# Question: Shigley’s Mechanical Engineering Design (8th Edition) – Free Chegg Question Answer

PShigley’s Mechanical Engineering Design (8th Edition)

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### Problem

A pressure-fed bearing has a journal diameter of 50.00 mm with a unilateral tolerance of -0.05 mm. The bushing; bore diameter is 50.084 mm with a unilateral tolerance of 0.10 mm. The length of the bushing is 55 mm. Its central annular groove is 5 mm wide and is fed by SAE 30 oil is 55^{o} C at 200 kPa supply gauge pressure. The journal speed is 2880 rev/min carrying a load of 10 kN. The sump can dissipate 300 watts per bearing if necessary. For minimum radial clearances, perform a design assessment using Trumpler’s criteria.

### Step-by-step solution

- Step 1 of 25 Calculate the journal speed in rev/sec. Comment
- Step 2 of 25 Calculate the minimum thickness. Here,
*b*is the bore diameter and*d*is the journal diameter. Substitute 50.084 mm for*b*and 50 mm for*d.*Calculate the radius of the journal. Substitute 50 mm for*d.*Comment - Step 3 of 25 Calculate the radial clearance ratio. Calculate the bearing dimension ,. Calculate the slenderness ratio. Comment
- Step 4 of 25 Calculate the nominal pressure. Here,
*W*is the load. Substitute N for*W*, for*d,*and for . Comment - Step 5 of 25 Calculate the nominal pressure in terms of psi. Substitute for
*W*, in for*d,*and in for . Comment - Step 6 of 25 Obtain the value of viscosity, for oil SAE 30 and assumed temperature from figure 12-13 “Viscosity – temperature chart in SI units”. Calculate the sommerfeld Number. Substitute 595.23 for , Pa.s for
*P*, and for*N.*Obtain the value of coefficient of friction variable from chart 12 – 18“coefficient of friction variable” at and . The coefficient of friction, Obtain the value of eccentricity ratio for and from figure 12-16“Chart for minimum film-thickness and eccentricity ratio” Eccentricity ratio, Comment - Step 7 of 25 Calculate the temperature rise in oil. Here, is the supply pressure. Substitute 0.85 for , 200 kPa for , 2.3 for , 0.055 for
*S,*N for*W,*and 25 mm for*r.*Comment - Step 8 of 25 Calculate the average temperature. Here, is the temperature of the sump. Substitute for and for . Comment
- Step 9 of 25 Obtain the value of viscosity, for oil SAE 30 and assumed temperature 12 – 13 from figure “Viscosity – temperature chart in SI units”. Obtain the value of eccentricity ratio for and from “Chart for minimum film-thickness and eccentricity ratio” Eccentricity ratio, Comment
- Step 10 of 25 Calculate the sommerfeld Number. Substitute 595.23 for , Pa.s for
*P*, for , and for*N.*Comment - Step 11 of 25 Obtain the value of coefficient of friction variable from figure 12-18 “chart coefficient of friction variable” at and . The coefficient of friction, Obtain the value of eccentricity ratio for and from figure 12-16“Chart for minimum film-thickness and eccentricity ratio” Eccentricity ratio, Comment
- Step 12 of 25 Calculate the temperature rise in oil. Substitute 0.9 for , 200 kPa for , 1.6 for , 0.0296 for
*S,*N for*W,*and 25 mm for*r.*Comment - Step 13 of 25Calculate the average temperature. Substitute for and for . Plot and on a graph and taking the intersection of these two lines gives a point where and are equal. Thus, and will be equal for Obtain the value of viscosity, for oil SAE 30 and assumed temperature from figure 12-13“Viscosity – temperature chart in SI units”. Calculate the sommerfeld Number. Substitute 595.23 for , Pa.s for
*P*, for , and for*N.*Comment - Step 14 of 25 Obtain the value of coefficient of friction variable from figure 12-18 “coefficient of friction variable” at and . The coefficient of friction, Obtain the value of eccentricity ratio for and from “Chart for minimum film-thickness and eccentricity ratio” Eccentricity ratio, Comment
- Step 15 of 25 Calculate the rise in temperature of oil. Substitute 0.875 for , 200 kPa for , 2.2 for , 0.04596 for
*S,*N for*W,*and 25 mm for*r.*Comment - Step 16 of 25 Calculate the average temperature. Substitute for and for Comment
- Step 17 of 25 Calculate a close value for final temperature. Obtain the value of viscosity, for oil SAE 30 and assumed temperature from figure 12-13 “Viscosity – temperature chart in SI units”. Calculate the sommerfeld Number. Substitute 595.23 for , Pa.s for
*P*, for , and for*N.*Comment - Step 18 of 25 Obtain the value of coefficient of friction variable from chart 12-18 “coefficient of friction variable” at and . The coefficient of friction, Comment
- Step 19 of 25Obtain the value of eccentricity ratio for and from figure 12-16 “Chart for minimum film-thickness variable and eccentricity ratio” Eccentricity ratio, Calculate the rise in temperature of oil. Substitute 0.874 for , 200 kPa for , 2.23 for , 0.0457 for
*S,*N for*W,*and 25 mm for*r.*Comment - Step 20 of 25 Calculate the average temperature for this rise in oil temperature. Substitute for and for . Comment
- Step 21 of 25 Calculate the volumetric side flow leakage rate. substitute 0.874 for , 200 kPa for ,
*,*for*c,*and 25 mm for*r*, and 25 mm for . Calculate the value of minimum film thickness, . Comment - Step 22 of 25 Assess using Trumpler criteria: Calculate the minimum film thickness. Substitute for
*d.*, this value is not greater than ( obtained from trumpler’s criteria). Thus, this condition is not satisfied. Comment - Step 23 of 25 Calculate the maximum temperature value. Substitute for and for . This value is less than maximum temperature specified by trumpler’s criterion. Thus, the condition is satisfied. Comment
- Step 24 of 25 Verify the nominal pressure. This value is greater than pressure stated by trumpler’s criterion. Thus, the condition is not satisfied. Comment
- Step 25 of 25 Verify the design factor. This value of design factor does not satisfy the design factor of trumpler’s criterion. Thus, this condition is not satisfied.Comment

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