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The purpose of this paper is to propose a new assembly variation analysis model to analyze assembly variation for sheet metal parts. The main focus is to analyze assembly processes based on the method of power balance.

Starting with issues in assembly variation analysis, the review shows the critical aspects of tolerance analysis. The method of influence coefficient (MIC) cannot accurately analyze the relationship between part variations and assembly variations, as the welding point is not a point but a small area. Therefore, new sensitivity matrices are generated based on the method of power balance.

Here two cases illustrate the processes of assembly variation analysis, and the results indicate that new method has higher accuracy than the MIC.

This study is limited to assembly variation analysis for sheet metal parts, which can be used in auto-body and airplane body.

This paper provides a new assembly variation analysis based on the method of power balance.

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.

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.

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.

The purpose of this paper is to propose a method to identify sources of variation in horizontal stabilizer assembly using FEA (finite element analysis) and PCA (principal component analysis).

The horizontal stabilizer is assembled by long and thin‐walled deformable aluminum components. Part‐to‐part assembly of these compliant components regularly causes difficulties associated with dimensional variations. Finite element modeling and PCA are employed to predict the propagation of variation from edge to horizontal stabilizer.

The variation analysis combined with pattern fitting method is demonstrated in a case study of the horizontal stabilizer assembly system and good performance is obtained. The results have shown that the FEA and PCA method has the capability of predicting, to an acceptable degree of accuracy, the overall geometrical variations propagation of the edges and trailing edge.

The results of this research will enhance the understanding of the compliant components deformation in assembly, and help to systematically improve the precision control efficiency in civil aircraft assembly.

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.

This study aims to present a model and analysis of automotive body outer cover panels (OCPs) assembly systems to predict assembly variation. In the automotive industry, the OCPs assembly process directly influences the quality of the automobile body appearance. However, suitable models to describe variation propagation of OCPs assembly systems remain unknown.

An adaptive state space model for OCPs assembly systems is introduced to accurately express variation propagation, including variation accumulation and transition, where two compliant deviations make impacts on key product characteristics (KPCs) of OCP, and the impacts are accumulated from welding process to threaded connection process. Another new source of variation from threaded connection is included in this model. To quantify the influence of variation from threaded connection on variation propagation, the threaded connection sensitivity matrix is introduced to build up a linear relationship between deviation from threaded connection and output deviation in KPCs. This matrix is solved by homogeneous coordinate transformation. The final deviation of KPCs will be transferred to ensure gaps and flushes between two OCPs, and the transition matrix is considered as a unit matrix to build up the transition relationship between different states.

A practical case on the left side body structure is described, where simulation result of variation propagation reveals the basic rule of variation propagation and the significant effect of variation from threaded connection on variation propagation of OCPs assembly system.

The model can be used to predict assembly variation or potential dimension problems at a preliminary assembly phase. The calculated results of assembly variation guide designers or technicians on tolerance allocation, fixture layout design and process planning.

Material variation is inevitable in volume production, especially the sheet metal thickness variation, which influences part stiffness characteristic. The purpose of this paper is to present a new variation model of compliant sheet metal assembly with consideration of material variation influence.

The theory of computational solid mechanics is used to obtain the relationship between part stiffness matrix and material characteristic. The method of influence coefficients is adopted to deduce the assembly variation model.

Material variation‐induced influence coefficients to assembly variation are obtained, and a variation model of compliant sheet metal assembly with sources of material variations, part geometric variations and fixture variations is presented. Analysis shows that material variation has an important influence to assembly variations.

A quantitative relationship between assembly variations and material thickness variations is firstly given and a new variation model of compliant sheet metal assembly is presented to help designers to more exactly predict the assembly variation and diagnose variation sources.