NEW SIMPLE EQUATIONS FOR DESIGNING OF FINITE FULL JOURNAL BEARING

INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING AND TECHNOLOGY (IJMET) International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 6340(Print), ISSN 0976 6340 (Print) ISSN 0976 6359 (Online) Volume 6, Issue 4, April (2015), pp. 134-142 IAEME: www.iaeme.com/ijmet.asp Journal Impact Factor (2015): 8.8293 (Calculated by GISI) www.jifactor.com IJMET I A E M E NEW SIMPLE EQUATIONS FOR DESIGNING OF FINITE FULL JOURNAL BEARING Anand D. Kalani 1 Rita K.Jani 2 Sandeep Soni 3 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. 134

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 For Q 0 (flow through maximum film thickness at θ = 0) use upper signs; For Q π (flow through maximum film thickness at θ = π) use lower signs; 135

Table-2 Values of I S and I C 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 *The upper value is Is and the lower value is Ic. 6.1373 31.9219 6.6295-32.8642 6.8881-33.2602 8.7210-33.5520 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) W = radial load N, L = Length of Bearing mm, D = diameter of bearing mm. 2.) Sommerfield Number is calculated by the equation: R = Bearing Radius mm, C = Radial Clearance mm, µ = viscosity N s/mm 2, N = Speed of journal rps, P = Bearing Unit Load N/mm 2. 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. (2) 136

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) 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 0.239-1.388 137

2) Value of Is which is dependent on eccentricity ε. Governing Equation: (4) A rational cubic to cubic polynomial equation. ε = Eccentricity ratio p 1,p 2,p 3,p 4,q 1,q 2 and q 3 = 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 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 3) Value of Ic which is dependent on eccentricity ε. Governing Equation for (5) A rational cubic to cubic polynomial equation. ε = Eccentricity ratio p 1,p 2,p 3,p 4,q 1,q 2 and q 3 = Constants whose values are given in Table 5. 138

Figure -3 Curve Fit for Ic on basis of Eccentricity Table 5 Values of Constant for Equation 5 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 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 139

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/mm 2 ] vii. Density of Lubricant ρ [kg/m 3 ] 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/mm 2 ] d) Sommerfield No. S e) ttitude ngle [ ] f) Min. Oil Film Thickness h 0 [mm] g) Coefficient of Friction [f] h) Power Lost in Friction P f [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 140

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/m 3 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/m 3, 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/mm 2 1.28 N/mm 2 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 h 0 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 141

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, 2 nd 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 142