Tài liệu Gears P1 pptx

1.0 INTRODUCTION 2.0 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 Pitches 3.0 GEAR TOOTH FORMS AND STANDARDS 3.1 Preferred Pitches 3.2 Design Tables 3.3 AGMA Standards 4.0 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 Fundamentals 5.0 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 Pitch T25 T25 T25 T27 T27 T28 T28 T28 T28 T29 T29 T29 T31 T37 T37 T38 T38 138 T39 144 144 145 145 T48 T52 T53 T53 T54 T54 T54 T55 T55 155 T55 T55 T55 156 156 T56 156 T21 5.9.3 Center Distance 5.9.4 Velocity Ratio 5.10 Axial Thrust of Helical Gears 6.0 RACKS 7.0 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 Gears 8.0 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 Ratio 9.0 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 Teeth 10.0 GEAR TYPE EVALUATION 11.0 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 Standards 12.0 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 Error 13.0 GEAR STRENGTH AND DURABILITY 13.1 Bending Tooth Strength 13.2 Dynamic Strength 13.3 Surface Durability 13.4 AGMA Strength and Durability Ratings T57 T57 T57 T58 T58 T59 T60 T61 T61 T62 T62 T62 T63 T63 T64 T64 T66 T66 T67 T68 T68 T70 T70 T73 T73 T76 T77 T77 T78 T78 T78 T82 T88 T88 T22 Catalog D190 file:///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 Comments 15.0 FINISH COATINGS 15.1 Anodize 15.2 Chromate Coatings 15.3 Passivation 15.4 Platings 15.5 Special Coatings 15.6 Application of Coatings 16.0 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 Lubricants 17.0 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 Gears 18.0 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 T91 T91 T91 T92 T92 T92 T92 T92 T92 T99 T99 T100 T100 T100 T100 T100 T101 T101 T101 T103 T103 T103 T105 T105 T105 T105 T106 T106 T107 T107 T107 T107 T107 T108 T108 T108 T108 T23 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 Standards 20.0 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 T109 T122 T124 T125 T126 T126 T126 T131 T132 T139 T139 T139 T139 T140 T141 T143 T146 T146 T147 T147 T147 T150 T150 T150 T150 T151 T151 T152 T152 T152 T153 T153 T158 T24 1.0 INTRODUCTION This section presents a technical coverage of gear fundamentals. It is intended as a broad coverage written in a manner that is easy to follow and to understand by anyone interested in knowing how gear systems function. Since gearing involves specialty components it is expected that not all designers and engineers possess or have been exposed to all aspects of this subject However, for proper use of gear components and design of gear systems it is essential to have a minimum understanding of gear basics 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 order presented so as to obtain a logical development of the subject. Subsequently, and for those already familiar with gears, this material can be used selectively in random access as a design reference. 2.0 BASIC GEOMETRY OF SPUR GEARS The fundamentals of gearing are illustrated through the spur-gear tooth, both because it is the simplest, and hence most comprehensible, and because it is the form most widely used, particularly in instruments and control systems. 2.1 Basic Spur Gear Geometry The 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 distance 2. the pitch circle diameters (or pitch diameters) 3. size of teeth (or pitch) 4. number of teeth 5. pressure angle of the contacting involutes Details of these items along with their interdependence and definitions are covered in subsequent paragraphs. 2.2 The Law of Gearing A primary requirement of gears is the constancy of angular velocities or proportionality of position transmission, Precision instruments require positioning fidelity. High speed and/or high power gear trains also require transmission at constant angular velocities 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. A geometric relationship can be derived (1,7)* for the form of the tooth profiles to provide cojugate action, which is summarized as the 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 a fixed 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 Curve There are almost an infinite number of curves that can be developed to satisfy the law of gearing, and many different curve forms have been tried in the past. Modem gearing (except for clock gears) based on involute teeth. This is due to three major advantages 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 a generating 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 is imagined that a point on a string, which is pulled taut in a fixed direction, projects its trace onto a plane that rotates with the base circle. See Figure 1.2. The base cylinder, or base circle as referred to in gear literature, fully defines the form of the involute and 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 one base circle and wound on to the other, as shown in Figure 1.3a Thus, a single point on the string simultaneously traces an involute on each base circles rotating plane. This pair of involutes is conjugate, since at all points of contact the common normal is the common tangent which passes through a fixed point on the line-of-centers. It a second winding/unwinding taut string is wound around the base circles in the opposite direction, Figure 1 .3b, oppositely curved involutes are generted which can accommodate motion reversal. When the involute pairs are properly spaced the result is the involute gear tooth, Figure 1.3c. 2.4 Pitch Circles Referring to Figure 1.4 the tangent to the two base circles is the line of contact, or line-of-action in gear vernacular. Where this line 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 = D 1 (1) D 2 T27 2.5 Pitch Essential to prescribing gear geometry is the size, or spacing of the teeth along the pitch circle. This is termed pitch and there are two basic forms. 2.5.1 Circular pitch — A naturally conceived linear measure along the pitch circle of the tooth spacing. Referring to Figure 1.5 it is the linear distance (measured along the pitch circle ar between corresponding points of adjacent teeth. it is equal to the pitch-circle circumference divided by the number of teeth: p c = 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 a measure of the number of teeth per inch of pitch diameter. This is simply: expressed as: P d = diametral pitch = N (3) D Diametral pitch is so commonly used with fine pitch gears that it is usually contracted simply to "pitch" and that it is diametral is implied. 2.5.3 Relation of pitches: From the geometry that defines the two pitches it can be shown that they are related by the product expression: P d x P e = 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 STANDARDS involute gear tooth forms and standard tooth proportions are specified in terms of a basic rack which has straight-sided teeth for involute 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 have been formulated, only a few are currently active and widely used. Symbols for the basic rack are given in Figure 1.6 and pertinent 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 Pitches Although there are no standards for pitch choice a preference has developed among gear designers and producers. This is given in 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 Tables For the preferred pitches it is helpful in gear design to have basic data available as a function of the number of teeth on each gear, Table 1.3 lists tooth proportions common to a given diametral pitch, as well as the diameter of a measuring wire. Table 1.6 lists pitch diameters and the over-wires measurement as a function of tooth number (which ranges from 18 to 218) and various diametral pitches, including most of the preferred fine pitches. Both tables are for 20° pressure-angle gears. 3.3 AGMA Standards In the United States most gear standards have been developed and sponsored by the AGMA. They range from general and basic standards, 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 by contacting the headquarters office at 1500 King Street; Suite 201; Alexandria, VA 22314 (Phone: 703-684-0211). a = Addendum b = Dedendum c = Clearance h k = Working Depth h t = Whole Depth P c = Circular Pitch r f = Fillet Radius t = circular Tooth Thickness φ = Pressure Angle Figure 1.6 Extract from AGMA 201.02 (ANSI B6.1 1968) T29 TABLE 1.1 TOOTH PROPORTIONS OF BASIC RACK FOR STANDARD INVOLUTE GEAR SYSTEMS Tooth Parameter Symbol in Rack Fig. 1.6 14-1/2º Full Depth involute System 20º Full Depth involute System 20º Coarse-Pitch involute Spur Gears 20º Fine-Pitch involute System 1. System Sponsors 2. Pressure Angle 3. Addendum 4. Dedendum 5. Whole Depth 6. Working Depth 7. Clearance. 8. Basic Circular Tooth Thickness on Pitch Line 9. Fillet Radius In Basic Rack 10. Diametral Pitch Range 11. Governing Standard: ANSI AGMA −− φ a b h t h k C t r f -- -- -- ANSI & AGMA 14-1/2° 1/P 1.157/P 2.157/P 2/P 0.157/P 1 5708/P 1-1/3 x not specified B6.1 201.02 ANSI 20° 1/P 1.157/P 2.157/P 2/P 0.157/P 1.5708/P 1-112 X not specified B6.1 -- AGMA 20° 1.000/P 1.250/P 2.250/P 2.000/P 0250/P π/2P 0.300/P not specified -- 201.02 ANSI & AGMA 20° 1.000/P 1.200/P + 0.002 2.200/P + 0.002 2.000/P 0.200/P + 0.002 1.5708/P not standardized not specified B6.7 207.06 TABLE 1.2 PREFERRED DIAMETRAL PITCHES Class Pitch Coarse 1/2 1 2 4 6 8 10 Class Pitch Medium- Coarse 12 14 16 18 Class Pitch Fine 20 24 32 48 64 72 80 96 120 128 Class Pitch Ultra-Fine 150 180 200 TABLE 1.3 BASIC GEAR DATA FOR 20° P.A. FINE-PITCH GEARS Diameter Pitch 32 48 64 72 80 96 120 200 Diameter of Measuring Wire* .0540 .0360 .0270 .0240 .0216 .0180 .0144 .0086 Circular Pitch Circular Thickness Whole Depth Addendum Dedendum clearance .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 .0030 Note: 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 [...]... AGMA 203 AGMA 374 Gear Classification Handbook Gear Classification And Inspection Handbook Tooth portions For Coarse-Pitch Involute Spur Gears Tooth Proportions For Fine-Pitch Involute Spur Gears And Helical Gears Design-Manual For Bevel Gears Fine-Pitch On-Center Face Gears For 20° Involute Spur Pinions Design For Fine-Pitch Worm Gearing 4.0 INVOLUTOMETRY Basic calculations for gear systems are included... This basic formula shows that the larger the pressure angle the smaller the base circle Thus, for standard gears, 14½° pressure angle gears have base circles much nearer to the roots of teeth than 20° gears It is for this reason that 14 ½° gears encounter greater undercutting problems than 20° gears This is further elaborated on in section 4.8 4.5 Tooth Thickness This is measured along the pitch circle... used to indicate tooth details and dimensions for the design of a hob to produce gears of a basic rack system HELIX ANGLE (ψ) is the angle between any helix and an element of its cylinder In helical gears a worms, it is at the pitch diameter unless otherwise specified (Figure 1.7) INVOLUTE TEETH of spur gears, helical gears, and worms are those in which the active portion of the profile in the transverse... cylindrical worms and teeth of helical gears (Figure 1.11) LENGTH-OF-ACTION (ZA) is the distance on an involute line of action through which the point of contact moves during the action of the tooth profiles (Figure 1.8) LEWIS FORM FACTOR (Y, diametral pitch; yc, circular pitch) Factor in determination of beam strength of gears LINE-OF-ACTION is the path of contact in involute gears It is the straight line... design and, in general, profile-shifted gears is a large and involved subject beyond the scope of this writing References 1, 3, 5 and 6 offer additional information For measurement and inspection Figure 1.18 Comparison of such gears, in particular, consult reference 5 4.10 Backlash Calculation Up to this point the discussion has implied that there is no backlash If the gears are of standard tooth proportion... operating AXIAL PITCH (pa) is the circular pitch in the axial plane and in the pitch surface between corresponding sides of adjacent teeth, in helical gears and worms The term axial pitch is preferred to the term linear pitch (Figure 1.7) AXIAL PLANE of a pair of gears is the plane that contains the two axes In a single gear, an axial plane may be any plane containing the axis and a given point BASE DIAMETER... cos θ1 where the value of θ1 is obtained from inv θ1 = T + invθ + dw - π D D cos θ Ν (11) (12) (13) Tabulated values of over-pins measurements for standard gears are given in Table 1.6 This provides a rapid means for calculating values of M, even for gears with slight departures trom standard tooth thicknesses When tooth thickness is to be calculated from a known over-pins measurement, M, the equations... between 2 and 3 means 2 or 3 pairs of teeth are always in contact Such as high contact ratio generally is not obtained with external spur gears, but can be developed in the meshing of an internal and external spur gear pair or specially designed non-standard external spur gears 4.8 Undercutting From Figure 1.16 it can be seen that the maximum length of the line-of-contact is limited to the length of the... standard gears with T44 tooth numbers below a critical value are automatically undercut in the generating process The limiting number of teeth in a gear meshing with a rack is given by the expression: Nc = 2 (19) sin²φ This indicates the minimum number of teeth free of undercutting decreases with increasing Pressure angle For 14½º the value of Nc is 32, and for 20° it is 18 Thus, 200 pressure angle gears. .. plane of another gear PITCH DIAMETER (D = gear, d = pinion) is the diameter of the pitch circle In parallel shaft gears, the pitch diameters can be determined directly from the center distance and the number of teeth by proportionality Operating pitch diameter is the pitch diameter at which the gears operate (Figure 1.1) The pitch radius (R = gear, r pinion) is one half the pitch diameter (Figure 11) PITCH . 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. Spur Gears Tooth Proportions For Fine-Pitch Involute Spur Gears And Helical Gears Non-Spur AGMA 2005-B88 AGMA 203 AGMA 374 Design-Manual For Bevel Gears