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The hydro-state thrust bearing consists of six pads; each pad can be approximated as circular area of 500 mm and 100 mm as outer and inner diameters respectively. The total thrust load is 900 kN and film thickness is 0.05 mm and the viscosity of the lubricant is 58.86 cp.
Q.
Determine the supply pressure
- a)15.36 MPa
- b)1.11 MPa
- c)2.56 MPa
- d)6.67 MPa
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
The hydro-state thrust bearing consists of six pads; each pad can be a...
Given data:
- Number of pads = 6
- Outer diameter of each pad (Do) = 500 mm
- Inner diameter of each pad (Di) = 100 mm
- Total thrust load (W) = 900 kN
- Film thickness (h) = 0.05 mm
- Viscosity of lubricant (μ) = 58.86 cp
Assumptions:
- The bearing is operating under hydrodynamic lubrication conditions.
- The lubricant film is fully developed.
- The pressure distribution between the pads is uniform.
Calculations:
Step 1: Determine the effective area of each pad
The effective area of each pad (A) can be calculated using the formula:
A = π * (Do^2 - Di^2) / 4
Substituting the given values:
A = π * (500^2 - 100^2) / 4
A = 392,699.08 mm^2
Step 2: Determine the average pressure between the pads
The average pressure (P) between the pads can be calculated using the formula:
P = W / (A * 6)
Substituting the given values:
P = 900,000 N / (392,699.08 mm^2 * 6)
P = 3.83 N/mm^2
Step 3: Convert the viscosity to Pascal-seconds (Pa·s)
The viscosity needs to be converted from centipoise (cp) to Pascal-seconds (Pa·s) using the conversion factor:
1 cp = 0.001 Pa·s
Therefore, the viscosity (μ) becomes:
μ = 58.86 cp * 0.001 Pa·s/cp
μ = 0.05886 Pa·s
Step 4: Calculate the supply pressure
The supply pressure (Ps) can be calculated using the formula:
Ps = (6 * h * μ * Do) / (P * Di)
Substituting the given values:
Ps = (6 * 0.05 mm * 0.05886 Pa·s * 500 mm) / (3.83 N/mm^2 * 100 mm)
Ps = 2.56 MPa
Answer:
The supply pressure is 2.56 MPa (option C).
- Number of pads = 6
- Outer diameter of each pad (Do) = 500 mm
- Inner diameter of each pad (Di) = 100 mm
- Total thrust load (W) = 900 kN
- Film thickness (h) = 0.05 mm
- Viscosity of lubricant (μ) = 58.86 cp
Assumptions:
- The bearing is operating under hydrodynamic lubrication conditions.
- The lubricant film is fully developed.
- The pressure distribution between the pads is uniform.
Calculations:
Step 1: Determine the effective area of each pad
The effective area of each pad (A) can be calculated using the formula:
A = π * (Do^2 - Di^2) / 4
Substituting the given values:
A = π * (500^2 - 100^2) / 4
A = 392,699.08 mm^2
Step 2: Determine the average pressure between the pads
The average pressure (P) between the pads can be calculated using the formula:
P = W / (A * 6)
Substituting the given values:
P = 900,000 N / (392,699.08 mm^2 * 6)
P = 3.83 N/mm^2
Step 3: Convert the viscosity to Pascal-seconds (Pa·s)
The viscosity needs to be converted from centipoise (cp) to Pascal-seconds (Pa·s) using the conversion factor:
1 cp = 0.001 Pa·s
Therefore, the viscosity (μ) becomes:
μ = 58.86 cp * 0.001 Pa·s/cp
μ = 0.05886 Pa·s
Step 4: Calculate the supply pressure
The supply pressure (Ps) can be calculated using the formula:
Ps = (6 * h * μ * Do) / (P * Di)
Substituting the given values:
Ps = (6 * 0.05 mm * 0.05886 Pa·s * 500 mm) / (3.83 N/mm^2 * 100 mm)
Ps = 2.56 MPa
Answer:
The supply pressure is 2.56 MPa (option C).
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The hydro-state thrust bearing consists of six pads; each pad can be approximated as circular area of 500 mm and 100 mm as outer and inner diameters respectively. The total thrust load is 900 kN and film thickness is 0.05 mm and the viscosity of the lubricant is 58.86 cp.Q.Determine the supply pressurea)15.36 MPab)1.11 MPac)2.56 MPad)6.67 MPaCorrect answer is option 'C'. Can you explain this answer?
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