SAE Gear Design Course - C0223_th003

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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


Intersection Point BetweenNormal and Line of Action

18

RotaryMotion

A B

Length ‘A’ > Length ‘B’

ζB = (B/A) * ζA

ζB < ζA

A B


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



• 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



• 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


Elliptical

Driver Driven

SpeedRatio


27

55

Scroll

Driver DrivenSpeed

Ratio

One Revolution of Driver One Revolution of Driver

56

Multiple Sector

Driver DrivenSpeedRatio


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


• 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


• 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


• Wrapped Around Base Cylinder

InvoluteHelicoid

HelixTangent

H

Helix

r

λ

75

Involute Helicoid



• Unwrapped as to Generate Involute

152

Involute Helicoid

76

Involute Helicoid



• 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


• 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


• Hand of Helix

• Helix Angle

81

Helix Angle

Pitch Cylinders

Lead Angle

Plane of Rotation

Helix

Contact Point


R.H.L.H.

Axis


• Hand of Helix

• Helix Angle

• Lead Angle

82

Lead Angle

Pitch Cylinders

Lead Angle

Plane of Rotation

Helix

Contact Point


R.H.L.H.

Axis


• Hand of Helix

• Helix Angle

• Lead Angle

• Lead

83

Lead

Pitch Cylinders

Lead Angle

Plane of Rotation

Helix

Contact Point


R.H.L.H.

Axis

Lead

Pitch Cylinders

Lead Angle

Plane of Rotation

Helix

Contact Point


R.H.L.H.

Axis

84


• Hand of Helix

• Helix Angle

• Lead Angle

• Lead


TransversePitch

85


• Hand of Helix

• Helix Angle

• Lead Angle

• Lead


• Normal Pitch

NormalPitch

86


• Hand of Helix

• Helix Angle

• Lead Angle

• Lead


• Normal Pitch


NormalPressure

Angle

87


• Hand of Helix

• Helix Angle

• Lead Angle

• Lead


• Normal Pitch



TransversePressure

Angle

88


• Pitch Helix

• Normal Plane


• NormalPressure Angle

• Normal Helix

• TransverseCircular Pitch

• NormalCircular Pitch


• Pitch Helix

89



• Pitch Helix

• Normal Plane

90



• Pitch Helix

• Normal Plane


91



• Pitch Helix

• Normal Plane



92



• Pitch Helix

• Normal Plane



• Normal Helix

93



• Pitch Helix

• Normal Plane



• Normal Helix


94



• Pitch Helix

• Normal Plane



• Normal Helix


• NormalCircular Pitch

95


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


196


98


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



• Internal Spur Gears


Method


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



• External Helical Gears


Method


Method



• Internal Helical Gears


Method


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


• 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


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


• 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


180

Red Liner Data


• Tooth to Tooth Composite Error

• Tooth to Tooth Error

362


181

Red Liner Data


• Tooth to Tooth Composite Error

• Tooth to Tooth Error

• Runout

364


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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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)

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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.

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