SAE Gear Design Course - C0223_th003

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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. 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 deve lopment specialists, and those involved in the design and application of geared systems and assemblies. a ssemblies. 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 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 o Gear Tooth Action Conjugacy o Profile curves o o Surface of action Profile sliding o Gear Geometry and Nomenclature Principle of planes o Tooth nomenclature o Blank nomenclature o Gear Arrangements Simple gear train o Compound gear train -- ratios o Epicyclic -- configurations (solar, planetary, star); ratios; tooth number o selection and build requirements; application Preliminary Design Considerations Gear type selection o Preliminary estimate of size o Stress formulations o o Gear Drawing Data

DAY TWO •

•

Gear System Design Process o Calculation of gear tooth data Gear rating practice o Gear Design Process Layout o Root geometry o Backlash o

•

•

Gear Measurement and Inspection Dimension over pins o Pin diameter o Modify pin diameter and dimension over pins o Pin contact point o o Charts - involute; lead; red liner Dimension sheet o Gear Design Systems and Best Practices o Common proportions Interchangeability o Tooling considerations o Mounting considerations o Best practices o 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 Co nsultants, 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 Co llege of Computing and Information Sciences at the Rochester Institute of Technology.

1.3 CEUs

Fundamentals of Gear Design and Application William M. McVea, Ph.D., P.E. SAE #C0223

Copyrighted 2001

Introductions • William Mark McVea, Ph.D., P.E. – Chief Technical Officer of KBE+, Inc. – 15+ Years of Geared Product Design and Development – Graduate Work: • Automated Design of Automotive & Off-Highway Transmissions Using the Techniques of Artificial Intelligence

1

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 Course What You Put Into It • Ask Lots of Questions When You Have Them

2

Who Is In Attendance? • Take Take a Moment Moment & Find Find Out Out Who Who Is Here Here I

Know, I Know . . . Nobody Ever Likes Audience Participation

Your Expectations • Let’s list all all the the points points and topics topics you want to cover during the next two days

3

Gears – Let’s Face It Ya’ Know Them Ya’ Love Them

Course Content • Prin Princi cipl ples es of of Gears Gears & Geari Gearing ng • Gear Gear Clas Classi sifi fica cati tion on • Toot Tooth h Form Forms s & Geom Geomet etry ry • Nomen Nomencl clat ature ure & Defi Defini niti tions ons • Desi Design gn Prin Princi cipl ples es • Drawin Drawing g & Layout Layout Techniq Techniques ues / Practic Practices es • Meas Measure uremen mentt & Inspec Inspecti tion on

4

Principles of Gears • Purp Purpos ose e of of Gea Gears rs • Basi Basic c Conc Concep epts ts – Law of Geari Gearing ng – Common Common Tooth Tooth Forms Forms

• Clas Classi sifi fica cati tion on of Gea Gears rs • Defini Definitio tions ns and and Terms Terms Used Used in Gear Gearing ing

Purpose of Gears • Transm Transmit it Motio Motion n Betwe Between en Shaf Shafts ts • Transm Transmit it Powe Powerr Betwe Between en Shaf Shafts ts • Modify Modify Torque Torque & Speed Speed by Rati Ratio o – Torque Increases Increases as Speed Decreases Decreases – Torque Decreases Decreases as Speed Speed Increases Increases

• Change Change Direct Direction ion of Powe Powerr Flow Flow • Chan Change ge Axi Axis s of Pow Power er Flo Flow w • Split Split Power Power Amon Among g Multip Multiple le Shaft Shafts s

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

Rotary Motion

A

B

Driver

Driven

Length ‘A’ = Length ‘B’ B

= (B/A) *

B

=

A

A

14

7

A

Rotary Motion

B

A

B

Driver

Driven

15

A

Rotary Motion

A

Driver

B

B

Driven

Normal to Centerline of Slot In Arm A

16

8

A

Rotary Motion

B

A

B

Intersection Point Between Normal and Line of Action Normal to Centerline of Slot In Arm A

17

A

Rotary Motion

B

A

B

Intersection Point Between Normal and Line of Action Normal to Centerline of Slot In Arm A

Length ‘A’ > Length ‘B’ B

= (B/A) *

B

<

A

A 18

9

A

Rotary Motion

B

A

Normal to Centerline of Slot In Arm A

B

A

B

Is Equal To Zero

Length ‘A’ > Length ‘B’ B

= (B/A) *

B

= 0

A 19

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 matches the input motion – Disregarding the effect ratio

11

Involute Profile Zero Transmission Error Theoretically

23

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 the Pitch 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

Gear Type Definition

STRAIGHT BEVEL

27

Parallel Axis Spur Gears

14

Parallel Axis Helical Gears

29

Parallel Axis Double 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

Non-Parallel Axis Gears

32

16

Intersecting Axes Straight Bevel

Intersecting Axes Zerol Bevel

34

17

Intersecting Axes Spiral Bevel

35

Intersecting Axes Face Gear

36

18

Classification of Gears • Parallel Axis

• Nonintersecting Nonparallel Axis

– Spur – Helical – Double Helical or Herringbone

– Cross-Helical – Worm • Single-enveloping

• Nonparallel Axis

• Double-enveloping

– Straight Bevel – Zerol Bevel – Spiral Bevel – Cross-Helical – Face Gears

– Hypoid – Spiroid

Nonintersecting Nonparallel Axes Cross-Helical

19

Nonintersecting Nonparallel Axes Worm

39

Nonintersecting Nonparallel Axes Worm

40

20

Nonintersecting Nonparallel Axes Single Enveloping Worm

41

Nonintersecting Nonparallel Axes Double Enveloping Worm

42

21

Nonintersecting Nonparallel Axes Hypoid

43

Nonintersecting Nonparallel Axes Hypoid

44

22

Nonintersecting Nonparallel Axes Spiroid

Nonintersecting Nonparallel Axes Spiroid

46

23

Nonintersecting Nonparallel Axes Helicon

47

Classification of Gears • Parallel Axis

• Nonintersecting Nonparallel Axis

– Spur – Helical – Double Helical or Herringbone

– Cross-Helical – Worm • Single-enveloping • Double-enveloping

• Nonparallel Axis

– Hypoid – Spiroid – Helicon

– Straight Bevel – Zerol Bevel – Spiral Bevel – Cross-Helical – Face Gears

• Nonintersecting Parallel Axis – Basic Rack

24

Nonintersecting Parallel Axes Basic Rack Spur

49

Nonintersecting Parallel Axes Basic Rack Helical

50

25

Specialty Gear Forms • Square or Rectangular • Triangular • Elliptical • Scroll • Multiple Sector

Square or Rectangular Speed Ratio

Driver

Driven One Revolution of Driver

26

Triangular Speed Ratio

Driver


Elliptical

Speed Ratio

Driver


27

Scroll

Speed Ratio

Driven

Driver

One Revolution of Driver


55

Multiple Sector

Speed Ratio

Driver

Driven


28

56

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

Creation of an Involute

59

Definition of Involute

60

30

Cycloidal

Cycloidal

31

Wildhaber-Novikov w1

Pinion

f

r 1

r 2 Gear

Lines of Centers

Formate Gearing Generated Form

Non-Generated Form

32

63

Gear Geometry & Nomenclature • Ratio • Tooth Nomenclature • Gear Nomenclature • Blank Nomenclature • Principle Planes

Ratios

It’s all about ‘Leverage’

Gears have a ‘radius’ Gears rotate ‘in mesh’ Gears are always in ‘pairs’

R That ‘radius’ Acts like a lever

R r Ratio = R / r

You can have multiple ‘gear pairs’ to make One overall ratio

The difference in the length of the lever Is the difference in the amount of torque or rotational force it can transmit Or the ‘ratio’ between the gears

33

Ratio • Number of Gear Teeth Number of Pinion Teeth • Pitch Diameter of Gear Pitch Diameter of Pinion • Base Circle Diameter of Gear Base Circle Diameter of Pinion

Gear Layout Nomenclature • Tooth Numbers

• Face Width

• Base Circle

• Diametral Pitch

• Pressure Angle

• Module

• Pitch Circle

• Base Pitch

• Line of Action

• SAP / EAP

• Center Distance

• 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 Teeth No. Pinion Teeth 7

Design Considerations Requires at least 25 o pressure angle and special design to avoid undercutting. Poor contact ratio. Use only in fine pitches If 20o, outside diameter should be reduced in proportion to tooth thickness to avoid pointed teeth Subject to high specific sliding and usually have poor wear characteristics

10

Smallest practical number with 20 o teeth. Takes about 145 percent long addendum to avoid undercut. Poor wear characteristics

15

Used where strength is more important than wear. Requires long addendum

19

No undercutting with 20 o standard-addendum design

25

Good balance between strength and wear for hard steels. Contact kept away from critical base-circle region.

35

Strength may be more critical than wear on hard steels—about even on medium-hard steels

50

Probably critical on strength on all but low-hardness pinions. Excellent wear resistance. Favored in high-speed work for quietness.

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 No. of Teeth in Pinion

No. of Teeth in Gear and Pressure Angle 14 1/2 Coarse Pitch*

20 Coarse Pitch+

20 Fine Pitch+

7

42++

8

39++

9

36++

25 Coarse Pitch+

10

25

33

15

11

24

30

14 12

12

52

23

27

13

51

22

25

14

50

21

23

15

49

20

21

16

48

19

19

17

47

18

18

18

46

19

45

Numbers of Teeth in Pinion and Gear vs. Pressure Angle and Center Distance No. of Teeth in Pinion

No. of Teeth in Gear and Pressure Angle 14 1/2 Coarse Pitch*

20

44

21

43

22

42

23

41

24

40

25

39

26

38

27

37

28

36

29

35

30

34

31

33

20 Coarse Pitch+

37

20 Fine Pitch+

25 Coarse Pitch+

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 Min. No. of Teeth to Avoid Undercut Helix Angle (deg)

Normal Pressure Angle, o n 14 1/2

20

22 1/2

25

0 (spur gears)

32

17

14

12

5

32

17

14

12

10

31

17

14

12

15

29

16

13

11

20

27

15

12

10

23

25

14

11

10

25

24

13

11

9

30

21

12

10

8

35

18

10

8

7

40

15

8

7

6

45

12

7

5

5

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

• Face Width

• Base Circle

• Diametral Pitch

• Pressure Angle

• Module

• Pitch Circle

• Base Pitch

• Line of Action

• SAP / EAP

• Center Distance

• Contact Ratio

Base Circle

40

Base Circle • Theoretical Circle – From which involute tooth profile is derived

Base Circle

82

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

Base Circle

84

42

Base Circle • Base Circle Diameter is the; – Pitch Diameter times

– Cosine of the Pressure Angle

D BaseCircle

=D

P

* cos(θ )

Base Circle

43

Pressure Angle P

Tangent to Tooth Surface at Pitch Line

Pitch Circle Pressure Line

r B r Base Circle

Pressure Angle • Angle of Tangent to Tooth Surface at Pitch ( phi ) Point: • 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

Normal Pitch

92

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

Pitch Point

94

47

Line of Action

Line of Action • In Gear Geometry – Path of Action for Involute Gears

48

Line of Action

97


• 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

Line of Action

99


• 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

Center Distance

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

Face Width

103

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 • Or

(Gear)

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

SAP / EAP

109

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 Action Pinion Driver

Angle of Approach

Angle of Approach Gear Driven

56

Angle of Recess

Angle of Recess

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

58

Gear Tooth Nomenclature • Addendum

• Chordal Addendum

• Dedendum

• Backlash

• Whole Depth

• Fillet Radius

• Working Depth

• Top Land

• Clearance

• Bottom Land

• Circular Thickness

• Circular Pitch

• Chordal Thickness

• 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

Chordal Thickness • Length of Chord of Circular Thickness • Used to Measure Tooth Thickness – With Chordal Addendum

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

Fillet Radius

136

68

Fillet Radius • Stress Concentration Reduction • Increases Tool Life

Top Land

138

69

Top Land • Product of Tooth Thickness and Depth • Minimum Required to Heat Treat • Possibly Limits Strength Balance

Bottom Land • Function of Point Width of Tool

Circular Pitch

140

70

Circular Pitch • Sum of; – Tooth Thickness of Pinion – Tooth Thickness of Gear – Backlash

• p =

/ Pd

Gear Tooth Nomenclature • Addendum

• Chordal Addendum

• Dedendum

• Backlash

• Whole Depth

• Fillet Radius

• Working Depth

• Top Land

• Clearance

• Bottom Land

• Circular Thickness

• Circular Pitch

• Chordal Thickness

• Tooth Flank

71

Tooth Flank

143

Nomenclature of Gear Tooth Details

144

72

Gear Circle Nomenclature

Helical Gears

146

73

Involute Helicoid • Paper Cut as Parallelogram Shape

Involute Helicoid Cylinder Axis

H

2 r

74

Involute Helicoid • Paper Cut as Parallelogram Shape • Wrapped Around Base Cylinder

Involute Helicoid

r

Helix

H

Helix Tangent

75

Involute Helicoid • Paper Cut as Parallelogram Shape • Wrapped Around Base Cylinder • Unwrapped as to Generate Involute

Involute Helicoid

152

76

Involute Helicoid • Paper Cut as Parallelogram Shape • Wrapped Around Base Cylinder • Unwrapped as to Generate Involute • Paper Edge Defines Involute Helicoid

Involute Helicoid

154

77

Involute Helicoid

Involute Curves

r b 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

Helical Gear Involute Surface and Line of Contact Face Width

t t a c n o f C o e i n L

Normal Base Pitch

Length of Action

Base Helix Angle 158

79

Helical Gear Nomenclature • Hand of Helix

• Transverse Pitch

• Helix Angle

• Normal Pitch

• Lead Angle

• Normal Pressure Angle

• Lead

• Transverse Pressure Angle


80

Hand of Helix Plane of Rotation

Pitch Cylinders Lead Angle

Helix

Contact Point

Axis L.H. R.H.

Lead – 6” Lead – 12”

Helical Gear Nomenclature • Hand of Helix • Helix Angle

81

Helix Angle Plane of Rotation


Helix

Contact Point

Axis L.H. R.H.


Helical Gear Nomenclature • Hand of Helix • Helix Angle • Lead Angle

82

Lead Angle Plane of Rotation


Helix

Contact Point

Axis L.H. R.H.


Helical Gear Nomenclature • Hand of Helix • Helix Angle • Lead Angle • Lead

83

Lead Plane of Rotation

Pitch Cylinders

Helix

Lead Angle Contact Point

Axis L.H. R.H.



Pitch Cylinders Lead Angle Contact Point

Axis L.H. R.H.


84

Helix



• Helix Angle • Lead Angle • Lead

Transverse Pitch

85



• Helix Angle

• Normal Pitch

• Lead Angle • Lead

Normal Pitch

86



• Helix Angle

• Normal Pitch

• Lead Angle


• Lead

Normal Pressure Angle

87



• Helix Angle

• Normal Pitch

• Lead Angle


• Lead


Transverse Pressure Angle

88

Helical Gear Nomenclature • Pitch Helix

• Normal Helix

• Normal Plane

• Transverse Circular Pitch


• Normal Circular Pitch



89

Helical Gear Nomenclature

Helical Gear Nomenclature • Pitch Helix • Normal Plane

90


Helical Gear Nomenclature • Pitch Helix • Normal Plane • Transverse Pressure Angle

91


Helical Gear Nomenclature • Pitch Helix • Normal Plane • Transverse Pressure Angle • Normal Pressure Angle

92



• Normal Helix

• Normal Plane • Transverse Pressure Angle • Normal Pressure Angle

93



• Normal Helix

• Normal Plane


• Transverse Pressure Angle • Normal Pressure Angle

94



• Normal Helix

• Normal Plane



• Normal Circular Pitch


95


Internal & External Gears

96

Internal Gear Nomenclature

Bevel Gear Nomenclature • Shaft Angle

• Crown

• Pitch Angle

• Pitch Apex

• Spiral Angle

• Pitch Apex to Crown

• Face Angle

• Outer Cone Distance

• Root Angle

• Mean Cone Distance

• Back Angle • Front Angle

97

Bevel Gear Nomenclature

195


196

98


See Nomenclature Listing in the Gear Handbook by 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

C d

Theoretical Center Distance C

Theo.

=

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

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 Diameters d

Oper.

=

D

2.0 * C

Oper.

=

mG * d

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

101

/ Pinion Teeth

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

Pitch Circles

Base Circles

Pressure Angle Pitch Points

102

Operating Pressure Angle =

cos-1 (cos

Oper.

Theo.)

m`

Where:

is the Pressure Angle m` is the Spread Ratio; Operating Pitch Diameter

/ Theoretical Pitch Diameter

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 Planes Spur 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 Planes Helical 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 Planes Helical 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 B without slipping • Specifically -- Trochoid is defined as the trace 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 on another curve B without slipping • Specifically -- Trochoid is defined as the trace of a point, fixed on a circle, that rolls along a line

Standard AGMA & ANSI Tooth Systems for Spur Gears Design Item

Coarse Pitch

Fine Pitch

[ up to 20 P f ull dep th ]

[ 20 P an d up ful l d ep th]

20o

20o

25o

Pressure Angle

φ

Addendum

a

1.000 / P

1.000 / P

Dedendum

b

1.250 / P

1.200 / P + 0.002

Working Depth

hk

2.000 / P

2.000 / P

Whole Depth (minimum)

ht

2.250 / P

2.200 / P + 0.002

Circular Tooth Thickness

t

π / (2 * P)

Fillet Radius

rf

0.300 / P

Not Standardized

Basic Clearance ( minimum)

c

0.250 / P

0.200 / P + 0.002

Clearance

r f

0.350 / P

0.350 / P + 0.002

1.5708 / P

(of Basic Rack)

(Shaved or Ground Teeth)

Minimum Number of Pinion Teeth

18

Minimum Number of Teeth per Pair

36

Minimum Top Land Width to

12

18

24

36

0.25 / P

111

Not Standardized

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 Pitch Plane

X1 Pitch Element

X2 Pitch Cylinders

113

Principle Planes Bevel Gears

Intersecting Axis Pitch Surfaces X1

Pitch Plane

Pitch Element

Pitch Cones

X2

228

114

Hyperboloid Pitch Surfaces

229

Gear Tooth Pitch Point Dedendum Circle Pitch Circle Base Circle Involute Addendum Circles

Involute Pitch Circle Base Circle Dedendum Circle

115

Line of Action

231

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

Surface of 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-Wise Contact Lines As Helix Tangents

Base Cylinder Helix

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 Type

Pinion

Of

Pinion

Gear

and Gear

Teeth

Pinion and Interand Internal changerack ability Gear

One

Pinion

Tooth

of 5

Pinion

Teeth

Pinion of 16 or More Teeth

Spur

Yes

Yes

Yes

Yes

No

No*

Yes

Helical

Yes

Yes

Yes

No

No*

No*

Yes

Straight Bevel

Yes

No*

No

No*

No

No*

Yes

Zerol Bevel

Yes

No

No

No

No

No*

Yes

Spiral Bevel

Yes

No

No

No

No*

No*

Yes

Hypoid

Yes

No

No

No

Yes

Yes

Yes

Gear Meshing Possibilities Type Of Gear Teeth

Pinion

Pinion Pinion Pinion and InterOne Pinion of 16 or and Internal change- Tooth and of 5 ability Pinion Teeth More Gear rack Gear Teeth

Face Gear

Yes

No

No

No

No

No*

Yes

Crossed Helical

Yes

Yes

No

Yes

Yes

Yes

Yes

Single-enveloping Worm

Yes

No*

No*

No

Yes

Yes

No*

Doubleenveloping Worm

Yes

No

No

No

Yes

Yes

No*

Beveloid

Yes

Yes

No

Yes

No

No*

Yes

Spiroid

Yes

No

No

No

Yes

Yes

No*

126

How to Obtain Ratios Kind of Arrangement

Single Reduction:

Minimum Number of Toothed Parts

Ratio Range 5:1

50:1

100:1

2

Spur

2

Yes

No

No

Helical

2

Yes

No

No

Bevel

2

Yes

No

No

Hypoid

2

Yes

Yes

Yes

Face

2

Yes

No

No

Worm

2

Yes

Yes

Yes

Spiroid

2

No

Yes

Yes

Planoid

2

Yes

No

No

3

Yes

No

No

Simple Eplicyclic

General Design Procedure for Parallel Axis Gears

127

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 –F

= Pinion Pitch Diameter = 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 Procedure for 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 NPmax

NP / NG

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 Kind of Arrangement

Nominal Maximum kW (hp)

Typical Efficiency, % 5:1 Ratio

50:1 Ratio

100:1 Ratio

Single Reduction: Spur

2,240 (3,000)

98

Helical

22,400 (30,000)

98

Straight Bevel

370 (500)

98

Zerol bevel

745 (1,000)

98

Spiral Bevel

3,730 (5,000)

98

Hypoid

745 (1,000)

95

80

60

Crossed Helical

75 (100)

95

80

60

Cylindrical Worm

560 (750)

95

80

60

95

80

60

Double-enveloping Worm 745 (1,000)

Gearbox Relative Size and Weight Ratio Range Kind of Arrangement

5:1

20:1

50:1

100:1

Small

Small Small

Small

Small Small

Small

Small Small

Single Reduction: Spur, Helical, Bevel

Small

Worm Hypoid

Small

Spiroid Planoid

Small

133

Gearbox Relative Size and Weight Ratio Range Kind of Arrangement

5:1

20:1

50:1

Double Reduction: Single Power Path, Helical Gears

Medium Size

Multiple Power Path, Helical Gears

Small

Very Small

Epicyclic Gears: Simple Planetary

Very Small

Compound Planetary

Very Small

Double-reduction Planetary

Very Small

Very Small

Compound Gear Train •

N – Number of Teeth

•

n –

Rotational Speed

– Note: Gears 4 & 5 Rotate at Same Speed

• Final Speed; n6 =

N 2 N 3 N 5 N 3 N 4 N 6

134

n2

(rpm)

100:1

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

• Single / Simple Epicyclic Trains

• Several Planet Pinions

– Planetary – Star – Solar

• Ring Gear • Planet-Pinion Carrier

• Compound Epicyclic

• Input & Output Shafts

– Planetary – Star – Solar

Simple Epicyclical Trains Ring Gear

Sun Gear

Planet Carrier Planet Pinion

136

Epicyclic Geartrain Planetary Configuration Planet Wheels Rotate About Spindles

Fixed Annulus or Ring Gear

Planet Carrier

Sun Gear

Epicyclic Geartrain Star Configuration Planets Rotate on Spindles Rotating Annulus

Rotating Sun Gear

Fixed Planet Carrier

137

Epicyclic Geartrain Solar Configuration Planets Rotate on Spindles Rotating Planet Carrier

Fixed Sun Gear

Rotating Annulus

Simple Epicyclical Train Ratio Ranges • Planetary – 3:1 to 12:1

• Star – 2:1 to 11:1

• Solar – 1.2:1 to 1.7:1

138

Simple Epicyclical Train Ratio Equations Revolution of Operational Condition

Sun

Carrier

Ring

Sun Fixed

0

1

1 + Ns / Nr

Carrier Fixed

1

0

- Ns / Nr

1 + Nr / Ns

1

0

Ring Fixed

Simple Epicyclical Train Build 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 Fixed Annulus or Ring Gear

Planet Gear

Housing

Sun Gear

Rotating Carrier Rotating Carrier

Compound Star Gear Rotating Annulus or Ring Gear

Star Gear

Housing Sun Gear

Fixed Carrier

Rotating Carrier

Star Pinion

140

Compound Epicyclical Train Ratio Ranges • Planetary – 6:1 to 25:1

• Star – 5:1 to 24:1

• Solar – 1.05:1 to 2.20:1

Compound Epicyclical Train Ratio Equations Revolution of Operational Condition

Sun

Carrier

Ring

Sun Fixed

0

1

1 + Ns * Npr Nps * Nr

Carrier Fixed

1

0

- Ns * Npr Nps * Nr

1 + Nps * Nr Ns * Npr

1

0

Ring Fixed

141

Compound Epicyclical Train Build 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 ) / q Must 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 Common Compound Epicyclical • Ravigneaux -- Planetary – Two Separate Sun Gears – Two Sets of Planet Gears – One Planet Carrier

Ravigneaux Compound Epicyclical Short Planet Gear

Long Planet Gear Reverse Sun Gear (Input)

Forward Sun Gear

Ring Gear (Output)

Rear View

143

Ravigneaux Compound Epicyclical Long Planet Gears

Ring Gear Planet Carrier

Input Reverse Sun Gear

Forward Sun Gear

Short Planet Gear

Rear Facing Output

Two Common Compound Epicyclical • Ravi Ravign gnea eaux ux -- Plan Planet etar ary y – Two Separa Separate te Sun Gears Gears – Two Sets Sets of Planet Gears – One Planet Planet Carri Carrier er

• Sim Simpson pson -- Plan Planet etar ary y – Two Separate Ring Gears – Two Separate Separate Planet Planet Carriers Carriers – One Commo Common n Sun Gear Gear

144

Simpson Compound Epicyclical Thrust Washer

Front Annulus

Driving Shell

Rear Annulus Gear

Rear Planet Gear Assembly

Sun Gear

Front Planet Gear

Low & Reverse Drum

Drive Shell Input Shell Thrust Washer Sun Gear Snap Ring

145

Snap Ring

Gear Selection Considerations Considerations • NVH NVH -- Nois Noise, e, Vib Vibra rati tion on & Hars Harshn hnes ess s • Durability • Powe Powerr Den Densi sity ty • Supp Suppor ortt Requi Require reme ment nts s • Lubri ubric catio ation n

NVH • Helical; – Smoothe Smootherr Operation Operation – Quiet Quieter er

• Toot Tooth h Cont Contac actt Rat Ratio io;; – Axial Axial Contact Contact ratio ratio – Transverse Transverse Contact Contact Ratio

• Spur Ge Gears; rs; – Only Transverse Transverse of 1.2 to 1.5 Typical 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 • Helica Helicall Gears Gears Requir Require e Axial Axial & Radial Radial Thrust Thrust • Spur Spurs s Only Only Radi Radial al • Double Double Helic Helical al Gears Gears Produ Produce ce Only Only Radia Radiall • Very Very Expen Expensi sive ve to Manu Manufac factu ture re • Spur Spur Gears Gears Most Most Toler Tolerant ant of of Misali Misalignme gnment nt

Lubrication • All Gear Gear Teeth Teeth Requir Require e Lubric Lubricant ant Flow Flow • Pres Pressu sure re Lubric Lubricat ation ion;; – 20% - 30% Incom Incoming ing Mesh Mesh (lubrica (lubrication tion)) – 70% - 80% Output Output Mesh (cooling (cooling))

• Spla Splash sh or Dip Dip Met Metho hod; d; – Case Design Design to Provide Adequate Adequate Supply Supply

• Forc Forced ed Lub Lubri rica cati tion on;; – Shaft Design Design to Put Put Lubrication Lubrication where where Needed Needed

148

Lubricant Cooling • Intern Internal al Lubri Lubrican cantt Circula Circulatio tion n • Convec Convectiv tive e Air-Co Air-Cooli oling ng In-S In-Situ itu • Natu Natura rall Flow Flow Exc Excha hang nge e • Forc Forced ed Cool Coolin ing g – Radi Radiat ator or – Circul Circulati ation on Pump

Drawing Information • Gear Gear Data Data Tabul Tabular ar Infor Informa matio tion n • Gear Gear Measur Measureme ement nt & Insp Inspect ection ion • Tolerances – Spur Spur – Heli Helica call – Beve Bevell • Stra Straig ight ht • Spira iral

149

300

150

Lead Tolerance Chart

Lead Tolerance Data

151

Tooth Profile Crown Note

304

152

Gear Measurement and Inspection Tooth 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 Inspection Tooth Thickness Pitch Check

Caliper Setting for chordal tooth thickness

Involute Test

Diameter Over Pins

o

360

Number of Teeth

154

Concentricity Runout Taken with a Ball Checker

Tooth Chordal Dimensions Addendum

Arc Thickness (t)

Chordal Addendum

Chordal Thicknes s (tc)

Gear Tooth Caliper

310

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 • Heli Helica call Ge Gears ars – Use Balls Balls or Dumbbell Dumbbell Pins – Due to Curvature Curvature of Tooth Space – Critical Critical for Odd Odd Number of Teeth

• Method Method for Para Paralle llell Axis Axis Gears Gears Only Only

Measurement Over Pins

157

Pin Sizes Used to Check the Tooth Thickness of Spur Gears Type of Tooth External, standard or near standard proportions

Pressure Angle

Pin Diameter Constant

14 ½ to 25o

1.728 1.920 1.680

External, long-addendum pinion design

14 ½ to 25o

1.920

Internal, standard designs

14 ½ to 25o

1.680 1.440

Calculate Dimension Over Pins • For Standa Standard rd Pin Pin Diam Diamete eter r • External Spur Gears • Even Even Toot Tooth h Num Numbe bers rs – Dudley Practica Practical, l, Pg. 9.21 – Table & Method

• Odd Odd Too Tooth th Numb Number ers s – Dudley Practica Practical, l, Pg. 9.21 – Table & Method

158

Calculate Dimension Over Pins • For Standa Standard rd Pin Pin Diam Diamete eter r • Internal Spur Gears • Even Even Toot Tooth h Num Numbe bers rs – Dudley Practica Practical, l, Pg. 9.27 – Table & Method

• Odd Odd Too Tooth th Numb Number ers s – Dudley Practica Practical, l, Pg. 9.27 – Table & Method

Pin Contact Point • Tangent Tangent Point of contact contact between between pin pin and and tooth, must be on tooth • Outside Outside edge edge of pin pin must must be be beyond beyond the tooth OD • Inner Inner edge edge of pin must must not conta contact ct root root • Pin should should contact contact tooth 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 M = 3 Pb + tP

BC

• Pb – Normal Base Pitch • tP – Circular Tooth Thickness at Base Circle BC

Where; tP

= B *

tP

= B *

BC BC

= tP

t

+

(for spur gears)

*

sin ( n) sin ( t )

(for helical gears)

Inv ( t ) PD

161

Gear Measurement and Inspection • Involute Chart • Lead Chart • Red Liner Chart

Involute Chart

o

0

162

o

6

o

12

o

18

Involute Chart

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 Involute

True Profile

Actual Involute

Form Diameter

“V” Type Chart

Theoretical or True Involute

0

+5

-5

Acceptable Involute Profiles

0

164

Equivalent Band Chart

0

-5 True Involute

Acceptable Involute Profiles

-5 329

0

“K” Type Chart -5

20% of Total Roll Angle

-5

0

165

Modified “K” Chart With Tip and Flank Relief

OD

-3

-8

-3

-8

1

2

PD

3

4

TIF

5

0

Involute Measurement Results Minus Pressure Angle

True Involute

Actual Profile

Actual Involute

Form Diameter

166

Involute Measurement Results Plus Pressure Angle

True Involute

Actual Profile

Actual Involute

Form Diameter

Involute Measurement Results Undercut & Tip Chamfer True Involute Actual Involute Actual Profile

Form Diameter

167

Gear Measurement and Inspection • Involute Chart • Lead Chart

Lead • Axial Advance of a Helix for One Complete Turn

168



Helix

Contact Point

Axis L.H. R.H.


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

Lead Chart Good Profile

340

170

Lead Chart Acceptable Profile

341

Lead Chart Concave Profile

342

171

Lead Chart Profile with Protuberance

Lead Chart Profile with Protuberance

172

Lead Chart Profile Outside 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

Crown Tolerance

348

174

Long & Short Lead

Lead of Crowned Teeth

Helical Gear

Spur Gear

175

Lead of Tapered Teeth

Helical Gear

Spur Gear

Lead & Involute Error Causes • 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 Liner Schematic of Gear Rolling Device

Red Liner • Double Flank Tester • Master Gear • Motion of Center of Test Gear – Recorded (Trace) – During Roll with Master

178

Red Liner Typical Chart

357

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 • Total Composite Error • Tooth to Tooth Composite Error • Tooth to Tooth Error


362

181

Red Liner Data • Total Composite Error • 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

Single Flank Gear Tester Schematic

367

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

Topological Plot of a Gear Tooth Surface from an Automated CMM

370

185

Gear Design Systems and Best Practices • Common Proportions • Interchangeability • Tooling Considerations • Mounting Considerations • Application

This Is The Slide We’ve Been Looking For • Questions ? • Did I Meet Your Expectations ? • Comments ? • Suggestions ? • Thanks !

186

Gear Seminar Reference List 1. “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 List 1. “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, McGrawHill, 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, McGrawHill 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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SAE Gear Design Course - C0223_th003

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