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AGMA 918-A93
/
c= Reproduced By GLOBAL
a ENGINEERINGDOCUMENTS
B z With The Permission Of AGM
-7 Under Royalty Agreement
AMERICAN GEAR MANUFACTURERS ASSOCIATIOiV
A Summary of Numerical Examples
Demonstrating the Procedures or
Calculating Geometry Factors for
Spur and Helical Gears
AGMA INFORMATION SHEE
(This InformationSheet s NOT an AGMA Standard)
8/15/2019 AGMA 918-A93
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918-A93, A Summary of Numerical Examples Demonstrating the Procedures for
Calculating Geometry Factors for Spur and Helical Gears
CAUTION NOTICE: AGMA standards are subject to constant improvement, revision, or withdrawal as
dictated by experience. Any person who refers to any AGMA Technical Publication should be sure that the
publication is the latest available from the Associat ion on the subject matter.
[Tables or other self-supporting sections may be quoted or extracted in their entirety. Credit line should read:
Extracted from AGMA 918-A93, A Summary of Numerical Examples Demonstrating the Procedures for
Calculathg Geometry Factors for Spur and Helical Gears, with the permission of the publisher, the American
Gear Manufacturers Association, 1500 King Street, Suite 201, Alexandria, Virginia 22314.1
ABSTRACT
This information sheet provides numeri cal examples for calculating the pitting resistance geometry factor, I,
and bending strength geometry factor,J, for typical gearsetsthat are generated by rack-type tools hobs, rack
cutters or generating grinding wheels) or piniowtype tools disk-type shaper cutters). The numerical
examples are shown in tabular form and provide thevaluesforall variables as calculated using the procedures
and equations in AGMA 908-B89. A flow chart, intended to assist in the development of a computer program
for these variables, is also included.
Copyright 0,1993 by American Gear Manufacturers Association
Published by
American Gear Manufacturers Association
1500 King Street, Suite 201, Alexandria, Virginia 22314
January, 1993
ISBN: 1-5558~17-0
ii
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Table of Contents
Page
Foreword . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
V
1 Scope
.........................................................................
1
1.1
Numericalexamples
.............................................................
1
1.2 Flow chart ...................................................................... 1
1.3
Exceptions
.....................................................................
1
2
Definitions and symbols
..........................................................
1
2.1
Definitions
......................................................................
1
2.2
Symbols
.......................................................................
1
3 Numericalexamples
.............................................................
4
3.1
Examples
......................................................................
4
3.2
Tabulation of examples
..........................................................
5
4 Flow chart
...................................................................
28
5 Cutting tool geometry
...........................................................
37
5.1
Rack type cutting tools
..........................................................
37
5.2 Pinion type cutting tools ......................................................... 37
5.3
Cutting tool drawings
...........................................................
37
Tables
I Symbols used in equations
....................................................... 2
2A Accurate spur gears, example 3.1 .l
...............................................
6
2B Accurate spur gears, example 3.1 l
...............................................
7
3A Inaccurate spur gears, example 3.1.2
..............................................
8
3B Inaccurate spur gears, example 3.1.2
..............................................
9
4A Conventional helical gears, example 3.1.3
..............
:
..........................
10
4B Conventional helical gears, example 3.1.3
......................................... 11
5A Low axial contact ratio LACR) helical gears, example 3.1.4
.........................
12
5B Low axial contact ratio LACR) helical gears, example 3.1.4 ......................... 13
6A Conventional helical gears, different tools, example 3.15
............................ 14
6B Conventional heli cal gears, different tools, example 3.1.5
............................
15
7A Spur sun and planet gear, example 3.1.6
..........................................
16
7B Spur sun and planet gear, example 3.1.6
..........................................
17
8A Spur planet and ring gear, example 3.1.7
..........................................
18
8B Spur planet and ring gear, example 3.1.7
..........................................
19
9A Helical sun and planet gear, example 3.1.8
........................................
20
9B Helical sun and planet gear, example 3.1.8
........................................
21
10A Helical planet and ring gear, example 3.1.9
........................................
22
1OB Helical planet and ring gear, example 3.1.9
........................................
23
11A Conventional double helical gears, example 3.1 .I 0 .................................
24
11B Conventional double helical gears, example 3.1
l 0
.................................
25
12.r Herringbone gears, example 3.1.11
...............................................
26
12B Herringbone gears, example 3.1 .ll
...............................................
27
Figures
1 Flow chart for Z and .Zsubroutines for AGlvlA 908-B89
... ...........................
28
2 Hobfor examples3.1.1 and3.1.2
................................................
37
3
Hobforexamples3.1.3and3.1.4
................................................
38
.
III
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Table of Contents cant)
4
5
6
7
8
9
10
11
12
Page
Hobfor example3.1.5
..........................................................
38
Helical pinion type shaper cutter for example 3.1.5
.................................
39
Hobforexamples3.1.6and3.1.7
................................................
39
Spur pinion type shaper cutter for example 3.1.7 ................................... 40
Hob for example 3.1.8
..........................................................
40
Helical pinion type shaper cutter for examples 3.1.8 and 3.1.9
.......................
41
Helical pinion type shaper cutter for example 3.1.9
.................................
41
Hobforexample3.1.10
.........................................................
42
Helical pinion type shaper cutter for example 3.1 .ll
................................
42
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[The foreword, footnotes, and annexes, if any, in this document are provided for informational purposes only
and are not to be construed to be part of AGMA 918A93,
A Summary of Numerical Examples Demonstrating
the Procedures for Calculating Geometry Factors for Spur and Helical Gears.]
This AGMA information sheet and related publications are based on typical or average data, conditions, or
application.
This information sheet, AGMA 918-A93, was prepared o assist designers in the proper use and interpretation
of AGMA 908B89 and to assist in the development of computer programs when calculating geometry factors
for pitting resistance, I, and bending strength, J. A flow chart provides a step by step procedure for the
calculation of these factors, either manually or by computer program. Several examples are provided to
demonstrate the calculation procedure for the various characteristics of geometry as described in AGMA
908-B89.
These include accurateand inaccurate spur gears, conventional and LACR helical gears, internal and external
gears, double helical and her ringbone Sykes) gears, and addendum modifications. The calculation of J-fac-
tor for internal gears is not defined in AGMA 908B89 and, therefore, is not covered in this information sheet. A
tabulation of all calculated variab les is provided for each example based on its design criieria.
This provides
the designer with known results to check against when calculating or programming these factors.
Suggestions for the improvement of this information sheet will be welcome. They should be sent to the
American Gear Manufacturers Association, 1500 King Street, Suite 201, Alexandria, Virginia, 22314.
V
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PERSONNEL of the AGMA Commit tee for Helical Gear Rating
Chairman: D. McCarthy (Dorris Company)
Vice Chairman: N. Hulse (General Electric)
ACTIVE MEMBERS
K. E. Acheson .......
The Gear Works-Seattle
M. Antosiewicz
...... Falk
J. Bentley ........... Peerless-Winsmith
E. S. Bemdt .........
C M of Indiana
J. D. Black
..........
GM/Allison Div.
E. J. Bodensieck
.....
Bodensieck Engineering
N. K. Burrel l .........
Metal Improvement Co.
M. F. Dalton .........
General Electric
G. DeLange .........
Emerson Power Trans.
J. Ft. DeMarai s
.......
Bison Gear
R. J. Drago ..........
Boeing
R. L. Errichello .......
Academic Member
H. Hagan ............
Cincinnati Gear
H. Ft. Johnson .......
Lufkin Industries
0. LaBath ........... Cincinnati Gear
ASSOCIATE MEMBERS
G. Lian ..............
L. Lloyd .............
D. R. McViiie ........
A. Milbum ...........
C. Moyer ............
R. Nay ..............
M. W. Neesley
.......
W. P. Pizzichil ........
J. W. Polder
.........
E. R. Sewal l .........
J. Tellman ...........
T. Tumbull ...........
W. Wagner ..........
C. C. Wang ..........
R. Wasilewski ........
J. Adamson .........
R. G. Allenby ........
J. Amendola .........
K. Beckman .........
D. L. Borden .........
E. R. Braun ..........
G. Buziuk ...........
A. Cardou ...........
M. R. Chaplin ........
J. Cianc i ............
A. S. Cohen .........
J. T. Cook
...........
R. DiRusso ..........
D. W. Dudiey ........
K. A. Evans ..........
R. Geary ............
R. Giuff ra ...........
L. L. Haas ...........
F. M. Hager ..........
TIW Systems
Hamilton Gear
MAAGlArtec
Lufkin Industries
Gear Research Institute
Eaton
Brad-Foote
Universite Lava1
Contour Hardening Inc.
General Electric
Engranes y Maquinaria
Power-Tech
Kaman
Honorary Member
GM-Saginaw Div.
Terre11 ear Drives
ABS
SPECO Corporation
Cummins Engine
A. C. Hayes .........
DACA
W. H. Heller .........
Peerless-Winsmith
G. Henriot ........... Engrenages et Reducteurs
M. Hirt ..............
Renk Tacke GmbH
D. R. Houser ........ Academic Member
. lrey ...............
New Angle Gear
T. W. Jessup
......... Lucas Western Inc./ATD
T. Kameyama
........
SeikiiKogyosho
M. Lawrenz
..........
Metal Improvement
J. Liesicki
...........
Falk Corporation
J. Maddock
..........
Consultant
D. Mairet
...........
Falk Corporation
T. J. Maiuri ..........
P. C. McAvoy ........
B. W. McCoy ........
F. Myers ............
D. Moser ............
B. L. Mumford
.......
W. Nagel i ...........
B. C. Newcomb
......
H. C. A. Nielsen
......
J. Nyerup ...........
. Okamoto ..........
G. E. Olson ..........
J. A. Pennell .........
A. E. Phillips .........
B. D. Pyeatt .........
V. Z. Rychlinski
......
E. Sandberg .........
Amarillo Gear Co.
Lufkin Industries
Gear Engineers, Inc.
Milbum Engineering
The Timken Co.
Pratt Whitney
WesTech Gear
Philadelphia Gear
Academic Member
Sewall Gear
Reliance Electric/Reeves
Mobile Pulley Machine
Sewall Gear
3E Software Engrg.
Arrow Gear
Gleason Works
Cummins Engine
Marathon Letourneau
Horsburgh Scott
Nuttall Gear
Alten-Foundry
MAAG
Chicago Gear-D-O-James
F. L. Smith
F. L. Smith
Nippon Gear
Cleveland Gear
Academic Member
Reliance Electric
Amarillo Gear
Brad Foote
Det Norske Veritas
W. F. Schierrenbeck . . Xtek Incorporated
A. Seireg ............
Academic Member
E. E. Shipley ......... Mechanica l Technology
D. A. Sylvester
....... Flender Corporat ion
D. Set for. ..........
Precision Gear
L. J. Smith ........... Invincible Gear
. A. Thoma .........
Honorary Member
W. J. Toner ..........
IMO Delaval, Inc.
H. J. Trapp ..........
Klingelnberg
F. C. Uherek .........
Flender Corporation
T. Urabe ............
Tsubakimoto Chain
D. A. Wagner ........
General Motors/AGT
H. Winter ............
Academic Member
vi
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AGMA919-493
A Summary of Numerical
Examples Demonstrating
the Procedures for Calculat-
ing Geometry Factors for
Spur and Helical Gears
1 Scope
This information sheet provides a set of numerical
examples which calculate the geometry factor for
pitting resistance, I, and bending strength, J, for a
variety of gearsets selected to demonstrate thevari-
ous gear geometries analyzed in AGMA 908-l389,
Geometry Factors for Determining the Pitting Resis-
tance and Bending Strength of Spur, Helical and
Herringbone Gear Teeth. A flow chart is also in-
cluded to formalize the calculation procedures for
the numerical examples and to assist in the practical
application of AGMA 908-889.
1 .l
Numerical examples
Numerical examples wer e selected to demonstrate
the following conditions: accurate and inaccurate
spur gears, conventional and LACR low axial con-
tact ratio) helical gears, internal and external gears,
double helical and herringbone Sykes) gears and
addendum modification. For simplification pur-
poses and for demonstrating the effect on resulting
geometry factors, similar examples were selected
with different load locations example 3.1 lvs3.12)
and face widths example 3.1.3 vs 3.1.4)
The results are presented in tabular form by provid-
ing the numerical results for each equation as pre-
sented in AGMA 908-689 and appropriate to that
gear geometry. Gear cutter data is presented for
each component in each numerical example. All
gearsets a re functional and do not violate any of the
exceptions stated n the scope of AGMA 908-B89.
The examples used are for demonstration purposes
only and are not intended to be recommendations
for gearset design.
12 Flow chart
The flow chart provides a step by step procedure for
calculating geometry factors, I and J, using the
equations and instructions from AGMA 908-B89.
The numerical value tables are formatted to coin-
cide with the flow chart procedures.
1.3 Exceptions
A procedure for the calculation of bending strength
geometry factor,
J,
for internal gears has not been
established by AGMA. For this reason, numerical
examples and flow chart procedures for such a cal-
culation are not included.
2 Definitions and symbols
2.1 Definitions
The terms used, wherever applicable, conform to
the following standards:
ANSI Y10.3-1968, Letter Symbols for Quantities
Used in Mechanics of Solids,
AGMA 904-B89, Metric Usage;
AGMA 1012-F90, Gear Nomenclature, Definitions
of Terms with, Symbols.
2.2 Symbols
The symbols used in the geometry factor formulas
are shown in table 1.
NOTE - The symbols, definitions and terminology
used in this information heet may differ from other
AGMA documents. The user should not assume that
familiar symbols can be used without a careful study of
these definitions.
Units of measure are not shown in table 1 because
the equationsare in terms of unity normal module or
unity normal diimetral pitch.
8/15/2019 AGMA 918-A93
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AGMA 919-A93
Symbols
C&,...C(j
Gzl, cm+ cnt
ch
cr
cv
Di
d
F
fi
F2
H
&lo
hF
Z
J
Kf
Kv
L
L
min
M
mF
mG
“N
mn
mP
II
n0
5 n2
*a
Plld
pb
PN
PX
R19R2
Rbl’ Rb2
Rbc
Table 1 - Symbols used in equations
Terms
distances along line of action (See figure 3-I of AGMA 9084389)
distances along line of action of virtual spur gear
helical factor
operating center distance
helical overlap factor
inside diameter of internal gear
pinion operating pitch diameter
effective face width
gear type code
spur gear load sharing code
parameter for stress correction factor
nominal tool addendum
height of Lewis parabola
pitting resistance geo metry factor
bending strength geometry factor
stress correction factor
helix angle factor
parameter for stress correction factor
minimum length of contact lines
parameter for stress correction factor
axial contact ratio
gear ratio
load sharing ratio
normal module
transverse contact ratio
virtual tooth number
virtual tooth number of tool
tooth numb er, pinion and gear
fractional part of
mF
tool tooth number
fractional part of
mp
normal diametral pitch
transverse base pitch
normal base pitch
axial pitch
standard pitch radii, pinion and gear
base radii, pinion and gear
base radius of tool
continued
2
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AGMA 919-A93
Table 1 (continued)
Symbols
Rc
Rrnl
ROL Ro2
R
oc
‘m rn2
I,
‘n
rm
II
5lo
rs
no
‘ha 9?&a2
rid, hb2
‘?lbO
rnL
SF
S,
Snl, Sn2
l
STlO
sns
Tl
To1
us
x
X17X2
xtz
X0
XgbXg2
Y
Y
Y'
z
O1n
ani
Pn
4
60
6
a0
qnF
Terms
standard pitch radius of tool
mean radius of pinion
addendum radii, pinion and gear, internal and external
outside radius of tool
reference pitch radii of virtual spur gear
generating pitch radius of virtual spur gear
reference pitch radius of virtual tool
generating pitch radius of virtual tool
radius to center “9” of tool tip radius
virtual outside radii
virtual base radii
virtual base radii of tool
virtual load radius
tooth thickness at criiical section
reference normal circular tooth thickness
reference no rmal circular tooth thickness, pinion and gear
tooth thickness at outside diameter
reference normal circular tooth thickness of tool
standard tooth thickness, thinned for backlash
temporary variable
temporary variable
stock allowance per side of tooth, for finishing
addendum modification coefficient at zero backlash
addendum modification coefficient, pinion and gear
generating rack shift coefficient
addendum modification coefficient of tool
generating rack shii coefficient, pinion and gear
tooth form factor
iteration function
derivative of iteration function
active length of line of action
angle of surface, normal
iteration ang le
angle between tangent to fillet and tooth center line
amount gear tooth is thinned for backlash
amount of p rotuberance, tool
amount of effective protuberance, tool
ordinate of criiical point “F
continued
3
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AGMA 91 &A93
Table
1 (concluded)
Symbols
en
em
KFKS
hns
z
Pla P2
bzl~ brl2
Pa0
PF
cp
bt
4::
4);
L
- blpo
r
4hs
hlW
+r
w
vb
yr
co
0 tool
1 pinion
2 gear
Terms
angular displacement of gear
angular displacement of tool
distance from pitch point to points “F’ and “S’
angle to center “S” of tool tip radius
auxiliary angle locating point “s”
abscissa of criiical point “F
radii of curvature of profiles at point of contact stress calculation
radii of curvature of profile at mean radius
tool tip radius
minimum radius of curvature of fillet curve
standard transverse pressure angle
standard normal pressure angle
generating pressure angle
iteration value for generating pressure angle
load angle
pressure angle at radius where tool tooth is pointed
operating normal pressure angle
pressure angle at point “s” on tool
pressure angle at load application point
operating transverse pressure angle
standard helix angle
base helix angle
operating helix angle
angle of inclination of helical contact line
Subscripts
n normal or virtual spur gear
r
0
El
erating or running
sence
of a subscript indicates transverse
3 Numerical examples
Eleven numerical examples, based on actual gear-
sets, are presented to demonstrate the calculation
of both geometry factors, I and
J,
using the proce-
dures outlined in AGMA 908-B89.
3.1 l Accurate spur gears
This example demonstrates a spur gearset which
meets the criteria of table 5-l in AGMA 908-B89 for
load sharing and is therefore considered loaded at
the highest point of single tooth contact.
3.12 Inaccurate spur gears
3.1 Examples
The following examples were selected to illustrate
the various types of gearing
and geometry eatures
found in most of today’s gearing.
This example, which uses the same geometry as
3.1 l, does not meet the criteria in table 5-l of
AGMA go&B89 for load sharing and is therefore
considered to be loaded at the tip of the teeth.
4
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AGMA 91 A93
3.1.3 Conventional helical gears
This example demonstrates a conventional helical
gearset wher e the mesh face width is greater than
the axial pitch.
It also includes an addendum
modification coefficient in the pinion and protuber-
ance in the rack cutter used to generate both
components.
3.1.4 Low axial contact ratio (LAM) helical
gears
This example, which uses the same basic geometry
as 3.1.3, demonstrates an LACR helical gearset
where the face width has been reduced to less than
the axial pitch. The effect on both geometry factors
under these conditions can readily be seen.
3.1.5 Conventional helical gears, different tools
This example demonstrates a conventional helical
gearset with addendum modification. The pinion is
generated by a hob and the gear by a pinion type
shaper cutter. Both cutters have protuberance.
3.1.6 Spur sun and planet gear
This example combines with 3.1.7 to demonstrate
the geometry factor calculation for a spur sun/planet
gear combination. Here, the I factor for the
sun/planet mesh and the J factor for each compo-
nent are calculated.
3.1.7 Spur planet and ring gear
This example combines with 3.1.6 and demon-
strates the effect on the I factor when the same
planet meshes with the internal ring gear of the
same set. The calculated J factor for the planet in
the planet/ring mesh is diierent from that in the
sun/planet mesh (3.1.6). TheJfactorcalculationfor
the ring gear is beyond the scope of this information
sheet (see 1.3).
3.1.8 Helical sun and planet gear
This example combines with 3.1.9 to demonstrate
the geometry factor calculation for a helical sun/
planet gear combination. The Z factor for the
sun/planet mesh along with the J factor for each
component is calculated.
3.1.9 Helical planet and ring gear
This example combines with 3.1.8 and demon-
strates the effect on the Z factor when the same
planet meshes with the internal ring gear of the
same set. The calculated J factor for the planet in
the planet/ring mesh is different from that in the
sun/planet mesh (3.1.8). TheJfactorcalcula tion for
the ring gear is beyond the scope of this information
sheet (see 1.3).
3.1 I0 Conventional double helical gears
This example demonstrates the method for consid-
ering the double face width encountered in this type
of gearing.
3.1 I1 Herringbone gears
This exampledemonstrateshow transverse diametral
pitch, usually associated with this type of gearing, is
accommodated.
3.2 Tabulation of examples
Tables 2B through 12B tabulate all the information
relating to each example as described in 3.1. The
format is based on the flow chart as presented in
clause 4 and includes all basic geometry (input
data) and results of the calculations for every
variable applicable to that gearset. These example
were calculated to 14 significant digits and the
results rounded as shown. For those variables
found by iteration, the final iterative value is listed.
See tables 2A through WA for the specific value of
each variable at each iteration loop. Figures 2
through 12 illustrate the various cutting tool profiles.
Specificdata relating o each gearset or component
is listed in the individual example tables.
5
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AGMA 91&A93
Table 2A - Accurate spur gears , example 3.1.1
Pinion: iteration for generating pressure angle
Variable 1 2 3 4 5 6
inv $; 0.014910 0.014910 0.014910 -
cp - 0.349386 -
nz
0.358675 0.349112
fb
n(i +l)
0.349386 0.349112 0.349111 -
Variable 1
a
Pn
no
K
S
P
If
c.F
P
UT
Y
IYl
ant
0.785398
0.000187
-1.325365
-1.761865
0.099917
0.685481
1.179814
24.257896
1.142721
4.452621
0.689143
0.689143
0.630626
Pinion: iteration for critical point
2 3
4
0.630626 0.605889
0.605442
0.000257 0.000270
0.000271
-1.589244 -1.645464
-1.646525
-2.025744 -2.081964
-2.083025
0.113499
0.116204
0.116255
0.517127 0.489685 0.489187
1.127191
1.119292
1.119150
24.334854 24.349198 24.349464
1.065763 1.051418 1.051153
3.441053 3.322607
3.320554
0.085121 0.001485
0.000000
0.085121 0.001485
0.000000
0.605889 0.605442
0.605442
Gear: iteration for generating pressure angle
6
Variable 1 2 3 4 5 6
inv $; 0.014894 0.014894 0.014894
v- 0.358546 0.349263 0.348989
nl
v -
n(i +l)
0.349263 0.348989 0.348988
Gear : iteration for critical point
Variable
1 2 3 4 5 6
an
ho
‘CS
9
(32
Bn
GlF
%F
k
Y’
Y
IYl
%i
0.785398
0.586171
0.541381 0.539939 0.539938
0.000232 0.000349
0.000386
0.000387
0.000387
-1.641409 -2.097854
-2.251830
-2.257242
-2.257248
-2.077909 -2.534354
-2.688330 -2.693742 -2.693748
0.053295 0.064581 0.068083 0.068205
0.068205
0.732103 0.521590 0.473298 0.471734
0.471733
1.224450 1.158420
1.144696
1.144259
1.144259
50.535758 50.627373
50.652661
50.653515
50.653516
1.239255
1.147640
1.122352 1.121498
1.121497
5.034538 3.586125
3.374076 3.367760
3.367754
1.003017 0.160620
0.004867 0.000005 0.000000
1.003017 0.160620 0.004667 0.000005 0.000000
0.586171 0.541381 0.539939
0.539938
0.539938
8/15/2019 AGMA 918-A93
13/49
AGMA 916-A93
Table 2B - Accurate spur gears , example 3.1.1
Gearset
Pinion
mn =
0.2WOW q = 51
on = 20.0000 n,1
= lWO0
Input data
g&g
kzol =
1.4565
n2 = 104
Pa01 =
0.4365
nc2
= low0
ha02 =
1.4
w = o.owo
, =
15.5000
F 2.5000
FI = I
53 = I
Rol
=
5.3225
%zol
=
0.0099
Ro2
= 10.5774
Pa02
=
0.4
Xl
=
0.1127
Asnl =
0.0215
x2
=
-0.1127
6
a02 =
0.0
x01 =
O.WW
x02 = o.owo
As,.,2 =
0.0
Cutter
figure
2
Cutter figure 2
62
%
w
cr
F
Rol
Ro2
“G
Rl
R2
9
Rbl
Rb2
%
‘b
pN
vb
‘6
Cl
%
c4
%
c,
z
“P
G3.64. G5
nr =
Px =
mF =
na =
L,h =
“zN =
Yr =
9
nr =
0.349066
o.owow
77.5WOW
12.500000
26.612500
52.887000
2.039216
25.5WOW
52.OWOW
0.349066
23.962162
48.664016
0.349066
2.952131
2.952131
o.owow
26.506561
6.274342
8.721514
9.226474
11.577563
8.625431
5.303220
1.796404
Z subroutine
d =
51 .WWW
Rml =
25.612750
Pl = 8.625431
P2 =
17.881130
P
ml =
9.045870
P
m2 =
17.460691
cy = 1 OOOOW
I = 0.107
G6 pinion
n1 = 51 .OOWW
Rol =
26.612500
RI =
25.5OWOO
Rbl =
23.962162
c4 =
9.226474
x =
0.112700
Asn =
O.o215W
nC = 10000.000000
h, =
1 A56500
x0 =
o.wwoo
Pa0 =
0.436500
sm =
O.W99W
J factor Pinion
n
=
51 .WWW
rn =
25.5OWW
0.796404 ‘& =
23.962162
cn4 = -
rd = -
r&2 = -
12.5WOW ‘~2 = -
l.OOOOW cn6 = -
O.OWOW Cnl = -
0.349066 ‘m = -
m@nW=
0.385043
5 =
0.083165
sn
$d
rnL
nO
=
1.631335
Y
= 0.904103
= 0.338152
J =
0.46
=
25.400616
= 10000.000000
gear6
‘no
‘nbo
$0
+ns
inv%zs
Sno
inv%zpo
hnsf2
ilV@;
+“ni
m”
r,“0
= 5Wo.W0000 ni
= 4698.463104 mG
= 5W1.02OWO To1
= 0.349626 R,l
= o.ol4wg
R,:
= 1.570796 T1
=
0.015061 R1
an
kzo
KS
KF
;:
h?.F
%F
hF
Y’
Y
“nl
pF
co
ch
SF
H
L
M
9
3f
=
-0.WOW8
= 0.014910
= 0.349111
= 25.500422
= 5000.082737
= 0.605442
= 0.00027 1
= -1.646525
= -2.083025
= 0.116255
= 0.489187
R2
Rbl
cfl
x
Asn
nC
h
a0
X0
Pa0
6
a0
=
104.000000
= 0.490385
= 26.612500
= 52.887000
= 26.612500
=
25.5WWO
=
52.OWWO
=
25.5WWO
= 48.864016
= 17.881130
= -0.112700
=
0.0215oo
= 10000.000000
= 1.456500
=
o.owwo
= 0.436500
= 0.009900
1.119150
24.349464
1.051153
3.320554
o.wowo
0.605442
0.469891
0.000000
1 ooowo
2.238300
0.18OWO
0.150ooo
0.45owo
1.955632
1 wowo
J factor aear
n
= 104.000000
rn
=
52.OWWO
‘nb =
48.864016
cn4 = -
‘n2 =
‘nb2 = -
‘na2 =
c,6
= -
C
nl = -
‘na =
fN)nW=
0.365937
5 = -0.142235
sn =
1.467257
+& =
0.336924
rnL =
51.7
nO
= 1 oooo.00
‘no = 5000.
‘nbo = 4698.4
GO
= 5001.0
qns =
0.3
invqns = 0.0
sno =
1.5
in3 npo = 0.0
hnsi
inv+n
vii
5i
GO
an
ho
KS
KF
;:
LF
qnF
hF
Y’
Y
anl
pF
0
ch
SF
H
L
M
9
KY
Y
J
=
-Q.O
= 0.0
= 0.3
= 51.9
= 4999.8
= 0.5
= 0.0
= -2.25
= -2.69
= 0.0
= 0.4
= 1.1
= 50.6
= 1.1
= 3.3
= 0.0
= 0.5
= 0.4
=
o.o
= 1 o
= 2.2
=
0.1
=
0.1
=
0.4
= 1.9
= 1 o
= 0.8
= 0.4
7
8/15/2019 AGMA 918-A93
14/49
8/15/2019 AGMA 918-A93
15/49
AGMA 916-A93
Table 3B - Inaccurate spur gears , example 3.1.2
Input data
Gearset
Pinion
m
m, =
0.200000
n1 = 51
ha01 = 1.4565
n2
= 104
hLlo2 =
1.456
0, = 20.0000
n,l = 10000
P
a01
=
0.4365
nc2
=lOooO
Pa02 =
0.436
w = 0.0000
Rol
=
5.3225
6
a01 = (
.0099
RA =
“A
10.5774
6 nn3 = 0.009
c, =
15.5000
LIv.2
0.1127
O.Ml5
=
F =
2.5000
Xl =
Asnl =
7
=
-0.1127
AS,2
0.021
Fl
1
x01 =
0.0000
x02 = 0.0000
F2
Cutter
figure
2
= 2
Cutter figure 2
62
%l
w
cr
F
Rol
%2
mG
Rl
R2
+
Rbl
Rb2
6
‘6
pN
vb
C6
Cl
c3
c,
C5
c2
2
“P
63.64. G5
nr =
Px =
mF =
na =
L,h =
mN =
Yr =
nr =
0.349066
0.000000
77.5ooooo
12.500000
26.612500
52.887000
2.039216
25.500000
52.OOOOOO
0.349066
23.962162
48.864016
0.349066
2952131
2.952131
0.000000
26.506561
6.274342
8.721514
9.226474
11.577563
8.625431
5.303220
1.796404
Z subroutine
d =
51.oooooo
Rml =
25.612750
Pl =
8.625431
P2 = 17.881130
P
ml =
9.045870
P&l =
17.460691
cy = 1.000000
I = 0.107
G6 pinion
nl = 51.000000
ROI = 26.612500
Rl =
25.5OOOOO
Rbl =
23.962162
c4 =
9.226474
x =
0.112700
Asn =
o.o215oo
nC = 10000.000000
h, =
1.456500
x0 = 0.000000
Pm =
0.436500
aa0 = 0.009900
J factor Pinion
n
=
51.000000
rn =
25.5OOOOO
0.796404 '& =
23.962162
C
n4 = -
rn2 = -
t-h2 = -
12.5OOOOO '~2 = -
l.OOOOOO cnfj = -
0.000000
C,l = -
0.349066 rm =
26.612500
@4)nW=
0.483160
xg =
osI83165
sn =
1.631335
Y
= 0.438626
qjjL = 0.436269
J = 0.30
rnL =
26.438538
no =
10000.000000 G6
‘no
‘nbo
rs
no
ns
inv4 zs
sno
‘“vOnpo
hnsli
iI-@;
Vni
4
Go
= 5000.000000
n1
= 4698.463104
mG
= 5001.020000
T,l
= 0.349626
Rol
= 0.01 979
4,~
= 1.570796
T1
,= o.015061 R1
an
ko
KS
KF
en
pn
%lF
%.F
hF
Y’
Y
anl
pF
w
ch
SF
H
L
M
Kf
KY
=
-o.oooou8
=
0.014910
= 0.349111
= 25.500422
= 5000.082737
= 0.413704
= 0.000427
= -2.330347
= -2.766847
= 0.146833
= 0.266871
R2
Rbl
c4
n
Asn
nC
h
a0
X0
Pa0
6
a0
=
104.000000
= 0.490385
= 26.612500
= 52.887000
= 26.612500
=
255OOOOO
=
52.OOOOOO
= 25.500000
= 48.864016
= 17.881130
= -0.112700
=
0.0215oo
=1oooo.oooooo
= 1.456500
= 0.000000
= 0.436500
= 0.009900
1.061951
24.496365
1.942172
5.404074
0.000000
0.413704
0.469891
0.000000
1.000000
2.123901
0.180000
0.150000
0.450000
1.485424
1.000000
J factor aear
n
= 104.000000
rn =
52.OOOOOO
‘nb =
48.864016
C
n4 = -
rn2 = -
‘nb2 = -
‘na2 =
c,fj = -
C,l = -
ma =
52.887000
mn4nW=
0.414051
xg = y-:5;
sn = .
d =
0.385039
rnL
nO
‘no
‘nbo
rs
no
+
ns
hv+ns
sno
inV npo
hns I2
in@‘;,
+Li
ri
Go
an
f-G20
KS
KF
en
Pn
LZF
^‘ln.F
hF
Y’
Y
“nl
PF
w
ch
SF
H
L
M
Kf
KY
Y
J
=
52.7242
=1oooo.ooooo
= 5ooo.ooam
= 4698.4631
= 5001.0200
= 0.349
= 0.014
= 1.570
= 0.015
= -0.0000
= 0.014
= 0.348
= 51.998
= 4999.8592
= 0.364
= 0.000
= -3.2540
= -3.6905
= 0.089
= 0.275
= 1.092
= 50.788
= 1.935
= 5.208
=
o.ooo
= 0.364
= 0.462
= 0.000
= 1.000
= 2.184
=
0.18O
= 0.150
=
0.45o
= 1.513
=
1.ooo
= 0.451
= 0.30
9
8/15/2019 AGMA 918-A93
16/49
Table 4A - Conventional helical gears, example 3.1.3
Pinion: iteration for generating pressure angle
Variable
1
2
3
4
5 6
inv @;
0.014937
0.014937
0.014937
$"-
0.358888
0.349589
0.349314
-
Ill
$”
n(i +l)
0.349589
0.349314
0.349313
Pinion: iteration for critical point
Variable
1
2
3
4
5 6
a
0.785398
0.530778
0.484332
0.483773
co
0.000102
0.000174
0.000194
0.000194
K
-0.801380
-1.119323
-1.216848 -1.218144
s
P
-1.210580.186208
-1.528523.220419
-1.626048.229993 -1.627344.230119
<
s"
0.599190
0.310360
0.254339
0.253654
c.F
1.157476
1.092056
1.082560
1.082451
IIs
F
10.767751.256396
10.903191.120957
10.935968.088180 10.936387.087760
Y'
7.558439
5.779360
5.652986
5.651830
Y
1.924528
0.268428
0.003165
0.000000
IYl
1.924528
0.268428
0.003165
0.000000
an1
0.530778
0.484332
0.483773
0.483773
Gear: iteration for generating pressure angle
Variable
1
2
3
4
5 6
inv i$;
0.014902
0.014902
0.014902
-
$2
0.358611 0.349324 0.349050 -
%(i + 1)
0.349324
0.349050
0.349050
-
Gear: iteration for critical point
Variable
1
2
3
4
5 6
an
0.785398
0.470846
0.370221
0.366647 0.366645
-
bl0
0.000198
0.000389
0.000510
0.000516 0.000516
-
%
-1.554759
-2.422778
-3.036768 -3.064963
-3.064981
-
KF
-1.963959
-2.831978
-3.445968 -3.474163
-3.474181
-
&
0.056632
0.078839
0.092918
0.093552 0.093552
-
fin
0.728766 0.392006 0.277303 0.273096 0.273093 -
&IF
1.235535
1.140587
1.112683
1.111685 1.111685
-
%lF
46.328373
46.482618
46.563564 46.567096
46.567098
-
F
2.223231
2.068985
1.988040
1.984507 1.984505
-
Y'
8.691103
5.665191
5.332131
5.325511 5.325507
-
Y
2.733809
0.570059
0.019054
0.000012 0.000000
-
IYl
2.733809
0.570059
0.019054
0.000012 0.000000
-
ani
0.470846
0.370221
0.366647
0.366645 0.366845
-
8/15/2019 AGMA 918-A93
17/49
AGMA 919-A93
Table 4B - Conventional helical gears, example 3.1.3
input data
Gearset
Pinion
@g
ln =
0.166667 q = 21
kzol =
1.4760 n2 = 86
ha02 =
1.4760
0, = 20.0000 n,1 =lOOOO P
a01 =
0.4092
nc2
=lOOOO
Pa02 =
0.4092
w =
15.0000
Rol
=
2.0667
~~~
6 ,A =
U”I
0.0061
Ro2
=
7.5865
=
0.0061
c, =
9.3175
6
a02
Xl = 0.5343
-
F =
3.7500
*w -
n n34n
“.“,s-T”
x2
=
- ----
o.uuuo
*
“Sn2
=
- _^~^
0.024u
Fl = I
F2
=Notrequireci
x01 =
0.0000
Cutter figure 3
x02 = 0.0000
Cutler figure 3
G2
%2
Y
cr
F
Rol
Ro2
“G
4
R2
4,
Rbl
Rb2
@r
i
)N
vb
c6
Cl
%
c4
C5
c,
Z
“P
63.64.65
nr =
Px =
“F =
na =
L,h =
mN =
Yj- =
0
nr =
0.349066
0.261799
55.904888
22.499955
12.400175
45.518909
4.095238
10.870400
44.516876
0.360356
10.172208
41.657612
0.384177
3.043517
2.952131
0.245674
20.952955
2.605900
4.112262
5.649417
7.091582
4.048065
4.485682
1.473848
0.473848
12.138182
1.853651
0.853651
33.224468
0.677210
0.264134
0.372068
I subroutine
d =
21.943975
Rml =
11.393077
Pl =
5.131121
P2 =
15.821834
P
ml = -
Pn.Q= -
cy = 1.000000
I = 0.242
G6 oinion
nl =
21.000000
ROI = 12.400175
Rl =
10.870400
Rbl =
10.172208
c4 = 5.649417
x = 0.534300
AS,, = 0.024000
nC
=10000.000000
h, =
1.476000
x0 = 0.000000
pa0 =
0.4092W
6
a0
=
0.006100
J factor Dinion
n =
23.301719
rn =
11.650859
rnb =
10.948227
C
n4 = -
rn2 = -
rnb2 = -
rna2 = -
c,,fj = -
C,l = -
ma =
13.180635
tantp,W =
0.670365
X8 =
0.501330
sn = 1.935735 Y = 0.580609
9d = 0.572388 .f = 0.58
rnL =
13.024147
no =
11096.056659 G6
‘no
‘nbo
GO
qns
inv4ns
Sn0
i”v%zPo
hnsi2
illV@;l
Vni
mt-i
GO
= 5548.028330
nl
= 5213.441281 mG
= 5549.095130
T,l
=
o.swi94 R,l
= o.ol4974
R,2
=
1.570796
T1
=
0.015046 R1
an
ko
KS
KF
%z
pn
%F
9n.F
hF
Y’
Y
anl
PF
w
ch
SF
H
L
M
Kf
KY
=
-0.000006 R2
=
0.014937
Rbl
=
0.349313
c4
=
11.651910 X
= 5548.528439 ASn
0.483773 nc
o.ooom ha0
-1.218144 X0
-1.827344
Pa0
0.230119 6ao
0.253654
=
86.000000
= 0.244186
= 12.400175
= 45.518909
= 12.400175
= 10.870400
= 44.516876
= 10.870400
= 41.657612
= 16.904890
= 0.000000
= 0.024000
=10000.000000
= 1.476000
= 0.000000
= 0.409200
= 0.006100
1.082451
10.936387
2.087760
5.651830
0.000000
0.483773
0.435535
5.236189
1.286597
2.164902
0.180000
0.150000
0.450000
1.472865
0.932426
J factor aear
n
=
95.426087
rn =
47.713044
‘nb =
44.835595
cn4 = -
rn2 = -
‘nb2 = -
‘na2 =
c,(j
= -
C,l = -
‘na =
48.715077
mOnW=
0.424901
xg = -y.ozo;;
s, = .
@A =
0.393787
rnL = 48.551604
nO = 11096.056659
'no = 5548.028330
‘nbo
= 5213.441281
GO = 5549.095130
9 ns = 0.34959
inv~,, =
0.014974
sno =
1.570796
inv+npo = 0.015046
hns6
in@ >
I;zi
r;
GO
an
kzo
KS
KF
;I
LF
qn.F
hF
Y’
Y
“nl
pF
0
ch
sF
H
L
M
9
KY
Y
J
= -0.000006
= 0.014902
= 0.349050
= 47.712763
= 5547.995640
= 0.366645
= 0.000516
= -3.064981
= -3.474181
= 0.093552
= 0.273093
= 1.111685
= 46.567098
= 1.984505
= 5.325507
= 0.000000
= 0.366645
= 0.434174
= 5.236189
= 1.286597
= 2.223369
= 0.180000
=
0.15OoO
= 0.450000
= 1.524664
= 0.932426
= 0.558144
= 0.54
11
8/15/2019 AGMA 918-A93
18/49
Table 5A - Low axial contact ratio (LACR) helical gears, example 3.1.4
Pinion: iteration for generating pressure angle
Variable 1 2 3 4 5 6
inv @; 0.014937 0.014937 0.014937 -
$ * 0.358888 0.349589 0.349314 -
nl
9” - -
n(i +l)
0.349589 0.349314 0.349313
Pinion: iteration for critical point
Variable 1
2 3 4 5 6
a 0.785398 0.664320 0.651858 0.651758
Pn 0.000102 0.000130 0.000134 0.000134
no
K -0.801380 -0.919094 -0.934027 -0.934149
s
3 -1.210580.186208 -1.328294.199679 -1.343227.201299 -1.343349.201312
P 0.599190 0.464641 0.460559 0.450446
CF 1.157476 1.123738 1.120528 1.120502
TlF 10.767751 10.825179 10.831698 10.831751 -
hF 1.222488 1.165060 1.158541 1.158488
Y' 4.231279 3.548075 3.492580 3.492145
Y 0.512316 0.044217 0.000348 0.000000 -
IYl 0.512316 0.044217 0.000348 0.000000
an1 0.664320 0.651858 0.651758 0.651758
Gear: iteration for generating pressure angle
Variable 1 2 3 4 5 6
inv Q; 0.014902 0.014902 0.014902
t$ - 0.358611 0.349324 0.349050 -
m
0”
n(i +l)
0.349324 0.349050 0.349050
Gear : iteration for critical point
Variable 1 2 3 4 5 6
an 0.785398 0.541421 0.476957 0.474521 0.474518 -
lllzo 0.000198 0.000329 0.000383 0.000386 0.000386 -
Ks -1.554759 -2.132880 -2.394107 -2.405443 -2.405456 -
KF
-1.963959 -2.542080 -2.803307 -2.814643 -2.814656 -
en 0.056632 0.071897 0.078164 0.078431 0.078432 -
Pn 0.728766 0.469524 0.398793 0.396090 0.396087 -
LF 1.235535 1.160451 1.142289 1.141610 1.141609 -
%.F 46.328373 46.439304 46.478542 46.480158 46.480160 -
hF 1.516735 1.405803 1.366566 1.364950 1.364948 -
Y' 6.035126 4.127370 3.848488 3.839332 3.839321 -
Y 1.472435 0.266065 0.009375 0.000011 0.000000 -
IYl 1.472435 0.266065 0.009375 0.000011 0.000000 -
ani 0.541421 0.476957 0.474521 0.474518 0.474518 -
12
8/15/2019 AGMA 918-A93
19/49
AGMA 916-A93
Table 5B - Low axial contact ratio (LACR) helical gears, example 3.1.4
Input data
Gearset
Pinion m
mn =
0.166667
q = 21
&Kd =
1.4760
n2 = 86
kw2 =
1.476
9, = 20.0000
n,l = 10000
pa01 =
0.4092
nc2 = 10000
Pa02 =
0.409
w =
15.oooo
Rol =
2.0667
6
a01
=
0.0061
ROIL
=
7.5865
FL-0 =
0 nm
.---,
c, = 9.3175
-uu.L
0.5343
O.o240
=
=
1.8750
Xl =
Asnl =
x2
0.0000
As,,2
0.024
1
= Nnt rpntk-od
x01
= 0.0000
Cutter figure 3
x02 = 0.0000
Cutter figure 3
L - ..-.,- l .
62
@n
w
cr
F
Rol
Ro2
mG
Rl
R2
cp
Rbl
Rb2
%
‘b
pN
vb
c6
Cl
%
G
C5
%
z
“P
0.349066
0.261799
55.904888
11.249978
12.400175
45.518909
4.095238
10.8704oo
44.516876
0.360356
10.172208
41.657612
0.384177
3.043517
2.952131
0.245674
20.952955
2.605900
4.112262
5.649417
7.091582
4.048065
4.485682
1.473848
63. G4. G5
nr =
0.473848
Px = 12.138182
mF
=
0.926826
na =
L,h =
mN =
: .oooooo
Yr =
0.264134
(4
nr =
0.372068
Z subroutine
d = 21.943975
Rml = 11.393077
Pl =
4.048065
P2 =
16.904690
P
ml =
5.131121
Pm2 =
15.821834
cy = 1.320561
I = 0.241
G6 pinion
nl =
21.oooooo
ROI =
12.400175
R1 =
10.870400
Rbl =
10.1722o6
c4 =
5.649417
x = 0.534300
Asn =
0.024000
nc
=1oooo.oooooo
h, =
1.476000
x0 =
0.000000
Pa0 =
0.409200
aa0 =
O.OO61OO
J factor pinion
n
=
23.301719
rn =
rnb =
cn4 =
i-d =
‘jIb2 =
rna2 =
cn6 =
cnl =
rm =
@@nW=
X8 =
11.650859
10.948227
5.670768
47.713044
44.835595
48.715077
21.769309
2.716636
0.517962
0.501330
sn = 1.935735
Y =
0.861107
4 & = 0.419985
J =
0.60
r-d = 11.990239
no
=11096.056659 G6
‘no
= 5548.028330
‘nbo
= 5213.441281
GO
= 5549.095130
0 ns = 0.349594
iin+,, = 0.014974
sno =
1.570796
hv+npo = 0.015046
hnsf2 = -O.OOOOO6
n1
mG
To1
Rol
Ro2
T1
Rl
R2
illV l;;
Vni
ri
60
=
0.014937
Rbl
=
0.349313
C4
=
11.651910 X
= 5S8.528439 A Sn
O1n
Clno
KS
KF
en
bz
LF
%F
hF
Y’
Y
“nl
pF
Co
ch
SF
H
L
M
Kf
%
0.651758 nc
0.000134
ha0
-0.934149 x0
-1.343349
Pa0
0.201312 ijao
0.450446
=
86.OOOOOO
= 0.244186
= 12.400175
= 45.518909
= 12.400175
= 10.870400
= 44.516876
=
10.8704oO
= 41.657612
= 16.904890
= 0.000000
= 0.024000
=1oooo.oooooo
= 1.476000
= 0.000000
= 0.409200
= 0.006100
1.120502
10.831751
1.158463
3.492145
0.000000
0.651758
0.435535
5.236189
1.000000
2.241005
0.180000
0.15oooo
0.45oooo
1.900525
1.000000
J factor aear
n
=
95.426087
rn =
47.713044
‘nb =
44.835595
Cn4 =
17.382131
‘n2
‘nb2
‘na2
cn6
cnl
=
11.650859
=
10.948227
=
13.180635
=
21.769309
=
14.430000
‘na =
QNnW=
0.387686
4 & =
0.356572
‘n.L
no
‘no
‘nbo
rs
4CS
inv@ns
sno
hv@npo
hns /2
invJ h
+‘;li
ri
GO
an
hlo
KS
KF
;:
hlF
q?lF
hF
Y’
Y
anl
pF
co
ch
sF
H
L
M
Kf
KY
Y
J
= 47.845
= 11096.056
= 5548.028
= 5213.441
= 5549.095
= 0.349
= 0.014
= 1.570
= 0.015
= -0.0000
= 0.014
= 0.349
= 47.712
= 5547.995
= 0.474
=
omo3
= -2.4054
= -2.8146
= 0.078
= 0.396
= 1.141
= 46.480
= 1.364
= 3.839
= 0.000
= 0.474
= 0.434
= 5.236
= 1.000
= 2.283
=
0.18O
=
0.15o
=
0.45o
= 1.796
= 1.000
= 0.706
= 0.52
13
8/15/2019 AGMA 918-A93
20/49
Table 6A - Conventional helical gears, different tools, example 3.1.5
Pinion: iteration for generating pressure angle
Variable
1
2
3
4
5
6
inv I$;
0.014923
0.014923
0.014923
cp -
0.358773
0.349479
0.349204
nz
v
n(i +l)
0.349479
0.349204
0.349204
Pinion: iteration for critical point
Variable
1
2
3
4
5
6
a
0.785398
0.489843
0.423246
0.422544
c
0.000161
0.000301
0.000356
0.000357
K
-1.428714
-2.146816
-2 A58926
-2.462757
S
3
-1.548714.108435
-2.266816.148603
-20.16439478926
-2.582757.164585
k
0.676963
0.341240
0.258852
0.257959
CF
1.174504
1.122203
1.108587
1.108439
IIg
Y<
20.907868.243744
21.006137.145476
21.050445.101167
21.051005.100608
8.228124
6.031137
5.929895
5.929600
Y
2.431867
0.401655
0.004159
0.000000
IYl
2.431867
0.401655
0.004159
0.000000
ani
0.489843
0.423246
0.422544
0.422544
Gear: iteration for generating pressure angle
Variable
1
2
3
4
5
6
inv $;
0.016894
0.016894
0.016894
-
V-
0.373767
0.363741
0.363431
nr
Q
n(i +l)
0.363741
0.363431
0.363430
Gear: iteration for critical point
Variable
1
2
3
4
5
6
an
0.785398
0.478334
0.388037
0.384560
0.384576
-
bw
0.039613
0.072843
0.089196
0.089925
0.089926
-
5
-1.549491
-2.268065
-2.662398
-2.680317
-2.680339
-
KF
-1.729491
-2.448065
-2.842398
-2.860317
-2.860339
-
en
0.068177
0.091832
0.103473
0.103992
0.103992
-
fin
0.717222
0.386503
0.284564
0280588
0.280583
-
ifl
1.237266
1.152564
1.124054
1.122925
1.122924
-
%.F
36.071536
36.215014
36.297514
36.301402r
36.301406
-
F
2.178133
2.034656
1.952155
1.948268
1.946263
-
V'
8.343913
5.576394
5.196610
5.183951
5.183935
-
;I
2.562113.562113
0.503535.503535
0.017965.017965
0.000022.000022
o.oooooo.000000
-
41
0.478334
0.388037
0.384580
0.384576
0.384576
-
8/15/2019 AGMA 918-A93
21/49
AGMA 919-A93
Table 6B - Conventional helical gears, different tools, example 3.1.5
Input data
Gearset
Pinion
j&&r
mn =
0.083333 nl = 35
hzol = 1.4460
n2
= 59
ha*: =
1.41
on = 20.0000
n,l =lOOOO
pa01 =
0.1200
nc2 = 42
Pa02 =
0.18
y = 22.1090
R,l = 1.6843
6
a01
=
0.0187
Ro2
=
3 7i?aFI
b.‘ .a..”
a%-A z
c,
4.2837
--UUL
-
n f-l1
-.-
0.3498
0.0240
=
F =
Xl =
Asnl =
x2 = 0.3523 Asn2 0.02
.8750
Fl = I
x01 =
0.0000
no2 =
0.0278
F2
=Notrequired
Cutter figure 4
Cutter figure 5
G2
+n
Y
cr
F
Rol
Ro2
“G
Rl
R2
+
Rbl
Rb2
%-
‘b
pN
wb
‘6
Cl
C3
c4
9
c2
z
“P
G3. G4.65
nr =
0.437722
Px =
8.347090
mF =
1.257928
na =
0.257928
L,h =
15.131716
mN =
0.693910
Yr =
0.390502
+
nr =
0.378768
0.349066
0.385875
51.404606
10.500042
20.211681
33.165733
1.685714
18.888911
31.841306
0.374334
17.580881
29.636343
0.406423
3.156112
2.952131
0.361494
20.321595
5.433579
7.566551
8.589692
9.971191
6.815079
4.537612
1.437722
I subroutine
d =
38.280025
Rml =
19.225277
Pl =
7.779710
f32 =
12.541885
P
ml = -
Pm2 = -
cy =
1.000000
I
=
0.166
G6 oinion
nl = 35.000000
ROI = 20.211681
Rl = 18.888911
Rbl = 17.560861
c4 = 8.589692
x = 0.349800
As, = 0.024000
*C
=10000.000000
ha0 =
1.446000
x0 = 0.000000
Pa0 =
0.120000
s
a0 =
0.018700
J factor oinion
n =
44.012358
rn =
22.006179
rnb =
20.679044
C
n4 = -
rn2 = -
rnb2 = -
rna2 = -
cn6 = -
C,l = -
rw =
23.328949
mOnW=
0.522216
xg =
0.316830
‘n
%?L
‘nL
nO
=
1.801430
Y
= 0.541648
'a = 38.24
= 0.466382
J =
0.46
no =
52.81
= 23.151612
‘no =
26.40
=12574.959321
G6 gear
‘nbo =
24.81
‘no
=
6287.479660
nl
‘nbo
= 5908.298240 mG
rs
no
= 6288.805660 To1
6
ns =
o.s.ms5 R,l
invqbns =
0.014981 R,2
sno =
1.570796
T1
hv4npo =
0.015029 R1
= 59.000000
rio =
27.66
= 0.593220
(Pns = 0.45
= 20.211681
inv~ns = 0.03
= 33.165733
sno =
1.59
= 20.211681
hv+
no0
= 0.04
=
18.888911
= 31.841306
= 18.888911
= 29.636343
= 13.506516
= 0.352300
= 0.024000
=
42.OCiWOO
= 1.411100
= 0.027800
= 0.180000
= 0.012700
hns 12
inVqJ’~
$‘;zi
r;
ri0
an
CLno
KS
KF
en
&2
blF
= 0.00
= 0.01
= 0.36
= 37.29
= 26.54
= 0.38
= 0.08
= -2.680
= -2.860
= 0.10
= 0.28
= 1.12
= 36.30
= 1.94
= 5.18
= 0.00
= 0.38
= 0.25
= 7.91
= 1.36
= 2.24
= 0.18
= 0.15
=
0.45
= 1.65
= 0.85
= 0.58
= 0.51
Ins I2
inV($
cP”ni
r;
GO
= 0.000031
= 0.014923
= 0.349204
= 22.007284
= 6287.795326
= 0.422544
= 0.000357
= -2.462757
= -2.582757
= 0.164565
= 0.257959
R2
Rbl
G
x
an
kzo
KS
KF
en
Bn
%lF
%F
hF
Y’
Y
“nl
PF
0
ch
SF
H
L
M
Kf
%f
Asn
nC
h
a0
x0
Pa0
6
a0
=
1.108439
= 21.051005
= 2.100608
= 5.929600
= 0.000000
= 0.422544
= 0.164496
= 7.910180
= 1.369671
= 2.216878
= 0.180000
= 0.150000
= 0.450000
= 1.693445
= 0.656723
J factor Qear
n
=
74.192260
rn =
37.096130
‘nb =
34.858960
Cn4
= -
rn2 = -
‘nb2 = -
rna2 = -
Cn6 = -
Cnl = -
‘na =
38.420556
m+nW=
0.463446
xg =
0.319330
sn =
1.803250
$& =
0.424237
“nl
PF
0
ch
SF
H
L
M
9
KY
Y
J
15
8/15/2019 AGMA 918-A93
22/49
Table 7A - Spur sun and planet gear, example 3.1.6
Pinion: iteration for generating pressure angle
Variable 1 2
3 4 5
6
inv $; 0.014928 0.014928
0.014928 -
0 . 0.358812 0.349517
0.349242 -
rzz
Q
n(i +l)
0.349517 0.349242
0.349241
Pinion: iteration for critical point
Variable 1 2
3 4 5
6
a 0.785398 0.602014
0.573238 0.572797
c 0.000151 0.000219
0.000233 0.000233
K -1.064773 -1.329401
-1.388073 -1.389022
S
3 -1.489773.168216 -1.754401.192695
-1.813073.197730 -1.814022.197810
ff 0.617182 0.409320
0.375509 0.374987
CF 1.129153 1.071762
1.063646 1.063524 -
P -
YC
12.941082.473364 13.043537.370909 13.063152.351294 13.063463.350983
5.246010 4.090220
3.970709 3.968983 -
Y 0.962033 0.117700
0.001753 0.000000 -
IYl 0.962033 0.117700
0.001753 0.000000
Qhl 0.602014 0.573238
0.572797 0.572797
Gear: iteration for generating pressure angle
Variable 1 2
3 4 5
6
inv $; 0.014928 0.014928
0.014928 -
4 . 0.358812 0.349517 0.349242
?ZZ
4
n(i +l)
0.349517 0.349242
0.349241
Gear : iteration for critical point
Variable 1 2
3 4 5
6
an 0.785398 0.602014
0.573238 0.572797
bzo 0.000151 0.000219
0.000233 0.000233
%
-1.064773 -1.329401
-1.388073 -1.389022 -
KF -1.489773 -1.754401
-1.813073 -1.814022 -
en
0.168216 0.192695
0.197730 0.197810
Bn 0.617182 0.409320
0.375509 0.374987
GZF 1.129153 1.071762
1.063646 1.063524
%F 12.941082 13.043537
13.063152 13.063463
4F 1.473364 1.370909
1.351294 1.350983
Y' 5.246010 4.090220
3.970709 3.968983
Y 0.962033 0.117700
0.001753 0.000000
IYl 0.962033 0.117700
0.001753 0.000000 -
ani 0.602014 0.573238
0.572797 0.572797
8/15/2019 AGMA 918-A93
23/49
AGMA 916-A93
Table 7B - Spur sun and planet gear, example 3.1.6
Input data
Gearset
Pinion Gear
m,
=
0.200000
q = 26
hzol =
1.4975 722
= 26
hao2 = 1.49
0,
= 20.0000
n,l =iwoo
Pml =
0.4250 nc2
=lOooO
Pa02 = 0.42
v
= o.owo
Rol
= 3.0750
6
a01
=
0.0245
Ro2
= 3.0750
8
a02 =
0.02
c, =
5.7500
= 0.4096
=
0.0650
0.06
F =
Xl
Asnl
x2 = 0.4098
2.5000
As,; =
Fl = I
J-01 =
O.WW
x02 =
o.owo
F2 = I
Cutter figure 6
Cutter figure 6
G.2
+n
v
cr
F
Rol
Ro2
mG
Rl
R2
$
Rbl
Rb2
b
‘b
pN
vb
c6
Cl
c,
c4
C5
ci
z
“P
63.64. G5
n, =
Px =
“F =
=
zti =
mN =
y- =
0
nr =
0.349066
o.owow
26.750000
12.500000
15.375000
15.375000
1.000000
14.000000
14.000000
0.349066
13.155697
13.155697
0.414645
2.952131
2.952131
0.000000
11.587626
3.630348
5.793613
6.562460
7.957276
5.005146
4.326929
1.465697
I subroutine
d = 26.750000
Rlnl = 14.375000
Pl = 5.005146
P2 = 6.582480
P
ml =
5.793613
Pm2 = 5.793813
cly = 1.000000
I = 0.091
G6 Dinion
nl =
26.000000
Rol =
15.375000
R1 =
14.000000
Rbl =
13.155697
c4 =
6.582480
x =
0.409600
Ass, =
0.065OW
%Z
=1oooo.oooooo
h, =
1.497500
x0 =
O.WWW
Pm =
0.425000
sao =
0.024500
J factor pinion
n
=
26.000000
rn = 14.000000
0.465697 '& =
13.155697
c,4 = -
rn2 = -
rnb2= -
12.500000 '& = -
1.000000 c&i = -
o.owow
C,l = -
0.414645 ma = -
mOnW=
0.500352
xg =
0.320507
sn =
1.804106 Y
= 0.634206
9d =
0.421015 J
= 0.37
rnL =
14.414446
nO
= 10000.000000 G6
rno
= 5000.000000 ni
‘nbo
= 4696.463104 'y%
GO
= 5001.072500
To1
@
s =
0.349655
ROl
irwjns = o.olaa3 R,2
sno =
1.570796
T1
invOnpo =
O.OISWI R1
Arts12
iIN+;
Vni
m”
m"0
=
-O.OOOOO6 R2
=
0.014926
Rbl
=
0.349241
C4
=
14.oooa95 x
= 5ooO.319SS A Sn
an
Vno
KS
KF
072
Pn
ClF
9n.F
hF
Y’
Y
anl
pF
co
ch
SF
H
L
M
Kf
Q
0.572797 n,
0.000233 ha0
-1.389022 x0
-1.614022
Pa0
0.197610 tjao
0.374967
=
26.000000
= 1.000000
= 15.375000
= 15.375000
= 15.375000
= 14.000000
= 14.000000
= 14.000000
= 13.155697
= 6.562480
= 0.409600
= 0.065000
= 10000.000000
= 1.497500
=
o.owwo
= 0.425000
= 0.024500
1.063524
13.063463
1.350963
3.966963
o.wowo
0.572797
0.463530
o.wowo
1.000000
2.127047
0.160000
0.15ooo0
0.450000
1.721566
1.000000
J factor ciear
n = 26.OOOOOO
rn =
14.000000
‘nb =
13.155697
C
n4 = -
rn2 = -
‘nb2 = -
‘na2 =
c,fj = -
C,l = -
ma =
m+nW =
osoo352
xg =
0.320507
sn = 1.604106
Q& =
0.421015
rnL = 14.41
nO = 10000.00
‘no = 5000.00
‘nbo = 4698.46
rs
o = 5001.07
$
ns =
0.34
inv(bns =
0.01
sno =
1.57
'"v&p, =
0.01
=
-0.00
=
0.01
=
0.34
=
14.00
= 5000.31
hns i
inv+ n
Tzi
r,”
GO
an
klo
KS
KF
%z
&z
LF
qnF
hF
Y’
Y
“nl
PF
co
ch
SF
H
L
M
Kf
%
Y
J
0.57
0.00
-1.38
-1.61
0.19
0.37
1.0
13.06
1.3
3.96
0.00
0.57
0.46
o.oo
1 o
2.12
0.1
0.15
0.4
1.7
l.W
0.6
0.3
17
8/15/2019 AGMA 918-A93
24/49
Table 8A - Spur planet and ring gear, example 3.1.7
Pinion: iteration for generating pmure angle
Variable
1 2
3 4
5
6
inv $;
0.014928 0.014928
0.014928
v-
0.358812 0.349517
0.349242
nr
v
n(i +l)
0.349517 0.349242
0.349241
Pinion: iteration for critical point
Variable
1 2
3 4
5
6
an
0.785398 0.661551
0.647725 0.647595
%o
0.000151 0.000193
0.000199 0.000199
K -1.064773
-1.225493
-1.247761 -1.247975
S
3 -10.168216.89773
-1.650493.183502
-1.672761.185507 -1.672975.185526
s
0.617182 0.478049
0.462218 0.462068
CF
1.129153 1.089338
1.085164 1.085125
TlF 12.941082 13.006523 13.014738 13.014816
hF
1.163157 1.097715
1.089501 1.089422
Y'
4.212840 3.485322
3.421318 3.420729
Y
0.521748 0.048189
0.000446 0.000000
lYl
0.521748 0.048189
0.000446 0.000000
ani
0.661551 0.647725
0.647595 0.647595
Gear: iteration for generating pressure angle
Variable
inv $;
9”.111
9”
n(i +l)
1
-
2
3 4
Gear : iteration for critical point
5
6
Variable
an
ho
5
KF
&
Bn
LF
%F
b
Y’
Y
IYl
clnl
1 2
3 4
5
6
8/15/2019 AGMA 918-A93
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AG MA 91&A93
Table 8B - Spur planet and ring gear, example 3.1.7
Gearset
Pinioq
Pn =
0.2WOW q = 28
t bn = 20.0000 n,l
=lOOW
Input data
Gear
huol =
1.4975
n2 = 85
&lo2 =
1.2629
ezol =
0.4250
4.2 = 30
Pa02 =
0.1500
w = o.oooo
c, =
5.7500
F =
2.5000
Fl = 2
F2
= I
Rol = 3.0750
Xl
= 0.4096
X01 =
O.WW
Cutter figure 6
%fol = 0.0245
Ro2
=
8.4250
6
o.oo
a02 =
Asnl
=
0.0650
x2
=
0.6678
Asn2 =
0.0650
x02 =
-0.2229
Cutter figure 7
Gz
+n
w
cr
F
Rol
Ro2
“G
Rl
R2
cp
Rbl
Rb2
4%
‘b
pN
vb
c6
Cl
c3
c4
C5
F.2
z
mP
63. G4.65
nr =
Px =
mF =
na =
L,b =
mN =
vr =
9
nr =
0.349066
o.owow
28.750000
12.5WOW
15.375000
42.125000
3.035714
14.000000
42.5WOW
0.349066
13.155697
39.936936
0.372222
2.952131
2.952131
o.owow
10.455989
2.943890
5.136275
5.896021
7.957278
5.005146
5.013388
1.698227
Z subroutine
d =
28.245614
Rml = 14.375000
PI = 5.005146
P2 =
15.461135
pml =
5.793613
P& = 16.249802
CyJ =
l.WWW
I = 0.244
G6 Dinion
nl =
28.WWW
Rol =
15.375000
Rl =
14.WWW
Rbl =
13.155697
c4 =
5.896021
X
=
0.409800
Asn =
0.065OW
nC
=10000.000000
h, =
1.497500
x0 =
O.WWW
P&,2 =
0.425000
aa0 =
0.024500
J factor pinion
n = 28.WWW
rn =
0.698227
‘& =
C
n4 =
‘n2 =
‘;Ib2 =
12.5WOW 'm2 =
: .owow
cn6 =
0.000000
Cnl =
0.372222 'na =
@e,w=
xg =
14.OOWW
13.155697
0.448172
0.320507
sn =
1.804106 Y =
0.825562
qnL =
0.368836
J =
0.43
rnL =
14.104239
no
=10000.000000
gear6
‘no
‘nbo
60
@
s
hv+ns
sno
im’%po
kI2
iIW$;f
cP”ni
r-i
GO
an
Cl?lO
KS
KF
en
bl
LF
%F
hF
Y’
Y
anl
pF
co
ch
SF
H
L
M
Kf
Kw
= 5WO.WOWO
n1
= 4698.463104 mG
= 5W1.072500
%l
=
0.349655
R,l
=
o.o14ga3 R,2
=
1.570796
*1
=
0.015061 R1
=
-0.WOOO6
= 0.014928
= 0.349241
=
14.WO895
= 5000.319535
= 0.647595
=
o.wo199
= -1.247975
= -1.672975
= 0.185526
= 0.462068
R2
Rbl
c4
X
Asn
nC
h
a0
X0
pa0
6
a0
1.085125
13.014816
1.089422
3.420729
o.wowo
0.647595
0.463530
o.wowo
l.WOWO
2.170249
0.18OWO
0.15owo
0.45owo
1.898920
l.WOOOO
J factor aear
n
=
rn =
‘nb =
cn4 =
‘n2 =
‘nb2 =
‘na2 =
cn6 =
C
nl =
‘na =
m+nW=
xi? =
sn =
$d =
rti =
no =
‘no =
rnbo =
r-i0 =
(4
s =
invQns =
sno =
hvOnoo =
hnsf2
in@ >
%i
G
GO
an
%zo
KS
KF
en
fin
%lF
qnF
hF
Y’
Y
anl
pF
w
ch
SF
H
L
M
Kf
%
Y
J
19
8/15/2019 AGMA 918-A93
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Table 9A - Helical sun and planet gear, example 3.1.8
Pinion: iteration for generating pressure angle
Variable 1 2
3 4 5
6
inv $; 0.030017 0.030017
0.030017
$". 0.451838 0.437112
0.436527
tll
v
n(i +l)
0.437112 0.436527
0.436526
Pinion: iteration for critical point
Variable 1 2
3 4 5
6
a 0.785398 0.550858
0.516528 0.516292
Pn 0.000092 0.000150
0.000163 0.000163
n0
K -0.755647 -1.020756
-1.081818 -1.082267
S
P -0.845647.183552 -1.110756.215756
-1.171818.222565 -1.172267.222614 -
s" 0.601846 0.335102
0.293964 0.293678 -
CF 1.203951 1.180769
1.177409 1.177386
P
YT
2.003974.761434 9.808402.957006
9.818742.946666 9.818818.946590
6.604027 5.308212
5.241281 5.240928
Y 1.548908 0.182230
0.001237 0.000000
IYl 1.548908 0.182230
0.001237 0.000000
ani 0.550858 0.516528
0.516292 0.516292 -
Gear: iteration for generating pressure angle
Variable 1 2
3 4 5
6
inv $; 0.026131 0.026131
0.026131 -
$"* 0.431629 0.418269
0.417773 -
Cli +I) 0.418269 0.417773
0.417772
Gear: iteration for critical point
Variable 1 2
3 4 5
6
Cr, 0.785398 0.532078
0.480780 0.479829 0.479829
-
blo 0.019982 0.033342
0.037361 0.037442 0.037442
-
KS -0.595631 -0.815390
-0.887999 -0.889483 -0.889484
-
9 -0.775631 -0.995390
-1.067999 -1.069483 -1.069484
-
&
0.132923 0.152962
0.158991 0.159112 0.159112
-
fb
0.652475 0.379116
0.321789 0.320717 0.320716
-
GlF 1.208512 1.173198
1.166728 1.166610 1.166610
-
SF 13.176464 13.239694
13.257422 13.257776 13.257776
-
F 1.837279 1.774049
1.756320 1.755966 1.755966
-
Y' 6.313286 4.684785
4.524943 4.522425 4.522424
-
Y 1.599280 0.240323
0.004303 0.000001 0.000000
-
IYl 1.599280 0.240323
0.004303 0.000001 0.000000
-
%i 0.532078 0.480780
0.479829 0.479829 0.479829
-
L
8/15/2019 AGMA 918-A93
27/49
AGMA 918-A93
Table 9B - Helical sun and planet gear, example 3.1.8
Input data
Gearset Pinion
@aJ
mn
=
0.111111
nl = 18
hzol =
1.1460 n2
= 24
ha02 = 1.128
on
= 25.0000
n,l =lOOOO
pa01 =
0.0900
nc2
= 36
Pa02 = 0.1800
w
= 17.7276
Rol
= 1.2154
6
a01
=
0.0000
c,
2.5500
Ro2
=
, F.4.c7
. “-.”
K.-n -
WaoL -
n nnnn
“.“““I
Xl
=
0.5420
Asnl =
0.0180
F =
x2
=
0.4316
.5000
Asn2 =
0.0180
=
Fl
.x01
0.0000
1
x02
= 4.6985
F2
= Not required
Cutter figure 8
Cutter figure 9
G2
%l
w
Cr
F
Rol
Ro2
“G
Rl
R2
0
Rbl
Rb2
Qr
‘b
pN
vb
c6
Cl
c3
c4
9
c,
z
“P
63.64. G5
n, =
0.145262
Px =
10.317491
??aF =
1.308459
na =
0.308459
L,h =
15.604712
mN =
0.865124
Yj- =
0.321240
0
nr =
0.507400
0.436332
0.309405
22.950023
13.500014
10.938611
13.911314
1.333333
9.448671
12.598228
0.455256
8.486309
11.315079
0.530005
2.962281
2.847250
0.279592
11.602094
3.509279
4.972326
6.471560
6.901867
3.939586
3.392587
1.145262
I subroutine
d
=
19.671448
Rml =
9.988660
Pl =
5.268385
l-3
=
6.333708
P
ml = -
Pnz; = -
cy =
1.000000
I
=
0.146
G6 pinion
nl =
18.000000
ROI = 10.938611
RI =
9.448671
Rbl = 8.486309
Cd = 6.471560
x = 0.542000
Asn = 0.018000
nC
=10000.000000
h, =
1.146000
x0 = 0.000000
Pm =
0.090000
sao =
0.000000
J
factor pinion
n = 20.828460
rn = 10.414230
rnb = 9.488498
C
n4 = -
rn2 =
‘nb2 =
‘na2 =
+j
= -
C
nl = -
ma =
11.904170
mOnW=
0.768580
xg =
0.522699
‘n
%.L
‘r2.L
nO
‘no
‘nbo
GO
@ns
inV4%s
sno
inv%zpo
hns I2
iIN@;;
@“ni
r?i
riY0
Orn
ho
KS
KF
en
pn
Gl.F
Q2.F
hF
Y’
Y
anl
pF
0
ch
SF
H
L
M
Kf
KY
=
2.058274
=
0.639785
=
11.765408
=11571X6413
=
5785.683206
=
5243.609743
=
5786.739206
=
0.436723
= 0.030060
=
1.570796
,=
0.030111
=
0.000033
=
0.030017
=
0.436526
=
10.415169
=
5786.204859
0.516292
0.000163
-1.082267
-1.172267
0.222614
0.293678
1.177386
9.818818
1.946590
5.240928
0.000000
0.516292
0.116121
7.694021
1.363320
2.354772
0.14oOOo
0.110000
0.500000
1.671480
0.903789
Y =
0.801215
J =
0.55
aear6
n1
mG
%l
Rol
Ro2
T1
Rl
R2
Rbl
c,
x
Asn
nc
ha0
X0
Pa0
6
a0
=
24.000000
= 0.750000
= 10.938611
= 13.911314
= 10.938611
= 9.448671
= 12.598228
= 9.448671
= 11.315079
= 7.662508
= 0.431600
= 0.018000
= 36.000000
= 1.128700
= -0.698500
= 0.180000
= 0.000000
J factor aear
n
=
27.771279
rn =
13.885640
‘nb =
12.584663
C
n4 = -
rn2 = -
‘nb2 = -
rna2 = -
c,fj = -
C,l = -
‘na =
15.198726
@NnW=
0.677188
xg =
0.412299
sn = 1.955313
(PnL =
0.576804
rnL =
no =
‘no =
‘nbo =
rs
no =
$
ns =
inv~,, =
sno =
inv@npo =
hns 12
iIn+ ;z
%i
ri
m”0
O1n
bzo
KS
KF
;:
&IF
‘lnF
hF
Y’
Y
anl
PF
0
ch
SF
H
L
M
9
Ku’
Y
J
15.0137
41.6569
20.8284
18.8769
21.0786
0.4611
0.0357
0.9193
0.0520
0.0067
0.0261
0.4177
13.7688
20.6532
0.4798
0.037
-0.8894
-1.0694
0.159
0.320
1.166
13.257
1.755
4.522
0.000
0.479
0.200
7.694
1.363
2.333
0.140
0.110
0.500
1.649
0.903
0.826
0.58
21
8/15/2019 AGMA 918-A93
28/49
Table 1OA - Helical planet and ring gear, example 3.1.9
Pinion: iteration for generating pressure angle
Variable 1 2 3 4 5 6
inv 4; 0.026131 0.026131 0.026131 -
4) . 0.431629 0.418269 0.417773 7
nr
4”
n(i +l)
0.418269 0.417773 0.417772
Pinion: iteration for critical point
Variable 1 2 3 4 5 6
an 0.785398 0.532078 0.480780 0.479829 0.479829 -
P 0.019982 0.033342 0.037361 0.037442 0.037442 -
no
K -0.595631 -0.815390 -0.887999 -0.889483 -0.889484 -
S
2 -0.775631.132923 -0.995390.152962 -1.067999.158991 -1.069483.159112 -1.069484.159112 -
s 0.652475 0.379116 0.321789 0.320717 0.320716 -
CF 1.208512 1.173198 1.166726 1.166610 1.166610 -
F 13.176464.837279 13.239694.774049 13.257422.756320 13.257776.755966 13.257776.755966 -
Y ; 6.313286 4.684785 4.524943 4.522425 4.522424 -
Y 1.599280 0.240323 0.004303 0.000001 0.000000 -
IYl 1.599280 0.240323 0.004303 0.000001 0.000000 -
ani 0.532078 0.480780 0.479829 0.479829 0.479829 -
Gear: iteration for generating pressure angle
Variable 1 2 3 4 5 6
inv $;
v- -
nr
C(i +l)
Gear: iteration for critical point
Variable 1 2 3 4 5 6
an
ha0
5
KF
%l
fin
&lF
%F
4F
Y’
Y
IYl
ani
8/15/2019 AGMA 918-A93
29/49
AGMA 916-A93
Table IOB - Helical planet and ring gear, example 3.1.9
mn
+n
Pinion
Input data
g@J
= 0.111111 nl = 24
haol =
1.1287 n2 = 69
hao2 =
1.1362
= 25.0000 n,l
=
36 P
a01 =
0.1800 nc2
=
36 Pa02
=
0.1080
w = 17.7276
ROI
= 1.5457 6
a01
= 0.0000
Ro2
= 3.8846 6
c, =
2.5500
a02 =
0.0000
= 0.4316
=
0.0180
=Xl
Asnl
-0.1972
Asn2 =
0.0180
1.5000
x2
Fl 2
x01
=
-0.6985
x02 =
0.1111
= Notrequired
Cutter figure 9
Cutter figure 10
62
+n
w
cr
F
Rol
Ro2
mG
Rl
R2
cp
Rbl
Rb2
b
‘b
pN
vb
c6
Cl
53
c,
%
c;
z
“P
G3. G4.65
n, =
0.362671
Px = 10.317491
mF =
1.308459
n, =
0.308459
L,h =
17.938456
mN =
0.752574
Y, =
0.301137
9
nr =
0.375282
0.436332
0.309405
22.950023
13.500014
13.911314
34.961435
2.875000
12.598228
36.219905
0.455256
11.315079
32.530852
0.391249
2.962281
2.847250
0.279592
8.751830
4.056199
4.667643
7.018480
8.092814
5.130533
4.036615
1.362671
I subroutine
d =
24.480024
Rml =
12.961363
Pl =
6.321860
P2 =
15.073690
Pm1 = -
l-J&= -
cy =
1.000000
I = 0.546
G6 oinion
n1 =
24.000000
ROI =
13.911314
Rl =
12.598228
Rbl =
11.315079
c4 =
7.018480
x =
0.431600
Asn =
0.018000
nc =
36.000000
h, =
1.128700
x0 =
4.698500
Pa0 =
0.180000
6
a0 =
0.000000
J factor Dinion
n =
27.771279
rn =
13.885640
rd = 12.584663
c,4 = -
rn2 = -
rnb2 = -
rna2 = -
cn6
= -
C,l = -
ma =
15.198726
tan(pnW=
0.677188
xg =
0.412299
‘n
%L
‘nL
nO
‘no
‘nbo
GO
@iZS
~VQ,,
Sno
i”%Zp0
Ins12
ilW&
Q”ni
ri
r"0
an
&ZO
KS
KF
072
pn
h.F
%F
hF
Y’
Y
“Rl
P
0
ch
SF
H
L
M
Kf
KY
1.955313 Y =
0.885141
0.576804
J =
0.71
15.013743
41.656919 G6
20.828460 ni
18.876995 mG
21.078660
To1
0.461130
Rol
0.035727
Ro2
Recommended