lecture_15 - MIT OpenCourseWare http/ocw.mit.edu 2.004...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

This note was uploaded on 02/23/2012 for the course MECHANICAL 2.004 taught by Professor Derekrowell during the Spring '08 term at MIT.

Page1 / 8

lecture_15 - MIT OpenCourseWare http/ocw.mit.edu 2.004...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online