HW9soln - ME 375 HW #9 SOLN SPRING 2009 PROBLEM 1 (40%):...

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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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(b) Draw the free body diagrams of the pinion and rack showing all relevant motions and forces. Be sure to incorporate the electromechanical coupling relationship. The free body diagrams of the pinion gear and rack are shown below. (c) Show that the following differential equations describe this system: 2 () T L E i JK M xf i rr K R iv t x r ⎛⎞ += + ⎜⎟ ⎝⎠ =− ±± ± The composite sketch of the system is shown below.
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This note was uploaded on 08/28/2010 for the course ME 375 taught by Professor Meckle during the Spring '10 term at Purdue University-West Lafayette.

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HW9soln - ME 375 HW #9 SOLN SPRING 2009 PROBLEM 1 (40%):...

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