A static analogy for 2D tolerance analysis

This paper aims to present a method for the tolerance analysis of mechanical assemblies that is suitable to nonlinear problems where explicit functional equations are difficult or even impossible to write down. Such cases are usually modelled by linearised tolerance chains, whose coefficients (or sensitivities) are calculated from assembly data.

The method is based on the free-body diagrams of force analysis, which are shown to be related to the sensitivities of linearised functional equations. Such an analogy allows the conversion of a tolerance chain into a corresponding static problem, which can be solved by common algebraic or graphical procedures.

The static analogy leads to a correct treatment of tolerance chains, as the analysis of several examples has confirmed by comparison to alternative methods.

Currently, the method has only been tested on two-dimensional chains of linear dimensions for assemblies with nonredundant kinematic constraints among parts.

The proposed method lends itself to ready application by using simple operations with minimal software assistance. This could make it complementary to current methods for calculating sensitivities, which are mathematically complex and require software implementation for deployment in industrial practice.

Analogy with force analysis, which has not been previously highlighted in the literature, is a potentially interesting concept that could be extended to a wider range of tolerancing problems.