A new calculation method for the worst case tolerance analysis and synthesis in stack-type assemblies

Productivity and industrial product quality improvements entail a rational tolerancing process to be applied as early as product design. Once functional conditions are defined, an optimal specification for each component in a mechanical system is to be developed. Despite numerous studies in this area, the problem is still far from solved. It may be decomposed into two stages: development of specifications based on standards, or qualitative synthesis, and calculation of tolerances. To the extent that these two sets of problems are related, we propose to address them in parallel. In this paper, we present an original method that enables us to solve these two problems for the case of serial assembly (stacking) without clearances. This method is based on the use of influence coefficients to obtain the relationship between the functional tolerance and the tolerances associated with the geometry of the mechanism’s interface surfaces. We will describe a calculation algorithm that helps obtain influence coefficients solely from the assembly’s geometric definition. Then, we will show that under our working hypothesis, this relationship is piecewise linear.

► Geometric deviations and clearance can be represented by domains.
► Minkowski sum complexity grows exponentially with the number of connecting surfaces.
► Obtain relations between geometric tolerances and functional requirement tolerance.
► Clearance can be taken into account in different manners, following their function.
► One functional requirement is represented by a system of linear inequalities.