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Creation European Article Number 13 in Software STRENGTH UNDER DYNAMIC CONDITIONS 29.33

STRENGTH UNDER DYNAMIC CONDITIONS 29.33
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STRENGTH UNDER DYNAMIC CONDITIONS
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These equations can be useful with rolling contact, such as occurs in cams, roller bearings, and gear teeth. The approach of the center of the rollers is = 2F 1 2 1 2 1 2 + E1 E2 ln d1 d 2 + ln 2 + b b 3 (29.38)
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The largest principal stress is compressive and located at the center of the rectangular flat and is pmax in magnitude. The largest shear stress is approximately 0.30pmax and is located at about 0.78b below the surface. The maximum compressive stress is repeatedly applied in rolling cylinders. At a position of z = 0.4b, y = 0.915b the shear stress has a magnitude of 0.242pmax but is completely reversed in rolling cylinders. The loss of surface integrity due to repeated application of hertzian contact stresses is called surface fatigue. The phenomenon is marked by the loss of material from the surface, leaving pits or voids. The onset of fatigue is often defined as the appearance of craters larger than a specified breadth. If Eq. (29.33) is substituted into Eq. (29.34) and the magnitude of pmax associated with the first tangible evidence of fatigue at a specified number of cycles is called the surface endurance strength Sfe, then F
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2 1 2 2 2 2 2 1 1 + = Sfe + =K E1 E2 d1 d2
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(29.39)
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The left-hand side of the equation consists of parameters under the designer s control. The right-hand side consists of materials properties. The factor K is called Buckingham s load-stress factor and is associated with a number of cycles. In gear studies a similar K factor is used and is related to K through Kg = K sin 4 (29.40)
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where = gear-tooth pressure angle. Note that pmax is proportional to other stresses present, and it is conventional to describe surface fatigue in terms of the strength Sfe. Reference [29.1] gives Kg information for pressure angles of = 141 2 degrees and = 20 degrees, as well as Sfe for various materials and numbers of cycles. The implication in the literature that above various cycles Kg does not change is unsupported. Log-log plots of K or Kg versus cycles to failure produce parallel lines with some consistency in slope for classes of material. AGMA standard 218.01 (Dec. 1982) suggests allowable contact-stress numbers for steel as high as ( )107 = 0.364HB + 27 kpsi for 10 cycles, and for the curve fit for other than 10 cycles, N = CL 107 = 2.46N 0.056(0.364HB + 27) kpsi (29.42) For applications where little or no pitting is permissible, the slope of 0.056 persists to 1010 (end of presentation). Another curve fit to Sfe data for steel at 108 cycles is (Sfe )108 = 0.4HB 10 kpsi (29.43) When a gear and pinion are in mesh, the number of cycles to which a point on the tooth surface is exposed is different. Consequently, the material strengths can be tuned to have both pinion and gear show tangible signs of wear simultaneously. For steel gears, using Eq. (29.43), the appropriate gear hardness BHN for a stipulated pinion hardness bhn is
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b/2 BHN = mG (bhn 25) + 25 7 7
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(29.41)
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(29.44)
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.
STRENGTH UNDER DYNAMIC CONDITIONS 29.34
LOAD CAPABILITY CONSIDERATIONS
where mG = gear ratio, i.e., teeth on the gear per tooth on the pinion. This matching can be done by controlling surface hardness. Strength matching for bending resistance is accomplished by control of core properties. When needle bearings are specified, the needle assembly is a vendor s product, but the roller track is supplied by the user and is a design concern. The equivalent load Feq accumulating the same damage as a variable radial load F is Feq = 1 2
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