Is the volume of fluid in the hydraulic system comprising the two cylinders, the tee, and the connecting hoses constant? In other words, is the actuating valve closed?
If so, perhaps you can use the knowledge that the volume of fluid in the system is constant, and if one assumes that the fluid is incompressible (a common assumption), then if the load on one cylinder causes it to compress (shorten) sufficient to displace say 1 inch**3 of fluid, then that same volume of fluid must be forced into the second cylinder. If the cylinder bores are the same diameter, that would mean that the second cylinder would extend by the same axial distance that the first cylinder was compressed. I haven't thought this through in any more detail than the superficial comments above, but using Mark's suggestions regarding springs and constraint equations, one could probably implement this behavior.
This method clearly will not work if the actuating valve is open, such that the fluid displaced from one cylinder could flow back into the hydraulic reservoir.
Mark Rodamaker wrote:
> Todd, > Yes I think you are right about not using a spring since the force > doesn't necessarily change as the nodes move relative to each other. The > problem is that there are too many DOF's to be handled by just adding one > CE. If there was another relationship between the translational DOF's, there > would be a lot better chance of it working. I'll think about this a little > more. There may be another approach. Starting with a spring may have been a > poor start.
> ----- Original Message ----- > From: > To: > Sent: Tuesday, November 28, 2000 8:31 PM > Subject: Re: [xansys] Modelling Tee'd Hydraulic cylinder
> > Mark, great idea. This shows some real inventive thinking.
> > However, I am not sure that we can treat the cylinders like a spring in > > this sense, can we?
> > The cylinders could effectively have two very different lengths but > exactly > > the same force in reality. k*x doesn't really apply since a either > cylinder > > could produce 1000 lbf at 30" or 100" if the structure it self were > > flexible enough to allow it.
> > I don't know where to go with this thing. I have been dealing with this > > type of problem for quite some time now. I do have some techniques that > > give reasonable results, but I am looking to refine and improve this > > process.
> > Your ideas are greatly appreciated, keep em comin! :)
> > I wonder if this could be handled with constraint equations. Align node > > DOF's to be along the cylinder axis. Assume it is the x direction. A > > cylinder acts as a spring with stiffness K. Assume nodes 1 and 2 are for > > cylinder 1 and nodes 3 and 4 are for cylinder 2.
> > F1=k(x2-x1) > > F2=k(x4-x3) > > F1=F2=k(x2-x1)=k(x4-x3) > > x2-x1=x4-x3 > > x2-x1-x4+x3=0 ! this is a constraint equation
> > I'm not sure whether you should also put the spring elements into the > > model - probably yes. The likely problem is this isn't enough of a > > mathematical condition and some additional relationships are necessary.
> > > Are you taking into account the reaction moments acting on your > > structure? > > > Without these, if I understand your problem, simple statics will not > > allow > > > the > > > cylinder forces to be equal.
> > > Terry Frankland
> > > Elliott Company
> > > Todd_Meidinger@i... on 11/28/2000 11:55:08 AM
> > > I have a question that I have not been able to find an elegant solution > > to.
> > > I need to include tee'd hydraulic cylinders in a model. The past > > solutions > > > that I have used to model this in the past are not entirely accurate nor > > > elegant so I am looking for some tips or tricks you may have > encountered.
> > > The situation is that in our structures we have hydraulic cylinders that > > > are tee'd together so that the pressure (thus force) is always equal in > > > each cylinder. Picture a tractor/loader with a cylinder on both (right > > and > > > left) its lift arms. When the load is applied at the center of the > bucket > > > (or whatever is on the machine) the cylinder lengths and forces are > equal > > > and this is easily calculated/analyzed. However, when the load is > shifted > > > to one side of the bucket (eccentric) the cylinder's lengths may become > > > unequal, but the force always remains equal. In the past I have used > link > > > 8's to analyze the structure with a center load to find the cylinder > > forces > > > (in this case the force and length are always equal due to symmetry). I > > > would get the reactions and replace them with a force and a light > spring > > > to overcome instability. This does not always work well as when the > > > structure twists (under unsymmetrical load ) the springs cause the > > cylinder > > > force to become unbalanced which is not possible in the real world.
> > > I have been experimenting with using Link 11's to do this by applying a > > > pressure load to face 2. This has not worked as the reactions still do > > not > > > balance due to the underlying stiffness of the Link 11.The force in the > > > link 11 is okay, but the force imparted to the structure is still > > > unbalanced due to the inability of the link 11 to adjust its length when > > > applying SFE to face 2. Once again, the force applied to the structure > > does > > > not remain equal between the two cylinder locations.
> > > In short, what I need to do is, keep the forces equal, but allow the > > > lengths/orientation to change based on the "tee'd" force.
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