Sandro Wartzack

Skin Model Shapes: A new paradigm shift for geometric variations modelling in mechanical engineering

Geometric deviations are inevitably observable on manufactured workpieces and have huge influences on the quality and function of mechanical products. Therefore, many activities in geometric variations management have to be performed to ensure the product function despite the presence of these deviations. Dimensional and Geometrical Product Specification and Verification (GPS) are standards for the description of workpieces. Their lately revision grounds on GeoSpelling, which is a univocal language for geometric product specification and verification and aims at providing a common understanding of geometric specifications in design, manufacturing, and inspection. The Skin Model concept is a basic concept within GeoSpelling and is an abstract model of the physical interface between a workpiece and its environment. In contrast to this understanding, established models for computer-aided modelling and engineering simulations make severe assumptions about the workpiece surface. Therefore, this paper deals with operationalizing the Skin Model concept in discrete geometry for the use in geometric variations management. For this purpose, Skin Model Shapes, which are particular Skin Model representatives from a simulation perspective, are generated. In this regard, a Skin Model Shape is a specific outcome of the conceptual Skin Model and comprises deviations from manufacturing and assembly. The process for generating Skin Model Shapes is split into a prediction and an observation stage with respect to the available information and knowledge about expected geometric deviations. Moreover, applications for these Skin Model Shapes in the context of mechanical engineering are given.

Discrete shape modeling for skin model representation

Nowadays, the management of product geometrical variations during the whole product development process is an important issue for companies’ competitiveness. During the design phase, geometric functional requirements and tolerances are derived from the design intent. Furthermore, the manufacturing and measurement stages are two main geometric variations generators according to the two well-known axioms of manufacturing imprecision and measurement uncertainty. GeoSpelling as the basis of the geometrical product specification standard enables a comprehensive modeling framework and an unambiguous language to describe geometric variations covering the overall product lifecycle thanks to a set of concepts and operations based on the fundamental concept of the “Skin Model.” In contrast, only few research studies have focused on the skin model representation and simulation. The skin model as a discrete shape model is the main focus of this work. We investigate here discrete shape and variability modeling fundamentals, Markov Chain Monte Carlo simulation techniques and statistical shape analysis methods to represent, simulate, and analyze skin models. By means of a case study based on a cross-shaped sheet metal part, the results of the skin model simulations are shown here, and the performances of the simulations are described.

A Comprehensive Framework for Skin Model Simulation

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.Copyright

Tolerance analysis of systems in motion taking into account interactions between deviations

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.

Approaches for the assembly simulation of skin model shapes

Even though they are weakly noticed, geometric part deviations accompany our everyday life. These geometric deviations affect the assemblability and functional compliance of products, since small part variations accumulate through large-scale assemblies and lead to malfunction as well as decreased product reliability and safety. However, the consideration of part deviations in the virtual modelling of mechanical assemblies is an ongoing challenge in computer-aided tolerancing research. This is because the resulting assembly configurations for variant parts are far more complicated than for nominal assemblies. In this contribution, two approaches for the relative positioning of point based models are highlighted and adapted to the assembly simulation of Skin Model Shapes, which are specific workpiece representatives considering geometric deviations. The first approach employs constrained registration techniques to determine the position of variant parts in an assembly considering multiple assembly steps simultaneously, whereas the second utilizes the difference surface to solve the positioning problem sequentially. The application of these approaches to computer-aided tolerancing is demonstrated, though their applicability reaches various fields of industrial geometry. Skin Model Shapes are digital part representatives comprising geometric deviations.Approaches for the relative positioning of point-based Skin Model Shapes are proposed.The approaches ground on algorithms from computational geometry and computer graphics.Applications for the assembly simulation in tolerancing are given.

Contact and Mobility Simulation for Mechanical Assemblies Based on Skin Model Shapes

Assembly modelling as one of the most important steps in the product development activity relies more and more on the extensive use of CAD systems. The modelling of geometric interfaces between the components of the assembly is of central importance in the simulation of mechanical assemblies. Over the past decades, many researchers have devoted their efforts to establish theories and systems covering assembly modelling. Although the product form or shape have been extensively investigated considering the nominal CAD geometry, inevitable limitations can be reported. Computer Aided Tolerancing systems provide simulation tools for modelling the effects of tolerances on the assembly but still lack of form deviation considerations. The skin model concept which stemmed from the theoretical foundations of Geometrical Product Specification and Verification (GPS) has been developed to enrich the nominal geometry considering realistic physical shapes. However, the digital representation of the skin model has been investigated only recently. This paper presents a novel approach for a skin model based simulation of contact and mobility for assemblies. Three important issues are addressed: the geometric modelling of the contact, the contact quality evaluation, and the motion analysis. The main contribution to computer aided tolerancing can be found in the analysis of the effects of geometric form deviations on the assembly and motion behaviour of solid mechanics, which comprises models for the assembly simulation, for the contact quality evaluation, and for the motion analysis. A case study is presented to illustrate the proposed approaches.

Improved Sheet Bulk Metal Forming Processes by Local Adjustment of Tribological Properties

This paper is focused on a combined deep drawing and extrusion process dedicated to the new process class of sheet bulk metal forming (SBMF). Exemplified by the forming of gearings, combined sheet and bulk forming operations are applied to sheet metal in order to form local functional features through an intended and controlled change of the sheet thickness. For investigations on the form filling and the identification of significant influencing factors on the material flow, a FE simulation model has been built. The FE model is validated by the results of manufacturing experiments using DC04 with a thickness of 2.0 mm as blank material. Due to the fact that the workpiece is in extensive contact to the tool surface and that the pressure reaches locally up to 2500 MPa, the tribological conditions are a determining factor of the process. Thus, their influence is discussed in detail in this paper. In the first instance, different frictional zones having a distinct effect on the resulting material flow are identified and their effect on improved form filling is demonstrated. Subsequently, a more comprehensive methodology is developed to define tribological zones of forming tools. For this, a system analysis of the digital mock-up of the forming process is performed. Besides friction, other relevant aspects of forming tool tribology like contact pressure, sliding velocity, and surface magnification are considered. The gathered information is employed to partition the tools into tribological zones. This is done by systematically intersecting and re-merging zones identified for each of the criterion. The so-called load-scanning test allows the investigation of the friction coefficient in dependence of the contact pressure and possible loading limits of tribological pairings. It provides an appropriate tribological model test to evaluate tribological measures like coatings, surface textures and lubricants with respect to their targeted application in particular zones. The obtained results can be employed in the layout of further forming processes to reach the desired process behavior. This can be, for example, an improved form filling, less abrasive wear and adhesive damage or lower forming forces, respectively tool load for an improved durability of the die.

Neural network based modeling and optimization of deep drawing --- extrusion combined process

A combined deep drawing–extrusion process is modeled with artificial neural networks (ANN’s). The process is used for manufacturing synchronizer rings and it combines sheet and bulk metal forming processes. Input–output data relevant to the process was collected. The inputs represent geometrical parameters of the synchronizer ring and the outputs are the total equivalent plastic strain (TEPS), contact ratio and forming force. This data is used to train the ANN which approximates the input-output relation well and therefore can be relied on in predicting the process input parameters that will result in desired outputs provided by the designer. The complex method constrained optimization is applied to the ANN model to find the inputs or geometrical parameters that will produce the desired or optimum values of TEPS, contact ratio and forming force. This information will be very hard to obtain by just looking at the available historical input–output data. Therefore, the presented technique is very useful for selection of process design parameters to obtain desired product properties.

Statistical Tolerance-Cost-Optimization of Systems in Motion Taking into Account Different Kinds of Deviations

The time-depending motion behavior of systems in motion is essentially affected by manufacturing-caused as well as operation-depending deviations (e.g., deformations), which appear during the system’s use. Consequently, it is almost impossible for the product developer to define the optimal tolerances, which both ensure the mechanism’s functionality and cause minimum manufacturing costs. This paper presents a methodology for the “statistical tolerance-cost-optimization of systems in motion”. Therefore two appropriate mathematical optimization concepts are developed. The practical use of the methodology is shown for a non-ideal crank mechanism which is subject to manufacturing-caused as well as operation-depending deviations.

How to determine the influence of geometric deviations on elastic deformations and the structural performance

Geometric deviations are observable on every manufactured part since manufacturing processes are inherently imprecise and measuring processes always involve uncertainties. These geometric deviations have influences on the function and the quality of the product. Therefore, allowable limits for these geometric deviations, depicted as geometric tolerances, have to be set. They define the allowable geometric deviations of a part for which the product function is guaranteed. In this context, elastic deformations and the structural performance are key aspects. However, the manufacturing-caused geometric deviations have an influence on the elastic deformations during use and the structural performance of the parts. In other words, there are interdependencies between geometric deviations and elastic deformations which affect the dimensional accuracy of a loaded part in an assembly. Therefore, this article proposes an approach for determining the impact of geometric deviations on the structural performance. This approach employs techniques such as sensitivity analysis, analysis of robustness and evaluation of reliability, and aims at providing information about the expectable elastic deformations and structural performance to geometric tolerancing. It can be concluded that geometric deviations can have a big impact on the structural performance, and thus, not only parametric deviations but also geometric deviations regarding the form and shape of a part itself should be taken into account within the structural performance analysis and tolerance simulations.