I am half way through designing a new product and need a custom belville. I can find information on force/axial deflection but nothing on radial deflection. As this is critial to the design I need to be able to calculate this for various OD/ID ratios, material thickness and cone angle. Where can I find this info. So far the spring manufacturers have not been able to provide it.
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Belville washer stress analysis 4
- Thread starter PurkisDan
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RichLeimbach
Mechanical
I've done a lot of work with Bellevilles and have never seen this calculation anywhere.
Should be able to calculate this yourself (depending on the amount of accuracy you need. You'll get very little reduction in the length of each side of your cone, so you should be able to use your deflection, starting angle and this length and trig it out to find the worst case diameter of this spring.
Should be able to calculate this yourself (depending on the amount of accuracy you need. You'll get very little reduction in the length of each side of your cone, so you should be able to use your deflection, starting angle and this length and trig it out to find the worst case diameter of this spring.
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Anthonyr has a good suggestion if you have software available. I didn't suggest this earlier, as it appeared you were looking for a closed-form solution. I have done such FE analyses on Belleville's before, with pretty good results.
A few pointers:
1) This is ABSOLUTELY a nonlinear geometric analysis (material nonlinearity is not important, but geometric nonlinearity is critical to get a meaningful answer).
2) This can be reduced without any loss of accuracy to an axisymmetric analysis for classic Bellevilles. This saves orders of magnitude in computation.
3) Proper element selection is critical to obtaining a good answer.
Brad
A few pointers:
1) This is ABSOLUTELY a nonlinear geometric analysis (material nonlinearity is not important, but geometric nonlinearity is critical to get a meaningful answer).
2) This can be reduced without any loss of accuracy to an axisymmetric analysis for classic Bellevilles. This saves orders of magnitude in computation.
3) Proper element selection is critical to obtaining a good answer.
Brad
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To complete the answer by RichLeimbach you can get a first approximation by assuming the spring rotates under load around a point situated at radius
ro=(R-r)/ln(R/r)
where R and r are respectively outer and inner radius of the undeformed spring.
If ho is the height of the spring (to be taken at mid thickness, this is called ho in DIN 2093, see the site below under 'Other' to see standard sizes), then you can find the following formula for the relative variation of inner radius (just derived on the spot, hope it is correct):
[(R/r-1)/ln(R/r)-1]ho2/R2
Now, as for commercial or standard Bellevilles R/r is normally close to 2 and ho/R is a few percent (say 0.02), the term in square brackets is of the order of 0.5 and the other term of the order of 0.0004. Hence the change in inner radius is of the order of 2 per ten thousands (of course the increase in outer radius behaves similarly).
I am curious to know what kind of application you are working on, as these changes of dimensions are really small and normally negligible (though some gap should normally be provided if the inner or outer radii are closely guided). prex
Online tools for structural design
ro=(R-r)/ln(R/r)
where R and r are respectively outer and inner radius of the undeformed spring.
If ho is the height of the spring (to be taken at mid thickness, this is called ho in DIN 2093, see the site below under 'Other' to see standard sizes), then you can find the following formula for the relative variation of inner radius (just derived on the spot, hope it is correct):
[(R/r-1)/ln(R/r)-1]ho2/R2
Now, as for commercial or standard Bellevilles R/r is normally close to 2 and ho/R is a few percent (say 0.02), the term in square brackets is of the order of 0.5 and the other term of the order of 0.0004. Hence the change in inner radius is of the order of 2 per ten thousands (of course the increase in outer radius behaves similarly).
I am curious to know what kind of application you are working on, as these changes of dimensions are really small and normally negligible (though some gap should normally be provided if the inner or outer radii are closely guided). prex
Online tools for structural design
Oops, my formula in the preceding post is lacking a divisor of 2, so the order of magnitude of the change in radius is 0.1 per mille... prex
Online tools for structural design
Online tools for structural design
PurkisDan,
I have two books that cover the design of disc springs - Roarks Forumulas for Stress and Strain, and the SAE Spring Design Manual. They approximately agree with each other on loading, and the SAE manual has equations for tensile stress at the outside of the disc spring. This ought to tell you that your increase in diameter is. Unfortuntately, you have to do some calculations, then read some numbers off a table, then do some more calculations. You need the book
Spring Design Manual
no author listed
Society of Automotive Engineers
ISBN 0-89883-777-4
JHG
I have two books that cover the design of disc springs - Roarks Forumulas for Stress and Strain, and the SAE Spring Design Manual. They approximately agree with each other on loading, and the SAE manual has equations for tensile stress at the outside of the disc spring. This ought to tell you that your increase in diameter is. Unfortuntately, you have to do some calculations, then read some numbers off a table, then do some more calculations. You need the book
Spring Design Manual
no author listed
Society of Automotive Engineers
ISBN 0-89883-777-4
JHG
- Thread starter
- #10
Thaks to everyone that took the time to respond. I have FEA and will use it later in the design as the belville is customised. I do not envisage the disc thickness being constant in the final design so FEA will be essential. I already have the books suggested but the radial deflection is not tackled. I would like to discuss this application further but patent issuse do not allow it. Once these are clear I will be happy to publish the details. The market sector is Oil and Gas where IP is highly valued. I have decided to build a first prototype tool to demo the basic concept of operation. If the customer likes it then the hard work begins in designing the full blown tool.
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