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
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138
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144
144
145
145
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155
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156
156
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156
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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
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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

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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

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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.
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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
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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.
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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)
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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.
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TABLE 1.4 SELECTED LIST OF AGMA STANDARDS
General
AGMA 390
AGMA
2000-A88
Gear Classification Handbook
Gear Classification And Inspection Handbook
spurs And
Helicals
AGMA 201
AGMA 207
Tooth portions For Coarse-Pitch Involute 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

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 in this section for ready reference in design. More advanced calculations are
available in the listed references.
4.1.1 GEAR NOMENCLATURE*
ACTIVE PROFILE is that part of the gear tooth profile which actually comes in contact with the profile of its mating tooth along the
line of action.
ADDENDUM (a) is the height by which a tooth projects beyond the pitch circle or pitch line; also, the radial distance between the
pitch circle and the addendum circle (Figure 1.1); addendum can be defined as either nominal or 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 (D
b
= gear, and d
b
= pinion) is the diameter of the base cylinder from which involute tooth surfaces, either
straight or helical, are derived. (Figure 1.1); base radius (R
b
= gear, r
b
= pinion) is one half of the base diameter.
BASE PITCH (p
b
) in an involute gear is the pitch on the base circle or along the line-of-action. Correspcndng sides of involute
gear teeth are parallel curves, and the base pitch is the constant and fundamental distance between them along a common
normal in a plane of rotation. (Figure 1.8)

BASIC RACK is a rack that is adopted as the basis for a system of interchangeable gears.
BACKLASH (B) is the amount by which the width of a tooth space exceeds the thickness of the engaging tooth on the pitch
circles. As actually indicated by measuring devices, backlash may be
______________
*Portions of this section are repented with permission from the Barber-Colman Co., Rockford, Ml.
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determined variously in the transverse, normal, or axial planes, and either in the direction of the pit circles or on the
line-of-action. Such measurements should be corrected to corresponding values a transverse pitch circles for general
comparisons. (Figure 1.9)
CENTER DISTANCE (C), Distance between axes of rotation of mating spur or helical gears.
CHORDAL ADDENDUM (a
c
) is the height from the top of the tooth to the chord subtending the circular-thickness arc. (Figure
1.10)
CHORDAL THICKNESS (t
c
) is the length of the chord subtending a circular-thickness arc. (Figure 1.10)
CIRCULAR PITCH (p
c
) is the distance along the pitch circle or pitch line between corresponding profiles of adjacent teeth. (Figure
1.1)
CIRCULAR THICKNESS (t) is the length of arc between the two sides of a gear tooth on the p4 circle, unless otherwise specified.
(Figure 1.10)
CLEARANCE-OPERATING (c) is the amount by which the dedendum in a given gear exceeds addendum of its mating gear. (Figure
1.1)
CONTACT RATIO (Spur) is the ratio of the length-of-action to the base pitch.
CONTACT RATIO (Helical) is the contact ratio in the plane of rotation plus a contact portion a tributted to the axial advance.
DEDENDUM (b) is the depth of a tooth space below the pitch line; also, the radial distance beta, the pitch circle and the root
circle. (Figure 1.1); dedendum can be defined as either nominal or operating.
DIAMETRAL PITCH (P

d
) is the ratio of the number of teeth to the number of inches in the pitch diameter. There is a fixed relation
between diametral pitch (P
d
) and circular pitch (p
c
): p
c
= π / P
d
FACE WIDTH (F) is the length of the teeth in an axial plane.
FILLET RADIUS (r,) is the radius of the fillet curve at the base of the gear tooth. In generated this radius is an approximate radius
of curvature. (Figure 1.13)
FULL DEPTH TEETH are those in which the working depth equals 2000"
diametral pitch
GENERATING RACK is a rack outline 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
plane is the involute of a circle.
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