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Linear Actuator Motion Profile

  1. Oct 27, 2013 #1
    1. The problem statement, all variables and given/known data
    The problem deals with a linear rail system not unlike the one displayed in the image below
    $(KGrHqEOKicE+d9)JjHUBS,efR3I9g~~60_3.JPG
    The relevant variables include:
    Load = 70 Lbs
    Load travel = 2.2 m
    Load speed required = 2.3 m/s
    Cycle time = 9 sec
    Capacity of actuator = 33,000 N

    With the given information:
    A. determine the values for the graph below
    trap.png
    B. ...and the life of the actuator in meters
    C. ...and the life of the actuator in hours
    2. Relevant equations
    Eq. 1
    20_1equation01.jpg
    Where:
    L10= actuator lifetime (in millions of revolutions)
    Cr = Dynamic Load Rating
    Pr = Equivalent Load Factor
    Eq. 2
    20_2equation01.jpg
    Where:
    n = rotation speed (min-1)
    this second equation results in unit of hours
    Eq. 3
    Vm = (V1q1+V2q2+....+Vnqn)/100%
    Where:
    V1,V2,...Vn = speed at phases of motion profile (in m/min)
    q1,q2,...qn = % of time for each phase

    Eq. 4
    L10 (hrs) var=(L10*105)/(60*Vm)
    Where:
    L10 (hrs) var = actuator life in hours modified for variable speed
    Vm = equivalent speed

    3. The attempt at a solution
    There are a few assumptions I've made in my solution attempt to this problem, but I don't know where else to start.

    First I assume that the dynamic load rating (Cr) is synonymous with the load capacity of the actuator
    Second I assume that the Equivalent Load factor (Pr) is synonymous with the load provided (because no details of load distribution were provided)

    To determine the life of the actuator in (millions of revolutions) I input the given values into Eq. 1:

    L10=(33,000N/311.5N)3=1.2*106

    Eq. 2:

    L10 (hrs)=(106/(60*n))*(L10)=(2.0*1010)/n

    I'm very unsure of how to determine n, but since the cycle time is 10 sec:
    n = 6(min-1) ???

    Assuming this, then:
    L10 (hrs)=3.3*(109)

    In order to use Eq. 3 account for the variable speed of the actuator, I believe I need to determine the values (time increments) of the graph given, but I'm unclear on how to do this with the given info.

    I realize this a very long post, but I wanted to be as clear as possible.
    Any pointers on how to where I have gone wrong in my process and/or how to proceed would greatly appreciated.
    Thank you
     
  2. jcsd
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