Abstract
The purpose of a ball bearing is to reduce the rotational friction and support radial and axial loading. But it can’t avoid the heat generation by the friction, the wear and the power loss it was caused by the relative motion between the metal materials. Heat is generated by the friction in the bearings, which causes the temperature inside the bearing to increase. If the heat is not appropriately removed from the bearing, elevated temperatures may give rise to premature failure. It is, therefore, important to be able to calculate the temperature in the bearings due to friction. Here, we describe a method to estimate the equilibrium temperature on the angular contact ball bearing in a spindle system using a numerical approach. The frictional torque of the bearing in a spindle system was calculated by use of a bearing analysis tool and thermal analysis of the spindle system including the bearings was achieved using the finite element method (FEM). The actual spindle system with the same layout of the FEA was built and the frictional torque, the bearing temperature were measured in the experiment. The bearing temperature was compared with measured data to verify the validity of finite element analysis.
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Abbreviations
- A :
-
Area (mm2)
- d M :
-
Bearing pitch diameter (mm)
- F a , F r :
-
Applied axial and radial loads (N)
- F 0a , F 0r :
-
Axial and radial static bearing loads (N)
- f 0 :
-
Factor depends on the bearing lubrication type
- f 1 :
-
Factor which is a function of the preload
- h :
-
Conductance (W/m2K)
- L :
-
Characteristic length (mm)
- M 1 :
-
Bearing frictional torque due to load (Nm)
- M 0 :
-
Bearing frictional torque due to lubrication (Nm)
- M R :
-
Bearing frictional torque (Nm)
- N R :
-
Frictional power loss (W)
- Nu :
-
Nusselt number
- n :
-
Rotational speed (rpm)
- P 1 :
-
Equivalent load depends on the value and direction of the load (N)
- \(\dot Q\) :
-
Heat dissipation rate (W)
- α :
-
Heat transfer coefficient (W/m2K)
- δ :
-
Gap width (mm)
- v :
-
kinematic viscosity of the lubricant (mm2/s)
- λ :
-
Thermal conductivity of air (W/mK)
- λ F :
-
Thermal conductivity of the fluid (W/mK)
- Δθ :
-
Temperature difference between the surface and the fluid (K)
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Kim, KS., Lee, DW., Lee, SM. et al. A numerical approach to determine the frictional torque and temperature of an angular contact ball bearing in a spindle system. Int. J. Precis. Eng. Manuf. 16, 135–142 (2015). https://doi.org/10.1007/s12541-015-0017-1
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DOI: https://doi.org/10.1007/s12541-015-0017-1