Chapter 14: Gears

Just stare at the machine. There is nothing wrong with that. Just live with it for a while. Watch it the way you watch a line when fishing and before long, as sure as you live, you’ll get a little nibble, a little fact asking in a timid, humble way if you’re interested in it. That’s the way the world keeps on happening. Be interested in it.Robert Piersig, Zen and the Art of Motorcycle Maintenance

Image: An assortment of gears.

Spur Gear Drive

Figure 14.1 Spur gear drive.

Text Reference: Figure 14.1, page 616

Helical Gear Drive

Figure 14.2 Helical gear drive.

Text Reference: Figure 14.2, page 616

Straight Tooth Bevel Gear Drive

Figure 14.3 Bevel gear drive with straight teeth.

Text Reference: Figure 14.3, page 616

Worm Gear Drive

Figure 14.4 Worm gear drive. (a) Cylindrical teeth; (b) double enveloping.

Text Reference: Figure 14.4, page 618

Spur Gear Geometry

Figure 14.5 Basic spur gear geometry.

Text Reference: Figure 14.5, page 620

Gear Tooth Nomenclature

Figure 14.6 Nomenclature of gear teeth.

Text Reference: Figure 14.6, page 621

Preferred Diametral Pitches

Table 14.1 Preferred diametral pitches for four tooth classes.

Text Reference: Table 14.1, page 621

Class Diametral pitch,pd, in.-1

Coarse 1/2, 1, 2, 4, 6, 8, 10Medium coarse 12, 14, 16, 18Fine 20, 24, 32, 48, 64,

72, 80, 96, 120, 128Ultrafine 150, 180, 200

Diametral Pitches

Text Reference: Figure 14.7, page 622

Figure 14.7 Standard diametral pitches compared with tooth size. Full size is assumed.

Addendum, Dedendum and Clearance

Parameter Symbol Coarse Pitch(pd<20in-1)

Fine pitch(pd �20in-1)

Metric modulesystem

Addendum a 1/ pd 1/ pd 1.00 mDedendum b 1.25/ pd 1.200/ pd+0.002 1.25 mClearance c 0.25/ pd 0.200/ pd+0.002 0.25 m

Table 14.2 Formulas for addendum, dedendum, and clearance (pressure angle 20°, full-depth involute.)

Text Reference: Table 14.2, page 623

Pitch and Base Circles

Figure 14.8 Pitch and base circles for pinion and gear as well as line of action and pressure angle.

Text Reference: Figure 14.8, page 624

Involute Curve

Figure 14.9 Construction of involute curve.

Text Reference: Figure 14.9, page 625

Contact Ratio

Figure 14.10 Illustration of parameters important in defining contact ratio.

Text Reference: Figure 14.10, page 629

Line of Action

Figure 14.11 Details of line of action, showing angles of approach and recess for both pinion and gear.

Text Reference: Figure 14.11, page 629

Backlash

Figure 14.12 Illustration of backlash in gears.

Text Reference: Figure 14.12, page 632

Recommended Minimum Backlash

Diametralpitch pd, in.-1

Center distance, cd, in.

2 4 8 16 32Backlash, bl, in.

181285321.25

0.0050.0060.007

----

0.0060.0070.0080.0100.014

--

-0.0090.0100.0120.0160.021

-

--

0.0140.0160.0200.0250.034

----

0.0280.0330.042

Table 14.3 Recommended minimum backlash for coarse-pitch gears.

Text Reference: Table 14.3, page 633

Externally Meshing Spur Gears

Text Reference: Figure 14.13, page 635

Figure 14.13 Externally meshing spur gears.

Internally Meshing Spur Gears

Figure 14.14 Internally meshing spur gears.

Text Reference: Figure 14.14, page 635

Simple Gear Train

Figure 14.15 Simple gear train.

Text Reference: Figure 14.15, page 636

Compound Gear Train

Figure 14.16 Compound gear train.

Text Reference: Figure 14.16, page 636

Example 14.7

Figure 14.17 Gear train used in Example 14.7.

Text Reference: Figure 14.17, page 637

Allowable Bending Stress vs. Brinell Hardness

Figure 14.18 Effect of Brinell hardness on allowable bending stress for two grades of through-hardened steel [ANSI/AGMA Standard 1012-F90, Gear Nomenclature, Definition of Terms with Symbols, American Gear Manufacturing Association, 1990.]

Text Reference: Figure 14.18, page 638

Contact Stress vs. Brinell Hardness

Figure 14.19 Effect of Brinell Hardness on allowable contact stress for two grades of through-hardened steel. [ANSI/AGMA Standard 1012-F90, Gear Nomenclature, Definition of Terms with Symbols, American Gear Manufacturing Association, 1990.]

Text Reference: Figure 14.19, page 639

Forces on Gear Tooth

Figure 14.20 Forces acting on individual gear tooth.

Text Reference: Figure 14.20, page 640

Bending Stresses

Figure 14.21 Forces and length dimensions used in determining bending tooth stresses. (a) Tooth; (b) cantilevered beam.

Text Reference: Figure 14.20, page 641

Lewis Form FactorsNumber of

TeetchLewis form

FactorNumber of

TeethLewis form

factor1011121314151617181920222426283032

0.1760.1920.2100.2230.2360.2450.2560.2640.2700.2770.2830.2920.3020.3080.3140.3180.322

34363840455055606570758090100150200300

0.3250.3290.3320.3360.3400.3460.3520.3550.3580.3600.3610.3630.3660.3680.3750.3780.382

Table 14.4 Lewis form factors for various numbers of teeth (pressure angle 20°, full depth involute).

Text Reference: Table 14.4, page 642

Spur Gear Geometry Factors

Figure 14.22 Spur gear geometry factors for pressure angle of 20° and full-depth involute. [ANSI/AGMA Standard 1012-F90, Gear Nomenclature, Definition of Terms with Symbols, American Gear Manufacturing Association, 1990.]

Text Reference: Figure 14.21, page 643

Application Factor

Driven Machines

Power Source Uniform Light shock Moderate shock Heavy shockApplication factor, Ka

UniformLight shockModerate shock

1.001.201.30

1.251.401.70

1.501.752.00

1.752.252.75

Table 14.5 Application factor as a function of driving power source and driven machine.

Text Reference: Table 14.5, page 643

Size Factor

Diametral pitch pd,in.-1

Module, m,mm

Size factor, Ks

≥5433

1.25

≤5681220

1.001.051.151.251.40

Table 14.6 Size factor as a function of diametral pitch or module.

Text Reference: Table 14.6, page 644

Load Distribution Factor

Figure 14.23 Load distribution factor as function of face widthand ratio of face width to pitch diameters. Commercial quality gears assumed. [From Mott (1992).]

Text Reference: Figure 14.23, page 645

Dynamic Factor

Text Reference: Figure 14.24, page 645

Figure 14.24 Dynamic factor as function of pitch-line velocity and transmission accuracy level number.

Helical Gear

Figure 14.25 Helical gear. (a) Front view; (b) side view.

Text Reference: Figure 14.25, page 651

Pitches of Helical Gears

Figure 14.26 Pitches of helical gears. (a) Circular; (b) axial.

Text Reference: Figure 14.26, page 652

Figure 14.27 Gears inside industrial mixer.

Text Reference: Figure 14.27, page 655

Gears Inside Industrial Mixer

Motor Torque and Speed

Figure 14.28 Torque and speed of motor as function of current for industrial mixer used in case study.

Text Reference: Figure 14.28, page 655