切削力建模方法综述

航空航天工程广泛采用薄壁复杂结构零件, 实现其高效精密数控加工关键技术具有重大的现 实意义. 传统的CAD/CAM软件在确定切削策略和规划刀位轨迹时, 一般仅基于零件的理想几 何形状. 由于切削力引起的刀具、零件显著的加工变形即``让刀'现象, 必然导致零件的实 际加工表面与理论值之间存在较大偏差. 工程师往往不得不通过选用比较保守的切削用量和 多次重复精加工过程来保证零件的加工精度. 为了能够从根本上解决这一问题, 很有必要通 过建立准确的切削力预报模型, 仿真切削加工的物理过程, 揭示工件和刀具的加工变形规律, 补偿原始数控刀具轨迹, 最终达到改善工件加工精度和提高加工效率的目的. 本文综述了各 种不同的切削力建模方法, 包括基于切屑形成机理的二维正交切削力模型、基于单位切削力 系数的铣削力模型、神经网络模型以及模糊灰色理论等. 目的是为实现薄壁复杂结构零件的 加工变形预测控制、关键工艺参数优化以及加工过程的物理仿真提供理论基础.     

Evolution of the Shape of the Anode Boundary under Electrochemical Dimensional Machining of Metals

This paper presents a method for calculating the anode boundary under unsteady conditions of electrochemical dimensional machining of metals. The plane quasistationary problem of determining the shape of the anode boundary for various machining times is considered.     

One scheme of electrochemical machining of metals by a curvilinear electrode tool

The nonlinear plane problem of the evolution of the shape of the metal surface (anode) during electrochemical machining by a curvilinear cathode of symmetric shape is solved. A condition is obtained which allows one to determine the position of the point of transition from the zone of anodic metal dissolution to the region in which machining stops.     

Analysis of Machining Stability for a Parallel Machine Tool

Abstract

Machine tool chatter is a self-excited vibration generated by chip thickness variation. It severely degrades the quality of the machined surface. The incidence of chatter is greatly affected by the dynamic characteristics of machine tool structure. This article extends chatter stability analysis to a machine tool equipped with a parallel mechanism. The vibration model of a parallel machine tool is derived, in which the legs of the parallel mechanism are considered as spring-damper systems. Then, the regenerative cutting dynamics is combined with the vibration model and stability analysis is performed. The chatter stability charts for various machining parameters are examined, with the example of the cubic parallel mechanism that is specially designed for machine tool use.     

An analytical study of nonlinear double-diffusive convection in a porous medium under temperature/gravity modulation

The article deals with nonlinear thermal instability problem of double-diffusive convection in a porous medium subjected to temperature/gravity modulation. Three types of imposed time-periodic boundary temperature (ITBT) are considered. The effect of imposed time-periodic gravity modulation (ITGM) is also studied in this problem. In the case of ITBT, the temperature gradient between the walls of the fluid layer consists of a steady part and a time-dependent periodic part. The temperature of both walls is modulated in this case. In the problem involving ITGM, the gravity field has two parts: a constant part and an externally imposed time-periodic part. Using power series expansion in terms of the amplitude of modulation, which is assumed to be small, the problem has been studied using the Ginzburg–Landau amplitude equation. The individual effects of temperature and gravity modulation on heat and mass transports have been investigated in terms of Nusselt number and Sherwood number, respectively. Further the effects of various parameters on heat and mass transports have been analyzed and depicted graphically.     

Rectangular tensile sheet with a center notch root crack

This paper deals with the rectangular tensile sheet with a center notch crack. Such a crack problem is called a center notch crack problem for short. By using a hybrid displacement discontinuity method (a boundary element method) proposed recently by Yan, two center notch models are analyzed in detail. By changing the geometrical forms and parameters of the center notch, and by comparing the SIFs of the center notch crack problem with those of the center cracked plate tension specimen (CCT), which is a model frequently used in fracture mechanics, the effect of the geometrical forms and parameters of the center notch on the stress intensity factors (SIFs) of the center cracked plate tension specimen, is revealed. Some geometric characterestic parameters are introduced here, which are used to formulate the notch length and the branch crack length, which are to be determined in mechanical machining of the center cracked plate tension specimen. So we can say that the geometric characterestic parameters and the formulae used to determine the notch length and the branch crack length presented in this paper perhaps have some guidance role for mechanical machining of the center cracked plate tension specimen. In addition, the numerical investigation proves that the conventional angular notched specimen is much less sensitive to the size of notch than is the circular notched specimen.     

Determination of Tool Profile for the Milling of Three-Screw Pump Rotor

The rotors of three screw pumps are commonly machined using shape milling cutters. The determination of the exact shape of the cutter is very important, since a high precision in the machining is required to obtain a high volumetric efficiency of the pump. This paper describes a method to determine the theoretical shape of the cutter, starting from the characteristic parameters of the pump. The rotors are modeled in space by helicoids. The contact line between the tool and the workpiece is then determined and this allows us to define the exact cutter profile, with a suitable reference system transformation.     

Modeling of Electrochemical Copying in a Finite-Width Cell

The problem of modeling of electrochemical machining is reduced to the solution of the Schwartz problem on a parametrical rectangle with the use of theta-functions. Various conditions (non-equipotentiality of electrodes and inconstancy of current efficiency) at the boundary of a processed surface are considered. Nonstationary, quasistationary, stationary, and limit solutions are studied. Results of machining of surfaces by tool electrodes of various shapes are given. It is shown that machining mode parameters significantly affect the dissolved layer size necessary for obtaining high-precision copying.     

Effect of electric field modulation on charge propagation in a low-conducting polar liquid

Unsteady processes of current propagation and formation of charge structures in a low-conducting polar liquid in the electric field of a horizontal capacitor are considered. Free charges are assumed to form in the liquid only owing to unipolar injection from the anode, which arises if the field strength on the anode is greater than a threshold value. The charge distribution in time and space and the evolution of the density of the current through the capacitor and the field strength on the anode are analyzed. It is demonstrated that the time intervals between two charge injections in a variable field (injection periods) may vary depending on the external field period. The density of the current through the capacitor is obtained as a function of the frequency and amplitude of the external field. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 1, pp. 3–12, January–February, 2008.     

Some problems in the antiplane shear deformation of bi-material wedges

The antiplane shear deformation of a bi-material wedge with finite radius is studied in this paper. Depending upon the boundary condition prescribed on the circular segment of the wedge, traction or displacement, two problems are analyzed. In each problem two different cases of boundary conditions on the radial edges of the composite wedge are considered. The radial boundary data are: traction–displacement and traction–traction. The solution of governing differential equations is accomplished by means of finite Mellin transforms. The closed form solutions are obtained for displacement and stress fields in the entire domain. The geometric singularities of stress fields are observed to be dependent on material property, in general. However, in the special case of equal apex angles in the traction–traction problem, this dependency ceases to exist and the geometric singularity shows dependency only upon the apex angle. A result which is in agreement with that cited in the literature for bi-material wedges with infinite radii. In part II of the paper, Antiplane shear deformation of bi-material circular media containing an interfacial edge crack is considered. As a special case of bi-material wedges studied in part I of the paper, explicit expressions are derived for the stress intensity factor at the tip of an edge crack lying at the interface of the bi-material media. It is seen that in general, the stress intensity factor is a function of material property. However, in special cases of traction–traction problem, i.e., similar materials and also equal apex angles, the stress intensity factor becomes independent of material property and the result coincides with the results in the literature.     

Steady sliding frictional contact problem for a 2d elastic half-space with a discontinuous friction coefficient and related stress singularities

The steady sliding frictional contact problem between a moving rigid indentor of arbitrary shape and an isotropic homogeneous elastic half-space in plane strain is extensively analysed. The case where the friction coefficient is a step function (with respect to the space variable), that is, where there are jumps in the friction coefficient, is considered. The problem is put under the form of a variational inequality which is proved to always have a solution which, in addition, is unique in some cases. The solutions exhibit different kinds of universal singularities that are explicitly given. In particular, it is shown that the nature of the universal stress singularity at a jump of the friction coefficient is different depending on the sign of the jump.     

Use of the time-establishment process when solving problems relating to the steady flow of gas around a cascade of profiles

The use of the time-establishment process in solving problems relating to the steady flow of an ideal (nonviscous and heat-insulating) gas around a cascade of profiles is considered. Chief attention is paid to the role of the Chaplygin-Zhukovskii condition, which is needed [1, 2] when solving these as steady-state problems. Results obtained during the time-establishment process with and without the application of the condition in question are presented. In both cases certain time-independent distributions of the parameters satisfying the equations and conditions of the steady-state problem (or more precisely their finite-difference analog) are produced during the establishment process. Comparison of the resultant distributions shows that the difference between the two cases lies within the limits of computing error, the results of the calculations agreeing quite well with experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 118–124, July–August, 1974.In conclusion, the authors wish to thank S. I. Ginzburg, G. Yu. Stepanov, and G. G. Chernov for taking part in discussions of this work.     

Reconstruction of inhomogeneous characteristics of a transverse inhomogeneous layer in antiplane vibrations

Direct and inverse problems of forced antiplane vibrations of a transverse inhomogeneous elastic layer are considered. The mechanical characteristics of the layer (density and shear modulus) are considered to be functions of the transverse coordinate. A method for solving the direct problem, based on using the integral Fourier transform and solving the boundary problem by the shooting method, is proposed. The inverse problem of determining the distributions of the mechanical parameters based on the known information on the wave field on some part of the upper surface is considered. Iterative sequences of integral equations are constructed. Results of numerical experiments and recommendations on the optimal choice of the vibration frequency and the interval, on which the displacements are determined, are given.     

Optimization of the response times of the feed kinematical linkages of the numerical control machine tools in order to minimize the path error

The main topic refers to enhancing the machining accuracy by minimizing the path error while machining through linear, circular or other interpolations on CNC machines for milling, boring and milling, grinding or turning. Currently the path error minimizing process while machining on CNC machine tools is a little explored, because of the absence of the dependence relations between the path error and the parameters of the kinematical axes taking part to the interpolation of the work piece contour. This work establishes and analyzes the relations of dependence between the path error and the response times of the kinematical axes that take part to the linear and circular interpolation. The theoretical results are experimentally verified by performing several machining operations through circular interpolation, where the moving speed along the contour and the response times of the kinematical axes are modified. The results of this research are intended for the machine tool designers and those who use such machines.     

Upper entropy bounds for transient forced convection

This article develops upper bounds for total entropy associated with convective heat transfer and transient fluid motion in an enclosure. Entropy production includes both friction and thermal irreversibilities due to fluid mixing in the enclosure. An integral formulation of entropy transport is developed in terms of the temperature excess (difference between the point-wise and spatially averaged temperature). The thermal irreversibility of entropy production is written in terms of the squared temperature excess. In this way, an upper entropy bound can be derived with respect to geometrical parameters and initial temperatures. Furthermore, this entropy bound is minimized by re-formulating the minimization problem in terms of a standard form of eigenvalue problem. Several example problems are considered and a spectral method is used to solve the governing energy equation. Theoretical predictions are compared successfully against numerical simulations for cases involving both Neumann and Dirichlet boundary conditions.     

Hybrid approach for dynamic model identification of an electro-hydraulic parallel platform

In this paper, a hybrid optimization algorithm is proposed to identify the dynamic parameters of a 6-DOF electro-hydraulic parallel platform. The dynamic model of a parallel platform with arbitrary geometry, inertia distribution and frictions is obtained based on a structured Boltzmann–Hamel–d’Alembert formulation, and then the estimation equations are explicitly expressed in terms of a linear form with respect to the identified inertial and the friction coefficients in accordance with a linear friction model. However, when nonlinear friction models are considered, the parameter identification of the electro-hydraulic parallel platform is considered as an optimization process with an objective function minimizing the errors between the measurement and identification, and then an effective combination of the particle swarm optimization (PSO) method and the local quasi-Newton method is proposed to solve the identification problem. Experimental identification processes are carried out for the identified parameters, and the identified models are compared by the predicted forces between the LS method and the optimization technique as well as between the linear and nonlinear friction models.     

On conditions of snow avalanching and landslides

The problem of elastic equilibrium of a wedge-shaped ground or snow massive on a rigid inclined plane under the action of gravity force and a constant force on its outer surface is considered in the three-dimensional statement. An exact solution that allows one to determine the displacements, strains, and stresses at each point of the massive is obtained in final form. An analysis shows that there are several critical relations between the problem input parameters at which the massive equilibrium is impossible. In this case, the earth or snow tears off from the slope and becomes a dangerous avalanche. In particular, this result can be used to predict formation of landslides and snow avalanching in mountains.     

Bifurcations of relative equilibria of a heavy bead on a rotating parabolic bowl with dry friction

The motion of a heavy bead on the surface of a parabolic bowl rotating at a constant angular velocity about its axis, which coincides with the vertical, is considered. It is assumed that the dry friction force acts between the bead and the bowl. The sets of nonisolated relative equilibria of the bead on the bowl are determined, and their dependence on the problem parameters is studied. The results are illustrated in the form of bifurcation diagrams.     

Formulation of strain gradient plasticity with interface energy in a consistent thermodynamic framework

In this work, the strain gradient formulation is used within the context of the thermodynamic principle, internal state variables, and thermodynamic and dissipation potentials. These in turn provide balance of momentum, boundary conditions, yield condition and flow rule, and free energy and dissipative energies. This new formulation contributes to the following important related issues: (i) the effects of interface energy that are incorporated into the formulation to address various boundary conditions, strengthening and formation of the boundary layers, (ii) nonlocal temperature effects that are crucial, for instance, for simulating the behavior of high speed machining for metallic materials using the strain gradient plasticity models, (iii) a new form of the nonlocal flow rule, (iv) physical bases of the length scale parameter and its identification using nano-indentation experiments and (v) a wide range of applications of the theory. Applications to thin films on thick substrates for various loading conditions and torsion of thin wires are investigated here along with the appropriate length scale effect on the behavior of these structures. Numerical issues of the theory are discussed and results are obtained using Matlab and Mathematica for the nonlinear ordinary differential equations (NODE) which constitute the boundary value problem.This study reveals that the micro-stress term has an important effect on the development of the boundary layers and hardening of the material at both hard and soft interface boundary conditions in thin films. The interface boundary conditions are described by the interfacial length scale and interfacial strength parameters. These parameters are important to control the size effect and hardening of the material. For more complex geometries the generalized form of the boundary value problem using the nonlocal finite element formulation is required to address the problems involved.     

Instability of an Oscillating Cylinder in a Circulation Flow of Ideal Fluid

The problem of the stability of a circular cylinder in a circulation flow is considered under the condition that the cylinder can perform both free (free cylinder) and forced oscillations (cylinder on a spring). It is shown that this simple system can be unstable in the presence of flow vorticity. Particular cases of vorticity distributions which make it possible to obtain an analytic solution are considered. The case of weak monotonically decreasing vorticity of an arbitrary form is analyzed for an arbitrary relation between the densities of the cylinder and the fluid. It turns out that the instability can develop only for a cylinder whose density is greater than that of the fluid. An approximate method of solving this problem based on consideration of the energy balance in the system is constructed. This makes it possible to obtain an expression for the growth rates and explain the physical mechanism realizing the instability, which is associated with the possibility of energy transfer from perturbations in the critical layer to the cylinder oscillations.