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### Plastic Spur Gearing Design Hp and Operating Stress Equations and Calculator

Plastic Spur Gearing Rated Design Hp, Operating Stress Equations and Calculator

Choice of plastics gear material depends on requirements for size and nature of loads to be transmitted, designated speeds, required life, working environment, type of cooling, lubrication, and operating precision. Because of cost plastics gears are sometimes not enclosed in sealed housings, so are often given only a single coating of lubricant grease. Overloading of lubricated plastics gear teeth will usually cause tooth fracture, and unlubricated teeth often suffer excessive wear. Thermoplastics strength varies with temperature, with higher temperatures reducing root stress and permitting tooth deformation. In calculating power to be transmitted by spur, helical, and straight bevel gearing, the following formulas should be used with the factors given in tables below.

Internal and External Spur Gears Rated Hp in US Customary Units

HP = ( Ss F Y V ) / ( ( 55 ( 600 + V ) P Cs )

Internal and External Spur Gears Rated Hp in Metric Units

KW = ( F Y m Ss V ) / ( 327 ( 3.05 + V ) Cs )

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

Ss = [ HP ( ( 55 ( 600 + V ) P Cs ) ] / ( F Y V )

Operating Stress Ss in Metric Units Internal and External Spur Gears

Ss  = [ KW ( 327 ( 3.05 + V ) 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