Modeling of 2D and 3D Assemblies Taking Into Account Form Errors of Plane Surfaces

The tolerancing process links the virtual and the real worlds. From the former, tolerances define a variational geometrical language (geometric parameters). From the latter, there are values limiting those parameters. The beginning of a tolerancing process is in this duality. As high precision assemblies cannot be analyzed with the assumption that form errors are negligible, we propose to apply this process to assemblies with form errors through a new way of allowing to parameterize forms and solve their assemblies. The assembly process is calculated through a method of allowing to solve the 3D assemblies of pairs of surfaces having form errors using a static equilibrium. We have built a geometrical model based on the modal shapes of the ideal surface. We compute for the completely deterministic contact points between this pair of shapes according to a given assembly process. The solution gives an accurate evaluation of the assembly performance. Then we compare the results with or without taking into account the form errors. When we analyze a batch of assemblies, the problem is to compute for the nonconformity rate of a pilot production according to the functional requirements. We input probable errors of surfaces (position, orientation, and form) in our calculus and we evaluate the quality of the results compared with the functional requirements. The pilot production then can or cannot be validated

A statistical tolerance analysis approach for over-constrained mechanism based on optimization and Monte Carlo simulation

Tolerancing decisions can profoundly impact the quality and cost of the mechanism. To evaluate the impact of tolerance on mechanism quality, designers need to simulate the influences of tolerances with respect to the functional requirements. This paper proposes a mathematical formulation of tolerance analysis which integrates the notion of quantifier: ‘‘For all acceptable deviations (deviations which are inside tolerances), there exists a gap configuration such as the assembly requirements and the behavior constraints are verified’’ & ‘‘For all acceptable deviations (deviations which are inside tolerances), and for all admissible gap configurations, the assembly and functional requirements and the behavior constraints are verified’’. The quantifiers provide a univocal expression of the condition corresponding to a geometrical product requirement. This opens a wide area for research in tolerance analysis. To solve the mechanical problem, an approach based on optimization is proposed. Monte Carlo simulation is implemented for the statistical analysis. The proposed approach is tested on an over-constrained mechanism

A New Methodology for Tolerance Synthesis of Parallel Manipulators

International audienceComputing the maximal pose error given an upper bound on perturbations is challenging for parallel robots, mainly because the direct kinematic problem has several solutions, which become unstable near or at parallel singularities. In this paper, we propose a local uniqueness hypothesis that will allow safely computing pose error upper bounds using nonlinear optimization. This hypothesis , together with a corresponding maximal allowed perturbation domain and a certified pose error upper bound valid over the complete workspace, will be proved numerically using a parametric version of Kantorovich theorem and certified nonlinear global optimization. We will then show how to synthesize tolerances reaching a prescribed maximal pose error over a workspace using approximate linearizations. This approximate tolerance synthesis will finally be checked using the certified pose error upper bound we propose. Preliminary experiments on a RPRPR and a 3RPR with fixed orientation parallel manipulators are presented

Functional and Behavioral Product Information Representation and Consistency Validation for Collaboration in Product Lifecycle Activities

Information models that represent the function, assembly and behavior of artifacts are critical in the conceptual development of a product and its evaluation. Much research has been conducted in this area; however, existing models do not relate function, behavior and structure in a comprehensive and consistent way. In this work, NIST\u27s Core Product Model (CPM) and the Open Assembly Model (OAM) are extended to integrate product information including function and behavior, with an emphasis on assembly, throughout all phases of product development. For function and flow classification, the NIST functional taxonomy is used to maintain consistency with the literature. The consistency validation of product information, and the verification of modified product information are discussed; these processes ensure that the product information has no contradictions and allows tracing through associations without any deficiency or disconnection. In other words, the information model has to be complete in terms of traceability of function, behavior, spatial relationships, etc., in order to support all information exchange activities. The product information representation provides a mechanism for capturing product information and storing it in a database. This representation schema also provides necessary information for any future decision making activities in the End of Life (EOL) environment, such as the replacement or reuse of any part or subassembly. When there is a need to replace one artifact with another, one must consider all of the associations of the existing artifact with other artifacts and the environment, not just functional and space requirements, and the relevant modification(s) of the associated objects has to verified. So one can manage product lifecycle activities in different perspectives by knowing how the product information is interconnected in various domains and how its characteristics affect each other

A study on the dynamics of a study on the dynamics of spatial mechanisms with frictional spherical clearance joints

An investigation on the dynamic modeling and analysis of spatial mechanisms with spherical clearance joints including friction is presented. For this purpose, the ball and the socket which compose a spherical joint are modeled as two individual colliding components. The normal contact-impact forces that develop at the spherical clearance joint are determined by using a continuous force model. A continuous analysis approach is used here with a Hertzian based contact force model, which includes a dissipative term representing the energy dissipation during the contact process. The pseudo-penetration that occurs between the potential contact points of the ball and the socket surface, as well as the indentation rate play a crucial role in the evaluation of the normal contact forces. In addition, several different friction force models based on the Coulomb’s law are revisited in this work. The friction models utilized here can accommodate the various friction regimens and phenomena that take place at the contact interface between the ball and the socket. Both the normal and tangential contact forces are evaluated and included into the systems’ dynamics equation of motion, developed under the framework of multibody systems formulations. A spatial four bar mechanism, which includes a spherical joint with clearance, is used as an application example to examine and quantify the effects of various friction force models, clearance sizes, and the friction coefficients.The first author expresses his gratitude to the Portuguese Foundation for Science and Technology through the PhD grant (PD/BD/114154/2016). This work has been supported by the Portuguese Foundation for Science and Technology with the reference project UID/EEA/04436/2013, by FEDER funds through the COMPETE 2020 – Programa Operacional Competitividade e Internacionalização (POCI) with the reference project POCI-01-0145-FEDER-006941.info:eu-repo/semantics/publishedVersio

A comprehensive survey of the analytical, numerical and experimental methodologies for dynamics of multibody mechanical systems with clearance or imperfect joints

"Available online 19 December 2017"A comprehensive survey of the literature of the most relevant analytical, numerical, and experimental approaches for the kinematic and dynamic analyses of multibody mechanical systems with clearance joints is presented in this review. Both dry and lubricated clearance joints are addressed here, and an effort is made to include a large number of research works in this particular field, which have been published since the 1960′s. First, the most frequently utilized methods for modeling planar and spatial multibody mechanical systems with clearance joints are analyzed, and compared. Other important phenomena commonly associated with clearance joint models, such as wear, non-smooth behavior, optimization and control, chaos, and uncertainty and links’ flexibility, are then discussed. The main assumptions procedures and conclusions for the different methodologies are also examined and compared. Finally, future developments and new applications of clearance joint modeling and analysis are highlighted.This research was supported in part by the China 111 Project (B16003) and the National Natural Science Foundation of China under Grants 11290151, 11472042 and 11221202. The work was also supported by the Portuguese Foundation for Science and Technology with the reference project UID/EEA/04436/2013, by FEDER funds through the COMPETE 2020 – Programa Operacional Competitividade e Internacionalização (POCI) with the reference project POCI-01-0145-FEDER-006941.info:eu-repo/semantics/publishedVersio

Computer-aided simulation and testing of spatial linkages with joint mechanical errors

Tolerance allocation influences production costs in a big way. For this reason it is very important to have an accurate study about the effects of manufacturing errors on the functioning and performances of linkages. In this paper, the authors present a computer-aided methodology based on a 3D geometrical approach using the dual-algebra fundamentals. The purpose is to give ail useful tool which can be integrated into CAD software in order to evaluate the performances of spatial mechanisms with mechanical errors. The proposed methodology has been validated by means of experimental tests on a Cardan joint mechanism with clearances, misalignments and dimensional errors. Copyright (c) 2005 John Wiley & Sons, Ltd