Search results

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.

The purpose of this study is to establish an assembly accuracy analysis model of deployable arms based on Jacobian–Torsor theory to improve the assembly accuracy. Spacecraft deployable arm is one of the core components of spacecraft. Reducing the errors in assembly process is the main method to improve the assembly accuracy of spacecraft deployable arms.

First, the influence of composite connecting rod, root joint and arm joint on assembly accuracy in the tandem assembly process is analyzed to propose the assembly accuracy analysis model. Second, a non-tandem assembly process of “two joints fixed-composite rod installed-flange gasket compensated” is proposed and analyzed to improve the assembly accuracy of deployable arms. Finally, the feasibility of non-tandem assembly process strategy is verified by assembly experiment.

The experiential results show that the assembly errors are reduced compared with the tandem assembly process. The errors on axes x, y and z directions decreased from 14.1009 mm, 14.2424 mm and 0.8414 mm to 0.922 mm, 0.671 mm and 0.2393 mm, respectively. The errors round axes x and y directions also decreased from 0.0050° and 0.0053° to 0.00292° and 0.00251°, respectively.

This paper presents an assembly accuracy analysis model of deployable arms and applies the model to calculate assembly errors in tandem assembly process. In addition, a non-tandem assembly process is proposed based on the model. The experimental results show that the non-tandem assembly process can improve the assembly accuracy of deployable arms.

Assembly errors of aeroengine rotor must be controlled to improve the aeroengine efficiency. However, current method cannot truly reflect assembly errors of the rotor in working state owing to difficulties in error analysis. Therefore, the purpose of this study is to establish an optimization method for aeroengine rotor stacking assembly.

The assembly structure of aeroengine rotor is featured. Rotor eccentricity is optimized based on Jacobian–Torsor model. Then, an optimization method for assembly work is proposed. The assembly process of the high-pressure compressor rotor and the high-pressure turbine rotor as the rotor core assembly is mainly considered.

An aeroengine rotor is assembled to verify the method. The results show that the predicted eccentricity differed from the measured eccentricity by 6.1%, with a comprehensive error of 8.1%. Thus, the optimization method has certain significance for rotor assembly error analysis and assembly process optimization.

In view of the error analysis in the stacking assembly of aeroengine rotor, an innovative optimization method is proposed. The method provides a novel approach for the aeroengine rotor assembly optimization and is applicable for the assembly of high-pressure compressor rotor and high-pressure turbine rotor as the rotor core assembly.

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 conventional statistical method of three-dimensional tolerance analysis requires numerous pseudo-random numbers and consumes enormous computations to increase the calculation accuracy, such as the Monte Carlo simulation. The purpose of this paper is to propose a novel method to overcome the problems.

With the combination of the quasi-Monte Carlo method and the unified Jacobian-torsor model, this paper proposes a three-dimensional tolerance analysis method based on edge sampling. By setting reasonable evaluation criteria, the sequence numbers representing relatively smaller deviations are excluded and the remaining numbers are selected and kept which represent deviations approximate to and still comply with the tolerance requirements.

The case study illustrates the effectiveness and superiority of the proposed method in that it can reduce the sample size, diminish the computations, predict wider tolerance ranges and improve the accuracy of three-dimensional tolerance of precision assembly simultaneously.

The proposed method may be applied only when the dimensional and geometric tolerances are interpreted in the three-dimensional tolerance representation model.

The proposed tolerance analysis method can evaluate the impact of manufacturing errors on the product structure quantitatively and provide a theoretical basis for structural design, process planning and manufacture inspection.

The paper is original in proposing edge sampling as a sampling strategy to generating deviation numbers in tolerance analysis.

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.

Assembly accuracy is the guarantee of mechanical product performance, and the characterization of the part with geometrical deviations is the basis of assembly accuracy analysis.

The existed small displacement torsors (SDT) model cannot fully describe the part with multiple mating surfaces, which increases the difficulty of accuracy analysis. This paper proposed an integrated characterization method for accuracy analysis. By analyzing the internal coupling relationship of the different geometrical deviations in a single part, the Monomer Model was established.

The effectiveness of the Monomer Model is verified through an analysis of a simulated rotor assembly analysis, and the corresponding accuracy analysis method based on the model reasonably predicts the assembly deviation of the rotor.

The Monomer Model realizes the reverse calculation of assembly deformation for the first time, which can be used to identify the weak links that affect the assembly accuracy, thus support the accuracy improvement in the re-assembly stage.

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.

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.

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.