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Research Papers: Design Automation

Product Family Design With Solution Spaces

[+] Author and Article Information
Markus Eichstetter

BMW AG,
Vehicle Dynamics, Preliminary Design,
München 80788, Germany
e-mail: markus.eichstetter@bmw.de

Steffen Müller

Professor
Institute for Motor Vehicles,
Technical University of Berlin,
Berlin 13355, Germany
e-mail: steffen.mueller@tu-berlin.de

Markus Zimmermann

BMW AG,
Vehicle Dynamics, Preliminary Design,
München 80788, Germany
e-mail: markusz@alum.mit.edu

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received December 28, 2014; final manuscript received September 8, 2015; published online October 16, 2015. Assoc. Editor: Massimiliano Gobbi.

J. Mech. Des 137(12), 121401 (Oct 16, 2015) (9 pages) Paper No: MD-14-1839; doi: 10.1115/1.4031637 History: Received December 28, 2014; Revised September 08, 2015

Design for optimal commonality in product families is different from design for optimal performance. While optimal performance may be achieved by the choice of appropriate design parameter values for all system components, optimal commonality requires a particular scheme of sharing components among systems. The number of possibilities to share components can be quantified by Bell's number and becomes large quickly, thus making optimization extremely expensive. This paper presents an approach to identify components that may be shared in order to optimize commonality for a product family of arbitrary high-dimensional nonlinear systems. Solution spaces are computed for each system using iterative Monte Carlo sampling. On these solution spaces, all design goals are reached. They are expressed as sets of permissible intervals for all design parameters. When parameter intervals from different systems overlap, they may assume the same value and components may be shared. The approach is applied to vehicle chassis design. A set of common components is computed for 13 vehicles with ten design parameters each, such that all design goals are satisfied and the number of different component designs is small.

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Figures

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Fig. 1

Front axle assembly of a midsize vehicle with (1) bump stop, (2) rebound stop, and (3) anti-roll bar

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Fig. 2

Vehicle response for particular driving maneuvers: (a) roll angle via lateral acceleration, (b) roll moment ratio via lateral acceleration, (c) side-slip angle via time, (d) vertical tire force via time, and (e) roll velocity via frequency

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Fig. 3

Solution spaces for the front (x-axis) and rear (y-axis) anti-roll bar stiffness. Designs are excluded by requirements from roll behavior, rollover, lateral stability, and self-steering behavior.

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Fig. 4

Solution spaces (lines), common designs (big dots), and performance optima from Sec. 3.2 (small dots) are shown inthe space of anti-roll bar stiffness values of the front (x-axis) and rear (y-axis) axle. Lines actually indicate boundaries of solution spaces.

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Fig. 5

Box-shaped solution space for a general design problem. Design points of the good region fulfill the inequality constraint f(x) ≤ fc.

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Fig. 6

Overlapping solution space and box-shaped solution space for a general design problem

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Fig. 7

Performance variation in a design space sample for vehicle 1. Shown are objective quantities (y-axis) and anti-roll bar stiffness ca,f (x-axis) of each sample point. All design variables are randomly chosen from the design space. Gray regions indicate design goal violation. The permissible interval of ca,f with respect to requirements on vehicle 1 is marked by dashed lines.

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Fig. 8

Solution spaces for (a) vehicles 1–3 and (b) all 13 vehicles shown as upper and lower limits for each design parameter. The units of stiffness values c and free lengths s are N/mm and mm, respectively. The connecting lines between limits of different parameters are only for the purpose of visualization.

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