Rigid-compliant hybrid variation modeling of sheet metal assembly with 3D generic free surface

• Assembly elements and coordinate systems that locate assembly elements are defined.
• Nominal and variational assembly spatial relationship is represented.
• Overall variation is represented by superposition of rigid and compliant variation.
• Rigid-compliant hybrid variation model of sheet metal assembly is built.
• A wing panel assembly case is studied following the proposed method.

Rigid and compliant variation models have been developed in parallel for different assembly processes all the time. However, sheet metal parts will generate not only rigid variation caused by rigid-body motion, but also compliant variation caused by deformation during the assembly process. In order to better evaluate the dimensional quality of sheet metal assembly, a rigid-compliant hybrid variation modeling methodology of sheet metal assembly is proposed in this paper. Parts, fixtures and features are considered as assembly elements in a sheet metal assembly process, and four types of coordinate systems are defined to locate them. The nominal and variational spatial relationships among assembly elements are then represented by relationships among different coordinate systems, which can be described by homogeneous transformation matrix. Based on two-dimensional stream-of-variation, the variation generation mechanism in every assembly step and the variation propagation mechanism between assembly steps are researched, and the mathematical relationship between the overall assembly variation and various variation sources is built accordingly. In this methodology, rigid variation is analyzed based on differential motion vector and homogeneous transformation matrix; compliant variation is analyzed based on method of influence coefficients; and their impact on each other is also considered. The proposed model has general applicability for sheet metal assembly with 3D generic-free surface. A case study on rigid-compliant hybrid variation modeling of a wing panel assembly is presented to demonstrate the modeling and analysis capability of the proposed methodology.