Mesh Parameters Research Articles

Numerical simulation of drive axles considering the nonlinear couplings between gears and bearings

The drive axle is the core of the powertrain in automotive vehicles, and numerical simulation is a common and effective approach for designing and analysing drive axles. This article develops a new numerical simulation method for drive axles considering the nonlinear couplings between gears and bearings. Two types of models are proposed and integrated: a reduced model with nonlinear bearing elements and equivalent gear elements, which is efficient for nonlinear bearing simulation, and a gear contact analysis model with equivalent bearing stiffnesses, which can accurately reflect the gear mesh conditions and system deflection. The equivalent gear mesh parameters used in the reduced model are derived from the contact analysis model, and the linear equivalent bearing stiffness matrices used in the contact analysis model are derived from the reduced model. Therefore, the static equilibrium condition of the entire drive axle system is obtained through an iterative calculation process involving the two models under the same load condition. The good correlation between the numerical and experimental results of the gear-loaded contact pattern indicates that the proposed method is reliable.

3D reconstruction of skeletal mesh models and human foot biomodel generation using semantic parametric-based deformation

ABSTRACTThis paper introduces two methodologies for the reconstruction of skeletal mesh models and for the generation of parametric bone models of the human foot. First, a new Parametric-Based Deformation methodology is presented, which deforms a template 3D mesh according to user-defined semantic parameters in order to derive a new bone model. The proposed method allows the parameterization of dense and detailed 3D meshes of human foot bones. An extensive evaluation is performed to examine the accuracy, quality, and performance of the proposed method with human and animal bones, and versus existing statistical-based methods in the literature. Also, a novel methodology is proposed for the generation of parametric bone models of the human foot using non-calibrated biplanar X-rays. The proposed method has been applied for the production of detail 3D foot biomodels from an initial template biomodel and has been evaluated using human and animal bones.

Recommendations for simulating microparticle deposition at conditions similar to the upper airways with two-equation turbulence models

The development of a CFD model, from initial geometry to experimentally validated results with engineering insight, can be a time-consuming process that often requires several iterations of meshing and solver set-up. Applying a set of guidelines in the early stages can help to streamline the process and improve consistency between different models. The objective of this study was to determine both mesh and CFD solution parameters that enable the accurate simulation of microparticle deposition under flow conditions consistent with the upper respiratory airways including turbulent flow. A 90° bend geometry was used as a characteristic model that occurs throughout the airways and for which high-quality experimental aerosol deposition data is available in the transitional and turbulent flow regimes. Four meshes with varying degrees of near-wall resolution were compared, and key solver settings were applied to determine the parameters that minimize sensitivity to the near-wall (NW) mesh. The Low Reynolds number (LRN) k-ω model was used to resolve the turbulence field, which is a numerically efficient two-equation turbulence model, but has recently been considered overly simplistic. Some recent studies have used more complex turbulence models, such as Large Eddy Simulation (LES), to overcome the perceived weaknesses of two-equation models. Therefore, the secondary objective was to determine whether the more computationally efficient LRN k-ω model was capable of providing deposition results that were comparable to LES. Results show how NW mesh sensitivity is reduced through application of the Green-Gauss Node-based gradient discretization scheme and physically realistic near-wall corrections. Using the newly recommended meshing parameters and solution guidelines gives an excellent match to experimental data. Furthermore, deposition data from the LRN k-ω model compares favorably with LES results for the same characteristic geometry. In summary, this study provides a set of meshing and solution guidelines for simulating aerosol deposition in transitional and turbulent flows found in the upper respiratory airways using the numerically efficient LRN k-ω approach.

Parameterization of triangulated surface meshes based on constraints of distortion energy optimization

Parameterization of triangulated surface meshes is a crucial problem in computer graphics, computer aided geometric design and digital geometric processing. This paper addresses the problem of planar parameterization, i.e., mapping a given triangulated surface onto a planar domain. We construct an optimized algorithm for parameterization of genus-zero meshes and aim to minimize the distortion of the parameterization. An energy functional is proposed in the paper, that quantities angle and area distortions simultaneously, while the relative importance between angle and area preservation can be controlled by the user through a parameter. The method is based on an iterative procedure that incrementally flattens mesh by growing region to obtain a parameterization result with free boundary. The result is then converted to a parameterization with regular boundary by conformal mapping. Application of the method to texture mapping is presented. Experiments show that the proposed method can obtain better results than some common parameterization methods.

Editable texture map generation and optimization technique for 3D visualization presentation

ABSTRACTThe mesh parameterization method has been widely used in computational geometry. It maps a three-dimensional (3D) model onto the parametric (UV) domain, on which various applications can be developed, such as texture mapping. The texture mapping technique is commonly used to create the 3D color model of an object by combining a 3D model with the object's texture map. However, the resolution and quality of the texture on the color model is important and requires careful consideration. The purpose of this study is to develop an integrated method for generating the 3D color model of an object based on the conformal mesh parameterization and a technique for direct texture mapping from the object images. Furthermore, an optimization process in texture mapping is developed to maintain the photo consistency at the transition of different images on the 3D color model. The proposed 3D color model is integrated with a 3D visualization method for a new easier and smoother presentation mode for 3D product pre...

Parametric Reshaping of Portrait Images for Weight-change.

We present an easy-to-use parametric image retouching method for thinning or fattening a face in a single portrait image while maintaining a close similarity to the source image. First, our method reconstructs a 3D face from the input face image using a morphable model. Second, according to the linear regression equation derived from the depth statistics of the soft tissue in the face and the user-set parameters of weight-change degree, we calculate the new positions of the feature points. The Laplacian deformation method is then used for non-feature points in the 3D face model. Our model-based reshaping process can achieve globally consistent editing effects without noticeable artifacts. We seamlessly blend the reshaped face region with the background using image retargeting method based on mesh parametrization. The effectiveness of our algorithm is demonstrated by experiments and user study.

Additive average Schwarz with adaptive coarse spaces: scalable algorithms for multiscale problems

We present an analysis of the additive average Schwarz preconditioner with two newly proposed adaptively enriched coarse spaces, which were presented at the twenty-third international conference on domain decomposition methods in Korea, for solving second-order elliptic problems with highly varying and discontinuous coefficients. It is shown that the condition number of the preconditioned system is bounded independently of the variations and the jumps in the coefficient while depending only on a prescribed threshold for the eigenvalues of the coarse space, and it depends linearly on the mesh parameter ratio H/h that is the ratio between the subdomain size and the mesh size thereby retaining the same optimality and scalability of the original additive average Schwarz preconditioner.

Scaling Invariance and Characteristics of the Cloud of Spherical Projectile Fragmentation Products upon High-Velocity Impact on a Thin Mesh Shield

In the present paper we consider the problem of the fragmentation of an aluminum projectile on a thin steel mesh shield at high-velocity impact in a three-dimensional (3D) setting. The numerical simulations are carried out by smoothed particle hydrodynamics method applied to the equations of mechanics of deformable solids. Quantitative characteristics of the projectile fragmentation are obtained by studying statistics of the cloud of fragments. The considerable attention is given to scaling laws accompanying the fragmentation of the projectile. Scaling is carried out using the parameter K which defines the number of the mesh cells falling within the projectile diameter. It is found that the dependence of the critical velocity Vc of fragmentation on the parameter K consists of two branches that correspond to two modes of the projectile fragmentation associated with the "small" and "large" aperture of the mesh cell. We obtain the dependences of the critical velocity Vc on the projectile diameter and the mesh parameters for the both modes of the fragmentation. It is shown that the average cumulative mass distributions constructed at Vc exhibit the property of scale invariance, splitting into two groups of distributions exactly corresponding to the modes of the projectile fragmentation. In each group, the average cumulative distributions show good coincidence in the entire mass region, moreover in the intermediate mass region the each group of distributions has a power-law distribution with an exponent tau different from that in the other group. The conclusion about the dependence of the exponent of the power-law distribution tau on the fragmentation mode is made.

Automated Analysis of Meshing Performance of Harmonic Drive Gears Under Various Operating Conditions

Accurate and efficient analysis of the meshing performance of harmonic drives (HDs) is the core and challenging problem for the improvement of the positioning accuracy of robots. This paper presents an integrated hardware and software system for an automated analysis of the meshing performance of the HD under various operating conditions. First, an optical measurement method based on the principle of periscope is proposed to capture the meshing images at a different driving speed and load torque. Next, a position tracking algorithm based on image processing and pattern recognition is designed to obtain the positions of the flexspline and circular spline teeth in the meshing process. Furthermore, a mathematical model based on the geometric relationship between the flexspline and the circular spline teeth is established to calculate the meshing backlash and depth. Last, the performance and advantages of the proposed method are demonstrated through uncertainty analysis and comparing with the conventional method. The results show that the error of the calculated meshing parameters is close to 0, and 1.59 s are required to track the FS teeth in each video frame with a laptop of 2.6-GHz CPU and 12-GB RAM. Moreover, the total rotation angle of the wave generator and the backlash and depth in the meshing process are seriously affected by the driving speed and load torque. Our method offers an effective tool for the HD manufacturers to examine the quality of products, and the obtained results can help to optimize the tooth profile of the HD.

Study on coupling effect between the time-varying gear backlash and the different time-varying mesh parameters on the gear system

The vibration excitation of the rolling mill mainly comes from the gearbox in the process of rolling strip, and the meshing excitation is the main excitation factor of the gearbox. And the gear backlash plays an important role in the meshing excitation. However, the backlash is inevitable in the process of designing the gear system. Therefore, it is important to select the appropriate gear backlash to reduce the vibration amplitude of the gearbox, to improve the rolling speed and the quality of the steel strip. So, in this paper, the effect of the different variation amplitudes for the time-varying gear backlash (TVGB) on the vibration characteristics of the gear system under various mesh parameters is studied. A new formulation for calculating nonlinear damping and time varying meshing stiffness is applied in this coupling model. The results show that increasing of the load torque, the damping ratio, the system parameter or decreasing the directional rotation radius variation or kinematic transmission error caused the effects of variation amplitudes for the (TVGB) on the dynamic characteristics of the gear system to decrease. Test data from a gearbox experimental table verifies the accuracy of the model. The model is shown to be capable of simulating the mutually coupled effect between the backlash and the different parameters on the gear system. So, the new coupled model can be used as guide to select the appropriate gear backlash values for the rolling mill under different operating conditions.

Sensitivity of Rotorcraft Hover Predictions to Mesh Resolution in Strand Grid Framework

The strand grid approach is a flow solution method where a prismatic like grid using “strands” is grown to a short distance from the body surface to capture the viscous boundary layer and the rest of the domain is covered using an adaptive Cartesian grid. The approach offers a potential for nearly automatic grid generation and adaptation requiring very few input parameters while, at same time, offering the ability to obtain fast and efficient flow solution. This paper explores the sensitivity of rotor hover predictions to various meshing parameters in the strand grid framework. Surface mesh resolution has minimal impact on the predictions, whereas both the outer extent of the strand mesh and the Cartesian mesh resolution have significant effect on rotor performance and wake predictions. A strand mesh extending out to half a chord distance away and a Cartesian mesh spacing of less than two times the outer boundary spacing of the strand mesh are recommended for most rotor blade simulations.

Optimization of a parameterized inexact Uzawa method for saddle point problems

ABSTRACTFor large sparse saddle point problems, Cao et al. studied a modified generalized parameterized inexact Uzawa (MGPIU) method (see [Y. Cao, M.Q. Jiang, L.Q. Yao, New choices of preconditioning matrices for generalized inexact parameterized iterative methods, J. Comput. Appl. Math. 235 (1) (2010) 263–269]). For iterative methods of this type, the choice of the relaxation parameter is crucial for the methods to achieve their best performance. In this paper, for an example of 2D Stokes equations, we derive the optimal relaxation parameter for the continuous version of the MGPIU method, by minimizing the corresponding convergence factor that is obtained using Fourier analysis. In addition, we find that the MGPIU method is mesh parameter independent, however, it depends asymptotically linearly on the viscosity ν, which suggests that the numerical methods for Stokes equations should be investigated with the presence of the viscosity ν, though it can be scaled out from the equations in advance. We use numerical experiments to validate our theoretical findings.

Sensitivity analysis on the effective stiffness properties of 3-D orthotropic honeycomb cores

ABSTRACTThe present study investigates the influences of representative volume element RVE mesh and material parameters, here cell wall elastic moduli, on the effective stiffness properties of three dimensional orthotropic honeycomb cores through strain driven computational homogenization in the finite element framework. For this purpose, case studies were carried out, for which hexagonal cellular RVEs were generated, meshed with eight node linear brick finite elements of varying numbers. Periodic boundary conditions were then implemented on the RVE boundaries by using one-to-one nodal match for the corresponding corners, edges and surfaces for the imposed macroscopic strains. As a novelty, orthotropic material properties were assigned for each cell wall by means of the transformation matrices following the cell wall orientations. Thereafter, simulations were conducted and volume averaged macroscopic stresses were obtained. Eventually, effective stiffness properties were obtained, through which RVE sensitivity analysis was carried out. The investigations indicate that there is a strong relation between number of finite elements and most of the effective stiffness parameters. In addition to this, cell wall elastic moduli also play critical role on the effective properties of the investigated materials.

Large-scale subject-specific cerebral arterial tree modeling using automated parametric mesh generation for blood flow simulation

In this paper, we present a novel technique for automatic parametric mesh generation of subject-specific cerebral arterial trees. This technique generates high-quality and anatomically accurate computational meshes for fast blood flow simulations extending the scope of 3D vascular modeling to a large portion of cerebral arterial trees. For this purpose, a parametric meshing procedure was developed to automatically decompose the vascular skeleton, extract geometric features and generate hexahedral meshes using a body-fitted coordinate system that optimally follows the vascular network topology. To validate the anatomical accuracy of the reconstructed vasculature, we performed statistical analysis to quantify the alignment between parametric meshes and raw vascular images using receiver operating characteristic curve. Geometric accuracy evaluation showed an agreement with area under the curves value of 0.87 between the constructed mesh and raw MRA data sets. Parametric meshing yielded on-average, 36.6% and 21.7% orthogonal and equiangular skew quality improvement over the unstructured tetrahedral meshes. The parametric meshing and processing pipeline constitutes an automated technique to reconstruct and simulate blood flow throughout a large portion of the cerebral arterial tree down to the level of pial vessels. This study is the first step towards fast large-scale subject-specific hemodynamic analysis for clinical applications.

A meshing strategy for a quadratic iso-parametric FEM in cavitation computation in nonlinear elasticity

The approximation properties of a quadratic iso-parametric finite element method for a typical cavitation problem in nonlinear elasticity in two dimensions are analyzed. More precisely, (1) the finite element interpolation errors are established in terms of the mesh parameters; (2) a mesh distribution strategy based on an error equi-distribution principle is given; (3) the convergence of finite element cavity solutions is proved. Numerical experiments show that, in fact, the optimal convergence rate can be achieved by the numerical cavity solutions.

Steady-State Heat-Flow Coupling Field of a High-Power Magnetorheological Fluid Clutch Utilizing Liquid Cooling

Compared with traditional speed regulation (SR) approaches like variable frequency and hydraulic coupling, magnetorheological clutch (MRC) provides a more superior solution for high-efficiency energy saving SR. However, recent developments have demonstrated that severe heating is an outstanding challenge for MRC, especially in high-power applications. Among commonly used cooling methods, liquid cooling offers a viable alternative for the problem. Aiming at pre-evaluating the cooling efficiency of a liquid-cooled MRC in high-power situations, this study introduces a heat-flow coupling simulation method. In this paper, theoretical basis for the simulation is presented first, which is followed by an illustration of the heat-flow coupling simulation. This paper details the simulation model establishment, finite element meshing (FEM), boundary conditions, and simulation parameters. After the simulations, the results concerning the steady flow field of the internal coolant, along with the steady-state temperature fields of MRC, magnetorheological (MR) fluids and the coolant are presented and discussed. Finally, several heating tests of an MRC prototype under various operation conditions are performed and the results verify the correctness and rationality of the simulation.

Nonrigid iterative closest points for registration of 3D biomedical surfaces

Advanced 3D optical and laser scanners bring new challenges to computer graphics. We present a novel nonrigid surface registration algorithm based on Iterative Closest Point (ICP) method with multiple correspondences. Our method, called the Nonrigid Iterative Closest Points (NICPs), can be applied to surfaces of arbitrary topology. It does not impose any restrictions on the deformation, e.g. rigidity or articulation. Finally, it does not require parametrization of input meshes. Our method is based on an objective function that combines distance and regularization terms. Unlike the standard ICP, the distance term is determined based on multiple two-way correspondences rather than single one-way correspondences between surfaces. A Laplacian-based regularization term is proposed to take full advantage of multiple two-way correspondences. This term regularizes the surface movement by enforcing vertices to move coherently with their 1-ring neighbors. The proposed method achieves good performances when no global pose differences or significant amount of bending exists in the models, for example, families of similar shapes, like human femur and vertebrae models.

OpenMP GNU and Intel Fortran programs for solving the time-dependent Gross–Pitaevskii equation

We present Open Multi-Processing (OpenMP) version of Fortran 90 programs for solving the Gross-Pitaevskii (GP) equation for a Bose-Einstein condensate in one, two, and three spatial dimensions, optimized for use with GNU and Intel compilers. We use the split-step Crank-Nicolson algorithm for imaginary- and real-time propagation, which enables efficient calculation of stationary and non-stationary solutions, respectively. The present OpenMP programs are designed for computers with multi-core processors and optimized for compiling with both commercially-licensed Intel Fortran and popular free open-source GNU Fortran compiler. The programs are easy to use and are elaborated with helpful comments for the users. All input parameters are listed at the beginning of each program. Different output files provide physical quantities such as energy, chemical potential, root-mean-square sizes, densities, etc. We also present speedup test results for new versions of the programs.

Weighted area/angle distortion minimization for Mesh Parameterization

PurposeMesh Parameterization is central to reverse engineering, tool path planning, etc. This work synthesizes parameterizations with un-constrained borders, overall minimum angle plus area distortion. This study aims to present an assessment of the sensitivity of the minimized distortion with respect to weighed area and angle distortions.Design/methodology/approachA Mesh Parameterization which does not constrain borders is implemented by performing: isometry maps for each triangle to the plane Z = 0; an affine transform within the plane Z = 0 to glue the triangles back together; and a Levenberg–Marquardt minimization algorithm of a nonlinear F penalty function that modifies the parameters of the first two transformations to discourage triangle flips, angle or area distortions. F is a convex weighed combination of area distortion (weight: α with 0 ≤ α ≤ 1) and angle distortion (weight: 1 − α).FindingsThe present study parameterization algorithm has linear complexity [\U0001d4aa(n), n = number of mesh vertices]. The sensitivity analysis permits a fine-tuning of the weight parameter which achieves overall bijective parameterizations in the studied cases. No theoretical guarantee is given in this manuscript for the bijectivity. This algorithm has equal or superior performance compared with the ABF, LSCM and ARAP algorithms for the Ball, Cow and Gargoyle data sets. Additional correct results of this algorithm alone are presented for the Foot, Fandisk and Sliced-Glove data sets.Originality/valueThe devised free boundary nonlinear Mesh Parameterization method does not require a valid initial parameterization and produces locally bijective parameterizations in all of our tests. A formal sensitivity analysis shows that the resulting parameterization is more stable, i.e. the UV mapping changes very little when the algorithm tries to preserve angles than when it tries to preserve areas. The algorithm presented in this study belongs to the class that parameterizes meshes with holes. This study presents the results of a complexity analysis comparing the present study algorithm with 12 competing ones.

Isometry‐Aware Preconditioning for Mesh Parameterization

AbstractThis paper presents a new preconditioning technique for large‐scale geometric optimization problems, inspired by applications in mesh parameterization. Our positive (semi‐)definite preconditioner acts on the gradients of optimization problems whose variables are positions of the vertices of a triangle mesh in ℝ2 or of a tetrahedral mesh in ℝ3, converting localized distortion gradients into the velocity of a globally near‐rigid motion via a linear solve. We pose our preconditioning tool in terms of the Killing energy of a deformation field and provide new efficient formulas for constructing Killing operators on triangle and tetrahedral meshes. We demonstrate that our method is competitive with state‐of‐the‐art algorithms for locally injective parameterization using a variety of optimization objectives and show applications to two‐ and three‐dimensional mesh deformation.