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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 55o 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

  1. Step 1 of 25 Calculate the journal speed in rev/sec. Comment
  2. 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
  3. Step 3 of 25 Calculate the radial clearance ratio. Calculate the bearing dimension ,. Calculate the slenderness ratio. Comment
  4. Step 4 of 25 Calculate the nominal pressure. Here, W is the load. Substitute N for W, for d, and for . Comment
  5. Step 5 of 25 Calculate the nominal pressure in terms of psi. Substitute for W, in for d, and in for . Comment
  6. 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
  7. 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
  8. Step 8 of 25 Calculate the average temperature. Here, is the temperature of the sump. Substitute for and for . Comment
  9. 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
  10. Step 10 of 25 Calculate the sommerfeld Number. Substitute 595.23 for , Pa.s for P, for , and for N. Comment
  11. 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
  12. 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
  13. 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
  14. 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
  15. 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
  16. Step 16 of 25 Calculate the average temperature. Substitute for and for Comment
  17. 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
  18. 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
  19. 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
  20. Step 20 of 25 Calculate the average temperature for this rise in oil temperature. Substitute for and for . Comment
  21. 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
  22. 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
  23. 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
  24. 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
  25. 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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