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

Manufacturing signature in jacobian and torsor models for tolerance analysis of rigid parts

An integrated open source CAT based on Skin Model Shapes

The modelling of nominal product geometry by computer-aided design tools has gained immense attention in industry during the last decades and is nowadays an integral part of the virtual product development process. However, the established geometry representation schemes for CAD imply severe drawbacks regarding the modelling of geometric part deviations, which are inevitably observed on every manufactured artefact. As a response, the concept of Skin Model Shapes, which stems from international standards for geometric product specification and verification, has been developed as a novel approach for the consideration of product shape variability. It employs discrete geometry methods and computational techniques, such as point clouds, surface meshes and geometric processing, to model shape variability and to facilitate the communication of geometric product information throughout the product design, manufacturing, and inspection processes. This paper highlights the foundations of this concept, demonstrates its potentials for the representation of product geometry considering geometric variations along the product lifecycle, and illustrates main applications in the context of computer aided product and process development. In this regard, a focus is laid upon recent results and contributions, such as contact modelling, tolerance analysis, and motion tolerancing based on Skin Model Shapes. Furthermore, challenges for future research, such as the application to complex shapes and compliant parts, as well as the consideration of novel manufacturing processes, are discussed.

The inevitable presence of geometrical part deviations and their effects on the product function and quality forces companies to manage these deviations along the product life-cycle. Computer-aided tolerancing and variation simulation tools support these activities by enabling the early prediction and assessment of the effects of such part deviations. However, available approaches for the tolerance analysis and variation simulation imply shortcomings regarding the consideration of form deviations, particularly when analysing mechanism and moving systems. This paper presents an approach for the motion tolerancing, i. e. for the tolerance analysis of mechanism and moving systems, employing discrete geometry representations of parts with geometrical deviations (Skin Model Shapes). In this regard, a novel method for the parametrization of form deviations is proposed and the use of meta-modelling techniques for the reduction of the computational effort is illustrated. Moreover, the presented approach is applied on two case studies. Based on the obtained results, it can be found, that the consideration of form deviations in the tolerance analysis for mechanism and moving systems may lead to more purposeful tolerancing decisions.

From solid modelling to skin model shapes: Shifting paradigms in computer-aided tolerancing

Nowadays, assembly tolerance analysis has become a challenging problem to predict the accuracy of a final assembly and examine whether specified tolerances satisfy assembly functional requirements (AFRs) for ensuring product assembly performance. Skin model shapes can be addressed to represent part geometric tolerances with manufacturing defects, thereby providing high fidelity surfaces that can replace nominal or ideal surfaces and significantly improve the accuracy and reliability of assembly tolerance analysis. However, their application in easy-to-use assembly simulation is limited by the level of detail required for manufacturing defect simulation and the complicated calculation process for integrating these defects into the tolerance analysis. Therefore, to overcome these issues in predicting assembly deviations in the early design stage, we propose a generic integrated approach of assembly tolerance analysis based on skin model shapes. First, two methods are introduced for modelling and generating skin model shapes according to different mate types of assembly key features. Second, a calculation method of assembly deviation propagation is developed by the integration of skin model shapes and stream-of-variation theory with accuracy and efficiency guarantees. Besides, a slightly modified relative contact positioning method is presented, based on different surface and progressive contact method, to obtain deterministic contact points and contact positioning errors between key mating joint surfaces. And then, the deviation values of AFRs are calculated, considering the inevitable manufacturing and assembly process errors. Finally, a typical mechanical assembly on assembly tolerance analysis is used as a case study to demonstrate the effectiveness of the proposed approach.

Possibilities of CMM Software to Support Proper Geometrical Product Verification

Tolerance analysis methods, which are important to achieve a balance between manufacturing costs and functional requirements, have been studied and improved over the last 30 years. This paper proposes a new method to improve the precision of assembly simulation for statistical assembly simulation; by investigating the effect of the geometric deviations and mechanical behaviors of assembly contact on the stack-up assembly deviation by combining the recent theories on the tolerance analysis of rigid bodies and local contact deformation. To improve the precision of the tolerance analysis, real parts with form defects were simulated with the help of non-nominal skin model shapes. The SMSs were first considered to be rigid, and a quadratic optimization-based method for the rigid body displacement was used to calculate the initial contact points of all the SMSs. Next, contact deformation, following Hertzian contact theory, occurred at the initial contact points, which changed the relative positions of the SMSs in the subsequent interactions. The iteration process was convergent, and the final simulation for tolerance analysis could be generated after several iterations. Case studies demonstrated the practicality of the proposed method. Their actual assembly deviations were simulated by combining the effects of geometric deviations and local surface deformations. Since the proposed tolerance analysis framework based on statistical assembly simulation, it is expected to control the functional requirements of mechanical assemblies with much rough tolerance design and help optimize the tolerance in the future.

An Approach to the Sensitivity Analysis in Variation Simulations considering Form Deviations

One of the most critical tasks within the scope of Design for Manufacturing (DfM) is to define the set of Geometrical Product Specifications (GPS) in the 3D model or in the engineering drawing that ensures the functionality and the interchangeability of parts, as well as the intended functional performance of an assembly. Several methodologies have been proposed for the optimal designation of such specifications; however, the majority of them do not effectively take into account the deformations that are inevitably induced during assembly and operation for the vast majority of mechanical components. Motivated by the widely accepted tolerancing practice for sheet metal parts in the automotive industry, where the distinction between free state and constrained state is considered, the paper investigates the influence of the deformations induced during assembly and operation on GPS. The effect of part stiffness in the resultant functional GPS of the assembly/component is explored, through CAD surfacing and non-linear numerical finite element analysis tools including the contact problem. The current stage of development of a novel, performance-based methodology for the GD&T design procedure is presented. The methodology is applied on a real-world mechanical assembly that is derived from tolerance stack up-related literature. This study illustrated is that for an unpredictably wide range of mechanical components the default, free-state GPS scheme should only be assigned after rigorous analysis of their compliance behaviour. The proposed approach will lead to deduce the correlation between production cost and performance through a further development in future study.

In accordance with the new generation geometrical product specification and verification (GPS), the specification design process and the measurement and verification process must satisfy with duality principle so as to avoid the ambiguous problems during the verification process. To solve the problems how to generate the specification surface model of planar feature and design and apply the corresponding specification operators. This paper firstly presents a method to generate the specification surface model of planar feature. The tolerance mathematic model of the planar factors should be established in first step. Then the influences of processing technology on the specification surface model need to be considered. The simulation points under the normal distribution are generated in the tolerance zone. By using the fitting approach of the least-squares B spline, the specification surface model is generated. Secondly, this paper makes a corresponding analysis and design on specification operators of plane feature with flatness requirement. Lastly takes the worktable of M7140 grinding machine as an example, builds its specification surface model and the specification design results by operations on specification surface model are given.

Geometrical Product Specifications (GPS): A Review of Teaching Approaches

The evolving technology of additive manufacturing (AM) is posing novel challenges in manufacturing practice since nowadays functional, end-use components, and assemblies are produced by commercially available AM equipment. In order to safeguard the functionality and the interchangeability of a part, the designer must clearly denote a set of Geometrical Product Specifications (GPS) in the 3D model or in the engineering drawing by using the existing standards, e.g., ISO 1101, ISO 5459, and ISO 1660. Apparently, the family of ISO GPS standards that are currently used in design, manufacture, and verification has been developed so as to address the needs of traditional manufacturing processes rather than AM. Supported by numerous recent publications, the argument that current standardization does not sufficiently support the geometrical specification and verification of AM parts is getting more and more popular. The paper investigates and questions the need for the development of AM process-specific standards, related to the tolerancing and verification of mechanical components, as encountered with castings, forgings, and composites. Focusing on the most critical issue of datum establishment and datum hierarchy, the capability of existing tolerancing tools, as provided by the ISO GPS standards, to serve the process-specific AM needs is systematically examined. Moreover, major AM process-specific parameters such as build direction, layer thickness, support structure, and hatching plan are linked with the datum system designation and datum hierarchy tasks through a design case study and analysis. The major findings of this research pointing towards the establishment of AM-specific design-for-accuracy good practices are presented and discussed.

Geometrical product specification and verification (GPS) is the only worldwide tolerancing specification language available for unambiguously communicating functional requirements and precisely expressing geometrical tolerances of workpieces on technical drawings. Although the understanding and application of GPS are of vital importance for modern manufacturing industry, the latest GPS standards contain huge amounts of data, information and knowledge that are obscurely linked together, so they are very difficult for designers, engineers and metrologists to understand, remember and comprehensively use them. This is especially true for surface texture that is one of the most complicated geometrical characteristics in GPS domain. To overcome the implementation barrier of GPS surface texture, a novel knowledge-based solution supported formally by a unified knowledge modeling of the complete GPS surface texture standard chain has been researched. This knowledge model can serve as a formal basis for developing more intelligent and reliable tolerance design and measurement systems. This paper starts with an introduction on how to build up a formal knowledge model based on category theory, called categorical fibration model, to unified acquisition and representation of all surface texture knowledge. It then moves on to define a recursive knowledge refinement process for the devised model to enable the recursive multi-level GPS knowledge transformations and refinements. This knowledge model is validated naturally by checking rules identified from category theoretic notions. Finally, this paper presents a general framework for applying the modeled GPS knowledge in practice, from the aspects of the integrated and complete modeling of all surface texture knowledge, detailed knowledge acquisition and modeling examples for four sub-knowledge bases of the proposed software solution, core functional features of this software, and a comprehensive case study for testing its validity and usability. This knowledge-based solution facilitates life cycle collaboration and integration of the complete GPS surface texture chain to reduce product development cost and lead time, and to ensure functional requirements of geometrical workpieces.

Least squares association of geometrical features plays an important role in geometrical product specification and verification. Most existing algorithms for the least squares association today usually do not give the covariance matrix associated with the parameters of the respective geometrical feature. The reason is that the complexity of these algorithms can be very high, because partial differential quotients are needed. If the necessary partial difference quotients are calculated by hand and subsequently coded into an algorithm, there is a high risk to introduce unwillingly errors. This paper shows how the least squares algorithm can automatically be generated solely from the equation specifying the distance function of the measured points from the geometrical feature.