612 Budynas-Nisbett:Shigley's Ill.Design of Mechanical 12.Lubrication and Journal T©The McGraw-Hill Mechanical Engineering Elements Bearings Companies,2008 Design,Eighth Edition 612 Mechanical Engineering Design The Raimondi and Boyd papers were published in three parts and contain 45 detailed charts and 6 tables of numerical information.In all three parts,charts are used to define the variables for length-diameter(/d)ratios of 1:4.1:2,and I and for beta angles of 60 to 360.Under certain conditions the solution to the Reynolds equation gives negative pressures in the diverging portion of the oil film.Since a lubricant can- not usually support a tensile stress,Part III of the Raimondi-Boyd papers assumes that the oil film is ruptured when the film pressure becomes zero.Part III also contains data for the infinitely long bearing;since it has no ends,this means that there is no side leak- age.The charts appearing in this book are from Part III of the papers,and are for full journal bearings (B=360)only.Space does not permit the inclusion of charts for par- tial bearings.This means that you must refer to the charts in the original papers when beta angles of less than 360 are desired.The notation is very nearly the same as in this book,and so no problems should arise. Viscosity Charts(Figs.12-12 to 12-14) One of the most important assumptions made in the Raimondi-Boyd analysis is that viscosity of the lubricant is constant as it passes through the bearing.But since work is done on the lubricant during this flow,the temperature of the oil is higher when it leaves the loading zone than it was on entry.And the viscosity charts clearly indicate that the viscosity drops off significantly with a rise in temperature.Since the analysis is based on a constant viscosity,our problem now is to determine the value of viscosity to be used in the analysis. Some of the lubricant that enters the bearing emerges as a side flow,which carries away some of the heat.The balance of the lubricant flows through the load-bearing zone and carries away the balance of the heat generated.In determining the viscosity to be used we shall employ a temperature that is the average of the inlet and outlet tempera- tures,or T Tv=1+2 (12-14) where T is the inlet temperature and AT is the temperature rise of the lubricant from inlet to outlet.Of course,the viscosity used in the analysis must correspond to Tav. Viscosity varies considerably with temperature in a nonlinear fashion.The ordinates in Figs.12-12 to 12-14 are not logarithmic,as the decades are of differing ver- tical length.These graphs represent the temperature versus viscosity functions for com- mon grades of lubricating oils in both customary engineering and SI units.We have the temperature versus viscosity function only in graphical form,unless curve fits are devel- oped.See Table 12-1. One of the objectives of lubrication analysis is to determine the oil outlet temper- ature when the oil and its inlet temperature are specified.This is a trial-and-error type of problem.In an analysis,the temperature rise will first be estimated.This allows for the viscosity to be determined from the chart.With the value of the viscosity,the analysis is performed where the temperature rise is then computed.With this,a new estimate of the temperature rise is established.This process is continued until the estimated and computed temperatures agree. To illustrate,suppose we have decided to use SAE 30 oil in an application in which the oil inlet temperature is Ti=180F.We begin by estimating that the temperature rise
Budynas−Nisbett: Shigley’s Mechanical Engineering Design, Eighth Edition III. Design of Mechanical Elements 12. Lubrication and Journal Bearings 612 © The McGraw−Hill Companies, 2008 612 Mechanical Engineering Design The Raimondi and Boyd papers were published in three parts and contain 45 detailed charts and 6 tables of numerical information. In all three parts, charts are used to define the variables for length-diameter (l/d) ratios of 1:4, 1:2, and 1 and for beta angles of 60 to 360◦. Under certain conditions the solution to the Reynolds equation gives negative pressures in the diverging portion of the oil film. Since a lubricant cannot usually support a tensile stress, Part III of the Raimondi-Boyd papers assumes that the oil film is ruptured when the film pressure becomes zero. Part III also contains data for the infinitely long bearing; since it has no ends, this means that there is no side leakage. The charts appearing in this book are from Part III of the papers, and are for full journal bearings (β = 360◦) only. Space does not permit the inclusion of charts for partial bearings. This means that you must refer to the charts in the original papers when beta angles of less than 360◦ are desired. The notation is very nearly the same as in this book, and so no problems should arise. Viscosity Charts (Figs. 12–12 to 12–14) One of the most important assumptions made in the Raimondi-Boyd analysis is that viscosity of the lubricant is constant as it passes through the bearing. But since work is done on the lubricant during this flow, the temperature of the oil is higher when it leaves the loading zone than it was on entry. And the viscosity charts clearly indicate that the viscosity drops off significantly with a rise in temperature. Since the analysis is based on a constant viscosity, our problem now is to determine the value of viscosity to be used in the analysis. Some of the lubricant that enters the bearing emerges as a side flow, which carries away some of the heat. The balance of the lubricant flows through the load-bearing zone and carries away the balance of the heat generated. In determining the viscosity to be used we shall employ a temperature that is the average of the inlet and outlet temperatures, or Tav = T1 + T 2 (12–14) where T1 is the inlet temperature and T is the temperature rise of the lubricant from inlet to outlet. Of course, the viscosity used in the analysis must correspond to Tav. Viscosity varies considerably with temperature in a nonlinear fashion. The ordinates in Figs. 12–12 to 12–14 are not logarithmic, as the decades are of differing vertical length. These graphs represent the temperature versus viscosity functions for common grades of lubricating oils in both customary engineering and SI units. We have the temperature versus viscosity function only in graphical form, unless curve fits are developed. See Table 12–1. One of the objectives of lubrication analysis is to determine the oil outlet temperature when the oil and its inlet temperature are specified. This is a trial-and-error type of problem. In an analysis, the temperature rise will first be estimated. This allows for the viscosity to be determined from the chart. With the value of the viscosity, the analysis is performed where the temperature rise is then computed. With this, a new estimate of the temperature rise is established. This process is continued until the estimated and computed temperatures agree. To illustrate, suppose we have decided to use SAE 30 oil in an application in which the oil inlet temperature is T1 = 180◦F. We begin by estimating that the temperature rise
Budynas-Nisbett:Shigley's lll.Design of Mechanical 12.Lubrication and Journal ©The McGraw-Hil 613 Mechanical Engineering Elements Bearings Companies,2008 Design,Eighth Edition Lubrication and Joumal Bearings 613 Figure 12-12 104 Viscosity-temperature chart in U.S.customary units. 532 (Raimondi and Boyd.] 10 32 lo SAE 70 0 0 30 0.5 0.4 0.3 020 50 100 150 200 250 300 Temperature (F) will be△T=30°E.Then,from Eq.(12-14), T Tv=1+2 =180+ 0 =195℉ From Fig.12-12 we follow the SAE 30 line and find that u=1.40 ureyn at 195F.So we use this viscosity (in an analysis to be explained in detail later)and find that the temperature rise is actually AT=54F.Thus Eq.(12-14)gives 54 7w=180+2=207F
Budynas−Nisbett: Shigley’s Mechanical Engineering Design, Eighth Edition III. Design of Mechanical Elements 12. Lubrication and Journal Bearings © The McGraw−Hill 613 Companies, 2008 Lubrication and Journal Bearings 613 Figure 12–12 Viscosity–temperature chart in U.S. customary units. (Raimondi and Boyd.) 30 50 100 150 200 250 300 0.2 0.3 0.4 0.5 1 2 3 4 5 10 2 3 4 5 2 3 5 2 3 5 102 103 104 A B SAE 70 Temperature (°F) Absolute viscosity (reyn) 40 30 20 10 50 60 will be T = 30◦F. Then, from Eq. (12–14), Tav = T1 + T 2 = 180 + 30 2 = 195◦ F From Fig. 12–12 we follow the SAE 30 line and find that μ = 1.40 μreyn at 195◦F. So we use this viscosity (in an analysis to be explained in detail later) and find that the temperature rise is actually T = 54◦F. Thus Eq. (12–14) gives Tav = 180 + 54 2 = 207◦ F
614 Budynas-Nisbett:Shigley's Ill.Design of Mechanical 12.Lubrication and Journal T©The McGraw-Hill Mechanical Engineering Elements Bearings Companies,2008 Design,Eighth Edition 614 Mechanical Engineering Design Figure 12-13 10 Viscosity-iemperature chart in Sl units.(Adapted from Fig.12-121 10 102 SAE 70 60 50 3 10 20 30 405060708090100110120130140 Temperature (C) This corresponds to point A on Fig.12-12,which is above the SAE 30 line and indi- cates that the viscosity used in the analysis was too high. For a second guess,try u=1.00 ureyn.Again we run through an analysis and this time find that AT =30F.This gives an average temperature of 30 7w=180+2=1959℉ and locates point B on Fig.12-12. If points A and B are fairly close to each other and on opposite sides of the SAE 30 line,a straight line can be drawn between them with the intersection locating the cor- rect values of viscosity and average temperature to be used in the analysis.For this illus- tration,we see from the viscosity chart that they are Tav=203F and u=1.20 ureyn
Budynas−Nisbett: Shigley’s Mechanical Engineering Design, Eighth Edition III. Design of Mechanical Elements 12. Lubrication and Journal Bearings 614 © The McGraw−Hill Companies, 2008 614 Mechanical Engineering Design 30 10 10 20 30 40 50 60 70 80 90 100 110 120 130 140 2 3 4 5 10 2 3 4 5 102 2 3 5 103 2 3 5 104 Temperature (°C) Absolute viscosity (mPa·s) 50 60 40 20 SAE 70 Figure 12–13 Viscosity–temperature chart in SI units. (Adapted from Fig. 12–12.) This corresponds to point A on Fig. 12–12, which is above the SAE 30 line and indicates that the viscosity used in the analysis was too high. For a second guess, try μ = 1.00 μreyn. Again we run through an analysis and this time find that T = 30◦F. This gives an average temperature of Tav = 180 + 30 2 = 195◦ F and locates point B on Fig. 12–12. If points A and B are fairly close to each other and on opposite sides of the SAE 30 line, a straight line can be drawn between them with the intersection locating the correct values of viscosity and average temperature to be used in the analysis. For this illustration, we see from the viscosity chart that they are Tav = 203◦F and μ = 1.20 μreyn
Budynas-Nisbett:Shigley's lll.Design of Mechanical 12.Lubrication and Journal ©The McGraw-Hill 615 Mechanical Engineering Elements Bearings Companies,2008 Design,Eighth Edition Lubrication and Journal Bearings 615 Figure 12-14 103 Chart for multiviscosity 54 lubricants.This chart was derived from known viscosities 32 at two points,100 and 103 210F,and the results are believed to be correct for other temperatures 20W 50 20w-40 I0w-30 03 0.2 100 150 200 250 300 Temperature (F) Table 12-1 Viscosity Constant Curve Fits*to Approxi- Oil Grade,SAE Hor reyn b,F mate the Viscosity versus 10 0.015810-41 1157.5 Temperature Functions for 20 0.013610-1 1271.6 SAE Grades 10 to 60 30 0.014110- 1360.0 Source:A.S.Seireg and S. 40 0.012110- 1474.4 Dandage,"Empirical Design 50 0.017010- 1509.6 Procedure for the Thermody namic Behavior of Journal 60 0.0187八10-61 1564.0 Bearings,"J.Lubrication Technology,vol.104,April *μ=p/T+95,InE 1982,pp.135-148
Budynas−Nisbett: Shigley’s Mechanical Engineering Design, Eighth Edition III. Design of Mechanical Elements 12. Lubrication and Journal Bearings © The McGraw−Hill 615 Companies, 2008 Lubrication and Journal Bearings 615 Figure 12–14 Chart for multiviscosity lubricants. This chart was derived from known viscosities at two points, 100 and 210°F, and the results are believed to be correct for other temperatures. 50 100 150 200 250 300 0.2 0.3 0.4 0.5 1 2 3 4 5 10 2 3 4 5 102 2 3 4 5 103 Temperature (°F) Absolute viscosity (reyn) 20W – 50 20W – 40 10W – 30 5W – 30 10W 20W Viscosity Constant Oil Grade, SAE 0, reyn b, °F 10 0.0158(10−6) 1157.5 20 0.0136(10−6) 1271.6 30 0.0141(10−6) 1360.0 40 0.0121(10−6) 1474.4 50 0.0170(10−6) 1509.6 60 0.0187(10−6) 1564.0 ∗ 0 exp [b/(T 95)], T in °F. Table 12–1 Curve Fits* to Approximate the Viscosity versus Temperature Functions for SAE Grades 10 to 60 Source: A. S. Seireg and S. Dandage, “Empirical Design Procedure for the Thermodynamic Behavior of Journal Bearings,” J. Lubrication Technology, vol. 104, April 1982, pp. 135–148.