Engineering Tribology Episode 1 Part 3 pdf

PHYSICAL PROPERTIES OF LUBRICANTS 25 υ = πr 4 glt / 8LV = k(t 2 − t 1 ) (2.15) where: υ is the kinematic viscosity [m 2 /s]; r is the capillary radius [m]; l is the mean hydrostatic head [m]; g is the earth acceleration [m/s 2 ]; L is the capillary length [m]; V is the flow volume of the fluid [m 3 ]; t is the flow time through the capillary, t = (t 2 − t 1 ), [s]; k is the capillary constant which has to be determined experimentally by applying a reference fluid with known viscosity, e.g. by applying freshly distilled water. The capillary constant is usually given by the manufacturer of the viscometer. Capillary tube Etched rings British Standard U-tube viscometer Capillary tube Capillary tube Etched rings Glass strengthening bridge Kinematic viscometers for transparent fluids for opaque fluids FIGURE 2.10 Typical capillary viscometers (adapted from [23]). In order to measure the viscosity of the fluid by one of the viscometers shown in Figure 2.10, the container is filled with oil between the etched lines. The measurement is then made by timing the period required for the oil meniscus to flow from the first to the second timing mark. This is measured with an accuracy to within 0.1 [s]. Kinematic viscosity can also be measured by so called ‘short tube’ viscometers. In the literature they are also known as efflux viscometers. As in the previously described viscometers, viscosity is determined by measuring the time necessary for a given volume of fluid to discharge under gravity through a short tube orifice in the base of the instrument. The most commonly used viscometers are Redwood, Saybolt and Engler. The operation principle of these viscometers is the same, and they only differ by the orifice dimensions and the volume of fluid discharged. Redwood viscometers are used in the United Kingdom, Saybolt in Europe and Engler mainly in former Eastern Europe. The viscosities measured by these viscometers are quoted in terms of the time necessary for the discharge of a certain volume of fluid. Hence the viscosity is sometimes found as being quoted in Redwood and TEAM LRN 26 ENGINEERING TRIBOLOGY Saybolt seconds. The viscosity measured on Engler viscometers is quoted in Engler degrees, which is the time for the fluid to discharge divided by the discharge time of the same volume of water at the same temperature. Redwood and Saybolt seconds and Engler degrees can easily be converted into centistokes as shown in Figure 2.11. These particular types of viscometers, are gradually becoming obsolete, since they do not easily provide calculable viscosity. A typical short tube viscometer is shown in Figure 2.12. In order to extend the range of kinematic, Saybolt Universal, Redwood No. 1 and Engler viscosity scales only (Figure 2.11), a simple operation is performed. The viscosities on these scales which correspond to the viscosity between 100 and 1000 [cS] on the kinematic scale are multiplied by a factor of 10 and this gives the required extension. For example: 4000 [cS] = 400 [cS] × 10 ≈ 1850 [SUS] × 10 = 18500 [SUS] ≈ 51 [Engler] × 10 = 510 [Engler] 2 2.5 3 3.5 4 4.5 5 6 7 8 9 10 15 20 25 30 35 40 45 50 60 70 80 90 100 150 200 250 300 350 400 450 500 600 700 800 900 1 000 2 2.5 3 3.5 4 4.5 5 6 7 8 9 10 15 20 25 30 35 40 45 50 60 70 80 90 100 150 200 250 300 350 400 450 500 600 700 800 900 1 000 Kinematic viscosity, cS Saybolt universal seconds Redwood Nº 1 seconds (standard) Engler degrees Saybolt furol seconds Redwood Nº 2 seconds (admiralty) Kinematic viscosity, cS 100 150 200 250 300 350 400 450 500 600 700 800 900 1 000 1 500 2 000 2 500 3 000 3 500 4 000 4 500 35 40 45 50 60 70 80 90 100 150 200 250 300 350 400 450 500 600 700 800 900 1 000 1 500 2 000 2 500 3 000 3 500 4 000 35 40 45 50 60 70 80 90 2 2.5 3 3.5 4 4.5 5 6 7 8 9 10 15 20 25 30 35 40 45 50 60 70 80 90 1.9 1.8 1.7 1.6 1.5 1.4 1.3 1.2 25 30 35 40 45 50 60 70 80 90 100 150 200 250 300 350 400 450 30 35 40 45 50 60 70 80 90 100 150 200 250 300 350 400 100 120 FIGURE 2.11 Viscosity conversion chart (compiled by Texaco Inc.). Rotational Viscometers Rotational viscometers are based on the principle that the fluid whose viscosity is being measured is sheared between two surfaces (ASTM D2983). In these viscometers one of the surfaces is stationary and the other is rotated by an external drive and the fluid fills the space in between. The measurements are conducted by applying either a constant torque and measuring the changes in the speed of rotation or applying a constant speed and measuring TEAM LRN PHYSICAL PROPERTIES OF LUBRICANTS 27 the changes in the torque. These viscometers give the ‘dynamic viscosity’. There are two main types of these viscometers: rotating cylinder and cone-on-plate viscometers. Stopper Capillary tube Lubricant sample Water bath Overflow rim FIGURE 2.12 Schematic diagram of a short tube viscometer. · Rotating Cylinder Viscometer The rotating cylinder viscometer, also known as a ‘Couette viscometer’, consists of two concentric cylinders with an annular clearance filled with fluid as shown in Figure 2.13. The inside cylinder is stationary and the outside cylinder rotates at constant velocity. The force necessary to shear the fluid between the cylinders is measured. The velocity of the cylinder can be varied so that the changes in viscosity of the fluid with shear rate can be assessed. Care needs to be taken with non-Newtonian fluids as these viscometers are calibrated for Newtonian fluids. Different cylinders with a range of radial clearances are used for different fluids. For Newtonian fluids the dynamic viscosity can be estimated from the formula: η = M(1/r b 2 − 1/r c 2 ) / 4πdω = kM / ω (2.16) where: η is the dynamic viscosity [Pas]; r b , r c are the radii of the inner and outer cylinders respectively [m]; M is the shear torque on the inner cylinder [Nm]; ω is the angular velocity [rad/s]; d is the immersion depth of the inner cylinder [m]; k is the viscometer constant, supplied usually by the manufacturer for each pair of cylinders [m -3 ]. When motor oils are used in European and North American conditions, the oil viscosity data at -18°C is required in order to assess the ease with which the engine starts. A specially adapted rotating cylinder viscometer, known in the literature as the ‘Cold Cranking Simulator’ (CCS), is used for this purpose (ASTM D2602). The schematic diagram of this viscometer is shown in Figure 2.14. TEAM LRN 28 ENGINEERING TRIBOLOGY Driving motor Pointer Torsion wire Graduated scale Fluid sample ω r c r b Inner cylinder (stationary) Outer cylinder (rotating) FIGURE 2.13 Schematic diagram of a rotating cylinder viscometer. Overload clutch Constant-power motor drive with tachometer Coolant (methanol) in Coolant out Nylon block Thermocouple ω Lubricant sample Rotating cylinder Stationary cylinder FIGURE 2.14 Schematic diagram of a cold cranking simulator. The inner cylinder is rotated at constant power in the cooled lubricant sample of volume about 5 [ml]. The viscosity of the oil sample tested is assessed by comparing the rotational speed of the test oil with the rotational speed of the reference oil under the same conditions. The measurements provide an indication of the ease with which the engine will turn at low temperatures and with limited available starting power. In the case of very viscous fluids, two cylinder arrangements with a small clearance might be impractical because of the very high viscous resistance; thus a single cylinder is rotated in a fluid and measurements are calibrated against measurements obtained with reference fluids. · Cone on Plate Viscometer The cone on plate viscometer consists of a conical surface and a flat plate. Either of these surfaces can be rotated. The clearance between the cone and the plate is filled with the fluid TEAM LRN PHYSICAL PROPERTIES OF LUBRICANTS 29 and the cone angle ensures a constant shear rate in the clearance space. The advantage of this viscometer is that a very small sample volume of fluid is required for the test. In some of these viscometers, the temperature of the fluid sample is controlled during tests. This is achieved by circulating pre-heated or cooled external fluid through the plate of the viscometer. These viscometers can be used with both Newtonian and non-Newtonian fluids as the shear rate is approximately constant across the gap. The schematic diagram of this viscometer is shown in Figure 2.15. The dynamic viscosity can be estimated from the formula: η = 3Mαcos 2 α(1 − α 2 /2) / 2πωr 3 = kM / ω (2.17) where: η is the dynamic viscosity [Pas]; r is the radius of the cone [m]; M is the shear torque on the cone [Nm]; ω is the angular velocity [rad/s]; α is the cone angle [rad]; k is the viscometer constant, usually supplied by the manufacturer [m -3 ]. Cone Driving motor Torque spring Plate α Test fluid r ω FIGURE 2.15 Schematic diagram of a cone on plate viscometer. Other Viscometers Many other types of viscometers, based on different principles of measurement, are also available. Most commonly used in many laboratories is the ‘Falling Ball Viscometer’. A glass tube is filled with the fluid to be tested and then a steel ball is dropped into the tube. The measurement is then made by timing the period required for the ball to fall from the first to the second timing mark, etched on the tube. The time is measured with an accuracy to within 0.1 [s]. This viscometer can also be used for the determination of viscosity changes under pressure and its schematic diagram is shown in Figure 2.16. The dynamic viscosity can be estimated from the formula: TEAM LRN 30 ENGINEERING TRIBOLOGY η = 2r 2 (ρ b − ρ)gF / 9v (2.18) where: η is the dynamic viscosity [Pas]; r is the radius of the ball [m]; ρ b is the density of the ball [kg/m 3 ]; ρ is the density of the fluid [kg/m 3 ]; g is the gravitational constant [m/s 2 ]; v is the velocity of the ball [m/s]; F is the correction factor. Liquid level Small hole Sphere Guide tube Glass tube Water bath Timing marks Start Stop FIGURE 2.16 Schematic diagram of a ‘Falling Ball Viscometer’. The correction factor can be calculated from the formula given by Faxen [19]: F = 1 − 2.104(d/D) + 2.09(d/D) 3 − 0.9(d/D) 5 (2.19) where: d is the diameter of the ball [m]; D is the internal diameter of the tube [m]. There are also many other more specialized viscometers designed to perform viscosity measurements, e.g. under high pressures, on very small volumes of fluid, etc. They are described in more specialized literature [e.g. 21]. 2.8 VISCOSITY OF MIXTURES In industrial practice it might be necessary to mix two similar fluids of different viscosities in order to achieve a mixture of a certain viscosity. The question is, how much of fluid ‘A’ TEAM LRN PHYSICAL PROPERTIES OF LUBRICANTS 31 should be mixed with fluid ‘B’. This can simply be worked out by using ASTM viscosity paper with linear abscissa representing percentage quantities of each of the fluids. The viscosity of each of the fluids at the same temperature is marked on the ordinate on each side of the graph as shown in Figure 2.17. A straight line is drawn between these points and intersects a horizontal line which corresponds to the required viscosity. A vertical line drawn from the point of intersection crosses the abscissa, indicating the proportions needed of the two fluids. In the example of Figure 2.17, 20% of the less viscous component is mixed with 80% of the more viscous component to give the ‘required viscosity’. Viscosity of fluid B 0 10050 % Less viscous component Kinematic viscosity Required viscosity υ [cS] 20 Viscosity of fluid A FIGURE 2.17 Determining the viscosity of a mixture. 2.9 OIL VISCOSITY CLASSIFICATION There are several widely used oil viscosity classifications. The most commonly used are SAE (Society of Automotive Engineers), ISO (International Organization for Standardization) and military specifications. SAE Viscosity Classification The oils used in combustion engines and power transmissions are graded according to SAE J300 and SAE J306 classifications respectively. A recent SAE classification establishes eleven engine oil and seven transmission oil grades [34,35]. The engine oil viscosities for different SAE grades are shown in Table 2.4. Note that the viscosity in column 2 (Table 2.4) is the dynamic viscosity while column 3 shows the kinematic viscosity. The low temperature viscosity was measured by the ‘cold- cranking simulator’ and is an indicator of cold weather starting ability. The viscosity measurements at 100°C are related to the normal operating temperature of the engine. The oils without a ‘W’ suffix are called ‘monograde oils’ since they meet only one SAE grade. The oils with a ‘W’ suffix, which stands for ‘winter’, have good cold starting capabilities. For climates where the temperature regularly drops below zero Celsius, engine and transmission oils are formulated in such a manner that they give low resistance at start, i.e. their viscosity is low at the starting temperature. Such oils have a higher viscosity index, achieved by adding viscosity improvers (polymeric additives) to the oil and are called ‘multigrade oils’. For example, SAE 20W/50 has a viscosity of SAE 20 at -18°C and viscosity of SAE 50 at 100°C as is illustrated in Figure 2.18. The problem associated with the use of multigrade oils is that they usually shear thin, i.e. their viscosity drops significantly with increased shear rates due to polymeric additives added. This has to be taken into account when designing machine TEAM LRN 32 ENGINEERING TRIBOLOGY components lubricated by these oils. The drop in viscosity can be significant, and with some viscosity improvers even a permanent viscosity loss at high shear rates may occur due to the breaking up of molecules into smaller units. The viscosity loss affects the thickness of the lubricating film and subsequently affects the performance of the machine. T ABLE 2.4 SAE classification of engine oils [34]. SAE viscosity grade Viscosity [cP] at temp [°C] max Kinematic viscosity [cS] at 100°C min max 0W 3 250 3.8at -30 - 5W 3 500 3.8at -25 - 10W 3 500 4.1at -20 - 15W 3 500 5.6at -15 - 20W 4 500 5.6at -10 - 25W 6 000 9.3at -5 - 20 5.6- < 9.3 30 9.3- < 12.5 40 12.5- < 16.3 50 16.3- < 21.9 60 21.9- < 26.1 Cranking Pumping at -35 at -30 at -25 at -20 at -15 at -10 - - - - - 30 000 30 000 30 000 30 000 30 000 30 000 15 000 5 000 15 6 SAE 50 SAE 40 SAE 30 SAE 20 SAE 10 SAE 20W/50 SAE 10W/50 Dynamic viscosity Tem p erature [°C] -18 100 η [cP] FIGURE 2.18 Viscosity-temperature graph for some monograde and multigrade oils (not to scale, adapted from [12]). SAE classification of transmission oils is very similar to that of engine oils. The only difference is that the winter grade is defined by the temperature at which the oil reaches the TEAM LRN PHYSICAL PROPERTIES OF LUBRICANTS 33 viscosity of 150,000 [cP]. This is the maximum oil viscosity which can be used without causing damage to gears. The classification also permits multigrading. The transmission oil viscosities for different SAE grades are shown in Table 2.5 [35]. T ABLE 2.5 SAE classification of transmission oils [35]. SAE viscosity grade Max. temp. for viscosity of 150 000 cP [°C] Kinematic viscosity [cS] at 100°C min max 75W 4.1-40 - 80W 7.0-26 - 85W 11.0-12 - 90 13.5- < 24.0 140 24.0- < 41.0 250 41.0- - 70W 4.1-55 - It should also be noted that transmission oils have higher classification numbers than engine oils. As can be seen from Figure 2.19 this does not mean that they are more viscous than the engine oils. The higher numbers simply make it easier to differentiate between engine and transmission oils. 5 10 15 20 25 75W 80W 85W 90 20 30 40 50 Transmission oils Engine oils Kinematic viscosity at 100°C [cS] FIGURE 2.19 Comparison of SAE grades of engine and transmission oils. ISO Viscosity Classification The ISO (International Standards Organization) viscosity classification system was developed in the USA by the American Society of Lubrication Engineers (ASLE) and in the United Kingdom by The British Standards Institution (BSI) for all industrial lubrication fluids. It is now commonly used throughout industry. The industrial oil viscosities for different ISO viscosity grade numbers are shown in Table 2.6 [36] (ISO 3448). 2.10 LUBRICANT DENSITY AND SPECIFIC GRAVITY Lubricant density is important in engineering calculations and sometimes offers a simple way of identifying lubricants. Density or specific gravity is often used to characterize crude oils. It gives a rough idea of the amount of gasoline and kerosene present in the crude. The oil density, however, is often confused with specific gravity. Specific gravity is defined as the ratio of the mass of a given volume of oil at temperature ‘t 1 ’ to the mass of an equal volume of pure water at temperature ‘t 2 ’ (ASTM D941, D1217, D1298). TEAM LRN 34 ENGINEERING TRIBOLOGY TABLE 2.6 ISO classification of industrial oils [36]. Kinematic viscosity limits [cSt] at 40°C ISO viscosity grade min. midpoint max. ISO VG 2 1.98 2.2 2.42 ISO VG 3 2.88 3.2 3.52 ISO VG 5 4.14 4.6 5.06 ISO VG 7 6.12 6.8 7.48 ISO VG 10 9.00 10 11.0 ISO VG 15 13.5 15 16.5 ISO VG 22 19.8 22 24.2 ISO VG 32 28.8 32 35.2 ISO VG 46 41.4 46 50.6 ISO VG 68 61.2 68 74.8 ISO VG 100 90.0 100 110 ISO VG 150 135 150 165 ISO VG 220 198 220 242 ISO VG 320 288 320 352 ISO VG 460 414 460 506 ISO VG 680 612 680 748 ISO VG 1000 900 1000 1100 ISO VG 1500 1350 1500 1650 For petroleum products the specific gravity is usually quoted using the same temperature of 60°F (15.6°C). Density, on the other hand, is the mass of a given volume of oil [kg/m 3 ]. In the petroleum industry an API (American Petroleum Institute) unit is used which is a derivative of the conventional specific gravity. The API scale is expressed in degrees which in some cases are more convenient to use than the specific gravity readings. The API specific gravity is defined as [23]: Degrees API = (141.5 / s) − 131.5 (2.20) where: s is the specific gravity at 15.6°C (60°F). As mentioned already the density of a typical mineral oil is about 850 [kg/m 3 ] and, since the density of water is about 1000 [kg/m 3 ], the specific gravity of mineral oils is typically 0.85. 2.11 THERMAL PROPERTIES OF LUBRICANTS The most important thermal properties of lubricants are specific heat, thermal conductivity and thermal diffusivity. These three parameters are important in assessing the heating effects in lubrication, i.e. the cooling properties of the oil, the operating temperature of the surfaces, etc. They are also important in bearing design. Specific Heat Specific heat varies linearly with temperature and rises with increasing polarity or hydrogen bonding of the molecules. The specific heat of an oil is usually half that of water. For mineral and synthetic hydrocarbon based lubricants, specific heat is in the range from about 1800 [J/kgK] at 0°C to about 3300 [J/kgK] at 400°C. For a rough estimation of specific heat, the following formula can be used [5]: TEAM LRN [...]... silicone oil 1 = 15 .14 [MPa0.5] and for air ∂2 = 6.69 [MPa0.5] Absolute oil temperature is 37 3K Substituting these values into the above equation yields the Ostwald coefficient of air in dimethyl silicone at 37 3K, i.e.: ln C0 = [0. 039 5 × (15 .14 − 6.69)2 − 2.66] × (1 − 2 73/ 3 73) − 0 .30 3 × 15 .14 − 0.02 41 × (17 .60 − 6.69) 2 + 5.7 31 = (2.8204 − 2.66) × 0.26 81 − 4.5874 − 2.8686 + 5.7 31 = − 1. 6820 C 0 = 0 .18 60 Which... conductivity at 10 0°C [W/mK] Thermal diffusivity at 10 0°C -6 2 [ × 10 m /s] 700 - 1 200 1 670 0 .14 Water 1 000 4 18 4 0.58 Steel 7 800 460 Bronze 8 800 38 0 50 - 65 14 .95 - 19 .44 Brass 8 900 38 0 80 - 10 5 23. 66 - 31 . 05 Aluminium (pure) 2 600 870 230 10 1.68 Aluminium (alloy) 2 700 870 12 0 - 17 0 51. 09 - 72 .37 46.7 0.059 - 0 .10 2 0 .16 13 .02 Pour Point and Cloud Point The pour point of an oil (ASTM D97, D2500) is... Transactions, Vol 24, 19 81, pp 232 - 238 16 D Klamann, Lubricants and Related Products, Publ Verlag Chemie, Weinheim, 19 84, pp 51- 83 17 K.E Bett and J.B Cappi, Effect of Pressure on the Viscosity of Water, Nature, Vol 207, 19 65, pp 620-6 21 18 J Wonham, Effect of Pressure on the Viscosity of Water, Nature, Vol 215 , 19 67, pp 10 53 -10 54 19 J Halling, Principles of Tribology, The MacMillan Press, 19 75 20 P.L O’Neill... Polychlorotrifluoro ethylene 15 .19 O2 7.75 Polychlorotrifluoro ethylene 15 .55 Ar 7.77 Polychlorotrifluoro ethylene 15 .77 CH4 9 .10 Dimethyl silicone 15 .14 CO2 14 . 81 Methyl phenyl silicone 18 . 41 Kr 10 .34 Perfluoropolyglycol 14 .20 Tri-2-ethylhexyl phosphate 18 .29 Tricresyl phosphate 18 .82 EXAMPLE Find the quantity of air that could be dissolved in one litre of dimethyl silicone oil at 10 0°C From Table 2 .10 , for dimethyl... composition TABLE 2 .10 Values of ‘ 1 and ‘∂2’ parameters for some typical lubricants and gases [37 ] 1 Lubricant ∂2 1 ∂2 [MPa 0.5 ] Gas [MPa 0.5 ] Di-2-ethylhexyl adipate 18 .05 He 3. 35 Di-2-ethylhexyl sebacate 17 .94 Ne 3. 87 Trimetholylpropane pelargonate 18 .18 H2 5.52 Pentaerythritol caprylate 18 .95 N2 6.04 Di-2-ethylhexyl phthalate 18 .97 Air 6.69 Diphenoxy diphenylene ether 23. 21 CO 7.47 Polychlorotrifluoro... 19 83 29 M.H Jones and D Scott, Industrial Tribology, The Practical Aspects of Friction, Lubrication and Wear, Elsevier, 19 83 30 T.I Fowle, Lubricants for Fluid Film and Hertzian Contact Conditions, Proc Inst Mech Engrs., Vol 18 2, Pt 3A, 19 67 -19 68, pp 508-584 31 R.S Porter and J.F Johnson, Viscosity Performance of Lubricating Base Oils at Shears Developed in Machine Elements, Wear, Vol 4, 19 61, pp 32 -40... Viscosity Classification, SAE J300, June 19 89 35 SAE Standard, Axle and Manual Transmission Lubricant Viscosity Classification, SAE J306, March 19 85 36 International Standard, Industrial Liquid Lubricants, ISO Viscosity Classification, ISO 34 48, 19 75 37 A Beerbower, Estimating the Solubility of Gases in Petroleum and Synthetic Lubricants, ASLE Transactions, Vol 23, 19 80, pp 33 5 -34 2 38 H Spikes, Lecture Notes,... Beerbower [37 ] Two new parameters were introduced in the formula: a measure of the solvation capacity of the lubricant ‘∂ 1 ’ and a gas solubility parameter ‘∂2 ’ The previously used formulae for the determination of the Ostwald coefficient for a particular lubricant were replaced by the following, single expression: lnC 0 =[0. 039 5(∂ 1 −∂ 2 ) 2 −2.66] × (1 2 73/ T)−0 .30 3∂ 1 −0.02 41( 17.6−∂ 2 ) 2 +5.7 31 (2.28)... cataoxygen present lysts 30 0 Oils containing anti-oxidants 200 Upper limit imposed by oxidation where the oxygen supply is unlimited 10 0 Oils without anti-oxidants 0 10 0 Life [hours] 10 000 20 30 40 50 3 000 4 000 5 000 10 2 000 3 4 5 1 000 2 30 0 400 500 1 200 Lower temperature limit imposed by the pour point which varies with oil, source, viscosity, treatment & additives -10 0 FIGURE 2. 23 Temperature-life... 273K are shown in Table 2.9 [37 ] TABLE 2.9 Ostwald coefficients ‘Co,d’ for typical gases dissolved in hydrocarbons at 273K [37 ] Gas Co,d Helium 0. 010 Neon 0.0 21 Hydrogen 0. 039 Nitrogen 0.075 Air 0.095 Carbon monoxide 0 .10 Oxygen 0 .15 Argon 0. 23 Methane 0. 31 Carbon dioxide 1. 0 Krypton 1. 3 One of the serious limitations of the method above is that it is limited only to mineral oils A more general formula . 000 3 500 4 000 35 40 45 50 60 70 80 90 2 2.5 3 3.5 4 4.5 5 6 7 8 9 10 15 20 25 30 35 40 45 50 60 70 80 90 1. 9 1. 8 1. 7 1. 6 1. 5 1. 4 1. 3 1. 2 25 30 35 40 45 50 60 70 80 90 10 0 15 0 200 250 30 0 35 0 400 450 30 35 40 45 50 60 70 80 90 10 0 15 0 200 250 30 0 35 0 400 10 0 12 0 FIGURE. 61. 2 68 74.8 ISO VG 10 0 90.0 10 0 11 0 ISO VG 15 0 13 5 15 0 16 5 ISO VG 220 19 8 220 242 ISO VG 32 0 288 32 0 35 2 ISO VG 460 414 460 506 ISO VG 680 612 680 748 ISO VG 10 00 900 10 00 11 00 ISO VG 15 00 13 50. 2 1. 98 2.2 2.42 ISO VG 3 2.88 3. 2 3. 52 ISO VG 5 4 .14 4.6 5.06 ISO VG 7 6 .12 6.8 7.48 ISO VG 10 9.00 10 11 .0 ISO VG 15 13 .5 15 16 .5 ISO VG 22 19 .8 22 24.2 ISO VG 32 28.8 32 35 .2 ISO VG 46 41. 4