Design of Bearing

Disc Wr
ω Bearing
Wa
Shaft

Support

Rolling Element Bearings

Many machine elements that are fluid film-lubricated have surfaces that do
not conform to each other well. The full burden of the load must then be
carried by the small lubricant area. Some example of nonconformal surfaces
are mating gear teeth, cams and followers, and rolling-element bearings.

Hydrodynamic Bearings (Journal Bearings)

Conformal surfaces fit snugly into each other with a high degree of
geometrical conformity, so that the load is carried over a relatively large
area. Fluid film journal bearings and slider bearings have conformal
surfaces.
24 September 2022 Design of Machine Elements 1
 Design of Bearing

Rolling Element Bearings Journal bearing

Magnetic bearing

24 September 2022 Design of Machine Elements 2

 Design of Bearing

24 September 2022 Design of Machine Elements 3

 Rolling Element Bearings

24 September 2022 Design of Machine Elements 4

 Rolling Element Bearings
Classification of rolling element bearings :
Based on geometry (type of rolling element):

Ball bearing Roller bearing Needle bearing

Based on loading:

Radial Thrust Combined radial and thrust

24 September 2022 Design of Machine Elements 5
 General Classification of rolling
element bearings :

Rolling Element Bearing Manufacturers

Check their websites for more

information !!!

24 September 2022 Design of Machine Elements 6

 Rolling Element Bearings
Deep groove Ball Bearing Angular contact Ball Bearing

24 September 2022 Design of Machine Elements 7

 Rolling Element Bearings
Cylindrical Roller Bearing Tapered Roller Bearing Spherical Roller Bearing

Large capacity Long endurance for heavy loads

Long-life requirements Long endurance for shock forces
Unless rollers are contoured, they can support load in only one direction (radial or thrust)
Most roller bearings support, both radial and thrust loads
If contact angle is less than 450, bearing has larger radial load capacity
24 September 2022 Design of Machine Elements 8
 Rolling Element Bearings
Thrust ball bearing Thrust Roller bearing

24 September 2022 Design of Machine Elements 9

 Rolling Element Bearings

Compensate for certain degree

of misalignment
Very limited axial load capacity,
only radial load

24 September 2022 Design of Machine Elements 10

 Rolling Element Bearings
Miniature bearings
Linear motion bearings

Precise linear motion

Used as liner actuators / sensors
Very low friction compared to
conventional screw arrangements
Both radial and axial load
capacity

24 September 2022 Design of Machine Elements 11

 Rolling Element Bearings

Radial Deep Groove Ball Bearing Angular Contact Ball Bearing Thrust Ball Bearing

Radial Deep Groove Ball Bearing Angular Contact Ball Bearing Cylindrical Roller Bearing
Filling Slot Filling Slot

Needle Roller Bearing with Self – Aligning Ball Bearing Tapered Roller Bearing
Hardened Raceways

Needle Roller Bearing Drawn Cup Thrust Needle Roller Bearing Self – Aligning Roller Bearing

Radial Deep Groove

Thrust Spherical
Thrust Roller Bearing Thrust Tapered Roller Bearing Ball Bearing
Roller Bearing
24 September 2022 Design of Machine Elements External Alignment 12
 Rolling Element Bearings
single-row deep groove ball bearing, light weight, with bore diameter 17mm, double shielded,

Bearing Nomenclature: Part number 6203ZZ

Type Code Series Bore Suffix

1 - Self-aligning ball bearing 7 - Not sure ** x 5 = bore Z - Single shielded

2 - Wide self-aligning ball bearing 8 - Extra thin section diameter ZZ - Double shielded
22 - Self-aligning roller bearing 9 - Very thin section RS - Single sealed
23 - Wide self-aligning roller bearing 0 - Extra light 09 - 45mm 2RS - Double sealed
3 - Double-row angular contact ball 1 - Extra light thrust 11 - 55mm V - Single non-contact seal
bearing 2 - Light VV - Double non-contact seal
4 - Double-row ball bearing 3 - Medium except DDU - Double contact seals
5 - Thrust ball bearing 4 - Heavy NR - Snap ring and groove
6 - Single-row deep groove ball bearing 00 - 10mm M - Brass cage
16 - Thin section single-row deep groove 01 - 12mm
ball bearing 02 - 15mm
7 - Single-row angular contact bearing 03 - 17mm

R - Inch (non-metric) bearing

24 September 2022 Design of Machine Elements 13

 Fluid Film Bearings: Hydrodynamic bearings

Full (3600) journal bearings are widely used bearings in industrial machinery. These bearings
can take up rotating radial load. As high speed is essential to generate fluid film self-action,
hydrodynamic bearings have found applications mostly in high speed machinery such as
turbines, turbogenerators, turbopumps etc.
24 September 2022 Design of Machine Elements 14
 Fluid Film Bearings: Hydrostatic bearings
Hydrostatic bearing is used to provide full film lubrication when the speed of the mating
surfaces is not large enough to create hydrodynamic lubrication. The load supporting film is
maintained by an external source. Hence these bearings are also called externally pressurized
bearings, can meet some extreme requirements, such as

24 September 2022 Design of Machine Elements 15

 Fluid Film Bearings: Hybrid fluid film bearings

Hydrodynamic thrust and

journal bearing

Externally pressurized multi-recess

journal bearings system

24 September 2022 Design of Machine Elements 16

 Fluid Film Bearings
Design a fluid film bearing: Multidisciplinary in nature > Chemist
Physicists
Mathematician
Material scientist
Mechanical Engineer

Design procedure:
• Purpose and type of bearing (journal, thrust pad, etc.)
• Type of lubrication technique (hydrodynamic, hydrostatic, etc.)
• Selection of material (refer to design data book) 7.30
• Selection of lubricant (refer to supplier data book) 7.28
• Structural design
• Apply lubrication technology, stability study and design optimization
24 September 2022 Design of Machine Elements 17
 Fluid Film Bearings

Selection of material (refer to design data book) 7.30

24 September 2022 Design of Machine Elements 18

 Fluid Film Bearings
Types of lubricant: Refer design data book 7.28
(i) Mineral oils , (ii) Greases , (iii) Synthetic oils , (iv) Solid lubricants

Mineral oil or liquid petrolatum is a by-product in the distillation of petroleum to produce

gasoline. It is a chemically inert, transparent, colorless oil.
Types: (a) Paraffins , (b) Napthenes , (c) Aromatics (Unsaturated)

Greases are oils that are thickened with solids to form semi-fluid products.

Solid lubricants are used for high temperature and/or low pressure, normal lubricants are unstable.
Should have (a) thermal stability, (b) low shear strength , (c) surface protection , (d) good bonding properties
Like graphite and molybdenum disulphide

Synthetic oil is oil consisting of chemical compounds which were not originally present in crude oil (petroleum) but
were artificially made (synthesized) from other compounds. Synthetic oil could be made to be a substitute for
petroleum or specially made to be a substitute for a lubricant oil such as conventional (or mineral) motor oil refined
from petroleum. When a synthetic oil is made as a substitute for petroleum, it is generally produced because of a
shortage of petroleum or because petroleum is too expensive.

24 September 2022 Design of Machine Elements 19

 Fluid Film Bearings: Properties of Lubricant
Viscosity, density, specific heat, thermal conductivity, acidity and alkalinity, oxidation stability, flash point, foaming, pour point, demulsibility, extreme
pressure properties, etc.

Viscosity is the resistance to flow, this resistance is mainly due to internal friction and is a molecular
phenomenon.
u
Newtonian fluids: At any point in a fluid the shear stress  is direct proportional to the rate of shear
y
u
 
y

Dynamic viscosity (Absolute viscosity):   cP , Pa s


Kinematic viscosity :   cSt , m 2 /s

Density: The relative density of a substance is the density of that substance divided by the density of water
at the same temperature and pressure

Measurement of fluid viscosity: Saybolt Universal Viscosity (7.28)

 180 
Dynamic viscosity     0.22  t   cP
 t 
24 September 2022 Design of Machine Elements 20
 Fluid Film Bearings: Properties of Lubricant
Effect of temperature on viscosity: Temperature OIL

ASTM: log10 log10   0.8  n log10 T  c

Kinematic viscosity, ν
L V.I. = 0
L U Test oil
Viscosity Index: V.I.  100 (7.28)
LH U

H
H Gulf coast oils V.I. = 100
100 210
L Pennsylvania oils
Temperature (0F)

Effect of pressure on viscosity:

Pressure OIL

Barus relationship:    0 e p

24 September 2022 Design of Machine Elements 21

 Fluid Film Bearings: Lubrication Technology
Reynolds equation
Ub
  h p    h p   U a  U b   h   h 
3 3
Ua
        
x  12 x  z  12 z   2  x t Two moving surfaces

FRICTION AND LUBRICATION REGIMES

24 September 2022 22
 Fluid Film Bearings: Lubrication Technology

Shaft rotating rapidly

Shaft stationary
Shaft rotating slowly – hydrodynamic lubrication
– metal contact
– Boundary lubrication - no metal contact
- forces and centers in line
- contact point leads centerline - fluid pumped by shaft
- shaft lags bearing centerline
24 September 2022 Design of Machine Elements 23
 Fluid Film Bearings: Lubrication Technology

Diametral clerance: Cd Radial clerance: C=Cd/2

Eccentricity: e (Maximum value of eccentricity is: C)
Eccentricity ratio: ε = e/C
Film thickness as a function of angular position (  ): h  C 1  cos  
Minimum and maximum film thickness: hmin  C 1   , hmax  C 1   

24 September 2022 Design of Machine Elements 24

 Fluid Film Bearings: Lubrication Technology
Pressure distribution in finite journal bearing Refer design data book 7.36 for numerical data

W
W

Pressure distribution

0.5
Numerical solution of finite journal 0.4
0.3
360
270
bearing using FDM (MATLAB) 0.2 180
0.1 90
0

24 September 2022 Design of Machine Elements 25

 Fluid Film Bearings: Lubrication Technology
Linearized method : Under static equilibrium condition and with no external force, equation of
motion of the journal is
x  Cxx C xy   x   K xx K xy   x  0 
 M 0  
W0          

   
0 M   y  C yx C yy   y   K yx K yy   y  0 
WC 2 M r C 2 p
where W0  , M  , 
22
 R 3
L W 0 
0.6
21
20 0.575

19
0.55
18 L/D=1

17 0.525
Mass param eter

16 L/D=0.5

W h irl ratio [ ]
0.5
15
14 0.475
13
0.45
12
11 Unstable 0.425
L/D=1 L/D=0.5
10
9 0.4

8
0.375
7
Stable
6 0.35
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3
24 September 2022 Sommerfeld number Design of Machine Elements Sommerfeld number [S] 26
 Fluid Film Bearings: Lubrication Technology

Nonlinear method : Trace the path of the journal centre

90
1 90
1 90
120 60 1
0.8 120 60 120 60
0.8 0.8
MW=11 0.6
MW=12 0.6 0.6
150 30 MW=13
0.4 150 Wr=0.36 30 150 30
0.4 0.4
0.2
0.2 0.2

180 0 180 0 180 0

1 3
4

210 330 210 2 330 210 330

240 300 240 300 240 300

270 270 270

Stable Marginally Stable Unstable

24 September 2022 Design of Machine Elements 27

 Design of Journal Bearing
Data available to designer:
Radial Load : W
Speed of journal : N
Diameter of shaft (journal) : D
Equivalent rigid mass of journal per bearing : M
Operating and environmental constrains:
Medical systems :water, bio-compatible lubricant
Space application, low temperature, high pressure :solid lubricant
Electronic devices, storage devices :low leakage (cooling system)
High functional characteristics to low weight ratio :miniature bearings
Central oil circulation systems :lubricant properties available

Pertinent non-dimensional parameters:

Eccentricity ratio :  e C Clearance ratio : C R Length to diameter ratio :L D
Minimum film thickness : hmin  hmin C Friction parameter : f  R C
Flow rate : Q  2Q UCL  Mass parameter : M  MC 2 W
2 Whirl ratio :   p 
N s  R 
Sommerfeld number : S   Bearing pressure : P  W 2 LR 
P C 
24 September 2022 Design of Machine Elements 28
 Design of Journal Bearing
Design Procedure:
1. Choose a suitable bearing material (refer 7.30 design data book)
based on: Operating conditions
Bearing pressure
Sliding speed

2. Assume suitable value of L/D and find L ? (refer 7.31 design data book)
based on: Load carrying capacity
Flow rate
Journal rigidity (rigidly supported bearings), Alignment problem
Space limitations (narrow bearings suitable for aircraft engines)
There is no general rule for the best L/D ratio, usually the value is taken as 1.
Calculate bearing pressure and check with the allowable value.

3. Selection of lubricant
based on: operating conditions (temperature, pressure, etc.)
Check for the recommended viscosity range in table 7.31 of design data book
Selected the available SAE grade oil in the same viscosity range, refer 7.28, 7.29
24 September 2022 Design of Machine Elements 29
 Design of Journal Bearing
Design Procedure:
4. Assume a suitable value of C/R ratio
based on: Surface condition
Load carrying capacity
Should be between 0.0005 – 0.001

5. Assume a suitable value of hmin (refer 7.36 design data book)

based on: Surface condition
Load carrying capacity

 hmin  0.005  0.00004 D mm

6. Find all design parameters

 R
hmin S design   Q
C 
col. 4 of 7.36 col. 6 of 7.36 col.7 x col.8
Assume   1  hmin Design data Design data of 7.36, Design
data book

24 September 2022 Design of Machine Elements 30

 Design of Journal Bearing
Design Procedure:
7. Friction force: F  W

8. Get the physical properties of oil, like mechanical equivalent of heat J, density 
and specific heat s
J Kg
Refer to oil supplier, design data book 7.36 s  1710 ,   830
Kg -0 C m3

9. Calculate equivalent viscosity of oil

heat generated = heat dissipated (goes to oil)
FU
Rise in oil temperature: T 
JsQ

Equivalent oil temperature (two-thirds approximation): Te  Ti  0.8T

From temperature-viscosity graph of the selected oil find the effective viscosity,
refer 7.41 design data book

2
N s  R  W
10. Calculate Sommerfeld number S   Bearing pressure P
P C  2 LR

24 September 2022 Design of Machine Elements 31

 Design of Journal Bearing
No
Is S > Sdesign ? Redesign

Yes

Design optimization No
(supplied in class,
Redesign

or page – 759 Shigley)

Yes

No
Calculate stability threshold speed, whirl ratio, is stable ? Redesign

Find mass parameter, whirl ratio from Figure – 1, supplied in class

MW
Stability threshold speed s 
MC

Journal speed should be less than stability threshold speed

Yes
Congratulations, you successfully designed a journal bearing

24 September 2022 Design of Machine Elements 32

 Design of Journal Bearing
Minimum film thickness (hmin/C)

Eccentricity ratio (ε)

Sommerfeld number (S)
24 September 2022 Design of Machine Elements 33
 Fluid Film Bearings: Lubrication Technology
Example:
Design a journal bearing with following specifications:
Journal diameter D = 100 mm
Journal speed N = 3000 rpm
Radial load W = 20 kN
Journal mass per bearing M = 100 kg
Operating temperature T = 60 0C

24 September 2022 Design of Machine Elements 34