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HW6 solution - EEL5225 Principles of MEMS Transducers HW6...

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Principles of MEMS Transducers Page 1 of 6 Prepared by D. Arnold November 5, 2010 v 1 = v 2 ω 1 R 1 = ω 2 R 2 ω 2 = R 1 R 2 ω 1 EEL5225 Principles of MEMS Transducers HW6 Fall 2010 Semester Assigned: Monday, 10/25 Due: Monday, 11/1 1. Consider the gear system shown below, with input angular velocity, ω 1 . Draw and completely label an appropriate equivalent circuit model for the system. (Hint: use rotational domain conjugate power variables). Note: The relation between the 2 gears is derived as: F 1 = F 2 T 1 R 1 = T 2 R 2 T 2 = R 2 R 1 T 1 These equations are represented by the first transformer with turns ratio R 2 /R 1 . Note the relations between force/torque and linear velocity/angular velocity: F = 1 R 2 T 2 and v = R 2 ω 2 These equations are represented by the second transformer with turns ratio 1/R 2 Now label the velocities at the nodes:
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Principles of MEMS Transducers Page 2 of 6 Prepared by D. Arnold November 5, 2010 Equivalent circuit model: + - + + - - T 1 w 1 w 2 1: R 2 R 1 T 2 F v 1 v 2 m 2 v1-v2 C 1 C 2 1: 1 w 1 R 2 Here, we assume massless gears and no loss in the rotational system. If you wanted, you could include an inductor (representing rotational inertia, J ) for each of the gears. 2. Consider the transfer function X ( s ) F ( s ) = 1 ms 2 + bs + k (displacement per force) for a standard underdamped 2 nd order mass-spring-damper system b .
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