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The purpose of this work is to present a variational model able to deal with form tolerances and assembly conditions. The variational model is one of the methods proposed in literature for tolerance analysis, but it cannot deal with form tolerances and assembly conditions that may influence the functional requirements of mechanical assemblies.

This work shows how to manage the actual surfaces generated by the manufacturing process and the operating conditions inside the variational model that has been modified to integrate the manufacturing signature left on the surfaces of the parts and the operating conditions that arise during an actual assembly, such as gravity and friction. Moreover, a geometrical model was developed to numerically simulate what happens in a real assembly process and to give a reference value.

The new variational model was applied to a three-dimensional case study. The obtained results were compared to those of the geometrical model and to those of the variational model to validate the new model and to show the improvements.

The proposed approach may be extended to other models of literature. However, its limitation is that it is able to deal with a sphere–plane contact.

Tolerance analysis is a valid tool to foresee geometric interferences among the components of an assembly before getting the physical assembly. It involves a decrease in the manufacturing costs.

The main contributions of the study are the insertion of a systematic pattern characterizing the features manufactured by a process, assembly operating conditions and development of a geometrical model to reproduce what happens in a real assembly process.

The purpose of this paper is to model how geometric errors of a machined surface (or manufacturing errors) are related to locators’ error, workpiece form error and machine tool volumetric error. A kinematic model is presented that puts into relationship the locator error, the workpiece form deviations and the machine tool volumetric error.

The paper presents a general and systematic approach for geometric error modelling in drilling because of the geometric errors of locators positioning, of workpiece datum surface and of machine tool. The model can be implemented in four steps: (1) calculation of the deviation in the workpiece reference frame because of deviations of locator positions; (2) evaluation of the deviation in the workpiece reference frame owing to form deviations in the datum surfaces of the workpiece; (3) formulation of the volumetric error of the machine tool; and (4) combination of those three models.

The advantage of this approach lies in that it enables the source errors affecting the drilling accuracy to be explicitly separated, thereby providing designers and/or field engineers with an informative guideline for accuracy improvement through suitable measures, i.e. component tolerancing in design, machining and so on. Two typical drilling operations are taken as examples to illustrate the generality and effectiveness of this approach.

Some source errors, such as the dynamic behaviour of the machine tool, are not taken into consideration, which will be modelled in practical applications.

The proposed kinematic model may be set by means of experimental tests, concerning the industrial specific application, to identify the values of the model parameters, such as standard deviation of the machine tool axes positioning and rotational errors. Then, it may be easily used to foresee the location deviation of a single or a pattern of holes.

The approaches present in the literature aim to model only one or at most two sources of machining error, such as fixturing, machine tool or workpiece datum. This paper goes beyond the state of the art because it considers the locator errors together with the form deviation on the datum surface into contact with the locators and, then, the volumetric error of the machine tool.

The purpose of this paper is to present a skin-based approach able to generate the variability model for a component in composite material due to its manufacturing process. It generates a skin-based model of the manufactured part. The skin model discretizes the part surfaces by points to take into account the geometric deviations, those points are the nodes of finite element analysis used for tolerance analysis of compliant assemblies.

The paper presents a general and systematic simulation model for generating a variability meta-model for a component in composite material due to its manufacturing process. The model is constituted by three steps: definition and pre-processing of the nominal model, generation of the manufacturing process model and evaluation of the part variability.

The advantage of this approach is related to the fact that it is designed as a part of a digital process that establishes a continuous and unambiguous flow of variation information from the part design to manufacturing and assembly and that takes into account the manufacturing signature. This is its uniqueness compared to other simulation approaches focused only on manufacturing.

Considering the variability around the nominal value of all the process parameters and parts with more complex geometries are not taken into account now, which will be modelled in practical applications.

To properly manage uncertainty since conceptual design of complex product, next generation geometry assurance requires simulation models to realistically consider process signatures due to the manufacturing process. This work focusses on this next generation tool for geometry assurance.

The literature is focused on metal sheets joined by welding or riveting. There are other materials widely used and typically compliant: the composite materials that typically used mechanical fixing elements (bolting, riveting) and structural adhesives to joint parts. No software tools exist in the literature to deal with uncertainty from manufacturing to assembly processes in products made by composite. This is the reason of the present work.

Selective laser sintering (SLS) has passed other techniques, thanks to its high print resolution, its ability to print microscale geometries without any additional support, its surface quality and its long-term thermal stability. However, despite the many advantages of SLS compared to fusion deposition modelling, there are still today some limitations on the materials to be printed. A limit critical from an industrial point of view is the aging of PA12 powder, i.e. the degradation of its physical and chemical performances, due to the high temperatures and the long printing cycles, thus involving a decrease of the mechanical properties of the printed parts. The purpose of this study was to charaterize mechanically and dimensionally specimens printed in PA12 through SLS by means of virgin or aged powder, i.e. powder just used for five printing cycles.

To achieve this aim, a set of specimens were designed, built, measured and mechanically tested; the obtained results were put into relationship with the values of the process parameters used to print them. Statistical tools to design the experiments and to analyse the obtained results were used.

The results show that the SLS process carried out through a Sintratec machine on PA12 powder has a good repeatability. To obtain the best dimensional and mechanical performances, it is needed to use virgin powder and place the part in the central zone of the printing area.

There are no scientific articles dealing with the influence of both the aging of the powder and the manufacturing parameters on the dimensional and mechanical characterization of specimens printed with SLS technique in PA12.

The purpose of this paper is to compare two different tools for tolerance analysis. Tolerance analysis is an important task to design and manufacture high-precision mechanical assemblies; it has received considerable attention in the literature. Many are the tools required to carry out a tolerance analysis, and may be divided into two categories: the analytical models and the statistical software packages. No comparison exists in the literature among these two categories.

This work presents a comparison between two different approaches to tolerance analysis: an analytical method, the variational model, and a statistical software, eM-Tolmate. The comparison has been developed on the same aeronautical case study that constitutes an actual product.

The proposed approach has been applied to an aeronautical case study. The results of the case study show how, when 2D tolerance analysis problems need to be solved, the two adopted tools give the same results. When the complexity of the tolerance analysis problems increases, the statistical software becomes the only choice to use. The new findings of the present paper are related to the fact that computer-aided tolerance analysis software packages remain the only choice to approach actual complex industrial products despite the extensive development of theoretical research.

This paper deals with a unique case study. However, the two adopted approaches and the obtained results are general, that is, they may be applied to any assembly.

Tolerance analysis is a valid tool to foresee geometric interferences among the components of an assembly, before getting the physical assembly. It involves a decrease of the manufacturing costs.

Many are the tools for tolerance analysis, such as different analytical models and different commercial software packages. Some are the comparisons among the different tools in the literature, but they are not exhaustive. Therefore, when a user has to solve an assembly problem to foresee the geometric interferences during the design stage, he/she does not know what to choose. The original contribution of the paper is to address the user’s choice through a comparison between an analytical model and a statistical software to solve the tolerance analysis problems of an actual aeronautical assembly.

The purpose of this paper is to carry out a tolerance analysis with geometric tolerances by means of the Jacobian model. Tolerance analysis is an important task to design and to manufacture high-precision mechanical assemblies; it has received considerable attention by the literature. The Jacobian model is one of the methods proposed by the literature for tolerance analysis. The Jacobian model cannot deal with geometric tolerances for mechanical assemblies. The geometric tolerances may not be neglected for assemblies, as they significantly influence their functional requirements.

This paper presents how it is possible to deal with geometric tolerances when a tolerance analysis is carried out by means of a Jacobian model for a 2D and 3D assemblies for which the geometric tolerances applied to the components involve only translational deviations. The three proposed approaches modify the expression of the stack-up function to overcome the shortage of Jacobian model that the geometric error cannot be processed.

The proposed approach has been applied to a case study. The results of the case study show how, when a statistical approach is implemented, the Jacobian model with the three developed methods gives results very similar to those due to other models of the literature, such as vector loop and variational.

In particular, the proposed approach may be applied only when the applied geometrical tolerances involve translational variations in 3D assemblies.

Tolerance analysis is a valid tool to foresee geometric interferences among the components of an assembly before getting the physical assembly. It involves a decrease of the manufacturing costs.

The original contribution of the paper is due to three methods to make a Jacobian model able to consider form and geometric deviations.