Real world friction/force problem... guiding pipe through a tunnel!

lupac

[b]1. Here is what I am trying to solve. I am not looking for a direct answer, I just need help solving the problem. I am a mechanical EIT working for a clean energy company. My boss (P Eng.) and I are trying to solve this problem but can't quite grasp the concept.

OK so, we have a tunnel with a 140m radius, the penstock for the powerplant will be travelling through this tunnel. The pipe lengths are 8m long each and the total tunnel distance is roughly 200m (this is not important). What we would like to do is push a section of pipe into the tunnel then weld the next section then push the whole assembly into the tunnel then weld the next section... and so and so forth. The pipes will be mitred to compensate for the 140m radius.

What we are trying to determine is the force required to push the pipe into the tunnel. This will be a friction force opposing the direction of travel. It is easy to find the force required to push the pipe on a flat section. Our problem is finding the force required to guide the pipe around the bend. The pipe will be bolted to two sliders (one on each end of each pipe). The sliders will slide on a track. There will be guide plate (similar to how a roller coaster stays on track) that will guide the pipe around the corners.

We are basically looking for the normal force pushing on the guide as it goes around the corner. How do you solve this problem??? Do you use a bending moment? We are stumped. Please help.

Attached my work so far to help you understand the problem!! Assume no elevation change. How to you find the force required to guide the pipe around the corner? Momentum can be ignored because the pipe will be travelling sooooo slowly as it is pushed through the tunnel

Attached Files

Scanned from a Xerox multifunction device001.pdf (279.9 KB, 19 views)

berkeman

Welcome to the PF.

(I moved your thread to the ME forum, where it should get better views and replies)

Is that a typo "140m radius"? That's a really big pipe! Maybe you meant 14.0m radius? Or is that the radius of the overall curvature of the pipe installation (where you have to go around bends)?

etudiant

It may be that a railway engineer could have some useful experience to contribute, because this seems a very tight curve for a tracked assembly.
The design apparently calls for pushing the pipe buildup around about a one and a half radian turn, so a lot of push will be against the guide track, rather than along it. That will make the assembly progressively more sticky as each pipe segment gets added.

It might be easier to move each segment to its position individually and assemble in situ, although presumably the pipe is on a slope, which complicates the task.
Still, an 8m diameter penstock should give plenty of room for a workcrew even inside the pipe.

nvn

lupac: Your question is already clear, as stated in post 1. I currently could not find an easy way to compute this using hand calculations. I hope someone will prove me wrong, because it would be interesting to see how to compute this fundamental problem.

I hate to give you the bad news, but I currently think this question might require a relatively advanced finite element model. It probably cannot be an all beam finite element model, because the guides and track contact points probably need to be modeled using surface contact, with friction. (The penstock pipeline, itself, can be modeled using beam finite elements.)

However, if your finite element program has gap elements that allow transverse friction, and has a robust solver, then the whole model could be an all beam finite element model, without using surface contact.

etudiant: Unless I am misinterpreting, the penstock pipe has a diameter of approximately 1.9 m, not 8 m.

etudiant

My mistake, the sections are 8m long, not 8m in diameter, so no interior assembly unless robotics capability makes a very sudden jump.
It still seems problematic to me to expect to push this several hundred foot long assembly around a quarter circle using sliding contacts. Sticktion is a real problem, especially in large assemblies such as this one and is very difficult to model.
Maybe vibrating the track might help unstick things, but that seems at odds with the idea of greasing the sliders.
Could the pipe assembly be floated in the tunnel, so the guide rail would be unloaded?

lupac

Thanks for the input. I agree that this problem is more complicated than a simple static problem. We would start at both ends of the tunnel and then meet the two sections in the middle.

etudiant

Was not the basis for the problem the difficulty in joining the pipe elements properly while inside the tunnel?
If the segments can be joined individually once in position in the tunnel, the problem becomes a lot more tractable. The force needed to move each segment is still not easily calculated, but should be approximated by sliding friction estimates.

lupac

No we would like assemble the pipe outside the tunnel and push it in as it is being assembled.

At first glance the problem doesn't seem to be very difficult. however, I haven't been able to produce a solution.

lupac

We want to assemble the pipe as it is pushed into the tunnel because it will be cheaper and also safer for the crew.

Travis_King

Can you pull from the other end while pushing from yours?

lupac

It depends which pipe we use. If it is the welded steel pipe then yes but if we use this new composite pipe the joints are couplers that can't be under significant tension.

etudiant

Well, now I'm confused.
If the pipe assembly will be done at both ends, the two sections must be joined in the middle of the tunnel. If that area is accessible, then so is the rest of the tunnel and the entire pipe can be joined in situ.
The composite pipe that is under consideration would be an extra complication.
Even if it were pushed through the tunnel, it would certainly put the joints under tension as the pipe assembly is forced to bend to conform to the tunnel and track.
The only solution I could envisage would be to hang the pipe from a single or dual track along the top of the tunnel, with the pipe entirely passive and under no stress, just carried by the metal sliders or rollers running along that track.
Given the requirement to push the pipe around a 90 degree tunnel, I doubt there will be a much easier way to put it into place.