Tolerances impose restrictions on the possible deviations of features from their nominal sizes/shapes. These variations of size/shape could be thought of as deviations of a set of generalized coordinates defined at some convenient point on a feature. Any tolerance specification for a feature imposes some kind of restrictions or constraints on its deviation parameters. These constraints, in general, define a bounded region in the deviation space. In this paper, a method has been presented for converting tolerance specifications as per maximum material condition (MMC)/least material condition (LMC)/regardless of feature size (RFS) material conditions for standard mating features (planar, cylindrical, and spherical) into a set of inequalities in a deviation space. Both virtual condition boundaries Virtual condition boundary: A constant boundary generated by the collective effects of a size feature's specified MMC or LMC material condition and the geometric tolerance for that material condition. (VCB) and tolerance zones are utilized for these mappings. The mapping procedures have been illustrated with an example. Note to Practitioners-This paper deals with methods to convert tolerance specification as per ASME Y14.5M into a set of generalized deviation of features and vice-versa. These are intermediate relationships that are required for use in deviation-based tolerance synthesis methods. In this work, different examples have been presented to show how different tolerance specifications (such as positional tolerance at maximum material condition (MMC), least material condition (LMC), etc.) applied to different features could be treated on a generalized basis for tolerancing of manufactured parts.

In this paper, a generic model for the synthesis of tolerances for manufactured parts is presented. The model uses a method of transforming traditional tolerance specifications (as defined in ASME Y14.5M) to a generalized coordinate system (hereinafter referred to as deviation space). Small displacement torsors (SDTs) have been used for representing the deviations. The tolerance synthesis method is formulated as a constrained nonlinear optimization process. Three different types of constraints have been considered for the optimization process: 1) representation of assemblability; 2) mapping of tolerance specification to deviations; and 3) functional requirements. A new deviation-based cost of manufacturing model has been proposed. A working module of the scheme has been implemented and the process has been elaborated with two examples. The possibility of extension of the model and scope for further generalization have been discussed. Note to Practitioners-This paper presents an optimization method for finding tolerance values for different features of an assembly of manufactured parts. Determination of different types of tolerances and their exact values for critical features of any part has been an ad-hoc process; it has been mostly experience-based till recent time. In this paper, efforts have been made to establish a strong mathematically oriented method for synthesis of tolerances. The procedure attempts to minimize cost of manufacturing while the functionality and assemblability are satisfied. It is a generalized method and could be applied for designing rigid manufacture parts. For practical usage, this method should be integrated with three-dimensional computer-aided design packages as a tolerance synthesis module for integrated tolerance design.

The Virtual Assembly Design Environment (VADE) is a virtual reality (VR) based engineering application which allows engineers to evaluate, analyze, and plan the assembly of mechanical systems. This system focuses on utilizing an immersive virtual environment tightly coupled with commercial computer aided design (CAD) systems. Salient features of VADE include: data integration (two-way) with a parametric CAD system; realistic interaction of the user with parts in the virtual environment; creation of valued design information in the virtual environment; reverse data transfer of design information back to the CAD system; significant interactivity in the virtual environment; collision detection; and physically-based modeling. This paper describes the functionality and applications of VADE. A discussion of the limitations of virtual assembly and a comparison with automated assembly planning systems are presented. Experiments conducted using real-world engineering models are also described.

Tolerancing decisions can profoundly impact the quality and cost of electro-mechanical assemblies. Existing approaches to tolerance analysis and synthesis in design entail detailed knowledge of geometry of the assemblies and are mostly applicable during advanced stages of design, leading to a less than optimal design process. During the design process of assemblies, both the assembly structure and associated tolerance information evolve continuously. Therefore, significant gains can be achieved by effectively using this information to influence the design of the assembly. Motivated by this, we identify and explore two goals for future research that we believe can enhance the scope of tolerancing for the entire design process. The first goal is to advance tolerancing decisions to the earliest possible stages of design. This issue raises the need for effective representation of tolerancing information during different stages of design and for effective assembly modeling. The second goal addresses the appropriate, synergistic use of available methods and best practices for tolerance analysis and synthesis, at successive stages of design. Pursuit of these goals leads to the definition of a multilevel approach that enables tolerancing to be addressed at successive stages of design in an incremental fashion. The resulting design process, which we call the design for tolerance process, integrates three important domains: (1) design activities at successive stages of design; (2) assembly models that evolve continuously through the design process; (3) methods and best practices for tolerance analysis and synthesis. We demonstrate major steps of our proposed approach through a simple, yet illustrative, example.

Tolerancing decisions during the design of electromechanical products profoundly affect cost and quality. Existing approaches to tolerance analysis and synthesis entail detailed knowledge of geometry of the assemblies and are mostly applicable during advanced stages of design, leading to a less than optimal design process. During design, both the assembly structure and associated tolerance information evolve continuously and significant gains can be achieved by effectively using this information to influence the design. We explore two goals of research to expand the scope of tolerancing to the entire design process. The first goal is to advance tolerancing decisions to the earliest possible stages of design. This issue raises the need for effective representation of tolerancing information during early stages. The second goal addresses the appropriate use of industry best practices and efficient computational approaches. Pursuit of these goals leads to the definition of a multilevel approach that enables tolerancing to be addressed at successive stages of design in an incremental, continuous ongoing fashion. The resulting design process, which we call the design-for-tolerance process, integrates three important domains: (1) design activities at successive stages of design; (2) assembly models that evolve continuously through the design process; and (3) methods and best practices for tolerance analysis and synthesis. We demonstrate major steps of our proposed approach through a simple, yet illustrative, example.