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Unformatted text preview: MIT OpenCourseWare http://ocw.mit.edu 2.004 Dynamics and Control II Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . i n K 9 Massachusetts Institute of Technology Department of Mechanical Engineering 2.004 Dynamics and Control II Spring Term 2008 Lecture 15 1 Reading: • Class Handout: Modeling Part 1: Energy and Power Flow in Linear Systems Sec. 3. • Class Handout: Modeling Part 2: Summary of One-Port Primitive Elements Nise: Secs. 2.4 and 2.6. • 1 Rotational Systems (continued) Example 1 The diagram shows a mechanical tachometer that uses frictional drag plates to create a torque proportional to angular velocity difference. The angular velocity is indicated by the displacement θ of a torsional spring. Find the transfer function relating the displacement of the indicator θ to the input angular velocity Ω in θ ( s ) H ( s ) = Ω in ( s ) and show that for a constant input angular velocity the steady-state indicated speed θ ss ∝ Ω i . Solution: There are two distinct angular velocities, and the system graph is: 1 copyright c D.Rowell 2008 15–1 J B K 9 = i n 9 Using impedances, redraw the graph combining the inertia and the spring into a single impedance Z 2 : Z Z 9 = i n 9 Then Z 2 Ω J = Ω in ( s ) Z 1 + Z 2 s/ ( Js 2 + K ) = Ω in ( s ) 1 /B + s/ ( Js 2 + K ) Bs = Ω in ( s ) . Js 2 + Bs + K But the angular displacement θ ( s ) = Ω J ( s ) /s so that B H ( s ) = Js 2 + Bs + K If the input velocity is a step function at t = 0, the...
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