A nonlinear spring has a defined nonlinear load-displacement function, which is also equivalent to its strain energy absorption rate. Various applications benefit from nonlinear springs, including prosthetics and microelectromechanical system devices. Since each nonlinear spring application requires a unique load-displacement function, spring configurations must be custom designed, and no generalized design methodology exists. In this paper, we present a generalized nonlinear spring synthesis methodology that (i) synthesizes a spring for any prescribed nonlinear load-displacement function and (ii) generates designs having distributed compliance. We introduce a design parametrization that is conducive to geometric nonlinearities, enabling individual beam segments to vary their effective stiffness as the spring deforms. Key features of our method include (i) a branching network of compliant beams used for topology synthesis rather than a ground structure or a continuum model based design parametrization, (ii) curved beams without sudden changes in cross section, offering a more even stress distribution, and (iii) boundary conditions that impose both axial and bending loads on the compliant members and enable large rotations while minimizing bending stresses. To generate nonlinear spring designs, the design parametrization is implemented into a genetic algorithm, and the objective function evaluates spring designs based on the prescribed load-displacement function. The designs are analyzed using nonlinear finite element analysis. Three nonlinear spring examples are presented. Each has a unique prescribed load-displacement function, including a (i) “J-shaped,” (ii) “S-shaped,” and (iii) constant-force function. A fourth example reveals the methodology’s versatility by generating a large displacement linear spring. The results demonstrate the effectiveness of this generalized synthesis methodology for designing nonlinear springs for any given load-displacement function.
Skip Nav Destination
e-mail: cvehar@umich.edu
e-mail: kota@umich.edu
Article navigation
August 2008
Research Papers
Design of Nonlinear Springs for Prescribed Load-Displacement Functions
Christine Vehar Jutte,
Christine Vehar Jutte
Department of Mechanical Engineering,
e-mail: cvehar@umich.edu
University of Michigan
, 2231 G.G. Brown Building, 2350 Hayward Street, Ann Arbor, MI 48109-2125
Search for other works by this author on:
Sridhar Kota
Sridhar Kota
Department of Mechanical Engineering,
e-mail: kota@umich.edu
University of Michigan
, 2231 G.G. Brown Building, 2350 Hayward Street, Ann Arbor, MI 48109-2125
Search for other works by this author on:
Christine Vehar Jutte
Department of Mechanical Engineering,
University of Michigan
, 2231 G.G. Brown Building, 2350 Hayward Street, Ann Arbor, MI 48109-2125e-mail: cvehar@umich.edu
Sridhar Kota
Department of Mechanical Engineering,
University of Michigan
, 2231 G.G. Brown Building, 2350 Hayward Street, Ann Arbor, MI 48109-2125e-mail: kota@umich.edu
J. Mech. Des. Aug 2008, 130(8): 081403 (10 pages)
Published Online: July 16, 2008
Article history
Received:
September 25, 2007
Revised:
April 21, 2008
Published:
July 16, 2008
Citation
Jutte, C. V., and Kota, S. (July 16, 2008). "Design of Nonlinear Springs for Prescribed Load-Displacement Functions." ASME. J. Mech. Des. August 2008; 130(8): 081403. https://doi.org/10.1115/1.2936928
Download citation file:
Get Email Alerts
Related Articles
Optimal Subassembly Partitioning of Space Frame Structures for In-Process Dimensional Adjustability and Stiffness
J. Mech. Des (May,2006)
Decomposition-Based Assembly Synthesis of Space Frame Structures Using Joint Library
J. Mech. Des (January,2006)
Topology Optimization of Multicomponent Beam Structure via
Decomposition-Based Assembly Synthesis
J. Mech. Des (March,2005)
Synthesis of Bistable Periodic Structures Using Topology Optimization and a Genetic Algorithm
J. Mech. Des (November,2006)
Related Proceedings Papers
Related Chapters
Supports
Process Piping: The Complete Guide to ASME B31.3, Third Edition
Supports
Process Piping: The Complete Guide to ASME B31.3, Fourth Edition
Mechanics of Long Beam Columns
Mechanics of Drillstrings and Marine Risers