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Mechanical Vibration Problem?

  1. Mar 7, 2014 #1
    Hi, I'm currently studying Mechanical Eng & have a class next semester 'Eng Analysis', which involves a large section on vibration. I've been trying to work my way through S.S.Rao, Mech Vibrations, 2nd edition. There's one specific problem; Project 5.51/Chapter 5/page 292.
    The problem concerns; two step cone pulleys connected by a belt. All relevent variables are given i.e. input/output shaft rpm, driven puley rpms, distance between centres,polar moments of inertia etc.
    I understand that this is a 2 Degrees of Freedom problem, & I should draw a free body diagram ( 2 pulleys connected by 2 springs). It's theinitial 'Equations of Motion' that I can't derive, & without these I can't really start the problem. I've attached a screen shot containing a clear example of the problem.
    Any help thats offered would be greatfully received.
     

    Attached Files:

    Last edited by a moderator: Mar 7, 2014
  2. jcsd
  3. Mar 7, 2014 #2

    berkeman

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    Staff: Mentor

    What does the textbook say about this kind of problem? What equations does the text use when describing this kind of problem?
     
  4. Mar 7, 2014 #3

    AlephZero

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    Science Advisor
    Homework Helper

    From the question:
    ??? Either I don't understand the question, or there is a typo somewhere. Those numbers don't seem to be consistent with each other.
     
  5. Mar 8, 2014 #4
    Same problem, updated rpm's & diameters...

    Hi, sorry here's the question with updated variables i.e. input shaft speed, output pulley speeds.
    Young's modulus for the belt: j1= 1x10^10 N/m^2, Drive step cone mass moment of inertia: j2=0.35 kg.m^2, Driven step cone mass moment of inertia: 0.6 kg.m^2, Distance between centres: c=2.8m, belt width: 19mm
    Please see attached for details.

    1st step: Free Body Diagram. this is essentially the 2 masses connected by 2 springs.
    2nd step: Using Newton's 2nd law (∑F=ma), write Eq's of motion.
    3rd: Assume simple harmonics. x=X sin (ωt+ø), x'=ωX cos (ωt+ø)
    4th: determine natural frequencies...
    I think it's 'Rayleigh's energy method', I should use to find the KE of the step cones & PE of the springs.
    It's the initial Eq's of motion that I can't derive.
     

    Attached Files:

  6. Mar 8, 2014 #5
    N=300rpm
    No1=650rpm
    No2=450rpm
    No3=250rpm
    No4=100rpm
    d1=400mm
    d2=300mm
    d3=200mm
    d4=100mm
     
  7. Mar 8, 2014 #6
    ..........
     
    Last edited: Mar 8, 2014
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