Design Example: Deciding Thickness of Lubricating Fluid in a Shaft

A rotating shaft operates inside a bearing housing. The shaft rotates at a specific speed and supports a load, requiring a lubricant with the correct viscosity to ensure smooth operation.

The objective is to determine the required thickness of the lubricating fluid to maintain the necessary shear stress within the fluid layer.

First, the shaft's tangential velocity is calculated by converting the rotational speed into angular velocity. This angular velocity is then multiplied by the shaft's radius, which provides the tangential velocity at the surface.

Next, the velocity gradient across the fluid is considered. The velocity gradient is determined by the difference in velocity between the rotating shaft and the stationary housing divided by the thickness of the lubricant layer.

The shear stress within the fluid is found by multiplying the velocity gradient by the fluid's viscosity.

Finally, the shear stress equation is rearranged to determine the fluid thickness. By dividing the tangential velocity by the shear stress, the appropriate thickness of the lubricant is calculated. The thickness value ensures proper lubrication between the shaft and the housing.