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WORCESTER POLYTECHNIC INSTITUTE

WORCESTER POLYTECHNIC INSTITUTE. MECHANICAL ENGINEERING DEPARTMENT. DESIGN OF MACHINE ELEMENTS ME-3320, C’2003. Lecture 20-22-23 February 17, 2003 C. Furlong. Journal bearings (short/long) and bushings. Thick-wall journal bearing. (Typically used in low-speed applications). Hard material.

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WORCESTER POLYTECHNIC INSTITUTE

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  1. WORCESTER POLYTECHNIC INSTITUTE MECHANICAL ENGINEERING DEPARTMENT DESIGN OF MACHINE ELEMENTS ME-3320, C’2003 Lecture 20-22-23 February 17, 2003 C. Furlong

  2. Journal bearings (short/long) and bushings Thick-wall journal bearing (Typically used in low-speed applications) Hard material Soft material Bearings and lubrication Journal bearings(short/long) -- sliding type Short journal bearings

  3. Friction Relative velocity Bearings and lubrication: friction Journal bearings(short/long) -- sliding type Friction as a function of velocity

  4. Note hardness difference between shaft and bearing material Bearings and lubrication: materials Journal bearings(short/long) -- sliding type

  5. Shear stresses: and for constant thickness, h, where, - is absolute viscosity - is linear (tangential) velocity - is film (lubricant) thickness Linear (tangential) velocity: (Analogy) Film (lubricant) thickness Bearings and lubrication: shear stresses in lubricant Journal bearings(short/long) -- sliding type

  6. Absolute viscosity: • Units of absolute viscosity in English system: lb-sec/in2 (reyn) • Units of absolute viscosity in SI system: Pa-sec • Typical values are expressed in µreyn and mPa-sec (1 centipoise (cP) = 1mPa-sec) • Kinematic viscosity ( ) and absolute viscosity are related as: • Units of kinematic viscosity are: in2/sec (English) and cm2/sec (stoke - SI) The term “viscosity” without modifiers refers to absolute viscosity Bearings and lubrication: viscosity Absolute/Relative

  7. Diametral clearance: Radial clearance: Eccentricity: (Maximum value of eccentricity is: ) Eccentricity ratio: Minimum and maximum film thickness: (Analogy: used to derive mathematical models) Bearings and lubrication: shear stresses in lubricant Reynold’s equation for eccentric journal bearings Definitions Film thickness as a function of angular position ():

  8. Reynold’s equation: Neglecting pressure gradient in the axial direction (assumption): Bearings and lubrication: shear stresses in lubricant Reynold’s equation for eccentric journal bearings Close-form solutions for Reynold’s equation do not exist, however, it can be solved numerically (e.g., with finite element methods). Particular close-form solutions for simplified Reynold’s equation do exist Involves solution of simplified Reynold’s equation:

  9. Pressure distribution, p, is: Total load, P,is: Average pressure, Pavg,is: Bearings and lubrication: Reynold’s equation Long bearing assumption: Sommerfeld solution No-leakage of lubricant at both ends of journal Important dimensionless quantity: Sommerfeld number, S ( n’ is rotational speed in revolutions per second)

  10. Bearings and lubrication: Reynold’s equation Short bearing assumption: Ocvirk solution Incorporates leakage of lubricant at both ends of journal Pressure distribution, p, is: Total load, P,is: Coefficient, K (dimensionless), is: Important dimensionless quantity: Ocvrick number, ON

  11. Bearings and lubrication: Reynold’s equation Short bearing assumption: Ocvirk solution Incorporates leakage of lubricant at both ends of journal Correcting eccentricity ratio (correction based on experimental observations):

  12. Bearings and lubrication Pressure distribution in journal bearings with Power loss:

  13. %P- distributions (approximations) in short and long bearings: (Short-bearing solution) %Pressure (Long-bearing solution) Bearings and lubrication Pressure distribution in short journal bearings

  14. Bearings and lubrication: design considerations Journal bearings(short/long) -- sliding type If shaft has been designed (for stress and/or deflection) If shaft has not been designed • Diameter and length of bearing can be found from iteration of bearing equations with and assumed Ocvirk number • A trial lubricant must be chosen and its viscosity defined Chose ratio l/d of bearing (based on packaging considerations) • Larger l/d ratios give lower film pressures • Clearance ratio (Cd/d) are typically in the range of 0.001 to 0.002 • Larger clearance ratios increase load number ON • Higher ON numbers give larger eccentricity, pressure, and torque • Larger clearance ratios used for better lubricant flow (increasing cooling conditions) • An Ocvirk number is chosen and lubricant is then selected • After bearing has been designed, heat and momentum (flow) analysis can be done… not in this course... Note: ON 30 ( =0.82) moderate loading (recommended) ON 60 ( =0.90) heavy loading ON 90 ( =0.93) severe loading

  15. Examples • Review and Master: Example 10-1

  16. Reading • Chapters 10 of textbook: Sections 10.0 to 10.13 • Review notes and text: ES2501, ES2502, ES2503 Homework assignment • Author’s: 10-2 • Solve: 10-9, 10-13, 10-19

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