Corporate Learning Solutions Discover what more than 100 companies already know: bringing SAE learning solutions in-house for groups of employees maximizes time, saves expense, enhances learning, and increases staff cohesion. Each year, we work with many companies to address their unique learning needs through custom designed in-house training. Customization is as simple as conducting one of our publicly offered seminars and incorporating company data; or as involved as assessing needs, designing a fresh curriculum, and measuring outcomes. Traditional classroom or blended delivery using e- learning formats are available. Seminars SAE regularly offers more than 100 high quality, 1-3 day technical seminars at our Automotive Headquarters in Troy, Michigan and at other select locations. Our instructors combine technical expertise with sound instructional practices to help individuals improve job performance, apply and stay abreast of new developments, and transfer new knowledge and skills to wisdom. Certain groupings of seminars have been packaged to create SAE Certificate Programs, another way to enhance one’s credentials. Engineering Academies SAE Engineering Academies are intensive week-long courses designed for newly hired engineers or experienced engineers in career transition who need to quickly develop new skills. Prior to the week, students engage in various e-learning activities to cover fundamental concepts. During the week, substantial hands-on practical exercises and case problems augment traditional classroom lecture to provide a truly applied learning experience. Engineering Academies are held once per year on Vehicle Interior Noise, Powertrain Noise, and Diesel Engine Technology. e-Learning SAE offers a variety of e-learning experiences that provide convenient, accessible, and cost-effective learning solutions for the busy professional. Formats include online courses, live telephone/webcasts, webinars, CD- ROMs, self-study workbooks, and videotapes. We are constantly looking for new and innovative ways to deliver lifelong learning opportunities directly to you. University Partnerships SAE has formed partnerships with Kettering University (formerly GMI Institute) and Walsh College which enable individuals to apply their SAE coursework towards graduate degree programs and professional certificates. Take SAE's applied, focused learning opportunities to keep you competitive on-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 meeting the learning needs of technical professionals around the world. Professional Development programs include customized in-house training, seminars, e-Learning, and engineering academies. Professional Development www.sae.org Toll Free 1-877-606-7323 or 724-776-4970 031614 [email protected]
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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.
The information, representations, opinions, and recommendations contained in the lectures
and hardcopy material are those of the speaker(s) and not of the Society of Automotive
Engineers. This material may be copyright protected. No part of this publication may be
reproduced in any form without the expressed, written permission of the speaker(s).
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
• 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
• 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
• 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.