New equations and software is developed to simplify the calculation of designing of finite length full journal bearing based on design methodology given by Reason and Narang. The equations given here calculate the values of eccentricity, Is and Ic.

1. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 6, Issue 4, April (2015), pp. 134-142© IAEME
134
NEW SIMPLE EQUATIONS FOR DESIGNING OF
FINITE FULL JOURNAL BEARING
Anand D. Kalani1
Rita K.Jani2
Sandeep Soni3
1
Assistant Professor, Mechanical Engineering Department, GEC, Palanpur, Gujarat
2
Associate Professor, Mechanical Engineering Department, SSEC, Bhavnagar Gujarat
3
Assistant Professor, Mechanical Engineering Department, SVNIT, Surat, Gujarat
ABSTRACT
New equations and software is developed to simplify the calculation of designing of finite length full
journal bearing based on design methodology given by Reason and Narang. The equations given
here calculate the values of eccentricity, Is and Ic. The performance parametric values calculated by
the new equations are compared with the values given by calculation given by Reason and Narang
method to validate the equations and software.
Key words: Eccentricity, Full Journal Bearing, IS, IC.
1. INTRODUCTION
Always a need is generated for developing a accurate and rapid method for designing of full
journal bearing. Reason and Narang developed a simplified method for designing a finite length full
journal bearing. On the basis of experimentation the values of the eccentricity, Is and Ic were given
in tabulated for specified values. The intermediate values other than values tabulated are to be
calculated with the help of langragian mean interpolation method and on the basis of values of
eccentricity, Is and Ic calculated the other performance parameters are calculated with hand held
calculator. Software is developed to rapidly and accurately generate the values and calculate the
performance parameters of the finite length full journal bearing.
2. REASON AND NARANG METHOD
Reason and Narang have developed an approximate technique that makes use of both long
and short journal bearing theories. The method can be used accurately to design steadily loaded
journal bearings.
INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING AND
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ISSN 0976 – 6340 (Print)
ISSN 0976 – 6359 (Online)
Volume 6, Issue 4, April (2015), pp. 134-142
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2. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
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The pressure and various performance parameters that can be obtained by this combined solution
approximation are presented in Table-1. The parameters are written in terms of two quantities Is and
Ic. Accurate values of these quantities are displayed in Table-2.
Table-1 Pressure and Various Performance Parameters Obtained by Combined Solution
Approximation
Performance
Parameters
Equation
S
Where,
For Q0 (flow through maximum film thickness at θ = 0) use upper signs;
For Qπ (flow through maximum film thickness at θ = π) use lower signs;

3. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 6, Issue 4, April (2015), pp. 134-142© IAEME
136
Table-2 Values of IS and IC for Values of L/D and ε
ε L/D 0.25 0.5 0.75 1.0 1.5 2 ∞
0.1
0.0032*
-0.0004
0.0120
-0.0014
0.0244
-0.0028
0.0380
-0.0041
0.0636
-0.0063
0.0839
-0.0076
0.1570
-0.0100
0.2
0.0067
-0.0017
0.0251
-0.0062
0.0505
-0.0118
0.0783
-0.0174
0.1300
-0.0259
0.1705
-0.0312
0.3143
-0.0408
0.3
0.0109
-0.0043
0.0404
-0.0153
0.0804
-0.0289
0.1236
-0.0419
0.2023
-0.0615
0.2628
-0.0733
0.4727
-0.0946
0.4
0.0164
-0.0089
0.0597
-0.0312
0.1172
-0.0579
0.1776
-0.0825
0.2847
-0.1183
0.3649
-0.1391
0.6347
-0.1763
0.5
0.0241
-0.0174
0.0862
-0.0591
0.1656
-0.1065
0.2462
-0.1484
0.3835
-0.2065
0.4831
-0.2391
0.8061
-0.2962
0.6
0.0363
-0.0338
0.1259
-0.1105
0.2345
-0.1917
0.3306
-0.2590
0.5102
-0.3474
0.6291
-0.3949
0.9983
-0.4766
0.7
0.0582
-0.0703
0.1927
-0.2161
0.3430
-0.3549
0.4793
-0.4612
0.6878
-0.5916
0.8266
-0.6586
1.2366
-0.7717
0.8
0.1071
-0.1732
0.3264
-0.4797
0.5425
-0.7283
0.7220
-0.8987
0.9771
-0.0941
1.1380
-1.1891
1.5866
-0.3467
0.9
0.2761
-0.6644
0.7079
-1.4990
1.0499
-2.0172
1.3002
-2.3269
1.6235
-2.6461
1.8137
-2.7932
2.3083
-3.0339
0.95
0.6429
-2.1625
1.3712
-3.9787
1.8467
-4.8773
2.1632
-5.3621
2.5455
-5.8315
2.7600
-6.0396
3.2913
-6.3776
0.99
3.3140
-22.0703
4.9224
-28.5960
5.6905
-30.8608
6.1373
31.9219
6.6295
-32.8642
6.8881
-33.2602
8.7210
-33.5520
*The upper value is Is and the lower value is Ic.
2.1 CALCULATION PROCEDURE ACCORDING TO REASON AND NARANG
The initial data required for designing Journal bearing is Radial load – W, Length of Bearing
– L, L/D Ratio, RPM – N, Clearance – C, Viscosity of Lubricant – μ, Density of Lubricant – ρ,
Specific Heat - C*.
1.) Unit Load P = W/(LD) (1)
Where,
W = radial load N, L = Length of Bearing mm, D = diameter of bearing mm.
2.) Sommerfield Number is calculated by the equation:
(2)
Where,
R = Bearing Radius mm, C = Radial Clearance mm, µ = viscosity N s/mm2
,
N = Speed of journal rps, P = Bearing Unit Load N/mm2
.
3.) On the basis of Sommerfield number S the value of Eccentricity ε, Is and Ic is found from the
Table-2. The values of Is and Ic other than given in the table are found on the basis of langragian
mean interpolation method.
4.) The bearing performance is computed by evaluating various parameters on the basis of
Table-1.

4. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 6, Issue 4, April (2015), pp. 134-142© IAEME
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The values of Is, Ic are evaluated on the value of eccentricity ε and the eccentricity value is evaluated
on the basis of Sommerfield Number calculated by Eq.-2
3 NEW EQUATIONS FOR CALCULATING THE VALUES OF ECCENTRICITY, Is AND
Ic
For the ease of handling software coding system, the curve fitting formulae are generated
with the help of curve fitting tool in MATLAB with goodness of fit of 1.0 or 0.999 is selected for the
evaluation of eccentricity, Is and Ic.
1) Value of eccentricity ε which is dependent on Sommerfield No. S.
Governing equation [Exponential Equation]
(3)
Where,
ε = Eccentricity ratio, S = Sommerfield Number
a,b,c & d = Constants whose values are given in Table-3.
Figure-1 Curve fit for Sommerfield Number to Eccentricity
Table-3 Values of Constant for Eq.-3
L/D a b c d
0.25 0.3966 -1.4 0.5665 -0.1265
0.5 0.4515 -3.796 0.5204 -0.4278
0.75 0.5095 -5.817 0.4718 -0.7767
1.0 0.5719 -7.202 0.4174 -1.073
1.5 0.6819 -8.873 0.3201 -1.411
2.0 0.7714 -9.712 0.239 -1.388

5. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 6, Issue 4, April (2015), pp. 134-142© IAEME
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2) Value of Is which is dependent on eccentricity ε.
Governing Equation:
(4)
A rational cubic to cubic polynomial equation.
Where,
ε = Eccentricity ratio
p1,p2,p3,p4,q1,q2and q3 = Constants whose values are given in Table-4.
Figure 2 Curve Fit for Is on basis of Eccentricity
Table 4 Values of Constant for Equation – 4
3) Value of Ic which is dependent on eccentricity ε.
Governing Equation for
(5)
A rational cubic to cubic polynomial equation.
Where,
ε = Eccentricity ratio
p1,p2,p3,p4,q1,q2and q3 = Constants whose values are given in Table – 5.
L/D p1 p2 p3 p4 q1 q2 q3
0.25 -32.59 97.82 -54.03 11.22 -138.1 -364.1 501.5
0.5 21.94 -35.29 64.44 -2.7 -160.4 -274 437.4
0.75 -195.9 267.4 -19.9 13.77 -187.7 -268.5 460.4
1.0 -132.6 101.9 52.96 12.73 140.7 -603.5 464.5
1.5 -88.5 -39.73 160.7 6.999 79.4 -457.9 381.2
2.0 222 -3098 3365 -92.19 788.3 -4502 3744

6. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 6, Issue 4, April (2015), pp. 134-142© IAEME
139
Figure -3 Curve Fit for Ic on basis of Eccentricity
Table 5 Values of Constant for Equation – 5
4. SOFTWARE - GRAPHIC USER INTERFACE
The GUI of the software developed, based on the Reason and Narang research is as shown in
Figure – 4.
Figure 4 GUI of Software for Reason and Narang Method
L/D p1 p2 p3 p4 q1 q2 q3
0.25 -108.7 61.69 22.66 -11.61 59.47 -403.4 341.7
0.5 -916.5 957.1 -340.3 23.69 -446 -307.2 749.5
0.75 348.4 -486 169.6 -29.14 963.3 -1913 948.5
1.0 -403.4 193 -179.9 16.37 -440.7 -385.9 824.4
1.5 -1778 2714 -1309 122.1 448.3 -1522 1074
2.0 -141.6 -16.18 -362.3 46.65 -421.5 -628.3 1048

7. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 6, Issue 4, April (2015), pp. 134-142© IAEME
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The GUI is alienated in two parts
1) Input Data
2) Output Data
INPUT DATA
The input data for the Journal bearing is:
i. Radial load – W [Newton]
ii. Length of Bearing – L [mm]
iii. L/D Ratio
iv. RPM – N
v. Clearance – C [mm]
vi. Viscosity of Lubricant – μ [N s/mm2
]
vii. Density of Lubricant – ρ [kg/m3
]
viii. Specific eat – [k /kg ]
OUTPUT DATA
The output data for the journal bearing is:
 Is and Ic Values
 Performance Parameters
a) Friction Variable [f (R/C)]
b) Flow Rate Variable [Q/RCNL]
c) Side Flow to Total Flow Rate [Qs/Q]
d) Temp. Rise Variable [ ρ ΔT/P]
 Performance Variables
a) Eccentric Ratio ε
b) Diameter of bearing D [mm]
c) Pressure Load P [N/mm2
]
d) Sommerfield No. S
e) ttitude ngle [ ]
f) Min. Oil Film Thickness h0[mm]
g) Coefficient of Friction [f]
h) Power Lost in Friction Pf [kW]
i) Total Flow Rate Q [ lit./min]
j) Side Leakage Qs [ lit./min]
k) Temperature Rise ΔT [ C]
5. COMPARISON OF RESULTS
Two numerical were taken from different books and the calculated results were compared
with the values generated by the software.
5.1 NUMERICAL – 1
Calculate performance parameters of a steadily loaded full journal bearing for the following
conditions.[3]
i. Length of bearing L = 1.5 inch
ii. Diameter of bearing D = 1.5 inch
iii. Rotation of bearing N = 1800 RPM
iv. Radial load W = 500 lbf

8. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 6, Issue 4, April (2015), pp. 134-142© IAEME
141
v. Clearance ratio C = 1.5 x 10-3
vi. Viscosity of lubricant μ = 4 x 10-6
reyn
vii. Lubricant SAE 20
a. Density = 875 kg/m3
b. Specific heat = 0 /kg
The output of the software is compared with the example given in standard hanbook of machine
design.
Table -6 Comparison Table for example – 1
Parameters Calculated output of book Software output
Unit load P 222 222.222
Sommerfield No. S 0.135 0.135
Is 0.3119 0.3171
Ic -0.2391 -0.2216
Eccentricity ε 0.582 0.5774
ttitude angle 52.5 55.09
Friction Variable [f (R/C)] 3.508 3.4935
Flow Rate Variable [Q/RCNL] 4.473 4.4602
Side Flow to Total Flow Rate [Qs/Q] 0.652 0.6288
Temp. Rise Variable [ ρ ΔT/P] 14.54 14.3491
5.2 NUMERICAL– 2
The following data is given for a 0 hydrodynamic journal bearing. [29]
Radial load = 3.2kN, Journal diameter = 50mm, Bearing length = 50mm, Journal speed = 1490 rpm,
Radial clearance = 50 microns, Viscosity of lubricant = 25 cP, Density of lubricant = 860 kg/m3
,
Specific heat of lubricant = . k /kg
Table 7 Comparison Table for example – 2
Parameters Calculated output of book Software output
Unit load P 1.28 N/mm2
1.28 N/mm2
Sommerfield No. S 0.121 0.1213
Eccentricity ratio ε 0.6 0.6052
Friction Variable [f (R/C)] 3.22 3.246
Flow Rate Variable [Q/RCNL] 4.33 4.5227
Side Flow to Total Flow Rate [Qs/Q] 0.68 0.628
Minimum oil thickness h0 0.02 mm 0.019 mm
Coefficient of friction f 0.00644 0.00649
Power lost in friction Pf 0.0804 kW 0.081 kW
Total flow rate of lubricant 0.4032 lit./min 0.421 lit./min
Side leakage 0.2742 lit./min 0.264 lit./min
Temperature rise . C . C

9. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 – 6340(Print),
ISSN 0976 – 6359(Online), Volume 6, Issue 4, April (2015), pp. 134-142© IAEME
142
6. CONCLUSION
The values generated by the software on the basis of the new equations and the values given
in the book generates a similarity, this validates the new equations for calculating the eccentricity, Is,
and Ic without referring the table given by Reason and Narang. This is a new rapid and accurate
method for designing a full journal bearing.
7 REFERENCES
1. Reason, B. R. and Narang. I.P., “Rapid Design and Performance Evaluation of Steady-State
Journal Bearings – A technique menable to Programmable and alculators”, SLE
Transactions, Vol. 25, No. 4, 1982, page 429-444.
2. Orthwein, W. ., “Machine omponent Design”, West Publishing o. St. Paul, 0.
3. vrahom arnoy, “Bearing Design in Machinery: Engineering Tribology and Lubrication”,
Marcel Dekker, Inc. New York, 2003.
4. E. Shigley and .R. Mischke ,“ ournal Bearings”, in Standard andbook of Machine Design,
2nd
edition , J. McGraw-Hill, Inc., New York, 1986.
5. ason Price and Mike Gunderloy, “Mastering Visual #.Net”, Sybex, lmeda, CA, 2002.
6. Ying Bai, “Pratical Database Programming with Visual #.NET”, ohn Wiley and Sons, Inc.
New Jersey, 2010.
7. ames Foxall, “Sams Teach Yourself Microsoft Visual #.NET in 24 ours”, Sams
Publishing, USA, 2004.
8. Anand Kalani, Sandeep Soni and Rita Jani, “Expert Knowledge-Base System For Computer
Aided Design of Full Hydrodynamic Journal Bearing”, International Journal of Mechanical
Engineering & Technology (IJMET), Volume 6, Issue 8, 2015, pp. 46 - 58, ISSN Print: 0976
– 6340, ISSN Online: 0976 – 6359.
9. Kanifnath Kadam, S.S. Banwait and S.C. Laroiya, “Thermohydrodynamic Analysis of Plain
Journal Bearing with Modified Viscosity -Temperature Equation”, International Journal of
Mechanical Engineering & Technology (IJMET), Volume 5, Issue 11, 2015, pp. 31 - 43,
ISSN Print: 0976 – 6340, ISSN Online: 0976 – 6359