Abstract
A Belleville spring is usually used in mechanical systems to obtain large loads for small distances of travel. Such a spring has a non-linear load-length curve. Moreover, Belleville springs are commonly stacked together in series or in parallel or both. Thus, defining a design that uses Belleville springs is not an easy matter. The existing assistance tool only checks whether a proposed design is acceptable or not. To improve design assistance, we show how optimization processes can be used in order to build a tool that interactively proposes an optimal design directly from the designer’s requirements. The tool presents both an optimal design using a Belleville spring taken from a catalogue and an optimal custom design. An illustrative example is presented to highlight the benefits of using such an assistance tool.
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Abbreviations
- D e :
-
Outside diameter (mm)
- D i :
-
Inside diameter (mm)
- d :
-
Density
- E :
-
Young’s modulus (MPa)
- F 1 :
-
External load at point 1 (N)
- F 2 :
-
External load at point 2 (N)
- i :
-
Number of alternating discs in stacked column
- l 0 :
-
Overall height of a single spring (mm)
- L 0 :
-
External free length (mm)
- L 1 :
-
External length at point 1 (mm)
- L 2 :
-
External length at point 2 (mm)
- M :
-
Mass of the arrangement (g)
- n :
-
Number of discs arranged in parallel (nested)
- s 1 :
-
Deflection at point 1 for a single disc (mm)
- s 2 :
-
Deflection at point 2 for a single disc (mm)
- s max :
-
Maximum allowable deflection to be compared to s 1; s 2
- S 1 :
-
External deflection at point 1 (mm)
- S 2 :
-
External deflection at point 2 (mm)
- S h :
-
External deflection (mm)
- t :
-
Spring thickness (mm)
- V e :
-
Overall volume of the arrangement (mm3)
- α s :
-
Safety factor related to stress at point I
- δ :
-
Diameter ratio (= D e /D i )
- μ :
-
Poisson’s ratio
- σ :
-
Maximum allowable stress (MPa)
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Paredes, M., Daidié, A. Optimal catalogue selection and custom design of belleville spring arrangements. Int J Interact Des Manuf 4, 51–59 (2010). https://doi.org/10.1007/s12008-009-0086-4
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DOI: https://doi.org/10.1007/s12008-009-0086-4