Deformable part inspection using a spring–mass system

• A spring–mass system is proposed for modeling deformation of shell parts.
• An expression to calculate the stiffness of the bending springs is presented.
• Radial basis functions are used to set the initial value for optimization.
• Radial basis functions are applied to speed up the calculation of deformations.

In order to inspect deformable parts, recent works use virtual deformation on a digitized version of a real-part to bring the part model back to its nominal shape. This simulation mimics the real process called fixturing, which is normally used by the manufacturer to bring back the part into its nominal shape once installed. To perform such virtual deformation Finite Element Methods (FEMs) are used in order to meet the precision requirements of the inspection process. This paper presents a method based on a spring–mass system, whose formulation is much simpler than the FEM, which allows the calculation of deformations of shell type parts with accuracy comparable to FEM. Furthermore, due to the simplicity in its formulation the algorithm can be implemented more easily than the FEM. The system is composed of two types of springs: one type models membrane behavior of the part’s mesh model and the second type models the flexion behavior between each mesh elements. We show that by applying the proposed mass-spring model, it is possible to reduce the calculation time by 80% over standard FEM calculation opening the door to real-time inspection.