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Expression for load

Expression for load. We have seen that under Sommerfeld’s condition W = W y In non-dimensional terms, W* = W y * = This is a function solely of the eccentricity ratio e . Putting back the dimensional quantities we get. Sommerfeld number. Which gives Where W = total load L = axial length

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Expression for load

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  1. Expression for load • We have seen that under Sommerfeld’s condition W = Wy • In non-dimensional terms, W* = Wy* = • This is a function solely of the eccentricity ratio e. Putting back the dimensional quantities we get

  2. Sommerfeld number • Which gives Where • W = total load • L = axial length • U = surface speed • h = viscosity • C = radial clearance • R = bearing radius The variable on the left hand side is known as the Sommerfeld number and is often designated by S or D. It is more usual to work with the reciprocal

  3. Sommerfeld’s number is used as abcissafor a number of design curves. • The ordinate can be selected to allow the friction value, film thickness, oil leakage, temperature rise etc to be determined. • Design curves have been produced of various variables against the Sommerfeldnumber using computer techniques by A.A Raimondi and J.Boyd of Westinghouse Research Labs(ASLE Transactions Vol 1 No 1 April 1958). • These graphs include compensation for end leakage and eccentricity.

  4. Friction coefficient Sommerfeld number Ref: http://www.roymech.co.uk/Useful_Tables/Tribology/Liquid_Lubrication.htm

  5. Reynold’s condition • p = 0, dp/dq = 0, at some value of q > p • The start of the curve is assumed at the point of maximum oil thickness q = 0 • The pressure equation obtained earlier is • If the pressure starts at q =0 (g = 0), then C = 0 • If p*= 0 at any other value of q, C will not be zero

  6. We know that h = c(1 + ecosq) and therefore ho = c(1 + ecosqo) where ho is the film thickness when dp/dq = 0 at q = qo • This equation is symmetrical about q = 180o, hence qocan have 2 values, one when pressure p is maximum and the other when p is minimum • Therefore we can write • On the gscale we can write • Where b on the gscale corresponds to a on the q scale • p* = 0 at g = p + b, sin(p+b) = -sinb and cos(p + b) = -cosb

  7. Reynold’s condition, p = 0, dp/dq = 0, at some value of q > p • = 0 Start of pressure curve Bearing Rdq q Wy Wx • = p+a (min. pressure = 0) W Y Shaft Pressure curve • = p-a (max. pressure)

  8. e in terms of b • Substituting the above in the pressure equation we get p* = 0 • Expanding and multiplying out we find that • Or • This equation can be used to determine b

  9. Values of b for different e (obtained by Cameron and Wood) • e = e/c = 1 when e = c(eccentricity = radial clearance) • = 0 when eccentricity = 0, i.e. the shaft and bearing are coaxial The values of b can be inserted into the pressure equation and integrated to give the loads Wxand Wy

  10. Now The first term is zero as p = 0 at q = 0 and (p+a). Using Sommerfeld substitution the required integral in terms of g comes out to be

  11. P = 0 at q = 0 and p + a, therefore the 1st. Term disappears. Using Sommerfeld’s substitution we get

  12. Therefore Once y has been found we can find W from Wsinyor Wcosy

  13. As e 1, The eccentricity  radial clearance, therefore the infinite journal bearing approaches the value for 2 discs with internal contact. • The expression is • Where • Now R1 - R2 = c, the radial clearance, so 1/Rred = c/R2, where R is taken as the radius of the shaft

  14. The minimum film thickness ho = c(1-e) • Hence the expression for load carried can be written as • Where D is the Sommerfeld number

  15. Dielectric strength • A measure of the electrical insulating strength • Measured as the maximum voltage it can withstand without conducting (expressed as volts/thickness) • Less moisture- better insulators • Dehydrating techniques are used to improve the dielectric strength

  16. Carbon residue • Carbon residue is formed by evaporation and oxidation of lubricant • The test of the tendency of a lubricant to form carbon residue is called the “Conradson” test • The test sample is heated until it is completely evaporated (cannot ignite) • The residue is cooled and weighed • Result interpreted as weight ratio of residue to oil sample

  17. Lubricant additives

  18. Lubricant additives or agents • Added to preserve, improve and/or provide additional useful properties to a lubricant • Protect the surface forming a film • Keep surfaces and lubricant passageways clean • Inhibitors prevent the formation of harmful products • Some are consumed (sacrificial), others are not (non-sacrificial)

  19. Lubricant additives- classification • Oxidation inhibitors • Viscosity index improvers • Boundary and extreme pressure additives • Rust inhibitors • Detergents • Dispersants • Pour point depressants • Anti-foaming agents • Friction modifiers

  20. Oxidation products • Sludge: Black tar-like substance consisting of water, carbon, engine oil, organic residue and dirt • Engine gum: Acts as a binder causing residue to stick to machinery components • Varnish: Petroleum gum exposed to high temperature and ironed out on surfaces • Laquer: Thin layer of reacted varnish • Carbon deposits: Combination of soot from fuel burning and oxidation of lubricating oil

  21. Oxidation prevention additives Oxygen reacts preferentially with additive molecules Oxygen • Preferential oxidation: Additive is more susceptable to oxidation than oil • Oil particles are therefore prevented from oxidising Oil Oil Additive

  22. Oxidation prevention additives Additive reacts with metal particles Metal catalyst Metal deactivators- • Metal particles in the oil act as catalysts for the oxidation reactions • The additives either react with the metal particles or form a coating over them Oil Oil Additives Additive covers metal particles by forming a coating

  23. Oxidation prevention additives- peroxide decomposers Hydrocarbon + oxygen Hydroxyperoxides Materials susceptible to oxidation by decomposed peroxides Hydroxyperoxides Decompose Additives + Hydroxyperoxides Non-oxidizing product

  24. Rust Inhibitors- effect of water • Below boiling point, water is present in a lubricating system. • Water contaminant can lead to formation of rust • Water enters by condensation and/or leakage from coolers or steam heating coils • Some oils are hygroscopic and therefore physically absorb moisture

  25. Rust prevention additives • Rust inhibitors neutralize acids formed by oxidation • Polar additives form a protective layer on the metal surface due to attraction by the surface • Chemically react with the metal surfaces to form a protective film • E.g. metal sulphonates, fatty acids, phosphates Rust prevention additive Acids formed by oxidation Harmless products Shield from air/water Polar additive layer or chemically reacted layer Metal

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