NEW ERA UNIVERSITY
COLLEGE OF ENGINEERING AND TECHNOLOGY
MECHANICAL ENGINEERING DEPARTMENT
ME 484
MACHINE DESIGN II
GEAR REDUCER DESIGN
Submitted by:
Vallejos, Dario Jr. C.
IV-BSME
Submitted to:
Engr. Nelio S. Gesmundo, Jr
Course Instructor
ACKNOWLEDGMENT
This work, though amateur at best, would not have been possible without the help of the
people within my immediate surroundings, that is, my family, professors, friends, and
acquaintances. Of special mention are the following individuals/persons:
My parents, without whose support this endeavor would surely fall apart in terms of
logistics and moral support,
My professors and instructors, without whom the knowledge and information taxed by this
task would not have been met,
My classmates/colleagues, without whom the ideas developed here would not have an
environment to thrive, improve, and grow,
My paramour, who kept me going, without whom this project would not have been rebuilt
each time it fell apart,
And to God, without whom all of these are otherwise physically void, intellectually
impossible, and mentally hopeless.
TABLE OF CONTENTS
I. DESIGN PROBLEM AND DESIGN SPECIFICATIONS
A. DESIGN PROBLEM
B. DESIGN SPECIFICATIONS
1. GEAR PAIR
2. SHAFTING
3. RIMS AND ARMS
4. GEAR HOUSING
II. DESIGN SKETCH/ILLUSTRATION
III. COMPUTATIONS
A. GEAR PAIR
1. PRELIMINARY GEAR DIMENSIONS, CONTACT RATIO, AND INTERFERENCE
2. TORQUE AND FORCES
3. BENDING STRENGTH
4. PITTING STRENGTH
5. MATERIAL SELECTION
B. SHAFTING
1. SHAFT
2. GEAR HUB
3. BEARING SELECTION
4. TOLERANCES AND FITS
5. KEYS AND COUPLINGS
C. RIMS AND ARMS
1. INITIAL DIMENSIONS
2. ARM GEOMETRY
D. HOUSING
1. INITIAL ILLUSTRATION
2. GEARBOX DIMENSIONS
IV. RECOMMENDATIONS
V. APPENDIX
I. DESIGN PROBLEM AND DESIGN SPECIFICATIONS
A. DESIGN PROBLEM
A gear-reduction unit is to be designed according to the data in the table and the
following specifications. The velocity ratio may be varied by an amount necessary to have
whole tooth numbers. The given center distance is the permissible maximum (but this
does not preclude asking the engineer in charge if a slightly larger one can be tolerated, in
case it looks impossible to satisfy this condition. The teeth are to be 20ᵒ F.D. with Np≥ 18
teeth, with 17 as the minimum acceptable. The service is continuous, with indefinite life.
Use Bucking ham’s dynamic load for average gears.
(a) Decide upon the material with its treatment, pitch, and face with. Start out being
orderly with your calculations so that you do not need to copy all of them for your report.
The report should show calculations for the final decisions first, but all significant
calculation should be in the appendix. These latter calculations should show: that a cheap
material (as cat iron) cannot be used; that through-hardened steel (minimum permissible
tempering temperature is 880ᵒF), flame or induction-hardened steel, and carburized
case-hardened teeth have all been considered in detail.
(b) To complete the design of the gears, a shaft size is needed. At the option of the
instructor: (i) compute shaft diameters for pure torsion only using a conservative design
stress, as Ss= 6 ksi (to cover stress concentration, minor bending, on the assumption that
the bearings will be quite close to the gears, etc.); or (ii) make a tentative assumption of
the distance between bearings, and design the shafts by a rational procedure. It would be
logical for the input and output to be via flexible couplings. Let the shaft material be cold-
finished AISI 1137. Design the keys for cold-drawn AISI C1118. Use better materials than
these only for good reason.
(c) Determine the dimensions of the hub, arms or webs, and rims and beads of both
gears.
(d) Make a sketch of each gear (on separate sheets of paper) including on it all
dimensions and information for its manufacture.
(e) At the instructor’s option (i) choose rolling type bearings, or (ii) design sleeve
bearings.
(f) Decide upon all details of the housing to enclose the gears, with sketches depicting
them.
(g) Your final report should be arranged as follows: (1) title page; (2) a summary of final
design decisions, and material specifications; (3) sketches; (4) final calculation; (5) other
calculations.
B. DESIGN SPECIFICATIONS
1. GEAR PAIR
MATERIAL
TABLE I.B.1-1
MATERIAL
Pinion AISI 6150 OQT 400
Gear AISI 6150 OQT 400
YIELD STRENGTH 270 ksi
HARDNESS
Pinion Approx 634 HB or 59 HRC
Gear Approx 670 HB or 61 HRC
CASE DEPTH .023 in
ALLOWABLE STRESS NUMBERS:
TABLE I.B.1-2.a
RATING METHOD ANSI/AGMA 2001-D04
ALLOWABLE BENDING STRESS NUMBER
Pinion ≳ 74.79 ksi
Gear ≳ 58.51 ksi
STRESS CYCLE FACTOR
Pinion .94
Gear .97
TEMPERATURE FACTOR 1.0
RELIABILITY FACTOR 1.0
BENDING STRESS NUMBER
Pinion 81614.24 psi
Gear 65881.37 psi
GEOMETRY FACTOR
Pinion .335
Gear .415
OVERLOAD FACTOR 1.75
DYNAMIC FACTOR 1.275
SIZE FACTOR 1.0
LOAD DISTRIBUTION FACTOR 1.181
RIM FACTOR 1.0
TABLE I.B.1-2.b
ALLOWABLE CONTACT STRESS NUMBER
Pinion ≳ 264.02 ksi
Gear ≳ 252.79 ksi
STRESS CYCLE FACTOR
Pinion .91
Gear .94
BENDING STRESS NUMBER
Pinion 237617.65 psi
Gear 237617.65 psi
GEOMETRY FACTOR
Pinion .109
Gear .109
GEOMETRY
TABLE I.B.1-3
PROFILE TYPE INVOLUTE
PRESSURE ANGLE 20°
DIAMETRAL PITCH, Pd 6
FACE WIDTH, F 2.67 in
CENTER DISTANCE, c 9.583 in
GEAR RATIO, mg 5.053
NUMBER OF PINION TEETH, Np 19
NUMBER OF GEAR TEETH, Ng 91
PINION SPEED, np 900 rpm
GEAR SPEED, ng 178.125 rpm
PINION DIAMETER, Dp 3.167 in
GEAR DIAMETER, Dg 8.00 in
PITCH LINE VELOCITY, v 776.44 rpm
DEDENDUM, b .2083 in
CLEARANCE, c .0413 in
WHOLE DEPTH, ht .334 in
WORKING DEPTH, hk .50 in
TOOTH THICKNESS, t .262 in
BASE CIRCLE DIAMETER (PINION) 2.976 in
BASE CIRCLE DIAMETER (GEAR) 7.516 in
CIRCULAR PITCH .5234 in
BACKLASH .015 in
2. SHAFTING
SHAFT MATERIAL
TABLE I.B.2-1
MATERIAL AISI 1137 CD
ULTIMATE TENSILE STRENGTH 98 ksi
YIELD STRENGTH 82 ksi
MODULUS OF ELASTICITY 30E6 psi
MODULUS OF RIGIDITY 11.5E6 psi
DESIGN STRESS 6 ksi
SHAFT DIMENSIONS
Pinion
TABLE I.B.2-2.a
D1 D1s D2 D3
DIMENSION 1.5475 in 1.8504 in 1.80 in 1.5475 in
HOLE + 0 No Adjustment + 0 + 0
SHAFT +.0024 in No Adjustment -.0030 in +.0024 in
Gear
TABLE I.B.2-2.b
D1 D1s D2 D3
DIMENSION 2.7559 in 3.0709 in 3.00 in 2.7559 in
HOLE + 0 No Adjustment + 0 + 0
SHAFT +.0029 in No Adjustment -.0037 in +.0029 in
GEAR HOB
TABLE I.B.2-3
DIAMETER LENGTH
PINION 2.70 in 2.25 in
GEAR 4.50 in 3.75 in
BEARINGS
TABLE I.B.2-4
MANUFACTURER/
MODEL NAME
DYNAMIC LOAD
CAPACITY
INNER
DIAMETER
OUTER
DIAMETER
BEARING
WIDTH
PINION SKF
NUP 2208 ECP
18300 lbsf 1.5748 in 3.1496 in .9055 in
GEAR SKF
NU 1014 ML
12600 lbsf 2.7559 in 4.3307 in .7874 in
COUPLINGS
TABLE I.B.2-5
MANUFACTURER/
MODEL NAME
TORQUE
CAPACITY
MINIMUM
DIAMETER
MAXIMUM
DIAMETER
COUPLING
WIDTH
PINION SKF
KD2-153
7884 lbs-in .748 in 2.874 in 2.008 in
GEAR SKF
KD2-303
37812 lbs-IN 1.4961 in 6.7323 in 3.386 in
KEYS MATERIAL
TABLE I.B.2-6
MATERIAL AISI 1137 CD
ULTIMATE TENSILE STRENGTH 80 ksi
YIELD STRENGTH 75 ksi
MODULUS OF ELASTICITY 30E6 psi
MODULUS OF RIGIDITY 11.5E6 psi
KEYS DIMENSIONS
TABLE I.B.2-7
PINION KEY GEAR KEY PINION
COUPLER KEY
GEAR
COUPLER KEY
ORIGINAL 1.12 in 2.26 in 2.084 in 2.46 in
ADJUSTED 2.00 in 3.50 in 2.00 in 3.25 in
3. RIM AND ARMS
Data for the rims and arms are summarized as follows:
TABLE I.B.3-1
MATERIAL AISI 6150 OQT 400
RIM THICKNESS .5864 in
RIM BEAD INCORPORATED IN RIM
HUB BEAD NONE
NUMBER OF ARMS 5
ARM LEGNTH 4.955 in
ARM GEOMETRY ELLIPTICAL (h = 1.06 in)
4. HOUSING
Summary of gearbox dimensions is as follows:
TABLE I.B.4-1
MATERIAL Cast iron
WALL THICKNESS .45 in
TOP COVER THICKNESS .36 in
COVER FLANGE THICKNESS .90 in
COVER FLANGE BOLT DIAMETER .75 in
COVER FLANGE WIDTH 1.875 in
COVER FLANGE BOLT SPACING 4.5 in
FOUNDATION FLANGE BOLT DIAMETER .875 in
FOUNDATION FLANGE THICKNESS 1.3125 in
FOUNDATION FLANGE WIDTH 2.1875 in
PINION BEARING HOUSING DIAMETER 3.80 in
GEAR BEARING HOUSING DIAMETER 5.20 in
II. DESIGN SKETCH/ILLUSTRATION
III. CALCULATIONS
A. GEAR PAIR
1. PRELIMINARY GEAR DIMENSIONS, CONTACT RATIO, AND INTERFERENCE
INITIAL CALCULATIONS FROM THE ORIGINAL PROBLEM SPECIFICATIONS
Original specifications given by the problem are as follows:
TABLE III.A.1-1
POWER 90 hp
GEAR RATIO 5
MAX CENTER DISTANCE 9.5 in
PINION RPM 900
LOAD TYPE Shock load
SAFETY FACTOR 1.4
PRESSURE ANGLE ϕ 20°
PINION TEETH ≥ 18
Using the tabulated values, we may assign initial values to the center distance, number
of gear teeth, diametral pitch, and the pinion and gear diameters using the following
equations and correlations, respectively:
C = (Dp + Dg)/2 Eqn III.A.1-1
mg = Ng/Np ∝ Dg/Dp Eqn III.A.1-2
∴ mg = Dg/Dp
5 = Dg/Dp = Ng/Np
5Dp = Dg
C = (Dp + 5Dp)/2 = (6Dp)/2
9.5 in = (6Dp)/2
Dp = 3.167 in (initial)
Ng = 5Np = 5 × 18
Ng = 90 (initial)
Dg = 5Dp = 5 × 3.167
Dg = 15.835 in (initial)
DIAMETRAL PITCH Pd
The diametral pitch is given by the formula:
Pd = N/D Eqn III.A.1-3
For this design, any value derived from Eqn III.A.1-3 will be rounded up in order to
meet a value for the center distance that is below the minimum. Hence:
Pd = ⌈N/D⌉ = ⌈18/3.167⌉ = ⌈5.684⌉
Pd = 6
CENTER DISTANCE C
The original maximum center distance C = 9.5 in will have to be adjusted with respect
to the adjusted diametral pitch. Modifying Eqn III.A.1-1:
C = (Dp + Dg)/2 = (Np + Ng)/2Pd = (18 + 90)/(2 × 6)
C = 9.00 in
DIAMETER ADJUSTMENT
Using Eqn III.A.1-3, the diameters for the gear pair may be derived as follows:
Dp = Np/Pd = 18/6
Dp = 3.00 in
Dg = Ng/Pd = 90/6
Dg = 15.00 in
Since the value for the center distance has not yet reached the maximum, these values
may still be increased without compromising the initial specifications.
The relations below logically follow if adjustments from the original gear pair diameters
are incrementally iterated in terms of the number of teeth:
Dp = (Np + ∆N)/Pd = (18 + ∆N)/(6) = (18 + ∆N)/6 Eqn III.A.1-4
Dg = 5Np = 5(18 + ∆N)/6 Eqn III.A.1-5
Np’ = (Np + ∆N) = 18 + ∆N Eqn III.A.1-6
Ng’ = 5Np = (Ng + ∆N) Eqn III.A.1-7
C = (Dp+Dg)/2=(Dp+5Dp)/2=6(18+∆N)/(2×6)=(18+∆N)/2 Eqn III.A.1-8
Summarizing the values for ∆N until C ≅ 9.50 in
TABLE III.A.1-1
∆N Dp (in) Dg (in) Np’ Ng’ C (in)
0 3.00 15.00 18 90 9
1 3.167 15.833 19 95 9.5
Only a single tooth can be added to the pinion, otherwise, the center distance limit will
be exceeded. This value will be checked if the resulting contact ratio has a range of 1.0
≤ mp ≤2.01, and no interference exists.
CONTACT RATIO
The contact ratio is given by the formula:
CR = AB/Pb Eqn III.A.1-9
Where:
AB = Line of contact = AP + BP
1 . ANSI/AGMA 2001-D04, Clause 1.2
Pb = (πD/N)cosϕ = (π/Pd)cosϕ
CR = (AP + PB)/(π/Pd)cosϕ Eqn III.A.1-10
To find the length of lines AP and BP, consider Fig III.A.1-12. An examination of the
figure yields the following relations:
Fig III.A.1-1
α = 90 + ϕ Eqn III.A.1-11
β3 = arcsin [(PO3sinα)/AO3] Eqn III.A.1-12
θ3 = 180 - (α - β3) Eqn III.A.1-13
AP = (AO3sinθ3)/sinα Eqn III.A.1-14
β2 = arcsin [(PO2sinα)/BO2] Eqn III.A.1-15
2 Kinematics and Dynamics of Machines, Martin, 2 ed., p. 251
θ2 = 180 - (α – β2) Eqn III.A.1-16
BP = (BO2sinθ2)/sinα Eqn III.A.1-17
The length of PO3, AO3, PO2, and BO2 can be expressed in term of the radii of the pinion
and the gear, and the addendum circle.
PO3 = Rg Eqn III.A.1-18
AO3 = Rg + 1/Pd Eqn III.A.1-19
PO2 = Rp Eqn III.A.1-20
BO2 = Rp + 1/Pd Eqn III.A.1-21
Considering the sum of the pinion and gear radii, the center distance, equals 9.00”, i.e.
Rg + Rp = 9.50 in Eqn III.A.1-22
Eqn III.A.1-22 has to be modified in anticipation of a hunting tooth. Considering the
length that a single tooth of the gear adds on the center distance:
(Rg + 1/2Pd) + Rp = 9.5 in +1/2Pd = 9.5 + 1/(2×6)
(Rg + 1/2Pd) + Rp = 9.583 in
let Rg’ = (Rg + 1/2Pd)
∴ C = Rg’ + Rp = 9.583 in Eqn III.A-1-23
Combining Eqn’s III.A.1-10~23, the final equation for the contact ratio of the gear pair
in term of the gear radius is given by Eqn III.A.-1-23. For the full derivation, see
Appendix A.
CR = ((Rg’+1/6) sin(70-arcsin(xsin110/( Rg’+1/6))) +
(9.75-Rg’)sin(70-arcsin((9.583-Rg’)sin110/(9.75-Rg’))))/ ((sin110)(cos20)(π/6))
Eqn III.A.1-24
Using Microsoft Mathematics confirms that valid values for Rg include {0 <mp < 9.0”}.
Fig III.A.1-2
Plotting the value of the contact ratio (y-axis) with respect to the gear radius (x-axis) =
(Rg + 1/2Pd) = (15.833 + 1/(2×6)) ≅ 8.00 in, a value of contact ratio mp ≅ 1.70 is
obtained. Therefore, the diameters of the gear and the pinion are valid values for the
design.
HUNTING TOOTH
The addition of a hunting tooth in the gear modified the gear ratio mg = 95/19 = 5, a
relatively poor distribution of load amongst the teeth, to mg = 96/19 = 5.053. This
means that for the same tooth from the gear and the pinion will mesh again for every 96
revolutions from the gear and 19 revolutions the pinion.
The angular speed of the gear also changes in correspondence with the hunting tooth.
From 180 rpm, the value changes to ng = 178.125 rpm.
ADDENDUM a
The addendum is identified early on because it will be used to find whether or not
interference exists. It is given by the formula:
a = 1/Pd = 1/6 Eqn III.A.1-25
a = .167 in.
INTERFERENCE
Using SolidWorks, interference with Rp = Dp/2 = 3.167/2 = 1.584 in and Rg = 8.00 in is
determined graphically. Looking at Fig III.A.1-3, points A and B do not exceed either
points E and F. Hence, no interference occurs.
Fig III.A.1-4
PITCH LINE VELOCITY
After finalizing both the diameters of the pinion and the gear, the pitch line velocity v
may now be determined.
v = 2πRpnp = 2π × 1.584 in × 900 rpm Eqn III.A.1-26
v = 8957.31 in/min = 776.44 fpm
FACE WIDTH
After finalizing the diametral pitch, the face width can now be determined. Using the
formula
F = (8 ~ 16)/Pd, say 16/Pd Eqn III.A.1-27
= 16/6
F = 2.67 in
Other geometric dimensions of particular concern are solved as follows:
DEDENDUM, b Eqn III.A.1-28
b = 1.25/Pd = 1.25/6
b = .2083 in
CLEARANCE, c Eqn III.A.1-29
c = b - a = .2083 - .167
c = .0413 in
WHOLE DEPTH, ht Eqn III.A.1-30
ht = a + b = .167 + .2083
ht = .3753 in
WORKING DEPTH, hk Eqn III.A.1-31
hk = 2a = 2 × .167
hk = .334 in.
TOOTH THICKNESS, t Eqn III.A.1-32
t = π/2 Pd =π/(2 × 6)
t = .262 in
BASE CIRCLE DIAMETER
Db = Dcosϕ Eqn III.A.1-34
Pinion
Dbp = 3.167cos(20)
Dbp = 2.976 in
Gear
Dbp = 8.00cos(20)
Dbp = 7.516 in
CIRCULAR PITCH
Pc = πD/N = π/Pd = π/6 Eqn III.A.1-35
Pc = .5234 in
BACKLASH
The 26th edition of Machinery’s Handbook provides a table to serve as a guide in
determining the amount of backlash of the gear:
TABLE III.A.1-2
For this design, an average between the two limits of the recommended gear backlash
value for gear pairs with diametral pitch Pd = 6~9.99, i.e., backlash bl = .015 in.
SAFETY FACTOR SF
The original specified safety factor SF = 1.4 will be reduced to unity. This is because the
design will use the rating method employed by the American Gear Manufacturer’s
Association (AGMA), an empirical approach to determine factors to be applied in the
design rating, i.e., uncertainties from which the safety factor was deemed fit to be
employed are now evaluated by empirical means.
UPDATED DIMENSIONAL SUMMARY
Preliminary dimensions for the involute spur gears are re-evaluated as follows:
TABLE III.A.1-3
POWER, P 90 hp
DIAMETRAL PITCH, Pd 6
FACE WIDTH, F 2.67 in
CENTER DISTANCE, c 9.583 in
GEAR RATIO, mg 5.053
NUMBER OF PINION TEETH, Np 19
NUMBER OF GEAR TEETH, Ng 91
PINION SPEED, np 900 rpm
GEAR SPEED, ng 178.125 rpm
PINION DIAMETER, Dp 3.167 in
GEAR DIAMETER, Dg 8.00 in
PITCH LINE VELOCITY, v 776.44 rpm
DEDENDUM, b .2083 in
CLEARANCE, c .0413 in
WHOLE DEPTH, ht .334 in
WORKING DEPTH, hk .50 in
TOOTH THICKNESS, t .262 in
BASE CIRCLE DIAMETER (PINION) 2.976 in
BASE CIRCLE DIAMETER (GEAR) 7.516 in
CIRCULAR PITCH .5234 in
SAFETY FACTOR, SF 1.0
DRIVEN LOAD Shock load
2. TORQUE AND FORCES
In order to proceed with the design, it will be necessary to find the value of the torque,
tangential force, radial force, and normal force acting on the gear pair assembly. These
are calculated by the following formulae, respectively:
T = 63000P/n; lbs-in Eqn III.A.2-1
Where
P = power in horsepower
n = angular speed in rpm
Wt = T/R; lbs Eqn III.A.2-2
Where
R = radius in inches
Wr = Wttanϕ; lbs Eqn III.A.2-2
Wn = Wt/cosϕ; lbs Eqn III.A.2-2
Applying the formulas for both the pinion and the gear:
PINION
T = 63000 × 90/900
T = 6300 lbs-in
Wt = 6300/1.584
Wt = 3977.27 lbs
Wr = 3977.27 × tan20
Wr = 1477.61 lbs
Wn = 3977.27/cos20
Wn = 4232.52 lbs
GEAR
T = 63000 × 90/178.125
T = 31831.58 lbs-in
Value for Wt, Wr, and Wn for the gear is the same with the pinion.
TABULAR SUMMARY
Summarizing the computed values on a table:
TABLE III.A.2-1
PINION GEAR
TORQUE, T 6300 lbs-in 31809.26 lbs-in
TANGENTIAL FORCE, Wt 3977.27 lbs 3977.27 lbs
RADIAL FORCE, Wr 1477.61 lbs 1477.61 lbs
NORMAL FORCE, Wn 4232.52 lbs 4232.52 lbs
3. BENDING STRENGTH
The bending strength is determined by the allowable bending stress number Sat, which,
in turn, is determined by the bending stress number St. The formula for the two are as
follows:
St = WtKOKVKS(Pd/F)(KmKB/J) Eqn III.A.3-1
Sat ≥ St × (SFKTKR/YN) Eqn III.A.3-2
Where
KO = Overload factor
KV = Dynamic factor
KS = Size factor
Km = Load distribution factor
KB = Rim factor
KT = Temperature factor
KR = Reliability factor
YN = Stress cycle factor
To proceed with the design, St is determined first. The factors are calculated next.
OVERLOAD FACTOR KO
The overload factor is determined by the use of the table below:3
TABLE III.A.3-1
3 Machine Elements in Mechanical Design, Mott, 4
th ed., p. 389
The given design problem specifi.e.s that the driven load is shock load. However, the
power source is not specified. The design will limit its application to uniform shock
power source, eg, electric motor. Therefore, KO =1.75.
DYNAMIC FACTOR KV
The dynamic factor is determined using the figure below4:
Fig III.A.3-1
Since the transmission grade QV is not specified, assumption will be made according to
the type of load and pitch line velocity. From TABLE III.A.3-25, shock load applications
usually fall under QV = 7 or below; by the pitch line velocity method, it is suggested to
have QV = {6, 7, 8} for pitch line velocity v < 800 fpm.
4 ANSI/AGMA 2001-D04, Appendix A
5 Machine Elements in Mechanical Design, Mott, 4
th ed., p. 389
TABLE III.A.3-2
For a high grade rating, QV = 8 will be used. Applying the formula for curves 5≤ QV ≤ 11
from Fig III.A.3-1:
KV = ((A + v.5)/A)B Eqn III.A.3-3
Where
B = .25 × (12 - QV).667 = .25 × (12 - 8).667 Eqn III.A.3-4
B = .6303
A = 50 + 56(1.0 - B) = 50 + 56(1.0 - .6306) Eqn III.A.3-4
A = 70.6864
KV = ((70.6864 + 776.44.5)/70.6864).7314
KV = 1.275
SIZE FACTOR, KS
The size factor may be taken as unity for most gears provided that the materials are
properly selected for the size.6 For this design, KS = 1.00.
6 ANSI/AGMA 2001-D04, clause 20.2
LOAD DISTRIBUTION FACTOR Km
ANSI/AGMA 2001-D04 defines the laod distribution factor as “...the peak load intensity
divided by the average, or uniformly distributed, load intensity; i.e., the ratio of peak to
mean loading.” It is affected by two components, namely the face load distribution
factor Cmf, which accounts for the distribution of load along the face width, and the
transverse load distribution factor Cmt, which accounts for the distribution of load
among the teeth that share the transmitted load instantaneously. I.e.,
Km = Cmf + Cmt Eqn III.A.3-5
Since there is no standard rating method for the transverse load distribution factor, it
can be assumed that Cmt = 1.00.
The empirical method of calculating for the Cmf may be used provided the design meets
certain criteria that are explained in Appendix C. Its formula is given as:
Cmf = Cmc(CpcCpm + CmaCe) Eqn III.A.3-6
Where
Cmc = lead correction factor
Cpf = pinion proportion factor
Cp = is pinion proportion modifi.e.r
Cma = mesh alignment factor
Ce = mesh alignment correction factor
The value of Cmc is rated either as 1.00 for unmodified loads or .8 for crowned leads. For
this design, with uncrowned leads, Cmc = 1.00.
For Cpf, Fig III.A.3-27 is used.
7 ANSI/AGMA 2001-D04, Fig 5
Fig III.A.3-2
For face width 1.0 < F ≤ 17, the curves from the table is defined by the formula:
Cpf = F/10Dp - .0375 +.0125F = 2.67/(10×3.167) -.0375 +.0125(2.67)
Cpf = .08 Eqn III.A.3-6
Cpm is based on the location of the gear pair from their respective distances from their
bearing centrelines. Consider the figure8:
Fig III.A.3-3
8 ANSI/AGMA 2001-D04, Fig 6
Cpm is 1.0 for straddle mounted pinions with (S1/S) < 0.175; Cpm is 1.1 for straddle
mounted pinions with (S1/S) ≥ 0.175. For this design, the pinions will be located at the
center of the bearing line, hence (S1/S) < 0.175. ∴ Cpm = 1.00.
The mesh alignment factor, Cma, can be obtained from the figure9 and table10 below:
Fig III.A.3-4
TABLE III.A.3-3
For this design, precision enclosed gear units will be used. Using the graph and the
empirical values above, the mesh alignment factor is computed with the formula:
Cma = A + BF +CF2 = .675E-1 +. 128E-1×2.67 - .822E-4 ×2.672 Eqn III.A.3-7
Cma = .101
9 ANSI/AGMA 2001-D04, Fig 7
10 ANSI/AGMA 2001-D04, Table 2
The mesh alignment correction factor Ce is used to modify the mesh alignment factor. It
is rated as either .8 if alignment is improved upon assembly, etc, or 1.00 if no further
improvement with the alignment is made. For this design, the latter scenario is
assumed, hence Ce = 1.00.
Substituting the obtained values for the factors in Eqn III.A.3-5 yields:
Km =1.0 + 1.0(.08×1.0+ .101×1.0)
Km = 1.181
RIM FACTOR KB
This factor is only modified for thin rimmed gears. Current information is insufficient to
find out whether or not rimmed gear is more appropriate for the design. However, the
graph11 shows that for a certain range of backup ratio mb = ht/tR ≥ 1.2 the rim factor is
at unity. Rimmed or not, this limit shall be observed so that KB = 1.0.
Fig III.A.3-5
11
ANSI/AGMA 2001/D04, Fig B.1
GEOMETRY FACTOR J
Calculation for the geometry factor for the bending stress of spur gears is relatively
complex. It is simplified, however, with the aid of the table12 below.
Fig III.A.3-6
It logically follows then that the pinion and the gear will each have a different geometry
factor J. Thru inspection:
Jp ≅ .335
Jg ≅ .415
Substituting all the calculated values of the factors from Eqn III.A.3-1 for the pinion
yields
Stp = WtKOKVKS(Pd/F)(KmKB/Jp) = 3977.27 × 1.75× 1.275× 1.0 × (6/2.67) ×
(1.181 × 1.0/.335)
Stp = 70303.20 psi
12
Machine Elements in Mechanical Design, Mott, 4th
ed., p. 389
For the gear, Stp is multiplied to Jp to cancel its value and divide the new value with Jg.
Stg = Stp (Jp/Jg) = 81614.24 (.335/.415) Eqn III.A.3-7
Stg = 56750.78 psi
RELIABILITY FACTOR KR
The reliability factor accounts for the normal statistical distribution of failure amongst
gear units. Refer to the TABLE III.A.3-213. For this design, a .99 reliability will be used,
i.e., one failure in 10000, hence, KR = 1.00.
TABLE III.A.3-4
TEMPERATURE FACTOR KT
The temperature factor is usually taken as unity for temperature range 32< °F <250 (0
< °C < 121). For this design, it will be assumed that the normal operating conditions
will observe this limit; hence, KT = 1.00.
STRESS CYCLE FACTOR YN
The bending stress number adjusts the allowable stress numbers for the required
cycles of operation. It is given Fig III.A.3-714:
For number of cycles N exceeding 107, the upper limit of the shaded region in the graph
will be used.
13
ANSI/AGMA 2001-D04, clause 18 14
ANSI/AGMA 2001-D04, Fig 18
Fig III.A.3-7
YN = 1.3558Nc-.0178 Eqn III.A.3-8
In which N shall be determined by the formula
Nc = 60Lnq Eqn III.A.3-9
Where
L = Number of life hours
q = Number of contacts per revolution
From Eqn III.A.3-9, it is obvious that different values of YN For this design, the number
of life hours will be designated as the upper limit of the design life of multi-purpose
gearing application (15000 hrs, or approx 5 years for 8-hour continuous, daily
operation) given by the TABLE III.A.3-515.
For q, a value of unity is designated because the gear pair only mesh with one another
in each revolution, i.e., q = 1.0 15
Machine Elements in Mechanical Design, Mott, 4th
ed., p. 396
TABLE III.A.3-5
Evaluating Eqn III.A.3-9 for both the gear and the pinion
Ncp = 60 × 15000 × 900 × 1
Ncp = 8.10E8
Ncg = 60 × 15000 × 178.125 × 1
Ncg = 1.60E8
Substituting the values of Np and Ng to Eqn III.A.3-8
YNp = 1.3558 × (8.10E8)-.0178
YNp = .94
YNg = 1.3558 × (1.60)-.0178
YNg = .97
Substituting the values of St, SF, KT, KR, and YN to Eqn III.A.3-2 for both the gear and the
pinion yields:
Satp ≥ 70303.20 × (1.0 × 1.0 × 1.00/.94)
Satp ≥ 74790.64 psi ≳ 74.79 ksi
Satg ≥ 56750.78 × (1.0 × 1.0 × 1.00/.97)
Satg ≥ 58505.96 psi ≳ 58.51 ksi
TABULAR SUMMARY
Summarizing the values for the bending strength in a table:
TABLE III.A.3-6
ALLOWABLE BENDING STRESS NUMBER
Pinion ≳ 74.79 ksi
Gear ≳ 58.51 ksi
STRESS CYCLE FACTOR
Pinion .94
Gear .97
TEMPERATURE FACTOR 1.0
RELIABILITY FACTOR 1.0
BENDING STRESS NUMBER
Pinion 81614.24 psi
Gear 65881.37 psi
GEOMETRY FACTOR
Pinion .335
Gear .415
OVERLOAD FACTOR 1.75
DYNAMIC FACTOR 1.275
SIZE FACTOR 1.0
LOAD DISTRIBUTION FACTOR 1.181
RIM FACTOR 1.0
4. PITTING STRENGTH
The pitting strength is determined by the allowable contact stress number Sac, which, in
turn, is determined by the contact stress number Sc. The formulae for the two are as
follows:
Sc = CP × (WtKOKVKS(Km/DpF)(Cf/I)).5 Eqn III.A.4-1
Sac ≥ Sc × (SFKTKR)/(ZNCH) Eqn III.A.4-2
Where
CP = elastic coeffici.e.nt
Cf = surface condition factor
I = pitting geometry factor
ZN = pitting resistance stress cycle factor
CH = hardness ratio factor.
All other variables have been previously identified. The remaining unknown factors
shall be accordingly identified.
ELASTIC COEFFICI.E.NT CP
The elastic coeffici.e.nt is defined by the equation16:
CP = (1/(π((1 - μp2)/Ep) + ((1 - μg2)/Eg))).5 Eqn III.A.4-3
Where
μp = Poisson’s ratio of the pinion
μg = Poisson’s ratio of the gear
Ep = Modulus of elasticity of the pinion
Eg = Modulus of elasticity of the gear
For steel, the design material, μ = .3 and E = 30000 ksi, CP = 2300.
16
ANSI/AGMA 2001-D04, Eqn 31
SURFACE CONDITION FACTOR Cf
This design assumes that the manufacturing of the gear allows for appropriate surface
finish. Hence, surface condition factor can be taken as Cf = 1.0.
PITTING GEOMETRY FACTOR I
Likewise with the bending geometry factor J, the pitting geometry factor I requires a
relatively complex procedure to identify. For this design, a simplified approach will be
taken based from the pressure angle and the number of teeth of the pinion and the gear
ratio. Consider the figure17:
Fig III.A.4-1
Plotting the corresponding value of I for Np = 20 and gear ratio 4.45, I ≅ .109
Substituting the unknown variables from Eqn III.A.4-1 with the values from TABLE
III.A.3-6 and the new calculated values yields:
Sc = 2300 × (3733.27 × 1.75 × 1.275 × 1.0 × (1.181/2.67 × 3.167)(1.0/.109)).5
Sc = 237617.65 psi
17
Machine Elements in Mechanical Design, Mott, 4th
ed., p. 402
STRESS CYCLE FACTOR ZN
The contact stress number also adjusts the allowable stress numbers for the required
cycles of operation. It is given by the graph18:
Fig III.A.4-2
For a number of load cycles greater than 107, the shaded region shall be used to identify
ZN. Using the formula for the upper region:
ZN = 1.4488Nc-.023 Eqn III.A.4-5
The values of Nc for the gear and the pinion have been previously identified, namely Ncp
= 8.10E8, and Ncg = 1.60E8. Substituting these values to Eqn III.A.4-5 yields:
ZNp = 1.4488(8.10E8)-.023
ZNp = .90
ZNg = 1.4488(1.60E8)-.023
ZNg = .94 18
ANSI/AGMA 2001-D04, Fig 18
HARDNESS RATIO FACTOR CH
The value of CH for the pinion is set at 1.0. The value of CH for the gear is either set at 1.0
or otherwise depending upon the gear ratio, surface finish of the pinion, and/or
hardness of the pinion and the gear.
For this design, it is initially assumed that the hardness ratio factor for the gear CH = 1.0
until further information regarding the material of the gear is decided.
Substituting the values for the variables in Eqn III.A.4-2:
Sacp ≥ 237617.65× (1.0 × 1.0 × 1.00)/(.90 × 1.0)
Sacp ≥ 264019.61 ≳ 264.02 ksi
Sacg ≥ 237617.65× (1.0 × 1.0 × 1.00)/(.94 × 1.0)
Sacg ≥ 252784.73 psi ≳ 252.79 ksi
TABULAR SUMMARY
TABLE III.A.4-1
ALLOWABLE CONTACT STRESS NUMBER
Pinion ≳ 264.02 ksi
Gear ≳ 252.79 ksi
STRESS CYCLE FACTOR
Pinion .91
Gear .94
BENDING STRESS NUMBER
Pinion 237617.65 psi
Gear 237617.65 psi
GEOMETRY FACTOR
Pinion .109
Gear .109
5. MATERIAL SELECTION
Given the allowable contact stress number and the allowable bending stress number
previously calculated, it will be necessary to select a relatively stronger type of steel.
With the contact stress as the governing stress for this design, consider the figure19
below:
Fig III.A.5-1
Required Brinell hardness number is calculated for both the gear and the pinion for
both Grades 1 and 2.
Grade 1
HB = (Sacp - 29100)/322 Eqn III.A.5-1
Pinion
HB = (264019.61 - 29100)/322
HB = 729.56
Gear
HB = (252784.73 - 29100)/322
19
ANSI/AGMA 2001-D04, Fig 3
HB = 694.67
Grade 2
HB = (Sacp - 34300)/349 Eqn III.A.5-2
Pinion
HB = (264019.61 - 34300)/349
HB = 658.22
Gear
HB = (252784.73 - 34300)/349
HB = 626.03
The Brinell hardness numbers, all well above 400, suggest that through hardening will
not be sufficient. Heat treatment case hardening will be required. In order to select the
appropriate heat treatment, consider the table20:
TABLE III.A.5-1
Only carburization hardening meets the requirement for the allowable contact stress,
namely Gear 3 for both the pinion and the gear. In this regard, a material with good heat
treatment hardening property and yield strength will be required for the gear pair.
20
ANSI/AGMA 2001-D04, TABLE 3
Upon inspection of the properties of AISI 6150 (tempered at 400 °F)21, it is conclusive
that it should serve well as the material for the gear pair.
Fig III.A.5-2
CASE DEPTH
ANSI-AGMA provides suggested case depth for carburized gear teeth. Consider Fig
III.A.5-322. For this design, normal case depth is selected for economy. Using the
equation for the normal case depth curve, the normal case depth is evaluated as
he = .119935Pd -.86105 = .119935 × (6 -.86105) Eqn III.A.5-2
he = .023 in
21
Machine Elements in Mechanical Design, Mott, 4th
ed., p. A-10 22
ANSI/AGMA 2001-D04, Fig 13
Fig III.A.5-3
TABULAR SUMMARY
Tabulating the new data23 for summary:
TABLE III.A.5-2
MATERIAL
Pinion AISI 6150 OQT 400
Gear AISI 6150 OQT 400
YIELD STRENGTH 270 ksi
HARDNESS24
Pinion Approx 634 HB or 59 HRC
Gear Approx 670 HB or 61 HRC
CASE DEPTH .023 in
23
See Appendix C for more details on metallurgical factors 24
See Appendix D for hardness conversion chart
B. SHAFTING
1. SHAFT
ORIGINAL SPECIFICATION FOR THE SHAFTS
The shaft material and the allowable design stress are given by the design problem. The
data are tabulated as follows:
TABLE III.B.1-1
MATERIAL AISI 1137 CD
ULTIMATE TENSILE STRENGTH 98 ksi
YIELD STRENGTH 82 ksi
MODULUS OF ELASTICITY 30E6 psi
MODULUS OF RIGIDITY 11.5E6 psi
DESIGN STRESS 6 ksi
INITIAL SHAFT DIAMETER
The design problem specifies that the design stress be limited to 6 ksi, only for pure
torsion, with the value covering for the stress concentration, minor bending, etc. Using
the torsion equation, initial shaft diameter is evaluated:
τd = 16T/(πd3) Eqn III.B.1-1
∴ d = (16T/(π τd))1/3
Evaluating d for the pinion and the gear:
dp = (16Tp/(π τd))1/3 = (16 × 6300/(π × 6000))1/3
dp = 1.749 in ≅ 1.75 in
dg = (16Tg/(π τd))1/3 = (16 × 31831.16/(π × 6000))1/3
dg = 3.00 in
INITIAL SHAFT LENGTH
The problem does not specify the length of the shaft. However, it does suggest keeping
the distance of the gear pair from each of their respective bearing as little as possible.
For this design, the distance of the gear pair from the bearing will be determined by
angular deflection, and synchronous vibration and transverse deflection.
The website roymech.co.uk provides data sheet for engineering application, including
recommended shaft deflection. From the table:25
TABLE III.B.1-2
The design specified the use of roller bearings. For this design, cylindrical roller
bearings will be used for economy, hence, the maximum angular deflection of .06°.
TORSIONAL DEFLECTION
Using the torsional deflection formula:
Θ = TL/JG Eqn III.B.1-2
∴ L = ΘJG/(T)
Where
L = Distance of gear pair from the bearing
J = Polar moment of inertia
25
http://www.roymech.co.uk/Useful_Tables/Drive/Shaft_design.html#Deflections
Θ = angular deflection in rads
Evaluating for the gear and the pinion shafts:
Pinion
L = ΘJG/(T) = (.06° × π/180°)(π(1.754/32))(30E6))/(6300)
= (.00105)(.9208)(30E6)/6300
L = 4.59 in
Gear
L = ΘJG/(T) = (.06° × π/180°)(π(3.004/32))(30E6))/(31831.16)
= (.00105)(7.9522)(30E/6)/6300
L = 7.85 in
SYNCHRONOUS VIBRATION
In order to design the shafts against critical speed, they must be designed such that
resonance starts to occur at about each of their fifth harmonics26, in which the impulses
are negligible, i.e.:
ns ≥ fn /2n-1 Eqn III.B.1-3
Where
ns = angular speed of the shaft
fn = natural frequency
n = nth harmonic (5th harmonic for this design)
∴fn ≥ ns × 25-1
For the pinion
fnp ≥ (900) × 25-1
fnp ≥ 14400 vib/min ≥ 240 vib/sec
26
Internal Combustion Engine, Maleev, 2 ed., p. 447
For the gear
fng ≥ (178.125) × 25-1
fng ≥ 2850 vib/min ≥ 47.5 vib/sec
The design natural frequencies of the pinion and the gear shafts are substituted to Eqn
III.B.1-4 in order to find the allowable transverse deflection.
fn = (12g/y).5/2π Eqn III.B.1-427
Where
g = 32.2 ft/s2
y = transverse deflection
∴ y = (12g)/(2πfn)2
For the pinion
yp = (12 × 32.2)/(2π × 240)2
yp = .00017 in
For the gear
yg = (12 × 32.2)/(2π × 47.5)2
yg = .00434 in
Using the acquired values of deflection, the distance of the gear pair from the bearings
may be obtained by the beam deflection formula for simply supported beams:
y = WnL3/48EI Eqn III.B.1-5
E = Modulus of elasticity
I = Moment of inertia
∴L = (48EIy/Wn)1/3
27
Internal Combustion Engine, Maleev, 2 ed., p. 460
Calculating the moment of inertia for both the pinion and the gear shaft using the
formula:
I = (πD4/64) Eqn III.B.1-6
Pinion
Ip = (π ×1.754/64)
Ip = .4604 in4
Gear
Ig = (π ×3.004/64)
Ip = 3.9761 in4
Substituting the values to Eqn III.B.1-5
Pinion
Lp = (48 × 30E6 × .4604 × .00017/4232.52)1/3
Lp = 2.99 in ≅ 3.00 in
Gear
Lg = (48 × 30E6 × 3.9761 × .00434/4232.52)1/3
Lg = 18.04 in
The evaluated distance of the pinion shaft from the bearing is also safe for the gear
shaft. For housing convenience, the same value will be used for both the pinion and the
gear shafts. Therefore, tentative shaft length = 2L = 6.00 in.
BEARING REACTION
To illustrate the initial set-up of the gear and shaft assembly, consider Fig III.B.1-1. The
combined radial and tangential forces are combined and are represented as the normal
force. The bearing reactions from the gear and the pinion will be the same since the
same amount of force acts on the shafts.
Using static moment equation to evaluate bearing reactions, with clockwise set as
positive:
MA = 3Wn - 6RB = 0
∴ RB = (3 × 4232.52)/6
Fig III.B.1-1
RB = 2116.26 lbs
MB = 6RA - 3Wn = 0
∴ RA = (3 × 4232.52)/6
RA = 2116.26 lbs
SHEAR AND MOMENT DIAGRAM
With the forces acting on the shaft already known, the shear and moment diagram may
now be determined. Using the shear and moment equation:
V = ΣFy Eqn III.B.1-7
Where
V = Shear force
Fy =Vertical forces
M = ΣM = ∫f(V) Eqn III.B.1-8
Evaluating the two equations:
V = 2116.26 - (4232.52) + 2116.26
V = 0
M = ∫f(V) = (∫ 2116.26
) - (∫ 4232.52
) = 2116.26(6) - 4232.52(6-3)
M = 0
Using Microsoft Mathematics, the shear and moment diagram are graphed as follows:
Fig III.B.1-2a
Shear diagram
Fig III.B.1-2b
Moment diagram
ACTUAL ENDURANCE STRENGTH Sn’
The actual endurance strength of the material must be evaluated in order to proceed
with the shaft design. Its value is evaluated as:
Sn’ = SnCmCstCRCs 28 Eqn III.B.1-9
Where
Sn = Endurance strength
Cm = Material factor
Cst = Stress type factor
CR = Reliability factor
Cs = Size factor
These variables are evaluated accordingly.
28
Machine Elements in Mechanical Design, Mott, 4th
ed., p. 174
ENDURANCE STRENGTH Sn
The endurance strength may be derived from Fig III.B.1-329
Fig III.B.1-330
Plotting the tensile strength of AISI 1137 CD against the surface finish condition,
endurance strength Sn = 38 ksi.
MATERIAL FACTOR Cm
According to its density and general characteristics, AISI 1137 CD can be classified as
wrought steel31. Hence, from TABLE III.B.1-3, its material factor Cm = 1.00.
TABLE III.B.1-3
29
Machine Elements in Mechanical Design, Mott, 4th
ed., p. 175 30
Machine Elements in Mechanical Design, Mott, 4th
ed., p. 175 31
http://www.steelforge.com/literature/ferrousnon-ferrous-materials-textbook/ferrous-metals/carbon-steel/
STRESS TYPE FACTOR Cst
Stress type factor is either evaluated 1.0 for bending or .80 for axial tension. For this
design, Cst = 1.0032.
RELIABILITY FACTOR CR
The same reliability from the gear pair shall be applied for the shafts. Hence, from the
table33 below, reliability factor CR = .81.
TABLE III.B.1-4
SIZE FACTOR CS
The size factor of the shaft shall be evaluated using the following range of values34:
TABLE III.B.1-4
Using the equation for .30 < D ≤ 2.0 for the pinion shaft and 2.0 < D < 10.0 for the gear
shaft:
Pinion Eqn III.B.1-10
Cs = (D/0.3) -.11 = (1.75/.3)-.11
32
Machine Elements in Mechanical Design, Mott, 4th
ed., p. 174 33
Machine Elements in Mechanical Design, Mott, 4th
ed., p. 175 34
Machine Elements in Mechanical Design, Mott, 4th
ed., p. 175
Cs = .8237
Gear Eqn III.B.1-11
Cs = .859 - .02125D = .859 - .02125 × 3.00
CS = .7953
Substituting the obtained values to Eqn III.B.1-9
Pinion
Sn’ = 38E3 (1.00)(1.00)(.81)(.8237)
Snp’ = 25353.49 psi
Gear
Sn’ = 38E3 (1.00)(1.00)(.81)(.7953)
Sng’ = 24479.33 psi
READJUSTED SHAFT DIAMETERS
The final shaft diameters left to be determined are those at the section of the bearing.
Considering that neither torque nor bending moment occurs at the bearings from both
the pinion and the gear shaft, the equation for the shaft diameter at these sections is
applied:
D = (2.94KtVN/Sn’).5 Eqn III.B.1-12
Where
N = Shaft factor of safety = 3 (shock load, certain data)
Kt = Stress concentration factor = 1.5 (round fillet)
Pinion
D = (2.94 × 1.5 × 2116.26 × 3/25353.49).5
D = 1.0501 in
Gear
D = (2.94 × 1.5 × 2116.26 × 3/24479.33).5
D = 1.0695 in
TABULAR SUMMARY
The acquired values for the shaft diameters, including the preferred basic sizes, are
summarized in a table:
TABLE III.B.1-5
Pinion
D1 D2 D3
Nominal Size 1.05 in 1.75 in 1.05 in
Preferred basic size 1.20 in 1.80 in 1.20 in
Gear
D1 D2 D3
Nominal Size 1.0695 in 3.00 in 1.0695 in
Preferred basic size 1.20 in 3.00 in 1.20 in
2. GEAR HUB
Mott and Faires recommend empirical methods for calculating the hub diameter and
hub length, respectively.
Dh = 1.5Ds Eqn III.B.2-135
Lh = 1.25 ~ 2Ds Eqn III.B.2-236
HUB DIAMETER
Substituting values of Ds for both the gear and the pinion to Eqn III.B.2-1
Pinion
Dhp = 1.50 × 1.80
Dhp = 2.70 in
Gear
Dhg = 1.50 × 3.00
Dhg = 4.50 in
HUB LENGTH
Substituting values of Ds for both the gear and the pinion to Eqn III.B.2-2
Pinion
Dhp = 1.7 5 × 1.80
Dhp = 2.25 in
Gear
Dhg = 1.25 × 3.00
Dhg = 3.75 in
35
Machine Elements in Mechanical Design, Mott, 4th
ed., p. 440 36
Design of Machine Elements, 4th
ed., p. 388
3. BEARING SELECTION
Bearings are selected next for the design. Note that bearing selection may affect pre-
determined shaft dimensions according to size compatibility.
BEARING DYNAMIC LOAD CB
The bearing dynamic load is given by the formula:
CB = V(Nc/1E6)1/k Eqn III.B.3-137
Where
CB = Rated bearing load
V = Shear force
Nc = Number of life cycle (See III.A.3, STRESS CYCLE FACTOR)
k = life-load ratio
Substituting the values accordingly for both the pinion and the gear, with k = 3.3 for
ball bearings, bearing dynamic load is evaluated as:
Pinion
CBp = 2116.26 (8.1E8/1E6)1/3.3
CBp = 16103.79 lbs
Gear
CBg = 2116.26 (1.6E8/1E6)1/3.3
CBg = 9851.09 lbs
SELECTION FROM BEARING CATALOGUE
For its local availability, this design will use bearings manufactured by Svenska
Kullagerfabriken (SKF). Select products from the catalogue are included in Appendix E.
37
Machine Elements in Mechanical Design, Mott, 4th
ed., p. 611
The bearings are selected according to their dynamic load capacity and bore diameter
such that stress concentration will be minimized, i.e. the bore should be only slightly
smaller than the diameters at the gear pair section.
The figure38 should serve as a guide in selecting bearings with respect to their bore
diameter:
Fig III.B.3-1
Note that to achieve stress concentration factor Kt = 1.5, the step ratio of the shaft
diameters must not exceed 1.25. Therefore, for the pinion shaft, the minimum bore
diameter:
D1p = D2p/1.25 = 1.80/1.25 Eqn III.B.3-2
D1p = 1.44 in
while for the gear, minimum bore diameter
D1g = D2g/1.25 = 3.00/1.25 Eqn III.B.3-3
D1g = 2.40 in
38
Machine Elements in Mechanical Design, Mott, 4th
ed., p. A-27
For the pinion shaft, the SKF NUP 2208 ECP roller bearing will be used.
Fig III.B.3-2
For the gear shaft, the SKF NU 1014 ML roller bearing will be used
Fig III.B.3-3
ADJUSTED DIAMETERS
The shaft diameters for both the pinion and the gear shafts are adjusted to
accommodate the selected bearings. The new dimensions are tabulated as follows:
TABLE III.B.3-1
D1 D1s D2 D3
PINION 1.5475 in 1.8504 in 1.80 in 1.5475 in
GEAR 2.7559 in 3.0709 in 3.00 in 2.7559 in
4. TOLERANCES AND FITS
Tolerances shall be applied to the gear pair sections of the shafts while fits shall be
applied to the bearing sections. Given the design load and speed, a tolerance of RC5 and
a force fit of FN2 will be used. For convenience, only the shaft dimensions will be
adjusted while the dimensions of the holes are maintained.
Using the ANSI/ASME Clearance Fits and Force Fits charts39, the clearances/fits for the
diameter:
Pinion
TABLE III.B.4-1a
D1 D1s D2 D3
Dimension 1.5475 in 1.8504 in 1.80 in 1.5475 in
Hole + 0 No Adjustment + 0 + 0
Shaft +.0024 in No Adjustment -.0030 in +.0024 in
Gear
TABLE III.B.4-1b
D1 D1s D2 D3
Dimension 2.7559 in 3.0709 in 3.00 in 2.7559 in
Hole + 0 No Adjustment + 0 + 0
Shaft +.0029 in No Adjustment -.0037 in +.0029 in
39
See Appendix F
5. KEYS AND COUPLINGS
ORIGINAL SPECIFICATION FOR THE KEYS
The problem specifies that the material for the keys is AISI C1118 CD. Summarizing its
properties:
TABLE III.B.5-1
MATERIAL AISI 1137 CD
ULTIMATE TENSILE STRENGTH 80 ksi
YIELD STRENGTH 75 ksi
MODULUS OF ELASTICITY 30E6 psi
MODULUS OF RIGIDITY 11.5E6 psi
For this design, the axial area for the shaft and coupling keys are empirically selected
from the TABLE III.B.5-240 whilst the key length is given by the formula:
Lk = (4TN)/(DsWSy) Eqn III.B.5-141
Where
W = face width
Value of T, W, and D are different for both the pinion and the gear. Hence, they shall be
solved separately. In all cases, factor of safety N = 3.00
PINION KEY
Upon inspection at TABLE III.B.5-2, nominal face width and height for a square key
configuration for the pinion shaft Ds = 1.80 in is obtained:
Wp = Hp = ½ in
Substituting the variables from Eqn III.B.5-1:
40
Machine Elements in Mechanical Design, Mott, 4th
ed., p. 495 41
Machine Elements in Mechanical Design, Mott, 4th
ed., p. 500
TABLE III.B.5-2
Lkp = (4 × 6300 × 3)/( 1.80 × .5 × 75000)
Lkp = 1.12 in
GEAR KEY
Upon inspection at TABLE III.B.5-2, nominal face width and height for a square key
configuration for the pinion shaft Ds = 3.00 in is obtained:
Wg = Hg = .75 in
Substituting the variables from Eqn III.B.5-1:
Lkg = (4 × 31809.26 × 3)/( 3.00 × .75 × 75000)
Lkg = 2.26 in
PINION COUPLER KEY
For this design, the diameter of the shaft that elongates to the coupling is given the
same diameter as the diameter of the section of the shaft that is adjacent to the bearing.
In this regard, axial dimension of the pinion coupler key for Ds = 1.5475 in is given as:
Wpc = Hpc = .3125 in
Substituting the variables from Eqn III.B.5-1:
Lkpc = (4 × 6300 × 3)/( 1.5475 × .3125 × 75000)
Lkpc = 2.084 in
GEAR COUPLER KEY
Axial dimension of the pinion coupler key for Ds = 2.7559 in is given as:
Wgc = Hgc = .75 in
Substituting the variables from Eqn III.B.5-1:
Lkgc = (4 × 31809.26 × 3)/( 2.7559 × .75 × 75000)
Lkgc = 2.46 in
COUPLING SELECTION
Manufactured couplings are selected accordingly for this design. See Appendix G for a
select catalogue range from Svenska Kullagerfabriken.
The parameters for the flexible coupling selection are the minimum allowed shaft
diameter, torque capacity, and angular speed capacity. Assigning a value of 4.00 in as
the distance of the elongated portion of the shafts from their respective bearings to
their couplings also limits possible and practical choices. For this design, disc flexible
couplings are employed.
For the pinion, the SKF KD2-153 satisfies all parameters for the pinion coupling.
Fig III.B.5-1
For the gear, the SKF KD2-303 satisfies all parameters for the gear coupling.
Fig III.B.5-2
READJUSTED KEY DIMENSIONS
The key lengths are further adjusted in order to be compatible with their respective
hubs.
TABLE III.B.5-2
PINION KEY GEAR KEY PINION
COUPLER KEY
GEAR
COUPLER KEY
ORIGINAL 1.12 in 2.26 in 2.084 in 2.46 in
ADJUSTED 2.00 in 3.50 in 2.00 in 3.25 in
C. RIM AND ARMS
1. PRELIMINARY DIMENSIONS
For this design, only the gear will use rim and arms in order to reduce mass and cost.
Rim thickness and the number of arms are determined empirically. This design will also
incorporate the ring bead to the rim for easier manufacturing and to keep the material
homogenous.
RIM THICKNESS
A suggested empirical value for the rim thickness is given by the formula:
tR = .56Pc = .56π/Pd Eqn III.C.1-142
Since this design incorporates the bead to the rim, and the bead having the same
formula for the rim thickness, Eqn III.C.1-1 is modified to:
tR = 2(.56π/Pd) = 2(.56π/6) Eqn III.C.1-2
tR = .5864 in
Note that this value of tR is within the prescribed range for the rim thickness factor
determined earlier. The radial distance will be subtracted from the dedendum line.
NUMBER OF ARMS
The number of arms is also empirically suggested43:
TABLE III.C.1-1
Gear diameter(mm) Arms
300-500 4-5
500-1500 6
42
Design of Machine Elements, Faires, 4th
ed., p. 390 43
Design of Machine Elements, Bhandari, 4th
ed., p. 670
1500-2400 8
>2400 10-12
The gear diameter, Dg = 16 in = 403 mm, suggests a recommended number of arms NA
= 4 ~ 5. For this design, NA = 4.
The figure illustrates the preliminary dimensions of the gear pitch diameter, hob, rim,
and shaft bore.
Fig III.C.1-1
2. ARM GEOMETRY
Appropriate arm dimensions are calculated such that the arms, acting as cantilever
beams, will be able to withstand the applied tangential forces. To proceed with the
design, the shape of the cross section must be determined. Faires lists common cross
section shapes for gear arms44. For this design, elliptical arms are selected for their
smaller tendency for stress concentration.
Using the stress formula for beams:
σ = M/S = Sy/N = M/S Eqn III.C.1-3
Where
M = Moment
S = Section modulus
N = Factor of safety = 4
∴ S = 4M/(270 ksi)
Solving for the value of the moment evenly distributed to the four arms:
M = WtL/NA = 3977.27 × 4.955 /5 Eqn III.C.1-4
M = 3941.48 lbs-in
The section modulus of an elliptical cross section in which the major diameter is twice
the minor diameter is given by the formula:
S = πh3/64 Eqn III.C.1-545
Substituting the values to Eqn III.C.1-3
πh3/64 = 4M/(270 ksi)
∴h = ((64 × 4 × 3941.48)/(270E3 × π))1/3
44
Design of Machine Elements, Faires, 4th
ed., p. 389 45
Design of Machine Elements, Faires, 4th
ed., p. 389
h = 1.06 in
TABULAR SUMMARY
TABLE III.C.2-1
RIM THICKNESS .5864 in
RIM BEAD INCORPORATED IN RIM
HUB BEAD NONE
NUMBER OF ARMS 5
ARM LEGNTH 4.955 in
ARM GEOMETRY ELLIPTICAL (h = 1.06 in)
To illustrate the assembly, consider the figure:
Fig III.C.1-2
D. HOUSING
1. INITIAL ILLUSTRATION
To proceed with the gearbox design, an initial illustration, determined by other
dimensions previously designated, e.g., bearings, is provided in order to have a general
idea of the gearbox configuration. Also note that a .5 in clearance from the gear pair is
provided.
Fig III.D.1-1
Further modifications will be made according to recommended dimensions and
material selection.
2. GEARBOX DIMENSIONS
Actual gearbox dimensions are solved as follows:
GEARBOX THICKNESS
Professors Gopinath and Mayuram of the Indian Institute of Technology, Madras,
provide a rule of thumb in determining gear house thickness. 46
TABLE III.D.1-1
Wall thickness ‘s’ in mm of the gearboxes Material
Non-case hardened gears
Case hardened gears
CI castings 0.007L + 6 mm 0.010 L + 6 mm
Steel castings 0.005L + 4 mm 0.007L + 4 mm
Welded construction 0.004L + 4 mm 0.005L + 4 mm
For this design, cast iron castings will be used. Using the empirical formula for CI
castings and case hardened gear, gearbox thickness s is determined:
s = 0.010 L + 6 mm Eqn III.D.1-1
Where
L = largest dimension of the housing
L = 20.167 in = 532.18 mm
s = 0.010 (532.18) + 6 mm
s = 11.122 mm = .44 in
s ≅ . 45 in
46
Indian Institute of Technology, Machine Design 2, Module 2, Lecture 17
2. OTHER DIMENSIONS
Other necessary dimensions for the gearbox are as follows47:
TOP COVER THICKNESS
sc = .8s = .8 × .45 in Eqn III.D.1-2
sc = .36 in
COVER FLANGE THICKNESS
scf = 2s = 2 × .44 Eqn III.D.1-3
scf = .9 in
COVER FLANGE BOLT DIAMETER Eqn III.D.1-4
Dcb = 1.5s = 1.5 × .44
Dcb = .675 in
Dcb = .75 in (standard)
COVER FLANGE WIDTH Eqn III.D.1-5
Wcf = 2.5Dcb = 2.5 × .75
Wcf = 1.875 in
COVER FLANGE BOLT SPACING
wcs = 6Dcb = 6 × .75
wcs = 4.5 in
FOUNDATION FLANGE BOLT DIAMETER Eqn III.D.1-6
Dfb = (1.38E-5Tg)1/3 = (1.38E-5 × 31809.26)1/3
Dfb = .7598 in
Dfb = .8750 in (standard)
47
Indian Institute of Technology, Machine Design 2, Module 2, Lecture 17
FOUNDATION FLANGE THICKNESS Eqn III.D.1-7
sff = 1.5Dfb = 1.5 × .8750
sff = 1.3125 in
FOUNDATION FLANGE WIDTH Eqn III.D.1-8
Wff = 2.5Dfb = 2.5 × .875
Wfc = 2.1875
BEARING HOUSING DIAMETER
Bearing housing diameter on the gearbox is given by:
Dbh = 1.2Dob Eqn III.D.1-10
Pinion
Dpbh = 1.2 × 3.1496
Dpbh = 3.80 in
Gear
Dgbh = 1.2 × 4.3307
Dgbh = 5.20 in
TABULAR SUMMARY
Summarizing the computed values of gearbox dimensions:
TABLE III.D.1-2
WALL THICKNESS .45 in
TOP COVER THICKNESS .36 in
COVER FLANGE THICKNESS .90 in
COVER FLANGE BOLT DIAMETER .75 in
COVER FLANGE WIDTH 1.875 in
COVER FLANGE BOLT SPACING 4.5 in
FOUNDATION FLANGE BOLT DIAMETER .875 in
FOUNDATION FLANGE THICKNESS 1.3125 in
FOUNDATION FLANGE WIDTH 2.1875 in
PINION BEARING HOUSING DIAMETER 3.80 in
GEAR BEARING HOUSING DIAMETER 5.20 in
To illustrate a general idea for the gearbox dimensions, consider the figure below. Note
that the illustration excludes the top cover and the holes.
Fig III.D.1-2
IV. RECOMMENDATIONS
1. Improve alignment upon assembly to avoid stress due to misalignment
2. Operate according to prescribed temperature determined for the temperature factor.
Properly insulate if extreme temperatures are unavoidable.
3. Apply lubricant appropriate with the operating temperature
4. Ensure case hardening is properly conducted.
5. Improve surface finish of shaft.
6. Refer to Fig III.B.3-1 for the appropriate fillet radii.
7. Also apply fillet radii on gear arm joints to avoid stress concentration.
8. Drill horizontal sluice on gearbox cover for ease of lubricant application.
9. Regular, commercially available retaining ring may be used for the unit.
10. Conduct cleaning according to the working environment of the unit.
V. APPENDIX
A. DERIVATION OF THE CONTACT RATIO FORMULA
CR = AB/Pb
AB = AB + PB
Pb = π/(Pdcosϕ)
CR = (AB + PB)/ (πcosϕ/Pd) = (AOgsinθ3 + BOpsinθ2)/(sinα πcosϕ/Pd)
AOg = Rg + 1/Pd
BOp = Rp + 1/Pd
CR = ((Rg + 1/Pd)sin(180 - (α + β3)) + (rp +1/Pd)sin(180 - (α + β2)))/(sinα πcosϕ/Pd)
CR = ((Rg + 1/Pd)sin(180 - α - sin-1(Rgsinα/(Rg + 1/Pd))) + (rp +1/Pd) sin(180- α - sin-1
(Rpsinα/(Rp + 1/Pd)))/(sinα πcosϕ/Pd)
Note that:
α = 90° + ϕ
c = Rg + Rp
Substituting these values yields a function for the contact ratio in terms of either the
pinion or the gear radius.
B. RESTRICTIONS FOR THE EMPIRICAL METHOD FOR Cmf
From ANSI/AGMA 2001-D04, clause 15.3:
“The face load distribution factor accounts for the non--uniform distribution of load
across the gearing face width. The magnitude of the face load distribution factor is
defined as the peak load intensity divided by the average load intensity across the face
width.
This factor can be determined empirically or analytically. This standard provides an
empirical method only, but includes a theoretical discussion for analytical analysis in
annex D. Either method can be used, but when using the analytical approach, the
calculated load capacity of the gears should be compared with past experience since it
may be necessary to re--evaluate other rating factors to arrive at a rating consistent with
past experience. Also see AGMA 927--A01.
The empirical method requires a minimum amount of information. This method is
recommended for relatively stiff gear designs which meet the following requirements:
-- Net face width to pinion pitch diameter ratio, F/d, ≤ 2.0. (For double helical gears the
gap is not included in the face width).
-- The gear elements are mounted between bearings (see following paragraph for
overhung gears).
-- Face width up to 40 inches.
-- Contact across full face width of narrowest member when loaded.
CAUTION: If F/d > 2.4 -- 0.002Kwhere K = the contact load factor (see equation 6), the
value of Km determined by the empirical method may not be sufficiently conservative.
In this case, it may be necessary to modify the lead or profile of the gears to arrive at a
satisfactory result. The empirical method shall not be used when analyzing the effect of a
momentary overload. See 16.3.
When gear elements are overhung, consideration must be given to shaft deflections and
bearing clearances. Shafts and bearings must be stiff enough to support the bending
moments caused by the gear forces to the extent that resultant deflections do not
adversely affect the gear contact. Bearing clearances affect the gear contact in the same
way as offset straddle mounted pinions. However, gear elements with their overhang to
the same support side can compound the effect. This effect is addressed by the pinion
proportion modifying factor, Cpm. When deflections or bearing clearances exceed
reasonable limits, as determined by test or experience, an analytical method must be
used to establish the face load distribution factor.
When the gap in a double helical gear set is other than the gap required for tooth
manufacture, for example in a nested design, each helix should be treated as a single
helical set.
Designs which have high crowns to centralize tooth contact under deflected conditions
may not use this method.
This method will give results similar to those obtained in previous AGMA standards.
Designs falling outside the above F/d ranges require special consideration.”
C. METALLURGICAL FACTORS FOR CARBURIZED CASE HARDENING
D. HARDNESS CONVERSION TABLE48
Hardness Conversion Chart
Rockwell Rockwell Superficial Brinell Vickers Shore
A B C D E F 15-N 30-N 45-N 30-T 3000 kg 500 kg 136 Approx Tensile
Strength (psi)
60kg Brale
100kg 1/16"
Ball 150kg Brale
100kg Brale
100kg 1/8" Ball
60kg 1/16"
Ball 15kg Brale
30kg Brale
45kg Brale
30 kg 1/16"
Ball
10mm Ball
Steel 10mm
Ball Steel Diamond Pyramid
Sciero-scope
86.5 --- 70 78.5 --- --- 94.0 86.0 77.6 --- --- --- 1076 101 ---
86.0 --- 69 77.7 --- --- 93.5 85.0 76.5 --- --- --- 1044 99 ---
85.6 --- 68 76.9 --- --- 93.2 84.4 75.4 --- --- --- 940 97 ---
85.0 --- 67 76.1 --- --- 92.9 83.6 74.2 --- --- --- 900 95 ---
84.5 --- 66 75.4 --- --- 92.5 82.8 73.2 --- --- --- 865 92 ---
83.9 --- 65 74.5 --- --- 92.2 81.9 72.0 --- 739 --- 832 91 ---
83.4 --- 64 73.8 --- --- 91.8 81.1 71.0 --- 722 --- 800 88 ---
82.8 --- 63 73.0 --- --- 91.4 80.1 69.9 --- 705 --- 772 87 ---
82.3 --- 62 72.2 --- --- 91.1 79.3 68.8 --- 688 --- 746 85 ---
81.8 --- 61 71.5 --- --- 90.7 78.4 67.7 --- 670 --- 720 83 ---
81.2 --- 60 70.7 --- --- 90.2 77.5 66.6 --- 654 --- 697 81 320,000
80.7 --- 59 69.9 --- --- 89.8 76.6 65.5 --- 634 --- 674 80 310,000
80.1 --- 58 69.2 --- --- 89.3 75.7 64.3 --- 615 --- 653 78 300,000
79.6 --- 57 68.5 --- --- 88.9 74.8 63.2 --- 595 --- 633 76 290,000
79.0 --- 56 67.7 --- --- 88.3 73.9 62.0 --- 577 --- 613 75 282,000
78.5 120 55 66.9 --- --- 87.9 73.0 60.9 --- 560 --- 595 74 274,000
78.0 120 54 66.1 --- --- 87.4 72.0 59.8 --- 543 --- 577 72 266,000
77.4 119 53 65.4 --- --- 86.9 71.2 58.6 --- 525 --- 560 71 257,000
76.8 119 52 64.6 --- --- 86.4 70.2 57.4 --- 500 --- 544 69 245,000
76.3 118 51 63.8 --- --- 85.9 69.4 56.1 --- 487 --- 528 68 239,000
75.9 117 50 63.1 --- --- 85.5 68.5 55.0 --- 475 --- 513 67 233,000
75.2 117 49 62.1 --- --- 85.0 67.6 53.8 --- 464 --- 498 66 227,000
74.7 116 48 61.4 --- --- 84.5 66.7 52.5 --- 451 --- 484 64 221,000
74.1 116 47 60.8 --- --- 83.9 65.8 51.4 --- 442 --- 471 63 217,000
48
Carbide Depot, https://www.carbidedepot.com/formulas-hardness.htm
73.6 115 46 60.0 --- --- 83.5 64.8 50.3 --- 432 --- 458 62 212,000
73.1 115 45 59.2 --- --- 83.0 64.0 49.0 --- 421 --- 446 60 206,000
72.5 114 44 58.5 --- --- 82.5 63.1 47.8 --- 409 --- 434 58 200,000
72.0 113 43 57.7 --- --- 82.0 62.2 46.7 --- 400 --- 423 57 196,000
71.5 113 42 56.9 --- --- 81.5 61.3 45.5 --- 390 --- 412 56 191,000
70.9 112 41 56.2 --- --- 80.9 60.4 44.3 --- 381 --- 402 55 187,000
70.4 112 40 55.4 --- --- 80.4 59.5 43.1 --- 371 --- 392 54 182,000
69.9 111 39 54.6 --- --- 79.9 58.6 41.9 --- 362 --- 382 52 177,000
69.4 110 38 53.8 --- --- 79.4 57.7 40.8 --- 353 --- 372 51 173,000
68.9 110 37 53.1 --- --- 78.8 56.8 39.6 --- 344 --- 363 50 169,000
68.4 109 36 52.3 --- --- 78.3 55.9 38.4 --- 336 --- 354 49 165,000
67.9 109 35 51.5 --- --- 77.7 55.0 37.2 --- 327 --- 345 48 160,000
67.4 108 34 50.8 --- --- 77.2 54.2 36.1 --- 319 --- 336 47 156,000
66.8 108 33 50.0 --- --- 76.6 53.3 34.9 --- 311 --- 327 46 152,000
66.3 107 32 49.2 --- --- 76.1 52.1 33.7 --- 301 --- 318 44 147,000
65.8 106 31 48.4 --- --- 75.6 51.3 32.5 --- 294 --- 310 43 144,000
65.3 105 30 47.7 --- --- 75.0 50.4 31.3 --- 286 --- 302 42 140,000
64.7 104 29 47.0 --- --- 74.5 49.5 30.1 --- 279 --- 294 41 137,000
64.3 104 28 46.1 --- --- 73.9 48.6 28.9 --- 271 --- 286 41 133,000
63.8 103 27 45.2 --- --- 73.3 47.7 27.8 --- 264 --- 279 40 129,000
63.3 103 26 44.6 --- --- 72.8 46.8 26.7 --- 258 --- 272 39 126,000
62.8 102 25 43.8 --- --- 72.2 45.9 25.5 --- 253 --- 266 38 124,000
62.4 101 24 43.1 --- --- 71.6 45.0 24.3 --- 247 --- 260 37 121,000
62.0 100 23 42.1 --- --- 71.0 44.0 23.1 82.0 240 201 254 36 118,000
61.5 99 22 41.6 --- --- 70.5 43.2 22.0 81.5 234 195 248 35 115,000
61.0 98 21 40.9 --- --- 69.9 42.3 20.7 81.0 228 189 243 35 112,000
60.5 97 20 40.1 --- --- 69.4 41.5 19.6 80.5 222 184 238 34 109,000
59.0 96 18 --- --- --- --- --- --- 80.0 216 179 230 33 106,000
58.0 95 16 --- --- --- --- --- --- 79.0 210 175 222 32 103,000
57.5 94 15 --- --- --- --- --- --- 78.5 205 171 213 31 100,000
57.0 93 13 --- --- --- --- --- --- 78.0 200 167 208 30 98,000
56.5 92 12 --- --- --- --- --- --- 77.5 195 163 204 29 96,000
56.0 91 10 --- --- --- --- --- --- 77.0 190 160 196 28 93,000
55.5 90 9 --- --- --- --- --- --- 76.0 185 157 192 27 91,000
55.0 89 8 --- --- --- --- --- --- 75.5 180 154 188 26 88,000
54.0 88 7 --- --- --- --- --- --- 75.0 176 151 184 26 86,000
53.5 87 6 --- --- --- --- --- --- 74.5 172 148 180 26 84,000
53.0 86 5 --- --- --- --- --- --- 74.0 169 145 176 25 83,000
52.5 85 4 --- --- --- --- --- --- 73.5 165 142 173 25 81,000
52.0 84 3 --- --- --- --- --- --- 73.0 162 140 170 25 79,000
51.0 83 2 --- --- --- --- --- --- 72.0 159 137 166 24 78,000
50.5 82 1 --- --- --- --- --- --- 71.5 156 135 163 24 76,000
50.0 81 0 --- --- --- --- --- --- 71.0 153 133 160 24 75,000
49.5 80 --- --- --- --- --- --- --- 70.0 150 130 --- --- 73,000
49.0 79 --- --- --- --- --- --- --- 69.5 147 128 --- --- ---
48.5 78 --- --- --- --- --- --- --- 69.0 144 126 --- --- ---
48.0 77 --- --- --- --- --- --- --- 68.0 141 124 --- --- ---
47.0 76 --- --- --- --- --- --- --- 67.5 139 122 --- --- ---
46.5 75 --- --- --- 99.5 --- --- --- 67.0 137 120 --- --- ---
46.0 74 --- --- --- 99.0 --- --- --- 66.0 135 118 --- --- ---
45.5 73 --- --- --- 98.5 --- --- --- 65.5 132 116 --- --- ---
45.0 72 --- --- --- 98.0 --- --- --- 65.0 130 114 --- --- ---
44.5 71 --- --- 100.0 97.5 --- --- --- 64.2 127 112 --- --- ---
44.0 70 --- --- 99.5 97.0 --- --- --- 63.5 125 110 --- --- ---
43.5 69 --- --- 99.0 96.0 --- --- --- 62.8 123 109 --- --- ---
43.0 68 --- --- 98.0 95.5 --- --- --- 62.0 121 107 --- --- ---
42.5 67 --- --- 97.5 95.0 --- --- --- 61.4 119 106 --- --- ---
42.0 66 --- --- 97.0 94.5 --- --- --- 60.5 117 104 --- --- ---
41.8 65 --- --- 96.0 94.0 --- --- --- 60.1 116 102 --- --- ---
41.5 64 --- --- 95.5 93.5 --- --- --- 59.5 114 101 --- --- ---
41.0 63 --- --- 95.0 93.0 --- --- --- 58.7 112 99 --- --- ---
40.5 62 --- --- 94.5 92.0 --- --- --- 58.0 110 98 --- --- ---
40.0 61 --- --- 93.5 91.5 --- --- --- 57.3 108 96 --- --- ---
39.5 60 --- --- 93.0 91.0 --- --- --- 56.5 107 95 --- --- ---
39.0 59 --- --- 92.5 90.5 --- --- --- 55.9 106 94 --- --- ---
38.5 58 --- --- 92.0 90.0 --- --- --- 55.0 104 92 --- --- ---
38.0 57 --- --- 91.0 89.5 --- --- --- 54.6 102 91 --- --- ---
37.8 56 --- --- 90.5 89.0 --- --- --- 54.0 101 90 --- --- ---
37.5 55 --- --- 90.0 88.0 --- --- --- 53.2 99 89 --- --- ---
37.0 54 --- --- 89.5 87.5 --- --- --- 52.5 --- 87 --- --- ---
36.5 53 --- --- 89.0 87.0 --- --- --- 51.8 --- 86 --- --- ---
36.0 52 --- --- 88.0 86.5 --- --- --- 51.0 --- 85 --- --- ---
35.5 51 --- --- 87.5 86.0 --- --- --- 50.4 --- 84 --- --- ---
35.0 50 --- --- 87.0 85.5 --- --- --- 49.5 --- 83 --- --- ---
34.8 49 --- --- 86.5 85.0 --- --- --- 49.1 --- 82 --- --- ---
34.5 48 --- --- 85.5 84.5 --- --- --- 48.5 --- 81 --- --- ---
34.0 47 --- --- 85.0 84.0 --- --- --- 47.7 --- 80 --- --- ---
33.5 46 --- --- 84.5 83.0 --- --- --- 47.0 --- 79 --- --- ---
33.0 45 --- --- 84.0 82.5 --- --- --- 46.2 --- 79 --- --- ---
32.5 44 --- --- 83.5 82.0 --- --- --- 45.5 --- 78 --- --- ---
32.0 43 --- --- 82.5 81.5 --- --- --- 44.8 --- 77 --- --- ---
31.5 42 --- --- 82.0 81.0 --- --- --- 44.0 --- 76 --- --- ---
31.0 41 --- --- 81.5 80.5 --- --- --- 43.4 --- 75 --- --- ---
30.8 40 --- --- 81.0 79.5 --- --- --- 43.0 --- 74 --- --- ---
30.5 39 --- --- 80.0 79.0 --- --- --- 42.1 --- 74 --- --- ---
30.0 38 --- --- 79.5 78.5 --- --- --- 41.5 --- 73 --- --- ---
29.5 37 --- --- 79.0 78.0 --- --- --- 40.7 --- 72 --- --- ---
29.0 36 --- --- 78.5 77.5 --- --- --- 40.0 --- 71 --- --- ---
28.5 35 --- --- 78.0 77.0 --- --- --- 39.3 --- 71 --- --- ---
28.0 34 --- --- 77.0 76.5 --- --- --- 38.5 --- 70 --- --- ---
27.8 33 --- --- 76.5 75.5 --- --- --- 37.9 --- 69 --- --- ---
27.5 32 --- --- 76.0 75.0 --- --- --- 37.5 --- 68 --- --- ---
27.0 31 --- --- 75.5 74.5 --- --- --- 36.6 --- 68 --- --- ---
26.5 30 --- --- 75.0 74.0 --- --- --- 36.0 --- 67 --- --- ---
26.0 29 --- --- 74.0 73.5 --- --- --- 35.2 --- 66 --- --- ---
25.5 28 --- --- 73.5 73.0 --- --- --- 34.5 --- 66 --- --- ---
25.0 27 --- --- 73.0 72.5 --- --- --- 33.8 --- 65 --- --- ---
24.5 26 --- --- 72.5 72.0 --- --- --- 33.1 --- 65 --- --- ---
24.2 25 --- --- 72.0 71.0 --- --- --- 32.4 --- 64 --- --- ---
24.0 24 --- --- 71.0 70.5 --- --- --- 32.0 --- 64 --- --- ---
23.5 23 --- --- 70.5 70.0 --- --- --- 31.1 --- 63 --- --- ---
23.0 22 --- --- 70.0 69.5 --- --- --- 30.4 --- 63 --- --- ---
22.5 21 --- --- 69.5 69.0 --- --- --- 29.7 --- 62 --- --- ---
22.0 20 --- --- 68.5 68.5 --- --- --- 29.0 --- 62 --- --- ---
21.5 19 --- --- 68.0 68.0 --- --- --- 28.1 --- 61 --- --- ---
21.2 18 --- --- 67.5 67.0 --- --- --- 27.4 --- 61 --- --- ---
21.0 17 --- --- 67.0 66.5 --- --- --- 26.7 --- 60 --- --- ---
20.5 16 --- --- 66.5 66.0 --- --- --- 26.0 --- 60 --- --- ---
20.0 15 --- --- 65.5 65.5 --- --- --- 25.3 --- 59 --- --- ---
--- 14 --- --- 65.0 65.0 --- --- --- 24.6 --- 59 --- --- ---
--- 13 --- --- 64.5 64.5 --- --- --- 23.9 --- 58 --- --- ---
--- 12 --- --- 64.0 64.0 --- --- --- 23.5 --- 58 --- --- ---
--- 11 --- --- 63.5 63.5 --- --- --- 22.6 --- 57 --- --- ---
--- 10 --- --- 62.5 63.0 --- --- --- 21.9 --- 57 --- --- ---
--- 9 --- --- 62.0 62.0 --- --- --- 21.2 --- 56 --- --- ---
--- 8 --- --- 61.5 61.5 --- --- --- 20.5 --- 56 --- --- ---
--- 7 --- --- 61.0 61.0 --- --- --- 19.8 --- 56 --- --- ---
--- 6 --- --- 60.5 60.5 --- --- --- 19.1 --- 55 --- --- ---
--- 5 --- --- 60.0 60.0 --- --- --- 18.4 --- 55 --- --- ---
--- 4 --- --- 59.0 59.5 --- --- --- 18.0 --- 55 --- --- ---
--- 3 --- --- 58.5 59.0 --- --- --- 17.1 --- 54 --- --- ---
--- 2 --- --- 58.0 58.0 --- --- --- 16.4 --- 54 --- --- ---
--- 1 --- --- 57.5 57.5 --- --- --- 15.7 --- 53 --- --- ---
--- 0 --- --- 57.0 57.0 --- --- --- 15.0 --- 53 --- --- ---
E. SELECTED BEARING CATALOG
Pinion
Gear
F. FITS AND TOLERANCE CHARTS
CLEARANCE FITS
FORCE FITS
F. SELECTED COUPLING CATALOG