Variation Propagation Model Research Articles

Geometric Deviation Representation and Variation Propagation Modeling in Multistage Machining Processes

Geometric Deviation Representation and Variation Propagation Modeling in Multistage Machining Processes

Modeling Variation in Multi-Station Compliant Assembly Using Parametric Space Envelope

Abstract Compliant parts have different characteristics from rigid parts and are used frequently in industries. One of the biggest challenges facing by industries is geometric variation management of these compliant parts which can directly impact product quality and functionality. Existing rigid body-based variation modeling approaches are not suitable for compliant assembly while finite element analysis-based methods have the disadvantages of requiring heavy computation efforts and detailed design information which is unavailable during preliminary design phase. Hence, this paper proposes a novel geometric variation propagation model of multi-station compliant assembly based on parametric space envelope. Three sources of variation: location-led positional variation, assembly deformation-induced variation, and station transition caused variation are analyzed. In this study, geometric variations are modeled indirectly through control points of constructed variation tool. Compared with existing methods where geometric variation is modeled by tracking key feature points on the manufacturing part, the proposed approach brings unique benefits. It can deal with arbitrary complex compliant part, and it provides a unified modeling framework for different types of variation. The method is illustrated and verified through a two-station three parts case study on a multi-station compliant panel assembly. The proposed method provides industries with a new way to manage geometric variation from compliant assembly.

Variation Analysis Considering the Partial Parallel Connection in Aero-Engine Rotor Assembly

The rotation precision of rotors determines the efficiency and quality of the overall aero-engine, as well as its long-term and reliable operation ability. As the terminal link of aero-engine manufacturing, the assembly is the last guarantee of precision control. Rotor assembly relates to the accurate expression of the connection form and design optimization of the assembly scheme. The existing variation model cannot adequately handle the partial parallel chain problem, ignoring the bayonet circular connector between the rotor parts, and it is still deficient in multistage gyration error control. In this paper, the partial parallel connection and multistage revolving characteristics of rotors were discussed, and a novel modeling and optimizing method for a partial parallel dimension chain was proposed. On the one hand, the variation expression of the connection features for the revolving components considering the partial parallel structure was researched. Contact point-based torsors were represented, and a system for locating points was regarded as an assembly to describe the partial parallel chain. On the other hand, the variation propagation modeling and control for the stacking of the multistage revolving components was researched. A revolution joint was introduced in the unified Jacobian–Torsor model, and a novel assembly technique for concentricity control was proposed. Therefore, a unified variation analysis and control method for rotor assembly has been developed. Experimental results show that through this method, the final concentricity variation is 0.0539 mm, far less than the 0.1595 mm of the traditional model, and is closer to the true value range of 0.030–0.040 mm. Moreover, the optimum installed angles can be calculated as 3.153 rad, 6.025 rad, and 2.590 rad, to obtain the highest concentricity of 0.040 mm, which has strong practical guiding significance.

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

PurposeThis 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/approachFirst, 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.FindingsThrough 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/valueIn 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 propagation modeling in multistage machining processes considering form errors and N-2-1 fixture layouts

Variation propagation modeling of multistage machining processes enables variation reduction by making an accurate prediction on the quality of a part. Part quality prediction through variation propagation models, such as stream of variation and Jacobian-Torsor models, often focus on a 3-2-1 fixture layout and do not consider form errors. This paper derives a mathematical model based on dual quaternion for part quality prediction given parts with form errors and fixtures with N-2-1 (N>3) layout. The method uses techniques of Skin Model Shapes and dual quaternions for a virtual assembling of a part on a fixture, as well as conducting machining and measurement. To validate the method, a part with form errors produced in a two-stationed machining process with a 12-2-1 fixture layout was considered. The prediction made following the proposed method was within 0.4% of the prediction made using a CAD/CAM simulation when form errors were not considered. These results validate the method when form errors are neglected and partially validated when considered.

Fault diagnosis for underdetermined multistage assembly processes via an enhanced Bayesian hierarchical model

Previous works have shown that only relying on measurement data is generally insufficient to identify root causes of the dimensional variation for the complex manufacturing system. It is also well known that for underdetermined multistage assembly processes (MAPs), the number of measurements is less than that of process errors so that the traditional methods are not available for the variation source identification. Therefore, there exists a substantial challenge for fault diagnosis of underdetermined MAPs, especially for the case with multiple fault patterns. To tackle this problem, a novel approach that integrates statistical analysis with domain knowledge is proposed in this paper. First, the variation propagation model is employed to reveal the inherent relationship between key control characteristics and key product characteristics, and then the corresponding variance model is constructed to interpret process faults by means of the abnormal variance of process errors. Considering that the probability of less process faults is far higher than that of more process faults in MAPs, the problem of fault diagnosis is further transformed into searching the sparse solution of abnormal variance changes for process faults. Afterwards, based on the non-negative property of the covariance matrix, an enhanced Bayesian hierarchical model is developed to favor sparse estimation of the variance for the underdetermined system in MAPs. Finally, experimental results of both the numeric simulation and practical case study demonstrate the proposed diagnosis methodology can effectively identify the process faults for different patterns with system noise.

Research on global coupling analysis and approximate decoupling of quality characteristics in the early design stage

Due to the existence of coupling relationships, quality characteristics form a variation propagation process, which increases the risk possibility of product quality. In order to improve the robustness of quality characteristics, this paper proposes a fuzzy clustering-based key quality characteristics decoupling planning considering risk criticality. Firstly, based on the design structure matrix, a modular correlation matrix of key quality characteristics was established to quantify the coupling relationships among them. Secondly, according to the variation characteristics of quality characteristics, the variation propagation model is constructed to identify the potential quality risk. Thirdly, the fuzzy clustering algorithm is used to obtain the optimal control sequence of key quality characteristics. Finally, the computerized numerical control machine tool is taken as an actual case, the effectiveness and superiority of this method are verified by the comparison of the numerical result and method. This method provides a new indicator system solution for the coupling analysis of product design.

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

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.

Variation Propagation in Multistage Machining Processes Using Dual Quaternions

The application of rigid transformations matrices in variation propagation has a long tradition in manufacturing community. However, the matrix-based modeling of variation propagation in multistage machining processes is complicated. Moreover, there is a need to improve the computational efficiency of manipulation of geometrical models for variation analysis purposes. This paper introduces the representation of rigid transformation by dual quaternions, which have a computational advantage and mathematical elegance compared to matrices. In comparison to a commercial tool, the implementation of the purposed method predicted parallelism with an average error of 4.3 % in a hypothetical two stage machining process. The proposed approach has a potential to be an alternative to matrix based rigid transformation practices in variation and tolerance analysis.

A quality-driven assembly sequence planning and line configuration selection for non-ideal compliant structures assemblies

In automotive body assembly systems, an optimum assembly sequence planning (ASP) not only increases production efficiency and product quality, but also decreases cost and process cycle time. Typically, ASP evaluation approaches are focused on design for assembly criteria, and very few studies have considered the impact of ASP on dimensional accuracy. The major challenges involving quality-driven ASP evaluation can be enumerated into three categories: (1) batch of compliant non-ideal parts to consider real part defects; (2) variation propagation modeling in multi-station assembly (MSA) system in the presence of stochastic manufacturing errors both at product and process levels; and, (3) the development of dimensional quality criteria for quantitative ASP comparisons. This paper proposes a methodology based on the modeling of dimensional errors propagation in MSA with a batch of compliant non-ideal parts to improve product dimensional quality through optimizing ASP and assembly line configuration. It entails three main steps: (i) assembly sequence generation by k-ary assembly operation method for a predetermined assembly line configuration; (ii) variation propagation simulation taking into account a batch of non-ideal parts, station-to-station repositioning errors, and spring-back phenomenon in MSA system; and, (iii) robust optimization of ASP based on developed quality criteria which contains two quantitative indices. The potential benefits of the proposed methodology are successfully demonstrated on automotive front-rail assembly process.

Three-Dimensional Tolerance Analysis Modelling of Variation Propagation in Multi-stage Machining Processes for General Shape Workpieces

The quality control of general shape workpieces has become one of research hotspots because of the increasing diversity of products. The theory of stream of variation (SoV) for machining processes is a successful method in researching variation propagation rule. However, with the consideration of all key elements in manufacturing system, there is no unified and integrated model for workpieces in different kinds of shapes. In this paper, a new variation propagation model in multi-stage machining processes for general shape workpieces is established. It visually demonstrates the variation propagation chain and expands the universality of current SoV models. The connection of all key elements in manufacturing system is defined as an assembly chain, in which the variations are defined and propagated by modified three-dimensional tolerance analysis method. The equivalent conversion of the connection between workpiece and fixture realizes the modelling of general shape workpiece regardless of its machining method and locating scheme. Real experiments validate the effectiveness and accuracy of the new SoV model for different shape workpieces. This model has great potential to be applied toward multi-scale variation modelling, process control, and fault diagnosis for general shape workpieces.

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

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.

Variation propagation modeling and analysis of automotive body outer cover panels assembly systems

PurposeThis 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.Design/methodology/approachAn 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.FindingsA 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.Originality/valueThe 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.

Twofold Variation Propagation Modeling and Analysis for Roll-to-Roll Manufacturing Systems

Roll-to-roll (R2R) manufacturing has emerged as one of the most cost-effective manufacturing techniques for high-volume production of flexible printing electronics, graphene films, thin-film batteries, and solar cells, as opposed to low-volume batch production. However, in practice, real-time monitoring of the R2R process and in situ measurement of fabricated materials during production are challenging because of the high speed and dynamic variation of the web. In addition, due to the lack of cost-effective sensors and in-line metrology systems with a large range and high resolution, effective quality control and defect diagnosis are difficult to achieve. To address these challenges, this paper aims to develop analytical models that can serve as virtual sensing and metrology tools to quantify process state variation and estimate product quality in R2R processes with limited accessibility of in situ sensor. First, the quality variation propagation mechanism in R2R processes is investigated. Second, a hybrid multistage modeling method is proposed to characterize the twofold variation propagation—product-centric and process-centric variations, and its relationship with product quality in R2R processes. Note to Practitioner s—The novel modeling method developed in this paper employs both physics-based analysis (e.g., web handling system dynamics) and regression methods [e.g., censored regression and linear/logistic regression (LG)] using multisensor signals. The estimation results from the model can serve as virtual sensing and virtual metrology tools to increase the system visibility and be applied for process monitoring and error detection in real time. A print registration unit of elastic film in a roll-to-roll system is employed to demonstrate and validate the proposed modeling method in terms of the accuracy of state estimates and quality prediction. Based on the comparison results, the hybrid modeling method shows higher accuracy in state estimation and quality prediction than do the models with data-driven methods only.

Cost-oriented process optimisation through variation propagation management for aircraft wing spar assembly

Overconstrained assemblies such as aircraft sub-assemblies present a challenge to production planners, as variations in parts and processes can make it difficult to achieve all assembly Key Characteristics (KCs) simultaneously. Despite assigning tight tolerances to sub-component manufacture, part variation propagation necessitates expensive and time-consuming variation management processes such as shimming in order to ensure the final assembly is within specification. This paper presents for the first time a variation propagation model for overconstrained assemblies, and develops a novel modelling method to connect variations with production costs. This facilitates a novel process optimisation method based on variation propagation, with the ability to analyse the trade-offs between the cost and achievable variation limits of the entire manufacturing chain in order to minimise the overall manufacturing cost. An overconstrained wing spar assembly is used as a case study to validate the methodology.

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

PurposeThis 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/approachBased 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.FindingsThis 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 implicationsThe 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/valueAlthough 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.

Quality-driven Optimization of Assembly Line Configuration for Multi-Station Assembly Systems with Compliant Non-ideal Sheet Metal Parts

Final product quality is affected by both defects generation as well as defects propagation through the multi-station assembly system. Less quantifiable understood is quality defects propagation which depends on assembly line configuration. This paper focuses on modelling and optimization of multi-station assembly line configuration for systems with compliant non-ideal sheet-metal parts. The proposed methodology is based on: (1) assembly sequence generation; (2) multi-station assembly variation propagation model and simulations considering batch of non-ideal parts, station-to-station repositioning error and spring-back phenomenon; (3) development of assembly configuration index; and, (4) calculation of optimal configuration based on stochastic robust optimization. The methodology is demonstrated using automotive front-rail subassembly process.

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

PurposeComplicated 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/approachTo 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.FindingsThe 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/valueThis 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.

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

Positioning variation modeling for aircraft panels assembly based on elastic deformation theory

Dimensional variation in aircraft panel assembly is one of the most critical issues that affect the aerodynamic performance of aircraft, due to elastic deformation of parts during the positioning and clamping process. This article proposes an assembly deformation prediction model and a variation propagation model to predict the assembly variation of aircraft panels, and it derives consecutive three-dimensional deformation expressions which explicitly describe the nonlinear behavior of physical interaction occurring in compliant components assembly. An assembly deformation prediction model is derived from equations of statics of elastic beam to calculate the elastic deformation of panel component resulted from positioning error and clamping force. A variation propagation model is used to describe the relationship between local variations and overall assembly variations. Assembly variations of aircraft panels due to positioning error are obtained by solving differential equations of statics and operating spatial transformations of the coordinate. The calculated results show a good prediction of variation in the experiment. The proposed method provides a better understanding of the panel assembly process and creates an analytical foundation for further work on variation control and tolerance optimization.