KEVOS® MAKEOS · Gears
Gear Backlash at Operating Temperature
How much backlash will this gear pair have when the housing and gears warm up, and could it jam?
Change in circular backlash of a spur gear pair when the housing and the gears expand differently: the change in centre distance of the housing bores, the growth of the gears’ pitch radii, the net change in operating centre distance and the resulting change in backlash (2 Δa tan φ), giving the hot backlash and a jamming check.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Module | mm | Module. |
| Pinion teeth | Pinion teeth. | |
| Gear teeth | Gear teeth. | |
| Pressure angle | ° | Pressure angle. |
| Cold circular backlash | mm | Circular backlash at assembly temperature. |
| Housing expansion coefficient | µm/m·K | Expansion coefficient of the housing (23 for aluminium, 11 for cast iron). |
| Housing temperature rise | K | Rise in housing temperature from assembly to running. |
| Gear expansion coefficient | µm/m·K | Expansion coefficient of the gears (11.5 for steel; plastics 50–100 or more). |
| Gear temperature rise | K | Rise in gear temperature (gears usually run hotter than the housing). |
Method and formulas
- Standard centre distance a = m (z₁ + z₂) ÷ 2.
- Housing bores move apart by a α_h ΔT_h; the gears’ pitch radii together grow by a α_g ΔT_g.
- Net operating centre distance change Δa = a (α_h ΔT_h − α_g ΔT_g).
- Backlash change Δj = 2 Δa tan φ (handbook relation between centre distance and backlash); hot backlash = cold + Δj.
- Example: 20/60 teeth, module 2, go from 0.08 mm to 0.10009 mm of backlash when warm.
Limitations
- Uniform temperatures; tooth thickness growth is included through the pitch radius approach.
- Bearing clearances and shaft deflection also change running backlash.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Set cold backlash for a gearbox with an aluminium housing
- Check plastic or bronze gears for jamming when warm
- Explain noise or rattle changes as a gearbox warms
Who it is for
- Gear designers
- Design engineers
- Maintenance engineers
What you get
- Centre distance change from the housing
- Pitch radius growth of the gears
- Hot backlash and jamming check
Interpreting the result
- An aluminium housing with steel gears gains backlash when warm; plastic gears in a steel housing lose it and can jam.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2163–2167, 375–378. Topic reference; no source tables or recommended settings are reproduced.
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