Examples of Torsion ShaftsPower generation shaftAutomotive power train shaftShip drive shaftTire shift driveComplex crank shaftScrewdriver6
6 Ship drive shaft Complex crank shaft Automotive power train shaft Screwdriver Power generation shaft Tire shift drive Examples of Torsion Shafts
Sign Convention of TorqueMeMeMe.MeMe: Sign (Positive) convention (right-hand rule): thumb - cross-section normal; rest fingers - torque
• Sign (Positive) convention (right-hand rule): thumb – crosssection normal; rest fingers – torque Sign Convention of Torque 7
Torque Diagram: Abscissa: cross-section position: Ordinate: torqueMeiMe2Me3Me4-Me4xMe1Mei+Me28
• Abscissa: cross-section position • Ordinate: torque Torque Diagram 8
Power & TorqueMotor. Transformation from electricpower to mechanical powerC motor power: P (kW); generated torqueM. (N-m):: n (rpm, revolutions per minute):1000 ×60 PPM。×2元n = P×1000×60= M。95492元nn: n (rps, revolutions per second):P1000 P159M,×2元n=P×1000=M2元nn· @ (rad/s, radian per second))PM。× =P×1000= M.=100009
• Transformation from electric power to mechanical power Power & Torque 9 1000 60 2π 1000 60 9549 2π e e P P M n P M n n • motor power: P (kW); generated torque: Me (N·m): • n (rpm, revolutions per minute): 1000 2π 1000 159 2π e e P P M n P M n n e e 1000 1000 P M P M • n (rps, revolutions per second): • ω (rad/s, radian per second):
Internal Torque & Stress - Static Indeterminacy. Net of the internal shearing stresses is aninternal torque, equal and opposite to theapplied torque,T=[pdF = p(t dA): Although the net torque due to the shearingstresses is known, the distribution of thedFstresses is not.: Distribution of shearing stresses is(a)statically indeterminate - must considerBshaft deformations.: Unlike the normal stress due to axial loadsthe distribution of shearing stresses due to(b)torsional loads can not be assumed uniform10
T dF dA • Net of the internal shearing stresses is an internal torque, equal and opposite to the applied torque, • Although the net torque due to the shearing stresses is known, the distribution of the stresses is not. • Unlike the normal stress due to axial loads, the distribution of shearing stresses due to torsional loads can not be assumed uniform. • Distribution of shearing stresses is statically indeterminate – must consider shaft deformations. Internal Torque & Stress - Static Indeterminacy 10