Brachistochrone for a rolling cylinder

The motion of a heavy homogeneous cylinder is considered as a no-slip rolling along the desired curve. We obtain a functional in the form of the total time of the cylinder rolling and solve the corresponding variational problem of minimizing this functional. We obtain an algebraic equation for the directional line of steepest descent, brachistochrone, in parametric form. We use the equation of motion of the cylinder with constraint reaction to determine the conditions of implementation of its pure rolling without separation and slip with respect to the brachistochrone.     

A general method for impact dynamic analysis of a planar multi-body system with a rolling ball bearing joint

Impact affects the dynamic characteristics of mechanical multi-body systems and damages those rotating parts, such as the joint rolling element bearings, which are high-precision, defect intolerant components. Based on multi-body dynamic theory, Hertzian contact theory, and a continuous contact model, this study proposed a modelling method that can describe the dynamic behaviour of planar mechanical multi-body systems containing a rolling ball bearing joint under impact. In this method, the rigid bodies and bearing joint were connected according to their joint force constraints; the impact constraint between the multi-body system and the target rigid body was constructed using a continuous contact force model. Based on this method, the reflection relationship between the external impacts of the mechanical multi-body system and the variation law governing the dynamic load on the rolling bearing joint were revealed. Subsequently, an impact multi-body system, which was composed of a sliding–crank mechanism containing a rolling ball bearing joint and the target rigid body with an elastic support, was analysed to explore the dynamic response of such a complex discontinuous dynamic system andthe relevant relationship governing the dynamic load on the rolling bearing joint. In addition, a multi-body dynamic simulation software was used to build a virtual prototype of the impact slider–crank system. Compared with the theoretical model, the prototype had an additional deep groove ball bearing. That is to say, the prototype model took account of the specific geometric structural characteristics and the complex contact relationship of the inner and outer races, rolling balls, and bearing cage. Finally, the effectiveness of the theoretical method proposed in this study was verified by comparative analysis of the results. The results suggested that the external impact of a mechanical multi-body system was prone to induce sudden changes in the equivalent reaction force on its bearing joint and the dynamic load carried on its rolling balls. This study provided an effective method for exploring the distribution characteristics of dynamic loads on rolling ball bearing joints under working impact load conditions. Moreover, it offered support for the parameter optimisation of geometric structure, performance evaluation, and dynamic design of the rolling ball bearings.     

光滑曲面点接触的理想约束推导

分析力学在讲述形状光滑的两刚性面保持点接触时,如果无摩擦或者纯滚动,使用了两个接触点的可能微小位移在接触点法向分量相等,或者接触点的相对速度为零的条件推导出接触为理想约束。本文从两曲面保持点接触时满足共点和相切的几何条件出发,获得这一结论,前提条件更加明确。     

Distinct element method investigation on mechanical behavior within shear bands in granulates under the Earth and the Moon conditions

This letter mainly aims to investigate the mechanical behavior within shear bands in regolith both under the Earth and the Moon conditions via the distinct element method, in which a novel contact model considering interparticle van der Waals forces and rolling resistance is employed. The results show that for regolith under both conditions the stress paths are almost identical inside and outside the shear bands but void ratio, average pure rotation rate, and strain paths are rather distinct with dilation, particle rotation and the second invariant of strain tensor mainly occurring within the bands. However, the regolith under the Moon condition has higher peak strength and more significant strain localization than those under the Earth condition.     

Quasiconvex envelopes of energies for nematic elastomers in the small strain regime and applications

We provide some explicit formulas for the quasiconvex envelope of energy densities for nematic elastomers in the small strain regime and plane strain conditions. We then demonstrate their use as a powerful tool for the interpretation of mechanical experiments. Analytical formulas characterizing the stress-strain response in pure shear are derived, providing an easily testable benchmark for future numerical and experimental investigations on the mechanics of nematic elastomers.     

The three-dimension model for the rock-breaking mechanism of disc cutter and analysis of rock-breaking forces

To study the rock deformation with threedimensional model under rolling forces of disc cutter,by carrying out the circular-grooving test with disc cutter rollingaround on the rock,the rock mechanical behavior underrolling disc cutter is studied,the mechanical model of disccutter rolling around the groove is established,and the theory of single-point and double-angle variables is proposed.Based on this theory,the physics equations and geometricequations of rock mechanical behavior under disc cutters oftunnel boring machine(TBM) are studied,and then the balance equations of interactive forces between disc cutter androck are established.Accordingly,formulas about normalforce,rolling force and side force of a disc cutter are derived,and their validity is studied by tests.Therefore,a newmethod and theory is proposed to study rock-breaking mechanism of disc cutters.     

Qualitative analysis of a rolling hoop with mass unbalance

The dynamical behavior of a rolling hoop with an unbalanced point mass under the influence of gravity is discussed. The whole process from rolling to hopping of the hoop is analyzed qualitatively. The conditions of slipping, hopping and touching down of the hoop are obtained. It is shown that the hoop cannot maintain a pure rolling before hopping up, and the slippage is unavoidable. The hoop has neither vertical velocity nor vertical acceleration at the moment when the normal constraint force vanishes. The hopping motion of the hoop can occur only when the derivative of the vertical acceleration with respect to time is positive. It requires that the angular velocity of the hoop should be larger than a critical value, and the mass point should be located in the fourth quadrant of the hoop circle at the moment of hopping. The whole process of the pure rolling, rolling with slipping, hopping and falling motions of the hoop is shown in the phase plane, and the physical explanation of the hopping motion is given.     

Heat transfer associated to a hot surface quenched by a jet of oil-in-water emulsion

In hot rolling, the mechanical properties of steel alloys are conditioned by the rolling process but a great part is ensured by the cooling of the hot strip mill. Well controlling this cooling rate and its homogeneity is thus of primary importance for obtaining steels with desired mechanical properties. As the water used in the cooling stage of the rolling process can be polluted by oil (in hot mill strip, some oil is used to lubricate the rolls and a part of it can pollute the water), it is important to know how much varies the cooling rates when water is polluted. In this study, transient cooling has been investigated during quenching of a hot metal disk with various subcooled oil-in-water emulsion jets. The aim of this work is to compare the cooling efficiency of oil-in-water emulsion jet with a pure water jet. Experimental investigations of axisymmetric jet impingements on a preheated hot metal disk (500-600 °C) have been performed with various oil-in-water emulsions. The transient cooling heat fluxes on the quenched side are estimated by coupling the measurement of the temperature field of the other side (rear face) with a semi-analytical inverse heat conduction model.     

Transient rolling friction model for discrete element simulations of sphere assemblies

The rolling resistance between a pair of contacting particles can be modeled with two mechanisms. The first mechanism, already widely addressed in the DEM literature, involves a contact moment between the particles. The second mechanism involves a reduction of the tangential contact force, but without a contact moment. This type of rotational resistance, termed creep-friction, is the subject of the paper. Within the creep-friction literature, the term “creep” does not mean a viscous mechanism, but rather connotes a slight slip that accompanies rolling. Two extremes of particle motions bound the range of creep-friction behaviors: a pure tangential translation is modeled as a Cattaneo–Mindlin interaction, whereas prolonged steady-state rolling corresponds to the traditional wheel–rail problem described by Carter, Poritsky, and others. DEM simulations, however, are dominated by the transient creep-friction rolling conditions that lie between these two extremes. A simplified model is proposed for the three-dimensional transient creep-friction rolling of two spheres. The model is an extension of the work of Dahlberg and Alfredsson, who studied the two-dimensional interactions of disks. The proposed model is applied to two different systems: a pair of spheres and a large dense assembly of spheres. Although creep-friction can reduce the tangential contact force that would otherwise be predicted with Cattaneo–Mindlin theory, a significant force reduction occurs only when the rate of rolling is much greater than the rate of translational sliding and only after a sustained period of rolling. When applied to the deviatoric loading of an assembly of spheres, the proposed creep-friction model has minimal effect on macroscopic strength or stiffness. At the micro-scale of individual contacts, creep-friction does have a modest influence on the incremental contact behavior, although the aggregate effect on the assembly's behavior is minimal.     

A study of mechanical properties of pure and nitrogen-doped ultrananocrystalline diamond films under various loading conditions

To better understand the mechanical responses of ultrananocrystalline diamond (UNCD) under various loading conditions, a numerical study is performed to investigate the size, loading rate and temperature effects on the material properties of pure and nitrogen-doped UNCD films. Since the UNCD growth mechanism is not completely understood yet, a simple procedure by combining kinetic Monte Carlo and molecular dynamics (MD) methods is developed to form a polycrystalline UNCD block with an artificial grain boundary (GB). By randomly inserting different numbers of nitrogen (N) atoms into the GB of the resulting polycrystalline UNCD films, N-doped UNCD films can be formed. The responses of the simulated pure and N-doped UNCD films with various grain sizes are then investigated by applying displacement-controlled tensile loading under different rates and temperatures in the MD simulations. The simulation results presented in this paper provide a better understanding of the combined size, rate and thermal effects on the material responses of pure and N-doped UNCD films.     

Rolling resistance of a rigid sphere with viscoelastic coatings

We present a novel three-dimensional boundary-element formulation that fully characterizes the mechanical behavior of the external boundary of a multi-layered viscoelastic coating attached to a hard rotating spherical core. The proposed formulation incorporates both, the viscoelastic, and the inertial effects of the steady-state rolling motion of the sphere, including the Coriolis effect. The proposed formulation is based on Fourier-domain expressions of all mechanical governing equations. It relates two-dimensional Fourier series expansions of surface displacements and stresses, which results in the formation of a compliance matrix for the outer boundary of the deformable coating, discretized into nodes. The computational cost of building such a compliance matrix is optimized, based on configurational similarities and symmetry. The proposed formulation is applied, in combination with a rolling contact solving strategy, to evaluate the viscoelastic rolling friction of a coated sphere on a rigid plane. Steady-state results generated by the proposed model are verified by comparison to those obtained from running dynamic simulations on a three-dimensional finite element model, beyond the transient. A detailed application example includes a verification of convergence and illustrates the dependence of rolling resistance on the applied load, the thickness of the coating, and the rolling velocity.     

Model of plastic anisotropy evolution with texture-dependent yield surface

Model of evolution of plastic anisotropy due to crystallographic texture development, in metals subjected to large deformation processes, is presented. The model of single grain with the regularized Schmid law proposed by Gambin is used. Evolution of crystallographic texture during drawing, rolling and pure shear is calculated. Phenomenological texture-dependent yield surface for polycrystalline sheets is proposed. Evolution of this yield surface is compared with evolution of phenomenological higher order yield surfaces proposed by Hill and Barlat with Lian for drawing, rolling and pure shear processes. The change of the Hill yield surface and the Barlat–Lian yield surface is obtained by replacing material parameters present in these conditions by texture-dependent functions.     

FeCrAl合金材料织构对其宏观力学本构关系的影响研究

FeCrAl合金具有优良的高温抗氧化性和耐辐照性能,是事故容错核燃料包壳的重要候选材料. 其在加工过程和热处理过程中易形成α纤维织构（<110>//RD）和γ纤维织构（<111>//ND）,会影响材料的宏观力学性能与深加工成形能力. 本研究针对具有不同织构的多晶FeCrAl合金,建立了代表性体元模型, 使用晶体塑性有限元方法,在ABAQUS/Explicit中模拟材料单轴加载下的宏观应力应变曲线,分析不同织构对FeCrAl合金宏观力学本构关系的影响. 计算结果表明,对于具有α织构、γ织构和晶粒无择优取向的材料,在轧向上的应力应变曲线差异较小. γ织构会引起材料强烈的各向异性,在轧面法向上的屈服强度远高于轧向和横向上的屈服强度,这是因为晶粒的<111>方向平行于加载方向,滑移系难以启动. 提高γ纤维织构的比例,将增大轧面法向上的屈服强度. 本研究可以为优化FeCrAl合金材料织构、加工条件和材料力学性能提供参考.     

FeCrAl合金材料织构对其宏观力学本构关系的影响研究

FeCrAl合金具有优良的高温抗氧化性和耐辐照性能,是事故容错核燃料包壳的重要候选材料. 其在加工过程和热处理过程中易形成α纤维织构（<110>//RD）和γ纤维织构（<111>//ND）,会影响材料的宏观力学性能与深加工成形能力. 本研究针对具有不同织构的多晶FeCrAl合金,建立了代表性体元模型, 使用晶体塑性有限元方法,在ABAQUS/Explicit中模拟材料单轴加载下的宏观应力应变曲线,分析不同织构对FeCrAl合金宏观力学本构关系的影响. 计算结果表明,对于具有α织构、γ织构和晶粒无择优取向的材料,在轧向上的应力应变曲线差异较小. γ织构会引起材料强烈的各向异性,在轧面法向上的屈服强度远高于轧向和横向上的屈服强度,这是因为晶粒的<111>方向平行于加载方向,滑移系难以启动. 提高γ纤维织构的比例,将增大轧面法向上的屈服强度. 本研究可以为优化FeCrAl合金材料织构、加工条件和材料力学性能提供参考.     

Simulation of parametric ship roll and hull twist oscillations

A new mechanical model for simulating both the ship oscillations and the induced twisting of the hull in the case of longitudinal seas is presented. Particular attention is given to the onset of parametric rolling, which may result from non-linearly coupled heave-pitch-roll motions. It is shown that in these sea conditions the phenomenon of twisting is likely to occur under a mechanism similar to that of parametric rolling.     

Multi-scale morphology analysis of acoustic emission signal and quantitative diagnosis for bearing fault

Monitoring of potential bearing faults in operation is of critical importance to safe operation of high speed trains. One of the major challenges is how to differentiate relevant signals to operational conditions of bearings from noises emitted from the surrounding environment. In this work, we report a procedure for analyzing acoustic emission signals collected from rolling bearings for diagnosis of bearing health conditions by examining their morphological pattern spectrum (MPS) through a multi-scale morphology analysis procedure. The results show that acoustic emission signals resulted from a given type of bearing faults share rather similar MPS curves. Further examinations in terms of sample entropy and Lempel-Ziv complexity of MPS curves suggest that these two parameters can be utilized to determine damage modes.     

纯水合物力学性质研究进展

纯水合物力学性质是含水合物沉积物力学性质研究的基础, 其与水合物开采、海底地质灾害防治、CO₂埋藏、气体储运等诸多方面都密切相关. 然而受水合物形成条件和样品本身影响, 目前对纯水合物力学性质研究还存在很多争议和不足, 其中最主要的问题就是难于获取高纯度的水合物实验样品. 据此本文从实验和理论计算两个方面对当前纯水合物力学性质的研究进展进行了总结和分析, 提出可从宏观实验技术改进和微观分子动力学模拟两方面结合来尽可能消除水合物样品本身的影响, 揭示纯水合物力学性质与冰异同的内在原因, 掌握水合物样品残余水气和微孔隙对其力学性质的影响机理, 从而实现水合物微观力学本质与宏观力学特性间的衔接, 为今后含水合物沉积物力学性质及水合物力学性质相关领域研究奠定坚实的理论基础.     

表面机械滚压处理(SMRT)316L不锈钢梯度纳米层在腐蚀介质下的摩擦学行为研究

采用表面机械滚压处理(surface mechanical rolling treatment,SMRT)技术在316L奥氏体不锈钢表面构筑了梯度纳米结构层. 利用透射电子显微镜(TEM)和纳米压痕仪等分析其微观组织、力学性能等基础上,重点探讨了SMRT前后316L在1 mol/L HCl溶液(以纯水环境作为对比组)中的摩擦学行为. 结果表明:经SMRT加工后316L表面梯度纳米晶层厚度达200 μm以上,表面硬化层厚度超过1.5 mm,表面硬度提升至基体近2倍;SMRT大大减缓了材料磨损,与基体试样相比,SMRT试样在腐蚀介质下减摩效果比纯水环境更明显,且在腐蚀环境下表现出优异的耐腐蚀性能,其磨损机制由处理前伴随严重剥落特征的疲劳磨损和磨粒磨损转变为轻微疲劳磨损. 因此,316L不锈钢机械滚压梯度纳米层在腐蚀服役环境下具有较高的潜在工程应用价值.      

Swing-up and positioning control of an inverted wheeled cart pendulum system with chaotic balancing motions

This paper explores the problem of swinging-up an inverted pendulum formed by a rod attached to a wheeled cart with a hanging bob at its opposite end. The system is driven by the wheeled cart platform system, which is formed by a cart, wheels with counterbalance and connecting-rods. The model of the system is initially obtained under the assumption of rolling without slipping of the wheels, which is then verified by computing the reaction forces. The motion of the wheeled cart is initially oscillating, whereas the rod can move freely giving rise to an under-actuated mechanical system. From the harmonic prescribed motion for the wheeled cart, necessary conditions for chaotic rod motion are deduced by means of the Melnikov function. Once the chaotic oscillation has been reached and the rod is close to the upright position, the force over the wheeled cart is commutated to a control law based on the pole-placement plus integrator technique. This procedure allows driving the rod and the wheeled cart system to the upright position and to a prescribed set point respectively. The onset of strange attractors is crucial in the design of the control law, whose performance to obtain rolling without slipping is researched by means of sensitive dependence, power spectral density, Lyapunov exponents and reaction forces. The results of the analytical calculations are verified by full numerical simulations.     

Simulation of parametric ship rolling: Effects of hull bending and torsional elasticity

An enhanced mechanical model for simulating ship body oscillations and both the induced fluxural and twisting vibrations of the hull in the case of longitudinal seas is presented. The onset of parametric rolling, which may result from nonlinearly coupled heave-pitch-roll motions, and the effects of bending and torsional elasticity of the hull are considered in detail. It is shown that in the above sea conditions the flexural and/or twisting vibrations are likely to occur under a mechanism similar to that of parametric rolling.