ELEMENTS OF METRIC GEAR TECHNOLOGY

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1 ELEMENTS OF METRIC GEAR TECHNOLOGY Gears are some of the most important elements use in machinery. There are few mechanical evices that o not have the nee to transmit power an motion etween rotating shafts. Gears not only o this most satisfactorily, ut can o so with uniform motion an reliaility. In aition, they span the entire range of applications from large to small. To summarize: Gears offer positive transmission of power. Gears range in size from small miniature instrument installations, that measure in only several millimeters in iameter, to huge powerful gears in turine rives that are several meters in iameter. Gears can provie position transmission with very high angular or linear accuracy; such as use in servomechanisms an military equipment. Gears can couple power an motion etween shafts whose axes are parallel. intersecting or skew. Gear esigns are stanarize in accorance with size an shape which provies for wiesprea interchangeaility. This technical manual is written as an ai for the esigner who is a eginner or only superficially knowlegeale aout gearing. It provies funamental theoretical an practical information. Amittely, it is not Intene for experts. Those who wish to otain further information an special etails shoul refer to the reference list at the en of this text an other literature on mechanical machinery an components. SECTION 1 INTRODUCTION TO METRIC GEARS This technical section is eicate to etails of metric gearing ecause of its increasing importance. Currently, much gearing in the unite States is still ase upon the inch system. However, with most of the worl metricate, the use of metric gearing in the Unite States is efinitely on the increase, an inevitaly at some future ate it will e the exclusive system. It shoul e appreciate that in the Unite States there is a growing amount of metric gearing ue to increasing machinery an other equipment imports. This is particularly true of manufacturing equipment. such as printing presses, paper machines an machine tools. Automoiles are another major example, an one that impacts tens of millions of iniviuals. Further sprea of metric gearing is inevitale since the worl that surrouns the Unite States is rapily approaching complete conformance. Englan an Canaa, once astions of the inch system, are well own the roa of metrication, leaving the Unite States as the only significant exception. Thus, it ecomes pruent for engineers an esigners to not only ecome familiar with metric gears, ut also to incorporate them in their esigns. Certainly, for export proucts it is imperative; an for omestic proucts it is a serious consieration. The U.S. Government, an in particular the military, is increasingly insisting upon metric ase equipment esigns. Recognizing that most engineers an esigners have een reare tan environment of heavy use of the inch system an that the amount of literature aout metric gears is limite, we are offering this technical gear section as an ai to unerstaning an use of metric gears. In the following pages, metric gear stanars are introuce along with information aout interchangeaility an non-interchangeaility. Although gear theory is the same for oth the inch an metric systems, the formulae hr metric 1.1 Comparison Of Metric Gears With American Inch Gears Comparison of Basic Racks In all moern gear systems, the rack is the asis for tooth esign an manufacturing tooling. Thus, the similarities an ifferences etween the two systems can e put into proper perspective with comparison of the metric an inch asic racks. In oth systems, the asic rack is normalize for a unit size. For the metric rack it is 1 moule, an for the inch rack it is 1 iametral pitch Metric ISO Basic Rack The stanar ISO metric rack is etaile in Figure 1-1. It is now the accepte stanar for the international community, it having eliminate a numer of minor ifferences that existe etween the earlier versions of Japanese. German an Russian moules. For comparison, the stanar inch rack is etaile in Figure 1-2. Note that there are many similarities. The principal factors are the same for oth racks. Both are normalize for unity; that is, the metric rack is specifie in terms of 1 moule, an the inch rack in terms of 1 iametral pitch. Fig. 1-1 The Basic Metric Rack From ISO 53 Normalize For Moule 1 h a =Aenum h f =Deenum c=clearance r=working Depth h=whole Depth p=circularpitch r f =Root Raius s=circular Tooth Thickness a = Pressure Angle Fig. 1-2 The Basic Inch Diametral Pitch Rack Normalize For 1 Diametral Pitch From the normalize metric rack, corresponing imensions for any moule are otaine y multiplying each rack imension y the value of the specific moule m. The major tooth parameters are efine y the stanar, as:

2 gearing take on a ifferent set of symols. These equations are fully efine in the metric system. The coverage is thorough an complete with the intention that this e a source for all information aout gearing with efinition in a metric format. Tooth Form: Pressure Angle: Straight-sie full epth, forming the asis of a family of full epth interchangeale gears. A 20º pressure angle, which conforms to worlwie acceptance of this as the most versatile pressure angle. 329

3 Aenum: Deenum: Root Raius: Tip Raius: This is equal to the moule m, which is similar to the inch value that ecomes 1/p. This is 1.25 m; again similar to the inch rack value. The metric rack value is slightly greater than the American inch rack value. A maximum value is specifie. This is a eviation from the American inch rack which oes not specify a rouning Comparison of Gear Calculation Equations Most gear equations that are use for iametral pitch inch gears are equally applicale to metric gears if the moule m is sustitute for iametral pitch. However, there are exceptions when it is necessary to use eicate metric equations. Thus, to avoi confusion an errors, it is most effective to work entirely with an within the metric system. 1.2 Metric Stanars Worlwie ISO Stanars International Stanars Organization (ISO). A listing of the most pertinent stanars is given in Tale Foreign Metric Stanars Most major inustrialize countries have een using metric gears for a long time an consequently ha evelope their own stanars prior to the estalishment of ISO an SI units. In general, they are very similar to the ISO stanars. The key foreign metric stanars are liste in Tale 1-2 for reference. 1.3 Japanese Metric Stanars In This Text Application of JIS Stanars Japanese Inustrial Stanars (JIS) efine numerous engineering sujects incluing gearing. The originals are generate in Japanese, ut they are translate an pulishe in English y the Japanese Stanars Association. Consiering that many metric gears are prouce in Japan, the JIS stanars may apply. These essentially conform to all aspects of tin ISO stanars. Metric stanars have een coorinate an stanarize y the Tale 1-1 ISO Metric Gearing Stanars ISO 53:1974 Cylinrical gears for general an heavy engineering - Basic rack Cylinrical gears for general an heavy engineering - Moules an iametral ISO pitches ISO 677: Straight evel gears for general an heavy engineering - Basic rack ISO 678: Straight evel gears for general an heavy engineering - Moules an iametral pitches ISO 701 : International gear notation - symols for geometrical ata ISO :1983 Glossary of gear terms - Part 1: Geometrical efinitions ISO 1328:1975 Parallel involute gears - ISO system of accuracy ISO 1340: ISO 1341: Cylinrical gears Information to e given to the manufacturer y the purchaser in orer to otain the gear require Straight evel gears - Information to e given to the manufacturer y the purchaser in orer to otain the gear require ISO 2203:1973 Technical rawings - Conventional representation of gears ISO 2490:1975 single-start soli (monoloc) gear hos with axial keyway, 1 to 20 moule an 1 to 20 iametral pitch - Nominal imensions ISO/TR 4467:1982 Aenum moification of the teeth of cylinrical gears for spee-reucing an spee-increasing gear pairs H5O 4468:1982 Gear hos - Single-start - Accuracy requirements ISO :1993 Acceptance coe for gears - Part 1: Determination of airorne soun power levels emitte y gear units ISO :1993 Acceptance coe for gears - Part 2: Determination of mechanical virations of gear units uring acceptance testing ISO/TR :1992 Cylinrical gears - Coe of inspection practice - Part 1: Inspection of corresponing flanks of gear teeth Tale 1-2 Foreign Metric Gear Stanars AUSTRALIA AS B 62 AS B 66 AS B 214 AS B 217 AS Bevel gears 1969 Worm gears (inch series) 1966 Geometrical imensions for worm gears - Units 1966 Glossary for gearing International gear notation symols for geometric ata (similar to ISO 701)

4 NF F NF E NF E NF E NF E NF E NFL FRANCE Glossary of gears (similar to ISO 1122) Glossary of worm gears Gearing - (similar to ISO 701) Tolerances for spur gears with involute teeth (similar to ISO 1328) Cylinrical gears for general an heavy engineering-basic rack an moules (similar to ISO 467 an ISO 53) Cylinrical gears - Information to e given to the manufacturer y the proucer Calculating spur gears to NF L Continue on following page

5 DIN 37 DIN 780 Pt 1 DIN 780 Pt 2 DIN 867 DIN 868 DIN 3961 DIN 3962Pt 1 DIN 3962 Pt 2 DIN 3962 Pt 3 DIN 3963 DIN 3964 DIN 3965 Pt 1 DIN 3965 Pt 2 DIN 3965 Pt 3 DIN 3965 Pt 4 DIN 3966 Pt 1 DIN 3966 Pt 2 DIN 3967 DIN 3970 Pt 1 DIN 3970 Pt 2 DIN 3971 DIN 3972 DIN 3975 DIN 3976 DIN 3977 DIN 3978 DIN 3979 DIN 3993 P11 DIN 3993 Pt 2 DIN 3993 Pt 3 DIN 3993 Pt 4 DIN 3998 Suppl 1 DIN 3998 Pt 1 DIN 3998 Pt 2 DIN 3998 Pt 3 DIN 3998 Pt 4 DIN Pt 1 Tale 1-2 (Cont.) Foreign Metric Gear Stanars GERMANY - DIN (Deutsches Institut für Normung) Conventional an simplifie representation of gears an gear pairs [4] Series of moules for gears - Moules for spur gears [4] Series of moules for gears - Moules for cylinrical worm gear transmissions [4] Basic rack tooth profiles for involute teeth of cylinrical gears for general an heavy engineering [5] General efinitions an specification factors for gears. gear pairs an gear trains [11] Tolerances for cylinrical gear teeth - Bases [8] Tolerances for cylinrical gear teeth-tolerances for eviations of iniviual parameters [11] Tolerances for cylinrical gear teeth-tolerances for tooth trace eviations [4] Tolerances for cylinrical gear teeth-tolerances for pitch-span eviations [4] Tolerances for cylinrical gear teeth-tolerances for working eviations [11] Deviations of shaft center istances an shaft position tolerances of casings for cylinrical gears [4] Tolerancing of evel gears-basic concept [5] Tolerancing of evel gears-tolerances for iniviual parameters [11] Tolerancing of evel gears-tolerances for tangential composite errors [11] Tolerancing of evel gears-tolerances for shaft angle errors an axes intersection point eviations [5] Information on gear teeth in rawings-information on involute teeth for cylinrical gears [7] Information on gear teeth in rawings-information on straight evel gear teeth [6] System of gear fits-backlash, tooth thickness allowances, tooth thickness tolerances-principles [12] Master gears for checking spur gears-gear lank an tooth system [8] Master gears for checking spur gears-receiving arors [4] Definitions an parameters for evel gears an evel gear pairs [12] Reference profiles of gear-cutting tools fit involute tooth systems accoring to DIN 867 [4] an efinitions for cylinrical worm gears with shaft angle 9Oº [9] Cylinrical worms-dimensions, correlation of shaft center istances an gear ratios of worm gear rives [6] Measuring element iameters for the raial or iametral imension for testing tooth thickness of cylinrical gears [8] Helix angles for cylinrical gear teeth [5] Tooth amage on gear trains-designation, characteristics, causes (11] Geometrical esign of cylinrical internal involute gear pairs - Basic rules [17) Geometrical esign of cylinrical internal involute gear pairs-diagrams for geometrical limits of internal gear-pinion matings [15] Geometrical esign of cylinrical internal involute gear pairs-diagrams for the etermination of aenum moification coefficients [15] Geometrical esign of cylinrical internal involute gear pairs-diagrams for limits of internal gear-pinion type cutter matings [10] Denominations on gear an gear pairs - Alphaetical inex of equivalent terms [10) Denominations on gears an gear pairs-general efinitions [11) Denominations on gears an gear pairs-cylinrical gears an gear pairs [11] Denominations on gears an gear pairs-bevel an hypoi gears an gear pairs [9] Denominations on gears an gear pairs-worm gear pairs[8] Spur gear rives for fine mechanics-scope, efinitions, principal esign ata, classification [7] Spur gear rives for fine mechanics-gear fit selection, tolerances, calculation [12] allowances [9] Spur gear rives for fine mechanics-inication in rawings, examples for

6 DIN Pt 2 DIN Pt Spur gear rives for fine mechanics-tales [15] Technical Drawings - Conventional representation of gears DIN Pt DIN ISO NOTES: 1. Stanars availale in English from: ANSI, 1430 Broaway, New York, 10018; or Beuth Verlag GmH. Burggrafenstrasse 6, D Berlin, Germany; or Gloal Engineering Documents. Inverness Way East, Englewoo, CO Aove ata was taken from: DIN Catalogue of Technical Rules Supplement, Volume 3, Translations UNI 3521 UNI 3522 UNI 4430 UNI 4760 UNI 6586 UNI 6587 UNI 6588 UNI 6773 Tale 1-2 (Cont.) Foreign Metric Gear Stanars ITALY Gearing - Moule series Gearing - Basic rack Spur gear - Orer information for straight an evel gear I Gearing - Glossary an geometrical efinitions Moules an iametral pitches of cylinrical an straight evel gears for general an heavy engineering (correspons to ISO 54 an 678) Basic rack of cylinrical gears for stanar engineering (correspons to ISO 53) Basic rack of straight evel gears for general an heavy engineering (correspons to ISO 677) International gear notation - for geometncal ata (correspons to 1970 ISO 701) Continue on following page 331

7 Catlog Q410 B 0003 B 0102 B 1701 B 1702 B 1703 B 1704 B 1705 B 1721 B 1722 B 1723 B 1741 B 1751 B 1752 B 1753 B 4350 B 4351 B 4354 B 4355 B 4356 B 4357 B Tale 1-2 (Cont.) Foreign Metric Gear Stanars JAPAN - JIS (Japanese Inustrial Stanars) Drawing office practice for gears Glossary of gear terms Involute gear tooth profile an imensions Accuracy for spur an helical gears Backlash for spur an helical gears Accuracy for evel gears Backlash for evel gears Shapes an imensions of spur gears for general engineering Shape an imensions of helical gears for general use Dimensions of cylinrical worm gears Tooth contact marking of gears Master cylinrical gears Methos of measurement of spur an helical gears Measuring metho of noise of gears Gear cutter tooth profile an imensions Straight evel gear generating cutters Single threa hos Single threa fine pitch hos Pinion type cutters Rotary gear shaving cutters Rack type cutters NOTE: Stanars availale in English from: ANSI, 1430 Broaway, New York, NY 10018; or International Stanarization Cooperation Center. Japanese Stanars Association, Akasaka, Minato-ku, Tokyo 107 Tale 1-2 (Cont.) Foreign Metric Gear Stanars UNITED KINGDOM - BSI (British Stanars Institute) BS 235 BS 436 Pt 1 BS 436 Pt 2 BS 436 Pt 3 BS 721 Pt 1 BS 721 Pt 2 BS 978 Pt 1 BS 978 Pt 2 BS 978 Pt 3 BS 978 Pt 4 BS 1807 BS 2007 BS 2062 Pt 1 BS 2062 Pt 2 BS 2518 Pt 1 BS 2518 Pt 2 BS 2519 Pt 1 BS 2519 Pt 2 BS 2697 BS 3027 BS 3696 Pt 1 BS 4517 BS 4582 Pt 1 BS 4582 Pt 2 BS 5221 BS 5246 BS Specification of gears for electric traction Spur an helical gears - Basic rack form, pitches an accuracy (iametral pitch series) Spur an helical gears - Basic rack form, moules an accuracy (1 to 50 metric moule) (Parts 1 & 2 relate ut not equivalent with ISO 53, 54, 1328, 1340 & 1341)Spur gear an helical gears-metho for calculation of contact an root ening stresses, limitations for metallic involute gears (Relate ut not equivalent with ISO/DIS 6336/1, 2 & 3) Specification for worm gearing - Imperial units Specification for worm gearing - Metric units Specification for fine pitch gears - Involute spur an helical gears Specification for fine pitch gears - Cycloial type gears Specification for fine pitch gears - Bevel gears Specification for fine pitch gears - Hos an cutters Specification for marine propulsion gears an similar rives: metric moule Specification for circular gear shaving cutters, 1 to 8 metric moule, accuracy requirements Specification for gear hos - Hos for general purpose: 1 to 20.p., inclusive Specification for gear hos - Hos for gears for turine reuction an similar rives Specification for rotary form relieve gear cutters - Diametral pitch Specification for rotary relieve gear cutters - Metric moule Glossary for gears - Geometrical efinitions Glossary for gears - Notation (symols for geometrical ata for use in gear rotation) Specification for rack type gear cutters Specification for imensions of worm gear units Specification for master gears - Spur an helical gears (metric moule) Dimensions of spur an helical geare motor units (metric series) Fine pitch gears (metric moule) - Involute spur an helical gears Fine pitch gears (metric moule) - Hos an cutters Specifications for general purpose, metric moule gear hos Specifications for pinion type cutters for spur gears-1 to 8 metric moule Specification for nonmetallic spur gears NOTE: Stanars availale from: ANSI, 1430 Broaway, New York, NY 10018; or BSI, Linfor Woo, Milton Keynes MK146LE, Unite Kingom 332

8 1.3.2 Gear parameters are efine y a set of stanarize symols that are efine in JIS B 0121 (1983). These are reprouce in Tale 1-3. Pressure Angle (General) Stanar Pressure Angle Working Pressure Angle Cutter Pressure Angle Raial Pressure Angle Pressure Angle Normal to Tooth Axial Pressure Angle Helix Angle (General) Stanar Pitch Cyliner Helix Angle Outsie Cyliner Helix Angle Base Cyliner Helix Angle Lea Angle (General) Stanar Pitch Cyliner Lea Angle Outsie Cyliner Lea Angle Base Cyliner Lea Angle The JIS symols are consistent with the equations given in this text an are consistent with JIS stanars. Most iffer from typical American symols, which can e confusing to the first time metric user. To assist, Tale 1-4 is offere as a cross list. Tale 1-3A The Linear Dimensions An Circular Dimensions Center Distance a Circular Pitch (General) P Lea Stanar Circular Pitch P Contact Length Raial Circular Pitch Pt Contact Length of Approach Circular Pitch Contact Length of Recess Perpenicular to Tooth Pn Contact Length of Overlap Axial Pitch Px Normal Pitch P Diameter (General) Raial Normal Pitch Pt Stanar Pitch Diameter Normal Pitch Working Pitch Diameter Perpenicular to Tooth Pn Outsie Diameter Whole Depth Aenum h ha Base Diameter Root Diameter Deenum hf Caliper Tooth Height h Raius (General) Working Depth h' hw Stanar Pitch Raius Tooth Thickness (general) s Working Pitch Raius Circular Tooth Thickness s Outsie Raius Base Raius ase Circle Circular Tooth Thickness S Root Raius Choral Tooth Thickness S Raius Curvature Span Measurement W Cone Distance (General) Root With e Cone Distance Top Clearance c Mean Cone Distance Circular Backlash j Inner Cone Disatance t Back Cone Distance Normal Backlash j n Blank With Working Face With ' w * These terms an symols are specific to JIS Stanar Tale 1-3B Angular Dimensions α α α' or αw Shaft Angle α Cone Angle (General) 0 Pitch Cone Angle α t Outsie Cone Angle αn Root Cone Angle αx Numer of Teeth Equivalent SpurGear Numer Of Teeth Numer Of Threas in Worm Numer of Teeth in pinion Numer of Teeth Ratio Spee Ratio Moule Raial Moule Normal Moule Axial Moule β β βa β γ γ γa γ P z g a g f g α g β ' w a f r r r' rw ra r r f p R Re Rm Ri Rv Mounting Distance *A Offset Distance *E Aenum Angle Deenum Angle Raial Contact Angle Overlap Contact Angles Overall Contact Angle Angular Pitch of Crown Involute Function Tale 1-3C Size Numers, Ratios & Spee z Contact Ratio zv Raial Contact Ratio zw Overlap Contact Ratio zl Total Contact Ratio u Specific Slie i Angular Spee m Linear or Tangential Spee mt Revolutions per Minute mn Coefficient of Profile Shift mx Coefficient of Center Distance Increase Continue on following page NOTE:The term "Raial" is use to enote parameters in the plane of rotation perpenicular to the axis. 333 Σ δ δ δa δt θa θf φa φ φr τ inv α ε εα εβ εγ *σ ω v n x y

9 Tale 1-3D Accuracy/Error Single Pitch Error fpt Normal Pitch Error Pitch Variation *fu or fpu Involute Profile Error Partial Accumulating Error Fpk Runout Error (Over Integral k teeth) Lea Error Total Accumulate Pitch Error Fp *These terms an symols are specific to JIS Stanars Tale 1-4 Equivalence of American an Japanese American Japanese Nomenclature Symol Symol American Japanese B Symol Symol j acklash, linear measure along pitch Nv Z v circle B LA j P t P acklash, linear measure along P line-of-action n P n ab j n acklash in arc minutes P t C a center istance R r C a change in center istance Co a C w operating center istance R r st stanar center istance Ro r a D pitch iameter R T D ase circle iameter T S Do a outsie iameter W D R f root iameter F face with Y i K k factor, general Z h L L length general; also lea a a of worm h f measurement over-pins c c M N z numer of teeth, usually gear w p Nc zc critical numer of teeth for no unercutting e ht h whole epth hk hw mp ε contact ratio yc n z1 numer of teeth, pinion γ δ nw zw numer of threas in worm θ Pa Px axial pitch λ γ P P ase pitch µ Pc P circular pitch ν Pcm Pn normal circular pitch φ α r r pitch raius, pinion φo αw r r ase circle raius, pinion ψ β rf rf fillet raius ro ra outsie raius, pinion t S tooth thickness, an for ω general use, for tolerance invφ invα Terminology use in metric gearing are ientical or are parallel to those use for inch gearing. The one major exception is that metric gears are ase upon the moule, which for reference may e consiere as the inversion of a metric unit iametral pitch. Terminology will e appropriately introuce an efine throughout the text. There are some terminology ifficulties with a few of the escriptive wors use y the Japanese JIS stanars when translate into English. Nomenclature fp ff Fr F virtual numer of teeth for helical gear iametral pitch normal iametral pitch horsepower, transmitte pitch raius, gear or general use ase circle raius, gear outsie raius, gear testing raius tooth thickness, gear eam tooth strength Lewis factor, iametral pitch mesh velocity ratio aenum eenum clearance pitch iameter, pinion pin iameter, for over-pins measurement eccentricity working epth Lewis factor, circular pitch pitch angle, evel gear rotation angle, general lea angle, worm gearing mean value gear stage velocity ratio pressure angle operating pressure angle helix angle (=ase helix angle;w = operating helix angle) angular velocity involute function One particular example is the Japanese use of the term "raial" to escrie measures such as what Americans term circular pitch. This also crops up with contact ratio. What Americans refer to as contact ratio in the plane of rotation, the Japanese equivalent is calle "raial contact ratio". This can e oth confusing an annoying. Therefore, since this technical section is eing use outsie Japan, an the American term is more realistically escriptive, in this text we will use the American term "circular" where it is meaningful. However, the applicale Japanese symol will e use. Other examples of giving preference to the American terminology will e ientifie where it occurs. 334

Metric Standards Worldwide Japanese Metric Standards In This Text

Metric Standards Worldwide Japanese Metric Standards In This Text ELEMENTS OF METRIC GEAR TECHNOLOGY Table of Contents Page SECTION 1 INTRODUCTION TO METRIC GEARS 329 1.1 Comparison Of Metric Gears With American Inch Gears 329 1.1.1 1.1.2 1.1.3 Comparison of Basic Racks