О влиянии конструктивных и геометрических характеристик концевых фрез на виброустойчивость процесса фрезерования

В статье выполнен анализ конструктивных и геометрических параметров концевых фрез, видов работ, выполняемых концевыми цилиндрическими фрезами. Проанализировано влияние этих параметров на виброустойчивость процесса фрезерования.This article gives an analysis of the structural and geometric parameters of end mills, types of work performed by the cylindrical end mills. The effect of these parameters on the vibration milling process

On the preservation of fibre direction during axisymmetric hyperelastic mass-growth of a finite fibre-reinforced tube

Several types of tube-like fibre-reinforced tissue, including arteries and veins, different kinds of muscle, biological tubes as well as plants and trees, grow in an axially symmetric manner that preserves their own shape as well as the direction and, hence, the shape of their embedded fibres. This study considers the general, three-dimensional, axisymmetric mass-growth pattern of a finite tube reinforced by a single family of fibres growing with and within the tube, and investigates the influence that the preservation of fibre direction exerts on relevant mathematical modelling, as well on the physical behaviour of the tube. Accordingly, complete sets of necessary conditions that enable such axisymmetric tube patterns to take place are initially developed, not only for fibres preserving a general direction, but also for all six particular cases in which the fibres grow normal to either one or two of the cylindrical polar coordinate directions. The implied conditions are of kinematic character but are independent of the constitutive behaviour of the growing tube material. Because they hold in addition to, and simultaneously with standard kinematic relations and equilibrium equations, they describe growth by an overdetermined system of equations. In cases of hyperelastic mass-growth, the additional information they thus provide enable identification of specific classes of strain energy densities for growth that are admissible and, therefore, suitable for the implied type of axisymmetric tube mass-growth to take place. The presented analysis is applicable to many different particular cases of axisymmetric mass-growth of tube-like tissue, though admissible classes of relevant strain energy densities for growth are identified only for a few example applications. These consider and discuss cases of relevant hyperelastic mass-growth which (i) is of purely dilatational nature, (ii) combines dilatational and torsional deformation, (iii) enables preservation of shape and direction of helically growing fibres, as well as (iv) plane fibres growing on the cross-section of an infinitely long fibre-reinforced tube. The analysis can be extended towards mass-growth modelling of tube-like tissue that contains two or more families of fibres. Potential combination of the outlined theoretical process with suitable data obtained from relevant experimental observations could lead to realistic forms of much sought strain energy functions for growth

Development of anisotropic structure in the Earth's lower mantle by solid-state convection

Seismological observations reveal highly anisotropic patches at the bottom of the Earth's lower mantle, whereas the bulk of the mantle has been observed to be largely isotropic(1-4). These patches have been interpreted to correspond to areas where subduction has taken place in the past or to areas where mantle plumes are upwelling, but the underlying cause for the anisotropy is unknown-both shape-preferred orientation of elastically heterogenous materials(5) and lattice-preferred orientation of a homogeneous material(6-8) have been proposed. Both of these mechanisms imply that large-strain deformation occurs within the anisotropic regions, but the geodynamic implications of the mechanisms differ. Shape-preferred orientation would imply the presence of large elastic (and hence chemical) heterogeneity whereas lattice-preferred orientation requires deformation at high stresses. Here we show, on the basis of numerical modelling incorporating mineral physics of elasticity and development of lattice-preferred orientation, that slab deformation in the deep lower mantle can account for the presence of strong anisotropy in the circum-Pacific region. In this model-where development of the mineral fabric (the alignment of mineral grains) is caused solely by solid-state deformation of chemically homogeneous mantle material-anisotropy is caused by large-strain deformation at high stresses, due to the collision of subducted slabs with the core-mantle boundary.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/62804/1/416310a.pd

A finite strain fibre-reinforced viscoelasto-viscoplastic model of plant cell wall growth

A finite strain fibre-reinforced viscoelasto-viscoplastic model implemented in a finite element (FE) analysis is presented to study the expansive growth of plant cell walls. Three components of the deformation of growing cell wall, i.e. elasticity, viscoelasticity and viscoplasticity-like growth, are modelled within a consistent framework aiming to present an integrative growth model. The two aspects of growth—turgor-driven creep and new material deposition—and the interplay between them are considered by presenting a yield function, flow rule and hardening law. A fibre-reinforcement formulation is used to account for the role of cellulose microfibrils in the anisotropic growth. Mechanisms in in vivo growth are taken into account to represent the corresponding biologycontrolled behaviour of a cell wall. A viscoelastic formulation is proposed to capture the viscoelastic response in the cell wall. The proposed constitutive model provides a unique framework for modelling both the in vivo growth of cell wall dominated by viscoplasticity-like behaviour and in vitro deformation dominated by elastic or viscoelastic responses. A numerical scheme is devised, and FE case studies are reported and compared with experimental data