Simulation of table tipping force

[140108654P9E]

I'm trying to simulate the stability of a table. I build a model that contains the table and a floor as well as a load on the tip of the table.

When the contact type between the table and the floor is separated or rough, it gives the following error  

STIFFNESS MATRIX SINGULAR OR NON-POSITIVE DEFINITE 

 The model only solves when the type of contact is bonded and it performs bending on the table top.
How can I solve this error?

[dsouzasujay]

Hi @140108654P9E ,

Can you attach design that you have already completed in Fusion 360? you File>Export your *.f3d/ *.f3z file to your local drive and then attach it here to a reply?

[140108654P9E]

Here you go. This is the model when the table and the floor are bonded. (Which doesn't simulate the tipping of the table .. The table performs bending)

[wmhazzard · Accepted solution]

Another way to figure the force would be just go to Inspect/Center of Mass, select your table and weight components. Adjust the weight until the center of mass falls outside the foot of the table. That is the amount of force needed to cause the table to tip. 

[Ex_Machina_Engineering · Accepted solution]

You don't need a simulation for this. Besides, a static simulation will not give you an answer to that question. But this is a very simple problem. By equating torques you will end up with a 1st-degree equation that can be solved very easily.

Torque is ForcexDistance. Force of gravity is Mass x g. But because you'll end up with g in both sides of the equation you can skip that.

So, on the plane of the table's top draw a line between the center of mass (Fusion provides that) and the center of mass of the weight. Then draw the vertical projection of the surface of the leg that is closest to the weight. The point the two meet is your tipping point.

Calculate Tor_A = Mass of table (Fusion provides this as well) x distance from tipping point. Then calculate Tor_B = Mass of weight x distance from tipping point.

When Tor_A is larger the table is stable. When Tor_B is larger the table will tip. Your dynamic balance is when:

Tor_A = Tor_B ==> Mass_tab x Dist_tab = Mass_w x Dist_w.

Solve for Mass_w to find the weight at which the table tips when the weight is applied to that location of the table.

[John_Holtz]

I agree with @Ex_Machina_Engineering  and @wmhazzard. The best solution is to not perform a simulation when a quick and easy hand calculation will suffice.

You mentioned "The table performs bending". Is the amount of displacement is small when the table tips? Or will the table be so flimsy that it bends significantly before it tips? Be aware that the amount of displacement and bending does not change the solution in the analysis type you are performing (static stress). Static analysis assumes small displacements; therefore, the results are linear. If you apply a load to cause 1 mm displacement, the results will be exactly 1000 times larger if you increase the load to cause 1 m displacement. That is not how the real world works, and if that type of effect is important, then you need to find an alternate solution.

If you have to calculate the tipping with a simulation, I can think of two possibilities:

1. A static analysis cannot calculate tipping because tipping is not a static condition. A static analysis can predict what load does not tip the table. Use a rough contact between the table and floor. Apply a small load and run the analysis. If it completes, the table does not tip. Increase the load. If it does not complete (and gives the stiffness matrix singular error), you know it should have tipped. Keep changing the load until you find the point where it solves and does not solve.
2. You do not need the floor; the floor adds complication to the analysis which causes it to run longer. Instead, add constraints to the two front edges and the back edge (actually split into two segments). The reaction at the front will always be positive because the floor holds the front legs up. When force is small, the back edge also has a positive reaction force because the floor is holding the table up. When the sum of the reaction force at the back constraint is negative, that indicates the floor needs to hold the table down. Since the floor cannot do that, you know the table is going to tip. 

John

[Ex_Machina_Engineering]

Actually using the fact that the simulation errors out to check whether you have tipped is a very clever approach to the problem. I like it.

Also, let me note that my calculations work only if the table is rigid. If the weight causes the table to bend, the complexity increases significantly.

[TheCADWhisperer]

@140108654P9E 

Check >>this simulation<< when the video is done compiling.

I used Autodesk Inventor Professional - Dynamic Simulation...

[140108654P9E]

Can you please share the file of this model?

[140108654P9E]

This is actually a very simple solution. However, I was looking to simulate it for an animation.

[140108654P9E]

Thank you for this solution. 

[Ex_Machina_Engineering]

If you want to do an animation with it and you don't require precise motion simulation:

1. Find the tipping point
2. Draw a sketch point on that exact location
3. Create a revolute joint on that point so that the table rotates around that point as it would do when tipping
4. Make a motion study with the change in angle of the joint follows the curve you need
5. Go to the render environment and render your animation (you can find additional info online on how to do that. It's easy

I hope this helped.

[TheCADWhisperer]

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@140108654P9E wrote:

Can you please share the file of this model?

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Do you have access to Autodesk Inventor Professional?

[PuregoldnerDsgn]

@wmhazzard Can you clarify what you mean by “until the center of mass falls outside the foot of the table.”

I am trying to do the same thing as well and want to know if someone’s feet will tip over a coffee table. Thanks!

[PuregoldnerDsgn]

 Can you clarify what you mean by “until the center of mass falls outside the foot of the table.”

I am trying to do the same thing as well and want to know if someone’s feet will tip over a coffee table. Thanks!

[wmhazzard]

It is shown in the photo. The white line is the edge of the bottom feet of the table, you can see that the center of mass icon is to the left of the line showing that the center of mass is outside of the bottom of the table foot which will cause the table to tip. 

[matthew]

Hi,

Can you show me your joint setup for this one or if you can send me the files I would be very grateful