Governing physics, pt II

In the last post we discussed cable tension resulting from acceleration and deceleration in both the arbor cables and power drum cable.  Now, lets discuss whether that acceleration and maximum velocity make sense considering winch capabilities and move time.

Since we defined our maximum linear velocity of the winch as 60 in/sec, we will accelerate up to that speed, coast there, then decelerate down to zero.  If you were to graph this as vertical velocity of the lift vs. time, it would look something like this…

Where the y-axis is velocity and the x-axis is time.  This is called a trapezoidal velocity profile (as opposed to a triangular velocity profile), and it’s the graph of the desired behavior of the lift during operation.  You can see from the graph that the 2 angled sides represent the acceleration and deceleration with respect to the maximum velocity. 

By drawing this shape and integrating over time (taking the area under the velocity curve), we can determine what the total move time should be given our parameters for acceleration and max velocity.  Here are the resulting equations for total move time, acceleration and deceleration time…

 Because we have the time in terms of move distance, acceleration and maximum velocity, we can change their values and observe how that change affects the move time.  We could also work backwards, specifying a move time and calculating the necessary acceleration.  This would be useful information as the applications of the elevator vary from show to show.

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