mathmatical equasion to find Circumference

This is an absolutely baffling question for a person who graduated from high school.

Circumference is equal to Pi * diameter.

I agree to #1, it indeed to be solved by a high school student. try to find your neirboor who is studying this class. and tell you that

angle speed multiply radius equal to linear speed.

try

If I'm understanding your question correctly, the equation you are looking for is:

v=πdα, where:

v=linear (face) velocity of the roller (also equals your belt velocity)

π=pi (3.14...)

α=shaft rotational speed (rpm)

I'm puzzled as to how and where you want to mount the encoder wheel. Does the encoder measure fpm (linear) or rpm (rotational)? You note a tachometer in the sketch, which leads me to think rotational measurement.

But here's how it works; it should be intuitively obvious to you that the roller circumference is moving at the same speed as the belt. Therefore, any wheel mounted to the roller shaft must be the same diameter as the roller to match the belt speed. Same deal if you want to match the shaft rpm by mounting another wheel driven by the belt, the new driven wheel must be the same diameter as the 80 rpm roller to match an 80 rpm shaft speed. Now, any wheel you mount to be driven by the belt will have the same face velocity as the belt (again, intuitively obvious). As you go larger than your roller diameter, this wheel's rpm's will decrease, smaller and they will increase. If what you have is an encoder with a wheel on it that reads linear velocity (like fpm), the encoder does all the work for you; it is already calibrated to the wheel it is supplied with. Just mount the encoder where the wheel is driven by the belt and start taking readings.

Does this answer your question, or did I completely misunderstand what you're looking for?

"I know the rpm of the shaft driving the belt and the feet per min of the belt speed. I need to manufacture a wheel to mount to the drive shaft that will drive a wheel at the same speed the belt is traveling."

This wheel on the drive shaft drives the wheel on the encoder? Is this the configuration?

If the drive shaft wheel is the same diameter as the drive roller, the rim of the wheel will travel at the same tangential velocity as the roller and, therefore, the same speed in linear feet/sec as the conveyor belt. If the encoder wheel is the same diameter as the wheel on the drive shaft, it too will have this velocity. But as long as both wheels are the same diameter - whether or not they have the same diameter as the drive roller - they will rotate at the same speed, ie, that of the drive shaft.

So what is it that you need to solve?

hi first of all let me thank you for not giving me the smart high school answer, since i spend allot of my day fixing real world problems caused bu such engineers, I thank you for your reply, for the others my equasion would be (shut + your = piehole)

normally the encoder wheel would ride directly on the belt....problem solved. what is missing is that the belt stretches on one end(driven) and retracts on the other so the ends do not match the speed of the product i am printing on in the middle... there is too much chatter in the middle from the motor drive chain and the belt seam also makes the wheel bounce and pulses the signal. I have tried measuring the diameter of the roller (say 4") and the thickness of the belt (say 1/4) and making a wheel 4 1/2 the combined diameter. every time i either need to mill of 1/16 or add 1/32 to 1/16 since there seems to be a variance in the belt width. the only true "real world" reading i can get is feet per min of the belt and rpm the wheel will turn when mounted. I just want to calculate a wheel diameter or circumference so i do not have to modify the wheel every time i make one. the encoder puts out 8000 ppr and a small variation changes the print pitch 2-4 inches so i am trying to get away from measuring the components.

At the risk of opening my piehole (sorry if my reply came off as high-handed, I was only trying to answer the question as you stated it...)

Would it be possible to take a reading off the product itself? I realize you would only get intermittent readings, but perhaps a filter could eliminate "gap" readings. Would not the speed of the product be the value you would be most interested in?

(Closing piehole now...)

CSM writes: "Would it be possible to take a reading off the product itself? I realize you would only get intermittent readings, but perhaps a filter could eliminate "gap" readings."

-----

My thoughts exactly - unless he must use an encoder for some reason (possibly because encoders are the most common type of position/velocity feedback element used with motion controllers).

But back to your suggestion: no filter is needed! If he took readings from two sensors a known distance apart, he can measure the time interval directly without interpolating. The first sensor starts a timer (possibly implemented in software) and the second one stops it. The sensor spacing divided by the time interval then gives the velocity of the product directly. As long as the distance between any two items is greater than the sensor spacing, the distance can vary at random without affecting the timing measurement.

Most of that info should have been in your original post!! GIGO!!!

Hi h2ocean,

If I understand your dillema correctly, you are using a closed printing system that prints at the speed the encoder (tach) turns so your product and encoder Must match or you get some strange looking print.

We had a similar problem trying to print small package flaps on a flat belt conveyor using a "Markem" system. Didn't seem to matter what kind of belting we tried or the drive type, the belt always seemed to slip or stutter occassionally messing up the print.

We finally broke down and purchased a flat plastic Slat type conveyor that is sprocket driven and that pretty much cured the problem as it effectively eliminated the belt slippage and gave us satisfactory, readable print.

Here's a site that will show you the type of conveyor I'm talking about in case you're not sure.

http://www.conveyor-center.com/hytrol/plastic.htm

Just make the wheel you make to drive your encoder wheel is the same diameter as the sprockets plus conveyor slats at the drive end as was stated by others here previously and it should work well.

Good luck to you.

Reply to CR4 Thread – "Mathematical equasion to find circumference"

H2ocean:

If my understanding is right, I think you are more interested in knowing the FPM of the conveyor belt in the middle of two pulleys, where you need to do the printing – right?

If it is so, then you will always have problem in synchronizing printing speed to the belt speed that is, if you are trying to pick up pulses from either of the rotating pulleys (I prefer to call it roller). There is bound to be slippage between the drive roller and belt, which could be one of the factors for gaps in printing. You have talked of width of the belt but have not provided its dimension. Another factor missing is the distance between two rollers. I assume you have a system where you are using the pulses of encoder to run the printing head.

What I am trying to arrive is, that, you need to have a non-slip mechanism which rides over the belt in the centre (may be at the bottom run of the belt, in case you are printing from top) and use rollers of this mechanism to pick up lateral speed of the belt which then can be converted as input to the encoder. I have designed such a system long time back. I call it "4-wheel – Non-slip mechanism". This mechanism provides a synchronized input to the printing head at all speed of conveyor belt.

Let me know in case you require further details.

I had a similar problem with conveyors for a venner lathe. I needed to know the position of the product on a 60 ft conveyor within an inch or two. It is problematic in that the belts slip on the conveyor drive wheels, especially during acceleration. For reference the belts run from 0 to 1200fpm. It was critical to keep the belts tight, and automatic belt tighteners helped tremendously. We used a pulse tach on the motor shaft, and it ran at 1800 rpm for 1200fpm. The pulse tach was 2 quadrant 4096 PPR, so you accumulate a pulse on the leading and trailing edge of both phases for 16384 pulses per revolution. Each foot of conveyor requires 1800/1200 x 16384 = 24576 pulses, or 2048 pulses per inch.

Now, the belts run over the drive wheel and assuming it is not a cogged belt will increase the diameter of the drive wheel by the thickness of the belt (ie radius increases by thickness / 2). No matter what, you need to both calculate the pulses per unit length. Speed is then justa calibrated pulses per length per unit time. Experience says you need to do your calculation to be in the ballpark, then verify with actual measurements to acount for belt tickness variation and slippage.

Don't let them bug ya, You seem to know what you want but are having trouble explaining it. Your question requires much deeper thinking than most want to give it.

I don't have the answers either but keep in mind.....

The top belt surface (above the drums) is stretching lengthwise (getting longer) because of load. Crosswise of the belt, this should be a rather uniform stretch but the thickness of the belt is getting thinner, but the thickness of of the belt does not materially affect the surface speed. The speed of the lower surface of the belt (and the top surface between drums) will be (assuming no slip) the exact speed as the surface speed of the drum. The thickness of the belt makes no difference.

The top surface of the belt will be same as the bottom surface of the belt at all points between the drums except when going around the drums. A this point, the top surface will accelerate and de-accelerate as it goes around the drum because the top surface has a further distance to go in the same time period.

I don't believe the average number of revolution's of the driven drum is any faster than the return drum but there is a constant angular change in the rotational position of the two drums as different loads are placed on the belt.

If the loading is constant on the belt, then there will be a slight acceleration of the product form on end to the other.

A measurement of belt stretch can be obtained by measuring the sag of the belt on the return. An idler pulley position sensor at this point could provide a signal for servo control.

You could also get this information by putting selsyn transmitters on each drum and runnin the signals through a phase comparator.

Ive loused up the wording of this, The wife is calling, It's time to go to bed,

These are just some things to think about.

Snakers

Maybe I have an answer to this, You need only one magnetic sensor to detect pulses, and a lot of small metallic clips. Fit the clips along one border of the belt (50cms between clips). Place your magnetic sensor in the critical printing area or before this (it depends on your delay time printing system). Every time a clip passes by the sensor, this will emit one pulse.

Using a very simply software and a system connected PC, you can know the time elapsed between pulses, and because you know the distance (50cm), the software can calculate accurately in real time the product speed travelling in the critical zone you want.

In the same way, you can collect and use the pulses directly like an electrical input to syncronize your printing system to the belt.

Best Regards

Jacam

i thank all for their input to my question. The markum man has hit the nail on the head unfortunatly i am just a grunt installing and the money needed to replace a conveyor is usualy not in the manufacturers project budget.

I only need an encoder because the product will slow/stop/restart with the flow of the production line once it is running and stays running i do not need the encoder but do not have the luxury of turning it on and off, printer software runs one way or the other. It would be wonderful to use some other method of detection or an encoder divider ratio that the manufacturer software will support.

Here is the current solution since my measurments to make the roller do not seem to work.

1. I take my line handheld tach and tach the belt
2. Drill and tap either roller on the conveyor at either end
3. mount a wheel my belt + roller diameter is equil to
4. put my tach on the roller
5. add tape to the roller until the belt speed and roller speed match
6. measure roller & tape with calipers
7. make new wheel
8. maont encoder drive wheel against mine. done

i was simply trying to see how to calculate from the feet per min of the belt and the rpm of the shaft what diameter wheel will give me the same reading.

Here is another Idea.. If your hand tach has a narrow wheel that will track on the surface of a disc or tapered surface. Design a speed changer adjuster by cutting the surface of the wheel on a slant (taper) and then fabricate an adjustable positioner to hold your tach against the surface. Depending on where the tach is positioned on the tapered rim of the wheel, your speeds will change and you can make small adjustments until you match speeds.

You could also do this by installing a disc (flat plate) on the end of the shaft and running your tach at right angles to the surface. Adjust your positioner so the tach will run approximately the same distance from the center as the drum radius. This will also give you a variable speed adjustment.

Forget about the calculations and just adjust it until you match the speed numbers. As the belt wears etc, you can adjust it.

I had a good nights sleep

Snakers.

god bless you!!!!!!! the taper would not work as it would wear the soft grip/traction surface applied tothe encoder wheel. However the running on the face is a brilliant suggestion i had not thought of. thanks thanks thanks.

We use adjustable rubber plugs for temporarily plugging pipe systems. There is a hole through the middle and by tightening the screw the rubber disc is diameter is increased plugging the pipe. It would seem that this type of config could serve you. By allowing a rubberized running surce with an adjustable diameter and modifying thru bolt as an axle.

Just a thought. It's quickly posted but I can elaborate if needed They are called expansion plugs. The one I am thinking of is very low tech ...actually here could you modify something like this or use this theory?