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# Estimating bearing operating temperature

If you are able to estimate a value for the heat dissipation from a bearing, Ws, then you can use the formula given in SKF model of bearing friction for calculating the bearing frictional power loss, Ploss, to estimate the operating temperature, Tbear, for a bearing in thermal equilibrium, under steady-state conditions, using

Tbear = (Ploss / Ws) + Tamb

where
 Tbear estimated average bearing operating temperature [°C] Ploss bearing frictional power loss [W] Ws total heat dissipation per degree above ambient temperature [W/°C] Tamb ambient temperature [°C]

Should the value of the estimated bearing operating temperature be too high for the application requirements – for example, resulting in a κ value that is too low, or a re-lubrication interval that is too short – a possible solution may be to reduce the operating temperature by means of a circulating oil lubrication system.

## Estimating heat dissipation from SKF plummer (pillow) blocks

For SKF plummer (pillow) block housings, you can use a model based on bearing size to estimate heat dissipation values.
Using diagram 1, you can estimate the heat dissipation per degree above ambient temperature Ws, for a bearing with bearing mean diameter dm in a plummer block housing, with the shaft exposed to the surrounding air.
The estimation is valid for SKF plummer block housings used with grease or oil bath lubrication and only where there is no significant heat input from external sources, such as steam heating of shafts or pronounced radiation from hot surfaces.

## Cooling via circulating oil

By circulating the oil, it is possible to cool it, and thereby remove heat from the bearing arrangement.
In diagram 2 the curved line shows the bearing frictional power loss (Ploss) and the angled line shows the heat dissipation (Ws).
Taking the heat dissipated via oil circulation into account, the bearing thermal equilibrium (diagram 2) under steady state conditions becomes:

Ploss = Ws (Tbear – Tamb) + Poil

where
 Ploss bearing frictional power loss [W] Ws total heat dissipation per degree above ambient temperature [W/°C] Tbear estimated required bearing operating temperature [°C] Tamb the ambient temperature [°C] Poil estimated power dissipated in the oil cooler [W]

Taking the heat dissipation via oil circulation into account, you can estimate the bearing operating temperature using

Tbear = ((Ploss – Poil) / Ws) + Tamb
You can estimate the power that must be dissipated by oil cooling, for a given bearing temperature, using

Poil = Ploss - Ws x (Tbear – Tamb)
You can estimate the required oil flow, for a given quantity of power that must be dissipated by oil cooling (Poil), using

Q = Poil / (27 x (Tout – Tin))

where
 Q required oil flow [l/min] Poil power dissipated in the oil cooler [W] Tout oil temperature at the housing oil outlet [°C] Tin oil temperature at the housing oil inlet [°C]

If you do not have values for Tout or Tin, you may assume a temperature difference of 5 to 10 °C (40 to 50 °F).
The limit of cooling that is possible via circulating oil is determined by the degree of heat transfer that can be obtained from a given bearing. As a rule of thumb, you can determine the maximum oil flow, above which no significant temperature reduction is obtained, using

Qmax = (D x B) / 12 500

where
 Qmax maximum oil flow [l/min] D bearing outer diameter [mm] B bearing width [mm]

## Further temperature related checks

After you have estimated the operating temperature, check:

• that the temperature assumption for calculating bearing life (operating viscosity) was correct
• the lubricant selection and temperature limits
• the grease or oil change interval
• the cage and seal material limits