Improving optimization of tool path planning in 5-axis flank milling using advanced PSO algorithms

This paper studies optimization of tool path planning in 5-axis flank milling of ruled surfaces using advanced Particle Swarm Optimization (PSO) methods with machining error as an objective. We enlarge the solution space in the optimization by relaxing the constraint imposed by previous studies that the cutter must make contact with the boundary curves. Advanced Particle Swarm Optimization (APSO) and Fully Informed Particle Swarm Optimization (FIPS) algorithms are applied to improve the quality of optimal solutions and search efficiency. Test surfaces are constructed by systematic variations of three surface properties, cutter radius, and the number of cutter locations comprising a tool path. Test results show that FIPS is most effective in reducing the error in all the trials, while PSO performs best when the number of cutter locations is very low. This research improves tool path planning in 5-axis flank milling by producing smaller machining errors compared to past works. It also provides insightful findings in PSO based optimization of the tool path planning.     

Optimize tool paths of flank milling with generic cutters based on approximation using the tool envelope surface

This paper presents a global optimization method to generate a tool path for flank milling free-form surfaces with a generic cutter based on approximation using the tool envelope surface. It is an extension of our previous work [Gong Hu, Cao Li-Xin, Liu Jian. Improved positioning of cylindrical cutter for flank milling ruled surfaces. Computer Aided Design 2005; 37:1205–13]. First, given initial tool path or tool axis trajectory surface, the grazing points of the tool envelope surface can be calculated. Second, the errors between the tool envelope surface and the designed surface along the normal direction of the tool envelope surface are calculated. Based on this new definition of error, an optimization model is established to get the global optimized tool axis trajectory surface. In order to simplify the calculation, two variants of this method based on the least square criterion are proposed to solve this model. Since this method is really based on the tool envelope surface, it can reduce the initial machining errors effectively. The proposed method can be used not only for cylindrical cutters and conical cutters, but also for generic cutters with a surface of revolution. In addition to ruled surfaces, it also can be used for machining non-ruled surfaces. Finally, several examples are given to prove its effectiveness and accuracy. The generated tool paths and calculated grazing points for test are available in supplementary files for the readers’ convenience in verifying this work in different CAD/CAM systems.     

Profile error-oriented optimization of the feed direction and posture of the end-effector in robotic free-form milling

In robotic milling of free-form surfaces, most existing studies tried to reduce the profile errors by optimizing the robot stiffness. However, the stiffness could not directly and rigorously reflect the milling performance to some content, especially, when the significant influence of feed direction on the profile error was ignored for robotic milling of free-form surfaces with large curvatures. In order to solve these problems, direct optimization of the feed directions and end-effector postures is theoretically formulated to seek the solution of a new profile error-oriented optimization model. This model characterizes the profile error in relation to the robot deformation caused by cutting forces, called force-induced profile error. The force-induced profile error is calculated and reduced at each cutter contact point on the free-form surface by comprehensively considering robot stiffness, free-form surface features, feed directions and cutting forces for generating feed direction and posture of the end-effector. The surface is partitioned into multiple sub-regions, in each of which the principle for determining the initial feed direction is proposed to ensure the smooth milling without abrupt change of feed direction. Robotic milling process of the workpiece with saddle contour is experimented. Feed direction and posture of the end-effector are generated by the proposed method and the existing method for comparative studies. Measured profile errors and photographs of machined surface indicate that the developed method can greatly improve the milling performance.     

Generation of reciprocating tool motion in 5-axis flank milling based on particle swarm optimization

This paper proposes a novel method for generation of optimized tool path in 5-axis flank milling of ruled surfaces based on Particle Swarm Optimization (PSO). The 3D geometric problem, tool path generation, is transformed into a mathematical programming task with the machined surface error as the objective function in the optimization. This approach overcomes the limitation of greedy planning methods employed by most previous studies. By allowing the cutter to move backforward, reciprocating tool path produces smaller machining error compared with the traditional one consisting of only forward cutter movement. A cutting experiment is conducted with different tool paths and the CMM measurement verifies the effectiveness of the proposed method.     

Tool path planning for 5-axis flank milling of ruled surfaces considering CNC linear interpolation

This paper investigates tool path planning for 5-axis flank milling of ruled surfaces in consideration of CNC linear interpolation. Simulation analyses for machining error show insights into the tool motion that generates a precision machined surface. Contradicting to previous thoughts, the resultant tool path does not necessarily produce minimal machining error when the cutter contacts the rulings of a developable surface. This effect becomes more significant as the distance between two cutter locations is increased. An optimizing approach that adjusts the tool position locally may not produce minimal error as far as the entire surface is concerned. The optimal tool path computed by a global search scheme based on dynamic programming supports this argument. A flank milling experiment and CMM measurement further validate the findings of this work.     

Analysis of improved positioning in five-axis ruled surface milling using envelope surface

This article covers side milling of ruled surfaces using a milling cutter. Flank milling is useful for machining objects such as impellers, turbine blades, fan vanes and all workpieces defined by non-developable, ruled surfaces. In the present article, we first introduce two types of positioning on ruled surfaces developed within the Toulouse Mechanical Engineering Laboratory. The positioning studied is taken from the geometric situation not taking the instantaneous speed of rotation of the milling cutter into account. The swept profile of the tool is then determined based on the tool motion. Having defined the envelope surface, we seek to analyse improved and standard positioning errors comparing envelope surfaces with the ruled surface. We then introduce an example to illustrate positioning developed through a first theoretical study before experimentation including machining and measurement of the test piece. Finally, we give our conclusions as to the validity of improved positioning without taking the instantaneous speed of rotation of the milling cutter into account.     

Analytical estimation of error in flank milling of ruled surfaces

This article introduces a method to estimate geometric error during flank milling of a ruled surface. The various positioning schemes developed by researchers are intended to reduce this geometric error in order to mill with larger sized milling cutters while respecting the tolerance interval. There are two trends in positioning: either positioning is simple and right from the start it is easy to determine design of the maximum allowed milling cutter radius, or positioning is complex and determination of the maximum milling cutter dimensions can only be conducted after digital calculations of the error. It will then be necessary to choose another milling cutter radius and recommence the positioning procedure and error calculation in order to validate the tool. In the present study, a method to estimate error in the scope of complex positioning is presented. The aim is to be capable of choosing a maximum cutting tool radius that respects the tolerance interval.     

Algorithms for selecting cutters in multi-part milling problems

This paper describes geometric algorithms for automatically selecting an optimal sequence of cutters for machining a set of 2.5-D parts. In milling operations, cutter size affects the machining time significantly. Meanwhile, if the batch size is small, it is also important to shorten the time spent on loading tools into the tool magazine and establishing z-length compensation values. Therefore, in small-batch manufacturing, if we can select a set of milling tools that will produce good machining time on more than one type of parts, then several unnecessary machine-tool reconfiguration operations can be eliminated. In selecting milling cutters we consider both the tool loading time and the machining time and generate solutions that allow us to minimize the total machining time. In this paper we first present algorithms for finding the area that can be cut by a given cutter. Then we describe a graph search formulation for the tool selection problem. Finally, the optimal sequence of cutters is selected by using Dijkstra's shortest path planning algorithm.     

Digital copy milling—autonomous milling process control without an NC program

Conventional NC machine tools do not generally allow the change of cutting conditions such as depth of cut and stepover during machining operations, once they are given machining commands as NC programs. For that reason, the NC programs must be prepared adequately and verified in advance, which requires extensive time and effort. It is therefore necessary to develop functions to generate the cutter path autonomously and control the cutting conditions adaptively during machining to optimize the cutting process, maintain stable cutting, and avoid cutting trouble. This paper proposes a new architecture to realize autonomous control of the cutting process without using NC programs. A technique called digital copy milling is developed to control the NC machine tool in real time. The digital copy milling system can generate tool paths in real time, based on the principle of copy milling. In addition, a new control strategy is developed to control the cutting conditions adaptively. A prototype of an autonomous controller was implemented in a three-axis control machining center. Thereafter, experimental milling tests were carried out to verify the effectiveness of the proposed system. The cutter paths were generated autonomously by the digital copy milling system. Results show that the cutting depth and stepover can be changed during milling tests. Cutting conditions were controlled adaptively.     

Towards efficient 5-axis flank CNC machining of free-form surfaces via fitting envelopes of surfaces of revolution

We introduce a new method that approximates free-form surfaces by envelopes of one-parameter motions of surfaces of revolution. In the context of 5-axis computer numerically controlled (CNC) machining, we propose a flank machining methodology which is a preferable scallop-free scenario when the milling tool and the machined free-form surface meet tangentially along a smooth curve. We seek both an optimal shape of the milling tool as well as its optimal path in 3D space and propose an optimization based framework where these entities are the unknowns. We propose two initialization strategies where the first one requires a user’s intervention only by setting the initial position of the milling tool while the second one enables to prescribe a preferable tool-path. We present several examples showing that the proposed method recovers exact envelopes, including semi-envelopes and incomplete data, and for general free-form objects it detects envelope sub-patches.     

Tool path generation for free form surfaces using Bézier curves/surfaces

Presented in this paper is a tool path generation method for multi-axis machining of free-form surfaces using Bézier curves and surfaces. The tool path generation includes two core steps. First is the forward-step function that determines the maximum distance, called forward step, between two cutter contact (CC) points with a given tolerance. The second component is the side step function which determines the maximum distance, called side step, between two adjacent tool paths with a given scallop height. Using the Bézier curves and surfaces, we generate cutter contact (CC) points for free-form surfaces and cutter location (CL) data files for post processing. Several parts are machined using a multi-axis milling machine. As part of the validation process, the tool paths generated from Bézier curves and surfaces are analyzed to compare the machined part and the desired part.     

An expert system approach for die and mold making operations

In the modern manufacturing of sophisticated parts with 3D sculptured surfaces, die and mold making operations are the most widely used machining processes to remove unwanted material. To manufacture a die or a mold, many different cutting tools are involved, from deep hole drills to the smallest ball nose end mills. Since the specification of each tool is very different from each other, each mold or die is specific with their complicated shapes and many machining rules exist to consider, a great deal of expertise is needed in planning the machining operations. An expert system (DieEX) developed for this purpose is described in the present work. The geometry and the material of the workpiece, tool material, tool condition and operation type are considered as input values and various recommendations about the tool type, tool specifications, work holding method, type of milling operation, direction of feed and offset values are provided.     

Constant scallop-height tool path generation for three-axis sculptured surface machining

This paper presents a new approach for the determination of efficient tool paths in the machining of sculptured surfaces using 3-axis ball-end milling. The objective is to keep the scallop height constant across the machined surface such that redundant tool paths are minimized. Unlike most previous studies on constant scallop-height machining, the present work determines the tool paths without resorting to the approximated 2D representations of the 3D cutting geometry. Two offset surfaces of the design surface, the scallop surface and the tool center surface, are employed to successively establish scallop curves on the scallop surface and cutter location tool paths for the design surface. The effectiveness of the present approach is demonstrated through the machining of a typical sculptured surface. The results indicate that constant scallop-height machining achieves the specified machining accuracy with fewer and shorter tool paths than the existing tool path generation approaches.     

Five-axis NC cylindrical milling of sculptured surfaces

In theory, the five-axis numerical control (NC) machining of sculptured surfaces can be classified into facing milling and cylindrical milling (or side milling). In general, the first one, using flat-end cutter, is suitable for the machining of large sculptured surfaces, e.g. the blade of hydraulic turbine, whose binding relations with drive surface (DS) and check surface (CS) are simple, and the second one, using cylindrical cutter, has wide applications for the milling of small and middle dimensional surfaces whose binding relations with DS and CS are more complex, such as the milling of integral turbine wheels. In practice, the second one suffers more difficulties than the first one, which are mostly related to gouge avoidance, interference avoidance and tool strength. This paper, on the basis of the theories of differential geometry and analytical geometry, describes research on algorithms for the toolpath generation of five-axis cylindrical milling of sculptured surfaces with cylindrical cutter. The approach includes (a) single point offset (SPO) algorithm, and (b) double point offset (DPO) algorithm for the cutter location data (CLDATA) calculation of five-axis cylindrical milling.     

Mechanistic modelling of the milling process using an adaptive depth buffer

A mechanistic model of the milling process based on an adaptive and local depth buffer is presented. This mechanistic model is needed for speedy computations of the cutting forces when machining surfaces on multi-axis milling machines. By adaptively orienting the depth buffer to match the current tool axis, the need for an extended Z-buffer is eliminated. This allows the mechanistic model to be implemented using standard graphics libraries, and gains the substantial benefit of hardware acceleration. Secondly, this method allows the depth buffer to be sized to the tool as opposed to the workpiece, and thus improves the depth buffer size to accuracy ratio drastically. The method calculates tangential and radial milling forces dependent on the in-process volume of material removed as determined by the rendering engine depth buffer. The method incorporates the effects of both cutting and edge forces and accounts for cutter runout. The simulated forces were verified with experimental data and found to agree closely. The error bounds of this process are also determined.     

A machining potential field approach to tool path generation for multi-axis sculptured surface machining

This paper presents a machining potential field (MPF) method to generate tool paths for multi-axis sculptured surface machining. A machining potential field is constructed by considering both the part geometry and the cutter geometry to represent the machining-oriented information on the part surface for machining planning. The largest feasible machining strip width and the optimal cutting direction at a surface point can be found on the constructed machining potential field. The tool paths can be generated by following the optimal cutting direction. Compared to the traditional iso-parametric and iso-planar path generation methods, the generated MPF multi-axis tool paths can achieve better surface finish with shorter machining time. Feasible cutter sizes and cutter orientations can also be determined by using the MPF method. The developed techniques can be used to automate the multi-axis tool path generation and to improve the machining efficiency of sculptured surface machining.     

An innovative approach to NC programming for accurate five-axis flank milling of spiral bevel or hypoid gears

To transfer power, a pair of spiral bevel or hypoid gears engages. From beginning to end of two tooth surfaces engaging with each other: for their rigid property, they contact at different points; and for their plastic property, they contact at small ellipses around the points. On each surface, the contact line (or called as contact path) by connecting these points and the contact area by joining these ellipses are critical to driving performance. Therefore, to machine these surfaces, it is important to machine the contact line and area with higher accuracy than other areas. Five-axis flank milling is efficient and is widely used in industry. However, tool paths for flank milling the gears, which are generated with the existing methods, can cause overcuts on the contact area with large machining errors. To overcome this problem, an innovative approach to NC programming for accurate and efficient five-axis flank milling of spiral bevel or hypoid gears is proposed. First, the necessary conditions of the cutter envelope surface tangent with the designed surface along a designed line are derived to address the overcut problem of five-axis milling. Second, the tooth surface including the contact line and area are represented using their machining and meshing models. Third, according to the tooth surface model, an optimization method based on the necessary conditions is proposed to plan the cutter location and orientation for flank milling the tooth surface. By using these planned tool paths, the overcut problem is eliminated and the machining errors of contact area are reduced. The proposed approach can significantly promote flank milling in the gear manufacturing industry.     

Three dimensional modeling and finite element simulation of a generic end mill

The geometry of cutting flutes and the surfaces of end mills is one of the crucial parameters affecting the quality of the machining in the case of end milling. These are usually represented by two-dimensional models. This paper describes in detail the methodology to model the geometry of a flat end mill in terms of three-dimensional parameters. The geometric definition of the end mill is developed in terms of surface patches; flutes as helicoidal surfaces, the shank as a surface of revolution and the blending surfaces as bicubic Bezier and biparametric sweep surfaces. The proposed model defines the end mill in terms of three-dimensional rotational angles rather than the conventional two dimensional angles. To validate the methodology, the flat end milling cutter is directly rendered in OpenGL environment in terms of three-dimensional parameters. Further, an interface is developed that directly pulls the proposed three-dimensional model defined with the help of parametric equations into a commercial CAD modeling environment. This facilitates a wide range of downstream technological applications. The modeled tool is used for finite element simulations to study the cutting flutes under static and transient dynamic load conditions. The results of stress distribution (von mises stress), translational displacement and deformation are presented for static and transient dynamic analysis for the end mill cutter flute and its body. The method described in this paper offers a simple and intuitive way of generating high-quality end mill models for use in machining process simulations. It can be easily extended to generate other tools without relying on analytical or numerical formulations.     

Automated process planning method to machine A B-Spline free-form feature on a mill–turn center

In this paper, we present a methodology for automating the process planning and NC code generation for a widely encountered class of free-form features that can be machined on a 3-axis mill–turn center. The free-form feature family that is considered is that of extruded protrusions whose cross-section is a closed, periodic B-Spline curve. In this methodology, for machining a part with B-Spline protrusion located at the free end, the part is first rough turned to the maximum profile diameter of the B-Spline, followed by rough profile cutting and finish profiling with axially mounted end mill tools. The identification and sequencing of machining volumes is completely automated, as is the generation of actual NC code. The approach supports both convex and non-convex profiles. In the case of non-convex profiles, the process planning algorithm ensures that there is no gouging of the work piece by the tool. The algorithm also identifies when sections of the tool path lie outside the work piece and utilizes rapid traverses in these regions to reduce cutting time. This methodology presents an integrated turn–mill process planning where by making the process fully automated from design with no user intervention making the overall process planning efficient. The algorithm was tested on several examples and test parts using the unmodified NC code obtained from the implementation were run on a Moriseiki mill–turn center. The parts that were produced met the dimensional specifications of the desired part.