Efficiency per stage and in the chain
The efficiency η describes the proportion of the input power that actually reaches the output shaft. The remainder is dissipated as frictional heat:
η = P_ab / P_an
P_ab = Output power · P_an = Drive power · η = Efficiency (0…1)
When there are multiple consecutive gear stages (such as a two-stage planetary gearbox), the stage efficiencies are multiplied to yield the overall efficiency—a common misconception is to add them together or calculate their average:
η_ges = η₁ · η₂ · … · η_n
Example: Two stages at 95% each result in η_ges = 0.95 · 0.95 = 0.9025 = 90.25%—not 95%.
The power loss, which must be dissipated as heat, is directly derived from the drive power and efficiency:
P_V = P_an · (1 − η)
P_V = Power loss (heat)
Where the losses come from
Four types of losses combine to form the total power loss of a gearbox:
- Gear losses—sliding friction between the tooth flanks; predominant in worm gearboxes, comparatively low in helical gearboxes.
- Bearing losses—friction in the rolling bearings of each shaft—increase with speed.
- Seal losses—friction at shaft seals, usually the smallest component.
- Churning losses—lubricating oil “sprayed” by the rotating gears; increases with speed.
| Gear Type | Efficiency per stage |
|---|---|
| Spur gear (straight-toothed/helical-toothed) | 95–99 % |
| Planetary, single-stage | 95–98 % |
| Planetary, two-stage | 90–96 % |
| Bevel gear, spiral-tooth gear | 94–97 % |
| Hypoid | 90–96 % |
| Worm gear (i = 10) | 60–90 % |
| Worm gear (i = 50) | 30–60 % |
Description and values of the figure
Spur and planetary gearboxes achieve the highest efficiencies (up to 99%). Worm gearboxes with high gear ratios (here, i=50) are highlighted because they are the only type whose efficiency range can fall below the 50% line: At that point, the gearset is self-locking even during operation (dynamically). Worm gearboxes can be statically self-locking even at higher operating efficiencies because, when stationary, the greater static friction comes into play. This is technically useful but results in noticeably more power loss than with other designs.
| Name | from (%) | to (%) |
|---|---|---|
| Stirnradgetriebe | 95 | 99 |
| Planetengetriebe, 1-stufig | 95 | 98 |
| Planetengetriebe, 2-stufig | 90 | 96 |
| Kegelradgetriebe, spiralverzahnt | 94 | 97 |
| Hypoidgetriebe | 90 | 96 |
| Schneckengetriebe i=10 | 60 | 90 |
| Schneckengetriebe i=50 | 30 | 60 |
Reverse efficiency and the 50% limit
The efficiency η given so far applies to the power flow from the drive to the output (forward). If the load acts in the opposite direction against the gearbox—for example, if a weight attempts to turn the output shaft backward—the reverse efficiency η′ applies, which can be roughly estimated from η:
η′ ≈ 2 − 1 / η
η′ = reverse efficiency (load drives) · η = forward efficiency (drive drives)
If η = 0.5 is substituted, this yields η′ = 2 − 1/0.5 = 0. Precisely at an efficiency of 50 %, the load can, mathematically speaking, no longer drive the gearbox backward—this is the theoretical limit of self-locking. The decisive factor is which efficiency value is used: For holding the load at a standstill, the static efficiency (start-up, static friction) is what counts, and this is significantly lower than the operating efficiency. A worm gearbox with a 60–70% operating efficiency can therefore be self-locking when stationary. If the operating efficiency is already below 50%, the gearbox locks even while in motion. The section “Self-locking: Benefits and Limitations” explains why this still does not replace a brake.
Mnemonic
Worked example
Given
A 7.5-kW motor drives a screw conveyor via a two-stage planetary gearbox. Stage efficiencies: η₁ = 0.96, η₂ = 0.95.
Calculation
- Overall efficiency: η_ges = η₁ · η₂ = 0.96 · 0.95 = 0.912 (91.2 %)
- Output power: P_ab = P_an · η_ges = 7.5 kW · 0.912 = 6.84 kW
- Power loss: P_V = P_an − P_ab = 7.5 kW − 6.84 kW = 0.66 kW (660 W)
The 660 W is dissipated as heat through the gear housing and helps determine how large and how well-ventilated the housing must be designed.
Description and values of the figure
The input power of 7.50 kW passes through two gear stages. After stage 1 (efficiency η1 =0.96), 7.20 kW remains, while the remainder (0.30 kW) is lost. After stage 2 (η2 =0.95), 6.84 kW remains, with an additional loss of 0.36 kW. The total loss across both stages is 0.66 kW, and the overall efficiency is 6.84/7.50 ≈ 91.2%.
| Level | Input (kW) | Efficiency | Output (kW) | Loss (kW) |
|---|---|---|---|---|
| Level 1 | 7,50 | η₁ = 0.96 | 7,20 | 0,30 |
| Level 2 | 7,20 | η₂ = 0.95 | 6,84 | 0,36 |
| Total | 7,50 | η_ges ≈ 0.912 | 6,84 | 0,66 |
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