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The purpose of this paper is to carry out a tolerance analysis with geometric tolerances by means of the Jacobian model. Tolerance analysis is an important task to design and to manufacture high-precision mechanical assemblies; it has received considerable attention by the literature. The Jacobian model is one of the methods proposed by the literature for tolerance analysis. The Jacobian model cannot deal with geometric tolerances for mechanical assemblies. The geometric tolerances may not be neglected for assemblies, as they significantly influence their functional requirements.

This paper presents how it is possible to deal with geometric tolerances when a tolerance analysis is carried out by means of a Jacobian model for a 2D and 3D assemblies for which the geometric tolerances applied to the components involve only translational deviations. The three proposed approaches modify the expression of the stack-up function to overcome the shortage of Jacobian model that the geometric error cannot be processed.

The proposed approach has been applied to a case study. The results of the case study show how, when a statistical approach is implemented, the Jacobian model with the three developed methods gives results very similar to those due to other models of the literature, such as vector loop and variational.

In particular, the proposed approach may be applied only when the applied geometrical tolerances involve translational variations in 3D assemblies.

Tolerance analysis is a valid tool to foresee geometric interferences among the components of an assembly before getting the physical assembly. It involves a decrease of the manufacturing costs.

The original contribution of the paper is due to three methods to make a Jacobian model able to consider form and geometric deviations.

The traditional precision design only takes the influence of geometric tolerance of the parts and does not involve the load deformation in the assembly process. This paper aims to analyze the influence mechanism of flexible parts deformation on the geometric precision, and then to ensure the reliability and stability of the mechanical system.

Firstly, this paper adopts the N-GPS to analyze the influence mechanism of flexible parts deformation on the geometric precision and constructs a coupling 3D tolerance mathematical model of the geometric tolerance and the load deformation deviation based on the SDT theory, homogeneous coordinate transformation theory and surface authentication idea. Secondly, the least square method is used to fit the deformation surface of the mating surface under load so as to complete the conversion from the non-ideal element to the ideal element.

This paper takes the horizontal machining center as a case to obtain the deformation information of the mating surface under the self-weight load. The results show that the deformation deviation of the parts has the trend of transmission and accumulation under the load. The terminal deformation cumulative amount of the system is up to –0.0249 mm, which indicated that the influence of parts deformation on the mechanical system precision cannot be ignored.

This paper establishes a comprehensive 3D tolerance mathematical model, which comprehensively considers the effect of the dimensional tolerance, geometric tolerance and load deformation deviation. By this way, the assembly precision of mechanical system can be accurately predicted.

The purpose of this paper is to present a new efficient method for the tolerance–reliability analysis and quality control of complex nonlinear assemblies where explicit assembly functions are difficult or impossible to extract based on Bayesian modeling.

In the proposed method, first, tolerances are modelled as the random uncertain variables. Then, based on the assembly data, the explicit assembly function can be expressed by the Bayesian model in terms of manufacturing and assembly tolerances. According to the obtained assembly tolerance, reliability of the mechanical assembly to meet the assembly requirement can be estimated by a proper first-order reliability method.

The Bayesian modeling leads to an appropriate assembly function for the tolerance and reliability analysis of mechanical assemblies for assessment of the assembly quality, by evaluation of the assembly requirement(s) at the key characteristics in the assembly process. The efficiency of the proposed method by considering a case study has been illustrated and validated by comparison to Monte Carlo simulations.

The method is practically easy to be automated for use within CAD/CAM software for the assembly quality control in industrial applications.

Bayesian modeling for tolerance–reliability analysis of mechanical assemblies, which has not been previously considered in the literature, is a potentially interesting concept that can be extended to other corresponding fields of the tolerance design and the quality control.

The purpose of this paper is to propose a novel mathematical model to present the three-dimensional tolerance of a discrete surface and to carry out an approach to analyze the tolerance of an assembly with a discrete surface structure. A discrete surface is a special structure of a large surface base with several discrete elements mounted on it, one, which is widely used in complex electromechanical products.

The geometric features of discrete surfaces are separated and characterized by small displacement torsors according to the spatial relationship of discrete elements. The torsor cluster model is established to characterize the integral feature variation of a discrete surface by integrating the torsor model. The influence and accumulation of the assembly tolerance of a discrete surface are determined by statistical tolerance analysis based on the unified Jacobian-Torsor method.

The effectiveness and superiority of the proposed model in comprehensive tolerance characterization of discrete surfaces are successfully demonstrated by a case study of a phased array antenna. The tolerance is evidently and intuitively computed and expressed based on the torsor cluster model.

The tolerance analysis method proposed requires much time and high computing performance for the calculation of the statistical simulation.

The torsor cluster model achieves the three-dimensional tolerance representation of the discrete surface. The tolerance analysis method based on this model predicts the accumulation of the tolerance of components before their physical assembly.

This paper proposes the torsor cluster as a novel mathematical model to interpret the tolerance of a discrete surface.

Addresses the need for a unified product information model and presents a new representation scheme for mechanical component modelling using shells as its principal geometric primitives for modelling form features. The representation scheme was implemented using the ACIS geometric modeller and C++ on a SUN SPARC/10 station. The advantage of using shells is that both surface and volume information of a form feature can be derived from a shell. Different levels of product data representation can be integrated into a single model. Therefore, it allows the user to model the geometry effectively and form features of a mechanical part on one system.

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.

This paper aims to propose a method to automate the tolerance analyses of mechanical assembly using STandard for the Exchange of Product model data-Application Protocol Part 242 (STEP AP 242) files derived from the 3-D computer-aided design (CAD) models.

Product manufacturing information and mating information available in ISO 10303 STEP AP242 files resulting from the 3-D CAD model of mechanical assembly are extracted. The extracted geometric attributes, geometric dimensioning and tolerancing (GD&T) and mating information are used to automatically generate assembly graph and mating edges required for the tolerance analyses of the mechanical assembly by using the matrix approach.

The feasibility of the proposed method is verified through two mechanical assembly case studies. The results of manual calculations and tolerance values computed by the automated method are very closely matching.

Tolerance analysis is an integral part of product development that directly influences the cost and performance of a product. Apart from the academic interest, the work is expected to have positive implications for the digital design and smart manufacturing industry that involve in the development of solutions for automation of design and manufacturing system functions.

The approach presented in the paper that aids the automation of tolerance analyses of mechanical assembly is an innovative application of the STEP AP 242 file. The automation of tolerance analyses would improve the productivity and efficiency of the product realization process.

Localization accuracy is a key concern in the design of a fixture to specify a locating scheme and tolerance allocation. This paper presents an analysis describing the impact of localization source errors on the potential datum‐related geometric errors of machined features. The analysis reveals the error sensitivity and error characteristics of critical points of multiple manufacturing features. It shows the importance to consider the overall error among the multiple critical points in fixture layout design. This paper also suggests an optimal approach to the locator configuration design for reducing geometric variations at the critical points of machined features.

This paper aims to comprehensively achieve the requirements of high assembly precision and low cost, a precision-cost model of assembly based on three-dimensional (3D) tolerance is established in this paper.

The assembly precision is related to the tolerance of parts and the deformation of matching surfaces under load. In this paper, the small displacement torsor (SDT) theory is first utilized to analyze the manufacturing tolerances of parts and the assembly deformation deviation of matching surface. In the meanwhile, the extracting method of SDT parameters is proposed and the assembly precision calculation model based on the 3D tolerance is established. Second, an integrated optimization model based on the machining cost, assembly cost (mapping the deviation domain to the SDT domain) and quality loss cost is built. Finally, the practicability of the precision-cost model is verified by optimizing the horizontal machining center.

The assembly deviation has a great influence on cost fluctuation. By setting the optimization objective to maximize the assembly precision, the optimal total cost is CNY 72.77, decreasing by 16.83 per cent from the initial value, which meets economical requirements. Meanwhile, the upper bound of each processing tolerance is close to the maximum value of 0.01 mm, indicating that the load deformation can be offset by appropriately increasing the upper bound of the tolerance, but it is necessary to strictly restrict the manufacturing tolerances of lower parts in a reasonable range.

In this paper, a 3D deviation precision-cost model of assembly is established, which can describe the assembly precision more accurately and achieve a lower cost compared with the assembly precision model based on rigid parts.

Determining whether a set of tolerances on a part can be met by a rapid prototyping (RP) machine is often difficult. To achieve a set of tolerances as closely as possible, relationships between part geometry, tolerances, and process variables must be understood quantitatively. This paper presents an empirical model for stereolithography apparatus (SLA) accuracy, as specified by geometric tolerances, and a process planning method based on response surface methodology and multiobjective optimization. Response surfaces are used to capture the relationships among part surfaces, tolerances, and process variables. These response surfaces were generated by extensive design‐of‐experiment studies for a variety of geometries. An annotated STL data format is also presented that enables the inclusion of tolerance and surface information in faceted representations. Application of the accuracy models and process planning method is illustrated on one part.