Configuration Tree Solver: A Technology for Automated Design and Configuration

Configuration is a process of generating a definitive description of a product or an order that satisfies a set of specified requirements and known constraints. Knowledge-based technology is an enabling factor in automation of configuration tasks found in the business operation. In this paper, we describe a configuration technique that is well suited for configuring “decomposable” artifacts with reasonably well defined structure and constraints. This technique may be classified as a member of a general class of decompositional approaches to configuration. The domain knowledge is structured as a general model of the artifact, an and-or hierarchy of the artifact’s elements, features, and characteristics. The model includes constraints and local specialists which are attached to the elements of the and-or-tree. Given the specific configuration requirements, the problem solving engine searches for a solution, a subtree, that satisfies the requirements and the applicable constraints. We describe an application of this approach that performs configuration and design of an automotive component.

Generation and Modification of Non-Uniform B-Spline Surface Approximations to PDE Surfaces Using the Finite Element Method

A PDE surface is generated by solving partial differential equations subject to boundary conditions. To obtain an approximation of the PDE surface in the form of a B-spline surface the finite element method, with the basis formed from B-spline basis functions, can be used to solve the equations. The procedure is simplest when uniform B-splines are used, but it is also feasible, and in some cases desirable, to use non-uniform B-splines. It will also be shown that it is possible, if required, to modify the non-uniform B-spline approximation in a variety of ways, using the properties of B-spline surfaces.

Tool Approach Directions for Machining Protrusion and Depression Features in an Object

The success of any industry in today’s highly competitive market is largely dependent on its ability to produce quality products, quickly and at low cost. Evaluating the effect of a product design on its manufacture is crucial in developing efficient designs. Any potential manufacturing problems detected at this stage can be corrected by modifying the design, leading to shorter product development cycles and lower production costs. This paper presents an algorithm to determine feasible tool approach directions. The algorithm is based on detecting if any part of the object obstructs the tool path. The basis for the algorithm is determining feasible approach directions and clearances around a planar polygonal face. The algorithm is applicable to both protrusions and depressions. The information is useful in performing manufacturability analysis of designs and develop process plans.

Probabilistic Optimal Design Using Successive Surrogate Probability Density Functions

Probabilistic optimization using the moment matching method and the simulation optimization method are discussed and compared to conventional deterministic optimization. A new approach based on successively approximating probability density functions, using recursive quadratic programming for the optimization process, is described. This approach incorporates the speed and robustness of analytical probability density functions and improves accuracy by considering simulation results. Theoretical considerations and an example problem illustrate the features of the approach. The paper closes with a discussion of an objective function formulation which includes the expected cost of design constraint failure.

An Interactive Graphical Approach to Feature Modeling Using Halfspaces and Geometric Constraints

Feature modeling enables the specification of a model with standardized high-level shape aspects that have a functional meaning for design or manufacturing. In this paper an interactive graphical approach to feature-based modeling is presented. The user can represent features as new CSG primitives, specified as a Boolean combination of halfspaces. Constraints between halfspaces specify the geometric characteristics of a feature and control feature validity. Once a new feature is defined and stored in a library, it can be used in other objects and positioned, oriented and dimensioned by direct manipulation with a graphics cursor. Constraints between features prevent feature interference and specify spatial relations between features.

Designing and Mapping Trimming Curves on Surfaces Using Orthogonal Projection

In the design and manufacturing of shell structures it is frequently necessary to construct trimming curves on surfaces. The novel method introduced in this paper was formulated to be coordinate independent and computationally efficient for a very general class of surfaces. Generality of the formulation is attained by solving a tensorial differential equation that is formulated in terms of local differential properties of the surface. In the method proposed here, a space curve is mapped onto the surface by tracing a surface curve whose points are connected to the space curve via surface normals. This surface curve is called to be an orthogonal projection of the space curve onto the surface. Tracing of the orthogonal projection is achieved by solving the aforementionned tensorial differential equation. For an implicitely represented surface, the differential equation is solved in three-space. For a parametric surface the tensorial differential equation is solved in the parametric space associated with the surface representation. This method has been tested on a broad class of examples including polynomials, splines, transcendental parametric and implicit surface representations. Orthogonal projection of a curve onto a surface was also developed in the context of surface blending. The orthogonal projection of a curve onto two surfaces to be blended provides not only a trimming curve design tool, but it was also used to construct smooth natural maps between trimming curves on different surfaces. This provides a coordinate and representation independent tool for constructing blend surfaces.

Automated Hybrid Analysis of Surface Mounted Electronic Assemblies

Simulations of surface mounted electronic assemblies under general mechanical loading conditions have been performed using an hybrid analytical/experimental analysis approach. This method combines analytical techniques with experimentally determined load-deformation characteristics of the surface-mounted assemblies to predict loadings and deformations of the assemblies. An automated analysis procedure which integrated the finite element method, optimization theory and the hybrid analysis approach was developed. This procedure can be used to study the strength of the surface mounted devices located anywhere on a printed circuit board subjected to the specified loading conditions.

A Formal Approach to Design Specifications

In this paper a methodology for the specification stage in conceptual design is presented. It allows for problem solving in an active interaction with the designer. An important part of the proposed methodology is the requiremental and functional tree representing the overall logic and structure of the design problem. The specification stage aims at providing requirements and transforming them into functions of the designed object. It occurs at the highest level of abstraction and it must provide enough information to begin the synthesis process where functions are transformed into design components that are further synthesized into the designed object. The proposed approach was motivated by the following problems: specification of requirements, specification of functions, incorporation of logic into functional and requiremental trees, representation of requirements-functions interaction, and optimization in the functional space. The methodology presented is illustrated with examples.

Automatic Generation of Tolerance Chains From Mating Relations Represented in Assembly Models

This paper presents an algorithm for generating tolerance chains from the mating relations between components of assemblies. The algorithm is developed upon a feature-based assembly modeling strategy that represents each component in close relation to its mating features, dimensions and tolerances. The mating relations within an assembly are described by a mating graph. Tolerance chains together with their dimensions and tolerances are generated automatically by searching through a mating graph for matching mating features. A prototype program package based on the presented algorithm has been developed, and several examples of various complexity have been tested with success.

The M-Space Theory of Tolerances

A rigorous mathematical theory of tolerances is an important step toward the automated solution of tolerancing problems. This paper develops a mathematical theory of tolerances in which tolerance specifications are interpreted as constraints on a normed vector space of model variations (M-space). This M-space provides concise representations for both dimensional and geometric tolerances, without deviating from the established tolerancing standards. This paper extends the authors’ previous work to include examples of geometric orientation and form tolerances. We show that the M-space theory supports the development of effective algorithms for the solution of tolerancing problems. Through the use of solid modeling technology, it is possible to automate the solution of such problems.