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.     

Tool path optimisation for flank milling ruled surface based on the distance function

This paper deals with optimised tool path generation for five-axis flank milling using signed point-to-surface distance function. The main idea is that the geometrical deviations between the design surface and the machined surface are minimised by fine tuning the cutter locations. Based on the tangency conditions in envelope theory, the analytic representation of the envelope surface of a cutter undergoing five-axis motion is first obtained. Then the geometrical deviations between the envelope surface (i.e. machined surface) and the design surface are calculated. Optimisation of the five-axis tool path is modeled as the fine tuning of the initial cutter locations under the minimum zone criterion recommended by ANSI and ISO, which requires minimisation of the maximum geometrical deviation between the design surface and the envelope surface. Using the signed point-to-surface distance function, tool path optimisation for finish milling is formulated as a constrained optimisation problem. Based on the first-order Taylor approximation of the signed distance function, two sequential approximation algorithms for the Minimax and Least Square optimisations are developed. Numerical examples, in which a conical tool is chosen as a special case of flank machining ruled surface, verify the proposed strategy.     

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.     

On a novel approach to planning cylindrical cutter location for flank milling of ruled surfaces

This paper presents a novel approach to planning cylindrical cutter location for flank (or side) milling of ruled surfaces. It contains two steps: tool positioning and re-positioning. In the former step, first an adaptive mesh is constructed on the designed ruled surface with the existing algorithm, and then a sequence of initial cutter locations (CLs) is determined using the offset points of the grid sampled points via semidefinite programming (SDP). In the latter step, a smooth tool axis surface is generated by interpolating the initial CLs using the dual mapping theory; afterwards, the tool is re-positioned by adjusting the offset value of each sampled point on the designed surface according to the predicted cutting errors. The cutter positioning methods for rough and finish milling are both developed in this framework. Example and numerical simulation illustrate the efficiency of the novel strategy.     

Fast tool path generation by the iso-scallop height method for ball-end milling of sculptured surfaces

This article reports on tool path generation by the iso-scallop height method for the three-axis ball-end milling of sculptured surfaces. In order to achieve the specified machining accuracy, constant scallop height machining requires an understanding of the three-dimensional machining geometry and the use of iterative approaches. Feng and Li have accomplished such work using the bisection method to search the scallop curves and the tool centre curves. This paper presents an analytic and geometric study of the machining aspects. Analysing the local properties of the distance functions, which indicate where the scallop point and the tool are centred, the bisection method can be replaced by the Newton iterative algorithm which converges faster. The derivatives of the functions are formulated by their Taylor approximations with a small error. The initial guesses are obtained by considering the local machining geometry. The proposed method significantly reduces the total computing time necessary to generate tool paths.     

球磨时间对镁碳复合储氢材料结构和性能的影响

采用氢气气氛中高能球磨反应法,制备了40Mg60C镁碳复合储氢材料,研究了球磨时间对材料粒度、晶体结构和放氢性能的影响.结果表明,球磨2h材料的粒度即可达纳米级,约10～20nm,球磨时间再延长,材料团聚程度加重;球磨2h的材料为纳米晶和非晶结构,当球磨时间增加到4h时,材料几乎成为非晶结构;球磨时间4h时,材料储氢量已趋于饱和,最大放氢量为3.15%(质量分数);材料放氢温度随球磨时间的增加而降低,球磨5h材料的初始放氢温度和放氢峰温降为275.18和314.94℃.     

Understanding production of fines in batch ball milling for mill scale-up design using the population balance model

The rate of production of fine material in the batch mode of grinding operation forms the basis for determination of the grindability parameter of the Bond approach and the breakage distribution function of the population balance model (PBM) approach to the mill scale-up design. For a given set of mill operating conditions, the rate of production of fines is determined by the breakage characteristics and production history of the material being ground. Another important aspect is the variation in the rate of production of fines with grinding time. With a view to developing a clear understanding of these aspects, a detailed analysis of variations in the rate of production of fines was carried out using the PBM framework and two well-known functional forms for the specific breakage rate and breakage distribution parameters. In this paper, it has been shown how the results of this analysis can be used for: (i) obtaining more accurate estimates of the breakage distribution parameters by performing just one short-duration batch grinding experiment, and (ii) explaining variation in the Bond Work index with the product size in terms of the exponent of particle size in the expression for the specific breakage rate function: $k_j=A^1{x}_j^{\alpha }$.     

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.