Helical Gears Project
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Transcript of Helical Gears Project
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CONTENTS
Abstract i
List of Figures ii
List of Tables ii
Nomenclature iii
1. INTRODUCTION 1
. LITERATURE SUR!E" #
.1Intro$uction to %&T #
.Establis'ment of Com(an)*s +ranc'es #
.#Com(an)*s &ilestones ,
.,About -raga Diision /
#. -o0er transmission
#.1T)(es of $ries
#.A$antage of gear $ries
#.#Disa$antages of gear $ries 2
,. INTRODUCTION TO 3EAR DRI!ES 4
,.1Intro$uction 4
,.3eneral classification of gears 15
,.#3ear terminolog) 1,
,.,S(ur gear 1
,./C'aracteristics of 'elical gears 12
/. -RO+LE& DEFINITION
/.1Design (roce$ure for 'elical gears #
/.calculations /
6. FINITE ELE&ENT &ET%OD. ANAL"SIS
2. RESULTS AND CONCLUTION /,
4. REFERENCES /6
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ABSTRACT
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This project involves the design of a set of helical gears for gearbox of a thread rolling
machine at HMT. Thread rolling is a cold forming process in which different types of threads
are formed by rolling action.
In this project problems posed by spur gears like noise, lack of free movement
during power transmission and high impact stresses at the time of engagement of gears
are eliminated by replacing them with helical gears.
The design constraints in this project work are centre distance between the gears,
tranmission ratio and the gearbox dimensions.
irst, set of helical gears to be designed theoretically using !"#I$ "%&'TI().
$tresses induced in those gears are to be evaluated and they should be within the safe limits.
!ater, inite element package ')$*$ will be used for analysis. 'im of the analysis is to
determine the maximum deflection and stresses induced in the helical gear. Tangential, radial
and axial loads are analy+ed using ')$*$ software. The stresses produced in the gears
should be with in the limits, if not the process would be repeated accordingly and the stress
produced in the gear which is within the limits should be achived.
i
LIST OF FIGURES
Figure 1 : Thread rolling machine
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Figure 2 : $pur gear
Figure 3 : Helical gear
Figure 4 : Herring bone gear
Figure 5 : $traight bevel gear
Figure 6 : Hypoid gear
Figure 7 : rossed gear
Figure 8 : #orm gear
Figure 9 : -ear terminology
Figure 10 : Meshed gear
Figure 11 : ompressive stress diagram
Figure 12 : eformed shape of helical gear
LIST OF TABLES
Ta!e 1: $pur gear results
Ta!e 2 : Helical gear results
ii
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"O#E"CLATURE
$ % /ressure angle, degrees
$& % )ormalpressure angle, degrees
' 0 Helix angle, degrees
a( 0 esign stress, )1mm2
)e 0 "ndurance limit stress, )1mm2
)e* 0 $urface endurance limit of a gear pair, )1mm2
a 0 enter distance, mm
0 ace width, mm
C 0 ynamic factor depending upon machining errors
C* 0 $ervice factor
C+ 0 #ear and lubrication factor
C, 0 3elocity factor
- 0 /itch circle diameter, mm
Fa 0 'xial thrust, )
F( 0 ynamic load on gear tooth, )
F. 0 Tangential load at pitch line, )
F* 0 ynamic strength of the gear, )
F+ 0 !imiting load for wear, )
/ 0 !oad stress factor
0 Module, mm
& 0 )ormal module, mm
" 0 $peed, rpm
0 ircular pitch
( 0 iametral pitch
0 ircular pitch, mm
iii
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& 0 )ormal circular pitch, mm
0 4atio factor
0 /itch line velocity, m1s
0 orm factor
0 !ewis form factor
0 )o. (f teeth on gear
e 0 "5uivalent no. of teeth
iv
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CATER 1
I"TRO-UCTIO"
The thread rolling is a cold forming process in which different types of threads are
formed by means of rolling action. The thread rolling machine can produce threads, worms,
knurls, serrations, annular forms, roll finishing and straightening. There are different types of
thred rolling machines like6
axial rolling,
radial rolling,
tangential rolling.
In the thread rolling machine rolls are pressed into the component,stressing the
material beyond its yield point. This causes the component material to be deformed
plastically, and thus, permanently. &nike thread cutting, the grain structure of the material is
displaced not removed. 's the material will be plastically deformed by pressure, it should
have a minimum elongation of 78 and a maximum tensile strength of 29:,;;; /$I. Materials
that have less than 78 elongation or a significant hardness greater than 9; H4c, such as cast
iron, hard brass alloys and other hardened materials are not suitable candidates for thread
rolling process. The only re5uirement for the rolling process is that either the component or
the rolling head, or both, are rotating towards one another. Thread rolling tools can be used
on a wide variety of standard and special machine tools.
Threads are produced in second and in only one pass, whereas ) single pointthread cutting re5uires numerous passes and a much longer cycle time. !ong roll
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ig = Thread rolling machine and thread rolling process
Ca.er 2
Li.era.ure *ur,e
2;1 I&.r
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company diversified into #atches, Tractors, /rinting Machinery, Metal orming /resses, ie
asting D /lastic /rocessing Machinery, ) $ystems D Aearings. In =B:;s, the company
set up new units at /injore, Ealamassery and Hyderabad. In =BF;s, they set up HMT
International !td as a subsidiary company to channel HMT>s products and technical services
abroad.
2;2 E*.a!i*e&.
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Machine Tools !td and HMT #atches !td have been incorporated and these subsidiaries will
take over the business of Machine Tools and #atches of the company.
In the year 2;;9, the company signed agreement with &E
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pace with the ever changing technology. In addition, the company also manufactures a wide
range of industrial forgings for railway, automotive and ordnance applications.
/4'-'$ wisest investment has been in it excellent collaboration with cutter and tool
grinders, gambian of france for milling machines, escofier of france for thread rolling
machines, george fisher of swit+erland for copying lathes,mitsubishi heavy industries of
japan for machining centres and keiyo seiki of japan for ) lathes. The collaborations have
culminated in /raga producing machine tools of the highest 5uality conforming to
international standards. Ay virtue of their dependability, precision engineering and proven
performance , praga machine tools are penetrating larger segments of foreign markets
including &E, I$, anada, Aulgaria,Indonesia, -ermany, apan, etc., praga is even more
proud of the fact that it has contributed to the development of the machine tool industry in the
country and the creation of a vast band of skilled technicians. Thus, /raga today, is a nam to
reckon within the machine tool industry.
HMT !imited has =G manufacturing units.The constituent subsidiaries are given
below while the holding company retains the tractors business group.HMTs tractor business
commenced its operations in =BF= in technical collaboration with
M(T(E(3, +echoslovakia. HMT started the operation with the manufacture of
27 H/ tractor at the manufacturing plant in /injore, Haryana state. (ver the years, it has
developed tractors ranging from 27 H/ to F7 H/.
HMT !imited took over /raga Tools !imited as one of its subsidiaries =BGG. /raga
Tools !imited was established in May, =B9C as /raga Tools orporation !imited to
manufacture machine tools with its head 5uarters at $ecunderabad. It was renamed as /raga
Tools !imited in =B:C. It is mainly involved in manufacture of machine tools including )
machines.
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CATER 3
O?ER TRA"S#ISSIO"
/ower transmission is transfer of rotary motion and power from one shaft to another. The
transmission of power can be done in different ways like belt drives, rope drives, chain drives
and gear drives.
3;1 Te*
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-ears offer positive power transmission.
-ear drives are compact in construction due to relatively small centre distance.
-ears provide power transmission with high angular or linear accuracy.
-ear drives can avail a wide range of power transmission beyond the range of belt
drives or chain drives.
-ears can change the rate of rotation of a machinery shaft.
-ears can change the direction of the axis of rotation.
-ears can change rotary motion to linear motion.
-ear drives have a provision for gear shifting thus changed the transmission ratio over
a wide range.
3;3 -i*a(,a&.age*
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CATER 4
I"TRO-UCTIO" TO GEARS
-ears are most common means of transmitting power in modern mechanical world.
They vary from a tiny si+e used in watches to the larger gears used in marine speed reducers,
bridge lifting mechanisms and rail road turn table drives. They form vital elements of main
and auxilary machanisms in many machines such as automobiles, tractors, metal cutting
machine tools, rolling mills, hoisting and transmitting machinery, marine engines etc.
Toothed are used to change the speed or power ratio as well as direction between input and
output.
4;1 -e=i&i.i
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Manufacturing of gears is complex, since special tools and e5uipment are necessary to
manufacture.
ue to errors and inaccuracy in their manufacture, the drive may become noisy
accompained by vibration and high speed.
They are not suitable for large center distances because the drive becomes bulky.
4;2 GE"ERAL CLASSIFICATIO" OF GEARS:
epending upon the relation between the axes, shape of the solid on which the teeth
are developed, curvature of the tooth trace and any other special features, gears are
categori+ed into the following types.
4;2;1 Sur gear*:
In a pair of mating spur gears the axes of the component gears are parallel, that is they
are mounted on shafts which are parallel to each other. The gear teeth are straight along the
length and parallel to the axes.
ig 2
4;2;2 e!ia! gear*:
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In these gears also the axes are parallel and the pitch solid is cylindrical. The traces or
the elements of teeth are helices and these may be left handed or right handed.
ig C
4;2;3 erri&g
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ig 7
4;2;5
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ig F
4;2;7 ?
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ig B
a@ i. ir!e:
/itch circle is an imaginary circle, which by pure rolling motions would give same
motion as the actual gear.
@ i. ir!e (iae.er:
It is the diameter of the pitch circle. The si+e of gear usually specified by the pitch
circle diameter. It is also called pitch diameter.
@ i.
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g@ -e((e&(u:
It is a radial distance of a tooth from pitch circle to the bottom of tooth.
@ A((e&(u ir!e:
It is the circle drawn through the top of tooth and is concentric with the pitch circle.
i@ -e(e&(u ir!e:
It is the circle drawn through the bottom of tooth and is concentric with the pitch
circle.
@ Ciru!ar i. :
It is the distance measured to the circumference of the pitch circle from a point of one
tooth the corresponding point on next tooth. It is denoted by /c .
/cKL)
#here /cK circular pitch
K diameter of pitch circle
)K no. (f teeth on wheel
@ -iae.ra! i. :it is the ratio of no. (f teeth to the pitch circle diameter in mm, it is
denoted by /d.
/dK )L K /c
!@ #
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It is the radial distance from addendum and the dedendum circle of a gear. It is e5ual
to the sum of addendum to the dedendum.
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It is the radius that connects the circle to the profile of the teeth.
@ a.
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proportional to the magnitude of the pitch error. This can be some what alleviated by
providing tip relief of teeth and lapping the teeth to have a crowning.
!onger duration of meshing period generally reduces noise level. Helical gears are
better than spur gears in this respect, because the engagement of teeth is gradual and more
teeth are mesh simultaneously which helps to cancel out the bad effects of tooth error
resulting in smoother operation.
-ears may become more prone to vibration due to resonance. Therefore, natural
fre5uency of the system must lie away from the critical +one or the inclination towards co
vibration should be corrected by providing appropriate shape and providing vibration
damping methods.
-ear box housing should be so designed that the resonance effect is avoided by
damping. #ebs and ribs should be appropriate placed to attain this objective.
4;5 CARACTERISTICS OF ELICAL GEARS :
Helical gears are analogous to a set of stepped gears which consist of a number of
identical spur gears so arranged that the teeth of each individual member are slightly out of
phase relative to each other. In such an arrangement there is an mesh at the pitch line, other
mating pairs of teeth are in different phases of contact including approach and recess
contacts. ' helical gear construction is approximated if a composite body is made up of an
infinite number of such stepped gears, each of which is a lamination of infinitesimal
thickness, placed side by side successively with a slight phase difference.
4;5;1 Tru*. ara.eri*.i*
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rotation of individual gears. $ince the axial force or thrust is created due to the helical
orientation of the teeth, there by altering the direction of main tooth force ?normal force@.
The helix angle should be chosen carefully. or single helical gear running on parallel
shafts it is prudent to confine the helix angle within 2; degrees.
4;5;2 F
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*oungs modulus K 2L "7 )1mm2.
/oissons ratio K ;.C
Maximum bending stress K 9;; )1mm2
Maximum design compressive stress K ==;; )1mm2
ensity K F.GBL"
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CATER 5
ROBLE# -EFI"ITIO"
The objective of this project is to give a design of helical gear drive, which has
interchangability with the existing spur gear drive. There are constraints to be taken care of
i.e, centre distance and transmission ratios. The existing gear box has a single gear drive,
which restricts its user to have variable speeds at a time, so a gear train is to be designed for a
minimum of 9 speeds.
The given data of the existing gear drive is as follows6
/ower ?/@ K CF2G.7 #
$peed ?)@ K =9C; rpm
entre distance ?a@ K ==; mm
ace width ?b@ K27 mm
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air* 21@ 7634 7139 6545 5852 3476 3971 4565 5258
Tra&*i**i
5;1 a@ -e.eri&a.i
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MnK O?tLw@1?PdLvLEL*@Q=12
#here
tK /Ls13
wK =.=7
PdK 7:.9 )1mm2
vK :.=1?:.=R3@
3 K SLpL)p
pK ?pLmn1cos@
a K O?pRg@Lmn12 osQ
E K b1mn
bK O?=.=7LSLmn@1sinQ
* K SLy
yK ;.=22
5;1 @ -e*ig&
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bK =.=7LSLmn1$in
eK 1osC
5;1 @ S.re&g.
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)2K :9; rpm
mnK O?tLw@1?$dLvLEL*@Q=12
tK /L=;;;13
sK =
3 K SLpL)p
K ?SLpLmnL)p@1?:;;;;Los@
pK O2aLosQ1OmnL?iR=@Q
K ?2L==;L;.B:@1C.2C7Lmn@
K :7.CF1mn
3 K ?C.=9L:7.CFL=9C;@1?;.B:L:;;;;@
K 7.;B m1s
K CF2G.7L=17.;B
K FC2.7 )
Pd K 7:.9 )1mm2
vK :.=1?:.=R3@
K :.=1?:.=R7.;B@
K ;.797
E K b1mn
b K O?=.=7LSLmn@1$inQ
K O?=.=7LC.=9Lmn@1;.2GQ
K =C.==
* K SLy
K S?;.=79< ;.B=21Te@
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y K ;.=22
K C.=9L;.=22
K ;.CGC;G
mn K O?FC2.7L=.=7@1?7:.9L;.797L=C.==L;.CGC@Q=12
K2.C9
m K mn1cos
K 2.C91;.B:
K 2.9C K 2.7 ?approx@
2.7 mm is selected as the standard module for all the gears as it is calculated for the highest
transmission ratio.
$ince standard modules are 2 , 2.7 , C , C.7 ......
1*. air :
a K O?=R2@Lmn12cosQ
==; K ?C.2C7L=L2.9@1?2L;.B:@ since 2K 2.2C7 =
There for =K GG1C.2C7
= K 2F
= K 2F, 2K :=
K Lm
pK 2FL2.7 K :F.7 mm
gK :=L2.7 K =72.7 mm
/ K 1 p
K 2F1:F.7
K ;.9
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/nK /1os
K ;.91;.B:
K ;.92
4oot diameter ?r@K osNn
rpK :F.7L;.B99 K :C.FC X :9 mm ? for pinion@
rgK =72.7L;.B99 K =9C.BB X =99 ? for gear @
(uter diameter ?o @K R2mn
op K :7.7R9.G K F2.C X F2 mm
og K =72.7R9.G K =7F.C X =7F mm
aK tL Tan
tK /Ls13
3 K SL pL)p
K ?C.=9L:7.7L=9C;@1?:;;;;@
K 7.;7 m1s
tK CF2G.7L=17.;B
K FCG.CG )
aK FCG.CGL;.2GF
K 2==.F )
rK tLtanN1cos
K FCG.CGLtan2;1cos=:
K 2FB.7G )
b K =.=7LSLmn1sin
K =C.==Lmn
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K C=.7 mm
eK 1cosC
epK C=
eg K :B
d K tRVOEC3?bos2Rt@osQ1OEC3R?bos
2 R t@=12QW
K 2G:.C7
KFCG.CGR
VO2;.:FL7.;7?2G:.C7LC=.7L;.B29RFCG.CG@QL;.B:12;.:FL7.;7R?2G:.C7LC=.7L;.B29RFCG.CG@=12
QW
K 7;=2.2 )
s K PeLbL*Lmn
Pe K A.H.)L=.F7 K 2;;L=.F7 KCG7 )1mm2
sK CG7LC=.7L;.C7GL2.9
sK =;929.= )
w K pLbL%Lk1cos2
% K 221?=R2@
K =.CB
E K OPes 2LsinN1=.9QLO?"=R"2@1"="2Q
K =.G:9
K:F.7LC=.7L=.CBL=.G:91;.B29
K 7B:2 )
2&(air :
a K O?=R2@Lmn12cosQ
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==; K ?2.G2=L=L2.9@1?2L;.B:@ since i K =.G2=
There for =K GG12.G2=
= K C=
= K C=, 2K 7F
K Lm
pK C=L2.7 K FF.7 mm
gK 7FL2.7 K =92.7 mm
/ K 1 p
K C=1FF.7
K ;.9
/nK /1os
K ;.91;.B:
K ;.92
rK osNn
rpK FF.7L;.B99 K FC.=: X FC mm
rgK =92.7L;.B99 K =C9.72X =C7 mm
o K R2mn
op K FF.7R9.G K G2.C X G2 mm
og K =92.7R9.G K =9F.C X =9F mm
aK tL Tan
tK /Ls13
3 K SL pL)p
K ?C.=9LFF.7L=9C;@1?:;;;;@
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K 7.G m1s
tK CF2G.7L=17.G
K :92.G7 )
a K :92.G7L;.2GF
K =G9.7 )
r K tLtanN1cos
K :92.G7Ltan2;1cos=:
K 29C.9; )
b K =.=7LSLmn1sin
K =C.==Lmn
K C=.7 mm
e K 1cosC
epK C7
eg K :9
d K tRVOEC3?bos2Rt@osQ1OEC3R?bos
2 R t@=12QW
K C9C.:
K :92.G7R
VO2;.:FL7.G?C9C.:LC=.7L;.B29R:92.G7@QL;.B:12;.:FL7.GR?C9C.:LC=.7L;.B29R:92.G7@=12
QW
K :=9=.B7 )
s K PeLbL*Lmn
Pe K A.H.)L=.F7 K 2;;L=.F7 KCG7 )1mm2
sK CG7LC=.7L;.CF=L2.9
sK =;FBG.CC )
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w K pLbL%Lk1cos2
% K 221?=R2@
K =.2B
E K OPes 2LsinN1=.9QLO?"=R"2@1"="2Q
K =.G:9
KFF.7LC=.7L=.2BL=.G:91;.B29
K :C72.G )
3r(
air :
a K O?=R2@Lmn12cosQ
K ?2.99L=L2.9@1?2L;.B:@ since 2K =.99=
There for =K GG12.99
= K C:
= K C:, 2K 72
K Lm
pK C:L2.7 K B; mm
gK 72L2.7 K =C; mm
/ K 1 p
K C:1B;
K ;.9
/nK /1os
K ;.91;.B:
K ;.92
rK osNn
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rpK B;L;.B99 K G9.B: X G7 mm
rgK =C;L;.B99 K =22.F2X =2C mm
o K R2mn
op K B;R9.G K B9.G X B7 mm
og K =C;R9.G K =C9.G X =C7 mm
aK tL Tan
tK /Ls13
3 K SL pL)p
K ?C.=9LB;L=9C;@1?:;;;;@
K :.F9m1s
tK CF2G.7L=1:.F9
K 7CC.=B )
aK 7CC.=BL;.2GF
K =7C.= )
rK tLtanN1cos
K 7CC.=BLtan2;1cos=:
K 2;=.GG )
b K =.=7LSLmn1sin
K =C.==Lmn
K C=.7 mm
eK 1cosC
epK 9=
eg K 7B
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d K tRVOEC3?bos2Rt@osQ1OEC3R?bos
2 R t@=12QW
K C9C.:
K 7CC.=BR
VO2;.:FL:.F9?C9C.:LC=.7L;.B29R7CC.=B@QL;.B:12;.:FL:.F9R?C9C.:LC=.7L;.B29R7CC.=B@=12QW
K :C:C.F2 )
s K PeLbL*Lmn
Pe K A.H.)L=.F7 K 2;;L=.F7 KCG7 )1mm2
sK CG7LC=.7L;.CB:L2.9
sK ==727.BF )
w K pLbL%Lk1cos2
% K 221?=R2@
K =.=G
E K OPes 2LsinN1=.9QLO?"=R"2@1"="2Q
K =.G:9
KB;LC=.7L=.=GL=.G:91;.B29
K :F9G.72 )
4.air :
a K O?=R2@Lmn12cosQ
K ?2.=2L=L2.9@1?2L;.B:@ since 2K =.=2=
There for =K GG12.=2
= K 92
= K 92, 2K 9:
K Lm
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pK 92L2.7 K =;7 mm
gK 9:L2.7 K ==7 mm
/ K 1 p
K 921=;7
K ;.9
/nK /1os
K ;.91;.B:
K ;.92
rK osNn
rpK =;7L;.B99 K BB mm
rgK ==7L;.B99 K =;B mm
o K R2mn
op K =;7R9.G K ==; mm
og K ==7R9.G K =2; mm
aK tL Tan
tK /Ls13
3 K SL pL)p
K ?C.=9L=;7L=9C;@1?:;;;;@
K F.G:m1s
tK CF2G.7L=1F.G:
K 9F9.C: )
aK 9F9.C:L;.2GF
K =C: )
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rK tLtanN1cos
K 9F9.C:Ltan2;1cos=:
K =FB.:= )
b K =.=7LSLmn1sin
K =C.==Lmn
K C=.7 mm
eK 1cosC
epK 9G
eg K 72
d K tRVOEC3?bos2Rt@osQ1OEC3R?bos
2 R t@=12QW
K 2G:.C7
K 9F9.C:R
VO2;.:FLF.G:?2G:.C:LC=.7L;.B29R9F9.C:@QL;.B:12;.:FLF.G:R?2G:.C:LC=.7L;.B29R9F9.C:@=12
QW
K 7GC9.77 )
s K PeLbL*Lmn
Pe K A.H.)L=.F7 K 2;;L=.F7 KCG7 )1mm2
sK CG7LC=.7L;.9;GL2.9
sK ==GF7.27 )
w K pLbL%Lk1cos2
% K 221?=R2@
K =.;7
E K OPes 2LsinN1=.9QLO?"=R"2@1"="2Q
K =.G:9
K=;7LC=.7L=.;7L=.G:91;.B29
K F;;7.GG )
F
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/ower K CF2G.7 #
$peed ?)=@ K =9C; rpm
enter distance ?a@ K ==; mm
ace width ?b@ K C=.7 mm
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See("1@ =9C; =9C; =9C; =9C; =9C; =9C; =9C; =9C;
See("2@ :CC FFG BB; =C;: C22G 2:2B 2;:F =7::
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