Influence of the tip mass on the tip-sample interactions in TM-AFM

This paper focuses on the influences of the tip mass ratio (the ratio of the tip mass to the cantilever mass), on the excitation of higher oscillation eigenmodes and also on the tip-sample interaction forces in tapping mode atomic force microscopy (TM-AFM). A precise model for the cantilever dynamics capable of accurate simulations is essential for the investigation of the tip mass effects on the interaction forces. In the present work, the finite element method (FEM) is used for modeling the AFM cantilever to consider the oscillations of higher eigenmodes oscillations. In addition, molecular dynamics (MD) is used to calculate precise data for the tip-sample force as a function of tip vertical position with respect to the sample. The results demonstrate that in the presence of nonlinear tip-sample interaction forces, the tip mass ratio plays a significant role in the excitations of higher eigenmodes and also in the normal force applied on the surface. Furthermore, it has been shown that the difference between responses of the FEM and point-mass models in different system operational conditions is highly affected by the tip mass ratio.     

Surface stresses and flow modes on contact surface in a combined double cup extrusion process

The main goal of this study is to examine the influence of geometrical parameters in double cup extrusion process (DCEP) on the surface stress profiles such as surface expansion, contact pressure, sliding velocity and distance. The flow modes, sliding over or sticking onto the punch surface, were also investigated to see the possibility of the metal-to-metal contact or the lubricant film breakdown along the punch and workpiece interface. Two major design factors chosen for analysis include the reduction in area in backward direction (RAB) and the wall thickness ratio (TR). A sequential operation has been also simulated to compare the surface stress profiles and flow modes with those in a combined operation.     

A new theorem on higher order derivatives of Lyapunov functions

The Lyapunov stability analysis method for nonlinear dynamic systems requires a non positive first derivative of the Lyapunov functions along the system’s trajectories. In this paper, a new method is developed to relax this requirement. A new sufficient condition is developed for the stability analysis of nonlinear systems, introducing some inequalities for higher order derivatives of the Lyapunov function. The differential inequalities can be considered as a new controllable canonical form linear time invariant system with negative inputs. The stability analysis of a given nonlinear system is then reduced to check if the characteristic equation for the new linear time invariant system is Hurwitz. Some examples are presented to establish the approach.     

Determination of NSIFs and coefficients of higher order terms for sharp notches using finite element method

An overdeterministic method was used for calculating the Notch Stress Intensity Factors (NSIFs) as well as the coefficients of the higher order terms for structures containing sharp notches. The series solution of displacement fields around the notch tip was fitted to a large number of nodal displacements obtained from finite element analysis. An over-determined set of simultaneous linear equations was then derived and the nodal displacements reduced to a small set of unknown coefficients by employing the concept of the least-squares method. The efficiency of the proposed method was assessed through analyzing several notched specimens under pure mode I, pure mode II and mixed modes I/II loading. The accuracy of the NSIFs and the coefficients of higher order terms was evaluated by comparing them with the results available in the literature, or the results obtained by the boundary collocation method. While the presented method is simple, it yields very good results.     

Sliding behavior of metallic glass: Part II. Computer simulations

Molecular dynamics (MD) calculations were used to simulate the sliding of a two-component 2D amorphous system interacting via Lennard–Jones potentials. The friction coefficient showed a transient before reaching an average steady state value. The steady state friction coefficient was observed to decrease with an increasing sliding velocity. Mixing was observed at the sliding interface. The mixed layer grew at a rate that scaled with the square root of time. A density decrease was recorded in the region adjacent to the sliding interface. This spatially corresponded to the softer layer detected experimentally near the worn surface in a Zr_41.2Ti_13.8Cu_12.5Ni_10.0Be_22.5 bulk metallic glass alloy after sliding. Subsurface displacement profiles produced in these simulations were similar to those observed in other material systems. The Navier–Stokes equation was used to analyze the material flow pattern, with results in agreement with data obtained from simulations. This suggests that the observed subsurface displacement profile may be a generic material flow pattern under combined compression and shear.     

接触角和横向载荷对轮轨粘着的影响

应用多层多支子结构技术建立轮对与轨道的多体接触模型,采用参变量变分原理和数学二次规划法求解轮轨接触力,根据不同的接触角和横向载荷计算得出轮轨接触力分布,分析接触角和横向载荷对纵向摩擦力(牵引力)以及粘着系数的影响。计算结果表明,轮对承受横向载荷时,轮轨接触点对之间摩擦力的方向在粘着区和蠕滑区有明显的不同,在粘着区其方向与钢轨纵向夹角较小,而在蠕滑区其方向与钢轨纵向夹角较大;当接触角较小时,粘着系数随着横向载荷的增加而减小;当接触角较大时,随着横向载荷的增加,粘着系数先增加后减小;在直线段粘着系数随着轮对承受横向载荷的增加而减小,在曲线段选取适当的横向载荷能够提高粘着系数。     

结构仿真高精度有限元网格划分方法

为了得到高精度计算结果的有限元网格,在有限元模型任一单元小片内将其误差分解为全局误差与局部误差两部分:局部误差是由于该单元小片内单元的残值所引起的,而全局误差是由单元小片外区域内单元的残值所导致。提出关键性区域的概念,并得出有限元求解模型中所有关键性区域的网格划分水平决定整个有限元模型的计算结果精度的论断。基于该结论建立高精度有限元网格划分方法流程。以连杆为实例,应用高精度有限元网格划分方法流程对连杆进行高精度网格划分。在压缩工况下,对其平面模型进行关键性区域的划分,并研究其误差特性,可知局部误差是连杆结构仿真误差的主导部分。划分疏密得当的高精度网格。应用实例证明了提出方法的可行性、实用性。     

Simulations on atomic-scale friction between self-assembled monolayers: Phononic energy dissipation

Atomic-scale friction between self-assembled monolayers (SAMs) on Au (1 1 1) has been studied through molecular dynamics simulations, with emphasis on the mechanism of energy dissipation. Results show that the shear stress and chain angle on commensurate SAMs exhibit a clean periodic pattern and atomic stick–slip friction, which manifests a gradual storage and sudden release of energy. Using a simple model of two atoms, analysis shows that the atomic stick–slip originates from the dynamic instability of molecule motion. Energy has been built up during the stick, followed by a sudden separation as the equilibrium becomes unstable, and most energy dissipates at the time of slip. Moreover, the simulations reveal that more energy is stored and released in commensurate sliding, resulting in much higher friction than that in incommensurate cases. The contradictory frictional behavior can be traced to the difference in the number and strength of the Van der Waals bonds, formed in the two types of contacts.     

齿轮箱箱体结构对其振动模态的影响研究

借助I-DEAS和NASTRAN软件平台对某齿轮箱进行了振动模态分析,研究并讨论了齿轮箱箱体结构型式对振动模态的影响,分析并验证了结构布局、大弧面和加强筋是提高齿轮箱箱体的抗振能力的重要途径,其结论可以为齿轮箱的动态设计提供参考。     

不同转速下变速箱齿轮齿根应力历程的特性分析

用有限元方法,建立汽车变速箱齿轮结构的三维动力学模型.模拟齿轮实际啮合过程中的连续冲击载荷,研究不同转速下齿轮齿根应力历程,得到随着转速变化,齿根应力的变化规律,对于齿轮强度及弯曲疲劳寿命计算具有一定的指导意义.     

Mixed-type finite element formulation of higher order shear deformation theory for the linear and nonlinear analyses of a laminated composite plate

For the linear and nonlinear analyses of a laminated composite plate structure, the mixed type finite element program is developed on the basis of higher order shear deformation theory of laminated plates. The accuracy of this program is checked by means of comparing with the existing results for laminated rectangular plates and is found to agree well with them. Deformations and interlaminar stresses of laminated plates are calculated according to the variation of layer numbers, fiber orientations, and plate thicknesses, so that the shear and nonlinear effects on their behaviors are studied. It is found that plate deformations are reduced by means of arranging the fiber direction into the angle-ply and increasing layer numbers.     

不同压制工艺对粉末冶金制品性能影响的有限元模拟

利用MSC/MARC有限元分析软件对金属粉末压制过程进行模拟分析.采用基于更新拉格朗日方法的热-力耦合分析不同工艺条件(温度、摩擦条件和压制方式等)对压坯性能的影响规律,同时对压制过程中的力学特征(压制力、脱模力、侧压力和应力分布等)进行分析.结果显示,摩擦条件是影响压坯密度大小及分布的关键因素,通过采用双向压制方法可以有效地改善单向压制压坯密度分布不均、差值较大的现象.温度的提高有利于提高粉末颗粒的塑性变形能力,但效果不明显.另外,由于温度影响润滑剂润滑性能,因此在制定压制工艺时需考虑温度对压坯性能的影响.此外温度的提高、摩擦的降低均有利于降低压制力,提高压坯密度均匀性,改善压坯应力集中现象.     

板式楔横轧接触区表面应力分布规律研究

楔横轧接触表面是形状复杂的空间曲面,接触表面应力分布变化规律相当复杂,对于其认识程度至今还局限于作较多假设的滑移线法分析结果,致使在模具设计和实际生产上主要依靠经验因素,阻碍楔横轧的应用和理论的发展。根据板式楔横轧的特点,在有限元ANSYS/DYNA软件基础上进行二次开发,编制模拟板式楔横轧轧制过程的命令流程序,模拟其轧制过程,获得接触区空间曲面形状,并较详细分析在楔横轧展宽段接触区的空间接触曲面上轧件接触表面应力的分布变化规律。研究结果为避免轧件表面产生缺陷、指导楔横轧模具设计和确定轧机力能参数等提供重要的理论依据。     

大型回转支承故障与外圈表面应力的变化规律

运用有限元分析软件对工作状态下双排异径球型回转支承发生故障前后的外圈应力分布及其表面应力变化的规律进行分析,基于对计算结果的数值分析提出回转支承局部损伤类故障可以通过监测回转支承外圈表面应力的变化来诊断。     

On the use of the asymptotic scaled modal analysis for time-harmonic structural analysis and for the prediction of coupling loss factors for similar systems

The paper presents the results of an ongoing research on a scaling procedure aimed at the reduction of the computational cost associated, in a deterministic approach, to the wavelength simulation. The adoption of the energy distribution approach allowed to completely define the way in which a scaled model can represent the mean response of a given original model. This goal is achieved through a reduction in the dimensions not involved in the energy propagation and accordingly in an increase of the original damping loss factors. Here, the coupled systems under observation are those in which the same wave is allowed to travel, exchange and reflect. Specifically the results coming from the classical modal response and the statistical energy analysis are compared with those in output from the scaling procedure. Some highlights with experimental test-case results and comparisons for a plate assembly are also given. The work presents also an investigation about the possibility of estimating the energy influence coefficients through scaled finite element models.     

Dynamic spring constants for higher flexural modes of cantilever plates with applications to atomic force microscopy

In atomic force microscopy (AFM) a sharp tip fixed close to the free end of a cantilever beam interacts with a surface. The interaction can be described by a point-mass model of an equivalent oscillator with a single spring located at the position of the tip. However, other spring constants have to be used to describe the oscillation behavior correctly if forces are acting on the cantilever over an extended lateral range. A point-mass model is then no longer valid. In the present study we derive expressions for the spring constants of cantilevers that can interact with any part of their plan view area along the beam and for all flexural modes. The equations describe the oscillation behavior in the corresponding mass model and are based on the eigenfrequencies and modal shapes of the free cantilever. The results are of high practical relevance, for example if an AFM is operated in a higher flexural mode, if the tip is not located at the free end of the cantilever beam, or if the external conservative forces affecting cantilever movement are not restricted to a single point. The limitations of the approach are discussed.     

冲击压路机压实效果的有限元分析法

利用有限元法计算了冲击压路机作用下土壤的应力状态,并与实测值进行了比较,认为利用有限元法可以预测冲击压路机压实深层土时的压实效果。     

纳米金属材料宏观弹性模量的数值模拟研究

将分子动力学模拟方法与连续体的有限元模拟技术相结合,进行"复合有限元"方法的探索与研究.首先,将纳米金属材料看作由晶粒、晶界、三叉晶界组成的复合材料,基体是具有不规则原子结构的界面相,夹杂是具有理想晶格的晶粒相,用有限元源程序自动生成系统fepg软件模拟材料的宏观弹性模量,并进一步调整晶粒尺寸,研究晶粒尺寸对材料宏观弹性模量的影响.研究结果表明,随着晶粒尺寸的减小,晶界、孔洞等所占的体积比增大,材料的弹性模量也随之下降.     

非线性转子-轴承系统的动力学特性及稳定性

研究非线性转子—轴承系统的动力学特性及稳定性。采用改进的自由界面模态综合技术给出一种自由度降阶方法,该方法将非线性油膜力及非线性自由度保留在物理空间,以增加非线性分析的精度,使降阶系统仍具有局部非线性特征。基于打靶法及将延续算法和打靶法相结合的轨迹预测追踪算法,研究系统非线性不平衡响应,结合Floquet理论分析非线性轴承—转子系统T周期运动的局部稳定性和分岔行为。     

车载武器发射底架的结构特性分析

采用有限元方法对某车载武器系统发射装置的底架在发射状态时的结构特性进行了研究。为了能够对底架的复杂结构进行深入分析 ,使用薄壳单元来建立底架的有限元模型 ,对其中的细节部分在建模时给予了充分的考虑。通过对计算结果的详细分析 ,指出了其结构设计存在的优缺点 ,并在此基础上提出了一些改进措施 ,为进一步的设计提供了理论依据