Set based robust design of mechanical systems using the quantifier constraint satisfaction algorithm

Embodiment design is an important phase of the design process where the initial design parameters and their feasible solution spaces with design configurations are decided for the design problem. This article presents a new approach of embodiment design space exploration of the product based on set based design with integration of robustness for the mechanical systems. The approach presented addresses the initial design phase of the mechanical systems design and provides a three step approach based on a formal expression syntax, transformation and evaluation engine and a computational algorithm for performing a domain search for sets of robust solutions for the product designs by taking into the account the variations and uncertainties related to the manufacturing process and material. The approach is based on the design domain exploration and reduction techniques. This is achieved by the utilization and integration of existential and universal quantifiers from the quantifier constraint satisfaction problem (QCSP) for the expression of the parameters and variables related to the product design and robustness. The quantifier notion has been used to develop the consistency check for the existence of a design solution and existence of a robust design solution. In order to compute the developed quantifier approach, an algorithm based on the transformation of the quantifier with interval arithmetic has also been developed. In order to demonstrate the capability of the developed approach, this article includes three examples of mechanical systems from earlier research works that apply the quantifier model and the resolution algorithm to successfully explore the design domain for robust solutions while taking into account different types of variations such as variations in mechanical/material properties, manufacturing variations or variations in geometric dimensions which may be of continuous or discrete type.