scholarly journals Numerical Approach for Detecting the Resonance Effects of Drilling during Assembly of Aircraft Structures

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2926
Author(s):  
Alexey Vasiliev ◽  
Sergey Lupuleac ◽  
Julia Shinder
Keyword(s):  
Contact Problem ◽  
Numerical Procedure ◽  
Numerical Approach ◽  
Mean Value ◽  
Assembly Process ◽  
Drilling Force ◽  
Resonance Effects ◽  
Stationary Analysis ◽  
Quadratic Programming Problems ◽  
Compliant Parts

This paper is devoted to the development of a numerical approach that allows quick detection of the conditions favorable for the beginning of noticeable vibrations during drilling. The main novelty of the proposed approach lies in taking into account the deviations of the assembled compliant parts during non-stationary contact analysis by means of variation simulation. The approaches to stationary analysis of assembly quality are expanded and generalized for modeling such non-stationary effects as vibration and resonance. The numerical procedure is based on modeling the stress–strain state of the assembled structures by solving the corresponding transient contact problem. The use of Guyan reduction, the node-to-node contact model and the application of the generalized α method allow the reformulation of the contact problem in terms of a series of quadratic programming problems. The algorithm is thoroughly tested and validated with commercial software. The efficiency of the developed numerical procedure is illustrated by analysis of the test joints of two aircraft panels. The unsteady process of drilling the panels with periodic drilling force was simulated. The influence of deviations in the shape of the parts on the non-stationary interlayer gap was modeled by setting different initial gaps between parts. It is shown that the oscillation amplitudes of the interlayer gap depend on the initial gaps and do not correlate with the mean value of the stationary residual gap. Thus, non-stationary analysis provides new information about the quality of the assembly process, and it should be applied if the assembly process includes periodic impact on the assembled parts.

Simulation of the Wing-to-Fuselage Assembly Process

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Sergey Lupuleac ◽  
Nadezhda Zaitseva ◽  
Maria Stefanova ◽  
Sergey Berezin ◽  
Julia Shinder ◽  
...  
Keyword(s):  
Statistical Analysis ◽  
Contact Problem ◽  
Assembly Process ◽  
Multistage Process ◽  
Stochastic Nature ◽  
Closing The Gap ◽  
Compliant Parts ◽  
Level Parallelism ◽  
Task Level

The paper presents a simulation of the Airbus A350-900 wing-to-fuselage assembly process. The latter is a complex multistage process where the compliant parts are being joined by riveting. The current research analyzes the quality of the temporary fastener arrangement. The fastener arrangement is being checked to ensure that the residual gap between joined parts is small, and the fastener loads closing the gap are calculated. The deviations of the part shape from nominal are modeled via initial gaps. A cloud of initial gaps is generated based on the statistical analysis of the available measurements assuming the stochastic nature of local gap roughness. Through the reduction of the corresponding contact problem to a quadratic programming (QP) problem and the use of efficient QP algorithms together with the task-level parallelism, the mass contact problem solving on refined grids is accomplished.

Simulation of Body Force Impact on the Assembly Process of Aircraft Parts

2019 ◽  
Author(s):  
Sergey Lupuleac ◽  
Aleksandr Smirnov ◽  
Maria Churilova ◽  
Julia Shinder ◽  
Nadezhda Zaitseva ◽  
...  
Keyword(s):  
Quadratic Programming ◽  
Contact Problem ◽  
Body Force ◽  
Numerical Approach ◽  
Manufacturing Technology ◽  
Assembly Process ◽  
Integration Process ◽  
Force Vector ◽  
Force Impact ◽  
Correction Terms

Abstract The manufacturing technology of some aircraft parts involves rotation of parts in assembly jig during the integration process. As the jig rotates, the gravity acting on the parts changes its direction. It can affect the residual gap between parts joined with temporary fasteners and lead to eccentricity of drilled holes for rivets. A numerical approach for simulation of airframe assembly process with account of this effect is discussed in the paper. The approach is based on reformulation of contact problem in terms of quadratic programming and introduction of special correction terms in the force vector. The developed approach is applied to evaluation of effect of assembly rotation on the contact quality.

scholarly journals The Indentation Rolling Resistance in Belt Conveyors: A Model for the Viscoelastic Friction

Lubricants ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 58 ◽  
Author(s):  
Nicola Menga ◽  
Francesco Bottiglione ◽  
Giuseppe Carbone
Keyword(s):  
Contact Problem ◽  
Finite Thickness ◽  
Numerical Procedure ◽  
Contact Problems ◽  
Accurate Solution ◽  
Rolling Contact ◽  
Viscoelastic Layer ◽  
Force Coefficient ◽  
Belt Conveyors ◽  
Energy Dissipated

In this paper, we study the steady-state rolling contact of a linear viscoelastic layer of finite thickness and a rigid indenter made of a periodic array of equally spaced rigid cylinders. The viscoelastic contact model is derived by means of Green’s function approach, which allows solving the contact problem with the sliding velocity as a control parameter. The contact problem is solved by means of an accurate numerical procedure developed for general two-dimensional contact geometries. The effect of geometrical quantities (layer thickness, cylinders radii, and cylinders spacing), material properties (viscoelastic moduli, relaxation time) and operative conditions (load, velocity) are all investigated. Physical quantities typical of contact problems (contact areas, deformed profiles, etc.) are calculated and discussed. Special emphasis is dedicated to the viscoelastic friction force coefficient and to the energy dissipated per unit time. The discussion is focused on the role played by the deformation localized at the contact spots and the one in the bulk of the thin layer, due to layer bending. The model is proposed as an accurate solution for engineering applications such as belt conveyors, in which the energy dissipated on the rolling contact of idle rollers can, in some cases, be by far the most important contribution to their energy consumption.

scholarly journals The dynamics of a new chaotic system through the Caputo–Fabrizio and Atanagan–Baleanu fractional operators

2019 ◽  
Vol 11 (7) ◽  
pp. 168781401986654 ◽  
Author(s):  
Muhammad Altaf Khan
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Order Parameter ◽  
Numerical Procedure ◽  
Numerical Approach ◽  
Fractional Operators ◽  
Fundamental Properties ◽  
Chaotic Model ◽  
New Chaotic System ◽  
Model Apply

The aim of this article is to analyze the dynamics of the new chaotic system in the sense of two fractional operators, that is, the Caputo–Fabrizio and the Atangana–Baleanu derivatives. Initially, we consider a new chaotic model and present some of the fundamental properties of the model. Then, we apply the Caputo–Fabrizio derivative and implement a numerical procedure to obtain their graphical results. Further, we consider the same model, apply the Atangana–Baleanu operator, and present their analysis. The Atangana–Baleanu model is used further to present a numerical approach for their solutions. We obtain and discuss the graphical results to each operator in details. Furthermore, we give a comparison of both the operators applied on the new chaotic model in the form of various graphical results by considering many values of the fractional-order parameter [Formula: see text]. We show that at the integer case, both the models (in Caputo–Fabrizio sense and the Atangana–Baleanu sense) give the same results.

Simulation and Optimization of Airframe Assembly Process

2018 ◽  
Author(s):  
Sergey Lupuleac ◽  
Nadezhda Zaitseva ◽  
Maria Stefanova ◽  
Sergey Berezin ◽  
Julia Shinder ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Statistical Analysis ◽  
Problem Solving ◽  
Contact Problem ◽  
Quality Measures ◽  
Assembly Process ◽  
Variation Analysis ◽  
Simulation And Optimization ◽  
The Mathematical Model ◽  
Variation Simulation

An approach for simulating the assembly process where compliant airframe parts are being joined by riveting is presented. The foundation of this approach is the mathematical model based on the reduction of the corresponding contact problem to a Quadratic Programming (QP) problem. The use of efficient QP algorithms enables mass contact problem solving on refined grids, which is needed for variation analysis and simulation as well as for the consequent assembly process optimization. To perform variation simulation, the initial gap between the parts is assumed to be stochastic and a cloud of such gaps is generated based on statistical analysis of the available measurements. The developed approach is illustrated with two examples, simulation of A350-900 wing-to-fuselage joining and optimization of A320 wing box assembly. New contact quality measures are discussed.

scholarly journals Assembly Variation Analysis of Aircraft Panels under Part-to-part Locating Scheme

2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
Xia Liu ◽  
Luling An ◽  
Zhiguo Wang ◽  
Changbai Tan ◽  
Xiaoping Wang ◽  
...  
Keyword(s):  
Elastic Deformation ◽  
Assembly Process ◽  
Variation Analysis ◽  
Kinematic Theory ◽  
Statistical Variation ◽  
Variation Propagation ◽  
Fixed Part ◽  
Compliant Parts ◽  
Aircraft Panels

A typical aircraft panel is the assembly consisting of a multitude of thin and lightweight compliant parts. In panel assembly process, part-to-part locating scheme has been widely adopted in order to reduce fixtures. By this locating scheme, a part is located onto the pre-fixed part/subassembly by determinant assembly (DA) holes, and temporary fasteners (e.g., spring pin) are used for joining these DA hole-hole pairs. The temporary fasteners can fasten DA hole-hole pairs in the axial and radial directions of DA holes. The fastening in the radial directions is realized by the expansion of temporary fasteners. Although the usage of temporary fasteners helps reduce the positional differences between hole-hole pairs, their clamping forces thereby may lead to elastic deformation of compliant parts/subassemblies. Limited research has been conducted on such elastic deformation produced by temporary fastener and its influence on assembly dimensional quality. This paper proposes a novel rigid-compliant variation analysis method for aircraft panel assembly, incorporating the deformation in part-to-part locating process. Based on the kinematic theory and linear elasticity deformation assumption, the variation propagation through the locating process, as well as the entire assembly process of an aircraft panel, is formulated. Then, the statistical variation analysis is performed with Monte Carlo (MC) simulation. Finally, the proposed method is validated by a case study. The result shows the deformation in the part-to-part locating process significantly impacts the assembly variations, and our method can provide a more accurate and reliable prediction.

scholarly journals Solving Nonholonomic Systems with the Tau Method

2019 ◽  
Vol 24 (4) ◽  
pp. 91 ◽  
Author(s):  
Alexandra Gavina ◽  
José M. A. Matos ◽  
Paulo B. Vasconcelos
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Numerical Procedure ◽  
Necessary Optimality Conditions ◽  
Transversality Condition ◽  
Nonholonomic Systems ◽  
Numerical Approach ◽  
Ease Of Use ◽  
Tau Method ◽  
Control Functions

A numerical procedure based on the spectral Tau method to solve nonholonomic systems is provided. Nonholonomic systems are characterized as systems with constraints imposed on the motion. The dynamics is described by a system of differential equations involving control functions and several problems that arise from nonholonomic systems can be formulated as optimal control problems. Applying the Pontryagins maximum principle, the necessary optimality conditions along with the transversality condition, a boundary value problem is obtained. Finally, a numerical approach to tackle the boundary value problem is required. Here we propose the Lanczos spectral Tau method to obtain an approximate solution of these problems exploiting the Tau toolbox software library, which allows for ease of use as well as accurate results.

scholarly journals An analytical and numerical approach to a bilateral contact problem with nonmonotone friction

2013 ◽  
Vol 23 (2) ◽  
pp. 263-276 ◽  
Author(s):  
Mikaël Barboteu ◽  
Krzysztof Bartosz ◽  
Piotr Kalita
Keyword(s):  
Contact Problem ◽  
Frictional Contact ◽  
Numerical Approach ◽  
Bundle Method ◽  
Nonconvex Problem ◽  
Proximal Bundle Method ◽  
Loss Of Contact ◽  
The Galerkin Method ◽  
Bilateral Contact ◽  
Numerical Approaches

We consider a mathematical model which describes the contact between a linearly elastic body and an obstacle, the so-called foundation. The process is static and the contact is bilateral, i.e., there is no loss of contact. The friction is modeled with a nonmotonone law. The purpose of this work is to provide an error estimate for the Galerkin method as well as to present and compare two numerical methods for solving the resulting nonsmooth and nonconvex frictional contact problem. The first approach is based on the nonconvex proximal bundle method, whereas the second one deals with the approximation of a nonconvex problem by a sequence of nonsmooth convex programming problems. Some numerical experiments are realized to compare the two numerical approaches.

Comparison of the Effects of Density and Sound Speed Variation in the Propagation of Planar Transient Waves

1992 ◽  
Vol 114 (3) ◽  
pp. 409-414
Author(s):  
J. H. Ginsberg
Keyword(s):  
Differential Equations ◽  
Material Properties ◽  
Sound Speed ◽  
Heterogeneous Media ◽  
Numerical Procedure ◽  
Mean Value ◽  
The Other ◽  
Transient Waves ◽  
One Dimensional ◽  
Spatial Grid

When expressed in the form of characteristic differential equations, the laws governing propagation of linear one-dimensional waves through heterogeneous media show that the only properties of significance are the sound speed c and the acoustic impedance ρc, either of which may vary spatially. The former occurs in the differential equations governing the (curved) characteristics, while the latter appears in the differential equations governing the evolution of particle velocity and stress along the characteristics. The present study employs an inherently stable finite difference representation of the characteristic equations, in which the spatial grid is obtained by evaluating the intersections in space-time of constant time lines with comparable increments of the characteristic variables. The numerical procedure is used to follow the propagation of a single-lobe sine pulse in cases where only ρ or c fluctuates spatially about a mean value while the other property is constant, and compares those results to the case were both material properties vary. Nonconstancy of c is shown to cause temporal shifts in waveforms, while spatial variation of ρc causes attenuation and distortion of the waveform.

Sign in / Sign up

Export Citation Format

Share Document