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.

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.

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.

An assembly sensitivity analysis method based on state space model

2017 ◽  
Vol 37 (2) ◽  
pp. 249-259 ◽  
Author(s):  
Xin Li ◽  
Jianzhong Shang ◽  
Hong Zhu
Keyword(s):  
Sensitivity Analysis ◽  
State Space ◽  
Process Parameters ◽  
State Space Model ◽  
System Level ◽  
System Response ◽  
Assembly Process ◽  
Content Type ◽  
Space Model ◽  
Variation Propagation

Purpose 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. Design/methodology/approach 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. Findings 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. Originality/value A case study of assembly sensitivity for a multi-station assembly process illustrates and validates the proposed methodology.

Combination modeling of auto body assembly dimension propagation considering multi-source information for variation reduction

2019 ◽  
Vol 39 (4) ◽  
pp. 514-522
Author(s):  
Yinhua Liu ◽  
Shiming Zhang ◽  
Guoping Chu
Keyword(s):  
Modeling Method ◽  
Propagation Model ◽  
Source Information ◽  
Content Type ◽  
Variation Reduction ◽  
Combination Model ◽  
Model Based ◽  
Variation Propagation ◽  
Variable Weight ◽  
Assembly Deviation

PurposeThis 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.Design/methodology/approachBased 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.FindingsThe 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.Originality/valueA combination modeling method could be used to provide more accurate variation predictions and new engineering tolerance design procedures for the assembly process.

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.

A modification of DMVs based state space model of variation propagation for multistage machining processes

2017 ◽  
Vol 37 (4) ◽  
pp. 381-390 ◽  
Author(s):  
Fuyong Yang ◽  
Sun Jin ◽  
Zhimin Li
Keyword(s):  
Current Model ◽  
Propagation Model ◽  
Machining Processes ◽  
Motion Vectors ◽  
Content Type ◽  
Model Based ◽  
Differential Motion ◽  
Variation Propagation ◽  
Current Variation ◽  
Differential Motion Vectors

Purpose Complicated workpiece, such as an engine block, has special rough locating datum features (i.e. six independent datum features) due to its complex structure. This locating datum error cannot be handled by current variation propagation model based on differential motion vectors. To extend variation prediction fields, this paper aims to solve the unaddressed variation sources to modify current model for multistage machining processes. Design/methodology/approach To overcome the limitation of current variation propagation model based on differential motion vectors caused by the unaddressed variation sources, this paper will extend the current model by handling the unaddressed datum-induced variation and its corresponding fixture variation. Findings The measurement results of the rear face with respect to the rough datum W and the pan face with respect to the hole Q by coordinate measuring machine (CMM) are −0.006 mm and 0.031 mm. The variation results for rear face and pan face predicted by the modified model are −0.009 mm and 0.025 mm, respectively. The discrepancy of model prediction and measurement is very small. Originality/value This paper modifies the variation propagation model based on differential motion vectors by solving the unaddressed variation sources, which can extend the variation prediction fields for some complicated workpiece and is useful in the future work for many fields, such as process monitoring, fault diagnosis, quality-assured setup planning and process-oriented tolerancing.

Research on risk spread model of industrial chain

2014 ◽  
Vol 4 (2) ◽  
pp. 328-338 ◽  
Author(s):  
Yanfeng Chu ◽  
Mei-Mei Dai
Keyword(s):  
Risk Communication ◽  
External Environment ◽  
Chain Complex ◽  
Propagation Model ◽  
Normal Operation ◽  
Design Algorithm ◽  
Content Type ◽  
Industry Chain ◽  
Industrial Chain ◽  
Spread Model

Purpose – The industrial chain network is a complex system consisted by many members of the enterprise, and the complex relationship and the interaction with the external environment among the node enterprises and the existence of various uncertainty all increase the risk of the industry chain. The risk of some individual node enterprises will not only affect the normal operation but also spread the risk to other enterprises by network relationship because of their own mismanagement or deterioration of the external environment. The purpose of this paper is to make an attempt to establish the risk spread model of the industrial chain based on complex networks. Design/methodology/approach – By improving Lobos disaster diffuse model, the paper introduces two indexes: the risk spread range and the risk propagation velocity to measure of industrial chain risk communication effects, and design algorithm for industrial chain complex network structure. The risk spread range can be used to measure the coverage of the risk communication influence produced by the propagation enterprises in the industry chain and to analyse the risk spread breadth on the industrial chain network .The speed index of risk communication represents the total numbers of infection enterprises in unit simulation time. Findings – This paper proposes the universal industrial chain risk propagation model. Originality/value – Through proposed algorithm constructs industrial chain network, and enterprise class divide, the importance of the product chain enterprises in the industry chain is strengthened.

Comprehensive identification of aircraft coordination feature based on complete importance modeling and its engineering application

2018 ◽  
Vol 38 (4) ◽  
pp. 398-411 ◽  
Author(s):  
Feiyan Guo ◽  
Fang Zou ◽  
Jian Hua Liu ◽  
Bo Zhao ◽  
Zhongqi Wang
Keyword(s):  
Engineering Application ◽  
Laboratory Method ◽  
Correction Coefficient ◽  
Assembly Process ◽  
Quality Loss ◽  
Content Type ◽  
Aircraft Manufacturing ◽  
Close Relationship ◽  
Geometric Size ◽  
Assembly Precision

Purpose Coordination feature (CF) is the information carrier in dimension and shape transfer process in aircraft manufacturing. The change of its geometric size, shape, position or other attributes would affect the consistency of accumulated errors between two or more assemblies. To identify these “key characteristics” that have a close relationship with the assembly precision, a comprehensive method was developed under digital manufacturing environment, which was based on importance calculation. The multi-hierarchy and multi-station assembly process of aircraft products were also taken into consideration. Design/methodology/approach First, the interaction and evaluation relationship between components at different manufacturing stages was decomposed with a hierarchical net. Second, to meet coordination accuracy requirements, with the integrated application of Taguchi quality loss function, accuracy principal and error correction coefficient H, the quality loss between target features and candidate features at adjacent assembly hierarchies were calculated, which was based on their precision variation. Third, the influence degree and affected degree of the features were calculated with DEMATEL (decision-making trial and evaluation laboratory) method, and the concepts of centrality degree index and cause degree index were proposed for calculating the complete importance degree to eventually identify the CFs. Findings Based on the proposed methodology, CFs, affecting the skin profile and the flush coordination accuracy, were successfully identified at different assembly hierarchies to a certain type of wing flap component. Originality/value Benefit results for the engineering application showed that the deviation of skin profile was more accurate than before, and the tolerance was also closer to the centerline of required assembly precision range. Moreover, the stability in the assembly process was increased by 26.9 per cent, which could bring a higher assembly quality and an enhancement on aircraft’s flight performance.

On the state independency and log-linearity of error propagation for discrete group affine systems with application to attitude estimation

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Jiaolong Wang ◽  
Chengxi Zhang ◽  
Jin Wu
Keyword(s):  
Error Propagation ◽  
Discrete Group ◽  
Attitude Estimation ◽  
The State ◽  
Propagation Model ◽  
Rigorous Proof ◽  
Affine Systems ◽  
Content Type ◽  
Physical Systems ◽  
Propagation Properties

Purpose This paper aims to propose a general and rigorous study on the propagation property of invariant errors for the model conversion of state estimation problems with discrete group affine systems. Design/methodology/approach The evolution and operation properties of error propagation model of discrete group affine physical systems are investigated in detail. The general expressions of the propagation properties are proposed together with the rigorous proof and analysis which provide a deeper insight and are beneficial to the control and estimation of discrete group affine systems. Findings The investigation on the state independency and log-linearity of invariant errors for discrete group affine systems are presented in this work, and it is pivotal for the convergence and stability of estimation and control of physical systems in engineering practice. The general expressions of the propagation properties are proposed together with the rigorous proof and analysis. Practical implications An example application to the attitude dynamics of a rigid body together with the attitude estimation problem is used to illustrate the theoretical results. Originality/value The mathematical proof and analysis of the state independency and log-linearity property are the unique and original contributions of this work.

Optimizing assembly sequence planning using precedence graph-based assembly subsets prediction method

2019 ◽  
Vol 40 (2) ◽  
pp. 361-375 ◽  
Author(s):  
Nan Zhang ◽  
Zhenyu Liu ◽  
Chan Qiu ◽  
Weifei Hu ◽  
Jianrong Tan
Keyword(s):  
High Efficiency ◽  
Prediction Method ◽  
Solution Space ◽  
Assembly Sequence Planning ◽  
Selection Strategy ◽  
Assembly Process ◽  
Assembly Sequence ◽  
Content Type ◽  
Sequence Planning ◽  
Precedence Graph

Purpose Assembly sequence planning (ASP) plays a vital role in assembly process because it directly influences the feasibility, cost and time of the assembly process. The purpose of this study is to solve ASP problem more efficiently than current algorithms. Design/methodology/approach A novel assembly subsets prediction method based on precedence graph is proposed to solve the ASP problem. The proposed method adopts the idea of local to whole and integrates a simplified firework algorithm. First, assembly subsets are generated as initial fireworks. Then, each firework explodes to several sparks with higher-level assembly subsets and new fireworks are selected for next generation according to selection strategy. Finally, iterating the algorithm until complete and feasible solutions are generated. Findings The proposed method performs better in comparison with state-of-the-art algorithms because of the balance of exploration (fireworks) and exploitation (sparks). The size of initial fireworks population determines the diversity of the solution, so assembly subsets prediction method based on precedence graph (ASPM-PG) can explore the solution space. The size of sparks controls the exploitation ability of ASPM-PG; with more sparks, the direction of a specific firework can be adequately exploited. Practical implications The proposed method is with simple structure and high efficiency. It is anticipated that using the proposed method can effectively improve the efficiency of ASP and reduce computing cost for industrial applications. Originality/value The proposed method finds the optimal sequence in the construction process of assembly sequence rather than adjusting order of a complete assembly sequence in traditional methods. Moreover, a simplified firework algorithm with new operators is introduced. Two basic size parameters are also analyzed to explain the proposed method.

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