Luc Laperrière

GAPP: A generative assembly process planner

Abstract This paper presents results of exhaustive research in automated assembly planning. A generative assembly process planner (GAPP) has been developed that takes as input a solid model of the product to be assembled and outputs its feasible assembly sequences. Once the product has been modeled as a solid using a commercial solid modeler, the resulting solid models boundary representation (B-Rep) file is interpreted by the GAPP to generate mating information among parts in the form of a relational graph. This graph becomes the input of a search graph process whose constrained expansion reveals all feasible assembly sequences from a geometric, stability, and accessibility point of view. The relative goodness of different feasible assembly sequences can be determined using pertinent criteria such as the number of reorientations involved or the clustering of similar assembly operations into successive ones. The expansion engine is very flexible and enables many different types of assembly problems to be handled uniformly, for example, finding disassembly repair sequences not requiring complete product disassembly or generating assembly sequences that force the building of predefined subassemblies. Examples with real industrial products are provided to illustrate the potential of using this tool.

Statistical tolerance analysis using the unified Jacobian–Torsor model

This paper presents the results of ongoing research aimed at developing an integrated computer-aided tolerancing tool. A unified Jacobian–Torsor approach has been developed for deterministic (worst case) computer-aided tolerancing. The paper describes how one can use the same set of interval-based deterministic equations in a statistical context. The nature of the resulting equations lends itself to very fast computations to determine the percentage of rejected assemblies produced given some statistical distribution of the tolerances of their constituent parts. An example application is also presented to illustrate the use of the developed tool.

Monte Carlo simulation of tolerance synthesis equations

This paper presents results on ongoing research aimed at developing an integrated computer-aided tolerancing tool. Starting with explicit tolerance analysis equations used to model the relationship between a parts functional elements and an assemblys functional requirements, the reverse synthesis equations are obtained using a simple Jacobian inversion scheme. The explicit nature of the resulting equations lend themselves to conventional Monte Carlo simulation techniques to determine the percentage of rejects being produced given some statistical distributions of the tolerances appearing in these equations. An example is presented that will provide insight on the merits of the developed method.

Re-Design of Mechanical Assemblies using the Unified Jacobian-Torsor Model for Tolerance Analysis

this paper describes how the unified Jacobian-Torsor model can be used for the redesign of assembly tolerances. Through a numerical and graphical approach, the designer is guided into choosing his tolerances. After having identified a functional requirement (FR) and the functional elements (FEs) of the dimensional chain, it becomes possible to compute the percentage contribution of each FE to the FR. A percentage contribution chart tells the designer how each dimension has contributed to the total FR. Once these contributions have been identified, we proceed to modify the most critical tolerance zones to respect the requirements imposed by the designer. The results are evaluated by comparing the predicted variation with the corresponding specified design requirements. Then, the contributions can be used to help decide which tolerance to tighten or loosen. This study has been developed for Worst-Case approach. Finally, an example application is presented to illustrate our methodology.

Tolerance Analysis And Synthesis Using Virtual Joints

This paper presents the results of a research aiming at mathematically modeling the effects of tolerances buildups in close kinematic tolerance chains. The model consists of associating a set of six virtual joints, three for small translations and three for small rotations, to every pair of functional elements in a tolerance chain. These virtual joints can therefore simulate the effects of positional and orientational inaccuracies between two functional elements of the same part which are assumed to result from manufacturing precision limits. The mathematical model is obtained by first associating a coordinate frame to every virtual joint. Transformations matrices describing the global position and orientation of every frame with respect to a base frame are then computed. The effects of small translations and small rotations of every virtual joint on a point of interest in the chain (in particular on the functional requirement) can be computed using standard Jacobian matrices, which are easily obtained once the transformations matrices have been figured out. The model is in the form of six equations relating the new position and orientation of a point of interest in the chain (in cartesian space) to the small dispersions of the functional elements of the chain (in joint space) as simulated by possible moves about their virtual joints. A detailed example is provided that will illustrate the use of the developed model.

Experimental characterization of short flax fiber mat composites: tensile and flexural properties and damage analysis using acoustic emission

AbstractnIn this work, tensile and flexural tests are realized on composites reinforced with short flax fibers mats produced by a papermaking process. Plates are molded with different fiber volume contents (Vf), and to support the analysis, acoustic emission (AE) is coupled to test samples to follow the evolution of different damage modes using a multivariable analysis to classify the acoustic events. It is shown that the tensile and flexural properties increase with Vf up to a critical value of about 40%, above which they start to decrease. The contribution of each damage mode in the global failure of the composites is calculated, and their effect in the evolution of mechanical properties is discussed. The results show that compared to the tensile tests, AE events of flexural tests appear at much higher strains, with considerably lower cumulated energies, reflecting the low level of AE events attributed to matrix microcracking. The AE analysis also reveals a clear domination of fiber–matrix friction and fiber pullout mode of fracture, raising the importance of the adhesion of flax fibers–epoxy matrix. The decrease in Young’s modulus and strength at Vf above 40% is in a large measure explained by a poor fiber–matrix adhesion.

A Unified Jacobian-Torsor Model for Analysis in Computer Aided Tolerancing

This paper presents a unified model for computer-aided tolerancing. It combines the benefits of the Jacobian matrix model and the torsor (or screw) model. The former is based on small displacements modeling of points using 6x6 transformation matrices of open kinematic chains in robotics. The latter models the boundaries of 3-D tolerance zones resulting from a feature’s small displacements using a torsor representation with constraints. The proposed unified model expands the functionalities of the Jacobian model under two important aspects. First, the punctual small displacement variables of the former Jacobian formulation are now considered as intervals formulated and solved using interval-based arithmetic. The equations describing the bounds within which the feature is permitted to move, which are the constraint equations of the torsor formulation, are applied on the unified model. Second, some of the small displacement variables used in the model are eliminated due to the invariant nature of the movements they generate with respect to the toleranced feature. This standard result of the torsor formulation is applied to the unified model. The effect of this is to significantly reduce the unified model size. A example application is also presented.

Modeling Dispersions Affecting Pre-Defined Functional Requirements of Mechanical Assemblies Using Jacobian Transforms

Assuming that a method exists for exhaustively generating 3-D tolerance chains around a desired functional requirement, this paper describes a method to mathematically quantify the relationship between the effects that the functional elements dispersions implied in a chain have on the dispersions of the desired functional requirement. This is achieved by using the concept of six virtual joints associated to each functional element implied in a chain. These virtual joints then become the basis for modeling virtual kinematic chains around the desired functional requirement. By associating each virtual joint with a coordinate frame, the impact of various small displacements of the individual functional elements on the overall functional requirement can be computed using a Jacobian matrix.

Identifying and Quantifying Functional Elements Dispersions During Functional Analysis

This paper presents a methodology for supporting the designer during one of the most important stages of mechanical design: functional analysis. The mechanism to be analysed is first represented in a Functional Element Graph. The designer must then identify some Functional Requirements between elements in this graph, typically in the form of critical toleranced dimensions or toleranced gaps. For each such Functional Requirement, a systematic graph growing algorithmic engine then traverses the Functional Element Graph in order to build a subgraph consisting of candidate Functional Element pairs possibly affecting the Functional Requirement. For each Functional Element pair identified in the process, a list of its possible dispersions is established through an associative table. Once the dispersions have been identified, a set of simple rules is finally used to quantify each dispersion and translate it into a possible dimensional or geometric tolerance interval on the corresponding Functional Element pairs. An example is used throughout the paper to illustrate the proposed approach.

Framework proposal for a modular approach to tolerancing

In current engineering practices, tolerancing activities are most often being done at the detail design phase, once drawings have been generated. The effects of tolerances are then propagated to other views of the product, such as process planning or quality control, where they will dictate choices of means and methods. Such an approach goes against current trend in product design processes and concurrent engineering.