Conception mécanique et usinage MECA0444-1 Hydrodynamic plain bearings Pr. Jean-Luc BOZET Dr. Christophe SERVAIS Année académique 2016-2017 1
Tribology Tribology comes from the greek word tribein, which means rubbing It appeared for the first time in march 1966 in a report of British Ministery of Science and Education: the Jost report Definition: tribology is the science and technology of interacting surfaces in relative motion and of its derived observed phenomena, which are friction and wear (tribology includes lubrication) Tribology is a discipline that traditionally belongs to mechanical engineering However, with the push towards more and more severe operating conditions in almost all technological fields (i.e.: mechatronics, biomechanics), tribology is becoming more and more interdisciplinary, embracing physics, chemistry, metallurgy, biology and engineering 2
Purpose of tribology [:3+,209 Z:3+9 )379 X/,5:>319 J+::a9/,5,20!7:<832,<3/!,24:+63<:9 :4<= F?-+,<34,.2 X?+63<:!<.34,209 [+3Q:9!!!!!!!!!)/?4<8:9 )/37@9!!!!!!!!!$1+:9 X8.:9 J+,<4,.23/!8:34,20!_:=0=!,2,4,34,.2.6!6,+:!-1!@+:8,94.+,<!@:.@/:` :4<= W:3+!+:9,94324 734:+,3/9 X3<+,6,<,3/ 734:+,3/9 f,2,7?7!6+,<4,.2 f,2,7?7!>:3+ WYK% k J%")$"&# f3;,7?7!>:3+ f3;,7?7!6+,<4,.2 Y2832<:7:24!.6 358:9,.2 g:2<,/9 ':@.9,4,.2!.6!9./,5!/?-+,<3249-1!9/,5,20!<.243<49 Y+39:+9 J+,<4,.2!9?+63<,20 3
Tribological systems Parameters Observed phenomena Wear process Type of contact (geometry) Contact pressure and stresses Adhesion Type of materials (hardness) Friction Abrasion Surface roughness Loss of weight (wear) Erosion Load (N) Vibration (stick-slip) Cavitation Sliding speed Thermal phenomena Deformation Environment (atmosphere, fluid, dirt) Bulk modification Surface transformation Fatigue Fretting Corrosion 4
Lubrication The role of a lubricant is to separate opposed surfaces decrease shear stress at the interface remove the heat generated by the rubbing remove the wear debris 5
Viscosity Consider 2 flat surfaces separated by a lubricant of thickness h The force F required to move the upper surface is proportional to the wetted area A, the upper surface velocity u and to the inverse of the film thickness h F / A u 1 h and the dynamic viscosity h is defined such that F = A u h () = u h $! # &<48<8A3>E!AD8< 4>;87!X>@E369Y @63@ " #(%) 6
Viscosity The SI unit of the dynamic viscosity is the Pascal-second [Pas] Historically, before the introduction of the SI system, the unit of the dynamic viscosity was the Poise [P], which is equal to 0.1 [Pas] An alternative viscosity also exists: the kinematic viscosity n The kinematic viscosity is equal to the dynamic viscosity h divided by the density of the lubricant r = The SI units of the kinematic viscosity is the Stoke [S], which is equal to 0.0001 [m/s 2 ] 7
Viscosity and temperature The viscosity of oils used as lubricant is extremely sensitive to temperature T Several viscosity-temperature relationships have been proposed in order to compute the dynamic viscosity h Name Equation Comments Reynolds = B exp AT Early equation, accurate only for a very limited temperature range Slotte = A (B + T ) C Reasonable, useful in numerical analysis Walther = A + BD 1 T C Forms the basis of the ASTM viscositytemperature chart Vogel = A exp T B C Most accurate, very useful in engineering calculations 8
Viscosity and pressure The viscosity of lubricants increases with pressure This pressure effect can be stronger than the effect of the temperature Globally speaking, the heavily loaded contacts are particularly concerned by the pressure effects, especially the ones related to elastohydrodynamic lubrication (ball bearings, gears,...) The equation of Barus is the best model to link the dynamic viscosity h to the pressure p = 0 exp ( p) where h0 is the dynamic viscosity at atmospheric pressure and where a is a parameter which may depend on pressure and temperature Unfortunately, the Barus equation is not always valid and the parameter a is not always easy to determine 9
Viscosity and shear rate It is often supposed that the viscosity is proportional to the shear rate (Newtonian fluid) However, lubricants are not perfectly Newtonian For example, a lot of oils experience non-newtonian behavior at high shear rates and greases cannot be considered as Newtonian fluids τ τ %D3@6!9A6399 91; α = η %D3@6!9A6399 α %D3@6!6@A39 #'! %D3@6!6@A39 #'! Newtonian fluid Non-Newtonian fluid 10
Lubrication regimes Fluid film lubrication Complete separation of mating surfaces by the lubricant film Mixed lubrication Incomplete separation of the mating surfaces by the lubricant film Boundary lubrication Surfaces only separated by lubricant molecules attached to the surfaces 11
Lubrication regimes h 0.0025 [µm] h 0.025 to 2.5 [µm] h>0.25 [µm] Stribeck curve 12
Lubrication regimes h 0.025 to 2.5 [µm] h 0.0025 [µm] h>0.25 [µm] 13
Elastohydrodynamic lubrication The elastohydrodynamic lubrication occurs in heavily loaded contacts The pressure and the lubricant film thickness are not only a function of the hydrodynamical laws governing the fluid behavior but also depend on the elastic deformation of the surfaces Typical examples: gears, ball bearings or roller bearings Sliding speed 3 "3456789:;7:9<4=>? G;B55@;B :>56;>A@6>7< (B;6P>4< G;B55@;B :>56;>A@6>7< /7<64?6><E 5@;C4?B5 L - /7<56;>?6>7< L @ N :9<4=>?!G;B55@;B!:>56;>A@6>7<!><!4<!B3456789:;7:9<4=>?!? Oil film thickness of a ball-on-disk contact (interferometry) 14
Lubrication regimes h 0.0025 [µm] h 0.025 to 2.5 [µm] h>0.25 [µm] 15
Hydrodynamic lubrication The hydrodynamic lubrication is the regime present in contact with surfaces separates by a fluid film Numerous applications use the oil wedge principle («coin d huile») in order to create a lift force and to separate the surfaces (example: plain bearing) The flow rate of a Newtonian lubricant within a contact is the combination of a Couette flow due to the relative motion of surfaces a Poiseuille flow due to a pressure gradient 1 dimension U Oil wedge 16
Hydrodynamic lubrication Example: journal bearing, which only supports radial loads 17
Hydrodynamic lubrication Example: thrust bearing, which only supports axial loads ω Bearing pad W t A A r o r i r o r i N a Sliding surface or runner Lubricant Thrust bearing l Bearing pad Pads 18
Oil wedge The simplest oil wedge is a surface inclined and moving with respect to another surface First, let us assume that there is no pressure fluctuation within the film, thus the speed distribution is linear (Couette flow) The volume flow rate at both inlet (Qe) and outlet (Qs) are given, for a width L, by Q e = Lh e U 2 and Q s = Lh s U 2 If the fluid is incompressible, then Qe = Qs, which is impossible because he is different from hs As a result, pressure is generated within the film, which tends to separate the surfaces p h e u e U h s u s p e =0 u e u s U p s =0 Couette flow 19 Oil wedge flow
Oil wedge The Reynolds equation governs the pressure distribution within thin fluid films A simplified equation of Reynolds may be derived by considering a 1D, laminar and isothermal flow in a steady-state configuration The equilibrium of a small element within the fluid may be written [p(x) p(x +dx)]dy +[ xy (y +dy) xy (y)]dx =0 because the film is thin and the pressure is supposed to be constant along the y-axis If the fluid is Newtonian with a constant viscosity, then a first order development gives dp dx dxdy + @ @u dxdy =0 () dp @y @y dx = @2 u @y 2 y h(x) dy dx U x 20
Oil wedge By integrating the resulting equilibrium equation, the speed profile can be obtained u = 1 2 dp dx y2 + C 1 y + C 2 where the constants C1 and C2 are determined by using the fact that for y = 0, u = U It follows that for y = h, u =0 u = 1 2 dp y y (y h)+h dx h U y h(x) dy dx U x 21
Oil wedge In any cross section, the volume flow rate by unit of length is given by q(x) = Q(x) L = q is constant because the fluid is supposed to be incompressible, thus h 3 12 Z h(x) where h * is the film thickness for which the pressure gradient is zero 0 dp dx + hu 2 u dy = h3 12 = constant = h U 2 dp dx + hu 2 Finally, one has dp dx =6 U h h 3 h y h(x) dy dx U x 22
Bearing comparison Classic Parameters Ball bearing plain bearing Porous plain bearing Incompressible fluid Compressible fluid Hydrodyn. Hydrostat. Aerodyn. Aerostat. High speed Low speed Alternate rotation High load Low load Combined load Change in load direction Change in load intensity Starting torque Nominal torque?????????????????????????????????????????? (1)???(2)?????????? (3)???????????????? (4) (4) (4) (4)??????????????????????????????????????????????????????????? Frequent starts and stops (1) Unless high speed (2) Unless low speed (3) Becomes unstable due to oil whip (4) Unless thrust bearing?????????????? 23?????? Not applicable Poor Good Excellent
Bearing comparison Classic Parameters Ball bearing plain bearing Porous plain bearing Incompressible fluid Compressible fluid Hydrodyn. Hydrostat. Aerodyn. Aerostat. External vibrations Source of vibrations Source of damping??????????????(1)?????(2)???????????????? Noise Centering Axial compactness Radial compactness Standardization Cost?????????? (3)????? (4)????????????????????????????????????????????????????????????? (1) Stick-slip (2) Becomes unstable due to oil whip (3) Special lubricant for T > 150 ºC (4) Pump?????? Not applicable Poor Good Excellent 24
Bearing comparison Classic Parameters Ball bearing plain bearing Porous plain bearing Incompressible fluid Compressible fluid Hydrodyn. Hydrostat. Aerodyn. Aerostat. High temperatures Low temperatures Humidity?? (1)???(2)?? (3)?? (3)?? (3)???????? (4)????(5)?(5)?(5)???????? (6)?????????????? Dust?? (6)????? (6)?? (7)???(7)?(7)?? (7) Vacuum Simplicity of lubrication and maintenance?(8)????(8)?? (9)?????????(10)????? (10) (1) Special lubricant for T > 150 ºC (2) Limited by material temperature (3) Oxidation, choice of adapted lubricant (4) Special lubricant for T < 30 ºC (5) High starting torque (6) Seal (7) Filtration (8) Special lubricant (9) For grease lubrication (10) Pump?????? Not applicable Poor Good Excellent 25