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Stress Analysis on Disc Spring

Stress Analysis on Disc Spring

Stress Analysis on Disc Spring

Anyone has experience with flexures (thin annular plate, with an etched design) that acts as a spring?  The flexure is used as a centering guide and provides a spring load.

I am not sure on how to approach a stress analysis.

Any input would greatly be appreciated.

RE: Stress Analysis on Disc Spring

I too could not find a closed formulation for such a spring.

You could write a computer program to analyze such a spring as a combination of curved cantilever springs in parallel. In this case the spring see torsion in addition to bending. Using this approach you can and check many design options systematically and come to the best or optimized spring with respect to the number of arms and strip thickness.

Another way is to use FEA analysis. This will be more time consuming mainly because you will need to check many design options.

Combining both approaches will give an optimized and accurate solution.

RE: Stress Analysis on Disc Spring

If I understand your application properly, you should be able to find some formulas for calculating forces, deflections, etc. in Roark's Formulas for Stress and Strain, specifically chapter 11 on Flat Plates.  These types of spring elements are commonly analyzed using finite element models.

RE: Stress Analysis on Disc Spring

Thanks guys for the input.

I have been looking at the formulas for annular plates on Roarks.  However, what throws me off is the spiral etching between the OD and the ID.  Do I need to analyze that as a separate beam?  My company has yet invested in an FEA package.

RE: Stress Analysis on Disc Spring

Roark's doesn't have formulation for spiral like etched arm integrated in circular plate with an inner hole. Can you give more information such as:
1. What will be the use of this spring
2. what range of forces and deflection you are looking for
3. Life cycle
4. Materials (environmental conditions)
5. Will you use one spring or two as an elastic bearing too
5. Dimension constraints (maximum outside diameter, Minimum inside diameter, etc.)


RE: Stress Analysis on Disc Spring


Unit is a bipropellant space component designed with no sliding parts.  The flat spring, which is identified as a flexure, it has an OD (3/4"), ID (1/4"), and in between there is an etched spiral type design that frees up some of the stiffness of the flat spring.  The flexure is clamped on the OD and the ID at assembly. It is used to guide a pin onto a seat and provide a load (less than 2 lbs)that adds back force to the seat .   Life cycles are specked out to be 10XE6 and tolerances are pretty tight.  There are a few flexures in the design with one other prodiving a different etch configuration.

RE: Stress Analysis on Disc Spring

Sorry I did not get your pic.

RE: Stress Analysis on Disc Spring

I tried but it didn't work

RE: Stress Analysis on Disc Spring

Actaully it is symetrical, the sketch is poorly drawn.  there are three symetrical bands. First band starts at 30 Deg. and ends 300 deg. The hole pattern is an old design sorry about that.


RE: Stress Analysis on Disc Spring

This design is not symmetrical too. See the area circled by the red circle. It appears only once on the disc.


The beam between the the red circle and the green circle is wider on the middle and narrower on both sides. This is not a good design, you want the beam to be wider on one side and narrower on the other-side to get the largest deflection and the a given force.

RE: Stress Analysis on Disc Spring

It is not symmetrical because it is an undimensioned hand drawn sketch. All three bands are 120 deg. apart and start start at a radius (.160) from the center. This has not been drawn onto a Solid Works model, I am having difficulty drawing the spiral design.  

There is a clamping land on the OD and ID.  The the spiral band start and end on between the clamping surface.

RE: Stress Analysis on Disc Spring


How much deflection is needed at the 2lb load?
Is the 2lb load is needed form one flexure spring or from two (1lb each)?
Will the spring be loaded (deflected) only in one direction or both directions from free position?


RE: Stress Analysis on Disc Spring


Deflection is what we are analyzing as well as stresses.

Installed the flexure is under .007" deflection. the spring force is 1.5 lbs and the two flexures are overcoming the spring force. The flexures are moving in both directions when the open/close poles are actuated.

RE: Stress Analysis on Disc Spring

I am a little bit confused.

What is the largest deflection that a flexure deflect?
How much force one flexure should give at that deflection?

RE: Stress Analysis on Disc Spring

This analysis is to find out how things change with thickness and load, so we can know what is acceptable. Attached is a more accurate sketch of the flexure.

We want it thick enough capable to handle 10XE6 cycles and finding the deflection with a 1 lb. load at the inner edge with the outer edge fixed.
The starting thickenss is .013' and material is 17-7 cres.


RE: Stress Analysis on Disc Spring

Mleo11- usually stresses drop off as thickness is decreased. Thus for the same deflection distance the life goes up as thickness goes down. (This is a completely general statement however.)

RE: Stress Analysis on Disc Spring


FEA analysis is needed to accurately find the deflection at 1 lb. At the same time the stresses need to be low enough for 10XE6 cycles which is basically infinite life.

Each point where the slot ends there is A high stress concentration which has a significant influence on the life cycle.

You didn't specify the desired slot width which affect how much wide each "spring" will have.

I assume you mean 17-7 condition C heat treated to CH900?

Modeling the many options and doing the analysis to find out how things (deflection, stresses, life cycle etc.) change with the thickness and load is a time consuming process.

I understand that you are designing a (solenoid?) valve, therefore, the spring deflection should be known from the flow requirements of the fluid. But at the same time the deflection is a function of the flow orifice diameter and the flow pressure. More than that, the valve (electromagnet) pulling force is the result of the orifice sealing diameter, the fluid pressure and the spring/s sealing forces. The valve opening and closing time response is a function of the forces, the plunger mass and distance movement. So, every thing is connected.

From your need to check the deflection at 1 lb for various metal thicknesses I understand that all other variables mentioned above are supposedly known and fixed. However, what will happen if the stresses needed to achieve 10XE6 cycles will dictate a deflection which will not allow the desired fluid flow? Then you will need to start all over again?


RE: Stress Analysis on Disc Spring


This is a solenoid type of valve design; however, I am not experienced with it and therefore my responses tend to be incomplete, thank you for bearing with me.

An FEA is the best way and we are pursuing that route. The slot width is .02" and the selected material is 17-7 ph cond. RH950.  The flexure has an installed axial load of 0.6lbf, additional working deflection of each operating cycle .006” (10XE6 cycles). We are looking for a spring rate less than 100lb/in. It is going to take some time to play with thicknesses and material to get the desired spring rate and not fail.

The material selection is up in the air. It must be compatible with nitrogen textroxide, monoethyl hydrozine and nitric acid.  Nitronic metals have been mentioned, but I am not familiar with it and need to do some more research.  Any recommendations?



RE: Stress Analysis on Disc Spring


I often designed this in two steps:
first: bending only (this is a good approximation if the beams are not very short);
then: adding torsion.
Any elastic calculation is suitable. (I prefer Castigliano.)
Some designs work better with straight beams as these have high radial stiffness.

Be cautious with materiels and fatigue: fatigue limit is sensitive to very slight corrosive attack and measured in benign environments.
Also: only materials with cubic room centered crystallinity exhibit a stable fatigue limit above 1 million cycles, all other materials go down further.


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