Compliant assembly variation analysis of sheet metal with shape errors based on primitive deformation patterns

2017 ◽  
Vol 232 (13) ◽  
pp. 2334-2351 ◽  
Author(s):  
Yunyong Li ◽  
Yong Zhao ◽  
Haidong Yu ◽  
Xinmin Lai
Keyword(s):  
Sheet Metal ◽  
Propagation Model ◽  
Surface Shape ◽  
Mode Analysis ◽  
Assembly Process ◽  
Variation Analysis ◽  
Compliant Assembly ◽  
Variation Propagation ◽  
Shape Errors ◽  
Deformation Patterns

In the compliant assembly of sheet metal, the performance of the product is highly related to the shape errors of surface. Therefore, variation analysis is generally required to reveal the influence principle of the components’ manufacturing variations on the surface shape errors of the product. The traditional compliant assembly variation analysis methods were used to build a variation propagation model based on characteristic points between parts and product without considering shape errors. In this paper, a new method based on primitive deformation patterns considering shape errors is proposed. The primitive deformation patterns of part can be obtained by natural mode analysis of ideal part, and the primitive deformation patterns of product can be calculated by the dynamic substructure method. The initial shape errors of part are decomposed into the individual contributions of primitive deformation patterns. Considering the force equilibrium relationship in assembly process, a variation propagation model is built based on the primitive deformation patterns between parts and product. This model reveals variation propagation in assembly process by the basic element of dimension error field (deformation patterns), which is convenient for evaluating the assembly quality. A case study on a panel parts assembly process is presented to demonstrate the proposed variation analysis method. The results show the effectiveness and accuracy of the proposed method compared with the method of finite element analysis conducted in commercial software ABAQUS.

Variation Analysis for Compliant Assembly

2000 ◽  
Author(s):  
S. Jack Hu ◽  
Yufeng Long ◽  
Jaime Camelio
Keyword(s):  
Sheet Metal ◽  
Assembly Line ◽  
Assembly Process ◽  
Variation Analysis ◽  
Assembly Lines ◽  
Compliant Assembly ◽  
Single Station ◽  
Dimensional Variation ◽  
Sheet Metal Assembly

Abstract Assembly processes for compliant non-rigid parts are widely used in manufacturing automobiles, furniture, and electronic appliances. One of the major issues in the sheet metal assembly process is to control the dimensional variation of assemblies throughout the assembly line. This paper provides an overview of the recent development in variation analysis for compliant assembly. First, the unique characteristics of compliant assemblies are discussed. Then, various approaches to variation modeling for compliant assemblies are presented for single station and multi-station assembly lines. Finally, examples are given to demonstrate the applications of compliant assembly variation models.

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.

Compliant assembly analysis including initial deviations and geometric nonlinearity, part II: Plate structure

2018 ◽  
Vol 233 (11) ◽  
pp. 3717-3732 ◽  
Author(s):  
Tao Liu ◽  
Zhi-min Li ◽  
Sun Jin ◽  
Wei Chen
Keyword(s):  
Geometric Nonlinearity ◽  
Mindlin Plate ◽  
Variation Analysis ◽  
Governing Equations ◽  
Plate Structures ◽  
Orthotropic Composite ◽  
Compliant Assembly ◽  
Variation Propagation ◽  
Springback Prediction ◽  
Assembly Analysis

Part I of this paper (Liu et al., “Compliant assembly analysis including initial deviations and geometric nonlinearity, part I: Beam structure”) has studied the variation propagation of beam structures with consideration of initial deviations and geometric nonlinearity. In practices, plate structures are more commonly used in manufacturing fields, and the attempt of this paper is to expand previous methodology for the assembly process of orthotropic composite plate structures. Similarly, initial deviations and von Kármán-type geometric nonlinearity are introduced into variation analysis model, with Mindlin plate theory accounting for shear effect. The analyzed plates are set as orthotropic composite materials, which also preserve the compatibility with isotropic metal materials. Governing equations and corresponding finite element expressions can be obtained by applying the principle of virtual work. Also, a linearized model or noninitial model can be regarded as a degradation of origin governing equations. A variation analysis approach for plate structures is proposed to make more refined assembly variation predictions with consideration of initial deviations, fixture errors, and matching deviations. The verification of the developed method is implemented with case studies on springback prediction of two composite plates assembly.

Propagation analysis of variation for fuselage structures in multi-station aircraft assembly

2018 ◽  
Vol 38 (1) ◽  
pp. 67-76 ◽  
Author(s):  
Liang Cheng ◽  
Qing Wang ◽  
Jiangxiong Li ◽  
Yinglin Ke
Keyword(s):  
Propagation Model ◽  
Analysis Approach ◽  
Good Prediction ◽  
Assembly Process ◽  
Content Type ◽  
Modeling And Analysis ◽  
Aircraft Assembly ◽  
Propagation Analysis ◽  
Variation Propagation ◽  
Large Aircraft

Purpose 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. Design/methodology/approach 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. Findings 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. Practical implications 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. Originality/value 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.

Compliant Assembly Variation Analysis Using Component Geometric Covariance

2004 ◽  
Vol 126 (2) ◽  
pp. 355-360 ◽  
Author(s):  
Jaime A. Camelio ◽  
S. Jack Hu ◽  
Samuel P. Marin
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Principal Component ◽  
Computational Effort ◽  
Deformation Pattern ◽  
Variation Analysis ◽  
Element Analysis ◽  
Compliant Assembly ◽  
Compliant Parts ◽  
Deformation Patterns

Dimensional variation is one of the most critical issues in the design of assembled products. This is especially true for the assembly of compliant parts since clamping and joining during assembly may introduce additional variation due to part deformation and springback. This paper discusses the effect of geometric covariance in the calculation of assembly variation of compliant parts. A new method is proposed for predicting compliant assembly variation using the component geometric covariance. It combines the use of principal component analysis (PCA) and finite element analysis in estimating the effect of part/component variation on assembly variation. PCA is used to extract deformation patterns from production data, decomposing the component covariance into the individual contributions of these deformation patterns. Finite element analysis is used to determine the effect of each deformation pattern over the assembly variation. The proposed methodology can significantly reduce the computational effort required in variation analysis of compliant assemblies. A case study is presented to illustrate the methodology.

Assembly variation analysis of the non-rigid assembly with a deformation gradient model

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Ibrahim Ajani ◽  
Cong Lu
Keyword(s):  
Deformation Gradient ◽  
Transformation Matrix ◽  
Propagation Model ◽  
Assembly Process ◽  
Content Type ◽  
Target Value ◽  
Gradient Model ◽  
Variation Propagation ◽  
Target Values ◽  
Gradient Models

Purpose 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. Design/methodology/approach 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. Findings 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. Originality/value 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.

Variation Analysis of Accumulative Stresses in Multistep Assembly Processes Using Output Transformation Matrices

2017 ◽  
Author(s):  
Jia Lin ◽  
Sun Jin ◽  
Cheng Zheng ◽  
Fuyong Yang ◽  
Siyi Ding
Keyword(s):  
Computer Aided Design ◽  
Structural Reliability ◽  
Single Case ◽  
Fe Model ◽  
Assembly Process ◽  
Variation Analysis ◽  
Transformation Matrices ◽  
Compliant Assembly ◽  
Geometric Variation ◽  
Output Transformation

Geometric variation produces gaps or interferences between the mating features of parts when assembling them. To accomplish the operation, forces need to be applied to deform the parts; while as a price, stresses arise around the structure and accumulate as the assembly process proceeds, which could impair the structural reliability. A tool modeling and analyzing the accumulation of assembly stresses can help us predict and control it. Associated with geometric variation, the levels of assembly stresses are variables as well, thus variation analysis of them is required rather than a single case analysis; however, research on assembly variation analysis has focused mainly on the geometric variation itself. In a previous study, we developed a compliant assembly variation analysis method which is based on a Finite Element (FE) model condensation technique of substructuring (Lin J, et al. “Compliant assembly variation analysis of aeronautical panels using unified substructures with consideration of identical parts.” Computer-Aided Design, 2014.). In this paper, by introducing Output Transformation Matrices (OTMs) into the unified substructure system, we add the analysis of assembly stresses onto that of assembly deviations: no extra modeling work is needed, but the assembly stresses within a part are recovered from its assembly deviations by OTMs. Though these OTMs need to be generated in advance, this one-off effort will be relatively small when the assembly process to be analyzed involves multiple steps. A case study on an aeronautical panel assembly is presented to illustrate the proposed method and investigate the characteristics of assembly stresses.

Dynamic prediction and compensation of aerocraft assembly variation based on state space model

2015 ◽  
Vol 35 (2) ◽  
pp. 183-189 ◽  
Author(s):  
Yujun Cao ◽  
Xin Li ◽  
Zhixiong Zhang ◽  
Jianzhong Shang
Keyword(s):  
State Space ◽  
State Space Model ◽  
Propagation Model ◽  
Small Displacement ◽  
Assembly Process ◽  
Dynamic Prediction ◽  
Content Type ◽  
Assembly Accuracy ◽  
Variation Propagation ◽  
State Space Theory

Purpose – 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. Design/methodology/approach – 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. Findings – The paper provides the predicting and compensating method for aeroplane assembly accuracy. Originality/value – This paper fulfils an identified need to study how the assembly variation propagates in the assembly process.

Modeling Variation Propagation of Multi-Station Assembly Systems With Compliant Parts

2003 ◽  
Vol 125 (4) ◽  
pp. 673-681 ◽  
Author(s):  
Jaime Camelio ◽  
S. Jack Hu ◽  
Dariusz Ceglarek
Keyword(s):  
Space Representation ◽  
Assembly Process ◽  
State Space Representation ◽  
Automotive Body ◽  
Compliant Assembly ◽  
Variation Propagation ◽  
Sources Of Variation ◽  
Dimensional Variation ◽  
Compliant Parts ◽  
And Performance

Products made of compliant sheet metals are widely used in automotive, aerospace, appliance and electronics industries. One of the most important challenges for the assembly process with compliant parts is dimensional quality, which affects product functionality and performance. This paper develops a methodology to evaluate the dimensional variation propagation in a multi-station compliant assembly system based on linear mechanics and a state space representation. Three sources of variation: part variation, fixture variation and welding gun variation are analyzed. The proposed method is illustrated through a case study on an automotive body assembly process.

Integration of in-plane and out-of-plane dimensional variation in multi-station assembly process for automotive body assembly

2019 ◽  
Vol 234 (6) ◽  
pp. 1690-1702
Author(s):  
Vahid Jandaghi Shahi ◽  
Abolfazl Masoumi
Keyword(s):  
Transfer Function ◽  
Sheet Metal ◽  
Assembly Process ◽  
Assembly Operation ◽  
Automotive Body ◽  
Variation Propagation ◽  
Out Of Plane ◽  
Dimensional Variation ◽  
Plane Direction ◽  
Assembly Operations

Automotive body assembly systems contain multiple operations in multi-station processes. One of the most critical challenges for such manufacturing systems is dimensional quality, which is affected by the accumulation and propagation of variation caused by manufacturing imperfections. However, sheet metal part compliancy behavior makes the variation modeling method extremely intricate when both rigid (in-plane) and compliant (out-of-plane) variations are considered. This paper develops a more accurate variation propagation model to describe dimensional variation of sheet metal assembly in multi-station assembly system through involving both the variation types simultaneously as well as the impacts of assembly operations on each other. In this methodology, three sources of deviations—non-ideal parts, fixture errors, and assembly operations effects—are taken into account. The variation generated in every assembly operation (placing, clamping, fastening, and releasing steps) and the variation propagation through station-to-station interaction (repositioning) are analyzed by the transfer function mechanism. In the in-plane direction, the stream of variation analysis is adopted to obtain the rigid transfer function to describe the position and orientation relationships between part and assembly element errors. For the simulation of part deformation during the assembly process in the out-of-plane direction, the compliant transfer functions are extracted by variation response methodology. A nested state space model is used to integrate the overall assembly variation by updating part geometry after each assembly operation. The capability of proposed method is illustrated through a case study on an automotive body side assembly process.

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