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Corporate Learning SolutionsDiscover what more than 100companies already know: bringing SAElearning solutions in-house for groupsof employees maximizes time, savesexpense, enhances learning, andincreases staff cohesion. Each year, wework with many companies to addresstheir unique learning needs throughcustom designed in-house training.Customization is as simple asconducting one of our publicly offeredseminars and incorporating companydata; or as involved as assessing needs,designing a fresh curriculum, andmeasuring outcomes. Traditionalclassroom or blended delivery using e-learning formats are available.
SeminarsSAE regularly offers more than 100high quality, 1-3 day technical seminarsat our Automotive Headquarters inTroy, Michigan and at other selectlocations. Our instructors combinetechnical expertise with soundinstructional practices to helpindividuals improve job performance,apply and stay abreast of newdevelopments, and transfer newknowledge and skills to wisdom.Certain groupings of seminars havebeen packaged to create SAE CertificatePrograms, another way to enhance one’scredentials.
Engineering AcademiesSAE Engineering Academies areintensive week-long courses designedfor newly hired engineers orexperienced engineers in career
transition who need to quickly developnew skills. Prior to the week, studentsengage in various e-learning activities tocover fundamental concepts. Duringthe week, substantial hands-on practicalexercises and case problems augmenttraditional classroom lecture to providea truly applied learning experience.Engineering Academies are held onceper year on Vehicle Interior Noise,Powertrain Noise, and Diesel EngineTechnology.
e-LearningSAE offers a variety of e-learningexperiences that provide convenient,accessible, and cost-effective learningsolutions for the busy professional.Formats include online courses, live
telephone/webcasts, webinars, CD-ROMs, self-study workbooks, andvideotapes. We are constantly lookingfor new and innovative ways to deliverlifelong learning opportunities directlyto you.
University PartnershipsSAE has formed partnerships withKettering University (formerly GMIInstitute) and Walsh College whichenable individuals to apply their SAEcoursework towards graduate degreeprograms and professional certificates.Take SAE's applied, focused learningopportunities to keep you competitiveon-the-job and, at the same time,advance towards a graduate credential!
Learning Solutions for Today’s Forward Thinking Engineers
For information on SAE’s full range of Professional Development options, call, email, or visit our website.
SAE Professional Development is an international resource for mobility engineering education dedicated to meetingthe learning needs of technical professionals around the world. Professional Development programs includecustomized in-house training, seminars, e-Learning, and engineering academies.
Professional Development
www.sae.orgToll Free 1-877-606-7323or 724-776-4970
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Please note that SAE policy prohibits the audio or videotaping of any of the presentations.
Fundamentals of Gear Design and Application
I.D. #C0223
Duration: 2 Days
Through informative discussions and detailed explanations, this seminar will provide a solid and fundamental understanding of gear geometry, types and arrangements, and design principles. Starting with the basic definitions of gears, conjugate motion, and the Laws of Gearing, those attending will be given the tools needed to understand the inter-relation and coordinated motion operating within gear pairs and multi-gear trains. Basic gear system design process and gear measurement and inspection techniques will also be explained. In addition, the fundamentals of understanding the step-wise process of working through the iterative design process required to generate a gear pair will be reviewed, and attendees will also briefly discuss the steps and issues involved in design refinement and some manufacturing considerations. Also, an explanation of basic gear measurement techniques, how measurement equipment and test machines implement these techniques, and how to interpret the results from these basic measurements will be covered.
Benefits of Attending By attending this seminar, attendees will be able to:
• Describe the "Law of Gearing," conjugate action and specifically, involute profiles • Review the various definitions and terms used in gearing • Identify the function and operation of all gear arrangements • Appraise preliminary design considerations and the gear system design process • Explain practical gear measurement and inspection techniques, tools and equipment • Recognize "Best Practices" in regards to gear system design • Discuss some of the new and automated gear design systems
Who Should Attend The intended audience for this seminar is powertrain engineers, engineering directors and managers, component suppliers, vehicle platform powertrain development specialists, and those involved in the design and application of geared systems and assemblies. This seminar will appeal to anyone who is interested in gears, gear systems, design development or measurement and inspection techniques.
More specifically, anyone responsible for the following will benefit:
• Mechanical power transmission system design, development, durability assessment and application
• Application and development of geared systems technologies • Management of transmission designers and manufacturers • Supply of components and sub-systems to mechanical power transmission system
manufacturers
Prerequisites Attendees should have an undergraduate engineering degree to attend this program. This seminar is intended for powertrain engineers, engineering directors and managers, component suppliers, vehicle platform powertrain development specialists, and those involved in the design and application of geared systems and assemblies. Anyone who is interested in gears, gear systems, design development or measurement and inspection techniques should attend.
Seminar Content DAY ONE
• Principles of Gears o Purpose of gears o Basic concepts -- Law of gearing; common tooth forms o Classification of gears o Definitions and terms used in gearing o Velocity ratio o Pitch surfaces
• Gear Tooth Action o Conjugacy o Profile curves o Surface of action o Profile sliding
• Gear Geometry and Nomenclature o Principle of planes o Tooth nomenclature o Blank nomenclature
• Gear Arrangements o Simple gear train o Compound gear train -- ratios o Epicyclic -- configurations (solar, planetary, star); ratios; tooth number
selection and build requirements; application • Preliminary Design Considerations
o Gear type selection o Preliminary estimate of size o Stress formulations o Gear Drawing Data
DAY TWO
• Gear System Design Process o Calculation of gear tooth data o Gear rating practice
• Gear Design Process o Layout o Root geometry o Backlash
• Gear Measurement and Inspection o Dimension over pins o Pin diameter o Modify pin diameter and dimension over pins o Pin contact point o Charts - involute; lead; red liner o Dimension sheet
• Gear Design Systems and Best Practices o Common proportions o Interchangeability o Tooling considerations o Mounting considerations o Best practices o Application
Instructor(s): W. Mark McVea Dr. William Mark McVea is founder and chief technical officer of KBE+, Inc., an organization that designs and develops complete powertrains for automotive and off-highway vehicles, and also develops and delivers professional development seminars for the automotive industry and its supplier base. Prior to founding KBE+, McVea was a manager of the CAE group within a tier one, powertrain supplier to world automotive markets; a consulting engineer in vehicle dynamics, with Gear Consultants, Inc.; a project manager of traction systems for off-highway vehicles with Clark-Hurth International; and a research laboratory supervisor, developing geared traction devices with Gleason Power Systems, Inc. He also taught and lectured at Purdue, Michigan State and Syracuse universities. Dr. McVea is published extensively on the topics of transmission systems, automated design assistant systems, knowledge systems and knowledge based engineering in general. Dr. McVea holds a BS in mechanical engineering from the Rochester Institute of Technology, a PhD in design engineering from Purdue University, and is a licensed professional engineer. Currently, he is a professor of information technology in the B. Thomas Golisano College of Computing and Information Sciences at the Rochester Institute of Technology.
1.3 CEUs
Fundamentals ofGear Design
andApplication
William M. McVea, Ph.D., P.E.SAE #C0223Copyrighted 2001
Introductions
• William Mark McVea, Ph.D., P.E.– Chief Technical Officer of KBE+, Inc.
– 15+ Years of Geared ProductDesign and Development
– Graduate Work:• Automated Design of Automotive & Off-Highway
Transmissions Using the Techniques of Artificial Intelligence
11
My Expectations
• #1: I want you to feel confident --
• Able to Understand & Correctly Use Gear Terminology
• Basic Concepts of;– Gears– Path of Motion– Transfer of Torque
• Gear Geometry, Development and Layout
• Inspection, Measurement & Application
My Expectations
• You Only Get Out of a CourseWhat You Put Into It
• Ask Lots of QuestionsWhen You Have Them
2
Who Is In Attendance?
• Take a Moment & Find Out Who Is HereI Know, I Know . . .
Nobody Ever Likes Audience Participation
Your Expectations
• Let’s list all the points and topics you want to cover during the next two days
3
Gears Gears ––LetLet’’s Face Its Face It
YaYa’’ Know ThemKnow Them
YaYa’’ Love ThemLove Them
Course Content
• Principles of Gears & Gearing
• Gear Classification
• Tooth Forms & Geometry
• Nomenclature & Definitions
• Design Principles
• Drawing & Layout Techniques / Practices
• Measurement & Inspection
4
Principles of Gears
• Purpose of Gears• Basic Concepts
– Law of Gearing– Common Tooth Forms
• Classification of Gears• Definitions and Terms Used in Gearing
Purpose of Gears
• Transmit Motion Between Shafts • Transmit Power Between Shafts• Modify Torque & Speed by Ratio
– Torque Increases as Speed Decreases– Torque Decreases as Speed Increases
• Change Direction of Power Flow• Change Axis of Power Flow• Split Power Among Multiple Shafts
5
Basic Concepts
• Law of Gearing
• Conjugate Action
• Common Gear Tooth Forms
• Gear Tooth Action
Law of Gearing
• To transmit uniform rotary motion from one shaft to another by means of gear teeth
• The normals of these teeth at all points of contact must pass through a fixed point in the common centerline of the two shafts
6
Rotary Motion
• Transmit rotary motion from one shaft – The Driver or Driving Member
• To a shaft attached to it– The Driven or Driven Member
14
RotaryMotion
A B
Length ‘A’ = Length ‘B’
ζB = (B/A) * ζA
ζB = ζA
Driver Driven
7
15
RotaryMotion
A B
A B
Driver Driven
16
RotaryMotion
A B
A B
Normal to Centerlineof Slot In Arm A
Driver Driven
8
17
RotaryMotion
A B
A B
Normal to Centerlineof Slot In Arm A
Intersection Point BetweenNormal and Line of Action
18
RotaryMotion
A B
Length ‘A’ > Length ‘B’
ζB = (B/A) * ζA
ζB < ζA
A B
Normal to Centerlineof Slot In Arm A
Intersection Point BetweenNormal and Line of Action
9
19
RotaryMotion
A B
Length ‘A’ > Length ‘B’
ζB = (B/A) * ζA
ζB = 0
A B
A BNormal to Centerlineof Slot In Arm A Is Equal
To Zero
Conjugate Action
• Transmit rotary motion from one shaft to a shaft attached to it
• A profile of two mating members that when run in contact produce uniform rotary motion
10
Conjugate Action
Conjugate Action• Transmit rotary motion from one shaft to
a shaft attached to it
• A profile of two mating members that when run in contact produce uniform rotary motion
• The output motion exactly matchesthe input motion
– Disregarding the effect ratio
11
23
Involute ProfileZero Transmission Error Theoretically
Conjugacy
• Conjugate Gear Tooth Action: Is the action between such profiles, which transmit uniform rotary motion
• In essence the gear tooth surfaces are cams in which the common normal to both profiles pass through thePitch Point
12
Definitions & Nomenclature
• Classification of Gears
• Basic Definitions and Terms
• Velocity Ratio
• Pitch Surfaces
Classification of Gears
• Parallel Axis– Spur– Helical– Double Helical
or Herringbone
13
27
Gear TypeDefinition
STRAIGHT BEVEL
Parallel AxisSpur Gears
14
29
Parallel AxisHelical Gears
Parallel AxisDouble Helical or Herringbone Gears
15
Classification of Gears• Parallel Axis
– Spur– Helical– Double Helical
or Herringbone• Nonparallel Axis
– Straight Bevel– Zerol Bevel– Spiral Bevel– Cross-Helical– Face Gears
32
Non-ParallelAxis Gears
16
Intersecting AxesStraight Bevel
34
Intersecting AxesZerol Bevel
17
35
Intersecting AxesSpiral Bevel
36
Intersecting AxesFace Gear
18
Classification of Gears• Parallel Axis
– Spur– Helical– Double Helical
or Herringbone• Nonparallel Axis
– Straight Bevel– Zerol Bevel– Spiral Bevel– Cross-Helical– Face Gears
• NonintersectingNonparallel Axis– Cross-Helical– Worm
• Single-enveloping• Double-enveloping
– Hypoid – Spiroid
NonintersectingNonparallelAxesCross-Helical
19
39
NonintersectingNonparallelAxesWorm
40
NonintersectingNonparallelAxesWorm
20
41
NonintersectingNonparallelAxesSingleEnvelopingWorm
42
NonintersectingNonparallelAxesDoubleEnvelopingWorm
21
43
NonintersectingNonparallelAxesHypoid
44
NonintersectingNonparallelAxesHypoid
22
NonintersectingNonparallelAxesSpiroid
46
NonintersectingNonparallelAxesSpiroid
23
47
NonintersectingNonparallelAxesHelicon
Classification of Gears
• Parallel Axis– Spur– Helical– Double Helical
or Herringbone• Nonparallel Axis
– Straight Bevel– Zerol Bevel– Spiral Bevel– Cross-Helical– Face Gears
• NonintersectingNonparallel Axis– Cross-Helical– Worm
• Single-enveloping• Double-enveloping
– Hypoid – Spiroid– Helicon
• NonintersectingParallel Axis– Basic Rack
24
49
NonintersectingParallel AxesBasic RackSpur
50
NonintersectingParallel Axes
Basic RackHelical
25
Specialty Gear Forms
• Square or Rectangular
• Triangular
• Elliptical
• Scroll
• Multiple Sector
Square or Rectangular
Driver Driven
SpeedRatio
One Revolution of Driver
26
Triangular
Driver Driven
SpeedRatio
One Revolution of Driver
Elliptical
Driver Driven
SpeedRatio
One Revolution of Driver
27
55
Scroll
Driver DrivenSpeed
Ratio
One Revolution of Driver One Revolution of Driver
56
Multiple Sector
Driver DrivenSpeedRatio
One Revolution of Driver
28
Definitions & Nomenclature
• Classification of Gears
• Basic Definitions and Terms
Common Profile Curves
• Involute• Cycloidal• Wildhaber-Novikov• Formate Gearing
• Infinite Number of Shapes that Produce Conjugate Action– With Involute Being the Most Common
29
59
Creation of an Involute
60
Definition ofInvolute
30
Cycloidal
Cycloidal
31
63
Wildhaber-NovikovPinion
Gear
w1
Lines ofCenters
r1
r2
f
Formate Gearing
Generated Form
Non-Generated Form
32
Gear Geometry & Nomenclature
• Ratio
• Tooth Nomenclature
• Gear Nomenclature
• Blank Nomenclature
• Principle Planes
Gears rotate ‘in mesh’Gears are always in ‘pairs’
Ratios
It’s all about‘Leverage’ Gears rotate ‘in mesh’
Gears have a‘radius’
RThat ‘radius’Acts like a lever
The difference in the length of the leverIs the difference in the amount of torque or rotational force it can transmitOr the ‘ratio’ between the gears
R
r
Ratio = R / r You can have multiple‘gear pairs’ to makeOne overall ratio
33
• Number of Gear TeethNumber of Pinion Teeth
• Pitch Diameter of GearPitch Diameter of Pinion
• Base Circle Diameter of GearBase Circle Diameter of Pinion
Ratio
Gear Layout Nomenclature
• Tooth Numbers• Base Circle• Pressure Angle• Pitch Circle• Line of Action• Center Distance
• Face Width• Diametral Pitch• Module• Base Pitch• SAP / EAP• Contact Ratio
34
Tooth Numbers
• Based on Ratio
• 40 Teeth Minimum in Pair Desired
• Minimum Number of Pinion Teeth Selected by Application
Tooth Numbers
• Pinion Tooth Numbers Based on Application
35
General Guide to Selection of Number of Pinion TeethNo. Pinion
TeethDesign Considerations
Probably critical on strength on all but low-hardness pinions. Excellent wear resistance. Favored in high-speed work for quietness.
50
Strength may be more critical than wear on hard steels—about even on medium-hard steels
35
Good balance between strength and wear for hard steels. Contact kept away from critical base-circle region.
25
No undercutting with 20o standard-addendum design19
Used where strength is more important than wear. Requires long addendum15
Smallest practical number with 20o teeth. Takes about 145 percent long addendum to avoid undercut. Poor wear characteristics
10
Subject to high specific sliding and usually have poor wear characteristics
If 20o, outside diameter should be reduced in proportion to tooth thickness to avoid pointed teeth
Requires at least 25o pressure angle and special design to avoid undercutting. Poor contact ratio. Use only in fine pitches
7
Tooth Numbers
• Pinion Tooth Numbers Based on Application• Based on Ratio and Center Diameters;
– Calculate Pitch Diameters– Then Tooth Numbers
36
Numbers of Teeth in Pinion and Gear vs. Pressure Angle and Center Distance
5251504948474645
151412
2524232221201918
42++
39++
36++
3330272523211918
789
10111213141516171819
25Coarse Pitch+
20Fine Pitch+
20Coarse Pitch+
14 1/2Coarse Pitch*
No. of Teeth in Gear and Pressure AngleNo. of Teeth in Pinion
Numbers of Teeth in Pinion and Gear vs. Pressure Angle and Center Distance
444342414039383736353433
202122232425262728293031
25Coarse Pitch+
20Fine Pitch+
20Coarse Pitch+
14 1/2Coarse Pitch*
No. of Teeth in Gear and Pressure AngleNo. of Teeth in Pinion
37
Tooth Numbers
• Pinion Tooth Numbers Based on Application• Based on Ratio and Center Diameters;
– Calculate Pitch Diameters– Then Tooth Numbers
• Spur –– Integer Diametral Pitch (i.e. 1, 2, 3 / use std. hobs)
• Helical –– Normal Diametral Pitch to be Integer
Minimum Number of Pinion Teeth vs. Pressure Angle and Helix Angle Having No Undercut
12
12
12
11
10
10
9
8
7
6
5
14
14
14
13
12
11
11
10
8
7
5
17
17
17
16
15
14
13
12
10
8
7
32
32
31
29
27
25
24
21
18
15
12
0 (spur gears)
5
10
15
20
23
25
30
35
40
45
2522 1/22014 1/2
Normal Pressure Angle, on
Min. No. of Teeth to Avoid UndercutHelix Angle
(deg)
38
Ratio Selection Considerations
• Hunting Tooth Ratio– Number of Teeth in Pinion– And Number of Teeth in the Gear– Have No Common Factor
• Example;– NP = 11– NG = 41
Ratio Selection Considerations
• Why Use A Hunting Tooth Ratio– Good if you intend to lap gears for smooth
running & long life– If a tooth develops a surface imperfection,
then there are multiple contact points to smooth and remove surface abnormality
• Why Not To Use A Hunting Tooth Ratio– If a tooth develops a surface imperfection
it may eventually damage all other teeth
39
Gear Layout Nomenclature
• Tooth Numbers• Base Circle• Pressure Angle• Pitch Circle• Line of Action• Center Distance
• Face Width• Diametral Pitch• Module• Base Pitch• SAP / EAP• Contact Ratio
Base Circle
40
Base Circle
• Theoretical Circle– From which involute tooth profile is derived
82
Base Circle
41
Base Circle
• Theoretical Circle– From which involute tooth profile is derived
• Involute Tooth Profile is Generated– By un-wrapping a string– From the base circle
84
Base Circle
42
Base Circle
• Base Circle Diameter is the;– Pitch Diameter
times– Cosine of the Pressure Angle
)cos(* θPBaseCircle DD =
Base Circle
43
Pressure Angle
PitchCircle
BaseCircle
PressureLine
P
rr
B
φ
φ
Tangent to Tooth Surfaceat Pitch Line
Pressure Angle
• Angle of Tangent to Tooth Surface at Pitch Point: φ ( phi )
• Typical Angles: 14.5, 20, 22.5, 25, 30
• Selection Based on Available Tooling
• Strength vs. Noise Requirements– Lower Pressure Angles Generally Quieter– Higher Pressure Angles are Stronger
44
Pressure Angle
• Select Based on Hob Availability
• Select from Standard Hob PA’s;– 14.5 degrees (older standard)– 20 degrees (common standard)– 25 degrees (for higher strength)– 30 degrees (special applications)
Pitch Circle
45
Pitch Circle
• Theoretical Surfaces of a Pair of Gears Which Would Roll without Slipping
• Pitch Circle Diameter –– Number of Teeth / Diametral Pitch– Circular Pitch
92
NormalPitch
46
Pitch Diameter
• Pitch Diameter =– Number of Teeth / Diametral Pitch
• Base Circle Diameter =– Pitch Diameter * cosine (PA)
• Addendum =– 1.0 / Dp
• Dedendum =– 1.25 / Dp
94
PitchPoint
47
Line of Action
Line of Action
• In Gear Geometry– Path of Action for Involute Gears
48
97
Lineof
Action
Line of Action
• In Gear Geometry– Path of Action for Involute Gears
• The Line of Action– Path of the Contact Point Between the Teeth– As Teeth Roll Through Mesh it Defines a Line
• Straight Line Passing Through Pitch Point• Tangent to Base Circles of Two Mating Gears
49
99
Line ofAction
Line of Action
• In Gear Geometry– Path of Action for Involute Gears
• The Line of Action– Path of the Contact Point Between the Teeth– As Teeth Roll Through Mesh it Defines a Line
• Straight Line Passing Through Pitch Point• Tangent to Base Circles of Two Mating Gears• Intersection of Two Base Circles
– Defines the Pitch Point
50
CenterDistance
Center Distance
Center Distance
• Distance Between the Centers of Two Mating Gears
• Distance Between the Center of the Support Shafts
• Sets Overall Dimension of Gearbox
51
103
Face Width
Face Width
• Width of Gear Tooth at Pitch Circle
• Actual is Measured Width
• Effective is Length of Contact Pattern
• Effective is Less than or Equal Actual
• Face Width is a Function of a Pair
• Effective is Equal for Pinion and Gear
52
Diametral Pitch
• Ratio - Teeth Number : Pitch Diameter
• Pd = N / D(D for Gear, d for Pinion)
• English Only Concept
• Corresponding SI Concept is Module
Module
• M = D / N (Gear)
• Or M = d / n (Pinion)
• M = 25.4 / Pd
• Inverse Relationship to Diametral Pitch
53
Base Pitch
Base Pitch
• Pitch Along Base Circle
• Pb is the Circumference of the Base Circle
/ Number of Teeth
• Any two gears with the same Base Pitch will roll together
54
109
SAP / EAP
SAP / EAP
• Start of Active Profile– Point on Tooth which is First Contacted by the
Tip of the Mate• End of Active Profile
– Point on Tooth which Contacts the SAP of the Mate
• EAP May be Tip of Tooth• Or Chamfer at Tip
55
Active Tooth Profile
• Define Active Tooth Profile
• Length of Tooth Profile– Which Actually Comes into Contact with the
Mating Tooth
Tooth ActionPinion
Driver
GearDriven
Angle ofApproach
Angle ofRecess
Angle ofApproach
Angle ofRecess
56
Tooth Action
• Angle of Approach– Arc of Pitch Circle – From Point of First Contact Along Pitch Circle– To the Pitch Point Between Gear & Pinion– Used to Calculate
• Length of Contact• Contact Ratio
Tooth Action
• Angle of Recess– Arc of Pitch Circle– From Pitch Point Between Gear & Pinion – To the Last Point of Contact Along Pitch
Circle– Used to Calculate
• Length of Contact• Contact Ratio
57
Contact Ratio
Contact Ratio
• Average Number of Teeth in Contact
• Length of Line of Action / Circular Pitch * Cosine of Pressure Angle
• mc = Lab / p * Cos φ
58
Gear Tooth Nomenclature
• Addendum• Dedendum• Whole Depth• Working Depth• Clearance• Circular Thickness• Chordal Thickness
• Chordal Addendum• Backlash• Fillet Radius• Top Land• Bottom Land• Circular Pitch• Tooth Flank
Addendum
59
Addendum
• Measured from;– Pitch Circle– Top of Tooth
• a = 1.0 / Pd– Standard Tooth Proportions
Dedendum
60
Dedendum
• Measured from;– Pitch Circle– Root of Tooth
• b = 1.25 / Pd– Standard Tooth Proportions
Whole Depth
61
Whole Depth
• Sum of;– Addendum– Dedendum
• Total Depth of Tooth
Working Depth
62
Working Depth
• Sum of;– Addendum of Gear– Addendum of Pinion
• Active Depth of Teeth
Clearance
63
Clearance
• Difference Between;– Whole Depth– Working Depth
• To Avoid Contact Between Top Land and Root of Mate
Circular Thickness
64
Circular Thickness
• Arc Tooth Thickness on Pitch Line
Chordal Thickness
65
Circular Thickness• Arc Tooth Thickness on Pitch Line
• Length of Chord of Circular Thickness• Used to Measure Tooth Thickness
– With Chordal Addendum
Chordal Thickness
Chordal Addendum
66
Chordal Addendum
• Dimension from;– Tip– Center Span of Chordal Thickness
Backlash
67
Backlash
• Clearance Between Tooth Profiles• Permits Smooth Operation• Address Manufacturing Tolerance Stack• Difference Between
– Circular Pitch– Sum of Circular Thickness of
• Gear• Pinion
136
Fillet Radius
68
Fillet Radius
• Stress Concentration Reduction
• Increases Tool Life
138
Top Land
69
Top Land
• Product of Tooth Thickness and Depth• Minimum Required to Heat Treat• Possibly Limits Strength Balance
• Function of Point Width of Tool
Bottom Land
140
Circular Pitch
70
Circular Pitch
• Sum of;– Tooth Thickness of Pinion– Tooth Thickness of Gear– Backlash
• p = π / Pd
Gear Tooth Nomenclature
• Addendum• Dedendum• Whole Depth• Working Depth• Clearance• Circular Thickness• Chordal Thickness
• Chordal Addendum• Backlash• Fillet Radius• Top Land• Bottom Land• Circular Pitch• Tooth Flank
71
143
Tooth Flank
144
Nomenclature of Gear Tooth Details
72
Gear Circle Nomenclature
146
Helical Gears
73
Involute Helicoid
• Paper Cut as Parallelogram Shape
Involute Helicoid
2πr
H
CylinderAxis
β
λ
74
Involute Helicoid
• Paper Cut as Parallelogram Shape
• Wrapped Around Base Cylinder
InvoluteHelicoid
HelixTangent
H
Helix
r
λ
75
Involute Helicoid
• Paper Cut as Parallelogram Shape
• Wrapped Around Base Cylinder
• Unwrapped as to Generate Involute
152
Involute Helicoid
76
Involute Helicoid
• Paper Cut as Parallelogram Shape
• Wrapped Around Base Cylinder
• Unwrapped as to Generate Involute
• Paper Edge Defines Involute Helicoid
154
Involute Helicoid
77
InvoluteHelicoid Involute
Curves
rb
r
Gear Contact Comparison
• Spur Gear– Initially a Line– Extends Across Entire Face– Parallel to Axis of Rotation
• Helical Gear– Initially a Point– Becomes a Line as Teeth Engage– Diagonal across Face of Tooth
78
Helical Gear Contact
• Gradual Engagement of Teeth
• Smooth Transfer of Load Tooth to Tooth
• Transmit Heavy Loads at High Speeds
• Contact Ratio– Face Contact Ratio– Transverse Contact Ratio– Modified (Total Effective) Contact Ratio
158
Helical GearInvolute Surface and Line of Contact
Face Width
Lengthof
Action
NormalBase Pitch
Line of Contact
Base HelixAngle
79
Helical Gear Nomenclature
• Hand of Helix
• Helix Angle
• Lead Angle
• Lead
• Transverse Pitch
• Normal Pitch
• Normal PressureAngle
• TransversePressure Angle
Helical Gear Nomenclature
• Hand of Helix
80
Hand of Helix
Pitch Cylinders
Lead Angle
Plane of Rotation
Helix
Contact Point
Lead – 6”Lead – 12”
R.H.L.H.
Axis
Helical Gear Nomenclature
• Hand of Helix
• Helix Angle
81
Helix Angle
Pitch Cylinders
Lead Angle
Plane of Rotation
Helix
Contact Point
Lead – 6”Lead – 12”
R.H.L.H.
Axis
Helical Gear Nomenclature
• Hand of Helix
• Helix Angle
• Lead Angle
82
Lead Angle
Pitch Cylinders
Lead Angle
Plane of Rotation
Helix
Contact Point
Lead – 6”Lead – 12”
R.H.L.H.
Axis
Helical Gear Nomenclature
• Hand of Helix
• Helix Angle
• Lead Angle
• Lead
83
Lead
Pitch Cylinders
Lead Angle
Plane of Rotation
Helix
Contact Point
Lead – 6”Lead – 12”
R.H.L.H.
Axis
Lead
Pitch Cylinders
Lead Angle
Plane of Rotation
Helix
Contact Point
Lead – 6”Lead – 12”
R.H.L.H.
Axis
84
Helical Gear Nomenclature
• Hand of Helix
• Helix Angle
• Lead Angle
• Lead
• Transverse Pitch
TransversePitch
85
Helical Gear Nomenclature
• Hand of Helix
• Helix Angle
• Lead Angle
• Lead
• Transverse Pitch
• Normal Pitch
NormalPitch
86
Helical Gear Nomenclature
• Hand of Helix
• Helix Angle
• Lead Angle
• Lead
• Transverse Pitch
• Normal Pitch
• Normal PressureAngle
NormalPressure
Angle
87
Helical Gear Nomenclature
• Hand of Helix
• Helix Angle
• Lead Angle
• Lead
• Transverse Pitch
• Normal Pitch
• Normal PressureAngle
• TransversePressure Angle
TransversePressure
Angle
88
Helical Gear Nomenclature
• Pitch Helix
• Normal Plane
• TransversePressure Angle
• NormalPressure Angle
• Normal Helix
• TransverseCircular Pitch
• NormalCircular Pitch
Helical Gear Nomenclature
• Pitch Helix
89
Helical Gear Nomenclature
Helical Gear Nomenclature
• Pitch Helix
• Normal Plane
90
Helical Gear Nomenclature
Helical Gear Nomenclature
• Pitch Helix
• Normal Plane
• TransversePressure Angle
91
Helical Gear Nomenclature
Helical Gear Nomenclature
• Pitch Helix
• Normal Plane
• TransversePressure Angle
• NormalPressure Angle
92
Helical Gear Nomenclature
Helical Gear Nomenclature
• Pitch Helix
• Normal Plane
• TransversePressure Angle
• NormalPressure Angle
• Normal Helix
93
Helical Gear Nomenclature
Helical Gear Nomenclature
• Pitch Helix
• Normal Plane
• TransversePressure Angle
• NormalPressure Angle
• Normal Helix
• TransverseCircular Pitch
94
Helical Gear Nomenclature
Helical Gear Nomenclature
• Pitch Helix
• Normal Plane
• TransversePressure Angle
• NormalPressure Angle
• Normal Helix
• TransverseCircular Pitch
• NormalCircular Pitch
95
Helical Gear Nomenclature
Internal & External Gears
96
Internal Gear Nomenclature
Bevel Gear Nomenclature
• Shaft Angle• Pitch Angle• Spiral Angle • Face Angle • Root Angle• Back Angle• Front Angle
• Crown• Pitch Apex• Pitch Apex to Crown • Outer Cone Distance• Mean Cone Distance
97
195
Bevel Gear Nomenclature
196
Bevel Gear Nomenclature
98
Bevel Gear Nomenclature
See Nomenclature Listing in the Gear Handbookby Darle Dudley 2nd Edition, Pg. 2.39, Table 2.7
Operating Dimensions
• Theoretical Center Distance
• Operating (Spread) Center Distance
• Operating Pitch Diameter of;– Pinion– Gear
• Theoretical Pressure Angle
• Operating Pressure Angle
99
Center Distance
Cd
Theoretical Center DistanceC = d + D
2.0
Where: C is the Theoretical Operating Center Distance
d is the Pitch Diameter of the Pinion
D is the Pitch Diameter of the Gear
Theo.
100
Operating (Spread) Center Distance
• Common Practice:– Increase Center Distance Slightly– Increases Operating Pressure Angle;
• If Operating Center Distance is 1.7116% Larger Operating Pressure Angle will be 22.5 deg.s Using 20 deg. Hobs
– Make use of available Tooling• Hobs• Cutters• Shapers
Operating Pitch Diametersd = 2.0 * C
mG + 1.0
Where: dOper. is the Operating Pitch Diameter of the Pinion
DOper. is the Operating Pitch Diameter of the Gear
C is the Theoretical Operating Center Distance
mG is the Ratio;Gear Teeth / Pinion Teeth
D = mG * dOper. Oper.
101
Theoretical Pressure Angle
• Given by Design
• Pressure Angle of Cutting Tool
• Angle Between Plane Normal to Pitch Surface and Normal to Tooth Surface at Pitch Point
Pressure Angle
BaseCircles
PitchCircles
PressureAngle
PitchPoints
φ
102
Operating Pressure Angleφ = cos-1 (cos φTheo.)
m`
Where: φ is the Pressure Angle
m` is the Spread Ratio;
Operating Pitch Diameter / Theoretical Pitch Diameter
Oper.
Gear Geometry & Nomenclature
• Principle Planes
• Blank Nomenclature
• Gear Nomenclature
• Tooth Nomenclature
103
Principle Planes
• Normal Plane– Normal to the tooth at the pitch point– Normal to the pitch plane
Principle PlanesSpur Gears
104
Principle Planes
• Normal Plane– Normal to the tooth at the pitch point– Normal to the pitch plane
• Transverse Plane– Plane perpendicular to both the axial and the
pitch planes
Principle PlanesHelical Gears
105
Basic Rack
• What is the Basic Rack• How is it used to
– Define Gears– Design gears– Design Cutters / Tools– Why would one use it
Basic Rack
• As the Pitch Circle increases in size, approaching infinite, it becomes a Rack
• Circle with an Infinite Radius is a Plane
106
Principle PlanesHelical Gears
Basic Rack
• As the Pitch Circle increases in size, approaching infinite, it becomes a Rack
• Circle with an Infinite Radius is a Plane
• Pitch Surface becomes a Plane– Which has Transnational Motion– While Rolling with the Pitch Cylinder of its
Mate
107
Function of a Rack
• A Rack is the Basic Member for a Family of Gears Conjugate to it
• Two Basic Racks are Complimentary if;– They can be fitted together face-to-face– With coincident pitch & tooth surfaces
Interchangeable Gears
• Basis for Interchangeability is that the Basic Member be Complimentary to Itself
108
Design of Gear Cutting Tools
• Hob design derived from the theory of Basic Rack
• Hobs have Straight Cutting Sides• Hob Representing the Basic Rack
– Rolls with the Work Piece– Through a specific Relationship of Motion– Such that it Generates the Involute Profile
• Motion is both relative Rotation and Translation
Interchangeable Gears
• Basis for Interchangeability is that the Basic Member be Complimentary to Itself
109
Fillet Curve
• Shape is a Trochoid– Generated by Radius at Corner of Hob / Tool– May be Produced With a Protuberance Hob
• Provides Greater Clearance for Shaving / Grinding
Definition of a Trochoid• Generally -- Trochoid is any curve that is
the locus of a point fixed to a curve A,while A rolls on another curve Bwithout slipping
• Specifically -- Trochoid is defined as thetrace of a point, fixed on a circle,that rolls along a line
110
Definition of a Trochoid• Generally -- Trochoid is any curve that is the locus
of a point fixed to a curve A, while A rolls onanother curve B without slipping
• Specifically -- Trochoid is defined as the trace of apoint, fixed on a circle, that rolls along a line
Standard AGMA & ANSI Tooth Systemsfor Spur Gears
Design Item Coarse Pitch Fine Pitch[up to 20P full depth] [20P and up full depth]
Pressure Angle φ 20o 25o 20o
Addendum a 1.000 / P 1.000 / PDedendum b 1.250 / P 1.200 / P + 0.002Working Depth hk 2.000 / P 2.000 / PWhole Depth (minimum) ht 2.250 / P 2.200 / P + 0.002Circular Tooth Thickness t π / (2 * P) 1.5708 / PFillet Radius rf 0.300 / P Not Standardized
(of Basic Rack)
Basic Clearance (minimum) c 0.250 / P 0.200 / P + 0.002Clearance rf 0.350 / P 0.350 / P + 0.002
(Shaved or Ground Teeth)
Minimum Number of Pinion Teeth 18 12 18Minimum Number of Teeth per Pair 36 24 36Minimum Top Land Width to 0.25 / P Not Standardized
111
Gear Pair Action
• Principle Plane
• Line of Action
• Surface of Action
• Sliding
Velocity Ratio
• Ratio of the Pitch Diameters
• Ratio of Tooth Numbers
• Ratio of Base Circle Diameter
112
Pitch Surfaces
• Imaginary Planes, Cylinders or Cones that roll together without slipping
• The Pitch Surfaces are:– Planes for the Basic Rack– Cylinders for Spur and Helical gears– Cones for Bevel Gears– Hyperboloids for Hypoid Gears
Parallel Axis Pitch Surfaces
PitchCylinders
X1
X2
PitchPlane
PitchElement
113
Principle PlanesBevel Gears
228
Intersecting Axis Pitch Surfaces
PitchCones
X1
X2
PitchPlane
PitchElement
114
229
Hyperboloid Pitch Surfaces
Gear Tooth Pitch Point
Involute
DedendumCircle
BaseCircle
PitchCircle
AddendumCircles
Involute
Base Circle
Pitch Circle
Dedendum Circle
115
231
Line of Action
Line of Action
• In Gear Geometry– The path of action for involute gears
• The Line of Action is– The path the contact point between teeth follows
while in contact during mesh
• It is the Straight Line passing through the Pitch Point– Tangent to base circles of the two mating gears– Intersection of base circles defines the Pitch Point
116
Surface of Action
• Point of Contact is Actually a Line– Called the Line of Contact
Surface of Action
117
Surface of Action
• Point of Contact is Actually a Line– Called the Line of Contact
• As Conjugate Action Progresses– Line of contact describes surface in space– Defined as the Surface of Action
Surfaceof Action
118
Sliding
• Efficiency Factor Due to Frictional Loss
• Failure Mechanism:– Wear / Scoring / Scuffing
– Heat Generation
– Lubricant Film Breakdown
• Two Types:– Profile– Length-Wise
Profile Sliding
• Due to the constant change in radius of involute relative to each gear (as they are in mesh)
• The point of instantaneous contact on one member must slide relative to the other
119
Length-Wise
• Sliding along the face length of the tooth
• Basic gear tooth geometry similar to screw thread action
Length-Wise
120
Length-WiseContact Lines As
Helix Tangents
Base CylinderHelix
Sliding Direction
• Spur Profile only
• Helical Profile only
• Bevel Profile only
• Cross-Helicals Both
• Spiroids Both
• Hypoids Both
• Worm Gears Length-Wise only
121
Preliminary Design Considerations
• Gear Type Selection
• Preliminary Estimate of Size
• Stress Formulations
• Gear Drawing Data
Gear Type Selection
• Why would I select a Spur Gear– Simplest Gear Form– Lower Cost– Lower Thrust Load
• Why would I select a Helical Gear– Greater Load Carrying Capacity– Quieter and Smoother Operation– More Uniform Motion Transmission
122
Gear Type Selection
• Why would I select a Bevel Gear– Transmit Power Through an Angle
• Non-Parallel Shaft Axes
Gear Type Selection
• Why would I select a Straight Bevel– Lower Cost– Lower Thrust Load– Simplest Design
• Why would I select a Spiral Bevel– Longer Effective Face Width– Greater Contact Ratio
• For Same Packaging
123
Gear Type Selection
• Why would I select a Hypoid Gear– Transmit Power Through an Angle– Transmit Power with Off-set Shafts
• Straddle Mount Both Members• Clearance Design Considerations• Alignment Design Considerations
Gear Type Selection
• Why would I select a Spiroid Gear / Helicon– High Number of Teeth in Contact– High Ratios Achieved (Dudley pg. 2-13)
• Why would I select a Worm Gear– Very High Ratios– Very High Contact
124
Other Types of Gears
• Skew Bevel Gears
• Face Gears
• Beveloid Gears
• Cross Axis Helical Gears
• Herringbone Gears
Other Types of Gears
• Worm Gearing– Cylindrical– Single - Enveloping– Double - Enveloping
125
Gear Meshing Possibilities
YesYesYesNoNoNoYesHypoid
YesNo*No*NoNoNoYesSpiral Bevel
YesNo*NoNoNoNoYesZerol Bevel
YesNo*NoNo*NoNo*YesStraight Bevel
YesNo*No*NoYesYesYesHelical
YesNo*NoYesYesYesYesSpur
Pinion of 16
orMoreTeeth
Pinionof 5
Teeth
OneToothPinion
Inter-change-ability
Pinionand
InternalGear
Pinion and rack
Pinionand Gear
TypeOf
GearTeeth
Gear Meshing Possibilities
YesNo*NoNoNoNoYesFace Gear
No*YesYesNoNoNoYesSpiroid
YesNo*NoYesNoYesYesBeveloid
No*YesYesNoNoNoYesDouble-enveloping Worm
No*YesYesNoNo*No*YesSingle-enveloping Worm
YesYesYesYesNoYesYesCrossed Helical
Pinion of 16
orMoreTeeth
Pinionof 5
Teeth
OneToothPinion
Inter-change-ability
Pinionand
InternalGear
Pinion and rack
Pinionand Gear
TypeOf
GearTeeth
126
How to Obtain Ratios
NoNoYes3Simple Eplicyclic
NoNoYes2Planoid
YesYesNo2Spiroid
YesYesYes2Worm
NoNoYes2Face
YesYesYes2Hypoid
NoNoYes2Bevel
NoNoYes2Helical
NoNoYes2Spur
2Single Reduction:
100:150:15:1
Ratio RangeMinimum Number of Toothed Parts
Kind of Arrangement
General Design ProcedureGeneral Design Procedurefor Parallel Axis Gearsfor Parallel Axis Gears
127
General Design Procedurefor Parallel Axis Gears
Gear Design Methodology
• Synthetic K Factor Method
• Proportional to Hertzian Contact Stress– Based on Roller Bearing Analysis
• Used to Estimate Preliminary Gear Size
• Based on Application and Material
Synthetic K Factor Method
• Synthetic K Factor
K = Wt * ( mG + 1 )d * F mG
– Where;– K = 1.5 to 1000 based on Material and Application– WT = Tangential Driving Load (Wt = 2 * TP / d)– D = Pinion Pitch Diameter– F = Face Width– mG = Ratio (NG / NP)
128
K Factor by Application
• Automotive Transmission– Steel, 58 HRC…………………………… K = 1.5
• General Purpose Industrial Drive– Steel 575 BHN / Steel 575 BHN...……. K = 800
• Small Commercial– Steel 350 BHN / Phenolic……………… K = 75
• Small Gadget– Steel 200 BHN / Zinc…………………… K = 25
• Small Gadget– Steel 200 BHN / Brass or Aluminum…. K = 25
Procedure
• For a Given Application• Assume a K Factor From;
– Use Table 2.15– On Pg. 2.45– “Handbook of Practical Gear Design” by
Darle Dudley
129
Derive Base Equation
• Solving for the Face Width and Pinion Diameter, as one term;
d * F = Wt * ( mG + 1 )K mG
Best Practices
• Good Practice;– The Ratio “F / d” Should Not Exceed 1.0
• F – Face Width• d – Diameter of the smallest diameter member
– If F / d > 1.0, Then;• The effect of shaft deflection must be checked• As it affects effective face width
130
General Design Procedurefor Parallel Axis Gears
• Compare Calculated Face Width, F to;– Packaging Requirements– Manufacturability Issues– Iterate As Required
• Procedure to Calculate Center Distance– More Involved– Requires More Iterations
Next Step
• Once Diameter, Face Width are Selected
• With Given Ratio, mG
• Use Chart to Select Initial Number of Pinion Teeth
131
Pinion Tooth Number Guideline
NP / NG
NPmax
Stress Formulations• The Synthetic K Factor Method Provides
Preliminary Sizing
• Next Step is to Calculate Bending and Contact Stress
• Surface Durability– Approximately 120 to 150 (ksi)
• Dudley Pg.s 13.17 thru 13.24
• Bending– Approximately 35 to 50 (ksi)
• Dudley Pg.s 13.28 thru 13.38
132
General Survey of Power and Efficiency
608095745 (1,000)Double-enveloping Worm
608095560 (750)Cylindrical Worm
60809575 (100)Crossed Helical
608095745 (1,000)Hypoid
983,730 (5,000)Spiral Bevel
98745 (1,000)Zerol bevel
98370 (500)Straight Bevel
9822,400 (30,000)Helical
982,240 (3,000)Spur
Single Reduction:
100:1 Ratio
50:1 Ratio
5:1 Ratio
Typical Efficiency, %Nominal Maximum kW (hp)
Kind of Arrangement
Gearbox Relative Size and Weight
SmallPlanoid
SmallSmallSmallSpiroid
SmallSmallSmallSmallHypoid
SmallSmallSmallWorm
SmallSpur, Helical, BevelSingle Reduction:
100:150:120:15:1Kind of ArrangementRatio Range
133
Gearbox Relative Size and Weight
Very Small
Compound Planetary
Very Small
Very Small
Double-reduction Planetary
Very Small
Simple Planetary
Epicyclic Gears:
Very Small
SmallMultiple Power Path, Helical Gears
Medium Size
Single Power Path, Helical GearsDouble Reduction:
100:150:120:15:1Kind of ArrangementRatio Range
Compound Gear Train
• N – Number of Teeth
• n – Rotational Speed– Note: Gears 4 & 5 Rotate at Same Speed
• Final Speed;
n6 = N2 N3 N5 n2
N3 N4 N6
(rpm)
134
Gear Arrangements
• Simple Gear Train• Compound Gear Train
– Ratios• Epicyclic
– Configurations (Solar, Planetary, Star)– Ratios– Tooth Number Selection and Build
Requirements– Application
Planetaries
135
Epicyclical Trains
• Sun Gear• Several Planet
Pinions• Ring Gear• Planet-Pinion Carrier• Input & Output Shafts
• Single / Simple Epicyclic Trains– Planetary– Star– Solar
• Compound Epicyclic– Planetary– Star– Solar
Simple Epicyclical Trains
Ring Gear
Sun Gear
PlanetCarrier
Planet Pinion
136
Epicyclic GeartrainPlanetary Configuration
Fixed Annulusor
Ring Gear
Planet WheelsRotate AboutSpindles
PlanetCarrier
Sun Gear
Epicyclic GeartrainStar Configuration
RotatingAnnulus
PlanetsRotate on Spindles
FixedPlanet Carrier
RotatingSun Gear
137
Epicyclic GeartrainSolar Configuration
RotatingPlanet Carrier
RotatingAnnulus
PlanetsRotate on Spindles
FixedSun Gear
Simple Epicyclical TrainRatio Ranges
• Planetary– 3:1 to 12:1
• Star– 2:1 to 11:1
• Solar– 1.2:1 to 1.7:1
138
Simple Epicyclical TrainRatio Equations
Revolution of
Operational Condition Sun Carrier Ring
Sun Fixed 0 1 1 + Ns / Nr
Carrier Fixed 1 0 - Ns / Nr
Ring Fixed 1 + Nr / Ns 1 0
Simple Epicyclical TrainBuild Requirements
• Nr -- Number of Ring Gear Teeth• Ns -- Number of Sun Gear Teeth• q -- Number of Planet Gears
• (Nr + Ns) / q Must Equal an Integer
139
Compound Planetary Gear
Planet Gear
Rotating Carrier
Sun Gear
Fixed Annulusor Ring Gear
Rotating Carrier
Housing
Compound Star Gear
Star Gear
Rotating Carrier
Sun Gear
Rotating Annulusor Ring Gear
Fixed Carrier
Housing
Star Pinion
140
Compound Epicyclical TrainRatio Ranges
• Planetary– 6:1 to 25:1
• Star– 5:1 to 24:1
• Solar– 1.05:1 to 2.20:1
Compound Epicyclical TrainRatio Equations
Revolution of
OperationalCondition Sun Carrier Ring
Sun Fixed 0 1 1 + Ns * Npr Nps * Nr
Carrier Fixed 1 0 - Ns * Npr Nps * Nr
Ring Fixed 1 + Nps * Nr Ns * Npr
1 0
141
Compound Epicyclical TrainBuild Requirements
• Nr -- Number of Ring Gear Teeth• Ns -- Number of Sun Gear Teeth• q -- Number of Planet Gears• Npr -- Number of Planet Gear Teeth in
contact with the Ring Gear• Nps -- Number of Planet Gear Teeth in
contact with the Sun Gear
• (Nr * Nps - Ns * Npr ) / qMust Equal an Integer
Epicyclical Design Considerations
• Load Share Between Planets• High Planet Pin Bearing Loads• Rotating Balance of Planet Carrier• Complicated Assembly• More Sensitive to Debris Entrainment• More Lubrication Required
142
Two CommonCompound Epicyclical
• Ravigneaux -- Planetary– Two Separate Sun Gears– Two Sets of Planet Gears– One Planet Carrier
RavigneauxCompound Epicyclical
ShortPlanet Gear
LongPlanet Gear
ReverseSun Gear(Input)Forward
Sun Gear
Ring Gear(Output)Rear View
143
RavigneauxCompound Epicyclical
Output
Input
RearFacing
LongPlanet Gears
Planet Carrier
Ring Gear
ForwardSun Gear
ShortPlanet Gear
ReverseSun Gear
Two CommonCompound Epicyclical
• Ravigneaux -- Planetary– Two Separate Sun Gears– Two Sets of Planet Gears– One Planet Carrier
• Simpson -- Planetary– Two Separate Ring Gears– Two Separate Planet Carriers– One Common Sun Gear
144
SimpsonCompound Epicyclical
FrontPlanetGear
ThrustWasher
FrontAnnulus
Sun Gear
Driving ShellRear PlanetGear Assembly
Rear AnnulusGear
Low & ReverseDrum
Drive Shell
SnapRing
SunGear
ThrustWasher
InputShell Snap Ring
145
Gear Selection Considerations
• NVH -- Noise, Vibration & Harshness
• Durability
• Power Density
• Support Requirements
• Lubrication
NVH
• Helical;– Smoother Operation– Quieter
• Tooth Contact Ratio;– Axial Contact ratio– Transverse Contact Ratio
• Spur Gears;– Only Transverse of 1.2 to 1.5 Typical
146
Durability
• Bending Stresses & Contact Stresses Should be Balanced for Application
• Helical will be Smaller than Spur
• Carburized or Carbo-Nitrided
• Surface Finish Key Control
Power Density
• Helical Planetaries Provide Highest PD
• Spur Gears Lowest Cost / Lowest PD
• Helical are More Expensive to Mfg.
• Helical Gears Require More Expensive Support
• Helical Require Better Control of Mounting and Positioning
147
Support
• Helical Gears Require Axial & Radial Thrust
• Spurs Only Radial
• Double Helical Gears Produce Only Radial
• Very Expensive to Manufacture
• Spur Gears Most Tolerant of Misalignment
Lubrication
• All Gear Teeth Require Lubricant Flow
• Pressure Lubrication;– 20% - 30% Incoming Mesh (lubrication)– 70% - 80% Output Mesh (cooling)
• Splash or Dip Method;– Case Design to Provide Adequate Supply
• Forced Lubrication;– Shaft Design to Put Lubrication where Needed
148
Lubricant Cooling
• Internal Lubricant Circulation
• Convective Air-Cooling In-Situ
• Natural Flow Exchange
• Forced Cooling– Radiator– Circulation Pump
Drawing Information• Gear Data Tabular Information
• Gear Measurement & Inspection
• Tolerances– Spur– Helical– Bevel
• Straight• Spiral
149
300
150
Lead Tolerance Chart
Lead Tolerance Data
151
Tooth Profile Crown Note
304
152
Gear Measurement and InspectionTooth Thickness
• Gear Tooth Caliper
• Pin Diameter
• Dimension Over Pins
• Modify Pin Diameter and Dimension Over Pins
• Pin Contact Point
• Span Measurement
153
Drawing Information
• Gear Data Tabular Information
• Gear Measurement & Inspection
Gear Measurement and InspectionTooth Thickness
InvoluteTest
ConcentricityRunout Takenwith a BallChecker
360o
Number of Teeth
DiameterOver Pins
Caliper Settingfor chordaltooth thicknessPitch Check
154
Tooth Chordal Dimensions
Addendum
ArcThickness
(t)
ChordalThicknes
s(tc)
Chordal Addendum
310
Gear ToothCaliper
155
Gear Tooth Caliper
• Used to Measure Gear Tooth Thickness
• At Pitch Line
• Affected by Gear Diameter Variance– Undersize Blank
• Measure Too Large– Oversize Blank
• Measure Too Small
• Technique Sensitive
Measurement Over Pins
• Most Accurate Method
• Not Affected by;– Blank Dimensional Variances– OD Run Out
• Affected by;– Tooth Spacing Errors– Profile Errors
156
Measurement Over Pins
• Helical Gears– Use Balls or Dumbbell Pins– Due to Curvature of Tooth Space– Critical for Odd Number of Teeth
• Method for Parallel Axis Gears Only
MeasurementOver Pins
157
Pin Sizes Used to Check the Tooth Thickness of Spur Gears
1.4401.68014 ½ to 25oInternal, standard designs
1.92014 ½ to 25oExternal, long-addendum pinion design
1.6801.920
1.72814 ½ to 25oExternal, standard or near standard proportions
Pin Diameter Constant
Pressure AngleType of Tooth
Calculate Dimension Over Pins
• For Standard Pin Diameter
• External Spur Gears
• Even Tooth Numbers– Dudley Practical, Pg. 9.21 – Table &
Method
• Odd Tooth Numbers– Dudley Practical, Pg. 9.21 – Table &
Method
158
Calculate Dimension Over Pins
• For Standard Pin Diameter
• Internal Spur Gears
• Even Tooth Numbers– Dudley Practical, Pg. 9.27 – Table &
Method
• Odd Tooth Numbers– Dudley Practical, Pg. 9.27 – Table &
Method
Pin Contact Point
• Tangent Point of contact between pin and tooth, must be on tooth
• Outside edge of pin must be beyond the tooth OD
• Inner edge of pin must not contact root
• Pin should contact tooth at or above the middle of the tooth height
159
Calculate Dimension Over Pins
• For Standard Pin Diameter
• External Helical Gears
• Even Tooth Numbers– Dudley Practical, Pg. 9.32 – Table &
Method
• Odd Tooth Numbers– Dudley Practical, Pg. 9.32 – Table &
Method
Calculate Dimension Over Pins
• For Standard Pin Diameter
• Internal Helical Gears
• Even Tooth Numbers– Dudley Practical, Pg. 9.27 – Table &
Method
• Odd Tooth Numbers– Dudley Practical, Pg. 9.27 – Table &
Method
160
Span Measurement
M
Block Measurement of Gear Teeth
• Pb – Normal Base Pitch
• tPBC– Circular Tooth Thickness at Base Circle
Where;tPBC
= B * ν (for spur gears)
tPBC= B * ν * sin (θn) (for helical gears)
sin (θt)
ν = tPt+ Inv (θt)
PD
M = 3 Pb + tPBC
161
Gear Measurement and Inspection
• Involute Chart
• Lead Chart
• Red Liner Chart
Involute Chart
0o 6o 12o18o
162
InvoluteChart
Involute Measurement
• Measure of Gear Tooth Profile• Rolling Gear on Base Circle• Produces Contact Traces of Profile• Relation Between Roll Angle / Profile• Variations in Tooth Geometry
– Deviations from Straight Line on Chart• Run Out / Gear Wobble Effect Trace• Measure at Several Axial Positions
163
Involute Measurement Results
True ProfileTrue Involute
Form Diameter
Actual Involute
+ 5 - 5
0
0
Theoreticalor
TrueInvolute
“V” Type Chart
AcceptableInvolute
Profiles
164
329
Equivalent Band Chart- 5
0
0
TrueInvolute
AcceptableInvolute
Profiles
- 5
“K” Type Chart
20% ofTotal
Roll Angle
- 5
0
- 5
165
Modified “K” ChartWith Tip
andFlank Relief
0
- 8- 3
- 8- 31
2
3
4
5
OD
PD
TIF
Involute Measurement ResultsMinus Pressure Angle
Actual ProfileTrue Involute
Form Diameter
Actual Involute
166
Involute Measurement ResultsPlus Pressure Angle
Actual ProfileTrue Involute
Form Diameter
Actual Involute
Involute Measurement ResultsUndercut & Tip Chamfer
Actual Profile
Form Diameter
True Involute
Actual Involute
167
Gear Measurement and Inspection
• Involute Chart
• Lead Chart
Lead
• Axial Advance of a Helix for One Complete Turn
168
Lead
Pitch Cylinders
Lead Angle
Plane of Rotation
Helix
Contact Point
Lead – 6”Lead – 12”
R.H.L.H.
Axis
Lead
• Axial Advance of a Helix for One Complete Turn
• Lead Tolerance– Is the total allowable lead variation
• Lead Variation– Is measured in the Direction Normal to the
Specified Lead of the Gear
169
Lead Chart
• Lead– Usually Specified Between Points– Represent 85% of Face Width
• Teeth are Often Chamfered– Points A & D
340
Lead ChartGood Profile
170
341
Lead ChartAcceptable Profile
342
Lead ChartConcave Profile
171
Lead ChartProfile withProtuberance
Lead ChartProfile withProtuberance
172
Lead ChartProfileOutside Gauge
Lead Chart
• Lead– Usually Specified Between Points– Represent 85% of Face Width
• Teeth are Often Chamfered– Points A & D
• Crest of Crown– Specifies Position Along Tooth– Differing Based on Design & Application
173
Crown Tolerance
348
Crown Tolerance
174
Long & Short Lead
Lead of Crowned Teeth
SpurGear
HelicalGear
175
Lead of Tapered Teeth
SpurGear
HelicalGear
Lead & Involute ErrorCauses
• Machine Setup
• Machine Capability & Condition
• Condition of Work Holding Equipment
• Die Wear / Dull Tooling
• Handling
• Heat Treat Changes
176
Gear Measurement and Inspection
• Involute Chart
• Lead Chart
• Red Liner Chart
Red Liner
• Double Flank Tester• Master Gear
177
Red LinerSchematic of Gear Rolling Device
Red Liner
• Double Flank Tester• Master Gear• Motion of Center of Test Gear
– Recorded (Trace)– During Roll with Master
178
357
Red LinerTypical Chart
Red Liner
• Double Flank Tester• Master Gear• Motion of Center of Test Gear
– Recorded (Trace)– During Roll with Master
• Measures Variation of Test Gear– Composite Test & Master Gear Error– Master Variation Assumed to be Negligible
179
Red Liner Data
• Total Composite Error
360
Red LinerTypical Chart
180
Red Liner Data
• Total Composite Error
• Tooth to Tooth Composite Error
• Tooth to Tooth Error
362
Red LinerTypical Chart
181
Red Liner Data
• Total Composite Error
• Tooth to Tooth Composite Error
• Tooth to Tooth Error
• Runout
364
Red LinerTypical Chart
182
Red Liner Limitations
• Test Run with Zero Backlash– Not at Operating Pitch Diameter
• Test Run with No-Load
• Both Flanks are Engaged
• Can Not Differentiate Between– Involute Errors– Lead Errors– Profile Modification Errors– Combination of Errors
Single Flank Gear Tester
• Measures Similar Parameters– With Backlash– On Operating Pitch Diameters
183
367
Single Flank Gear TesterSchematic
Single Flank Gear Tester
• Measures Similar Parameters– With Backlash– On Operating Pitch Diameters
• Measures Transmission Error
• More Accurate Representation of Error
184
CMM
• Index Variation
• Lead Variation
• Involute Variation
• Topological Plots
• Generates Surface of Actual Tooth Form
370
Topological Plotof a Gear ToothSurface from anAutomated CMM
185
Gear Design Systems and Best Practices
• Common Proportions
• Interchangeability
• Tooling Considerations
• Mounting Considerations
• Application
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186
Gear Seminar Reference List1. “Gear Handbook” by Darle W. Dudley. First Edition, McGraw-Hill, Inc. 1962.
2. “Dudley’s Gear Handbook, Second Edition” by Dennis P. Townsend. McGraw-Hill, Inc. 1992. (ISBN: 0-07-017903-4)
3. “Spur Gears” by Earle Buckingham. First Edition, McGraw-Hill, Inc. 1928.
4. “Handbook of Practical Gear Design” by Darle W. Dudley. First Edition, Technomic Publication, Inc. 1994. (ISBN: 1-56676-218-9)
5. “A Treatise of Gear Wheels” by George B. Grant. Twenty-First Edition, Philadelphia GEAR Works Inc. 1899. Reprinted 1980.
6. “Gear Geometry and Applied Theory” by Faydor Litvin. First Ed, Prentice-Hall, Inc. 1994.(ISBN: 0-13-211095-4)
7. “The Internal Gear”, by The Fellows Corporation. Seventh Ed, Fellows Corporation. 1978.
8. “Encyclopedic Dictionary of Gears and Gearing” by D.W. South and R.H. Ewert. McGraw-Hill, Inc., New York, New York. 1994. (ISBN: 0-07-059795-0)
9. “MAAG Gear Book” by MAAG Gear Company Ltd. 1990.
10.“Gleason Fachworter” by The Gleason Works. Alfred Wentzky & Co. 1967.
Gear Seminar Reference List1. “Mechanical Engineers Reference Handbook” by Edward H. Smith. Twelfth Edition, Society of
Automotive Engineers, Inc. 1994. (ISBN: 1-56091-450-5)
2. “Machinery’s Handbook” by Erik Oberg, Franklin Jones, and Holbrook Horton. Twenty-third Edition, Industrial Press, Inc. 1914. Revised 1989. (ISBN: 0-8311-1200-X)
3. “Engineering Unit Conversions” by Micheal Lindeburg. Professional Publications, Inc. 1988.(ISBN: 0-932276-89-X)
4. “Mechanics of Materials” by E. P. Popov. Second Edition, Prentice-Hall, Inc. 1976.
5. “Formulas for Stress and Strain” by Raymond Roark and Warren Young. Fifth Edition, McGraw-Hill, Inc. 1975. (ISBN: 0-07-053031-9)
6. “Mechanical Engineering Design” by Joseph Shigley. Third Edition, McGraw-Hill, Inc. 1977.(ISBN: 0-07-056881-2)
7. “Mechanical Designs and Systems Handbook”, by Harold Rothbart. Second Edition, McGraw-Hill Inc. 1985. (ISBN: 0-07-054020-9)
8. “Mark’s Standard Handbook for Mechanical Engineers ” by Eugene Avallone and Theodore Baumeister. McGraw-Hill Inc. 1978. (ISBN:0-07-004127-X)
187
Gear Seminar Reference List9. “Rules of Thumb for Mechanical Engineers” by J. Edward Pope. Gulf Publishing Company.
1997.
10.“Mechanisms and Mechanical Devices Sourcebook” by Nicholas Chironis and Neil Sclater. Second Edition, McGraw-Hill, Inc. 1996. (ISBN: 0-07-011256-4)
11. “Stress Concentration Factors” by R. E. Peterson. John Wiley and Sons, Inc. 1974.
188