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Designing With Plastic Gears and General Considerations of Plastic Gearing

General Considerations of Plastic Gearing

Plastic gears are continuing to displace metal gears in a widening arena of applications. Their unique characteristics are also being enhanced with new developments, both in materials and processing. In this regard, plastics contrast somewhat dramatically with metals, in that the latter materials and processes are essentially fully developed and, therefore, are in a relatively static state of development.

Plastic gears can be produced by hobbing or shaping, similarly to metal gears or alternatively by molding.

Among the characteristics responsible for the large increase in plastic gear usage, the following are probably the most significant:
  1. Cost effectiveness of the injection-molding process.
  2. Elimination of machining operations; capability of fabrication with inserts and integral designs.
  3. Low density: lightweight, low inertia.
  4. Uniformity of parts.
  5. Capability to absorb shock and vibration.
  6. Ability to operate with minimum or no lubrication.
  7. Relatively low coefficient of friction.
  8. Corrosion-resistance.
  9. Quietness of operation.
  10. Tolerances often less critical than for metal gears, due in part to their greater resilience.
  11. Consistency with trend to greater use of plastic housings and other components.
  12. One step production; no preliminary or secondary operations.
At the same time, the design engineer should be familiar with the limitations of plastic gears relative to metal gears. The most significant of these are the following:

  1. Less load-carrying capacity.
  2. Lower accuracy.
  3. Greater dimensional instabilities, due to their larger coefficient of thermal expansion and moisture absorption.
  4. Reduced ability to operate at extremely high and low temperatures.
  5. Initial high mold cost in developing correct tooth form and dimensions.
  6. Can be negatively affected by certain chemicals and even some lubricants.
  7. Improper molding tools and process can produce residual internal stresses at the tooth roots,resulting in over stressing and/or distortion with aging.
  8. Costs of plastics track petrochemical pricing, and thus are more volatile and subject to increases in comparison to metals.

Choice of Pressure Angles and Modules

Pressure angles of 14.5°, 20° and 25° are used in plastic gears. The 20° pressure angle is usually preferred due to its stronger tooth
shape and reduced undercutting compared to the 14.5° pressure angle system. The 25° pressure angle has the highest load-carrying
ability, but is more sensitive to center distance variation and hence runs less quietly. The choice is dependent on the application.

The determination of the appropriate module or diametral pitch is a compromise between a number of different design requirements.
A larger pitch is associated with larger and stronger teeth. For a given pitch diameter, however, this also means a smaller number of
teeth with a correspondingly greater likelihood of undercut at very low number of teeth. Larger teeth are generally associated with more sliding than smaller teeth.

On the other hand, smaller pitches, which are associated with smaller teeth, tend to provide greater load sharing due to the compliance
of plastic gears. However, a limiting condition would eventually be reached when mechanical interference occurs as a result of too much compliance. Smaller teeth are also more sensitive to tooth errors and may be more highly stressed.

A good procedure is probably to size the pinion first, since it is the more highly loaded member. It should be proportioned to support the required loads, but should not be over designed.

Strength of Plastic Spur Gears

In the following text, main consideration will be given to Nylon MC901 and Duracon M90. However, the basic equations used are applicableto all other plastic materials if the appropriate values for the factors are applied.

Bending Strength of Spur Gears

Nylon MC901 and Duracon M90
The allowable tangential force F (kgf) at the pitch circle of the spur gear can be obtained from the Lewis formula:

Lewis Formula

Allowable Bending Stress

Table18-1 Form Factor, y

Fig. 18-2 Maximum Allowable Bending Stress Under Ideal Conditions

Table 18-3 Working Factor

Figure 18-3 Speed Factor

Fig 18-4 Temperature Factor

Tables 18-4 and 18-5 Lubrication and Material Factor

Application Notes

In designing plastic gears, the effects of heat and moisture must be given careful consideration. The related problems are:
  1. Backlash: Plastic gears have larger coefficients of thermal expansion. Also, they have an affinity to absorb moisture and swell. Good design requires allowance for a greater amount of backlash than for metal gears.
  2. Lubrication: Most plastic gears do not require lubrication. However, temperature rise due to meshing may be controlled by the cooling effect of a lubricant as well as by reduction of friction. Often, in the case of high-speed rotational speeds, lubrication is critical.
  3. Plastic gear with metal mate: If one of the gears of a mated pair is metal, there will be a heat sink that combats a high temperature rise. The effectiveness depends upon the particular metal, amount of metal mass, and rotational speed.

Surface Strength of Plastic Spur Gears Duracon M90

Duracon gears have less friction and wear when in an oil lubrication condition. However, the calculation of strength must take into consideration a no-lubrication condition. The surface strength using Hertz contact stress, SC, is calculated by Equation (18-3).
Equation 18-3 Surface Strength of Plastic Gears

If the value of Hertz contact stress, SC , is calculated by Equation (18-3) and the value falls below the curve of Figure 18-6,
then it is directly applicable as a safe design. If the calculated value falls above the curve, the Duracon gear is unsafe.

Bending Strength of Plastic Bevel Gears Nylon MC901 and Duracon M90

The allowable tangential force at the pitch circle is calculated by Equation (18-4).

Equation 18-4 Bending Strength of Plastic Bevel Gears

Other variables may be calculated the same way as for spur gears.

Bending Strength of Plastic Worm Gears Nylon MC901

Generally, the worm is much stronger than the worm gear. Therefore, it is necessary to calculate the strength of only the worm gear. The allowable tangential force F (kgf) at the pitch circle of the worm gear is obtained from Equation (18-7).

Equation 18-7 Bending Strength of Plastic Worm Gears

Worm meshes have relatively high sliding velocities, which induces a high temperature rise.
This causes a sharp decrease in strength and abnormal friction wear. This is particularly true of an all plastic mesh.
Therefore, sliding speeds must be contained within recommendations of Table 18-6.

Sliding Speed

Lubrication of plastic worms is vital, particularly under high load and continuous operation.

Figure 18-5 Modulus of Elasticity in Bending of Duarcon. 18-6 Maximum Allowable Surface Stress (Spur Gears)

Table 18-6 Maximum Combiations and Limits of Sliding Speed

Strength Of Plastic Keyway

Fastening of a plastic gear to the shaft is often done by means of a key and keyway.
Then, the critical thing is the stress level imposed upon the keyway sides. This is calculated by Equation (18-9).

Equation 18-9 Strength Of  Plastic Keyway

The maximum allowable surface pressure for MC901 is 200 kgf/cm2, and this must not be exceeded. Also, the keyway's corner must have a suitable radius to avoid stress concentration. The distance from the root of the gear to the bottom of the keyway should be at least twice the tooth whole depth, h.

Keyways are not to be used when the following conditions exist:
    Excessive keyway stress
    High ambient temperature
    High impact
    Large outside diameter gears
When above conditions prevail, it is expedient to use a metallic hub in the gear. Then, a keyway may be cut in the metal hub. A metallic hub can be fixed in the plastic gear by several methods:
    Press the metallic hub into the plastic gear, ensuring fastening with a knurl or screw.
    Screw fasten metal discs on each side of the plastic gear.
    Thermofuse the metal hub to the gear.

Effect of Part Shrinkage on Plastic Gear Design

The nature of the part and the molding operation have a significant effect on the molded gear. From the design point of view, the most important effect is the shrinkage of the gear relative to the size of the mold cavity.

Gear shrinkage depends upon mold proportions, gear geometry, material, ambient temperature and time. Shrinkage is usually expressed in millimeters per millimeter. For example, if a plastic gear with a shrinkage rate of 0.022 mm/mm has a pitch diameter of 50 mm while in the mold, the pitch diameter after molding will be reduced by (50)(0.022) or 1.1 mm, and becomes 48.9 mm at its final size after cooling.

Depending upon the material and the molding process, shrinkage ratescan range from about 0.001 mm/mm to 0.030 mm/mm occur in plastic gears (see Table 18-1 and Figure 18-7). Sometimes shrinkage rates are expressed as a percentage. For example, a shrinkage rate of 0.0025 mm/mm can be stated as a 0.25% shrinkage rate.

The effect of shrinkage must be anticipated in the design of the mold and requires expert knowledge. Accurate and specific treatment of this phenomenon is a result of years of experience in building molds for gears; hence, details go beyond the scope of this presentation. In general, the final size of a molded gear is a result of the following factors:
    1. Plastic material being molded.
    2. Injection pressure.
    3. Injection temperature.
    4. Injection hold time.
    5. Mold cure time and mold temperature.
    6. Configuration of part (presence of web, insert, spokes, ribs, etc.).
    7. Location, number and size of gates.
    8. Treatment of part after molding.
From the above, it becomes obvious that with the same mold – by changing molding parameters – parts of different sizes can be produced.

The form of the gear tooth itself changes as a result of shrinkage, irrespective of it shrinking away from the mold, as shown in Figure 18-8. The resulting gear will be too thin at the top and too thick at the base. The pressure angle will have increased, resulting in the possibility of binding, as well as greater wear.

In order to obtain an idea of the effect of part shrinkage subsequent to molding, the following equations are presented where the primes refer to quantities after the shrinkage occurred:

Equation part shrinkage

Equation 18-13 Shrinkage

It follows that a hob generating the electrode for a cavity which will produce a post shrinkage standard gear would need to be of a nonstandard configuration.

The shrinking process can give rise to residual stresses within the gear, especially if it has sections of different thicknesses. For this reason, a hubless gear is less likely to be warped than a gear with a hub.

If necessary, a gear can be annealed after molding in order to relieve residual stresses.
However, since this adds another operation in the manufacturing of the gear, annealing should be considered only under the following circumstances:
    1. If maximum dimensional stability is essential.
    2. If the stresses in the gear would otherwise exceed the design limit.
    3. If close tolerances and high-temperature operation makes annealing necessary.
Annealing adds a small amount of lubricant within the gear surface region.
If the prior gear lubrication is marginal, this can be helpful.

Figure 18-7 Shrinkage for Delrin in Air

Figure 18-8 Change of Tooth Profile

Proper Use of Plastic Gears Backlash

Due to the thermal expansion of plastic gears, which is significantly greater than that of metal gears, and the effects of tolerances, one should make sure that meshing gears do not bind in the course of service. Several means are available for introducing backlash into the system. Perhaps the simplest is to enlarge center distance. Care must be taken, however, to ensure that the contact ratio remains adequate.

It is possible also to thin out the tooth profile during manufacturing, but this requires careful consideration of the tooth geometry.

To some extent, the flexibility of the bearings and clearances can compensate for thermal expansion. If a small change in center distance is necessary and feasible, it probably represents the best and least expensive compromise.

Environment and Tolerances

In any discussion of tolerances for plastic gears, it is necessary to distinguish between manufacturing tolerances and dimensional changes due to environmental conditions.

As far as manufacturing is concerned, plastic gears can be made to high accuracy, if desired. For injection molded gears, Total Composite Error can readily be held within a range of roughly 0.075 – 0.125 mm, with a corresponding Tooth-to-Tooth Composite Error of about 0.025 – 0.050 mm. Higher accuracies can be obtained if the more expensive filled materials, mold design, tooling and quality control are used.

In addition to thermal expansion changes, there are permanent dimensional changes as the result of moisture absorption. The coefficient of thermal expansion of plastics is on the order of four to ten times those of metals (see Tables 18-3 and 18-10) and some plastics are hygroscopic. Dimensional changes on the order of 0.1% or more can develop in the course of time, if the humidity is sufficient. As a result, one should attempt to make sure that a tolerance which is specified is not smaller than the inevitable dimensional changes which arise as a result of environmental conditions. At the same time, the greater compliance of plastic gears, as compared to metal gears, suggests that the necessity for close tolerances need not always be as high as those required for metal gears.

Avoiding Stress Concentration

In order to minimize stress concentration and maximize the life of a plastic gear, the root fillet radius should be as large as possible, consistent with conjugate gear action. Sudden changes in cross section and sharp corners should be avoided, especially in view of the possibility of additional residual stresses which may have occurred in the course of the molding operation.

Metal Inserts

Injection molded metal inserts are used in plastic gears for a variety of reasons:
    1. To avoid an extra finishing operation.
    2. To achieve greater dimensional stability, because the metal will shrink less and is not sensitive to moisture;
        it is, also, a better heat sink.
    3. To provide greater load-carrying capacity.
    4. To provide increased rigidity.
    5. To permit repeated assembly and disassembly.
    6. To provide a more precise bore to shaft fit.
    7. As a durable support for fasteners, such as set screws to affix the gear to the shaft.

Inserts can be molded into the part or subsequently assembled. In the case of subsequent assembly, stress concentrations may be present and lead to cracking of the parts. The interference limits for press fits must be obeyed depending on the material used; also, proper minimum wall thicknesses around the inserts must be observed. The insertion of inserts may be accomplished by ultrasonically driving in the insert. In this case, the material actually melts into the knurling at the insert periphery.

Inserts are usually produced by screw machines and made of aluminum or brass. It is advantageous to attempt to match the coefficient of thermal expansion of the plastic to the materials used for inserts. This will reduce the residual stresses in the plastic part of the gear during contraction while cooling after molding.

Attachment of Plastic Gears to Shafts

Several methods of attaching gears to shafts are in common use. These include splines, keys, integral shafts, set screws, and plain and knurled press fits. Table 18-7 lists some of the basic characteristics of each of these fastening methods.

Table 18-7 Characteristics of Various Shaft Attachment Methods


Depending on the application, plastic gears can operate with continuous lubrication, initial lubrication, or no lubrication. According to L.D. Martin ("Injection Molded Plastic Gears", Plastic Design and Processing, 1968;
Part 1, August, pp 38-45; Part 2, September, pp. 33-35):
    1. All gears function more effectively with lubrication and will have a longer service life.
    2. A light spindle oil (SAE 10) is generally recommended as are the usual lubricants; these include silicone and hydrocarbon
        oils, and in some cases cold water is acceptable as well.
    3. Under certain conditions, dry lubricants such as molybdenum disulfide, can be used to reduce tooth friction.
Ample experience and evidence exist that substantiates that plastic gears can operate with a metal mate without the need of a lubricant, as long as the stress levels are not exceeded. It is also true that in the case of a moderate stress level, relative to the materials rating, plastic gears can be meshed together without a lubricant. However, as the stress level is increased, there is a tendency for a localized plastic-to-plastic welding to occur, which increases friction and wear. The level of this problem varies with the particular type of plastic.

A key advantage of plastic gearing is that, for many applications, running dry is adequate. When a situation of stress and shock level is uncertain, using the proper lubricant will provide a safety margin and certainly will cause no harm. The chief consideration should be in choosing a lubricant's chemical compatibility with the particular plastic. Least likely to encounter problems with typical gear oils and greases are: nylons, Delrins (acetals), phenolics, polyethylene and polypropylene. Materials requiring caution are: polystyrene, polycarbonates, polyvinyl chloride and ABS resins.

An alternate to external lubrication is to use plastics fortified with a solid state lubricant. Molybdenum disulfide in nylon and acetal are commonly used. Also, graphite, colloidal carbon and silicone are used as fillers.

In no event should there be need of an elaborate sophisticated lubrication system such as for metal gearing. If such a system is contemplated, then the choice of plastic gearing is in question. Simplicity is the plastic gear's inherent feature.

Elimination of Gear Noise

Incomplete conjugate action and/or excessive backlash are usually the source of noise. Plastic molded gears are generally less accurate than their metal counterparts. Furthermore, due to the presence of a larger Total Composite Error, there is more backlash built into the gear train. To avoid noise, more pliable material, such as urethane, can be used.