Bánh răng

Tài liệu tham khảo công nghệ chế tạo bánh răng nội dung bao gồm các vấn đề như: khái niệm về các loại bánh răng, phương pháp gia công,

1.0 INTRODUCTION2.0 BASIC GEOMETRY OF SPUR GEARS 2.1 Basic Spur Gear Geometry 2.2 The Law of Gearing 2.3 The Involute Curve 2.4 Pitch Circles 2.5 Pitch 2.5.1 Circular Pitch 2.5.2 Diametral Pitch 2.5.3 Relation of Pitches3.0 GEAR TOOTH FORMS AND STANDARDS 3.1 Preferred Pitches 3.2 Design Tables 3.3 AGMA Standards4.0 INVOLUTOMETRY 4.1.1 Gear Nomenclature 4.1.2 Symbols 4.2 Pitch Diameter and Center Distance 4.3 Velocity Ratio 4.4 Pressure Angle 4.5 Tooth Thickness 4.6 Measurement Over-Pins 4.7 Contact Ratio 4.8 Undercutting 4.9 Enlarged Pinions 4.10 Backlash Calculation 4.11 Summary of Gear Mesh Fundamentals5.0 HELICAL GEARS 5.1 Generation of the Helical Tooth 5.2 Fundamental of Helical Teeth 5.3 Helical Gear Relationships 5.4 Equivalent Spur Gear 5.5 Pressure Angle 5.6 Importance of Normal Plane Geometry 5.7 Helical Tooth Proportions 5.8 Parallel Shaft Helical Gear Meshes 5.8.1 Helix Angle 5.8.2 Pitch Diameter 5.8.3 Center Distance 5.8.4 Contact Ratio 5.8.5 Involute Interference 5.9 Crossed Helical Gear Meshes 5.9.1 Helix Angle and Hands 5.9.2 PitchT25 T25T25T27T27T28T28T28T28 T29T29T29 T31T37T37T38T38138T39144144145145T48 T52T53T53T54T54T54T55T55155T55T55T55156156T56156T21 5.9.3 Center Distance 5.9.4 Velocity Ratio 5.10 Axial Thrust of Helical Gears 6.0 RACKS7.0 INTERNAL GEARS 7.1 Development of the Internal Gear 7.2 Tooth Parts of Internal Gear 7.3 Tooth Thickness Measurement 7.4 Features of Internal Gears8.0 WORM MESH 8.1 Worm Mesh Geometry 8.2 Worm Tooth Proportions 8.3 Number of Threads 8.4 Worm and Wormgear Calculations 8.4.1 Pitch Diameters, Lead and Lead Angle 8.4.2 Center Distance of Mesh 8.5 Velocity Ratio9.0 BEVEL GEARING 9.1 Development and Geometry of Bevel Gears 9.2 Bevel Gear Tooth Proportions 9.3 Velocity Ratio 9.4 Forms of Bevel Teeth10.0 GEAR TYPE EVALUATION11.0 CRITERIA OF GEAR QUALITY 11.1 Basic Gear Formats 11.2 Tooth Thickness and Backlash 11.3 Position Error (or Transmission Error) 11.4 AGMA Quality Classes 11.5 Comparison With Previous AGMA and International Standards12.0 CALCULATION OF GEAR PERFORMANCE CRITERIA 12.1 Backlash in a Single Mesh 12.2 Transmission Error 12.3 Integrated Position Error 12.4 Control of Backlash 12.5 Control of Transmission Error13.0 GEAR STRENGTH AND DURABILITY 13.1 Bending Tooth Strength 13.2 Dynamic Strength 13.3 Surface Durability 13.4 AGMA Strength and Durability RatingsT57T57T57 T58 T58T59T60T61 T61T62T62T62T63T63T64 T64T66T66T67T68 T68T70T70T73T73 T76T77T77T78T78 T78T82T88T88T22Catalog D190file:///C|/A3/D190/HTML/D190T22.htm [9/27/2000 4:11:52 PM] 14.0 GEAR MATERIALS 14.1 Ferrous Metals 14.1.1 Cast Iron 14.1.2 Steel 14.2 Non Ferrous Metals 14.2.1 Aluminum 14.2.2 Bronzes 14.3 Die Cast Alloys 14.4 Sintered Powder Metal 14.5 Plastics 14.6 Applications and General Comments15.0 FINISH COATINGS 15.1 Anodize 15.2 Chromate Coatings 15.3 Passivation 15.4 Platings 15.5 Special Coatings 15.6 Application of Coatings16.0 LUBRICATION 16.1 Lubrication of Power Gears 16.2 Lubrication of Instrument Gears 16.3 Oil Lubricants 16.4 Grease 16.5 Solid Lubricants 16.6 Typical Lubricants17.0 GEAR FABRICATION 17.1 Generation of Gear Teeth 17.1.1 Rack Generation 17.1.2 Hob Generation 17.1.3 Gear Shaper Generation 17.1.4 Top Generating 17.2 Gear Grinding 17.3 Plastic Gears18.0 GEAR INSPECTION 18.1 Variable-Center-Distance Testers 18.1.1 Total Composite Error 18.1.2 Gear Size 18.1.3 Advantages and Limitations of Variable-Center-Distance Testers . 18.2 Over-Pins Gaging 18.3 Other Inspection Equipment 18.4 Inspection of Fine-Pitch Gears 18.5 Significance of Inspection and Its Implementation T91T91T91T92T92T92T92T92T92T99 T99T100T100T100T100T100 T101T101T101T103T103T103 T105T105T105T105T106T106T107 T107T107T107T107T108T108T108T108T23 19.0 GEARS, METRIC 19.1 Basic Definitions 19.2 Metric Design Equations 19.3 Metric Tooth Standards 19.4 Use of Strength Formulas 19.5 Metric Gear Standards 19.5.1 USA Metric Gear Standards 19.5.2 Foreign Metric Gear Standards20.0 DESIGN OF PLASTIC MOLDED GEARS 20.1 General Characteristics of Plastic Gears 20.2 Properties of Plastic Gear Materials 20.3 Pressure Angles 20.4 Diametral Pitch 20.5 Design Equations for Plastic Spur, Bevel, Helical and Worm Gears 20.5.1 General Considerations 20.5.2 Bending Stress - Spur Gears 20.5.3 Surface Durability for Spur and Helical Gears 20.5.4 Design Procedure - Spur Gears 20.5.5 Design Procedure Helical Gears 20.5.6 Design Procedure - Bevel Gears 20.5.7 Design Procedure - Worm Gears 20.6 Operating Temperature 20.7 Eftect of Part Shrinkage on Gear Design 20.8 Design Specifications 20.9 Backlash 20.10 Environment and Tolerances 20.11 Avoiding Stress Concentration 20.12 Metal Inserts 20.13 Attachment of Plastic Gears to Shafts 20.14 Lubrication 20.15 Inspection 20.16 Molded vs Cut Plastic Gears 20.17 Elimination of Gear Noise 20.18 Mold Construction 20.19 Conclusion T109T122T124T125T126T126T126 T131T132T139T139T139T139T140T141T143T146T146T147T147T147T150T150T150T150T151T151T152T152T152T153T153T158T24 1.0 INTRODUCTIONThis section presents a technical coverage of gear fundamentals. It is intended as a broad coverage written in a manner that iseasy to follow and to understand by anyone interested in knowing how gear systems function. Since gearing involves specialtycomponents it is expected that not all designers and engineers possess or have been exposed to all aspects of this subjectHowever, for proper use of gear components and design of gear systems it is essential to have a minimum understanding of gearbasics and a reference source for details. For those to whom this is their first encounter with gear components, it is suggested this section be read in the orderpresented so as to obtain a logical development of the subject. Subsequently, and for those already familiar with gears, thismaterial can be used selectively in random access as a design reference.2.0 BASIC GEOMETRY OF SPUR GEARSThe fundamentals of gearing are illustrated through the spur-gear tooth, both because it is the simplest, and hence mostcomprehensible, and because it is the form most widely used, particularly in instruments and control systems.2.1 Basic Spur Gear GeometryThe basic geometry and nomenclature of a spur-gear mesh is shown in Figure 1.1. The essential features of a gear mesh are:1. center distance2. the pitch circle diameters (or pitch diameters)3. size of teeth (or pitch)4. number of teeth5. pressure angle of the contacting involutesDetails of these items along with their interdependence and definitions are covered in subsequent paragraphs.2.2 The Law of GearingA primary requirement of gears is the constancy of angular velocities or proportionality of position transmission, Precisioninstruments require positioning fidelity. High speed and/or high power gear trains also require transmission at constant angularvelocities in order to avoid severe dynamic problems. Constant velocity (i.e. constant ratio) motion transmission is defined as “conjugate action” of the gear tooth profiles. Ageometric relationship can be derived (1,7)* for the form of the tooth profiles to provide cojugate action, which is summarized asthe Law of Gearing as follows: “A common normal to the tooth profiles at their point of contact must, in all positions of the contacting teeth, pass through afixed point on the line-of-centers called the pitch point.” Any two curves or profiles engaging each other and satisfying the law of gearing are conjugate Curves.___________*Numbers in parenthesis refer to references at end of text.T25 T26 2.3 The Involute CurveThere are almost an infinite number of curves that can be developed to satisfy the law of gearing, and many different curve formshave been tried in the past. Modem gearing (except for clock gears) based on involute teeth. This is due to three majoradvantages of the involute curve:1. Conjugate action is independent of changes in center distance.2. The form of the basic rack tooth is straight-sided, and therefore is relatively simple and can be accurately made; as agenerating tool ft imparts high accuracy to the cut gear tooth.3. One cutter can generate all gear tooth numbers of the same pitch.The involute curve is most easily understood as the trace of a point at the end of a taut string that unwinds from a cylinder. It isimagined that a point on a string, which is pulled taut in a fixed direction, projects its trace onto a plane that rotates with thebase circle. See Figure 1.2. The base cylinder, or base circle as referred to in gear literature, fully defines the form of the involuteand in a gear it is an inherent parameter, though invisible. The development and action of mating teeth can be visualized by imagining the taut string as being unwound from onebase circle and wound on to the other, as shown in Figure 1.3a Thus, a single point on the string simultaneously traces aninvolute on each base circles rotating plane. This pair of involutes is conjugate, since at all points of contact the common normalis the common tangent which passes through a fixed point on the line-of-centers. It a second winding/unwinding taut string iswound around the base circles in the opposite direction, Figure 1 .3b, oppositely curved involutes are generted which canaccommodate motion reversal. When the involute pairs are properly spaced the result is the involute gear tooth, Figure 1.3c.2.4 Pitch CirclesReferring to Figure 1.4 the tangent to the two base circles is the line of contact, or line-of-action in gear vernacular. Where thisline crosses the line-of-centers establishes the pitch point, P. This in turn sets the size of the pitch circles, or as commonly called,the pitch diameters. The ratio of the pitch diameters gives the velocity ratio: Velocity ratio of gear 2 to gear 1 = Z = D1 (1) D2T27 2.5 PitchEssential to prescribing gear geometry is the size, or spacing of the teeth along the pitch circle. This is termed pitch and there aretwo basic forms. 2.5.1 Circular pitch — A naturally conceived linear measure along the pitch circle of the tooth spacing. Referring to Figure1.5 it is the linear distance (measured along the pitch circle ar between corresponding points of adjacent teeth. it is equal to thepitch-circle circumference divided by the number of teeth:pc = circular pitch = pitch circle circumference = Dπ (2) number of teeth N 2.5.2 Diametral pitch — A more popularly used pitch measure, although geometrically much less evident, is one that is ameasure of the number of teeth per inch of pitch diameter. This is simply: expressed as: Pd = diametral pitch = N (3) DDiametral pitch is so commonly used with fine pitch gears that it is usually contracted simply to "pitch" and that it is diametral isimplied. 2.5.3 Relation of pitches: From the geometry that defines the two pitches it can be shown that they are related by theproduct expression: Pd x Pe = π (4)This relationship is simple to remember and permits an easy transformation from one to the other.T28 3.0 GEAR TOOTH FORMS AND STANDARDSinvolute gear tooth forms and standard tooth proportions are specified in terms of a basic rack which has straight-sided teeth forinvolute systems. The American National Standards Institute (ANSI) and the American Gear Manufacturers Association (AGMA)have jointly established standards for the USA. Although a large number of tooth proportions and pressure angle standards havebeen formulated, only a few are currently active and widely used. Symbols for the basic rack are given in Figure 1.6 andpertinent standards for tooth proportions in Table 1.1. Note that data in Table 1.1 is based upon diametral pitch equal to one. To convert to another pitch divide by diametral pitch.3.1 Preferred PitchesAlthough there are no standards for pitch choice a preference has developed among gear designers and producers. This is givenin Table 1.2. Adherence to these pitches is very common in the fine- pitch range but less so among the coarse pitches.3.2 Design TablesFor the preferred pitches it is helpful in gear design to have basic data available as a function of the number of teeth on eachgear, Table 1.3 lists tooth proportions common to a given diametral pitch, as well as the diameter of a measuring wire. Table 1.6lists pitch diameters and the over-wires measurement as a function of tooth number (which ranges from 18 to 218) and variousdiametral pitches, including most of the preferred fine pitches. Both tables are for 20° pressure-angle gears.3.3 AGMA StandardsIn the United States most gear standards have been developed and sponsored by the AGMA. They range from general and basicstandards, such as those already mentioned for tooth form, to specialized standards. The list is very long and only a selected few,most pertinent to fine pitch gearing, are listed in Table 1.4. These and additional standards can be procured from the AGMA bycontacting the headquarters office at 1500 King Street; Suite 201; Alexandria, VA 22314 (Phone: 703-684-0211).a = Addendumb = Dedendumc = Clearancehk = Working Depthht = Whole DepthPc = Circular Pitchrf = Fillet Radiust = circular Tooth Thicknessφ = Pressure AngleFigure 1.6 Extract from AGMA 201.02 (ANSI B6.1 1968)T29 TABLE 1.1 TOOTH PROPORTIONS OF BASIC RACK FORSTANDARD INVOLUTE GEAR SYSTEMSTooth ParameterSymbolinRackFig. 1.614-1/2ºFull DepthinvoluteSystem20ºFull DepthinvoluteSystem20ºCoarse-PitchinvoluteSpur Gears20ºFine-PitchinvoluteSystem1. System Sponsors2. Pressure Angle3. Addendum4. Dedendum5. Whole Depth6. Working Depth7. Clearance.8. Basic Circular Tooth Thickness on Pitch Line9. Fillet Radius In Basic Rack10. Diametral Pitch Range11. Governing Standard: ANSI AGMA −−φabhthkCt rf -- ----ANSI & AGMA14-1/2°1/P1.157/P2.157/P2/P0.157/P1 5708/P 1-1/3 x not specified B6.1201.02ANSI20°1/P1.157/P2.157/P2/P0.157/P1.5708/P 1-112 X not specified B6.1--AGMA20°1.000/P1.250/P2.250/P2.000/P0250/Pπ/2P 0.300/P not specified --201.02ANSI & AGMA20°1.000/P1.200/P + 0.0022.200/P + 0.0022.000/P0.200/P + 0.0021.5708/P not standardized not specified B6.7207.06TABLE 1.2 PREFERRED DIAMETRAL PITCHESClass PitchCoarse1/21246810Class PitchMedium-Coarse12141618Class PitchFine2024324864728096120128Class PitchUltra-Fine150180200TABLE 1.3 BASIC GEAR DATA FOR 20° P.A. FINE-PITCH GEARSDiameter Pitch32 48 64 72 80 96 120 200Diameter ofMeasuring Wire*.0540 .0360 .0270 .0240 .0216 .0180 .0144 .0086Circular PitchCircular ThicknessWhole DepthAddendumDedendumclearance.09817.04909.0708.0313.0395.0083.06545.03272.0478.0208.0270.0062.04909.02454.0364.0156.0208.0051.04363.02182.0326.0139.0187.0048.03927.01963.0295.0125.0170.0045.03272.01638.0249.0104.0145.0041.02618.01309.0203.0083.0120.0037.01571.00765.0130.0050.0080.0030Note: Outside Diameter for N number of teeth equals the Pitch Diameter far (N+2) number at teeth.*For 1.7290 wire diameter basic wire system.T30 123doc.vn