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A new deviation propagation model considering the form defects in compliant assembly process is proposed. The purpose of this paper is to analyze the deviation propagation by using the basic deviation fields. In particular, each basic deviation field is defined with a generalized compliance matrix of part.

First, the form defects of parts may be decomposed into a linear combination of basic deviation fields, which are constructed by the eigen-decomposition of the structure stiffness of parts with ideal dimensions. Each basic deviation field is defined with a generalized compliance of part. Moreover, by analyzing the relationship between the basic deviation fields before and after assembling process, a new sensitive matrix is obtained in which each value expresses the correlation of a basic deviation field between the parts and the assembly.

This model may solve the deviation propagation problems of compliant assembly with considering form defects. Here, one case is used to illustrate the deviation propagation in the assembly process. The results indicate that the proposed method has higher accuracy than the method of influence coefficient when the entire deviation fields of parts are considered. Moreover, the numerical results with the proposed method basically agree with the experimental measurements.

Owing to the hypothesis of linear superposition of basic deviation fields, the research in this paper is limited to the parts with linear elastic deformation. However, the entire form defects of parts are considered rather than the deviations of the local feature points. It may be extended to analyze the three-dimensional deviations of complex thin-walled parts.

A deviation propagation model considering parts form defects is developed to achieve more accurate predictions of assembly deviation by using the basic deviation fields.

The structure stiffness is greatly affected by the fixture constraints during assembly due to the flexibility of large-scale thin-walled structures. The compliant deformation of structures is usually not consistent for the non-uniform stiffness in various clamping schemes. The purpose of this paper is to investigate the correlation between the assembly quality and the clamping schemes of structures with various initial deviations and geometrical parameters, which is based on the proposed irregular quadrilateral plate element via absolute nodal coordinate formulation (ANCF).

Two typical clamping schemes are specified for the large-scale thin-walled structures. Two typical deviation modes are defined in both free and clamping states in the corresponding clamping schemes. The new irregular quadrilateral plate element via ANCF is validated to analyze the compliant deformation of assembled structures. The quasi-static force equilibrium equations are extended considering the factors of clamping constraints and geometric deviations.

The initial deviations and geometrical parameters strongly affect the assembly deviations of structures in two clamping schemes. The variation tendencies of assembly deviations are demonstrated in details with the circumferential clamping position and axial clamping position in two clamping schemes, providing guidance to optimize the fixture configuration. The assembly quality of structures with deviations can be improved by configuration synthesis of the clamping schemes.

Typical over-constraint clamping schemes and deviation modes in clamping states are defined for large-scale thin-walled structures. The plate element via ANCF is extended to analyze the assembly deviations of thin-walled structures in various clamping schemes. Based on the proposed theoretical model, the effects of clamping schemes and initial deviations on the deformation and assembly deviation propagation of structures are investigated.

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.

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.

Thin-walled structures inevitably always have manufacturing deviations, which affects the assembly quality of mechanical products. The assembly quality directly determines the performances, reliability and service life of the products. To achieve the automatic assembly of large-scale thin-walled structures, the sizing force of the structures with deviations should be calculated, and its assembling ability should be studied before assembly process. The purpose of this study is to establish a precise model to describe the deviations of structures and to study the variation propagation during assembly process.

Curved thin-walled structures are modeled by using the shell element via the absolute nodal coordinate formulation. Two typical deviation modes of the structure are defined. The generalized elastic force of shell elements with anisotropic materials is deduced based on a continuum mechanics approach to account for the geometric non-linearity. The quasi-static method is introduced to describe the assembly process. The effects of the deviation forms, geometrical parameters of the thin-walled structures and material properties on assembly quality are investigated numerically.

The geometric non-linearity of structure and anisotropy of materials strongly affect the variation propagation and the assembly quality. The transformation and accumulation effects of the deviations are apparent in the multiple assembly process. The constraints on the structures during assembly can reduce assembly deviation.

The plate element via the absolute nodal coordinate formulation is first introduced to the variation propagation analysis. Two typical shape deviation modes are defined. The elastic force of structures with anisotropic materials is deduced. The variation propagation during the assembly of structures with various geometrical and material parameters is investigated.

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.

The assembly quality of complex products is pivotal to their lifecycle performance. Assembly precision analysis (APA) is an effective method used to check the feasibility and quality of assembly. However, there is still a need for a systematic approach to be developed for APA of kinematic mechanisms. To achieve more accurate analysis of kinematic assembly, this paper aims to propose a precision analysis method based on equivalence of the deviation source.

A unified deviation vector representation model is adopted by considering dimension deviation, geometric deviation, joint clearance and assembly deformation. Then, vector loops and vector equations are constructed, according to joint type and deviation propagation path. A combined method, using deviation accumulation and sensitivity modeling, is applied to solve the kinematic APA of complex products.

When using the presented method, geometric form deviation, joint clearance and assembly deformation are considered selectively during tolerance modeling. In particular, the proposed virtual link model and its orientation angle are developed to determine joint deviation. Finally, vector loops and vector equations are modeled to express deviation accumulation.

The proposed method provides a new means for the APA of complex products, considering joint clearance and assembly deformation while improving the accuracy of APA, as much as possible.

Manufacturing errors, which will propagate along the assembly process, are inevitable and difficult to analyze for complex products, such as aircraft. To realize the goal of precise assembly for an aircraft, with revealing the nonlinear transfer mechanism of assembly error, a set of analytical methods with response to the assembly error propagation process are developed. The purpose of this study is to solve the error problems by modeling and constructing the coordination dimension chain to control the consistency of accumulated assembly errors for different assemblies.

First, with the modeling of basic error sources, mutual interaction relationship of matting error and deformation error is analyzed, and influence matrix is formed. Second, by defining coordination datum transformation process, practical establishing error of assembly coordinate system is studied, and the position of assembly features is modified with actual relocation error considering datum changing. Third, considering the progressive assembly process, error propagation for a single assembly station and multi assembly stations is precisely modeled to gain coordination error chain for different assemblies, and the final coordination error is optimized by controlling the direction and value of accumulated error range.

Based on the proposed methodology, coordination error chain, which has a direct influence on the property of stealthy and reliability for modern aircrafts, is successfully constructed for the assembly work of the jointing between leading edge flap component and wing component at different assembly stations.

Precise assembly work at different assembly stations is completed to verify methodology’s feasibility. With analyzing the main comprised error items and some optimized solutions, benefit results for the practical engineering application showing that the maximum value of the practical flush of the profiles between the two components is only 0.681 mm, the minimum value is only 0.021 mm, and the average flush of the entire wing component is 0.358 mm, which are in accordance with theoretical calculation results and can successfully fit the assembly requirement. The potential user can be the engineers for manufacturing the complex products.

This paper aims to provide a precision assembly method to improve the aircraft engine quality of initial unbalance with the purpose of founding the process for mass eccentricity propagation and demonstration of assembly process. The proposed method can be used for assembly guidance, tolerance allocation and so on, especially for the assembly with a large number of rotors and the assembly requirements of initial unbalance and coaxiality in high precision.

This paper proposes a constrained optimization-build method to minimize initial unbalance of aircraft engine assembly, which takes amount of unbalance and concentricity of each rotor into account. A constrained nonlinear programming model is extracted by choosing the initial unbalance as the objective function, and choosing the coaxiality and assembly orientations as the nonlinear constraints. The initial unbalance is reduced stage-by-stage by controlling the assembly angle of each rotor.

The validity and accuracy of the proposed method is verified by the multistage rotors assembly through experiments run with the measuring instruments. Compared with the direct-build method, the initial unbalance of final assembly using proposed method is reduced by 22.2% in four rotors assembly.

Different from the geometric eccentricity propagation control methods to reduce the initial unbalance indirectly, this paper establishes mass eccentric propagation model in multistage rotors assembly of aircraft engine for the first time. It provides a new idea to establish the relationship between the amount of unbalance of each rotor and the initial unbalance of multistage rotors.

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.