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LECTURE+13+COE-3001-A

Strains in circular bar vary linearly

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Unformatted text preview: LUTION: WORKED OUT ON BOARD ⌧ ⌧ ⌧ (pure shear) ⌧ =G 45° element T C (no shear) T C 2/1/13 M. Mello/Georgia Tech Aerospace 5 GIVEN: •  CIRCULAR TUBE (Aluminum 7075- T6) Ø།  di = 60mm (inside diameter) Ø།  do = 80 mm (outside diameter) •  T = 4 kNm = 4000Nm DETERMINE: (A)  maximum shear, tensile, and compressive stresses in the tube (B)  corresponding maximum shear, tensile, and compressive strains reference element SOLUTION: WORKED OUT ON BOARD ⌧ ⌧ (pure shear) ⌧ ⌧ ⌧ =G 45° element T C (no shear) 2/1/13 M. Mello/Georgia Tech Aerospace C 6 T POWER TRANSMISSION ²་  MOST IMPORTANT USE OF CIRCULAR DRIVE SHAFTS IS TO TRANSMIT MECHANICAL POWER FORM ONE DEV ICE OR MACHINE TO ANOTHER. •  SHIP PROPELLER SHAFT •  AUTOMOBILE DRIVE SHAFT •  BICYCLE AXLE ²་  TYPICAL DESIGN PROBLEM: DETERMINE REQUIRED DIAMETER OF CIRCULAR SHAFT TRANSMIT REQUIRED POWER AT SPECIFIED ROTATIONAL SPEED, WITHOUT EXCEEEDING ALLOWABLE STRESSES TORQUE SHOWN IN FIGURES IS REACTION TORQUE EXERTED ON THE SHAFT BY THE DEVICE 2/1/13 M. Mello/Georgia Tech Aerospace 7 TORQUE – POWER RELATIONSHIPS FROM ELEMENTARY PHYSICS Work done by torque of constant magnitude (3- 36) W =T Applied torque Power: rate at which Work is done P= Angle of rotaZon dW d =T dt dt angular speed (ω) in rad/s Recall, ! = 2⇡ f (f = Hz = s- 1) P = 2⇡ f T (3- 40) also, n = # of revoluZons/minute and so, n = 60f and … P= 2/1/13 2⇡ nT 60 (3- 42) M. Mello/Georgia Tech Aerospace P = T ! (3- 36) Power Units: N ewton = 1W att second horsepower = 550f t lb/s 8 A QUICK NOTE ON GEAR RATIOS AND TORQUE MULTIPLICATION linear speed at the rim is the same on both gears i.e., v1 = v2 = v P1 = P2 T1 !1 = T2 !2 v v T1 = T2 r1 r2 T1 T2 = r1 r2 v1=v2=v !1 !2 Energy is conserved Linear speed at the rim is same in both gears r2 T2 = T1 r1 Torque is mulZplied by the raZo of the gear diameters hap://en.wikipedia.org/wiki/File:Gears_animaZon.gif 2/1/13 M. Mello/Georgia Tech Aerospace 9 GIVEN: •  SOLID STEEL AXLE: shear modulus G=80GPa •  d = 50mm (diameter) •  Motor transmits 5OkW to shaP at 10Hz. •  Gears B and C drive machinery requiring 35kW and 15kW, respecZvely. DETERMINE: (A)  maximum shear stress (τmax) in the axle (B)  Angle of twist φAC (between motor and gear at C) SOLUTION: WORKED OUT ON BO...
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