Line Ramp Up/Ramp Down?

[jj28west]

Hello PLCS Nation,

I am hoping you can help a newbie find calculations on how to determine Line Ramp Up & Ramp down Speed.

We have a machine that has a manual payoff, capstan, dancer and takeup winder spooler that winds metal strip/wire.

I am looking for when the operator is either in tension mode (no dancer) or dancer mode...how do I calculate the ramp up or down speed (deceleration) weather he is running at 100 FPM or 1000 FPM.

For example...if he wanted to set a footage length of 5,000 Feet, how do we determine the deceleration when the footage is at 4,900 Feet.

Or maybe the speed will dictate the footage when to begin ramp up or ramp down as a set point?

My hopes is that there is a theoretical rule of thumb as a starting point and then we must tweak from there.

Thanks all for reading and I apologize if this is a trivial question but google wasn't my controls physics friend here.

 

[drbitboy]

You want the last 100ft (4,900 to 5000) to be wound while linearly(assumed?) decelerating from V to 0 ft/min?

If the linear deceleration is D, ft/min², then the time to decelerate from V to 0 will be T (minutes) = V/D minutes.

If the length to be wound while decelerating is L (ft), then formula relating T and V to that length is L = ½ T (V - 0) = ½ T V = ½ (V/D) V = ½ V² / D.

Solving for D = ½ V² / L, ft/min²

We get the same result starting with the traditional L = ½ D T² and substituting V/D for T, but starting with L = ½ T (V - 0) is easier to see graphically (area of a triangle).

Converting that to RPM on a roll with varying diameter is left as an exercise for the user.

P.S. Yes, I was lazy with the signs.

P.P.S. Yes this assumes infinite jerk at the start and end of the deceleration; if you want to ramp the decel up and down from 0 for a few seconds the calculation is only slightly more complex.

 

[kamenges]

The equation I usually use is:

D = V²/(2*a) + ((V*a) / (2 * j))
where:
D = distance to decel
a = accel or decel rate
j = jerk rate (s-curve rate)

This is basically the drbitboy formula with s-curve acceleration added and using the variables you most likely have to work with. This formula doesn't work at very low speeds if s-curve acceleration is used and constant accel is not reached. But for most cases it will work. Just make sure you use consistent units for everything, especially with time. Accel rate, for example, should be in distance/sec² NOT distance/min/sec.

Keith

 

[drbitboy]

Ooh, nice!

If we push to the limit of where that formula breaks down*, so we start with negative constant jerk, -j, i.e. increasing deceleration, to decrease velocity from its initial V by half, then positive constant jerk, +j, i.e. decreasing deceleration, to decrease velocity from that half-of-initial-V to 0, then

L = V²/a_max

N.B. My L is @kamenges' D
​

or

a_max = V²/L
​

and jerk is then

j = V³/L²
​

Both of those have L, the remaining material to wind, in the denominator. Since L is decreasing and V is likely more or less constant,and both L and V are known, both a_max and j as calculated by those formulae will increase as the process approaches the end of the roll.

If OP can figure out what their target maxima are for a_max and j, then when either hits its maximum, they can calculate the matching jerk magnitude from the second formula above.

The time to apply negative jerk -j, to decelerate from V to V/2 is

t_j = L/V
​

which is half the time to finish the wind, then an equal time applying positive jerk +j to decelerate from V/2 to 0 finishes the wind.

* The formula assumes V/a_max ≥ a_max/j, and the limit described above occurs when V/a_max = a_max/j

 

[Peter Nachtwey]

There are two cases for ramping down. One is that the deceleration is jerk limited. In this case there is no constant deceleration segment.
If the jerk is high enough the deceleration rate will be reached so there will be a constant deceleration section.


This example assumes the acceleration and deceleration limits are reached so there are 7 motion segments or states. State 0 is stopped.
https://deltamotion.com/peter/wxMaxima/Seg1234567.html

 

[MaxK]

I guess jj28west doesn't understand the issue too well. So I will make two assumptions:

1. jj28west will not be able to implement complex algorithms
Do you really think that jj28west will be able to programmatically apply logic / mathematics:

If
l <= j * (2 * V / j)^(1.5) / 6
then
Deceleration Mode := true

If Deceleration Mode = true
then
V = j* ( 6*l / j )^(2/3) /2

j – jerk
V – velocity
l = desired length – current length

On what basis do you think that jj28west has the ability to fine speed control?


2. The question is not formulated correctly

I dare to suggest that the jj28west needs to ensure smooth braking (without critical loads on the units).

Decelerate "comfortably" (without critical loads on the units). Calculate deceleration:

d = V^2 / (2 * l )

when the machine is working, determine the distance to stop

l = V^2 / (2 * d )

with deceleration = d