Machining Strip Width Research Articles

Constant Scallop Height Algorithm of Self-Adaptive Tool Orientation with Toroidal Cutter

Using a 5-axis NC machining tool enables the tool to be oriented in any spatial direction to access a given point. This means interference can be avoided and the position of the tool can be optimized. This paper presents a new approach to generate gouging-free tool paths for constant scallop-height machining using 5-axis toroidal milling. We consider cutter positions, which guarantee local gouging avoidance. Based on second order approximations of the machined strip width, we present locally optimal cutting positions for cutting directions. The largest machined strip width of constant scallop height and the corresponding gouging-avoidance tool orientation are calculated. The effectiveness of the present approach is demonstrated through the comparing of tool path, velocity curve and acceleration curve of a typical sculptured surface, which generated by the present approach and the conventional constant scallop height. The results indicate that the present constant scallop-height machining achieves the specified machining accuracy with fewer and shorter tool paths than the existing tool path generation approaches. The dynamics is better, too.

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.

Study on Methods for Calculating Tool Position Error Distribution during 5-Axis Machining of Sculptured Surfaces

With the continuous improvement of the calculation speed of computer, tool positioning methods based on numerical calculation in five-axis NC programming will play a greater role. First, this paper introduces three numerical methods for calculating tool position error distribution between a torus cutter and design surface in 5-axis machining of sculptured surfaces, namely a method for discretizing design surface, a method for discretizing the torus central circle, and a longitude method. At the same time, the detailed calculating steps are also given. An example of a cylindrical surface machined with torus tool is then conducted to compare and analyze the calculation accuracy and efficiency of the above methods. Results obtained show that the calculating deviation for computing tool position error distribution using the method for discretizing the torus central circle is minimum, while that using another two methods are larger; the calculation time of the method for discretizing the torus central circle is shortest, while that of the longitude method is longest; within the given programming tolerance, the machining strip widths calculated by the above methods are appropriately same, and the maximum deviation of actual machining strip width is within 2% of the theoretical value.

Tool Positioning Algorithm Based on Smooth Tool Paths for 5-axis Machining of Sculptured Surfaces

The current research of the 5-axis tool positioning algorithm mainly focuses on searching the local optimal tool position without gouging and interference at a cutter contact(CC) point, while not considering the smoothness and continuity of a whole tool path. When the surface curvature varies significantly, a local abrupt change of tool paths will happen. The abrupt change has a great influence on surface machining quality. In order to keep generated tool paths smooth and continuous, a five-axis tool positioning algorithm based on smooth tool paths is presented. Firstly, the inclination angle, the tilt angle and offset distance of the tool at a CC point are used as design variables, and the machining strip width is used as an objective function, an optimization model of a local tool positioning algorithm is thus established. Then, a vector equation of tool path is derived by using the above optimization model. By analyzing the equation, the main factors affecting the tool path quality are obtained. Finally, a new tool position optimization model is established, and the detailed process of tool position optimization is also given. An experiment is conducted to machine an aircraft turbine blade by using the proposed algorithm on a 5-axis blade grinding machine, and the machined blade surface is measured with a coordinate measuring machine(CMM). Experimental and measured results show that the proposed algorithm can ensure tool paths are smooth and continuous, improve the tool path quality, avoid the local abrupt change of tool paths, and enhance machining quality and machining efficiency of sculptured surfaces.

Effective Determination of Feed Direction and Tool Orientation in Five-Axis Flat-End Milling

This paper addresses the challenging problem of determining feed direction and tool orientation at a given cutter contact (CC) point in five-axis free-form surface machining with flat-end mills. The objective is to efficiently determine a feed direction and tool orientation that will avoid both local and global tool gouging and yield a near maximum machining strip width at the CC point. Concurrent determination of the optimal feed direction and tool orientation is a very computationally intensive task and searching for the correct solution would involve exhaustive evaluations of the machining strip width at many feed directions and tool orientations. In this paper, the optimal feed directions and analytical solutions for the optimal tool orientations in five-axis flat-end milling of spherical, cylindrical, and toroidal surfaces are identified first. A toroidal surface inscription method is devised to approximate the local surface geometry at a CC point on a free-form surface by an inscribed toroidal surface. Analytical solutions for toroidal surface machining are then employed to position the flat-end mill at the CC point with the tool feeding in the best toroidal surface inscribing direction. Case studies have demonstrated that the proposed method can efficiently determine a feed direction and tool orientation, corresponding to a near maximum machining strip width.

Dual Drive Curve Tool Path Planning Method for 5-axis NC Machining of Sculptured Surfaces

The problem of finished surface being not first-order continuous commonly exists in machining sculptured surfaces with a torus cutter and some other types of cutters. To solve this problem, a dual drive curve tool path planning method is proposed in this article. First, the maximum machining strip width of a whole tool path can be obtained through optimizing each tool position with multi-point machining (MPM) method. Second, two drive curves are then determined according to the obtained maximum machining strip width. Finally, the tool is positioned once more along the dual drive curve under the condition of tool path smoothness. A computer simulation and cutting experiments are carried out to testify the performance of the new method. The machined surface is measured with a coordinate measuring machine (CMM) to examine the machining quality. The results obtained show that this method can effectively eliminate sharp scallops between adjacent tool paths, keep tool paths smooth, and improve the surface machining quality as well as machining efficiency.

Third-order point contact approach for five-axis sculptured surface machining using non-ball-end tools (II): Tool positioning strategy

Based on the mathematical model describing the third-order approximation of the cutter envelope surface according to one given cutter location (CL), a tool positioning strategy is proposed for efficiently machining free-form surfaces with non-ball-end cutters. The optimal CL is obtained by adjusting the inclination and tilt angles of the cutter until its envelope surface and the design surface have the third-order contact at the cutter contact (CC) point, which results in a wide machining strip. The strategy can handle the constraints of machine joint angle limits, global collision avoidance and tool path smoothness in a nature way, and can be applied to general rotary cutters and complex surfaces. Numerical examples demonstrate that the third-order point contact approach can improve the machining strip width greatly as compared with the recently reported second-order one.

Optimization of tool positions locally based on the BCELTP for 5-axis machining of free-form surfaces

The Basic Curvature Equations of Locally Tool Positioning (BCELTP) are an accurate description of the relationships between the second order approximations of the cutter surface, the tool envelope surface and the designed surface, which was proposed in our previous paper [Gong Hu, Cao Li-Xin, Liu Jian. Second order approximation of tool envelope surface for 5-axis machining with single point contact. Computer-Aided Design 2008;40:604–15]. Based on them, for a given tool path with single cutter contact point, a new local optimization method of tool positions is presented to maximize the machining strip width by minimizing the relative normal curvature between the tool envelope surface and the designed surface. Since the BCELTP are accurate analytical expressions, the proposed optimization method of tool positions is accurate and effective in computation. Furthermore, another new optimization method of tool positions based on a dual-parameter envelope is subsequently proposed. The most interesting point is that it will result in the same results as the method based on the BCELTP. It also proves the correctness of the method based on the BCELTP from a different angle. Finally, several examples are given to prove its effectiveness and accuracy.

Machining of Composite Surface Based on Z-buffer Method with Torus Tools

A new tool path generation method based on Z-buffer method is proposed for composite surface machining by using torus cutters.Firstly,the examining area is determined by means of Z-buffer method.Then interference-free tool positions with optimal machining strip width are obtained by matching the end surface of the torus cutter to the model surface as close as possible.The discretized points within the examining area are efficiently read in and stored directly by the computer hardware;no extra searching and iterative methods are needed.Interference checking and avoiding methods are combined with the adjusting process of the cutter,so the tool positions generated are interference-free.Triangulated model is used in the newly developed method which is particularly suitable for tool path generation of composite surface.The new method is used to generate tool path for a mold surface and the result shows that,comparing to traditional machining method with ball end cutter,the new method raises efficiency by ten times.Finally,simulation and cutting test are performed.

Flank Milling for Blisk with a Barrel Ball Milling Cutter

To satisfy the requirement in blisk machining, a barrel-ball milling (BBM) cutter suitable for machining both blade and hub is presented in this paper. The selection of cutter parameter and calculation of cutter location were put forward. The new efficient machining cutter location via the advanced optimization on cutter machining strip width was gained. By the numerical simulation of blisk blade machining, the feasibility of the BBM cutter and cutter location strategy were verified. The result showed that the efficiency of this method was increased to more than three times compared to the machining with a ball cutter.

Five-Axis Flank Milling of Sculptured Surface with Barrel Cutters

A flank milling tool positioning method using a barrel cutter is proposed. An offset point is used as the first anchor point. Two rotary angles of the barrel cutter are adjusted to find the optimized tool position with the largest machining strip width. The result tool position calculated using the proposed method is gouge-free because the local interference avoidance method is integrated inside the tool positioning procedure. Error distribution beneath the barrel cutter is well estimated by virtual of the instant envelope curve of the cutter. The envelope curve is discretized into points. The distances between these points and the model surface are the machining errors beneath the cutter. The employment of the envelope curve also largely reduces the computational load of the algorithm. Finally, numerical implementation and simulation are performed to validate the feasibility of the method.

Flank Milling for Blisk with a Barrel Ball Milling Cutter

To satisfy the requirement in blisk machining, a barrel-ball milling (BBM) cutter suitable for machining both blade and hub is presented in this paper. The selection of cutter parameter and calculation of cutter location were put forward. The new efficient machining cutter location via the advanced optimization on cutter machining strip width was gained. By the numerical simulation of blisk blade machining, the feasibility of the BBM cutter and cutter location strategy were verified. The result showed that the efficiency of this method was increased to more than three times compared to the machining with a ball cutter.

Effect of tool tilt angle on machining strip width in five-axis flat-end milling of free-form surfaces

This paper examines the effect of tool tilt angle on machining strip width in the determination of optimal tool orientation and feed direction in five-axis flat-end milling. The machining strip width is evaluated using the swept profile of the flat-end mill, avoiding both local and global gouging of the tool. An optimization problem is formulated to maximize the machining strip width over feasible gouge-free tool orientations for a constant-feed direction. By solving the optimization problem and analyzing the geometry of the machining strip width, it is shown that identifying the optimal tool tilt angle, instead of following the common practice of setting the tool tilt angle as zero, can significantly increase the machining strip width, especially for 3D free-form surface machining. The optimization has also been extended to identify the optimal feed direction that maximizes the machining strip width at a given cutter contact (CC) point. The minimum curvature direction has been considered as the optimal feed direction at a CC point by researchers. Our results indicate that although the minimum curvature direction is mostly not the optimal feed direction in free-form surface machining, the minimum curvature direction does represent a good approximation of the optimal feed direction at a CC point, in particular for a free-form surface with low-curvature relative to the tool size.

Quadric method for cutter orientation in five-axis sculptured surface machining

Existing orientation strategies in 5-axis sculptured surface machining mostly limit the cutter to incline in one direction and lack an effective approach to assess the orientation. This paper presents the quadric method (QM) that exploits fully the two orientation angles to maximise the machining efficiency at a cutter contact point. The geometric construction assumes that the local shape of a sculptured surface can be suitably approximated by two quadrics. An upper quadric lying above the surface is used to orient the cutter, and a lower quadric lying below the surface is used to evaluate machined strip width. Then, the cutter orientation is optimised with respect to the width and is guaranteed to give no gouging. Both flat-end cutter and fillet-end cutter are considered. Simulated examples demonstrate the improved machining efficiency of the QM over current published methods.

Multiple-axis sculptured surface machining

This paper presents swept envelope techniques to generate optimal tool paths for multiple-axis sculptured surface machining. The properties of the swept envelopes are analysed. The results help us to realise the geometric matching in tool-tip machining and understand the geometric machinability in tool-side machining. The target surfaces are classified into open-boundary sculptured surfaces and closed-boundary pocket surfaces, based on the existence of the surrounding obstacles. The objective of the open-boundary sculptured surface machining is to maximise the machining strip width of the fillet-end tools for tool-tip machining and, thus, to optimise the machining efficiency. On the other hand, the goal of the closed-boundary pocket machining is to smooth the tool axes of the ball-end tools for both tool-tip and tool-side machining and, therefore, to optimise the tool path variation. The complement of the swept envelope, which represents the in-process workpiece, is also addressed. It finally demonstrates the developed techniques and illustrates the application examples.

Tool path generation for five-axis NC machining using adaptive space-filling curves

We present the concept of an adaptive space-filling curve for tool path planning for five-axis NC machining of sculptured surfaces. Generation of the adaptive space-filling curves requires three steps: grid construction, generation of the space-filling curve, and tool path correction. The space-filling curves, adapted to the local optimal cutting direction, produce shorter tool paths. Besides, the tool path correction stage makes it possible to eliminate the effect of sharp angular turns which characterize standard space-filling curve patterns. Our space-filling curve method is endowed with a new modification of techniques for computing the machining strip width along with a modified formula for the minimum tool inclination angle to avoid gouging. Finally, we show that the adaptive space-filling curves are more efficient compared with the traditional iso-parametric scheme. The numerical experiments are complemented by real machining as well as by test simulations on Unigraphics 18.

Tool tip gouging avoidance and optimal tool positioning for 5-axis sculptured surface machining

This article deals with locally optimal cutting positions and cutting directions for tool tip gouging avoidance in 5-axis sculptured surface machining. In order to measure the quality of tool positioning, this paper suggests a new concept of 'machined region width', which does not have the drawbacks of 'machined strip width'. The method evaluates the optimal cutting position of a flat endmill or toroidal endmill, where optimality is with respect to the avoidance of tool tip gouging. It is based on a second-order Taylor approximation of the design surface and multipoint tool positioning. The implementation and some illustrative examples are discussed.

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.

Locally optimal cutting positions for 5-axis sculptured surface machining

The paper presents a local condition for collision-free 5-axis milling of sculptured surfaces. We consider cutter positions, which guarantee local gouging avoidance. This can replace concepts such as ‘cutting profile’ or ‘effective cutting shape’ which are of approximate nature. Based on second order approximations of the machined strip width, we also present locally optimal cutting positions for cutting directions.

Surface interrogation and machining strip evaluation for 5-axis CNC die and mold machining

This research is focused on the investigation of robust surface interrogation tools which can support the planning and programming of 5-axis die/mold surface machining. Surface curvature information is evaluated to determine optimal tool orientation for 5-axis machining. A method for calculating machining strip width is proposed for 5-axis cutter path generation. This paper is focused on the development of computational geometry techniques and their application to design, analysis, and manufacturing automation. The proposed planning and programming methodology consists of three phases: (1) surface interrogation; (2) machining strip width evaluation; and (3) optimum tool orientation for 5-axis machining. This proposed research can be used to improve the quality of 5-axis die/mold machining.