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### Transcript of Gear Analysis

Analysis of Spur and Helical Gears prepared by Wayne Book based on Norton, Machine Design and Mischke and Shigley Mechanical Engineering Design The Gnashing of Teeth Simple model for loaded gears Beam for bending stress Cylinders in contact for surface contact stress Idealized Shape of a Tooth for Stress Analysis Simple model: cantilever beam with applied force W Tooth thickness t Length l Face width F Max stress at root (a) l Wt F t a 2 36) 12 / (2 / ) (Ftl WFtt l WIMct t= = = oConsider the Shape of a Tooth Uncertainties include: point of load application l point of maximum stress appropriate load component beam thickness Depends on pitch P, number of teeth N and pressure angle | Conservative assumptions are made Y = Lewis form factor Introduce Lewis Shape Factor t l Wr Wt W x 3264 2 /2 /iangles similar tr By 212 6222 2xPYFYP WlP tFP WltxtlxtPtlFP WFtl Wt tt t== == == =ooRather than calculate Y(P,, N), create a table, e.g. 14-2 Lewis equation has been improved by AGMA Velocity Effect (Its Barth not Barf) Purely empirical adjustment for non-zero velocity Barths equation (1800s) has been modified to account for current practice and accuracy V is velocity in ft/sec at the pitch line Kv= 1200/(1200+V)(Modified Barth) Metric form Kv= 6.1/(6.1+V), V in m/sec Compare to endurance strength (reversing) or use Goodman diagram (one direction) Apply notch sensitivity, Marin factors. the works FY KP Wvt= oSurface Durability:Contact Stress Analyzed as two cylinders of length l in rolling contact with specified force Cylinder radii r1 and r2 vary with contact point Depends on elastic material properties and radii of cylinders Translate into gear nomenclature as shown on right factor velocityCpinion and gearrefer to subscripts P G,modulus s Young' Eratio s Poisson'1111 1cosv2 / 1222 / 12 1===((((((

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