Excel Belleville Spring Calculator

Belleville Springs (aka “Belleville Washers”, “Spring Washers”, or “Disk Springs”) are wonderfully useful mechanical devices, but with one minor drawback – their properties are difficult to calculate – until now!  Almen and Laszlo were the first to develop a workable calculation method, but it can only loosely be described as “workable.”  (This is the method used in the DIN 2092 standard.)

The most common approach to designing with disk springs is to use a manufacturers catalog (e.g. Schnorr, Key Bellevilles, McMaster-Carr) and choose from the available options using the published values for load at maximum deflection.  This method is insufficient for many applications though because of the non-linear nature of the load-deflection curve, and it is precisely this non-linear behavior that is one of the most useful features of Belleville Springs!

The figure below describes the variety of spring characteristic curves that can be obtained by varying the ratio of formed height (ho) to material thickness (t).  At a ratio of of ho/t=0.5 the spring curve is nearly linear but if the ratio is ~1.5, the spring will provide nearly it’s full load at 50% of its stroke and then continue to deliver approximately that same load for the second half of the stroke.  (This property is sometimes used to retain bearings in the presence of large amounts of axial shaft play.)

Radigan Engineering - Belleville Spring Calculator

The Excel workbook can be used to calculate the load-deflection curves of any Belleville Spring.  Start by entering your desired spring measurements in the yellow-highlighted boxes and then select one of the material options from the dropdown menu in D12.  The Excel workbook is unprotected so it’s easy to add, edit, or tweak the material options as well as include these calculations in a larger design workbook.

I should note that the terminology used in this tool follows the pattern set in the Schnorr Disk Spring handbook (which can be found here).  There are a few different conventions in use, but the small screenshot images in the worksheet should be sufficient explanation.


Belleville Spring Calculator (14311 downloads)

If this calculator is useful to you, please send me a note or leave a comment below.  I should also point out that this implementation of the calculation method is licensed under the Creative Commons 3.0 CC-BY-SA.

Happy Calculating!

EDIT (2015_06_30): The spreadsheet has been updated with cell highlighting (for inputs and outputs) as well as comments regarding spreadsheet usage.  Please let me know in the comments section if you have improvements to offer to the community at large.

7 Comments Permalink
7 comments on “Excel Belleville Spring Calculator
  1. Hello,
    First of all thank you very much for this useful calculation to understand the concept of disc spring design.
    I need to ask you one doubt in calculation:
    Our target Desired Load at 80% defl. was 13345 N (cell M5) but in stack spring force we got 24981 N (Cell K57).
    in the same way , our target Desired Total Stack defl. was 25.4mm (cell M4) but for 80 % of stack compression it is 34.56 mm (cell K61).

    Why we have got different values than our target design???
    Please do the needful .

    Best regards
    Saurabh Shriavstava

    • Hi Saurabh,

      This tool was created a while back to help in a set of design calculations that I was working through repeatedly, but I’m afraid that I can’t offer any advice on your particular situation. I admit that the tool isn’t as easy to follow as I want it to be, and I’m sorry for any difficulty you encounter using it. Best Regards, – William

  2. Your spread sheet on Belliville washer/springs is probably the best app I’ve seen on any calculation I’m interested in. thank you. As an old engineer I was to lazy to dig out a slide rule and Roark and Young (like I said I’m old). In any case in my retirement I’m building a house which uses some large timber trusses. In the bolted connections I’m using belliville washers to take up timber shrinkage and keep the fasteners tight. Your spread sheet allowed me to calculate the stacking and loads.

    Thanks Again

    • Hi Randy,

      Thanks for the reply, I’m glad that you find the tool useful. Please double-check your final design using another tool, a manufacturers table, or hand calculations. This Excel tool is accurate to the best of my knowledge, but responsibility for overhead loads is a whole different ballgame. Good luck with your house project!

      -William

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