Journal bearings/sliding bearings

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1 Journal bearings/sliding bearings Operating conditions: Advantages: - Vibration damping, impact damping, noise damping - not sensitive for vibrations, low operating noise level - dust tight (if lubricated by grease) - simple design; separable into two parts, easy to handle - small total required space, adjustable to different design demands and conditions - for big shaft diameters cheaper than rolling bearings - with good lubrication very high rotational speed possible - with good and appropriate lubrication nearly free of wear Disadvantages: - without sufficient lubrication very quickly failure of bearing - in certain cases expensive and complicated lubrication system required - high consumption of lubricant - run-in time necessary - surface quality of shaft surface very important Friction conditions in sliding bearings: (Slide 01) : Friction conditions between a moving and non-moving surface LEC-DT3-Journal_Bearings.doc Seite 1 von 25

2 Case a): hydrodynamic lubrication (Flüssigkeitsreibung) - complete separation of both surfaces by a lubricant film, the bearing pressure is entirely supported by the fluid pressure in the film generated by the relative motion of both surfaces - film thickness: mm mm - typical friction coefficients: µ = (Optimum condition: desired situation) Case b): mixed-film lubrication (Mischreibung) - surface roughness peaks get in contact and their is partial hydrodynamic support under certain proper conditions the surface wear can be mild - coefficients of friction : µ = Case c): boundary lubrication (Trockenreibung) - surfaces are in contact continuously by and extensively, the lubricant is continuously smeared over the surfaces and provides a continuously renewed absorbed surface film that reduces friction and wear - typical coefficients of friction: µ = 0,05-0,20 Slide 02): Situation of a sliding bearing: - a fixed bearing enclosed the rotating shaft - rotating journal (shaft) and sleeve are separated by a lubricant - shaft and sleeve has a eccentricity - the gap continuously narrow - the lubricant is drawn in to this gap in the direction to the minimum thickness - the lubricant is sheared, there is a velocity gradient in the film LEC-DT3-Journal_Bearings.doc Seite 2 von 25

3 -shear stresses in the lubricant are Proportional to the velocity gradient τ ~ dv = µ v dy h h: thickness of lubricant film v: rotational speed of shaft µ: proportional factor dynamic viscosity ( acc. to DIN 1342 and 51550) Measured by falling sphere viscometer (Kugelfallviskosimeter), a ball falls inside an oil filled tube: v τ = µ h = Ns η = µ = 1 Pa s 2 m N Ns m mm = mm Sm. 2 2 A derivate unit is often used µ η ' = µ ' = kinematic viscosity ρ m S 2 LEC-DT3-Journal_Bearings.doc Seite 3 von 25

4 (Slide 03): Viscosity and density of oils and lubricants depending on temperature - SAE 70: oil type (Society of Automobile Engineers) Old dimensions for viscosity: 1 stokes = 1 St = 1 cm 2 /s Kinematic viscosity 1 Centistokes= 1 cst = 1 mm 2 /s =1 Z LEC-DT3-Journal_Bearings.doc Seite 4 von 25

5 - High viscosity : Higher forces can be taken at low speeds with high loads but high friction values - Low viscosity : Smaller loads can be taken but higher speeds are possible with less internal friction Density and specific heat of oil is also temperature-depended: (acc. to VDI-2204) 5 ( ( t t )) ρ = ρ t to o ρ t : ρ : to Density at temperature t Density at temperature t 0 = 15 C ; t = actual temperature C C p p = ρ t (ρ 0 > 896 kg/m 3 ) o = ρ t (ρ kg/m 3 ) o (Slide 04): Geometry and pressure distribution for a journal bearing LEC-DT3-Journal_Bearings.doc Seite 5 von 25

6 Geometrical definitions of bearings - length of bearing : l or (b) - sleeve diameter of bearing: d 1, d 1 d 2 d - shaft diameter: d 2 (d) - clearance S = d 1 -d 2 - related clearance: ψ = S/d = (d 1 -d 2 )/d (d 1 -d 2 )/d 2 - minimum film thickness of lubricant film: S d h 0 = h min = δ = 2 2 ψ δ δ = related thickness of lubricant film h h δ = = S /2 ψ 0 0 d 2 - eccentricity of bearing: e = S/2 h 0 = d ψ ε 2 - related eccentricity e ε = = 1 δ S /2 - angular speed of bearing ω = 2π n rad 60 sec n: rpm revolutions per minute - sliding speed of bearing n=π d n n : operating rpm of bearing [ 1/ s ] - specific pressure in the bearing P L = P = F bd i F: bearing force; b: width of bearing; d: diameter of bearing LEC-DT3-Journal_Bearings.doc Seite 6 von 25

7 (Slide 05): Design data for journal bearings LEC-DT3-Journal_Bearings.doc Seite 7 von 25

8 Design data for journal bearings: - tabulated data for sliding bearings for different conditions in engineering - determining conditions for bearings are: Max. design pressure P = P L in MPa diameter clearance ratio ( related clearance) ψ = C d bearing ratio: l d or b d = β Some simple bearings: Bearing material grease lubrication Lubrication by hand N/mm 2 dropped oil Sliding speed u (m/s) pressure P L u P L Cast iron Bronze, Cu alloy Al alloy Pb Sn alloy Sinter material (oil filled) LEC-DT3-Journal_Bearings.doc Seite 8 von 25

9 (Slide 06): Data about bearing materials (Babbitt metal: Lagerweissmetall: Zinnlager) LEC-DT3-Journal_Bearings.doc Seite 9 von 25

10 (Slide 07): Demands on bearing materials fatigue strength in operation good sliding properties seizure resistance (Notlaufeigenschaft) corrosion resistance embedability: hard partials are embedded in the soft outer layer compatibility: the bearing sleeve fits itself to rotating journal during run in time LEC-DT3-Journal_Bearings.doc Seite 10 von 25

11 (Slide 08): Bearing geometries: a) full bearing 360 bearing b) partial bearing 180 bearing LEC-DT3-Journal_Bearings.doc Seite 11 von 25

12 Specific load for a sliding bearing: (mean) Sliding bearings / Oil film bearings: P = P B = F d b F: Bearing force (Lagerkraft) b: Bearing width (Lagerbreite) d: bearing diameter (Lagerdurchmesser) P = N mm 2 mean pressure The journal rotates in the bearing with the sliding speed u : m u= d π n s Angular speed of journal (Lagerzapfen) n : journal rps [ 1/ s ] n =n M /60, n M =rpm 1 min ω = 2 π n = 2 π n 60 s 1 LEC-DT3-Journal_Bearings.doc Seite 12 von 25

13 Due to friction a certain friction power is generated in the bearing: Nm Pf = F µ u = W s [ ] µ: friction factor u: sliding speed P f : friction power For the capacity if a sliding bearing a dimensionless factor is defined: p ψ F S F S S0 = = = 2 b d 2 3 η ω d η b d S: diameter difference: d 1 - d 2 (Lagerspiel) P : mean pressure of bearing η: viscosity of oil Pa s d: journal diameter (bearing diameter) F: bearing force ω: angular speed of journal S 0 : Sommerfeld-Number A lot of design data for sliding bearings are related to the Sommerfeld number S 0 : The Sommerfeld number S 0 can be calculated as a function of the relative eccentricity ε and the width ratio β = b/d of the bearing. Calculation of Sommerfeld number S ( ε ) ( ) b ε α1 = π 1 ε + 16ε d 2 1 α with : ( ε 1) 2 + ε e ε = = 1 δ with S /2 h δ = 0 and e = h 0 = ψ ε S / 2 S d 2 2 α 1 = f(b/d) and α 2 = f (b/d) LEC-DT3-Journal_Bearings.doc Seite 13 von 25

14 (Slide 10) Calculation acc. to DIN ( for full bearings) ( see also slide 10a,b) LEC-DT3-Journal_Bearings.doc Seite 14 von 25

15 (Slide 10a) The Sommerfeld number S = f( ε, b/ d ) with pure rotation o L LEC-DT3-Journal_Bearings.doc Seite 15 von 25

16 (Slide 10b) - heavy loaded bearings big S 0 -numbers - low loaded bearings small S 0 -numbers Practically: S 0 > 1 ; only with high sliding speeds and low bearing loads S 0 > 1! LEC-DT3-Journal_Bearings.doc Seite 16 von 25

17 Some practical values for the minimum oil film thickness in the bearing h omin (Slide 11) : Experimental data for h omin[ µm ] acc. to DIN T3 for different shaft diameter and sliding speeds Empirical value of smallest allowable h 0min acc. to DIN T3 The value h 0 for the smallest gap in the bearing is given by 2 formulas: For S 0 > 1: h0 = S 1 2β 2 2 S 1+ β 0 For 0 < β 2 with β = b/d (width ratio of bearing) And for S 0 < 1 : h 0 S S0 1+ β = β For 0.5 β 2 These formulas give good approximation for h 0 During operation of the bearing is necessary: h 0 h 0min The rotational speed n min, which is necessary to ensure h omin is given by: h0min nmin = in s h 0 [ 1/ ] Minimum rotational speed The value of n is calculated by use of the S 0 -number for S 0 < 1 ( ) n S = = 0 1 ~ P ψ 2 η 2π LEC-DT3-Journal_Bearings.doc Seite 17 von 25

18 The transition rotational speed n T is given by: n T h0 T = n for h 0 > h 0min > h 0T h 0 A thumb-rule equation for the relative bearing clearance ψ is given by: S d1 d2 4 ψ = = 0.8 u u: sliding speed d d 1 Where ψ is given 1/1000 (promille) Practical conditions are: Small ψ-values for high speeds and loads, greater ψ-values for small loads and high speeds Some values for ψ in relation to ISO-fits for shafts and bearings are given in (Slide 12a,b) (solide 12a) LEC-DT3-Journal_Bearings.doc Seite 18 von 25

19 (Slide 12b) Any sliding bearing do have friction in the oil film in the bearing gap. Some thumb rules for a related friction factor is: For S 0 < 1 (high speed bearing) µ ψ = 3 S 0 For S 0 >1 (high load bearing) µ 3 ψ = S0 LEC-DT3-Journal_Bearings.doc Seite 19 von 25

20 See also (slide 13): Vogelpohl diagram (Slide 13) LEC-DT3-Journal_Bearings.doc Seite 20 von 25

21 The related friction factor can also be calculated acc. to DIN to a formula system: ( see slide 14) The related friction factor µ / ψ eff depending on the related excentricity ε and the related bearing width B/D acc. to DIN µ 10 y ψ = where y = f (factor: based on S 0 and b/d - ratio ) With this data the friction power is calculated d Pf = µ F u = µ F ω 2 LEC-DT3-Journal_Bearings.doc Seite 21 von 25

22 The total friction power generates heat in the bearing, this heat must transferred out of the bearing partly by convection through the bearing housing and partly by the oil flow through the bearing: P f = P A +P Q P A : P Q : cooling power by convection cooling power by oil flow - bearings without pressured flow of oil: convection - bearings with pressured oil flow: oil cooling If P f = P A µ F u = α * A v v = ( ) 0 α* : heat transition factor Nm W = 2 2 s m K m K by surrounding air α * = Vw with V w : air speed [ m/ s ] Vw 1.25 m/ s Max. values for α* are 20 W 2 mk and A: surface area of bearing housing For a cylindrical bearing housing: (DIN 31652) 2 2 ( ) A = π d d + π d b 2 H B H H d H : d B : b H : diameter of housing bearing diameter width of housing For a pedestal bearing (Stehlager) A π H bh + H 2 H: height of pedestal LEC-DT3-Journal_Bearings.doc Seite 22 von 25

23 A bearing in a machine compound: ( ) A = db bb θ o : ambient temperature ( 20 c) θ : max. bearing temperature 70 c 100 c If cooling is done by oil flow, the necessary oil flow is: Q c = P f ( ) c ρ ϑ ϑ 2 1 Q c : oil flow m s 3 c: specific heat of oil = f (θ) ρ: density of oil = f (θ) θ 2 : run out temperature of oil θ 1 : run in temperature of oil (θ 2 -θ 1 ) should be K For regular lubrication conditions in a oil film bearing a certain necessary oil flow is required in the bearing: u QL ϕ h0 b 2 ψ: oil flow rate factor 1,5 h 0 : min. oil film thickness b: bearing width u: sliding speed Acc. to DIN31652 the calculation is as follows: Q L =Q 1 +Q 2 Where: Q = d ϕ ω q 3 1 b b q1 = ε 4 d d q 1 : related oil flow due to internal bearing pressure Q 2 is: 3 3 ( ψ E / η) Q = d P q (see slide 15) 2 2 LEC-DT3-Journal_Bearings.doc Seite 23 von 25

24 The related oil flow q 1 due to intrinsic pressure in the gap a relation of related eccentricity ε and related bearing ratio B/D acc. to DIN Where P e is the entry oil pressure from lubrication system and for q 2 see (slide 16) With the oil flow rate the bearing temperature is controlled, if the temperature is too high bearing conditions must be changed!! LEC-DT3-Journal_Bearings.doc Seite 24 von 25

25 The related oil rate q 2 depending on the series of the lubricant entries (Slide 16) LEC-DT3-Journal_Bearings.doc Seite 25 von 25

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