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This paper aims to develop a method to improve the accuracy of tolerance analysis considering the spatial distribution characteristics of part surface morphology (SDCPSM) and local surface deformations (LSD) of planar mating surfaces during the assembly process.

First, this paper proposes a skin modeling method considering SDCPSM based on Non-Gaussian random field. Second, based on the skin model shapes, an improved boundary element method is adopted to solve LSD of nonideal planar mating surfaces, and the progressive contact method is adopted to obtain relative positioning deviation of mating surfaces. Finally, the case study is given to verify the proposed approach.

Through the case study, the results show that different SDCPSM have different influences on tolerance analysis, and LSD have nonnegligible and different influence on tolerance analysis considering different SDCPSM. In addition, the LSD have a greater influence on translational deviation along the z-axis than rotational deviation around the x- and y-axes.

The surface morphology with different spatial distribution characteristics leads to different contact behavior of planar mating surfaces, especially when considering the LSD of mating surfaces during the assembly process, which will have further influence on tolerance analysis. To address the above problem, this paper proposes a tolerance analysis method with skin modeling considering SDCPSM and LSD of mating surfaces, which can help to improve the accuracy of tolerance analysis.

The purpose of this paper is to carry out an assembly tolerance analysis by means of a combined Jacobian model and skin model shape. The former is based on small displacements modeling of points using 6 × 6 transformation matrices of open kinematic chains in robotics. The latter easily models toleranced features with all kinds of geometric deviations.

This paper presents the procedure of performing tolerance analysis by means of the Jacobian model and skin model shape for assemblies. The point cloud-based discrete representative is able to model the actual toleranced surfaces instead of the ideal or associated ones in an assembly, which brings the simulation tools closer to reality.

The proposed method has the advantage of skin model shape which is suitable for geometric tolerances management along the product life cycle and contact analysis of kinematic small variations, as well as, with the Jacobian, enabling transformation of locally expressed parts deviations to globally expressed functional requirements. The result of the case study shows the accuracy of the method.

The proposed approach has not been developed fully; other functional features such as the pyramid are still ongoing challenges.

It is an effective method for supporting design, manufacturing and inspection by providing a quantitative analysis of the effects of multi-tolerances on the final functional key characteristics and for predicting the quality level.

The paper is original in taking advantages of both Jacobian model and skin model shape to consider all geometric tolerances in assembly.

The purpose of this paper is to present a skin-based approach able to generate the variability model for a component in composite material due to its manufacturing process. It generates a skin-based model of the manufactured part. The skin model discretizes the part surfaces by points to take into account the geometric deviations, those points are the nodes of finite element analysis used for tolerance analysis of compliant assemblies.

The paper presents a general and systematic simulation model for generating a variability meta-model for a component in composite material due to its manufacturing process. The model is constituted by three steps: definition and pre-processing of the nominal model, generation of the manufacturing process model and evaluation of the part variability.

The advantage of this approach is related to the fact that it is designed as a part of a digital process that establishes a continuous and unambiguous flow of variation information from the part design to manufacturing and assembly and that takes into account the manufacturing signature. This is its uniqueness compared to other simulation approaches focused only on manufacturing.

Considering the variability around the nominal value of all the process parameters and parts with more complex geometries are not taken into account now, which will be modelled in practical applications.

To properly manage uncertainty since conceptual design of complex product, next generation geometry assurance requires simulation models to realistically consider process signatures due to the manufacturing process. This work focusses on this next generation tool for geometry assurance.

The literature is focused on metal sheets joined by welding or riveting. There are other materials widely used and typically compliant: the composite materials that typically used mechanical fixing elements (bolting, riveting) and structural adhesives to joint parts. No software tools exist in the literature to deal with uncertainty from manufacturing to assembly processes in products made by composite. This is the reason of the present work.

This paper aims to propose a framework for optimizing the pose in the assembly process of the non-ideal parts considering the manufacturing deviations and contact deformations. Furthermore, the accuracy of the method would be verified by comparing it with the other conventional methods for calculating the optimal assembly pose.

First, the surface morphology of the parts with manufacturing deviations would be modeled to obtain the skin model shapes that can characterize the specific geometric features of the part. The model can provide the basis for the subsequent contact deformation analysis. Second, the simulated non-nominal components are discretized into point cloud data, and the spatial position of the feature points is corrected. Furthermore, the evaluation index to measure the assembly quality has been established, which integrates the contact deformations and the spatial relationship of the non-nominal parts’ key feature points. Third, the improved particle swarm optimization (PSO) algorithm combined with the finite element method is applied to the process of solving the optimal pose of the assembly, and further deformation calculations are conducted based on interference detection. Finally, the feasibility of the optimal pose prediction method is verified by a case.

The proposed method has been well suited to solve the problem of the assembly process for the non-ideal parts with complex geometric deviations. It can obtain the reasonable assembly optimal pose considering the constraints of the surface morphological features and contact deformations. This paper has verified the effectiveness of the method with an example of the shaft-hole assembly.

The method proposed in this paper has been well suited to the problem of the assembly process for the non-ideal parts with complex geometric deviations. It can obtain the reasonable assembly optimal pose considering the constraints of the surface morphological features and contact deformations. This paper has verified the method with an example of the shaft-hole assembly.

The different surface morphology influenced by manufacturing deviations will lead to the various contact behaviors of the mating surfaces. The assembly problem for the components with complex geometry is usually accompanied by deformation due to the loading during the contact process, which may further affect the accuracy of the assembly. Traditional approaches often use worst-case methods such as tolerance offsets to analyze and optimize the assembly pose. In this paper, it is able to characterize the specific parts in detail by introducing the skin model shapes represented with the point cloud data. The dynamic changes in the parts' contact during the fitting process are also considered. Using the PSO method that takes into account the contact deformations improve the accuracy by 60.7% over the original method that uses geometric alignment alone. Moreover, it can optimize the range control of the contact to the maximum extent to prevent excessive deformations.

One major problem preventing further application and benefits from additive manufacturing (AM) nowadays is that AM build parts always end up with poor geometrical quality. To help improving geometrical quality for AM, this study aims to propose geometrical deviation identification and prediction method for AM, which could be used for identifying the factors, forms and values of geometrical deviation of AM parts.

This paper applied the skin model-based modal decomposition approach to describe the geometrical deviations of AM and decompose them into different defect modes. On that basis, the approach to propose and extend defect modes was developed. Identification and prediction of the geometrical deviations were then carried out with this method. Finally, a case study with cylinders manufactured by fused deposition modeling was introduced. Two coordinate measuring machine (CMM) machines with different measure methods were used to verify the effectiveness of the methods and modes proposed.

The case study results with two different CMM machines are very close, which shows that the method and modes proposed by this paper are very effective. Also, the results indicate that the main geometrical defects are caused by the shrinkage and machine inaccuracy-induced errors which have not been studied enough.

This work could be used for identifying and predicting the forms and values of AM geometrical deviation, which could help realize the improvement of AM part geometrical quality in design phase more purposefully.

The purpose of this paper is to propose an assembly coordination modelling approach based on measured data for assembly quality control of multi-constrained objects in aircraft assembly. This approach aims to establish a high-precision digital mirror of physical assembly system in the virtual environment, with which the assembly process in the virtual environment can be performed synchronously with that in the physical world.

This paper presents a realistic geometrical representation model based on measured point cloud, as well as the multiple constraints modelling methods for local and global constraints with the proposed representation model. For the assembly target optimization, a novel optimization method based on the evaluation of multi-dimensional tolerance zone is proposed, where the particle swarm optimization and simulated annealing algorithm are combined to calculate the optimal solutions.

As shown in the validation results, the minimum easiness value for easiness model in global optimization is 3.01, while the best value for weighting model by adjusting weights for more than 10 times is 1.94. The results verify that the proposed coordination modelling approach is effective to the assembly of multi-constrained objects, and the optimization model has an obvious advantage over the traditional weighting method.

This paper provides a new idea for the fine control of assembly quality of non-ideal components by introducing the measured data into the on-line assembly process. Besides, a novel optimization method based on the evaluation of multi-dimensional tolerance zone is proposed, which overcomes the problem of traditional weighting model wherein the weightings are difficult to determine.

The assembly simulation in tolerance analysis is one of the most important steps for the tolerance design of mechanical products. However, most assembly simulation methods are based on the rigid body assumption, and those assembly simulation methods considering deformation have a poor efficiency. This paper aims to propose a novel efficient and precise tolerance analysis method based on stable contact to improve the efficiency and reliability of assembly deformation simulation.

The proposed method comprehensively considers the initial rigid assembly state, the assembly deformation and the stability examination of assembly simulation to improve the reliability of tolerance analysis results. The assembly deformation of mating surfaces was first calculated based on the boundary element method with optimal initial assembly state, then the stability of assembly simulation results was assessed by the density-based spatial clustering of applications with noise algorithm to improve the reliability of tolerance analysis. Finally, combining the small displacement torsor theory, the tolerance scheme was statistically analyzed based on sufficient samples.

A case study of a guide rail model demonstrated the efficiency and effectiveness of the proposed method.

The present study only considered the form error when generating the skin model shape, and the waviness and the roughness of the matching surface were not considered.

To the best of the authors’ knowledge, the proposed method is original in the assembly simulation considering stable contact, which can effectively ensure the reliability of the assembly simulation while taking into account the computational efficiency.

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.

The purpose of this paper is to model how geometric errors of a machined surface (or manufacturing errors) are related to locators’ error, workpiece form error and machine tool volumetric error. A kinematic model is presented that puts into relationship the locator error, the workpiece form deviations and the machine tool volumetric error.

The paper presents a general and systematic approach for geometric error modelling in drilling because of the geometric errors of locators positioning, of workpiece datum surface and of machine tool. The model can be implemented in four steps: (1) calculation of the deviation in the workpiece reference frame because of deviations of locator positions; (2) evaluation of the deviation in the workpiece reference frame owing to form deviations in the datum surfaces of the workpiece; (3) formulation of the volumetric error of the machine tool; and (4) combination of those three models.

The advantage of this approach lies in that it enables the source errors affecting the drilling accuracy to be explicitly separated, thereby providing designers and/or field engineers with an informative guideline for accuracy improvement through suitable measures, i.e. component tolerancing in design, machining and so on. Two typical drilling operations are taken as examples to illustrate the generality and effectiveness of this approach.

Some source errors, such as the dynamic behaviour of the machine tool, are not taken into consideration, which will be modelled in practical applications.

The proposed kinematic model may be set by means of experimental tests, concerning the industrial specific application, to identify the values of the model parameters, such as standard deviation of the machine tool axes positioning and rotational errors. Then, it may be easily used to foresee the location deviation of a single or a pattern of holes.

The approaches present in the literature aim to model only one or at most two sources of machining error, such as fixturing, machine tool or workpiece datum. This paper goes beyond the state of the art because it considers the locator errors together with the form deviation on the datum surface into contact with the locators and, then, the volumetric error of the machine tool.

Digital twin (DT) is an emerging technology that enables sophisticated interaction between physical objects and their virtual replicas. Although DT has recently gained significant attraction in both industry and academia, there is no systematic understanding of DT from its development history to its different concepts and applications in disparate disciplines. The majority of DT literature focuses on the conceptual development of DT frameworks for a specific implementation area. Hence, this paper provides a state-of-the-art review of DT history, different definitions and models, and six types of key enabling technologies. The review also provides a comprehensive survey of DT applications from two perspectives: (1) applications in four product-lifecycle phases, i.e. product design, manufacturing, operation and maintenance, and recycling and (2) applications in four categorized engineering fields, including aerospace engineering, tunneling and underground engineering, wind engineering and Internet of things (IoT) applications. DT frameworks, characteristic components, key technologies and specific applications are extracted for each DT category in this paper. A comprehensive survey of the DT references reveals the following findings: (1) The majority of existing DT models only involve one-way data transfer from physical entities to virtual models and (2) There is a lack of consideration of the environmental coupling, which results in the inaccurate representation of the virtual components in existing DT models. Thus, this paper highlights the role of environmental factor in DT enabling technologies and in categorized engineering applications. In addition, the review discusses the key challenges and provides future work for constructing DTs of complex engineering systems.