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HW9soln

# HW9soln - ME 375 HW#9 SOLN SPRING 2009 PROBLEM 1(40 You are...

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ME 375 HW #9 SOLN SPRING 2009 PROBLEM 1 (40%): You are given the electromechanical system shown below with input voltage v i (t) and output displacement x(t). This device is used to position the rack in a desired location. The circuit has resistance R, the pinion gear has moment of inertia J, and the translating rack has mass M. The motor has torque constant K T and back emf constant K E . The rack and gear mesh with no backlash at radius r of the gear. There is a load f L (t) that resists motions of the rack. (a) Draw the circuit diagram with +/- signs and current flow indicated. Be sure to include the electromechanical coupling relationship. The circuit diagram is shown below with voltage drops and current flow indicated. v i (t) - + R i + - + - Voltage drop K E ω from EM coupling v i (t) R J (pinion gear) r x(t) M (rack) f L

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