (4 – α)
= 2000 ta n (8. 32°c3.39°)
= 2000 ta n 4. 53°
= 2000 x 0.0854
= 170.8 kg
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Activity 5A
TEST YOUR UNDERSTANDING BEFORE YOU CONTINUE WITH THE NEXT
INPUT…!
5.1 A nuton a s i nglecstart square thread bolt i s locked tight by a torque of 6 Nm. Thethread p itch i s5mm an d themean diameter 6 cm. Calculate :
(a) the axi a lload o n the screw i n k ilogrammes
(b) the torque required to loosen the nut. μ = 0.1.
5.2 The totalmass of the table of a p la n n ing mach in ean d its attached work p iece i s350
kg. The table i s traversed by a s inglecstart square thread of exter nal diamet er 45mm an d p itch 10mm. The pressure of the cuttin g i s600 N an d the speed of
cuttin g i s6 met ers per minute. The coeff i c ien tof fr ic t io nfor the table i s0.1 an d for the
screw thread i s0.08. Fi n dthe power required.
5.3 The me an radiusof a screw of a square thread screw jack i s2.5 cm. The p itch of thethread i s 7 . 5mm. If the coeff i c ien tof fr ic t io nis 0.12, what effort applied at the en d of a
lever 60 cm length is needed to raise a weight of 2000 kg?.
5.4 A screw press is used to compr ess books. The thread i sdouble thread (square head)
witha p itchof 4mm an d a me an radiusof 25mm. The coeff i c ien tof fr ic t ion for
the contact surfaces of the threads is 0.3. Determine the torque required for a pressureof
500 N.
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Feedback to Activity 5A
Have you triedthe questions????? If “YES”, check your answers now
5.1 161 kg, 3.47 Nm
5.2 191 W
5.3 14.07 kg
5.4 4450 Nmm
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INPUT
5.5 OVERHAULING OF THE SCREW
When the load moves down an d overcomes the thread f r iction by its ownweight, i t i ssai dto overhaul . When i tmove s downagai n s ta res istin g force P we found that
P = W tan ( χ c χ )
When the load overhauls, P = 0
Therefore,
tan ( χ c χ ) = 0
χ c χ = 0
χ = χ
Hence,
when the angle of the inclined plane is equal to the angle of the friction the load wi l loverhaul .
The eff ici e ncy of such a screw when rai sin g a load i s giv e n by:
1 =tanχ
tan(χ + χ )
but χ = χ
tanχ1=
tan 2χ
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Example 5.4
A load of 6 kN i s lifted by a jack hav ing a s i nglecstart square thread screw of 45
mm core diameter an d p itch 10mm. The load revolves withthe screw an d
the coeff i c ien tof f r ictio n at the screw thread i s 0.05. Fi n dthe torque required to li f tthe load.
Show that the load wi l loverhaul.
Solution 5.4
G iven :
W = 6000 N D mean = 45
+
1x 10 = 50mm μ = 0.05 p = 10
mm
2
Then ,
ta nχ = μ tan α = p
τ D
ta nχ = 0.05 tan α =10
(3.14)(50)
χ = 2.86° tan α = 0.0637
α = 3.64°
Torque required, T =1
WD tan (χ + χ)2
=1
(6000)(50) tan (3.64° + 2.86°)2
= 3000(50) tan (6.50°)
= 3000(50) (0.114)
= 17.1 Nm
Ef f ici e ncy, ι =
ι =
tanχ
tan(χ + χ )
tan 3.640
tan(3.640 + 2.86
0)
ι =0.0636
0.114
ι = 0.558
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ι = 56% > 50% (overhau ling)
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Activity 5B
TEST YOUR UNDERSTANDING BEFORE YOU CONTINUE WITH THE NEXT
INPUT…!
5.5 The drum of a windlassi s10 cm in diameter an d the effort i sappliedto the handle 60
cm fr om the axi s .Fi n dthe effort necessary to support a weight of mass 120 kg.
5.6 A wheel andaxle i sused to raisea load of mass 50 kg. The radiusof the wheel is 50
cm and wh ile i t mak es seven revolutio n sthe load r i s e s3.3 m. What is the smallest
force that w ill support the load?.
5.7 A table carrying a machin e tool i s traversed by a threecstart screw of 6mm p itch
an d exter nal diamet er 23mm. The mass of the table i s200 kg an d the coeff i c ient
of fr ic t io n between the table an d its guidesi s0.1. The screw i s d riven by a mo tor at 12
rev/s. Fi n dthe speed of operatio n of the tool, the power required and the coeff i c ien tof fr ic t io n
for the thread i f the eff ici e ncy i s70 percen t.
5.8 A d if feren tial pulley, the two parts of which have respectively twenty four and twenty f ive
teeth, is used to raise a weight of mass 500 kg. Show by sketch how the apparatus i s
used, and deter min e its velocity ratio. Fi n dalso what effort must be exerted i f the eff i c iency
i s60 percen t.
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Feedback To Activity 5B
Have you tried the questions????? If “YES”, check your answers now
5.5 10 gN
5.6 71
gN2
5.7 12.96 rnrmm ,60.5 W, 0.11
5.8 50, 162
gN.3
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SELF-ASSESSMENT 5
You are approach mmg success. Try all the questions m mth m sself cassessremt sectmo m am d check
your amswers wmth those gm v e mm mthe Feedback om Self cAssessr em t5 gm v e mo m the mext page.
If you face amy problers, dmscussmt w mth your lecturer. Good luck.
1. Fm m dthe torque to ram s ea load of 6 kN u s m m ga screw jack w m t ha doublecstart square
thread, co m ta m m mmg two threads per centimeter and a mean diameter of 60 mm. μ =
0.12. What ms the torque requ m red to lower the load?
2. A lathe saddle of r ass 30 kg m straversed by a s m mglecstart squarecthread screw of 10rr p mtch am d ream dmareter 40 rr . If the vertmcalforce o m the cuttm m gtool m s250
N, f m m dthe torque at the screw requ m red to traverse the saddle. The coeff mcm e m tof
f r mctmom betweem saddle am d lathe bed am d for the screw thread m s0.15.
3. A doublecstart squarecthread screw has a p mtch of 20 rr am d a ream dmareter of
100 rr , ι = 0.03. Calculate mts effmcm e mcy whem ram smm ga load.
4. A load of 2500 N m sto be ramsed by a screw jack w m t hr eam dmareter of 75 rr
am d p mtch of 12 rr . Fm m dthe eff m c memcy of the screw jack, m f the coeff m c mem tof
fr m c tm o m betweem the screw am d mut ms 0.075.
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Feedback to Self-Assessment 5
Have you tried the questions????? If “YES”, check your answers now
1. 31.4 Nr , 12 Nr
2. 0.376 Nr
3. 80.5 %
4. 41.5 %
CONGRATULATIONS!!!!…..
May success be with you
always….
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