Two-dimensional representation of machining geometry and tool path generation for ball-end milling of sculptured surfaces

This article applies a two-dimensional representation of the machining geometry relevant to tool path generation for the three-axis ball-end milling of sculptured surfaces. A two-dimensional geometric model detecting the machined strip is suggested as the concept for the ‘effective cutting profile’ which fits well into the three-dimensional machining geometry. The model is the same as the intersection of the cutter with the plane perpendicular to the tangent direction of the cutter location curve and incident with the cutter location point. In order to achieve the specified machining accuracy, an iterative approach is needed. The paper also presents a new iterative method to generate tool paths with a constant scallop height. It is based on the proposed model which resorts to a two-dimensional representation of the three-dimensional machining geometry. The proposed method reduces significantly the computing time to generate tool paths. Implementations and illustrated examples are discussed.     

Integrated method for tool path generation in five-axis sculptured surface machining

Five-axis machining allows continuous adjustment of cutter orientation along a tool pass. Unfortunately, the flexibility has not been fully exploited due to the separate consideration of tool path generation and cutter orientation in current machining methods. This paper presents an integrated method (IM) for tool path generation, which is tightly integrated with the orientation strategy, to minimise tool path length under the constraint of smooth cutter orientation. Distinctively, cutter orientation along a tool pass is optimised by balancing considerations of maximum material removal and smoothness of cutter movement. Further, the intervals between successive tool passes are maximised according to the optimised orientation. In the paper, the IM is combined with the quadric method, a recently developed cutter orientation strategy, for iso-parametric machining with a flat-end cutter. However, the method could be applied to other orientation strategies with different machining mechanisms and cutter types. Simulated examples illustrate that the IM is more efficient in machining than established methods.     

Tool path generation via the multi-criteria optimisation for flat-end milling of sculptured surfaces

A method of generating optimal tool paths for sculptured surface machining with flat-end cutters is presented in this paper. The inclination and tilt angles, as well as the feed directions of the cutter at each cutter contact point on a machining path are optimised as a whole so that the machining width of the tool path can be as large as possible, and concerns such as smooth cutter motion, gouging avoidance, scallop height and machining widths overlap are also considered when calculating a path. A multi-criteria tool path optimisation model is introduced, and it is converted into a single objective optimisation with the weighted sum method. The Differential Evolution (DE) algorithm is suitable for solving this highly non-linear problem. However, the searching process of the DE algorithm may be trapped in local minima due to large number of design variables. Therefore, an algorithm combining the DE algorithm and the sequence linear programming algorithm is developed to solve this optimisation model. The proposed method is applied to two freeform surfaces to illustrate its effectiveness.     

Cutter size optimisation and interference-free tool path generation for five-axis flank milling of centrifugal impellers

Strategies for cutter size optimisation and interference-free tool path generation are proposed for five-axis flank milling of centrifugal impellers. To increase the material removal rate and provide a stronger tool shank during flank milling, the cutter size is first maximised under a set of geometric constraints. The tool path is then globally optimised in accordance with the minimum zone criterion for the determined optimal cutter size. Aside from the local interference of the cutter with the design surface, the global interferences with the hub surface and the adjacent blade surface are also considered in the optimisation models. Interference is indicated by the signed distance from the sampled point on the blade surface to the tool envelope surface. This distance is calculated without constructing the envelope surface. On the basis of the differential property of the distance function, we choose a sequential linear programming method in implementing the optimisations. This approach applies to generic rotary cutters, such as cylindrical and conical tools. Simulations are conducted to obtain the optimal cutter size and generate an interference-free tool path for a practical impeller. Simultaneously, a software module that can generate tool envelope surfaces and verify geometric errors is used to validate the proposed method.     

Integrated tool positioning and tool path planning for five-axis machining of sculptured surfaces

In this paper a new approach to tool path planning is presented for five-axis machining of sculptured surfaces. The positioning of the cutting tool along a machining pass is determined in an attempt to produce the most efficient machining pass with respect to the entire tool path. In this way the tool positioning strategy is an integral part of the path planning strategy. This differs from current methods, where tool positioning and path planning are two separate tasks. In the present work, various tool orientations are evaluated for cutter locations along the machining pass. The evaluation and eventual selection are made with respect to the completion of the overall tool path. An example part was simulated using the proposed integrated method which resulted in improved efficiency over a more traditional approach. The proposed method was also verified experimentally using cutting tests.     

Non-productive tool path optimisation for four-axis milling using the simulated annealing algorithm

The paper concerns the development of generic computer aided optimisation techniques for the minimisation of residence time of a multi-component pallet in a horizontal machining centre. A general methodology has been established to take a part program for a multi-faced pallet, that involves many components, typically 20–30, and tool changes, segment it to extract the position and machining conditions embedded in it, automatically re-sequence the machining operations to find the optimum total tool path, and regenerate a new part program with the optimised machining sequence. A range of case studies has been used to: validate the software, and to demonstrate its ability to minimise the total pallet residence time. The techniques developed can be used for semi-automatic part programming of the entire pallet with multi-components, and with an auto-selection multi-tool facility. The software is capable of achieving a large reduction in part programming time, as well as reducing the non-machining time. It is shown that the use of the optimisation package with a range of part programs reduces the total pallet residence time by a factor between 9.5 and 36%, and consequently has the potential to achieve considerable economic gains.     

多轴微细铣削机床的精度设计方法研究

高精度机床是实现微细加工的基础,目前对其设计主要还是依赖于经验或直观地根据加工精度要求来选取各个运动轴的精度,不能满足多轴微细铣削机床设计的需要. 以精度分析与精度分配为主要内容的精度设计方法,针对一种新型桌面五轴联动微细铣削机床,构建主要包括各运动轴定位精度的运动误差模型,求解各运动轴精度对末端精度的影响分布趋势,完成精度分析. 基于末端运动精度要求和关键设计参数,合理设置直线轴与旋转轴的精度要求,在工作空间内分别对B轴和C轴依次进行精度求解,实现各运动轴的运动精度优化与分配, 指导设计时科学地对各运动轴零部件进行选型.此设计方法对于多轴联动的中大型机床设计也具有一定的推广价值．     

Flank milling model for tool path programming of turbine blisks and compressors

In this paper, a methodology for complex surface machining based on cutting forces prediction is presented. The work is focused on blade finishing operations. The cutting forces model developed can be applied to three axis and five axis milling cases. For three-axis cases, the chip thickness is calculated according to traditional analytical methods. On the contrary, for five-axis cases the chip thickness is obtained from a geometric method developed in the paper. The cutting forces values can be calculated for the complete toolpath, but the presented model can also provide the programmer information about the cutting forces in a single point of the toolpath. The cutting force model is integrated in the CAM software in order to provide an extra tool that helps the programmer to decide which the optimal milling strategy is, based on the minimum cutting forces. In the last section, results of a case study based on impeller and blisk blades flank milling are discussed. Model predicted forces and real measured forces of flank milling operations are compared for model validation. Applying this methodology, cutting forces can be taken into account as a decisive criterion for optimal tool path selection.     

Using the global optimisation methods to minimise the machining path length of the free-form surfaces in three-axis milling

During the machining of free-form surfaces using three-axis numerically controlled machine (NC), several parameters are chosen arbitrary and one of the most important is the feed motion direction. The main objective of this study is to minimise the machining time of complex surfaces while respecting a scallop height criteria. The analytical expression of the machining time is not known and by hypothesis, it is assumed to be proportional to the path length crossed by the cutting tool. This path length depends on the feed direction. To have an optimal feed direction at any point, the surface is divided into zones with low variation of the steepest slope direction. The optimization problem was formulated aiming at minimizing the global path length. Furthermore, a penalty reflecting the time loss due to the movement of the tool from one zone to another one is taken into account. Several heuristics are used to resolve this problem: Clarke and Wrights, Greedy randomized adaptive search procedure, Tabu search and Nearest neighbour search. An example illustrates our work by applying the different heuristics on a test surface. After simulations, the results obtained present a significant saving of paths length of 24% compared to the machining in one zone.     

Refining of copper powder by a novel micro-abrasive milling method conducted in the air

The pure copper powder was milled by conventional high-energy ball milling (CM) and micro-abrasive milling (MAM) methods in the air or vacuum. The refining behavior of copper powder milled using these different methods has been studied, and the morphologies, microstructures, compositions, and properties of the milled powders have been thoroughly investigated. The results show that, as compared to CM, the MAMed copper powder had a better refinement behavior and contained a smaller number of agglomerates. After milling in the air for 30 h by MAM, whole copper powder was converted into Cu₂₊₁O. In addition, under the synergistic effects of micro-abrasion and exposure to oxygen, the Cu₂₊₁O powder was soft-agglomerated and had a specific surface area of 15.1031 m²/g and an average size of 375.4 nm. During the dispersion process, Cu₂₊₁O was partly converted into CuO and the microstructural evolution characteristics were disclosed. The dispersed powder had an average particle size of 179.5 nm. The refining mechanism of the copper powder prepared by the micro-abrasive milling method was also discussed.     

A radius compensation method of barrel tool based on macro variables in five-axis flank machining of sculptured surfaces

Barrel tool radius compensation is very important to improve the five-axis CNC machining precision and efficiency of sculptured surfaces. By combining macro variables and math function of CNC controller, a radius compensation method of barrel tool based on macro variables in five-axis flank machining of sculptured surfaces was presented. The basic principle of barrel tool radius compensation in five-axis flank machining was firstly investigated. For a specific five-axis CNC machine tool with dual rotary tables, a relationship equation between compensated cutter location (CL) data and machine control (MC) data could be derived. A post-processor with the function of five-axis barrel tool radius compensation was then developed by using the C++ language, which could generate the NC programme with macro variables of barrel tool radius compensation. Finally, the NC programme was obtained automatically by the developed post-processor for the aero-engine blade surface machining. The machining process was simulated on the software VERICUT, and machining experiments were also conducted on the five-axis machine tool. Both the simulation and experimental results showed that the proposed method could perform the function of barrel tool radius compensation in the NC programme for five-axis flank machining.     

高能球磨法合成纳米晶NiZn铁氧体的结构和磁性

报告了作者利用机械球磨方法成功制备纳米晶NiZn铁氧体软磁材料的实验结果。实验样品具有很好的单相结构,所形成材料典型晶粒尺度为10～50nm。结合纯Fe3O4球磨样品,初步估算其样品的合成效率大约为27%～44%,这一结果可利用两步合成及中间纳米颗粒的高活性给予理解。对本实验利用球磨方法直接获得的NiZn铁氧体样品表现出较低的磁化强度σm和较大的矫顽力Hc,其典型值为43Am2kg-1和377×103(4π)-1A/m。从实用化角度而言,必要的热处理将是必要的。实验进一步证明,除了传统的机械合金化制备纳米晶软磁合金材料以外,利用高能球磨制备纳米晶NiZn软磁铁氧体也将是一种有效可行的新方法。     

A fictitious domain method for the simulation of thermoelastic deformations in NC‐milling processes

This paper presents a (higher‐order) finite element approach for the simulation of heat diffusion and thermoelastic deformations in NC‐milling processes. The inherent continuous material removal in the process of the simulation is taken into account via continuous removal‐dependent refinements of a paraxial hexahedron base‐mesh covering a given workpiece. These refinements rely on isotropic bisections of these hexahedrons along with subdivisions of the latter into tetrahedrons and pyramids in correspondence to a milling surface triangulation obtained from the application of the marching cubes algorithm. The resulting mesh is used for an element‐wise defined characteristic function for the milling‐dependent workpiece within that paraxial hexahedron base‐mesh. Using this characteristic function, a (higher‐order) fictitious domain method is used to compute the heat diffusion and thermoelastic deformations, where the corresponding ansatz spaces are defined for some hexahedron‐based refinement of the base‐mesh. Numerical experiments compared to real physical experiments exhibit the applicability of the proposed approach to predict deviations of the milled workpiece from its designed shape because of thermoelastic deformations in the process.     

A freeform surface manufacturing approach by integration of inspection and tool path generation

Freeform surfaces have been widely used in various engineering applications. Increasing requirements for the accuracy of freeform surfaces have led to significant challenges for the manufacturing of these surfaces. A method for manufacturing of freeform surfaces is introduced in this paper by integrating inspection and tool path generation to improve manufacturing quality while reducing manufacturing efforts. Inspection is conducted by comparing the digitised manufactured surface with the design surface to identify the error regions. In this new inspection technique, the areas on the manufactured surface that are beyond the design tolerance boundaries are used as the objective function during the localisation process, in order to minimise post-inspection machining efforts. The tool path generation methods are then selected based on the geometric characteristics of the identified error regions, for creating tool paths to remove the errors. Computational efficiency, machining efficiency, and quality are considered in this integrated method.     

Application of variational mesh generation approach for selecting centers of radial basis functions collocation method

In this paper, a two-dimensional variational mesh generation method is applied to obtain adaptive centers for radial basis functions (RBFs). At first, a set of uniform centers is distributed in the domain, then mesh generation differential equations are used to move the centers to region with high gradients. An iterative algorithm is introduced to solve steady-state mesh generation differential equations with RBFs. Functions with steep variation in the domains are used to validate the adaptive centers generation method. In addition to the centers adaption process is applied to solve elliptic partial differential equations via RBFs collocation method. Numerical results of Helmholtz differential equation show a clear reduction in the error, when the adaptive centers are used for RBFs.     

反应球磨法制备镁/碳纳米复合储氢材料

将无烟煤进行脱灰和碳化,制备微晶碳, 再将微晶碳和铝添加到镁中,用氢气反应球磨法制取镁/碳纳米复合储氢材料.用透射电子显微镜、选区电子衍射、X射线衍射和差示扫描量热分析对储氢材料的粒度、晶体结构和放氢温度进行了测定.结果表明,微晶碳是镁粉的高效助磨剂,添加40%(质量分数)的微晶碳,球磨3h,即可将镁磨至20～40nm;添加微晶碳和铝能降低储氢材料的放氢温度;微晶碳具有类似石墨结构,较易磨至纳米级,层片之间能够储氢.     

Bordering method for solving systems of linear equations generated by the finite element method in the plate bending problem

A combined iteration algorithm based on the bordering and conjugate gradient methods is proposed to solve systems of linear equations generated by the finite element method in the plate bending problem. The numerical results for the analysis of the convergence rate of the iterative process are presented in the solution of model problems using a classical and modified algorithm of the method of conjugate gradients. The possibility of acceleration of the iterative algorithm is shown. __________ Translated from Problemy Prochnosti, No. 4, pp. 137–145, July–August, 2007.     

An efficient method for analyzing second harmonic generation with the consideration of pump depletion

We propose a simple method to analyze second harmonic generation (SHG) in general quasi-phase-matching media with the consideration of pump depletion. It allows us to conveniently predict precise result from undepleted pump approximation solution. Based on this method, multi-wavelength generation with arbitrary target efficiency and wavelength spacing is engineered. The effect of pump depletion on the performance of constructed multi-wavelength generator is analyzed. We demonstrate that it is efficient to design nonlinear device for multi-wavelength SHG by proposed method.