Gear101

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Society of
Manufacturing
Engineers
1999
MR99-262
Basic Gear Review
author
MICHAEL G. TENNUll-I
Chief Engineer
Star Cutter Company
Farmington Hills, Michigan
abstract
This paper is a short and brief description of gear nomenclature. It touches on the
gear motion and conjugate action of gear sets having involutes and non-involute
profiles. Subjects of gear ratios, descriptors, tooth systems, contact ratios and gear
inspection are also briefly discussed.
conference
ADVANCED GEAR PROCESSING & MANUFACTURING
June 8-9, 1999
Romulus, Michigan
terms
Gear Motion
Gear Ratios
Descriptors
Tooth Systems
Contact Ratios
Gear Inspection
Society of Manufacturing Engineers
One SME Drive l P.O. Box 930 l Dearborn, Ml 48121
Phone (313) 271-l 500

SME TECHNICAL PAPERS
This Technical Paper may not be reproduced in whole or in part in
any form without the express written permission of the Society of
Manufacturing Engineers. By publishing this paper, SME neither
endorses any product, service or information discussed herein, nor
offers any technical advice. SME specifically disclaims any warranty
of reliability or safety of any of the information contained herein.

IGt99-262
BASIC GEAR REVIEW
Presented by: Michael (5. Tennutti
There are many different types of gears in terms of size and material. The gears can be
made from steel, cast iron and different types of plastics, to name just a few. (See Fig. I>
What do all these gears have in common? Basically, the need is to have a minimum of
two gears in contact together to cause rotation. There is usually some type of power or
input, to one gear to cause rotation with the other, or output. The gears wiil cause
transmission of motion. This rotation will or should be uniform in motion depending on
the quality of the gears manufactured. (See Fig. 2}
IUniform Transmission of iuloticn
Fig. 2
There are two types of gears when discussing a parallel type gear set. One type is a
spur gear. The spur gear has its teeth parallel to the axis of the gear. The other type is
a helical gear where the teeth are skewed to the axis of the gear. The helical gears
have left or right hand of helix.
together in a parallel gear set.
It requires a left and a right hand helical gear to run
I
(See Fig. 3-4)
When observing a gear set that contains only one tooth in each gear, the pattern of uniform
motion will not be constant. When contact is made with the driven gear, the tip or edge of this
gear will make contact with the form of the other. The gear form will be pushing the other and
the form of each will not be in true contact. The driver gear will rotate further and when the
conjugate forms are in true contact then there will be uniform motion. When the gears are
rotated further, the uniform motion will be lost when the tip of the driver gear is only in contact
with the driven gear. This can apply to involute and non-involute type gears. The main fact to
observe is that in each case the gears must be conjugate to have uniform motion. (See Fig. 5 -
21)
The above can also be observed with a gear set with only two teeth. The biggest difference is
that with a two tooth gear set there will be a portion where there is a slight overlap.
will cause transfer from one tooth to the other.
The overlap
This shows the tooth to tooth action of this gear
set. When having more teeth in the gear, the tooth to tooth transfer will be constant and there
will be a constant uniform motion with the gear set.

m99-262-2
INVOLUTE GEAR SET
.:-.
‘ ‘.
‘
,
Line depicting Uniform Motion
-7-----K-
Line depicting Uniform
-i ‘I-
Line dedctino Uniform
-/7---i--
. “.
Line derktina Uniform Motion
Line derktina Uniform Motion
-- - ..“-
Tip and Profite in
Contact, No Uniform
Motion.
Profiles Coming Out
of Contact, Ending
Uniform Motion.
-
/’
/’ 1 ZZi!Z! FZZ, Loss I
,/’ I of Uniform Motion. I‘
‘
/,.’
/’/.
‘
‘,/ //’
[Fig.1

MR99-262-3
NON-INVOLUTE GEAR SET
Profiles are Conjugate at Fixed Center Distance.
1.

‘1
Line depicting Uniform Motion-- .__ -...._I
--jT---‘-
--.lm--
---ii
I Profiles coming in
Contact, starting
i
Profiles In Contact
having Uniform
Motion.
/
/’ I
/’/
I Tip and Profile
/ / Contact of set, Loss
1of Uniform Motion. 1
‘i /’ i I
‘1.
/’

//
Q,//
f ,
1 Fig. IO-14 1

HR99-262-4
1NVO~UTE GEAR SET

‘,
‘.
‘1
--j7---
Profifes of First Tooth
fn Contact, Causing
~~~forrn Motion.
Profiles of Second
Tooth Coming In
Contact.
L-_
/
/
I
/I’// Profiles of Both
/’ I
/’ 1 Teeth In Contact.
Uniform hotbox
Using Both Teeth.

, /’
1
‘,/’
i-1

MR99-262-5

-

.

INVOLUTE GEAR SET
First Tooth Out of Contact.
Second Tooth Still In
Contact Causing Uniform
Motion. Over lap transfer
of teeth
Second Tooth Coming Out
of Action Causing Lack of
Uniform Motion.
Tip and Profile on
Second Tooth In
Contact, No Uniform
Motion.
-_-.
//

?R99-262-6
Gear Ratios:
The gear ratio is based upon the number of teeth in the gear
set. When there is a gear ratio of one to one (1 :I) the
number of teeth in each gear are the same. This is typical of
a pump gear set. (See Fig. 22)
The gear teeth that have different number of teeth will have
a lower or higher ratio depending on the application. An
example of this is when a two gear set has twice the number
of teeth in one gear verses the other gear. Depending on
which gear is the driver, this can be a “Reduction” set or a
‘Step up” set. (See Fig. 23)
The gear set has a Pinion and a Gear.
The pinion being the smaller member
and the gear being the larger member.
The gear set ratio can also be
described in different terms.
(See Fig. 24)
GEAR RATIO
t NGINP = RATIO
, poo/pbp= L,
+ OpPDG/OpPDP= L(
l BDG/BDP= ,c
t LG/LP= II
Fig. 24
Examples:
Subscripts of “g” is for the gear and “p”
is for the pinion
N =Number of teeth
PD =Theoretical pitch diameter
OpPD =Operating pitch diameter
BD =Base Diameter
L =Lead on a helical gear
Ratio can be calculated then using:
Ratio =Ng/Np
U
=Pdg/PDp
“
=OpPDg/OpPDp
‘L
=BDg/BDp
it
=Lg/Lp

?fR99-262-7
The gear ratio will be different depending on the number of
teeth in the gear train. When the gear set are composed of
four gears it will change the ratio altogether compared to a
two gear set. (See Fig. 25)
When the gear is composed of three gears, the ratio is
based upon the end gears. The middle gear, called an idler,
will only change direction. (See Fig. 26)
DESCRIPTORS:
involute Gears
The involute gear is the most common gear. The involute
curve can be described by unwinding a string from a circle
and tracking the locus of points from the tip of the string.
The circle from which the curve is generated is the Base
circle or diameter. (See Fig 27)
The involute gear has certain attributes that other gears do
not have. (See Fig. 28) Namely the involute gears are truly
conjugate. Conjugate by definition is something, which is
compatible with or interchangeable.
An involute gear can be manufactured by generating
methods. A hob, for example, having a certain definition can
generate different numbers of gear teeth. One tool can
produce different number of gear teeth.
The involute gear system is also interchangeable. Meaning
that the gear teeth produced by the one hob above can be
placed together and ran together and will be conjugate.
The biggest factor using the involute gear system is that the
gears when placed in gear sets do not have to set a very
close tolerance center distance. The involute gear system
has center distance flexibility. When the center distance
varies, within reason, the gear teeth will still function
properly. (See Fig. 29)
INVOLUTE
PROPERTIES
+ True Conjugacy
+ Generateable
+ Center Distance
Flexible Fig 28
,Y--...,,
,_‘--.. _
:2._.__.,
~ ” ;: i ,>$ J.,;-”
./
t.&$~ ‘-+-.
ti’->%,‘-- ‘3
/I,
___II C.D.2
,( II
t i ^ < +-.+ :
: 8
x.._* i’ $ -- !...A-
: ’ --sig. 29

MR99-262-8
Certain etements describe the gear in terms of depth and
shape. An involute gear can be described in terms of
Diametral Pitch. Simply stated the Diametraf Pitch (DP)
tells how big the gear is. A gear with a low number
associated with a DP is a large gear in terms of tooth depth
and size. A I-DP gear is a large gear and a 20-DP is a
small gear. Gears with a diametral pitch iess than 20 is
considered a coarse pitch gear and those of 20 diametral
pitch and greater are fine pitch. (See Fig. 30)
The gear Pressure angle tells the shape of the gear
tooth. A gear with a 14.5 degree pressure angle (PA) will
have less slope than a gear with a 25 PA. (See Fig. 31)
A gear with an infinite number of teeth is called a rack.
When measuring the PA on a rack it is accomplished by
taking the angie amount between a vertical line and the
side of the rack form.
Measuring a gear pressure angle is more difficult. The
gear has an infinite number of pressure angles on its form.
The gear PA ie normally measured at the theoretical gear
Pitch Diameter (PD). This is accomplished by taking a radia4
line (a line from the center of the gear) through the pitch
diameter and tangent to the involute form. The PA is then
measured from the radial line and the angle formed by a
second line tangent to the involute from at the p4tch
diameter. (See Fig. 32)
Tooth Sysfems
There are numerous different gear tooth depth systems, which
can be applied to the involute gears. Some common gear
systems are:
FULL DEPTH
STUB DEPTH
FLAT ROOT
ELLIPTIICAL ROOT
FULL FILLET
I T4’h” PA & 20~ PA
‘_-‘*Ar
-/4/,,.+// I,WP1
j/- --I‘--,
/
/’ mrrq,
i’
s
,/
&% ,, ‘1-
i
,;’
~UYIT
ttlJ)E IlADtus i
I
IWVFA = rm m - ARC PA Fig. 32
Fig. 33
A.G.M.A. FULL DEPTH
EkR TSITH HO3 TDIIT~

MR99-262-9
One most commonly used system is the A.G.M.A.
system.
(See Fig. 33)
The depth constant for:
the gear addendum is 1.OO/DP
the gear dedendum is I .Z/DP
and the whole depth is 2.251DP
If the gear had a IO DP
the gear addendum is 1.OO/lO = .I00
the gear dedendum is 1.25/l 0 = .I25
and the whole depth is 2.25/10 = .225
The depth of a fult fillet system is based upon
adding extra depth to the standard system and
maintaining approximately the same fil4et tangent
point. The full fillet was designed to add strength
to the fillet area in the root of the gear.
(See Fig. 34)
Total Contact Ratio:
The involute contact ratio on a gear set is based
upon the number of teeth in contact along the line
of action of the gears. This is calculated by taking
the total line of action and dividing by the base
pitch of the gear. The minimum involute
theoretical contact ratio must be greater than 1.O
to have the gears run properly. Depending on
which source is read, the minimum contact ratio
is usually stated as 1.1. This contact ratio
number states how many teeth are in contact at
what percent of the time. A contact ratio of 1.1
states that there are 2 teeth in contact 10% of
the time.
(See Fig. 35)
When there are heiical gears being used there is
another contact ratio to consider. The number
of teeth in contact along the axis in the face
width of the gear is called the helical contact
ratio. The higher the helix of the gear, the
higher the helical contact ratio. (See Fig. 3s)
20” PA
Fig. 34
outside~lu52 7
‘: BASE 2
Contact Ratio Fig. 35

MR99-262-10
The total contact ratio is adding the involute and helical
contact ratio together. It is obvious that a hefical gear
having the same definition as a spur gear in terms of
depth, normal diametral pitch and pressure angie will
have a theoretically bigher contact ratio. Normally, a
helical gear set with the same quality Ieve ti44 be quieter
than a spur gear set due to the higher total contact ratio.
There will be more teeth engaged in the helical gear set.
The Fig. 37 and Fig. 38 show a rotor having oniy a .05”’
involute portion. The cafculation on invotute contact ratio
is fess than ‘4.0, but the rotors will still operate together.
The total contact ratio, due to the helical contact ratio, is
greater than one and will operate smoothly.
Gears to assure the proper quality based upon
application will be inspected to certain standards.
Certain industries or companies will have their internal
standards that they use.
I Fig. 38 f
- -&es>-
rrdllr
,.rp*cti*n
Data Fig. 39
Companies that do not have internal standards may
use industry standards such as American Gear
Manufacturing Association (A.G.M.A.). This standard
has a certain “Q” number associated with the quality
of the gear. The “Q” number varies from Q3 through
Ql5, where Q15 is a closer tolerance on the gears.
Certain tolerance vvilf apply on elements such as
involute, lead, runout, spacing and total composite
error.
involute and lead checks are made on a gear using
an ana4yti~4 measuring ~nst~ment. An involute and
lead instrument measures the deviations from the true
path of the gear on its elements. Today a C.N.C.
machine can accomplish this same task. The
deviations on the gear must be within the specified
tolerance. {See Fig. 39 - 43)

MFC99-262-11
-+xy I ;;/
” ..-... -~ ” ,~ !
: i
“7
; -5
3
: ‘“-1
2
:
‘~ !
: 1
F
1
” ;
I/: --.A. _ > /
i
;‘.i ,._...~ . !
4---.-..--iLi
-
, _
- .- :.
LEAD CIiECK Fig. 42
The functional composite check is used to check several elements at the same time.
This is done by using a master gear of known quality and running at tight center
distance to detect errors. These errors detect the variation in the center distance of the
gears. This is referred to dual flank testing. The errors are described as tooth to tooth
and total composite errors. Runout errors can also be detected.
(See Fig. 44-45)
Camposite Test Fig. 45
RUNOUT
q&&&Q.. ^ .-.^-.-..L
-- 5
vv&$&A&b;
TCE T-TCE
.- - !TOOTCt
- .._. -__I_
- 1 TURN - ...._
TCE = TOTtALCORlPOSlTE ERROR
T-TCE = TQOTH TO TUOTH C~~~~~US~TE ERROR
Toofh Sizing
The thickness of the gear tooth can be measured in
several different manners.
One method is to use two size-controlled pins or bails.
This is done by placing the balls or pins in the space of
the gear and taking a measurement over them. The
reading then can be translated to a circular tooth
thickness on the gear at the theoretical pitch diameter.
(See Fig. 46)
/Fig. 46 b&Y?p;<.y*p&;
*’Ii,I
r‘ ’ ‘7 :
,-
>
7% #’
21
+? ,(
j,
4,,w ?I

MR99-262-12
A second method is to use a caliper and set it to a chordal
addendum on the gear to obtain a chordal tooth thickness.
These readings can be calculated to a circular tooth
thickness at the pitch diameter of the gear. A caution must
be noted using this method. The actual outside diameter
on the gear must be known using this method. If the gear
outside diameter is smaller or larger it will effect the
position on the chordal addendum and yield an incorrect
reading. (See Fig. 47)
A third method is to use span measurements over a certain
number of teeth. To do this properly the anvils on the
micrometer must be tangent to the invoiute curve to obtain
a good reading. This method uses the fact that on an
involute curve a line tangent to the involute curve will
contact the base circle. The two anvils would be tangent to
the involute curve on each tooth and a line perpendicular to
that tangent point would be tangent to the base diameter.
The calculation will transform the reading into a tooth
thickness at the pitch diameter on the gear. (See Fig. 48)
Depending on the size of the gear, one method may be
better than the other. The caliper reading method is most
sensitive to the gear size and operator expertise.

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