Tool path generation device, tool path generation method, processing machine, and program

Abstract

This tool path generation device comprises: a machining surface shape information acquisition unit that acquires machining surface shape information indicating the shape of a machining surface; a potential generation unit that generates a potential in a coordinate space, which is a space of a parameter indicating the orientation of a tool, on the basis of machining strategy information that indicates a strategy for machining control on the basis of the orientation of the tool and / or a portion of the tool; and a path generation unit that generates a tool path on the basis of the machining surface shape information and the potential.

Description

Tool path generation device, tool path generation method, machining center, and program

[0001] The present invention relates to a tool path generation device, a tool path generation method, a machining center, and a program. This application claims priority based on Japanese Patent Application No. 2025-037393, filed in Japan on March 10, 2025, the contents of which are incorporated herein by reference.

[0002] Conventionally, cutting systems that process workpieces quickly and accurately are known (Patent Document 1).

[0003] Japanese Patent Publication No. 2025-004718

[0004] However, conventional cutting systems have not adequately considered how to generate tool paths that correspond to the machining control strategy.

[0005] The present invention has been made in view of the above points, and provides a tool path generation device, a tool path generation method, a machining machine, and a program that can generate tool paths according to a machining control strategy.

[0006] One aspect of the present invention is a tool path generation device comprising: a machined surface shape information acquisition unit that acquires machined surface shape information indicating the shape of a machined surface; a potential generation unit that generates a potential on a configuration space which is a space of parameters indicating the orientation of a tool, based on machined strategy information that indicates a machining control strategy based on the orientation of the tool and at least one of the parts of the tool; and a path generation unit that generates a tool path based on the machined surface shape information and the potential.

[0007] One aspect of the present invention is a machining machine equipped with the above-described tool path generation device.

[0008] One aspect of the present invention is a method for generating a tool path, comprising: a step of acquiring tool surface shape information indicating the shape of a machined surface; a step of generating a potential on a configuration space, which is a space of parameters indicating the orientation of a tool, based on machining strategy information indicating a machining control strategy based on the orientation of the tool and at least one of the parts of the tool; a step of generating a tool path based on the tool surface shape information and the potential.

[0009] One aspect of the present invention is a program for causing a computer to perform the following steps: a machined surface shape information acquisition step for acquiring machined surface shape information indicating the shape of a machined surface; a potential generation step for generating a potential on a configuration space, which is a space of parameters indicating the orientation of a tool, based on machined strategy information indicating a machining control strategy based on the orientation of the tool and at least one of the parts of the tool; and a path generation step for generating a tool path based on the machined surface shape information and the potential.

[0010] According to the present invention, tool paths can be generated according to the machining control strategy.

[0011] This shows an example of the tool feed direction and pick feed direction of the machined surface S according to an embodiment of the present invention. This is a diagram showing an example of PNF data according to an embodiment of the present invention. This is a diagram showing an example of the cutting point coordinate system according to an embodiment of the present invention. This is a diagram showing an example of CL data according to an embodiment of the present invention. This is a diagram showing an example of the tool shape data format according to an embodiment of the present invention. This is a diagram showing an example of the procedure for generating tool shape data according to an embodiment of the present invention. This is a diagram showing an example of the application of the tool shape data format according to an embodiment of the present invention. This is a diagram showing an example of the positional relationship between the cutting point and the command point according to an embodiment of the present invention. This is a diagram showing an example of the command point calculation flow based on the tool shape data format according to an embodiment of the present invention. This is a diagram showing an example of the cutting edge portion according to an embodiment of the present invention. This is the tool tip point O according to an embodiment of the present invention θ This figure shows an example of the process for determining the tool tip O according to an embodiment of the present invention. θThis figure shows an example of rotational movement around the normal vector. This figure shows an example of an Euler angle according to an embodiment of the present invention. This figure shows an example of a C-Space representing appropriate and inappropriate cutting edge portions for machining according to an embodiment of the present invention. This figure shows an example of discretization of a C-Space according to an embodiment of the present invention. This figure shows an example of calculation of two-dimensional C-Spaces with different resolutions according to an embodiment of the present invention. This figure shows an example of set operations in an SDF according to an embodiment of the present invention. This figure shows an example of a method for representing the shape of a shaped tool using an SDF according to an embodiment of the present invention. This figure shows an example of a color map of a shaped tool converted to an SDF according to an embodiment of the present invention. This figure shows an example of discretization of a NURBS surface using a point cloud according to an embodiment of the present invention. This figure shows an example of coordinate transformation of an interference point cloud to a cutting point coordinate system according to an embodiment of the present invention. This figure shows an example of coordinate transformation of an interference point cloud to a tool coordinate system according to an embodiment of the present invention. This figure shows an example of projection of interference points according to an embodiment of the present invention. This figure shows an example of projection of interference points according to an embodiment of the present invention. This figure shows an example of interference determination using a two-dimensional SDF according to an embodiment of the present invention. This figure shows an example of a three-dimensional array of threads according to an embodiment of the present invention. This figure shows an example of a composite R-shaped shaped tool according to an embodiment of the present invention. This figure shows an example of a machined target shape according to an embodiment of the present invention. This figure shows an example of machining conditions according to an embodiment of the present invention. This figure shows an example of the calculation conditions for C-Space according to an embodiment of the present invention. This figure shows an example of C-Space according to an embodiment of the present invention. This figure shows an example of the tool path obtained as a result of calculation based on C-Space according to an embodiment of the present invention. This figure shows an example of the tool posture according to an embodiment of the present invention. This figure shows an example of the machining simulation according to an embodiment of the present invention. This figure shows an example of the analysis results of over-machining and under-machining according to an embodiment of the present invention. This figure shows an example of a photograph of the finished surface after machining and the measurement results of the surface roughness according to an embodiment of the present invention. This figure shows an example of machining using a barrel-lens composite tool according to an embodiment of the present invention. This figure shows an example of setting the boundary of C-Space according to an embodiment of the present invention. This figure shows an example of the distance within a two-dimensional C-Space according to an embodiment of the present invention.This figure shows an example of a Gaussian distribution according to an embodiment of the present invention. This figure shows an example of a discretized C-Space according to an embodiment of the present invention. This figure shows an example of an artificial potential field according to an embodiment of the present invention. This figure shows an example of a tool path using an artificial potential field according to an embodiment of the present invention. This figure shows an example of the distance to cutting points belonging to the same tool path according to an embodiment of the present invention. This figure shows an example of a modified artificial potential field according to an embodiment of the present invention. This figure shows an example of a tool path using a modified artificial potential field according to an embodiment of the present invention. This figure shows an example of the configuration of a machining center 1 according to an embodiment of the present invention. This figure shows an example of the flow of the tool path generation process according to an embodiment of the present invention. This figure shows an example of the potential field of each machining strategy according to an embodiment of the present invention. This figure shows an example of the appearance of a barrel tool according to an embodiment of the present invention. This figure shows an example of the shape of a workpiece according to an embodiment of the present invention. This figure shows an example of machining conditions according to an embodiment of the present invention. This figure shows an example of calculation conditions according to an embodiment of the present invention. This figure shows an example of an artificial potential field according to an embodiment of the present invention. This figure shows an example of an artificial potential field in a single tool path according to an embodiment of the present invention, arranged in the tool feed direction. This figure shows an example of a model of the shape of a tool and machined surface according to an embodiment of the present invention. This figure shows an example of a part of the generated tool axis vector This figure shows an example of a tool path generated for wall surface machining using a barrel blade according to an embodiment of the present invention. This figure shows an example of a tool path generated for bottom surface machining using a lens tool according to an embodiment of the present invention. This figure shows an example of the results of analyzing the amount of over-machining according to an embodiment of the present invention. This figure shows an example of the results of analyzing the amount of unmachined material according to an embodiment of the present invention. This figure shows an example of a machined surface created by a tool path generated by the tool path generation method according to an embodiment of the present invention.This figure shows an example of the results of measuring the surface roughness according to an embodiment of the present invention.

[0012] (Embodiments) Embodiments of the present invention will be described in detail below with reference to the drawings. In recent years, the sophistication and diversification of products in the market have been remarkable. Production technology in manufacturing sites is required to achieve both sophistication and cost reduction. One useful technology that is attracting attention is the use of irregularly shaped tools in 5-axis controlled machining. Barrel tools, which are typical irregularly shaped tools, have a cutting edge shape of a large diameter even in small diameter tools, and it is possible to set a large pick feed amount equivalent to that of a large diameter tool, so that machining efficiency can be greatly improved. Not only is machining time shortened, but it also leads to the omission of post-processing such as grinding, and contributes to a significant reduction in lead time.

[0013] Conventional techniques for tool path generation in 5-axis controlled machining have proposed tool path generation methods that take into account the avoidance of interference between the tool and the workpiece (tool interference) and interference with the structure of the machine tool, such as the spindle and pivot axis (structural interference). Furthermore, from the perspective of machining quality, methods have been proposed for generating tool paths that minimize and smoothly change the tool position in order to obtain a continuous surface texture, and for generating tool paths that avoid deterioration of surface texture caused by backlash of the rotating axis. Such policies for tool path generation that address objectives such as interference avoidance, quality, and cost are called "machining strategies." Many of the proposed machining strategies target ball end mills, which are the most common tool used in 5-axis controlled machining.

[0014] In 5-axis controlled machining using a ball end mill, the positional relationship between the machining point and the command point is always constant, making it easy to determine the command point. However, with irregularly shaped tools, the positional relationship between the machining point and the command point changes depending on the tool orientation, requiring the calculation of an appropriate command point based on the tool shape. Furthermore, irregularly shaped tools are diverse, including barrel tools specialized for flank machining using the tool's side surface and lens tools that use only the tool's bottom surface, each requiring a different tool orientation suitable for machining. Currently, tool path generation is handled on a case-by-case basis by defining the tool shape for each type of irregularly shaped tool. To take advantage of the characteristics of irregularly shaped tools, such as selecting the appropriate cutting edge and maximizing machining speed, operators need to be well-versed in the complex tool shapes and usage methods, requiring high skill. From the above, it can be said that the procedure for work design when using irregularly shaped tools is not standardized due to the complexity of the tool shapes.

[0015] In this embodiment, the objective is to generate a strategic tool path that provides the optimal tool orientation for the tool shape to bring out its characteristics, in order to achieve highly efficient machining with a wide variety of irregularly shaped tools. Similar to conventional ball end mills, the aim is to achieve 5-axis controlled machining that can be applied to irregularly shaped tools of any shape using a standardized work procedure.

[0016] First, we will describe a tool shape data format that can define the shape of any irregularly shaped tool by extending the German industrial standard DIN 66215. Next, we will show a method for calculating command points based on the tool shape data format described above. By showing a single, general-purpose calculation method, it will not only be possible to calculate command points using a standardized procedure that is independent of the tool shape, but it will also be possible to easily apply it to 5-axis control machining for new irregularly shaped tools that will be developed in the future.

[0017] In this embodiment, the tool path generation method based on C-Space is extended to map information about the cutting edge of a non-standard tool. Since non-standard tools have cutting edge portions that are unsuitable for machining, each point in the discretized C-Space is classified as suitable for machining or not. This enables strategic tool path generation that selects the appropriate cutting edge portion while avoiding interference at each cutting point.

[0018] Furthermore, by considering C-Space as an artificial potential field, a tool path generation method called the "safety-first machining strategy" is applied to irregularly shaped tools. A repulsive field is set on C-Space to move away from tool positions that cause interference and tool positions corresponding to cutting edge parts unsuitable for machining. By selecting a tool position from the minimum value of the potential, a tool path is automatically generated that selects an appropriate cutting edge part while avoiding interference. For the practical application of the developed method, speeding up the interference calculation, which requires enormous processing, is a crucial challenge. In this embodiment, in order to parallelize the enormous interference calculation using a GPGPU and achieve high-speed interference calculation, a method for converting the shape of an irregularly shaped tool, defined based on the tool shape data format, into a format suitable for parallel computation of the GPU is described. The usefulness of the method described above is verified in terms of machining quality and computation time by performing machining simulations and machining experiments.

[0019] [Cutting Point Data] In this embodiment, we refer to the iso-parametric method, which generates tool paths based on isoparametric curves on a parametric surface. The surface to be machined is defined by CAD as a non-uniformed rational B-spline (NURBS) and is represented by the following equation (1).

[0020]

[0021] Here N ｉ，ｐ (u)N ｊ、ｑ (v) is the B-spline basis function in the u and v directions, P ｉ，ｊ is a control point, w ｉ，ｊ The weights of each control point are shown, and p and q indicate the order in the u and v directions. As shown in Figure 1, here the parameter for the pick feed direction of the machined surface S is u, and the parameter for the tool feed direction is v. The cutting point is P ｉ，ｊ This is expressed as follows, where i = {0, 1, ..., M} corresponds to the pick feed direction and j = {0, 1, ..., N} corresponds to the tool feed direction. The unit normal vector n at any point can be found by the following equation (2).

[0022]

[0023] A vector F indicating the tool feed direction is obtained from the following formula (3) so as to be perpendicular to the normal vector n.

[0024]

[0025] Here, R(x, α) represents a transformation matrix that rotates a vector by α around vector x. P ｉ，ｊ＋１ represents the next cutting point relative to the cutting point P ｉ，ｊ .

[0026] Cutting point data that can be handled by the CAM software implemented in the present embodiment is composed of cutting point coordinates P ｉ，ｊ , a normal vector n, a tool feed vector F, and a cutting code. The cutting code indicates either cutting feed ("80") or rapid traverse ("7f"). In the present embodiment, this cutting point data is referred to as "PNF data". FIG. 2 shows an example of PNF data.

[0027] [Tool path data] As shown in FIG. 3, with the cutting point P ｉ，ｊ as the origin, the tool feed direction F is defined as the X ｃ axis, the direction of the normal vector n is defined as the Z ｃ axis, and the direction of the cross product of X ｃ and Z ｃ is defined as the Y ｃ axis to set a coordinate system {X ｃ , Y ｃ , Z ｃ}. This is referred to as a cutting point coordinate system. The tool posture at the cutting point P ｉ，ｊ is represented by a tool axis vector T. T is determined by two parameters, an inclination angle θ relative to the Z ｃ axis and a turning angle φ around the Z ｃ axis, and can be obtained by the following formula (4).

[0028]

[0029] A command point O to be input to a machine tool is a point on the tool axis vector T, and for example, in the case of a drill tool, it is often set as the tip point of the tool, and in the case of a ball end mill, it is often set as the center point of the ball. In the present embodiment, the tip point of the tool is used as the command point.

[0030] In this embodiment, the tool path (Cutter location: CL) data consists of a command point O, a tool axis vector T, and a code representing the cutting feed ("80") or rapid traverse ("7f"). An example of CL data is shown in Figure 4.

[0031] [Tool Shape Data Format] In this embodiment, the tool contour shape is defined by two straight lines and a single fillet radius. A tool shape data format that extends the DIN 66215 to include n arc sections, as shown in Figure 5, will be described. By using the tool shape data format according to this embodiment, not only can the tool shape be defined parametrically, but a NURBS model of the tool used for interference calculations required when generating the tool path can also be created.

[0032] Figure 6 shows the procedure for generating tool shape data using given parameters. First, the tip of the tool is set as the origin, and the tool radius direction is set as X. ｔ The axis and tool axis direction are Z ｔ Tool coordinate system with axis {X ｔ , Z ｔ Define} (step S10). Next, input tool shape information into the tool model (step S20). The tool shape information includes the tool name and n cutting edge radii r. ０ ,r １ , ..., r ｎ－１ , tangential angle ψ of the cutting edge ０ ψ １ ,…,ψ ｎ＋２ , bottom diameter d ｂ It consists of the following. Irregularly shaped tools may have cutting edges that are suitable for machining and cutting edges that are not. Therefore, tool shape information for irregularly shaped tools includes parameter a, which indicates whether each cutting edge is suitable for machining. ０ , a １ , ..., a ｎ＋１ Further includes ∈{0,1}. The value is 1 if the cutting edge portion is suitable for machining, and 0 otherwise. a ０ This corresponds to the flat part of the tool's bottom surface, and the arc-shaped cutting edge portion r ｉ a ｉ＋１ This corresponds to the last a. ｎ＋１This corresponds to the shank portion. Next, we calculate the tool's contour line. X ｔ -Z ｔ On a plane, given d ｂ and ψ ０ A flat portion of the tool bottom surface is generated using this method (step S30).

[0033] Next, given {r ０ ,r １ , ..., r ｎ－１} and {ψ １ ψ ２ ,…,ψ ｎ＋１ Using}, the arc center O ｉ = {O ｉｘ , O ｉｚ} is calculated (step S40). Given {r ０ ,r １ , ..., r ｎ－１} and {ψ １ ψ ２ ,…,ψ ｎ＋１ Using}, the center O of the arc ｉ The contour of the cutting edge portion with the arc centered at r ｉ The number of arcs is calculated (step S50). Then, it is determined whether the number of arcs is less than n (step S60). If the number of arcs is less than n (step S60; YES), the arc center O ｉ and the contour of the cutting edge part r ｉ Repeat the calculation. This will give you the center of the arc O. ｉ and the contour of the cutting edge part r ｉ The n pairs of values ​​are calculated sequentially from the tool tip towards the shank.

[0034] If the number of arcs becomes n or greater (step S60; NO), ψ ｎ＋２ The flat portion corresponding to the shank portion is defined using (step S70). With the above processing, the tool contour line is completed. The obtained contour line is Z ｔ By rotating it around the axis, a NURBS model is obtained as a tool model for the irregularly shaped tool (step S80). Finally, the tool name and various parameters (r ｉ ψ ｉ d ｂ , a ｉ , O ｉ) and the NURBS model of the tool are stored in memory as tool shape data (step S90).

[0035] Figure 7 shows an example of applying the tool shape data format according to this embodiment. It can be seen that NURBS curved surfaces of various irregularly shaped tools can be obtained.

[0036] [Calculation of Command Points Based on Tool Shape Data Format] In conventional 5-axis controlled machining using a ball end mill, the positional relationship between the cutting point and the command point is always constant regardless of the tool orientation, as shown in Figure 8(A). Therefore, the command point can be easily determined by offsetting the given cutting point by the ball radius in the direction of the normal vector of the machined surface. On the other hand, in the case of 5-axis controlled machining using a non-standard shaped tool, the positional relationship between the cutting point and the command point changes depending on the tool orientation, as shown in Figure 8(b). Therefore, it is necessary to calculate the coordinates of the command point accurately based on the tool shape.

[0037] Since a wide variety of irregularly shaped tools have been proposed, it is necessary to derive a calculation formula for the command point that is suitable for each shape each time. However, in order to standardize work design, it is desirable that the command point can be obtained from a single calculation formula. In this embodiment, a method is shown for obtaining the command point of a wide variety of irregularly shaped tools from a single calculation formula based on the tool shape data format according to this embodiment.

[0038] Figure 9 shows the flow of command point calculation based on the tool shape data format according to this embodiment. This procedure also includes the process of converting the tool model to the cutting point coordinate system for interference calculation. First, the tool model (NURBS model) of the tool is moved to the origin and rotated (step S100). Next, the inclination angle θ and the tangent angle ψ of the cutting edge portion are calculated. ｉ By comparing these, the cutting edge portion that contacts the cutting point is identified (step S110). Here, it is determined whether the inclination angle θ is outside the machining range (step S120). If the inclination angle θ is outside the machining range (step S120; YES), an error is output and the process is terminated.

[0039] When the inclination angle θ falls within the machining range (step S120; NO), the tool tip point O is determined by ignoring the rotation angle φ and applying only the inclination angle θ.θ The tool axis vector Z is calculated (step S130). Next, the command point O is calculated using the rotation angle φ and the cutting point P (step S140). Furthermore, the tool axis vector T is calculated using the inclination angle θ and the rotation angle φ (step S150). Next, the tool axis vector Z is calculated. ｔ The cross product of the normal vector n is calculated (step S160), Euler angles α, β, and γ are calculated (step S170), and these are used to convert the NURBS model of the tool to the cutting point coordinate system.

[0040] Here, a branching process is performed to avoid singularities in the Euler angle (step S180). In this branching process, it is determined whether or not the Euler angle β is 0. If the Euler angle β is 0 (step S180; YES), the tool model is translated to the cutting point coordinates (step S1120).

[0041] On the other hand, if it is determined that the Euler angle β is not 0 during the branching process (step S180; NO), the tool model is set to the tool coordinate system Z ｔ Rotate the tool model by an Euler angle α (step S190) and move it to the tool coordinate system Z. ｔ The tool model is rotated by an Euler angle β in a direction perpendicular to the normal vector n (step S1100), and then rotated by an Euler angle γ around the normal vector n (step S1110). After that, the tool model is translated to the cutting point coordinates (step S1120).

[0042] [Application of Inclination Angle] With milling tools, the cutting speed decreases at the cutting edge near the tool axis. At low cutting speeds, not only does tool wear progress, but tearing and burrs occur, worsening the surface roughness. By applying an inclination angle to the tool, it is possible to maintain an appropriate cutting speed and improve the surface roughness. In the case of barrel cutting, flank cutting, which involves increasing the inclination angle θ and machining on the side of the tool, is common.

[0043] The command point O at a certain cutting point P is determined by the inclination angle θ and the rotation angle φ. First, the tool position is calculated by applying only the inclination angle θ. In the process of step S110 in Figure 9, the inclination angle θ and the tangent angle ψ of the tool shape data format are compared, and the cutting edge r tangent to the machined surface is determined. ｉis specified. For example, in FIG. 10(a), ψ ２ <θ<ψ ３ , therefore the cutting edge portion r １ is selected, and in FIG. 10(b), ψ ３ <θ<ψ ４ , therefore the cutting edge portion r2 is selected.

[0044] Subsequently, in the process of step S130 in FIG. 9, as shown in FIG. 11, using the selected cutting edge portion r ｉ and the inclination angle θ, the tool tip point O θ is obtained. First, the unit normal vector of the machined surface at the cutting point is multiplied by the cutting edge radius r ｉ to obtain the arc center O ｉ of the cutting edge portion r ｉ . By using the component representation O ｉ ={O ｉｘ , O ｉｚ} in the tool coordinate system, the angle formed between O θ -O ｉ and the Z ｔ axis can be expressed as Tan-1(O ｉｘ / O ｉｚ ). Therefore, the relationship between the inclination angle θ and the tool tip point O θ can be obtained from equation (5).

[0045]

[0046] [Application of Swing Angle] The swing angle φ can control the orientation of the tool without changing the contact point of the tool, so it is useful for avoiding interference, and it also affects cusp height and cutting resistance, so its control is important.

[0047] As the process of step S140 in FIG. 9, as shown in FIG. 12, the command point O output as CL data is a coordinate value obtained by rotating the tool tip point O θ obtained by applying the inclination angle θ by φ around the normal vector n, then translating the coordinate P of the cutting point. The calculation of the command point O to which the swing angle φ is applied is shown in equation (6).

[0048]

[0049] [Rotation of the Tool Model] To use the tool model for interference calculations with the machined surface model, the generated NURBS surface of the tool is transformed into a cutting point coordinate system using Euler angles. In this embodiment, Euler angles of the type that rotate in the order of Z-axis, X-axis, Z-axis were used. In the procedure from step S160 in Figure 9 onwards, the NURBS surface of the tool is rotated in the order of angles α, β, γ. Here, as shown in Figure 13, angle α is X ｔ and Z ｔ The angle β is the angle made by ×n. ｔ The angle between n and γ is Z. ｔ This is the angle between ×n and F. As shown in the following procedure, branching is necessary to avoid singularities when using Euler angles. (1) Tool axis vector Z ｔ The cross product of the normal vector n and Z ｔ (2) Find ×n. (3) When angle β = 0, it is a singularity of the Euler angle, so no further rotation is performed. ｔ Rotate it by an angle α around the axis. (4) Z ｔ Rotate by an angle β around the n axis. (5) Rotate by an angle γ around the n axis. Note that Z ｔ The axis is the tool axis vector Z. ｔ This is the axis that indicates the direction of Z. ｔ The ×n axis represents the cross product Z. ｔ The x-axis indicates the direction of n, and the n-axis indicates the direction of the normal vector n.

[0050] [C-Space Generation and Speed ​​Improvement through Parallel Computing] As described above, this embodiment describes a general-purpose tool shape data format that can describe a wide variety of irregularly shaped tools, and shows a method for calculating command points based on this format. In this embodiment, the tool path generation method based on configuration space (C-Space) is further extended to describe cutting edge information of irregularly shaped tools, realizing strategic tool path generation that selects appropriate cutting edge locations while avoiding interference. Furthermore, a method for speeding up calculations by converting the shape of irregularly shaped tools into a format suitable for parallel computing on GPUs based on the tool shape data format described above is explained. Finally, a tool path generation and machining experiment is performed as a case study to demonstrate the usefulness of the method according to this embodiment in terms of quality and calculation speed.

[0051] [Extension of 2D C-Space to accommodate irregularly shaped tools] C-Space is a parameter space for uniquely representing the position and orientation of a moving object. In this embodiment, the C-Space developed for application to 5-axis controlled machining is extended to accommodate irregularly shaped tools. In the case of an irregularly shaped tool with multiple cutting edges R, the cutting edge portion R in Figure 14 Ｓ As shown above, there may be areas that are unsuitable for finishing due to their small radius. Ｓ When cutting, the amount of pick feed required to achieve the desired cusp height becomes small, and the high machining efficiency expected with the application of irregularly shaped tools cannot be obtained. As shown in the RS area of ​​Figure 14, the region of tool posture corresponding to an inappropriate cutting edge area is mapped onto the C-Space, and the free region is classified into appropriate and inappropriate regions. By selecting a tool posture from the appropriate region, a tool posture without interference corresponding to an appropriate cutting edge area for finishing can be obtained.

[0052] In this embodiment, a two-dimensional C-Space is discretized with an arbitrary resolution, and interference and whether or not the cutting edge portion is suitable for machining are determined for each discrete point, thereby generating an interference-free tool path corresponding to an appropriate cutting edge portion. In this embodiment, as shown in Figure 15, the resolution of the rotation angle φ is set to be higher as the distance from the origin of the C-Space increases, thereby discretizing it into a uniform distribution in a concentric circle.

[0053] A uniform discretization in a concentric circle can be obtained by the following procedure: (1) Discretization of the inclination angle θ Based on the resolution Δθ of the given inclination angle θ, the set of discretized inclination angles θ ｉ We find this as shown in equation (7).

[0054]

[0055] Here, N θ This is the number of divisions of the inclination angle θ, and is calculated using equation (8) so that it is an integer.

[0056]

[0057] θ ｍａｘ θ is the maximum value of the inclination angle θ. Also, in the right-hand side of equation (8), θ ｍａｘ The floor function used is the largest integer less than or equal to the value obtained by dividing by the inclination angle θ. (2) Discretization of the rotation angle φ Resolution of the rotation angle φ Δφ ｉ This is determined by dividing the circumference into equal parts, as shown in equation (9).

[0058]

[0059] Here, Nφ ｉ θ indicates the number of divisions of the rotation angle φ. Discretized inclination angle θ ｉ A uniform division is achieved by calculating it using equation (10) accordingly.

[0060]

[0061] The constant "6" was chosen because dividing the circumference into multiples of 6 yields the densest partitioning. Finally, the discretized rotation angle φ ｉ，ｊ We find this using equation (11).

[0062]

[0063] (3) Generating a list of tool positions All combinations (θ ｉ ､φ ｉ，ｊ Using this, a list of tool positions TAll is created as shown in equation (12), and this is set to the discretized C-Space.

[0064]

[0065] Figure 16 shows an example of discrete calculation of a two-dimensional C-Space. Red indicates the interference region, purple indicates the boundary of the interference region, blue indicates the region corresponding to an inappropriate cutting edge, and green indicates the region corresponding to an appropriate cutting edge. It can be seen that the definition domain of the C-Space is discretized uniformly and concentrically in accordance with the given resolution.

[0066] Figure 16(A) shows the result with a resolution of 5°, where the C-Space was divided into 1027 regions. Figure 16(B) shows the result with a resolution of 1°, where the C-Space was divided into 24571 regions. The tool path generation method according to this embodiment calculates the free region by calculating interference for all tool position points in advance, and then plans the tool path. In order to clarify the free region of the entire machined surface, interference calculations are required a number of times equal to the number of C-Space divisions multiplied by the number of cutting points. Although it depends on the shape of the workpiece and the machining conditions, the number of interference calculations is thought to be several million to tens of millions, and sequential processing by a CPU takes several minutes to several hours.

[0067] [Speeding up Interference Calculation] This section describes how to speed up interference detection using parallel processing with a GPU. One method of high-speed computation using a GPU is Sphere Tracing, which is one of the Ray Tracing techniques. In Sphere Tracing, the shortest distance to an object is calculated for each pixel, and interference is determined if that distance falls below a threshold. This is a rendering technique for obtaining realistic images by acquiring information such as color and normals from the interfering objects. A shape representation technique called the Signed Distance Function (SDF) is used to calculate the shortest distance. SDF is a function that takes an arbitrary point as input and returns the signed distance from the surface of the object. If the sign of the distance is positive, it can be determined that the point is outside the object, and conversely, if it is negative, it can be determined that it is inside. In other words, interference detection between a point and an object is possible.

[0068] As a basic example of an SDF, we show an SDF of a sphere centered at the origin. The SDF F(p) that takes an arbitrary point p as input can be expressed using the radius r of the sphere as shown in equation (13).

[0069]

[0070] In SDF, translation and rotation operations are equivalent to moving and rotating a point in the opposite direction. For F(p), these can be expressed using the translation vector t and rotation matrix R as shown in equation (14).

[0071]

[0072] One of the features of SDF is that it allows for set operations. As shown in Figure 17, the sum, product, and difference shapes can be easily obtained from multiple SDFs. By combining SDFs of basic shapes, it is possible to construct SDFs of complex shapes. By combining SDFs FA(p) and FB(p) with an arbitrary point p as input, the sum shape (Funion), product shape (Fintersection), and difference shape (Fdifference) can be obtained as shown in equation (15), respectively.

[0073]

[0074] Since SDF is generally used for graphics processing, it is implemented in a way that is suitable for GPUs. Because SDF can detect interference between points and objects and can construct complex shapes through set operations, we will explain its application to interference detection of irregularly shaped tools.

[0075] This section describes a high-speed interference calculation method using SDF for interference detection between irregularly shaped tools and interfering surfaces. Since SDF is a distance function that takes any point as input, interference detection is performed by treating either the tool or the interfering surface as an SDF and the other as a point cloud, and calculating the signed distance for all points in the point cloud. Irregularly shaped tools can be represented as SDFs by considering them as solids of revolution. Here, interference detection is accelerated by representing the irregularly shaped tool as an SDF and the interfering surface as a point cloud.

[0076] First, we will describe how to represent a non-standard tool using SDF. The tool coordinate system is defined as the tool coordinate system with the tip of the non-standard tool as the origin, and the shape of the non-standard tool is represented in SDF on the tool coordinate system. Since a non-standard tool is composed of multiple straight line and arc segments, the SDF of the non-standard tool is obtained by finding the union of each segment represented in the SDF. For example, in the case of a barrel-shaped non-standard tool, the arc portion can be represented as the product of a sphere and a height range, as shown in Figure 18(a). The shank portion can be found as the product of a cylinder and a height range, as shown in Figure 18(b). By finding the union of Figures 18(a) and 18(b), the SDF of the entire tool shape is obtained, as shown in Figure 18(c).

[0077] As an example of a tool with an irregular shape converted to SDF, Figure 19 shows its application to a tapered barrel tool. Figure 19 represents the negative values ​​of SDF as a color map, and it can be seen that the negative values ​​become larger as you move further into the tool.

[0078] Next, point cloud generation is performed on the interference surface given as a NURBS surface. As shown in Figure 20, the NURBS surface is discretized into a point cloud by equally dividing it according to the parameters (u, v). This conversion of the interference surface into a point cloud will be called the interference point cloud. A coordinate transformation is performed in order to determine the interference between the interference point cloud and the irregularly shaped tool represented in SDF. Three coordinate systems are defined: world coordinates, cutting point coordinate system, and tool coordinate system. The world coordinate system is the coordinate system of the CAD model representing the workpiece. The interference point cloud is described there. The cutting point coordinate system is a coordinate system with the cutting point as the origin. The tool coordinate system is an SDF coordinate system with the tip of the irregularly shaped tool tangent to the cutting point as the origin.

[0079] In order to input the interference point cloud into the SDF, it is necessary to determine the coordinate values ​​of the interference point cloud in the tool coordinate system. In this embodiment, as shown in Figure 21, the interference point cloud described in the world coordinate system is converted to the cutting point coordinate system, and then further converted to the tool coordinate system.

[0080] First, a coordinate transformation is performed from the world coordinate system to the cutting point coordinate system. Using the vectors P, n, F, and (n × F) that define the cutting point coordinate system, one point p in the interference point group in the world coordinate system is defined. ｗ The point p in the cutting point coordinate system is as shown in equation (16) below. ｃ It is converted to this.

[0081]

[0082] Here, M ｗ２ｃ This is the coordinate transformation matrix from the world coordinate system to the cutting point coordinate system, and is defined as shown in equation (17).

[0083]

[0084] Next, as shown in Figure 22, a coordinate transformation is performed from the cutting point coordinate system to the tool coordinate system. As shown in equation (18), the coordinate axis X represents the tool coordinate system on the cutting point coordinate system. ｔ and Y ｔ To obtain.

[0085]

[0086] Here, Mposture is a rotation matrix that represents the orientation of the tool coordinate system in the cutting point coordinate system, and is defined as shown in equation (19) using the tool's inclination angle θ and rotation angle φ.

[0087]

[0088] Next, a coordinate transformation is performed from the cutting coordinate system to the tool coordinate system. The tool tip point O in the cutting point coordinate system. ｔ Using this, the input coordinate value p in the tool coordinate system is shown in equation (20). ｔ You can obtain this.

[0089]

[0090] Here, M ｃ２ｔ This is the coordinate transformation matrix from the cutting point coordinate system to the tool coordinate system, and is defined as shown in equation (21).

[0091]

[0092] Combining equations (16) and (20) above, we get equation (22) as follows: the interference point group p in the world coordinate system ｗ From there, input coordinate p to the SDF in the tool coordinate system ｔ You can obtain this.

[0093]

[0094] Next, the interference point p in the obtained tool coordinate system. ｔ As shown in Figures 23 and 24, the norm of the x and y components is X ｔ To the axis, the z component is Y ｔ The image is projected onto the axis. This projection makes it possible to determine interference using a two-dimensional SDF, as shown in Figure 25.

[0095] [Implementation of Interference Detection Processing using GPGPU] This section describes the implementation of interference detection using General-Purpose computing on Graphics Processing Units (GPGPU). First, it is necessary to transfer the data required for general-purpose computing from the CPU to the video memory (VRAM) on the GPU. In interference detection processing for irregularly shaped tools, data such as interference point cloud, PNF data, tool shape data, and an empty interference detection result array are required, and each is transferred to VRAM as a buffer object of the appropriate data type. The interference point cloud stores each coordinate value in the order of (x, y, z) in a float-type array. The PNF data consists of the coordinates P of the cutting point, the normal vector n, and the tool feed direction vector F, and each is stored in a float-type array. The tool shape data is the bottom diameter d according to the tool shape data format. ｂ The data consists of an array of arc radii r, an array of tangent angles ψ, and an array of tool positions (θ, φ), which are stored in float type and float type arrays, respectively. To determine whether or not interference occurs for all combinations of cutting points and tool positions, the array length of the interference determination result data is the product of the number of cutting points and the number of tool positions. After data transfer, the general-purpose calculation is executed on the GPU by specifying the number of parallel executions.

[0096] As shown in Figure 26, each calculation thread is placed on a Workgroup grid, which is a three-dimensional array of threads called Workgroup. By specifying the size of each three-dimensional array according to the size of the data to be transferred, the same processing can be executed in parallel for different data.

[0097] [Processing Simulation and Processing Experiment] Below, we present the results of evaluating the tool path generation method for irregularly shaped tools based on C-Space according to this embodiment, from the viewpoint of processing quality and computation time, through processing simulation and processing experiments.

[0098] For the case study, we selected the "PolyBall" composite R-shaped irregular tool manufactured by OSG Corporation. As shown in Figure 27, this tool has a large radius at the cutting edge, making it suitable for machining. Ｌ And, the radius R is smallＳ This is a throwaway tool with a complex shape in which alternating elements are arranged. Due to its extremely complex shape, CAM operation is difficult. Radius R Ｌ The tool diameter is designed to be very large relative to the tool diameter, and in the PolyBall selected this time, the R is for a tool diameter of φ12 [mm]. Ｌ = 24 [mm], R Ｓ = 1.2 [mm].

[0099] The shape to be machined was a smoothly curving groove shape with a radius of R24, as shown in Figure 28(a). This shape ideally results in zero cusp height for a PolyBall with a cutting edge of R24. The tool path was set to a down-cut across the entire machined surface, as indicated by the arrow in Figure 28(b). Other machining conditions are shown in Figure 29.

[0100] The calculation conditions for C-Space are shown in Figure 30. In this case study, as a machining strategy for PolyBall, the following four conditions were set to attempt to generate tool paths: (1) No interference (2) Always an appropriate cutting edge radius Ｌ (3) Down-cutting across the entire area (4) Maximum cutting speed at each cutting point

[0101] As shown in Figure 30, the number of interference calculation trials across the entire machined surface reached 48,269,880,000, but as a result of parallel computing using GPGPU, the calculation could be completed in a sufficiently practical time of 8.5 [s]. Figure 31 shows the C-Space calculated in the center of the workpiece. The red area with a large inclination angle θ is calculated as the interference region, indicating that interference occurs when the tool is tilted. Also, PolyBall is the radius used in machining. Ｌ (R24) and inappropriate R Ｓ Because the cutting edge portions of (R1.2) are arranged alternately, the R on C-Space Ｓ The region appears as stripes. Interference region and R Ｓ By describing the region in C-Space, the free region was classified into stripes. By selecting one point within the free region, interference was eliminated, and the cutting edge portion R was determined. ＬThis allows us to obtain a tool position that contacts the machined surface. Here, we selected the tool position in the free region where the inclination angle θ is largest and the rotation angle φ is closest to 3π / 2. φ = 3π / 2 corresponds to a tool position that minimizes cusp height because it is perpendicular to the feed direction.

[0102] Figure 32 shows the tool path obtained by calculating the C-Space for all cutting points on the machined surface. While the actual cutting points are more densely spaced, Figure 32 only shows some of the data. It can be seen that the tool axis vector T is significantly inclined relative to the machined surface, as the tool orientation that maximizes the cutting speed is selected for each cutting point.

[0103] The advantages of the method according to this embodiment will be compared with commercially available CAM software from the perspectives of ease of use and machining quality. First, the advantages from the perspective of ease of use will be described. As an example, with the commercially available CAM software Mastercam, as of 2024, it is possible to handle tools with complex shapes such as PolyBall if the operator can directly input the inclination angle relative to the normal vector of the machining surface. In order to correctly input the normal vector, the operator needs to be familiar with the shape of the tool and plan how to incline the tool relative to the machining surface. Currently, it is not easy to handle irregularly shaped tools with complex shapes. On the other hand, in the tool path generation method according to this embodiment, the tool posture is automatically determined based on the tool shape data format and C-Space. The operator can automatically obtain a tool path based on the machining strategy without having to be aware of the details of the tool such as its shape.

[0104] Next, let's discuss the advantages from the perspective of machining quality. As mentioned earlier, commercially available CAM software determines the tool orientation of a non-standard tool by specifying a constant inclination angle relative to the normal vector of the machined surface. In other words, it is not possible to generate a tool path that changes the tool orientation at each cutting point when machining with a non-standard tool. In machining groove shapes like the one in this case study, if the tool is tilted too much, the workpiece and the shank will interfere. To avoid interference across the entire machined surface, it is necessary to raise the tool orientation as shown in Figure 33(A). At some cutting points, even if there is room to use the outer circumference of the tool which allows for a faster cutting speed, it is difficult to provide such a tool orientation.

[0105] On the other hand, in the tool path generation method according to this embodiment, the most inclined tool position that maximizes the cutting speed is determined based on the C-Space of each cutting point. As a result, as shown in Figure 33(B), it is possible to determine a deeply inclined tool position that maximizes the cutting speed for each cutting point. By using C-Space, it is possible to generate a tool path with a higher degree of freedom in which the tool position is controlled for each cutting point.

[0106] Figure 34 shows a machining simulation using VERICUT. It was confirmed that the tool avoided interference and performed as expected. Figure 35 shows the analysis results of over-cutting and under-cutting. As a result, no over-cutting or under-cutting exceeding 1 [μm] was observed. The simulation confirmed that tool interference was avoided and that the tool was correctly positioned according to the machining strategy.

[0107] Figure 36 shows a photograph of the finished surface after machining and the results of the surface roughness measurement. A Mitutoyo SURFTEST SV-2100 stylus-type surface roughness measuring instrument was used. The cutting speed was at its maximum and the cutting edge radius was R. ＬAs a result of machining with a tool position that made contact with the material, a glossy and smooth appearance was obtained. The surface roughness in the pick-feed direction was Rz 6.0 μm and Ra 1.1 μm. These values ​​can be said to be good values ​​for cutting. For example, in the case of finishing turbine blades where a strict surface roughness is required, a surface roughness of Ra 3 μm is required, and the machining results obtained this time meet this high standard. From the above results, it was confirmed that it is possible to generate a strategic tool path at high speed using the method according to this embodiment for machining PolyBall with a complex shape.

[0108] As described above, the tool path generation method based on C-Space was extended to map cutting edge radius information to C-Space in order to apply it to 5-axis controlled machining using irregularly shaped tools. Furthermore, irregularly shaped tools defined based on the tool shape data format described in this embodiment were represented in SDF format, which can return the distance from the tool surface. By comparing the interference point cloud obtained by discretizing the machined surface with the SDF, the speed of interference detection for a large number of points was increased. Finally, in order to confirm the usefulness of the method according to this embodiment, machining simulations and machining experiments were conducted and the following results were obtained. (1) By mapping cutting edge radius information to C-Space, it became possible to generate tool paths that always utilize the appropriate cutting edge portion in 5-axis controlled machining using irregularly shaped tools, and it was confirmed that strategic tool path generation is possible that allows the selection of the optimal tool posture at each cutting point. (2) By representing the tool shape in SDF format based on the tool shape data format according to this embodiment, a high-speed interference detection method using GPGPU was described, and it was confirmed that interference detection for a large number of points can be performed in a practically acceptable time.

[0109] [Strategic Toolpath Generation Based on C-Space] As described above, the toolpath generation method based on a configuration space (C-Space) that represents the relationship between tool orientation and interference at each cutting point has been extended to apply to machining with irregularly shaped tools by adding information on the cutting edge portion that indicates whether it is suitable for machining. For complex-shaped PolyBalls, we have demonstrated a toolpath generation method that requires determining the tool orientation at each cutting point, which cannot be handled by commercially available CAM software.

[0110] The following describes a method for generating tool paths that reflect machining strategies using irregularly shaped tools. By applying the artificial potential method, which is used in robot manipulator motion planning, to path generation, we describe a tool path generation method that reflects a machining strategy of machining with a safe tool position away from interference surfaces and with a cutting edge suitable for machining. As a case study, we show the results of machining an overhanging pocket shape using a barrel tool and a lens tool.

[0111] [Application of Artificial Potential Method to Irregularly Shaped Tools] The following describes the application of the artificial potential method to the C-Space of an irregularly shaped tool. As described above, the C-Space of the irregularly shaped tool in this embodiment represents whether the cutting edge portion is suitable for machining or unsuitable. By using this information, a potential field is formed that not only avoids tool interference but also allows for the selection of a cutting edge portion suitable for machining. In this section, a tool path generation method using the artificial potential method according to this embodiment is shown, using machining with a barrel-lens composite tool as shown in Figure 37 as an example.

[0112] First, as shown in Figure 38(A), the C-Space at each cutting point is discretized, and the list of tool position points T is created. Ａｌｌ = {(θ) ｉ ､φ ｉ，ｊ )|i=0,1,...,N θ ,j=0,1,...,N φｉ Generates} -1}. T Ａｌｌ These are classified into one of the following four types: (1) Interference region T Ｉｎｔｅｒｆｅｒｅｎｃｅ (2) Boundary T of the interference region Ｂｏｕｎｄａｒｙ (3) Tool position T corresponding to an inappropriate cutting edge areaＩｎａｐｐｒｏｐｒｉａｔｅ (4) Tool position T corresponding to the appropriate cutting edge area Ａｐｐｒｏｐｒｉａｔｅ Here is the boundary T of the interference region. Ｂｏｕｎｄａｒｙ The determination of whether it is an interference region is made by the tool position point (θ) determined to be an interference region, as shown in Figure 38(B). ｎ ､φ ｎ，ｍ )'s four neighboring points (θ ｎ－１ ､φ ｎ－１ ,m), (θ ｎ＋１ , φn+1, m), (θ ｎ ､φ ｎ，ｍ－１ ), (θ ｎ ､φ ｎ，ｍ＋１ ) If any of them is in the free area T Ｆｒｅｅ = T Ｉｎａｐｐｒｏｐｒｉａｔｅ ∪T Ａｐｐｒｏｐｒｉａｔｅ This is the case where it belongs to [a certain category].

[0113] Next, we introduce the concept of distance within a two-dimensional C-space. The distance d between two points {θ, φ} and {θ', φ'} on the C-space is calculated from the following equation (23), as shown in Figure 39.

[0114]

[0115] The artificial potential is designed to decay with respect to distance d. In this embodiment, the function F(d) for calculating the artificial potential from the distance d in C-Space is given by a Gaussian distribution that has a smooth peak shape as shown in Figure 40, according to the following equation (24).

[0116]

[0117] Here, σ is the standard deviation of the Gaussian distribution and is a parameter that determines the distance over which the potential decays. The Gaussian distribution is suitable for creating artificial potential fields because its decay design is easy and its shape is smooth.

[0118] Next, the potential is calculated for all free regions on the discretized C-Space as shown in Figure 41. For a certain tool orientation (θ, φ) ∈ TFree, the lists of distances dBoundary and dInappropriate to TBoundary and TInappropriate are obtained by equations (25) and (26), respectively.

[0119]

[0120]

[0121] Here, N represents the number of boundary points in the interference region, and M represents the number of tool positions corresponding to inappropriate cutting edge portions. Using this list of distances, the potential is calculated using a Gaussian distribution. Here, the boundaries of the interference region have a large weight w Ｂｏｕｎｄａｒｙ A small weight wInappropriate is assigned to each inappropriate cutting edge portion. The potential U(θ,φ) at a point (θ,φ) in a certain free region can be obtained by the following equation (27).

[0122]

[0123] After calculating the potential for all free regions on the C-Space, the artificial potential field is normalized to the range of 0 to 1 as shown in equation (28).

[0124]

[0125] The potential in the interference region is set to 1, as shown in equation (29).

[0126]

[0127] Following the above procedure, an artificial potential field is formed as shown in the color map of Figure 42. Minimum value U ｍｉｎ By using a tool position with this configuration for machining, the safest tool path, furthest from the interference surface, can be obtained. Figure 43 is a diagram in which the artificial potential field shown in Figure 42 is arranged in three-dimensional space along the tool feed direction, and the yellow broken line represents the minimum value U ｍｉｎ This shows a tool position with a potential field. A problem is that this artificial potential field is formed independently at each cutting point, causing the tool position to change abruptly, as shown in Figure 43.

[0128] To solve this problem, we introduce a repulsive force from other artificial potential fields belonging to the same toolpath. For a potential U(θ, φ) at a certain cutting point, the potential U at another cutting point belonging to the same toolpath is... ｋFrom (θ, φ), we consider that a repulsive force is received corresponding to the distance D between the cutting points. Figure 44 shows an example of the distance D between cutting points belonging to the same tool path. First, the cutting point P of interest and a list of cutting points belonging to the same tool path {P ０ , P １ , ..., P Ｋ－１ The list D of distances to} is calculated as shown in equation (30).

[0129]

[0130] Here, K represents the number of cutting points belonging to the same tool path. Using this list of distances D, the potential U(θ) at the cutting point P obtained in equation (27) is used. ｉ ､φ ｉ，ｊ ) is corrected using the following equation (31).

[0131]

[0132] Here, lol Ｏ This indicates the repulsive force weights corresponding to other artificial potential fields belonging to the same tool path. Finally, the artificial potential field is normalized again to the range of 0 to 1 by equation (28). The modified artificial potential field is shown in Figure 45.

[0133] This modification reflects the repulsive forces from interference surfaces at future and past cutting points in the artificial potential field. As the tool approaches an interference surface, a tool position is selected that avoids anticipated interference in the future, resulting in the continuity of the tool position, as shown in Figure 46. Conversely, as the tool moves away from an interference surface, it gradually releases the interference avoidance actions experienced in the past.

[0134] From the artificial potential fields U(θ,φ) obtained as described above, the minimum value U ｍｉｎ By selecting a tool position with the appropriate characteristics, it is possible to avoid interference, machine at a cutting edge suitable for machining, and generate a tool path that also considers the continuity of the tool position.

[0135] [Configuration of the machining center] Figure 47 shows an example of the configuration of the machining center 1 according to this embodiment. The machining center 1 is, for example, a 5-axis controlled machining center. The machining center 1 comprises a control unit 2, a tool path generation unit 3, a machining unit 4, an operation reception unit 5, a display unit 6, and a storage unit 7.

[0136] The control unit 2 performs various controls on the processing machine 1. The control unit 2 controls the processing unit 4. For example, the control unit 2 controls the processing unit 4 based on a tool tip point control function. The control unit 2 also includes a GPU (Graphics Processing Unit).

[0137] The control unit 2 includes a tool path generation unit 3. The tool path generation unit 3 includes a tool shape information acquisition unit 30, a machining surface shape information acquisition unit 31, a cutting point information generation unit 32, a command point information generation unit 33, a cutting point information acquisition unit 34, a command point information acquisition unit 35, a machining strategy information acquisition unit 36, a configuration space generation unit 37, an interference determination unit 38, a region classification unit 39, a potential generation unit 310, a path generation unit 311, a potential correction unit 312, and an output unit 313. Each of these functional units is realized, for example, by the GPU reading a program from ROM (Read Only Memory) and loading it into RAM (Random Access Memory), and then executing processing according to that program. The ROM and RAM are included in the storage unit 7.

[0138] The tool shape information acquisition unit 30 acquires tool shape information. The tool shape information includes information indicating the shape of the tool. For example, the tool shape information includes the tool name, cutting edge radius of 1 or more, tangent angle of the cutting edge, and base diameter. The tool shape information also includes information indicating whether each part of the tool is suitable for machining. This information is referred to as part information.

[0139] The machined surface shape information acquisition unit 31 acquires machined surface shape information. Machined surface shape information is information that indicates the shape of the machined surface. As an example, the machined surface shape information is represented by a NURBS curved surface.

[0140] The cutting point information generation unit 32 generates cutting point information based on the machined surface shape information. The cutting point information is information indicating a cutting point. Note that the cutting point is just one example of a machined point.

[0141] The command point information generation unit 33 generates command point information. Command point information is information that indicates the position of the command point in a coordinate system based on the cutting point. The command point is the reference point for tool control and is generated based on tool shape information.

[0142] The cutting point information acquisition unit 34 acquires the cutting point information generated by the cutting point information generation unit 32.

[0143] The command point information acquisition unit 35 acquires the command point information generated by the command point information generation unit 33.

[0144] The machining strategy information acquisition unit 36 ​​acquires machining strategy information. Machining strategy information is information that indicates the machining control strategy. In this embodiment, the machining strategy information indicates the machining control strategy based on at least one of the tool's orientation and the tool's part.

[0145] The configuration space generation unit 37 generates a configuration space for each cutting point based on tool shape information and command point information. The configuration space is a parameter space that indicates the orientation of the tool. The configuration space is, as an example, the C-Space described above.

[0146] The interference determination unit 38 determines whether or not interference occurs between the tool and the workpiece surface.

[0147] The region classification unit 39 classifies the regions included in the coordination space.

[0148] The potential generation unit 310 generates a potential in the coordination space based on machining strategy information. The potential generation unit 310 generates a potential in the coordination space for each cutting point. In the following description, the potential in the coordination space may be simply referred to as "potential".

[0149] The path generation unit 311 generates a tool path based on the machining surface shape information and potential.

[0150] The potential correction unit 312 corrects the potential based on the potential of a cutting point of interest that is different from the cutting point of interest among the cutting points belonging to the tool path.

[0151] The output unit 313 outputs the tool path generated by the path generation unit 311 to the machining unit 4.

[0152] The machining unit 4 is controlled by the control unit 2 to perform machining. The machining unit 4 is controlled by the control unit 2 to perform machining based on the tool path generated by the tool path generation unit 3.

[0153] The operation reception unit 5 receives various operations from the user. The operation reception unit 5 includes, for example, a touch panel, operation buttons, a mouse, or a keyboard.

[0154] The display unit 6 displays various types of information. The display unit 6 includes, for example, a liquid crystal display or an organic electroluminescent (EL) display.

[0155] The memory unit 7 stores various types of information. The memory unit 7 is configured using, for example, a memory device such as a semiconductor memory device.

[0156] The machining strategy information may also be stored in the storage unit 7. In that case, the machining strategy information acquisition unit 36 ​​may be omitted from the configuration of the tool path generation unit 3.

[0157] Furthermore, at least one of the cutting point information generation unit 32 and the command point information generation unit 33 may be omitted from the configuration of the tool path generation unit 3 and provided in an external device (such as a server) separate from the machining center 1.

[0158] The tool path generation unit 3 is described as being provided in the control unit 2 of the machining center 1 as an example, but it is not limited to this. The tool path generation unit 3 may be provided as a separate personal computer (PC) or server, or other computer. In that case, the tool path generation unit 3 outputs the generated tool path to the machining center 1. The tool path generation unit 3 communicates with the machining center 1 via wireless or wired communication.

[0159] [Tool Path Generation Process] Figure 48 shows an example of the tool path generation process by the tool path generation unit 3 according to this embodiment. In this embodiment, as an example, the tool is a non-standard shaped tool. That is, the tool is a tool having either multiple arcs or two straight lines. The tool may be a tool other than a non-standard shaped tool, such as a ball end mill.

[0160] Step S210: The tool shape information acquisition unit 30 acquires tool shape information. Tool shape information, such as the tool name, cutting edge radius of 1 or more, tangent angle of the cutting edge, bottom diameter, and part information, is input by the user via the operation reception unit 5. The tool shape information acquisition unit 30 generates tool shape data based on the acquired tool shape information. The tool shape information acquisition unit 30 generates tool shape data from tool shape information based, for example, the procedure for generating tool shape data described above (Figure 6). In the following processes, the tool shape information is used as tool shape data.

[0161] Alternatively, one or more tool shape information may be pre-stored in the storage unit 7, and the tool shape information acquisition unit 30 may acquire tool shape information selected by the user from among the one or more tool shape information.

[0162] Step S220: The tool path generation unit 3 starts the process of generating a tool path for each cutting point. The cutting points are indicated by cutting point information. The cutting point information is generated by the cutting point information generation unit 32 based on the machined surface shape information and acquired by the cutting point information acquisition unit 34.

[0163] Step S230: The configuration space generation unit 37 generates a configuration space for each cutting point based on the tool shape information and the command point information. Here, the command point information is generated by the command point information generation unit 33 and acquired by the command point information acquisition unit 35. As an example, the command point information generation unit 33 generates command point information based on the process described in the command point calculation flow (Figure 9) above.

[0164] As described above, the configuration space generation unit 37 generates a configuration space by discretizing a two-dimensional configuration space (C-Space) with an arbitrary resolution (Figure 15). In the generated configuration space, the orientation of the tool relative to the cutting point is indicated by the inclination angle θ and the rotation angle φ, based on the tool shape information and the command point information.

[0165] Step S240: The interference determination unit 38 determines whether or not interference occurs between the tool and the machined surface. As an example, the interference determination unit 38 determines whether or not interference occurs by representing the tool as an SDF and the machined surface as a point cloud (Figures 21 to 24). For speed improvement, it is preferable that the interference determination process by the interference determination unit 38 uses parallel computing by a GPU.

[0166] The interference determination unit 38 may determine whether interference occurs by representing the tool as a point cloud and the machined surface as an SDF. Therefore, the interference determination unit 38 determines whether interference occurs between the tool and the machined surface by representing either the tool or the machined surface as an SDF. However, since representing the diverse shapes of the machined surface as an SDF is computationally intensive, it is preferable to represent the tool as an SDF and the machined surface as a point cloud, as in this embodiment. The interference determination unit 38 may also determine whether interference occurs by representing both the tool and the machined surface as point clouds.

[0167] The domain classification unit 39 classifies the domains included in the configuration space. The classification result by the domain classification unit 39 is, for example, one of the following: interference domain, appropriate domain, inappropriate domain, and boundary domain. An interference domain is a domain where interference occurs between the tool and the workpiece surface. The domain classification unit 39 determines the interference domain based on tool shape information, workpiece surface shape information, and command point information. An appropriate domain is a domain corresponding to a part of the tool that is suitable for machining. An inappropriate domain is a domain corresponding to a part of the tool that is unsuitable for machining. The domain classification unit 39 determines the appropriate domain and the inappropriate domain based on the part information included in the tool shape information. Therefore, the domain classification unit 39 classifies the domains included in the configuration space based on whether each part of the tool is suitable for machining or not, based on the tool shape information. A boundary domain is a domain within the interference domain that is adjacent to a domain other than the interference domain (appropriate domain or inappropriate domain).

[0168] Step S260: The potential generation unit 310 generates a potential in the configuration space based on the processing strategy information. In this embodiment, as an example, a processing strategy is used that avoids interference regions (and boundary regions) and inappropriate regions. The potential generation unit 310 generates a potential in the configuration space using the classification result from the region classification unit 39 as processing strategy information.

[0169] The potential generation unit 310 generates a potential represented by equation (27) as an example. Therefore, the potential includes the sum of a second repulsive potential representing the repulsion from the interference region and a first repulsive potential representing the repulsion from the inappropriate region. This sum is a weighted sum. As described above, the weight for the second repulsive potential representing the repulsion from the interference region is greater than the weight for the first repulsive potential representing the repulsion from the inappropriate region. This is because, in this embodiment, the machining strategy includes a safety-first machining strategy that prioritizes avoiding interference between the tool and the machined surface.

[0170] Furthermore, the weight for the second repulsive potential may be smaller than the weight for the first repulsive potential. The weights for the second repulsive potential and the first repulsive potential may be equal. In addition, the function representing the potential may be a function of a shape other than a Gaussian distribution as shown in equation (24).

[0171] Furthermore, the potential may include an attractive potential that represents the attractive force from an appropriate region. For example, the attractive potential may be added to the potential shown by equation (27) with a predetermined weight. As another example, in the potential shown by equation (27), the attractive potential may be included with a predetermined weight instead of the first repulsive potential that represents the repulsive force from an inappropriate region.

[0172] Furthermore, the potential only needs to include one of the following: a second repulsive potential representing the repulsive force from the interference region, an attractive potential representing the attractive force from the appropriate region, and a first repulsive potential representing the repulsive force from the inappropriate region. For example, the potential does not need to include the second repulsive potential representing the repulsive force from the interference region. In that case, the potential may be a weighted sum of the attractive potential representing the attractive force from the appropriate region and the first repulsive potential representing the repulsive force from the inappropriate region.

[0173] Step S270: The path generation unit 311 generates a tool path based on the minimum potential value. The path generation unit 311 determines the position in the configuration space where the potential is at its minimum for the cutting point of interest. The path generation unit 311 determines the orientation indicated by that position as the orientation of the tool.

[0174] Step S280: The tool path generation unit 3 completes the process of generating a tool path for each cutting point.

[0175] Step S290: The output unit 313 stores the tool path generated by the path generation unit 311 as CL data in the storage unit 7. The CL data stored in the storage unit 7 is read by the control unit 2 and used to control the machining unit 4. With this, the tool path generation unit 3 completes the tool path generation process.

[0176] The path generation unit 311 may generate a tool path based on the potential modified by the potential generation unit 310. As described above, the path generation unit 311 modifies the potential based on the potential of cutting points on the tool path that are different from the cutting point of interest. The potential modification unit 312 modifies the potential based on a third repulsive potential that indicates the repulsive force corresponding to the distance between the cutting points on the tool path and the cutting point of interest. The potential modification unit 312 modifies the potential based on the third repulsive potential, for example, based on equation (31). The weight of the third repulsive potential can be adjusted to a desired magnitude by the user. For example, the path generation unit 311 generates a tool path based on the modified potential after the processing in step S280.

[0177] In this embodiment, an example has been described in which, in modifying the potential, all cutting points belonging to the tool path that are different from the cutting point of interest are selected, including cutting points that have been machined in the past of the cutting point of interest and cutting points that will be machined in the future of the cutting point of interest. However, this is not the only example. Not all cutting points belonging to the tool path that are different from the cutting point of interest are selected. For example, only cutting points that have been machined in the past of the cutting point of interest are selected, or only cutting points that will be machined in the future of the cutting point of interest are selected. In modifying the potential, it is sufficient that at least one cutting point belonging to the tool path that is different from the cutting point of interest is selected.

[0178] In this embodiment, an example has been described in which the classification result by the area classification unit 39 is used as machining strategy information, but the embodiment is not limited to this. The machining strategy information may indicate a machining control strategy based on the tool's orientation. The potential generation unit 310 may also generate a potential based on the sum of potentials based on each of the multiple machining strategy information. The potential can be expressed as a linear sum of multiple potentials. Therefore, according to the tool path generation unit 3 of this embodiment, when it is desired to generate a tool path by combining multiple machining strategy information, it is easy to represent each of the multiple machining strategy information as a potential and express the multiple machining strategy information as a linear sum of multiple potentials.

[0179] The following describes an example where the potential is generated based on the sum of potentials derived from machining strategy information, which indicates a machining control strategy based on the tool's orientation, and machining strategy information, which avoids interference regions.

[0180] To efficiently generate interference-free tool paths in 5-axis machining, three types of potential fields were designed. First, there is an interference avoidance potential to prevent tool interference. Outside the interference region, a potential value is set according to the proximity to the interference region boundary, as shown in equation (32), and within the interference region, a value of +∞ is assigned to ensure reliable interference avoidance.

[0181]

[0182] Secondly, there is a 90° tilt avoidance potential to prevent excessive tilting of the tool. As shown in equation (33), it suppresses the tilt angle θ from approaching π / 2 [rad].

[0183]

[0184] Thirdly, a forward / backward tilt suppression potential that suppresses excessive tilting in the tool feed direction and its reverse direction is defined as shown in equation (34). By inducing such a posture, a reduction in the amount of change in tool posture can be expected.

[0185]

[0186] The three potentials have a scaling constant k. ｉｎｔ , k ｔｉｌｅ９０ , k ｆ．ｂ． It is synthesized as shown in equation (35) using the formula.

[0187]

[0188] By adjusting these constants, it becomes possible to control the priority of each potential field, i.e., the emphasis on each processing strategy. Figures 49(A) to 49(c) show the distribution of each individual potential field on a two-dimensional C-space, and Figure 49(d) shows the result of their combination.

[0189] Note that one or more of the three potentials included on the right-hand side of equation (35) may be omitted. In other words, it is sufficient that one or more of the processing strategies considered in the potential shown in equation (35) are considered.

[0190] [Processing Simulation and Processing Experiment] Processing experiments were conducted using irregularly shaped tools with tool paths generated by the artificial potential method based on the safety-first processing strategy according to this embodiment. Overhanging pocket shapes requiring interference avoidance were processed using barrel tools and lens tools.

[0191] The following two irregularly shaped tools were used for machining: (1) Barrel tool: OSG PFB100R150-BR-ST (throwaway tool) (2) Lens tool: EMUGE FRANKEN 3544L.10020A (solid tool) Both were used mounted on MS Corporation's HSK shank shrink-fit holder "Slimline". The appearance of the barrel tool is shown in Figure 50(A). The appearance of the lens tool is shown in Figure 50(B).

[0192] The shape of the workpiece is an overhanging pocket shape, as shown in Figure 51. Although this shape is overhanging, it can be machined using the tool selected for this project.

[0193] The machine tool used for machining was a DMG MORI NMV 5000 DCG. Other machining conditions are shown in Figure 52.

[0194] Tool paths were generated using C-Space under the calculation conditions shown in Figure 53. First, a tool path for finishing the wall surface with a barrel cutting edge was generated. The NURBS surface of the CAD model corresponding to the wall surface was divided equally using the u and v parameters so that the cusp height was less than 10 [μm], which is the target cusp height, to generate cutting points for contour machining. Figures 54 to 57 show the tool paths generated for wall surface machining with a barrel cutting edge. Figure 54 shows the artificial potential field calculated at one cutting point. Figure 55 shows the artificial potential field in one tool path arranged in the tool feed direction. Figure 56 shows the model of the tool and the shape of the machined surface. Figure 57 shows a part of the generated tool axis vector. It can be seen that a continuous tool orientation is obtained because the generated artificial potential field takes into account the potential value at another cutting point belonging to the same tool path.

[0195] Next, a tool path was generated for finishing the bottom surface with a lens blade. The CAD model corresponding to the bottom surface was divided equally using the u and v parameters so that the target cusp height was less than 10 [μm], and cutting points for scanline machining were generated. Figures 58 to 61 show the tool paths generated for bottom surface machining with a lens blade. Figure 58 shows the artificial potential field calculated at one cutting point. Figure 59 shows the artificial potential field in one tool path arranged in the tool feed direction. Figure 60 shows the model of the tool and the shape of the machined surface. Figure 61 shows a part of the generated tool axis vector. Similar to the barrel blade, the tool position with the minimum potential value was selected.

[0196] Here, since pocket machining is performed with the workpiece surrounded on all four sides by the workpiece surface, it is necessary to consider the entry path (lead-in) and retraction path (lead-out). If the tool enters in a straight line, the cutting area increases rapidly, causing a sudden change in cutting resistance and an instantaneous increase in tool deflection. To avoid this problem, it is common to start machining gradually with an arc-shaped or ramp-shaped entry path. Similarly, when retracting, machining is also ended gradually with an arc-shaped or ramp-shaped retraction path. In this case, an arc-shaped entry path and retraction path were generated. Figure 62 shows the tool path generated for wall machining with a barrel cutting edge. As shown in Figure 62(A), the tool enters in an arc shape, and as shown in Figure 62(C), it retracts in an arc shape.

[0197] Furthermore, in the scanning line machining path for finishing the bottom surface with a lens blade, there is no space for the tool to enter or retract in an arc shape. Therefore, a tool path was generated in which the tool enters linearly in the direction of the tool axis vector as shown in Figure 63(a) and retracts as shown in Figure 63(c). Since entry in the direction of the tool axis is disadvantageous for the lens tool due to the large cutting resistance, the tool feed rate was reduced to 50% in the entry path.

[0198] Machining simulations using VERICUT confirmed that the tool could machine the workpiece without interfering with it. Figure 64 shows the results of the analysis of the amount of material removed, and no problematic over-machining was observed. Figure 65 shows the results of the analysis of the amount of material left unmachined. In both the lens tool machined on the bottom surface and the barrel tool machined on the side surface, blue appeared, indicating the target cusp height of 10 [μm], confirming that the intended tool position was accurately achieved.

[0199] Figures 66 and 67 show the machined shape. In the machining experiment, as in the machining simulation, the pocket shape could be machined without interference until the end. The tool path generation method using the artificial potential method according to this embodiment is characterized by the ability to maintain the continuity of the tool position by setting repulsive forces corresponding to interference surfaces in the future and past. As a result, as shown in Figure 66, regular cutting marks were observed on the obtained machined surface, and a high-quality finished surface was obtained. As shown in Figure 67, when the workpiece was cut and the surface roughness was measured, the surface roughness in the pick feed direction by the lens blade and barrel blade was Rz 10 [μm], respectively. This value matches the target value of the cusp height, confirming that the cutting tool was accurately positioned by the method according to this embodiment. The safety-first machining strategy shown in this embodiment can be applied to machining using any irregularly shaped tool.

[0200] As described above, the tool path generation device according to this embodiment (tool path generation unit 3 in this embodiment) comprises a machining surface shape information acquisition unit 31, a potential generation unit 310, and a path generation unit 311. The machining surface shape information acquisition unit 31 acquires machining surface shape information indicating the shape of the machining surface. The potential generation unit 310 generates a potential on the configuration space (C-Space), which is a parameter space indicating the orientation of the tool, based on machining strategy information indicating a machining control strategy based on the orientation of the tool and at least one of the parts of the tool. The path generation unit 311 generates a tool path based on the machining surface shape information and the potential.

[0201] With this configuration, the tool path generation device according to this embodiment can generate tool paths based on potentials generated based on machining strategy information, and therefore can generate tool paths that correspond to the machining control strategy.

[0202] As in this embodiment, the tool path generated based on potential by the tool path generation device according to this embodiment automatically obtains the tool position that maximizes the cutting speed and the optimal cutting edge contact point for each cutting point. In the conventional technology, the user had to manually input the tool position that maximizes the cutting speed.

[0203] In the tool path generation device according to this embodiment, the type of machining that can be performed can be calculated in advance by inputting the shape of the tool. In other words, it is possible to experiment with various tool shapes to see what kind of machining can be performed. Therefore, the tool path generation device tool according to this embodiment can also be used to allow the user to pre-select the shape of the tool.

[0204] On the other hand, for tool manufacturers, the tool path generation device according to this embodiment allows them to simulate and test what kind of machining is possible, which can be useful in designing the shape of the tool. In other words, the tool path generation device according to this embodiment is also suitably used as a design tool.

[0205] In this embodiment, an example has been described in which the interference region is the area where the tool and the workpiece come into contact, but it is not limited to this. The interference region may also be the area where the tool comes into contact with a jig or other tool, in addition to the workpiece.

[0206] While embodiments of the present invention have been described in detail above with reference to the drawings, the specific configuration is not limited to these embodiments, and design changes and the like are also included within the scope of the gist of the present invention. For example, a computer program for realizing the functions of each of the above-described devices may be recorded on a computer-readable recording medium, and the program recorded on this recording medium may be read by a computer system and executed. The term "computer system" as used herein may include hardware such as an operating system and peripheral devices.

[0207] Furthermore, "computer-readable recording media" refers to writable non-volatile memory such as flexible disks, magneto-optical disks, ROM, and flash memory, portable media such as DVDs (Digital Versatile Discs), and storage devices such as hard disks built into computer systems. In addition, "computer-readable recording media" also includes volatile memory (for example, DRAM (Dynamic Random Access Memory)) within computer systems that act as servers or clients when programs are transmitted via networks such as the Internet or communication lines such as telephone lines, which retains programs for a certain period of time.

[0208] Furthermore, the above program may be transmitted from a computer system that stores the program in a memory device or the like to another computer system via a transmission medium or by transmission waves within the transmission medium. Here, the "transmission medium" for transmitting the program refers to a medium that has the function of transmitting information, such as a network (communication network) such as the Internet or a communication line (communication line) such as a telephone line. Also, the above program may be for the purpose of realizing a part of the functions described above. Furthermore, it may be a so-called differential file (differential program) that can realize the above functions in combination with a program already recorded in the computer system.

[0209] 1... Machining machine, 2... Control unit, 3... Tool path generation unit, 4... Machining unit, 5... Operation reception unit, 6... Display unit, 7... Memory unit, 30... Tool shape information acquisition unit, 31... Machining surface shape information acquisition unit, 32... Cutting point information generation unit, 33... Command point information generation unit, 34... Cutting point information acquisition unit, 35... Command point information acquisition unit, 36... Machining strategy information acquisition unit, 37... Configuration space generation unit, 38... Interference determination unit, 39... Region classification unit, 310... Potential generation unit, 311... Path generation unit, 312... Potential correction unit, 313... Output unit

Claims

1. A tool path generation device comprising: a machined surface shape information acquisition unit that acquires machined surface shape information indicating the shape of a machined surface; a potential generation unit that generates a potential on a configuration space, which is a space of parameters indicating the orientation of a tool at a machining point, based on machining strategy information that indicates a machining control strategy based on the orientation of the tool and at least one of the parts of the tool; and a path generation unit that generates a tool path based on the machined surface shape information and the potential.

2. The tool path generation device according to claim 1, further comprising a region classification unit that classifies the regions included in the coordination space based on tool shape information including information indicating whether each part of the tool is suitable for machining, wherein the potential generation unit generates a potential in the coordination space using the classification result by the region classification unit as machining strategy information.

3. The tool path generation apparatus according to claim 2, wherein the classification result by the area classification unit includes an inappropriate area corresponding to a part of the tool that is unsuitable for machining, and the potential includes a first repulsive potential indicating a repulsive force from the inappropriate area.

4. The tool path generation apparatus according to claim 3, wherein the classification result by the region classification unit includes interference regions where interference occurs between the tool and the machined surface, and the potential includes the sum of a second repulsive potential indicating repulsion from the interference region and the first repulsive potential.

5. The tool path generation device according to claim 1, further comprising a potential correction unit that corrects the potential based on the potential of a machining point of interest that is different from the machining point of interest among the machining points belonging to the tool path, wherein the path generation unit generates a tool path based on the potential corrected by the potential correction unit.

6. The tool path generation device according to claim 5, wherein the potential correction unit corrects the potential based on a third repulsive potential that indicates a repulsive force corresponding to the distance between a machining point belonging to the tool path and a machining point of interest.

7. The tool path generation device according to claim 1, wherein the potential generation unit generates the potential based on the sum of the potentials based on each of the plurality of machining strategy information.

8. The tool path generation device according to claim 1, further comprising an interference determination unit that determines whether or not interference occurs between the tool and the machined surface by representing either the tool or the machined surface with a signed distance function.

9. The tool path generation device according to claim 1, wherein the tool is a tool having either a plurality of arcs or two straight lines.

10. A machining center equipped with a tool path generation device according to any one of claims 1 to 9.

11. A method for generating a tool path, comprising: a step of acquiring machined surface shape information that indicates the shape of a machined surface; a step of generating a potential in a configuration space, which is a space of parameters indicating the orientation of a tool, based on machining strategy information that indicates a machining control strategy based on the orientation of the tool and at least one of the parts of the tool; a step of generating a tool path based on the machined surface shape information and the potential; and a method for generating a tool path.

12. A program for causing a computer to perform the following steps: a machined surface shape information acquisition step for acquiring machined surface shape information indicating the shape of a machined surface; a potential generation step for generating a potential in a configuration space, which is a space of parameters indicating the orientation of a tool, based on machined strategy information indicating a machining control strategy based on the orientation of the tool and at least one of the parts of the tool; and a path generation step for generating a tool path based on the machined surface shape information and the potential.

Images