Date post: | 28-Feb-2018 |
Category: |
Documents |
Upload: | manda-ramesh-babu |
View: | 230 times |
Download: | 0 times |
of 39
7/25/2019 Chapter 4 Spur Gears Gear Profiles
1/39
1
It is essential for correctly
meshing gears, the size of the
teeth ( the module ) must be
the same for both the gears.
Another requirement - the
shape of teeth necessary for
the speed ratio to remain
constant during an increment
of rotation; this behaior of thecontacting surfaces (ie. the
teeth flan!s) is !no"n as
conjugate action.
7/25/2019 Chapter 4 Spur Gears Gear Profiles
2/39
#
7/25/2019 Chapter 4 Spur Gears Gear Profiles
3/39
$
Although many tooth
shapes are possible
for "hich a mating
tooth could bedesigned to satisfy the
fundamental la", only
t"o are in general use%
the cycloidal andinvoluteprofiles.
7/25/2019 Chapter 4 Spur Gears Gear Profiles
4/39
&
7/25/2019 Chapter 4 Spur Gears Gear Profiles
5/39
'
7/25/2019 Chapter 4 Spur Gears Gear Profiles
6/39
7/25/2019 Chapter 4 Spur Gears Gear Profiles
7/39
*he portion of the
Inolute +ure that"ould be used to
design a gear tooth
7/25/2019 Chapter 4 Spur Gears Gear Profiles
8/39
7/25/2019 Chapter 4 Spur Gears Gear Profiles
9/39
lue arro"s sho"s
the contact forces.
*he force line runs
along commontangent to base
circles.
7/25/2019 Chapter 4 Spur Gears Gear Profiles
10/391/
7/25/2019 Chapter 4 Spur Gears Gear Profiles
11/39
11
7/25/2019 Chapter 4 Spur Gears Gear Profiles
12/39
1#
7/25/2019 Chapter 4 Spur Gears Gear Profiles
13/39
1$
7/25/2019 Chapter 4 Spur Gears Gear Profiles
14/39
1&
7/25/2019 Chapter 4 Spur Gears Gear Profiles
15/39
1'
7/25/2019 Chapter 4 Spur Gears Gear Profiles
16/39
1
*he inolute profile of gears has important
adantages;
0 It is easy to manufacture and the centerdistance bet"een a pair of inolute gears
can be aried "ithout changing the elocity
ratio. *hus close tolerances bet"een shaft
locations are not required. *he most
commonly used conjugate tooth cure is
the involute curve.(rdman 2 3andor).
7/25/2019 Chapter 4 Spur Gears Gear Profiles
17/39
1
#. In inolute gears, the pressure angle, remains
constant bet"een the point of tooth engagement
and disengagement. It is necessary for smooth
running and less "ear of gears.ut in cycloidal gears, the pressure angle is
ma4imum at the beginning of engagement,
reduces to zero at pitch point, starts increasing
and again becomes ma4imum at the end of
engagement. *his results in less smooth running
of gears.
7/25/2019 Chapter 4 Spur Gears Gear Profiles
18/39
1
7/25/2019 Chapter 4 Spur Gears Gear Profiles
19/39
1
7/25/2019 Chapter 4 Spur Gears Gear Profiles
20/39
#/
$. *he face and flan! of inolute teeth are
generated by a single cure "here as in cycloidal
gears, double cures (i.e. epi-cycloid and hypo-
cycloid) are required for the face and flan!respectiely. *hus the inolute teeth are easy to
manufacture than cycloidal teeth.
In inolute system, the basic rac! has straight
teeth and the same can be cut "ith simple tools.
7/25/2019 Chapter 4 Spur Gears Gear Profiles
21/39
#1
7/25/2019 Chapter 4 Spur Gears Gear Profiles
22/39
##
1. 3ince the cycloidal teeth hae "ider flan!s,
therefore the cycloidal gears are stronger than
the inolute gears, for the same pitch. 5ue to this
reason, the cycloidal teeth are preferred speciallyfor cast teeth.
7/25/2019 Chapter 4 Spur Gears Gear Profiles
23/39
#$
#. In cycloidal gears, the contact ta!es place
bet"een a cone4 flan! and a concae surface,
"here as in inolute gears the cone4 surfaces
are in contact. *his condition results in less "earin cycloidal gears as compared to inolute gears.
6o"eer the difference in "ear is negligible.
7/25/2019 Chapter 4 Spur Gears Gear Profiles
24/39
#&
$. In cycloidal gears, the interference does not
occur at all. *hough there are adantages of
cycloidal gears but they are out"eighed by the
greater simplicity and fle4ibility of the inolutegears.
7/25/2019 Chapter 4 Spur Gears Gear Profiles
25/39
#'
1.A normal dra"n to an inolute at pitch point is
a tangent to the base circle.
#. 7ressure angle remains constant during themesh of an inolute gears.
$. *he inolute tooth form of gears is insensitie
to the centre distance and depends only onthe dimensions of the base circle.
7/25/2019 Chapter 4 Spur Gears Gear Profiles
26/39
#
&. *he radius of curature of an inolute is equal
to the length of tangent to the base circle.
'. asic rac! for inolute tooth profile has straightline form.
. *he common tangent dra"n from the pitch
point to the base circle of the t"o inolutes is
the line of action and also the path of contact of
the inolutes.
7/25/2019 Chapter 4 Spur Gears Gear Profiles
27/39
#
. 8hen t"o inolutes gears are in mesh and
rotating, they e4hibit constant angular elocity
ratio and is inersely proportional to the size of
base circles. (9a" of :earing or conugateaction)
.
7/25/2019 Chapter 4 Spur Gears Gear Profiles
28/39
#
*he follo"ing four systems of gear teeth are commonly used
in practice%
1. 1&=> +omposite system
#. 1& => ?ull depth inolute system
$. #/> ?ull depth inolute system
&. #/>3tub inolute system
7/25/2019 Chapter 4 Spur Gears Gear Profiles
29/39
#
*he 1&=> composite system is used for generalpurpose gears.
It is stronger but has no interchangeability. *he tooth
profile of this system has cycloidal cures at the top
and bottom and inolute cure at the middle portion.
*he teeth are produced by formed milling cutters or
hobs.
*he tooth profile of the 1&=> full depth involutesystem"as deeloped using gear hobs for spur and
helical gears.
7/25/2019 Chapter 4 Spur Gears Gear Profiles
30/39
$/
*he tooth profile of the #/ofull depth involute system
may be cut by hobs.
*he increase of the pressure angle from 1&=oto #/o
results in a stronger tooth, because the tooth actingas a beam is "ider at the base.
*he 20o stub involute system has a strong tooth to
ta!e heay loads.
7/25/2019 Chapter 4 Spur Gears Gear Profiles
31/39
$1
r
A
O
Gear
CB
F
E
Base Circle
Addendum Circle
Pitch Circle
ra
*he study of the geometry ofthe inolute profile for a gear
teeth is called inolumetry.
+onsider an inolute of base
circle radius ra and t"o points and + on the inolute as
sho"n in figure. 5ra"
normal to the inolute from
the points and +. *henormal and +? are
tangents to the ase circle.
7/25/2019 Chapter 4 Spur Gears Gear Profiles
32/39
$#
D
ra
r
A
OGear
C
B
rbrc
F
E
Base Circle
Addendum Circle
Pitch Circle
cb
Let
ra= base circle radius
of gear
rb= radius of point B
on the involute
rc= radius of point Con the involute
bt
ct
7/25/2019 Chapter 4 Spur Gears Gear Profiles
33/39
$$
bt
ct
D
ra
r
A
OGear
C
B
rbrc
F
E
Base Circle
Addendum Circle
Pitch Circle
cb
bt
ct
and
!b= pressure angle for
the point B
!c= pressure angle for
the point C
tb= tooth thic"nessalong the arc at B
tc= tooth thic"ness
along the arc at C
7/25/2019 Chapter 4 Spur Gears Gear Profiles
34/39
$&
bt
ct
D
ra
r
A
OGear
C
B
rbrc
F
Ecb
Base Circle
Addendum Circle
Pitch Circle
( )cos
#$%cos
cca
bba
rr
rr
OCFandOBEFrom
=
=
ccbb rr
Therefore
coscos =
bt
ct
7/25/2019 Chapter 4 Spur Gears Gear Profiles
35/39
$'
bt
ct
r
O
Base Circle
ra
Gear
Ecb F
B
rc
rbA
Addendum Circle
Pitch CircleC
D
?rom the properties of the Inolute%
Arc AE = Length BE and
Arc AF = Length F
( )
=
==
===
functioninvolutecalled
isExpression
Inv
AOEAOB
OE
BE
OE
ArcAEAOE
bb
bbb
bbb
b
tan
tan&
tan
tan
bt
ct
7/25/2019 Chapter 4 Spur Gears Gear Profiles
36/39
$
bt
ct
r
O
Base CircleraGear
E
bc
F
B
rbrc A
Addendum Circle
Pitch Circle
CD3imilarly%
ccc
CCc
c
Inv
AOFAOC
OF
BE
OF
ArcAFAOF
=
==
===
tan&
tan
tan
b
bbb
b
b
r
t
r
tAOBAOD
BpotheAt
tan
int
+=
+=
bt
ct
7/25/2019 Chapter 4 Spur Gears Gear Profiles
37/39
$
r
O
Base Circlera
Gear
E
bc
F
B
rbrc A
Addendum Circle
Pitch Circle
C D
c
ccc
b
c
rt
r
tAOCAOD
CpotheAt
tan
int
+=
+=
bt
ct
7/25/2019 Chapter 4 Spur Gears Gear Profiles
38/39
$
Catthicknesstooth
rr
t
invinvt
r
tinvr
tinv
r
t
r
tequationsabovetheEquating
c
b
b
cbc
c
cc
b
bb
c
ccc
b
bbb
=
+=
+=+
+=+
&&
&
&
tan
tan
'
7/25/2019 Chapter 4 Spur Gears Gear Profiles
39/39
Base Circle
Addendum Circle
r
O
ra
Gear
E
F
B
rc
rbA
CD
cb
Pitch Circle
bt
ct
@sing this equation
and !no"ing tooth
thic!ness at any point
on the tooth, it is
possible to calculate
the thic!ness of the
tooth at any point