Automatic method for milling complex channel-shaped cavities via coupling flank-milling positions

Abstract

Methods and devices for milling a channel-shaped cavity by a five-axis computer numerical control (CNC) machine by selecting a workpiece to be machined, determining cutting tool flow along the channel-shaped cavity, determining cutting tool in-depth penetration, determining a trochoid path, and determining auxiliary movements.

Claims

1. A method comprising: selecting a workpiece to be machined, wherein the workpiece has a bottom surface of a channel, a left wall of the channel, a right wall of the channel, and an entry point of a cutting tool; determining a set of extrapolated sequence of points based on extracting a sequence of points from a set of limit curves representing the left wall of the channel and the right wall of the channel; determining a primary set of flank-milling positions of the cutting tool based on a set of surfaces, the set of surfaces determined based on the set of extrapolated sequence of points; determining a trochoidal path for the cutting tool based on the determined primary set of flank-milling positions of the cutting tool and coupling the set of determined primary flank-milling positions; and outputting one or more cutting tool movements as one or more machine instructions, wherein the one or more cutting tool movements is based on the determined primary set of flank-milling positions and the determined trochoidal path.

2. The method of claim 1, wherein there is a high relative displacement between the left wall of the channel and the right wall of the channel.

3. The method of claim 2, further comprising: determining a paired set of tool-positions for displaced portions of the left wall of the channel and the right wall of the channel.

4. The method of claim 1, further comprising: replicating, for each depth-level of an incrementally lower depth-level, at least one of: determining a primary set of flank-milling positions of the cutting tool and determining a trochoidal path for the cutting tool.

5. The method of claim 1, wherein the set of limit curves is determined based on the left wall of the channel and the right wall of the channel.

6. The method of claim 5, wherein each curve of the set of limit curves comprises a set of points associated with the left wall of the channel and the right wall of the channel.

7. The method of claim 1, wherein the set of surfaces is determined based on the set of extrapolated sequence of points having a corresponding point on an opposing wall.

8. The method of claim 1, wherein a method of milling the channel-shaped cavity is performed by a five-axis computer numerical control (CNC) machine.

9. A device for generating instructions for a five-axis machining tool, the device comprising a processing module having addressable memory, the processing module configured to: repeat the following steps for a channel-shaped cavity, while at least one machining limitation parameter is not satisfied: determine cutting tool flow along the channel-shaped cavity, wherein the cutting tool flow is based on a set of extrapolated sequence of points extracted from a set of limit curves; determine cutting tool in-depth penetration from a top surface of the channel-shaped cavity towards a bottom surface of the channel-shaped cavity; determine a trochoid path for the cutting tool based on the determined cutting tool flow along the channel-shaped cavity and the determined cutting tool in-depth penetration; and outputting one or more cutting tool movements as one or more machine instructions, wherein the one or more cutting tool movements is based on the determined cutting tool flow along the channel-shaped cavity and the determined trochoidal path.

10. The device for generating instructions for a five-axis machining tool of claim 9, wherein the processing module is further configured to: select the channel-shaped cavity to be machined, wherein the channel-shaped cavity has a bottom surface, a left wall, a right wall, and an entry point of the cutting tool.

11. The device for generating instructions for a five-axis machining tool of claim 9, wherein the determined trochoid path for the cutting tool is further determined based on coupling positions produced on a left wall and positions produced on a right wall of the channel-shaped cavity.

12. A device for generating instructions for a five-axis machining tool comprising a processing module having addressable memory, wherein the processing module is configured to: select a workpiece to be machined, wherein the workpiece has a bottom surface of a channel, a left wall of the channel, a right wall of the channel, and an entry point of a cutting tool; determine a set of extrapolated sequence of points based on extracting a sequence of points from a set of limit curves representing the left wall and the right wall of the channel; determine a primary set of flank-milling positions of the cutting tool based on a set of surfaces, the set of surfaces determined based on the set of extrapolated sequence of points; determine a trochoidal path for the cutting tool based on the determined primary set of flank-milling positions of the cutting tool and coupling the set of determined primary flank-milling positions; and outputting one or more cutting tool movements as one or more machine instructions, wherein the one or more cutting tool movements is based on the determined primary set of flank-milling positions and the determined trochoidal path.

13. The device for generating instructions for a five-axis machining tool of claim 12, wherein the set of surfaces is determined based on the set of extrapolated sequence of points having a corresponding point on an opposing wall.

14. The device for generating instructions for a five-axis machining tool of claim 12, wherein the processing module is further configured to: determine a paired set of tool-positions for displaced portions of the left wall of the channel and the right wall of the channel, wherein there is a high relative displacement between the left wall of the channel and the right wall of the channel.

15. The device for generating instructions for a five-axis machining tool of claim 12, wherein the processing module is further configured to: determine the set of limit curves based on the left wall of the channel and the right wall of the channel wherein each curve of the determined set of limit curves comprises a set of points associated with the left wall of the channel and the right wall of the channel.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Embodiments may be illustrated by way of example and not limitation in the figures of the accompanying drawings, and in which:

(2) FIG. 1 depicts, in a functional block diagram, an exemplary computer aided manufacturing system;

(3) FIG. 2 depicts, in a top-level flowchart, an exemplary method of five-axis machining;

(4) FIG. 3 depicts, in a top-level flowchart, an exemplary method of selecting the workpiece;

(5) FIG. 4 depicts, in a top-level flowchart, an exemplary symmetry propagation and synchronization step;

(6) FIG. 5 depicts, in a top-level flowchart, an exemplary flank pass step;

(7) FIG. 6 depicts, in a functional block diagram, an exemplary trochoid generation step;

(8) FIG. 7 depicts, in a functional block diagram, an exemplary iteratively feedback driven positioning process;

(9) FIG. 8A depicts an exemplary channel-shaped cavity comprising an exemplary trochoidal tool path;

(10) FIG. 8B depicts an exemplary channel-shaped cavity comprising an exemplary displacement of the channel walls;

(11) FIG. 8C depicts an exemplary workpiece channel-shaped cavity comprising an exemplary channel with a left wall and a right wall showing a high relative displacement along with instances of the tool positions;

(12) FIG. 8D depicts an exemplary workpiece channel-shaped cavity comprising an exemplary channel with a left wall and a right wall showing a high relative displacement with a pseudo-circular trochoidal path;

(13) FIGS. 8E-8H depict a pre-processing step showing extending of the left wall and right wall wherever needed;

(14) FIG. 9A depicts an exemplary tool path trajectory in a portion of an exemplary channel-shaped cavity;

(15) FIG. 9B depicts an exemplary tool path trajectory in a portion of an exemplary channel-shaped cavity with a displacement of the walls;

(16) FIG. 10 illustrates, in a top-level flowchart, an exemplary auxiliary movements step; and

(17) FIGS. 11A-11D depict an exemplary polishing finish pass operation.

DETAILED DESCRIPTION

(18) The present embodiments may utilize a structured combination of: 5-axis flank-machining, high speed machining allowed by adaptive analysis of geometrical data and technological constraints, and a channel-dedicated roughing cycle. 5-axis numerically controlled (5-axis NC) machines may be characterized by three translational axes and two rotary axes: the two rotary positions, which may be designated with the letters A, B or C, define, depending on the mechanical configuration of the particular machine tool, respectively the position about the axis X, Y or Z. The two rotary axes add two degrees of freedom to the range of spatial movements that the cutting tool is able to perform; in particular, they represent a technological enhancement when compared to 3-axis NC machines, where two rotary axes are missing and only translational movements of the cutting tool are possible. This increased flexibility of the cutting tool positions may result in: a) shorter machining times; and b) the rough material being removed in a way to reproduce the desired target shape more consistently.

(19) The cost for these improvements is that the calculated trajectory of the cutting tool must satisfy more constraints than in the 3-axis case, i.e., there is much more to control in terms of possible unwanted collisions between the cutting tool apparatus and the rough material. In addition, the amount of cutting load, i.e., the so-called tool-engagement that represents the amount of rough material instantly removed by the cutting tool, may, more readily than in the 3-axis case, increase beyond the mechanical limits sustainable by the cutting tool apparatus. Moreover, the cutting portion of the tool typically comprises its tip and a portion of the shank. The tip may be flat, spherical, or torical, where torical is an intermediate shape between a flat-shaped cutting tip and a spherical cutting tip. A portion of the shank may be a portion of either a cylindrical or conical lateral surface. Accordingly, the tool may cut rough material either with its tip or with its shank. Flank milling may be more productive, since it allows larger removal rates of rough material, and it exploits more effectively the cutting sub-area of the cutting tool. The tool-engagement may be split into a radial component, corresponding to tip point milling, and an axial component, corresponding to flank milling.

(20) Exemplary embodiments may comprise a channel-shape suited cutting-tool trajectory calculation, which is called 5-axis-Trochoidal-Channel-Roughing (5-axis TCR). A trochoid is the path traced by a point fixed on a circle that rolls along a line. This definition is generalized to a circle rolling along a general three-dimensional curve which is continually adapted to the shape of the channel being machined, in particular: to its left wall, right wall, and bottom surface.

(21) Trochoidal motion has several advantages. One advantage is that the cutting tool always removes material with its flank, which allows for a higher machining speed. Another advantage is that only a small area of the cutting tool is engaged at any one time. Trochoidal motion presents many complications when applied to 5-axis NC.

(22) To calculate an efficient 5-axis continual or continuous trochoidal roughing movement of the cutting tool, 5-axis TCR may perform five steps. This first step is called symmetry propagation and automatic synchronization, and it involves a thorough geometrical analysis of the specific features of the channel to be machined. In particular, a) the information about possible elements of symmetry of the bottom surface may be propagated to the channel walls; and b) the relative position of the left wall and right wall of the channel may be assessed, and a resulting correspondence of sub-portions of the right side of the channel with counterparts on the left side of the channel may be established.

(23) The second step is flank pass production. In this step, a) a primary set of flank-milling tool positions relative to the right wall is calculated; and b) a primary set of flank-milling tool positions relative to the left wall is calculated. In some embodiments, there may be a high relative displacement between the left wall and the right wall of the channel. For example, the left wall may start and end before the corresponding right wall. Accordingly, this step may also comprise a pre-processing operation or step in which an array of paired set of tool-positions, one flank-milling the left wall and the other flank-milling the right wall, may be determined. The determined array may correspond to flank-milling rails on the channel. In one embodiment, the determined flank-milling rails may signify the directional movement of the cutting tool toward the inside of the channel. In an embodiment utilizing 5-axis machining, each position may be represented by a pair of tool positions, a tool-end position, e.g., a three dimensional point, and a tool-axis direction, e.g., a three dimensional vector, issued in that position. Accordingly, a set of subsequent positions may be determined based on the pair of tool positions to form the left rail for the left wall and right rail for the right wall. Once the positions are determined, each left position may be coupled with a corresponding right position to form pseudo-circular patterns that may be used in the next step, i.e., the trochoid generation step. That is, the determined pseudo-circular patterns may be based on the generated pair of tool positions that may comprise a set of extrapolated sequence of points, where the extrapolated sequence of points may be an extrapolation process for estimation beyond the original workpiece and its complex channel-shaped cavities. The extrapolated sequence of points may be based on the channel's left lateral wall and right lateral wall whose baselines are joined by a bottom surface, and further on the basis of the relationship between the left lateral wall and the right lateral wall. For example, flank-milling rails on the channel may be an interpolation based on estimates between known sets of flank-milling tool positions.

(24) Additionally, in this embodiment, the coupling of the left tool positions with the right tool positions may be based on the tool position's displacement, which may be intrinsically produced by the relative shift of the walls. That is, the pseudo-circular patterns resulting in the trochoidal paths may be further adjusted based on the misalignment of the channel walls or the resulting patterns may contain stretched pseudo-circular trochoidal patterns with spiking portions and/or sharp increase/decrease in local curvatures. Accordingly, the step of flank pass production may further comprise determining a set of pseudo-circular patterns based on a smoothing out of the resulting patterns subsequent to determining a set comprising the pair of subsequent tool positions. In effect, the determining of the set of pseudo-circular patters may be akin to a symmetrization of the channel parts that are to be machined, where the channel's left lateral wall and right lateral wall may be extended based on the limit curves from the surfaces representing the channel's left lateral wall and right lateral wall.

(25) The third step is the trochoid generation step. In this step, the corresponding elements of the first step and the second step may be joined via pseudo-circular patterns; patterns that typically yield a characteristic trochoidal path. During this step, the tool engagement is point-wise evaluated and the trochoidal passes may be adaptively changed e.g., in the event that the limit engagement threshold is exceeded.

(26) The fourth step is the incremental step. In this step, the previous three-step sequence, i.e., synchronizationflank passtrochoid, is repeatedly replicated, i.e., iterated at lower levels of amplitude, or cutting load, and done so inside the channel. This process allows a gradual removal of the rough material by keeping a low rate of cutting load. There may be many of these replications, and the number of them depends on the geometric shape of the channel, the mechanical characteristics of the cutting tool used, and the degree of precision, i.e., the so-called machining tolerance, the 5-axis TCR machining is asked to provide. These parameters will also affect the relative depth-distance of two adjacent levels.

(27) The fifth step is the auxiliary movements step. This step comprises the addition of auxiliary movements to the tool trajectory; where the auxiliary movements desired of the tool are calculated according to the above specification, e.g., with respect to cutting loads and target dimensions. The fifth step may include the execution of an optional finishing pass.

(28) The symmetry propagation and automatic synchronization step takes into account the tool flow along the channel, whereas the flank pass production step considers the transversal direction instead: that is, it produces the tool in-depth penetration from the top of the channel toward its bottom surface. The trochoid generation step may deal with various technological aspects including tool engagement, i.e., axial and radial engagement, tool high-speed motion, and interaction of the bottom surface of the channel with the cutting tool trajectory. The incremental step repeats the prior steps to complete a roughing operation, depending on the depth of the channel, as it may be impracticable to remove all the rough material from the channel through a single synchronizationflank passtrochoid sequence. The auxiliary movements step may yield the necessary links and offers the possibility to polish the final result by exploiting the same geometric information, and in particular the flank pass production step, used for producing the trochoidal passes.

(29) Embodiments include an exemplary CAM system 100, as illustrated in a functional block diagram in FIG. 1. The system comprises a machining apparatus 130 and a device 102 comprising a planning module 110 and a numerical code generator 120. The planning module 110 has a processing module and the numerical code generator 120 may be a separate processing module or may be embodied as computer-executed instructions that are executed by the processing module of the planning module. Numerically controlled machines are automatically operated by commands received by their processing units. The machining apparatus 130 may provide a machining tool or cutting tool, and may reorient the cutting tool relative to a workpiece according to instructions provided by the numerical code generator 120. The position of the cutting tool may be expressed in three absolute positions, i.e., XYZ, and two rotary positions, i.e., Aa rotary position about X, and Ba rotary position about Y. The numerical code generator may be responsive to the output of the planning module 110. The planning module may have access to one or more databases 140 comprising computer-based models of: (a) features defining the channel workpiece to be machined 141 (typically left wall and right wall plus a bottom surface); (b) geometric options 142 relative to the analysis of the channel surface being machined and the way that information may affect the shape the curve described by the end point of the cutting tool will have (such a curve is known as the tool-path); (c) technological options 143 expressing: i) the relative position between the cutting tool of the machining apparatus 130 and the workpiece, and ii) the overall evolution of the roughing strategy; and (d) auxiliary movements 144 that may include: (1) instructions for approaching the workpiece; (2) instructions for departing the workpiece; and (3) instructions for movements linking machining sub-areas.

(30) Via a user interface 150, a user of the system 100 may select files or objects from the databases 140 for application by the planning module 110 to generate the numerical code 121 that may for example be G-code. The machining apparatus 130 may then receive the G-code and execute the coded instructions to drive the machine tool. For example, the device may have a user interface 150 adapted to receive a user selection from a first menu 151 where the first menu may be displayed via a touch screen, or a display and indicating device, and where the first menu 151 includes the definition of essential elements of a channel shape, e.g., a left wall, a right wall, and a bottom surface, and the device may have a user interface 150 configured to receive input from a second menu 152 where the second menu may be presented via a touch screen, a display and indicating device, a first menu 151, via a separate touch screen, or via a separate display and indicating device. The second menu 152 may include a plurality of technological options that specify the relative position and axial orientation of the tool reference points with respect to the channel shaped workpiece.

(31) Embodiments may include an exemplary method of 5-axis machining 200, as illustrated in a top-level flowchart of FIG. 2. A 5-axis TCR machining cycle, including a planning or programming process, may comprise seven steps which may then be followed by the generation of CNC code. The exemplary seven planning steps of the 5-axis TCR machining comprise the following (a) to (g) sequence detailed below. Of the exemplary seven planning steps, only step (a) may require the direct intervention of a machine CAM operator, with the definition of simple and limited input information. All subsequent steps, steps (b)-(g), may be automatically handled by the system. The process may consist of the following steps: (a) defining or selecting the area of the channel-shaped workpiece to be machined (step 210); (b) propagating the symmetry of the bottom surface and synchronizing the left wall and right wall of the selected channel-shaped workpiece, i.e., the symmetry propagation and automatic synchronization step (step 220); (c) producing the flank-milling tool positions relative to the right wall and left wall, i.e., the flank pass production step and pre-processing of a paired set of tool-positions for a high relative displacement between the left wall and the right wall of the channel (step 230); (d) join the flank passes through pseudo-circular patterns, i.e., the trochoid generation step (step 240); (e) repeated replication of the previous steps (iteration) at lower levels inside the channel, i.e., the incremental step (step 250); (f) defining the auxiliary movements, i.e., the auxiliary movements step (step 260) that may include: (1) approaching the workpiece; (2) departing the workpiece; (3) movements linking machining sub-areas; and (4) finishing passes; and (g) generating the CNC code (step 270).

(32) With the present 5-axis TCR machining method, a great variety of channel-shaped workpieces may be efficiently cut by a 5-axis CNC machine. The preliminary geometric definition step and analysis step, i.e., step 210 and step 220, allows for a channel shape to be decomposed into a flow component, which is representative of the left wall and right wall of the channel, and a depth component, all of which is influenced by the wall's shape and is representative of the channel bottom surface. The geometric analysis phase and the above-described decomposition allow the channel shape surfaces to be processed as a simpler entity to produce the corresponding trajectory of the tool. The adaptive modification of the trochoid passes according to tool engagement and curvature analysis is a further element characterizing the extreme flexibility of 5-axis TCR, wherein this machining method may be able to cope with a wide variety of channel-shaped workpieces.

(33) An exemplary method of selecting the workpiece 300 is illustrated in a top-level flowchart of FIG. 3. The part geometry selection may be the only task in the process that requires an explicit intervention of the CAM operator, as all of the other steps and stages may be automatically handled by the system. The exemplary steps comprise: (a) selecting an area of the channel-shaped workpiece to be machined (step 310); (b) selecting a right wall and a left wall of the channel via a defined set of surfaces (step 320); (c) selecting a bottom surface of the channel via a defined set of surfaces (step 330); and (d) defining an entry point of the channel, which may be used to specify the flow direction of the trochoidal passes inside the channel (step 340).

(34) An exemplary method of symmetry propagation and synchronization 400 is illustrated in a top-level flowchart of FIG. 4. This step may be completely automated and may not require any direct actions of the CAM operator. The exemplary steps comprise: (a) the analysis of the bottom surface and the detection of possible geometric symmetries (step 410); (b) the propagation of such information concerning the bottom surface to the left wall and right wall (step 420); (c) the detection of the relative shift position of the left wall and right wall and the definition of a three-dimensional curve describing the flow direction of the channel and equidistant from the channel walls, i.e., called a spine curve, it carries all the information about the relative shift between the walls (step 430); and (d) the generation of an updated geometric database containing the symmetrized and synchronized versions of the left and right wall surfaces, on the basis of the information collected in step 420 and step 430 (step 440). Possible symmetries in step 410 may include, for example, cylindrical, spherical, generic revolution surfaces, or others.

(35) An exemplary method of flank pass production 500 is illustrated in a top-level flowchart of FIG. 5. This may be a completely automated step involving no direct actions of the CAM operator. The exemplary steps comprise: (a) production of a set of tool positions flank milling the right wall (step 510); (b) verification of the positions previously produced against the bottom surface, and coherent reproduction of any possibly existing symmetries on the bottom surface (step 520); (c) adaptive modification of the positions previously produced in case of collision with the bottom surface, or of violation of other technological constraints, according to minimal distance criteria (step 530); and (d) application of the same procedure, i.e., step 510, step 520, and step 530, to the left wall of the channel (step 540). Optionally, in an embodiment having a high relative displacement between the left wall and the right wall of the channel, a further step of pre-processing operations to determine a paired set of tool-positions for the displaced portions of the left wall and the right wall may be performed (step 550). The set of tool positions in step 510 may be produced according to the geometric properties of the wall surface previously computed (see FIG. 4).

(36) FIG. 6 depicts an exemplary functional block diagram of the content of the trochoid generation step 600. This may be a completely automated step involving no direct actions of the CAM operator. The exemplary steps comprise: (a) the left and right wall positions produced, and coupled, in the flank pass production step (see FIG. 5) form the start point and end point of pseudo-circular patterns (step 610); (b) the pseudo-circular patterns are verified to yield positions that do not collide with the left wall and right wall of the channel (step 620); (c) the pseudo-circular patterns are verified to yield positions that do not generate a tool engagement larger than that sustainable by the cutting tool (step 630); (d) the pseudo-circular patterns may be verified to have local curvatures that allow the cutting tool being moved at high speed, e.g., high speed machining (HSM), while cutting (step 640); and (e) the pseudo-circular patterns are verified to yield positions that do not collide with the bottom surface of the channel (step 650). The shape of the patterns in step 610 may be built according to the technological constraints specified in 152 (see FIG. 1) and/or the symmetry features determined in step 420 and step 440 (see FIG. 4). In case of collisions in step 620, the patterns may be continually or continuously and adaptively modified, i.e., an iteratively feedback driven positioning algorithm: see FIG. 7, in order to produce a close, or the closest possible, collision-free tool positions configuration. In case of over-engagement in step 630, the patterns may be continuously and adaptively modified in order to produce the closest possible controlled-engagement tool positions configuration. In case of excess of curvatures in step 640, the patterns may be continually or continuously, and adaptively modified in order to produce the closest possible controlled-curvature tool positions configuration. In case of collision with the bottom surface in step 650, each position may be shifted along its axis to produce the closest non-colliding position.

(37) FIG. 7 illustrates in a functional block diagram, an exemplary, and iteratively feedback-driven positioning process 700. The exemplary steps comprise: (a) geometrically calculating a cutting tool position (CTP) (step 760); (b) an external routine calculates the relative interaction of the target workpiece (WP) and cutting tool position, or improved cutting tool position (ICTP): if coming from step 790 (step 770); (c) determining whether the relative position of the WP versus the CTP, or ICTP, satisfies the technological constraints (step 780); (d) if the technological constraints are not satisfied in step 780, then an improved position ICTP may be produced, e.g., via testing on the relative interaction of the target WP and the CTP (or ICTP), according to the information acquired in step 770 and step 780 (step 785); (e) the improved ICTP is passed as new input back to step 770, and the cycle from step 785 to step 790 to step 770 and back to step 780 continues until the technological constraints are satisfied in step 780 (step 790); and (f) if the technological constraints are satisfied, then the cutting tool position is accepted (step 795).

(38) FIG. 8A depicts an exemplary channel-shaped cavity comprising an exemplary trochoidal tool path 800. The exemplary channel comprises a left (inner) wall 811, a right (inner) wall 812, and a bottom surface 813, which may be input by a CAM operator. An entry point 818 of the trochoidal path 815 may also be input by a CAM operator.

(39) FIG. 8B depicts an exemplary channel-shaped cavity comprising an exemplary trochoidal tool path 830. The exemplary channel comprises a left (inner) wall 811, a right (inner) wall 812, and a bottom surface 813, where one wall, right wall 812, extends further out as compared to the other wall, left wall 811. An entry point 818 of the trochoidal path 815 may also be input by a CAM operator, however, given the misalignment of the left wall 811 and the right wall 812, a pre-processing operation in which an array of a set of paired tool-positions, one flank-milling the left wall and the other flank-milling the right wall, may be necessary. That is, the figure depicts the walls as being shifted, where the last flank milling position 832 relative to the right wall 812 may be much beyond the last flank milling position 831 relative to the left wall 811. As part of the flank pass production step, a set of subsequent positions may be determined to form a left rail 835 and if necessary, a right rail (not shown in FIG. 8B). Then each position of the determined left rail 835 extending the left wall 811 may be coupled with a correspondent position on the right wall 812, thereby forming a cubic (pseudo-circular) passes, resulting in a trochoidal path 815. Accordingly, the misalignment of the channel walls, i.e., left wall 811 and right wall 812, may be avoided, and rectified via the determined left rail 835 causing a smoother coupling of the left tool position and right tool position. That is, a resulting pseudo-circular trochoidal path comprising uneven and stretched sharp local curvatures that may be undesirable for the cutting tool (see FIG. 8D) may be prevented.

(40) FIG. 8C depicts an exemplary workpiece channel-shaped cavity 850 comprising an exemplary channel with a left wall 851 and a right wall 861 showing a high relative displacement along with instances of the tool positions. The exemplary embodiment may comprise a pre-processing step, where the production of an array comprising a paired set of tool-positions, one for flank-milling the left wall 851 and one for flank-milling the right wall 861, may define a set of flank-milling rails 852, 862. In this embodiment, the flank-milling rail 852 may be associated with a left wall 851 and the flank-milling rail 862 may be associated with a right wall 861. The figure also shows a set of arrows along the dotted paths signifying the direction of movement toward the inside of the channel. Additionally, a few exemplary instances of the tool positions 854, 856, 858 for the left wall 851 and a few exemplary instances of the tool positions 864, 866, 868 for the right wall 861 are shown. Accordingly, the tool moves along the flank-milling rails 852, 862 in the directly of the arrows.

(41) Referring to two starting tool positions 854, 864 for each wall, given the shift in the position of the walls, the first flank-milling position 854 may be beyond the first flank position 864, relative to each other. That is, in an exemplary 5-axis milling machine, each tool position may be represented by a pair of vectors, a tool-end position, and a tool-axis direction guide the cutting tool. As depicted, the left most tool position 854 for the left wall 851 may be coupled with the left most tool position 864 for the right wall 861, forming the cubit (pseudo-circular) passes resulting in a trochoidal toolpath. Following the same calculation, tool position 856 and tool position 866 may be paired together. Thereafter, tool position 858 and tool position 868 may also be paired together; keeping in mind that the tool positions depicted in FIG. 8C are only an exemplary subset of the entire set of tool positions.

(42) FIG. 8D depicts an exemplary workpiece channel-shaped cavity 870 comprising an exemplary channel with a left wall 851 and a right wall 861 showing a high relative displacement with a pseudo-circular trochoidal path 872. The exemplary embodiment depicts a coupling of the left tool positions with the right tool positions (described above and in FIG. 8C) without considering the tool position displacement caused by the relative shift of the walls. The pseudo-circular trochoidal path 872 shows spiking portions supplemented by sharp local curvatures with increasing and decreasing angles. As it is evident, the depicted pseudo-circular trochoidal path 872 may be undesirable for any cutting machine. Accordingly, an array of adjusted positions to correspond to flank-milling rails on the channel may be determined.

(43) FIGS. 8E-8H depict a pre-processing step or method where the device for generating instructions for a five-axis machining tool may suitably extend the left wall and the right wall, wherever needed, in order to provide a symmetrization of the channel part to be machined via the Automatic Method for Milling Complex Channel Shaped Cavities algorithm.

(44) FIG. 8E depicts an exemplary workpiece channel-shaped cavity 880 comprising an exemplary channel with a left wall 851 and a right wall 861 showing an extracted view of the four limit curves from the surfaces representing the left wall and the right wall. Each wall may comprise two limit curves, i.e., the left wall 851 may comprise a first limit curve 883 and a second limit curve 884, and the right wall 861 may comprise a first limit curve 886 and a second limit curve 887. In one embodiment, the left wall 851 first limit curve 883 may be an upper limit curve and the second limit curve may be a lower limit curve with respect to each other. Similarly, the right wall 861 first limit curve 886 may be an upper limit curve and the second limit curve 887 may be a lower limit curve.

(45) FIG. 8F depicts the four limit curves of FIG. 8E, where a sequence of points has been extracted from the limit curves to form four chains of points. The extracting of the points from the limit curve may be done via, for example, digitalization of a sequence of points having a fixed distance along the curves. Accordingly, the first limit curve 883 and the second limit curve 884 of the left wall 851 (see FIG. 8E), along with the first limit curve 886 and the second limit curve 887 of the right wall 861 (see FIG. 8E) may be represented as a series of points along the curves.

(46) FIG. 8G depicts the exemplary workpiece channel-shaped cavity 880, with a slightly different angle of view as previous figures, comprising an exemplary channel with a left wall 851 and a right wall 861 showing a set of new points 885, 888, i.e., extra points, that may have been drawn that do not have corresponding points on the opposite limit curve. That is, new points 885, 888 are copied and translated at both the extremities of the curves and, via an exemplary translation vector, points of the upper chain may be copied and translated along with points of the upper lower chain that may also be copied and translated. Accordingly, once the copying and translating step has been completed, each new point 885, 888 may be obtained as the result of a vector translation as shown.

(47) FIG. 8H depicts the exemplary workpiece channel-shaped cavity 890 comprising an exemplary channel with a left wall 851 and a right wall 861 showing the extrapolated data points (see FIG. 8G, 885, 888) forming an extension for each wall based on the flank-milling rails 893, 894 and formed from the extending of the limit curves (see FIG. 8E, 883, 884, 886, 887). That is, the left wall 851 may be extended by the determined flank-milling rail 893 and the right wall 861 may be extended by the determined flank-milling rail 894. As can be seen, the relative displacement between the input walls has now disappeared and the channel algorithm may produce a correct, consistent, and non-stretched, pseudo-trochoidal path 898.

(48) In the embodiment where the left wall and the right wall are extracted and drawn as four limit curves representing the edge of each wall, the limit curves form the surfaces that represent the left wall and the right wall. Once the limit curves are determined, a sequence of points may then be extracted from the limit curves to form four chains of points. In order to determine an efficient 5-axis continual or continuous trochoidal roughing movement of the cutting tool, the 5-axis TCR may then take into consideration the points on the four limit curves that do not have a corresponding point on the opposite wall, i.e., extra points. Accordingly, the extra points may be copied and subsequently translated at both of the extremities of the limit curves to form a set of new points. Thereby, each new point may be obtained as a result of a vector translation onto to the opposing wall. This process may be performed for each of the four limit curves to determine a complete set of points for both the left wall and the right wall. A set of curves are defined based on the newly determined set of points, for example, a set totaling four curves for two walls, and therefore a set of two new surfaces, i.e., walls, may be determined based on the newly defined set of curves. The newly defined set of curves may now determine the left wall and the right wall of the channel. The coupling of flank-milling positions on the left wall with those on the right wall may be used for the trochoid generation step. Accordingly, the relative displacement between the inner walls may now be eliminated and the channel algorithm may produce a correct, consistent, and non-stretched pseudo-circular patterns trochoidal toolpath for the roughing movement of the cutting tool.

(49) FIG. 9A depicts an exemplary tool path trajectory in a portion of an exemplary channel-shaped cavity 900. The exemplary channel-shaped cavity comprises a left (inner) wall 911, a right (inner) wall 912, and an entry point 918. Start points and end points, generated during the trochoid generation step, form the left tool path axes boundary 916, right tool path axes boundary 917, and bottom tool path axes boundary 914 of the pseudo-circular trochoidal patterns 915. An exemplary flank milling tool 921,922,923 is depicted in three positions along its trochoidal path 915. In the first milling tool position 921, the milling tool is positioned according to a calculated tool path on axis 931. The milling tool then moves into a second milling tool position 922 on axis 932. The milling tool then moves into a third milling tool position 923 on axis 933. The milling tool positions move along a trochoidal path constructed based on the previously determined set of flank milling tool positions.

(50) The incremental step described in step 250 (see FIG. 2) is a replication of the steps described in at least one of FIG. 4, FIG. 5, and FIG. 6 at a lower depth-levels inside the channel. The number of replications depends on the geometric shape of the channel, the mechanical characteristics of the cutting tool used, and the degree of precision, i.e., the so-called machining tolerance, the 5-axis TCR machining is asked to provide. These parameters will affect also the relative depth-distance of two adjacent levels.

(51) FIG. 9B depicts an exemplary tool path trajectory in a portion of an exemplary channel-shaped cavity 900 with a disparity between the channel walls. The exemplary channel-shaped cavity comprises a left (inner) wall 911, a right (inner) wall 912, and an entry point 918. Start points and end points, generated during the trochoid generation step may also include the determined paired set of tool-positions for the displaced portions of the left wall and the right wall generated during the pre-processing operations. The aggregate of the points may then form the left tool path axes boundary 916, 946, right tool path axes boundary 917, 947, and bottom tool path axes boundary 914 of the upper and lower pseudo-circular trochoidal patterns 915. An exemplary flank-milling tool is depicted in three positions 921,922,923 along its trochoidal path 915. In the first milling tool position 921, the milling tool is positioned according to a calculated tool path on axis 931. The milling tool then moves into a second milling tool position 922 on axis 932. The milling tool then moves into a third milling tool position 923 on axis 933. The milling tool positions move along a trochoidal path constructed based on the previously determined set of flank milling tool positions.

(52) The left (inner) wall 911 may now comprise a set of extrapolated points in addition to the ones directly corresponding to the wall 911 itself in order to determine a left tool path axes boundary 916. The number of extrapolated points needed depends on the geometric shape of the channel, the mechanical characteristics of the cutting tool used, and the degree of precision, i.e., the so-called machining tolerance, the 5-axis TCR machining is asked to provide.

(53) FIG. 10 illustrates in top level flowchart an addition to the tool position trajectory calculated in the auxiliary movement step. The approaches and detaches are selected as motion about a radius or radiused (step 1010). The connection between large portions, i.e., sub-areas, of the tool path may be selected as rapid links (step 1020). A polishing finish pass operation may be added to each incremental level (step 1030). With the planning complete, the tool path may be determined (step 1040). The auxiliary movement step may be checked for collision detection.

(54) FIGS. 11A-11D depict, in a top-view of a channel, an exemplary polishing finish pass operation. The exemplary polishing finish pass operation may be performed right after the cutting tool 1110 performs the trochoidal passes 1120 of the trochoidal tool path (FIG. 11A). The finish pass may remove rough material 1131,1132,1133,1134,1135, e.g., creases, left by the trochoidal passes of the cutting tool on the left wall 1101 and the right wall 1102. The tool positioning used to generate the trochoidal tool path may be to generate the tool path for the finish pass (FIG. 11C). The cutting tool 1110 may remove the rough material 1133,1134,1135, e.g., peeling, from a right wall 1102, left wall 1101, and/or bottom surface (FIG. 11D). This finishing pass may produce the desired final shape with a minimum of machining effort.

(55) It is contemplated that various combinations and/or sub-combinations of the specific features and aspects of the above embodiments may be made and still fall within the scope of the invention. Accordingly, it should be understood that various features and aspects of the disclosed embodiments may be combined with or substituted for one another in order to form varying modes of the disclosed invention. Further, it is intended that the scope of the present invention herein disclosed by way of examples should not be limited by the particular disclosed embodiments described above.