Five-axis Sculptured Surface Machining Research Articles

Collision-free and smooth path generation method of five-axis ball-end milling considering effective tool diameter change

Ball-end cutters are widely used in five-axis sculptured surface machining. It is desired to avoid drastic changes of rotary axis movements for improving the kinematics performance of machine tools while ensuring collision-free during five-axis machining. It cannot acquire the optimum solution when cutter orientations are first generated and then adjusted to avoid collisions. The cutter orientations should be generated and optimized in their feasible regions wholly while the computation load is usually large. Different relative postures between a ball-end cutter and workpiece during the machining process will produce different effective tool diameters of the ball-end cutter, resulting in different cutting speeds. Using a variable cutting speed along a tool path can unfavorably affect the process' technological effects (e. g. surface quality, tool life). It is desired to keep the effective tool diameter constant or at a very slightly varying value during five-axis ball-end machining. Moreover, it is also desired to make the cutting point in a high position of the ball-end cutter tool edge, increasing the effective tool diameter. A smooth and collision-free tool path generation method of five-axis ball-end machining while minimizing the effective tool diameter variation and increasing the effective tool diameter of the ball-end cutter along a tool path is proposed. Tool orientations along a tool path are generated and optimized within their feasible regions and the proposed method solves the smoothness tool path generation problem by applying sequentially for the rough and fine search spaces to reduce the computing time. The numerical examples and the machining experiment illustrate the effectiveness of the proposed method.

A G3 continuous tool path smoothing method for 5-axis CNC machining

The chain of short linear tool path segments is the most common form for the five-axis machining by Computer Numerical Control (CNC) machines. The connection points of the linear path segments lead to the discontinuities in position, velocity, acceleration, and jerk, resulting in fluctuation of machine motion which leaves undesired marks on the finished surface. This paper presents a geometric smoothing algorithm by enforcing the continuity of first, second, and third geometric derivatives of the splined path segments at their meeting points for the five-axis machining of curved surfaces. The linear tool path segments are first smoothed by Bezier splines while constraining the path errors within a set tolerance. The tool path segments, that cannot be smoothed within the path error limit, are smoothly connected at the connection points. The tooltip position and tool axis orientation displacements are synchronized to avoid discontinuous displacements along the tool axis. The proposed algorithms are demonstrated with simulations and experiments in following a five-axis, curved tool path on a CNC machine tool. It is shown that the proposed G3 continuous tool path algorithm gives smoother tool-tip and tool axis orientation, reduces the tracking errors, contour errors and amplitudes of jounce at the connections of segments along the tool path, leading to the smoother surface for the precision five-axis machining of sculptured surfaces.

Compact radial zigzag for five-axis machining of STL surfaces

The paper presents a new method to generate efficient milling toolpaths for five-axis sculptured surface machining in an important case when the vector field of preferred directions (VFPD) forms a star-like, radial configuration. To optimize the toolpath, a new modification of the radial toolpath aligned with the VFPD called the compact radial zigzag (CRZ) has been proposed, analyzed, and verified practically. The CRZ is combined with transfinite interpolation (TFI) to treat an irregular VFPD. The method is designed for the machining of industrial stereolithography (STL) part surfaces characterized by complex geometries and sharp extrema. A demo of the algorithm is at https://drive.google.com/open?id=1OM_z4cAOUqGu2RPAzkZOIBcEnfptdTq7.

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.

Estimation of Cutter Deflection Based on Study of Cutting Force and Static Flexibility

In the tool orientation planning for five-axis sculptured surface machining, the geometrical constraints are usually considered. Actually, the effect of nongeometrical constraints on tool orientation planning is also important. This paper studied one nongeometrical constraint which was cutting force induced static deflection under different tool orientations, and proposed a cutter deflection model based on that. In the study of the cutting force, the undeformed chip thickness in filleted end milling was modeled by geometrical analysis and coordinate transformation of points at the cutting edge. In study of static flexibility of multi-axis machine, static flexibility of the entire machining system was taken into consideration. The multi-axis machining system was divided into the transmission axes-handle (AH) end and the cutting tool end. The equivalent shank method was developed to calculate the static flexibility of the AH end. In this method, static flexibility anisotropy of the AH end was considered, and the equivalent lengths of the AH end were obtained from calibration experiments. In cutter deflection modeling, force manipulability ellipsoid (FME) was applied to analyze the static flexibility of the AH end in arbitrary directions. Based on the synthetic static flexibility and average cutting force, cutter deflections were derived and estimated through developing program realization. The predicted results were compared with the experimental data obtained by machining 300 M steel curved surface workpiece, and a good agreement was shown, which indicated the effectiveness of the cutter deflection model. Additional experiments of machining flat workpiece were performed, and the relationship of cutter deflections and tool orientations were revealed directly. This work could be further employed to optimize tool orientations for suppressing the surface errors due to cutter deflections and achieving higher machining accuracy.

Reducing fluctuation of machining strip width by tool position modification for five-axis NC machining of sculptured surfaces

This paper presents a method to reduce the fluctuation of machining strip width by modifying tool position. When the machining strip width varies rapidly within a tool path, the fluctuation of cutting force brings negative influence on the workpiece and cutter. Furthermore, as the tool path interval is always defined conservatively to avoid undercut, the machined strips of adjacent tool paths have unnecessary amount of overlap. Rapid changing machining strip width usually creates too much overlap at some location, which causes repeated cutting. A method is proposed to modify tool position and reduce the fluctuation of machining strip width. Besides, tilt angle smoothness along the tool path is also taken into account. The computation result of a blade surface verified the validity of the proposed method.

Smooth trajectory generation for five-axis machine tools

This paper presents a smooth spline interpolation technique for five-axis machining of sculptured surfaces. The tool tip and orientation locations generated by the CAM system are first fitted to quintic splines independently to achieve geometric jerk continuity while decoupling the relative changes in position and orientation of the cutter along the curved path. The non-linear relationship between spline parameters and displacements along the path is approximated with ninth order and seventh order feed correction splines for position and orientation, respectively. The high order feed correction splines allow minimum deviation from the reference axis commands while preserving continuous jerk on three translational and two rotary drives. The proposed method has been experimentally demonstrated to show improvements in reducing the excitation of inertial vibrations while improving tracking accuracy in five-axis machining of curved paths found in dies, molds and aerospace parts.

Bézier polygons for the linearization of dual NURBS curve in five-axis sculptured surface machining

Motivated by the excellent performance of three-axis NURBS interpolation, this paper presents a numerically efficient and accuracy controllable five-axis sculptured surface machining method with dual NURBS curve. Unlike the traditional three-axis NURBS interpolation, a dual NURBS format of the five-axis toolpath is developed to accurately and smoothly describe the tool movement in the part coordinate system. Different from the subdivision methods using the Taylor series expansion or inverse function, a piece-wise Bézier curve method is implemented to fast subdivide the NURBS curve within the user-defined tolerance. A generic rotation tool center point management module is also designed to realize the coordinate transformation and adaptive nonlinear error control for major five-axis machine tools. The overall effectiveness of the proposed five-axis NURBS machining scheme is demonstrated by the five-axis machining of an impeller’s flow channel.

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.

Integrated method for tool path generation in five-axis sculptured surface machining

Five-axis machining allows continuous adjustment of cutter orientation along a tool pass. Unfortunately, the flexibility has not been fully exploited due to the separate consideration of tool path generation and cutter orientation in current machining methods. This paper presents an integrated method (IM) for tool path generation, which is tightly integrated with the orientation strategy, to minimise tool path length under the constraint of smooth cutter orientation. Distinctively, cutter orientation along a tool pass is optimised by balancing considerations of maximum material removal and smoothness of cutter movement. Further, the intervals between successive tool passes are maximised according to the optimised orientation. In the paper, the IM is combined with the quadric method, a recently developed cutter orientation strategy, for iso-parametric machining with a flat-end cutter. However, the method could be applied to other orientation strategies with different machining mechanisms and cutter types. Simulated examples illustrate that the IM is more efficient in machining than established methods.

Generating tool-path with smooth posture change for five-axis sculptured surface machining based on cutter’s accessibility map

In five-axis high speed milling, one of the key requirements to ensure the quality of the machined surface is that the tool-path must be smooth, i.e., the cutter posture change from one cutter contact point to the next needs to be minimized. This paper presents a new method for generating five-axis tool-paths with smooth tool motion and high efficiency based on the accessibility map (A-map) of the cutter at a point on the part surface. The cutter’s A-map at a point refers to its posture range in terms of the two rotational angles, within which the cutter does not have any interference with the part and the surrounding objects. By using the A-map at a point, the posture change rates along the possible cutting directions (called the smoothness map or S-map) at the point are estimated. Based on the A-maps and S-maps of all the sampled points of the part surface, the initial tool-path with the smoothest posture change is generated first. Subsequently, the adjacent tool-paths are generated one at a time by considering both path smoothness and machining efficiency. Compared with traditional tool-path generation methods, e.g., iso-planar, the proposed method can generate tool-paths with smaller posture change rate and yet shorter overall path length. The developed techniques can be used to automate five-axis tool-path generation, in particular for high speed machining (finish cut).

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.

Third-order point contact approach for five-axis sculptured surface machining using non-ball-end tools (I): Third-order approximation of tool envelope surface

In this paper, the geometric properties of a pair of line contact surfaces are investigated. Then, based on the observation that the cutter envelope surface contacts with the cutter surface and design surface along the characteristic curve and cutter contact (CC) path, respectively, a mathematical model describing the third-order approximation of the cutter envelope surface according to just one given cutter location (CL) is developed. It is shown that at the CC point both the normal curvature of the normal section of the cutter envelope surface and its derivative with respect to the arc length of the normal section can be determined by those of the cutter surface and design surface. This model characterizes the intrinsic relationship among the cutter surface, cutter envelope surface and design surface in the neighborhood of the CC point, and yields the mathematical foundation for optimally approximating the cutter envelope surface to the design surface by adjusting the cutter location.

Tool path generation for five-axis sculptured surface machining with a toroidal cutter

This paper presents an algorithm to generate tool paths for five-axis sculptured surface machining with a toroidal cutter based on optimal tool position and orientation. The toroidal cutting surface offers a large range of radius of curvatures. Furthermore, the cutter orientation varies depending on the curvature of surface. Thus, the proposed method is much better than the conventional method with a fixed orientation. To verity the usefulness of the developed algorithm, a computer simulation program is coded using C++ language. The proposed method can be integrated into CAM systems to improve five-axis sculptured surfaces machining.

Combined reparameterization-based spiral toolpath generation for five-axis sculptured surface machining

Reparameterization-based toolpath generation methods are usually adopted for machining triangular meshes, trimmed surfaces and compound surfaces. The quality of the reparameterization has an important effect on that of the surface. In this paper, a combined reparameterization procedure is introduced to generate an optimal mapping between the designed surface and a specified planar circular region with relatively less distortion both in length and in angle. Then, for five-axis sculptured surface machining the mathematical model of spiral guide path with maximum path interval is constructed in the circular region. Cutter contact paths are obtained by inversely mapping the guide path onto the designed surface. Under constraints of gouging and collision, continuous and optimal cutter orientations are subsequently calculated. Finally, the results of simulation and experiment of the machining process are given to illustrate the feasibility and applicability of the proposed method.

Feed optimization for five-axis CNC machine tools with drive constraints

Real time control of five-axis machine tools requires smooth generation of feed, acceleration and jerk in CNC systems without violating the physical limits of the drives. This paper presents a feed scheduling algorithm for CNC systems to minimize the machining time for five-axis contour machining of sculptured surfaces. The variation of the feed along the five-axis tool-path is expressed in a cubic B-spline form. The velocity, acceleration and jerk limits of the five axes are considered in finding the most optimal feed along the tool-path in order to ensure smooth and linear operation of the servo drives with minimal tracking error. The time optimal feed motion is obtained by iteratively modulating the feed control points of the B-spline to maximize the feed along the tool-path without violating the programmed feed and the drives’ physical limits. Long tool-paths are handled efficiently by applying a moving window technique. The improvement in the productivity and linear operation of the five drives is demonstrated with five-axis simulations and experiments on a CNC machine tool.

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.

Penetration–elimination method for five-axis CNC machining of sculptured surfaces

In this paper, a new tool positioning strategy for five-axis machining, called the penetration–elimination method (PEM), is introduced. The PEM gains from two innovative techniques that can considerably improve the computational efficiency during the calculation of the optimal tool orientations. The first technique includes developing a quantitative definition for the gouging concept and using this definition in conjunction with powerful numerical root-finder algorithms to determine the optimized tool orientations. The second technique dynamically detects the ineffective grid points and drops them from calculations and consequently takes a great role in reducing the computational burden. The ability of the PEM in removing various types of gouging has been shown via several examples. The computational efficiency of the PEM has been compared with another recently described method named the arc-intersect method (AIM). This comparison shows that although the two methods reach the same solution for the tool orientation, the PEM is averagely 7.5 times faster than the AIM.

An improved tool path discretization method for five-axis sculptured surface machining

In five-axis machining of sculptured surfaces, the cutting tool is unable to continuously trace the intended curved tool path due to limitations of existing controllers for the commercial machine tools. Current industrial practice is thus to discretize the continuous tool path into a finite number of cutter contact (CC) points. An improved method of tool path discretization for five-axis sculptured surface machining is presented in this paper. While the tool posture along a tool path is tuned to ensure maximized material removal rate and to avoid gouging to the machined surface, the forward step lengths, characterized by the consecutive discretized CC points, are determined by maintaining the machined surface error within the specified tolerance. The conventional method employs chordal deviations to estimate the machined surface errors of the interpolated tool movements between consecutive CC points, which have been referred to as the geometry-based errors. It has been found that chordal deviations are not reliable estimations of the geometry-based errors. As such, the geometry-based errors are accurately evaluated in this work and the related algorithms are implemented to the machining of a typical Bezier surface patch. The results showed a reduction of about 30% in the number of discretized tool path segments compared with those of the conventional method.

On the B-spline interpolated tool trajectories for five-axis sculptured surface machining

B-spline interpolation scheme is now available on modern five-axis Computer Numerical Control (CNC) machine tools. With this newly implemented interpolation scheme, a cutting tool can be directly commanded to trace B-spline trajectories, which approximate ideal 3D curved trajectories, in sculptured surface machining. The approximation of ideal tool trajectories by B-spline interpolated tool trajectories inevitably leads to machining errors, referred to as the geometry-based errors in the present work. It is essential to ensure synchronisation of the movements of the three translational and two rotational joints of a five-axis machine tool to reduce the geometry-based errors. This paper presents an effective method to achieve synchronisation of the machine joint movements. It first fits a 3D B-spline for the three translational joints and then uses a knot inheriting procedure to fit a 2D B-spline for the two rotational joints. Evaluation of the presented method was made through the machining of a typical bi-cubic Bezier surface on a five-axis machine tool capable of performing non-uniform B-spline interpolation. It was found that the resulting geometry-based errors, which were varying along the given isoparametric tool paths, were able to be maintained below 25m.