An Expert System Framework for Economic Evaluation of Machining Operation Planning

Recognising the importance of combining manufacturing and management systems for machining operation planning, this paper presents a new methodology for the evaluation of economic aspects in an operation plan. To ensure that the quality of machined parts satisfies the required specifications, the manufacturing system acts as an alternative generator that provides meaningful and practical plans. Through cost analysis, the variable, fixed, and total costs associated with the machining operation are quantitatively determined. The management system, which functions as an evaluation mechanism, then selects the optimal plan based on the defined goal. The proposed methodology has been applied in the framework design of an expert system. The program establishes a sequence of machining operation planning and searches for the optimal plan. This optimal plan integrates considerations from both managers and production engineers, and balances their needs for efficient machining of a quality product.     

On algorithms for estimating computable error bounds for approximate periodic solutions of an autonomous delay differential equation

Machine tool chatter has been characterized as isolated periodic solutions or limit cycles of delay differential equations. Determining the amplitude and frequency of the limit cycle is sometimes crucial to understanding and controlling the stability of machining operations. In Gilsinn [Gilsinn DE. Computable error bounds for approximate periodic solutions of autonomous delay differential equations, Nonlinear Dyn 2007;50:73–92] a result was proven that says that, given an approximate periodic solution and frequency of an autonomous delay differential equation that satisfies a certain non-criticality condition, there is an exact periodic solution and frequency in a computable neighborhood of the approximate solution and frequency. The proof required the estimation of a number of parameters and the verification of three inequalities. In this paper the details of the algorithms will be given for estimating the parameters required to verify the inequalities and to compute the final approximation errors. An application will be given to a Van der Pol oscillator with delay in the non-linear terms.     

Queueing models of certain manufacturing cells under product-mix sequencing rules

This paper considers a manufacturing cell composed of a machining center and several parallel downstream production stations. In the machining center, there is an ample supply of raw material for a number of different part-types. For each type, parts are first processed in the machining center, and then in one of parallel production stations (one for each type). The decision to determine which type to produce (production sequence) occurs whenever the machining center completes the process of a part. The production sequencing rules under consideration are rotation rules and random rules, respectively. By using such rules, the resulting product-mix meets a preset level. Based on a decomposition technique, solution procedures are developed to compute the response time of parallel stations in the manufacturing cell using such product-mix sequencing rules. Numerical examples are given to demonstrate the solution procedures and to investigate the impact of the production sequence on the overall average response time.     

模的弱消去问题和Exchange环的弱稳定条件

本文研究模的弱消去问题和exchange环的弱稳定条件,给出了wsrl条件的新刻划,证明了对具有有限exchange性质的模,外弱消去等价于内弱消去并等价于自同态环满足wsrl条件.     

Analytical modeling of chatter stability using multi-dimensional approach

Machining is one of the most common manufacturing processes in industry due to its high flexibility and ability to produce parts which excellent quality. Chatter, a type of self excited vibrations arising in metal cutting operations, is a major limitation in machining resulting in poor quality and reduced productivity. Under certain conditions, the cutting process may become unstable yielding oscillations with high amplitudes and cutting forces. Stability analysis of the dynamic cutting process can be used to determine chatter-free machining conditions with high material removal rate. Usually, one dimensional models are used for stability analysis of machining. However, based on the geometry of the actual machining process, multi-directions would have to be used for accurate modeling of the process dynamics and the stability. In this presentation, multi directional models for turning and milling processes are presented. The effects of multi directional process mechanics on the stability are demonstrated by applications. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

强预不变凸函数的充要条件

本文讨论了强预不变凸函数与预不变凸函数、严格预不变凸函数及半严格预不变凸函数之间的关系,得到它的三个充要条件：(i)在一定条件下,f是强预不变凸函数的充分必要条件是f是预不变凸函数且f满足中间点强预不变凸性；(ii)在一定条件下,f是强预不变凸函数的充分必要条件是f是严格预不变凸函数且f满足中间点强预不变凸性；(iii)在一定条件下,f是强预不变凸函数的充分必要条件是f是半严格预不变凸函数且f满足中间点强预不变凸性．     

Subdivision Schemes and Irregular Grids

The present paper deals with subdivision schemes associated with irregular grids. We first give a sufficient condition concerning the difference scheme to obtain convergence. This condition generalizes a necessary and sufficient condition for convergence known in the case of uniform and stationary schemes associated with a regular grid. Through this sufficient condition, convergence of a given subdivision scheme can be proved by comparison with another scheme. Indeed, when two schemes are equivalent in some sense, and when one satisfies the sufficient condition for convergence, the other also satisfies it and it therefore converges too. We also study the smoothness of the limit functions produced by a scheme which satisfies the sufficient condition. Finally, the results are applied to the study of Lagrange interpolating subdivision schemes of any degree, with respect to particular irregular grids.     

Heat content and Hardy inequality for complete Riemannian manifolds

Upper bounds are obtained for the heat content of an open set D in a complete Riemannian manifold, provided the Dirichlet-Laplace-Beltrami operator satisfies a strong Hardy inequality, and the distance function on D satisfies an integrability condition.     

On a two-weighted estimation of maximal operator in the Lebesgue space with variable exponent

We study two-weight inequalities with general-type weights for Hardy-Littlewood maximal operator in the Lebesgue spaces with variable exponent. The exponent function satisfies log-Holder-type local continuity condition and decay condition in infinity. The right-hand side weight to the certain power satisfies the doubling condition. Sawyer-type two-weight criteria for fractional maximal functions are derived.     

Mathematical Theory of Electrochemical Machining 2. Anodic Shaping

Present address: Department of Mechanical Engineering, Strathclyde University, Glasgow, C.I. Further solutions to the potential equation with moving boundaryconditions, applicable to the electrochemical machining process,are presented. A theory is proposed for the machining of anarbitrary distribution of irregularities on to an anode forthe cases where the cathode profile is specified and the resultantanode shape must be found, and where a cathode profile mustbe designed to give a required anode shape. Limitations on theapplication of this theory are discussed. The effects of overpotentialare also discussed; overpotential only at the cathode is shownto reduce the limiting amplitude which can be obtained on theanode, and to increase the machining time required to achieveit. Overpotential only at the anode has no effect on this limitingamplitude, but again increases the necessary machining time.     

强预拟不变凸函数的充要条件

本文引入了一类新的广义凸函数—强预拟不变凸函数.讨论了强预拟不变凸函数与预拟不变凸函数、严格预拟不变凸函数及半严格预拟不变凸函数之间的关系,得到它的三个充要条件:(i)当条件P_1满足时,f是强预拟不变凸函数的充分必要条件是f是预拟不变凸函数且f满足中间点强预拟不变凸性;(ii)当条件P_2满足时,f是强预拟不变凸函数的充分必要条件是f是严格预拟不变凸函数且f满足中间点强顶拟不变凸性;(iii)当条件P_2满足时,f是强预拟不变凸函数的充分必要条件是f是半严格预拟不变凸函数且f满足中间点强预拟不变凸性.     

Determining the optimal procurement policy and maximum allowable lifespan for machining tools with stochastically distributed toollife

For high-value added products, machining tools’ lifespan significantly influences the quantity of procurement in machining process. Preemption of tools from the workpiece while processing is continuing is sometime beneficial to safeguard the product from the damage due to tool failure or its malfunction. Also an early discard of a tool is costly for the manufacturing operation. Therefore an optimal strategy for the tool life is sought here to determine the maximum allowable tool lifespan to preempt from the workpiece and to have an appropriate amount of tool stock in the crib to ascertain the proper running of the production schedule and tool inventory. Therefore, an impact of the machining tool lifespan on the production-inventory policy of the system is investigated in this paper. An integrated lifespan related inventory model for machining tools is developed to meet the responding accurate requirement of procurement and inventory. Two numerical examples are presented to illustrate the integrated model. The results show that the practical lifespan adoption of machining tools has significant impact on the whole quantity of procurement, and eventually influences the coordinating economic decision making.     

Equivalence of the Local Markov Inequality and a Kolmogorov Type Inequality in the Complex Plane

We prove that a compact subset of the complex plane satisfies a local Markov inequality if and only if it satisfies a Kolmogorov type inequality. This result generalizes a theorem established by Bos and Milman in the real case. We also show that every set satisfying the local Markov inequality is a sum of Cantor type sets which are regular in the sense of the potential theory.     

A new bounding mechanism for the CNC machine scheduling problems with controllable processing times

In this study, we determine the upper and lower bounds for the processing time of each job under controllable machining conditions. The proposed bounding scheme is used to find a set of discrete efficient points on the efficient frontier for a bi-criteria scheduling problem on a single CNC machine. We have two objectives; minimizing the manufacturing cost (comprised of machining and tooling costs) and minimizing makespan. The technological restrictions of the CNC machine along with the job specific parameters affect the machining conditions; such as cutting speed and feed rate, which in turn specify the processing times and tool lives. Since it is well known that scheduling problems are extremely sensitive to processing time data, system resources can be utilized much more efficiently by selecting processing times appropriately.     

Optimal structural design of a planar parallel platform for machining

Parallel manipulators have many advantages over traditional serial manipulators. These advantages include high accuracy, high stiffness and high load-to-weight ratio, which make parallel manipulators ideal for machining operations where high accuracy is required to meet the requirements that modern standards demand.Recently, the finite element method has been used by some workers to determine the stiffness of spatial manipulators. These models are mainly used to verify stiffness predicted using kinematic equations, and are restricted to relatively simple truss-like models. In this study, state-of-the-art finite elements are used to determine the out of plane stiffness for parallel manipulators. Euler–Bernoulli beam elements and flat shell elements with drilling degrees of freedom are used to model the platform assembly.The main objective of this study is to quantify the stiffness, particularly the out of plane stiffness, of a planar parallel platform to be used for machining operations. The aim is to obtain a design that is able to carry out machining operations to an accuracy of 10 μm for a given tool force.Reducing the weight of a parallel manipulator used in machining applications has many advantages, e.g. increased maneuverability, resulting in faster material removal rates. Therefore the resulting proposed design is optimized with respect to weight, subject to displacement and stress constraints to ensure feasible stiffness and structural integrity. The optimization is carried out by means of two gradient-based methods, namely LFOPC and Dynamic-Q.     

Scheduling of a machining center

A machining center is an advanced NC (Numerical Control) machine that has the capability to perform a variety of operations on a part by automatically changing the cutting tools. Because of its versatile processing capabilities, a machining center is often a production bottleneck, and effective scheduling can result in significant improvement of system performance. The problem, however, is very difficult since many factors such as machine setups, pallets, tool magazine, and possible tool overlapping among different part types, etc., have to be considered. This paper presents an optimization-based approach for the scheduling of a machining center with two pallets. A novel “separable” problem formulation that considers the above mentioned factors is presented. Lagrangian relaxation is applied to decompose the problem into simple subproblems, which are efficiently solved without encountering complexity difficulties. The subgradient method is then used to update the multipliers. Testing results indicate that the approach is effective, and the algorithm provides a valuable tool for solving stand-alone machining center problems. The approach also points out a direction on how to consider machining centers within a job shop environment.     

Scheduling flexible machining and assembly systems

Most scheduling papers consider flexible machining and assembly systems as being independent. In this paper, a heuristic two-level scheduling algorithm for a system consisting of a machining and an assembly subsystem is developed. It is shown that the upper level problem is equivalent to the two machine flow shop problem. The algorithm at the lower level schedules jobs according to the established product and part priorities. Related issues, such as batching, due dates, process planning and alternative routes, are discussed. The algorithm and associated concepts are illustrated on a number of numerical examples.     

A “micro” process planning system based on integer programming for prismatic parts produced on horizontal machining centers

An automated process planning system is developed for manufacturing prismatic parts on a Horizontal Machining Center. The goal is to demonstrate the feasibility of using the integer (0–1) programming technique to determine the optimal sequence of machining operations. The final process sequence reflects constraints on tool life. Precedence relationships due to fixturing and/or process requirements are also taken into account. Decision logic for selection of cutting tools and calculation of necessary machining parameters are also developed. Process plans for test workpieces are produced and the effectiveness of the system demonstrated.     

On a Kohn-Vogelius like formulation of free boundary problems

The present paper is concerned with the solution of a Bernoulli type free boundary problem by means of shape optimization. Two state functions are introduced, namely one which satisfies the mixed boundary value problem, whereas the second one satisfies the pure Dirichlet problem. The shape problem under consideration is the minimization of the L ²-distance of the gradients of the state functions. We compute the corresponding shape gradient and Hessian. By the investigation of sufficient second order conditions we prove algebraic ill-posedness of the present formulation. Our theoretical findings are supported by numerical experiments.     

Chain conditions in modules with krull dimension

Any ring with Krull dimension satisfies the ascending chain condition on semiprime ideals. This result does not hold more generally for modules. In particular if Ris the first Weyl algebra over a field of characteristic 0 then there are Artinian R-modules which do not satisfy the ascending chain condition on prime submodules. However, if Ris a ring which satisfies a polynomial identity then any R-module with Krull dimension satisfies the ascending chain condition on prime submodules, and, if Ris left Noethe-rian, also the ascending chain condition on semiprime submodules.