mechanical "strange oscillator" problem

[XDN]

Hi all

I have a mechanical problem, but i don't a have a mathematical skill to solve it, I hope that someone could help me👃

in first, see simplified drawing:

1. 

    in yellow box , is a winch

2.  wire betwen winch and pulley (steel cable,the length is low, the elongation can be a constant, maybe )
3. pulley connected to ground with spring
4. wire betwen mechanical elbow and pulley (steel cable,the length is high, i need to use Hooke's law for evaluate elongation, and correct this to calculate good Lw parameter)
   
5. mechanical elbow
6. mechanical load mg ( for simplify what happens in mechanicel elbow, we consider un traction forces on wire node at elbow)

At t0 system at rest  : it is as if the spring is a bar

At t1, the winch pulls to make an ordered value for alpha

Find Lw according to alpha angle, the object of the game is that the winch gives a Lw length which allows to maintain alpha angle according to the instructions (angle ordered)

What i feel : variable is a function f(x)=k(x) , here is a differential equation

I do not know, neither to pose this problem nor to solve it😓

this is above my skills, but it's very interesting

Anyone can help me ? I would like to learn how to solve this

[XDN]

i can add this comment:

At t0 we have a small load in wire. (prestressing)

This small load it make by traction spring, and it is nessary to avoid the cable goes out of the winch

Of course the winch is connected to a motor, and motor is connected to ground

the speed is low, and the system has time to equilibrate, it can be considered static I think

[XDN]

Another one things, for show the scale, the wire cable diameter is 1 millimeter

and the systeme is small, the pulley (made with steel)  diameter is 40mm and this  thickness is 4 milimeter

I think that we can neglect the masses and the inertia of different part.

sorry for the multiple messages, but it seems that we can no edit the post

[LucMeekes]

You should be able to edit your own posts, within about one day from first posting. Just go to the (three dots) menu in the upper right corner of the posting and select edit.

Regarding the topic: I wouldn't know where to start, but if you give me the (set of) differential equation(s) I'll be happy to help solve it.

Success!

Luc

[XDN]

Thanks for your answer !

Unfortunately, i can't write this equation 😩

I think it's possible to reduce the problem to the equations of statics, and not to consider a dynamic system

If the point of view is :  the system not move for each step time

In real world, it's possible to wait the system stabilisation between  to step

I'll try to breakdown my system step by step to better identify the problem

[Fred_Kohlhepp]

Need one more clarification:

What is the force reaction at this point?

[XDN]

This point is not a pulley, is a hinge

and this hinge had a linear guidance on z_axis with ground

in the same way, the pulley (blue circle) have a linear guidance on z_axis with ground

i calculated reaction forces at this point in terms of alpha angle (resulting moment theorem)

and i finally, i find the lenght cable for alpha angle value 0° to 90°, it's no linear.

i translate my worksheet, after this, post it .

[Fred_Kohlhepp]

This point is not a pulley, is a hinge

and this hinge had a linear guidance on z_axis with ground

in the same way, the pulley (blue circle) have a linear guidance on z_axis with ground

If that hinge is constrained in x, then the tension in the cable is constant equal to the weight m g.

[XDN]

Yes I agree

But my problem is not the calculation of this force reaction.

My problem is behaviour of pulley and spring

if I consider the static system at each step of time

I must respect the first Newton's law : sum of external forces = 0

and my system (pulley + spring) subjected 3 forces

but for my spring F=ku

If F spring are lower or higher Fload (force reaction elbow), the alpha angle will vary

and the system will oscillate because of F=ku

and finally , the question is:

what is the offset of lenght cable winch to keep alpha constant

of course the hook law must be considered for the elongation of the cable

[Fred_Kohlhepp]

My point is this

    If the angle of the weight does not alter the cable tension, then the spring extension length will not change (since the force on the spring is simply twice the cable weight.)  You can wind the winch to slide the rig  up and down to your heart's content, but FT_aval will not change, so the pulley stays in the same place (DL/2 = zero) regardless of DL.

That does not mean that there isn't a resonant frequency--you have a mass suspended on a spring.  But you don't have anything that will change the force acting on the spring.

[Fred_Kohlhepp]

Attached is an analysis (Prime 4.0)

[XDN]

Thanks Fred

i going to look you file...

But your premisces are not correct, it is normal that it is not understandable, because,

to simplify the problem I said only that the tensile force was variable.

In reality at P7 point in the drawing, we have another same elbow system.

I did not want to increase the problem, but I see that it is not a good idea

[XDN]

in any case, a big thank you to the community because your sheets are always a wonderful way for me to learn a lot of things