A natural-circulation pillow-block bearing with l/d = 1 has a journal diameter D of 2.500 in with a unilateral tolerance of ‒0.001 in. The bushing bore diameter B is 2.504 in with a unilateral tolerance of 0.004 in. The shaft runs at an angular speed of 1120 rev/min; the bearing uses SAE grade 20 oil and carries a steady load of 300 lbf in shaft-stirred air at 70°F with α = 1. The lateral area of the pillow-block housing is 60 in2. Perform a design assessment using minimum radial clearance for a load of 600 lbf and 300 lbf. Use Trumpler’s criteria.
The design for load
The design for load
Answer to Problem 15P
The design has been successful for load
The design has been successful for load
Explanation of Solution
Write expression for minimum thickness.
Here, bore diameter is
Write expression for journal radius.
Write expression for radial clearance ratio.
Write expression for nominal pressure.
Here, length of bearing is
Write expression for viscosity.
Here, viscosity is
Write expression for Somerfield number.
Here Somerfield number is
Write expression for heat generated due to friction.
Here, Coefficient of friction is
Write expression for heat loss.
Here, overall coefficient of radiation and convection radiation is
Write expression for heat loss by linear approximation.
Here, constant is
Write expression for inlet temperature.
Here, film temperature is
Write expression for maximum temperature of the lubricant.
Here, the sump temperature is
Conclusion:
Substitute
Substitute
Substitute
Design for
Substitute
The nominal pressure
Refer to figure 12.1 “Viscosity-temperature chart in SI units”, obtain the value of viscosity
Substitute
Substitute
Substitute
Substitute
Calculate the value of
Substitute
The value of
Write expression for minimum film thickens.
Solve Equation (XII) for
Substitute
Refer to figure 12-24 “Temperature rise and Somerfield graph”
Write expression for temperature rise.
Here, Temperature rise is
Substitute
Substitute
Thus, the inlet temperature of the lubricant is
Substitute
Since the maximum temperature
Write expression for minimum film thickness using Trumpler’s criteria.
Substitute
The minimum radial clearance
Write the equation for
Substitute
So, the Trumpler’s criteria satisfied.
Thus, the design is successful for load
Design for
Substitute
The nominal pressure
Refer to figure 12.1 “Viscosity-temperature chart in SI units”, obtain the value of viscosity
Substitute
Substitute
Substitute
Substitute
The value of
Substitute
The value of
Write expression for minimum film thickens.
Solve Equation (XVII) for
Substitute
Thus, the minimum radial clearance is
Write expression for temperature rise.
Substitute
Substitute
Thus, the inlet temperature of the lubricant is
Substitute
Since the maximum temperature
Write expression for minimum film thickness using Trumpler’s criteria.
Substitute
Since the minimum radial clearance
Write equation for
Substitute
So, the Trumpler’s criteria is satisfied.
Thus, the design is successful for load
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Chapter 12 Solutions
Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
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