Question

Windmills and watermills were often used to harness the power of natural forces and provide a source of mechanical energy. This energy was transferred using a series of gears and shafts to typically turn a grindstone to crush grains. Below is a simplified diagram of the drive-system within a windmill. Gear 1 has a diameter D₁ =2.2 m, Gear 3 has a diameter D₃ = 1.75 m, and Gear 4 has a diameter D₄ =1 m. Items 2 and 5 are the shafts the gears rotate on. A torque of T₁ = 4000 N.m is applied to Gear 1 and Gear 4 turns by an angular velocity of w = 15 rpm as a result.

U

What is the magnitude of generate power by the windmill?

Answer 1

Soln: Since velocities at contact point of gear 3 & 4 will be equal to both = Wu ru = W38 or wady = W3 d3 - W₂ = Wydu / dz • Wy = 15 rpm = 27x15 rad/s = 1.5708 rad/s & du = lm & dz = 1.75m =) W3 = 1.5708x1 = 0.8976 rad/s 1.75 = Gear since gear 1 & 3 & same will be angular velocity of are attached to same shaft 2 . 7 W, = 0.8976 rad/s & since torgue on gear 1 = Ti= > Power generated Tiw, = P = 3590:4 watts 4000 N.m 1000 X 0.8976 watts