Gear

Designing gears can be very complex since many interfacing load factors are involved. There are bending, shear, rolling, tension, and sliding stresses all acting upon a mechanism whose purpose is to transmit uniform motion and power. This situation is well understood by those designing gears. For over a century plastic gears have been extensively used in all industries worldwide and with time passing the plastic industry has provided lightweight and quieter operating gears. They provide a means of cutting cost, weight, and noise without reducing performance.

Information on designing gears is extensive. Knowledge of gear fundamentals is a prerequisite for the understanding of applying appropriate plastic information into the gear formulas so that the application results in favorable operation. Textbooks, technical handbooks, and industrial literature of gear suppliers provide information such as teeth load requirements, transmitting motion and power by means of gears, their construction, and detail performance requirements. Reviews on teeth of heavily loaded gears require tip relief to reduce effects of deflection, and have full fillet radii to reduce stress concentrations. If the pinion in a pair of gears has a small number of teeth, undercutting may result. Undercutting weakens teeth, causes undue wear, and may affect continuity of action.

Designing gears involves ribbing, coring, and shaping material. When going from a metal to a plastic gear it is redesigned to meet the behaviors of plastics. The popular injection molded plastic gear saves material, eliminates stresses from having thick and thin sections, provides uniform shrinkage in teeth and the remainder of the gear, and provides a full load-carrying capacity for the teeth. Plastic gears are dimensioned so that they will provide sufficient backlash at the highest temperatures likely to be encountered in service.

Wear, scoring, material flow, pitting, fracture, creep, and fatigue cause plastic and metal gears to fail. Continuous lubrication can increase the allowable bending stress by a factor of at least 1.5. However there are plastics (acetals, nylons, fluoropolymers, and others) that operate efficiendy with no lubrication. There are plastics with wear resistance and durability of plastic gears makes them exceptionally useful.

The bending stress in engineering TPs is based on fatigue tests run at specific pitch-line velocities. A velocity factor should be used if the operating pitch-line velocity exceeds the test speed. Plastic gears should have a full fillet radius at the tooth root, so they are not subjected to stress concentration as are metal gears. If a gear is lubricated, bending stress will be important to evaluate. As with bending stresses, calculating surface-contact stress requires using a number of correction factors. As an example, a velocity factor is used when the pitch-line velocity exceeds the test velocity. A correction factor is also used to account for changes in operating temperature, gear materials, and the pressure angle. Stalled torque, another important factor, could be considerably more than the normal loading torque.

A damaging situation for gears is to operate over a specified temperature for the plastic used. Reducing the rate of heat generation or increasing the rate of heat transfer will stabilize the gear's temperature so that they will run indefinitely until stopped by fatigue failure. Using unfilled engineering plastics usually gives them a fatigue life on an order of magnitude higher than metal gears.

Plastic gears are subject to hysteresis heating, particularly at high speeds (Chapter 3). If the proper plastic is not used to meet the gears service requirements the hysteresis heat may be severe enough that the plastic melts. Avoid this failure by designing the gear drive so that there is favorable thermal balance between the heat that is generated and that which is removed by cooling processes. Hysteresis heating in plastics can be reduced by several methods, the usual one being to reduce the peak stress by increasing the tooth root area available for torque transmission. Another way to reduce stress on the teeth is by increasing the gear's diameter.

Materials used such as sdffer plasdcs can reduce hysteresis heating. Crystalline TPs for example (the popularly used acetal and nylon) can be stiffened by 25 to 50% with the addition of fillers and reinforcements. Others used include ABS, polycarbonates, polysulfones, phenylene oxides, polyurethanes, and thermoplastic polyesters. Additives, fillers, and reinforcements are used in plastics gears to meet different performance requirements (Chapter 1), Examples include glass fiber for added strength, and fibers, beads, and powders for reduced thermal expansion and improved dimensional stability. Other materials, such as molybdenum disulfide, polytetrafluoroethylene (PTFE), and silicones, may be added as lubricants to improve wear resistance.

Choice of plastics gear material depends on requirements for size and nature of loads to be transmitted, speeds, required life, working environment, type of cooling, lubrication, and operating precision. The strength of these TPs varies with temperature. If the incorrect plastic is used, the higher temperatures can reduce root stress and permit 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 Table 4.5.

For internal and external spur gears:

55(600 + VjPCs

For internal and external helical gears,

S^FYV

423(78 + W)P„C5 For straight bevel gears, SsFYV(C- F)

55(600 + i/)PCCs where S = safe stress in bending (Table 4.5a); F = face width in inches; Y= tooth form factor (Table 4.5b); C= pitch cone distance in inches; C, = service factor (Table 4.5c); P= diametral pitch; P. = normal diametral pitch; and V = velocity at pitch circle diameter in ft/min.

The surrounding condition, whether liquid, air, or oil (most efficient) will have substantial cooling effects. A fluid like oil is at least ten times better at cooling than air. Agitating these mediums increases their cooling rates, particularly when employing a cooling heat exchanger.

Methods of fabricating gears involve cutting/hobbing from processed blocks or sheet plastics, compression molding laminated (RP) material, or the most popular injection molding. Use is made of unfilled and

Plastic gear (a) safe bending stress (psi), (b) tooth form examples of Y factors, and (c) service factors

Plastics Type

Safe Stress Unfilled Glass-filled

ABS Aceta I Nylon

Polycarbonate

Polyester

Polyurethane

6,000 7,000 12,000 9,000 8,000

Number of Teeth

M'/s-deg Involute or Cycloidal

20-deg Full

Depth

Involute

20-deg Stub

Tooth

Involute

20-deg 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

50

0.352

0.480

0.474

0.437

0.613

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

Type of load

8-10 hr/day

24 hr/day

Intermittent 3 hr/day

Occasional '/? hr/day

Steady

1.00

1.25

0.80

0.50

Light shock

1.25

1.5

1.00

0.80

Medium shock

1.5

1.75

1.25

1.00

Heavy shock

1.75

2.00

1.5

1.25

filled or reinforced laminated TPs or TSs. Phenolic laminated gears are in a class of their own. One can make all the perfect calculations and insert the necessary values for plastic gears, but if molding conditions and molding materials are not processed properly one may end up with mediocre or even unsatisfactory results.

Being not as strong as steel, plastics perform far closer to their design limits than do metal gears. Metal and plastic in gear design differ. Designs for metal are based on the strength of a single tooth, but plastic shares the load among the various gear teeth to spread it out. In plastics the allowable stress for a specific number of cycles to failure increases as the tooth size decreases to a pitch of about 48. Very littie increase is seen above a 48 pitch, because of the effects of size and other considerations.

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