ADDITIONAL THEORY Gears are used to transmit motion, and therefore power, between one shaft and another shaft. The funtion of a !ear bo" is to transmit rotationa# motion from a dri$in! prime mo$e to a dri$en mahine. Gear a#so %nown as toothed whee# desi!ned to transmit tor&ue to another !ear or toothed omponent. Di'erent si(e !ears are often used in pairs, a##owin! the tor&ue of the dri$in! !ears to produe a #ar!e tor&ue in the dri$en !ear at #ower speed, or a sma##er tor&ue at hi!her speed. The #ar!e !ear %nown as whee# and the sma##er !ear as a pinion.
N 1
N 2
And another theor) of !ear is a omponent within a transmission de$ie that transmits rotationa# tor&ue b) app#)in! a fore to the teeth of another !ear or de$ie. A !ear is di'erent from a pu##e) in that a !ear is a round whee# that has #in%a!es that mesh with other !ear teeth, a##owin! fore to be fu##) transferred without s#ippa!e. Dependin! on their onstrution and arran!ement, !eared de$ies an transmit fores at di'erent speeds, tor&ue, or in a di'erent diretion, from the power soure. The !ear*s most important fe ature is that !ears of une&ua# si(es +diameters an be ombined to produe a mehania# ad$anta!e, so that the rotationa# speed and tor&ue or the seond !ear are di'erent from those of the -rst.
O/ER0ATION/ • •
•
•
•
Gear with di'erent si(e produe di'erent motor speed +rpm /peed motor with the same si(e or di'erent si(e !ear 1 to 2, the $a#ue of speed motor from resu#t wi## derease unti# the #owest $a#ue in the data from the !ear 1 to 2. The hi!hest speed +rpm is at !ear 3. At !ear set 3, 411 motor speeds reorded 351.5 rpm and at !ear set 6 on 411 motor speed states at 226.6 rpm. Eah b#o% !ear set are two hea$), it ma) omp#iated if the entire !roup member are !ir#s. 7ontat tahnometer for !ear 2 on#) deteted at speed 211 unti# 411 rpm at 8 se
The hi!her speed produe a sma##er tor&ue mean whi#e #ar!e tor&ue in the dri$en !ear produe #ower speed.7AL79LATION 7a#u#ation for sta!e !ear with di'erent si(e !ear +!ear at set 6 Gear ratio +theoretia#
Gear Ratio =
Gear 1=
18
Gear 2=
18
Gear 3 =
38
78
input speed N 1 = output speed N 2
=0.474
× ( gear 1 )=
18 118
18 78
× ( gear 2 )=
( 0.474 )= 0.109
18 118
( 0.109 )=0.016
Gear ratio +e"periment
Gear Ratio =
gear 1 =
(
gear 2
input speed N 1 = output speed N 2
46.7 100
) =
+ 97.3 + 149.9 + 190.3 + 239.3 + 282.5 + 332.3 200
300
400
500
600
700
7
(=
11.0 100
+
21.1 200
+
32.8 300
+
44.7 400 7
+
52.9 500
+
66.8 600
+
74.2 700
)=
0.479
0.380
gear 3
(=
2.5 100
+
3.7 200
+
6.7 300
+
6.9 400 7
+
8.4 500
+
10.1 600
+
11.6 700
)=
0.019
7a#u#ation for sta!e !ear with same si(e !ear +!ear at set 3 Gear ratio +theoretia#
Gear Ratio =
Gear 1=
18
Gear 2=
18
Gear 3 =
78
input speed N 1 = output speed N 2
=0.231
78
× ( gear 1 )=
18 118
18 78
× ( gear 2 )=
( 0.231 )=0.053
18 118
( 0.053 )=0.012
Gear ratio +e"periment
Gear Ratio =
gear 1
(=
24.1 100
gear 3
+
48.8 200
+
70.0 300
+
92.6
+
400
121.8 500
+
136.7 600
+
) =
160.6 700
7
gear 2 =
(=
input speed N 1 = output speed N 2
(
12.2 100
11.7 100
+
11.6 200
+
16.5 300
+
21.3 400
+
26.1 500
+
31.7 600
+
38.3 700
7
+
7.8 200
+
8.1 300
+
4.9 400 7
+
6.3 500
+
7.4 600
+
8.6 700
)=
)=
0.033
0.236
0.064
DI/79//ION a. :rom tab#e 2.3 and 2.6, a#u#ate !ear ratio theoretia##) and e"perimenta##) and ompare the resu#ts. /et 3
G.R +theoretia# G.R +e"periment
Gear 3 1.623 1.625
Gear 6 1.182 1.15;
Gear 2 1.136 1.122
Gear 3 1.;4; 1.;4<
Gear 6 1.31< 1.2=1
Gear 2 1.135 1.13<
/et 6
G.R +theoretia# G.R +e"periment
On the a#u#ations, the resu#t for both set 3 and set 6 ha$e s#i!ht#) di'erent from the theoretia# $a#ues.
b. what are the input torque and the output torque of the gear system. Given that the input power pin equal to 20 kW and the eciency, η equal to 0.
η=
Power output Power input
0.7 =
Pout 20 × 10
3
P out =14000 N /et 3 > same si(e !ear Gear 1,
w=
2 πN 60
=
2 π ( 100 ) 60
=10.47 rad / s
P ( 20 × 10 ) =1910.2 Nm ( I nput torque ) T = = w 10.47 3
w=
Gear 3,
T =
60
=
2 π ( 24.1 ) 60
=2.52 rad / s
P ( 14000 ) = =55547.31 Nm ( Out put torque ) 24.1 w
w=
Gear 6,
T =
2 πN
2 πN 60
=
2 π ( 5.5 ) 60
=1.37 rad / s
P ( 14000 ) = =10958.21 Nm ( Output torque ) w 1.37
Gear 2,
w=
T =
2 πN 60
=
2 π ( 11.7 ) 60
=1.23 rad / s
P ( 14000 ) = =11426.5 Nm ( Output torque ) 1.23 w
N +rpm 311 611 211 ;11 811 511 411
a$ !
;11
Gear 1 w +Nm
T +Nm
31.; 4 61.< ; 23.; 6 ;3.= < 86.2 5 56.= 2 42.2 1
3<31 .6 <88. 3 525. 8 ;45. ; 2=3. < 23=. 2 646. = 414. 23
N +rpm 6;.3
Gear 3 w +Nm 6.86
;=.=
8.33
41.1
4.22
<6.5
<.41
363. = 325. 4
36.4 8 3;.2 6 35.= 6
1
51.5 <2.8
T +Nm 88;4 .2 642< .5 3<1< .< 3;;2 .4 31<4 .5 <44. < =26. ; 614= .;
N +rpm 36.6
Gear 6 w +Nm 3.6=
33.5
3.63
35.8
3.46
63.2
6.62
65.3
6.42
23.4
2.26
2=.2
;.13
66.8
T +Nm 31<8= .6 33868 .1 =316. ; 5645. 8 8366. 6 ;634. ; 2;<1. 5 41<=. <3
N +rpm 33.4
Gear 2 w +Nm 3.62
4.=
1.=6
=.3
1.=8
;.<
3.8;
5.2
1.55
4.;
1.44
=.5
1.<1
4.=
T +Nm 33;65. 8 3432<. = 3581;. < 646=2. 4 63661. 4 3=155. 6 388;8. 24 3=35<. 5
/et 6 > di'erent si(e !ear Gear 1,
w=
2 πN 60
=
2 π ( 100 ) 60
=10.47 rad / s
P ( 20 × 10 ) =1910.2 Nm ( Input torque ) T = = 10.47 w 3
w=
Gear 3,
T =
60
=
2 π ( 46.7 ) 60
=4.8904 rad / s
P ( 14000 ) = =2862.74 Nm ( Output torque ) w 4.8904
w=
Gear 6,
T =
2 πN
2 πN 60
=
2 π ( 11.0 ) 60
=1.1519 rad / s
P ( 14000 ) = =12153.65 Nm ( Output torque ) w 1.1519
Gear 2,
w=
T =
2 πN 60
=
2 π ( 2.5 ) 60
=0.2618 rad / s
P ( 14000 ) = =53476.06 Nm ( Output torque ) w 0.2618
N +rpm 311 611 211 ;11
Gear 1 w +Nm
T +Nm
31.; 4 61.< ; 23.; 6 ;3.= <
3<31 .6 <88. 3 525. 8 ;45. ;
N +rpm ;5.4 <4.2 3;<. < 3<1. 2
Gear 3 w +Nm ;.=< 31.3 < 38.5 < 3<.< 2
T +Nm 6=56 .4 3246 .< =<3. < 416. 8
N +rpm 33.1
Gear 6 w +Nm 3.38
63.3
6.63
26.=
2.;2
;;.4
;.5=
T +Nm
N +rpm
36382 .4 5225. 1 ;148. < 6<<1. =
6.8
Gear 2 w +Nm 1.65
2.4
1.2<
5.4
1.41
5.<
1.46
T +Nm 82;4 .3 2532 .8 3<<8 .= 3<24 .;
811 511 411 a$ !
;11
86.2 5 56.= 2 42.2 1
2=3. < 23=. 2 646. = 414. 2
62<. 2 6=6. 8 226. 6 3<3. 3<
68.1 5 6<.8 = 2;.4 <
88=. 4 ;42. 6 ;16. 26 3124 .<
86.<
8.8;
55.=
5.<<
4;.6
4.44
;2.;
6864. 6 6113. ; 3=13. = ;888. 2
=.;
1.==
31.6
3.15
33.5
3.63
4.3
38<3 .8 3262 .4 3386 .1 6;62 .4
c. !alculate the eciency of gear system "gear set # and set 2$ of the following combination gear. Given
P¿ =20 kW and system
are idle,
a Gear 3 to !ear 1
Average Speed Gear 0, ( gear set 1 ∧2 )
speed =
100+ 200 + 300 + 400 + 500 + 600 + 700 7
N 1= 400 rp m
Average Speed Gear 1, ( same gear )
speed gear 1=
( 24.1+ 48.8 + 70.0 + 92.6 + 121.8 + 136.7 + 160.6 ) 7
N 2=93.5 rp m
Average Speed Gear 1, ( different gear )
speed gear 1=
( 46.7 + 97.3 + 149.9 + 190.3 + 239.3 + 282.5 + 332.3 )
N 2=191.19 rp m
effiien! gear 1− 0 ( samegear )
η=
( 2 π N T × 60 ) ( 2 π N T × 60 ) 2
2
1
1
7
¿
[ 2 π ( 93.5 ) ( 2078.4 ) ( 60 ) ] [2 π ( 400 ) ( 707.31 ) ( 60 ) ]
¿ 0.69 effiien! gear 1− 0 ( different gear )
η=
¿
( 2 π N T × 60 ) ( 2 π N T × 60 ) 2
2
1
1
[ 2 π ( 191.19 ) ( 1037.91 ) ( 60 ) ] [ 2 π ( 400 ) ( 707.31 ) ( 60 ) ]
¿ 0.70 b Gear 6 to 1
Average Speed Gear 2, ( same gear )
speed gear 2=
( 12.2+ 11.6 + 16.5 + 21.3 + 26.1 + 31.7 + 38.3 ) 7
N 2=20.79 rp m
Av erage Speed Gear 2, ( different gear )
speed gear 2=
( 11.0 +21.1 + 32.8 + 44.7 + 52.9 + 66.8 + 74.2 )
N 2= 43.36 rp m
effiien! gear 2 −0 ( samegear )
7
η=
¿
( 2 π N T × 60 ) ( 2 π N T × 60 ) 2
2
1
1
[ 2 π ( 20.79 ) ( 7098.91 ) ( 60 ) ] [ 2 π ( 400 ) ( 707.31 ) ( 60 ) ]
¿ 0.5216 effiien! gear 2 −0 ( different gear )
η=
¿
( 2 π N T × 60 ) ( 2 π N T × 60 ) 2
2
1
1
[ 2 π ( 43.36 ) ( 4555.3 ) ( 60 ) ] [ 2 π ( 400 ) ( 707.31 ) ( 60 ) ]
¿ 0.6981
Gear 2 to 1
Average Speed Gear 3 " ( same gear )
speed gear 3=
( 11.7 + 7.8+ 8.1 + 4.9 + 6.3 + 7.4 + 8.6 ) 7
N 2=6.16 rp m
Av erage Speed Gear 2, ( different gear )
speed gear 3=
( 2.5 + 3.7 + 6.7 + 6.9 +8.4 + 10.1+ 11.6 ) 7
N 2=7.13 rp m
effiien! gear 3 −0 ( samegear )
η=
¿
( 2 π N T × 60 ) ( 2 π N T × 60 ) 2
2
1
1
[ 2 π ( 6.16 ) ( 18169.6 ) ( 60 ) ] [ 2 π ( 400 ) (707.31 ) ( 60 ) ]
¿ 0.3956 effiien! gear 3 −0 ( different gear )
η=
¿
( 2 π N T × 60 ) ( 2 π N T × 60 ) 2
2
1
1
[ 2 π (7.13 ) ( 24230.7 ) ( 60 ) ] [ 2 π ( 400 ) ( 707.31 ) ( 60 ) ]
¿ 0.6106
?9E/TION
a. %eside that compound gear train, give another type of gearbo& constructions and also describe the applications. @orm !earbo" > worm !ears @orm !ears are ab#e to withstand hi!h sho% #oads, #ow in noise #e$e# and maintenanefree but are #ess frition than other !ear t)pes. @orm !ear an be used in ri!ht an!#e on-!uration. The worm !earbo" on-!uration a##ows the worm to turn the !ear with easeB howe$er, the !ear annot turn the worm. The pre$ention of the !ear to mo$e the worm an be used as a bra%in! s)stem. @hen the worm !earbo" is not ati$e, it is he#d in a #o%ed position. In additiona#, worm !ears are used in app#iations in minin!, ro##in! mi##s, presses and esa#ator dri$e s)stem. In e#e$ators, worm !ears an often be found in the mahiner) of ommon e#e$ators beause of their ompat si(e and non re$ersib#e properties. As the !earC#oad annot transmit motion ba% throu!h the wormChoist, usin! this t)pe of !ear an at as a seondar) bra%in! s)stem. This means the #oad annot free fa## and #oad speed is easi#) re!u#ated.
7ON7L9/ION :rom the e"periment, the obeti$e ha$e been ahie$ed whih are desribe the di'erent t)pe of !ear s)stem and some of their app#iation. Other than that, we are ab#e to impro$e our %now#ed!e about the onept of !ears s)stem, t)pe of !ears and it re#ated funtion and its app#iations. :urthermore, from the a#u#ations, a## the eien) has been stated. @hen we do this e"periment, we faed some prob#em that was to !et aurate rpm and to ho#d the tahnometer. The prob#em from that, ma%e a readin! in error readin!s. :urthermore, the tehnometer aura) are not in !ood ondition espeia##) pointin! reFetor for #ow speed !ear. ) su!!estion is impro$e the &ua#it) of tehnometer suh as do maintenane. In this wa), it ma) !i$e on aurate readin! in other e"periment.
RE:EREN7E 3. 6. 2. ;. 8.
En.wi%ipedia.or!Cwi%iCwormdri$e www.ho#ro)d.omCb#o!Cworm!earapp#iationsusesC www.anaheimautomation.omCmanua#sCformsC!earbo"!uide www.srib.omCdoC61566;54Computeri(ed!ears)stem www.!earsandstu'.omCt)peof!ear.htm
