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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.

The purpose of this paper is to focus on optimal sensor placement for the fixture variation diagnosis of compliant sheet metal assembly process. Fixture variations are the main sources for complex automotive body dimensional failures. An effective measurement strategy can help exactly and timely diagnose these fixture variations. Research on sensor placement strategy of compliant sheet metal assembly process is not much stated formerly.

The impact principle of fixture variations is analyzed to set up the relationship between the assembly variation and fixture variations applying the method of influence coefficients and the effective independence (EI) method is used to find the optimal sensor positions based on the impact principle analysis of fixture variations.

The obtained fixture variation sensitivity matrix describes the influence of fixture variations to compliant sheet metal assembly variation and can be used for diagnosing fixture variations. The EI method can effectively solve the optimal sensor positions for compliant sheet metal assembly by a case demonstration.

The proposed method can solve the sensor placement of online assembly station for diagnosing fixture variations. It takes the compliant characteristics of sheet metal parts into account and the sensor information has much greater diagnosability than that from applying other methods.

This paper aims to clarify the predicting and compensating method of aeroplane assembly. It proposes modeling the process of assembly. The paper aims to solve the precision assembly of aeroplane, which includes predicting the assembly variation and compensating the assembly errors.

The paper opted for an exploratory study using the state space theory and small displacement torsor theory. The assembly variation propagation model is established. The experiment data are obtained by a real small aeroplane assembly process.

The paper provides the predicting and compensating method for aeroplane assembly accuracy.

This paper fulfils an identified need to study how the assembly variation propagates in the assembly process.

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.

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.

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.

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.

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.

This paper aims to present a combination modeling method using multi-source information in the process to improve the accuracy of the dimension propagation relationship for assembly variation reduction.

Based on a variable weight combination prediction method, the combination model that takes the mechanism model and data-driven model based on inspection data into consideration is established. Furthermore, the combination model is applied to qualification rate prediction for process alarming based on the Monte Carlo simulation and also used in engineering tolerance confirmation in mass production stage.

The combination model of variable weights considers both the static theoretical mechanic variation propagation model and the dynamic variation relationships from the regression model based on data collections, and provides more accurate assembly deviation predictions for process alarming.

A combination modeling method could be used to provide more accurate variation predictions and new engineering tolerance design procedures for the assembly process.