A product's functionality depends largely on the interaction of its components and their geometries. Hence, tolerance analyses are used to determine the effects of deviations on functional key characteristics of mechanisms. However, possible interactions between the different deviations and the resulting effects on themselves as well as on the functional key characteristics have not yet been considered.This article considers the extension of the existing ''integrated tolerance analysis of systems in motion'' approach. By means of the methodology, the interactions between appearing deviations can be identified and integrated into a tolerance analysis functional relation. Therefore, the appearing interactions are represented by meta-models that can be easily integrated into the functional relation. Consequently, the product developer is able to gain information about the effects of deviations on functional key characteristics, as well as the effects of the deviations among themselves. In order to show the methodology's practical use, the interactions between deviations of a nonideal crank mechanism inside a four-stroke combustion engine are considered. For this purpose, two different meta-modeling techniques are used: response surface methodology and artificial neural networks.

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Simulations not only facilitate new and unprecedented insights in highly sophisticated science areas, but also support product design in engineering in terms of improved functionality, cost and time issues. However, as a matter of fact, simulations examine limited excerpts of real systems with accompanying simplifications, abstractions and idealizations. Hence, there is a distinct need to be aware of upcoming risks in simulation outcomes caused by uncertainties. These influence every step of forward-thinking simulation design which is not only restrained by modeling practice but begins with reality perception itself.The intention of the paper is to embed an awareness of uncertainty in the context of simulation by linking major classes of uncertainty with uncertainties within simulations in engineering design. Besides the decisive inclusion of reality as the starting point, mathematic approaches are also used to understand how those uncertainty classes evolve through exponential knowledge creation of systems. The transfer to statistical tolerance analysis shall finally put emphasis on the practical classification of uncertainty, starting from data preparation via concept design and mathematical implementation to result depiction. In the end, the reader's conception of possible uncertainties in special simulation cases shall be sharpened which, vice versa, shall lead to even better and well-thought-out simulation outcomes.

The need for geometrical variations management is an important issue in design, manufacturing and all other phases of product development. Two main axioms cover geometrical variations, namely the axiom of manufacturing imprecision and the axiom of measurement uncertainty. Therefore, this paper reviews common models for the description of non-ideal geometry (shape with geometric deviations) and shows how the random field theory can be applied to create more realistic skin models (a model which comprises these geometric deviations). Furthermore, methods to estimate and to express the underlying random field from a sample population are shown. These can be used to create and simulate random shapes considering systematic and random deviations observed through measurement or gathered from manufacturing process simulations. The proposed approach incorporates given information from manufacturing process simulations or prototypes. Based on these information, skin model samples are created which can represent the “realistic” part in assembly simulations or other geometrical analyses. This can help to identify the optimal tolerance sets within every stage of the product development process. The efficiency of the introduced approaches is shown in a case study.

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