The Datum Flow Chain: A systematic approach to assembly design and modeling

Current CAD systems are part-centric and do not capture the underlying logic of an assembly at an abstract level. We need to make CAD systems assembly-centric. To be able to lay out, analyze, outsource, assemble and debug complex assemblies, we need ways to capture their fundamental structure in a top-down design process, including the designer's strategy for constraining the parts kinematically and locating them accurately with respect to each other. We describe a concept called the Datum Flow Chain to capture this logic. Most assembly problems occur due to ineffective datum logic or the choice of assembly procedures that are not consistent with the datum logic, if any, that was used to design the parts. The DFC relates the datum logic explicitly to the product's key characteristics, assembly sequences, and choice of mating features, and provides the information needed for tolerance analyses. Two types of assemblies are addressed: Type-1, where the assembly process puts parts together at their pre-fabricated mating features, and Type-2, where the assembly process can incorporate in-process adjustments to redistribute variation. Two types of assembly joints are defined: mates that pass dimensional constraint from part to part, and contacts that merely provide support. The scope of DFC in assembly planning is presented using several examples. Analysis tools to evaluate different DFCs and select the ones of interest are also presented.     

Structure and Matrix Models for Tolerance Analysis from Configuration to Detail Design

A substantial amount of all quality problems that arise during assembly can be referred back to the geometrical design, and especially the geometrical concept of the product, i.e. the way in which parts are designed and located with each other. Special emphasis should thus be put on geometry design, especially during the early design phases, to try to find robust concepts and avoid solutions that may cause down-stream production problems.  This paper presents a generic set of evaluation tools for robust geometry design encountering (i) potential tolerance chain detection in configuration design, (ii) assembly robustness evaluation in concept design, and (iii) tolerance sensitivity analysis in detail design. Special attention is given to the development of a new matrix-based evaluation tool for the configuration design part. The tool presented is based on a new way of representing geometry variation constraints in an enhanced function-means tree structure model. Different parts of the function-means tree that are of interest for analysis purposes are then extracted and converted to matrix representation. The reason for doing this is that the structure model is most suitable for modeling, but becomes unsuitable for analysis as the model complexity increases. For this latter purpose, the matrix representation is far better. The use of the different tools is demonstrated in the design of a new vehicle front system for which the geometry a priori is unknown.     

Makespan estimation and order acceptance in batch process industries when processing times are uncertain

Batch process industries are characterized by complex precedence relationships between operations, which renders the estimation of an acceptable workload very difficult. A detailed schedule based model can be used for this purpose, but for large problems this may require a prohibitive large amount of computation time. We propose a regression based model to estimate the makespan of a set of jobs. We extend earlier work based on deterministic processing times by considering Erlang-distributed processing times in our model. This regression-based model is used to support customer order acceptance. Three order acceptance policies are compared by means of simulation experiments: a scheduling policy, a workload policy and a regression policy. The results indicate that the performance of the regression policy can compete with the performance of the scheduling policy in situations with high variety in the job mix and high uncertainty in the processing times. Correspondence to: C.V. Ivanescu     

Advanced production scheduling for batch plants in process industries

An Advanced Planning System (APS) offers support at all planning levels along the supply chain while observing limited resources. We consider an APS for process industries (e.g. chemical and pharmaceutical industries) consisting of the modules network design (for long–term decisions), supply network planning (for medium–term decisions), and detailed production scheduling (for short–term decisions). For each module, we outline the decision problem, discuss the specifi cs of process industries, and review state–of–the–art solution approaches. For the module detailed production scheduling, a new solution approach is proposed in the case of batch production, which can solve much larger practical problems than the methods known thus far. The new approach decomposes detailed production scheduling for batch production into batching and batch scheduling. The batching problem converts the primary requirements for products into individual batches, where the work load is to be minimized. We formulate the batching problem as a nonlinear mixed–integer program and transform it into a linear mixed–binary program of moderate size, which can be solved by standard software. The batch scheduling problem allocates the batches to scarce resources such as processing units, workers, and intermediate storage facilities, where some regular objective function like the makespan is to be minimized. The batch scheduling problem is modelled as a resource–constrained project scheduling problem, which can be solved by an efficient truncated branch–and–bound algorithm developed recently. The performance of the new solution procedures for batching and batch scheduling is demonstrated by solving several instances of a case study from process industries.     

Assembly modeling as an extension of feature-based design

The advantages and limitations of procedural and declarative approaches for product modeling are discussed. Concepts are developed for modeling all levels of product relations with a uniform set of structures and relationships. It is shown that five basic structures,Part-of, Structuring relation, Degrees of freedom, Motion limits, andFit can be used to define relationships between assemblies, parts, features, feature volume primitives, and evaluated boundaries. Generic relations which facilitate constraint specification between target and reference entities are also presented. Methods for the derivation of the location of an assembly unit from high level constraint specifications, such as mating conditions, and techniques for determining the degrees of freedom, motion limits, and assemblability are required. This can be done by uni-directional parameter derivation in the procedural approach, or by symbolic geometric reasoning or numerical equation solution in the declarative approach. The former is less expensive, easy to implement, avoids conflicts, but leads to combinatorial explosion. The latter is general, flexible, decouples constraint specification from validation, but is expensive, and may require conflict resolution.     

On the steady state of the replicating portfolio: accounting for a growth rate

For the risk management and transfer pricing of non-maturity liabilities, banks in Europe often use a so-called replicating portfolio technique. A commonly used implementation is replication of a fixed investment rule every time period. This paper deals with the development of the portfolio in the long run, when using this methodology. Applying this replicating portfolio technique yields, after a while, a steady state. Besides the straightforward result when volume is constant, we solve the steady states for the case where the funds (volume) grow with a fixed rate (e.g. due to credited interest or growth in GDP). We therefore define a system growth process, alternative to the Markov process (when volume is constant). From a transfer pricing and risk-management point of view, the resulting portfolio should satisfy certain requirements concerning return and flexibility. Once the steady state can be calculated for given growth rates, the investment policy can be specified. The importance of taking account of a growth rate is illustrated. Growth in volume implies that a different rule will converge to the desired steady state. This is illustrated analytically and with numerical examples. The purpose of the paper is not to find the ideal hedge strategy for non-maturity liabilities, but to improve the existing risk management without any implementation costs for the banks. Given the currently used methodology, accounting for a growth rate can significantly improve the risk management of non-maturity liabilities. RID="*" ID="*" I thank Anja De Waegenaere, Peter Kort and an anonymous referee for useful comments on an earlier draft.     

Automated Design and Parametrization of Mechanical Part Geometry

Variational methods for evaluating the design of mechanisms were first introduced by this group in the form of mathematical formulations generally applicable to open- and closed-loop mechanisms. This method is extended here, and demonstrated on the design of mechanical parts in the context of automatic parametrization of the geometry. The formulation is based on the development of constraint equations that govern the relationships between geometry in a mechanical part as dictated by a designer. Instead of the tedious method of specifying mathematical relations between any two geometries of the part, it is proposed to use the notion of kinematic relations inherent in the formulation relating the connectivity between joints and links. Cut-joint constraints are introduced, kinematic joints in the formulation are combined, their variations evaluated, and a Jacobian is determined. Constraint violations are then compensated to compute an assembled mechanism, hence redesigning the part. It is shown that this kinematically-driven formulation is broadly applicable to 2D and 3D models. The method and algorithm are illustrated through a number of examples.     

An introduction to smart assemblies for robust design

Research conducted over the past decade has resulted in a suite of methods for robust design which can be applied during different design stages. These methods focus on reducing the sensitivity of the design to variation without removing its causes.In this paper we propose an additional and very powerful means for achieving robustness that complements other methods developed to date. We have called this approach smart assemblies. A smart assembly has features, not otherwise required by the function of the design, which allow the design to absorb or cancel out the effects of variation.This paper provides an introduction to smart assemblies. Specifically, we define passive and active smart assemblies and provide examples of each. We discuss the close connection between smart assembly design and exactly constrained design. We present an example from industry illustrating the benefits of exactly constrained smart assemblies. We discuss a design methodology for smart assembly design and present the beginnings of a classification system for 2D smart features.     

A Mathematical Framework for the Key Characteristic Process

To maximize product quality, a product design team selects concepts and dimensions to minimize a product’s sensitivity to variation. However, even for the most robust products, it is rarely possible to transition a product into production without encountering any variation-related problems. In a complex product, it is not economically or logistically feasible to control and/or monitor the thousands of tolerances specified in a product’s drawing set. To address this problem, many organizations are using Key Characteristic (KCs) methods to identify where excess variation will most significantly affect product quality, and what product features and tolerances require special attention from manufacturing. As simple as this principle seems, most companies struggle to effectively implement KC methods because no quantitative methods to prioritize KCs exist. This paper develops a mathematical definition of a KC based on a variation propagation model. In addition, it develops a quantitative effectiveness measure used to prioritize where verification, variation reduction, and on-going monitoring should be applied. The effectiveness measure incorporates the cost of control, the benefit of control, and the expected change in process capability. The methods are illustrated using an automotive door assembly.     

Scheduling vehicles in automated transportation systems Algorithms and case study

One of the major planning issues in large scale automated transportation systems is so-called empty vehicle management, the timely supply of vehicles to terminals in order to reduce cargo waiting times. Motivated by a Dutch pilot project on an underground cargo transportation system using Automated Guided Vehicles (AGVs), we developed several rules and algorithms for empty vehicle management, varying from trivial First-Come, First-Served (FCFS) via look-ahead rules to integral planning. For our application, we focus on attaining customer service levels in the presence of varying order priorities, taking into account resource capacities and the relation to other planning decisions, such as terminal management. We show how the various rules are embedded in a framework for logistics control of automated transportation networks. Using simulation, the planning options are evaluated on their performance in terms of customer service levels, AGV requirements and empty travel distances. Based on our experiments, we conclude that look-ahead rules have significant advantages above FCFS. A more advanced so-called serial scheduling method outperforms the look-ahead rules if the peak demand quickly moves amongst routes in the system. Received: June 21, 2000 / Accepted: January 22, 2001     

A Taxonomy for Design Requirements from Corporate Customers

We have developed a taxonomy that classifies those needs of a corporation that impact product design. We call these needs corporate requirements. In contrast to the consumer or end-user requirements, corporate requirements come from internal sources such as marketing, finance, manufacturing, and service. This taxonomy allows for an organized method of gathering, managing, and retrieving the requirements. The taxonomy also helps to facilitate a broader, clearer form of Quality Function Deployment. Generic in nature, this taxonomy provides a template with which to create taxonomies for a given product within a given company or industry. We include an industrial case study to demonstrate this concept.     

Representation of geometric variations using matrix transforms for statistical tolerance analysis in assemblies

The goal of this article is to develop a tolerance representation for assemblies compatible with tolerance analysis based on a closed-form algorithm used in robotic applications. A methodology is described that represents standard Y14.5M-1982 tolerances using homogeneous 4×4 matrix transforms. Transforms represent both the nominal relations between parts and the variations caused by geometric deviations allowed by the tolerances. The analysis calculates a statistical estimate of the location of theNth part in an assembly starting from the first part or a fixture. Except forform tolerances, most types of tolerance specifications are compatible with the proposed representation. This approach is well suited to integration with CAD systems and feature-based design. Since assembly apparatus errors can be calculated using the same methodology, one can predict the relative position and angle errors between two parts about to be mated. This permits useful evaluation of assembly equipment errors, comparison of different product tolerance assignments, and calculations of assembly process capability.     

‘Signposting’, A Parameter-driven Task-based Model of the Design Process

This paper addresses the need for computer support in aerospace design. A review of current design methodologies and computer support tools is presented, and the need for further support is discussed, with particular reference to the early formative stages of the design process. A parameter-based model of design is proposed, founded on the assumption that a design process can be constructed from a predefined set of tasks. This is supported by knowledge of possible tasks in which the confidence in key design parameters is used as a basis for identifying, or signposting, the next task. A prototype implementation of the signposting model, for use in the design of helicopter rotor blades, is described and results from trials of the tool are presented. Further areas of research are discussed.     

Evaluation Metrics for the Rating and Optimization of Snap-fits

Current snap-fit design guides recommend sizing snap-fit features on the basis of insertion force and allowable strain during assembly. Retention force information in such guides is often inaccurate, although this is considered to be the primary attribute of the snap-fit after assembly. The authors contend that these (insertion force, allowable strain, retention force) are not the only critical performance criteria for snap-fit features. Designers have to contend with several other constraints and design requirements. Additional performance metrics for snap-fit features are proposed by drawing upon considerable experience with plastic part design issues. Locking ratio, dimensional and volumetric retention force, consideration of the characteristic dimension of the joint and snap-fit, feature stiffness, required over-insertion and consideration of snap-fit strength relative to part strength are proposed to supplement currently used metrics for evaluating and rating snap-fit designs. The applicability of these metrics is illustrated with real-life examples, and their merits and demerits discussed. A chart of achievable locking ratios for different snap-fit topologies is presented for use as a design tool for the initial selection of snap-fit topologies. Its use as a rational basis for selection and optimization of snap-fits is suggested. Adoption of proposed metrics will allow designers to better quantify, and thereby optimize the performance of, snap-fit features. These ideas will be built upon in the future, and used as a basis for a comprehensive snap-fit selection and detailed design tool.     

Assembly sequence influence on geometric deviations propagation of compliant parts

This paper presents a non-rigid part variation simulation method for fulfilling functionnal requirements on compliant assemblies. This method is based on the propagation of different geometrical deviations (manufacturing and assembly process defects) using the method of influence coefficient. Tolerance analysis of compliant assemblies is also achieved very early in the design stage. As a consequence, designers and manufacturing engineers can efficiently analyse the assembly design principles both in terms of installed stresses and geometric variation clearance. They can also set optimised sequences that enable ridding of geometric variations.     

On crack arrest in ceramic / metal assemblies

Brittle parts of ceramic/metal assemblies are subjected to a residual stress field generated by the fabrication. During that process, cracks are initiated and the key question is whether they propagate through the whole brittle part. The use of classical probabilistic fracture models applied to the ceramic (i.e., based on a weakest link hypothesis), allow one to conclude that cracks are likely to initiate after the manufacturing process. Consequently, a crack arrest model is proposed, based on a random toughness distribution. Applied to micro-hardness experiments, the statistical parameters are identified, and the predictive capacity of the model is analyzed. The model is then used to study the reliability of ceramic/metal assemblies during the fabrication stage.     

Numerical Modeling of a Post & Dome Snap-Fit Feature

Snap-fits are often designed using guides that rely on classic beam theory, with the basic assumption that the beam undergoes small rotations and displacements. This is a poor assumption, for they typically experience both large rotations and displacements due to loading offset from the neutral axis and axial loading. This paper investigates the performance of the post & dome feature, establishes its nomenclature, and derives the equations needed to intelligently design different variations of it. The post & dome feature was selected for analysis because it is a high performance snap-fit that is self-datuming and can withstand some shear loading in addition to retention. The design equations were generated in three steps. First, an experimental array was created using a design of experiments approach. Finite element methods and multiple regression techniques were used in lieu of beam equations models for each of the trials in the experimental array. Finally, response surface methods were used to develop response curves based on the performance data generated by the finite element models. Sensitivity data was plotted for both the main effects and selected variable interactions. The traditional benchmarks for defining high performance snap-fits are retention strength, insertion force, and insertion strain. This paper uses an expanded definition of these benchmarks that also includes locking ratio (the ratio of retention force to insertion force).     

Optimal tax depreciation lives and charges under regulatory constraints

Depreciation is not only a representation of the loss in asset-value over time. It is also a strategic tool for management and can be used to minimize tax payments. In this paper we derive the depreciation scheme that minimizes the expected value of the present value of future tax payments for two types of constraints on the depreciation method. We show how the optimal scheme depends on the discount factor and the cash flow distributions. Moreover, we find the somewhat surprising result that the way in which the optimum is affected by uncertainty depends crucially on the type of regulatory constraint. Received: January 9, 2001 / Accepted: Feburary 25, 2002     

A Theory of Complexity, Periodicity and the Design Axioms

One of the topics that has received the attention of mathematicians, scientists and engineers is the notion of complexity. The subject is still being debated, as it lacks a common definition of complexity, concrete theories that can predict complex phenomena, and the mathematical tools that can deal with problems involving complexity. In axiomatic design, complexity is defined only when specific functional requirements or the exact nature of the query are defined. Complexity is defined as a measure of uncertainty in achieving a set of specific functions or functional requirements. Complexity is related to information, which is defined in terms of the probability of success of achieving the Functional Requirements (FRs). There are two classes of complexity: time-dependent complexity and time-independent complexity. There are two orthogonal components of time-independent complexity, i.e., real complexity and imaginary complexity. The vector sum is called absolute complexity. Real complexity of coupled design is larger than that of uncoupled or decoupled designs. Imaginary complexity can be reduced when the design matrix is known. As an example of time-independent imaginary complexity, the design of a printing machine based on xerography is discussed. There are two kinds of time-dependent real complexity: time-dependent combinatorial complexity and time-dependent periodic complexity. Using a robot-scheduling problem as an example, it is shown that a coupled design with a combinatorial complexity can be reduced to a decoupled design with periodic complexity. The introduction of periodicity simplifies the design by making it deterministic, which requires much less information. Whenever a combinatorial complexity is converted to a periodic complexity, complexity and uncertainty is reduced and design simplified.     

Tolerance analysis and design of nesting forces for exactly constrained mechanical assemblies

In this research we investigate the analysis and design of nesting forces for exactly constrained mechanical assemblies. Exactly constrained assemblies have a number of important advantages over other assemblies including the ability to assemble over a wide range of conditions. Such designs often require nesting forces to keep the design properly seated. To date, little theory has been developed for the analysis and design of nesting forces. We show how the effects of tolerances on nesting forces, a key issue, can be analyzed and then apply the analysis to two example problems. Good agreement is obtained between the method and Monte Carlo simulation.