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GEARING
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FIGURE 10.53 Surface-distress probability chart as a function of pitch line velocity and specific film thickness. Curves represent 80, 40, and 5 percent probability of distress. The region above the 80 percent line is unsatisfactory; the region below the 5 percent line is good.
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q= where
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(10.87)
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q = wear, in nT = number of cycles Sy = yield strength of gear material, psi K = factor from Eq. (10.88)
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and 3.1 K 1.645 109 1.8 (10.88)
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In applying these equations, greater emphasis should be placed on the trend indicated than on the absolute value of the numbers. For example, a new design might be compared with an existing similar design for which the wear characteristics have been established. This could be accomplished by calculating the q value for each by
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Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website.
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HELICAL GEARS 10.55
HELICAL GEARS
Eqs. (10.87) and (10.88) and then comparing them, rather than looking at absolute values of either. The ratio of the two q values is far more accurate than the absolute value of either. Scoring. Very few data concerning the scoring behavior of gears are available in an easily usable form. Scoring is normally a problem for heavily loaded, high-speed steel gears.The exact mechanism by which scoring occurs is not yet fully understood. At high speeds, the calculated film thickness is often quite large. Yet a wearlike failure mode sometimes occurs. Under high-speed conditions, the sliding motion of one gear tooth on another may create instantaneous conditions of temperature and pressure which destroy the film of oil separating the tooth flanks. When this occurs, the asperities on the surfaces of the mating teeth instantaneously weld. As the gears continue to rotate, these welds break and drag along the tooth flanks, causing scratches, or score marks, in the direction of sliding. If the damage which occurs is very slight, it is often referred to as scuffing or frosting. In some cases, light frosting may heal over and not progress; however, scoring is generally progressively destructive. Though never a catastrophic failure itself, scoring destroys the tooth surface, which leads to accelerated wear, pitting, and spalling. If scoring is allowed to progress unchecked, tooth fracture may ultimately occur. Note that scoring is not a fatigue phenomenon; that is, its occurrence is not timedependent. In general, if scoring does not occur within 15 to 25 minutes (min) at a certain operating condition, usually it will not occur at that condition at all. Only a change in operating condition, and not the accumulation of cycles, will cause scoring. A theory known as the critical-temperature theory, originally proposed by Harmen Blok, is usually used in the evaluation of scoring hazard for a set of helical gears. If we consider a simple analogy, the concept of critical temperature will become clear. Consider the old method of making fire by rubbing two sticks together. If the sticks are held together with only light pressure and/or they are rubbed slowly, they will simply wear. If, however, the pressure is increased and the sticks are rubbed more rapidly, then the temperature at the mating surfaces will increase. If the pressure (load) and the rubbing speed (sliding velocity) are progressively increased, eventually the sticks will ignite. At the point of ignition, the sticks have reached their critical temperature. Quite obviously, the critical temperature will vary with the type of wood, its moisture content, and other factors. In a similar manner, as gear-tooth sliding velocity and load are increased, eventually a point will be reached at which the temperature at the conjunction attains a critical value, and then the film separating the tooth flanks will be destroyed. At this point the teeth are in metal-to-metal contact, and instantaneous welding of the surface asperities occurs. The continued rotation of the mesh rips apart these microscopic welds and produces the scored appearance from which this failure derives its name. The critical temperature varies with the type of gear material, surface hardness, surface finish, type and viscosity of oil, additives in the oil, etc. When the film is destroyed, it is sometimes referred to as flashing; thus the parameter used to evaluate this condition has come to be known as the flash temperature. When the flash temperature reaches its critical value, failure by scoring will occur. Note that the flash temperature referred to here is not related in any way to the flash point of the oil, and the oil flash point shown on some manufacturers specification sheets is in no way related to the allowable flash temperature discussed here. Many refinements have been made to Blok s original theory, and it is currently accepted as the best method available for evaluating scoring resistance for spur, helical, and bevel gears. Reference [10.9] presents a method of analysis for steel spur and
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