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Stiffness for vertical pumps using Pro/E


New member

I have a problem to which i donn whether pro/e can solve it.

It is a vertical pump which is subjected to lateral gravity loads. My question is --can we find the stiffness ( spring rate) of the pump.I have performed structural and modal analysis. But iam not sure how to intrepret theoutput data. Which no. do i need tolook for to get the stiffness.

Can any one help me out.



New member
To carry out a stiffness analysis, apply a unit load in the direction you are interested in. Add a measure to measure the deflection in the same direction. Run the analysis, find the result of the measure and then calculate the stiffness:

Stiffness = Unit Load/Displacement

I normally choose 1000 N for my load to make sure I get good convergence.




New member
hi rod,

thanks for the reply,

actually the formula i know to find the stiffness as load/ displacement as you said. Do you think i can use this

(mass*gravity in the lateral direction)/ displacement in the lateral direction.

So like this i donn need to re run the analysis with unit load.

Am i right.

And the other formula i have for stiffness is

(natural frequency)^2 = Stiffness/mass

so can i use this???????????

Please give me some suggestions.

thanks in advance.



New member

You can't use the latest, unless you know the vibration direction. It is easy for a spring-mass system, but for a solid ... You have to remember that in FEA you are working with a stiffness array, not with a scalar quantity.

The method that Rod suggested seems to be the right one. Also make sure you distibute the unit load over the volume, since each node in your system needs to carry a gravity load.


New member
One more thing, Sari,

If you are trying todetermine a scalar number for stiffness this should be related to a certain location (node) in your model and to a certain loading case.

Hope this helps,



New member
hi Ibotez,

"You can't use the latest, unless you know the vibration direction. It is easy for a spring-mass system, but for a solid ... You have to remember that in FEA you are working with a stiffness array, not with a scalar quantity."

with this statement do u mean that i cannot use both the equations i mentioned in my previous reply.

When you are talking about the stiffness matrix, i think, i understood, but some think is not really clear. Can you explain me in details. Do you mean that if i need to calculate the stiffness of a body, i need to take the displacment at the point at which i apply the load in the required direction????

You also suggested me to apply unit load to the whole volume. How can i do that in Pro/E????

The main problem is that i dont have the parts to do the analysis, i only have the results for structural analysis( when only lateral gravity is applied) and modal analysis ( when only lateral gravity is applied). so now i have to figure out whether i can extract the stiffness of the pump with this data.

Sorry for too many questions.

Thanks in advance.



New member
I'll try to make it as simple as possible, so I don't make this e-mail too long.

For a spring: F=k*dx

Note that the system is unidimensional: one nodal force (F), one DOF (x)! The stiffness will be a scalar quantity.

For aFE model: {F}=[K]*{dx}


{F} - the nodal force array, all nodal loads included: force, andtorque on x,y, and z;

{dx} - the nodal displacement, all nodal DOFs included, and

[K] - stiffness matrix.

How you determine the stiffness matrix is not important now, quite complex by the way, and let's leave it for the pros.

As you can tell from the latest equation a nodal force will determinedisplacements on all nodes. Therefore, if you want to determine the a scalar quantity for the stiffness you'll have to refer to one certain DOF at a certain node and one nodal load.

As far as how to apply a volume load in Pro/E, just use gravity load.
Edited by: lbotez


New member

thanks for the patience. I understood what you said.

As you said i have the displacement in the direction of the applied gravity. ( i performed a stress analysis by applying a gravity force in the lateral direction).

So now can i use this formula :

stiffness = (mass of the body * lateral gravity)/(displacement in the direction of the applied lateral gravity)



New member
hai Ibotez,

i applied a gravity load in a particular direction and recorded the displacement in that particular direction. but how to input this gavity load in the formula load/ displacment. bcos the units of gravity load is inch^2/sec.

Please guide me. i am totally relaying on your reply.

help meee

thanks in advance



New member
I don't really understand. The unit should be in/sec^2. Could you please explain where from did you get that in^2/sec?


New member
hey ,

i am sorry for such silly questions. I will be happy if you can tell me whether i am right.

stiffness = mg/disp.

= (lb) * (inch/sec^2)/inch

= lbf/inch

Do u think what i mean i correct.

PLease guide me.