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Both calculate an approximation of the first natural frequency of vibration, which is assumed to be nearly equal to the critical speed of rotation. The Rayleigh–Ritz method is discussed here. For a shaft that is divided into n segments, the first natural frequency for a given beam, in rad/s , can be approximated as:
Dunkerley's method [1] [2] is used in mechanical engineering to determine the critical speed of a shaft-rotor system. Other methods include the Rayleigh–Ritz method . Whirling of a shaft
Dynamic Runabout 7 shaft-driven bicycle Drive-shaft housing. A shaft-driven bicycle is a bicycle that uses a drive shaft instead of a chain to transmit power from the pedals to the wheel. Shaft drives were introduced in the 1880s, but were mostly supplanted by chain-driven bicycles due to the gear ranges possible with sprockets and derailleurs ...
From a mechanical viewpoint, up to 99% of the mechanical energy delivered by the rider into the pedals is transmitted to the wheels (clean, lubricated new chain at 400 W), although the use of gearing mechanisms reduces this by 1–7% (clean, well-lubricated derailleurs and a straight chainline), 4–12% (chain with 3-speed hubs), or 10–20% (shaft drive with 3-speed hubs).
In 1991, a two-wheel drive bicycle was marketed under the Legacy name. It used a flexible shaft and two bevel gears to transmit torque from the rear wheel, driven by a conventional bicycle chain with derailleurs, to the front wheel. [11] In 1994, Steve Christini and Mike Dunn introduced a two-wheel drive option. [12]
Bicycle and motorcycle dynamics is the science of the motion of bicycles and motorcycles and their components, due to the forces acting on them. Dynamics falls under a branch of physics known as classical mechanics. Bike motions of interest include balancing, steering, braking, accelerating, suspension activation, and vibration. The study of ...
Analysis shows that there are well-damped critical speed at lower speed range. Another critical speed at mode 4 is observed at 7810 rpm (130 Hz) in dangerous vicinity of nominal shaft speed, but it has 30% damping - enough to safely ignore it. Analytically computed values of eigenfrequencies as a function of the shaft's rotation speed. This ...
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