Basic Training for Designing Plastic Gears

Dan Fritzinger
Mechanical Engineer
Grabill, Ind.

While metal gears date back centuries, engineers have only a few decades of experience using plastics to design gears. At first, manufacturers tried to replace metals with plastics using the same gear designs. They quickly discovered that plastics couldn’t be used as a simple drop-in replacement for metals because of vast differences in material properties and manufacturing processes. The molding process for making plastic gears gives engineers more freedom with gear shapes and sizes. However, plastics behave differently than metals when loaded, so engineers must change tooth profiles to compensate for these differences.

MATERIAL MATTERS
Engineers select materials for plastic gears based on such factors as moisture absorption, impact strength, tensile strength, and cost. A variety of qualities makes nylon and acetal the most common resins for gears. Both resist chemicals well, letting engineers lubricate gear trains with oil or grease. Gear trains often contain a combination of nylon and acetal gears, since the coefficient of friction is lower when the two materials mesh together than when each meshes against itself. Even though this eliminates the need for external lubrication, engineers can design gear trains from one material by adding a little grease or oil.

Moisture absorption is another factor that drives material selection. Since nylon is hygroscopic, or absorbs moisture, workers must completely dry resin before molding, or finished parts will be brittle. Even gears molded with properly dried nylon tend to expand when exposed to humid environments, immersed in fluids, or lubricated. Swelling causes gears to bind, therefore engineers consider such growth when designing clearances in gears or housing centerlines.

One way to avoid moisture expansion is by using acetal instead of nylon. However, each material has its strengths and weaknesses. When nylon absorbs moisture, loadcarrying capacity decreases while impact strength increases. Although acetal does not expand significantly when exposed to moisture, it is typically more brittle than nylon, which means acetal gears can’t withstand as much shock as nylon gears.

GETTING IN GEAR
Besides material selection engineers must determine gear ratio and choose gear type. Motor input speed and desired output speed depend on the application and are the driving factors for selecting gear ratio. Common gear types include external tooth, internal tooth, spur, bevel, helical, and worm. The most common tooth profile is the involute curve. Most engineers choose external spur gears with involute-tooth profiles for first-time applications or material substitutions.

The next step is to select a diametral pitch, which is the ratio of the number of teeth per inch as measured at the pitch diameter. Gears with less than 20DP are coarse pitch and those of 20DP and higher are fine pitch. Fine-pitch gears are generally smaller and have higher contact ratios, while coarsepitch gears tend to be less efficient but carry higher loads. Common DPs for steel gears are 16, 24, 32, and 48. Although the molding process lets engineers design gears with any DP, including fractional values, using common pitches is recommended.

Next, the gear pressure angle must be determined. The line of action is the line along which forces between mating teeth always lie. Pressure angle is the angle between the line of action and the line perpendicular to the line connecting the centers of mating gears. Common pressure angles are 14½, 20, and 25°. Gears with a 14½° pressure angle tend to have thin, weak teeth, but work well where design calls for precise motion and high efficiency. Comparatively, gears with a 25° pressure angle are strong but inefficient. They are used in high-power transfer applications. A pressure angle of 20° is most commonly used.

Gear manufacturing methods typically create sharp corners at the tooth root. This is not much of a concern with many steel gear applications, but can lead to failure with plastic gears, because they’re highly notch sensitive. To boost strength, the plastic gear root should have a smoothly curved radius, known as a full-root radius or full-fillet radius.

Another difference between metal and plastic gears is the way gear teeth tend to mesh. Plastic gear teeth deflect significantly more than metal ones under heavy loads. When this happens, teeth coming into mesh become misaligned and tips dig into each other. When excessive deflection is expected, plastic gear teeth tips should be thinned. This is known as tip relief and it produces a “sled-runner” shape that smoothly guides gear teeth into mesh.

SIZING UP GEARS
The next step determines maximum circular tooth thickness, a gear characteristic related to pitch diameter. Circular tooth thickness is the width of each gear tooth, measured as the length of an arc concentric with the gear. Circular tooth space is the distance between teeth, measured along the same arc. Pitch diameter is a theoretical diameter where circular tooth thickness and circular tooth space are equal. As circular tooth thickness increases, so does pitch diameter and overall gear size. While several methods exist for determining maximum circular tooth thickness, AGMA 2000A88 lists standard circular tooth thicknesses for various diametral pitches.

Next, determine root and outer diameters at maximum circular tooth thickness. For standard tooth proportions, use the following procedure:

Standard pitch diameter is determined by:

D = N/P

where D = standard pitch diameter, N = number of teeth, and P = diametral pitch. Now, find the standard addendum height (a), which is the gear tooth portion that lies above the standard pitch diameter:

a = 1/P

Next, find whole depth (h_t), which is the gear tooth’s total height — addendum plus dedendum:

h_t = 2.33/P

Then, find standard circular tooth thickness (c_t):

c_t = π/2P

Now, find outside diameter (d_o) using values for standard pitch diameter and standard addendum:

d_o = D + 2a

Next, find root diameter (d_r):

d_r = D − 2h_t

The close mesh center distance (C_d) is the minimum centerline dimension between two gears at their largest sizes. This occurs at maximum circular tooth thickness, when gears are in tight mesh, assuming exact dimensions. The value is the sum of standard pitch radii of mating gears:

C_d = (D₁/2) + (D₂/2)

At this point, gears are dimensionally perfect and mated at their largest sizes mounted on a centerline in close mesh. Although this value should be the minimum centerline on the gear-housing drawing, there are several factors that may cause gears to bind. The first is total composite tolerance of the pinion and gear, which is the sum of all gear errors including runout, ovalization, wobble, and tooth spacing. Other factors include moisture expansion, thermal expansion, and bearing runout of the mounting shafts.

The sum of these factors is ΔC, the required increase in close mesh center distance to avoid binding, which is added to C_d. The result is the true minimum operating center distance to avoid binding in all cases. The following equation represents this:

C_m = C_d + ΔC

Just as maximum circular-tooth thickness affects gear parameters, so does minimum circular-tooth thickness. AGMA 2000A88 lists standards for this value, but a ±^0.000/_0.001-in. tolerance is common for finepitch plastic gears. Using the same equations for maximum outer and root diameters, determine minimum values for each, based on minimum circular tooth thickness. This defines the smallest allowable sizes for gears.

Next, calculate maximum centerline for an acceptable contact ratio when gears are at their minimum sizes. Contact ratio refers to the number teeth in mesh during rotation of mating gears. A value of 1.0 should be the minimum allowable, since this means there is exactly one pair of teeth in mesh at all times. A contact ratio lower than 1.0 means there are gaps between pairs of teeth leaving and approaching mesh. This causes gear noise, low efficiency, and excessive wear. A conservative minimum for contact ratio is 1.2. Using an iterative process, assume an operating center distance and calculate contact ratio until it stays above the minimum allowable value.

Finally, determine the face width required to handle input power. This should be based on hours to failure, pinion and gear speed, material strength, and a safety factor. Published values for materials’ tensile strengths tend to be exaggerated and should be used with caution when designing gears. Fortunately, safety factors usually don’t need to be very high for plastic gears. A minimum safety factor of 1.0 is recommended, but gear designers might use a value of 1.5 or more for first-time applications.

OTHER GUIDELINES
Besides dimensioning gears properly, it is important to use good molding practices when making plastic gears. Though engineers use radial ribs and spokes to help strengthen plastic parts, these features cause uneven shrinkage, which results in oblong and out-of-round gears. By properly designing webs and rims designers can eliminate support ribs. Weight-reduction holes, often used to cut material costs, cause parts to shrink unevenly and create knit lines that weaken gears. Knit lines form as two streams of molten plastic meet and begin to flow together in the mold. Features such as holes produce knit lines because they create barriers to flow.

Mold design for gears also requires special attention. In a standard gear reduction there’s a group of progressively larger gears. To cut tooling costs, engineers may try to mold all the gears in one mold, known as a family mold. While these are suitable for low-tolerance parts, family molds don’t work well for different-sized gears and should only be used for identical gears.

Molten plastic flows into a mold through a series of distribution channels called runners. The runner attaches to the part at the gate. To help molds fill designevenly, engineers should locate gates at the center of the part. Offset gating tends to produce egg-shaped gears. When center gating is not possible, multiple gating spaced equally and as close to the gear’s center should be used.

Almost all gears require ejector pins to remove parts from the mold. The pins rest flush inside the mold cavity and push behind the part to remove it as the two halves separate. Engineers should design as many ejector pins as possible and make them large to avoid warping gears during ejection.

INSPECTION AND TESTING
When companies that don’t focus on gearing decide to make gears, their qualitycontrol labs usually don’t have specialized gear-measuring equipment to measure finished parts. Instead, they check gear size using calipers to measure outer diameter and a dial indicator to measure gear runout. These two measurements aren’t enough to accurately measure a gear’s quality.

OD checks with calipers don’t measure location of the gear center. The gear could be perfectly round based on OD, but useless because its bore is off-center. Caliper OD checks also can’t measure the involute curve, where the meshing action takes place. Though the gear could fall within OD tolerances, errors in tooth thickness, involute curve, or tooth spacing can prevent it from mating properly. Dial indicator measurements of OD runout don’t work effectively because they measure runout at gear tooth tips, not along tooth flanks.

A double-flank roll tester is a piece of equipment that can measure all critical gear dimensions. It works by tightly meshing the measured gear against a master gear that has been precisely ground and is virtually free of profile errors. The gears are kept in tight mesh while they rotate against each other. The master gear mounts to an arbor that moves on linear slides. If there are imperfections in the test gear, a dial indicator measures linear movement, which is compared to standards in AGMA 2000A88. This process measures total composite tolerance, which is the sum of all gear errors, and tooth-to-tooth error, or inaccuracy between two adjacent teeth. Double flank roll testers are fast and easy to use, and can be set up quickly to measure a wide variety of gears. New users can learn the measurement process in a matter of hours.

The only way to truly test molded designs is with molded gears. Machined prototypes show some similarities for product performance, but won’t give a true indication of molded-gear behavior. Because nylon and acetal parts both continue to crystallize and strengthen for a few days after molding, tests should not begin until parts fully crystallize.

Nylon gears that will be exposed to moisture may require testing in wet conditions. Boiling accelerates moisture effects and helps predict long-term gear behavior. Material manufacturers often have performance data for moisture absorption when boiled and when exposed to various humidity levels. As a guideline, boiling nylon gears for 2 hr simulates moisture absorption that occurs at 73°F for six months at 50% relative humidity.

Several other tests are recommended for all gears. Dimensional checks are important to ensure gears and housing meet specifications. If the gearbox will be connected to an electric motor, no-load current-draw tests effectively check for binding. Although this quick, simple, and reliable test comes in handy on the shop floor, it first requires a history of current draws for in-spec and out-ofspec motor/gearbox assemblies. A suddenstall test helps check gearbox strength. In this test, the output shaft couples to a brake that applies and releases repeatedly, placing a sudden, impact-style load on the gear train. Dynamometers are also useful tools to measure efficiency at various loads, although it’s difficult to find off-the-shelf dynamometers to match expected torque and speed ranges.

Engineering Polymers.

© 2010 Penton Media, Inc.