Shock absorber forces

[mrguyman]

Hi everyone! There’s a problem that I can’t find an answer to. I need to test the integrity of a skid landing gear after a fall from 500 mm height.

For a better understanding I simplified forward crosstube and it looks as follows: there’s a horizontal beam of 1,5 m length supporting the mass of around 300 kg, on the edges to the beam there is a shock absorber perpendicularly attached on each side, they are seen here as springs. The shock absorbers should damp all the energy of impact, namely 1.471,5 J by moving its full length of 100 mm. In order to do it, each shock absorber produces 7357,5 N. I calculated it using: m*g*h=0,5*kx^2=0,5*F_Spring*x.

Even if I assume that the collision will be 0.1 s long from: F=m*delta(v)/delta(t), I get that force of collision is 9396 N, which is significantly lower than the force produced by both shock absorbers. This means that the bending moment with the shock absorbers is far bigger than without them, which makes no sense. I understand that it’s a dynamic problem and I try to solve it in a static way but it makes no sense to me.

I guess that all the force produced by the shock absorbers is going to the ground but I’m not sure. I need to find a deflection of the beam and the bending moment. The material is Aluminum.
Thank you for your help, it’s highly appreciated!

 

[berkeman]

Welcome to PF.

Do you have a sketch or mechanical drawing of the setup? That would help this discussion a lot. Use the "Attach files" link below the Edit window to upload the file(s).

Also, a skid landing gear is subjected to both vertical and horizontal forces when contacting the ground (assuming whatever vehicle it's attached to is moving forward as it lands). Is that part of your calculation somehow?

 

[mrguyman]

Welcome to PF.

Do you have a sketch or mechanical drawing of the setup? That would help this discussion a lot. Use the "Attach files" link below the Edit window to upload the file(s).

Also, a skid landing gear is subjected to both vertical and horizontal forces when contacting the ground (assuming whatever vehicle it's attached to is moving forward as it lands). Is that part of your calculation somehow?

Thank you for advice. The landing gear is meant for vertical landing so I’m only assuming vertical forces. Here’s the quick sketch

 

[jack action]

You should look at the harmonic oscillator to solve this problem.

Although you talk about shock absorbers - usually called dampers - you only refer to springs. You probably will have to include damping as well in your equation.

Here is a 5-min video to summarize your case:

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The only difference would be that in your case you would have an initial velocity $v_0$ as well, found with $mg\Delta h = \frac{1}{2}mv_0^2$, where $\Delta h$ is the vertical distance traveled by the fallen object before the landing gear hits the ground.

Of course, plenty of online solvers, like this one.

 

[tech99]

I tend to think that conservation of momentum will apply in this case. Average spring force x stopping distance = falling velocity x mass of helicopter. The spring must be sufficient to stop the aircraft hitting the ground, and the damping must then be enough to provide critical damping so it does not rebound.