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Plastic Helical Gears Design Hp, Operating Stress Equations and Calculator

Plastics Engineering and Design
Mechanical Gear Design and Engineering

Plastic Helical Gears Rated Design Hp, Operating Stress Equations and Calculator

 

Preview Plastic Helical Gears Rated Design Hp, Calculator

Internal and External Helical Gears Rated Hp in US Customary Units

HP = ( Ss F Y V ) / ( ( 423 ( 78 + V1/2 ) Pn Cs )

Internal and External Helical Gears Rated Hp in Metric Units

KW = ( F Y m Ss V ) / ( 179 ( 5.56 + V1/2 ) Cs )

Operating Stress Ss in US Customary Units Internal and External Helical Gears

Ss = [ HP ( 423 ( 78 + V1/2 ) Pn Cs )  ] / ( F Y V )

Operating Stress Ss in Metric Units Internal and External Helical Gears

Ss  = [ KW ( 179 ( 5.56 + V1/2 ) Cs ) ] / ( F Y m V ) 

Where:

Ss = safe stress in bending (lbs/in2, (from Table 2);
F = face width in inches (mm);
Y = tooth form factor (from Table 1);
m = module, (mm); = Ref. Dia / No. teeth
C = pitch cone distance in inches (mm);
Cs = service factor (from Table 3);
P = diametral pitch in inches (mm);
Pn = normal diametral pitch in inches (mm);
V = velocity at pitch circle diameter in ft/min (m/s).

V = ( rpm π D ) / 12 = ft/min

 

Table 1 Tooth Form Factors Y for Plastic Gears

Number
of Teeth
14 - 1⁄2° Involute
or Cycloidal
20° Full Depth
Involute
20° Stub Tooth
Involute
20° Internal
Full Depth
Pinion
Gear
12
0.210
0.245
0.311
0.327
13
0.220
0.261
0.324
0.327
14
0.226
0.276
0.339
0.330
15
0.236
0.289
0.348
0.330
16
0.242
0.259
0.361
0.333
17
0.251
0.302
0.367
0.342
18
0.261
0.308
0.377
0.349
19
0.273
0.314
0.386
0.358
20
0.283
0.320
0.393
0.364
21
0.289
0.327
0.399
0.371
22
0.292
0.330
0.405
0.374
24
0.298
0.336
0.415
0.383
26
0.307
0.346
0.424
0.393
28
0.314
0.352
0.430
0.399
0.691
30
0.320
0.358
0.437
0.405
0.679
34
0.327
0.371
0.446
0.415
0.660
38
0.336
0.383
0.456
0.424
0.644
43
0.346
0.396
0.462
0.430
0.628
50
0.352
0.480
0.474
0.437
0.613
60
0.358
0.421
0.484
0.446
0.597
75
0.364
0.434
0.496
0.452
0.581
100
0.371
0.446
0.506
0.462
0.565
150
0.377
0.459
0.518
0.468
0.550
300
0.383
0.471
0.534
0.478
0.534
Rack
0.390
0.484
0.550
  • These values assume a moderate temperature increase and some initial lubrication.
  • With bevel gearing, divide the number of teeth by the cosine of the pitch angle and use the data in the table.
  • For example, if a 20-deg PA bevel gear has 40 teeth and a pitch angle of 58 deg, 40 divided by the cosine of 58 deg = 40 รท 0.529919 ≈ 75, and Y = 0.434.

 

Table 2 Recommended Bending Stress Values for Plastic Gears

Plastic
Type
Recommended Stress
Unfilled Glass-Filled
(lb/in2) (MPa) (lb/in2) (MPa)
ABS 3,000 20.68 6,000 41.37
Acetal 5,000 34.47 7,000 48.26
Nylon 6,000 41.37 12,000 82.74
Polycarbonate 6,000 41.37 9,000 62.05
Polyester 3,500 24.13 8,000 55.16
Polyurethane 2,500 17.24 ... ...

 

Table 3 Service Factors Plastic Gears

Load 8-10 hr/day 24 hr/day Intermittent
3 hr/day
Occasional
1/2 hr/day
Steady 1.00 1.25 0.80 0.50
Light Shock 1.25 1.50 1.00 0.80
Medium Shock 1.50 1.75 1.25 1.00
Heavy Shock 1.75 2.00 1.50 1.25

 

References:

Machinerys Handbook, 29th Edition

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