1.0
Objective • •
2.0
To determine the coefficient of friction between belt and pulley. To differentiate differentiate the efficiency between V-belt and flat-belt. Introduction
Belt is flexible ban which is in power transmission transmission.. It is able to transfer transfer the power from one point to the other points with minimum power loss. The belt is able to work smoothly and quietly even without the requirement of lubrication. The earliest belt used in the world was the flat belt. In flat belt, only the bottom part of the belt is in contact with the pulley surface. The disadvantae of flat belt is that the flat belt pulley needs to be carefully alined to prevent the belt from fr om slippin. In order to solve the problem encountered by the flat belt, V belt is introduced. !ormally, the V-belt V-belt is placed on the roove of a pulley. In V-belt, V-belt, both sides of the belt are in contact with the pulley roove. This can prevent or minimi"e the chances of the belt from slippin. #lat belts require sinificantly hiher pre-tensionin in order to transmit a certain torque without slippae. This especially applies to lare transmission ratios and thereby low anles of contact. Tension pulleys with defined contact pressure are recommended in cases of this kind to reduce the transverse force. V-belts are characteri"ed by their trape"ium shaped $v-shaped% cross-section. They consist of a tensionin section of multiple layers of endlessly wound polyester fibre cord threads, the core which is made of a hih-quality rubber mixture and the enclosure which is made of rubberi"ed cotton or synthetic fabric. &ependin on the intended intended use, different different desins are used.#lat used.#lat belts are not advisable advisable for hih outputs outputs at hih speeds. This experiment is done to determine the coefficient of friction between belt and pulley. The factors to be discussed are the use of belt and the anle of contact between belt and pulley. Two types of belt used in this experiment are a flat belt and V-shaped belt. This experiment experiment was initiated by placin a fixed weiht of '.() k mass at one end of a flat belt. The value is recorded as tension, T'. The other end of sprin was placed at anles of (*+ to '*+. nylon rope was attached on the rim of the pulley clockwise and end freely suspended with a weiht of value which is . The weiht of the lead pulley is taken when the pulley starts to rotate at constant velocity. Then the tension, T/ is obtained by subtractin the total value from T'. The ratio of T'0T/ is taken and the value of ln $T'0T/% is calculated. 1
raph of ln $T'0T/% aainst contact anle was plotted to find the coefficient of slidin friction between belt and pulley.
3.0
Equipment & Material
1prin scale, belt holder, anle display, sprin scale holder, pulley with different rooves, sprin scale with screw strut, screw strut holder, win nut and safety door
2
4.0
Procedure
4.1: o determine t!e belt "riction coe""icient "or #lat$belt
'. 2pen the safety door. $&o not open the door usin the bottom riht end as it may break the acrylic cover.% /. Insert the sprin scale screw strut into the inner side hole of the screw strut holder. Tihten it with win nut. 3. 4lace the sprin scale to the sprin scale holder at 5+. (. 6lose the safety acrylic door. *. pply the load to belt by turnin the win nut. $7ake sure the weiht is in k% . 4lace the sprin scale to the sprin scale holder at (*+. 8. Take the readin at the other sprin scale. ). 9epeat the experiment with other anle and take the readin. 4.2: o determine t!e belt "riction coe""icient "or %$belt
'. 2pen the safety door. $&o not open the door usin the bottom riht end as it may break the acrylic cover.% /. Insert the sprin scale screw strut into the inner side hole of the screw strut holder. Tihten it with win nut. 3. 4lace the sprin scale to the sprin scale holder at 5+. (. 6lose the safety acrylic door. *. pply the load to belt by turnin the win nut. $7ake sure the weiht is in k% . 4lace the sprin scale to the sprin scale holder at (*+. 8. Take the readin at the other sprin scale. ). 9epeat the experiment with other anle and take the readin.
3
.0
'E()*(
*.'
#lat Belt
6ontac t anle ᵦ$+%
1prin scale
1prin scale
T'$!%
T/$!%
(*
*8
5
-5.5*'3
'.'(
8*
*
5
5.5)55
'.585
'5*
8/.*
5
5.');/
'.)5/5
'3*
8*
5
5.//3'
/.;8(8
'*
85
5
5.'*(/
;.3(**'
ln $T/0T'%
6oefficient of static friction, :s
×
'5-3
× ×
×
'5-3 '5-3 '5-3
×1
5-
3
*./
V-belt
6ontact anle ᵦ$+%
1prin scale
1prin scale
T'$!%
T/$!%
(*
*
5
5.5)55
-'./;(
8*
85
5
5.'*(/
-'.))(( × '5-3
'5*
85
5
5.'*(/
-'.3((5
'3*
)5
5
5./)88
-'.;*3/ × '5-3
'*
8*
5
5.//3'
-'./3;/
ln $T/0T'%
4
6oefficient of static friction,:s
×
×
×
'5-3
'5-3
'5-3
+.0
,I(-)((IO/E%*)IO
+.1
,I(-)((IO
Belt is a loop of flexible material used to link two or more rotatin shafts mechanically, most often parallel. Belts may be used as a source of motion, to transmit power efficiently, or to track relative movement. Belts are looped over pulleys and may have a twist between the pulleys, and the shafts need not be parallel. In a two pulley system, the belt can either drive the pulleys normally in one direction or the belt may be crossed, so that the direction of the driven shaft is reversed. s a source of motion, a conveyor belt is one application where the belt is adapted to carry a load continuously between two points. Belt friction is a term describin the friction forces between a belt and a surface, such as a belt wrapped around a bollard. hen one end of the belt is bein pulled only part of this force is transmitted to the other end wrapped about a surface. The friction force increases with the amount of wrap about a surface and makes it so the tension in the belt can be different at both ends of the belt. Belt friction can be modeled by the Belt friction equation. In practice, the theoretical tension actin on the belt or rope calculated by the belt friction equation can be compared to the maximum tension the belt can support. This helps a desiner of such a ri to know how many times the belt or rope must be wrapped around the pulley to prevent it from slippin. 7ountain climbers and sailin crews demonstrate a standard knowlede of belt friction when accomplishin basic tasks. This experiment conducted to study the belt friction coefficient for V-belt and flat belt. The experimental results obtained are plotted in two different raphs.
The fact that hih standard forces between pulleys and belts occur at low pretension offers advantaes for the V-belt. These advantaes include low bearin load and reliable operation even in the case of small anles of contact. The V-belt is less efficient in comparison with the flat belt, as it is restricted by the hih amount of flexin required.
6
.0
)E(IO(
.1
Plot t!e 2 rap!: -oe""icient o" tatic "riction5 6 v -ontact nle 7 "or "lat$belt.
>nhanced coefficient of friction, :s vs 6ontact nle ? for V-belt
.2
8!en t!e coe""icient o" tatic "riction 9ill be equal to ero "or "lat belt;
Based on the raph, the coefficient of static friction will be equal to "ero when the value of contact anle decreases if the flat belt is contact to the overall surface of circumferences of pulley. Therefore no tension on the belt and the rotation of the pulley does not occur.
.3
a%
The relation between coefficient of static friction vs contact anle for flat belt.
Based on the raph coefficient of static friction vs contact anle for flat belt, the curve show the relation between coefficient of static friction and contact anle are inversely proportional. s the value of contact anle increases, the value of coefficient of static friction also increase. Therefore the enhancement of the value coefficient of static friction depends on the value of contact anle. b%
The relation between coefficient of static friction vs contact anle for V-belt.
Based on the raph of coefficient of static friction vs contact anle for V belt, the curve show the relation between coefficient of static friction and contact anle are fluctuate. This means that the coefficient of static friction increase or decrease are not depends on the increase or decrease contact anle.
7
.4
8!ic! belt i able to tranmit more po9er i" bot! are operatin in t!e ame
anular peed5 =; E>plain ?our an9er.
V belt is able to transmit more power than flat belt to transmit more power if both are operatin in the same anular speed due to wedin action in the rooves, limitin ratio of tensions is hiher and thus, more power transmission can be produced. 2win to wedin action, V-belts need little adAustments and transmit more power, without slip as compared to flat belt.
.
,erive equation o" coe""icient o" tatic "riction5 6 "or %$@elt b? taAin normal Σ F y = 5
Σ F x = 5
"orce
and
.
In case of a V-belt, there are two normal reactions so that the radial reaction is equal to /9 sin . Thus total frictional force C /$:9% C /:9. 9esolvin the forces tanentially, 2 μR + T cos
δθ δθ −( T + δT ) cos =0 2 2
#or small anle of DE, cos
δθ ≈1 2
δT = 2 μR
9esolvin the forces radially, 2 Rsinα −T sin
s DE is small,
sin
δθ δθ −( T + δT ) sin =0 2 2
δθ δθ ≈ 2 2
8
2 Rsinα −T
δθ 2
−
T
δθ 2
=
0
R=
Tδθ 2 sinα
2r #rom $iii% and $iv%,
DT
Tδθ 2sin α
¿ 2 μ
δT μδθ = T sin α
or
Interratin between proper limits, T 1
θ
dT μdθ ∫ T =∫ sin α T 0 2
log e
T 1 T 2
=
μθ sin α
2r
T 1 T 2
.+
μθ / sin α
=e
8!at are t!e advantae and diadvantae uin "lat belt;
a% dvantaes usin flat belt i. &oes not require rooves ii. 7inimi"in the enery loss and wear from the belt wedin in iii. iv. v.
and pullin out from the rooves. >nery savins lon service life of belts and pulleys Fess down time and hih productivity 9
vi. Fow noise eneration from a smooth belt operation vii. 6an be installed simply and securely. b% &isadvantaes usin flat belt i. hih belt tension required to transmit power often shortens ii.
bearin life failure to track properly since they tend to climb towards the hiher side of the pulley
.
8!at are t!e advantae and diadvantae uin v$belt;
a% dvantaes usin v-belt i. 4ositive drive as slip between belt and pulley is neliible ii. !o Aoint troubles as V-belts are made endless iii. 2peration is smooth and quite iv. Gih velocity ratio up to '5 can be obtained v. &ue to wedin action in the rooves, limitin ratio of tensions vi. vii. viii.
is hiher and thus, more power transmission. 7ultiple V-belt drive increases the power transmission manifold. 7ay be operated in either direction with tiht siht at the top or bottom. 6an be easily installed and removed.
b% &isadvantaes usin v-belt i. 6annot be used for lare centre distances ii. 6onstruction of pulley is not simple iii. !ot as durable as flat belts iv. 6ostlier as compared to flat belts
10
B.0
-O-*)(IO
s conclusion, our obAective which is to determine the coefficient of friction between belt and pulley and to differentiate the efficiency between v-belt and flat-belt was achieved. Based on the raph of coefficient of static friction versus contact anle for v-belt and the raph of coefficient of static friction versus contact anle for flat-belt, we can conclude that there is a sinificant of increasin of coefficient of static friction to the contact anle for flat belt and for v-belt there is fluctuated up and down contact anle. By comparin for both type of belt, the flat-belt have hiher coefficient than v-belt. e can say that V-belt is better than the flat belt as V-belt will have lower the chances of slip occur. The hih standard forces between pulleys and belts occur at low pretension offers low bearin load and reliable operation in the small anles of contact. Therefore, the V-belt is less efficient in comparison with the flat belt, as it is restricted by the hih amount of flexin required.
11
C.0
'E#E'E-E(
'. 9.6. Gibbeler, Engineering Mechanics: Statics, '/th >dition in 1.I. Hnit $/5'5%, 4erson >ducation 1outh sia 4te, Ftd. /. #erdinand 4. Beer, >. 9ussell ohnston, r., Vector Mechanics for Engineers, Static and Dynamics, International Edition 1996 , 7c
12
10.0
PPE,I-E(
Figure 1 V-belt
Figure 2Flat Belt
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