[lec dt3 journal bearings

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IAM-DT-3: SS 2005 Prof. Dr.- Ing. P. J. MaukUniversitt Duisburg-Essen Institut fr Angewandte Materialtechnik

LEC-DT3-Journal_Bearings.doc Seite 1 von 25

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


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Case a): hydrodynamic lubrication (Flssigkeitsreibung)

- complete separation of both surfaces by a lubricant film, the bearingpressure is entirely supported by the fluid pressure in the film generated by the

relative motion of both surfaces- film thickness: 0.008 mm - 0.020 mm- typical friction coefficients: = 0.002 - 0.010

(Optimum condition: desired situation)

Case b): mixed-film lubrication (Mischreibung)

- surface roughness peaks get in contact and their is partial hydrodynamicsupport under certain proper conditions the surface wear can be mild

- coefficients of friction : = 0.004 - 0.10

Case c): boundary lubrication (Trockenreibung)

- surfaces are in contact continuously by and extensively, the lubricant iscontinuously smeared over the surfaces and provides a continuouslyrenewed absorbed surface film that reduces friction and wear

- typical coefficients of friction: = 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


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-shear stresses in the lubricant areProportional to the velocity gradient

~dv v

dy h =

h: thickness of lubricant filmv: rotational speed of shaft: proportional factordynamic viscosity

( acc. to DIN 1342 and 51550)

Measured by falling sphere viscometer (Kugelfallviskosimeter), a ball falls insidean oil filled tube:

v

h =

21

NsPa s

m = =

=

2 2 .

N Ns m

S mmm mm=

A derivate unit is often used

' '

= = kinematic viscosity2

m

S


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(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 cm2/s Kinematic viscosity

1 Centistokes= 1 cSt = 1 mm2/s =1 Z


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- High viscosity :Higher forces can be taken at low speedswith high loads but high friction values

- Low viscosity :Smaller loads can be taken but higher speeds arepossible with less internal friction

Density and specific heat of oil is also temperature-depended: (acc. to VDI-2204)

( )( )51 65 10 = t to ot t

t : Density at temperature t

to : Density at temperature t0 = 15 C ; t = actual temperature

3856 2.345 4.605p oC t= + (0 > 896 kg/m

3)

2910 1.290 4.605p oC t= + (0 896 kg/m

3)

(Slide 04): Geometry and pressure distribution for a journal bearing


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Geometrical definitions of bearings

- length of bearing : l or (b)- sleeve diameter of bearing: d1, d1 d2 d- shaft diameter: d2(d)

- clearance S = d1-d2- related clearance: = S/d = (d1-d2)/d (d1-d2)/d2- minimum film thickness of lubricant film:

h0 = hmin =2 2

S d =

= related thickness of lubricant film

= =

0 0

/ 2

2

dS

h h

- eccentricity of bearing:

e = S/2 h0= 2

d

- related eccentricity

= =/ 2

1S

e

- angular speed of bearing

2

60 sec

n rad

= n: rpm revolutions per minute

- sliding speed of bearing

n=d n n: operating rpm of bearing [ ]1/ s

- specific pressure in the bearing

PL = P=i

F

b d F: bearing force; b: width of bearing; d: diameter of bearing


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(Slide 05): Design data for journal bearings


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Design data for journal bearings:

- tabulated data for sliding bearings for different conditions in engineering- determining conditions for bearings are:

Max. design pressure P= PLin MPa diameter clearance ratio ( related clearance)

=C

d

bearing ratio:

l

d or =

b

d

Some simple bearings:

Bearing material grease lubricationLubrication by hand N/mm

2dropped oil

Sliding speed u (m/s) pressure PL u PL

Cast iron 1 0.4 3 0.8

Bronze, Cu alloy 2 0.6 2 1.2Al alloy 2 0.3 2 0.4Pb Sn alloy 3 0.1 3 0.3Sinter material 1 1 3 1.8(oil filled)


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(Slide 06): Data about bearing materials

(Babbitt metal: Lagerweissmetall: Zinnlager)


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(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 intime


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(Slide 08): Bearing geometries:

a) full bearing 360 bearingb) partial bearing 180 bearing


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Sliding bearings / Oil fi lm bearings:

Specific load for a sliding bearing: (mean)

P= PB =F

d b F: Bearing force (Lagerkraft)

b: Bearing width (Lagerbreite)

d: bearing diameter (Lagerdurchmesser)

P =2

N

mm

mean pressure

The journal rotates in the bearing with the sliding speed u :

u= d nm

s

n: journal rps [ ]1/ s n=nM/60 , nM=rpm1

min

Angular speed of journal (Lagerzapfen)

= 2 n =12

60

ns


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Due to friction a certain friction power is generated in the bearing:

[ ]fNm

P F u Ws

= =

: friction factoru: sliding speedPf: friction power

For the capacity if a sliding bearing a dimensionless factor is defined:

2 2 2

0 2 32

F S F SS

b dd b d

p

= = =

S: diameter difference: d1 - d2(Lagerspiel)P: mean pressure of bearing: viscosity of oil Pasd: journal diameter (bearing diameter)F: bearing force: angular speed of journalS0: Sommerfeld-Number

A lot of design data for sliding bearings are related to the Sommerfeld number S0:

The Sommerfeld number S0 can be calculated as a function of the relativeeccentricity and the width ratio = b/d of the bearing.

Calculation of Sommerfeld number

( )( )

( )2 2 2 2 10 2

2

11 16

2 1

bS

d

= +

+

with :

/ 21

e

S = = with 0

/ 2

h

S = and = = 0

2 2

S de h

1= f(b/d) and 2= f (b/d)


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(Slide 10)

Calculation acc. to DIN31652-2 ( for full bearings) ( see also slide 10a,b)


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(Slide 10a)

The Sommerfeld number ( , / )o L

S f b d = with pure rotation


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(Slide 10b)

- heavy loaded bearings big S0-numbers- low loaded bearings small S0-numbers

Practically: S0 > 1 ; only with high sliding speeds and low bearing loads S0 > 1 !


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Some practical values for the minimum oil film thickness in the bearing homin

(Slide 11) : Experimental data for homin[ ]m acc. to DIN 31652 T3 for different

shaft diameter and sliding speedsEmpirical value of smallest allowable h0minacc. to DIN 31652 T3

The value h0for the smallest gap in the bearing is given by 2 formulas:

For S0 > 1: 00

1 2

2 2 1

Sh

S

=

+

For 0 2< with = b/d (width ratio of bearing)

And for S0 < 1 :0

0

11

2 2 2

S Sh

+=

For 0.5 2These formulas give good approximation for h0During operation of the bearing is necessary:

h0h0min

The rotational speed nmin, which is necessary to ensure hominis given by:

[ ]= i0minmin0

1/h

n n sh

Minimum rotational speed

The value of n is calculated by use of the S0-number for S0 < 1

( )

~2

01

2

Pn S

= =


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The transition rotational speed nTis given by:

0

0

TT

hn n

h= for h0 > h0min > h0T

A thumb-rule equation for the relative bearing clearance is given by:

41 2

1

0.8S d d

ud d

= = u: sliding speed

Where is given 1/1000 (promille)Practical conditions are:

Small -values for high speeds and loads, greater -values for small loads and highspeedsSome values for in relation to ISO-fits for shafts and bearings are given in(Slide 12a,b)

(solide 12a)


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(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 S0 < 1 (high speed bearing)

0

3

S

=

For S0>1 (high load bearing)

=

0

3

S


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See also (slide 13): Vogelpohl diagram

(Slide 13)


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A bearing in a machine compound:

( )15 20 B BA d b=

o : ambient temperature ( 20c): max. bearing temperature 70c 100c

If cooling is done by oil flow, the necessary oil flow is:

( )2 1

fc

PQ

c =

Qc: oil flow

3m

s

c: specific heat of oil = f ()

: density of oil = f ()2: run out temperature of oil1: run in temperature of oil

(2-1) should be 10 20 K

For regular lubrication conditions in a oil film bearing a certain necessary oil flow isrequired in the bearing:

0

2L

uQ h b

: oil flow rate factor 1,5h0: min. oil film thicknessb: bearing widthu: sliding speed

Acc. to DIN31652 the calculation is as follows:

QL=Q1+Q2

Where:

=

=

3

31 1

1

10.223

4

b b

d d

Q d q

q

q1: related oil flow due to internal bearing pressure

Q2is:

( )3 32 2/EQ d P q = (see slide 15)


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The related oil flow q1due to intrinsic pressure in the gap a relation of relatedeccentricity and related bearing ratio B/D acc. to DIN 31652

Where Peis the entry oil pressure from lubrication system and for q2see (slide 16)

With the oil flow rate the bearing temperature is controlled, if the temperature is toohigh bearing conditions must be changed!!


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The related oil rate q2depending on the series of the lubricant entries

(Slide 16)

[lec dt3 journal bearings

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