9/5/07 1 Compliant Mechanism as an Automotive Seat Cushion Christine Vehar Jutte Faculty sponsor: Sridhar Kota Compliant Systems Design Laboratory (CSDL) University of Michigan September 5, 2007

9/5/07 2 Original Design Rigid Seat Pan Multi-piece stamped and welded steel pan (No foam or cover shown) 4-inch foam cushion (Expensive to store and ship) Reduce foam thickness from 4” to 2” without compromising passenger’s comfort and safety Anti-submarine geometry

9/5/07 3 Passenger Comfort Automotive company force-displacement data measured at the center of the seat cushion. [1] 4-inch foam cushion

9/5/07 4 New Design Model Nonlinear spring: A compliant mechanism where the input force and the measured output displacement share the same location and have a nonlinear relationship.

9/5/07 5 Problem Definition Spring in Parallel Spring in series with foam Design a nonlinear spring: 1)Match load-displacement function 2)Fit within prescribed design space

9/5/07 6 Functional Description In-plane thickness = 0.027in (0.69mm) Out-of-plane thickness = 12in (304.8mm) Material = MartINsite M130 (E = 200 GPa) Max stress = 605MPa (< yield 930 MPa) Safety factor =1.5 Disp. = 29% of largest footprint dimension Final Spring Design Spring within new assembly

9/5/07 7 Functional Description Final Spring Design’s Assembly in Prototype Nonlinear springs Connecting Plate Anti-Submarine feature

9/5/07 8 Functional Description Final Spring Design’s Load-Displacement Function

9/5/07 9 Functional Design Validation Instron 8516 Nonlinear spring assembly (No foam included)

9/5/07 10 Functional Design Validation (Instron 8516) Nonlinear spring assembly (Foam included)

9/5/07 11 Novel Features Long, slender curvilinear shape (Enables large geometric nonlinearities with low stress) Horizontal constraint at input (Activates the axial mode of the spring for stiffening effect) Free rotation at input (Enables large rotations with low bending stress) 1)Generates nonlinear response by varying effective stiffnesses of beam elements - Geometric nonlinearities (large displacements and rotations) - Boundary conditions Tradeoff between bending (flexible) and axial (stiff) modes

9/5/07 12 Novel Features 2) Matches a prescribed load-displacement function at one point on the mechanism (Separate input and output point)

9/5/07 13 Novel Features 3) Distributed compliance - Large displacement relative to footprint (29%) - Easier manufacturing Various large-displacement compliant mechanism synthesis methodologies Nonlinear load-displacement relationship at single point (lumped compliance) Howell (2001) – Constant-force mechanism/spring Pedersen, Fleck, and Ananthasuresh (2006) – Compliant mechanism and actuator system with constant-force output

9/5/07 14 Procedure Objective function (0.98): - Minimizes error relative to prescribed load-displacement function - Includes penalty functions for displacement, stress, and buckling Developed a generalized nonlinear spring synthesis methodology for matching any prescribed load displacement function

9/5/07 15 Procedure Shape and size optimization of spline determines final design (Full scale nonlinear spring synthesis methodology includes a network of 9 splines for topology optimization) Genetic algorithm (optimization) ABAQUS’s modified Riks method (nonlinear finite element analysis) Hybrid beam elements (for increased efficiency)

9/5/07 16 Benefits Nonlinear spring design –Reduces storage and shipping costs of seat cushion Nonlinear spring synthesis methodology –Reduces design process cost & time New seat assembly –Recommendations made to reduce manufacturing costs [1] Stamp springs using permanent dye Use lightweight, high-strength composite for connecting plate Integrate the hinges into connecting plate Integrate the support bars into either (i) seat frame or (ii) nonlinear spring via a modified stamping process.

9/5/07 17 Possible Applications Freedom Innovations Otto Bock Statically Balanced Mechanisms Nature’s Nonlinear Compliance MEMS Devices Artificial Implants and Prosthetics - Structures with synthesized nonlinear elasticities - Mimic nonlinear and viscoelastic materials Constant-Force Springs Shock absorbers Design for crashworthiness

9/5/07 18 Acknowledgements Senior design team: Trevor Knauf, Rachel LaValley, Ben Sivulka, and Joe Thomas [1] Knauf, T., LaValley, R., Sivulka, B., and Thomas, J. “Compliant Seat Cushion Pan for an Automotive Seat.” University of Michigan. December Faculty sponsor: Sridhar Kota

9/5/07 19 THANK YOU