Design of Sliding Contact Bearings

Dr. Chandan SharmaDepartment of Mechanical Engineering

Engineering College Ajmer

Contents

• Basic modes of lubrication – Thick and Thin film lubrication

• Common bearing materials

• Desirable properties of a good bearing material

• Bearing design – Selection of parameters

• Properties of lubricating oils

• Bearing failures – Causes and Remedies

• Comparison of Sliding and Rolling Contact Bearings

• Design procedure of hydrodynamic bearing

Basic modes of lubrication

The objectives of lubrication are as follows:

To reduce friction

To reduce or prevent wear

To carry away heat generated due to friction

To protect the journal and bearing from corrosion

The lubricants can be :

Liquid lubricant like mineral or vegetable oils

Semi-solid lubricants like grease

Solid lubricants like graphite or Molybdenum disulphide

Basic modes of lubrication

There are two basic modes of lubrication:

Thick film lubrication

Thin film lubrication

Further thick film lubrication can be of two types:

Hydrodynamic lubrication

Hydrostatic lubrication

Hydrodynamic lubrication

Also called as self-acting

bearings

Used in bearings mounted

on engines and centrifugal

pumps

Hydrodynamic journal bearings

These bearings can be of two types:

Full journal bearing

Partial bearing

Full journal bearing versus partial bearings

The advantages of partial bearings compared to full journal bearing are as follows:

Partial bearings are simple in construction

It is easy to supply lubricating oil to Partial bearing

The frictional losses in partial bearing are less hence temperature rise is low

But

Partial bearings can take load in only one radial direction

Clearance bearings (diameter of bearing > diameter of journal)

Fitted bearings (diameter of bearing = diameter of journal)

Hydrostatic lubrication

Also called as externally pressurized

bearings

Used in vertical turbo-generators,

centrifuges and ball mills

Hydrodynamic bearings versus Hydrostatic bearings

Hydrodynamic bearings:

Simple in construction

Easy to maintain

Lower in initial as well as maintenance cost

Hydrostatic bearings:

High load carrying capacity even at low speeds

No starting friction

No rubbing action at any operating speed or load

Thin film lubrication

• Also called as boundary lubrication

• There is partial metal to metal contact

• Found in door hinges and machine tool slides

Newton’s law of viscosity

The constant of proportionality μ is called

as absolute viscosity (N-sec/m2 or MPa-sec).

Popular unit is Poise (Dyne-sec/cm2)

Viscosity in centipoise (cp) denoted by z.

h

UA or P

h

U

A

P

h

U

h

U

h

U

2

2

1

1

910

z

Petroff’s equation

It is used to determine coefficient of friction in journal bearings. It is based on following assumptions:

Shaft is concentric with the bearing

The bearing is subjected to light load

Petroff’s equation

Petroff’s equation indicates that there are two important dimensionless parameters namely (r/c) and (μns/p).

They govern the coefficient of friction and other frictional properties like frictional torque, frictional power loss and temperature rise in the bearing.

p

n

c

r)(2 f s2

Mckee’s investigation

• In region BC, there is partial metal to metal contact (thin or boundarylubrication)

• In region CD, there is relatively thick film of lubricant and hydrodynamiclubrication takes place

• Coefficient of friction is minimum at C. Bearing characteristic no. correspondingto minimum coefficient of friction is called as Bearing modulus (K)

Mckee’s investigation

• In thin film or unstable region, variations are compounding.

• In thick film or stable region, variations are self-correcting

• In order to avoid seizure, operating value of bearing characteristic numbershould be at least 5 to 6 times bearing modulus.

• If the bearing is subjected to fluctuating of impact loads, it should be 15 timesbearing modulus.

Reynold’s equation

The theory of HD lubrication is based on differential equation derived byReynolds. This equation is based on following assumptions:

• Lubricant follows Newton’s law of viscosity

• The lubricant is incompressible

• The viscosity of lubricant is constant

• It is assumed that the film is so thin that the pressure is constant across the filmthickness

• The shaft and the bearing are rigid

• There is continuous supply of lubricant

Reynold’s equation

• There is no exact analytical solution for this equation for bearings with finite

length.

• Theoretically exact solution can be obtained if the bearing is assumed to be

either infinitely long or very short

• Approximate solutions using numerical methods are available for bearings with

finite length

Raymondi and Boyd method

• Reynolds equation was solved on computers using iterative technique

• This method predicts that performance of the bearing can be expressed in termsof dimensionless parameters

c

h - 1 or

c

h 1

hc cor he c

h e r - R

hre RSince

c

e ratioty Eccentrici

r - Rc

00

00

0

0

Dimensionless parameters

Length to diameter ratio L/D

Radial clearance ratio r/c

Coefficient of friction variable (CFV) (r/c)f

Flow variable (FV) Q/rcnL

Sommerfeld number (S) (r/c)2(μns/p)

Minimum film thickness variable h0/c

Eccentricity ratio (ε) e/c

Pressure ratio pmax/p

Dimensionless performance parameters

L/D ε h0/c S φ (r/c)f Q/rcnL Qs/Q p/pmax

1.0

0.1 0.9 1.33 79.5 26.4 3.37 0.150 0.540

0.2 0.8 0.631 74.02 12.8 3.59 0.280 0.529

Desirable properties of a good bearing material

• Should not stick or weld to the journal surface in case of metal to metal contact

• Should have high compressive strength

• Should have high fatigue strength

• Should have high ‘Conformability’ (ability to adapt shape of journal)

• Should have high ‘Embeddability’ (accommodating dirt particles in oil)

• Should have high ‘Bondability’ (ability to bond with high strength steel shell)

• Should have sufficient corrosion resistance

• Should have high thermal conductivity and low thermal expansion

• Should have low coefficient of friction

• Should be of reasonable cost and easily available

Common bearing materials

• Babbits or white alloys (Sn 89.3% + Sb 8.9% + Cu 1.8%)

Tend to loose their strength quite rapidly at higher temperature

Have relatively low fatigue strength

Have excellent ‘Conformability’ and ‘Embeddability’

• Copper lead alloys (more hardness and fatigue strength, used in heavy duty applications)

• Bronzes (2nd most preferred after Babbits, excellent casting and machining properties)

• Aluminium alloys

• Silver (most costly)

• Cast Iron

• Teflon (low coefficient of friction and requires no external lubricant)

• Rubber (used in marine applications)

Bearing design – Selection of parameters

• Length to diameter ratio (L/D)

• Unit Bearing Pressure

• Start up load

• Radial clearance

• Minimum oil film thickness

• Maximum oil film temperature

Length to diameter ratio (L/D)

• Length to diameter ratio affects the performance of the bearing

• A long bearing has more load carrying capacity but are more susceptible

to metal to metal contact

• A short bearing has greater side flow

• L/D > 1 (long bearing)

• L/D < 1 (short bearing)

• L/D = 1 (square bearing)

Unit Bearing Pressure

• It is load per unit of projected area of the bearing in running condition

• It depends on bearing materials, operating temperature, nature and

frequency of load and service conditions.

• The values of unit bearing pressure based on past experience is provided

in the design data book

Start up load

• It is static load when the shaft is stationary

• Mainly consist of dead weight of shaft and its accessories

• The unit bearing pressure for the starting conditions should not exceed

2 MPa

Radial clearance (c)

• Should be small to provide the necessary velocity gradient

• This requires:

• Costly finishing operations

• Rigid mounting of the bearing assembly

• Clean lubricating oil without any foreign particle

• Practical value of c is 0.001 r

Material Radial clearance

Babbits 0.001 r to 0.00167 r

Copper lead 0.001 r to 0.01 r

Aluminium alloys 0.002 r to 0.0025 r

Minimum oil film thickness (h0)

• The surface finish of the journal and the bearing is governed by the

value of minimum oil film thickness selected by the designer and vice

versa.

• There is a lower limit for the minimum oil film thickness below which

metal to metal contact occurs and hydrodynamic film breaks

• The lower limit is given by

h0 = 0.0002 r

Maximum oil film temperature

• The lubricating oil tends to oxidize when operating temperature exceeds 120°C

• Also the surface of the bearing material tends to soften at 125°C

• Therefore, operating temperature should be kept within limits

• The limiting temperature is 90°C for bearings made of Babbit material

L/D ratio ho/c

(for max. load)

ho/c

(for min. friction)

1 0.53 0.30

0.5 0.43 0.12

0.25 0.27 0.03

Properties of lubricating oils

• Can be mineral oil or vegetable oil

• Should be available in wide range of viscosities

• Should have little change in viscosity with temperature

• Should be chemically stable

• Should have sufficient specific heat to carry away frictional heat

• Should be commercially available at reasonable cost

Bearing failures – Causes and Remedies

• Abrasive failure

• It is scratches in the direction of motion often

with embedded particles

• Occurs when lubricated oil is contaminated

with dust, rust or foreign particles

• Proper enclosure, cleanliness of housing

and use of high viscosity oil can prevent abrasive

failure

Bearing failures – Causes and Remedies

• Wiping of bearing surface

• Excessive rubbing of journal results in melting in surface of the bearing

• This occurs in the form of surface melting and flowing of bearing material

• Causes are inadequate clearance, excessive load and insufficient oil supply

• Remedy is to keep these factors under control

Bearing failures – Causes and Remedies

• Corrosive failure

• Caused by chemical attacks of reactive agents present in the lubricating oil

• Oxidation products corrode materials such as lead, copper, cadmium and Zinc

• Causes are inadequate clearance, excessive load and insufficient oil supply

• Remedy is to keep these factors under control

Bearing failures – Causes and Remedies

• Distortion failure

• Caused by misalignment and improper fit

• When fit is too tight, bore distortion occurs

• When foreign particles are trapped between the bearing and the housing during

the assembly, local bore distortion occurs

• The failure can be avoided by correct selection of fit and adopting proper assembly

procedure

Comparison of Sliding and Rolling Contact Bearings

Comparison of Sliding and Rolling Contact Bearings

Criteria Hydrodynamic Bearing Rolling element bearing

High Load bearing capacity √

Low starting torque √

Frequent start √

Low cost √

Low noise √

Low maintenance √

Less space √

Design procedure of Hydrodynamic Bearings

a. Choose appropriate value of L/D for the given application

b. Check bearing pressure for the chosen value of L/D

c. For the bearing material choose appropriate value of c/r

d. Choose h0/c for either maximum load or minimum friction

e. For this value of h0/c, find Sommerfeld no. from either tables or charts

f. From Sommerfeld no., calculate viscosity and select appropriate lubricating oil and its operating temperature (should be between 40 - 80°C)

g. For this Sommerfeld no., find CFV and FV and estimate friction coefficient and other parameters

h. Calculate Hg = f.W.v and Hd = mcp∆t

i. List all the selected and/or calculated parameters

Design procedure of Hydrodynamic Bearings

a. Choose appropriate value of L/D for the given application

b. Check bearing pressure for the chosen value of L/D

Design procedure of Hydrodynamic Bearings

c. For the bearing material choose appropriate value of c/r

Design procedure of Hydrodynamic Bearings

d. Choose h0/c for either maximum load or minimum friction

Design procedure of Hydrodynamic Bearings

e . For this value of h0/c, find Sommerfeld no. from either tables or charts

L/D ε h0/c S φ (r/c)f Q/rcnL Qs/Q p/pmax

1.0

0.1 0.9 1.33 79.5 26.4 3.37 0.150 0.540

0.2 0.8 0.631 74.02 12.8 3.59 0.280 0.529

Design procedure of Hydrodynamic Bearings

e . For this value of h0/c, find Sommerfeld no. from either tables or charts

Design procedure of Hydrodynamic Bearings

• Sommerfeld Number:

Where S = Sommerfeld number

μ = viscosity of lubricant (MPa-sec or N-sec/m2)

ns = journal speed (rev/sec)

p = unit bearing pressure (MPa)

p

n

c

r S s

2

Design procedure of Hydrodynamic Bearings

f. From Sommerfeld no., calculate viscosity and select appropriate lubricating oil and its operating temperature (should be between 40 - 80°C)

Design procedure of Hydrodynamic Bearings

g. For this Sommerfeld no., find Coefficient of friction variable (CFV) and Flow variable (FV) and estimate friction coefficient and other parameters

h. Calculate Hg = f.W.v and Hd = m.cp.∆t

i. List all the selected and/or calculated parameters

f c

r CFV

lrcn

Q FV

s

Thanks for your kind attention