cable_hoist_1 - REVIEW NETWORK MODELING OF PHYSICAL SYSTEMS...

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REVIEW NETWORK MODELING OF PHYSICAL SYSTEMS a.k.a. "lumped-parameter" modeling E XAMPLE : VIBRATION IN A CABLE HOIST Problem switch motor geartrain compliant cable drum elevator cage voltage supply g The cage of an elevator is hoisted by a long cable wound over a drum driven through a gear-set by an electric motor. The motor is relay-operated (i.e., either on or off) and the resulting abrupt transients cause the cage to oscillate on the hoisting cable. Because the cable has low internal friction, the oscillations persist for many cycles. Even more important, the peak stress in the cable is almost double the steady- state stress required to support the weight of the cable. Modeling and Simulation of Dynamic Systems Cable Hoist Example page 1
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Scenario To solve this problem it has been proposed to introduce an electrical R-C filter between the relay and the motor terminals. The designer claims that this will smooth the transient, thereby reducing the oscillation amplitude to acceptable levels. Your task is to evaluate this proposal. abruptly engaging the motor excites oscillation does electrical filtering help? Modeling goal The simplest model competent to elucidate the effect of electrical filtering on the mechanical oscillation. Modeling and Simulation of Dynamic Systems Cable Hoist Example page 2
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First reproduce the problem To keep things simple assume that: • variation of weight supported with length change may be ignored (i.e., consider small changes in elevation) • weight is concentrated (“lumped”) in the cage variation of cable compliance with length change may be ignored • neglect cable internal damping (first, that emphasizes tendency to oscillation; second, it’s small anyway; and third, it’s easy to add later if necessary) • drum and gear inertia may be neglected • DC electric motor with constant magnetic field • motor armature resistance & inductance may be neglected • relay resistance may be neglected • voltage supply “internal resistance” may be neglected Modeling and Simulation of Dynamic Systems Cable Hoist Example page 3
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Direct approach (i.e., just “write down” the differential equations) Newtonian mechanics: m cage ¨x cage := k cable (x rim – x cage ) – m cage g Transmission ˙ x rim := r drum ω drum ω drum := n gear ω motor Motor transduction characteristic: ω motor := e motor / K motor Switch: e motor := e supply if switch closed; 0 if switch open.
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cable_hoist_1 - REVIEW NETWORK MODELING OF PHYSICAL SYSTEMS...

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