1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Link with spring-mass-damper system

  1. Nov 15, 2012 #1
    From this mechanical part (attached), I need to derive a differential equation relating mass 'x' position to hinge 'y' position.

    [itex]\ddot{x}m + b\dot{x} + cx = F[/itex]

    The link l would be rotating. I am confused about considering the displacement of x with reference to y. Would this change the differential equation by replacing x with (x-y) ?

    I derived an equation to relate 'y' with [itex]\theta[/itex] ;

    [itex]y = lsin(\theta)[/itex]

    Finally I also need to derive a differential equation from the previous two to relate the loading torque on the shaft for some rotation theta.

    [itex]\tau = (\ddot{x}m + b\dot{x} + cx)lcos(\theta)[/itex]

    I would really appreciate if you can give me some hints on my work. thanks
     

    Attached Files:

    Last edited: Nov 15, 2012
  2. jcsd
  3. Nov 15, 2012 #2

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Damped-driven harmonic motion with feedback?
    Is the servo "active" (it is being driven by a motor and the second mass is just a counter-balance?) ... the it is just providing the f(t) in the standard equations.
     
  4. Nov 16, 2012 #3
    I need to investigate some tight control on an open loop modelling of a servo motor linked with a spring mass damper system.
    The linkage with spring mass damper is stable with a counterbalance on the other side. The aim is to shift the mass (by the servo) of the s-m-d system and eliminate oscillations as much as possible. The servo is modeled as having a feedback loop with theta. I will also be implementing a PID loop in the servo controller but the spring-mass-damper is open loop.

    I already derived the transfer functions and state space for the servo which is simply a DC motor with a 10:1 gearbox.

    My main confusion right now are the equations in my previous post. I need these in order to simulate everything together in simulink. attached
     

    Attached Files:

  5. Nov 16, 2012 #4

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Gotcha:
    The F in the above relation is being applied at y - y moving up and down is what is generating it.
    If ##\theta## is expected to be small enough that you can discount lateral movement then ##\sin(\theta)\approx \theta##
    considering the idea is to minimize oscillations, that seems reasonable.

    measure x from some equilibrium/rest position and y likewise ... then you'll see better how they interact.
     
  6. Nov 16, 2012 #5
    I cannot assume this. The system has to remain non linear that is why it will be simulated via simulink. Dont worry, I will not be working any calc with a non linear system.


    Do you mean [itex]y-y_{o}[/itex] ? Then how would the differential equation be?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook