Two-dimensional problem of electrochemical metal machining

The two-dimensional problem of the electrochemical dimensional machining of a metal is investigated within the framework of the model of an ideal stationary process, which makes it possible to use the analogy with the problems of fluid flows with free surfaces. In the problem considered the cathode (machining tool) takes the form of two parallel semi-infinite rectangular electrodes. The blank (anode) is a half-plane whose boundary is perpendicular to the cathodes. Depending on the relationship between the physical and geometrical parameters of the problem, on the machined part (anode) a projection symmetrical about the center line between the cathodes may be formed. Additional mechanical machining of the part is then required. In order to exclude such solutions, a condition is obtained for the mathematical parameters which determine the solution of the problem in the auxiliary complex plane. General and particular limiting cases are considered. For the cases considered the calculation results are presented in the form of plots of the shape of the part machined.     

Current distribution of permeable electrodes in the presence of the hall effect in a stream of electrically conducting medium

The two-dimensional problem of the current distribution on the surface of permeable electrodes contiguous with a stream of incompressible medium with Hall effect is considered. An electrically conducting medium with the same physical properties as those of the main stream is pumped in (out) through the electrodes.This problem was solved in [1] for one particular case when the electrodes are impermeable. It was established that due to the Hall effect in magnetohydrodynamic channels the current is distributed non-uniformly on the electrodes; for values of the Hall parameter of the order of several units or greater, the current flows into an isotropically conducting medium mainly from a small portion on the edge of the electrode. It was also noted that this phenomenon creates unfavorable conditions for the operation of electrodes in magnetohydrodynamic devices.It is shown in what follows that the current distribution on the electrodes may be controlled, and in particular made more uniform, by injecting an electrically conducting medium.     

Anode-Shape Determination with Allowance for Electrolyte Properties in Problems of Dimensional Electrochemical Machining of Metals

Based on the boundary-element technique, a method for determining the contour of an anode-workpiece with a prescribed shape of a cathode-tool is suggested for plane problems of dimensional electrochemical machining of metals. Within the scope of the assumptions made, the original problem is reduced to the problem of a fictitious flow of an ideal fluid with free surfaces. The allowance for the machining mode and electrolyte properties yields a nonlinear condition at the free surface.     

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.     

Deviations Induced by Tool Sharpening in the Profile of Three Screw Pump Rotors

Three screw pumps represent an important family of positive displacement rotary pumps. They are quite easy to construct, even if the use of a shaped milling cutter for the rotor machining can cause some problems when the tool is not new. In fact the sharpening of the tool modifies the total geometry of the milling cutter by reducing its diameter. The shape of the single cutter does not change, but the cutter radial position is shifted towards the tool center. This causes deviations in the profile cut and the screws consequently need a long breaking-in. In this paper, the problem is analyzed from a quantitative point of view, using a method that allows us to determine the machining error as a function of the tool-geometry variation. Moreover, some alternative solutions to this problem are suggested.     

Simulation of precision electrochemical machining of metals by a segmented cathode

Bulge formation in the process of electrochemical machining by a flat tool electrode with an insulated area is studied. Based on a step function of the current efficiency, precision machining is simulated. The solution of a nonstationary problem shows that a limiting mode with the current density equal to its critical value is established in a finite time.     

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.     

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.     

配置环形线电极的单极机中的磁流体力学流动

给出配置了环形线电极的单极机中的磁流体力学解析解. 由于问题是线性的, 求解可简化为基本解的叠加, 可利用单极机在两个区域中的基本解的衔接来求得解析解. 讨论了基本解的性质. 利用非完全电极可改善Hartmann 边界层、增加装置中的质量流量. 应用基本解讨论了连续电极的单极机.     

Charge formation in a dielectric liquid in the case of a weak electrolyte

The problem of electric charge formation in a dielectric liquid placed between two electrodes is solved. Several simple formulas are derived for the electric charge density, the electric potential, and the current.     

Modeling of electrochemical machining with the use of a curvilinear electrode and a stepwise dependence of the current efficiency on the current density

An analytical solution of the problem of electrochemical machining of metals by a curvilinear cathode tool with allowance for a discontinuous function that describes the dependence of the current efficiency on the current density is obtained. According to the hydrodynamic interpretation, the original problem reduces to the problem of the theory of ideal fluid flows with a free surface. It is demonstrated that the use of the proposed dependence of the current efficiency on the current density ensures the existence of three domains on an unknown treated surface; these domains have different laws of the distribution of the charge fraction spent on metal dissolution. Results calculated for various particular cases are presented.     

Concentration of electric field near electrodes on piezoelectric layer

This paper aims at the study of electric field concentration near the edge of the electrodes for a piezoelectric layer. For simplicity, attention is focussed on a piezoelectric layer that is bonded to a rigid, conductive substrate and then covered by a pair of conductive electrodes on the surface. The analysis is performed within the scope of linear piezoelectricity. Fourier transform technique is applied to reduce the boundary value problem to a pair of dual integral equations. An analytical solution to the integral equations is obtained by using an iteration method. Numerical results for distributions of stresses and electric fields are displayed and discussed.     

Electroelastic analysis for a piezoelectric layer with surface electrodes

An electroelastic analysis of a transverse isotropic piezoelectric layer with surface electrodes is made. The piezoelectric layer is infinite long along the poling direction, and the top surface is perfectly bonded to a rigid electrode. The problem is solved via the conformal mapping technique for two cases of elastic boundary conditions on the bottom surface with two spaced electrodes, and the distribution of the electrostatic field in the entire piezoelectric layer is determined in an explicit analytic form, respectively. It is found that for the bottom surface electrodes with vanishing stiffness, the induced strain is singular, but no stress. Instead, for the bottom electrodes with stiffness as infinity, the induced stress is singular, but no strain.     

Transient oscillations of a multimode cylidrical piezoelectric transducer with a disconnected electrode section

The transient excitation of a cylindrical piezoelectric transducer with sectional electrodes is considered. A signal is supplied to one of the electrode sections while the electrodes of the other section are disconnected. The problem is solved by applying the Laplace integral time transform and representing the functions to be determined in the form of a series in natural oscillation modes. Calculation results are given for some transient signal profiles and different electrode-section sizes. Institute of Pulse Processes and Technology, National Academy of Sciences of Ukraine, Nikolaev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 4, pp. 73–79, April, 1999.     

有限厚压电层表面金属电极脱层的屈曲研究

基于弹性有限变形理论和压电弹性体偏场理论,对上、下表面有金属电极的压电材料板内存在穿透脱层的屈曲问题进行了分析.采用平面应变模型,远处作用有均匀压应变载荷.用Fourier积分变换,界面连续条件和上、下电极表面的边界条件将问题归为第二类Cauchy型奇异积分方程组.利用Gauss-Chebyshev积分公式将该方程组变为一齐次线性代数方程组,以确定脱层屈曲载荷.算例给出了中间层为PZT-4,上、下电极为Pt的结构在不同脱层长厚比时的临界应变及相应屈曲形状.同时分析了压电层的机电耦合效应对临界应变的影响.     

磁悬浮灌封胶新配方的研制

针对经高低温循环处理后定子磁芯材料齿根处开裂的技术难题,开展径向悬浮定子组件灌封胶新配方的研制攻关。根据径向悬浮定子组件的结构特点,要求灌封胶既具有良好的韧性,能耐高低温冲击,又要求具有刚性,保证加工精度的要求,这本身就是一对矛盾,是解决问题的关键和难点所在。通过工艺试验,提高环氧树脂灌封胶的综合性能,自主研制出灌封胶新配方,有效解决了定子磁芯高低温处理后自身开裂的问题。现新配方已成功地应用于实际批量生产中,对近二年所有批次采用新配方灌封的径向悬浮定子组件进行全面质量跟踪、计量检测和数据统计,产品的成活率由以前的25%～35%提高到90%以上,有效解决了磁悬浮的生产瓶颈问题,为我所科研生产提供了有效的技术保障。     

Influence of the hall effect on the characteristics of a MHD generator with two pairs of electrodes

The characteristics of segmented-electrode MHD generators with Hall currents are at present the object of considerable interest. Various types of electrode connections ate being examined: ordinary segmented-electrode generators, Hall generators, mixed-type generators, and Montardy generators. Research is being pushed in several directions. In some cases infinitely fine segmentation is assumed [1--4]. In these studies it is considered that the current density j in the duct is everywhere uniform; the net characteristics or the most favorable electrode connection angle are determined. In another group of studies periodic problems are solved, it being assumed that the processes taking place in a single elementary celi are repeated in the other ceils; fringe effects are not taken into account. In this case it is usually assumed that the lengths of the electrodes and insulators are finite, but small as compared with the duct height [5–7 ]. Finally, in a last group of studies nonperiodic problems are considered. In [3] Vatazhin solves the problem of the current distribution in a duct with a single pair of electrodes between infinitely long insulators. In [8] a general expression is found for the current density function in the case of an arbitrary number of electrode pairs and for any scheme of electrode connection at finite electrode and insulator dimensions. However, numerical calculations are made only for the periodic problem, whose solution is also obtained in [8]; the effect of segment pitch on the characteristics of a Montardy generator is studied.The present author has investigated the influence of the Hall effect on the characteristics of a MHD generator having two pairs of electrodes with symmetrical and crossed electrode connections. Although it is obvious that in practice only multisegment ducts will be employed, the examination of a generator with two pairs of electrodes makes possible the qualitative anatysis of the various effects observed in segmented-electrode ducts in which the electrodes are connected in different ways. Numerical calculations, based on formulas obtained by solving the corresponding problems, have been made on a M-20 computer. Integrated characteristics of the various generator systems have been obtained as a function of electrode and insulator length, external loads, and Hall parameter w.In conclusion, the author thanks A. B. Vatazhin and A. N. Kraiko for their helpful advice.     

Determination of the Inhomogeneous Preliminary Stress–Strain State in a Piezoelectric Disk

The problem of steady radial vibrations of a thin electroelastic hollow disk in the presence of a preliminary inhomogeneous plane stress–strain state is solved. Vibrations are induced by applying a potential difference across the electrodes placed on the end surfaces of the disk. Equations of the vibrations and boundary conditions are formulated. The preliminary stress state corresponding to the solution of the Lam´e problem was investigated. The direct problem of determining the displacement function is solved numerically by the shooting method. The inverse problem of determining a pre-stress parameter from the change in the natural frequency of the disk is formulated and solved. The accuracy of determining the prestressed state for initial data specified with an error is analyzed.     

Identification of the shock load on an electroelastic bimorph disk

A numerical–analytic method for the identification of the axisymmetric mechanical shock load on a disk-shaped metal–piezoceramic bimorph transducer is proposed. A problem is formulated based on the theory of thin two-layer plates. The solution is found using the Laplace transform. By recovering the original function analytically, the problem is reduced to a system of Volterra equations, solved numerically using Tikhonov’s regularization algorithm. The finite-element solution of the direct problem is used as input data (potential difference between the electrodes of the piezoceramic layer). The results are analyzed     

An analytical model for electrode–ceramic interaction in multilayer piezoelectric actuators

The present paper develops an analytical model for multi-electrodes in multi-layered piezoelectric actuators, in which the electrodes are vertical to and terminated at the edges of the medium and electroelastic field concentrations ahead of the electrodes in the multilayer piezoelectric actuators are examined. By considering a representative unit in realistic multilayers, the problem is formulated in terms of electric potential between the electrode tips and results in a system of singular integral equations in which the electric potential is taken as unknown function. Effects are investigated of electrode spacing and piezoelectric coupling on the singular electroelastic fields at the electrode tips, and closed-form expressions are given for the electromechanical field near the electrode tips. Exact solution for un-coupled dielectrics is provided, where no piezoelectric coupling is present. The English text was polished by Yunming Chen.