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1 – 10 of 481Yoshihiro Kawase, Tadashi Yamaguchi, Masashi Watanabe, Naotaka Toida, Tu Zhipeng and Norimoto Minoshima
This paper aims to describe a novel 3D finite element mesh modification method for motors with the skewed rotor in detail, the method having been developed by solving the Laplace…
Abstract
Purpose
This paper aims to describe a novel 3D finite element mesh modification method for motors with the skewed rotor in detail, the method having been developed by solving the Laplace equation.
Design/methodology/approach
Using the mesh of the skewed squirrel‐cage induction motor created by the novel method, the torque, the bar‐current, the electrical losses and so on are analyzed by the 3D finite element method.
Findings
It was found that the torque ripple, the bar‐current ripple and the losses of the motor with the skewed rotor are smaller than those of the motor with the no‐skewed rotor. In addition, the validity of the analysis is clarified by comparing the calculated and the measured results.
Originality/value
The usefulness of the method is clarified by the 3D finite element analysis of a skewed squirrel‐cage induction motor.
Details
Keywords
Lei Yin, Xiaolin Zheng, Dongxing Tang, Yanfeng Han, Rui Zhao and Yi Chen
This study aims to develop a new method to treat the numerical singularity at the critical nodes of two skew coordinates, and optimize the leakage of micro herringbone grooved…
Abstract
Purpose
This study aims to develop a new method to treat the numerical singularity at the critical nodes of two skew coordinates, and optimize the leakage of micro herringbone grooved journal bearings (MHGJBs) with this method.
Design/methodology/approach
A side leakage numerical algorithm is proposed by using the skew meshes with a virtual node (SMVN) method to evaluate the effects of groove angle, bank/groove ratio, groove depth and groove number on load capacity, friction and side leakage of MHGJB.
Findings
The SMVN method is effective in treating the numerical singularity at the critical nodes of two skew coordinates. Besides, a group of optimized parameters of micro herringbone groove is obtained which can not only minimize the side leakage but also improve the load capacity and friction force.
Originality/value
A virtual node method was proposed, which can significantly improve the calculation accuracy in the side leakage model.
Details
Keywords
Ajay Vadakkepatt, Sanjay R. Mathur and Jayathi Y. Murthy
Topology optimization is a method used for developing optimized geometric designs by distributing material pixels in a given design space that maximizes a chosen quantity of…
Abstract
Purpose
Topology optimization is a method used for developing optimized geometric designs by distributing material pixels in a given design space that maximizes a chosen quantity of interest (QoI) subject to constraints. The purpose of this study is to develop a problem-agnostic automatic differentiation (AD) framework to compute sensitivities of the QoI required for density distribution-based topology optimization in an unstructured co-located cell-centered finite volume framework. Using this AD framework, the authors develop and demonstrate the topology optimization procedure for multi-dimensional steady-state heat conduction problems.
Design/methodology/approach
Topology optimization is performed using the well-established solid isotropic material with penalization approach. The method of moving asymptotes, a gradient-based optimization algorithm, is used to perform the optimization. The sensitivities of the QoI with respect to design variables, required for optimization algorithm, are computed using a discrete adjoint method with a novel AD library named residual automatic partial differentiator (Rapid).
Findings
Topologies that maximize or minimize relevant quantities of interest in heat conduction applications are presented. The efficacy of the technique is demonstrated using a variety of realistic heat transfer applications in both two and three dimensions, in conjugate heat transfer problems with finite conductivity ratios and in non-rectangular/non-cuboidal domains.
Originality/value
In contrast to most published work which has either used finite element methods or Cartesian finite volume methods for transport applications, the topology optimization procedure is developed in a general unstructured finite volume framework. This permits topology optimization for flow and heat transfer applications in complex design domains such as those encountered in industry. In addition, the Rapid library is designed to provide a problem-agnostic pathway to automatically compute all required derivatives to machine accuracy. This obviates the necessity to write new code for finding sensitivities when new physics are added or new cost functions are considered and permits general-purpose implementations of topology optimization for complex industrial applications.
Details
Keywords
Di Yang and Zhiming Gao
A finite volume scheme for diffusion equations on non-rectangular meshes is proposed in [Deyuan Li, Hongshou Shui, Minjun Tang, J. Numer. Meth. Comput. Appl., 1(4)(1980)217–224…
Abstract
Purpose
A finite volume scheme for diffusion equations on non-rectangular meshes is proposed in [Deyuan Li, Hongshou Shui, Minjun Tang, J. Numer. Meth. Comput. Appl., 1(4)(1980)217–224 (in Chinese)], which is the so-called nine point scheme on structured quadrilateral meshes. The scheme has both cell-centered unknowns and vertex unknowns which are usually expressed as a linear weighted interpolation of the cell-centered unknowns. The critical factor to obtain the optimal accuracy for the scheme is the reconstruction of vertex unknowns. However, when the mesh deformation is severe or the diffusion tensor is discontinuous, the accuracy of the scheme is not satisfactory, and the author hope to improve this scheme.
Design/methodology/approach
The authors propose an explicit weighted vertex interpolation algorithm which allows arbitrary diffusion tensors and does not depend on the location of discontinuity. Both the derivation of the scheme and that of vertex reconstruction algorithm satisfy the linearity preserving criterion which requires that a discretization scheme should be exact on linear solutions. The vertex interpolation algorithm can be easily extended to 3 D case.
Findings
Numerical results show that it maintain optimal convergence rates for the solution and flux on 2 D and 3 D meshes in case that the diffusion tensor is taken to be anisotropic, at times heterogeneous, and/or discontinuous.
Originality/value
This paper proposes a linearity preserving and explicit weighted vertex interpolation algorithm for cell-centered finite volume approximations of diffusion equations on general grids. The proposed finite volume scheme with the new interpolation algorithm allows arbitrary continuous or discontinuous diffusion tensors; the final scheme is applicable to arbitrary polygonal grids, which may have concave cells or degenerate ones with hanging nodes. The final scheme has second-order convergence rate for the approximate solution and higher than first-order accuracy for the flux on 2 D and 3 D meshes. The explicit weighted interpolation algorithm is easy to implement in three dimensions in case that the diffusion tensor is continuous or discontinuous.
Details
Keywords
David A. Lowther, Behzad Forghani and Uday Deshpande
Two‐ and three‐dimensional computations of the cogging torque in a brushless dc motor are compared with measurements for both skewed and unskewed stators. The modeling of stator…
Abstract
Two‐ and three‐dimensional computations of the cogging torque in a brushless dc motor are compared with measurements for both skewed and unskewed stators. The modeling of stator skew is considered both using a full three dimensional model with and without material anisotropy and using a set of displaced two‐dimensional slices. The errors inherent in the latter approach are discussed. A cost/benefit trade‐off between three‐dimensional and two‐dimensional analyses is considered.
Details
Keywords
D. McBride, N. Croft and M. Cross
To improve flow solutions on meshes with cells/elements which are distorted/ non‐orthogonal.
Abstract
Purpose
To improve flow solutions on meshes with cells/elements which are distorted/ non‐orthogonal.
Design/methodology/approach
The cell‐centred finite volume (FV) discretisation method is well established in computational fluid dynamics analysis for modelling physical processes and is typically employed in most commercial tools. This method is computationally efficient, but its accuracy and convergence behaviour may be compromised on meshes which feature cells with non‐orthogonal shapes, as can occur when modelling very complex geometries. A co‐located vertex‐based (VB) discretisation and partially staggered, VB/cell‐centred (CC), discretisation of the hydrodynamic variables are investigated and compared with purely CC solutions on a number of increasingly distorted meshes.
Findings
The co‐located CC method fails to produce solutions on all the distorted meshes investigated. Although more expensive computationally, the co‐located VB simulation results always converge whilst its accuracy appears to grace‐fully degrade on all meshes, no matter how extreme the element distortion. Although the hybrid, partially staggered, formulations also allow solutions on all the meshes, the results have larger errors than the co‐located vertex based method and are as expensive computationally; thus, offering no obvious advantage.
Research limitations/implications
Employing the ability of the VB technique to resolve the flow field on a distorted mesh may well enable solutions to be obtained on complex meshes where established CC approaches fail
Originality/value
This paper investigates a range of cell centred, vertex based and hybrid approaches to FV discretisation of the NS hydrodynamic variables, in an effort characterize their capability at generating solutions on meshes with distorted or non‐orthogonal cells/elements.
Details
Keywords
Changsheng Wang, Xiaoxiao Sun, Xiangkui Zhang and Ping Hu
A higher-order Reissner-Mindlin plate element method is presented based on the framework of assumed stress quasi-conforming method and Hellinger-Reissner variational principle. A…
Abstract
Purpose
A higher-order Reissner-Mindlin plate element method is presented based on the framework of assumed stress quasi-conforming method and Hellinger-Reissner variational principle. A novel six-node triangular plate element is proposed by utilizing this method for the static and free vibration analysis of Reissner-Mindlin plates.
Design/methodology/approach
First, the initial assumed stress field is derived by using the fundamental analytical solutions which satisfy all governing equations. Then the stress matrix is treated as the weighted function to weaken the strain-displacement equations after the strains are derived by using the constitutive equations. Finally, the arbitrary order Timoshenko beam function is adopted as the string-net functions along each side of the element for strain integration.
Findings
The proposed element can pass patch test and is free from shear locking and spurious zero energy modes. Numerical tests show that the element can give high-accurate solutions, good convergence and is a good competitor to other models.
Originality/value
This work gives new formulations to develop high-order Reissner-Mindlin plate element, and the new strategy exhibits advantages of both analytical and discrete methods.
Details
Keywords
Tomasz Kwiatkowski, Pawel Flaszyński and Jerzy Zoltak
The simulations of grid-resolved rod vortex generators (RVGs) require high computational cost and time. Additionally, the computational mesh topology must be adjusted to rods…
Abstract
Purpose
The simulations of grid-resolved rod vortex generators (RVGs) require high computational cost and time. Additionally, the computational mesh topology must be adjusted to rods geometries. The purpose of this study is to propose the new source term model for RVG.
Design/methodology/approach
The model was proposed by modification of Bender, Anderson, Yagle (BAY) model used to predict flows around different type of vortex generators (VGs) – vanes. Original BAY model was built on lifting line theory. The proposed model was implemented in ANSYS Fluent by means of the user-defined function technique. Additional momentum and energy sources are imposed to transport equations.
Findings
The computational results of source term model were validated against experimental data and numerical simulation results for grid-resolved rod. It was shown that modified BAY model can be successfully used for RVG in complex cases. An example of BAY model application for RVG on transonic V2C airfoil with strongly oscillating shock waves is presented. Aerodynamic performance predicted numerically by means of both approaches (grid resolved RVG and modeled) is in good agreement, what indicates application opportunity of the proposed model to complex cases.
Practical implications
Modified BAY model can be used to simulate the influence of RVGs in complex real cases. It allows for time/cost reduction if the location or distribution of RVG has to be optimized on a profile, wing or in the channel.
Originality/value
In the paper, the new modification of BAY model was proposed to simulate RVGs. The presented results are innovative because of original approach to model RVGs.
Details
Keywords
Bernhard Weilharter, Oszkár Bíró and Siegfried Rainer
The purpose of this paper is to analyse the surface vibrations of an induction machine due to force waves acting on the stator and rotor core. The focus lies on the investigation…
Abstract
Purpose
The purpose of this paper is to analyse the surface vibrations of an induction machine due to force waves acting on the stator and rotor core. The focus lies on the investigation of the influence of force waves with axial variation and with higher spatial ordinal numbers on the surface vibration of an induction machine and thus its emitted noise.
Design/methodology/approach
Unit force waves with different spatial ordinal numbers and varying in axial direction are set up and applied on the stator and rotor teeth of a structural finite element model of an induction machine. Structural harmonic analyses with different frequencies are performed and the deformation of the machine is determined. After that, the root mean square of the normal component of the velocity on the surface of the machine's housing is determined and compared for the different force waves.
Findings
The influence of force waves with spatial ordinal numbers of higher order can have a significant influence on the structural vibration, especially if the spatial ordinal number is near the number of teeth. Furthermore, it is shown that the structure may react sensitively to axial variations of the forces, particularly near distinct structural resonances.
Originality/value
The presented investigations show relevant issues influencing the noise behaviour of electrical machines.
Details
Keywords
Bak Leong Wong and Ted Belytschko
An alternative stabilization approach has been developed for the 9‐node Lagrange plane and plate elements. In this approach, a stabilization stiffness is formulated using…
Abstract
An alternative stabilization approach has been developed for the 9‐node Lagrange plane and plate elements. In this approach, a stabilization stiffness is formulated using functions associated with the spurious zero‐energy modes. Efficiency has been increased by employing the same uniformly‐reduced integration scheme on the stabilization and underintegrated stiffness matrices. The results obtained using this rank‐sufficient element, termed the γ‐ψ element, appear to surpass those obtained with other rank‐sufficient 9‐node elements in accuracy.