1Shafts & Keys Shafts in general Fatigue Deflection Keys Critical FrequenciesShaftsshoulders, keys, bending, torsion, deflectionShaft PowerP=TωPower = (Torque)(Angular Velocity)W = (Nm)(radians/s)1 hp = 745.7 WStresses in Shafts normal, bending, alternating,σa normal, bending, mean, σm shear, torque, alternating, τa shear, torque, mean, τmFatigue DataStatic TorsionReversed TorsionShaft Fatigue Failure2Shaft Design Strategy Find correct equation for dshaft Identify critical points along shaft¾Find Ma, Mm, Ta, Tm¾Find Kf,Kfs,Kfm, Kfsm Find Se(as a function of dshaft) Solve for dshaft(iterative) Some General Rules of Shaft Design Length/positioning¾ keep length as short as possible, avoid overhangs/cantilevered sections Hollow shafts¾ greater stiffness/mass and higher natural frequency (but has greater cost and diameter) Stress concentrations¾ place where bending moment is low, use generous radiiMore General Rules Gears¾ deflection less than 0.005 in., relative slope differ by less than 0.03 degrees Bearings¾ deflection important for sleeve/journal bearings¾ slope important for roller bearings Natural Frequency¾ first natural frequency > 3x(forcing frequency)Key Design Strategy For Direct Shear Failure¾ Find Fkeyfrom F=T/rshaft» you now have Faand Fm¾ Find τaand τb(=F/Ashear)¾ Find σ´a and σ´m For Bearing Failure¾ F=Fm+Fa¾ Find σ (=F/Abearing)utmeafSSNσσ′+′=1σysSN =Natural Frequencies Bending¾Lateral¾Whirl TorsionalLateralassumes external excitationset potential energy equal to kinetic energyweighteachatweighteachatdeflectionweightSUMdeflectionweightSUMgravityFrequencyNatural)*()*( 2⋅=∑∑==⋅=niiiniiinwwg121δδω3Shaft Whirl22)/(1)/(nneωωωωδ−=Whirl22)/(1)/(nneωωωωδ−=Bending Frequency Strategy Find maximum static deflection¾static, but be realistic Find ωnusing Lateral Deflection Find ω/ωnTorsional Frequency Strategy Find Imof mass (ignore shaft) Find Kt¾Find J for each section¾Kt,section=GJ/L¾Find 1/Kt,total = 1/K1 + 1/K2 + 1/K3 +
View Full Document
Unlocking...