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 generation for five-axis machining of blisks with barrel cutters

A barrel cutter has a cutting segment with a large radius on its profile, and this arc segment allows the cutter to tilt away from the part surface, avoiding the collisions of the tool with the part. Therefore, barrel cutters are suitable for five-axis blisk machining. However, the barrel cutters are more challenging for CAM software to generate paths. A method of generating collision-free and large-machining width flank milling paths with smooth axes movements for blisk machining with barrel cutters is proposed. Local gouge between the tool flute surface and the blade to be machined is considered, and the collisions of the blisk with the non-cutting parts of the tool, i.e. tool shank and holder, are also detected. The machined part geometry is the complement of the cutter’s swept envelope from the stock. Accordingly, the swept profile of the cutter at each cutter contact point is employed to evaluate the machining width naturally. Thereafter, a multi-criteria tool path generation model is established, and it is converted into a single-objective optimization with the weighted sum method. An algorithm based on the Differential Evolution algorithm is developed to solve this model. The numerical example illustrates the effectiveness of the proposed method.     

Simultaneous optimization of the feed direction and tool orientation in five-axis flat-end milling

The two additional rotational motions of five-axis machining make the determination of the optimal feed direction and tool orientation a challenging task. A new model to find the optimal feed direction and tool orientation maximising the machining width and avoiding local gouging at a cutter contact (CC) point with a flat-end cutter considering the tool path smoothness requirement is developed in this paper. The machining error is characterised by a signed distance function defined from a point on the bottom tool circle of the cutter to the design surface. With the help of the differential evolution approach, the optimisation model can be resolved to determine the optimal tool orientation and feed direction at a given CC point, and generate the smooth tool paths following the optimal feed direction. Simulation examples demonstrate the developed techniques can improve the tool orientation and feed direction at a CC point to increase the machining width, improving the efficiency of freeform surface machining.     

New criteria for tool orientation determination in five-axis sculptured surface machining

The problem of optimal tool orientation determination in five-axis flat-end milling of sculptured surfaces is examined in this paper. The optimal tool orientation avoids local and global gouging of the tool and maximises a specific criterion related to machining efficiency. Two new criteria are introduced in this paper to quantify the tool orientation quality at a cutter contact point: infinitesimal machining volume (IMV) and infinitesimal machining area (IMA). The IMV criterion is used to maximise the material removal at the cutter contact point. The IMA criterion attempts to identify tool orientations that would lead to minimised overall tool path length. Using one of these criteria, an optimisation problem can be formulated to determine the optimal tool orientation among feasible gouge-free orientations. It is shown that the commonly adopted criterion of machining strip width in the determination of the optimal tool orientation cannot contribute towards maximising the material removal and does not really result in minimum overall tool path length. Results from various case studies have indicated that the newly introduced criteria can be used to generate optimal tool orientations that significantly increase machining efficiency.     

Adaptive nonlinear tool path optimization for five-axis machining

Current tool path computation in the CAM algorithms approximates the surface by piecewise linear interpolation. In the case of three-axis machining on a CNC machine the tool will exactly reproduce this computed tool path. However in the case of five-axis simultaneous machining the real tool path on the CNC machine will not follow the linear approximation computed by the conventional CAM algorithm. A new CAM algorithm is proposed which approximates the surface to be machined by a piecewise curved approximation. This curve represents the real tool path followed on the five-axis machine. This piecewise curved approximation is further optimized by formulating the tool path computation as the generation of a grid based on a variational smoothness penalty function. This new algorithm considerably improves the accuracy and reduces the number of blocks and machining time.     

曲面匹配方法在刀具加工轨迹优化中的应用

为减小非可展直纹面侧铣过程中产生的原理误差，提出一种新的刀具加工轨迹优化方法，将曲面匹配方法应用于初始刀具加工轨迹的优化过程，并使用序列二次规划算法求解曲面匹配问题。首先，采用现有的刀具加工轨迹生成方法得到刀轴轨迹曲面；其次，对刀轴轨迹曲面进行法向偏移得到对应的刀具加工包络面并进行原理误差计算，使用基于序列二次规划算法的曲面匹配方法对加工包络面与设计曲面进行曲面逼近，得到空间变换矩阵；再次，通过空间变换和法向偏移，得到优化后的刀轴轨迹曲面及其对应的刀具加工包络面，以及对应的优化刀具加工轨迹及加工误差分布数据；最后，使用MATLAB进行仿真，并与基于最小二乘法的曲面匹配方法进行对比验证。仿真结果表明该优化方法有效地减小了初始刀具加工轨迹产生的原理误差，这说明提出的方法能够用于减小非可展直纹面侧铣加工时产生的原理误差。研究成果为提高非可展直纹面侧铣的精度提供了新的技术支持。     

New method of tool orientation determination by enveloping element for five-axis machining of spatial cam

A new methodology is presented for the determination of a feasible tool orientation of a ball-end milling cutter for collision and gouging avoidance in five-axis machining of spatial cam. Since the meshing element is used as a generating element for a spatial cam, the meshing element is in tangency with the spatial cam. The notion of the proposed collision-free method is that the ball-end milling cutter is confined within the meshing element. Based on envelope theory, homogeneous coordinate transformation and differential geometry, curvatures of the cam surface and the cutting tool are evaluated for interference checking. To evaluate machining efficiency, the contact length is calculated for various tool orientations. The toolpath is verified through a solid cutting simulation. The proposed methodology can be used to automate the programming of tool paths for five-axis machining of spatial cam.     

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.     

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.     

Design,evaluation and optimisation of cutter path strategies when high speed machining hardened mould and die materials

The use of high speed milling (HSM) for the production of moulds and dies is becoming more widespread. Critical aspects of the technology include cutting tools, machinability data, cutter path generation and technology. Much published information exists on cutting tools and related data (cutting speeds, feed rates, depths of cut, etc.). However, relatively little information has been published on the optimisation of cutter paths for this application. Most of the research work is mainly focused on cutter path generation with the main aim on reducing production time. Work with regards to cutter path evaluation and optimisation on tool wear, tool life, surface integrity and relevant workpiece machinability characteristics are scant. Therefore, a detailed knowledge on the evaluation of cutter path when high speed rough and finish milling is essential in order to improve productivity and surface quality. The paper details techniques used to reduce machining times and improve workpiece surface roughness/accuracy when HSM hardened mould and die materials. Optimisation routines are considered for the roughing and finishing of cavities. The effects of machining parameters notably feed rate adaptation techniques and cutting tools are presented.     

A review of numerically controlled methods for finish-sculptured-surface machining

This paper presents a mathematical review of methods and algorithms used to compute milling cutter placement for multi-axis finished-surface machining. In general, these methods and algorithms compute tool path points based on tangent-plane contact between the milling cutter and the surface while maintaining a fixed tool orientation. This tangent-plane method of tool positioning and orientation is examined by discussing its strengths and weaknesses. Errors resulting from the tangent-plane approach are typically determined using a posteriori cutter path checking and graphic visualization techniques. Although these checking techniques have proved useful in identifying the tool path errors before actual machining, the problem of generating an error-free tool path remains. In this paper, we discuss the analysis of tool path position and orientation data as they are generated. This a priori analysis method is used to show error locations along the lateral face of the tool. The conclusion is reached that additional research is needed in the area of simultaneous multi-axis tool path planning, if errors are to be eliminated and the efficiency of the milling machine is to be improved. The reader is referred to research efforts that extend beyond the traditional or computer-aided design (CAD, vendor supplied) tool path planning methods. Some of these efforts show great promise in eliminating gouging and improves machine tool efficiency.     

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.     

The optimal feedrate planning on five-axis parametric tool path with geometric and kinematic constraints for CNC machine tools

The optimal feedrate planning on five-axis parametric tool path with multi-constraints remains challenging due to the variable curvature of tool path curves and the nonlinear relationships between the Cartesian space and joint space. The methods for solving this problem are very limited at present. The optimal feedrate associated with a programmed tool path is crucial for high speed and high accuracy machining. This paper presents a novel feedrate optimisation method for feedrate planning on five-axis parametric tool paths with preset multi-constraints including chord error constraint, tangential kinematic constraints and axis kinematic constraints. The proposed method first derives a linear objective function for feedrate optimisation by using a discrete format of primitive continuous objective function. Then, the preset multi-constraints are converted to nonlinear constraint conditions on the decision variables in the linear objective function and are then linearised with an approximation strategy. A linear model for feedrate optimisation with preset multiple constraints is then constructed, which can be solved by well-developed linear programming algorithms. Finally, the optimal feedrate can be obtained from the optimal solution and fitted to the smooth spline curve as the ultimate feedrate profile. Experiments are conducted on two parametric tool paths to verify the feasibility and applicability of the proposed method that show both the planning results and computing efficiency are satisfactory when the number of sampling positions is appropriately determined.     

Efficient tool path planning for five-axis surface machining with a drum-taper cutter

This paper presents a new efficient approach to NC tool path generation for five-axis surface machining. First, an efficient cutter, named a drum-taper cutter, is proposed; its key dimension is determined to avoid gouging in surface machining according to the maximum curvature of the surface calculated with a genetic algorithm. Then, based on the drum-taper cutter, the tool paths are generated so that the scallop height formed by adjacent tool paths in machining is kept constant, and an improved algorithm for calculating the interval between tool paths is presented. Finally, an example of tool path generation with the above method for arbitrary surface impeller machining is conducted, and the results show that the presented method leads to a significant reduction in the total tool path length and is accompanied by a reduction in machining time.     

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.     

基于曲率的曲面加工刀位轨迹生成算法

提出了一种自由曲面五轴数控加工无干涉刀位轨迹的生成算法。该方法利用曲面的曲率来确定环形刀的刀具姿态,使得刀具随被加工曲面的形状变化而倾斜,从而生成无干涉的刀位轨迹。     

Optimierung der Schneckenradfertigung durch Prozesssimulation

The simulation program developed in recent years allows the complete worm wheel manufacturing process to be simulated. Depending on the state of wear of the grinding tool, the simulation provides optimum machine setting data – and more precisely the center distance when milling and the milling tool swivel angle. The target gear flank topography of the worm wheel can now also be calculated using this machine setting data. Instead of the previous contact pattern check using special blueing paste and a master worm, the actual flank topography of the gearwheel can be determined on a gear measuring center. A comparison then identifies the deviations between the actual and target flank topographies. The simulation program calculates optimized machine setting data from the values that are determined. This technique has an inestimable advantage due to the fact that it also essentially compensates topography errors caused by deviations at the milling tool, deformation of the milling machine etc. A subjective assessment of the tooth contact pattern by the machinist is now replaced by an objective measurement and a simulation of the milling process.     

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.     

机器人外形复杂曲面的加工刀具的研究

探讨了机器人外形美观设计的重要性和外型复杂曲面加工的可行性,从而阐述了研制“S”形球面铣刀的意义,然后研究了加工刀具的前刀面和后刀面的数学模型与工业实现的机构可行性,并给出了相关的数学公式和加工数据,最后得出结论用简单的2轴完全可以实现在传统上用4轴数控机床才能加工的“S”形球头刀,为简化复杂刀具的加工进行探讨。     

Diffusion wear in milling titanium alloys

Abstract

In this paper, diffusion wear during milling of titanium alloys is reported. In high speed milling, tool wear is mainly caused by diffusion. The wear pattern is characterised by the combined extension of crater wear on the rake face and glacier wear on the flank. Evidence of diffusion of cobalt and carbon at the interface between the milling cutter and the workpiece has been obtained. It was demonstrated for the first time that, as diffusion wear occurred, a carbon rich layer was formed at the tool/workpiece interface while the tool material below the flank wearland was depleted in carbon. Wear occurred as a result of embrittlement and weakening of the tool surface resulting from the diffusion process.

MST/674