Lubrication & Journal Bearings

Chapter 12

Lubrication & Journal bearings

(7 - 8 Lectures)(7 - 8 Lectures)

TOPICS1. Definitions and Objectives2. Types of Lubrication 3. Dynamic Viscosity 4. Bearing Characteristic Number5. Stable & Unstable Lubrication 6. Hydrodynamic Lubrication 7. Design Considerations 8. Heat Balance-Self-Contained Bearings9. Clearance10. Pressure-Fed Bearings11. Loads and Materials12 Boundary lubrication13. Types of Journal Bearings

Announcements

1. HWK 3 Due Wed. 15/11

2. Quiz 3 on Monday 13/11 Ch 14

Definitions and objectives• The role of a bearing is to provide relative positioning and

rotational freedom while transmitting a load between a shaft and a housing.

• There are two general types of bearings: 1. Rolling-contact bearings (anti-friction bearings, rolling bearings).

In the rolling-contact bearings the load is transmitted by rolling rather than by sliding.

2. Journal Bearings (plain bearings, bushings, sleeve bearings).

In journal bearings, the load is transmitted by sliding and the

problem of this class of bearings is essentially a lubrication problem.

Definitions and objectives

• Journal Bearings: cylindrical or semi-cylindrical bushing made of a suitable material.

– The Journal is the part of shaft or gear in bearing

• Among applications:1. High speed, high temperature, high varying loads:

• Automotive engines: connecting rod, crankshaft,…Metal alloys

• Turbo machinery: Metal alloys

2. Light loads, low speeds with little or no lubrication:• Nylon, Teflon, rubber

3. HydrostaticLow speed, light load

4. Elastohydrodynamic

For rolling contact

(gears, rolling bearings)

5. Solid Film

Extreme Temperatures

(Graphite or Molybdenum disulfide))

Types of Lubrication

Types of Lubrication 1. Hydrodynamic Lubrication

(HDL) (a) Full, thick Fluid film lubrication - surfaces separated by bulk lubricant film; Film conditions required for lubrication.

2. Boundary (Thin Film)Lubrication (b) partial lubrication (mixed) - both bulk lubricant and boundary film play a role; (c) boundary lubrication - performance depends essentially on boundary film

Viscosity

dy

du

A

F

is absolute or dynamic viscosity (lbf.s/in2 or reyn. In ips system and

Pa.s in SI system)

du/dy is the rate of shear or velocity gradientIf rate of shear is constant: du/dy = U/h With h= c (clearance)

Fig. 12.1

Shear Stress

c

U

h

U

A

F

c=

Viscosity v.s. temperature

In general, Viscosity decreases with temperature increase.The increase in temperature comes from friction

Petroff’s Law

cr

PNfsf

f

s

s

TT

rl

WPrlPrffWrT

c

lNrlrT

rlArAT

c

rN

c

U

22

2;)2(

4)(2

2;)(

2

322

Bearing Characteristic Number (Sommerfeld Number)

Scrf

cr

PNS

22

2

Petroff used a concentric shaft to define a group of dimensionless parametersThat allow the prediction of an acceptable coefficient of friction.

r/c = clearance ratio

Shear torque in lubricant

Friction torque

0.08-0.14For steel onBronze

a

bc

12

1’

2’f = 0.001-0.005Similar to precision BB

Stable and unstable lubricationThe McKee Brothers Plot

(a) Full, thick Fluid film lubrication - surfaces separated by bulk lubricant film; Film conditions required for lubrication.

(b) partial lubrication (mixed) - both bulk lubricant and boundary film play a role;

(c) boundary lubrication - performance depends essentially on boundary film

• Boundary lubrication should be expected for slow speeds:

U<10 ft/min (0.05 m/s)

Hydrodynamic Lubrication (HDL)

• For lubricated bearing the minimum film thickness h0 occurs to the left of load line because the shaft is pushed by the pressure build up on the right. The shaft is playing the role of a pump.

Fig. 12.6

1. e: eccentricity

2. h0 minimum film thickness

3. = e/c = eccentricity ratio

4. ß bearing angular length

Hydrodynamic Lubrication (HDL)Nomenclature

• Tower investigated bath-type lubrication in 157° partial bearing. He was able to determine the pressure distribution in oil film in axial and radial directions.

• Reynolds used Tower’s findings to propose a relationship between friction, pressure and velocity. His work is given under mathematical form in the following.

Hydrodynamic Lubrication (HDL)-Theory B. Tower

Hydrodynamic Lubrication (HDL): theoryO. Reynolds

• Assuming pressure varies in x-direction only (no leakage)

• Assuming Velocity varies in x & y directions

)1(

0

ydxdp

dxdzdxy

dxdzpdydzdydzdxdxdppFx

• Assuming Newtonian viscous fluid + u = u(x,y)

• Assuming Constant viscosity and substituting Eq. (1) into (2):

• Integrating (3) twice (holding x constant):

• Assuming no slip at boundaries:

Hydrodynamic Lubrication (HDL): theory

)2(y

u

)3(12

2

2

2

dxdp

y

uory

udxdp

)4(121

2

2CyCy

dx

dpu

)5(2

@

00@0

1

2

dx

dph

h

UChyUu

Cyu

• The velocity distribution in film is:

• Flow rate:

• Incompressible flow:

The above is the Reynolds Eq. For one-dimensional flow.

Considering Leakage (2-D):

Hydrodynamic Lubrication (HDL): theory

)6(2

1 2 yh

Uhyyudxdp

)8(0 adx

Qd

)1112(633

dx

dhUz

ph

zx

ph

x

)7(122

3

0 dxdphUhudyhQ

)1012(63

dx

dhUdx

dph

dx

d

Hydrodynamic Lubrication (HDL):Theory

• There are no general analytical solutions to the 2-D Reynolds Equation.

• The Summerfeld Solution to Eq. 12-11

)1212(2

P

N

c

rfc

r

Design ConsiderationsTwo groups of variables in the design of sliding bearings (eq:12.12)

A- The independent variables:1. The viscosity ,2. The load per unit of projected bearing area, P The speed N3. The bearing dimensions r, c, and l

B- The dependent Variables or performance factors:1. The coefficient of friction f2. The temperature rise T 3. The volume flow rate of oil Q

4. The minimum film thickness ho

The first (A) are somewhat under designer control and the second (B) are not.

Design Criteria for Journal Bearings (See Lab Manual for details)

1. The value of the important parameter l/d is taken between 0.25 and 1.5. Values up to 2 were used in earlier designs. Nowadays the value of l/d is confined between 0.25 and 0.75. Short bearings are preferred when shaft deflections and misalignments are expected.

2. The nominal value of clearance ratio r/c can be taken approximately as: 1000 for precision bearings when 25<d<150 mm 500 for general machinery 250 for rough machineryThe choice of the values of r/c depends on the tolerances and

surface roughness of shaft and bearing.

Design Criteria for Journal Bearings (See Lab Manual for details)

3. The minimum film thickness h0 can be estimated from one of these equations (Trumpler’s design criteria):

or

4. The outlet temperature of the oil should be kept below 250F (121C). A value of 70C (160F) is usually specified as the average operating temperature

5. Starting unit load Pst=Wst/ld is kept below 300 psi6. Design factor on starting load should be at least 2.

)(0004.0005.0

)(00004.00002.0

0

0

mmdh

indh

)(00025.00 indh

Relationship between variables

Viscosity ChartsIn IPS units


Viscosity ChartsIn SI Units


Viscosity Charts


Minimum Film Thickness & Eccentricity ratio Chart

Optimal designZone


Minimum Film Thickness Angular position vs. S


Coefficient of friction variable vs. S


Flow variable vs. S


Maximum pressure ratio vs. S

Relationship between variablesTerminating Position of film pressure & maximum film pressure vs. S

Relationship between variablesLubricant Temperature rise T

)(2

112

aQsQ

TQCTsQQCTQC ppsplossH

Taking T1 as reference temperature:

)(Pr42 bc

fr

J

lNc

J

TNlossH

The heat loss due to friction

)(

//5.01

/

4c

rcNlQQsQ

cfr

P

CJ Tp

Equating (a) to (b)

)1512(

//5.01

/70.9

rcNlQQsQ

cfr

Ppsi

FTWith = 0.0311 lbm/in3 & Cp = 0.42 Btu/lbm.Ffor petroleum lubricants and J=9336 lbf.in/Btu

Relationship between variablesLubricant Temperature rise vs. S

Sample problems on HDL

The analysis problems are of two general categories:

1) When the viscosity is specified as in example 12-1 through 12-4 of 7th ed. The solution is straight forward.

2) The problem becomes more complex when only the lubricant inlet temperature is specified. To solve this type of problem an iterative procedure has to be followed. An example of the procedure is given in the following.

Problem # 12-12 (Modified)A 2-1/2 x2-1/2-in sleeve bearing uses grade 20 lubricant. The axial-

groove sump has an inlet temperature of 110° F. The shaft journal has a diameter of 2.500 in and the radial clearance is 0.002 in. lf journal speed is 1120 rev/min and the radial load is 1200 Ibf. Estimate

(a) The magnitude and location of the minimum oil-film thickness.(b) The eccentricity.(c) The coefficient of friction.(d) The power loss rate.(e) Both the total and side oil-flow rates.(f) The maximum oil-film pressure and its angular location.(g) The terminating position of the oil film.(h) The average temperature of the side flow.(i) The oil temperature at the terminating position of the oil film.

• Given: d = 2.5 in, b = 2.504 in, cmin = 0.002 in, W = 1200 lbf, SAE = 20, T1 = 110°F,N = 1120 rev/min, and l = 2.5 in.

• Required (see list)• Solution: to find any of these performance

factors we need to have the bearing characteristic number: S.

• To find average viscosity (From Fig. 12-11; 12) we need to have the average operating film temperature Tf (Eq. 12-14):

Procedure: (good for IPS and SI system)1. For a first trial assume T = (General) 20 – 80 °F (10-

50°C) For our case take T = 40 °F

2. Tf =130 °F

Problem # 12-12

avavavav

P

N

c

rS 42 108.3

192

67.18625

5.25.2120067.182

002.

25.12

21T

f TT

3. Find µav = 3.8 reyn (From Fig. 12-11; 12) using Tf = 130°F

4. Calculate S = 3.8x104x3.8x10-6 = 0.144

5. Calculate TF or TC using 12-18 or Fig 12-23; 24 with S=0.144 and l/d =1

6. Recalculate Tfcal = 110+25.7/2122.85 °F

7. Compare Tfcal to Tfassum if |difference| less than 6 °F or 3 °C Recalculate, For our case Tfassum -Tfcal = 130-122.85= 7.15 >6 °F

need to re-iterate:

1’ assume T =30 °F

2’ Tf = 125°F 5’ TF 27 °F

3’ µav 4.3 reyn 6’ Tfcal = 110+27/2123.5°F

4’ S 0.163 7’ Tfassum -Tfcal = 125-

123.5=1.5<6 °F ACCEPT: Tf = 125°F or Tf

= (125+123.5)/2= 124.25 °F

FT oFP

T

psi

F 7.2570.9/3.11923.170.9

Problem # 12-12

µav = 4.3 reyn (From Fig. 12-11 for oF; 12 for oC) using Tf = 125°F yielding S=0.163

a) Using Fig 12-16 with S=0.163 and l/d =1 h0/c = 0.49 h0 = 0.0098 in

Using Fig 12-17 = 56 °

b) e= c- h0 =.002-.00098 = 0.001in. or using Fig. 12-16 =e/c = 0.5 e = 0.001 in.

c) f :Fig 12-18 (r/c)f= 4f= 4/625=0.0064

d) Power loss: H=(2TN)/(778x12)= (2fWrN)/778x12=H = 0.121 Btu/s =436 Btu/hrH = 126 j/s=453 KJ/hr

Problem # 12-12

e) Using Fig 12-19 with S=0.163 and l/d =1

Q/rcNl = 4.15 Q = 4.15x1.25x0.002x18.67x2.5=0.48 in3/s

Using Fig 12- 20 Qs/Q=0.61Qs = 0.29 in3/s

f) Using Fig 12-21 P/Pmax = 0.44 Pmax = 192/0.44=436 psig

g) Using Fig 12-22 Pmax = 18° & p0 = 82°

h) See part (a) Tav = 125°F

i) T2= 110+30=140 °F

Problem # 12-12

NOTE: In cases where l/d curve is not available the interpolation equation (12-15; 16)

may be used when necessary.

Sample problem on Design of HDL Journal Bearings (to be solved during help session)

• Design a journal bearing to carry a radial load of 1500 lb while the shaft rotates at 850 rpm. The shaft stress analysis determines that the minimum acceptable diameter at the journal is 2.10 in.

• The shaft is part of a machine requiring good

precision.• Power loss in the bearing should not exceed 1%

of the 15 hp driving power.

Procedures for design of oil lubricated journal bearings

• A- Full-film (Hydrodynamic) Lubrication• Step1: Often, the shaft diameter at the bearing

is determined by strength and deflection analyses. If the shaft diameter is not known Table 12-5 or Table 28-8 of the Standard Handbook of Machine Design can be utilized to get a rough estimate of the unit load P=W/ld (with W being the applied load). This value is combined with the value of l/d (ratio of bearing length to bearing diameter), determined in the next step, to find the dimensions of the bearing.


• Step2: The value of the important parameter l/d is taken between 0.25 and 1.5. Values up to 2 were used in earlier designs. Nowadays the value of l/d is confined between 0.25 and 0.75. Short bearings are preferred when shaft deflections and misalignments are expected.

• Step3: The minimum film thickness h0 can be estimated from one of these equations: )(00025.00 indh

)(0004.0005.0

)(00004.00002.0

0

0

mmdh

indh


Step4: The nominal value of clearance ratio r/c (r = bearing radius and c = clearance) can be taken approximately as:1000 for precision bearings when 25<d<150 mm500 for general machinery250 for rough machineryThe choice of the values of r/c depends on the tolerances and surface roughness of shaft and bearing. This guideline when combined with the results of steps 1 and 2 will allow you to get the nominal value of c.


• Step5: Now the bearing characteristic number (S = Sommerfeld number) can be determined from the chart of Fig. 12.164 .

• Step6: Next, the viscosity of the oil is determined using:

Where:P (unit load) = W/ld, with W being the applied load. N = speed in revolutions per second.

N

P

r

cS

2


• Step7: The outlet temperature of the oil should be kept between 200F (93C) and 250F (121C). A value of 70C (160F) is usually specified as the average operating temperature [2, 9, 18-20]. The chart of Fig 12-11 or 12-12 [3,4]) can be entered to select an oil grade. If the selected lubricant has a viscosity higher than the value computed in step 6, recalculate S and find the new h0.

• Step8: Now, find the friction coefficient from Fig. 12-17. The friction coefficient should be kept as low as possible consistent with h0 (i.e. in the optimum zone between the minimum friction line and the maximum load line in Fig. 12.14 [3,4]. As a general rule friction coefficients below 0.01 are acceptable (see Table 28-1 of the Standard Handbook of Machine Design [5]).


• Step9: Power loss due to friction can be calculated from:

•• Its value can be compared to the input power to take a

decision concerning f and h0. • Step10: Select a suitable bearing material from Table

12-5 [3,4] or from Tables 28-2 to 28-4 of the Handbook [5]. Unit load, maximum operating temperature and conditions should be used as criteria for material selection.

• Step11: Write a summary of your design results.

)(1050

hpfWrN

H

Self-Contained Bearings

Examples of Pillow-blocks withPolymer Bearings

Ring oiled bearing

Pillow-blocks or pedestal bearings are used for:•Fans,•Blowers•Pumps and small motors

Self-Contained Bearings

)(Pr42

bc

fr

J

lNc

J

TNgenH

Two general types of lubrication: 1) Oil-Ring and 2) Oil BathSince the warm lubricant stays within the bearing housing; it shouldbe designed such that the heat generated by friction is dissipated.

As seen above the heat generated (in Btu/s) by friction can be estimated:

Where J= 9336 in.lbf/Btu

The heat to be dissipated & surface temperature of housing are respectively:

)19;1712(1

)19;1712()(1

bbTT

T

aaTTA

fb

fCR

lossH

)(1050

hpinfWrN

genH

Tf is the average film temperature which is unknown and found by trial and error to satisfy Hgen=Hloss as in the following example.See also (Eq. 12-20) for Tf

Or in (hp)

See Eq. 12-18 for ħCR and Table 12-2 for

Example on self-contained bearings



ClearanceAmong the independent variables under designer’s control, clearance is the most difficult to hold accurate during manufacture and It may also increase during service because of wear.

When selecting a clearance for a JB a number of performance variables and expected in service wear should be taken into account.

Bearing Noisy+ h0 decreases

ClearanceTable 12-3: Max., Min. & Average Clearances for 1.5 in. dia. JB based on fit

Clearance

Temperature limits for mineral oils

Oils with antioxidants + O2 supply unlimited

O2 insignificant

Pressure-Fed Bearings

•At high bearing loads and high temperature: turbo machinery, car engines, ESP, ….•Lubricant is supplied at supply pressure Ps through supply hole drilled opposite to load bearing area side.


w

Unit load

2

''

2312'4'2

2/

wll

rl

W

rl

WP

Velocity Profile

)2112(4'8

22

yc

l

pu s


Example of pressure-fedGrooved bearings

Centrally located full annular groove

Circumferential groove axial pressure distribution


Use charts with l/d

)6(2

1 2 yh

Uhyyu

dxdp

'8

)2112(4'8

2

max

22

l

cpu

ycl

pu

s

s

)2212(5.11'3

23

l

rcpsQ s

2312'4'2

2/ rl

W

rl

WPrl

WP

2

Qs from Fig. 12-19; 20

Pressure-Fed lubricantNatural circulation of oil

Velocity

Side-Flow

Unit load

Use charts with l’/d

)2912(

5.11

/)10(978

)2812(5.11

/0123.0

42

26

42

2

rp

WScfrT

rp

WScfrT

s

C

s

F

Temperature rise

T from Fig. 12-23; 24

• An eight-cylinder diesel engine has a front main bearing with diameter 3.5 in. and length 2 in. The bearing has a central annular oil groove 0.250 in. wide. It is pressure-lubricated with SAE 30 oil at an inlet temperature of 180°F and at a supply pressure of 50 psi. Corresponding to a radial clearance of 0.0025 in, a speed of 2800 rev/min, and a radial load of 4600 lb, find the temperature rise and the minimum oil-film thickness.

Example on Pressure-Fed BearingsProblem 12-34; 16 (modified)

• Given: d = 3.5 in, l = 2.0 in, Ps = 50 psi, w = 0.25 in; cmin = 0.0025 in, W = 4600 lbf, SAE = 20, T1 = 180°F; N = 2800 rpm

• Required: TF, h0, Pmax, Pmax & p0

• Solution: Use Eq. 12-28 to compute TF

Problem # 12-34; 16 (modified)

avavP

N

c

r avS

410045.375160

28002700

2

psirl

WP

c

r

inwl

l

751875.075.14

4600

'4

7000025.0

75.1

875.02

'

)2812(

5.11

/0123.042

2

rp

WScfrT

s

F

1. For a first trial assume T = 30 °F 2. Tf = 180+30/2 = 195 °F 3. Find µav = 1.4 reyn (From Fig. 12-11; 12) using Tf = 195°F4. Calculate S = 0.04265. Use S = 0.0426 and l’/d = ¼ to find = 0.93 from Fig. 12-15;

16 & (r/c)f = 2.2 from Fig. 12-17; 18

6. Calculate TF

6. Recalculate Tfcal = 180+22.64/2191.3 °F

7. Compare Tfcal to Tfassum if |difference| >6 °F Recalculate, For our case

Tfassum -Tfcal = 195-191.3= 3.7 <6 °F

ACCEPT: T = 30 °F

Problem # 12-34; 16

FTF

64.22

75.15093.05.11

246000426.02.20123.042

• Using Fig 12-14; 16 with S=0.0426 and l/d =1/4 h0/c = 0.07 h0 = 0.000175 in

Trumpler’s Criteria satisfied?Trumpler’s Criteria satisfied?

1)1) hh00 0.0002+0.00004(3.5)=0.00034 in 0.0002+0.00004(3.5)=0.00034 in not not satisfied?satisfied?

2)2) TTmaxmax = T = Tss+ + T= 180+22.64=202.64 °F T= 180+22.64=202.64 °F <250<250 °F °F OKOK

3)3) PPstst = 751 psig = 751 psig <350 psi <350 psi not satisfied?not satisfied?

• Using Fig 12-20; 21 P/Pmax = 0.16 Pmax =

751/0.16=4694 psig • Using Fig 12-21; 22 Pmax = 8° & p0 = 24°

Problem # 12-34; 16

A- Loads: Typical values of unit load P

JOURNAL BEARING LOADS & MATERIALS

JOURNAL BEARING LOADS & MATERIALS

B- Materials: To minimize wear of journal bearings, Metallic Materials (Table 12-5 for Hydrodynamic Lubrication and 12-6 for Boundary Lubrication) are selected for:

1. Mechanical Properties

Conformability: to compensate for small shaft misalignments and deflections (i.e. Low E and yield: Lead base Babbit=90% Pb + 10% Cu)

Embeddability: to allow foreign particles to become embedded into the bearing which prevents scratching of shaft and sleeve (Tin base and Lead base Babbit)

High Fatigue Strength: to support the compressive cyclic loading (Trimetal, Silver, Steel base, Solid Brass…)

JOURNAL BEARING MATERIALS 2. Thermal Properties High Thermal Conductivity: to remove heat rapidly from the

bearing (Ag, Cu, Pb). Thermal Coefficient of Expansion not too different from that

of casing and shaft. 3. Metallurgical Properties Compatibility: to avoid fusing under heat and contact dissimilar

materials (Mainly not same melting point) for shaft and bearing are more compatible than similar materials.

4. Chemical Properties Corrosion Resistant: to resist corrosion by lubricant

improvement additives (Sn, Al, Ag...).

Non-Metallic Materials (Table 12-6) such as Wood, Rubber, Carbon Graphite, Derlin, Teflon, Nylon… Most have low thermal conductivity.

JOURNAL BEARING MATERIALS

Boundary (thin-film)-Lubrication • In certain applications boundary lubrication should be

designed for (see your lab manual for the procedure of boundary lubrication design).

• Boundary lubrication should be expected for slow speeds (start ups and shut downs) : U<10 ft/min (0.05 m/s)..

• In boundary lubrication the bearing performance depends essentially on boundary film.

• The coefficient of friction is reduced by using animal and vegetable oils containing fatty acids that stick to metal surfaces.

Materials for Boundary (thin-film, boundary friction, oilite, oiles and bushed pins)-Lubrication

To minimize metal-to-metal contact in boundary lubrication:•Mix animal or vegetable oils with lubricant•Use porous metallic materials (Table)•Use non-metallic materials•Use indented bearings

Table 12-8

Sample problem on Design of Boundary-Lubricated Journal Bearings

• Design a boundary lubricated plain-surface bearing to carry a radial load of 2.5 kN from a shaft rotating at 1150 rpm. The nominal minimum diameter of journal is 75 mm.

Given: Boundary lubricated JB. W=2.5 kN; n= 1150 rpm; d = 75 mm

• Solution: (see class work)

Types of Radial Journal Bearings

Radial

(Plain Bearings, sleeves)

Thrust Journal Bearing

Thrust

Journal Bearings

Types of bearings

Plain Bearings

Journal Bearings

Self-lubricated Journal Bearings

Bushes Polymer Bearings

Types of Bearings

Radial Journal Bearings for Pinion Shaft in Gear Box for GE Turbine

• Housing for Gear Box showing Radial Journal Bearing Supports

Types of Bearings

Types of Bearings

Radial Journal Bearings for Pinion Shaft in Gear Box for GE Turbine




Typical Groove Patterns


• Thrust Bearing for GE

Turbine Shaft


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Lubrication & Journal Bearings

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