Interval computation and constraint propagation for the optimal design of a compression spring for a linear vehicle suspension system

Abstract

In this paper an optimization design method based on existing intervals and constraint satisfaction problem “CSP” computer tools is proposed. The method was used in the preliminary design to size a compression spring implemented in a linear vehicle suspension system. Compared to conventional design methods, our design method avoids the passing through two stages of sizing (static and dynamic). Using the numeric CSP approach, static and dynamic requirements can be coupled in the same step of sizing. It also avoids the falling on the loop “design–simulate–back to the initial step in case of failure”, as the design parameter values of the compression spring generated by the numeric CSP satisfy all imposed requirements, and the simulation results of the system behavior are always successful and respect all posted constraints. This is due to the fact, that in the CSP, all analytical relation types static and/or dynamic defining the product and its behavior are implemented and integrated from the beginning. So the production of a qualifying system can be achieved from the first time without any need for resizing the system. The general idea of the proposed design method consists of expressing the design variables by intervals; integrate all imposed constraints of different types before the simulation step and solve the problem using the CSP. The generated intervals represent the domains of possible values for the design variables of the product. The obtained result which can be a solution or set of solutions, affirms that the suggested method is valid and potentially useful to size dynamic systems easily and effectively.