BIZOMAT MAKEOS · Power Transmission
Gearbox or Hydraulic Unit Heat Balance and Cooling
How hot will this gearbox or hydraulic power unit run, and does it need a cooler?
Thermal balance of an enclosed gearbox or hydraulic power unit: heat generated from the power and efficiency, equilibrium oil temperature from the housing or tank surface area and a heat transfer coefficient (natural or fan-cooled), the thermal power limit for the maximum oil temperature, and the cooler duty and oil flow needed when the surface alone is not enough.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Unit | choice | Gearbox or hydraulic power unit (affects wording only). |
| Input power | kW | Power going into the unit. |
| Efficiency (gearbox) or overall system efficiency (hydraulics) | % | Share of input power delivered usefully; the rest becomes heat (worm gears can be 50–90%, spur and helical about 95–98% per stage; hydraulic systems often 60–80%). |
| Heat-dissipating surface area | m² | External surface area of the housing or reservoir that sheds heat (exclude the base on a foundation). |
| Heat transfer coefficient | W/m²·K | Heat transfer coefficient: about 10–15 W/m²·K in still air, 20–40 with a shaft fan or good air flow. |
| Ambient temperature | °C | Surrounding air temperature. |
| Maximum oil temperature | °C | Highest oil temperature you accept (from the lubricant and seals). |
| Oil temperature drop across the cooler | K | Temperature drop of the oil through the cooler. |
| Oil specific heat | kJ/kg·K | Specific heat of the oil. |
| Oil density | kg/m³ | Density of the oil. |
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: Unit
- What it is
- Whether the unit being checked is a gearbox or a hydraulic power unit. It changes only the wording of the result; the heat balance is the same.
- Units and format
- Choose one of 2 options from the list: Gearbox; Hydraulic power unit.
- Example
- The form opens with “Gearbox” selected as a worked example. Choose the option that matches your case.
What this means: Input power
- What it is
- Mechanical or shaft power going into the unit at the duty being checked, for example the motor output at the working load.
- Units and format
- Enter a number in kW: kilowatts. The form accepts 0.000001 kW to 100000 kW. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 15 kW as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Heat generated rises in direct proportion, raising the equilibrium oil temperature.
- Get it right
- Use the power actually transmitted in service rather than the motor nameplate if the unit runs part loaded.
What this means: Efficiency (gearbox) or overall system efficien…
- What it is
- Share of the input power delivered as useful output. Everything else is lost inside the unit as heat that the housing or reservoir must shed.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 10% to 99.9%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 92% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Heat generated is P × (1 − η), so a few points of efficiency change the heat load a lot.
- Get it right
- For a hydraulic unit use the overall system efficiency (pump, valves and actuators), since all those losses end up heating the oil.
What this means: Heat-dissipating surface area
- What it is
- Outside surface of the housing or reservoir that is exposed to air and sheds heat, measured from the drawings or by tape.
- Units and format
- Enter a number in m²: square metres. The form accepts 0.000001 m² to 10000 m². Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 m² as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More area raises h A, lowering the equilibrium temperature and raising the thermal power limit.
- Get it right
- Leave out a base that sits on a foundation and surfaces shielded by guards or other equipment.
What this means: Heat transfer coefficient
- What it is
- Watts shed by each square metre of surface for every kelvin it runs above the surrounding air. It combines convection and radiation and depends on air movement around the unit.
- Units and format
- Enter a number in W/m²·K: watts per square metre per kelvin. The form accepts 0.000001 W/m²·K to 500 W/m²·K. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 15 W/m²·K as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Works with area: doubling h A halves the oil temperature rise above ambient.
- Get it right
- A shaft fan or forced air raises it markedly; still air in an enclosure lowers it. Take it from the unit maker or a heat transfer reference.
What this means: Ambient temperature
- What it is
- Temperature of the air around the unit at its hottest working condition, for example inside an enclosure or plant room in summer.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -40 °C to 80 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The equilibrium oil temperature moves up degree for degree with ambient.
What this means: Maximum oil temperature
- What it is
- The highest oil temperature you will accept in service, set by the lubricant’s rating, the seal material and the unit maker’s limits.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts 20 °C to 150 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 80 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher limit raises the thermal power limit and reduces the cooler duty.
What this means: Oil temperature drop across the cooler
- What it is
- How much cooler the oil leaves the cooler than it enters. It is used only to turn the cooler duty into an oil flow through the cooler.
- Units and format
- Enter a number in K: kelvin (a difference of 1 K equals 1 °C). The form accepts 0.000001 K to 50 K. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5 K as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger drop needs proportionally less oil flow for the same cooler duty.
- Get it right
- This is the oil-side temperature drop, not the difference between the oil and the cooling air or water.
What this means: Oil specific heat
- What it is
- Heat needed to warm one kilogram of the oil by one kelvin, from the oil supplier’s data sheet. Used only to size the oil flow through the cooler.
- Units and format
- Enter a number in kJ/kg·K: kilojoules per kilogram per kelvin. The form accepts 0.000001 kJ/kg·K to 5 kJ/kg·K. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1.9 kJ/kg·K as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Check the unit: kJ/kg·K, not J/kg·K.
What this means: Oil density
- What it is
- Mass of one cubic metre of the oil at working temperature, from the supplier’s data sheet. Used only for the oil flow through the cooler.
- Units and format
- Enter a number in kg/m³: kilograms per cubic metre. The form accepts 0.000001 kg/m³ to 1500 kg/m³. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 870 kg/m³ as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
Method and formulas
- Heat generated = P (1 − η).
- Equilibrium oil temperature = T_amb + heat ÷ (h A).
- Thermal power limit = h A (T_max − T_amb) ÷ (1 − η).
- Cooler duty = heat − h A (T_max − T_amb); oil flow = duty ÷ (ρ c_p ΔT).
- Example: 15 kW at 92% efficiency on 2 m² settles at about 70 °C.
Limitations
- Steady state with uniform surface temperature; churning and fan effects are in the coefficient.
- Gear makers publish thermal ratings that supersede this estimate.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check whether a worm gearbox will overheat at full power
- Size an oil cooler for a hydraulic power unit
- Compare natural and fan cooling
Who it is for
- Design engineers
- Mechanical engineers
- Maintenance engineers
What you get
- Heat generated and equilibrium temperature
- Thermal power limit
- Cooler duty and oil flow
Interpreting the result
- If the thermal limit is below the mechanical rating, the thermal limit governs (as the handbook notes for worm gearing).
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 3339–3340, 2430–2436. Topic reference; no source tables or recommended settings are reproduced.
Learn the Concepts Behind This Tool
These BIZOMAT Library readings explain the method this tool uses, with worked examples.
Useful alongside · BIZOMAT original book
Follow the heat out
In Electronics Packaging by the Numbers
What it covers: Build a simple thermal-resistance network for a sealed enclosure on a hot machine in the sun, find the internal temperature and choose a mounting that balances heat against vibration.
BIZOMAT tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
Open the Gearbox or Hydraulic Unit Heat Balance and Cooling calculator