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Article
Publication date: 1 February 2016

Wilma Polini and Andrea Corrado

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…

Abstract

Purpose

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.

Design/methodology/approach

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.

Findings

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.

Research limitations/implications

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

Practical implications

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.

Originality/value

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

Details

Assembly Automation, vol. 36 no. 1
Type: Research Article
ISSN: 0144-5154

Keywords

Article
Publication date: 3 June 2019

Ting Liu, Yan-Long Cao, Qijian Zhao, Jiangxin Yang and Lujun Cui

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…

Abstract

Purpose

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.

Design/methodology/approach

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.

Findings

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.

Research limitations/implications

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

Practical implications

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.

Originality/value

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

Details

Assembly Automation, vol. 39 no. 2
Type: Research Article
ISSN: 0144-5154

Keywords

Article
Publication date: 23 January 2023

Roshith Mittakolu, Sarma L. Rani and Dilip Srinivas Sundaram

A higher-order implicit shock-capturing scheme is presented for the Euler equations based on time linearization of the implicit flux vector rather than the residual vector.

Abstract

Purpose

A higher-order implicit shock-capturing scheme is presented for the Euler equations based on time linearization of the implicit flux vector rather than the residual vector.

Design/methodology/approach

The flux vector is linearized through a truncated Taylor-series expansion whose leading-order implicit term is an inner product of the flux Jacobian and the vector of differences between the current and previous time step values of conserved variables. The implicit conserved-variable difference vector is evaluated at cell faces by using the reconstructed states at the left and right sides of a cell face and projecting the difference between the left and right states onto the right eigenvectors. Flux linearization also facilitates the construction of implicit schemes with higher-order spatial accuracy (up to third order in the present study). To enhance the diagonal dominance of the coefficient matrix and thereby increase the implicitness of the scheme, wave strengths at cell faces are expressed as the inner product of the inverse of the right eigenvector matrix and the difference in the right and left reconstructed states at a cell face.

Findings

The accuracy of the implicit algorithm at Courant–Friedrichs–Lewy (CFL) numbers greater than unity is demonstrated for a number of test cases comprising one-dimensional (1-D) Sod’s shock tube, quasi 1-D steady flow through a converging-diverging nozzle, and two-dimensional (2-D) supersonic flow over a compression corner and an expansion corner.

Practical implications

The algorithm has the advantage that it does not entail spatial derivatives of flux Jacobian so that the implicit flux can be readily evaluated using Roe’s approximate Jacobian. As a result, this approach readily facilitates the construction of implicit schemes with high-order spatial accuracy such as Roe-MUSCL.

Originality/value

A novel finite-volume-based higher-order implicit shock-capturing scheme was developed that uses time linearization of fluxes at cell interfaces.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 33 no. 5
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 3 May 2013

Gianpietro Granelli and Mario Montagna

The purpose of this work is that of providing the guidelines of an efficient implementation of power flow computations using the MATLAB computation environment.

1204

Abstract

Purpose

The purpose of this work is that of providing the guidelines of an efficient implementation of power flow computations using the MATLAB computation environment.

Design/methodology/approach

The goal of obtaining high efficiency from MATLAB programs often proves elusive unless special care is taken in exploiting the vectorising capability of MATLAB programming. In the present paper the implementation of Newton‐Raphson power flow in MATLAB is examined with particular emphasis on the way of obtaining a vectorisable code capable of achieving effective numerical performance by exploiting its formulation in terms of complex variables.

Findings

Tests on actual networks with up to 1,300 buses are presented. They show that the complex power flow is as efficient as the best implementations of the Newton Raphson power flow using real variables, as long as the operations involved are reordered with the aim of exploiting the vectorisation capabilities of the MATLAB environment.

Originality/value

It is shown that improved numerical efficiency in the MATLAB can be obtained through its formulation in terms of complex variables. The complex Newton‐Raphson load flow, not very common in practical uses, is shown to have many desirable qualities from the point of view of MATLAB programming and is presented in detail.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 32 no. 3
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 6 June 2023

Ligang Lu, Pengfei Li, Dongbo Wu, Jiawei Liang, Hui Wang and Pengpeng He

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…

Abstract

Purpose

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.

Design/methodology/approach

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.

Findings

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.

Originality/value

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.

Details

Robotic Intelligence and Automation, vol. 43 no. 3
Type: Research Article
ISSN: 2754-6969

Keywords

Open Access
Article
Publication date: 21 July 2023

M. Neumayer, T. Suppan, T. Bretterklieber, H. Wegleiter and Colin Fox

Nonlinear solution approaches for inverse problems require fast simulation techniques for the underlying sensing problem. In this work, the authors investigate finite element (FE…

Abstract

Purpose

Nonlinear solution approaches for inverse problems require fast simulation techniques for the underlying sensing problem. In this work, the authors investigate finite element (FE) based sensor simulations for the inverse problem of electrical capacitance tomography. Two known computational bottlenecks are the assembly of the FE equation system as well as the computation of the Jacobian. Here, existing computation techniques like adjoint field approaches require additional simulations. This paper aims to present fast numerical techniques for the sensor simulation and computations with the Jacobian matrix.

Design/methodology/approach

For the FE equation system, a solution strategy based on Green’s functions is derived. Its relation to the solution of a standard FE formulation is discussed. A fast stiffness matrix assembly based on an eigenvector decomposition is shown. Based on the properties of the Green’s functions, Jacobian operations are derived, which allow the computation of matrix vector products with the Jacobian for free, i.e. no additional solves are required. This is demonstrated by a Broyden–Fletcher–Goldfarb–Shanno-based image reconstruction algorithm.

Findings

MATLAB-based time measurements of the new methods show a significant acceleration for all calculation steps compared to reference implementations with standard methods. E.g. for the Jacobian operations, improvement factors of well over 100 could be found.

Originality/value

The paper shows new methods for solving known computational tasks for solving inverse problems. A particular advantage is the coherent derivation and elaboration of the results. The approaches can also be applicable to other inverse problems.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 42 no. 5
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 1 March 2002

Johan Driesen and Kay Hameyer

A general framework for the application of the Newton methods in non‐linear coupled electromagnetic‐thermal problems solved with the FEM on independent subproblem meshes is…

Abstract

A general framework for the application of the Newton methods in non‐linear coupled electromagnetic‐thermal problems solved with the FEM on independent subproblem meshes is presented. The explicit derivation of the Jacobian matrix is outlined and discussed. A matrix‐free quasi‐Newton method, to be used along with linear system solvers built around Jacobian‐vector products is presented. This method does not require explicit derivatives and can be parallelised. The numerical aspects of these methods are discussed. The different Newton methods are demonstrated using a steady‐state conductive heating example problem.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 21 no. 1
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 14 October 2020

Yew-Chung Chak, Renuganth Varatharajoo and Nima Assadian

The paper aims to address the combined attitude control and Sun tracking problem in a flexible spacecraft in the presence of external and internal disturbances. The attitude…

Abstract

Purpose

The paper aims to address the combined attitude control and Sun tracking problem in a flexible spacecraft in the presence of external and internal disturbances. The attitude stabilization of a flexible satellite is generally a challenging control problem, because of the facts that satellite kinematic and dynamic equations are inherently nonlinear, the rigid–flexible coupling dynamical effect, as well as the uncertainty that arises from the effect of actuator anomalies.

Design/methodology/approach

To deal with these issues in the combined attitude and Sun tracking system, a novel control scheme is proposed based on the adaptive fuzzy Jacobian approach. The augmented spacecraft model is then analyzed and the Lyapunov-based backstepping method is applied to develop a nonlinear three-axis attitude pointing control law and the adaptation law.

Findings

Numerical results show the effectiveness of the proposed adaptive control scheme in simultaneously tracking the desired attitude and the Sun.

Practical implications

Reaction wheels are commonly used in many spacecraft systems for the three-axis attitude control by delivering precise torques. If a reaction wheel suffers from an irreversible mechanical breakdown, then it is likely going to interrupt the mission, or even leading to a catastrophic loss. The pitch-axis mounted solar array drive assemblies (SADAs) can be exploited to anticipate such situation to generate a differential torque. As the solar panels are rotated by the SADAs to be orientated relative to the Sun, the pitch-axis wheel control torque demand can be compensated by the differential torque.

Originality/value

The proposed Jacobian control scheme is inspired by the knowledge of Jacobian matrix in the trajectory tracking of robotic manipulators.

Details

Aircraft Engineering and Aerospace Technology, vol. 93 no. 1
Type: Research Article
ISSN: 1748-8842

Keywords

Article
Publication date: 24 June 2021

Chuanyuan Zhou, Zhenyu Liu, Chan Qiu and Jianrong Tan

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…

Abstract

Purpose

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.

Design/methodology/approach

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.

Findings

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.

Research limitations/implications

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

Practical implications

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.

Originality/value

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

Details

Assembly Automation, vol. 41 no. 4
Type: Research Article
ISSN: 0144-5154

Keywords

Article
Publication date: 8 November 2022

Zesheng Wang, Dongbo Wu, Hui Wang, Jiawei Liang and Jingguang Peng

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…

Abstract

Purpose

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.

Design/methodology/approach

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.

Findings

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.

Originality/value

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.

Details

Assembly Automation, vol. 42 no. 6
Type: Research Article
ISSN: 0144-5154

Keywords

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