Flat belt and inclined puley 1

[thegasperus]

Dear fellow engineers!

I have a simple question about operating principle of flat belt and pulley that has inclined pulley. Visualization on the picture. The smaller(lower) pulley is driving pulley and the bigger one is driven. The axis of the bigger pulley gets inclined for few degrees because of operating conditions and wear. The lower pulley is fixed and the belt cannot slide off there, as it cannot slide of the bigger pulley since it is very big. The picture shows exaggerating case when it comes angle.

My questions are: If that happens, is the belt trying to slide up on the bigger pulley in direction x on the photo?

And if so, than there is some opposite force that would make the bigger slowly slide out on off the system in negative x direction on the photo. If of course the bigger pulley can move freely in +-x direction.

Thank you.

TheGasperus

 

[desertfox]

Hi

Well you could use flanged pulleys, all you have in the diagram stopping sliding is friction of the belt on the pulley, how many degrees is the upper pulley tilting?

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

 

[jlnsol]

The belt will run to the side where the belt tension is the lowest, so in opposite direction of x.

 

[thegasperus]

This is an actual and quite delicate problem. The pulleys will definitely stay the same, because the bigger pulley is wide enough to overcome the problem of belt slipping of. The problem that bothers me that it seems like the bigger pulley is getting dragged/pushed in the negative x direction on the picture. And when that movement happen (cca. 5mm in negative x) a collision appears with some other part in assembly.

My goal is to determine if the force of the belt on the bigger pulley exists and later on how big that force is after approx. 20000000 spins. I will have to get into account that at the beginning the pulleys axes are norizontal and in correct position, only later with time we get the bigger one inclined.

Basically I just want to confirm the principle her, that the belt is always trying to get higher up the bigger and therefore the bigger pulley is being pushed to one side.

Thank you.

TheGasperus

 

[thegasperus]

@jlnsol

Ok, then I am completely lost... Why do we use crowned pulleys then? Isnt't the principle the same than with my bigger pulley that is not crowned? Always trying to put the tension in the middle and get to the top of the cone - which I dont have in my case, but you can look at it like half cone... the other half is imaginary cut away

Ohh, and the angle is 2°max...

 

[berkshire]

As you already know. The crowning on the lower pulley changes the circumference of the belt, the belt will always try to run at a position where the tension on both sides of the belt is equal. But first it will migrate to where the tension is lowest before the changing angle increases the tension on that side. The crowning height and angle on the lower pulley is important. Too high a crown and the belt becomes unstable, as does too low a crown. The belt must be able to find an equilibrium where a tangent drawn across the crowned pulley is parallel to the flat pulley ,no matter what angle the flat pulley is running at, and the tension on both sides of the belt is equal. And no the belt will not climb up in the direction of X.
B.E.

You are judged not by what you know, but by what you can do.

 

[thegasperus]

@berkshire

Thank you for explaining this problem to me. You answered my basic question.

I guess the problem for me still remains, but I got rid of one of the possible causes for pulley movement.

 

[dvd]

The belt will try to align perpendicularly with the downstream pulley. The pulley axes need to be parallel.

 

[thegasperus]

@dvd

We cannot get axes to become parallel as I said after 20000000 spins there is always an angle. That is why I thought this may be the the reason for sliding our bigger pulley in the negative x direction shown in the picture.

There is of course some other possible causes that my result in pulley sliding, but they are probably not appropriate for this thread.

 

[Compositepro]

I guess your dotted line are just showing the orientation of the crowned pulley and not an actual belt path. Your terminology is also confusing. Belt walking and sliding are two very different things. Sliding is not often an important factor in controlling belt path.

The first principle of belt tracking is that a belt will approach a flat pulley at a 90 degree angle to the axis of rotation and it comes from "its point of origin". In this case the point of origin is that the belt is close-to-centered on the crowned pulley. If the alignment of the flat pulley changes, the belt will walk to its new tracking position where it is approaching the flat pulley at 90 degrees. The reason for this is that all the points on the pulley surface are moving at 90 degrees to the axis of rotation, and when the belt contacts the roller surface, it moves exactly the same way, if there is no slippage. Belts are designed to not slip. The belt follows the surface motion of the flat pulley until it separates and is suspended in air between the pulleys. It is pulled toward the crowned pulley.

So how does a crowned pulley work? This is what few people truly understand. Once the belt touches the crowned pulley, it behaves just as it does on a flat pulley. What the crown does is that it distorts the belt as it approaches the pulley. The belt becomes slightly curved. This curvature, combined with belt tension cause the belt that is approaching the pulley to move slightly toward the center of the crown. And then the belt touches the pulley. For this to work the belt must have certain properties. It must have stretch and some in-plain shear rigidity. A round belt or string will not work. All this is difficult to understand without pictures, so here are some links.

https://woodgears.ca/bandsaw/crowned_pulleys.html

https://www.youtube.com/watch?v=6sM0Qjumyro

https://www.lockhaven.edu/~dsimanek/make/crowned.htm

Now, if there is slippage on the pulley this will affect belt tracking. There are devices called turning bars where a web of paper in a printing press can be turned upside down and the path changed 90 degrees. The bar does not rotate and the web slides on its surface. In this case the web will side to the lowest point on the bar where the path is shortest to approaching the next roller at 90 degrees to the roller's axis of rotation.

https://www.google.com/search?sxsrf...lAhVPI6wKHe5KDtgQsAR6BAgIEAE&biw=1366&bih=604

In the real world tracking is due to a balance of forces caused by friction on rotating rollers, slippage, web distortion, and web tension.