ABSTRACT
The wear life of a gear box can be greatly extended with a good gear replacement selection and a preventive maintenance program that consists of periodic inspection of the gear tooth wear, the amount of contamination in the lubricant, bearing end play, and operating temperature.
LUBRICATION
The lubrication of the gears and bearings is the most important contributing factor to long life. The functions of the lubricating oil are described below:
1. SEPARATION OF METAL:
Oil provides a very thin film, that could be anywhere from several millionths of an inch to perhaps several tenths of one thousandth of an inch, to prevent the gear teeth and bearing metals from contacting each other. While this appears to be an extremely thin oil film, it is sufficient to keep the metals from touching each other. If the oil film breaks due to heavy loads, water in the oil, too low an oil viscosity due to high shearing temperature, or extremely heavy shock loads, the gear teeth or bearings may spot weld to each other then immediately break the spot weld due to continuous motion and result in scoring and pitting.
2. LUBRICATION:
A gear oil that provides the thickest film for the operating conditions should be selected. A thicker oil film offers more protection from spot welding, scoring, or wear due to abrasive, fine particles of foreign material in the oil. An even greater advantage provided by a thick oil film, is that the forces at the gear teeth and the bearings are transferred from one component to another through an improved hydrostatic load transfer. When the hydrodynamic oil film is over three times greater than the surface asperity, concentrated loads at high points of asperity are avoided. When the oil film thickness is less than two times the surface asperities, mechanical load transfer occurs because the high spots on one tooth will contact the high spots on the mating tooth. This results in higher localized forces that cause higher stresses that lead to an earlier fatigue failure. Fatigue failure begins at metal disparities where the resistance to strain is lower. (Disparities may be caused by small layers of low strength inclusions such as copper, silicon, etc.) The thicker hydrodynamic oil film increases the fatigue life of the steel in gears and bearings.
The preference should always be for the heaviest gear oil so long that the operating temperature is not below the oil pour point in order to avoid channeling. (Oil channeling is defined as exposure to low temperature where the oil becomes thick like grease and no longer flows. When the gears rotate, the oil will not flow back between the gear teeth and bearing rollers to provide continuous lubrication. Therefore, even though there is a sufficient amount of oil in the gear box, the gear teeth and bearings could be starved and overheat because oil thick like grease does not flow.) It should also be considered that at the high temperature end the heavier oils generate more heat, because it takes more energy to shear the oil. For example, if the gear box continuously operates at temperatures above 200°F, it may be preferable to go to a lighter weight oil in order to reduce the operating temperature. In the end, the same oil film thickness could be achieved. Figure 3 shows that the same oil film thickness can be achieved with SAE 90 oil at 128°F as with SAE 140 at 172°F. A high-speed shaft may develop a thicker oil film due to the velocity factor of the hydrodynamic film properties of oil.
During NASA testing it was found that oils with extreme pressure (EP) additives of sulfur phosphorous oxide increase surface durability by a factor of five. For this reason, it is recommended that only oils with EP additives be used. These additives also have the quality of further enhancing the metal-to-metal separation and in turn increase wear and fatigue life¹.
A guide to types of oil to be selected for operating temperatures should be used from Figure 1. A guide for oil change intervals for various continuous operating temperature is presented in Figure 2. Figure 3 shows various hydrodynamic oil film thicknesses calculated to develop between gear teeth under heavy loads. This figure is made to illustrate how the oil film thickness varies with temperature and with viscosity. Figure 4 shows the kinematic viscosity property of various grades of gear oils.
Some gears and bearings are lubricated with grease, which is adequate for slow operating components. Medium and high-speed components cannot be lubricated properly with grease because the centrifugal force would throw the grease away from the gears and bearings. They could soon become dry and then fail due to lack of lubrication because the grease is like a very thick paste and it does not flow freely back between the gear teeth and bearing rollers like oil does.
3. CARRY AWAY HEAT:
Another function of the lubricant is to carry the heat away from the metal gear teeth and bearings in order to reduce their operating temperatures. Heat is generated when a load is transferred from one gear tooth to another or from one bearing component to another. The heat must be carried away from the generating point into the air or water in order to reduce the temperature of the metal as much as possible.
Inevitably, even with the best lubrication, the gears and bearings will wear due to sliding. Gear teeth have pure rolling at the pitch diameter only. Sliding increases proportionally to the distance away from the pitch diameter. Some sliding occurs at the bearings when the rollers skew and also by design such as at the thrust end of the rollers. Spherical rollers and balls also have sliding because of the different amount of circumferential length travel between the ball or roller and race at contact point. Bushings also produce heat due to sliding. When sliding occurs, metal particles are rubbed off the sliding surfaces and mixed with the oil. If the oil film thickness is less than two to three times greater than the surface asperities, the particles that are larger than the oil film thickness may cause depressions on the gear teeth or bearing surfaces when trapped under load. They are further reduced in size under heavy loads until they are about the size of the oil film thickness. Sometimes such large metal particles will make a depression on the gear teeth or bearing surfaces, however, if cracks are not produced the metal fatigue life may not be affected. This illustrates how good filtration can increase the gear box operating life. A chemical analysis can be done when the oil is inspected to determine whether the suspected metal particles came from gears and bearings or from other sources. (This is done by determining the amount of a particular alloy such as chrome or nickel.) If some components are subjected to heavy wear, the periodic chemical analysis will alert you when the number of metal particles begins to increase rapidly. At this point, the gear box should be shut down for preventive maintenance and/or repair. Foreign particles in oil that are less than 10,000 per million are acceptable. The oil need not be changed until the contaminants exceed 10,000 parts per million.
A simple way to inspect a gear box and determine if the wear is normal or if there may be an imminent failure is to install a magnetic plug at the bottom of the case where the oil is in motion and use the following guidelines:
1. Remove the plug once a week to inspect the metallic deposit on the magnet and to detect wear or damage at its beginning stage to initiate preventive maintenance.
Normal Wear:Pick up the metallic deposit off the magnet and rub it between your fingers. If it looks like silver paint it is caused by normal wear. Clean the plug. Return it to the gear box and continue to operate the gear box.
Abnormal Wear:If the metallic deposit appears to have steel crumbs when you rub it between your fingers, it is an indication that gear teeth, bearings, or other components are disintegrating. The gear box must be removed from service immediately and inspected for repair. When the gear teeth or bearings disintegrate into crumbs they may break into pieces or pits are formed that will not self-heal. The pits will only grow like a pothole in the road grows. The gear box must be promptly repaired.
2. Check the oil level every time you inspect the magnetic plug. Add or change oil if necessary.
To simplify this inspection, Power Engineering & Manufacturing, Ltd. has designed and currently manufactures a magnetic plug with a check valve to stop the oil flow after the magnetic plug is removed, such as the one shown on Figure 5.
BEARINGS
In order for bearings to operate properly they must be correctly installed as well as adequately lubricated. Endplay is defined as axial movement of a shaft. During normal operation the outside walls of the case will be operating at a lower temperature than the gears and shafts. (The reason for this is because heat is generated at the gear teeth and at the bearings and the case is exposed to outside air that is cooler.) The metal of the shaft, bearings, and gears operates at a higher temperature than the case itself. The heat is carried away to the case walls by the oil. For that reason, we expect the shafts to grow in length more than the case walls. If we do not have clearance at the bearings, defined as endplay, or the case has flexible walls, then this shaft growth can impose extremely high loads on the bearings and lead to lower life and failure.
For example, tapered roller bearings operate best with .001 – .005 endplay, unless the gear box manufacturer recommends a different setting or perhaps even no (.000) endplay. Endplay can be set by using a dial indicator and shims. See Figure 6.
Cylindrical roller bearings must have some endplay as well as radial clearance between the rollers and the outer race. (Figure 7 shows how the bearing roller clearance is checked after installation. This inspection should be made at twelve o’clock on the bearing, or in other words vertically above the centerline where gravity has no effect on the clearance measurement.) This clearance must be at least .002. When it exceeds .0 IO for a small or medium sized bearing or .015 for a bearing larger than one foot in diameter the bearing should be replaced due to excessive wear.
Spherical bearings should be treated in a similar manner as the straight cylindrical bearing, requiring a minimum of several thousandths endplay and over .002 radial clearance between the roller and the outer race, again when measured directly above the centerline of the shaft (vertically up at twelve o’clock). Refer to Figure 8.
Bushings should have a minimum of .005 clearance with provisions for oil flow so that the oil can circulate through the bearing and carry away the heat generated by the sliding due to shaft rotation under load.
For good gear box durability, the bearing endplay and shaft clearances should be checked periodically as deemed necessary for each operation, preferably prior to the start of the season. For bearings, corrective action must be taken whenever necessary because under heavy loads if a bearing fails, gears may fail as well. The resulting failure could lead to an expense many times greater than the cost of replacing a bearing or two.
GEARS
Gears that are in good operating condition must have smooth surfaces with a good involute profile. Although a small amount of wear may be acceptable, heavy involute wear can cause vibrations or damage to the mating gear. In a speed reducing gear box where the gear has many more teeth than the pinion, the pinion undergoes a larger number of load cycles and will consequently wear and fatigue sooner than the big diameter gear. For this reason, it is often economical to replace a worn or fatigued pinion in order to enable a longer life for the mating gear. For example, in a five to one reduction ratio gear set the gear will have a wear and fatigue life five times longer than the pinion. Through adequate maintenance it would be possible to replace the pinion five times before needing to replace the gear. This is more economical than allowing the pinion to operate to failure, resulting in damage or destruction of the gear and possibly other adjacent gears and bearings.
Metal fatigue of gear teeth or bearings can be observed if the surfaces have spalling. Spalling is a condition where the metal just flakes away leaving pits that have a rather rough surface. The pits usually grow fast due to the heavy loads that are applied at the periphery of the pit. (These pits grow in a similar manner as a pothole grows in a road under constant traffic.) When spalling is observed the gears should be removed from operation promptly because the metal particles that fall and mix with the oil can damage other components in the gear box. Figure 9 shows spalling due to end loading caused by misalignment.
Figure 10 shows a line of spalling at the start of active profile near the pinion root diameter caused by excessively high surface compressive stress combined with high sliding. Note that a large pit, marked “A”, grew rapidly from the small pits initiated at the start of active profile due to the pothole effect. This gear tooth failed by pitting without having any wear. You may see that the grinding marks still show.
CARBURIZED HIGH HARDNESS PINION WITH MEDIUM HARDNESS GEARS
When a pair of gears operate with a high reduction ratio, such as 6 or 7: 1, the pinion will accumulate a larger number of load cycles than the gear proportional to the reduction ratio of those two gears. Consequently, the pinion will be subjected to a higher number of surface fatigue cycles, bending stress cycles, and surface wear due to sliding. If the pinion and the gear are at nearly the same hardness, in a 6: 1 reduction ratio the pinion will have to be replaced six times before the gear is replaced. However, many times a pinion that has advanced surface wear or possibly even broken teeth may damage the gear to the extent that the gear will not last long enough to be used with five or six pinions. This condition can lead to a costly premature replacement of the gear.
A common practice is to make the pinion somewhat harder than the gear. Often the pinion is through hardened to 270-310 BHN and the gear is hardened to 230-280 BHN. This difference in the hardness average of about 35 BHN points will double to triple the surface fatigue life of the pinion, but this is not enough to equal the gear life when the reduction ratio is greater than 3: 1.
A better service life may be obtained from both the pinion and the gear if a carburized or induction hardened pinion, with an adequate depth of case hardness, and a through hardened gear, that is of medium hardness, are used. In such a combination the gear teeth and pinion teeth should be designed so that the fatigue and wear life of the pinion and the gear wear out at the same time, after a long life.
Figure 11 illustrates the strength and fatigue characteristics of a carburized steel and of a medium hardness steel. The fatigue properties of the carburized steel are very much higher than the fatigue properties of the medium carbon steel. (Carburized steel heat treated to Rc56-62 and medium carbon steel heat treated to BHN 310.) The surface fatigue behavior of metals has been proven in research done by bearing manufacturers to be to the power of 3.33. The metal fatigue behavior of gears and bearings is similar because both have rolling and sliding under heavy pressure and with an oil film for lubrication.
The relationship of material fatigue behavior in relation to the force to which it is subjected, is to the power of 3.33, as shown in Equation 1. However, when calculating the surface compressive stress, the force appears under the square root, as shown in Equation 2. Therefore, when the fatigue properties of the metal are correlated based on surface compressive stress properties and not force properties, the relationship goes to the power of 6.66 as shown in Equation 3, which is derived by substituting stress in place of force and simplifying the equation.
As shown in Equation 4, a 100% difference in the material fatigue properties yields an effect of the 6.66 power. Therefore, if the fatigue surface compressive stress doubles, due to material higher hardness, and is raised to the 6.66 power the life increases by a factor of 100, not just six times longer relating to the gear ratio. Conversely, if the operating surface compressive stress is doubled, the fatigue life goes down by a factor of 100. The hundred-fold effect of doubling or reducing to half the operating surface compressive stress, which is controlled by the 6.666 power, should be distinguished from doubling or reducing to half the horsepower. The horsepower or load effect on surface fatigue life is controlled by the 3.333 power, therefore, when the horsepower is doubled or reduced to half the fatigue life of the gears or bearings is reduced or increased tenfold as shown in Equation 5.
Another advantage of combining ground carburized and high hardness pinion with fully hardened medium hardness gear is illustrated in Figure 12. The yield strength of the carburized steel at Rc 56-62 is 266,000 psi while the yield strength of a medium hardened pinion at BHN 310 is 77,000 psi. This shows that mechanical properties of the carburized and case-hardened pinion tooth surface is nearly three times higher and similarly in ultimate strength. Therefore, under heavy loading the gear material may yield but the pinion material will yield at a much higher load. Such a pinion is desirable because it is necessary to maintain the curvature of the involute profile intact so that load can be transferred without generating vibrations, that in effect are higher forces that shorten the fatigue life. The fatigue stress levels and load cycles may not correspond to the AGMA numbers because PEM developed its own theoretical calculations based on scientific analytical fundamentals that correlate well with our product experience.
It is further desired to have the carburized pinion tooth profile ground so that it would have a smooth surface. The yield properties of the medium hardness gear, being much lower than the carburized gear, would smooth out the gear tooth surface. This will improve the oil film thickness between the teeth and eliminate localized stress rising points that can lead to a shorter fatigue life.
A carburized, non-yielding pinion will retain the involute profile and cause the gear to also retain the involute profile. As mentioned at the beginning of the paper, the principle feature of the involute profile is that it provides a means of attaining constant angular velocity.
Figure 13 shows a rough surface on the teeth. The metal flowed to form peaks and valleys in a herringbone pattern. Under heavy loads with insufficient lubrication the sliding coefficient of friction may increase by as much as fivefold or more. As the gears rotate and the teeth contact to transfer the load, sliding action takes place at the tooth surface.
The coefficient of friction at the teeth is about .04 when the lubrication is good. A coefficient of friction between .10 and .20, or even higher, can be expected when the lubrication is poor. Note from Figure 14 that the friction force (FF) at the teeth increases in proportion to the coefficient of friction. NF is the normal force generated by the torque an µ is the sliding coefficient of friction. This force causes shearing action that makes the metal flow. At the pitch diameter the sliding is zero and it increases in magnitude the further the point of contact is away from the pitch diameter. In Figure 13 you can see a clear channel like line, that is the pitch diameter. In Figure 13, above and below the pitch diameter, the material flow is in a “V” shape along the tooth or herringbone pattern. This condition is caused by the fact that the sliding between teeth is in the radial direction. This is a helical gear, and the line of load contact is in a diagonal direction on the tooth. (See Figure 15.) Furthermore, each tooth has sliding in both directions starting at zero at the pitch diameter and increasing in magnitude linearly as the contact between teeth moves away from the pitch diameter. (See Figure 16.) The combination of radial sliding in opposite directions and diagonal load contact gives rise to the herringbone pattern. When such involute profile distortion occurs, it is recommended that the gears be removed and a minimum layer of material be machined off to restore the involute profile. If the gears are allowed to continue to operate with the herringbone pattern, the fatigue life will be shorter because the contact area of load transfer is smaller, as shown on Figure 17, and consequently the operating stresses will be higher. This will result in a shorter fatigue life. In this case, the surface stresses exceeded the material yield properties and the material moved. If the pinion would have been carburized and consequently, of a much higher hardness than the gear, then the pinion surface would have not yielded and would have allowed the gear to maintain its surface profile.
In Figure 17 the high peaks and valleys along the surface of the gear tooth result in an uneven surface contact. The forces transferred from one tooth to another will now be applied over a much smaller length or area of contact because the voids subtract from the surface that carries the load. Consequently, stresses will be very high resulting in more rapid, localized fatigue. A carburized pinion would have maintained the smooth surface without yield on the pinion. Without a mechanism to create peaks and valleys on the gear, the surface would have remained smooth. Figure 18 illustrates a smooth surface where we expect a load transfer to take place over a much longer line or larger area of contact. The stresses remain lower; therefore, surface fatigue will not be promoted as fast, and the life of the gear will be extended.
SHAFT AND GEAR ALIGNMENT
In order to have good and even load distribution over the entire length of the gear teeth and the entire length of the bearing rollers, the shafts must operate parallel to each other. If the shafts are not parallel and the gears do not have good load distribution, end loading develops as shown on Figure 9. In extreme conditions it is possible that only half (or even less) of the gear tooth face may carry the load. This condition is the same as having a gear that is half as wide. Since gears and bearings behave in a similar manner, the life to load relationship is such that when the load is doubled the life is reduced by a factor of ten. Equation 5, on page 11, governs the life load relationship for bearings as well as gears.
When gear box maintenance is performed on parallel shaft gear boxes, a load pattern inspection is recommended using a spray powder penetrant and developer (such as Magnaflux® SpotCheck®). Under extreme conditions where heavy loads are applied, the gear box case could permanently distort. When this happens, one side of the gear case may distort more than the other side leading to permanently positioning the shafts in a non-parallel condition of operation. In order to maintain good load distribution at the gear teeth, shaft and gear misalignment must be avoided.
The bearing pockets must be square with the shafts in order to have good load distribution for the full length of the rollers so that the bearings attain their full designed life. If, by the load pattern test, a parallel shaft gear box is found to have uneven load distribution at the gear teeth the situation may be improved by raising one corner of the gear box with shims in order to physically bring the walls into a squarer position and again enable the shafts to operate parallel to each other. Once the raised position is found that will provide better load distribution, all of the bolts that fasten the gear case to the foundation should be shimmed so that no additional distortion is imposed when tightening the retaining bolts. If this mounting adjustment cannot be done, the gear case should be re-machined, or the gear life will be shortened.
When planetary gear boxes are installed, opening the gear box is not necessary because a planetary gear box that has three planet gears, automatically align themselves and will have good load distribution over the entire length of the gear tooth. A planetary with three planet gears is like a three-legged stool; no matter how uneven the floor the three-legged stool will always be stable and not rock. In this regard, the planetary reducer is superior to the parallel shaft reducer. Throughout the life of the gear box the parallel shaft reducer may experience distortion resulting from large radial and axial forces at the gear teeth. A planetary reducer will not have this distortion because the radial forces at the mesh between the sun pinion and the planet gears cancel out by the radial forces at the planet to ring mesh due to being equal and in opposite direction. The tangential force generates the output carrier torque. The planetary case is also stronger and stiffer because the ring gear forms the case.
Figures 23 and 24 show a planetary type gear box. This gear box does not need re-alignment at installation time because the internal components are such that either the sun pinion, the planetary carrier, or both are floating in order to provide equal load distribution between the three planet gears, the sun, and the ring gear. This type of gear box will always maintain good load distribution by its inherent design.2 The planetary has three principal members: a sun pinion, a planetary carrier assembly which includes three planet gears, and a ring gear, as shown on Figure 19.
The ring gear is stationary, the planetary carrier is the member that rotates the output shaft, and the sun pinion is the input member. Figure 20 shows how the gears are nested together during operation.
Figure 21 shows one planet gear, one planet shaft, and a triple row cylindrical bearing. To maximize the bearing capacity for long life, the shaft becomes the bearing inner race and the bore inside the planet gear becomes the outer race. The three rows of cylindrical rollers are used without a cage so that the number of rollers can be maximized and thus increase the bearing life. This is an economical bearing construction, and the bearing life is calculated so that it will be as long or longer than the gear life. In addition, a planetary gear box has a high-power density and is smaller in size than a parallel gear box due to the advantage of having three gears in the planet carrier carrying the load simultaneously as compared to only one gear in a parallel reducer or two gears in a herringbone arrangement.
Figure 22 shows the ring gear, the three planet gears, and the sun pinion. Each planet gear has two arrows on the teeth and each planet gear bore has one longer ai-row. The two arrows on each planet gear, marked “F”, designate the forces that act upon the teeth of the planet gear. The force near the center is the force from the input torque, marked “T”. This force is generated at the sun pinion teeth and acts upon the planet gear teeth. Because the planet gear is mounted on an anti-friction bearing, an equal force is generated 180° away from the sun pinion gear tooth mesh at the planet to ring mesh. At that point, the reaction force, marked “F”, also acting by the ring gear upon the planet gear tooth, is equal in magnitude to the force near the sun pinion. The magnitude of the force seen by the planet gear shaft, marked “2F”, is the sum of the two forces acting upon the planet gear teeth. This is the action and reaction sum of the forces acting on the planet gear. Because the planet gear shaft is mounted in the planet carrier and because there are three such planet shafts, the output carrier torque is proportional to the sum of those three planets bore reaction forces multiplied by the radius at which they operate.
This clearly shows that in a planetary there are six gear teeth in mesh simultaneously. At all times the forces on the teeth are equal in magnitude. This is the fundamental and principal advantage of a planetary construction gear reducer. Having six teeth carry the load simultaneously, the individual forces are lower than they would be if only one or two teeth carried the load, as is the case with spur and helical or herringbone parallel shaft gear sets. In addition to that, all the radial forces, except those acting on the ring gear, are self-canceling thus reducing the gear box distortion. Planetary gear boxes will become more popular because of their power density, smaller space requirement, and consequently lower cost.
CONCLUSION
In conclusion, the gear box wear life can be increased by a factor of 100% to as much as 500% with proper and complete preventive maintenance. Whenever an unusual problem exists with gears or bearings in a gear box, contact Power Engineering & Manufacturing, Ltd. for free consultation.
REFERENCES
1. Huffaker, G.E., “Compressive Failures in Transmission Gearing”, Presented at SAE Summer Meeting, June 17, 1959.
2. Moyer, Charles A., “The Use of Elastohydrodynamic Lubrication in Understanding Bearing Performance”, SAE Trans. Volume 80 (1971 ).
3. Townsend, D.P., Zaretsky, E. V., and Scibbe, H.W., “Lubricant and Additive Effects on Spur Gear Fatigue Life” ASME Trans. Volume 108 (1986).
4. Moyer, Charles A. and Bahney, L. L., “Modifying the Lambda Ratio to Functional Line Contacts”, Tribology Transactions Volume 33 (1990).
5. Moyer, Charles A., “Using the Modified Lambda Ratio to Advance Bearing and Gear Performance”, SAE Technical Paper Series 901625 (1990).
6. Herscovici, Saul (Power Engineering & Manufacturing, Ltd.), “High Horsepower Planetary Gear Boxes for Reduced Cost and Improved Efficiency in Sugar Cane Mill Applications”, American Society of Sugar Cane Technologists Annual Meeting of the Louisiana Division (1995).
January 1997