Simultaneous Optimal Uncertainty Apportionment and Robust Design Optimization of Systems Governed by Ordinary Differential Equations

The inclusion of uncertainty in design is of paramount practical importance because all real-life systems are affected by it. Designs that ignore uncertainty often lead to poor robustness, suboptimal performance, and higher build costs. Treatment of small geometric uncertainty in the context of manufacturing tolerances is a well studied topic. Traditional sequential design methodologies have recently been replaced by concurrent optimal design methodologies where optimal system parameters are simultaneously determined along with optimally allocated tolerances; this allows to reduce manufacturing costs while increasing performance. However, the state of the art approaches remain limited in that they can only treat geometric related uncertainties restricted to be small in magnitude. This work proposes a novel framework to perform robust design optimization concurrently with optimal uncertainty apportionment for dynamical systems governed by ordinary differential equations. The proposed framework considerably expands the capabilities of contemporary methods by enabling the treatment of both geometric and non-geometric uncertainties in a unified manner. Additionally, uncertainties are allowed to be large in magnitude and the governing constitutive relations may be highly nonlinear. In the proposed framework, uncertainties are modeled using Generalized Polynomial Chaos and are solved quantitatively using a least-square collocation method. The computational efficiency of this approach allows statistical moments of the uncertain system to be explicitly included in the optimization-based design process. The framework formulates design problems as constrained multi-objective optimization problems, thus enabling the characterization of a Pareto optimal trade-off curve that is off-set from the traditional deterministic optimal trade-off curve. The Pareto off-set is shown to be a result of the additional statistical moment information formulated in the objective and constraint relations that account for the system uncertainties. Therefore, the Pareto trade-off curve from the new framework characterizes the entire family of systems within the probability space; consequently, designers are able to produce robust and optimally performing systems at an optimal manufacturing cost. A kinematic tolerance analysis case-study is presented first to illustrate how the proposed methodology can be applied to treat geometric tolerances. A nonlinear vehicle suspension design problem, subject to parametric uncertainty, illustrates the capability of the new framework to produce an optimal design at an optimal manufacturing cost, accounting for the entire family of systems within the associated probability space. This case-study highlights the general nature of the new framework which is capable of optimally allocating uncertainties of multiple types and with large magnitudes in a single calculation

Automating Tolerance Synthesis: A Framework and Tools

This paper describes CASCADE-T—a new approach to tolerance synthesis that uses a complete representation of the conditional tolerance relations that exist between features of a part under design. Conditional tolerances are automatically determined from functional requirements and shape information. Tolerance primitives based on the virtual boundary requirements approach to tolerance representation are composed to form more complex tolerance relationships. Artificial intelligence techniques, including a constraint network, frame-based system, and dependency tracking are used to support flexible and detailed computation for tolerance analysis and synthesis

Allocation of geometric tolerances in one-dimensional stackup problems

Many tolerancing problems on mechanical assemblies involve a functional requirement depending on a chain of parallel dimensions on individual parts. In these one-dimensional cases, simple methods are available for the analysis and the allocation of dimensional tolerances. However, they are difficult to extend to geometric tolerances, which must be translated into equivalent dimensional tolerances; this allows the analysis but makes the allocation generally impossible without Monte Carlo simulation and complex search strategies. To overcome this difficulty, the paper proposes a way of dealing directly with geometric tolerances in the allocation problem. This consists in expressing the functional requirement as a linear model of geometric tolerances rather than equivalent dimensional tolerances; the coefficients of the model (sensitivities) are calculated considering both the dimension chain and the standard definition of the geometric tolerances. The approach can be combined with any constrained optimization method based on sensitivities. The optimal scaling method, previously proposed for dimensional tolerances, is extended to geometric tolerances and used in two examples to demonstrate the simplicity of the overall workflow and the quality of the optimal solution

Numerical and Geometric Optimizations for Surface and Tolerance Modeling

Optimization techniques are widely used in many research and engineering areas. This dissertation presents numerical and geometric optimization methods for solving geometric and solid modeling problems. Geometric optimization methods are designed for manufacturing process planning, which optimizes the process by changing dependency relationships among geometric primitives from the original design diagram. Geometric primitives are used to represent part features, and dependencies in the dimensions between parts are represented by a topological graph. The ordering of these dependencies can have a significant effect on the tolerance zones in the part. To obtain tolerance zones from the dependencies, the conventional parametric method of tolerance analysis is de-composed into a set of geometric computations, which are combined and cascaded to obtain the tolerance zones in the geometric representations. Geometric optimization is applied to the topological graph in order to find a solution that provides not only an optimal dimensioning scheme but also an optimal plan for manufacturing the physical part. The applications of our method include tolerance analysis, dimension scheme optimization, and process planning. Two numerical optimization methods are proposed for local and global surface parameterizations. One is the nonlinear optimization, which is used for building the local field-aware parameterization. Given a local chart of the surface, a two-phase method is proposed, which generates a folding-free parameterization while still being aware of the geodesic metric. The parameterization method is applied in a view-dependent 3D painting system, which constitutes a local, adaptive and interactive painting environment. The other is the mixed-integer quadratic optimization, which is used for generating a quad mesh from a given triangular mesh. With a given cross field, the computation of parametric coordinates is formulated to be a mixed-integer optimization problem, which parameterizes the surface with good quality by adding redundant integer variables. The mixed integer system is solved more efficiently by an improved adaptive rounding solver. To obtain the final quadrangular mesh, an isoline tracing method and a breadth-first traversal mesh generation method are proposed so that the final mesh result has face information, which is useful for further model processing

Feature Cluster Algebra and Its Application for Geometric Tolerancing

abstract: The goal of this research project is to develop a DOF (degree of freedom) algebra for entity clusters to support tolerance specification, validation, and tolerance automation. This representation is required to capture the relation between geometric entities, metric constraints and tolerance specification. This research project is a part of an on-going project on creating a bi-level model of GD&T; (Geometric Dimensioning and Tolerancing). This thesis presents the systematic derivation of degree of freedoms of entity clusters corresponding to tolerance classes. The clusters can be datum reference frames (DRFs) or targets. A binary vector representation of degree of freedom and operations for combining them are proposed. An algebraic method is developed by using DOF representation. The ASME Y14.5.1 companion to the Geometric Dimensioning and Tolerancing (GD&T;) standard gives an exhaustive tabulation of active and invariant degrees of freedom (DOF) for Datum Reference Frames (DRF). This algebra is validated by checking it against all cases in the Y14.5.1 tabulation. This algebra allows the derivation of the general rules for tolerance specification and validation. A computer tool is implemented to support GD&T; specification and validation. The computer implementation outputs the geometric and tolerance information in the form of a CTF (Constraint-Tolerance-Feature) file which can be used for tolerance stack analysis.Dissertation/ThesisM.S. Mechanical Engineering 201

Virtual manufacturing: prediction of work piece geometric quality by considering machine and set-up

Lien vers la version éditeur: http://www.tandfonline.com/doi/full/10.1080/0951192X.2011.569952#.U4yZIHeqP3UIn the context of concurrent engineering, the design of the parts, the production planning and the manufacturing facility must be considered simultaneously. The design and development cycle can thus be reduced as manufacturing constraints are taken into account as early as possible. Thus, the design phase takes into account the manufacturing constraints as the customer requirements; more these constraints must not restrict the creativity of design. Also to facilitate the choice of the most suitable system for a specific process, Virtual Manufacturing is supplemented with developments of numerical computations (Altintas et al. 2005, Bianchi et al. 1996) in order to compare at low cost several solutions developed with several hypothesis without manufacturing of prototypes. In this context, the authors want to predict the work piece geometric more accurately by considering machine defects and work piece set-up, through the use of process simulation. A particular case study based on a 3 axis milling machine will be used here to illustrate the authors’ point of view. This study focuses on the following geometric defects: machine geometric errors, work piece positioning errors due to fixture system and part accuracy

Review of dimensioning and tolerancing: representation and processing

The paper surveys the current state of knowledge of techniques for representing, manipulating and analysing dimensioning and tolerancing data in computer-aided design and manufacturing. The use of solid models and variational geometry, and its implications for the successful integration of CAD and CAM, are discussed. The topics explored so far can be grouped into four categories: (a) the representation of dimensioning and tolerancing (D & T), (b) the synthesis and analysis of D & T, (c) tolerance control, and (d) the implications of D & T in CAM. The paper describes in detail the recent work in each group, and concludes with speculation on a general framework for future research.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/29159/1/0000204.pd

Feature-based hybrid inspection planning for complex mechanical parts

Globalization and emerging new powers in the manufacturing world are among many challenges, major manufacturing enterprises are facing. This resulted in increased alternatives to satisfy customers\u27 growing needs regarding products\u27 aesthetic and functional requirements. Complexity of part design and engineering specifications to satisfy such needs often require a better use of advanced and more accurate tools to achieve good quality. Inspection is a crucial manufacturing function that should be further improved to cope with such challenges. Intelligent planning for inspection of parts with complex geometric shapes and free form surfaces using contact or non-contact devices is still a major challenge. Research in segmentation and localization techniques should also enable inspection systems to utilize modern measurement technologies capable of collecting huge number of measured points. Advanced digitization tools can be classified as contact or non-contact sensors. The purpose of this thesis is to develop a hybrid inspection planning system that benefits from the advantages of both techniques. Moreover, the minimization of deviation of measured part from the original CAD model is not the only characteristic that should be considered when implementing the localization process in order to accept or reject the part; geometric tolerances must also be considered. A segmentation technique that deals directly with the individual points is a necessary step in the developed inspection system, where the output is the actual measured points, not a tessellated model as commonly implemented by current segmentation tools. The contribution of this work is three folds. First, a knowledge-based system was developed for selecting the most suitable sensor using an inspection-specific features taxonomy in form of a 3D Matrix where each cell includes the corresponding knowledge rules and generate inspection tasks. A Travel Salesperson Problem (TSP) has been applied for sequencing these hybrid inspection tasks. A novel region-based segmentation algorithm was developed which deals directly with the measured point cloud and generates sub-point clouds, each of which represents a feature to be inspected and includes the original measured points. Finally, a new tolerance-based localization algorithm was developed to verify the functional requirements and was applied and tested using form tolerance specifications. This research enhances the existing inspection planning systems for complex mechanical parts with a hybrid inspection planning model. The main benefits of the developed segmentation and tolerance-based localization algorithms are the improvement of inspection decisions in order not to reject good parts that would have otherwise been rejected due to misleading results from currently available localization techniques. The better and more accurate inspection decisions achieved will lead to less scrap, which, in turn, will reduce the product cost and improve the company potential in the market

Reverse Engineering of a Racing Motorbike Connecting Rod

The following scientific paper aims to analyze in detail the methodology for reverse engineering of a racing motorcycle connecting rod. The objective is to start with a product available on the market as a spare part, reconstruct its CAD model with a high standard of accuracy, then proceed with lightening modifications to arrive at a new, improved design. The innovative aspect of the procedure lies in the fact that in order to ensure accuracy on the order of a tenth of a millimeter during reconstruction, it was decided to use a FARO articulated arm laser to scan the component’s outer surface. By taking advantage of appropriate redesign CAD software (Geomagic Design X), a reconstruction can proceed within the high standard of accuracy imposed. In conclusion, the modifications made through material removal allow an improvement in product efficiency, ensuring high performance