Transcript
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
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