On-Chip Assessment of Scattering in the Response of Si-Based Microdevices

The response of micromachines to the external actions is typically affected by a scattering, which is, on its own, induced by their microstructure and by stages of the microfabrication process. The progressive reduction in size of the mechanical components, forced by a path towards (further) miniaturization, has recently enhanced the outcomes of the aforementioned scattering, and provided a burst in research activities to address issues linked to its assessment. In this work, we discuss the features of an on-chip testing device that we purposely designed to efficiently estimate the two major sources of scattering affecting inertial, polysilicon-based micromachines: the morphology of the silicon film constituting the movable parts of the device, and the etch defect or over-etch induced by microfabrication. The coupled electro-mechanical behavior of the statically determinate movable (micro)structure of the on-chip device has been modeled via beam bending theory, within which the aforementioned sources of scattering have been accounted for through local fluctuating fields in the compliant part of the structure itself, namely the supporting spring. The proposed stochastic model is shown to outperform former ones available in the literature, which neglected the simultaneous and interacting effects of the two mentioned sources on the measure response. The model can fully catch the scattering in the C–V plots up to pull-in, hence, also in the nonlinear working regime of the device.

Nonlinear mechanical model of the shaft of a roll forming mill and parameter identification

Roll forming is a continuous process in which a moving metal sheet passes through numerous pairs of opposing forming rolls. The shafts of the roll forming mill are equipped with these rolls and must be set up and aligned to achieve the required final profile of the sheet. The practically relevant task of predicting the profile geometry of this incremental rolling process with varying characteristics of the metal sheet entering the mill requires an accurate description of the stiffness behavior of the shaft with rolls, which is the most compliant part of the roll forming mill. In this paper, the measured force-deflection characteristic of the shaft without rolls is compared with predictions of various theoretical models, followed by the adoption of the shear deformable beam model of the shaft with nonlinear elastic supports in the bearings. The coefficients of the cubic stiffness characteristics of the rotational springs as well as the effective length between the supports are identified based on the experimental data for the deflections, measured along the shaft for various loading levels. The theoretical predictions are obtained via the nonlinear finite element model of the shaft. The model thus provided shows high accuracy compared with the measurements. The paper’s results serve as a foundation for models to predict the stiffness of shafts with rolls.

Optimal Design of Fixture Layout for Compliant Part With Application in Ship Curved Panel Assembly

In a ship assembly process, a large number of compliant parts are involved. The ratio of the part thickness to the length or the width is typically 0.001–0.012. Fixture design is a critical task in the ship assembly process due to its impact on the deformation and dimensional variation of the compliant parts. In current practice, fixtures are typically uniformly distributed under the part to be assembled, which is non-optimal, and large dimensional gaps may occur during assembly. This paper proposed a methodology for the optimal design of the fixture layout in the ship assembly process by systematically integrating direct stiffness method and simulated annealing algorithm, which aims to minimize dimensional gaps along the assembly interface to further improve the quality and efficiency of seam welding. The case study shows that the proposed method significantly reduced the dimensional gaps of the compliant curved panel parts in a ship assembly process.

Numerical and experimental investigation of bulk stress distribution in edge under different clamping sequence

Purpose The edge is a typical aero-structural compliant part, whose length-width ratio is about 60:1 and height-thickness ratio is about 30:1. Distortion of the edge is mainly caused by the bulk stresses which come from the manufacturing process of the plates. This paper aims to investigate the effect of clamping sequence on the bulk stress distribution in the edge. Design/methodology/approach The paper conducts the numerical and experimental investigations to predict the bulk stress distribution in the edge under different clamping sequences. A finite element model of the plate with residual stress after quenching and stretching is constructed. The edge is milled from the plate numerically and is ready for clamping. The contact model between the clamper and the edge is constructed to simulate the clamping process. Then the edge is virtually clamped in different clamping sequences, and different deformations and bulk stresses are obtained. An experimental edge milled from the plate and a designed clamping platform are used to precisely control clamping force to verify the effect of clamping sequence on the bulk stress distribution in the edge. The experimental edge’s distortions, relative displacements between the edge and the clamper and clamping forces validate the proposed numerical model. Findings The primary cause of bulk stress redistribution is the friction between the rigid clamper and the compliant edge. The edge exhibits different deformation under different clamping sequences because of its compliant characteristics. Originality/value The proposed numerical model of the edge could predict the bulk stress distribution in the edge under different clamping sequence. The developed clamping platform could be used to conduct clamping experiments, including experiments with different clamping forces, sequences and different clamping positions. It will help to systematically improve the compliant assembling efficiency in civil aircraft industry.

Study on the Effect of Clamping Sequence on Bulk Stress Redistribution of Long Edge

For a given assembly process, fixture-related operations contribute to the dimensional variations of compliant part. When the manufactured components are within the specified tolerances, the bulk stresses distribution of the assembly are respected. In addition to fixture geometric errors and clamping forces, the clamping sequence can also affect part bulk stress redistribution. This paper presents a numerical simulation of bulk stress redistribution in a long edge assembling with different clamping sequences. A finite element model of the plate with residual stresses after quenching and stretching is constructed. The edge is milled from the numerical plate, and the edge with the initial deformation and residual stresses is ready for clamping. The contact model between the clamper and edge is constructed to simulate the practical clamping process, especially considering the friction contact between the clamper and edge. Then the edge is virtually clamped in different clamping sequences, and its deformation and bulk stresses are obtained. The simulation results show that there are differences in the stains of edge under different clamping sequences, and the edge’s bulk stresses under different clamping sequences are different with each other also. The proposed numerical model could predict the edge’s bulk stresses under different clamping sequences. It will help obtaining optimal stresses of the edge by certain clamping sequence, and help systematically improving the compliant assembling efficiency in civil aircraft industry.

Fault Failure Diagnosis for Compliant Assembly Structures Using Statistical Modal Analysis

This paper develops a new diagnostics methodology for N-2-1 fixtures used in assembly processes with compliant parts. The developed methodology includes: (i) the predetermined CAD-based dimensional variation fault patterns model; (ii) data-based dimensional variation fault model; and (iii) the fault mapping procedure isolating the unknown fault. The CAD-based variation fault pattern model is based on the piece-wise linear bi-partitioning of compliant part into deformed (faulty) and un-deformed regions. Data-based dimensional variation fault models are based on the statistical modal analysis (SMA) which allow to model part deformation with varying number of deformation modes. It is proved in the paper that these independent deformation modes are equivalent to the CAD-based faults models obtained in (i). The fault mapping procedure allows to diagnose the unknown fault by comparing the unknown fault variation pattern obtained from the SMA model with one of the predetermined CAD-based fault patterns. One industrial case study from an automotive roof framing assembly illustrates the proposed method.

Variation Simulation of Fixtured Assembly Processes for Compliant Structures Using Piecewise-Linear Analysis

While variation analysis methods for compliant assemblies are becoming established, there is still much to be done to model the effects of multi-step, fixtured assembly processes statistically. A new method is introduced for statistically analyzing compliant part assembly processes using fixtures. This method yields both a mean and a variant solution, which can characterize an entire population of assemblies. The method, called Piecewise-Linear Elastic Analysis, or PLEA, is developed for predicting the residual stress, deformation and springback variation resulting from fixtured assembly processes. A comprehensive, step-by-step analysis map is presented for introducing dimensional and surface variations into a finite element model, simulating assembly operations, and calculating the error in the final assembly. PLEA is validated on a simple, laboratory assembly and a more complex, production assembly. Significant modeling issues are resolved as well as the comparison of the analytical to physical results.

Modeling Compliant Part Assembly: Mechanics of Deformation and Contact

This paper describes an approach to model the mechanics of assembly by assuming parts are compliant. The approach involves a model of contact between compliant bodies based on variational inequalities. This approach has a number of advantages over current finite element codes, which rely on traditional variational approaches such as penalty force methods and Lagrange multipliers to resolve multiple unknown contact conditions. From a mathematical point of view, contact problems among compliant parts are particularly difficult to handle due to the fact that contact constraints are not permanently active, but depend on deformations. They are inherently non-linear and irreversible in character. To obtain a more mathematically robust way of modeling contact, we present a variational inequalities based approach that produces a quadratic programming (QP) problem. The QP is solved to resolve contact situations and obtain the mechanics of parts during assembly. We apply the method to simulate and design aircraft assembly processes.