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.     

Isophote-based ruled surface approximation of free-form surfaces and its application in NC machining

This paper presents a method to approximate free-form surfaces using piecewise ruled surface and its application in five-axis NC machining. New concepts of isophote, iso-inclination curve and iso-inclination angle are introduced to facilitate the generation of the piecewise ruled surfaces. The resulting ruled surfaces are adaptive to the surface features, such as peaks and valleys. Adjusting the isoinclination angle controls the error of this approximation. The application of the isophote-based ruled surface approximation in five-axis NC machining is also studied. The tapered tools are suggested to cut the ruled surfaces. Methods for selecting appropriate tools and generating tool paths are presented. The present case studies show that the new approach may lead to the integration of rough, semi-finish and finish machining of free-form surfaces.     

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.     

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.     

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.     

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.     

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.     

Tool path generation for triangular meshes using least-squares conformal map

Tool path generation is an interesting and challenging task in free-form surface machining. Iso-planar tool path generation is one of the common approaches to dealing with this task. However, it suffers from an inherent drawback that intersecting intervals of the iso-planar method are limited to surface geometric features. This results in poor machining efficiency in flat regions due to redundant machining paths. For this problem, a new tool path generation method for triangular meshes is proposed based on the least-squares conformal map (LSCM). After LSCM parameterisation with minimal stretching energy, the triangular meshes are unfolded on a plane, where the principal component analysis (PCA) technique is employed to determine a suitable drive line for calculating cutter contact paths by the iso-planar strategy. Therefore, the tool paths are generated in a plane and the unevenness of the traditional iso-planar method is improved. The feasibility and effectiveness of the developed method is demonstrated through a test experiment.     

Tool path re-planning in free-form surface machining for compensation of process-related errors

Free-form surfaces are widely used in many applications in today’s industry. This paper presents a new approach to identify and compensate process-related errors in machining of free-form surfaces. The process-related errors are identified online by a newly developed in-process inspection technique. In this technique, the surface is first machined through an intermediate semi-finishing process that is specifically designed to machine different geometric shapes on the surface with different process parameters. An inspection method is developed to identify the process-related errors in the selected regions on the semi-finished surface. The relationship between the machining/surface parameters and process-related error is then achieved using a neural network. This relationship is used to predict the process-related errors in the finishing process. The process-related errors, together with the machine tool geometric errors identified using a method developed in our previous work, are compensated in the finishing tool paths through tool path re-planning. Experiment has been conducted to machine a part with a free-form surface to show the improvements in the machining accuracy.     

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.     

Interference-free tool path generation for 5-axis sculptured surface machining using rational Bézier motions of a flat-end cutter

This paper presents a new approach that uses rational Bézier motions to generate 5-axis tool path for sculptured surface machining (finish cut) with a flat-end cutter. By using dual quaternion to represent a spatial displacement, the representation of kinematic motions for the cutter bottom circle of the flat-end cutter is formulated. Based on that, a new approach for tool path generation using rational Bézier cutter motions is described, in which key issues such as interference avoidance and surface accuracy requirement are addressed. First, a set of cutter contact points on an iso-parametric curve of the designed surface is obtained based on a given fitting tolerance. The associated cutter locations (CLs) are then obtained by finding the suitable cutter orientations that avoid any gouging. The conversion from the CLs to dual quaternion representation is carried out and the rational Bézier dual quaternion curve for cutter motion is generated. The entire tool path is therefore established based on the cutter undergoing the rational Bézier motion. Next, the whole tool path is checked to find (1) if there is any interference between the cutter and the designed surface, and (2) whether the deviation between the surface generated by the cutter motion and the designed surface is larger than the given tolerance. The problematic CLs, which cause either gouging or accuracy problem, are then modified. The process of tool path checking?→?CLs modification?→?tool path regeneration continues until the whole tool path is interference-free and satisfies the accuracy requirement. Furthermore, a more accurate representation of the effective cutting shape is proposed, which is used to evaluate the scallop height between adjacent tool paths. A method for constructing the adjacent tool path has been developed by considering the allowable scallop height. Finally, computer implementation and an illustrative example are presented to demonstrate the efficacy of the approach.     

A new machine strategy for sculptured surfaces using offset surface

A new CNC tool path planning method is developed for accurate and efficient finishing cutting of sculptured surfaces. The proposed method generates CNC tool paths based on an offset surface of an object instead of the actual surface. The new algorithm consists of two main computational techniques: offset surface generation technique and offset CNC tool path planning technique. In offset surface generation, approximate parametric offset surfaces are generated accurately from an original parametric surface by employing bi-cubic surface patch, surface conversion, and surface subdivision algorithms. In offset CNC tool path planning, the precise geometric models of chordal deviation and cusp height on an offset surface are established. The effectiveness of this proposed CNC tool path planning method is verified by geometric simulation and verification which detect and identify errors in CNC tool paths.     

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.     

Combining physical shell mapping and reverse-compensation optimisation for spiral machining of free-form surfaces

Machining of free-form surfaces has an important role in industrial manufacturing, but conventional tool-path generation strategies for free-form surfaces machining have the drawbacks of serious flattening distortion and poor tool-path continuity. Therefore, a novel method is developed to generate a spiral tool path for the machining of free-form surfaces by improving surface-flattening distortion and tool-path continuity. First, physical shell mapping is presented to flatten a free-form surface into a plane, which takes stretching energy, bending energy, and global energy into account. Then, the spatial spiral polyline is rounded to generate a spiral path by proposing reverse-compensation optimisation. Therefore, the free-form surfaces can be quickly flattened with less distortion, remaining free of overlap, and can in addition be machined at high speed along a C² continuous spiral tool path. Further, the flattening error, tool-path length, mean curvature, mean scallop-height error of the spiral path, machining time and surface roughness are obviously reduced. Finally, simulation results are given to show the effectiveness and feasibility of the presented strategy.     

Globally optimal tool paths for sculptured surfaces with emphasis to machining error and cutting posture smoothness

Global optimisation for manufacturing problems is mandatory for obtaining versatile benefits to facilitate modern industry. This paper deals with an original approach of globally optimising tool paths to CNC-machine sculptured surfaces. The approach entails the development of a fully automated manufacturing software interface integrated by a non-conventional genetic/evolutionary algorithm to enable intelligent machining. These attributes have been built using already existing practical machining modelling tools such as CAM systems so as to deliver a truly viable computer-aided manufacturing solution. Since global optimisation is heavily based on the formulation of the problem, emphasis has been given to the definition of optimisation criteria as crucial elements for representing performance. The criteria involve the machining error as a combined effect of chord error and scallop height, the tool path smoothness and productivity. Experiments have been designed considering several benchmark sculptured surfaces as well as tool path parameters to validate the aforementioned criteria. The new approach was implemented to another sculptured surface which has been extensively tested by previous research works. Results were compared to those available in the literature and it was found that the proposed approach can indeed constitute a promising and trustworthy technique for the global optimisation of sculptured surface CNC tool paths.     

Computer-aided design,manufacturing and inspection system integration for optical lens production

The main objectives of this research are the development of an integrated manufacturing strategy and the construction of a database management system for the design, machining and inspection of sculptured surfaces. Specifically, the optical lens for colour display tube/colour picture tube is selected as an application example to show the effectiveness and efficiency of the developed manufacturing strategy and database construction methods. In the machining strategy, the total machining time reduction method is proposed for the rough cutting operation based on the optimum tool path planning. In the finish cutting operation, a modified cutter contact variable step method is employed, and optimal tool paths are generated by selecting the proper tool radius within the given tolerance of a designed model. In the inspection strategy, the shortest measuring path is calculated to reduce the inspection time in CMM. In addition, an efficient database management system, which conducts the process from the surface design stage to the inspection result analysis stage, is constructed for the optimization of the sculptured surface manufacturing process. Finally, the required simulation and experimental works are carried out to verify the proposed 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.     

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.     

Approximation of planar offset curves with globally bounded error for B-spline NC tool paths

The topic of representing the offset of a 2D B-spline curve in the same form has been a topic of research for a long time, and it has many industrial applications, especially in NC tool path generation for pocketing. For B-spline tool paths, it is often required that the tool paths have fewer control points, lower base function degree, and the approximation error is guaranteed within a given tolerance over the entire curve. However, the existing methods utilising global error control approximate the offsets of 2D free-form curves with high function degree and many control points. Although these offsets are useful in computer-aided design, they are inappropriate for the use of CNC machining. To address the problems in order to generate high quality B-spline tool paths, this original work formulates an error function of the offset approximation and then constructs a NURBS curve to globally bound the errors. By checking the maximum coefficient of the bounding curve, the upper bound of all the approximated offset errors is found and the errors can be reduced by segmenting the curve at appropriate knot values. The proposed new approach is more efficient, and the resulting offset approximations are more accurate, with fewer control points and lower function degree. It is useful to generate B-spline tool paths for CNC pocketing, which have the potential for other applications in industry.     

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.