4-20ma, hz, dwell, inverse slope.

ghriver · Jul 9, 2007

I am hoping someone can explain, well actually point me in the correct direction to be able to do the math on an inverse slope. This is was I have.

4-20ma output to a vfd turning an auger. The augers speed needs to be set via dwell time. (The amount of time the product is in the auger).

The numbers:
vfd scaling = 20 - 60hz
analog scaling = 4 - 20ma

ok, the vfd running at 20 hz equates to 53 seconds of dwell time.
the vfd running at 60 hz equates to 18 seconds of dwell time.

so if 20=53 and 60=18 you would think that the middle vfd scale of 40hz would equal the middle scale of dwell. It doesn't.

This is what i got.
20 hz = 53 seconds of dwell
40 hz = 24 seconds of dwell (middle would be 35.5 seconds)
60 hz = 18 seconds of dwell

so the slope i got m=y2-y1/x2-x1 equates to -1.1428571429. But that would be for a linear slope and from what i see in the output the slope isn't linear. Can some one help?

bernie_carlton · Jul 9, 2007

40hz is the middle of the numbers but isn't the middle of the range. 20hz to 60hz is * 3. You found that the dwell at 40hs (twice 20hz) was about 1/2 (53 / 24) the time as it should be. The jump from 40hz to 60hz is times 1.5 so you should see the time go DOWN by a factor of 1.5 (24 / 18). Dwell is the time to go a distance at a certain speed. Dwell is therefor inversely proportional to the speed (hz). The 'middle' hz for 11/2 dwell is about 34.641016151377545870548926830117 hz. (20 * square-root(3))

Bob O · Jul 9, 2007

You could plot your data in excell and add a trend line which will give you the equation of the line that fits the points.

kamenges · Jul 9, 2007

This isn't really an inverse slope thing. An inverse slope is when the slope value is negative. This is an inversely proportional thing.

This means that the speed times the dwell time is a constant. You can use this constant to go back and forth. Don't try and do this in one piece. It can be done but it will tend to make things more confusing. Also, if you had all the physical parameters of the system you could calculate this constant directly. But we will use your imperical data.

The base equation ot get speed from time is:

V_M = C/T_d

Solving for C we have:
C = V_M * T_d

Using your data we get:
60 * 18 = 1080
40 * 24 = 960
20 * 53 = 1060

Given the above results I am going to consider the 40Hz data an anomoly and use 1070 as the constant. Substitute this constant into the first equation to get a command RPM. Based on the 1070 conversion constant I would have expected the 40Hz dwell time to be 26.75 seconds.

Now you can take the command RPM and linearly scale it to 4-20 mA. This will have a scvale factor as well as a y-intercept other than zero. I get a slope of 0.4 mA/Hz and a y-intercept of -4mA.

Incidentally, C is a linear feed constant. It breaks down to:

feet of auger/(feet of feed / auger rev) * gear ratio * (motor Hz/motor RPM) * (60 sec/min)

Granted, this doesn't account for any material slip past the auger. However, since the 20Hz and 60Hz dwell times are so close to each other I don't think there is much of that.

Keith

russrmartin · Jul 9, 2007

ghriver said:
The numbers:
vfd scaling = 20 - 60hz
analog scaling = 4 - 20ma

ok, the vfd running at 20 hz equates to 53 seconds of dwell time.
the vfd running at 60 hz equates to 18 seconds of dwell time.

so if 20=53 and 60=18 you would think that the middle vfd scale of 40hz would equal the middle scale of dwell. It doesn't.

This is what i got.
20 hz = 53 seconds of dwell
40 hz = 24 seconds of dwell (middle would be 35.5 seconds)
60 hz = 18 seconds of dwell

so the slope i got m=y2-y1/x2-x1 equates to -1.1428571429. But that would be for a linear slope and from what i see in the output the slope isn't linear. Can some one help?

Your slope is correct, but to put what the other guys are saying into simple terms, you didn't bother with the offset. Remember, equation for a line is y=mx+b. You need to determine what b is. I believe you forgot about b, which is what threw your number off. Use the point slope method to solve for b, then I think you'll find that your numbers match.

bernie_carlton · Jul 9, 2007

An OFFSET has nothing to do with it. The error was in thinking that a constant (screw length) divided by a linearly changing speed value (Hz) would give a linear value (time). It doesn't.

Plug the requested dwell time into an equation as suggested by kamenges then use the result.

ghriver · Jul 9, 2007

Thanks so much, we have a working formula now. I really appreciate it.

ghriver · Jul 9, 2007

kamenges said:
This isn't really an inverse slope thing. An inverse slope is when the slope value is negative. This is an inversely proportional thing.

This means that the speed times the dwell time is a constant. You can use this constant to go back and forth. Don't try and do this in one piece. It can be done but it will tend to make things more confusing. Also, if you had all the physical parameters of the system you could calculate this constant directly. But we will use your imperical data.

The base equation ot get speed from time is:

V_M = C/T_d

Solving for C we have:
C = V_M * T_d

Using your data we get:
60 * 18 = 1080
40 * 24 = 960
20 * 53 = 1060

Given the above results I am going to consider the 40Hz data an anomoly and use 1070 as the constant. Substitute this constant into the first equation to get a command RPM. Based on the 1070 conversion constant I would have expected the 40Hz dwell time to be 26.75 seconds.

Now you can take the command RPM and linearly scale it to 4-20 mA. This will have a scvale factor as well as a y-intercept other than zero. I get a slope of 0.4 mA/Hz and a y-intercept of -4mA.

Incidentally, C is a linear feed constant. It breaks down to:

feet of auger/(feet of feed / auger rev) * gear ratio * (motor Hz/motor RPM) * (60 sec/min)

Granted, this doesn't account for any material slip past the auger. However, since the 20Hz and 60Hz dwell times are so close to each other I don't think there is much of that.

Keith

^^^^^^ Special Thx.

russrmartin · Jul 10, 2007

An OFFSET has nothing to do with it. The error was in thinking that a constant (screw length) divided by a linearly changing speed value (Hz) would give a linear value (time). It doesn't.

Why wouldn't dividing a constant by a linearly changing speed give a linear value? That sentence makes no sense. It should give a linear value. I agree with kamenges method, buy I don't understand or agree with that statement.

kamenges · Jul 10, 2007

Originally posted by russmartin:

Why wouldn't dividing a constant by a linearly changing speed give a linear value?

You said you agreed with the method as I proposed it. That means you agree that the dwell time is inversely proportional to speed. That means that if I double my speed, the dwell time is cut in half. If this is true I could double my speed nearly infinitely and the dwell time will never reach zero. It just gets smaller and smaller. The exact opposite is true if I cut my speed in half. The dwell time doubles. I can keep cutting my speed in half and my dwell time will keep doubling keeps.

If this were a linear relationship the slope of the curve would be the same at all points. The curve you get from an inversely proportional relationship has a constantly changing slope. Take the simple equation y=1/x.

Look at some pairs and their slopes:



 

x     y     slope

0.5   2

             2

1     1    

             .5

2     .5    

             .166666666 

3     .33333

It is an inversely proportional relationship. The easiest way to see this is to type some numbers into Excel using an inverse proportion and do an X-Y Scatter plot of them. You will see a curve that is assymptotic to the X and Y axes, assuming you use all positive values for X.

While the result changes in a clearly defined way the result is not linear.

Now, the relationship of desired speed to milliamp command is linear and has an offset.

Keith

russrmartin · Jul 11, 2007

duh

Yup, you're right. I was having a blonde moment I guess.

ghriver · Jul 11, 2007

I am still having a little trouble getting this down. I have tried to find the vm=c/td by searching google to get a little more explanation but havent had any luck. Can someone help me understand this better. I need to understand whats going on because i have to do this for multiple scales and devices.

kamenges · Jul 11, 2007

ghriver-

Your original post covered a couple of interrelated items. I'm not sure specifically what you are having trouble with. At this point you may want to ask some very specific questions about what you don't understand and we can go from there.

The big thing to get a handle on is the inversely proportional relationship between speed and time given a constant distance and how to represent that in equation form. With a fixed distance, if I double my speed my time to travel the distance is cut in half. That relationship holds for all speeds and times (within reason). All the rest is scaling to make the physical units come out.

Keith

ghriver · Jul 11, 2007

I am actually having trouble understanding the math. I am currently only 2 years into my 4 years of college and I am lacking a little in the math department.

For this particular machine i have the following data.

18 seconds of dwell relates to a decimal value of 30840.
53 seconds of dwell relates to a decimal value of 0.

i understand y=mx+b no problem but the inversely proportional relationship i haven't been able to get a handle on.

Its the same as before if the operator requests a dwell of 40 seconds i need the decimal equivalent.

ghriver · Jul 11, 2007

I have one more value i just went out to the field to calculate. A decimal value of 2643 equates to 45 seconds

4-20ma, hz, dwell, inverse slope.

ghriver

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