Optimal angle to guide pallets with the least friction

[RobinDP]

Homework Statement

Image below is a sketch of the situation. A pallet is vertically moved towards the conveyor. The purpose is that this stack of pallets (about 15 pallets) gets guided by 2 plate structures so that the stack is ligned out.

Homework Equations

I'm wondering now what the optimal angle (alpha) would be so that the pallets will slide down the fastest and easiest way with the least friction.

The Attempt at a Solution

I already tried things as replacing the situation with forces (gravity, friction force,...) in order to get a solution where the friction is the least but the thing is that the optimale angle would be 89° in theory.. I figured out what the minimum angle should be: alpha = inversetan(coefficient of friction), what is around 20°. I'm wondering if there is a math solution to this rather than just saying I choose that angle because I want to guide pallets that are stacked very badly.

Thanks in advance,
Kind regards,

R.

 

[berkeman]

Welcome to the PF.

What keeps the pallets from tilting as they are dropped down into the conveyor chute? What keeps the stack of pallets from tilting and getting stuck in the chute?

 

[RobinDP]

Welcome to the PF.

What keeps the pallets from tilting as they are dropped down into the conveyor chute? What keeps the stack of pallets from tilting and getting stuck in the chute?

Thanks! The pallets are guided with a forklift towards the conveyor. On the side of the forklift, the pallets are hold by 2 plates. The forks of the forklift can pass through it. The other side is fully open since the whole stack is guided towards a pallet dispenser. The only thing that can hold up the pallets is friction but I added a tolerance of 25 mm each side so that the pallet can't get stuck.

 

[haruspex]

Thanks! The pallets are guided with a forklift towards the conveyor. On the side of the forklift, the pallets are hold by 2 plates. The forks of the forklift can pass through it. The other side is fully open since the whole stack is guided towards a pallet dispenser. The only thing that can hold up the pallets is friction but I added a tolerance of 25 mm each side so that the pallet can't get stuck.

As I read it, the reason for the shoulders is that the plates might not be lined up properly as the forklift attempts to lower the pallets. So while sliding on a shoulder, the pallet is still on one arm of the forklift. Thus there are two normal forces and two frictional forces to think about. Also, we need to know where the forklift arms are in relation to the full width of the pallet in order to get the geometry right...
Edit: ... and what the maximum displacement we need to allow for is.

 

[berkeman]

Do you have any more detailed sketches or pictures? And how many pallets can be in a single stack?

http://c8.alamy.com/comp/F698A3/for...n-pallets-shot-on-white-background-F698A3.jpg

 

[RobinDP]

@haruspex @berkeman: As Berkeman shows in the picture, the stack of pallets (15 euro pallets ~ 450 kg) is lowered and should be guided by the angled plates. The maximum displacement that the pallets can be in disorder (side ways) is around 10 cm. The forks are in the middle as shown in the picture.

 

[berkeman]

So you are carrying 15 stacked pallets on a forklift, and want to set them down so that they are lined up well. Does the forklift then back up and leave the stack on the ground? Where does each pallet stack go after that?

 

[RobinDP]

So you are carrying 15 stacked pallets on a forklift, and want to set them down so that they are lined up well. Does the forklift then back up and leave the stack on the ground? Where does each pallet stack go after that?

Yes, so the red cross indicates where the forklift will be when dropping the pallets. He lifts the whole stack above the structure and lowers them behind the 2 plates as you can see. The thing is that the sides are not guided which let the stack end up as not being aligned sideways. After that, the whole stack goes further to a pallet dispenser where the bottom pallet is taken off and goes further to stack products on.

 

[berkeman]

Huh, I hadn't seen those before. I did a google search on Pallet Dispenser, and got lots of hits.

What you show in your picture looks like the rear of the dispenser, right? Does the front look more like this?

https://www.bastiansolutions.com/blog/wp-content/uploads/2016/08/dual-pallet-dispensers.jpg
https://www.bastiansolutions.com/blog/wp-content/uploads/2016/08/dual-pallet-dispensers.jpg

 

[RobinDP]

Huh, I hadn't seen those before. I did a google search on Pallet Dispenser, and got lots of hits.

What you show in your picture looks like the rear of the dispenser, right? Does the front look more like this?

https://www.bastiansolutions.com/blog/wp-content/uploads/2016/08/dual-pallet-dispensers.jpg

The dispenser is fully independent to this structure. It looks like that but it's done in a slight different way. Let's assume it's pre-aligning the pallets before they enter the dispenser.

 

[berkeman]

Anything like this video?

 

[RobinDP]

Anything like this video?

Yes, the destacking is done with pistons so it's comparable to that.

 

[berkeman]

Okay, we're getting closer, thanks. But I still don't understand the picture you posted. Does the forklift approach that apparatus from the other side? And how high are the forklift's forks when it deposits the pallets into the alignment chute? From the picture, it looks like the forks would need to be many meters off the ground to clear the two side panels, and the forks could only be less than a meter apart to fit in that slot...

 

[haruspex]

The forks are in the middle as shown in the picture.

They might be in the middles of the holes (I can't see it that clearly in the picture) but they're not in the middle of the pallets, and I do not know the dimensions of the holes. I could make a guess from the picture.

But the numbers do not matter yet, we can just assign unknowns.
Let the forks be distance f from the centre of the pallet, the full width of the pallet be 2p, and the distance between the shoulders be 2s. Suppose the centre of the pallet is displaced x > s-p from the centre of the gap between the shoulders. Can you draw the force diagram and write some equations?

 

[RobinDP]

They might be in the middles of the holes (I can't see it that clearly in the picture) but they're not in the middle of the pallets, and I do not know the dimensions of the holes. I could make a guess from the picture.

But the numbers do not matter yet, we can just assign unknowns.
Let the forks be distance f from the centre of the pallet, the full width of the pallet be 2p, and the distance between the shoulders be 2s. Suppose the centre of the pallet is displaced x > s-p from the centre of the gap between the shoulders. Can you draw the force diagram and write some equations?

I don't quite understand what you mean, is this information relevant to the problem? Let's say the pallets have enough space to move between the forks.

 

[haruspex]

I don't quite understand what you mean, is this information relevant to the problem? Let's say the pallets have enough space to move between the forks.

If the pallets are displaced such that one edge lands on a shoulder of the guide, the stack will be supported by the shoulder on the one side and the far arm of the fork on the other side. No weight will be on the arm near the shoulder the stack hits.
We need to know how the weight of the pallets will be distributed between these two contact points. Also, as the forks continue down, we need to know what angle the pallet stack will lean at for a given height. These will both depend on where the forks are in relation to the edges of the gap into which the pallets are to descend. If you draw suitable diagrams you will see this.

 

[RobinDP]

If the pallets are displaced such that one edge lands on a shoulder of the guide, the stack will be supported by the shoulder on the one side and the far arm of the fork on the other side. No weight will be on the arm near the shoulder the stack hits.
We need to know how the weight of the pallets will be distributed between these two contact points. Also, as the forks continue down, we need to know what angle the pallet stack will lean at for a given height. These will both depend on where the forks are in relation to the edges of the gap into which the pallets are to descend. If you draw suitable diagrams you will see this.

Ok I understand what you mean now but I assume the angle that the stack will lean, depends on the angle of the plate. The thing is also that the forks will not always be in the same position as before. It could be that the forklift operator lifts it up with one fork next to the wooden block. But basically, if I know the angle of which the pallet on the forks can lean, let's say 20° then the angle of the plate must be 70° in order to not disturb this? If the angle is too low, the pallet will be guided by the force of the forklift and not by the friction with the plate?

 

[RobinDP]

Ok I understand what you mean now but I assume the angle that the stack will lean, depends on the angle of the plate. The thing is also that the forks will not always be in the same position as before. It could be that the forklift operator lifts it up with one fork next to the wooden block. But basically, if I know the angle of which the pallet on the forks can lean, let's say 20° then the angle of the plate must be 70° in order to not disturb this? If the angle is too low, the pallet will be guided by the force of the forklift and not by the friction with the plate?

Edit: I say 70° because most of the guiding plates used in the production line there have an angle of 70 - 75°, it's just that I'm trying to figure out a math calculation why exactly that angle.

 

[haruspex]

Edit: I say 70° because most of the guiding plates used in the production line there have an angle of 70 - 75°, it's just that I'm trying to figure out a math calculation why exactly that angle.

I don't think it can be simply a matter of the best angle for ensuring the pallets slide into position. The steeper you make the shoulders the more readily the plates will slide. It will be a compromise, probably so as to avoid having to lift the pallets very high. So perhaps it is the least angle such that the pallets will always slide.
On that basis, you can consider the worst case in regard to how the pallets are positioned on the forks, etc.