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SURFACE STRESSES• Mating gear have acombination of rollingand sliding at theirinterface. The stressesat tooth surface aredynamic Hertziancontact stresses incombined rolling andsliding.• The surface stresses inthe gear teeth wereinvestigated byBuckingham whorecognized that twocylinders having thesame radius ofcurvature as the gearteeth at the pitchpoint and radiallyloaded in rollingcontact.
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SURFACE STRESSES• Where Wt is tangentialload or force.• D is the pitch diameter ofthe two gears in mesh. F isthe face width. I is thedimensionless surfacegeometry factor forpitting resistance.• Cp is an elasticcoefficient thataccounts for differencesin the gear and pinionmaterial constants.
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SURFACE STRESSES• The factors Ca , Cm ,Cv and Cs are equalrespectively to Ka, Km,Kv and Ks.• Surface geometry factorI: This factor takes intoaccount the radii ofcurvature of the gearteeth and pressureangle.ρp and ρg are radii ofcurvature of the pinionand gear . The radii of thecurvature of the teeth arecalculated from the meshgeometry.
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SURFACE STRESSES• Elastic CoefficientCp: The elasticcoefficientaccounts fordifferences in toothmaterials.• Ep and Eg aremoduli of elasticityfor pinion andgear.Ѵp and Ѵg are thePoisson’s ratios.
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SURFACE STRESSES• Surface FinishFactor Cf: It is usedto account forunusually roughsurface finishes ongear teeth. For theconventionalmethods of gearCf be set to 1.
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SURFACE STRESSES ANALYSIS OF SPURGEAR TRAIN• EXAMPLE:• Determine the surfacestresses in the gearteeth of the 3-geartrain containing apinion, an idler andgear. The transmittedload on the gear teethis 432 lb. The pinion has14 teeth , a 25˚ pressureangle , and pd = 6.• The idler has 17 teethand gear has 49 teeth.Pinion speed is 2500rpm. Face width is 2inches.• Assumptions: The teethare standard AGMA fulldepth profiles. The loadand source are bothuniform in nature. Aquality index of 6 willbe used. All gears aremade of steel with Ѵ =0.28.
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MATERIAL STRENGTHS• Since both of the gear failure modes involve fatigueloading, material fatigue strength data are needed,both for bending stresses and for surface contactstresses. Test data for fatigue strengths of most gearmaterials have been compiled by AGMA.• AGMA BENDING FATIGUE –STRENGTHS FOR GAERMATERIALS:• The published AGMA data for both bending andsurface- strengths are in effect, partially correctedfatigue strengths, since they are generatedappropriately sized parts having the samegeometry, surface finish etc.
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• LIFE FACTOR KL:• Since the test data are for a life of 1E7 cycles. Ashorter or longer cycle life will requiremodification of the bending fatigue strengthbased on the S – N relationship for the material.The number of load cycles in this case is definedas the number of mesh contacts.• Figure shows the S – N curves for the bendingfatigue strength of steels having several differenttensile strengths as defined by their Brinellhardness numbers. Curve fitted equations arealso shown in the figure for each S – N line. Theseequations can be used to compute theappropriate KL factor for a required number ofload cycles N.
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• The upper portion of the shaded zone can beused for commercial applications. The lowerportion of the shaded zone is typically used forcritical service applications where little pittingand tooth wear is permissible and where smoothness of operation and low vibration levels arerequired.• TEMPERATUE FACTOR KT:• The lubricant temperature is reasonable measureof gear temperature. For steel materials in oiltemperatures up to about 250ºF, KT can be set to1. For higher temperature KT can be estimatedfrom
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• SURFACE – LIFE FACTOR CL :• Since the test data are for a life of 1E7 cycles. Ashorter or longer cycle life will requiremodification of the bending fatigue strengthbased on the S – N relationship for the material.The number of load cycles in this case is definedas the number of mesh contacts.• Figure shows the S – N curves for the surfacefatigue strength of steels having several differenttensile strengths as defined by their Brinellhardness numbers. Curve fitted equations arealso shown in the figure for each S – N lines. Theseequations can be used to compute theappropriate CL factor for a required number ofload cycles N.
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• The upper portion of the shaded zone can beused for commercial applications. The lowerportion of the shaded zone is typically used forcritical service applications where little pittingand tooth wear is permissible and where smoothness of operation and low vibration levels arerequired.• HARDNESS RATIO FACTOR CH: This factor is afunction of the gear ratio and relative hardness ofpinion and gear, CH is always 1.0. CH is onlyapplied to the gear- tooth strength. Two formulasfor its calculation are suggested in the standard.
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