introduction to gear design - bd tech...

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Introduction to

Gear Design2nd

Edition

Charles D. Schultz, p.e.

Beyta Gear Service

Winfield, IL

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ii Introduction to Gear Design

For information, contact:

Beyta Gear ServiceCharles D. Schultz, p.e.0N230 County Farm RoadWin�eld, IL 60190

[email protected](630) 209-1652

Visit Beyta Gear Service on the web:http://BeytaGear.com

©1987, 2004 Charles D. SchultzAll rights reserved.

Self-published by Charles D. Schultz, Beyta Gear Service.Document typesetting and diagram conversions by BD Tech Concepts LLC — 2015.

Statement of Non-Liability Due to today’s legal climate, it is necessary to state that this bookhas been written for general education purposes only. Nothing written in these pages should beconsidered to be de�nitive advice about any speci�c situation.

mailto://[email protected]

http://BeytaGear.com/

http://BeytaGear.com/

http://bdtechconcepts.com/

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Dedication

One of the things I have enjoyed most about being in the gear industry is the opportunity to learnfrom some really great people. It isn’t possible to list them all here but I’m sure they know who theyare. It was their example that lead me to write this book. Whatever good comes from this e�ort I oweto them.

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Contents

Dedication iii

Introduction ix

About the 2nd Edition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix

1 How to Use This Book 1

2 What Kind of Gears Should I Use? 3

Parallel-Shaft Gears . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3Intersecting-Shaft Gears . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Non-Intersecting-Shaft Gears . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3 What Should They Be Made Of? 9

Rating Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Gear Materials and Heat Treatment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9The Gear-Design Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4 What Should They Look Like? 17

Mounting Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17Backlash . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17Blank Tolerancing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17Quality Classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Surface Finish . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Blank Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Tooth-Form Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

5 How Should They Be Made? 29

Milling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29Hobbing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29Shaping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33Broaching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40Lapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40Shaving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40Honing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Gear Grinding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Form Grinders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Generating Grinders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Bevel Gears . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46Worm Gears . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

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vi Introduction to Gear Design

6 How Should They Be Inspected? 49

7 Where Do I Look For Help? 53

8 Acknowledgments 55

9 About the Author 57

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List of Figures

2.1 Parallel-Shaft Gear Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Intersecting-Shaft Gear Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.3 Non-Intersecting-Shaft Gear Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3.1 Critical Sections in Typical Parts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.2 Mid-Band Jominy Hardness vs. Alloy . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.3 Approximate Min. Core Hardness vs. Alloy . . . . . . . . . . . . . . . . . . . . . . . . 133.4 Jominy Position vs. Critical Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.5 AISI Numbering System for Steel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

4.1 Anti-Backlash Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

5.1 Hob Nomenclature — 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345.2 Hob Nomenclature — 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355.3 Hobbing-Clearance Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365.4 Double-Helical Gap-Width Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375.5 Shaper-Cutter Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385.6 Shaper-Cutter Clearance Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395.7 Shaving-Cutter Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425.8 Hob-Dipping Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445.9 Tooth Modi�cations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445.10 Gear Grinder Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455.11 Grinding-Wheel Interference on Cluster Gears . . . . . . . . . . . . . . . . . . . . . . 465.12 Bevel-Cutter Interference with Front Shaft . . . . . . . . . . . . . . . . . . . . . . . . 485.13 Worm-Gear Throat Diameter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

6.1 Bearing Pattern Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

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List of Tables

2.1 Relative Characteristics of Gear Types . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3.1 Popular Gear Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.2 Approximate Minimum Hardenability of 1045, 4140, 4150, & 4340 . . . . . . . . . . . 15

4.1 Typical Gear-Blank Tolerances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204.2 Outside-Diameter Tolerances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.3 Gear-Blank Standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224.4 Minimum-Suggested Quality Level vs. Pitch-Line Velocity . . . . . . . . . . . . . . . 234.5 Achievable AGMA 2000 Quality Levels by Manufacturing Method . . . . . . . . . . . 234.6 Achievable Tooth-Surface Finishes by Manufacturing Method . . . . . . . . . . . . . 244.7 Surface-Finish Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254.8 Surface Finish vs. Tolerance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264.9 Popular Tooth Forms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

5.1 Normally-Available Milling Cutters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305.2 Normally-Available Gear Hobs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315.3 Normally-Available Spline Hobs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325.4 Minimum Number of Teeth to Avoid Undercutting . . . . . . . . . . . . . . . . . . . . 395.5 Shaper-Cutter Teeth vs. Minimum Internal Gear Teeth to Avoid Interference . . . . . 41

6.1 Sampling Plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

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Introduction

Albert Einstein once said:

“Things should be made as simple as possible, but no simpler.”

This book is an attempt to apply that principle to gear design by presenting information from amanufacturing point-of-view rather than a theoretical one. There are no great advances in geartechnology described here. The topics discussed are all covered in greater detail in other books, someof which are listed in the “reference” section. The author hopes that this little volume will be of useto the occasional gear designer as a source of handy information and direction to more completeanswers to the questions that arise during the design process.

About the 2nd EditionAfter �nishing this book in 1987 I vowed never to write another gear book. During the years since,however, I came to look at this little volume with a more critical eye and decided it needed just a littleupdating. What started out as a simple “scan it into the computer and make it look more modern”project grew into a major re-writing e�ort. I’ve tried to incorporate the lessons learned in 10 years ofbusy engineering practice at Milwaukee Gear and Pittsburgh Gear. I hope the additional �guresand tables will be of value.

Despite the modern convenience of spell check, I’m sure there are a few typos left, and that a 3rd

edition will be needed in a few years to correct them.1

1Editor’s note: This document is a 2015 revision based on a scan of the 2nd Edition. All content has been preserved, buthas been converted to PDF text and vector diagrams, along with new editing, numbering, formatting, typesetting, andinternal and external hyperlinks.

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Chapter 1

How to Use This Book

Every gear engineer must answer a series of ques-tions before he can complete a design. The in-formation in this book is organized in the usualsequence of these questions:

1. What kind of gears should I use?

2. What should they be made of?

3. What should they look like?

4. How should they be made?

5. How should they be inspected?

Somewhere between questions 1 and 2 thesize of the gears must be determined througha rating-calculation procedure. This subject isnot covered in this book for reasons that will bediscussed later. A list of references has been pro-vided to assist you in getting the answer to thatquestion, and any others which this book raisesfor you.

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Chapter 2

What Kind of Gears Should I Use?

Successful gear systems often depend as muchon selecting the right gear for the job as on theproper design of the individual parts. Gears canbe made in a wide variety of forms, each with itsown strengths and weaknesses. In some applica-tions di�erent gear types can be used with equalsuccess. There are other cases where a speci�c

type of gear has become the “standard” due toits unique characteristics. Table 2.1 shows themost common kinds of gears, organized by shaftorientation, showing their relative characteristicscompared to other types of the same shaft orien-tation. Additional comments on each are madein the following paragraphs.

Parallel-Sha� GearsSpur gears are by far the most common type ofparallel-shaft gear. They are simple to design,highly e�cient, and relatively forgiving of mount-ing errors. Spur gears can handle high horse-power and shock loads but are not the most com-pact way to transmit power due to the relativelylow contact ratio that can be obtained. Contactratio is a measure of smoothness of operation andis related to the number of teeth in contact (andsharing the load) at any one time. Well-designedspur gears should never have a contact ratio ofless than 1.2, but it is hard to get a contact ratiomuch over 1.8 without employing a non-standard“high contact ratio” tooth form, for which specialtooling is required. Spur gears do not generatethrust forces (loads in the direction of the shaftaxis), which allows for much simpler housing andbearing arrangements.

Helical gears are often thought of as “twisted”spur gears because the teeth run at an angle tothe shaft axis. This “helix angle” is produced bysetting the cutting tool at an angle to the work-piece and using a di�erential to vary the relativespeed of rotation between the tool and the work-piece. The helix angle raises the contact ratioby bringing more teeth into contact across the

face of the gear. This “face” contact ratio is addedto the “pro�le” contact ratio of the spur gear togive a “total” contact ratio that can be tailoredto meet higher load requirements and operatingspeeds. There is a thrust load created by the helixangle that complicates bearing selections, how-ever. Analysis of bearing loads can be complex.Consult your bearing manufacturer or one of thereference books for suggested analysis methods.

Double-helical gears have two “opposite-hand” helical gears on a single shaft. This theo-retically creates equal and opposite thrust forcesthat cancel each other, giving the advantages ofhelical gears without the bearing-load problems.In practice, however, it can be di�cult to insurethat each “helix” carries an equal load. Externalthrust loads caused by coupling miss-alignmentsor imbalance can interfere with the ability of thegears to “�oat” axially and �nd their equilibriumpoint. This causes one side of the gear to carrymore load and wear out sooner. The design ofmounting and bearing arrangements for double-helical gears turns out to be just as di�cult asfor helical gears. These gears can handle veryhigh loads and operating speeds, which accountsfor their popularity in pump drives and marinepropulsion units. A great deal of research has

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4 Introduction to Gear Design

Table 2.1: Relative Characteristics of Gear Types

1 = Best 5 = Worst

Ratio Power Speed Relative Space Approx. MountingType Range Capacity Range Cost Required E�ciency Costs

Parallel Shafts

Spur 1 to 10 4 4 1 4 95 to 98 % 1Helical 1 to 10 3 2 2 3 95 to 98 % 3Double-Helical 1 to 10 2 1 4 2 95 to 98 % 2Internal 2.5 to 12 5 5 3 5 90 to 95 % 4Planetary 2.5 to 12 1 3 5 1 85 to 95 % 5

Intersecting Shafts

Straight-Bevel 1 to 8 2 2 1 2 95 to 98 % 1Spiral-Bevel 1 to 8 1 1 2 1 95 to 98 % 2Face 3 to 8 3 3 3 3 90 to 95 % 3

Non-Intersecting Shafts

Worm 3 to 120 1 3 1 1 50 to 90 % 2Crossed-Helical 1 to 10 5 5 5 5 50 to 95 % 1Hypoid 2.5 to 10 2 1 3 2 90 to 95 % 2“Face” Worm 3 to 120 3 2 2 3 50 to 95 % 4Face 3 to 8 4 4 4 4 90 to 95 % 5

Notes:1 The ratio ranges shown are the extreme limits. For high-power applications and manufacturing

economy the designer is advised to limit spur and helical gearsets to a maximum of 5.5:1. Wormsshould be 5:1 to 70:1.

2 Internal gearsets over 8:1 are not recommended.3 Planetary gearsets lower than 4:1 or higher than 7:1 present some unique design problems that

the novice designer is advised to avoid.4 Consult the appropriate AGMA standard or a reference book to satisfy yourself that the pro-

posed design maintains the recommended relationships between various gear parameters such asface-width-to-pitch-diameter.

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Chapter 2 — What Kind of Gears Should I Use? 5

(a) Spur (b) Helical (c) Double-Helical (With Gap)

Herringbone (No Gap)

(d) Internal (e) Planetary

Figure 2.1: Parallel-Shaft Gear Types

been published on the system dynamics of thesedrives but much of it may be di�cult for the non-expert to use.

Internal gears can be made in spur or helicalforms. Contact ratios are slightly higher thanfor external gears of the same proportions, butload-carrying capacity su�ers from face-widthlimitations and an inability to mount adequatebearing on the pinion. The internal gear is alsovery awkward to mount, which can make thedrive di�cult to package.

Planetary gears use multiple gear meshes in-side an internal gear. These meshes have thee�ect of canceling the “separating” loads (forcestending to push the gears apart), which reducesthe bearing loads. As power capacity is calcu-lated on a “per mesh” basis the planetary-geardesign allows for very high loads in a compactspace. The “down side” of all this is that lubri-cation requirements and thermal losses can putlimits on the allowable operating speeds unlessexternal cooling and lube systems are employed(which reduces the “compactness” advantage). Inaddition, a high degree of precision is required inpart manufacture to insure that the load is shared

equally. There are some speci�c mathematicalrelationships that must be maintained in the de-sign of planetary gearsets, which can restrict theability to obtain exact ratios. The best approachfor the novice designer is to read everything men-tioned about planetaries in the reference booksand to look carefully at existing installations.

Intersecting-Sha� GearsBevel gears are the most popular means of con-necting intersecting shafts. Straight-bevel gears(including Coni�ex) have much in common withspur gears, while spiral-bevel gears (includingZerols) are similar to helical gears in operatingcharacteristics. All bevel gears are extremely sen-sitive to mounting accuracy, and require carefulanalysis of bearing loads. The Gleason Workshas a lot of information on the design of bevelgears and mountings. The published limitationson proportions and numbers of teeth should bestrictly observed. Doing otherwise can lead tounsolvable manufacturing and �eld problems.

Face gears are not commonly used in power-transmission designs due to their low power ca-

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pacity and lack of standardized calculation proce-dures. Face-gear design information is availablein some of the reference books listed at the endof this manual. These gears can be useful in sometiming and indexing applications. Consult anexperienced manufacturer before designing any“new” face gears, as tooling considerations arecritical.

Non-Intersecting-Sha� GearsWorm gears were originally designed as “jacks”for raising and lowering weights. They are uni-quely suited for static-load applications becauseof their tendency to “self lock” under certain con-ditions. “Self locking” occurs when the worm canturn the gear but the gear cannot turn the worm— the load cannot cause the drive to backup. Thisphenomenon does not occur in all wormgear setsand should not be counted upon to take the placeof a brake for safety-related applications. Wor-mgears can also provide the highest possible re-duction ratio in a single “pass” and are just aboutthe only type of gear where the gear-diameter-to-pinion-diameter ratio does not correspond tothe reduction ratio. This allows modern power-transmission wormgear boxes to be very compactin comparison to other gearboxes of similar reduc-tion. The large amount of sliding action in wormmeshes can result in low e�ciency and powerlimitations due to thermal losses. The meshingaction is very smooth, making these gears idealfor indexing applications. Calculation procedures

are available through AGMA and in most refer-ence books.

Crossed-helical gears can be thought of as asimple form of “non-enveloping” wormgear. Loadcapacity is severely limited because of the smallcontact area between the gear and the pinion.These gears are inexpensive to make and are veryforgiving of mounting errors, however, whichmakes them popular for low-power “takeo�s” ortiming purposes (like packaging machines). Cal-culation procedures are not standardized throughAGMA but can be found in some reference books.

Hypoid gears are a modi�ed form of spiral-bevel gear. All comments made about bevel gearsapply here as well. Rear-wheel-drive auto andtruck axles are the most popular use of Hypoidgears.

“Face worm” gears have been sold under thetrade names “Helicon” and “Spiriod”. The origi-nal design patents have now expired and thereis nothing to prevent a “second source” from de-veloping similar gears. The proprietary natureat these gears has tended to make them more ex-pensive than worms or Hypoids, and less wellunderstood. The design and rating methods thathave been published for these gears have not beenindependently tested or sanctioned by AGMA. Itappears these gears share some characteristicswith worms and Hypoids, but may have otherweaknesses or strengths.

Face gears can also be designed for non-inter-secting shafts. The comments previously madeabout face gears apply here as well.

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Chapter 2 — What Kind of Gears Should I Use? 7

(a) Bevel (b) Face

Figure 2.2: Intersecting-Shaft Gear Types

(a) Straight or Coni�ex (b) Zerol (c) Spiral

(d) Worm (e) Helicon (f) Spiroid

(g) Crossed Helical (h) Hypoid (i) O�set Face

Figure 2.3: Non-Intersecting-Shaft Gear Types

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Chapter 3

What Should They Be Made Of?

Rating CalculationsGear-rating calculation procedures have beenspeci�cally excluded from this manual. The au-thor feels that there is no simple way to coverthis subject without compromising the adequacyof the analysis. Anyone designing gears withoutaccess to the appropriate AGMA standards and awillingness to spend some time studying them isasking for a lot of trouble. There are a number ofpackages available for personal computers thatclaim to perform “complete gear analysis” accord-ing to the current AGMA standards. These aregreat time savers, but their use by inexperienceddesigners can be dangerous. There are many fac-tors in the rating formulas that must be carefullyconsidered for each application — factors whicheven the “experts” may disagree on. The best pol-icy is maintain a skeptical attitude in using anyrating method, manual or computerized. Believein what works, not in computer printouts!

Gear Materials andHeat TreatmentWhile material and heat-treatment selection arean important part of any rating calculation, theyalso have a major impact on the manufacturingprocesses required. Table 3.1 lists the relativecharacteristics of some popular gear materialsso that comparisons can be made of the man-ufacturing di�culties of alternate choices. Forgeneral applications it is best to con�ne mate-rial selections to those listed in the table. Lots ofother materials (including aluminum, powderedmetal, stainless steel, and exotic “tool steel” al-

loys) have been used to make gears, but theirallowable stresses and lubrication requirementshave not been standardized. If you choose to usea material not listed, you must be prepared to dosome digging to get that information and spendthe time and money needed to verify its accuracy.

Through-hardening steels are the most popu-lar gear materials because they can be cut afterreaching their �nal hardness. This eliminatesheat-treating distortion that can require expen-sive �nishing operations. The through-hardeningsteels are listed in order of relative power capacity(lowest to highest), with fully-annealed 1018 steelbeing used as the “baseline”. Very soft steels areoften “gummy” and can be di�cult to cut accu-rately. Cutting steel over 350 bhn can also be aproblem.

Steel alloys have di�erent “hardening pro�les”(the relationship of hardness to distance from thesurface) that must be matched to the size of thepart and the hardness needed (see Figure 3.1).Generally speaking, the lower the alloy is on thelist, the better the hardening pro�le. It is im-portant that highly-stressed parts have uniformhardness — soft “cores” can lead to �eld serviceproblems. The author prefers to limit the use of1045 material to parts requiring less than 240 bhn.Do not use 1045 for parts that will be operated atlow temperatures. 4140 works well for parts up to3 ndp and for critical sections up to about 4′′. Forcoarser pitches and larger critical sections 4340is preferred rather than 4150. The author doesnot advocate the use of re-sulphurized steels, asthey have an elevated notch sensitivity.

Some alloys, such as 4140 and 4150, can be-come extremely brittle if hardened over 430 bhn.

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Table 3.1: Popular Gear Materials

Relative Relative Maximum Di�culty of Heat-TreatDesignation Cost1 Durability2 Strength3 Hardness Manufacture Distortion

Through-Hardening Steels

1018 1.00 1.00 1.00 180 bhn 1.10Not a concernwith through-

hardenedsteels. (Severe

if �ame orinductionhardened.)

1117 1.00 1.00 1.00 180 bhn 1.101045 1.05 1.46 1.25 270 bhn 1.001137 1.05 1.46 1.25 270 bhn 1.001141 1.05 1.46 1.25 270 bhn 1.004140 1.10 2.50 1.50 335 bhn 1.204150 1.15 2.80 1.60 360 bhn 1.304340 1.20 3.00 1.60 390 bhn 1.404350 1.25 3.20 1.65 400 bhn 1.50

Nitriding Steels

4140 1.50 3.50 1.35 48 hrc 1.25 Minor4340 1.50 3.40 1.42 48 hrc 1.25 MinorNitralloy 1.75 4.20 1.45 64 hrc 1.25 Minor

Carburizing Steels

4130 1.50 3.50 1.60 50 hrc 2.50 Severe4620 1.65 4.00 1.85 55 hrc 2.50 Severe8620 1.35 4.50 1.97 62 hrc 2.50 Severe4320 1.50 5.60 2.15 62 hrc 2.50 Severe4820 1.75 5.60 2.25 62 hrc 2.75 Severe9310 2.00 5.50 2.12 61 hrc 3.00 Severe

Iron

G4000 Grey 0.80 0.80 0.40 200 bhn 0.85 Not a concernwith iron.Ductile 1.20 81 % of steel 81 % of steel 260 bhn Same as steel.

Malleable 1.00 0.95 0.51 240 bhn 1.00

Bronze

Sand-Cast 3.00 0.10 0.17 160 bhn 1.00 Not aconcern.Aluminum Bronze 5.00 0.47 0.72 220 bhn 1.10

Notes:1 Cost of material and heat treating relative to non-heat-treated 1018 steel.2 Durability relative to non-heat-treated 1018 steel.3 Strength relative to non-heat-treated 1018 steel.

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Chapter 3 — What Should They Be Made Of? 11

JOMINY POSITION FORHARDNESS PREDICTION IS J6FOR 8620H MID-BAND IS 27.6 R c

⌀ 2.468

⌀ 6.936

JOMINY POSITION FORHARDNESS PREDICTION IS J12FOR 4320H MID-BAND IS 24 R c

(a) Critical Section on Shaft/Pinions

⌀ 2.880 ⌀ 1.480

WEBBED GEARJOMINY POSITIONFOR TOOTH CORE HARDNESS=J5

FOR 8620 J5= 30

SOLID DISK GEARJOMINY POSITION FORHARDNESS AT TOOTH CORE= J7

FOR 8620 J7= 26.5

(b) Critical Section on Webbed Gears

Figure 3.1: Critical Sections in Typical Parts

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Always check the “notch sensitivity” of any mate-rial that is through-hardened above 375 bhn. Anyapplication for use at extreme temperatures (be-low 0 °F or above 250 °F) requires careful analysisof the material properties under those conditions.This analysis should be done by a competent met-allurgist.

While the AGMA standards do not (at thetime this is being written) have di�erent allow-able stresses for the various carburizing steelgrades, there is ample evidence to suggest thatall alloys do not perform equally. Figure 3.2 is agraph of the average (or mid-band) hardness po-tential of the most popular carburizing steels asfound in the “Jominy” hardenability test. Thereis a signi�cant di�erence in the curves from onealloy to another. This is important because forcarburized gears to perform well the tooth-corehardness must be greater than 25 hrc. Figure 3.3is a graphical representation of a table in theAGMA 2004 Materials and Heat Treat Manual.It clearly shows, for example, that the popular8620 alloy will not result in a tooth-core hard-ness of 25 hrc when the tooth size is larger than4.5 ndp. Figure 3.4 is a typical graph of jominyposition vs. critical-section size.

The actual hardness results will vary depend-ing upon the exact chemistry of the material, thespeci�cs of the heat-treat process, and the criticalsection (see Figure 3.1) of the part. Alloy selectionand critical-section analysis are a very importantpart of carburized-gear design. The author doesnot advise using high-performance alloys in allcases, but suggests 8620 not be used for teethlarger than 4.5 ndp or for parts with critical sec-tions over 3′′. For coarser-pitch application 4320is preferred.

While nitrided gears can’t carry as much loadas carburized and hardened ones, they o�er theadvantage of minimal heat-treat distortion. Thisusually allows them to be used “un-ground”, andgreatly reduces manufacturing costs. Materialselection for nitrided gears is generally made onthe basis of the durability rating required. Ni-

triding produces a very hard, shallow case thatcan be susceptible to cracking if overloaded. Thisprocess is most successful on teeth smaller than6 dp.

Carburized, hardened, and ground gears arethe ultimate in power capacity. Gear grindingis usually required to correct for heat-treat dis-tortion. Attempts at predicting distortion levelsand controlling it during the heat-treating pro-cess generally have been unsuccessful. Withoutgrinding it is di�cult to maintain AGMA Q-10tolerance levels. Selective hardening is speci�edto keep some areas of the part “soft”, and thiscan be done through the use of copper plating orcarburizing, machining the case o� the desiredsurfaces, and hardening. Special “stop-o�” paintshave also been used with great success. Materialselections are made on the basis of the durabilityrating and the case depth required. The AGMAstandards and some of the reference books canprovide guidance in those areas.

Cast iron is used in many industrial and au-tomotive gear applications because of low mate-rial cost. Casting methods have been developedthat can produce the required core hardness rightfrom the mold, saving an expensive heat-treat op-eration. (If not done properly, however, the partsbecome as hard as tool steel and unusable dueto brittleness.) These materials are getting betterevery year as a result of the research money be-ing spent on them. Some experts feel these newiron formulations can carry the same loads asthrough-hardened gears of the same core hard-ness. For high-volume uses the cost savings maymake these materials very attractive to those will-ing to verify the lab results.

Bronze is the material of choice for most wor-mgears, but is seldom used on other gear types un-less the power requirement is low. Some bronzealloys can be heat treated to improve their ca-pacity. Casting methods can greatly a�ect thematerial properties, and the gear designer mustmake sure the drawing speci�es the method de-sired.

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Figure 3.2: Mid-Band Jominy Hardness vs. Alloy

Figure 3.3: Approximate Min. Core Hardness vs. Alloy

(per ANSI/AGMA 2004 Table 5-3)

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Figure 3.4: Jominy Position vs. Critical Section

(for oil quench with good agitation)

Furnace TypeA — Basic Open-Hearth Alloy SteelB — Acid Bessemer Carbon SteelC — Basic Open-Hearth Carbon SteelD — Acid Open-Hearth Carbon SteelE — Electric Furnace Alloy Steel

Alloy Type10xx — Plain Carbon Steel11xx — Free-Cuing Carbon Steel3xxx — Nickel-Chrome Steel4xxx — Molybdenum Steel41xx — Chrome Moly Steel43xx — Chrome Nickel Moly Steel46xx — Nickel Moly Steel48xx — High Nickel Moly Steel86xx — Chrome Nickel Moly Steel93xx — Chrome Nickel Moly Manganese Steel

Harden-ability Restriction(None) noneH — H-band Jominy

Carbon Contentxx = .xx% carbon

E8620H

Figure 3.5: AISI Numbering System for Steel

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Table 3.2: Approximate Minimum Hardenability

of 1045, 4140, 4150, & 4340

Brinell ScaleJominyPosition 1045 4140 4150 4340

1 555 525 630 5252 390 525 630 5253 295 514 630 5254 270 495 620 5255 260 495 615 5256 250 480 595 5257 250 455 595 5258 245 444 575 5149 240 410 575 51410 235 390 555 51411 230 370 540 49512 220 360 525 49513 355 495 48014 345 480 46515 335 455 46516 330 444 45518 320 420 44420 310 400 43022 310 380 42024 300 370 41026 300 360 40028 295 350 39030 295 350 38032 285 350 370

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The Gear-Design Process

1. Determine Loads and Speeds• Prime-mover nameplate power and

speed• Duty cycle• Reliability• Smoothness of operation• External loads• Experience with similar applications

2. Determine Gear Type• Physical arrangement• E�ciency• Bearing considerations• Noise and vibration• Experience with similar applications

3. Determine Material and Heat Treatment• Strength vs. wear requirements• Lubrication issues• Space limitations• Process limitations• Cost issues• Delivery issues

4. Determine Quality Needed• Operating speed• Noise and vibration• Reliability and failure mode issues

5. Basic Gear Design• Space available• Standardized tooling• Process capabilities

6. Detail Design• Stress analysis• Raw material form• Assembly issues• Design for manufacturing• Cost review

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Chapter 4

What Should They Look Like?

Mounting CharacteristicsNo matter how much care is taken in the designand manufacture of gears, they are sure to fail ifimproperly assembled or inadequately mounted.Many “gear” problems are caused by lack of atten-tion to the accuracy required in machining thehousing, in assembling the gears and bearingsto the shafts, and in aligning the sub-assemblies.The author knows of gearboxes that, after giving30 years of excellent service, have failed withinhours of “�eld” rebuilding by inexperienced me-chanics. If you are not sure how to handle a par-ticular aspect of a design or maintenance project,ask for help or check the reference books listed inthis manual. Most bearing manufacturers will behappy to review your drawings and bearing selec-tions at little or no charge. If your gear supplierhas an engineering department, they may also beavailable to “consult” on your design project or totrain your maintenance and assembly people inproper methods of handling and adjusting gears.

BacklashBacklash is one of the most misunderstood con-cepts in gearing. An individual gear cannot havebacklash — it can only have a tooth thickness.Backlash occurs when gears are mated togetheron a given center distance and the sum of theirtooth thicknesses is less than their circular pitch.The backlash of a pair of gears will vary at somepoints in the rotational cycle due to run-out andcutting inaccuracies. If the center distance is in-creased the backlash will increase; if it is reducedthe backlash will decrease. Don’t confuse “lowbacklash” with “high quality”. Except for appli-

cations that require positioning accuracy, suchas index tables or radar drives, or that are sub-ject to frequent reversing loads, “too much” back-lash seldom e�ects gear performance. Not havingenough backlash can result in the gears “binding”under some conditions, especially at low temper-atures when steel gears are used in an aluminumhousing. Gears that bind are certain to fail.

When low backlash is required, the best ap-proach is to use “anti-backlash” gears or adjust-able centers (see Figure 4.1). Tight tolerances ontooth thicknesses and center distances are sel-dom e�ective and can be very expensive. Anti-backlash gears consist of two gear halves thatare spring loaded to adjust the “e�ective” tooththickness to �ll in the space available on the mat-ing part. These gears are not used to transmitsigni�cant amounts of power, as the requiredspring pressures become hard to obtain in thespace available. Adjustable centers can handleslightly higher loads but are expensive to manu-facture. The reference books discuss “backlash”extensively and some manufacturers include alimited range of anti-backlash gears for instru-ment use in their catalogs.

Blank TolerancingThe di�erence between a “good” gear and a “bad”one can often be traced to how accurately theblank was machined. In a production run of gears,for example, those having bores close to the lowlimit (or maximum material condition) will �t thecutting arbor more snugly and usually exhibit theleast “run-out”. If gears are to be cut in a “stack”the perpendicularly of the blank sides to the bore

17

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(a) “Scissors Gear”

(b) Adjustable Centers (c) Spring-Loaded Centers

(Illustrations extracted fromAGMA Design Manual for Fine Pitch Gearing [AGMA 370.01].

Used by permission of AGMA.)

Figure 4.1: Anti-Backlash Methods

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Chapter 4 — What Should They Look Like? 19

will similarly in�uence the results. It is importantto “match” the tolerancing of those part features— which will be used for work-locating duringthe machining process — to the accuracy neededin the �nal part. Your gear supplier may havesome speci�c requirements in this area, but thevalues shown in Tables 4.1 to 4.3 are a good placeto start.

�ality ClassesSelecting the proper quality class for a particularapplication is one of the most controversial areasof gear design. AGMA has provided a chart inAGMA 2000 (formerly AGMA 390.03) that can beused to select the quality level needed. Many ofthe texts listed in the reference section of thisguide have additional information on this topic.Quality level should be a function of application,power level, and operating speed. Table 4.4 is theauthor’s suggestion for minimum quality levelvs. maximum pinion pitch-line velocity whenrelatively smooth applications are considered.

It is very important to remember that in-creased quality levels cost money. If you wantcost-e�ective designs you must resist the urge to“solve” your gear problems by over-specifyingquality levels. Even the “best” gears will failif they are not mounted accurately, or properlysized for the load and system dynamics. Table 4.5shows the quality levels normally achievable forvarious gear elements by modern manufacturingtechniques. The column on “relative cost” re�ectsnot only the additional time and e�ort needed tomake the gear teeth, but also the extra expenseof increased blank accuracy.

Surface FinishThe surface �nish of gear teeth is another contro-versial aspect of gear design. One common mis-conception is that specifying an AGMA qualityclass also speci�es a tooth-surface �nish. AGMA2000 does not include surface �nish in its toler-

ancing. Table 4.6 shows the surface �nishes nor-mally produced by common production methods.Comparing this table with the one on quality vs.production method (Table 4.5) shows that thereis an indirect relationship between “quality” and“surface �nish”.

When you specify a tooth surface �nish (Ta-ble 4.7) you are often requiring costly gear-�nish-ing processes (Table 4.8) that do not increase“quality” as de�ned by AGMA 2000. It is impor-tant to satisfy yourself, by studying whateverinformation is available (or through �eld testing),that you need a particular �nish to meet yourperformance objectives. Surface �nish has ane�ect on lubricant �lm-thickness requirements.While no consensus “standard” has been pub-lished on what lubricant viscosities are neededwith what surface �nishes, it is clear that heavieroil is needed when coarser �nishes are present.The use of the heavier lube may or may not bepossible in some applications due to cold-startingconditions, thermal considerations, or other is-sues.

Blank DesignOne thing that all gear experts agree on is thatyou can’t make a good gear from a bad blank.“Bad” doesn’t just mean poor workmanship: italso refers to poor design or poor tolerancing. Agood way to prevent these problems is to becomefamiliar with the processes used to make gearsand make provisions in the design of the part touse those processes to your advantage. Once youunderstand the manufacturing techniques you’llbe able to determine which parts of your gearsystem are likely to be problems while there isstill time to make design changes. This is a goodtime to remember the old adage “If it looks rightit probably is.” Many gear problems are really“proportion” problems. Long spindly shafts, largegears with small rim or web thicknesses, inad-equate housing supports, and poor “packaging”have caused more “gear failures” than anyone

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Table 4.1: Typical Gear-Blank Tolerances

(Courtesy of �aker City Gear Works)

AGMA Q6 Q7 Q8 Q9 & Q10 Q11 & up

Diameter ofBore .002 .001 .0007 .0005 .0002

Taper of Bore(No portion toexceedtolerance)

.001/in oflength

Max .002

.0007/in oflength

Max .001

.0005/in oflength

Max .0007

.0003/in oflength

Max .0005.0002

Concavity ofMounting &RegisterSurfaces

.001/in of radius for rigid blanks.0005/in of radius for �exible blanks

Total .003

.0005/in of radius for rigidblanks

.0003/in of radius for �exibleblanks

Total .0015

Convexity ofMounting &RegisterSurfaces

None for any class

Lateral Runoutof Bevel & FaceGears

.001/in ofradius

Max .002

.0008/in ofradius

Max .0016

.0005/in ofradius

Max .001

.0004/in ofradius

Max .0008

.0003/in ofradius

Max .0005

Lateral Runoutof Spur &Helical Gears

.002/in ofradius

Max .004

.0015/in ofradius

Max .0025

.001/in ofradius

Max .002

.0007/in ofradius

Max .0015

.0005/in ofradius

Max.001

Non-Parallelism

.002/in ofradius

Max .004

.0015/in ofradius

Max .0025

.001/in ofradius

Max .002

.0007/in ofradius

Max .0015

.0005/in ofradius

Max.001

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Table 4.2: Outside-Diameter Tolerances


(a) Runout of Outside Diameter with Bore or Centers

Diametral Pitch AGMA Q5 TO Q8 AGMA Q9 & up

1 – 4 0.015 0.0095 – 8 0.010 0.0069 – 13 0.006 0.00414 – 19 0.004 0.00320 – 39 0.003 0.00240 – 79 0.002 0.0015

80 & �ner 0.001 0.001

(b) Tolerance of Outside Diameters

D.P. +0 D.P. +0

3 −0.020 40 −0.0055 −0.015 48 −0.0048 −0.010 64 −0.00310 −0.008 72 −0.00312 −0.007 80 −0.00214 −0.007 96 −0.00218 −0.007 120 −0.00220 −0.007 124 & up −0.00132 −0.006

cares to count. Take a careful look at the general“appearance” of your design before making the�nal drawings.

Tooth-Form SelectionOne of the �rst steps in designing a gear is the se-lection of the tooth form to be used. To a certainextent this decision is based upon rating require-ments, but the choice made will also e�ect themanufacturing processes used. Table 4.9 showsthe “popular” tooth forms in use today. Thereare many other forms available, and each hasits proponents. The author urges caution on thepart of anyone who is thinking of using a tooth

form not on Table 4.9, as the availability of cut-ting tools will be limited. The actual variationin tooth strength from one form to another isslight. For critical applications tooth form mightmake the di�erence between success and failure,but those instances are rare, and should be leftto the “real experts.” Unless very low numbersof pinion teeth are involved, the author sees lit-tle need to use anything other than 20 full-depthteeth on new designs. If low numbers of pinionteeth (< 20) are needed, 25 full-depth is the bestchoice. When making modi�cations to existingdesigns, you may have to work with the otherforms shown on Table 4.9, but they should beconsidered “obsolete” for new designs.

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Table 4.3: Gear-Blank Standards


Outside Diameter Tolerances:

Straight-Bevel Gears — All Classes

D.P. Tol. ±.000

20 – 30 −0.00531 – 40 −0.00441 – 56 −0.00357 – 94 −0.002

95 & �ner −0.001

Back-to-Corner Tolerances:

Bevel GearsD.P. Tol. ±.000

20 – 46 −0.00247 & �ner −0.001

Back-Angle Tolerances — Bevel Gears: ±1°

Surface Finishes — All Types and Classes:

Machine Finish: max. 125 Micro

Grind Finishes by Tolerances:

0.0000 – 0.0002 8 Micro0.0002 – 0.0005 16 Micro0.0005 – 0.0010 32 Micro

Threads: All units to be chamfered for:141⁄2° P.A. 15°20° P.A. 20°60° P.A. 30°

Radii: Sharp corners to be broken to 0.005 – 0.015′′radius.

Decimals:0 – 6′′ ±.0056 – 12′′ ±.010

Angular: ±1⁄2°

Thread Tolerances: Class 2 �t

Flatness: Mill Standard

Concentricity of Bearing Journals:

Concentricity of bearing journals, in respect totrue center of part, shall be held within thetotal tolerance of bearing journal diametersize.Examples:

• Bearing diameter size .125 ± .0003• Concentricity to true centerline

.0003 T.I.R.• Bearing diameter size .500 ± .0005• Concentricity to true centerline

.0005 T.I.R.

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Table 4.4: Minimum Suggested Quality Level vs. Pitch-Line Velocity

For uni-directional service and relatively smooth power �ow:(

Peak LoadNominal Load ≤ 1.25

)(If these conditions are not present, a higher quality level may be needed.)

Maximum Minimum-Suggestedplv in ft/min AGMA Quality Level

250 6500 71500 82500 93500 105000 117500 1210000 13

plv in ft/min = pitch diameter × .262 × revolutions per minute

Table 4.5: Achievable AGMA2000 Quality Levels

by Manufacturing Method

Manufacturing Involute Spacing RelativeMethod Run-out Pro�le Lead (Pitch) Cost

Hobbing (Class b Hob) 8 to 10 8 to 9 8 to 9 8 to 9 1.0 to 1.25Hobbing (Class a Hob) 9 to 11 8 to 9 9 to 11 8 to 10 1.25 to 1.5Hobbing (Class aa Hob) 9 to 12 8 to 11 9 to 11 9 to 11 1.5 to 1.75Shaping (Commercial Cutter) 8 to 10 8 to 10 8 to 11 8 to 10 1.25 to 1.5Shaping (Precision Cutter) 9 to 11 9 to 10 9 to 11 9 to 11 1.5 to 1.75Shaving 10 to 12 8 to 10 8 to 12 8 to 12 2.0 to 2.5Grinding 9 to 14 9 to 14 8 to 14 9 to 14 3.0 to 4.0

Notes:1 Lower quality levels are generally achievable under most conditions.2 Upper quality levels require special controls on blanks, tooling, and machinery.

This can increase costs signi�cantly.3 Relative costs compared to Class b hobbing for operations needed to �nish gear

teeth only. Material and heat-treat costs are not included in this comparison.4 If heat treating is done after tooth �nishing, quality level can drop by two levels or

more.

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Table 4.6: Achievable Tooth-Surface Finishes

by Manufacturing Method

Tooth E�ortSize Required Hobbing Shaping Shaving Grinding

1 to 3 dp Normal 125 80 to 125 63 32Extra 80 80 32 16

3 to 10 dp Normal 80 63 to 80 63 32Extra 63 63 32 16

10 to 24 dp Normal 80 63 to 80 50 to 32 32Extra 63 63 16 16

24 to 40 dp Normal 80 63 50 to 32 32Extra 63 63 to 32 16 16

40 dp and up Normal 80 63 not practical 32Extra 63 63 to 32 16

Notes:1 Normal e�ort involves typical production feeds and speeds.2 Extra e�ort involves special controls and procedures on tools and machines.

Cycle time may increase signi�cantly.3 Finishes shown are for through-hardened steel of 230 – 310 bhn.4 Finish may be poorer on steel below 230 bhn or above 310 bhn.5 Surface �nish may be slightly better in brass, bronze, aluminum, or stainless

steel, provided proper feeds and speeds are selected.6 Surface �nish for surface-hardened gears that are not �nished after heat

treating may be slightly worse due to scale-removal operations.

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Table 4.7: Surface-Finish Description

Symbol Description

1,000√ Indicates that the surface is very rough and uneven within the dimensional requirements.500√ Indicates that the surface is rough and uneven within the dimensional requirements.250√ Indicates that the surface must be smooth and even to a degree obtainable by tools re-

moving large chips or shavings. Machining marks and grooves discernible to the eye andto touch are permitted, if the surface meets dimensional requirements.

125√ Indicates that the surface must be smooth and even to a degree obtainable by tools re-moving medium chips or shavings. Machining marks and grooves discernible to the eyeare permitted, if the surface meets dimensional requirements.

63√ Indicates that the surface must be smooth and even to a degree obtainable by tools re-moving small chips. Machining marks and grooves discernible to the eye are permitted,if the surface meets the dimensional requirements.

32√ Indicates the surface must be smooth and even to a degree obtainable by tools removingsmall particles. Machining marks such as grooves must not be discernible to the eye ortouch, if the surface meets the dimensional requirements.

16√ Indicates that the surface must be very smooth and even to a degree obtainable by toolsremoving very small particles. Machining marks such as grooves must not be discernibleto the eye or touch, if the surface meets the dimensional requirements.

8√ Indicates that the surface must be even to a degree obtainable by tools removing minuteparticles, generally by grinding. Machining marks such as the �ne patterns resultingfrom grinding must not be discernible to the eye or touch and the surface must have apolished appearance and meet dimensional requirements.

4√ Indicates that the surface must be even to a degree obtainable by tools removing veryminute particles, generally by honing, lapping, or super-�nishing. Machining marks suchas very �ne patterns must not be discernible to the eye or touch and the surface musthave a highly polished appearance and meet dimensional requirements.

ref: Gear Handbook by Dudley, Table 9-16

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Table 4.8: Surface Finish vs. Tolerance

SymbolQualityclass Description

Max. rmsvalue,

micro in.

Suitablerange of total

toleranceTypical fabricationmethods

Approx.relativecost to

produce1,000√ Extremely

roughExtremely crude surfaceproduced by rapidremoval of stock tonominal dimension

1,000 0.063 – 0.125 Rough sand casting,�ame cutting

1

500√ Veryrough

Very rough surfaceunsuitable for matingsurfaces

500 0.015 – 0.063 Sand casting, contoursawing

2

250√ Rough Heavy toolmarks 250 0.010 – 0.015 Very good sand casting,saw cutting, very roughmachining

3

125√ Fine Machined appearancewith consistenttoolmarks

125 0.005 – 0.010 Average machining —turning, milling,drilling; rough hobbingand shaping; die casting,stamping, extruding

4

63√ Fine Semi-smooth withoutobjectionable toolmarks

63 0.002 – 0.005 Quality machining —turning, milling,reaming; hobbing,shaping; sintering,stamping, extruding,rolling

6

32√ Smooth Smooth, wheretoolmarks are barelydiscernible

32 0.0005 –0.002

Careful machining;quality hobbing andshaping; shaving;grinding; sintering

10

16√ Ground Highly smooth �nish 16 0.0002 –0.0005

Very best hobbing andshaping; shaving;grinding, burnishing

15

8√ Polish Semi-mirror-like �nishwithout any discerniblescratches or marks

8 0.0001 –0.0002

Grinding, shaving,burnishing, lapping

20

4√ Super-�nish

Mirror-like surfacewithout tool grinding orscratch marks of anykind

4 0.00004 –0.0001

Grinding, lapping, andpolishing

25

ref: Gear Handbook by Dudley, Table 9-17

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Table 4.9: Popular Tooth Forms

Dimensions shown are for 1 ndp.For other sizes, divide dimensions shown by ndp needed.

NormalTooth Pressure Whole Fillet CircularForm Angle Depth Addendum Dedendum Radius Pitch

Full Depth 14.5° 2.157 1.00 1.157 0.21 3.1416

Full Depth 20° 2.157 1.00 1.157 varies 3.1416Full Fillet 20° 2.250 1.00 1.250 0.30 3.1416Pre-Shave or

Pre-Grind20° 2.350 1.00 1.350 0.30 3.1416

Stub 20° 1.800 0.80 1.000 0.20 3.1416

Full Depth 25° 2.250 1.00 1.250 0.25 3.1416Full Fillet 25° 2.300 1.00 1.300 0.30 3.1416

Fellows Stub(x ⁄ y)

20° 2.25 ⁄ y 1.00 ⁄ y 1.25 ⁄ y varies 3.1416 ⁄ x

Nutall 20° 1.728 0.79 .943 varies 3.1416

Notes:1 Fellows stub is also called “combination pitch.”2 Nutall system should not be used for new designs.

Circ. PitchCirc. Pitch / 2

Addendum

Dedendum

WholeDepth

FilletRadius Normal

PressureAngle

Basic Rackon Hob

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Chapter 5

How Should They Be Made?

Gears can be made by a number of machiningand “near-net shape” processes. The “near-netshape” processes (plastic molding, powder-metalforging, and stamping ) require large “upfront” in-vestments in tooling, and are usually restricted tovery high volume (5000+ pieces) applications. Itis very expensive to make changes to these tools,so it is advisable to make prototypes by less ex-pensive methods, usually machining them fromthe same material as planned for the �nal prod-uct. Each “near net” process has its own uniquerequirements, and it is best to work closely witha couple of suppliers to make certain the part de-sign is compatible with the process desired. Thepower capacity of plastic and powdered metalgears is not well “standardized”, and a thoroughtesting program is suggested for all new applica-tions.

The machining methods used to make gearteeth can be divided into a number of subcate-gories, each of which must be well understoodif the gear designer is to avoid manufacturingproblems and high production costs. Careful se-lection of tooth size (Diametral Pitch or Module),for example, can avoid the need for special hobsand shave 8 to 12 weeks o� the required leadtime. Asking for a ground tooth when there isonly clearance for a 3-inch diameter cutter mighttriple the cost of the part, double the lead time,and restrict you to a couple of suppliers. The fol-lowing paragraphs will provide some insight intothe most common machining methods, and helpyou select the best process for your gears.

MillingMilling gear teeth with a cutter having the samepro�le as the tooth space is the oldest methodstill in current use. Milling is most commonlyused to produce special course-pitch (less than1 dp) gears or unusual non-involute forms thatare di�cult to generate with a hob. Milling cut-ters are available to cut a “range” of tooth num-bers (see Table 5.1). If more accuracy is required,special cutters with the form of an exact toothnumber can be made. Modern cutter manufac-turing techniques can produce excellent results,but it is di�cult to produce much better thanan AGMA Class 7 gear by this method. It is ad-visable to make both mating parts of a gearsetby milling to avoid meshing problems related to

pro�le errors. Most of the machines used to millgear teeth are unable to provide “double plunge”cutting cycles, so it is important to allow plentyof cutter clearance on one end of the part. Specialsmall-diameter cutters can be made, but there arelimitations, so make sure to consult your gearsupplier or a tool manufacturer.

HobbingHobbing is the most popular gear-manufacturingmethod, combining high accuracy with high pro-duction speed. A wide variety of cutting tools areavailable “o� the shelf” (see Tables 5.2 and 5.3)in quality levels to match part-quality require-ments, making it easy to get the tooth form youneed without having to wait for or pay for custom

29

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Table 5.1: Normally-Available Milling Cutters

O�ered in 14.5° and 20°npa.

Normal MinimumCutter Cutter

ndp Diameter Diameter

1 8.5 8.51.25 7.75 7.751.5 7 71.75 6.5 6.52 5.75 5.752.25 5.75 5.752.5 5.75 5.752.75 4.75 4.753 4.75 4.753.5 4.5 4.54 4.25 3.54.5 3.5 3.55 3.75 3.3756 3.5 3.1257 2.875 2.8758 3.25 2.8759 2.75 2.7510 2.75 2.37512 2.625 2.2514 2.5 2.12516 2.375 2.12518 2.375 220 2.375 224 2.25 1.7528 2.25 1.7532 2.25 1.7536 2.25 1.7540 1.75 1.7548 1.75 1.7556 1.75 1.7564 1.75 1.75

Minimum MaximumCutter Number Number

Number of Teeth of Teeth

1 135 Rack2 55 1343 35 544 26 345 21 256 17 207 14 168 12 13

Note: Teeth smaller than 3.5 ndp are seldom milled.

Image courtesy of Ash Gear & Supply

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Chapter 5 — How Should They Be Made? 31

Table 5.2: Normally-Available Gear Hobs

(a) Diametral-Pitch Hobs

O�ered in 14.5°, 20°, and 25°npa.

Normal Minimumndp Module Diameter Diameter

1 25.4 10.75 10.751.25 20.32 8.75 8.751.5 16.9333 8 81.75 14.5143 7.25 7.252 12.7 5.75 5.752.25 11.2889 5.5 5.52.5 10.16 5 52.75 9.2364 5 53 8.467 4.5 4.53.5 7.257 4.25 4.254 6.35 4 44.5 5.644 4 45 5.08 3.5 3.56 4.233 3.5 3.57 3.6286 3.25 3.258 3.175 3 29 2.822 3 210 2.54 3 1.87512 2.1167 2.75 1.87514 1.8143 2.5 1.87516 1.5875 2.5 1.87518 1.4111 2.5 1.2520 1.27 2.5 1.2524 1.0583 2.5 0.937528 0.9071 2.5 0.937532 0.7938 2.5 0.937536 0.7056 2.5 0.7540 0.635 2.5 0.7548 0.5292 2.5 0.7556 0.4536 1.875 0.7564 0.3969 1.625 0.7572 0.3528 1.625 0.7580 0.3175 1.625 0.7596 0.2646 1.5 0.75

4NDP

8NDP

16NDP

(b) Module (Metric) Hobs

O�ered in 20°npa.

Normal MinimumModule ndp Diameter Diameter

0.2 127 1.25 0.93750.3 84.6667 1.625 0.93750.4 63.5 1.875 0.93750.5 50.8 1.875 0.8750.6 42.3333 1.875 0.8750.7 36.2857 1.875 0.8750.75 33.8667 2.5 1.1250.8 31.75 1.875 1.250.9 28.2222 1.875 1.251 25.4 2.5 1.251.25 20.32 2.5 1.8751.5 16.9333 2.5 1.8751.75 14.5143 2.5 1.8752 12.7 2.75 1.8752.25 11.2889 2.75 1.8752.5 10.16 2.75 1.8752.75 9.2364 3 23 8.4667 3 23.25 7.8154 3 33.5 7.2571 3 33.75 6.7733 3 34 6.35 3.5 3.54.25 5.9765 3.25 3.254.5 5.6444 3.5 3.54.75 5.3474 3.5 3.55 5.08 3.5 3.55.5 4.6182 3.5 3.56 4.2383 4 46.5 3.9077 4 47 3.5286 4.25 4.258 3.175 4.5 4.59 2.8222 5 510 2.54 5 511 2.3091 5.5 5.512 2.1167 5.75 5.7514 1.8143 6.5 6.515 1.6933 6.5 6.516 1.5875 8 818 1.4111 8.25 8.2520 1.27 8.75 8.7522 1.1545 9.5 9.524 1.0583 10.75 10.7525 1.016 10.75 10.7527 0.941 10.75 10.75

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Table 5.3: Normally-Available Spline Hobs

(a) Diametral-Pitch Hobs

O�ered in 30°npa.Normal Minimum


2.5/5 4 43/6 4 44/8 3.5 3.55/10 3 36/12 3 38/16 2.75 1.87510/20 2.5 0.87512/24 2.5 0.87516/32 2.5 0.87520/30 2.5 0.87520/40 2.5 0.87524/48 2.5 0.7532/64 2.5 0.7540/80 2.5 0.7548/96 2.5 0.625

(b) Diametral-Pitch Hobs

O�ered in 37.5° and 45°npa.Normal Minimum


6/12 3 38/16 2.75 2.7510/20 1.875 1.2512/24 1.875 1.2516/32 2.5 1.2520/40 2.5 1.2524/48 1.875 1.2532/64 1.875 1.12540/80 1.875 1.12548/96 1.875 1.125

64/128 1.875 1.125 45° only80/160 1.875 1.125 45° only

(c) Module (Metric) Hobs

O�ered in 30°, 37.5°, and 45°npa.

Normal MinimumModule Diameter Diameter

0.4 1.875 1.1250.5 1.875 1.1250.6 1.875 1.1250.7 1.875 1.1250.75 1.875 1.1250.8 1.875 1.1250.9 1.875 1.1251 2.5 1.251.25 2.5 1.8751.5 2.5 1.8751.75 2.5 1.8752 2.75 1.8752.25 2.75 1.8752.5 2.75 1.8752.75 2.75 1.8753 3 23.5 3 34 3.25 3.254.5 3.25 3.255 3.5 3.56 3.5 3.57 3.75 3.758 3.75 3.7510 4 4

(d) Spline Forms

Flat Root:

Fillet Root:

Sample — BD Tech

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tooling. Hobbing is a “generating” process — thetooth pro�le is developed in a series of cuts as thehob ( a threaded worm with slots or gashes thatact as cutting edges (see Figures 5.1 and 5.2) ro-tates and is fed at an angle to the workpiece. Dueto this “swivel” angle the hob must have room to“approach” and “overrun” the needed face widthand insure that “full depth” teeth are cut in thatarea. (This is one of the �rst things to investigateif load-distribution or noise problems appear.)Allowances must also be made so that the hobdoes not destroy other features on the part whenentering or exiting the cut (see Figure 5.3).

Undercutting is another problem that occursin the hobbing process. On parts with low num-bers of teeth (the limiting number of teeth varieswith the pressure and helix angles), the tip of thehob can remove or “undercut” the lower portionof the part tooth, destroying the involute pro�leand reducing the strength of the tooth. This prob-lem is usually corrected by changing to a higherpressure angle, increasing the number of teeth(with a corresponding reduction in tooth size),or “enlarging” the pinion teeth and “contracting”the gear teeth (also called the “long and shortaddendum” system). If the number of teeth onyour part is less than that shown on Table 5.4,you may want to read the information on under-cutting found in the books listed in the referencesection of this guide.

Hobbing is used to produce spur, helical, anddouble-helical gears. The helix angle of helicalgears necessitates larger approach, overrun, andclearance allowances. For double-helical gearsthere is the additional complication of determin-ing the “gap width” required to avoid the hobcutting one side of the gear from damaging theother side when it reaches the end of its cut (seeFigure 5.4). The analysis of these situations isquite complex. Several di�erent methods are de-tailed in the reference books, including graphicaltechniques that may be adaptable to cad systems.Where little or no gap width can be allowed, a

shaped or assembled double-helical gear can beused. Use of “staggered” rather than “in-line”teeth slightly reduces the gap required for hobbedgears.

ShapingShaping involves a reciprocating pinion-like cut-ter (see Figure 5.5) which is rotated and in-fedagainst the rotating blank to generate the toothpro�le. Spur, helical, and double-helical gears canbe produced by this method with either internalor external teeth. Cutting-tool availability is notas great as with hobbing, and machine capabili-ties are far more limited, especially with regardto helix angle. Special “guides” are needed foreach helix angle to be cut — at a cost of severalthousand dollars each — along with matching cut-ting tools. To minimize these expenses severalstandard helix angles have been adopted (23°, 30°,and 45° are most common). Special “herringbone”machines have been developed to cut both sidesof a double-helical gear at the same time withlittle or no “gap” at all. Larger gears (6 dp andlower) can also be produced on “rack”-shapingmachines which use a straight “rack” of cutterteeth to generate the tooth pro�le.

Except for herringbone gears, all shaped teethrequire a chip-clearance groove beyond the toothface (see Figure 5.6). The cutter must also haveopen access to the start of the cut. Shaped partscan be cut between centers, on an arbor, or in alocating �xture. Fixtures are also used when thegear teeth must be aligned with another featureon the part. It is usually easier to cut the teeth�rst and then produce the aligned feature, butwhere this cannot be done it is much simpler toshape the teeth rather than hob them. If align-ment is required, remember to make a specialnote of the relationship to be maintained and atolerance on that alignment. Normal operatingprocedure in the gear industry is to assume thatno alignment requirement exists unless speci�-cally noted on the drawing. Any alignment shown

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CamRelief

Gash

Keyway

OutsideDiameter

Hole

ToothFace

Depth of Gash

PitchDia.

ThreadHelix

Lead Angle

HubDia.

Lead

Active Length

Length

NormalPressure Angle

Straight Portion

NormalTooth Thickness

Top Radius

Hob Addendum

Hob Dedendum

Approach

Whole Depthof Cut

Courtesy of Ash Gear & Supply Corporation

Figure 5.1: Hob Nomenclature — 1

Sample — BD Tech

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AxialPitch

Normal

Pitch

CenterLine

Flute Helix

AxialPitch

Normal

Pitch

FluteAngle

Straight Flute Helical Flute

Gear

Hob

Base CirclePitch Circle

Pitch Line

Line ofActionThe Hobbing Process

Pitch Circle

GearTooth

GearTooth

The Generating Action of a Hob

Courtesy of Ash Gear & Supply Corporation

Figure 5.2: Hob Nomenclature — 2

Sample — BD Tech

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HobCenter

HobLength

SwivelAngle

HobDiameter

WholeDepth

FaceWidth

Overrun

Clearance Required

TopView

SideView

Figure 5.3: Hobbing-Clearance Diagram

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HobCenter

HobLength

SwivelAngle

Gap Width Hob Diameter

WholeDepth

FaceWidth

Overrun

Groove DiameterLess Than

Root Diameter

Clearance Required

TopView

SideView

Figure 5.4: Double-Helical Gap-Width Diagram

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Cuer & Holder

Shank Cuer

Corr. Add.

InvoluteProfile

Cordal ToothThickness

ToothSpacing

Hole

C ' BoreRoot DiameterBase DiameterPitch Diameter

Outside Diameter

SideClearance Web Top Angle

Wid

th

Gear Shaper Cuer

Gear Being Generated

Base Circle Pitch Circle

BaseCircle

Shape of Gear Shaper-Cuer Chip

PitchCircle

Figure 5.5: Shaper-Cutter Nomenclature

Sample — BD Tech

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Table 5.4: Minimum Number of Teeth to Avoid Undercutting

NormalPressureAngle

WholeDepth @

1 ndp

Helix Angle

0° 10° 15° 20° 25° 30° 35° 40° 45°

14.5° 2.157 32 31 30 29 27 25 23 20 1720° 1.8 15 14 14 13 12 12 11 10 820° 2.25 18 18 17 17 16 15 13 12 1125° 2.25 13 12 12 11 11 10 9 8 8

Undercut tooth:

WorkingDepth

Relative tooth shape — Same ndp:

14 1⁄2°Full

Depth

20°Stub

Depth

20°Full

Depth

25°Full

Depth

WholeDepth

FaceWidth

ChipClearanceGroove

GrooveDiameterLess Than

RootDiameter

StrokeLength

EnteringClearance

RootDiameter

Figure 5.6: Shaper-Cutter Clearance Diagram

Sample — BD Tech

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on the drawing but not noted is assumed to be a

drafting convenience only. Tooth alignment ofhobbed teeth is very di�cult.

Another important design aspect of the shap-ing process is the need to relate cutter size tothe number of teeth on internal gears to prevent“trimming” of the teeth by the exiting cutter tooth.Table 5.5 shows the minimum number of partteeth that can be cut by a given number of cutterteeth. This varies according to the tooth form,and can be adjusted slightly by enlarging the mi-nor or inside diameter of the internal gear. Thiscan reduce the contact ratio and must be analyzedvery carefully. Methods for this are outlined inseveral of the reference books.

Small shaper cutters are typically made as“shank” cutters (one piece with the tool holder)which have very speci�c face-width limitations.Wide face widths can cause cutter life and rigid-ity problems. These parts may be more suitablefor the “broaching” method described below. It isbest to avoid designing parts that require shapercutters with less than �ve teeth.

BroachingThe broaching process is used to produce inter-nal spur gears and splines. A broach having thesame shape as the required tooth spaces is pushedor pulled through a pilot hole with each row ofteeth removing a little more metal. Some partsmay require more than one “pass“ with a seriesof broaches to reach the �nal size. The processis very fast and accurate but requires expensivetools and careful blank preparation. Some ma-chines are susceptible to “broach drift” and re-quire �nal machining after broaching. Part sizeis limited by the “tonnage” or power capacityof the broaching machine and the length of thebroach that can be pulled. Fixtures can be madeto align part features and the teeth, or to broachmore than one part at a time. Broaching is usu-ally limited to parts under 45 hrc, and toolingdesign can be very tricky if allowances must be

made for heat-treat distortion on parts broachedbefore heat treatment. Broaches are very expen-sive to make so it is wise to check if your gearmanufacturer has an existing broach before �-nalizing your design. It is important to tell themthe length of cut involved as there must be atleast two broach pitches in the part at all timesto avoid trouble. Give the maximum amount oftooth-thickness tolerance possible, as broachescannot be adjusted to vary the depth of cut like ashaper.

LappingLapping — the oldest gear “�nishing” method —involves running a set of gears with an abrasive�uid in place of the lubricant. This process wasdeveloped to adjust for cutting inaccuracies, in-crease backlash, and improve surface �nish. Lap-ping is no longer widely used, as sophisticatedgear inspection techniques have revealed that ex-cessive lapping can destroy the involute form cutinto the teeth. Modern gear-cutting equipmentcan usually produce parts that do not require lap-ping, and lapping requirements noted on olderdrawings are frequently ignored. The most com-mon use at lapping today is as a “last resort” insolving �eld problems or in making very �ne ad-justments in backlash for pump or instrumentgears. In some cases gears are lapped with “dum-mies” (made of cast iron or another soft material)to replicate the mating part. This reduces thetendency to damage the involute form.

ShavingShaving is a gear “�nishing” method that is usedto improve surface �nish and gear geometry (leadand involute). A serrated gear-like cutter (see Fig-ure 5.7) is rotated and led axially while in meshwith the part. The part teeth must be cut witha special “pre-shave” hob or shaper cutter that�nishes the root area at the part but leaves “stock”on the sides of the teeth. The cutter axis is at an

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Table 5.5: Shaper-Cutter Teeth vs.

Minimum Internal Gear Teeth

to Avoid Interference

# teeth incutter (Nc )

# teeth in internal gear

14.5° fd 20° fd 20° Stub 25° fd 30° ff 30° fr

3 15 11 11 10 9 94 18 13 13 12 12 105 20 15 15 14 13 116 22 17 16 15 14 127 24 19 17 17 16 138 26 21 18 19 17 149 28 23 20 21 18 1510 30 24 22 22 19 1611 32 26 23 23 20 1712 34 27 24 24 21 1813 36 29 25 25 22 1914 38 31 26 26 23 2015 39 33 27 27 24 2116 41 34 28 28 25 2218 44 36 30 30 27 2420 47 38 32 32 29 2621 49 39 33 33 30 2724 54 42 36 36 33 3025 55 43 37 37 34 3127 58 45 39 39 36 3328 59 46 40 40 37 3430 62 48 42 42 39 36

over 30 Nc+32 Nc+18 Nc+12 Nc+12 Nc+9 Nc+6

Note: Small shank cutters (Nc<10) do not produce a true involuteform.

Sample — BD Tech

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Clearance Holes

Key Way

MarkingZone

Hole Dia.Outside Dia.

Serrations

FaceWidth

HelixAngle

a

a

bc

(a) Work and cutter rotation(b) Axial sliding motion caused by crossed axes(c) Direction of chip removal

Undercut

ShavingStock

Gear Tooth

Undercut required prior to shaving.

(Courtesy of Ash Gear & Supply Corporation)

Figure 5.7: Shaving-Cutter Nomenclature

Sample — BD Tech

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angle to the part axis which creates a shaving orplaning action as the cutter moves axially acrossthe gear face. Spur, helical, and double-helical(with gap) gears can be shaved. Both internal andexternal teeth can be accommodated if propertooling can be designed. Tool clearance is an im-portant consideration, as shaving cutters are veryfragile and expensive. Internal gears are subjectto the same cutter-size limitations discussed inthe “shaping” section of this manual. Shavingcutters are often designed for a speci�c applica-tion, and “o� the shelf” tooling availability maybe limited.

On hobbed parts, care must be exercised toavoid hitting the hob runout area. A techniqueknown as “hob dipping” (feeding the hob past �n-ish depth at the ends of the cut) is sometimes usedto minimize this problem (see Figure 5.8). This issimilar in principle to crown hobbing. Shavingis often used to provide “crowned” or “tapered”teeth for special applications where shaft mis-alignment or adjusting backlash is desired. Shav-ing is most successful on parts less than 50 hrc.

HoningThe honing process is similar to shaving exceptthat the cutters are coated with an abrasive mate-rial. As shaving machines can also be adapted tohoning most of the limitations discussed abovestill apply. Honing has been used to producevery �nely polished surface �nishes (as low as6 aa) and to �nish surface-hardened gears thatare not suitable for gear grinding. This is a very“hot” area of gear research and is best studiedby reading technical papers and manufacturer’sliterature.

Gear GrindingGear grinding is the “Cadillac” of gear-�nishingprocesses. High accuracy, excellent surface �nish,and special features (see Figure 5.9) like crowning,tooth taper, and pro�le modi�cation (tip relief)

are possible with most grinding methods. Whilethere are many di�erent brands of grinding ma-chines (see Figure 5.10), each with a slightly di�er-ent operating principle, they can be divided intotwo basic types — form grinders and generatinggrinders.

Form GrindersForm grinders employ a thin wheel that has been“dressed” with the pro�le of the desired toothspace. This method is very versatile and canbe used to grind internal and external teeth ofalmost any type, including non-involute forms.Form grinding is also used to produce racks andgear segments that cannot be done by generatingmethods. Wheels as small as 1.5 inches in diam-eter can be �tted on some machines, allowingone piece “cluster” gears and small internal gearsto be processed. Dressing the proper form intothe wheel requires a high degree of operator skillor an expensive cnc control. Wheels must bere-dressed frequently, adding time to an alreadyslow process. Newer form grinding machines areable to use longer-lasting abrasive-coated steelwheels which may make form grinding more costcompetitive. Form grinding should be avoided inthe design of new parts if at all possible.

Generating GrindersOne type of generating grinder employs a large di-ameter (8 to 14 inches is most common) threadedwheel that acts much like an abrasive hob. Arelatively simple dressing mechanism is usedto maintain a very accurate straight-sided rackwith the proper pressure angle and depth in thewheel. The large diameter provides a long life be-tween dressings, but creates clearance problemson many parts (see Figure 5.11). Small diameter“solid-on-shaft” pinions and the pinion on one-piece “cluster” gears are often impossible to grindby this method.

Other generating grinders use either one ortwo narrow grinding wheels, which simulate arack. These wheels are very easy to dress but re-

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Amountof Dip

ActiveFace

Width

Finishing“Dipped”

Centerline

TrueHobbing

Centerline Starting“Dipped”

Centerline

Figure 5.8: Hob-Dipping Diagram — (Pre-Shave)

Crown

Taper

Figure 5.9: Tooth Modi�cations

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Grinding Wheel

GearGrinding Profile

OnlyGrinding Root

and Profile

(a) Form Grinders

(National, Orcutt, Detroit,

Kapp, Gear Grind, Michigan)

0°45° 45°

(b) Threaded Wheel

(Reishauer, Okomoto, She�eld)

(c) Two Wheel

(Maag)

(d) Single Wheel

(Hoe�er, Niles, Pratt & Whitney)

(Courtesy of American Pfauter’s Gear Process Dynamics)

Figure 5.10: Gear Grinder Types

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GrindingWheel

Hob

One-Piece Design Two-Piece Design

Figure 5.11: Grinding-Wheel Interference on Cluster Gears

quire more frequent attention than the threadedtype discussed above. Cycle times are slightlyslower also, although they are much faster thanform grinding. The same wheel-interferenceproblems are also encountered. For new designsit is best to consult several gear suppliers andread as much as you can on the method to beused before �nal drawings are prepared.

There are other problems that crop up fre-quently with all ground gears. Improper feeds,speeds, wheel materials, and coolants can causegrinding cracks and re-tempering (also called softspots or grinding burns). Nital etching is usedas an in-process check on grinding quality, andgear designers are wise to note a nital etch re-quirement on the drawing. It is also di�cult tomaintain tight controls on tooth thickness andalignments with other part features because heat-treat distortion may not occur uniformly, and theamount of stock removed from each side of thespace may not be equal. These tolerances shouldbe discussed with the supplier before �nalizing adesign.

Bevel GearsBevel-gear-cutting methods fall into two gen-eral categories — the reciprocating-blade methodfor straight bevels, and rotating-cutter methods

for straight, spiral, and Hypoid bevels. Bevelgears are probably the most di�cult to manu-facture. The theoretical “summary” (a computercalculated set of machine adjustments) is justthe starting point for developing the proper con-tact pattern between the gear and pinion. Dur-ing a production run this contact pattern mustbe constantly monitored and adjustments madefor cutter wear and diameter changes due to re-sharpening. It is very important that the samemating part or master gear be used for thesechecks if the parts are to be interchangeable.Many �eld problems are caused by attempts touse non-interchangeable parts as a gearset. Sub-tle di�erences in cutting methods can often resultin wide variations in contact pattern. The bestpolicy is to order bevel gears as a set and to re-place them as a set. If that is not possible, the useof a master gear and a speci�ed cutting method,complete with a proven summary, is the next-bestchoice.

Cutter clearance is an important considera-tion in the design of bevel-gear blanks, especiallyon parts with a through shaft or hub on the “smallend” of the gear (see Figure 5.12). Consult yourgear supplier early in the design process, andreview all parts that might have this problem. Mi-nor changes in hub or shaft diameters can oftenresult in considerable cost reductions.

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Worm GearsWormgear sets consist of a threaded worm anda mating gear. The worms can be produced byrolling, milling, or grinding, and usually presentno signi�cant manufacturing problems. Wor-mgears, on the other hand, can be almost as trickyto make as bevel gears. Successful developmentof the contact pattern and tooth thickness de-pends on proper initial tool design and accurateadjustment of the hobbing machine to accountfor cutter re-sharpening. Fly tools, commonlyused on low-volume jobs due to lower tool cost,are particularly prone to this problem due to theshort life of the single cutting point per lead. Thismethod requires low tool loads and relativelylong cycle times to produce an accurate gear. Wor-mgear hobs are custom-designed to replicate themating worm and have very distinct limits onthe number of times they can be re-sharpenedwithout compromising the tooth geometry. Many

�eld problems are caused by trying to use a hobwhich has been sharpened below the acceptablelimits of outside diameter.

Wormgears are usually checked against a mas-ter worm at both the mounted center distance (forbacklash) and a “tight mesh” center distance (fortotal composite error). If no master worm is avail-able, it is acceptable to use a representative mat-ing worm. Cutter clearance is not a problem withwormgear hobbing but part tolerancing shouldbe watched carefully. Excessive runout can causethe contact pattern to “wander” across the facewidth. Parts cut with a topping hob will havefairly wide variations in “throat diameter” (seeFigure 5.13) depending upon how many times thehob has been sharpened. As long as the contactpattern is good and the backlash is within lim-its, this should not cause a functional problem.Throat diameters should usually be “reference”dimensions.

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Apex

RootAngle

RotaryCuer

Figure 5.12: Bevel-Cutter Interference with Front Shaft

OutsideDiameter

ThroatDiameter

(Reference)

Ref. Throat Radius

Figure 5.13: Worm-Gear Throat Diameter

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Chapter 6

How Should They Be Inspected?

“Quality levels” have been established by theAmerican Gear Manufacturer’s Association(AGMA) to provide a common basis upon whichto compare parts made by di�erent methods andfrom di�erent suppliers. The current standard ongear inspection (AGMA 2000) contains informa-tion on selecting quality levels, calculating toler-ances, and measuring gear elements. When youput an AGMA quality level on a drawing you arespecifying that inspections be done in accordancewith the provisions of AGMA 2000. The standardoutlines many di�erent ways of certifying that aquality level has been met, and the manufactureris free to select from those methods unless yourequire speci�c inspections on your drawing.

Tooth thickness measurements, for example,can be made with �ve di�erent methods. If youplan to use a particular method for receiving in-spection, that is what should be noted on thedrawing. The gear manufacturer may then usewhatever method he wants for in-process checks,but the �nal inspection report will contain mea-surements that are directly comparable to yourresults.

Most gear purchasers are not equipped to per-form detailed gear inspections, and must rely onthe supplier to certify the “quality” of the deliv-ered goods. The gear designer has the option ofrequiring either “composite” or “individual ele-ment” (such as lead, pro�le, spacing, or runout)checks on the drawing, and may request copiesof the “charts” (the graphical output of the gearinspection machine) from these checks. Mak-ing charts is very time consuming and most gearsuppliers pass the cost of this labor on to thepurchaser in the form of higher part prices or

separate inspection fees. If you require charts besure to indicate the sampling plan desired. 100%inspections are seldom cost e�ective. Table 6.1 isan example of a typical sampling plan.

Modern inspection equipment can determinepart characteristics with far greater accuracy thanmanufacturing can make the parts. Some types ofgears, such as bevels and worms, have not beensubjected to “individual element” checks becauseof equipment limitations and have always beenaccepted based upon “composite” methods. Justbecause it is possible to inspect the individualelements of spur and helical gears does not meanit is practical. It is not uncommon for a gearpair accepted by such methods to have “additiveerrors” that result in unacceptable performance.Conversely, a pair of “rejected” gears may have“complementary errors” and provide very accept-able performance.

“Elemental” checks provide valuable infor-mation for in-process control of manufacturing,but may not be the “best” criteria for �nal ac-ceptance. The “composite” method of checkinga gear against its mate or a master gear on a“tight mesh” center distance considers lead, pro-�le, spacing, and runout errors. Both “�anks”of a tooth space are checked at the same time,however, when in actual operation only one isin mesh at a time. “Single �ank”, also knownas “transmitted error” testing is far more realis-tic but is not widely available. The author feelsthat a combination of composite checks and oc-casional contact-pattern checks (see Figure 6.1)under simulated “assembled” conditions is themost practical way to qualify a gearset and avoid�eld problems.

49

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Table 6.1: Sampling Plans

Lot Size 1% aql 4% aql

2 to 8 100% 1 of 29 to 15 100% 1 of 416 to 25 100% 1 of 726 to 50 1 of 2 1 of 751 to 90 1 of 4 1 of 1291 to 150 1 of 7 1 of 18151 to 280 1 of 7 1 of 21281 to 500 1 of 7 1 of 40501 to 1200 1 of 9 1 of 701201 to 3200 1 of 10 1 of 140

3201 to 10,000 1 of 16 1 of 400

Based on Level II-A of Mil-STD-105D.Modi�ed for in-process inspection.

(a) Worm Gear (b) Bevel Gear

Figure 6.1: Bearing Pattern Checks

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Chapter 6 — How Should They Be Inspected? 51

“Quality” costs when it comes to gears. Be-fore you put a quality requirement on a drawing,make sure you really need it. Attempting to solveyour “gear” problems by increasing quality re-quirements can be expensive and ine�ective. The“right” quality level for you is the one that worksin your application. It you �nd that one aspectof your gears (such as lead, pro�le, spacing, or

runout) needs to be controlled more closely thanthe others, it is your option to tighten the toler-ance on just that element. It is not uncommon, forexample, to order a Quality 8 gear with Quality 10spacing as long as it is noted on the drawing. Thereference books listed at the end of this manualhave extensive discussions on various aspects ofgear quality.

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Sample — BD Tech

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Chapter 7

Where Do I Look For Help?— Reference Material

Cutting Tool Catalog

Ash Gear & Supply Company21380 Bridge StreetSouth�eld, MI 48034(313) 357 – 5980

This catalog covers “o�-the-shelf” gear-cuttingtools, and contains a lot of practical informationon gear design.

Machinery’s Handbook

By Erik Oberg, Franklin D. Jones, and HolbrookL. HortonIndustrial Press Inc.200 Madison AvenueNew York, NY 10157ISBN 0–8311–1155–0

This “machine-shop bible” contains a good dealof information on gears. While some of it is dated,it still provides a “common denominator” for gearusers throughout industry.

Gear Handbook

Darle W. Dudley, Editor-in-ChiefMcGraw-Hill Book CompanyNew York, NYLibrary of Congress Number: 61–7304

This 1962 publication is a classic in gear litera-ture, and is a “must-read” for any gear designer’slibrary.

Practical Gear Design

By D.W.DudleyMcGraw-Hill Book CompanyNew York, NYLibrary of Congress Number: 53–11476

This book may hard to locate, and is somewhatdated, but its tool-design section is an excellentreference for special applications.

Handbook of Practical Gear Design

By Darle W. DudleyMcGraw-Hill Book CompanyNew York, NYISBN 0–07–017951–4

This 1984 revision of Practical Gear Design hasa lot of new information to o�er, including themost complete reference section ever published.

Gear Process Dynamics

By Geo�rey Ashcroft, Brian W. Clu�, Dennis R.Gimpert, and Claude LutzAmerican Pfauter Corporation925 East Estes AvenueElk Grove Village, IL 60007

This is the textbook from American Pfauter’sGear Process Dynamics Clinic, an excellentcourse for engineers involved in gear manufac-turing.

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Revised Manual of Gear Design

By Earle BuckinghamBuckingham Associates591 Parker Hill Road Spring�eld, VT 05156

This three-volume work has some excellent ba-sic information on gear concepts. Section Twocovers planetary gears in great detail.

Standards

American Gear Manufacturers Association1500 King Street, Suite 201Alexandria, VA 22314(703) 684 – 0211

AGMA maintains standards on many aspects ofgear design, including ratings, materials, inspec-tion, and cutting tools. Don’t start an importantdesign project without the latest standards forreference.

Engineer To Win

By Carroll SmithMotorbooks InternationalOsceola, WI 54020ISBN 0–87938–186–8 (pbk.)

While this book is about materials for race cars,it has the most understandable explanation ofmaterials and heat treating I have ever read.

Systematic Analysis of Gear Failures

By Lester E. AlbanAmerican Society for MetalsMetals Park, Ohio 44073ISBN: 0–87170–200–2

If you want to learn why things didn’t work outas planned, this is the book to read.

Steel Selection

By Roy F. Kern and Manfred E. SuessJohn Wiley & Sons, Inc.New York, NYISBN: 0–471–04287–0

This book may contain more than you ever wantto know about steel selection, but it is easy toread and explains a great deal about why we usethe steels that have become “popular”.

Design of Weldments

By Omer W. BlodgettThe James F. Lincoln Arc-Welding Founda-tionP.O. Box 3035Cleveland, Ohio 44117

If you are going to design or use welded gearblanks or housings, you are going to need a copyof this book.

Plastics Gearing

ABA/PGT Publishing1395 Tolland TurnpikeManchesler, CT 06040

For information on plastic gears, this is the bookto read.

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Chapter 8

Acknowledgments

This book would not have been possible without the help of:The Pittsburgh Gear CompanyThe American Gear Manufacturers’ AssociationAsh Gear and Supply CorporationAmerican Pfauter CorporationDon BordenCam DrecollDon GoodlandEd HahlbeckJim HoltDon McVittieBrad NewcombTom Trudell

Coni�ex, Zerol, and Hypoid are trademarks of The Gleason Works.Spiroid and Helicon are trademarks of the Spiroid Division of The Illinois Tool Works.

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Chapter 9

About the Author

Charles D. Schultz has been active in the gear industry since 1971. A registered professional engineerin Wisconsin and Pennsylvania, Mr. Schultz has presented four papers at AGMA Fall TechnicalMeetings. His work has included engineering over �ve hundred custom gearboxes, supervising a largeindustrial-engineering department, managing a custom-drive-system division, designing heat-treatequipment, conducting �eld-service operations, writing a product catalog, supervising a sales andmarketing department, cost estimating, and teaching gear and heat-treat courses for co-workers andcustomers.

He has experience with a wide range of gear drives ranging from medical devices to bridgemachinery, including metal-processing equipment and wind-turbine gearboxes.

Since 2008 he has owned and operated an engineering consulting �rm, Beyta Gear Service.Mr. Schultz is a technical editor and blogger for Gear Technology magazine.

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http://www.geartechnology.com/

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