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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 ÷ 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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