Gear grinding simulation method and device

Abstract

To provide gear grinding simulation method and device in gear grinding that grinds a work-piece by using a screw-shaped grindstone.SOLUTION: An intersection point between an object segment with a work-piece definition point, which is determined to be positioned in a grindstone definition point interval passage area that is represented by a grindstone definition point interval Se(i, tn) between adjacent two grindstone blade sectional points Pt(i, tn), Pt(i+1, tn) constituting a grindstone blade sectional point group at a time tn in a coordinate system based on a work-piece model Mw and grindstone definition point interval Se(i, tn+1) between adjacent two grindstone blade sectional points Pt(i, tn+1), Pt(i+1, tn+1) at a time tn+1 after Δt from the time tn, as one end and a surface constituting a grindstone definition point interval passage area is calculated, and by using a surface grinding model on the basis of a distance of the work-piece definition point before and after change with respect to each work-piece definition point, a grinding resistance in a mesh including the work-piece definition point after change is calculated on the basis of a grinding resistance parameter.SELECTED DRAWING: Figure 7

Description

[Technical field]

[0001] The present invention relates to a gear grinding simulation method and device. [Background technology]

[0002] Patent Document 1 describes a gear grinding method in which a workpiece is ground with a threaded grinding wheel to generate a gear tooth surface. The workpiece and the threaded grinding wheel are moved relative to each other while the workpiece and the threaded grinding wheel are also rotated, thereby grinding the tooth surface of a workpiece on which a gear tooth profile has been formed in advance by rough machining. In addition to finishing the tooth surface by grinding a certain amount of machining allowance, the gear grinding process can also modify the tooth profile direction and the tooth trace direction.

[0003] Patent Document 2 discloses a configuration for detecting grinding resistance in a grinding machine using a cylindrical grinding wheel, and Patent Document 3 discloses a configuration for performing machining in a gear cutting machine taking cutting resistance into consideration. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] JP 2015-123569 A [Patent Document 2] JP 2015-208812 A [Patent Document 3] JP 2020-069622 A Summary of the Invention [Problem to be solved by the invention]

[0005] In gear grinding using a threaded grinding wheel, waviness may occur on the tooth surface. One of the causes of the waviness is thought to be fluctuations in grinding resistance. However, in gear grinding using a threaded grinding wheel, the values ​​of parameters related to the grinding resistance change from moment to moment, so it cannot be considered the same as the grinding resistance in grinding using a cylindrical grinding wheel disclosed in Patent Document 2. In addition, the gear cutting disclosed in Patent Document 3 and the gear grinding have different machining mechanisms, so the knowledge about the gear cutting disclosed in Patent Document 3 cannot be applied to gear grinding using a threaded grinding wheel.

[0006] The present invention has been made in consideration of the above-mentioned problems, and aims to provide a gear grinding simulation method and device for simulating grinding resistance in gear grinding, which uses a threaded grinding wheel to grind a workpiece. [Means for solving the problem]

[0007] One aspect of the present invention is 1. A gear grinding simulation method for simulating a gear grinding process in which a workpiece is ground with a threaded grinding wheel to generate a gear, the method comprising the steps of: generating a grindstone blade cross-sectional point cloud that defines a cross-sectional shape of a convex blade of the threaded grindstone in an axial cross-section of the threaded grindstone; generating a grindstone model in which the convex blade of the threaded grindstone is three-dimensionally modeled by arranging the grindstone blade cross-sectional point cloud in an extension direction of the convex blade of the threaded grindstone; generating a workpiece model defined by a workpiece definition point cloud on a surface of the workpiece and a group of line segments each having one end at each point of the workpiece definition point cloud and extending in a radial direction of the workpiece; In a coordinate system based on the workpiece model, at time t n (n is an ordinal number), two adjacent grinding wheel blade cross-section points Pt(i,t n ),Pt(i+1,t n ) is the interval of the wheel definition point interval Se(i,t n ) and time t nAt time t, which is Δt after n+1 Two adjacent grinding wheel blade cross-section points Pt(i,t n+1 ),Pt(i+1,t n+1 ) is the interval of the wheel definition point interval Se(i,t n+1 ) and determine the wheel definition point section passing area represented by performing an inclusion check as to whether or not each workpiece definition point of the workpiece definition point group constituting the workpiece model is located within the grinding wheel definition point section passing area when viewed from the direction of a line segment having the workpiece definition point as one end; calculating an intersection between a target line segment having the workpiece definition point determined to be located inside in the inclusion check as one end and a surface constituting the grinding wheel definition point section passing area; The workpiece definition point located at one end of the target line segment is changed to the coordinates of the intersection point; Calculating a grinding force parameter for each of the workpiece definition points based on a distance between the workpiece definition point before the change and the workpiece definition point after the change, the grinding force parameter being used to calculate a grinding force in a surface grinding model; The gear grinding simulation method includes defining an area having a center at one of the workpiece definition points on the surface of the workpiece and a boundary connecting midpoints of adjacent workpiece definition points as a mesh, and calculating, using the surface grinding model, the grinding resistance in the mesh including the changed workpiece definition point among the plurality of meshes based on the grinding resistance parameters.

[0008] Another aspect of the present invention is a gear grinding simulation device that executes the gear grinding simulation method. Effect of the Invention

[0009] According to the above aspect, for each workpiece definition point, a grinding resistance parameter used for calculating the grinding resistance in the surface grinding model is calculated based on the distance between the workpiece definition point before the change and the workpiece definition point after the change, and the grinding resistance in a mesh including the changed workpiece definition point among a plurality of meshes defined on the surface of the workpiece is calculated based on the grinding resistance parameter using the surface grinding model. As a result, since the grinding resistance parameter reflects the state that changes from moment to moment in a gear grinding process in which a workpiece is ground using a threaded grinding wheel to generate a gear, the grinding resistance in the mesh can be calculated to calculate the grinding resistance with high accuracy during the gear grinding process. As a result, it becomes easy to analyze the cause of the tooth surface error caused by the grinding resistance and to determine the rigidity of each axis of the machine tool.

[0010] As described above, according to the above aspects, it is possible to provide a gear grinding simulation method and device that are capable of simulating fluctuations in grinding resistance in gear grinding, which uses a threaded grinding wheel to grind a workpiece to create a gear. [Brief description of the drawings]

[0011] [Figure 1] FIG. 2 is a diagram showing a gear grinding apparatus. [Diagram 2] FIG. 2 is a diagram showing the gear machining device, as viewed from the left side of FIG. 1. [Diagram 3] FIG. 2 is a functional block diagram of the gear grinding simulation device. [Figure 4] 4 is a flowchart showing processing by a calculation processing unit constituting the gear grinding simulation device, i.e., a gear grinding simulation method. [Diagram 5] 4 is a flowchart showing processing by a calculation processing unit constituting the gear grinding simulation device, i.e., a gear grinding simulation method. [Figure 6] 4 is a flowchart showing processing by a calculation processing unit constituting the gear grinding simulation device, i.e., a gear grinding simulation method. [Figure 7] 4 is a flowchart showing processing by a calculation processing unit constituting the gear grinding simulation device, i.e., a gear grinding simulation method. [Figure 8] FIG. 2 is a perspective view of one target tooth profile of a gear, which is a workpiece. [Figure 9] FIG. 11 is a diagram showing a group of target tooth profile cross-sectional points. [Figure 10] 1A is a diagram showing a cross-sectional point cloud of a grindstone blade, in which (a) shows a single-start thread, (b) shows a double-start thread, and (c) shows a triple-start thread. FIG. [Figure 11] FIG. 4 is a perspective view showing a contact state between a target tooth profile and a convex blade of a threaded grinding wheel. [Figure 12] 11A and 11B are diagrams illustrating a coordinate system for generating a grindstone model and division lengths of the grindstone model. [Figure 13] FIG. 1A shows a cross-sectional point cloud of the grinding wheel blade when the threaded grinding wheel has a single start thread, and FIG. 1B shows a model of the grinding wheel that forms a single start thread. [Figure 14] FIG. 1A shows a cross-sectional point cloud of the grinding wheel blade when the threaded grinding wheel has a double-thread, and FIG. 1B shows a model of the grinding wheel that forms a double-thread. [Figure 15] FIG. 1A shows a cross-sectional point cloud of the grinding wheel blade when the threaded grinding wheel has a triple-thread, and FIG. 1B shows a model of the grinding wheel that forms a triple-thread. [Figure 16] FIG. 2 is a diagram for explaining a coordinate system for generating a workpiece model. [Figure 17] FIG. [Figure 18] FIG. 18 is a workpiece model diagram shown in a coordinate system different from that of FIG. 17. [Figure 19] FIG. 2 is a diagram showing a workpiece model in a three-dimensional polar coordinate system (θ-Le-Zw). [Figure 20] 1 is a diagram showing a grindstone definition point section Se and a grindstone definition point section passing area At in a grindstone model in a three-dimensional orthogonal coordinate system (Xt-Yt-Zt) of the grindstone model. FIG. [Figure 21]1 is a diagram showing a grindstone definition point section passing area At and a rectangular inclusion area At' including the grindstone definition point section passing area At in a state in which the grindstone model is transformed into a two-dimensional polar coordinate system (θ-Zw) of the workpiece. FIG. [Figure 22] FIG. 2 is a diagram showing a state in which a workpiece model Mw, a grindstone definition point section passing area At, and a rectangular inclusion area At′ are arranged in a two-dimensional polar coordinate system (θ-Zw) of the workpiece. [Diagram 23] FIG. 13 is a diagram showing a state in which one of the line segments constituting a workpiece model Mw is included in a grindstone definition point section passing area At in a two-dimensional polar coordinate system (θ-Zw). [Figure 24] FIG. 13 is a diagram showing a state in which one of the line segments constituting the workpiece model Mw is not included in the grindstone definition point section passing area At in a two-dimensional polar coordinate system (θ-Zw). [Diagram 25] 1 is a diagram showing the intersections of line segments constituting a workpiece model Mw and a grindstone definition point section passing area At in a two-dimensional polar coordinate system (θ-Le). FIG. [Figure 26] 1 is a diagram showing the intersections between line segments constituting the workpiece model Mw and a grindstone definition point section passing area At in a three-dimensional orthogonal coordinate system (Xw'-Yw'-Zw) of the workpiece model Mw. FIG. [Figure 27] FIG. 13 is a diagram showing a state in which the workpiece definition points constituting the workpiece model Mw are changed to intersection points in a two-dimensional polar coordinate system (θ-Le). [Figure 28] 13 is a diagram showing a state in which the workpiece definition points constituting the workpiece model Mw are changed to intersection points in a three-dimensional orthogonal coordinate system (Xw'-Yw'-Zw) of the workpiece model Mw. FIG. [Figure 29] 1A to 1C are diagrams showing the state of a workpiece model Mw and a part of a grinding wheel model Mt during a gear grinding simulation. [Diagram 30] FIG. 13 is a diagram showing the final shape of the workpiece model Mw. [Diagram 31] FIG. 2 is a diagram for explaining an outline of a horizontal axis surface grinding model. [Diagram 32] FIG. 13 is a conceptual diagram illustrating a removal volume in a workpiece model. [Diagram 33]FIG. 4 is a conceptual diagram illustrating a principal force vector and a thrust force vector. [Diagram 34] (a) is a conceptual diagram illustrating the mesh area in a workpiece model, (b) is a partially enlarged view of (a), and (c) is a top view of (b). [Diagram 35] FIG. 2 is a conceptual diagram illustrating a conical abrasive grain model. [Diagram 36] 11 is a conceptual diagram illustrating a grinding resistance calculation position in a workpiece model. FIG. [Figure 37] FIG. 4A is a conceptual diagram illustrating a group of machining points for all tooth grooves in the first embodiment. [Figure 38] FIG. 4 is a conceptual diagram showing grinding resistance occurring in one tooth groove of a workpiece model Mw. [Figure 39] FIG. 13 is a conceptual diagram in which the grinding resistance of one tooth groove in a workpiece model Mw is arranged with phase shifts. [Diagram 40] FIG. 1 is a conceptual diagram showing the grinding resistance of all tooth grooves in a workpiece model Mw. [Diagram 41] FIG. 13 is a diagram for explaining an overview of another surface grinding model. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0012] (Embodiment 1) 1. Gear grinding equipment 1 The configuration of the gear grinding apparatus 1 will be described with reference to Figures 1 and 2. The gear grinding apparatus 1 grinds a workpiece W using a threaded grinding wheel T to generate a gear tooth profile on the workpiece W. In detail, the gear grinding apparatus 1 rotates the threaded grinding wheel T about the central axis of the threaded grinding wheel T, and while the workpiece W is rotated about the central axis of the workpiece W, moves the threaded grinding wheel T relatively in the central axial direction of the workpiece W to grind the gear tooth profile on the workpiece W.

[0013] Therefore, the gear grinding apparatus 1 is configured to enable relative movement between the workpiece W and the threaded grinding wheel T in each of the directions of three orthogonal axes. Furthermore, the gear grinding apparatus 1 is configured so that the workpiece W is rotatable about the central axis of the workpiece W, the threaded grinding wheel T is rotatable about the central axis of the threaded grinding wheel T, and the workpiece W or the threaded grinding wheel T is rotatable to change the relative position between the workpiece W and the threaded grinding wheel T.

[0014] The gear grinding device 1 is a six-axis machine, i.e., a machine having three linear axes and three rotational axes. In this embodiment, the gear grinding device 1 is capable of rotating the workpiece W around the B axis, and the threaded grinding wheel T around the A axis and the C axis, and is capable of moving the threaded grinding wheel T in the X-, Y-, and Z-axis directions. The A axis is an axis perpendicular to the central axis of the workpiece W and the central axis of the threaded grinding wheel T. The B axis coincides with the central axis of the workpiece W. The C axis coincides with the central axis of the threaded grinding wheel T.

[0015] The gear grinding device 1 includes a bed 2, a column 3, a Y-axis slide 4, a rotating member 5, a grinding wheel support member 6, a threaded grinding wheel T, and a workpiece support member 7. The bed 2 is placed on an installation surface. The column 3 is guided by an X-axis guide provided on the upper surface of the bed 2 and is provided so as to be movable in the X-axis direction (horizontal direction) relative to the bed 2. Although not shown, the column 3 is driven by a ball screw mechanism or a linear motor or the like.

[0016] The Y-axis slide 4 is guided by a Y-axis guide provided on a side surface of the column 3 extending in the vertical direction, and is provided so as to be movable in the Y-axis direction (up and down direction) relative to the column 3. The rotating member 5 is provided on the Y-axis slide 4 and is provided so as to be rotatable around the A-axis, which is a horizontal axis. The rotating member 5 is provided so as to be rotatable within a range of 360°, for example.

[0017] The grindstone support member 6 is provided so as to be movable in the Z-axis direction, guided by a Z-axis guide provided on the rotating member 5. The Z-axis direction changes direction as the rotating member 5 rotates around the A-axis. In the initial state, the Z-axis direction is horizontal and perpendicular to the X-axis and Y-axis directions.

[0018] The grinding wheel support member 6 supports the threaded grinding wheel T rotatably around the C axis. The C axis coincides with the central axis of the threaded grinding wheel T and is an axis parallel to the Z axis. The threaded grinding wheel T has a helical convex blade that protrudes radially outward. The threaded grinding wheel T may have a single thread or a multiple thread. In the case of a multiple thread, the threaded grinding wheel T will have multiple helical convex blades. The workpiece support member 7 is provided on the bed 2 and supports the workpiece W rotatably around the B axis.

[0019] Grinding by the gear grinding device 1 is performed as follows: The workpiece W and the threaded grinding wheel T are rotated synchronously. More specifically, the workpiece W is rotated about the B axis, and the threaded grinding wheel T is rotated about the C axis, and the rotations of both are synchronized.

[0020] Next, in this embodiment, the rotating member 5 is rotated a predetermined angle around the A axis to place the workpiece W and the threaded grinding wheel T in a grinding posture having a cross angle. Next, the column 3 is moved in the X-axis direction, the Y-axis slide 4 is moved in the Y-axis direction, and the grinding wheel support member 6 is moved in the Z-axis direction to move the threaded grinding wheel T to an initial grinding position. Next, the Y-axis slide 4 is moved to move the threaded grinding wheel T toward the central axis of the workpiece W, and the tooth profile of the workpiece W is ground.

[0021] 2. Gear grinding simulation device 10 The gear grinding simulation device 10 will be described with reference to Figures 3 to 40. The gear grinding simulation device 10 is configured by a computer, and is configured by, for example, an arithmetic processing device, a storage device, an interface, and the like.

[0022] 3, the gear grinding simulation device 10 includes an input unit 11, a calculation processing unit 12, a workpiece model storage unit 13, a grinding wheel model storage unit 14, and an output unit 15. The input unit 11 inputs various information used in the simulation. The various information includes, for example, the final shape of the workpiece W, i.e., target tooth profile information of the gear G, the material shape of the workpiece W, the outer diameter, axial width, and number of threads of the threaded grinding wheel T, the mechanical configuration of the gear grinding device 1, and the like.

[0023] The calculation processing unit 12 executes a gear grinding simulation using the information input by the input unit 11. In the gear grinding simulation in this embodiment, in order to facilitate calculation processing, the workpiece W is assumed to be fixed and the threaded grinding wheel T is assumed to move relative to the workpiece W. That is, in the gear grinding simulation, the threaded grinding wheel T is assumed to rotate about the central axis of the threaded grinding wheel T and to rotate around the workpiece W about the central axis of the workpiece W. However, the gear grinding simulation can also be performed such that the workpiece W and the threaded grinding wheel T perform the same operations as in actual gear grinding.

[0024] The workpiece model storage unit 13 stores the workpiece model Mw. In detail, the workpiece model storage unit 13 stores the workpiece model Mw generated initially, and then sequentially updates and stores the workpiece model Mw changed by the gear grinding simulation executed by the calculation processing unit 12. Note that all of the workpiece models Mw in the process of being updated may be stored.

[0025] The grindstone model storage unit 14 stores the grindstone model Mt generated initially. In this embodiment, the shape of the grindstone model Mt does not change in the gear grinding simulation. Therefore, the shape of the grindstone model Mt is not updated. However, it is also possible to change the shape of the grindstone model Mt. The output unit 15 outputs information generated by executing the gear grinding simulation by the arithmetic processing unit 12. For example, the output unit 15 outputs the updated workpiece model Mw, outputs the grindstone model Mt, or outputs the grinding amount for each micro-portion of the grindstone model Mt.

[0026] 2-1. Gear grinding simulation The grinding gear processing simulation will be described with reference to the flowcharts of Fig. 4 to Fig. 7. The grinding gear processing simulation is a simulation method executed by the arithmetic processing unit 12 in Fig. 3.

[0027] First, as shown in FIG. 4, a target tooth profile cross-sectional point cloud W_tar is generated that defines the cross-sectional shape of a target tooth profile of the gear G in the cross section (Xw-Yw plane) of the gear G in the direction perpendicular to the axis (S1). The target tooth profile of the gear G is shown in FIG. 8. For example, the target tooth profile of the gear G is formed by an involute surface. However, the target tooth profile of the gear G is not limited to an involute, and any tooth flank shape can be applied. As shown in FIG. 8, in the target tooth profile of the gear G, any point on the tooth flank is represented by a tooth flank normal vector Ga, a tooth trace tangent vector Gb, and a tooth depth tangent vector Gc. Then, as shown in FIG. 9, the target tooth profile cross-sectional point cloud W_tar is defined as a point cloud in the cross section (Xw-Yw plane) of the gear G in the direction perpendicular to the axis.

[0028] Next, the grindstone blade cross-sectional point group Pt_g is generated (S2). As shown in FIG. 10(a), the grindstone blade cross-sectional point group Pt_g defines the cross-sectional shape of the convex blade of the threaded grindstone T in the axial cross-section of the threaded grindstone T. One grindstone blade cross-sectional point group Pt_g is composed of a plurality of grindstone blade cross-sectional points Pt. The grindstone blade cross-sectional point group Pt_g shown in FIG. 10(a) is for a case where the threaded grindstone T has a single thread and a lead of the threaded grindstone T is L1. Therefore, the grindstone blade cross-sectional point group Pt_g is generated based on information about the threaded grindstone T inputted by the input unit 11.

[0029] Here, as shown in Fig. 11, each point Pt of the grinding wheel blade cross-sectional point group Pt_g is generated so that the tooth surface normal vector Ga of the target tooth profile of the gear G and the grinding wheel blade normal vector Ta of the convex blade of the threaded grinding wheel T are positioned coaxially in a state where each point Pt of the grinding wheel blade cross-sectional point group Pt_g coincides with each point of the target tooth profile cross-sectional point group W_tar. In Fig. 11, the tooth surface normal vector Ga and the grinding wheel blade normal vector Ta of the threaded grinding wheel T are vectors in opposite directions. Note that the tooth surface normal vector Ga and the grinding wheel blade normal vector Ta are unit vectors, and therefore their vector lengths (vector magnitudes) are the same.

[0030] When the threaded grinding wheel T has a double-thread thread, the grinding wheel blade cross-sectional point group Pt_g as shown in FIG. 10(b) is generated. The lead of the threaded grinding wheel T at this time is L2. When the threaded grinding wheel T has a three-thread thread, the grinding wheel blade cross-sectional point group Pt_g as shown in FIG. 10(c) is generated. The lead of the threaded grinding wheel T at this time is L3. In this manner, the grinding wheel blade cross-sectional point group Pt_g is generated according to the number of threads of the threaded grinding wheel T. When the threaded grinding wheel T has a multiple-thread thread, the grinding wheel blade cross-sectional point group Pt_g defines the cross-sectional shapes of the multiple convex blades that make up the multiple-thread thread.

[0031] Next, a grindstone model Mt is generated (S3), as shown in Fig. 4. The grindstone model Mt is a 3D model of the convex blade of the threaded grindstone T, obtained by arranging the grindstone blade cross-section point group Pt_g in the extension direction of the convex blade of the threaded grindstone T.

[0032] The grindstone model Mt is generated by arranging the grindstone blade cross-section point group Pt_g for each predetermined angle of the threaded grindstone T and for each predetermined axial position determined from the leads L1 to L3 of the threaded grindstone T. The coordinate system of the grindstone model Mt is defined as shown in FIG. 12. The grindstone model Mt is then divided into multiple parts in the axial direction of the grindstone model Mt for each predetermined axial position. The axial lengths of adjacent predetermined axial positions, i.e., the axial division length Ldt of the grindstone model Mt, are set in advance. The axial length Wt of the grindstone model Mt coincides with the axial length of the threaded grindstone T.

[0033] FIG. 13 shows a case where the threaded grinding wheel T has a single thread. FIG. 13(a) shows the grinding wheel blade cross-sectional point group Pt_g formed by a single thread, and FIG. 13(b) shows the grinding wheel model Mt generated using the grinding wheel blade cross-sectional point group Pt_g shown in FIG. 13(a). FIG. 14 shows a case where the threaded grinding wheel T has a double thread. FIG. 14(a) shows the grinding wheel blade cross-sectional point group Pt_g formed by a double thread, and FIG. 14(b) shows the grinding wheel model Mt generated using the grinding wheel blade cross-sectional point group Pt_g shown in FIG. 14(a). FIG. 15 shows a case where the threaded grinding wheel T has a triple thread. FIG. 15(a) shows the grinding wheel blade cross-sectional point group Pt_g formed by a triple thread, and FIG. 15(b) shows the grinding wheel model Mt generated using the grinding wheel blade cross-sectional point group Pt_g shown in FIG. 15(a).

[0034] Next, a workpiece model Mw is generated (S4) as shown in Fig. 4. The workpiece model Mw is defined by a workpiece definition point group Pw_g on the surface of the workpiece W and a group of lines LS_g extending in the radial direction of the workpiece W with each point of the workpiece definition point group Pw_g as one end.

[0035] As shown in FIG. 16, the workpiece model Mw has an initial shape, for example, a cylindrical shape. The axial length Ww of the workpiece model Mw coincides with the axial length of the workpiece W. The outer diameter and inner diameter of the cylindrical shape of the workpiece model Mw correspond to the radial range to be ground. In other words, the workpiece model Mw is represented as a cylindrical shape that defines only the range required for grinding. Furthermore, as shown in FIG. 16, the workpiece model Mw is divided at equal intervals in the direction of the central axis of the workpiece W (Zw direction). The axial length Ldw to be divided is set arbitrarily.

[0036] Then, on each of the divided surfaces, workpiece definition points Pw are arranged at equal intervals in the circumferential direction on the outer peripheral surface of the cylindrical shape. However, there are multiple tooth profiles generated on the workpiece W in the circumferential direction, and the multiple tooth profiles are identical. Therefore, as shown in Fig. 17, the workpiece model Mw arranges the workpiece definition points Pw only for an angle range Δθ that can represent one tooth profile. The angle range Δθ is set to a range from a start angle θs to an end angle θe corresponding to one tooth profile in the coordinate system of the workpiece model Mw.

[0037] The workpiece definition point Pw can be changed within a radial range from the outer peripheral surface to the inner peripheral surface of the cylindrical shape by the gear grinding simulation. Since the workpiece definition point Pw is a point located on the outer peripheral surface of the workpiece model Mw, it is a point that represents the shape of the outer peripheral surface of the workpiece model Mw.

[0038] As described above, the workpiece model Mw is defined by the workpiece definition point group Pw_g and the line segment group LS_g. That is, as shown in Fig. 17, a line segment LS is arranged with each of the workpiece definition points Pw as one end and the central axis of the workpiece model Mw as the other end. Therefore, the hatched area in Fig. 17 is the area that defines the workpiece model Mw.

[0039] Here, Fig. 18 shows the workpiece model Mw in a coordinate system of the workpiece model Mw as Xw'-Yw'-Zw. Yw' is located at the center of the angle range Δθ, and Xw' is a direction perpendicular to Yw'. In Fig. 18, the white circle is located on the inner peripheral surface of the workpiece model Mw defined as a cylindrical shape.

[0040] Next, as shown in FIG. 4, a workpiece divided area Ad(h) is generated (S5). The workpiece divided area Ad(h) is an area obtained by dividing the workpiece model Mw so as to include a plurality of workpiece definition points Pw that are part of the workpiece definition point group Pw_g. As shown in FIG. 19, in this embodiment, the workpiece divided area Ad(h) is defined in the workpiece model Mw that has been coordinate-transformed into a three-dimensional polar coordinate system (θ-Le-Zw). That is, in FIG. 19, the horizontal axis is the angle θ, the vertical axis is the line segment length Le of the line segment LS, and the axis in the depth direction is the Zw axis obtained by dividing the workpiece model Mw. FIG. 19 shows a case where the workpiece is divided into nine workpiece divided areas Ad(1) to Ad(9). The shape, size, and number of divisions of the workpiece divided area Ad(h) are set arbitrarily.

[0041] In the following, in order to simplify the calculation process, the workpiece model Mw is converted into a three-dimensional polar coordinate system (θ-Le-Zw) for processing. However, the workpiece model Mw can also be processed in a three-dimensional orthogonal coordinate system (Xw'-Yw'-Zw). The workpiece division area Ad(h) can also be defined in the three-dimensional orthogonal coordinate system (Xw'-Yw'-Zw).

[0042] Next, a time counter n (n is an ordinal number) is set to 0 as an initial value (S6). Time advances as the gear grinding process is performed. Therefore, the time t n The time counter n is used as an index representing the maximum value n_max-1. Then, it is determined whether the time counter n is the maximum value n_max-1, i.e., a value that is 1 less than the maximum value n_max (S7). If the time counter n is not the maximum value n_max-1 (S7: No), the time counter n is incremented by 1 (S8).

[0043] Next, the workpiece divided area number h (h is an ordinal number) is set to 0 as an initial value (S9). As shown in FIG. 19, the workpiece model Mw is divided into a plurality of workpiece divided areas Ad(h). In other words, the workpiece divided area number h is a number representing the workpiece divided area Ad(h). Next, it is determined whether the workpiece divided area number h is the maximum value h_max (S10). If the workpiece divided area number h is not the maximum value h_max (S10: No), the workpiece divided area number h is incremented by 1 (S11) as shown in FIG. 5.

[0044] Next, the grindstone blade cross-sectional point cloud number m (m is an ordinal number) is set to 0 as an initial value (S12). As shown in Figs. 13 to 15, the grindstone model Mt is composed of a plurality of grindstone blade cross-sectional point clouds Pt_g(m). The grindstone blade cross-sectional point cloud number m is a number representing a plurality of grindstone blade cross-sectional point clouds Pt_g(m) in the grindstone model Mt. Next, it is determined whether the grindstone blade cross-sectional point cloud number m is the maximum value m_max (S13). If the grindstone blade cross-sectional point cloud number m is not the maximum value m_max (S13: No), the grindstone blade cross-sectional point cloud number m is incremented by 1 (S14).

[0045] Next, the grindstone blade cross-section point number i (i is an ordinal number) is set to 0 as an initial value (S15). As shown in FIG. 10, one grindstone blade cross-section point group Pt_g is composed of a plurality of grindstone blade cross-section points Pt(i). The grindstone blade cross-section point number i is a number that represents the grindstone blade cross-section point Pt(i) in one grindstone blade cross-section point group Pt_g. Next, it is determined whether the grindstone blade cross-section point number i is the maximum value i_max-1, that is, a value that is 1 less than the maximum value i_max (S16). If the grindstone blade cross-section point number i is not the maximum value i_max-1 (S16: No), the grindstone blade cross-section point number i is incremented by 1 (S17).

[0046] Next, as shown in FIG. 5, at time t n In the wheel definition point interval Se(i,t n ) is calculated (S18). n ) is the time t in the coordinate system based on the workpiece model Mw. n In the grinding wheel blade cross-section point group Pt_g(t n) are the two adjacent points Pt(i,t n ),Pt(i+1,t n ) section. n ) means that at time t n The grindstone blade cross-sectional point group Pt_g in the n ) at time t n The i-th grindstone blade cross-section point Pt in the grindstone blade cross-section point group Pt_g in the

[0047] In this embodiment, the grindstone definition point interval Se(i,t n ) is expressed in the three-dimensional polar coordinate system (θ-Le-Zw) of the workpiece model Mw. In FIG. 20, multiple grinding wheel blade cross-section points Pt(i,t n ) is composed of the grinding wheel blade cross-section point cloud Pt_g(t n 20 shows the grindstone definition point interval Se(3,t n ) is shown. n ) at time t n Adjacent grinding wheel blade cross section points Pt(3,t n ), Pt(4,t n ) interval.

[0048] Furthermore, as shown in FIG. 5, at time t n At time t, which is Δt after n+1 In the wheel definition point interval Se(i,t n+1 ) is calculated (S18). n+1 ) is the time t in the coordinate system based on the workpiece model Mw. n+1 In the grinding wheel blade cross-section point group Pt_g(t n+1 ) are the two adjacent points Pt(i,t n+1 ),Pt(i+1,t n+1 ) section. n+1 ) means that at time t n+1 The grindstone blade cross-sectional point group Pt_g in the n+1 ) at time t n+1The i-th grindstone blade cross-section point Pt in the grindstone blade cross-section point group Pt_g in the

[0049] In this embodiment, the grindstone definition point interval Se(i,t n+1 ) is the wheel definition point interval Se(i,t n ), the workpiece model Mw is expressed in a three-dimensional polar coordinate system (θ-Le-Zw). In FIG. 20, multiple grinding wheel blade cross-section points Pt(i,t n+1 ) is composed of the grinding wheel blade cross-section point cloud Pt_g(t n+1 20 shows the grindstone definition point interval Se(3,t n+1 ) is shown. n+1 ) at time t n+1 Adjacent grinding wheel blade cross section points Pt(3,t n+1 ), Pt(4,t n+1 ) interval.

[0050] Next, as shown in Fig. 5, the wheel definition point section passing area At(i,t n ) is determined (S19). n In the wheel definition point interval Se(i,t n ) and time t n+1 In the wheel definition point interval Se(i,t n+1 ) The area represented by the wheel definition point section passing area At(i,t n ) at time t n and time t n+1 20, for example, the grindstone definition point section passing area At(3,t n ) is shown.

[0051] Next, as shown in FIG. 5, for each workpiece division area Ad(h), the grinding wheel definition point section passing area At(i,t n) is checked for interference with the workpiece model Mw (S20). In this embodiment, in order to facilitate calculation processing, the interference check is performed in a two-dimensional polar coordinate system (θ-Zw) of the workpiece model Mw, that is, a coordinate system represented by the circumferential angle θ of the workpiece model Mw and the axial position Zw of the workpiece model Mw.

[0052] The interference check will be described with reference to Figs. 21 and 22. For ease of explanation, the grinding wheel definition point section passing area At(3,t n First, as shown in FIG. 21, in the two-dimensional polar coordinate system (θ-Zw) of the workpiece model Mw, the grinding wheel definition point section passing area At(i,t n ) is the rectangular area At'(i,t n ) is generated. n ) is used to facilitate calculation processing. That is, the rectangular inclusion area At'(i,t n ) in the wheel definition point section passing area At(i,t n ) and process it accordingly.

[0053] In FIG. 21, the grinding wheel definition point section passing area At(3,t n ) containing the rectangular area At'(3,t n ) is generated. n ) is the point Pt'(3,t n ), point Pt'(3,t n+1 ), point Pt'(4,t n ), point Pt'(4,t n+1 ) in FIG. 21. n ) and point Pt'(4,t n The θ coordinate of the point Pt(3,t n In FIG. 21, the θ coordinate of point Pt'(3,t n+1 ) and point Pt'(4,t n+1 The θ coordinate of the point Pt(4,t n+1 ) corresponds to the θ coordinate of

[0054] In FIG. 21, the point Pt'(3,t n) and point Pt'(3,t n+1 The Zw coordinate of the point Pt(3,t n+1 In FIG. 21, the Zw coordinate of point Pt'(4,t n ) and point Pt'(4,t n+1 The Zw coordinate of the point Pt(4,t n ) Zw coordinates. However, the correspondence of the points is the same as that of the grinding wheel definition point section passing area At(3,t n ) depends on the shape.

[0055] As shown in FIG. 22, in the two-dimensional polar coordinate system (θ-Zw) of the workpiece model Mw, the workpiece model Mw and the grinding wheel definition point section passing area At(3,t n ) is the rectangular area At'(3,t n At this time, the grinding wheel definition point section passing area At(i,t n ) is the rectangular area At'(i,t n ) to check whether they interfere with each other.

[0056] For example, in FIG. 22, the workpiece division area Ad(5) and the grinding wheel definition point section passing area (3, t n ) is the rectangular area At'(3,t n ) interferes with the workpiece division area Ad(5). n On the other hand, the other workpiece divided areas Ad(1) to Ad(4) and Ad(6) to Ad(9) are included in the rectangular inclusion area At'(3,t n 5, the workpiece divided area Ad(1) currently being processed does not interfere with the rectangular inclusion area At'(1,t1) currently being processed.

[0057] In the above, in order to facilitate the calculation process, the interference check is performed by dividing the workpiece division area Ad(h) currently being processed and the rectangular inclusion area At'(i,t nIn addition, the interference check is performed for the workpiece division area Ad(h) currently being processed and the wheel definition point section passing area At(i,t n ) can also be used as an interference check.

[0058] 6, if the result of the interference check is that there is no interference (S21: No), the process returns to S17 and repeats. For example, if the rectangular inclusion area At'(1, t1) does not interfere with the workpiece divided area Ad(1), then an interference check is performed between the workpiece divided area Ad(1) and the rectangular inclusion area At'(2, t1).

[0059] On the other hand, in S21 of Fig. 6, if the interference check results in interference (S21: Yes), the initial value of the work definition point number q in the work divided area Ad(h) is set to 0 (S22). As shown in Fig. 22, one work divided area Ad(h) is made up of multiple work definition points Pw(q). The work definition point number q is a number that represents a work definition point Pw(q) in one work divided area Ad(h).

[0060] 22, one workpiece divided area Ad(h) is made up of 16 workpiece definition points Pw(1) to Pw(16). However, when the workpiece definition point Pw(q) is located on the boundary of the workpiece divided area Ad(h), it is common to multiple workpiece divided areas Ad(h), so it may be considered to constitute only one workpiece divided area Ad(h).

[0061] Next, it is determined whether the workpiece definition point number q is the maximum value q_max (S23). If the workpiece definition point number q is not the maximum value q_max (S23: No), the workpiece definition point number q is incremented by 1 (S24).

[0062] Next, as shown in FIG. 6, when each workpiece definition point Pw constituting the workpiece model Mw is viewed from the extending direction of a line segment LS having the workpiece definition point Pw as one end, the grinding wheel definition point section passing area At(i,t n) (S25).

[0063] The inclusion check will be described with reference to Fig. 23 and Fig. 24. Fig. 23 shows the relationship between the workpiece definition point Pw(6) constituting the workpiece model Mw and the grindstone definition point section passing area At(3,t n ) is included in the workpiece model Mw. FIG. 24 shows the state in which the workpiece definition point Pw(7) constituting the workpiece model Mw is located within the grinding wheel definition point section passing area At(3,t n ), i.e., not contained within.

[0064] The inclusion check can be easily performed by performing the calculation in the two-dimensional polar coordinate system (θ-Zw) of the workpiece model Mw as shown in Figures 23 and 24. As shown in Figures 23 and 24, in the two-dimensional polar coordinate system (θ-Zw), the workpiece definition points Pw(6) and Pw(7) are located within the grinding wheel definition point section passing area At(3,t n ) to see if it is located inside the

[0065] For example, in a two-dimensional polar coordinate system (θ-Zw), the workpiece definition point Pw(q) and the grinding wheel definition point section passing area At(i,t n ) n ), point Pt(i,t n+1 ), point Pt(i+1,t n ), point Pt(i+1,t n+1 Calculate the vectors v1, v2, v3, and v4 that connect each of the points.

[0066] Then, the cross product of two adjacent vectors in one circumferential direction centered on the workpiece definition point Pw(q) is calculated. The cross products of the two adjacent vectors are, for example, v1×v2, v2×v3, v3×v4, and v4×v1. If the signs of all four cross products are the same, the workpiece definition point Pw(q) is determined to be within the grinding wheel definition point section passing area At(i,t n On the other hand, if the four cross products have different signs, the workpiece definition point Pw(q) is determined to be located within the wheel definition point section passing area At(i,t n ) is not determined to be located inside the

[0067] As shown in FIG. 23, in the case of the workpiece definition point Pw(6), the signs of the cross products of two adjacent vectors in one circumferential direction centered on the workpiece definition point Pw(6) are all the same, so the workpiece definition point Pw(6) is located within the grinding wheel definition point section passing area At(3,t n On the other hand, as shown in FIG. 24, in the case of the workpiece definition point Pw(7), the cross product of two adjacent vectors in one circumferential direction centered on the workpiece definition point Pw(7) has a different sign, so the workpiece definition point Pw(7) is determined to be located within the grinding wheel definition point section passing area At(3,t n ) is not determined to be located inside the

[0068] Next, as shown in Fig. 6, the result of the inclusion check is that the workpiece definition point Pw(q) is in the wheel definition point section passing area At(i,t n If it is determined that the workpiece definition point Pw(1) constituting the workpiece divided area Ad(5) is not located within the grindstone definition point section passing area At(1,t1) (S26: No), the process returns to S23 and is repeated. For example, if the workpiece definition point Pw(1) constituting the workpiece divided area Ad(5) is not located within the grindstone definition point section passing area At(1,t1), then an inclusion check is performed to determine whether or not the workpiece definition point Pw(2) constituting the workpiece divided area Ad(5) is located within the grindstone definition point section passing area At(1,t1).

[0069] On the other hand, in S26 of FIG. 6, as a result of the inclusion check, the workpiece definition point Pw(q) is in the grinding wheel definition point section passing area At(i,t nIf it is determined that the intersection point Px is located within the grinding wheel definition point section passing area At(i,t) (S26: Yes), the intersection point Px is calculated (S27). n ), the target line segment LS(q) with the workpiece definition point Pw(q) as one end, and the grinding wheel definition point section passing area At(i,t n ) is the intersection point.

[0070] The calculation of the intersection point Px will be described with reference to Figs. 25 and 26. n ) is the point Pt(i,t n ), point Pt(i,t n+1 ), point Pt(i+1,t n ), point Pt(i+1,t n+1 If the four points are on the same plane, the wheel definition point passing area At(i,t n ) can be expressed by a single plane. However, if the four constituent points do not exist on the same plane, the grinding wheel definition point section passing area At(i,t n ) cannot be represented by a single plane.

[0071] Therefore, as shown in Fig. 25, the wheel definition point passing area At(i,t n The surfaces constituting the grindstone definition point section passing area At(i,t) are two triangular planes represented by lines connecting adjacent points among the four constituting points and lines connecting two diagonal points of the four constituting points. n ) is composed of points Pt(3,t n ), point Pt(3,t n+1 ), point Pt(4,t n ) and point Pt(4,t n ), point Pt(4,t n+1 ), point Pt(3,t n ) and a triangular plane with vertices at vertices.

[0072] Then, in the two-dimensional polar coordinate system (θ-Le) shown in FIG. 25, the intersection point between the target line segment LS(6) and one of the two triangular planes is calculated. n ) is the intersection point between the target line segment LS(6) and one of the two triangular planes. In the three-dimensional orthogonal coordinate system (Xw'-Yw'-Zw), it is as shown in FIG. 26. Note that the intersection point Px may also be calculated in the three-dimensional orthogonal coordinate system (Xw'-Yw'-Zw). However, the calculation process in the two-dimensional polar coordinate system (θ-Le) is easier.

[0073] Next, as shown in FIG. 6, when the workpiece definition point Pw(q) is changed to the intersection point Px, it is determined whether the line length of the line segment LS(q) is shorter than the original line length (S28). If the line length is shorter (S28: Yes), the workpiece definition point Pw(q) is changed to the coordinate of the intersection point Px, and the line length of the target line segment LS(q) is changed (S29). After these changes, the grinding resistance parameters are calculated (S40). After the calculation of the grinding resistance parameters, the process returns to S23 and the process is repeated. When the workpiece definition point Pw(6) and the target line segment LS(6) are changed, the result is as shown in FIG. 27 and FIG. 28. The grinding resistance parameters calculated in S40 will be described later.

[0074] If the line length of the line segment LS(q) is not shorter than the original line length (S28: No), the process returns to S23 and repeats the process without changing the line length of the workpiece definition point Pw(q) and the target line segment LS(q).

[0075] For example, if the workpiece definition point Pw(6) constituting the workpiece dividing area Ad(5) is located inside the grinding wheel definition point section passing area At(3,t1), then after changing the workpiece definition point Pw(6) and the target line segment LS(6), an inclusion check is performed to determine whether the workpiece definition point Pw(7) constituting the workpiece dividing area Ad(5) is located inside the grinding wheel definition point section passing area At(3,t1).

[0076] When steps S24 to S29 in Fig. 6 are repeatedly executed, if the workpiece definition point number q reaches the maximum value q_max in S23 in Fig. 6 (S23: Yes), the process returns to S16 in Fig. 5 and is repeated. That is, it is determined whether the grinding wheel blade cross-section point number i currently being processed has reached the maximum value i_max-1 (S16), and if it has not yet reached that value (S16: No), the grinding wheel blade cross-section point number i is incremented by 1 (S17), and the process from S18 onwards is carried out.

[0077] In S16, if the grindstone blade cross-section point number i currently being processed has reached the maximum value i_max-1 (S16: Yes), the process returns to S13 and is repeated. That is, it is determined whether the grindstone blade cross-section point group number m currently being processed has reached the maximum value m_max (S13), and if it has not yet reached the maximum value m_max (S13: No), the grindstone blade cross-section point group number m is incremented by 1 (S14), and the process from S15 onwards is carried out.

[0078] In S13, if the grinding wheel blade cross-section point group number m currently being processed has reached the maximum value m_max (S13: Yes), the process returns to S10 and repeats the process as shown in Fig. 4. That is, it is determined whether the workpiece divided area number h currently being processed has reached the maximum value h_max (S10), and if it has not yet reached the maximum value h_max (S10: No), the workpiece divided area number h is incremented by 1 (S11), and the process from S12 onwards is carried out.

[0079] In S10, if the workpiece divided area number h currently being processed has reached the maximum value h_max (S10: Yes), the process returns to S7 and is repeated. That is, it is determined whether the time counter n currently being processed has reached the maximum value n_max (S7), and if it has not yet reached the maximum value n_max (S7: No), the time counter n is incremented by 1 (S8), and the process from S9 onwards is carried out.

[0080] In S7, when the time counter n currently being processed reaches the maximum value n_max (S7: Yes), the workpiece model Mw defined by the changed workpiece definition point group Pw_g is output (S30). In addition to outputting the workpiece model Mw, the grindstone model Mt may be output in S30. Furthermore, the grinding amount for each grindstone definition point section Se(i) in each of the grindstone blade cross section point group Pt_g of the grindstone model Mt may be output.

[0081] For example, Fig. 29 is a diagram showing the state of the workpiece model Mw and a part of the grinding wheel model Mt in the middle of the gear grinding simulation in a three-dimensional polar coordinate system (θ-Le-Zw), and Fig. 30 is a diagram showing the final shape of the workpiece model Mw in a three-dimensional orthogonal coordinate system (Xw'-Yw'-Zw).

[0082] After outputting the workpiece model Mw, the grinding resistance parameters are output as shown in FIG. 7 (S41). The grinding resistance parameters are the grinding resistance parameters calculated in each mesh at each time in S40. The grinding resistance parameters are parameters necessary for calculating the grinding resistance in a predetermined surface grinding model. The type of surface grinding model used here is not limited, but for example, a horizontal axis surface grinding model shown in FIG. 8 may be used as the surface model. In this case, the principal component force vector ft and the thrust component force vector fn are expressed as follows using the specific grinding resistance Cp, table speed v, cutting amount (depth direction) Δ, thickness b, grinding wheel peripheral speed V, friction coefficient μ, and grinding wheel cutting edge tip half angle α, respectively.

[0083]

number

[0084] In applying the horizontal axis surface grinding model to this simulation, as shown in FIG. 33 and FIG. 34(a) and (b), the relative velocity vector in this simulation is defined as the principal force vector ft, and the vector perpendicular to the grindstone section vector and the relative velocity vector is defined as the thrust force vector fn. In FIG. 33, the open circles indicate four adjacent grindstone blade section points Pt at a given time. The solid circles indicate three adjacent workpiece definition points Pw at a given time. The relative velocity vector indicating the principal force vector ft is calculated for each workpiece definition point Pw in the workpiece model Mw. In this embodiment, the relative velocity vector is considered to be the velocity vector when the workpiece definition point Pw moves when the grindstone model Mt is fixed. The thrust force vector fn is also calculated for each workpiece definition point Pw. The grindstone cross-sectional vector for calculating the thrust force vector fn is a vector on the grindstone shaft cross section including the workpiece definition point Pw, and can be calculated from the grindstone cross-sectional vectors at times tn and tn+1.

[0085] Further, vΔb in the formula (1) can be expressed as the removal volume Vcut per unit time of the workpiece model Mw by the grindstone model Mt. Therefore, in this simulation, it can be expressed as the following formula (2).

[0086]

number

[0087] Here, the removal volume Vcut per unit time is calculated based on the removal length Lcut, which is the distance between the workpiece definition points before and after the change shown in FIG. 34(b). More specifically, first, as shown in FIG. 34, the surface of the workpiece model Mw is defined by a plurality of meshes, and one workpiece definition point Pw corresponds to one mesh. One mesh is defined as an area having a boundary that is centered on one workpiece definition point Pw on the surface of the workpiece model Mw and connects the midpoints of adjacent workpiece definition points Pw. The surface of the workpiece model Mw is defined in a state in which the meshes are connected together. Then, the removal volume Vcut per unit time can be calculated based on a first mesh area Sm1, which is the area of ​​the mesh including the workpiece definition point Pw before the change, a second mesh area Sm2, which is the area of ​​the mesh including the workpiece definition point Pw (Px) after the change, and the distance between the workpiece definition points before and after the change (i.e., the removal length Lcut).

[0088] Furthermore, in this embodiment, Vcut is calculated using the following equation (3) based on the mesh area Smesh, which is the mesh area median, which is the median between the first mesh area Sm1 and the second mesh area Sm2, the removal length Lcut, and the time increment t, as shown in Figure 34(b).

[0089]

number

[0090] Meanwhile, in formula (2), the specific grinding resistance Cp, the friction coefficient μ, and the half angle α of the cutting edge of the grindstone can be preset values ​​or can be set by the user each time. For example, the friction coefficient μ can be set appropriately according to the type of grindstone. Also, the half angle α of the cutting edge of the grindstone can be set based on the conical grindstone model shown in FIG. 35 for the abrasive grains provided on the grindstone.

[0091] The equations for Vcut and Smesh in equation (3) can also be derived based on the sector model shown in Fig. 34(c). In other words, if the radii of the first mesh Sm1 and the second mesh Sm2, which are circular arcs with the workpiece center O as the center, are r1 and r2, respectively, and the central angle of the sector is a, the area S1 of the sector before removal, the area S2 of the sector after removal, and the area ΔS of the removed portion can be expressed by the following equation (4).

[0092]

number

[0093] Since the removal length Lcut = r1 - r2 and the length of the arc Li = 2πr × (a / 2π), the following formula (5) can be derived from the above formula (4).

[0094]

number

[0095] And, Vcut can be expressed as Vcut = ΔS × t using ΔS. This is the same as the above formula (3). Therefore, formula (3) calculates an accurate value, not an approximate value.

[0096] From the above, in S40, the grinding resistance parameters, which are parameters necessary for calculating the grinding resistance based on the surface grinding model, include the relative velocity vector as the principal force vector, the grindstone cross-section vector used to calculate the thrust force vector, the mesh area Smesh used to calculate the removal volume per unit time, and the removal length Lcut. In addition, the grinding resistance parameters also include the machining point coordinates used to distinguish the tooth groove of the workpiece model Mw described later, and the machining time used to add up the grinding resistance at the same time described later.

[0097] Then, after outputting the workpiece model Mw shown in FIG. 4, the above-mentioned grinding resistance parameters are output in S41 shown in FIG. 7. In S41, data for one or more rotations of the workpiece when the grindstone model Mt is at any grindstone feed position can be output. This allows the amount of calculation to be reduced compared to when parameters are output at all feed positions. The grindstone feed positions at which parameters are output are not limited, but preferably include three positions near the start of grinding, near the middle, and near the end of grinding. In this embodiment, parameters are output at five grindstone feed positions including three positions near the start of grinding, near the middle, and near the end of grinding, as shown in FIG. 36.

[0098] Next, in S42 shown in Fig. 7, one tooth slot is extracted from the workpiece model Mw output in S30. For example, as shown in Fig. 37(a), the machining points of one tooth slot shown in Fig. 37(b) are extracted from the simulation results of the machining points for one rotation of the workpiece in the workpiece model Mw. The machining points of one tooth slot can be extracted by specifying the definition angle of the workpiece model Mw and extracting one tooth slot that is completely modeled.

[0099] Then, in S43 shown in Fig. 7, the grinding resistance for each mesh of the workpiece model Mw is calculated. In Fig. 18, the mesh is a substantially lattice-like plane partitioned by the workpiece definition point group Pw_g on the surface of the workpiece W. Then, in S44, the grinding resistances at the same time are added up. The sum of the grinding resistances is calculated for each three-dimensional component as shown in the following formula (6). In addition, in formula (6), ρ is a number assigned to each mesh.

[0100]

number

[0101] Then, the grinding resistance of one tooth groove during one rotation of the workpiece is calculated in S45 of Fig. 7. The grinding resistance of one tooth groove is calculated based on the workpiece rotation angle for one tooth groove, as shown in Fig. 38.

[0102] Thereafter, in S46 of FIG. 7, the grinding resistance of one tooth groove during one rotation of the workpiece is summed up multiple times to calculate the grinding resistance of all tooth grooves in the workpiece model Mw. The calculation of the grinding resistance of all tooth grooves is performed by changing the phase of the grinding resistance of one tooth groove and summing up multiple times. The amount of change in phase can be determined in consideration of the number of teeth of the workpiece model Mw. In this embodiment, the number of meshing teeth between the workpiece model Mw and the grinding wheel model Mt is 1 and 2 alternately. Therefore, the grinding resistance of all tooth grooves is calculated by first shifting the grinding resistance of one tooth groove by one pitch of the workpiece as shown in FIG. 39, duplicating it, and summing them up as shown in FIG. 40. Note that instead of calculating the grinding resistance of all tooth grooves, the grinding resistance of multiple tooth grooves may be calculated. The simulation ends when the calculation of the grinding resistance of all tooth grooves is completed.

[0103] In this embodiment, the relational expression shown in formula (1) is used as the surface grinding model. However, instead of this, the grinding resistance theoretical expression shown in FIG. 41 and the following formula (7) may be used.

[0104]

number

[0105] Then, Vcut, Ks, and λ are defined as shown in the following equation (8).

[0106]

number

[0107] Then, from the above formula (7) and formula (8), the above formula (7) becomes as shown in the following formula (9).

[0108]

number

[0109] As shown in the above formula (9), by using λ and Ks instead of Cp, μ, and α in this embodiment, the present invention can also be applied when the grinding resistance theoretical formula shown in formula (5) is used as a surface grinding model.

[0110] 3.Effects According to the gear grinding simulation method of the present embodiment, for each workpiece definition point Pw, a grinding resistance parameter used to calculate the grinding resistance in the surface grinding model is calculated based on the distance between the workpiece definition point Pw before the change and the workpiece definition point Pw(Px) after the change, and the grinding resistance in a mesh including the changed workpiece definition point Pw(Px) among a plurality of meshes defined on the surface of the workpiece model Mw is calculated based on the grinding resistance parameter using the surface grinding model. As a result, since the grinding resistance parameter reflects the state that changes from moment to moment in the gear grinding process in which the workpiece W is ground using the threaded grinding wheel T to generate a gear, the grinding resistance in the mesh can be calculated to calculate the grinding resistance with high accuracy during the gear grinding process. As a result, it becomes easy to analyze the cause of the tooth surface error caused by the grinding resistance and to determine the rigidity of each axis of the machine tool.

[0111] In the first embodiment, the grinding resistance parameter includes a removal volume Vcut per unit time by the grindstone model Mt in the workpiece model Mw, which is calculated based on the distance Lcut between the workpiece definition points before and after the change. This makes it possible to easily calculate the grinding resistance parameter.

[0112] In the first embodiment, the removal volume Vcut is calculated based on a first mesh area Sm1 which is the area of ​​the mesh including the workpiece definition point Pw before the change, a second mesh area Sm2 which is the area of ​​the mesh including the workpiece definition point Pw (Px) after the change, and a distance Lcut between the workpiece definition points before and after the change. This makes it possible to accurately calculate the removal volume Vcut.

[0113] In the first embodiment, the removal volume Vcut is calculated as the product of the mesh area median, which is the median of the first mesh area Sm1 and the second mesh area Sm2, and the distance Lcut between the workpiece definition points before and after the change. This makes it possible to accurately calculate the removal volume Vcut with a small amount of calculation.

[0114] In the first embodiment, the grinding force in the mesh including the coordinates of the intersection at a given time is calculated based on the grinding force vector in the mesh including the changed workpiece definition point Pw (Px) at the given time, which makes it easy to use a surface grinding model in the gear grinding simulation.

[0115] In the present embodiment, the grinding resistance vector includes a principal component vector, which is a relative velocity vector between the workpiece model Mw and the grindstone model Mt at the intersection Px, and a thrust component vector fn, which is orthogonal to the grindstone cross-section vector, which is a cross-section including the intersection Px in the grindstone model Mt, and the principal component vector ft. This makes it possible to calculate the grinding resistance with high accuracy.

[0116] Furthermore, in the first embodiment, the grinding resistance of one tooth groove during one revolution of the workpiece in the workpiece model Mw is calculated based on the grinding resistance in the mesh including the changed workpiece definition point Pw (Px). This makes it possible to reduce the amount of calculation compared to the case where the grinding resistance of all tooth grooves is directly calculated without calculating the grinding resistance of one tooth groove.

[0117] The grinding resistance of one tooth groove during one rotation of the workpiece in the workpiece model with the phase changed is added up multiple times to calculate the grinding resistance of multiple tooth grooves or all tooth grooves in the workpiece model. This makes it possible to reduce the amount of calculation compared to the case where the grinding resistance of all tooth grooves is directly calculated without calculating the grinding resistance of one tooth groove.

[0118] Also, in the first embodiment, a gear grinding simulation device 10 for executing the gear grinding simulation method is disclosed. The gear grinding simulation device 10 can perform the above-mentioned gear grinding simulation.

[0119] As described above, according to the above-mentioned aspects, it is possible to provide a gear grinding simulation method and device capable of simulating the variation in grinding resistance in gear grinding, in which a workpiece W is ground using a threaded grinding wheel T to create a gear. [Explanation of symbols]

[0120] W Workpiece Mw Workpiece model Pw Workpiece definition point Pw_g Workpiece definition point group LS Target line segment T Threaded grinding wheel Mt grinding wheel model Pt Grindstone blade cross section Pt_g Grindstone blade cross section point cloud Se Grindstone definition point interval At Grindstone definition point section passing area Px intersection ft Principal force vector fn Thrust force vector

Claims

1. 1. A gear grinding simulation method for simulating a gear grinding process in which a workpiece is ground with a threaded grinding wheel to generate a gear, the method comprising the steps of: generating a grindstone blade cross-sectional point cloud that defines a cross-sectional shape of a convex blade of the threaded grindstone in an axial cross-section of the threaded grindstone; generating a grindstone model in which the convex blade of the threaded grindstone is three-dimensionally modeled by arranging the grindstone blade cross-section point cloud in an extension direction of the convex blade of the threaded grindstone; generating a workpiece model defined by a workpiece definition point cloud on a surface of the workpiece and a group of line segments each having one end at each point of the workpiece definition point cloud and extending in a radial direction of the workpiece; In a coordinate system based on the workpiece model, time t ｎ (n is an ordinal number), two adjacent grinding wheel blade cross-section points Pt(i, t ｎ ), Pt(i+1,t ｎ ) ｎ ) and time t ｎ At time t, which is Δt after ｎ＋１ Two adjacent grinding wheel blade cross-section points Pt(i, t ｎ＋１ ), Pt(i+1,t ｎ＋１ ) ｎ＋１ ) and determining a wheel definition point section passing area represented by performing an inclusion check as to whether or not each workpiece definition point of the workpiece definition point group constituting the workpiece model is located within the grinding wheel definition point section passing area when viewed from the direction of a line segment having the workpiece definition point as one end; calculating an intersection between a target line segment having the workpiece definition point determined to be located inside in the inclusion check as one end and a surface constituting the grinding wheel definition point section passing area; The workpiece definition point located at one end of the target line segment is changed to the coordinates of the intersection point; Calculating a grinding force parameter for each of the workpiece definition points based on a distance between the workpiece definition point before the change and the workpiece definition point after the change, the grinding force parameter being used to calculate a grinding force in a surface grinding model; a gear grinding simulation method comprising: defining, as a mesh, an area having a center at one of the workpiece definition points on the surface of the workpiece and a boundary connecting midpoints of adjacent workpiece definition points; and calculating, using the surface grinding model, grinding resistance in a mesh that includes the changed workpiece definition point among the plurality of meshes, based on the grinding resistance parameters.

2. 2. The gear grinding simulation method according to claim 1, wherein the grinding resistance parameter includes a removal volume per unit time of the workpiece model by the grinding wheel model, the removal volume being calculated based on a distance between workpiece definition points before and after the change.

3. 3. The gear grinding simulation method according to claim 2, wherein the removed volume is calculated based on a first mesh area which is an area of ​​a mesh including the workpiece definition point before the change, a second mesh area which is an area of ​​a mesh including the workpiece definition point after the change, and a distance between the workpiece definition points before and after the change.

4. 4. The gear grinding simulation method according to claim 3, wherein the removed volume is calculated as a product of a mesh area median, which is a median of the first mesh area and the second mesh area, and a distance between the workpiece definition points before and after the change.

5. 3. The gear grinding simulation method according to claim 1, wherein the grinding force in the mesh including the changed workpiece definition point at a predetermined time is calculated based on a grinding force vector in the mesh including the changed workpiece definition point at the predetermined time.

6. 6. The gear grinding simulation method according to claim 5, wherein the grinding resistance vector includes a principal force vector which is a relative velocity vector between the workpiece model and the grinding wheel model at the intersection, and a thrust force vector which is perpendicular to a grinding wheel cross-section vector which is a cross-section including the intersection in the grinding wheel model and to the principal force vector.

7. 3. The gear grinding simulation method according to claim 1, further comprising the steps of: calculating a grinding resistance of one tooth groove during one rotation of the workpiece in the workpiece model based on the grinding resistance in the mesh including the changed workpiece definition point.

8. 8. The gear grinding simulation method according to claim 7, further comprising adding up a plurality of grinding resistances of one tooth groove during one rotation of the workpiece in the workpiece model with the phase changed, to calculate grinding resistances of multiple tooth grooves or all tooth grooves in the workpiece model.

9. A gear grinding simulation device for executing the gear grinding simulation method according to claim 1 or 2.

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