BIZOMAT MAKEOS · Gears
Plastic Gear Drive Check (Power Rating and Backlash at Temperature)
Will this plastic gear carry the power, and will the mesh still have backlash when the gears warm up and absorb moisture inside a metal housing?
Check of a plastic spur, helical or bevel gear in a metal housing: power rating by the handbook plastic gear formula with the service factor (as the plastic gear power tool) against the power required, the growth of the gear pitch radii from temperature and moisture swell against the growth of the housing centre distance (the plastic–metal mismatch, as the plastic thermal mismatch tool), the resulting loss of backlash through the pressure angle, and the backlash left at the hot, wet condition.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Gear type | choice | Gear type for the rating formula. |
| Face width | mm | Face width. |
| Lewis form factor | Lewis form factor for the tooth count. | |
| Module | mm | Module. |
| Safe stress for the plastic | MPa | Safe bending stress of the plastic at the running temperature (your value from the resin maker). |
| Pinion pitch diameter | mm | Pitch diameter of the plastic pinion (the gear rated). |
| Gear pitch diameter | mm | Pitch diameter of the mating gear (taken as plastic too). |
| Pinion speed | rpm | Speed of the pinion. |
| Service factor | Service factor for the duty. | |
| Cone distance (bevel) | mm | Cone distance for bevel gears. |
| Power to transmit | W | Power the drive must carry. |
| Backlash | ||
| Pressure angle | ° | Pressure angle. |
| Backlash at assembly | mm | Circular backlash set at assembly at room temperature, dry. |
| Plastic expansion coefficient | µm/m·K | Expansion coefficient of the gear plastic. |
| Housing expansion coefficient | µm/m·K | Expansion coefficient of the housing that sets the centre distance. |
| Temperature rise in service | K | Rise from assembly to running temperature. |
| Linear swell from moisture | % | Linear growth from moisture absorption (nylons swell; acetal very little). |
| Least backlash allowed | mm | Least backlash that must remain. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Gear type
- What it is
- The gear type, which selects the spur, helical or bevel version of the handbook plastic gear rating formula.
- Units and format
- Choose one of 3 options from the list: Spur; Helical; Bevel.
- Example
- The form opens with “Spur” selected as a worked example. Choose the option that matches your case.
What this means: Face width
- What it is
- The face width of the plastic gear teeth, measured along the tooth parallel to the axis.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 500 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- For spur and helical gears the rated power rises in direct proportion.
What this means: Lewis form factor
- What it is
- The Lewis form factor of the pinion tooth, a tabulated value that depends on the number of teeth and the tooth form.
- Units and format
- Enter a plain number with no unit. The form accepts 0.1 to 0.6. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.308 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Rated power is directly proportional to it.
- Get it right
- Take it from a Lewis factor table for the pinion’s tooth count.
What this means: Module
- What it is
- The module of the gears, which sets tooth size: pitch diameter divided by number of teeth.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.2 mm to 20 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.5 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Rated power is directly proportional to the module.
What this means: Safe stress for the plastic
- What it is
- The safe bending stress of the gear plastic at the running temperature, from the resin maker’s data.
- Units and format
- Enter a number in MPa: megapascals (1 MPa = 1 N/mm²). The form accepts 0.000001 MPa to 300 MPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 40 MPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the value at running temperature; plastic strength falls as it warms.
What this means: Pinion pitch diameter
- What it is
- The pitch diameter of the plastic pinion, the gear that is rated. It sets the pitch-line speed and, with the gear, the centre distance.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 2000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 45 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Gear pitch diameter
- What it is
- The pitch diameter of the mating gear, used with the pinion for the centre distance; the tool treats it as plastic too.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 5000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 90 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Pinion speed
- What it is
- The rotational speed of the pinion, which with its pitch diameter gives the pitch-line speed.
- Units and format
- Enter a number in rpm: revolutions per minute. The form accepts 0.000001 rpm to 100000 rpm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 600 rpm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Service factor
- What it is
- The service factor for the duty, allowing for shock, running hours and starts, from the gear handbook or your practice.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 3. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.25 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Rated power is inversely proportional to it.
What this means: Cone distance (bevel)
- What it is
- The cone distance of a bevel gear, from the cone apex to the outer end of the teeth along the pitch cone. Used only for bevel gears.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 2000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 60 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- It must exceed the face width.
What this means: Power to transmit
- What it is
- The power the gear drive must transmit in service, compared with the rated power of the pinion.
- Units and format
- Enter a number in W: watts. The form accepts 0 W to 1000000 W. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 W as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Backlash
What this means: Pressure angle
- What it is
- The pressure angle of the gear teeth. It converts a change in centre distance into a change in backlash.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 14.5° to 30°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Backlash at assembly
- What it is
- The circular backlash set at assembly, at room temperature with dry gears.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 5 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.3 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Plastic expansion coefficient
- What it is
- The linear thermal expansion coefficient of the gear plastic, from the resin maker’s data.
- Units and format
- Enter a number in µm/m·K: micrometres per metre per kelvin. The form accepts 0 µm/m·K to 300 µm/m·K. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 80 µm/m·K as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- µm/m·K is the same as 10⁻⁶ per kelvin.
What this means: Housing expansion coefficient
- What it is
- The linear thermal expansion coefficient of the housing material that fixes the centre distance.
- Units and format
- Enter a number in µm/m·K: micrometres per metre per kelvin. The form accepts 0 µm/m·K to 50 µm/m·K. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 23 µm/m·K as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Temperature rise in service
- What it is
- The temperature change from assembly to running. A negative value means the drive runs colder than when it was assembled.
- Units and format
- Enter a number in K: kelvin (a difference of 1 K equals 1 °C). The form accepts -50 K to 200 K. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 40 K as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Linear swell from moisture
- What it is
- The linear growth of the plastic gears from moisture absorbed in service, from the resin maker’s data for your humidity.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 0% to 3%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.2% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More swell takes away more backlash.
What this means: Least backlash allowed
- What it is
- The least backlash that must remain at the hot, wet condition so the gears do not bind.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 2 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0.02 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Method and formulas
- Spur rating P = F Y m S V ÷ [327 (3.05 + V) C_s] kW-form (helical and bevel variants) with V the pitch-line speed (as the plastic gear power tool).
- Centre distance a = (d₁ + d₂) ÷ 2; gear growth = a (α_p ΔT + swell); housing growth = a α_m ΔT (as the plastic thermal mismatch tool).
- Backlash change Δj = −2 tan α × (gear growth − housing growth); backlash in service = assembly backlash + Δj.
- Example: the pinion is rated 143.19 W against 100 W; warming and swelling take 0.2103 mm of backlash, leaving 0.089698 mm.
Limitations
- Handbook rating formula; resin makers’ data give better limits for modern materials.
- Uniform temperature of gears and housing; gears run hotter than the housing in practice.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Size a nylon or acetal gear pair
- Set the cold backlash so a plastic mesh does not bind
- Check a plastic gear for a power increase
Who it is for
- Design engineers
- Product designers
- Plastics engineers
What you get
- Power rating against the power required
- Change in backlash from temperature and moisture
- Backlash left in service
Interpreting the result
- Nylon gears in an aluminium housing lose backlash as they warm and soak: set enough cold backlash or use a lower-swell resin.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 604–606, 578–580. Topic reference; no source tables or recommended settings are reproduced.
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Open the Plastic Gear Drive Check (Power Rating and Backlash at Temperature) calculator