Program Crowned and Straight External Involute Gear EHL Film Thickness

Transcription

1 Program Crowned and Straight External Involute Gear EHL Film Thickness Introduction Lubrication film thickness is obviously an important factor in the lubrication of gears, because it determines the amount of contact between asperities (high spots) on the surfaces of the working flanks of the teeth. The ability of gears to operate without contact between the teeth has been noted since lubricated metal gears have been used. In many cases the initial machining marks on gears that have been in service for years are still visible. The obvious separation between the teeth cannot be accounted for by hydrodynamic theory alone. Because, for parallel axis external involute gears, the surfaces of the teeth are non-conformal (both convex) the separation predicted by hydrodynamic theory is too small to account for the separation of the teeth. The mode of lubrication between highly loaded gear teeth is not hydrodynamic but elastohydrodynamic (EHL). This theory takes into account not only the hydrodynamic character of the contact but the elastic deformation of the teeth as well. EHL theory successfully predicts the separation (or lack of separation) between gear teeth. The viscosity of lubricating oils increases with pressure. This effect is not very important in contacts such as journal bearings where the pressure in the oil film is relatively low. However, in gear tooth contacts the contact pressure may be in the range of 20,000 to 300,000 psi. At these pressures the viscosity of the lubricant increases dramatically and is responsible for the separation of the surfaces. In order to estimate the film thickness between gear teeth, two sets of data are necessary. First, we must know the relevant design and operating conditions for the gears. Second, we must know how the viscosity of the lubricant changes with both temperature and pressure. The first set of data is available from the design and loading data for the gear set. The second is available in the form of a lubricant parameter, developed for each lubricant, that takes into account the pressure and temperature effects on viscosity. These lubricant parameters have been determined by the Mobil Oil Corporation for most of their products and are used in this model. See reference 3 for more information. Once the thickness of the film has been estimated, it must be compared to the roughness of the contacting surfaces to determine the probability of asperity contact. The ratio of the film thickness to the composite roughness of the surfaces is called the specific film thickness and is used, along with speed and shear heating factors, to determine the probability of contact. (Since ALL factors affecting the film thickness are not known with certainty it is necessary to predict the amount of asperity contact using statistical methods.)

2 UTS Integrated Gear Software When the film thickness is too low the gear set may suffer from cold scoring. Cold scoring occurs when asperities on the tooth surfaces contact each other through the lubricant film. Subsequent rolling and sliding of the tooth surfaces produce radial score lines and surface contour is finally destroyed. (Cold scoring must not be confused with hot scoring as they are two different modes of tooth contact failure. See UTS Model or reference 2 for information on hot scoring.) Reference 3 uses the EHL film thickness at the operating pitch diameters to assess the probability of cold scoring. This model uses the EHL film thickness at the center of the length of the contact interval. This is done because some gears sets are designed so that the operating pitch point is quite far from the center of mesh. For example, full recess action gears have the outside diameter of the driven gear at the operating pitch point and the operating pitch point is at the very end of the contact interval. Ideal uniform load distribution along gear teeth is seldom obtained due to many factors, including dimensional errors and elasticity in the gear teeth themselves and in supporting elements such as shafts, bearings and housings. Even if parallelism between the teeth is achieved at a specific load condition it cannot be maintained if the load changes because of deflections in the supporting structure. Thermal effects, centrifugal deflections and external shaft bending moments also play a role in causing face mismatch. Of course, any deviation from a perfectly parallel condition between mating teeth causes a non-uniform load distribution along the teeth. The usual design procedure for assessing the compressive stress on teeth with no longitudinal (lead) modification is to use the Hertz equations for parallel cylinders and then to apply a multiplier based on the face mismatch to obtain the maximum compressive stress in the misaligned position. (The use of the parallel cylinder equations is not quite correct as the radii of curvature on involute teeth change across the load footprint when under load.) AGMA Standard 218 of the American Gear Manufacturers Association provides a multiplier (designated Face Load Distribution (FLD) Factor, labeled Cmf in the TK Solver model) to account for the increase in compressive stress due to face mismatch above the stress calculated with the Hertz equations. The FLD Factor is defined as the peak load intensity divided by the average load intensity across the face width of the gears. The FLD Factor determined by the analytical method in this standard assumes a linear load distribution across the teeth and is based on the stiffness of the teeth along with the load (for helical gears the effect of the profile contact ratio is also included). This method is valid for any design and teeth with crowns must use this method. This model uses the FLD factor to analyze gears with straight teeth. 2

3 Crowned and Straight External Involute Gear EHL Film Thickness When straight teeth are misaligned the load at the tooth ends is, of course, higher than the average load. One widely used method of relieving the load on the tooth ends caused by mismatch is called lead crowning. With this method the tooth ends of one or both gears are made thinner than the center. The sides of a section parallel to the axis of the gear through the tooth are more or less elliptical or circular rather than straight. The actual shape of the tooth depends on the machining method used and how it is applied. The crown is specified and measured as a lead deviation in transverse planes. In this model a circular arc with a specified rise in the center of the tooth is assumed for the lead deviation. For spur gears, of course, the lead deviation is normal to the tooth and is the actual shape of the tooth. For helical gears, however, the lead deviation is not normal to the tooth. The circular arc deviation for a helical tooth in a direction normal to the tooth is the circular arc obtained by dividing the radius of the deviation by the cosine of the operating helix angle. As we said, for straight teeth, the Hertz equations for parallel cylinders are used for the compressive stress calculation. Here, it is assumed that the shape of the contact zone is a rectangle with the long dimension along the length of the tooth. The width of the rectangle is determined by the load and the curvature of the involute profiles for a given combination of materials. The stress distribution is semi-cylindrical. When the teeth are misaligned the contact zone is no longer a rectangle. The stress distribution is then semi-conical. The multiplier, the FLD Factor, gives us the stress at the wide end of the trapezoidal or triangular load pattern. When we have two surfaces in contact with curvature in all directions (crowned teeth) it is necessary to use the Hertz equations for elliptical contacts instead of the parallel cylinder equations. In this case the zone of contact is assumed to be an ellipse with the long dimension along the tooth (direction of least curvature) and the short dimension in the normal direction of the involute profile. The dimensions of the ellipse are determined by the load, the radius of the crown (or crowns) and the radii of the involute profiles for a given combination of materials. The stress distribution is a semi-ellipsoid. If the contact ellipse (under load) is cut off by the end(s) of the teeth(spur) or by the start or end of the contact zone (helicals) the stress distribution is assumed to be a truncated ellipsoid cut by a plane (or planes) parallel to the minor axis of the contact ellipse. The stress and the minor dimension of the contact pattern are then adjusted to keep the same volume for the truncated ellipsoid and the full contact ellipsoid. (The numerical eccentricities of the elliptical sections are held constant.) This model incorporates both conditions and uses the parallel cylinder equations for straight teeth and the elliptical contact equations for teeth with crown on one or both gears. 3

4 UTS Integrated Gear Software The equations from reference 3 are used for both straight and crowned contacts to obtain a valid comparison of film thickness for the two types of contact. When stress for gears with straight teeth is being calculated, the FLD Factor will also be calculated (or must be input). The stress is then calculated by the methods from reference 3 for straight line contacts. For crowned gears the center of the crown is assumed to be in the center of the face width. (If the teeth are chamfered from the root to the tip at the ends use the mean value for the face widths.) If the initial (no load) contact of the crowned profile(s) falls off the end of the tooth due to the lead mismatch the model will not be solved and the note INITIAL TOOTH CONTACT OFF END will appear. Spur Gears If the contact ellipse (under load) falls off one or both ends of the gear tooth the calculated stress will be increased due to the reduced contact pattern. CROWNED TOOTH CONTACT OFF END will appear if the ellipse is off one end of the tooth. If the ellipse falls off both ends of the tooth the comment CROWN CONTACT OFF BOTH ENDS will appear. Helical Gears The contact ellipse is always truncated at the start and end of the contact zone. It is assumed that the initial contact of the CROWN is closest to the start of the contact zone. (In many cases the ellipse is truncated for the entire mesh cycle.) As an example a 12 normal diametral pitch, AGMA quality Q8, helical gear set with 27 teeth in the pinion and 108 teeth in the gear will be used. The gears are steel. The design load is 100 horsepower and the pinion speed is 3600 RPM. The initial temperature will be 200 F. (The initial or inlet temperature is the temperature of the lubricant as it enters the contact zone. This temperature may be somewhat higher than the sump temperature (for splash fed gears) or manifold temperature (for pressure fed gears). NOTE: If the actual value of the surface finish on the gears after break-in is not known, a suggested composite surface finish is available from table Finish from the reference. The individual surface finishes should be left blank if the composite finish is used. The face mismatch is.002 inch across a 2 inch face for the gear. The first calculation will be with straight teeth. 4

5 Crowned and Straight External Involute Gear EHL Film Thickness Examples Open a new analysis and enter the data shown in Figure 1. Since the gears are steel we can use the default values for Young s Modulus and Poisson s Ratio and do not have to enter them. For other materials they must be entered or they will default to the values for steel. Fig. 1 Because we have not chosen a lubricant, we do not know what the lubricant parameter (LP) is. Let s suppose we wish to hold the cold scoring probability to about 20%. Since TK Solver will solve in any direction, we can set the scoring probability to 20% and solve for a lubricant parameter. However, when solving in this direction the equations cannot be solved directly, so an iterative solution technique must be used. To do this we must toggle to TK Solver and work directly in the Variable Sheet. We will make a guess for the LP of 50. Input 50 for the LP, move the cursor to the status column and type G, or double-click the cell and pick Guess from the drop-down list of input value types. This will tell TK Solver that 50 is a guess at a starting point and TK's Iterative Solver will be used to solve the equations. 5

6 UTS Integrated Gear Software NOTE: The values that may be used for input for probability of scoring are about 6% to 49% or you may get an error message. If an error occurs with probability set between these values make a different guess for the LP. Your Variable Sheet entries should look like Sheet 1. Sheet 1 Return to the Integrated Gear Software interface and click the toolbar Solve button. Report 1 shows the inputs and outputs for this model. Report 1 COMMON DATA Quality Class 8 PINION Speed Power rpm HP 6

7 Crowned and Straight External Involute Gear EHL Film Thickness Normal pitch Normal Pressure Angle Helix Angle Operating Center Distance /in ` deg deg in Total Lead Mismatch Between Teeth in FILM THICKNESS & SCORING PROBABILITY : Crowned Teeth Actual Width of Contact Ellipse Length of Full Contact Ellipse NA in NA in Length of Actual Contact Ellipse NA in FILM THICKNESS & SCORING PROBABILITY : Straight Teeth Contact Length Maximum Contact Width in in Lubricant Parameter 68.7 Set Lube Parameter Table to Initial Lubricant (Inlet) Temp EHL Film at Center of Interval Composite Surface Finish y 200 C uin uin Correction Factor (Inlet Shear) 0.93 Specific Film Thickness 0.75 Probability of Cold Scoring 20 % PINION DATA Number of Teeth 27 Outside Diameter Face Width in in 7

8 UTS Integrated Gear Software Surface Finish,rms (After break-in) GEAR DATA uin Number of Teeth 108 Outside Diameter Face Width Surface Finish,rms (After break-in) in in uin An oil with an LP of about 69 will hold the cold scoring probability to 20%. The next step is to find a lubricant with an LP of about 69 at a temperature of 200 F. The model contains a table of all Mobil lubricants contained in reference 3. When we solved the model this table was updated to 200 degrees F. Sheet 4 is the table in printed form. 8

9 Crowned and Straight External Involute Gear EHL Film Thickness Sheet 4 Mobil Lubricant Parameter AUTOMOTIVE_GEAR_OILS Lube_SHC 38 EP Lube_HD_80W 28 EP Lube_HD_80W_90 50 EP Lube_FE_80W_ EP Lube_HD_85W_ EP Lube_HD_90 65 EP Lube_HD_ EP INDUSTRIAL_GEAR_OILS Cyl_600W 127 Sp_Cyl_600W 143 Sp_Cyl_Minrl_600W 164 X_HECLA_Sp_Cyl 206 X_HECLA_Sp_Cyl_Mnrl 241 DTE_Light 12 DTE_Medium 16 DTE_Hvy_Med 24 DTE_Heavy 34 DTE_Extra_Hvy 45 DTE_BB 67 DTE_AA 102 DTE_HH 140 Glygoyle_11 33 Mild_EP Glygoyle_22 70 Mild_EP Glygoyle_30 96 Mild_EP Glygoyle_ Mild_EP SHC_ Mild_EP SHC_ Mild_EP SHC_ Mild_EP SHC_ Mild_EP 9

10 UTS Integrated Gear Software Mobil Lubricant Parameter SHC_ Mild_EP Gear_ EP Gear_ EP Gear_ EP Gear_ EP Gear_ EP Gear_ EP Gear_ EP AUTOMATIC_TRANS_FLUID ATF_ AUTOMOTIVE_ENGINE_OILS Mobil_1 18 Delvac_1 17 Delvac_ Delvac_ Delvac_ Delvac_ Delvac_ Delvac_ Delvac_ Delvac_ Delvac_ Delvac_ Delvac_ Delvac_ Delvac_ Delvac_ Delvac_ Oil_10W 12 Oil_20W_

11 Crowned and Straight External Involute Gear EHL Film Thickness Mobil Lubricant Parameter Oil_30 34 Oil_40 48 Oil_50 69 Special_10W_30 18 Super_10W_40 18 GAS_ENGINE_OILS Pegasus_360_385_ Pegasus_100_30 30 Pegasus_460_485_ Pegasus_100_40 41 DIESEL_ENGINE_OILS DTE_Oil_#3 33 DTE_Oil_#4 47 DTE_Oil_#5 65 Gard_ Gard_ Gard_ Gard_ Gard_ Gard_ Gard_ Gard_ Gard_ Gard_ Gard_ Gard_ Gard_ Gard_443_ Gard_ Gard_

12 UTS Integrated Gear Software Mobil Lubricant Parameter Gard_ Gard_ Gard_444_ Gard_448_ HYDRAULIC_OILS DTE_21 4 DTE_ DTE_24 11 DTE_25 15 DTE_26 22 DTE_27 36 Vacuoline_ Vacuoline_ Vacuoline_ AIRCRAFT_JET_ENGINE_OILS Jet_ Jet_II 11 TURBINE_OILS DTE_ DTE_ SHC_ SHC_ SPINDLE_OILS Velocite_C 9 Velocite_D 7.3 Velocite_E 3.5 Velocite_S 5.6 Velocite_#3.9 12

13 Crowned and Straight External Involute Gear EHL Film Thickness Mobil Lubricant Parameter Velocite_#6 3.5 Velocite_#8 5.6 Velocite_# Velocite_#12 9 COMPRESSOR_OILS DTE_ DTE_ Rarus_ Rarus_ Rarus_427_US 36 Rarus_427_ID 25 Rarus_ Rarus_ Rarus_ Rarus_ Rarus_ AIR_TOOL_OILS Almo_ Mild_EP Almo_ Mild_EP Almo_ Mild_EP Almo_ Mild_EP Almo_ Mild_EP MACHINE_OILS Etna_#2 34 Etna_#3 50 Etna_#4 70 Etna_#6 140 Vactra_Light 12 Vactra_Medium 17 13

14 UTS Integrated Gear Software Mobil Lubricant Parameter Vactra_Hvy_Med 24 Vactra_Heavy 35 Vactra_Extra_Hvy 46 Vactra_BB 69 Vactra_AA 103 Vactra_HH 141 Viscolite_Hvy 27 Viscolite_Ex_Hvy 50 Viscolite_BB 77 Viscolite_AA 96 Viscolite_HH 136 Viscolite_SS 294 CIRCULATION_OILS Paper_Mach_J 41 Paper_Mach_K 58 Vacuoline_X28 50 Vacuoline_X33 72 Vacuoline_X37 99 Vacuoline_X Vacuoline_X Vacuoline_ MIST_OILS Mist_24 15 EP Mist_27 43 EP Mist_30 59 EP Mist_32 83 EP Mist_ EP REFRIGERATION_OILS Gargoyle_Arctic_Lt

15 Crowned and Straight External Involute Gear EHL Film Thickness Mobil Lubricant Parameter Gargoyle_Arctic_C 15 Gargoyle_Arctic_C_Hvy 18 Gargoyle_Arctic_Ex_Hvy 23 Gargoyle_Arctic_ Gargoyle_Arctic_ METAL_CUTTING_FLUIDS Mobilmet_Omicron 11 Mobilmet_Upsilon 4.2 WAY_OILS Vactra_#1 12 Mild_EP Vactra_#2 23 Mild_EP Vactra_#3 32 Mild_EP Vactra_#4 69 Mild_EP INITIAL_TEMP degf 167 INITIAL_TEMP degc 75 Note that the temperature to which the LP s are set appears at the bottom of the table. (The listing of lubricants in the table does not imply that they are suitable for the temperature listed. Lubricants must be selected on the basis of high and low temperatures to which they will be exposed. Check your selection with a qualified lubricant supplier.) Since we need an LP of about 69 we will choose Mobil Gear 634. Blank the scoring probability, input 65 for the LP on the data input form and solve. The completed data input form is shown in Figure 2, the report for the solved model in Report 2. 15

16 UTS Integrated Gear Software Fig. 2 Report 2 Message Field Message Field Message Field Message Field Message Field COMMON DATA STRAIGHT TEETH TEMP HIGH Quality Class 8 _ 16

17 Crowned and Straight External Involute Gear EHL Film Thickness PINION Speed PINION Torque Power Tangential Load at Operating PD Pitch Line Velocity Normal pitch Normal Module Normal Pressure Angle Helix Angle Transverse Pitch Transverse Module Transverse Pressure Angle Base Helix Angle Operating Center Distance Operating Trans Pressure Angle Operating Helix Angle Effective Face Width Total Lead Mismatch Between Teeth rpm lbf-in HP lbf ft/min /in ` mm ` deg deg /in ` mm ` deg deg in deg deg in in Face Load Distribution Factor Tooth Stiffness Constant psi Distance from Center of Tooth to Initial in Tooth Contact Gear Ratio Profile Contact Ratio (Theoretical) Helical Contact Ratio (Theoretical)

18 UTS Integrated Gear Software FILM THICKNESS & SCORING PROBABILITY : Crowned Teeth Actual Width of Contact Ellipse Length of Full Contact Ellipse NA in NA in Length of Actual Contact Ellipse NA in FILM THICKNESS & SCORING PROBABILITY : Straight Teeth Contact Length Maximum Contact Width in in Lubricant Parameter 65.0 Set Lube Parameter Table to Initial Lubricant (Inlet) Temp EHL Film at Center of Interval Composite Surface Finish y 200 C uin uin Correction Factor (Inlet Shear) 0.93 Specific Film Thickness 0.73 Probability of Cold Scoring 23 % PINION DATA Number of Teeth 27 Outside Diameter Transverse Crown Rise (Default=0) Face Width Tooth End to Initial Contact Point Tooth End to Crown Contact Ellipse With Crown Centered On Tooth Surface Finish,rms (After break-in) in in in in in uin 18

19 Crowned and Straight External Involute Gear EHL Film Thickness Young's Modulus (Default=steel) psi Poisson's Ratio (Default=.3) Operating Pitch Diameter Start of Active Profile-No Undercut Base Diameter GEAR DATA in in in Number of Teeth 108 Outside Diameter Transverse Crown Rise (Default=0) Face Width Tooth End to Initial Contact Point Tooth End to Crown Contact Ellipse With Crown Centered On Tooth Surface Finish,rms (After break-in) Young's Modulus (Default=steel) in in in in in uin psi Poisson's Ratio (Default=.3) Operating Pitch Diameter Start of Active Profile-No Undercut Base Diameter ROLL ANGLES : Pinion in in in Start of Active Profile Low Single Tooth Contact Pitch Diameter, Operating Center of Contact Interval High Single Tooth Contact deg _ deg deg deg _ deg 19

20 UTS Integrated Gear Software Outside Diameter, Effective ROLL ANGLES : Gear deg Start of Active Profile Low Single Tooth Contact Pitch Diameter, Operating Center of Contact Interval High Single Tooth Contact Outside Diameter, Effective deg _ deg deg deg _ deg deg With Mobil DTE HH we have about a 23% chance of scoring. (If the scoring probability is 20% or higher a message will be given in the message field suggesting the use of an extreme pressure lubricant instead of a non-reactive lubricant.) The film thickness is about microinch and the specific film thickness about.73. This is probably a good choice of lubricant for this application, as the table shows that Mobil Gear 634 is classed as an extreme pressure (EP) oil. The pour point and viscosity should be checked to make sure that they are OK for this application. EP additives are meant to react with the tooth surfaces at high temperatures and form a film to prevent welding. EP lubricants were developed primarily for prevention of hot scoring due to high temperatures at the tooth contact from high speed and load but have been found to help in cold scoring also. (This is probably due to the hot scoring characteristics of the asperity contact.) Let s put.0015 inch crown on the pinion and see what change this will make in the cold scoring probability. (Crown should not be added without consideration of the change in compressive and bending stress. See UTS TK Solver model ) Figure 3 shows a portion of the data input form with the crown added. Click the toolbar Refresh Values button, then the Solve button. The solved model is shown in Report 3. 20

21 Crowned and Straight External Involute Gear EHL Film Thickness Fig. 3 Report 3 Message Field Message Field Message Field Message Field Message Field COMMON DATA CROWNED TEETH TEMP HIGH _ Quality Class 8 PINION Speed rpm 21

22 UTS Integrated Gear Software PINION Torque Power Tangential Load at Operating PD Pitch Line Velocity Normal pitch Normal Module Normal Pressure Angle Helix Angle Transverse Pitch Transverse Module Transverse Pressure Angle Base Helix Angle Operating Center Distance Operating Trans Pressure Angle Operating Helix Angle Effective Face Width Total Lead Mismatch Between Teeth Face Load Distribution Factor lbf-in HP lbf ft/min /in ` mm ` deg deg /in ` mm ` deg deg in deg deg in in Tooth Stiffness Constant psi Distance from Center of Tooth to Initial in Tooth Contact Gear Ratio NA Profile Contact Ratio (Theoretical) Helical Contact Ratio (Theoretical)

23 Crowned and Straight External Involute Gear EHL Film Thickness FILM THICKNESS & SCORING PROBABILITY : Crowned Teeth Actual Width of Contact Ellipse Length of Full Contact Ellipse in in Length of Actual Contact Ellipse in FILM THICKNESS & SCORING PROBABILITY : Straight Teeth Contact Length Maximum Contact Width Lubricant Parameter 65.0 Set Lube Parameter Table to Initial Lubricant (Inlet) Temp EHL Film at Center of Interval Composite Surface Finish NA in NA in y 200 C uin uin Correction Factor (Inlet Shear) 0.93 Specific Film Thickness 0.75 Probability of Cold Scoring 21 % PINION DATA Number of Teeth 27 Outside Diameter Transverse Crown Rise (Default=0) Face Width Tooth End to Initial Contact Point Tooth End to Crown Contact Ellipse With Crown Centered On Tooth Surface Finish,rms (After break-in) in in in in in uin 23

24 UTS Integrated Gear Software Young's Modulus (Default=steel) psi Poisson's Ratio (Default=.3) Operating Pitch Diameter Start of Active Profile-No Undercut Base Diameter GEAR DATA in in in Number of Teeth 108 Outside Diameter Transverse Crown Rise (Default=0) Face Width Tooth End to Initial Contact Point Tooth End to Crown Contact Ellipse With Crown Centered On Tooth Surface Finish,rms (After break-in) Young's Modulus (Default=steel) in in in in in uin psi Poisson's Ratio (Default=.3) Operating Pitch Diameter Start of Active Profile-No Undercut Base Diameter ROLL ANGLES : Pinion in in in Start of Active Profile Low Single Tooth Contact Pitch Diameter, Operating Center of Contact Interval High Single Tooth Contact deg _ deg deg deg _ deg 24

25 Crowned and Straight External Involute Gear EHL Film Thickness Outside Diameter, Effective ROLL ANGLES : Gear Start of Active Profile Low Single Tooth Contact Pitch Diameter, Operating Center of Contact Interval High Single Tooth Contact Outside Diameter, Effective deg deg _ deg deg deg _ deg deg With the crown on the pinion and Mobil DTE HH we have about a 21% chance of scoring. The film thickness is about microinch and the specific film thickness about.75. The addition of crown helped the scoring probability somewhat. This will not always be the case. In some gear sets the addition of crown makes matters worse. (See UTS Model ) This example is not meant to imply that a 20% chance of scoring is suitable for gear sets. This choice must be made by the gear engineer for each application. References: 1. AGMA , AGMA Standard for Rating the Pitting Resistance and Bending Strength of Spur and Helical Involute Gear Teeth 2. AGMA , AGMA Information Sheet - Gear Scoring Design Guide for Aerospace Spur and Helical Power Gears Data extracted from reference 1 and 2 with the permission of the publisher, the American Gear Manufacturers Association, 1500 King Street, Suite 201, Alexandria, VA Mobil EHL Guidebook, Third Edition Mobil Oil Corporation Commercial Marketing Technical Publications 3225 Gallows Road Fairfax, VA