THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING THERMAL EFFECTS IN JOURNAL BEARINGS Elsayed Morsi Aly Afify April, 1959 IP-366

Doctoral Committee: Professor Frank L. Schwartz, Chairman Professor Jack R. Britton, University of Colorado Professor Ruel V. Churchill Professor Stuart W. Churchill Professor Arnet B. Epple Professor Rune L. Evaldson ii

ACKNOWLEDGMENTS The writer wishes to express his gratitude to Professor F. L. Schwartz, Chairman of the Doctoral Committee for his advice, guidance and encouragement. throughout this investigation. The writer also expresses his appreciation to the members of the committee, Professor R. V. Churchill, Professor S. W. Churchill, Professor A. B. Epple and Professor R. L. Evaldson for their interest and cooperation. The valuable help of Mr. W. G. Huizinga, Mr. M. W. Kaufman, and W. K. Salva during the construction of the experimental apparatus is appreciated. The patience and devotion of the writer's wife during this period is greatly appreciated. Last of all, the writer is indebted to the Industry Program of the College of Engineering for the typing and the printing of the dissertation. iii

TABLE OF CONTENTS Page ACKNOWIEDGEMENTS.................1.......*.*............. iii LIST OF TABLES............................................ vi LIST OF FIGUR ES...................vii NOMENCLATUIRE...a..**............................x I. INTRODUCTION................... 1:...i................. 1 II. THEORETICAL INVESTIGATION.......5,............... * 5 The Unloaded Bearing Solution................... 7 Boundary Conditions........................... 10 Constant Viscosity Theory................... 14 The Loaded Bearing Solution...,.................. 16 The Empirical Solution........................ 18 III. EXPERIMENTAL APPARATUS................................ 21 General Description of the Apparatus.................. 21 Driving Mechanism.......................... 21 Test Journal and Bearing.................,. 21 Oil Flow System................. 27 Loading Device...................30 Method of Estimating Film Breakdown............ 30 Heating System,....... 33 Cooling Water System......................... 33 Temperature Measurements.................... 36 IV. EXPERIMENTAL PROCEDURE................................. 42 Series A............... 42 Series B..........*..................... 42 Series C.....*................................ 42 Procedure of Tests................................... 42 Series A.................. 42 Series B.......*..*............................. 44 Series B... 44 Series C.....aeele..l.e l.a.......~....... 44 Operating Conditions.......................... 44 iv

TABLE OF CONTENTS (CONT'D) Page V. EXPERIMENTAL RESULTS........................ 46 Series A*.................... 46 Series B................................ 56 Series C.......................... 56 Data Reduction for the Heat Balance Analysis........... 56 Series A....56...................................... 6 Series B...3....... J... 63 VI. ANALYSIS AND DISCUSSION OF RESUL TS.......**...*... 76 Effect of Load on the Average Oil Film Temperature..... 76 Effect of Speed on the Average Oil Film Temperature.... 77 Effect of Speed on the Circumferential Temperature Distribution....a..................*.*..** a.aa*. 78 Effect of Load on the Circumferential Temperature Distribution.,............................. 78 Effect of Speed on Oil Flow Rate.......,...........,.. 79 Effect of Load on Oil Flow Rate......,........... 80 Effect of Speed and Load on the Heat Convected........ 80 Effect of Speed and Load on the Heat Dissipated Hc..... 81 Effect of the Average Oil Film Temperature on the Heat Dissipated Hc.................................. 81 Heat Balance...............o. J..................... 82 VII. CONCLUSIONS AND RECOMMENDATIONS...,.......,*O........ 83 Recommendati ons.............. X,......o v..o.X....oo... 84 APPENDICES: "A" - Journal and Bearing Dimensions................. 85 "B" - Properties of Gulfpride No. 30 Oil........ooO.... 86 "C" - Laminar Flow Criterion in Journal Bearings...... 90 "D" - Estimation of the Average Oil Film Temperature... 91 "E" - The Journal Frictional Heat Generation........... 93 "F" - Thermal Expansion Effect on Clearance........... 96 "G" - Determination of the Theoretical Journal Temperature.........*........................ 101 "H" - Experimental Data and Calculations............... 102 "I" - Exact Solution of Equation (2.6) for the No Heating Case1,.2....**............,....... 112 BIBLIOGRAPHY..e*................................................. 16

LIST OF TABLES Table Page T Thermal Expansion Effect on Clearance.................. 00 TI Comparison Between the Experimental and Theoretical (Journal Temperature-Bearing Temperature).............. 101 TII Temperature Data. 104-105 iV Oil Flow Data...... 106-1.07 rV Calculation of the Sommerfeld Number, the Load Number, and the Eccentricity Ratio........108-109 Vti Summary of Correlation Calculations.......... 110-111'VIt. Calculation of the Temperature Difference (TJ - TB) 115 vi

LIST OF FIGURES Figure Page 1 Lubricant Element and Co-ordinate System.............. 5 2 The Velocity Distribution.......................... 8 3 Temperature Distribution Across the Oil Film..........11 4 Comparison Between the Theoretical and Experimental (Journal Temperature-Bearing Temperature) at Different Speeds - N............. *.............. 13 5 Temperature Distribution Across the Oil Film for the External Heating Case at Different Products of Pr.E..............*.*........................ 15 6 Position of Journal Under Load........................ 16 7 General Layout of the Experimental Apparatus.......... 22 8 The Experimental Apparatus Showing the Film Breakdown Detection Instrumentation................... 23 9 The Temperature Measurement Instrumentation........... 24 10 Journal and Bearing Assembly.......................... 25 11 The Test Journal, Showing the Thermocouple Locations, the Heater, and the Self-Aligning Ball Bearings....... 26 12 The Bearing, Showing the Thermocouple Locations, Inlet and Outlet Oil Holes.................. 28 13 Schematic Sketch of the Oil Supply System and the Loading Device.......................... 29 14 Schematic Sketch of the Electric Circuit for the Estimation of the Film Breakdown.................. 31 15 Oscillographic Record for Normal Operation............ 32 16 Oscillographic Record for Metal-to-Metal Contact...... 32 17 Schematic Diagram of the Heating Circuit.............. 34 18 Schematic Diagram of the Cooling System............... 35 19 Slip-Ring and Brush Assembly......................... 37 vii

LIST OF FIGURES (CONT'D) Figure Page 20 Schematic Diagram of the Temperature Measuring CircuitO e a o a o 0 6 e a o 0 * a. e.... 0 a e o. a * o e a......... 39 21 Calibration Curve for Iron-Constantan Thermocouples...................................... 40 22 Average Oil Temperature vs. Eccentricity Ratio "n" for Different Speeds.....,.......... * * 47 23 Average Oil Temperature vso Speed'"N" for Different Eccentricity Ratios t"n.... 0 0. 0...............* 48 24 Circumferential Temperature Distribution for Different Eccentricities at 750 rpm..,.......... 49 25 Circumferential Temperature Distribution for Different Eccentricities at 000 rmp......... 50 26 Comparison Between Theoretical and Experimental Oil Flow at No-Load..................... 52 27 Oil Flow Rate vs. Calculated Eccentricity at Different Speeds.. o..,...................... 53 28 The Nondimensional Flow Number; T N vs. the Sommerfeld Number S 0 0. cP 54 29 Change in Diametrical Clearance x 104 vs. Temperature Elevation -.............................. 55 30 Average Oil Film Temperature vs. Calculated Eccentricity at Different Speeds................... 57 31 Circumferential Temperature Distribution for Different Eccentricities at 750 rpm....o..*... 58 32 Circumferential Temperature Distribution for Different Eccentricities at 1250 rpm............. 59 33 Oil Flow Rate vs. Calculated Eccentricity-n at Different Speeds-N........................... 60 34 Heat Generated Hj vs. Petroff Heat Generated.......... 61 35 Heat Dissipated Hc vs. Temperature Elevation LTT....... 62 viii

LIST OF FIGURES (CONT' D) Figure Page 36 Heat Convected by Oil vs. Calculated Eccentricity at Different Speeds....................... 64 37 Nondimensional Heat Convection Ratio HO/Hp vs. Load Number 1/S.................................... 65 38 Nondimensional Heat Convection Ho/Hp vs. Load Number 1/S.......,...o.................... 66 39 Heat Dissipated Ho vs. Load Number 1/S............. 67 40 The Heat Dissipation Ratio Hc/Hp vs. Load Number 1/S............................................ 68 41 Heat Balance Sheet....................,.............. 69 42 Heat Convected by Oil Flow vs. Calculated Eccentricity at Different Speeds..................... 71 43 Heat Convection Ratio Ho/Hp vs. Load Number 1/S....... 72 44 Heat Dissipated Hc vs.. Load Number 1/S................ 73 45 The Ratio Hc/Hp vs. the Load Number 1/S..........o...o 74 46 Heat Balance Sheet............................. 0 75 47 Variation of Specific Heat with Temperature for Gulfpride No. 30 Oil......o*a. oa............... 87 48 Variation of Specific Gravity with Temperature for Gulfpride No. 30 Oil............................ 88 49 Variation of Kinematic Viscosity with Temperature for Gulfpride No. 30 Oil........a.................... 89 50 Forces Tending to Cause Rotation of the Oil Film in a Full Journal Bearing................. 93 51 Bearing Construction.......................... 96 52 Bearing Thermocouple Positions.o..................... 102 53 Eccentricity Ratio vs. Load Number 1/S,.............. 103 ix

NOMENCLATURE BTU a Empirical constant. hr(BF)mftU c Radial clearance. inches cd Diametral clearance. inches BTU Ch Average specific heat of oil. lb OF d Nominal diameter of the bearing. inches e Eccentricity. inches F Frictional force. lbs h Oil film thickness. inches Hc Rate of heat dissipation through the bearing. BTU/hr He Rate of heat addition by the heater. BTU/hr Hj Rate of heat generation. BTU/hr Ho Rate of heat carried away by the oil. BTU/hr EHp Rate of heat generation at no-load. BTU/hr Hw Rate of heat carried away by the cooling water. BTU/hr J The mechanical equivalent of heat = 778. ft lb/BTU fBTU k Average coefficient of thermal conductivity of oil. hr hr ft ~F i Bearing length. inches L Nondimensional bearing length = i/c. m Empirical constant. MJ Journal friction torque. n Eccentricity ratio. N Speed of rotation. rpm N' Speed of rotation. rps p Unit pressure on projected area psi

NOMENCLATURE (CONT' D) qI Oil flow rate. in3/hr Q Oil flow rate. in3/hr r Bearing radius. inches R Nondimensional radius E r/c. S Sommerfeld number = CN'/p (d/cd)2. 1/S Load Number. T Temperature at any point in the oil film. ~F Ta Average oil film temperature. ~F TB Temperature of the oil film at bearing inner surface. ~F Tj Temperature of the oil film at journal surface. ~F T1 Oil inlet temperature. ~F T2 Oil outlet temperature. ~F Average oil film temperature - ambient temperature. ~F u Linear velocity at any point in the x-direction. in/sec v Linear velocity at any point in the y-direction. in/sec V Linear velocity at the journal surface. in/sec w Linear velocity at any point in the z-direction. in/sec W Load. lbs p. Oil viscosity. Reyns. 1gB Oil viscosity at the bearing at the bearing temperature. Reyns. 10o Oil viscosity at an arbitrary constant temperature. Reyns. ea Angle. degrees Viscosity exponent index. 1/OF f' Nondimensional index = P(TJ-TB). Attitude Angle degrees xi

NOMENC LATTRE (C ONT D) T Shear stress. psi p Average density of the oil. lb/ft3 v Kinematic viscosity. in2/sec E Nondimensional temperature = T - TB Tj - TB xii

I. INTRODUCTION To determine the temperature at which a bearing will run, the removal of frictional heat has to be studied first. The question of the removal of heat from journal bearings has been the subject of experimental and analytical investigations. Two approaches have been used in analyzing the problem. One approach considers that the heat generated in the oil film is removed only be conduction. The other approach treats the problem from the point of adiabtic flow, that is, all the heat generated by friction remains in the oil, raising its temperature and is carried away by convection. In practice, the heat generated is by no means confined within the clearance space, neither is it entirely carried away by the oil. It is partly carried away in the film itself and partly by conduction, at first from the interior of the film to the inner bearing surface and then through the bearing to the atmosphere. The present investigation explored some of the aspects not discussed by most of the previous investigators. Both the heat conducted through the bearing and that convected by the oil flow were considered in the study of the effect of speed, load and external heating on the average oil film temperature, oil flow and correspondingly the heat balance of journal bearings. Most of the early investigators based their work on the assumption that the heat generated by the internal viscous shear stresses was entirely dissipated from the bearing by conduction; and the oil flow through the bearing played no part.

-2In 1903, Lasche(ll) represented the first detailed investigation of thermal effects in bearings. He measured the friction loss in bearings running at peripheral speeds up to 80 fps, and considered the heat dissipation characteristics of the bearing. He found out that the heat dissipation was proportional to the 1.3 power of the temperature difference between the bearing and the surroundings. Muskat and Morgan(l2) carried out tests at low peripheral speeds up to 10 fps on a lightly loaded bearing to determine the correlation between the qlassical petroff formula for heat generation in journal bearings and their experimental results. This was accomplished by measuring the bearing friction torque, and comparing the results with those calculated using the Petroff formula. The close correspondence of their results and the theory is noteworthy. They included in their work the effect of speed on the transient temperature of the bearing and the heat balance. Hagg(10) conducted an analytical and experimental investigation on the heat conduction effects in concentric bearings. He derived an equation for the temperature distribution across the oil film in terms of velocity and viscosity variations. McKee(13), working on his four bearing friction machine, proposed an empirical method to determine the safe operating load for journal bearings taking into consideration the maximum allowable bearing temperature and the minimum Hersey number (XN'/p). However, in 1941 Christopherson(5) extended the hydrodynamic theory of lubrication to include thermal effects using the method of relaxation. His solution was obtained under two restricted assumptions:

-31. The heat generated by friction remained in the oil for film and no heat was lost to the surroundings. 2. The temperature distribution across the oil film was constant. Pinkus and Sternlicht(18), using the same assumptions, derived mathematically an expression for the circumferential temperature distribution in journal bearings based on the Sommerfeld infinitely wide journal bearing theory. Analogous investigation was made by Purvis, Meyer, and Benton(l9) using the narrow bearing approximation theory which was suggested by Michell(l4) and developed by Ocvirk and DuBois.(l7) Clayton and Wilkie(6) carried out tests with speeds up to 35 fps to measure the temperature distribution in Journal bearings. Their work was largely of an exploratory nature. Boyd and Robertson(3) were the first to consider both the heat conducted through the bearing and that convected by oil flow in their analysis. Their work was restricted to the study of the effect of speed and oil inlet pressure on lightly loaded Journal bearings. Cameron(4) carried out a preliminary investigation on Journal bearings with oil pockets to determine the equilibrium temperature of the bearing, considering the overall heat balance. He found out that more detailed investigation had to be made on the heat conduction part and also on the effect of oil pocketing in deciding the partition of the amount of heat between convection and conduction. For this investigation, a simple journal bearing was constructed with means to measure the journal and bearing temperatures as well as the

-4oil flow rate. A slip-ring and brush arrangement was used in the measurement of the journal temperature. Devices for loading the bearing and varying the speed of rotation were provided. A method of detecting metalto-metal contact between the journal and the bearing was used. As a result of this investigation, a better understanding of the effect of load, speed, and external heating on the heat dissipation through the bearing and that convected by the oil flow was achieved. The hydrodynamic effect on the average oil film temperature was also established. A mathematical treatment of the unloaded bearing was derived, while experimental correlations from the test results were obtained to calculate the heat convected by the oil flow, the heat conducted through the bearing, and the oil flow rate. A method, for estimating the average temperature of the bearing, was also presented.

II. THEORETICAL INVESTIGATION The fundamental starting point for the analysis will be the general energy equation for an element of lubricant(7) Developed Touvno-I SurRa.ce Y I __________ Developecd Brevin Surocte, x Figure 1. Lubricant Element and Co-ordinate System. -5

-6between the boundaries shown in Figure 1, namely, aT 6T aT _(k T + kT k 6T pChU - + Pchv - + pchW) + (k )) + - (k ax by aZ ax ax by by az az + ~ ~... (2.1) where - is the dissipation function. 6U 2 + v 2 + w 2 + v 6u 2 6w 6v2 D 2[( 6 + z)+ ( x + (T + ) + () + 2 ax y a~Z ax by by az +a + -2 2(a av + 2~ The first group of terms in Equation (2.1) represents the rate of change of internal energy; the second the rate at which heat is conducted away; and the third the rate at which energy is being dissipated through the action of viscosity. The following assumptions are introduced in order to simplify the mathematical analysis: 1. The change of the coefficient of thermal conductivity with temperature of ordinary lubricants is small and will be considered negligible. 2. The flow is considered laminar in view of the small dimensions of the clearance and the high viscosity of the oil. In Appendix C a numerical analysis for the validity of this assumption is given in detail. 3. The lubricant is Newtonian, that is, the shear stress is proportional to the rate of shear. 4. The change of the density of the oil with temperature is neglected. The specific gravity of the oil used changes

-7very little with temperature, as can be seen from the properties of the oil given in Appendix B. 5. The heat conducted in the x and z directions can be neglected with respect to the heat conducted in the y direction. 6. The velocity v in the y direction can be neglected when compared to the velocity u in the x direction. 7. The velocity gradients across the film are much more important than velocity gradients parallel to it. That is, it is assumed that 6u >> _u by ax When the above assumptions have been applied to the fundamental Equation (2.1), one gets: aT 6T a2T au 2 6w 2 pchu-+ p-hw k - + [ Y) + (y) 1 (2.2) Pchwyax a v y ay There are two desired solutions for the above equation. These are: 1. The unloaded bearing solution. 2. The loaded bearing solution. The Unloaded Bearing Solution When the bearing is not loaded, the journal will run concentrically with respect to the bearing. The following assumptions will be made in connection with this case: 1. The oil film is so thin that the curvature of the bearing surface may be ignored, that is, the distinction between

-8the polar and rectangular coordinates can be neglected and the problem can be considered as equivalent to that of the flow between parallel plates. 2. The viscosity of the oil is dependent on its temperature. It is sufficiently accurate for our purpose to use Reynolds empirical formula: 1 = t1oe-T (2.3) 3. As the parabolic velocity distribution, due to the pressure gradient, is small compared to the velocity distribution due to the journal motion, the flow of the lubricant in the clearance space will be considered as a Couette flow, that is, the velocity distribution will be linear. The velocity distribution will be expressed as follows: u =U (2.4) Journal y = h, u = U T / Bearing y = O, u = 0 Figure 2. The Velocity Distribution. 4. The oil supply pressure adopted for the experimental investigation is low. This will justify the negligence of the velocity w in the z direction.

5. The temperature gradient aT/6x will be neglected for the following reasons: a. The journal runs concentrically in the bearing and the problem can be considered symmetrical. b. As the thermal coefficient of conductivity of the bearing material is high, thermal recirculation in the bearing will tend to smooth out the small variations in the oil film temperature. When the above assumptions have been applied to Equation (2,2), it becomes d2T -PT u2 k y -2 oe h2 (2.5) To represent Equation (2.5) in a dimensionless form let: T - TB e - Tj - TB i' = (TJ - TB) Y = Y h Prandtl Number = Pr. = h B k Eckert Number = E. - iT2 ch(TJ TB) Substituting the above values in Equation (2.5) gives: d2e = - Pr.Eoe -eI dY2 or'e d 2 ep' = -Pr.E. (2.6) This is a nonlinear second order differential equation, To linearize the above equation, the following substitution is introduced.(9)

-10= e - 1 0 dm =,( eP' de (2.7) The last term in the above equation can be neglected compared to the second by the order of magnitude analysis. The above equation, then be.. o.me s d2 PI d2a Substituting in Equation (2.6) gives: d - PI Pr.E (2.8) dY Integrating Equation. (2,8) with respect to Y twice one gets: D - P2' Pr.E Y Y + c1 (2.9) Int order to eval.uate the constants of integration co and cl, the boundary conditions have to be specified. Boundary Condit i.on.s Two cases will be considered in the choice of the boundary condition.s i a. The no heating case, b. The external heating case. d=d The No Heating waseuaIthio case th s e boundary conditions can be described as fol lows o

-111.0 0.8 w 0.6 0.4 0 a0 I 0.20 0 0.2 0.4 0.6 0.8 1.0 DIMENSIONLESS TEMPERATURE, 9 Figure 3. Temperature Distribution Across the Oil Film.

-12The first boundary condition is based on assumption number (5) in the analysis. The second boundary condition is established from the consideration that, as the steady condition is reached, the journal can be regarded as virtually insulated since the rate of loss of heat from the journal is relatively very small. Solution of the No Heating Case.-Applying the first boundary condition to Equation (2.9) gives: C1 = 0 Applying the second boundary condition gives: Co = I' Pr.E. =, Pr.~E. y2 + I' Pr.E.Y. 2 But 8 = n(O + 1) pt2 8 = I n [P' Pr.E.(Y-. -) + 1] (2.12) This is the temperature distribution across the oil film, expressing the temperature as a function of the film thickness. Figure 3 gives the form the temperature distribution across the oil film will take, according to Equation (2.12). In Appendix I an exact solution for Equation (2.6) is carried out and an evaluation of the experimental results shown in Figure 4 and the theoretical result is given. The External Heating Case. —In this case the boundary conditions can be expressed as follows: 1. at Y = 0 e = O 0 c = 0 O (2.10) 2. at Y =1, =1, =e - 1 (2.13)

-137 6 5 THEORETICAL -3 T EXPERIMENTAL 2 Bearing Temp HEORETICAL -, I 0 250 500 750 1000 1250 1500 SPEED N Figure 4. Comparison Between the Theoretical and Experimental (Journal TemperatureBearing Temperature) at Different Speeds - N.

-14Applying the above boundary conditions to Equation (2.9) gives: C1 = 0 Co = (I' Pr.E. + en' -1) 2 substituting the values of the constants in Equation (2.9) one gets: =' Pr.E. y2 + (I' Pr.E. + e:' - 1) Y 2 2 But = 1!n (O + 1) AB'~~~~~~ ~(2.14) n [1- Pr.E. Y2 + (_ Pr.E. + e:' 1)Y] P' 2 2 This is the temperature distribution across the film for the external heating case which is presented in Figure 5 for different values of E.Pr. Constant Viscosity Theory If the viscosity of the oil is not appreciably affected by the temperature differences within the film, the following simplified equations for the temperature distribution across the film for both cases can be written as follows: a. The no heating case: 2 B = Pr.E. (Y - 2 (2.15) b. The external heating case: = Y + Pr E. (y_y2) (2.16) 2 The above equations are derived using the same analysis as above except for the variable viscosity assumption. It is worthy of mention that the temperature distribution for the external heating case, Equation (2.16), consists of a linear term which

1.0 >-.8 K. E-22.6Z Cn Pr. Eft 2.91 C, Co w z Pr. Ez- 3.31 C.).6 -J 4 Pr. E=3.31 z _IJ <i O.4 z w z 0 O~ z~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 0 2 4 6 *8 [0 1-2 1.4 NONDIMENSIONAL TEMPERATURE- e Figure 5. Temperature Distribution Across the Oil Film for the External Heating Case at Different Products of Pfr.E.

-16is the same as in the case of mere conduction with no frictional. heat generation. Superimposed on this is a parabolic distribution, represented by the last term in the equation, which is due to the heat generation by friction. The Loaded Bearing Solution In this case, the journal will run eccentrically with respect to the bearing as shown in Figure 6. The simplified general energy Oil InletBearing Journal 6 Figure 6. Position of Journal. Under Load. Equation (2t2) will describe to a good approximation. the he at effects in the lubricating film. For mathematical simplicity, the following assumptions are made: 1. The velocity distribution across the oil film is linear, that is u U Y (24,I 2. As the velocity u in the x-directil.on is greater than the velocity w in the z-direction, the term (aw/6y) can be neglected with respect to the term (au/ay)2

Substituting for the value of w, h, and dx by: w = 2 y(y-h) 6 h = C(l+n cos Ca) dx = r d a in Equation (2.2) one gets: U y T + p c y[y-(l+n cos a)] ap/ z aT _ 2T Ch (l+n cos a)r aaP 2 az U2 (2.17) + C1 cd(1+n cos 0)2. assuming a linear pressure gradient in the z-direction and dividing the above equation by PChU/c on gets: y _ + cyfy-c(l+n cos a)]p aT = kc a2T r(l+n cos a) 2a 2kt U Y 6z PChU + U (2.18) + chc(l+n cos) (.18) At this point, it is convenient to introduce dimensionless variables. Let =T - TB z= Z TJ - TB c Y Y c r R = c c = 1B e-e c also let R _ pUc G pc - B G=BU U2 ch(TJT - T B)

-18-.ch'B Pr - pe = Dk Ch U c Substitution in Equation (3.18) gives: Y ao Y[Y - (l+n cos a)] e 1 2a~ E e-5'$ R(+n- + G ---- + R(l+n co s a) a 25 L e-P'$ 6Z Pe ay2 Re(l+n cos a)2 multiplying the above equation by elf' yields: e'tO Y __ Y e2e'O[Y- (l+n cos a)] G 6 R(l+n cos a) ~a 2 L az eB't b2~ E 6y2 8 a 8 E(2.19) Pe ay2 Re(l+n cos a)2 After trying a few practical relationships, the writer was unsuccessful in proceeding with the solution. The reason for this difficulty is that Equation (2.19) is a non-linear non-homogeneous differential equation, added to that the difficulty in expressing the boundary conditions for the problem. For the above reasons, an empirical method is adopted for this case. The Empirical Solution The heat generated due to the viscous resistance of the lubricant film to the rotation of the shaft is carried away, after thermal equilibrium has been reached, partly in the oil film itself to the outlet end of the bearing, and partly by conduction, at first from the oil film to the bearing and then through the bearing to the atmosphere. The heat balance can be expressed by: H = Hc + Ho (2.20)

-19where H is the rate of heat generation in the film, Hc is the rate of heat dissipation through the bearing and surroundings and Ho is the rate at which heat is carried away by the oil flow. From Appendix E the rate of heat generation is given by: H 300 8 r3r3, N2 + (W e sin Y) 2N'] (2.21) LJ c (1-n2)2 2J j The rate of heat dissipation Hc can be described by a power of the temperature elevation of the oil film over the ambient, Hc = a(2Arj) (AT)m (2.22) where a and m are empirical constants, depending upon the type of housing and surroundings. The rate at which heat is carried away by the oil flow can be written as: Ho = pqch(T2 - T1) (2.23) Substituting Equations (2.21), (2.22), and (2.23) in Equation (2.20) yields: 300 8 lr3 l/N'2 + (W e sin y) 2xN'j a(2Tr) ()m (1-n2)1/2 2J (2.24) + Pqch(T2 - T1) This is the general heat balance equation for the loaded bearing. The numerical values for the empirical constants a and m will be determined experimentally.

-20For the external heating case the heat balance equation can be written as: 8 3r35 4N' + (W e sin 7) 2nN,] = a' (2rr)(T)m' He + 300 [J c (1-n2)l/ + 2 J + pqc (T2 - T1) (2.25) where He is the external heat applied. For the unloaded bearing, the heat balance equation can be obtained from Equation (2.24) and (2.25) when substituting zero for the value of e. For Qthe no heating case: 2400 O3r3 hN2 = a(2rre)(AT)m + pqch(T2 - T1) (2.26) J c For the external heating case: He + -2400 =r3r 2 = a(21trre)(AT)m + pqCh(T2 - T1) (2.27) J c

III. EXPERIMENTAL APPARATUS General Description of the Apparatus The test apparatus consisted mainly of the equipment shown in Figures 7 through 9. The heart of the apparatus is the test journal and bearing as indicated in Figure 10. Figure 13 illustrates diagrammatically the loading device and the means for collecting the oil flowing through the test bearing. The temperature measuring circuit is shown in Figure 20. The slip-ring and brush assembly used in the measurement of the journal surface temperature is sketched in Figure 19. In addition, Figure 14 illustrates the equipment used in detecting film breakdown. In the following paragraphs, the details of the various systems are described. Driving Mechanism The journal was driven by a 3/4 horsepower variable speed hydraulic transmission unit which was connected to a one horsepower, 1725 rpm, three phase electric motor. The motor and the speed reducer were mounted on a separate frame to prevent the vibration from being transmitted to the test bearing unit. The frame can be raised or lowered for leveling purposes by means of four screws located at the corners. Test Journal and Bearing The test journal and bearing are shown in Figure 10. The journal was made of number 4615 steel. A hole one inch in diameter was -21

-22 - Chle l 4, 1 0 t00"'itl':jt:0'; Figure 7. General Layout of the Experimental Apparatus.

-23-,Martinique!~~~~~~~~~~~~~~~~i Ao"~ Nt:...........t 0 0 f t iS. — H: ~ ~ ii:..:iii ia~:~.-! Figure 8. The Experimental Apparatus Showing the Film Breakdown Detection Instrumentation.

-24-!:: Fja if Figure 9.The Temperature Measurement Instrumentation.

COOLING WATER JACKET WATER LOADING ARM OUTLET LOADING ARM SELF ALIGNING BALL BEARING SELF ALIGNING BALL BEARING JOURNAL EXTENSION'k-l THERMOCOUPLE THERMOCOUPLE THERMOCOUPLE OIL OUTLET | Et/////';OIL OUTLET OIL RESERVOIR INLET TSURFACE PLATE TO WEIGHING TANK FTO WEIGHING TANK Figure 10. Journal and Bearing Assembly.

CARTRIDGE HEATER I " JOURNAL SELF ALIGNING -2 4 I4 BALL BEARING THERMOCOUPLE r LEADS - ) r I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~R JOURNAL EXTENSION SLF ALIGNING I5 BALL BEARING FIBER GLASS INSULATING RING THER MOCOUPLE Figure 11. The Test Journal, Showing the Thermocouple Locations, the Heater, and the Self-Aligning Ball Bearings.

-27bored centrally to provide for a 500 watt cartridge type electric heater to fit snugly, so that metal-to-metal contact is insured over the whole surface of the unit. Four iron-constantan thermocouples were silver soldered to the journal surface, as shown in Figure 11, to measure the temperature at the surface. In order to reduce the heat conduction in the axial direction, two fiber glass insulating rings of 1/4 inch thickness were placed between the journal and the journal extension at each end of the journal. After assembly, the journal was ground in a centerless grinder to the required dimensions. The exact dimensions of the bearing and the journal, and the constructional details are given in Appendix A. The bearing, shown in Figure 12, was made of Bunting Bronze because of its adequate lubricating properties. Thermocouples were silver soldered to 12, 1/4 inch diameter, fine thread plugs, which were made of the same material as the bearing. The plugs were then screwed and secured in place in the bearing, such that the final boring would just clear the thermocouple beads. At both ends of the bearing a groove was made for collecting the oil flowing outwards. A hole at the bottom of each groove was drilled to allow the oil to be collected in a pan. The bearing was supported at both ends and provision was made for cooling the bearing as shown in Figure 10. Oil Flow System As shown in Figure 13, a storage tank of 30 gallons capacity was used to feed the oil to the bearing.

THERMOCOUPLE THERMOCOUPLE H S: oou e POSITION OIL ONLET HOLE 4 OilE OIL OUTLE T HOLE OIL OUTLET HOLE * 6 Figure 12. The Bearing, Showing the Thermocouple Locations, Inlet and Outlet Oil Holes.

REGULATING VALVE NITROGEN BOTTLE OIL PRESSURE GAGES FEED TANK // HAIR VENT I'_../-, ~. -VINYLITE TUBING TEST BEARING and the Loading Device. and the Loading Device.

-30A 1700 psi nitrogen cylinder with a pressure regulating valve was connected to the oil tank to raise the pressure of the oil to the desired value. Two filters and a strainer were installed in the line to remove any dirt and contaminants in the oil. Two pressure gauges, placed before and after the filters in the feed line, gave the inlet oil pressure. After lubricating the bearing, the oil issued through a hole at each end of the bearing and flowed down into a container from which it was collected and weighed on a balance graduated in fiftieths of a pound. Loading Device The load was applied at both ends of the journal by means of two levers and dead weights. This arrangement insured a symmetrical loading of the journal ends. The load was transmitted to the journal through two self-aligning ball bearings mounted on the shaft. The levers were pivoted at their front ends, while the dead weights were placed on a pan suspended on a hardened knife-edge at the back ends. The loading arm was chosen to give a 10 to 1 leverage ratio. As the levers were pivoted at their front ends, the loading system could be raised from the shaft and placed over the hooks, shown in Figure 13, in the case of the no load tests. Method of Estimating Film Breakdown It is essential in this investigation that the bearing should be working under hydrodynamic lubrication conditions. An electric potential was applied between the bearing and the journal to detect any metal-to-metal contact. An audio frequency

CATHOD-IAY OSCILLOSCOPE AUDIO FREQUENCY.l I OSCILLATOR BEARING BRUSH CONTACT ZJOURNAL Figure 14. Schematic Sketch of the Electric Circuit for the Estimation of the Film Breakdown.

-32Figure 15. Oscillographic Record for Normal Operation. Figure 16. Oscillographic Record for Metal-to-Metal Contact. _~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~oii liMnmz

-33oscillator was used as the voltage source. The applied voltage was observed on a cathode-ray oscilloscope screen. A schematic diagram of the electric circuit is illustrated in Figure 14. The audio frequency oscillator delivered up to 50 volts and was operated at 20,000 cycles. Figure 15 shows an oscillographic record for normal operation under hydrodynamic conditions. If metal-to-metal contact occurred, the journal was shorted and a picture as illustrated in Figure 16 showed on the cathode-ray oscilloscope screen, indicating film breakdown. Heating System The cartridge heater, which was snugly fitted in the journal, was connected to the electric circuit through a slip-ring and brush assumbly. A variac was used to control the input voltage to the heater. A wattmeter was connected to measure the amount of wattage consumed. Figure 17 shows a schematic diagram of the heating circuit. Cooling Water System Water from the supply main was used in cooling the bearing. Two needle valves were installed in the pipe line between the main and the cooling jacket to shut-off and regulate the amount of water flow. After cooling the bearing the water was collected in a 20 gallon tank and weighed on a balance graduated in fiftieths of a pound. Two thermocouples placed at the inlet and outlet of the cooling jacket registered the temperature of the inlet and outlet water respectively. Figure 18 shows a schematic sketch of the system.

CARTRIDGE HEAD SLIP - RING,- BRUSH WATTM ETE R VARIAC JOURNAL L I — " Figure 17. Schematic Diagram of the Heating Circuit.IOV Figure 17. Schematic Diagram of the Heating Circuit.

WATER SUPPLY SHUT- OFF VALVE REGULATING ) BALANCE VALVE THERMOCOUPLE BEARING THERMOCOUPLE WEIGHING TANK FRAME DRAtic Diagram of the ooing System. Figure 18. Schematic Diagram of the Cooling System.

Temperature Measurements Twenty-three thermocouples were used to measure the temperature at various locations in the test apparatus. All the thermocouples used were made from number 24 gauge duplex iron-constantan wire with fiber glass on asbestos insulation, manufactured by the Leeds and Northrup Company. The temperature of the bearing inner surface was measured by means of 12 thermocouples arranged in four rows placed 90 degrees apart, as shown in Figure 12, to detect any variation in the axial as well as the circumferential temperature distribution. To measure the temperature of the journal surface while running, the journal thermocouple leads were laid in grooves in the extension journal shaft, and led through the coupling and the bearing to the collector-ring of a slip-ring and brush arrangement. Figure 19 shows a schematic sketch of the unit. Coin silver slip-rings were used for their durability, low resistivity and excellent dry friction property. Each ring was pressfitted onto an insulating plexiglas ring which in turn was press-fitted on an aluminum shaft. The shaft was mounted at its ends in two selfaligning ball bearings. Thermocouple wires were soldered to the sliprings and were brought out to the collector-ring through holes equally spaced around the circumference of the insulating ring as shown in Figure 19. Two brushes, placed 180 degrees apart, were used per slip-ring to insure constant contact. Silver "Graphalloy" brushes were chosen for their excellent performance from the standpoint of low coefficient of friction.

SELF ALIGNING BALL- COIN SILVER SLIP P- LEXIGLAS BEARING RING INSULATION /BRUSH HOLDER —!A BRUSH HOLDER GUIDE A COIN SILVER SUP RING t6 4M in R6 An ii I I I 4'1 i| ii INSULATING RING a4~~ T T+ +TEOOLTHERMOCOUPLE WIRE FOR JOURNAL THERMOCOUPLES lei Y" I f ~ ~ ~ ~ ~ ~ ~ 1-SLIP RING DETAIL ERMOCOUPLE WIRES CALIBRATING THERMOCOUPLE Figure 19. Slip-Ring and Brush Assembly.

-38Eleven slip-rings were employed, eight of which were used for the journal thermocouple connections. One slip-ring was used to feed the audio oscillator signal to the journal. The remaining two were used for calibrating the system against the extraneous emf generated in the thermocouple circuit due to the frictional heating of the brush and slipring at different speeds. This was done by measuring the temperature of the ambient air by means of a thermocouple, connected through the slipring and brush arrangement as indicated in Figure 19. The reading was checked against a calibrated thermometer graduated in one-tenth of a degree fahrenheit. The maximum error involved in the thermocouple readings was about.04 millivolt. The temperature of the inlet oil was measured by a thermocouple inserted in the inlet oil line near the bearing housing. The oil outlet temperature was measured by two thermocouples arranged to contact the oil as it was leaking out as shown in Figure 10. The temperature of the inlet and outlet cooling water was measured by two thermocouples placed at the inlet and outlet of the cooling jacket respectively. The temperature of the housing was measured by means of a thermocouple firmly attached to the support four inches from the bearing center. The leads from the thermocouples were connected to terminal boards from which they were brought to three Leeds and Northrup, 2-pole, 10 position selector switch units. The circuit diagram is shown in Figure 20. This arrangement allowed any thermocouple to be connected into the measuring circuit. The measurement of the thermocouple emf's was made

SELECTOR SWITCH PORTABLE 2* 2 PRECISION 3 3 POTENTIOMETER G + T HTHERMOCOUPLE WIRES SPOT LIGHT THER GALVAN OM FT ER ~~~~~~~~THERMINAL BOAIRDS ___________ ~ _ I_ I ~~~~~~~~~~~~~~~~I THERMOCOUPLE T.C.I. COLD JUNCTION THERMOS BOTTLE Figure 20. Schematic Diagram of the Temperature Measuring Circuit.

5.0 -J 4.0 i 0 ICI 0. 3.0 220 Io I 2.0 0 0 25 50 75 100 125 150 175 200 TEMPERATURE F Figure 21. Calibration Curve for Iron-Constantan Thermocouples.

with a manually balanced Leeds and Northrup portable precision potentiometer type 8622, and a spotlight Leeds and Northrup galvanometer as illstrated in Figure 9. The overall sensitivity of the apparatus was estimated about one microvolt. The melting point of ice was used as the cold junction reference temperature. The cold junction thermocouple was immersed in purified kerosene in a thin glass tube, which was placed six inches deep, side-by-side with a calibrated thermometer in melting ice in a well insulated thermos bottle. To nullify the effect of introducing dissimilar metals into the circuit, optimum care was taken to keep the temperature measuring equipment at a uniform temperature by placing them in a well insulated cabinet covered from the inside with aluminum lining. The calibration of the thermocouples were made at the Sohma Laboratory of the Chemical and Metallurgical Engineering Department. The thermocouples were calibrated in a constant temperature both against a thermometer calibrated at the National Bureau of Standards. The thermocouple calibration is shown in Figure 21. It agrees very closely with that given by the Leeds and Northrup Company for their iron-constantan wire.(12)

IV. EXPERIMENTAL PROCEDURE The procedure used to obtain the data required for determining the effect of speed, load, and external heating on the average oil film temperature and the oil flow rate is described in the following paragraphs. Briefly, three series of experiments were conducted from which the heat convected by the oil flow and the heat dissipated through the bearing and housing could be determined for different combinations of speed and load. Series A The external heating was not applied during this series of tests. The heat generated was mainly due to the viscous shear stresses. Series B The external heating was applied during this series of tests. The heat generated was. due to both the introduction of external heating and that generated due to the viscou.s shear stresses. Series C This series of tests was carried out to check the validity of Petroff's formula. No external heating was applied. The test bearing was running at no load. Cooling water was used to measure the amount of heat conducted through the bearing. Procedure of Tests Series A Before starting the test, the cathode-ray oscilloscope and the audio frequency oscillator were turned on. Oil was then allowed to pass

-43from the storage tank to the bearing unit by opening valves A and B as shown in Figure 13. After adjusting the oil inlet pressure to the desired value, the motor was then started with the load completely relieved. This was done by raising the loading levers from the shaft and placing them over the hooks shown in Figure 13. The speed was then adjusted by means of the speed reducer and checked by a General Radio Strobotac type 631-BL, which has a range of 60 to 14,500 rpm. To detect the thermal equilibrium condition, the temperature of a thermocouple in the loaded half of the bearing was checked every halfhour until no temperature variation was noticed for two consecutive checks. On the average, the thermal equilibrium was reached in about 5 to 7 hours. This limited the number of runs to one or two runs per day. After the thermal equilibrium condition was attained, the following data were taken for each run: 1. The ambient temperature. 2. The temperature of the journal. 3. The temperature of the bearing. 4. The temperature of the inlet oil. 5. The temperature of the outlet oil. 6. The temperature of the housing. 7. The oil flow rate. 8. The speed of rotation.

-44When loading the bearing, the motor was always started at noload, and the load was then applied. After each loading, the speed was checked and the load was recorded. The same experimental procedure used in the no-loading tests was then followed, Series B In all the runs performed in this series the heater was turned on. By means of the variac, the input voltage to the heater was so adjusted that the total wattage, indicated by the wattmeter, was kept constant at 100 watts. The procedure used for this series of tests was similar to that just described for Series A. Series C This series of tests was carried out at different constant speeds under no-load condition. Before starting the test, water was allowed to pass through the cooling jacket for about three hours to reach a steady state temperature. It was noticed that the variation in the inlet water temperature during the tests did not exceed 0.2'F. The motor was then started after following the same experimental procedure adopted in the no-load test series. In addition, the inlet and outlet temperatures of the cooling water and the water flow rate were recorded. Operating Conditions For both series of tests A and B, 71 runs were performed. On the average, five different speeds and seven different loads were used for each series of tests. The following ranges and conditions were covered in the experiments:

-45The speed was varied from 500 to 1500 rpm. The load applied was varied from 0 up to 3429 lbs. The inlet oil pressure was kept constant at 1 psig. The oil used was Gulfpride Motor Oil No. 30. Its physical properties are given in Appendix B. The experimental results are given in Appendix F.

V. EXPERIMENTAL RESULTS This chapter is primarily concerned with the presentation and reduction of the experimental results. Comments and explanations are included wherever necessary, but analysis and discussion are deferred to the next chapter. The experimental results are presented in a manner which shows the effect of the variables encountered in the investigation on the temperature, oil flow, and correspondingly the heat balance of the test bearing. Series A The effect of speed and load on the average oil film temperature is presented in Figures 22 and 23. The average oil film temperature used in this investigation is the average of the journal and bearing thermocouple readings. In Figure 22, the average oil film temperature is plotted against the calculated eccentricity ratio. The short bearing approximation was adopted for the calculation of the eccentricity ratio. The theory was developed by Michell(l4) and Cordullo(8) and was used later by Ocvirk and DuBois(l7). Their extensive experimental work on journal bearing performance was in good agreement with the theory for bearings having ~/d ratio up to two. The effect of speed and load on the circumferential temperature distribution of the oil film is shown in Figures 24 and 25. The temperature, plotted at each of the four positions in these figures, is the -46

-47200 SERIES-A 190 180 I0. 170 0 0 iLo 140 130 150 1 120 100 0 0.1 0.2 0.3 0.4 0.5 0.6 ECCENTRICITY RATIO-n Figure 22. Average Oil Temperature vs. Eccentricity Ratio "n" for Different Speeds.

-49SERIES-A 150 148 146 IL Io 144 I 142 w iC 140 z i- 138 1 3 6~\\;\~ 136 134 132 130 0 2I 2 THERMOCOUPLE POSITIONS Figure 24. Circumferential Temperature Distribution for Different Eccentricities at 750 rpm.

166 SERIES-A 164 162 U. 160 - IJ 158 w 0L z 154 THERMOCOUPLE POS ITIONS 146 Figure 25. Circumferential Temperature Distribution for Different Eccentricities at 1000 rpm.

-51average of the axial temperature indicated by three thermocouples placed flush with the bearing inner surface. The load is represented by the eccentricity ratio n. Detailed calculations for the load number and the eccentricity ratio are given in Appendix H, Table V. The effect of speed and load on the oil flow rate is illustrated in Figures 26, 27, and 28. Figure 26 shows a comparison between the experimental results and the theoretical flow derived by Muskat and Morgan(16) for concentric bearings. In Figure 27 the oil flow rate is given as a function of the calculated eccentricity ratio at different speeds. While in Figure 28 a straight line relationship is correlated when the nondimensional parameter 2Q N is plotted on log paper c p 500 against the Sommerfeld number S. The equation of the correlating line can be written as: 375 79 (51) c3p 500 p cd The method of least square was used in determining the empirical constants. The result of the calculations is given in Table VI. It is to be noticed that the effect of the change in bearing clearance with temperature was taken into consideration, as the journal and the bearing were of dissimilar metals. The equations derived by Von Gersdorfer(23) were used in calculating the change in clearance. Figure 29 gives the result of the calculations presented in Appendix F. The viscosity of the oil was also considered as a variable. At each load, the viscosity of the oil was determined from the average oil film temperature.

-523.0 2.8 2.6 2.4 G 2.2 2.0 = 1.8 — EXPERIMENTAL 3: 1.6 NO HEATING) 0 W 1.6 o 1.4 - THEORETICAL 1.2 1.0 0.8, 250 500 750 1000 1250 1500 SPEED, N Figure 26. Comparison Between Theoretical and Experimental Oil Flow at No-Load.

-539 6 - 0 a w 0O -J -i 0 r,, I,, I,,,, I I 0 0.1 0.2 0.3 0.4 0.5 0.6 CALCULATED ECCENTRICITY "n" Figure 27. Oil Flow Rate vs. Calculated Eccentricity at Different Speeds.

'50 Q40- SERIES-B O 500 rpm. 0( 750 rpm. 0 A 1000 rpm. V 1250 rpm..20 ~z ~1500 rpm. XtiZ, | rBSeries-A I A z ~O ~5 SERIES-A LZ | /tZ9e* 500 rpm. | i/ 0o 750 rpm. O | / *A 1000 rpm. z o V 1250 rpm. z.02 X 1500 rpm..01 I I I.02.04.06.08.10.20.40 60 SOMMERFELD NUMBER-S Figure 28. The Nondimensional Flow Number hQ; N vs. the Sommerfeld Number S. UCp 500

-55160 140 120 100 0 z 80 i.w -J w w 60 40 20 0 2 4 6 8 10 CHANGE IN DIAMETRAL CLEARENCE X 104 Figure 29. Change in Diametrical Clearance x 104 vs. Temperature Elevation - ST.

Series B The combined effect of external heating, speed, and load on the average oil film temperature, circumferential temperature distribution, and oil flow rate is shown in Figures 30 through 33. Series C The result of the comparison between the heat generated as calculated by Petroff's formula and the total heat dissipated through the bearing and convected by the oil flow as determined from the experimental data is shown in Figure 34. Data Reduction for the Heat Balance Analysis Series A To determine the heat dissipation characteristics of the bearing and housing, the heat balance Equation (2.26) for the unloaded bearing was used. The heat convected by the oil flow was calculated from the experimental data. The results of the calculations are shown in Table VI. Petroff's formula was used in determining the heat generated. To determine the empirical constants a and m, the temperature elevation AT is plotted against HJ - Ho on log paper as shown in Figure 35. It is noticed that all the data points are well correlated by a single straight line. The method of least square was used in fitting the line and determining the constants a and m. The correlating equation is found to be of the form: Hj - Ho = H = 3.26 (AT)1l43 (5.2)

-57230 SERIES-B 220 210 200 I o w 0 _ 0190 ~ ~ ~ ~ ~0 4 0.180 14 _ 140 130 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 CALCULATED ECCENTRICITY-n Figure 30. Average Oil Film Temperature vs. Calculated Eccentricity at Different Speeds.

-58SERIES-B: OIL INLETt 140 ~Ii. 160 i50~a70 - r OIL INLET W 140 0 I 2 3 THERMOCOUPLE POSITIONS Figure 31. Circumferential Temperature Distribution for Different Eccentricities at 750 rpm.

-59SERIES-B 230 220 210 200 140 0 I 2 3 at 1250 rpm. OIL INLET W 140 0 at 1250 rpm.

-6010 SERIES-B 0 0 ~, \0s0'? _ 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 CALCULATED ECCENTRICITY "n" Figure 33. Oil Flow Rate Vs. Calculated Eccentricity-n at Different Speeds-N.

-613600 SERIES-A 3200 2800 - Ia. U 2400 1600 i81600 4004 U. 1200 Generated. 400 0 400 800 1200 1600 2000 2400 2800 Generated.

l000 900 800 700 600 u 500TEP — SERIES, A 400 SERIES, B w 300 (0 o 5 I ~ r I 200 I00 10 20 30 40 50 60 70 80 90 100 200 300 TEMPERATURE ELEVATION tAT Figure 35. Heat Dissipated Hc vs. Temperature Elevation AT.

The effect of speed and load on the heat convected by the oil flow is indicated in Figures 36 through 38. In Figure 36, the heat convected by oil flow is plotted against the calculated eccentricity ratio n. The data are reduced to a single curve when the nondimensional heat convection parameter Ho/Ip is described as a function of the load number 1/S as shown in Figure 37. Plotting the same parameters on log paper in Figure 38, yields a straight line relationship. The correlating equation can be expressed as follows: Ho/Xp =.1845 (1/S).2146 (53) The effect of speed and load on the heat dissipated through the bearing and housing is presented in Figures 39 and 40. Figure 39 shows the heat dissipated Hc as a function of the load number 1/S at different speeds. The heat dissipated IHe was determined by the use of the empirical Equation (5.2) which is presented graphically in Figure 35. The data shown in Figure 39 are reduced to a single curve, when the nondimensional heat ratio Hc/Hp is plotted, instead of HE, against the load number 1/S as illustrated in Figure 40. A comparison, between the analytical heat generation ratio HJ/Hp and the total heat dissipation ratio (Hc + Ho)/Hp, is given in Figure 41. Equation (2.21) was used in calculating Hj/Hp. The total heat dissipation ratio (He+ Ho)/Hp was obtained by the addition of the smoothed data of Ho/Hp and Hc/Hp, presented in Figures 37 and 40 respectively. Series B The heat dissipation characteristics were determined using Equation (2.27). When the heat dissipated Hc was plotted against the

-64SERIES-A 320 300 I w 280 240 "200 IJ 4~~~~~~~~~0 240 0 0.1 0.2 0.3 0.4 0.5 0.6 CALCULATED ECCENTRICITY "n Figure 36. Heat Convected by Oil vs. Calculated Eccentricity at Different Speeds.

-65-.375 SERIES-A.350.325.300.275 x O s X.250 7 4L:.225 o.200 G,5 500 RPM..175 Z / S 750 RPM. FO A150|-/ 1000 RPM. W /150 T 1250 RPM. 8 X 1500 RPM. Ez. 100.075.050.025 0 0 2 4 6 8 10 12 14 16 18 20 LOAD NO - Figure 37. Nondimensional Heat Convection Ratio HJHp vs. Load Number 1/S.

-65-.375 - SERIES-A.350.325.300.275.250 vx.225 0.200 a.175 |/o 500 RPM. z S 70 RP7M. 0.7 150 _ 15000 RPM. 1.25 0 I_ 100 I 0 2 4 6 8 10 12 1 16 RP18 20 LOA El'N Ratio vs. 00ad Number 1/S. Ratio HJ% vs. Load Number 1/S.

1.0 SERIES-A 0. l ) C o. LC I.01.0.1. 1.0 10 100 LOAD NUMBER - I/S Figure 38. Nondimensional Heat Convection Ho/Hp vs. Load Number 1/S.

-67800 SERIES-A 700 600 IjL ~~~~~o P 500 400 300 0 200 100 0 2 4 6 8 10 12 14 16 18 20 LOAD NUMBER — Figure 39. Heat Dissipated Ho vs. Load Number 1/S.

-681.3 SERIES-A 1.2 1.1,n I / o 1.0 0 O fe o 0.8 X 00.f 8 O 500 RPM zre 0 750 RPM. 0.7 A 1000 RPM. v 1250 RPM. X 1500 RPM 0.6 0.5 0 2 4 6 8 10 12 14 16 18 20 22 LOAD NUMBER, Figure 40. The Heat Dissipation Ratio HJ% vs. Load Number 1/S.

-69SERIES-A 1.4 Hj/Hp (ANALYTICAL) 1.2 (Hc+ Ho)/Hp (EXPERIMENTAL) 1.0 HC/Hp 0.8 0.64 0.4 - - Hc/Hp 0.2 0 2 4 6 8 10 12 14 16 18 20 22 LOAD NUMBER t I/S Figure 41. Heat Balance Sheet. Total Heat Dissipation Ratio (Hc + HO)/p and Heat Generation Ratio Hj/Hp vs. Load Number.

-70temperature elevation AT on log paper, a straight line relationship was obtained as presented in Figure 35. The effect of speed and load on both the heat dissipated through the bearing and housing, and the heat convected by the oil flow is shown in Figures 42 through 45. In Figure 46 a heat balance between the analytical heat generation by friction as suggested by Barwell(l) and the total heat dissipation is made. The data is presented in a nondimensional form by expressing both quantities in terms of the heat generated at no-load.

-71500 SERIES-B 450 400:: 350 O 300 250 > 20o 100 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 CALCULATED ECCENTRICITY-n Figure 42. Heat Convected by Oil Flow vs. Calculated Eccentricity at Different Speeds.

-720.8 SERIES - 8 0.7 0.6, 0.5 A z 0.4- o I A x w 0.2 0 500 RPM. e 750 RPM. A 1000 RPM. V 1250 RPM. X 1500 RPM. 0 5 10 15 20 25 30 35 LOAD NO, I S Figure 43. Heat Convection Ratio Ho/IHp vs. Load Number 1/S.

-73SERIES-B 700 600 500 0W U) i 500 0 400 300 0 5 10 15 20 25 30 35 LOAD NUMBER- - Figure 44. Heat Dissipated Hc vs. Load Number 1/S.

ZI.'I I I I I IIIII II I I IIIIII I II-74SERIES - B 1.0 0. 9 0 7 I- 0'. _ 0 z 0.6 0 500 RPM. 0. e 750 RPM. 4 A 0 RPM. v 1250 RPM. 0.5, X 1500 RPM. 0.4 0.5 0 5 10 15 20 25 30 35 LOAD NO, I S Figu~re 145. The Ratio He/Hp vs. the Load Number i/S.

-75SERIES-B 1.6 1.4 Hj /Hp ( ANALYTICAL 1.2 Hc+H,/Hp (EXPERIMENTAL) I. ~- L Hc/HF, 0.8 0.6 HC/Hp 0.4 0.2 0 5 10 15 20 25 30 35 LOAD NUMBER, I/S Figure 146. Heat Balance Sheet. Ratio at' Total Heat Dissipated iCH + Ho/Hp and Heat Generation Ratio HYT/Hp vs. koad Numb er.

VI. ANALYSIS AND DISCUSSION OF RESULTS Effect of Load on the Average Oil Film Temperature Due to the increase in heat generation by load application, the average oil film temperature is expected to increase correspondingly. Actually, the average oil film temperature decreases to a certain minimum and then starts to increase as shown in Figure 22 and 23. The difference between the pressure developed in the axial direction, to support the load, and the atmospheric pressure at the ends of the bearing causes a rapid increase in the oil flow. This, in turn, increases the amount of heat carried away by the oil, causing the bearing to run at a cooler temperature. At heavy loads, the rate of heat generation is greater than the increase in the oil flow rate. Accordingly, the temperature of the bearing starts to rise again. This observation seems to have passed unnoticed by most of the previous investigators. This can be attributed to the following reasons: 1. The most detailed work on heat effects on journal bearings was done on unloaded or lightly loaded bearings. The technique, used in carrying out the lightly loaded bearing tests, was performed in such a way that this observation could not be detected. Muskat and Morgan(15) varied the speed while keeping the load and inlet oil pressure constant. Boyd and Robertson(3) changed the oil supply pressure and the speed while keeping the load constant. -76

-772. In other related investigations in the field of lubrication the lack of sufficient temperature measurements of the bearing was reported. Besides, there is some doubt about the time given for the thermal equilibrium condition to be reached. 3o The use of high oil supply pressure with the adoption of the oil outlet temperature as a true representation of the bearing temperature tends to give misleading results. This is mainly due to the excess oil flow which leaves the bearing almost immediately without contributing effectively to the cooling of the bearing. It is worthy of note that Rosenblatt and Wilcock(20), working on a different type of sleeve-bearing, were the first to report this observation in their study on oil flow. In the external heating case, the same phenomena is noticed as shown in Figure 30. The only difference between the 2 cases is that the average oil film temperature in the case of external heating starts to increase at a greater loado Effect of Speed on the Average Oil Film Temperature When the bearing is running under hydrodynamic lubrication conditions, the average temperature of the oil film is influenced more by variations in speed than by variations in load. This is due to the fact that the heat generated in the film is a function of the square of the speed as can be seen from Equation (3.24). This can be illustrated by comparing the difference in the average oil film temperature due to the

-78variation of speed with that due to the variation of load. From Figure 22 the level of the average oil film temperature has increased by about 550F due to the variation of speed from 500 to 1500 rpm, while the average oil film temperature has increased by about 10'F due to the variation of load from zero to 3429 pounds. This result is also confirmed when the effect of speed and load on the average oil film temperature for the external heating case, shown in Figure 30, are compared. From this result, it can be concluded that the speed of rotation has an important effect on the heat condition of journal bearings. Effect of Speed on the Circumferential Temperature Distribution As shown in Figures 24, 25, 31, and 32, for both series of tests performed, it is noticed that the variation in the circumferential temperature distribution, for the no load tests, at different speeds, can be considered negligible when compared to the corresponding variation for the loaded bearing tests. The small temperature variation recorded is mainly due to the introduction of fresh oil supply to the bearing. From these experimental results, the assumption that the temperature gradient aT/6x is negligible, as considered in the theoretical investigation for the case of the unloaded bearing, has been justified. Effect of Load on the Circumferential Temperature Distribution When the load is applied to the journal, the circumferential temperature ceases to be constant, and starts to vary around the circumference. This variation becomes more pronounced when the load is increased as shown in Figures 24, 25, 31, and 32.

-79It is noted in all the experimental results, that the maximum temperature is located within the vicinity of the minimum film thickness, confirming the results obtained by Stephen.(22) Effect of Speed on Oil Flow Rate At no load, the oil flow increases with the increase in speed, Figure 26 gives a comparison between the experimental results and the theoretical flow predicted by M1skat and Morgan. (16) Their equation is written here for convenience: Ap it cadj (6.1) loge di 1 4 3p~2 - 2 loge d - 1 b-(i-+e) ] where Ap - Inlet pressure - ambient pressure psi di Oil inlet hole diameter inches b = An integer with values 1, 2, 3, 4,..... The agreement between the theory and experiments is fairly close. The most probable reason for the discrepancy is that the clearance in Equation (6.1) is raised to the third power. Any small error in the measurement of the clearance will have a great effect on the calculated oil flow rate. It is to be noted that the speed does not enter explicitly as a variable in the above equation, in spite of the fact that the experimental results do show a positive increase in the oil flow rate with the increase in speed. This can be explained by the following reasoning: Increasing the speed will raise the average oil film temperature level.

-80As the viscosity of the oil is strongly related to the oil temperature, a corresponding decrease in the viscosity will result causing an increase in the oil flow rate. By the same reasoning, the increase in the oil flow for the external heating series, as illustrated in Figure 33, over the no heating series can be explained. Effect of Load on Oil Flow Rate When the load is applied on the journal, the oil flow rate increases rapidly as indicated in Figure 27. This can be attributed to the increase in the hydrodynamic oil flow with the increase in load. The equation of the correlating line (5.1), in Figure 28, can be used in predicting the oil flow in similar bearings working under low oil feed pressure. For the external heating case, the oil flow increases, following the same trend observed in the above case, as shown in Figure 33. It is noticed that the correlating line, for this case, is very close to the no heating case correlating line, as illustrated in Figure 28. Although the effect of load is considered small with respect to the effect of speed on the average oil film temperature, it is interesting to note that it has a greater influence on the oil flow rate than that of speed. Effect of Speed and Load on the Heat Convected The increase in oil flow, with speed and particularly load, is the main reason for the increase of the amount of heat convected by the oil flow as indicated in Figures 36 and 37.

The equation of the straight line (5.3), correlated from the data plotted in Figure 38, can be used in estimating the heat convection ratio Ho/Hp as a function of the load number in similar bearings. To illustrate the effect of external heating, a comparison is made between the results obtained in Series A and Series B runs. It is noticed in Figures 37 and 43 that the heat convection ratio in the case of external heating is about seven percent greater than in the case of no heating. This is mainly due to the decrease of the oil viscosity with external heating, causing the amount of oil flow to increase. This will accordingly increase the amount of heat convected by the oil flow and the heat convection ratio Ho/Hp. Effect of Speed and Load on the Heat Dissipated He From Figures 40 and 45, for both Series A and B, it is noticed that the heat dissipated through the bearing decreases at light load and then increases with the increase in load. The decrease in the heat dissipation is mainly attributed to the increase in the rate of heat convection due to the rapid increase in the hydrodynamic oil flow at light loads. At heavy loads, the rate of increase in the heat generation rate is much greater than that of the heat convection rate. This, correspondingly, causes the heat dissipation through the bearing and housing to rise again. Effect of the Average Oil Film Temperature on the Heat Dissipated Hc From Figure 355 the heat dissipation rate through the bearing and housing increases with the increase of the average oil film temperature. The empirical equation, relating the two variables is: He 3= e26(hT)e43

-82This confirms the assumption, first introduced by Lasche(ll), that the heat dissipation can be described by a power of the temperature elevation of the oil film over the ambient. The low value of the exponent gives an indication of the small role played by the radiation heat transfer. Comparing the values of the empirical constants with those determined by the following investigators: Lasche(ll) a = 2.9 m 1.30 Muskat and Morgan(l5): a = 2.0 m = 1.35 Burwell(2): a - 2.9 m = 1.5 McKee(l3): a = 3.42 m = 1.65 shows that the values obtained in this investigation lie within the range of the above results. It is interesting to note that the heat dissipation rate for the case of external heating is less than that for the no heating case as illustrated in Figure 35. This is mainly due to the increase in the rate of heat convection by the oil flow and the decrease in the heat generation rate due to external heating. Heat Balance Under thermal equilibrium condition, the heat generated in the oil film balances the total heat dissipated from the bearing. From Figures 41 and 46, it is noted that the experimental results are in agreement with the analytical, for both series of tests A and B. This confirms the validity of Barwell formula, Equation (2.21), in calculating the heat generated in loaded bearings.

VII. CONCTLUSIONS AND RECOMMENDATIONS Conclusions The following conclusions may be drawn from the results of this investigation: 1. The consideration of the heat dissipated through the bearing and housing, and that convected by oil flow, in the analysis of the exper~riment~al results, gives a better understanding of the effect of speed, load, and external heating on the avrerage oil film. tempe:rature and the heat balance. 2. The phenomena, that the bearing w-ill run cooler at light loads than at no load is well established and confirmed experimentally. 5. The average oil film temperature is affected more by variations in speed than by va-rations in load. The level of the average oil fflm temrperatrur e has increased by about 55~F due to the variation of speed from 500 to 1500 rpm, while it has increased only by about 10~F due to the varia-',ion of load from zero to -4.29 pounds. 4. The oil flow rate is influenced more by changes in load than by changes in speed. The oil flow rate has increased by about 350 percent due to the change in load from zero to 3429 pounds, while it has increased only by about 200 percent due to the change in speed from 500 to 1500 rpm. 5. The heat convected by the oil flow increases by external heating application~

-846. The heat dissipated through the bearing and housing for the external heating case is less than that for the no heating case, when the temperature elevation of the bearing over the ambient is the same in both cases. Recommendat ions It is recommended that further investigations of the same nature be made to cover larger ranges of speeds and oil inlet pressures. The study of the effect of the following variables, 1. the diametral clearance 2. the bearing length/diameter ratio 3. water cooling 4. oil grooves, on the temperature and heat balance of journal bearings is also needed in order that the problem of heat removal from journal bearings can be completely solved.

APPENDIX A JOURNAL AND BEARING DIMENSIONS The dimensions of the journal and bearing are given in Figure 11 and 12 respectively. The machining and grinding of the bearing and journal was made at the U.M.R.I. machine shop. The dimensions of the journal diameter was measured at three different positions. The average diameter was found to be 3.001 inches. The surface roughness was measured by means of a profilometer. Its value was 9 RMS microinch. The bearing bore was measured along two perpendicular planes at the two ends and at the middle section. The average value was 3.0068 inches. The surface roughness was found to be 14 RMS microinch. Summary of the Major Dimensions The journal diameter = 3.001 inches The journal length = 5.000 inches The bearing bore = 3.0068 inches The diametral clearance =.0058 inches

APPENDIX B PROPERTIES OF GULFPRIDE NO. 30 OIL The properties which entered the analysis of the experimental data are: 1. The Specific Heat - The specific heat was considered constant. An average value covering the range of temperature used, is chosen from Figure 47. The average specific heat = 0.515 BTU 2. The Specific Gravity - As shown in Figure 48, the variation of the specific gravity, within the range of the temperature used$ can be neglected. The following average value is adopted. The average specific heat = 0.858 3. The Coefficient of Thermal Conductivity - The following formula, given by Wilcock and Booser(25), were used in estimating the coefficient of thermal conductivity. k = 0.812 [1 -.0003 (T-32)] BTU per inch P60 hr ft2 F~F where P60 = density in gm/cc An average value covering the range of temperatures used (120~F - 2000F) was used. k =.0737 rTU ft hr ft2 OF =.0159 lb sec ~F 4. The Kinematic Viscosity - The kinematic viscosity temperature relationship was furnished by the manufacturer, as shown in Figure 49. To check the accuracy of the curve, the encircled points in the figure were determined experimentally. -86

0.60 UL. o 0.58 T5 0.56 co 0.54 0.52 I 0.50 O 0.48 La. Cn 0.46 0.44 0.42 0 50 100 150 200 250 300. 350 400 TEMPERATURE, OF Figure 47. Variation of Specific Heat with Temperature for Gulfpride No. 30 Oil.

0.92 0.90 0.88 0.86 0.84 0.82 " 0.80 a) 0.78 0.76 0.74 0 50 100 150 200 250 300 TEMPERATURE, OF Figure 48. Variation of Specific Gravity with Temperature for Gulfpride No. 30 Oil.

APPENDIX C LAMINAR FLOW CRITERION IN JOURNAL BEARINGS In 1923 Taylor analyzed the problem for the liquid between two concentric cylinders, and developed a criterion for the initiation of turbulence under these circumstances. This criterion, fortunately, can also be applied to journal bearings with sufficient accuracy as has been demonstrated by Wilcock(24). The transition between normal laminar behavior and turbulence takes place at a Reynolds number given by Re = N' DC = 41.1 (D) and the transition speed can be written as: N = 1.57 x 103 V rpm D1/2 CD2/3 To evaluate the speed at which turbulence initiates, the following substitutions are made. D = 3 inches CD =.00649 inches = 1L 24 x 10-7 x (12)3 x 386 3.0 x 10-2 in2/sec p.858 x 62.4 N = 1.57 x103x 3.00 x lO-2 1.73 x (.00649)3/2 = 1.57 x 103x 3.00 x 1-2 1.73 x 5.23 x 10-4 = 5.21 x 104 rpm As the maximum speed used in this investigation is 1500 rpm, it can be concluded that the flow is highly laminar. -90

APPENDIX D ESTIMATION OF THE AVERAGE OIL FILM TEMPERATURE As a result of this investigation, the average oil film temperature can be estimated. When the heat balance Equation (2.2)) is divided by the rate of heat generation at no load, one gets Hi H5 + Ho (D.1) Substituting for the values of He and Ho/Hp, in Equations (5.2) and (5.3) respectively, in the above equation gives: Hj _ 3.26(LT)1.43 +.1845 (/S).2146 (D.2) To determine Hp, the average oil film temperature for the unloaded bearing must first be evaluated. For the unloaded bearing Equation (6.2) reduces to: 1 3.26((AT)1 43 +.1845(1/S).2146 (D3) The above equation contains two unknown; the viscosity of the oil t which is included in the Hp and 1/S terms; and the temperature elevation AT. If a suitable viscosity-temperature relationship or an A.S.T.M. viscosity-temperature chart is used, the value of the temperature elevation LT can be evaluated graphically. After determining Hp, the average oil film temperature for the loaded bearing can then be estimated. Substituting for the value of HJ in Equation (2.21) in Equation (6.3) one gets: 300 [81trS3N'2 + (We sin7) 2 t Nt] p J c(l-n2 +) 2 J _ 3.26(aT)1'43 +.1845(1/S).2146 (D.4) -91

-92Making use of Ocvirk and DuBois results(l7), the value of n and a can be obtained. The temperature elevation AT can then be determined, when the same procedure used in its evaluation for the unloaded bearing case is followed.

APPENDIX E THE JOURNAL FRICTIONAL HEAT GENERATION From equilibrium conditions, the bearing frictional torque is less than the journal frictional torque. This can be shown when moments are taken about the center of the bearing 0 in Figure 50. IL. ~:j ru.FF Figure 50. Forces Tending to Cause Rotation of the Oil Film in a Full Journal Bearing. r FJ - r FB = W e sin y where Fj = Frictional force on journal surface, lbs. FB = Frictional force on bearing surface, lbs. The eccentricity of the journal is thus seen to be the source of the difference in the frictional torque between the journal and the bearing. The short bearing approximation theory does not indicate a difference between the journal and bearing frictional torques because of the assumption that the velocity distribution across the oil film is linear. -93

To estimate the journal frictional torque Ocvirk and DuBois(17) gave the following equation 4X2 r3 r N' MJ = c (- 2)1 2 + W e sin y c (ln The second term is the frictional torque obtained, using the short bearing approximation theory. The third term is the load couple caused by the eccentricity of the journal. Barwell(l) suggested the following modified form of Ocvirk's equation 4-A2 r3 g N' W MJ 2=1/2 + -e sin y c (l-n2)1/2 2 He based his equation on the assumption that the short bearing approximation theory, while underestimating the journal frictional torque, it overestimates the bearing frictional torque. It can, then, be considered as an average value between the journal and bearing frictional torques. As a closer approximation to the true journal frictional torque, he added one half of the load couple to the frictional torque derived, using the short bearing approximation theory. Barwell's equation was derived analytically by Mack and Shaw(21) without the use of the short bearing approximation theory. For this reason his equation was used in the prediction of the journal heat generation. Multiplying the journal frictional torque by 2n N', and using appropriate conversion factors, the journal frictional heat generation can be expressed as Hj = 300 [8 jr e 7 +N (W e sin 7) 2i N'] (2.21)'J c~ l -2')iJ/ + 2 J..

-95Sample Calculations for Run Number 5 The journal frictional heat generation = 300 [83 r3 N' (W e sin ) 2 (2.21) J c (_1-n2)12 + 2 J ) 2 N' (2.21) The short bearing approximation theory was used to calculate the eccentricity ratio n and the attitude angle y. Ocvirk and DuBois(l7) derived the following equation which expresses the attitude angle y as a function of the eccentricity ratio n tan y = it (ln2)1/2 This equation was used in estimating the attitude angle y. For Run 5: r = 1.5 inches = = 5.00 inches c =.00306 inches Nt = 8.34 rps n=.48 la =66.3 x 10-7 Reyns. W = 1727 lbs. tan y = 1.434 sin y =.82 Substituting the above values in Equation (2.21) yields Hj = 208 + 21 = 301 BTU/hr Similar calculations were made for the other runs as shown in Table VI.

APPENDIX F THERMAL EXPANSION EFFECT ON CLEARANCE As the journal and the bearing were made of dissimilar metals, the effect of the change of bearing clearance with temperature was taken into consideration. The method used by Von Gersdorfer(23) was adopted. Beca;ng (Bronze) WI supportn Fro.me Figure 51. Bearing Construction. The Effect of Thermal Expansion on the Journal The following equation will be used to determine the change in the journal diameter: ADj = DJ x aJ x ATJ where ADJ = The increase in the diameter of the journal due to ATJ. DJ = Journal diameter at room temperature inches aJ = Coefficient of thermal expansion of journal material = 6.2 x 10-6 l/~F ATJ = Temperature elevation of the journal over the ambient. -96

-97The Effect of Thermal Expansion on the Bearing According to the way the bearing unit is constructed, the bearing mid-section is free to expand, while the ends are constrained by the supporting frame as illustrated in the above figure. Expansion at the mid-section = 6DBi = DB x aB ATB = B 1 Expansion at the ends of the bearing = B~2 = DB W1E1lalAT1 + W2EBCBATB WlEl + W2E2 where W1 = Radial thickness of the supporting frame = 2". E1 = Youngs Modulus of elasticity of the support material= 30 x 106 lb/in2 EB = Youngs Modulus of elasticity of the bearing material 15.9 x 106 lb/in2. ^T1 = Temperature elevation of support over ambient. ATB = Temperature elevation of bearing over ambient. gB = Coefficient of thermal expansion of the bearing material = 12.2 x 10-6 1/OF. W2 = Thickness of the bearing at the end. Sample Calculation at 1500 rpm: From Table I LTB = 93.2 "F AT1 = 148-88 = 60~F. Bearing expansion at the mid-section AB1 = 3.0068 x 12.2 x 10'6 x 93.2 = 3.4188 x 10-3 inches

-98Bearing expansion at the ends = A32 = 3.0068 x 2 x 30 x 106 x 6.2 x 10-6 x 60 +.625 x 15.9 x 106 x 12.2 x 10-6 x 93.2 2 x 30 x 106 +.625 x 15.9 x 106 = 1.4477 x 10-3 inches The increase in the bearing diameter was taken as the average of the increase of the mid-section and that at the ends. Average bearing increase in diameter = AD =(- + e,2) 2 = 3.-4188 + 1.4477 x 10-3 2 2.4332 x 10-3 inches The change in journal diameter = ADJ = DJ x aJ x ATj 4 3.001 x 6.2 x 10-6 x 93.2 = 1.73409 x 10-3 inches The change in diametral clearance = IDBm - ADj = (2.43320 - 1.73409) 10-3 =.69911 x 10-3 The new diaftetral clearance = Cd + (AIBm - aDj) =.00580 +.00069911 =.006499 inches Following the same method of calculation, the change in diametral clearance with temperature can be evaluated. As the average oil film temperature was influenced more by the variation in speed than by the variation in load, the value of the

-99diametral clearance at constant speed under no-load condition was substituted for the diametral clearance at the corresponding speed for any load. The result of the calculations is given in Table I and presented graphically in Figure 29.

TABLE I TBERMAL EXPANSION EFFECT ON CLEARANCE 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 j Dj a x 10-6 A~j D Ct5 x 10-6 &Tj W1E1 W1Ea1,1 WBEB WBEBaB4TJ 9+11 8+10 12/13 ADB1 AIB2 ADBm CD C N Inches Inches Itches V'0F x 106 x 103 x 1o5 x 103 x lo3 x 106 x 10-3 lo-3 x 10-3 x jo-3 x lo-3 Inches rpm Inches Inches Inches Inches 42.2 3.001 6.2.78518 3.0068 12.2 30.2 60 11.2344 9.9375 5.1162 16.3506 69.9375.23378 1.54808.7029 1.12545 6.13030 3.065 50 6 H 59.9 3.001 6.2 1.1145 3.0068 12.2 40 60 14.880 9.9375 7.2621 22.142 69.9375.3166 2.197309.95195 1.5744 6.2599 3.1299 750 0 0 73 3.001 6.2 1.35825 3.0068 12.2 50.5 60 18.7860 9.9375 8.8503 27.636 69.9375.39515 2.67785 1.1881 1.9329 6.36465 3.1823 1000 84.2 3.001 6.2 1.56292 3.0068 12.2 55 60 20.460 9.9375 10.1839 30.6439 69.9375.43816 3.081368 1.31746 2.1994 6.4365 3.2182 1250 93.2 3.001 6.2 1.73409 3.0068 12.2 60 60 22.320 9.9375 11.2993 33.6193 69.9375.48070 3.4188 1.4477 2.4332 6.4991 3.2490 1500

APPEN7DIX G DETERMINATION OF THE THEORETICAL JOURNAL TEMPERATURE Equation ( 2.12) was used in the calculation of the theoretical journal temperature, 8 = 1 in [P' Pr.E (Y ) + 1] (2.12) multiplying the above equation by T7 - TB and. substituting for Y by 1, gives TJ -TB -In B + 1] B 2k The details of the calculations are presented in Table II. TABLE II COMPARISON BE'IWEEN TPIE EXPERIMENTAL AND THEORETICAL (JOTJRNAL TEMiPERATJE-BEARING TEMPERATURE) Speed IJLB k U2 2 AT AT Tav N TB x107 lb U x 104 1 + BU Calc. Exp. rpm ~F Reyns. sec ~F in/sec 2 k ~F ~F 128 500 127.2 69.6.0159 78.5.6162 1.0237 1.21 1.6 143.5 750 142.2 51.0159 117.8 1.385 1.039 2.23 2.7 157.5 1000 155.77 39.8 o0159 157 2,46 1.054 3.00 3.6 169.1 1250 166.7 32.4.0159 196.3 3.85 1.069 3.8 4.5 181.7 1500 178.5 26.15.0159 235.7 5-54 1.080 4.38 5.40 -10l

APPENDIX H EXPERIMENTAL DATA AND CAWIULATIONS This appendix contains all the original data for all the experiments. The data and the results of the calculations are given in the following tables: Table III - Temperature Data Table IV - Oil Flow Data Table V - Calculation of the Sommerfeld Number, the Load Number, and the Eccentricity Ratio Table VI - Summary of Correlation Calculations Figure 52 describes the positions of the bearing thermocouples given in Table III, q Thev ocovzs I | I I"oSlPosionolosiHo n. _ q 5IO o 15 16 17 (6 — 8)(15-f-I7) 7hevmocourles Post;h"-(a I31314) ta 3 14 Figure 52. Bearing Thermocouple Positions. while Figure 53 was used in evaluating the eccentricity ratio-n from the load number 1/S. -102

LO 0, z LU..2 0 0 5 10 15 20 25 30 35 40 LOAD NUMBER- Figure 53. Eccentricity Ratio vs. Load Niumber V/S (After DuBois and Ocvirk).

TAKIE III TEMPERATURE DATA: SERIES A Bearing Thermocouple Readings -. v.. Calibrating Journal Thermocouple Readings AveragePoiin-0ostn-3Pston 1oiin-2 big Speed Ambient Thermocouple Correc- Teaperature Corrected P~to oiin-3Psto oiin-2~sn Nun N Temp. tion 1 2 3 1. Tj Temp. Tj 6 7 8 9 10 11 12 13 11. 15 16 17 Average Temp. Loa NO rpm *F? m.v.'F *F MIN, ayv. m~v. m.v. m.v. ~27 ~F TB Tav, M.V. ls 1 500 85.8 1.55 86.2 2.812 2.729 2.185 2.831 P. 2.79 129 328.2 2.718 2.732 2.722 2.752 2.722 2.767 2.718 2.752 2.701. 2.722 2.762 2.733 127.2 1L28 2.4.17 0 2 500 86.9 1.575 87.5.6 2.801 2.71P 2.727 2.786 2.757 127.9 327.3 2.622 2.612 2.618 2.656 2.622 2.662 2.668 2.693 2.665 2.655 2.701. 2.700.12~4.5 125.8 2.369 12 3 500 86.9 1.575 87.5.6 2.811 2.71.3 2.771. 2.796 2.181 128.7 1.28.1 2.638 2.631 2.637 2.663 2.632 2.672 2.712 2.738 2.713 2.679 2.739 2.732 125.1. 126.25 2.382 97 1. 500 87.1 1.581 87.7.6 2.835 2.811. 2.825 2.830 2.826 130.3 129.7 2.685 2.682 2.686 2.705 2.673 2.713 2.769 2.800 2.782 2.729 2.791 2.790 1.27.1 128.1 2.1.19 1.2 5 500 86.9 1.572 87.1..5 2.881. 2.865 2.879 2.880 2.877 131.9 131.1. 2.707 2.712 2.716 2.729 2.698 2.739 2.798 2.832 2.814. 2.755 2.822 2.815 128 129.7 2.1.32 12 6 500 89.7 1.653 90.1.1. 3.120 2.960 2.989 3.050 3.030 137 136.6 2.81.0 2.863 2.81.6 2.81.7 2.810 2.862 2.992 3.009 2.972 2.892 2.963 2.952 132.9 131..1 2,538 22 7 500 88.3 1.611. 88.8.5 3.150 2.961. 3.020 3.080 3.051 137.7 137.2 2.851 2.879 2.866 2.860 2.828 2.875 2.989 3.021 2.996 2.912 2.981 2.967 133.3 135.3 2.550 22 8 750 83.6 1.1.83 81..1.5 3.31.8 3.223 3.21.2 3.275 3.272 11.5.1. 11.1.9 3.153 3.159 3.165 3.203 3.159 3.221 3.151. 3.2CR 3.11.8 3.161 3.218 3.179 11.2.2 11.3.5 2.632 0 9 750 81. 1.501 81..7.7 3.181. 3.110 3.128 3.150 3.11.3 11.1.1 11.0.1. 2.967 2.917 2.972 2.993 2.978 3.01.0 3.01.1 3.0o63 3.085 3.031 3. 110 3.098 136.8 138.6 2.588 12 10 750 81..8 1.519 85.3. 5 3.218 3.121 3.138 3.179 3.161. 11.1.8 11.1.3 2.976 2.912 2.958 3.012 2.985 3.029 3.057 3.083 3.063 3.01.1 3. 110 3.107 137 139.2 2.597 72 11 750 85.2 1.537 85.9.7 3.221. 3.189 3.199 3.200 3.203 11.3.1 11.2.1. 2.976 2.922 2.978 3.023 2.988 3.031. 3.088 3.120 3.1C2 3.072 3.138 3.130 137.7 11.0 2.611. 1R 12 750 85.6 1.51.0 86.1. 3.265 3.207 3.220 3.288 3.21.5 l141.5 11.1.1 2.993 2.951 3.008 3.01.5 3.009 3.057 3.1.70 3.162 3.11.8 3.108 3.172 3.160 138.8 141.1.5 2.61.4 13 13 750 85.6 1.51.0 86.1. 3.298 3.238 3.286 3.318 3.285 11.5.6 11.5.2 3.026 2.997 3.01.9 3.076 3.01.3 3.091 3.173 3.217 3.202 3.158 3.218 3.196 11.0.3 14.2.7 2.672 13 11. 750 85.7 1.51.9 86.3.6 3.371 3.289 3.31.3 3.1.09 3.353 11.8.1 11.7.5 3.082 3.066 3.121 3.131. 3.100 3.150 3.21.1 3.290 3.278 3.221. 3.281. 3.259 11.2.6 11.5 2.720 23 15 750 86 1.558 86.6.6 3.4.23 3.34.7 3.1.10 3.1.72 3.1.13 150.1 11.9.5 3.163 3.121 3.185 3.206 3.152 3.212 3.333 3.368 3.350 3.266 3.355 3.353 l144.8 11.7.1 2.751. 212 16 750 85.1 1.531 85.7.6 3.4.87 3.388 3.1.39 3.1.8 3.1.49 151.3 150.7 3.198 3.160 3.227 3.238 3.168 3.21.5 3.370 3.41.11 3.41.11 3.312 3.1.05 3.398 11.6.2 11.8.1. 2.768 28 17 1000 81..5 1.516 85.2.7 3.71.2 3.663 3.701 3.731. 3.710 160 159.3 3.551. 3.51.9 3.577 3.622 3.566 3.61.1 3.51.9 3.601. 3.51.7 3.565 3.632 3.588 155.7 157.5 2.977 0 18 1000 88.7 1.629 89.3.6 3.711. 3.657 3.688 3.673 3.683 159.1 158.5 3.1.90 3.1.28 3.1.28 3.510 3.5CR 3.51.8 3.5CR 3.51.0 3.500 3.518 3.600 3.593 153.1. 155.7 2.938 12 19 1000 87 1.581 87.7.7 3.701 3.629 3.628 3.656 3.656 158.2 157.5 3.31.5 3.283 3.31.1 3.1.11 3.362 3.1.26 3.1.65 3.1.98 3.1.82 3.1.55 3.51.0 3.538 150.7 151..1 2.888 97 20 1000 88.5 1.629 89.3.8 3.811, 3.761. 3.773 3.796 3.786 162.55 161.75 3.371. 3.362 3.1.12 3.1.53 3.1.00 3.1.70 3.557 3.610 3.591 3.538 3.621 3.600 152.8 157.6 2.941. 1.2 21 1000 86 1.567 86.9.9 3.861. 3.829 3.81.2 3.861 3.81.9 164.65 163.75 3.1.62 3.350 3.1.76 3.526 3.1.61 3.528 3.61.8 3.678 3.693 3.583 3.682 3.703 155.3 159.6 2.998 2R 22 1000 83.9 1.1.98 81..6.7 3.885 3.81.1 3.862 3.873 3.866 165.2 164.5 3.1.89 3.369 3.522 3.563 3.503 3.566 3.698 3.3 3.758 3.650 3.737 3.752 156.8 160.9 3.01.8 23 23 1000 83.9 1.501 86.7.8 4.0CR1 3.987 4..00i 4..004. 4.004. 169.8 169 3.608 3.1.57 3.639 3.669 3.605 3.669 3.833 3.852 3.882 3.763 3.850 3.868 160.1. 165.2 3.137 32 21. 1250 84.9 1.522 85.1..5 4.0o81 4..045s 4.057 4..070 1..064. 171.8 171.3 3.87 3.862 3.903 3.953 3.879 3.971. 3.876 3.91.7 3.890 3.891 3.977 3.928 166.9 169.1 3.1, 0, 25 1250 85.9 1.558 86.6.7 3.91.9 3.916 3.930 3.91.5 3.935 167.5 166.8 3.750 3.700 3.717 3.808 3.759 3.831. 3.816 3.861 3.820 3.817 3.926 3.915 163.2 165 3.071 12 26 1250 86.2 1.56 87.8 4.0CR2 1..007 4.009 1.0o14 1.0o13 170.1 169.3 3.767 3.773 3.71.7 3.810 3.763 3.850 3.871. 3.950 3.901. 3.853 3.981 3.959 166.7 166 3.082 62 27 1250 87 1.587 87.9.9 4..053 4.0.o2 4.0CR8 1.0o13 4..034. 170.8 169.9 3.750 3.777 3.753 3.810 3.750 3.81.6 3.908 3-8 3.91.2 3.872 1..00 3.977 165.1 167.5 3.098 82 28 1.250 87 1.581. 87.8.8 4.07T6 4..034. 4.01.8 4..068 4..056 171.1. 170.6 3.768 3.811 3.790 3.832 3.770 3.867 3.960 1.01.2 3.998 3.919 1.01.5 1.0o12 166.1. 168.5 3.127 1R 29 1250 87.8 1. 61 88.7.9 4..134. 4.098 4..107 1..109 4..112 173.1. 172.5 3.785 3.81.3 3.822 3.851. 3.791 3.890 4.0o02 4.OB 1.01.2 3.955 4..08o 1.01.0 167.5 170 3.150 12 30 1250 88.8 1.61.1 89.7.9 1..286 1..21.8 1.261. 1..266 1..266 178.1. 177.5 3.805 3.868 3.849 3.875 3.811 3.908 1.01.0 4.129 4..081. 3.992 4..112 4..061 168.5 173 3.168 1.2 31 1250 88.2 1.617 88.9.7 4.45.3 1..398 1..399 4.41.1 4.391 182.7 182 3.850 3.920 3.900 3.921 3.855 3.953 1.112 4.198 1.156 4.056 4.172 1..1l5 170.1.0 176 3.210 12 32 1500 88 1.611. 88.8.8 1..188 4.44.12 1..162 1..172 1..166 185.2 166.1. 1..227 1.223 1..287 4..330 4.24.2 4.352 1..21.2 1..323 1..273 4.21.9 1..31.5 1..297 179 181.7 3.31.3 0 33 1500 88.3 1.629 89.3 1.0 4..318 1..299 4..301. 1.3o7 4..307 179.9 178.9 4.037 3.885 3.963 4..106 4.0o58 1..129 1..085 4.078 4.061 41..oo 4.182 4..19l 172.3 175.6 3.262 12 31. 1500 86.9 1.59 88 1.1 1..307 1..276 1..282 4.297 1..289 179.3 178.2 3.905 3.751. 3.888 4.0CR3 3.91.1 4..CR3 1.01.9.019 4.039 1.01.9 4.136 41..62 169.6 173.9 3.22 2 35 1500 89 1.65 90 1.0 1..389 1..358 1..372 4.385 1..376 182.2 181.2 3.91.8 3.890 3.978 4.0o78 3.990 4.090 4..158 4.185 4.183 4.150 1..265 4.261 172.8 177 3.280 1R 36 1500 89.1 1.656 90.2 1.1 1..535 4.514. 4.519 4.525 1..523 187.1 186 4.012 4.013 4.o62 4.133 4.05o 4.157 4.263 4.331 4.313 4.250 4.372 1.31.5 176 181 3.333 12 37 1500 90.7 1.701. 91.8 1.1 4..883 4.841 1..860 4.866 4.862 188.1. 187.3 4.230 4.282 4.268 4.282 4.148 4.300 4.660 4.677 4.613 4.400 1..587 4.570 182.7 185 3.386 17.

TABLE III5 (CONTID) TEMPERATURE DATA: SERIES B Bearing Thermcoule2 Readings - mv Calibrating Journal TheroouplOeB Readings Average oiin-0 Psto 3Psto 1Psto Speed Amb8ent TherocBouple Correc- Temperature Csorreted Housing Pot~ B6to 150110Run N Cemp. tion 1 2 3 4 Tj Temp. T2 6 7 8 9 2.0 51 22 23 12 2.5 16 2.7 Average Tomp. Load NO. rpm ~F so. -F ~ F so. M.o. msv. MV. sV. -F.F TB Tav soV. lbs. 38 580 81.2 1.188 81.2 B 3.886 3.746 3.754 3.812 3.8B7 163.2 163.2 3.664 3.718 3.7BB 3.790 3.668 3.782 3.6624 3.759 3.695 3. 673 3. 782 3.75B 168.1 161.8 3.682. B 39 508 81.8 1.51B 85 B.B B.557 3.622 3.582 3.584 3.586 155.9 155.7 3.362 3.260 3.361 3.438 3.357 3.432 3.153 3.518 3. 517 3.131 3. 536 3.5 7 150.9 153.1 B.898 lB7 18 588 81.1 1.5B1 81.7 B.3 3.524 3.509 3.501 3.511 3.35.2 153.1 153.1 3.241 3.221 3.213 3.284 3.256 3.276 3.152 3.426 3.4202 3.398 3.117 3.4056 147.1 150.25 2.922 835 11 500 85.8 1.552 86.1 B.6 3.637 3.626 3.620 3.624 3.6267 157.B 156.6 3.37B 3.B88 3.188 3.458 3.382 3.456 3.508 3.58B 3.582 3.482 3.B590 3. 608 155 151.3 B.968 1136 42 588 86.6 1.561 86.8 B.B 3.761 3.767 3.754 3.763 3.761 161.7 161.5 3.440 3.379 3.171 3.583 3.448 3.5B8 3.578 3. 659 3.657 3. 549 3.667 3. 679 154.8 158.1 2.997 BB36 13 soo 86.1 1.555 86.5 B.1 3.790 3.791 3.788 3.792 3.791 165.7 162.6 3.459 3.108 3.586 3.539 3.472 3.547 3.631 3.715 3. 715 3.608 3.722 3.7B8 155.8 159.2 3.002 2610 44 500 86.1 1.558 86.6 B.B 3.882 3.87B 3.829 3.907 3.871 165.1 165.2 3.601 3.588 3.596 3.636 3.586 3.656 3.7B8 3.825 3.811 3.7B3 3.853 3.766 159.1 162. 3 3.01S 3537 15 758 88.2 1.518 86.2 0 1.173 4.179 1.161 1.178 4.171 175 175 3.922 3.950 3.985 4.059 3.933 4.055 3.919 4I010 3.914 3. 938 4.B5o 4.o18 169 172 3.263 B 16 758 88.6 1.56 87 8.1 3.922 3.903 3.872 3.863 3.890 166 165.6 3.621 3.582 3.585 3.817 3.790 3.866 3.858 3.870 3.829 3.594 3. 633 3. 679 16o2. 169 3.174 157 17 758 87.1 1.581 87.8.1 3.855 3.851 3.792 3.801 3.818 163.6 163.2 3.516 3.338 3.517 3.638 3.158 3.600 3.655 3.685 3. 698 3.632 3.729 3.779 156.6 165 3.815 835 48 758 87.1 1.581 87.8.4 3.906 3.900 3.88 3.86 3.886 165.9 165.5 3.516 3.33 3.537 3.631 3.533 3.613 3.712 3.711 3.763 3. 669 3.778 3.858 157.5 161.5 3.958 1136 19 758 88 1.586 88.2 0.2 4.819 4.029 3.952 3.912 3.985 169.5 169 3.610 3.413 3.675 3.739 3.658 3.714 3.885 3.899 3.938 3.822 3.906 3.958 165 165.5 3.177 5836 50 750 87.8 1.591 88.05 8.55 4.029 4.026 3.971 3.968 3.999 169.35 169.1 3.703 3.178 3.727 3.761 3.681 3.748 3.948 3.965 4.008 3.868 3. 963 1.08 163. 7 166.1 3.185 2658 51 758 88.8 1.593 88.10 8.18 1.112 1.161 3.981 3.956 1.060 171.7 171.6 3.717 3.677 3.761 3.803 3.698 3.885 1.811 4.o64 1.o61 3.885 4.o15 1.859 165.8 168.7 3.283 3537 52 1808 87.7 1.587 87.9.2 4.572 1.578 1.562 4.568 1.568 188.6 188.1 4.279 1.387 1.317 4.122 1.288 4.426 4.271 41.364 1.297 1.598 1.118 4.368 181 181.7 3.492 8 53 1888 89.3 i.611 89.8.5 4.393 1.335 1.342 1.338 1.351 181.1 185.9 1.025 3.858 3.968 4.114 1.o18 1.118 4.o18 1.681 1.875 1.872 1.171 1.285 171.8 176.3 3.311 157 51 1080 88 1.59 88 8 1.186 1.161 1.151 1.187 1.152 171.1 171.1 3.79 3.543 3.788 3.919 3.818 3.907 3.917 3.938 3. 979 3.952 4.033 4.085 166. 3 178.3 3.568 987 55 1000 98.5 1.665 98.5 8 1.378 1.353 1.315 1.365 4.359 181.6 181.6 3.858 3.613 3.879 3.999 3.929 3.992 1.086 4.896 4.147 4.093 4.163 4.197 169.6 175. 6 3.413 1157 56 1000 88.6 1.65 89.1 1.399 4.379 4.389 1.381 1.387 185.6 185.2 3.883 3.55 3.883 1.885 3.919 3.980 4.140 1.139 1.196 1.8090 1.176 4. 198 178 176.1 3.10 5885 57 1808 88.6 1.635 89.1.8 1.503 1.191 1.581 4.49o 4.497 188 185.2 3.918 3.685 3.969 1.868 3.968 1.018 1.553 1.238 1.-3o6 1.165 4.258 1.319 175.8 179 3.150 2756 \J 58 looo 88.7 1.632 89.1.7 4.638 1.851 1.619 1.610 4.,629 198.6 189.9 1.171 3.809 1.288 1.260 4.171 4.241 1.185 1.185 4.561 4.386 4.485 1.535 185 181.9 3.658 3159 59 1550 87 1.56 87 0 1.885 1.878 1.796 4.819 1.858 197.2 197.2 4.489 1.158 1.521 4.616 1.505 1.62-2 1.186 1.551 1.185 1.5o6 4. 60o 1.557 187.1 192.3 3.713 8 68 2250 87 1.575 87.1.1 1.510 1.538 4.529 1.519 1.531 187.1 187 1.187 3.930 41.27 1.268 1.235 1.278 4.233 1.508 1.553 4.278 1.31 4.372 177.5 185. 1 3.569 157 61 1250 88.2 1.566 87.2 1.0 1.508 1.185 1.173 1.198 1.189 188 185 3.978 3.698 3.988 1.118 1.o68 1.113 4.168 41.225 1.205 1.192 1.218 4.290 173 179 3.511 835 68 1250 88.3 1.659 89.3 1.0 1.603 4.609 1.687 4.605 1.6o6 199.9 188.9 1.098 3.892 1.138 1.256 1.500 1.567 4.316 41.369 1.122 1.385 1.452 4.447 178.7 183.8 3.698 1136 63 1250 89 1.656 98.2 1.2 1.738 1.768 1.751 1.776 1.757 191.8 193.6 4.181 4.012 1.515 1.328 1.231 4.296 1.587 1.557 1.588 1.522 1.580 1.558 185.1 188 3.898 2036 61 1250 88.9 1.587 87.9 1.0 1.858 4.679 4.759 1.878 1.811 196.7 195.7 1.561 4.061 4.327 1.358 1.317 1.375 4.611 4.618 1.661 4.6oo 1.653 4.598 181.7 189.2 1.883 5618 65 1500 87.9 1.598 88 0.1 5.131 5.218 5.150 5.181 5.i68 268.6 268.5 4.767 1.725 1.851 1.981 1.788 1.988 4.769 1.831 1. 768 4.787 1.885, 1.837 198.7 200.6 3.875 8 66 1500 88.3 1.635 89.1 1.1 1.897 1.913 1.985 4.955 4.925 288.5 199.1 1.397 1.569 1.198 4.574 5.558 4.566 4.511 1.518 1.555 1.587 1.688 4.636 187.4 193.1 3.611 157 67 1588 88.8 1.638 89.6 0.8 1.817 1.891 1.881 4.889 1.877 198.9 198.1 1.213 4.187.5224 4.420 4.402 1.126 1.171 1.185 4.183 4.512 1.585 1.568 183.5 198.8 3.198 835 68 1500 89.5 1.659 98.3.8 1.983 4.910 1.919 4.932 4.916 288.2 199.1 1.241 1.203 4.261 4.432 4.419 1.439 4.559 1.561 1.575 1.657 4.658 1.635 185.2 198.3 3.522 1136 69 1588 89.8 1.671 98.8 1.0 5.001 4.997 5.088 5.818 5.006 203.2 200.2 1.311 4.245 4.356 1.578 1.561 1.583 1.681 4.695 1.722 1.781 4.821 1.798 189.3 195.8 3.589 2036 70 1500 89.9 1.671 98.7 0.8 5.110 5.168 5.112 5.226 5.111 568.8 206 1.117 1.325 4.176 1.611 1.588 1.658 4.767 1.771 1. 793 4.875 4.921 4.883 192 199 3. 677 2618 71 1588 91.2 1.713 98.1 0.9 5.257 5.245 5.278 5.288 5.267 211.9 211 1.198 1.388 4.583 4.676 1.658 1.711 5.008 5.811 5.047 5.869 5.222 5.879 197 581 3.725 3537 TEMPERATURE DATA: 088100 C Journal Theroouosople Readings Average Bearinlg Theroousople Readinsg -m.v Spoed Ambient Thormoosuplo Correos- Tomporaturo Corrected Postin -0 osiio - 3 Positisn - 1 Average Housin Ran N Coop. tion 1 2 3 4 Tj Temp. Tj 6 7 8 9 18 11 22 13 14 15 16 17 TB Tav Comp. No. rpm m2.v. -F -F sov. m.v. MsV, ms. M.. F Fo.. -F M.V 75 752 75 1.232 75.1.4 2.124 2.o65 2.107 2.122 5.100 105.1 185 2.851 2.o18 2.810 2.118 5.090 2.130 1.974 2.01 1.988 5.008 2.050 1. 988 2.8033 103 181 1.675 73 1888 75.6 1.256 76.5.6 5.187 2.377 2.391 2.188 2.395 115.5 111.9 5.358 2.295 2.388 2.395 2.377 2.417 2.25 2.261 2.229 2.281 5.310 2.238 5.295 1122.1 1.13.5 1.888 71 1258 76.6 1.289 77.3.7 5.783 2.671 2.691 2.699 2.691 225.7 225 2.651 2.681 2.621 2.729 2.709 2.752 2.520 2.570 2.133 2.598 2.633 2.543 2.613 223 1221 2.113 75 1500 77.5 1.308 78.5 1.8 2.593 2.562 2.577 2.588 5.588 222 221 2.445 2.372 2.410 2.395 2.407 2.430 2.410 2.427 2.190 2.388 2. 362 2.375 2.381 115 118 1.468

TABLE IV OIL FLOW DATA: SERIES A Speed Oil Outlet Thermocouple Readings Avg. Outlet Inlet Oil Inlet Oil Oil ~~~~~~~~Run N ~Oil Temp. Thermocouple Temp. Flow Rate No. rpm m.v. m.v. m.v. ~F Reading F lb/hr. m.v. 1 500 2.474 2.478 2.476 118.2 1.534 85.8 1.2 ~2 500 2.454 2.492 2.473 118.1 1.546 86.2 2.95 3 500 2.489 2.517 2.503 119.1 1.549 86.3 3.80 ~4 500 2.502 2.522 2.512 119.4 1.558 86.6 4.2 5 500 2.512 2.528 2.52 120 1.564 86.8 4.35 6 500 2.518 2.546 2.532 120.4 1.561 86.7 4.50 ~7 500 2.531 2.569 2.550 121.0 1.564 86.8 4.65 8 750 2.797 2.843 2.820 130 1.468 83.6 1.59 9 750 2.782 2.828 2.805 129.5 1.495 84.5 3.5 10 750 2.789 2.809 2.799 129.3 1.516 85.2 3.96 ~~11 750 2.792 2.818 2.805 129.5 1.528 85.6 4.6 12 750 2.741 2.779 2.76 128 1.537 85.9 4.98 13 750 2.788 2.816 2.802 129.4 1.546 86.2 5.48 14 750 2.794 2.840 2.817 129.9 1.549 86.3 5.4 15 750 2.832 2.868 2.850 131 1.560 87 5.61 16 750 2.820 2.850 2.835 130.5 1.546 86.2 5.64 17 1000 3.174 3.226 3.200 143 1.495 84.5 1.95 18 1000 3.015 3.081 3.048 137.6 1.522 85.4 3.8 19 1000 2.989 3.019 3.004 136.1 1.513 85.1 4.65 20 1000 3.021 3.087 3.054 137.8 1.522 85.4 5.49 21 1000 3.024 3.066 3.045 137.5 1.510 85 5.75 22 1000 3.011 3.031 3.021 136.7 1.477 83.9 5.97 23 1000 3.030 3.072 3.051 137.7 1.495 84.5 6.22 24 1-250 3.401 3.425 3.413 150.2 1.507 84.9 2.325 25 1250 3.321 3.367 3.344 147.8 1.510 85 4.05 26 1250 3.318 3.322 3.320 147 1.534 85.8 4.80 27 1250 3.219 3.241 3.230 144 1.531 85.7 5.40 28 1250 3.244 3.294 3.269 145.3 1.540 86 5.60 29 1250 3.272 3.296 3.284 145.8 1.540 86 5.88 30 1250 3.291 3.331 3.311 146.7 1.552 86.4 6.0 31 1250 3.199 3.211 3.205 146.5 1.540 86 6.3 32 1500 3.641 3.689 3.665 158.5 1.590 88 2.64 33 1500 3.521 3.665 3.593 156.1 1.593 88.1 4.72

-107TABLE IV (CONT' ) OIL FLOW DATA: SERIES B Speed Oil Outlet Thermocouple Readings Avg. Outlet Inlet Oil Inlet Oil Oil Run N Oil Temp. Thermocouple Temp. Flow Rate No. rpm m.v. m.v. m.v. ~F Reading OF lb/hr m.v. M.V 38 500 3.295 3.405 3.35 148 1.486 84.2 1.48 39 500 3.224 3.362 3.293 146.1 1.486 84.2 3.75 40 500 3.198 3.220 3.209 143.3 1.480 84 4.75 41 500 3.214 3.330 3.272 145.4 1.501 84.7 5.25 42 500 3.327 3.403 3.365 148.5 1.510 85 5.30 43 500 3.400 3.438 3.419 150.3 1.519 85.3 5.40 44 500 3.425 3.509 3.467 151.9 1.516 85.2 5.50 45 750 3.597 3.607 3.602 156.4 1.546 86.2 2.05 46 750 3.449 3.533 3.491 152.7 1.549 86.3 4.4 47 750 3.451 3.477 3.464 151.8 1.561 86.7 5.4 48 750 3.498 3.526 3.512 153.4 1.561 86.7 5.83 49 750 3.548 3.596 3.572 155.4 1.564 86.8 6.1 50 750 3.602 3.644 3.623 157.1 1.561 86.7 6.25 51 750 3.619 3.645 3.632 157.4 1.552 86.4 6.65 52 1000 3.866 3.914 3.890 166 1.552 86.4 2.33 53 1000 3.744 3.790 3.767 161.9 1.567 86.9 5.15 54 loo1000 3.858 3.898 3.878 165.6 1.558 86.6 6.15 55 1000 3.908 3.950 3.929 167.3 1.587 87.9 6.65 56 1000 3.933 3.979 3.956 168.2 1.566 87.2 6.85 57 1000 3.964 4.014 3.989 169.3 1.563 87.1 7.05 58 1000 4.002 4.o24 4.013 170.1 1.563 87.1 7.25 59 1250 4.008 4.192 4.100 173 1.560 87 2.92 60 1250 3.829 3.879 3.854 164.8 1.563 87.1 5.50 61 1250 3.767 3.815 3.791 162.7 1.560 87 6.90 62 1250 3.859 3.909 3.884 165.8 1.566 87.2 7.40 63 1250 3.941 3.995 3.958 168.6 1.578 87.6 8.1 64 1250 3.962 3.998 3.980 169 1.560 87 8.3 65 1500 4.237 4.287 4.262 178.4 1.599 88.3 3.44 66 1500 3.974 4.016 3.995 169.5 1.605 88.5 6.10 67 1500 4.010 4.046 4.028 170.6 1.608 88.6 7.35 68 1500 4.101 4.153 4.127 173.9 1.617 88.9 8.15 69 1500 4.149 4.249 4.199 176.3 1.617 88.9 8.5 70 1500 4.201 4.245 4.223 177.1 1.62 89 8.75 71 1500 4.304 4.346 4.325 180.5 1.65 90 8.8 OIL FLOW A1D WATER FLOW DATA SERIES C Speed Oil Flow Outlet Oil Thermocouple Readings Outlet Oil Temp. Inlet Oil Temp. WAter Flow Outlet Water Inlet Water Run N Rate Rate Temp. Temp. No. rpm lb/hr m.v. m.v. m.v. ~F m.v. ~F lb/hr m.v. OF m.v. ~F 72 750 1.09 1.700 1.688 1.694 91.5 1.175 73.5 29.1 1.80 95.838 61.6 73 1000 1.50 1.915 1.878 1.896 98.5 1.193 74.1 29.2 2.147 106.9.805 60.5

TABLE V CALCULATION OF THE SOMMERFELD NUMBER, THE LOAD NUMBER. AND THE ECCENTRICITY RATIO SERIES - A Run N N' Tav x 10-7 W p Cd nlO-3 d 2 d 2 No. rpm rps ~ F C.S. Reyn. lbs. lbs/in2 in. T-X x O5 S./ n 1 500 8.34 2.8 54 67.2 12.83.855 6.13 4.98 2.48 16.25.0616 0 2 500 8.34 125.5 59 73.4 427 28.5 6.13 4.98 2.48.533 1.878.17 3 500 8.34 126.3 57 70.9 927 61.8 6.13 4.98 2.48.237 4.22.33 4 500 8.34 128.4 54 67.2 1427 95 6.13 4.98 2.48.1462 6.84.425 5 500 8.34 129.7 53.3 66.3 1727 115 6.13 4.98 2.48.1192 8.4.48 6 500 8.34 134.7 48 59.8 2127 141.8 6.13 4.98 2.48.0873 11.47.54 7 500 8.34 135.3 47 58.5 2627 175 6.13 4.98 2.48.069. 14.5.58 8 750 12.5 143.5 40 51 12.83.855 6.26 4.80 2.30 20.10.0498 0 9 750 12.5 138.6 45 56 427 28.5 6.26 4.80 2.30.565 1.77.170 10 750 12.5 139.2 44 54.8 727 48.5 6.26 4.80 2.30.325 3.08.26 11 750 12.5 140 43 53.55 1029 68.65 6.26 4.80 2.30.224 4.46.34 12 750 12.5 141.45 42 52.1 1330 88.6 6.26 4.80 2.30.169 5.92.40 13 750 12.5 142.7 41 51 1630 208.75 6.26 4.8 2.3.1348 7.42.45 14 750 12.5 145 39 48.6 2030 135.2 6.26 4.8 2.3.1031 9.7.505 15 750 12.5 147.1 37.5 46.64 2429 162 6.26 4.8 2.3.0827 12.1.545 16 750 12.5 148.4 37 46 2780 185 6.26 4.8 2.3.0714 14.57 17 1000 16.67 157.5 31 38.6 12.83.855 6.36 4.72 2.225 16.74.0598 0 18 1000 16.67 155.7 32 39.8 427 28.5 6.36 4.72 2.225.516 1.94.175 2.9 2.000 2.6.67 1.56.1 32.8 60.8 927 61.8 6.36 6.72 2.225.2667 6.09.32. 20 2.000 2.6.67 2.57.6 32. 38.6 2.627 95 6.36 6.72 2.225.2.505 6.65.61' 21 2.000 2.6.67 159.6 30 37.35 2027 2.35 6.36 6.72 2.225.2.025 9.75.51 22 2.000 2.6.67 2.60.9 29.6 36.6 2632. 2.75.5 6.36 6.72 2.225.0776 12.92.56 23 2.000 2.6.67 2.65.2 27 33.6 3329 222 6.36 6.72 2.225.0561. 17.82..61.5 26 1250 20.82. 2.69.2. 25 31.2. 12.83.855 6.636 6.665 2.2.75 2.6.5.0606 0 25 1250 20.82. 2.65 27 33.6 627 28.5 6.636 6.665 2.2.75.526 1.90.18 26 1250 20.82. 166 26.5 33 625 61.6 6.636 6.665 2.175.359 2.785.25 27 1250 20.82. 2.67.5 26 32.6 826 55.2. 6.636 6.665 2.2.75.266 3.76.305 28 1250 20.82. 2.68.5 25.5 31.75 2.027 68.5 6.636 6.665 2.2.75.22.0 6.76.36 29 1250 20.82. 2.70 25 31.2. 1227 81.8 6.636 6.665 2.2.75.2.72 5.82..397 30 1250 20.82. 2.73 23.5 29.25 2.627 95 6.636 6.665 2.2.75.2.392 7.2.7.665 32. 1250 20.82. 2.76 22 27.35 2.929 128.3 6.636 6.665 2.175.0965 10.6.520 32 2.500 25 181.7 20.5 25.5 12,.83.855 6.698 6.62 2.2.3 15.9.0629 0 33 2.500 25 2.75.6 22.5 28 627 28.5 6.698 6.62 2.2.3.526 1.92..2.87 36 2.500 25 2.73.9 23.5 29.25 726 68.6 6.698 6.62 2.2.3.322 3.108.27 35 2.500 25 2.77 21.5 26.75 2.028 68.55 6.698 6.62 2.2.3.208 6.82..36 36 2.500 25 182. 20.5 25.5 2.529 2.02 6.698 6.62 2.2.3.2.332 7.50.655 37 2.500 25 185 2.9.3 26 2.769 12.6.2 6.498 6.62 2.13.2.10 9.10.50

-109TABlE V (CONT'In) CAWUTATION OF THE SO2MERFELD INUMBER, THE LOAD NUNMBER, AND TwE ECCENTRICITY RATIO SERIES - B Run N N' Tav x l1-7 W P cdX d d 2 No. rpm rps ~F C.S. Reyn. lbs. lbs in2 in. Tdx 102 (a)105 S 1/S n 38 500 8.34 161.8 28.85 35.9 12.83.855 6.335 4.745 2.25 7.9.127 0 39 500 8.34 153.4 34 42.3 427 28.5 6.335 4.745 2.25.2785 3.59.27 40 500 8.34 150.25 35 43.6 835 55.7 6.335 4.745 2.25.147 6.8.435 41 500 8.34 154.3 33 41.1 1436 95.6 6.335 4.745 2.25.0806 12.4.555 42 500 8.34 158.1 30.6 38.1 2036 135.7 6.335 4.745 2.25.0528 19.0 6.3 43 500 8.34 159.2 30 37.4 2640 176 6.335 4.745 2.25.0398 25.1 6.7 44 500 8.34 162.3 28.5 35.5 3237 215 6.335 4.745 2.25.031 32.3 7.09 45 750 12.5 172 24 29.8 12.83.855 6.44 4.66 2.17 9.44.106 0 46 750 12.5 163 27.5 34.2 427 28.5 6.4k 4.66 2.17.326 3.076.266 k7 750 12.5 160 29.5 36.7 835 55.7 6.4k 4.66 2.17.1783 5.64.392 k8 750 12.5 161.5 28.5 35.45 1436 95.6 6.44 4.66 2.17.1005 9.95.51 49 750 12.5 165.5 26.5 33 2036 135.6 6.44 4.66 2.17.066 15.15.59 50 750 12.5 166.4 26.3 32.7 2640 176 6.44 4.66 2.17,0504 19.87.632 51 750 12.5 168.7 25.5 31.74 3237 215 6.44 4.66 2.17.0k0 25.67 52 1000 16.67 183.75 19.8 24.6 12.83.855 6.55 4.58 2.1 10 0.10 0 53 1000 16.67 176.3 22.5 28 427 28.5 6.55 4.58 2.1.276 3.62.3 54 1000 16.67 170.3 24.7 30.8 927 61.8 6.55 4.58 2.1.14 7.15.445 55 1000 16.67 175.6 22.7 28.25 1k27 95 6.55 4.58 2.1.0835 12.55 56 1000 16.67 176.1 22.5 28 2OA-5 135 6.55 4.58 2.1.0583 17.15.612 57 1000 16.67 179 21 26.15 2726 181.8 6.55 k.58 2.1 okok 2k.75.668 58 1000 16.67 i8k.9 19.6 24.k 3k29 228.5 6.55 k.58 2.1.03 33.3.713 59 1250 20.81 192.3 17.5 21.8 12.82.855 6.55 k.56 2.079 11.0k.0905 0 60 1250 20.81 182.1 20 24.9 k27 28.5 6.55 k.56 2.079.3786 2.6k.2k 61 1250 20.81 179 21 26.1 835 55.7 6.55 k.56 2.079.203 k.938.365 62 1.250 20.81 183.8 19.5 2k.25 1436 95.6 6.55 4.56 2.079.11 9.1.k92 63 1250 20.81 188 18.5 23 2036 135.7 6.55 k.56 2.079.0735 13.62.570 6k 1250 20.81 189.2 18.2 22.75 26k0 176 6.55 4.56 2.079.056 17.88.62 65 1500 25 202A.6 15 18.65 12.83.855 6.66 k.5 2.03 11.08.093 0 66 1500 25 193.4 17.1 21.3 k27 28.5 6.66 k.5 2.03.379 2.6k.2k 67 1500 25 190.8 18 22.k 835 55.7 6.66 4.5 2.03.20k k.9.37 68 1500 25 192.3 17.5 21.78 1k36 95.6 6.66 k.5 2.03.11k6 8.65.k9 69 1500 25 195.8 16.75 20.82 2036 135.7 6.66 4.5 2.03.0781 1L2.8.56 70 1500 25 199 15.9 19.8 2640 176 6.66 k.5 2.03.0571 17.5.615 71 1500 25 20k 1k.7 18.3 3237 215 6.66 4.5 2.03.0k33 23.1.656

-110TABLE VI SUMMARY OF CORRELATION CAICULATIONS SERIES A Speed Run N &T S 1/S n He H HO/Hp Hc/Hp H0+Hc Hj Hj/Hp jQ _N_ No. rpm OF BTU/hr BTU/hr BThr Hp c3p 500 1 500 42.2 16.25 O.0616 0 20 226 246.081.918.999 246 1 2.96 2 500 38.6.533 1.878.17 48.5 195 246.197.792.989 251.7 1.021.238 3 500 39.35.237 4.22.33 64.2 203 246.262.825 1.087 268.65 1.091.1363 4 500 41.3.1462 6.84.425 71.0 220 246.289.895 1.184 288.1 1.170.093 5 500 42.8.1192 8.4.48 74.4 231 246.303.938 1.241 301 1.222.0786 6 500 45.0873 11.47.54 78.0 249.5 246.317 1.012 1.329 320.5 1.300.0596 7 500 47 o0691 14.5.58 82.0 264.3 246.333 1.0715 1.404 336.8 1.370.0487 8 750 59.9 20.1.0498 0 38 372 410.0926.907.999 410 1 3.06 9 750 54.5.565 1.77.17 81 327 410.1975.7965.994 419.42 1.021.2478 10 750 54.4.325 3.08.26 90 326 410.2194.795 1.014 432.64 1.053.1622 11 750 54.8.224 4.46.34 104 328 410.2536.80 1.053 451.45 1.100.130 12 750 55.85.169 5.92.4 108 338 410.2634.825 1.088 469.4 1.144.106 13 750 57.1.1348 7.42.45 122 350 410.2978.854 1.151 489.8 1.191.093 14 750 59.3.1031 9.7.505 121 368 410.295.8965 1.191 514.65 1.252.0704 15 750 61.1.0827 12.1.545 127 388 410.310.946 1.256 537.5 1.308.0584 16 750 63.3.0714 14.57 128.5 404 410.314.985 1.299 556.2 1.355.0506 17 1000 73 16.74.0598 0 58.7 484.3 543.109.910 1.019 543 1 3.10 18 1000 67.516 1.94.175 102 439 543.1915.8075.999 551.68 1.012.21 19 1000 67.1.2447 4.09.31 122 440 543.227.81 1.037 58305 1.072 1 20 1000 69.1.1505 6.65.41 148 459.6 543.275.845 1.120 621.6 1.141.0876 21 1000 73.6.1025 9.75.51 155 500 543.288.920 1.208 678.9 1.249.0o628 22 1000 77.0774 12.92.56 162 535.7 543.301.984 1.285 721.75 1.328.0491 23 1000 81.3.0561 17.81.615 170 581.5 543.316 1.070 1.386 775.5 1.427.0372 24 1250 84.2 16.5.0606 0 81 606 687.1179.882 1.00 687 1.00 3.22 25 1250 79.1.526 1.90.18 131 559 687.211.814 1.025 704.1 1.025.2032 26 1250 79.8.359 2.785.25 151 561 687.233.815 1.048 721.05 1.049.162 27 1250 80.5.266 3.76.305 162 568 687.25.826 1.076 739.97 1.077.1352 28 1250 81.5.210 4.76.36 171 578 687.2675.841 1.108 761.95 1.108.1108 29 1250 82.2.172 5.81.397 181 589 687.279.856 1.135 780.75 1.136.095 30 1250 84.2.1392 7.17.445 186 607.5 687.294.884 1.178 809.55 1.179.0788 31 1250 88.8.0965 10.4.520 196 653 687.313.950 1.263 868.15 1.212.0570 32 1500 93.7 15.9.0629 0 94 707 801.1174.883 1.00 801 1.00 2.06 33 1500 87.3.524 1.91.187 165 640 801.206.799 1.005 821.63 1.025.210 341 I r1500 87.322 3.10.2ft 7 195~r 634l 80%1.243I.79 1.033 84.2 1.6l15

-111TABLE VI (CONT'D) SUMMARY OF CORRELATION CALCULATIONS SERIES B Speed Run N AT S /s n N Ho HN Ho/Hp Nc/Hp Ho+Hc N Nj/Hp LQ, N No. rpm ~F BT hr BTU/hr BTU/hr Np D 50 38 500 77.6 7.9.127 0 48.6 420 468.6.1037.9133 1.0170 468.6 1 1.76 59 500 68.6.2785 5.59.27 119.4 560 468.6.255.7682 1.0252 476.7 1.018.157 40 500 65.85.147 6.8.435 145 340 468.6.31.7255 1.0555 492.3 1.05.105 41 500 68.5.0806 12.4.555 164 360 468.6.350.7682 1.1182 515.4 1.094.0657 42 500 71.5.0528 19.0.63 173.3 382 468.6.570.8151 1.1851 53355.6 1.158.0422 45 500 72.8.0398 25.67 180.4 590 468.6.386.8322 1.2182 550.4 1.175.0525 44 500 75.9.031 52.5.709 188 412 468.6.401.8792 1.2802 566.9 1.210.0256 45 750 85.8 9.44.106 0 74.2 501 575.2.1289.8692.9981 575.2 1 2.35 46 750 76.4.526 3.076.266 150 420 575.2.2607.7501.9908 590 1.025.1752 47 750 72.6.1783 5.64.592 181 590 575.2.3146.6780 0.9926 609.4 1.058.117 48 750 74.1.1005 9.95.510 200 403 575.2.5477.7006 1.0485 642.1 1.114.071 49 750 77.5.066 15.15.59 215 428 575.2.5737.7440 1.1177 672.9 1.168.0489 50 750 78.4.0504 19.87.652 220.4 458 575.2.585.7614 1.1444 700.5 1.218.03815 51 750 81.040 25.670 243 460 575.2.4224.7997 1.2221 719.6 1.25.0323 52 1000 96 10 10 0 96.6 582.6 679.2.1422.8686 1.0108 679.2 1 2.42 53 1000 87.276 5.62.30 198.6 507 679.2.2924.7464 1.0388 703 1.033.182 54 looo1000 82.5.140 7.15.445 248 470 679.2.5651.6919 1.0570 756.2 1.082.1105 55 1000 85.1.0855 12.0.55 272 490 679.2.400.7214 1.1214 776.4 1.142.0715 56 looo00 87.5.0585 17.15.612 286 510 679.2.421.7508 1.1718 813.4 1.198.0514 57 1000 90.4.0404 24.75.668 299 558 679.2.44.7921 1.2321 855.2 1.258.05665 58 1000 96.2.05 533.5.715 502 580 679.2.444.8559 1.2979 895.2 1.518.0279 59 1250 105.5 11.04.0905 0 129 676.2 805.2.160.8520.9920 805.2 1 5.02 60 1250 95.1.578 2.64.24 220 577 805.2.275.7165.9895 827.5 1.028.1898 61 1250 92.8.203 4.938.365 269 558 805.2.334.6929 1.0269 865.8 1.075.1275 62 1250 95.5.110 9.1.492 300 580 805.2.5725.7205 1.0928 922.8 1.145.0757 63 1250 99.0.0735 13.62.570 338 610 805.2.420.7575 1.1775 977.7 1.212.0544 64 1250 102.3.056 17.88.620 350 635 805.2.455.7886 1.2256 1031.5 1.28.0424 65 1500 114.7 11.08.095 0 159.8 752.4 912.2.175.8245 0.9995 912.2 1 3.17 66 1500 105.1.379 2.64.24 254 680 912.2.2785.7454 1.0239 939 1.028.191 67 1500 102.204 4.9.57 312 640 912.2.542.7016 1.0456 982.9 1.076.124 68 1500 102.8.1146 8.65.49 557 645 912.2.591.7070 1.098 1052.8 1.152.0780 69 1500 106.0781 12.8.56 583 670 912.2.420.7344 1.1544 1117.2 1.222.0547 70 1500 109.1.0571 17.5.615 597 702 912.2.4355.7695 1.2050 1180.4 1.292.0412 71 1500 112.8.0433 25.10.656 410 750 912.2.450.8002 1.2502 1259.4 1.558.0332 SERIES C Speed Run N RV H0 Hw+Ho Hp Percentage No. rpm BTU/hr BTU/r T/hr BU BTU/hr Error 72 750 973 l0 983 1027 4.28 73 1ooo 1355 18,8 1575.8 1410 2.54

APPENDIX I EXACT SOLUTION OF EQUATION (2.6) FOR THE NO HEATING CASE Pe)' d28a e - = - Pr. E.6) 12 ~~Let ~Pr. E. = 12' 2 d28 1 2 E) e' = - -n q edy2 2 Multiplying both sides of the above equation by 2 d@ dY one gets: dY 2 d d28 Y = 2,I e-'e d( dY- dY Integrating both sides yields: (de)2 = 2 e-'e -2 A a S 71 2 (I.2) dY' where ~ is a constant of integration. Separating the variables and. multiplying both sidies of the above equation by n j- one gets: 2 2 =d ~ Y (I-3) - ~2 eP' 2 Integrating one gets: T1 ~~2 where b is a constant of integration. eP eB/2

-113~~and. a = 2 in I sin ( Y + P' t 2 This is the general solution of Equation (2.6). Boundary Conditions 1) atY =0 8 = 0 dB 2) Y = 1 -- =0 8- =1 dY Applying the first boundary condition on Equation (I-) one gets: sin 5 - (5) T1 Applying the second boundary condition gives: dB 2 l 2 cos (n + t( Y _Y=l sin (, + 5) which has 2 - 5. as a solution. 2 2 and. cos T1 =sinb=5 (I.6) 2 T From Equation (I-6)~, the values of b and.3 can be d~etermined. f or d~if ferent values of the nond~imensional number ri.The result of the calcula2 tions is shown in Table VII. To d~etermine the temperature d~if'ference between the journal and. bearing surfaces, the following substitution is mad~e in Equation (I-4) = 1 at Y l 1= n-sIn( -+B)

-114But (T - T) 2 Ti Tj - TB = 2 n sin (T I + )7) 2 The above equation was used in the determination of the temperature difference between the journal and the bearing surface. The result of the calculations is given in Table VII. It is noted that the results obtained, using the exact solution, are higher than those from the approximate theory represented in Chapter II. The maximum relative difference isabout 1 percent. This is due to the neglect of the higher order term in the linearization process of Equation (2.6). Comparison Between the Theoretical and Experimental Temperature Difference (Tj - TB) From Table VII', it is seen that the maximum experimental temperature difference is higher than the theoretical by about 20 percent. This discrepancy can be attributed to the following: 1. TIhe introduction of simplified assumptions, such as the neglect of the end leakage and the adoption of a linear velocity distribution, in carrying out the mathematical analysis. 2. The assumption that the clearance space is completely filled with oil is doubtful., especially when the oil is fed through a single hole in the bearing under low pressure. This explains the reason for the hi h values of the temperature difference (Tj - TBp) obtained experimentally.

-115TABLE VII CALCULATION OF THE TEMPERATURE DIFFERENCE (Tj - TB) N TJ- TB TJ- TB TJ- TB Percent rpm b /A Theoretical Exp. Approx. Difference 1 2 3 4 5 6 (5-4)/4 500 1.416 1.012 1.340 1.60 1.21 19.4 750 1.373 1. 021 2.28 2.70 2.25 19.5 1000 1.3 1.05 3.57 3.6 3.0o 6.84 1250 1.307 1.037 4.10 It.5 3.80 9.75 1500 1.287 1.04-2 4t.67 5.4 4t.38 15

BIBLIOGRAPHY 1. Barwell, F. T., Trans. A.S.M.E., 77, 1178 (1955). 2. Burwell, J. T., "Effect of Diametrical Clearance on the Load Capacity of a Journal Bearing," Trans. A.S.M.E., 64, 458, 1942. 3. Boyd, J. and Robertson, B. P., "Oil Flow and Temperature Relations in Lightly Loaded Journal Bearing," Trans. A.S.M.E., 70, 257-262, 1948. 4. Cameron, A., "Heat Transfer in Journal Bearings: A Preliminary Investigation," Proc. General Discussion on Heat Transfer, arranged by I.M.E. and A.S.M.E., 194-197, 1951. 5 Christopherson, D. G., "A New Mathematical Method for the Solution of Film Lubrication Problems," Proc. I.M.E., 146, 126, 1941. 6. Clayton, D., and Wilkie, M. J., "Temperature Distribution in the Bush of a Journal Bearing," Engineering, 166, 49, 1948. 7. Cope, W. F., "The Hydrodynamical Theory of Film Lubrication," Proc. Royal Society of London, Series A, 197, 201, 1949. 8. Cordullo F. E. "Some Practical Deductions from Theory of Lubrication of Short Cylindrical Bearings," Trans. A.S.M.E., MSP-52-12, 52, 143-153, 1930. 9. Dizioglu., B.., "Temperatur-,$ Zahigkeits-und Reibungsverhaltnisse in raschlaufenden Gleitlagern.," 50 Jahre Grenzschichtforschung,, F. Viewey and Sohn, 241, 1954. 10. Hagg, A. C.., "Heating Effects in Lubricating Films,tt J. Applied Mechanics, 11, A72-A76, 1944. 11. Lasche, 0.,, ttDie Reibungsverhaltnicse in Lagern mit Hoher Um~fangsgeschwindigkeit,." Forschungsh. Ver. dtsh. Ing.., 46, 1881-1890, 1932-19381, and 1961-1971, 1902. 12. Leeds and Northrup, Conversion Tables for Thermocouple, Issue 2. 13. McKee, S. A-, "Fpriction and Temperature as Criteria for- Safe Operation of Journal Bearings,'t Nat.,Bur. Stds. J. Res..* 24, 491., 1940. 14. Michell, A. G. M., "Progress in Fluid-Film Lubrication,tt Trans.. A.S.M.E., MSP-51-21, 51., 153-163., 1929. 15 Muisat,- M4, andMraFt mprtrIeaiuTo ora ern

BIBLIOGRAPHY (CONT' D) 16. Muskat, M., and Morgan, F., "The Theory of Thick Film Lubrication of a Complete Journal Bearing, of Finite Length with Arbitrary Positions of the Lubricant Source," J. Applied Physics, 10, 51 and 60, 1939. 17. OcirkF. W., and DuBois, G. B., "Experimental Investigation of Eccentricity Ratio, Friction, and Oil Flow of Long and Short Journal Bearings with Load-Number Charts," N.A.C.A., T.N.3491 1955. 8. Pinkus., and Sternlicht, B., "The Maximum Temperature Profile in Journal Bearings," Trans. A.S.M.E., 79, 337-342, 1957. 19. Purvis, M. B., Meyer, W. E., and Benton, T. C., "Temperature Distribution in the Journal Bearing Lubricant Film," Trans. A.S.M.E., 79, 343-350 1957. 20. Rosenblatt, M., and Wilcock, D. F., "Oil Flow, Key Factor in SleeveBearing Performance," Trans. A.S.M.E., 74, 849-866, 1952 21. Shaw, C. M., and Macks, F., t'Analysis and Lubrication of Bearings," st Ed., New York: McGraw-Hill Book Co., 177,206'-258, 1949. 22. Stephan, H., "Temperatur und Verdagerung von Zylindrischen Gleitlagern bei hoher Drehzahl," Forschungsh. Ver. dtsch. Ing. 439, 1953. 23. Von Gersd~orfer, 0.,?TDas Gleitlager. Wirkungsweise, Konstruktion., Baustoffe und. Berechnung.," Ind~ustrie-und. Fachverlag., S.89., 1954. 24. Wilcock, D. F.,. "Turbulence in High Speed. Journal Bearings," Trans. A.S.M.E., 72,~ 825-834, 1950. 25. Wilcock.$ D. F., and. Booser, E. R., Bearing Design and. Application, 1st Ed.., New York: McGraw-Hill Book Co.,, 410,, 1957.