Stress Function of a Rotating Variable-Thickness Annular Disk Using Exact and Numerical Methods

In this paper, the exact analytical and numerical solutions for rotating variable-thickness annular disk are presented. The inner and outer edges of the rotating variable-thickness annular disk are considered to have free boundary conditions. Two different annular disks for the radially varying thickness are given. The numerical Runge-Kutta solution as well as the exact analytical solution is available for the first disk while the exact analytical solution is not available for the second annular disk. Both exact and numerical results for stress function, stresses, strains and radial displacement will be investigated for the first annular disk of variable thickness. The accuracy of the present numerical solution is discussed and its ability of use for the second rotating variable-thickness annular disk is investigated. Finally, the distributions of stress function, displacement, strains, and stresses will be presented. The appropriate comparisons and discussions are made at the same angular velocity.

浸入运动边界-格子Boltzmann方法4种固含率计算方法对比研究

为了达到流固耦合,格子Boltzmann方法(LBM)可采用浸入运动边界法(IMB)实现移动颗粒边界上的无滑移条件.该耦合方式(IMB-LBM)中固含率计算方法对流固耦合计算精度和效率有影响.对常用的固含率4种计算方法,即蒙特卡洛法(MCM)、单元分解法(UDM)、近似多边形法(APM)和闭合边界法(CBM),分别阐述其具体算法,对比了它们的计算精度和计算效率;最后通过圆盘颗粒非连续变形分析方法(DDDA)与IMB-LBM耦合模型下的一个多颗粒沉降流固耦合算例,对比分析了它们在流固耦合计算过程中的耗时.结果表明:1)CBM无误差,MCM和UDM在随机点数取1000,子单元数取100时误差稳定在1%以下,APM在颗粒直径大于格子长度10倍时,误差小于0.44%;2)MCM和UDM的计算精度及耗时分别与随机点数和子单元数相关,它们的计算耗时大于APM和CBM;3)计算效率上,APM>CBM>UDM>MCM,其中CBM计算耗时略微大于APM,APM和UDM计算耗时分别比MCM少2个和1个数量级.该结果可为IMB-LBM耦合模型中固含率计算方法优选提供借鉴.

基于Hot Disk方法测量热导率的影响因素

基于hot disk方法测量材料的热导率时,探头热容及时间延迟的存在会直接影响热导率测量的准确度.为了有效地评估这种影响的程度,本文基于探头表面平均温升理想模型提出了一种可实现热容补偿及时间补偿的修正模型,并利用hot disk热物性分析仪的数据采集系统分别搭载两个不同半径的探头对Pyroceram 9606标准材料在常温常压条件下的热导率进行了测量.实验结果表明,对于测试时间比较短的情况,对理想模型进行探头热容补偿及时间补偿能够较大幅度地提高热导率的测量准确度,并且与hot disk热物性分析仪的测量结果非常接近,探头四线电阻散热的影响是造成差距的主要原因.

Hot disk探头热容对热导率测量的影响

Hot disk探头热容的存在会直接影响热导率测量的准确度。为有效地评估这种影响的程度,在基于瞬态点热源格林函数法得到探头表面平均温升理想模型的基础上,提出了一种能够修正探头热容对实际加热功率影响的改进模型,并利用三种不同大小及热容值的探头及Hot disk数据采集系统对Pyroceram 9606标准材料的热导率进行了测量。测量结果表明,Hot disk探头热容对热导率测量精度的影响会随探头半径、测量时间及加热功率等测量参数的不同而发生变化,对理想模型进行探头热容补偿可以有效提高热导率测量准确度,且探头热容相对实验总加热量的大小是影响热导率测量准确度的决定因素。

角色动画中基于隐式曲面的皮肤变形方法

提出了一种角色动画中基于隐式曲面的皮肤变形方法,主要面向具有骨骼层次以及相关蒙皮权重的动画模型,利用隐式曲面来驱动皮肤变形.首先,采用埃尔米特径向基函数和泊松圆盘采样对给定骨骼绑定的网格部分进行重建,把角色模型的体积近似当作一组局部的三维标量场,并保留原有的网格属性;其次,构造场函数,通过场函数纠正几何蒙皮技术的结果;最后,结合两种组合算子,使用隐式方法在人体模型上形成合理可信的皮肤变形效果.本方法不会产生糖纸扭曲和关节膨胀的问题,并且可以生成皮肤接触效果和肌肉凸起.由于该方法是后处理,因此非常适合标准动画制作流程.

如何用Diskedit找回失去的硬盘

介绍了用软件Diskedit找回失去的硬盘的方法与技巧,具有很强的可操作性与实用性。

Hot Disk测量法对苯板导热系数测定分析

本文基于Hot Disk测量法基本原理,通过正确选取设备加热功率和探测时间对聚苯乙烯泡沫板导热系数进行测定,实验过程比稳态法热流计法方便、快捷、准确且增大了选取聚苯乙烯泡沫板厚度的测定范围,分析了聚苯乙烯泡沫板热物理性能对实验结果的影响.

Mode II fracture analysis of double edge cracked circular disk subjected to different diametral compression

A detailed analysis of mode II stress intensity factors(SIFs) for the double edge cracked Brazilian disk subjected to different diametral compression is presented using a weight function method. The mode II SIFs at crack tips can be obtained by simply calculating an integral of the product of mode II weight function and the shear stress on the prospective crack faces of uncracked disk loaded by a diametral compression. A semi-analytical formula for the calculation of normalized mode II SIF, f _Ⅱ, is derived for different crack lengths (from 0.1 to 0.7) and inclination angles (from 10° to 75°) with respect to loading direction. Comparison between the obtained results and finite element method solutions shows that the weight function method is of high precision. Combined with the authors previous work on mode I fracture analysis, the new specimen geometry can be used to study fracture through any combination of mode I and mode II loading by a simple alignment of the crack relative to the diameter of compression loading, and to obtain pure mode II crack extension. Another advantage of this specimen geometry is that it is available directly from rock core and is also easy to fabricate.

Analytical and Numerical Solutions for a Rotating Annular Disk of Variable Thickness

In this paper, the analytical and numerical solutions for rotating variable-thickness solid disk and numerical solution for rotating variable-thickness annular disk are presented. The outer edge of the solid disk and the inner and outer edges of the annular disk are considered to have clamped boundary conditions. Two different cases for the radially varying thickness of the solid and annular disks are given. The numerical solution as well as the analytical solution is available for the first case of the solid disk while the analytical solution is not available for the second case of the annular disk. Both analytical and numerical results for displacement and stresses will be investigated for the first case of radially varying thickness. The accuracy of the present numerical solution is discussed and its ability of use for the second case of radially varying thickness is investigated. Finally, the distributions of displacement and stresses will be presented and the appropriate comparisons and discussions are made at the same angular velocity.

Evaluation of Stress Intensity Factors for Multiple Cracked Circular Disks Under Crack Surface Tractions with SBFEM

Stress intensity factors (SIFs) for the cracked circular disks under different distributing surface tractions are evaluated with the scaled boundary finite element method (SBFEM). In the SBFEM, the analytical advantage of the solution in the radial direction allows SIFs to be directly determined from its definition, therefore no special crack-tip treatment is necessary. Furthermore anisotropic material behavior can be treated easily. Different distributions of surface tractions are considered for the center and double-edge-cracked disks. The benchmark examples are modeled and an excellent agreement between the results in the present study and those in published literature is found. It shows that SBFEM is effective and possesses high accuracy. The SIFs of the cracked orthotropic material circular disks subjected to different surface tractions are also evaluated. The technique of substructure is applied to handle the multiple cracks problem.

Mass flow in a circumbinary disk with a gap around supermassive binary black holes

We study the interaction between supermassive binary black holes in an elliptical orbit and their surrounding disk with a gap.The gap in the disk is a low density region formed due to the tidal effects of the less massive black hole.The binary we have investigated has a sub-parsec separation and is coplanar with the disk.We find that the maximum variation of the surface density in the gap reaches 50%during an orbital period.However,in other regions of the disk,the density variation is much less than 1%.Furthermore,we calculate the corresponding variation of spectral energy distribution within a period,but little variation is found.The reason for these results is that the viscosity timescale of the disk at the binary radius is much longer than the orbital period of the binary.

Dust growth in protoplanetary disks-a comprehensive experimental / theoretical approach

More than a decade of dedicated experimental work on the collisional physics of protoplanetary dust has brought us to a point at which the growth of dust aggregates can-for the first time-be self-consistently and reliably modeled. In this article, the emergent collision model for protoplanetery dust aggregates, as well as the numerical model for the evolution of dust aggregates in protoplanetary disks, is reviewed. It turns out that, after a brief period of rapid collisional growth of fluffy dust aggregates to sizes of a few centimeters, the protoplanetary dust particles are subject to bouncing collisions, in which their porosity is considerably decreased. The model results also show that low-velocity fragmentation can reduce the final mass of the dust aggregates but that it does not trigger a new growth mode as discussed previously. According to the current stage of our model, the direct formation of kilometer-sized planetesimals by collisional sticking seems unlikely, implying that collective effects, such as the streaming instability and the gravitational instability in dust-enhanced regions of the protoplanetary disk, are the best candidates for the processes leading to planetesimals.

Mapping the Milky Way with LAMOSTⅠ:method and overview

We present a statistical method to derive the stellar density profiles of the Milky Way from spectroscopic survey data,taking into account selection effects.We assume the selection function,which can be altered during observations and data reductions,of the spectroscopic survey is based on photometric colors and magnitude.Then the underlying selection function for a line-of-sight can be recovered well by comparing the distribution of the spectroscopic stars in a color-magnitude plane with that of the photometric dataset.Subsequently,the stellar density profile along a line-of-sight can be derived from the spectroscopically measured stellar density profile multiplied by the selection function.The method is validated using Galaxia mock data with two different selection functions.We demonstrate that the derived stellar density profiles reconstruct the true ones well not only for the full set of targets,but also for sub-populations selected from the full dataset.Finally,the method is applied to map the density profiles for the Galactic disk and halo,using the LAMOST RGB stars.The Galactic disk extends to about R=19 kpc,where the disk still contributes about 10% to the total stellar surface density.Beyond this radius,the disk smoothly transitions to the halo without any truncation,bending or breaking.Moreover,no over-density corresponding to the Monoceros ring is found in the Galactic anti-center direction.The disk shows moderate north–south asymmetry at radii larger than 12 kpc.On the other hand,the R–Z tomographic map directly shows that the stellar halo is substantially oblate within a Galactocentric radius of 20 kpc and gradually becomes nearly spherical beyond 30 kpc.

Robust Optimum Design of Thrust Hydrodynamic Bearings for Hard Disk Drives

This paper describes the robust optimum design which combines the geometrical optimization method proposed by Hashimoto and statistical method. Recently, 2.5″ hard disk drives (HDDs) are widely used for mobile devices such as laptops, video cameras and car navigation systems. In mobile applications, high durability towards external vibrations and shocks are essentials to the bearings of HDD spindle motor. In addition, the bearing characteristics are influenced by manufacturing error because of small size of the bearings of HDD. In this paper, the geometrical optimization is carried out to maximize the bearing stiffness using sequential quadratic programming to improve vibration characteristics. Additionally, the bearing stiffness is analyzed considering dimensional tolerance of the bearing using statistical method. The dimensional tolerance is assumed to distribute according to the Gaussian distribution, and then the bearing stiffness is estimated by combining the expectation and standard deviation. As a result, in the robust optimum design, new groove geometry of bearing can be obtained in which the bearing stiffness is four times higher than the stiffness of conventional spiral groove bearing. Moreover, the bearing has lower variability compared with the result of optimum design neglecting dimensional tolerance.

Theoretical investigation of micropolar fluid flow between two porous disks

The steady, laminar, incompressible and two dimensional micropolar flow between two porous disks was investigated using optimal homotopy asymptotic method(OHAM) and fourth order Runge–Kutta numerical method. Comparison between OHAM and numerical method shows that OHAM is an exact and high efficient method for solving these kinds of problems. The results are presented to study the velocity and rotation profiles for different physical parameters such as Reynolds number, vortex viscosity parameter, spin gradient viscosity and microinertia density parameter. As an important outcome, the magnitude of the microrotation increases with an increase in the values of injection velocity while it decreases by increasing the values of suction velocity.

Flow of micropolar fluid between two orthogonally moving porous disks

The unsteady,laminar,incompressible,and two-dimensional flow of a micropolar fluid between two orthogonally moving porous coaxial disks is considered.The extension of von Karman's similarity transformations is used to reduce the governing partial differential equations(PDEs) to a set of non-linear coupled ordinary differential equations(ODEs) in the dimensionless form.The analytical solutions are obtained by employing the homotopy analysis method(HAM).The effects of various physical parameters such as the expansion ratio and the permeability Reynolds number on the velocity fields are discussed in detail.

RELIABILITY ANALYSIS FOR AN AERO ENGINE TURBINE DISK UNDER LOW CYCLE FATIGUE CONDITION

Reliability analysis methods based on the linear damage accumulation law (LDAL) and load-life interference model are studied in this paper. According to the equal probability rule, the equivalent loads are derived, and the reliability analysis method based on load-life interference model and recurrence formula is constructed. In conjunction with finite element analysis (FEA) program, the reliability of an aero engine turbine disk under low cycle fatigue (LCF) condition has been analyzed. The results show the turbine disk is safety and the above reliability analysis methods are feasible.

Numerical Investigation of Flow Structure Interaction Coupling Effects in Hard Disk Drives

This paper studies the flow structural interaction (FSI) within a hard disk drive (HDD) through the use of a novel coupling method. The interaction studied was the fluid induced vibration in the HDD. A two step coupling approach was used, where the fluid and structural components were solved sequentially. The result obtained was a ratio of 0.65 between the vibration amplitudes of a fixed head stack assembly (HSA) and a moving HSA. The ratio was next applied on a real 3.5 inch HDD, to allow the parameter to be further improved upon. A new benchmark index of 0.69 was developed from this. This parameter may allow future researchers to model the out of plane vibrations of a HSA easily, saving precious time. A 31% more accurate simulation of FSI within 3.5 inch HDD at 15000 rpm is achieved by the use of this new coupling method and benchmark index.

The analysis of disk core from the Maoping 800 m bore hole

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Two solutions for the BVP of a rotating variable-thickness solid disk

This paper presents the analytical and numerical solutions for a rotating variable-thickness solid disk. The outer edge of the solid disk is considered to have free boundary conditions. The governing equation is derived from the basic equations of the rotating solid disk and it is solved analytically or numerically using finite difference algorithm. Both analytical and numerical results for the distributions of stress function and stresses of variable-thickness solid disks are obtained. Finally, the distributions of stress function and stresses are presented and the appropriate comparisons and discussions are made at the same angular velocity.