A pump fitted with 50mm bore ball bearings uses an oil whose viscosity ranges from 100cSt at cold pump start-up to 7.5Cst when running at maximum speed and load. If these viscosities are the safe limits for the oil, specify the maximum start-up speed and the maximum running speed you would recommend for the pump.
Given that the the bore diameterof the ball bearing=50mm
At cold start-up the viscosity of oil= 100cST = 100 centistokes= 100 mm2/sec
At maximum speed condition viscosity of oil =7.5 cST= 7.5 centistokes= 7.5mm2/sec
From the viscosity formula we know that= τ = μ dc / dy
where
τ = shearing stress (N/m2)
μ = dynamic viscosity (N s/m2)
dc = unit velocity (m/s)
dy = unit distance between layers (m)
Lets assume the shearing stress be 1kpa.
So,from the 1st condition we get, velocity=Shear stress*unit distance/dynamic viscosity
So,the maximum start up speed is=1000*50/100 =500mm/sec
And, Maximum running speed will be = 1000*50/7.5 =6666.6667mm/sec
To determine the maximum start-up speed and maximum running speed for the pump, we need to consider the safe viscosity limits provided for the oil.
Viscosity is a measure of a fluid's resistance to flow. In this case, the oil used in the pump has a viscosity range specified as 100cSt (centistokes) at cold start-up and 7.5Cst when running at maximum speed and load.
Typically, the viscosity of oil decreases as temperature increases. So, at cold start-up, the oil is thicker (higher viscosity) than when the pump is running at maximum speed and load.
To determine the maximum start-up speed, we need to use the highest viscosity limit, which is 100cSt at cold start-up. The start-up speed should be chosen to ensure that the oil can effectively lubricate the ball bearings without causing excessive friction and wear.
The recommended maximum start-up speed can be determined by referring to the manufacturer's guidelines or specifications for the pump and the ball bearings. These guidelines will provide the recommended viscosity limits for the ball bearings. Once we have the viscosity limit for the ball bearings, we can calculate the maximum start-up speed using the following formula:
Maximum Start-up Speed = (Viscosity Limit at Cold Start-up) / (Viscosity of Oil at Cold Start-up)
For example, if the manufacturer's guidelines specify a maximum viscosity limit of 250cSt for the ball bearings, and the oil viscosity at cold start-up is 100cSt, then the maximum start-up speed would be:
Maximum Start-up Speed = 250cSt / 100cSt = 2.5 times the maximum start-up speed.
To determine the maximum running speed, we need to use the lowest viscosity limit, which is 7.5Cst when the pump is running at maximum speed and load. The running speed should be chosen to ensure that the oil maintains sufficient lubrication properties and does not become too thin, leading to inadequate lubrication.
Similarly, the recommended maximum running speed can be determined by referring to the manufacturer's guidelines or specifications for the pump and the ball bearings, taking into account the minimum viscosity limit. Again, once we have the viscosity limit for the ball bearings, we can calculate the maximum running speed using the following formula:
Maximum Running Speed = (Viscosity Limit at Running) / (Viscosity of Oil at Running)
Please note that the values used in these calculations are hypothetical and may vary depending on the specific pump and ball bearings used. It is important to consult the manufacturer's recommendations for accurate values.
In summary, to specify the maximum start-up speed and maximum running speed for the pump, we need to determine the viscosity limits for the ball bearings and then use the formulas mentioned above. Consulting the manufacturer's guidelines or specifications for the pump and ball bearings is essential to ensure the appropriate selection of speeds within the given viscosity limits for the oil.