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Assembly variation analysis generally demands probability distributions of variation sources. However, due to small production volume in aircraft manufacturing, especially prototype manufacturing, the probability distributions are hard to obtain, and only the small-sample data of variation sources can be consulted. Thus, this paper aims to propose a variation analysis method driven by small-sample data for compliant aero-structure assembly.

First, a hybrid assembly variation model, integrating rigid effects with flexibility, is constructed based on the homogeneous transformation and elasticity mechanics. Then, the bootstrap approach is introduced to estimate a variation source based on small-sample data. The influences of bootstrap parameters on the estimation accuracy are analyzed to select suitable parameters for acceptable estimation performance. Finally, the process of assembly variation analysis driven by small-sample data is demonstrated.

A variation analysis method driven by small-sample data, considering both rigid effects and flexibility, is proposed for aero-structure assembly. The method provides a good complement to traditional variation analysis methods based on probability distributions of variation sources.

With the proposed method, even if probability distribution information of variation sources cannot be obtained, accurate estimation of the assembly variation could be achieved. The method is well suited for aircraft assembly, especially in the stage of prototype manufacturing.

A variation analysis method driven by small-sample data is proposed for aero-structure assembly, which can be extended to deal with other similar applications.

This paper aims to present a modeling and analysis approach for multi-station aircraft assembly to predict assembly variation. The variation accumulated in the assembly process will influence the dimensional accuracy and fatigue life of airframes. However, in digital large aircraft assembly, variation propagation analysis and modeling are still unresolved issues.

Based on an elastic structure model and variation model of multistage assembly in one station, the propagation of key characteristics, assembly reference and measurement errors are introduced. Moreover, the reposition and posture coordination are considered as major aspects. The reposition of assembly objects in a different assembly station is described using transformation and blocking of coefficient matrix in finite element equation. The posture coordination of the objects is described using homogeneous matrix multiplication. Then, the variation propagation model and analysis of large aircraft assembly are established using a discrete system diagram.

This modeling and analysis approach for multi-station aircraft assembly reveals the basic rule of variation propagation between adjacent assembly stations and can be used to predict assembly variation or potential dimension problems at a preliminary assembly phase.

The modeling and analysis approaches have been used in a transport aircraft project, and the calculated results were shown to be a good prediction of variation in the actual assembly.

Although certain simplifications and assumptions have been imposed, the proposed method provides a better understanding of the multi-station assembly process and creates an analytical foundation for further work on variation control and tolerance optimization.

Assembly variations, which will propagate along the assembly process, are inevitable and difficult to analyze in Aeronautical Thin‐Walled Structures (ATWS) assembly. The purpose of this paper is to present a new method for analyzing the variation propagation of ATWS with automated riveting.

The paper addresses the variation propagation model and method by first, forming a novel Stage‐State model to represent the process of automated riveting. Second, the effect of positioning error on assembly variation is defined as propagation variation (PV), and propagation matrix of key characteristic points (KCP) is discussed. Third, the effect between the variations in each stage is defined as expansion variation (EV). According to the analysis of mismatch error and the reference transformation, the expansion matrix is formed.

The model can solve the variation propagation problem of ATWS with automated riveting efficiently, which is shown as an example of this paper.

The variation obtained by the model and method presented in this paper is in conformity with the variation measured in experiments.

The propagation variation and expansion variation is proposed for the first time, and variations are studied according to novel propagation matrix and expansion matrix.

This paper aims to consider a problem of assembly sensitivity in a multi-station assembly process. The authors focus on the assembly process of aircrafts, which includes cabins and inertial navigation system (INSs), and establish the assembly process state space model for their assembly sensitivity research.

To date, the process-related errors that cause large variations in key product characteristics remains one of the most critical research topics in assembly sensitivity analysis. This paper focuses on the unique challenges brought about by the multi-station system: a system-level model for characterizing the variation propagation in the entire process, and the necessity of describing the system response to variation inputs at both station-level and single fixture-level scales. State space representation is used to describe the propagation of variation in such a multi-station process, incorporating assembly process parameters such as fixture-locating layout at individual stations and station-to-station locating layout change.

Following the sensitivity analysis in control theory, a group of hierarchical sensitivity indices is defined and expressed in terms of the system matrices in the state space model, which are determined by the given assembly process parameters.

A case study of assembly sensitivity for a multi-station assembly process illustrates and validates the proposed methodology.

Dimensional variation management is a major challenge in multi‐station sheet metal assembly processes involving complex products such as automotive body and aircraft fuselage assemblies. Very few studies have explored it at a preliminary design phase taking into consideration effects of part deformation on variation propagation, since early design phase involves the development of imprecise design models with scant or incomplete product and process knowledge. The objective of this paper is to present a variation model which can be built into the preliminary design phase taking into consideration all of the existing interactions between flexible parts and tools in multi‐station sheet metal assembly process.

The paper addresses this problem by first, presenting a beam‐based product and process model which shares the same data structure of the B‐Rep CAD models, and therefore can be embedded in CAD systems for automatic product skeletal design; second, determining the influence of part deformation, for various, differing joining and releasing schemes, on variation propagation; and third, utilizing this information to generate a vector‐based variation propagation model for multistation sheet metal assemblies.

This paper presents a beam‐based product and process model which shares the same data structure of the B‐Rep CAD models, and therefore can be embedded in CAD systems for automatic product skeletal design; determines the influence of part deformation, for various, differing joining and releasing schemes, on variation propagation; and utilizes this information to generate a vector‐based variation propagation model for multistation sheet metal assemblies.

A truck cab assembly is presented to demonstrate the advantages of the proposed model over the state‐of‐the‐art approach used in industry for sheet metal assemblies.

Modeling and analysis of dimensional variation propagation is a crucial support technology for variation reduction, product/process design evaluation and recognition of variation source. However, owing to the multi-deviation (i.e. part deviations and fixture deviations) and multi-interaction (i.e. part-to-part interaction, part-to-fixture interaction and station-to-station interaction) in assembly processes, it is difficult for designers to describe or understand the variation propagation (or accumulation) mechanism clearly. The purpose of this paper is to propose a variation propagation modeling and analysis (VPMA) method based on multiple constraints aiming at a single station.

Initially, part-to-part constraints (PPCs) and part-to-fixture constraints (PFCs) are applied for the multi-interaction of assembly, and multiple constraints graph (MCG) model is proposed for expressing PPCs, PFCs, parts, as well as the variation propagation relation among them. Then, locating points (LPs) are adopted for representing the deviations in constraints, and formulas for calculating the deviations of LPs are derived. On that basis, a linearized relation between LPs’ deviations and part’s locating deviations is derived. Finally, a wing box is presented to validate the proposed method, and the results indicate the methodology’s feasibility.

MCG is an effective tool for dimensional VPMA, which is shown as an example of this paper.

Functions of geometric constraints in dimensional variation propagation are revealed, and MCG is proposed to formulize dimensional variation propagation.

This paper aims to develop a mathematical method to analyze the assembly variation of the non-rigid assembly, considering the manufacturing variations and the deformation variations of the non-rigid parts during the assembly process.

First, this paper proposes a deformation gradient model, which represents the deformation variations during the assembly process by considering the forces and the self-weight of the non-rigid parts. Second, the developed deformation gradient models from the assembly process are integrated into the homogenous transformation matrix to model the deformation variations and manufacturing variations of the deformed non-rigid part. Finally, a mathematical model to analyze the assembly variation propagation is developed to predict the dimensional and geometrical variations due to the manufacturing variations and the deformation variations during the assembly process.

Through the case study with a crosshead non-rigid assembly, the results indicate that during the assembly process, the individual deformation values of the non-rigid parts are small. However, the cumulative deformation variations of all the non-rigid parts and the manufacturing variations present a target value (w) of −0.2837 mm as compared to a target value of −0.3995 mm when the assembly is assumed to be rigid. The difference in the target values indicates that the influence of the non-rigid part deformation variations during the assembly process on the mechanical assembly accuracy cannot be ignored.

In this paper, a deformation gradient model is proposed to obtain the deformation variations of non-rigid parts during the assembly process. The small deformation variation, which is often modeled using a finite-element method in the existing works, is modeled using the proposed deformation gradient model and integrated into the nominal dimensions. Using the deformation gradient models, the non-rigid part deformation variations can be computed and the accumulated deformation variation can be easily obtained. The assembly variation propagation model is developed to predict the accuracy of the non-rigid assembly by integrating the deformation gradient models into the homogeneous transformation matrix.

Aircraft assembly demands high position accuracy of drilled fastener holes. Automated drilling is a key technology to fulfill the requirement. The purpose of the paper is to conduct positioning variation analysis and control for an automated drilling to achieve a high positioning accuracy.

The nominal and varied connective models of automated drilling are constructed for positioning variation analysis regarding automated drilling. The principle of a strategy for reducing positioning variation in drilling, which shortens the positioning variation chain with the aid of an industrial camera-based vision system, is explored. Moreover, other strategies for positioning variation control are developed based on mathematical analysis to further reduce the position errors of the drilled fastener holes.

The propagation and accumulation of an automated drilling system’s positioning variation are explored. The principle of reducing positioning variation in an automated drilling using a monocular vision system is discussed from the view of variation chain.

The strategies for reducing positioning variation, rooted in the constructed positioning variation models, have been applied to a machine-tool based automated drilling system. The system is developed for a wing assembly of an aircraft in the Aviation Industry Corporation of China.

Propagation, accumulation and control of positioning variation in an automated drilling are comprehensively explored. Based on this, the positioning accuracy in an automated drilling is controlled below 0.13 mm, which can meet the requirement for the assembly of the aircraft.

The aim of this paper is to present a new variation modeling method for fuselage structures in digital large aircraft assembly. The variation accumulated in a large aircraft assembly process will influence the dimensional accuracy and fatigue life of airframes. However, in digital large aircraft assembly, variation analysis and modeling are still unresolved issues.

An elastic structure model based on beam elements is developed, which is an equivalent idealization of the actual complex structure. The stiffness matrix of the structure model is obtained by summing the stiffness matrices of the beam elements. For each typical stage of the aircraft digital assembly process, including positioning, coordinating, joining and releasing, variation models are built using the simplified structure model with respective loads and boundary conditions.

Using position errors and manufacturing errors as inputs, the variations for every stage of the assembly process can be calculated using the proposed model.

This method has been used in a large fuselage section assembly project, and the calculated results were shown to be a good prediction of variation in the actual assembly.

Although certain assumptions have been imposed, the proposed method provides a better understanding of the assembly process and creates an analytical foundation for further work on variation control and tolerance optimization.

Driven by the development in sensing techniques and information and communications technology, and their applications in the manufacturing system, data-driven quality control methods play an essential role in the quality improvement of assembly products. This paper aims to review the development of data-driven modeling methods for process monitoring and fault diagnosis in multi-station assembly systems. Furthermore, the authors discuss the applications of the methods proposed and present suggestions for future studies in data mining for quality control in product assembly.

This paper provides an outline of data-driven process monitoring and fault diagnosis methods for reduction in variation. The development of statistical process monitoring techniques and diagnosis methods, such as pattern matching, estimation-based analysis and artificial intelligence-based diagnostics, is introduced.

A classification structure for data-driven process control techniques and the limitations of their applications in multi-station assembly processes are discussed. From the perspective of the engineering requirements of real, dynamic, nonlinear and uncertain assembly systems, future trends in sensing system location, data mining and data fusion techniques for variation reduction are suggested.

This paper reveals the development of process monitoring and fault diagnosis techniques, and their applications in variation reduction in multi-station assembly.