A survey of research in the application of tolerance analysis to the design of mechanical assemblies

Abstract

Tolerance analysis is receiving renewed emphasis as industry recognizes that tolerance management is a key element in their programs for improving quality, reducing overall costs and retaining market share. The specification of tolerances is being elevated from a menial task to a legitimate engineering design function. New engineering models and sophisticated analysis tools are being developed to assist design engineers in specifying tolerances on the basis of performance requirements and manufacturing considerations. This paper presents an overview of tolerance analysis applications to design with emphasis on recent research that is advancing the state of the art. Major topics covered are:1) New models for tolerance accumulation in mechanical assemblies, including the Motorola Six Sigma model. 2) Algorithms for allocating the specified assembly tolerance among the components of an assembly.3) The development of 2-D and 3-D tolerance analysis models. 4) Methods which account for non-Normal statistical distributions and nonlinear effects. 5) Several strategies for improving designs through the application of modern analytical tools.

Tolerance analysis — Form defects modeling and simulation by modal decomposition and optimization

“…Furthermore, the substituted-surface model is used to simulate geometric defects in a real surface by situation and dimension deviations. 'Situations deviations' can be mathematically represented with the help of the vectors [13], by a small displacement torsor SDT [12], by a matrix [14] or by a metric torsor [15]. Also, the deviations between two surfaces potentially in contact can be formalized based on the SDT and substituted models cannot take form defects into account when characterizing geometrical defects.…”

Discrete tolerance allocation for product families

“…Many different cost functions have been suggested which define the relationship between the cost and the size of the tolerance. A numerous selection of cost functions has appeared in the literature; see for example Chase and Parkinson (1991). If one of these functions describes the true manufacturing cost correctly, solving the optimization problem will indeed result in a minimized production cost for the manufacturer.…”

Modeling of 2D and 3D Assemblies Taking Into Account Form Errors of Plane Surfaces

“…From the most simple model based on a one-dimensional description assembly to a several dimensional one (discrete decomposition of features), we can find increasing data (and process) models. The one-dimensional models ( [1], [2]) are used to solve size variations. With those scalar models the analyses can be done with the worst cases or the statistic solving.…”