Machining shape simulation device

Abstract

A machining shape simulation device (100) for generative gear cutting comprises: a cylindrical coordinate system lattice prescribing unit (111) that prescribes a cylindrical coordinate system lattice that comprises a radial distance R component, an axial coordinate Z component, and an azimuth angle θ component and in which the lattice pitch of the radial distance R is set; a workpiece shape model prescribing unit (120) that prescribes a workpiece shape model defined by the axial direction as the axial coordinate Z direction in the cylindrical coordinate system lattice and the azimuth angle θ specified with respect to the radial distance R and the axial coordinate Z; a tool shape model prescribing unit (121); an interference region calculation unit (130) that calculates, on the basis of the workpiece shape model, a tool shape model, and the trajectory of relative movement of the tool and the workpiece, an interference region between the tool shape model and the workpiece shape model during generative gear cutting; and a machining result prediction unit (190) that predicts the machining result of the workpiece on the basis of the calculation result of the interference region calculation unit.

Description

Machining shape simulation device

[0001] The present invention relates to a machining shape simulation device.

[0002] Patent Document 1 discloses a configuration for generating a workpiece shape model to predict the machining results in gear grinding. In this configuration, since the gear has a substantially cylindrical shape, the workpiece shape model is expressed in a cylindrical coordinate system consisting of an azimuth angle θ, an axial coordinate Z, and a radial distance R. In particular, the workpiece shape model is defined by setting a grid pitch of the azimuth angle θ to a predetermined value and specifying the radial distance R for the azimuth angle θ and the axial coordinate Z of the set grid pitch. In this specification, the workpiece shape model expressed in this coordinate system is defined as a "θZ-R system model." In this θZ-R system model, the axial coordinate Z in the cylindrical coordinate system coincides with the axis of the gear to be generated, and the radial distance R indicates the radius of the surface on which the gear teeth are formed, centered on the gear axis. In other words, in the θZ-R system model, the azimuth angle θ and the axial coordinate Z are specified values, and the radial distance R is a value corresponding to the azimuth angle θ and the axial coordinate Z.

[0003] Japanese Patent Application Laid-Open No. 2023-33825

[0004] A gear profile is primarily composed of the tooth root and tip, which are on circular arcs, and the tooth flank, which is the curved portion connecting the two, and the shape of the tooth flank is important for performance evaluation. Therefore, to improve the prediction accuracy of the tooth flank shape in a gear performance simulation using a workpiece shape model for gear grinding, it is necessary to represent the tooth flank in detail in the workpiece shape model, i.e., to increase the data density of the tooth flank.

[0005] In order to increase the data density of the tooth flank in the θZ-R system model disclosed in Patent Document 1, it is conceivable to divide the azimuth angle θ component at a very small pitch. However, dividing the azimuth angle θ component at a very small pitch in the θZ-R system model increases the data density not only of the tooth flank but also of the tooth bottom and tooth tip, where there is little need to increase the data density, and this tends to increase the computational load. When the number of teeth is large, the tooth flank approaches a shape that follows the radial distance R, so the pitch of the azimuth angle θ component needs to be made smaller, and this tendency becomes more pronounced. Therefore, there is room for improvement in order to reduce the computational load while improving the prediction accuracy of gear performance and machining results.

[0006] Furthermore, in gear generating cutting, in addition to static behavior such as displacement caused by the average processing load occurring between the tool and workpiece at the processing point and the relative static stiffness between the tool and workpiece, dynamic behavior caused by fluctuations in the processing load occurring between the tool and workpiece and the relative dynamic characteristics between the tool and workpiece, i.e., vibrations such as forced vibrations and self-excited vibrations, occur.

[0007] However, the configuration disclosed in Patent Document 1 does not fully take such vibrations into consideration, which is one of the factors that causes a discrepancy between the actual machining results and the results predicted by simulation, reducing the prediction accuracy. Therefore, in order to improve the prediction accuracy of the machining results in gear-generating cutting, it is necessary to predict the vibrations at the machining point with high accuracy, but no attempt has been made to predict such vibrations in gear-generating cutting with high accuracy, which has been a challenge in improving the prediction accuracy of gear-generating cutting.

[0008] The present disclosure has been made in consideration of the above circumstances, and aims to provide a machining shape simulation device that can achieve both improved prediction accuracy of gear performance and machining results in gear generating cutting and reduced calculation load.

[0009] One aspect of the present disclosure is a machining shape simulation device that predicts a machining shape in gear generating cutting work in which a gear is generated by cutting a workpiece with a tool, the device comprising: a cylindrical coordinate system lattice definition unit that defines a cylindrical coordinate system lattice consisting of a radial distance R component, an axial coordinate Z component, and an azimuth angle θ component, with the lattice pitch of the radial distance R set to a predetermined value; a workpiece shape model definition unit that defines a workpiece shape model that is defined in the cylindrical coordinate system lattice based on analysis conditions including tool specifications, workpiece specifications, and machining conditions, such that the axial direction of the gear to be generated is parallel to the direction of the axial coordinate Z, and the azimuth angle θ is specified for the radial distance R and the axial coordinate Z of the set lattice pitch; a tool shape model definition unit that defines a tool shape model based on the analysis conditions; and an interference region calculation unit that calculates an interference region between the tool shape model and the workpiece shape model during gear generating cutting work based on the workpiece shape model, the tool shape model, and a relative movement trajectory of the tool and the workpiece. and a machining result prediction unit that predicts a machining result of the workpiece based on the calculation result of the interference region calculation unit.

[0010] A machining shape simulation device according to one aspect of the present disclosure defines a cylindrical coordinate system lattice in which the lattice pitch of the radial distance R is set to a predetermined value, and uses a workpiece shape model defined by specifying an azimuth angle θ with respect to the radial distance R and axial coordinate Z of the lattice pitch set in the cylindrical coordinate system. In this specification, this workpiece shape model is defined as an "RZ-θ system model." In this RZ-θ system model, by reducing the lattice pitch of the radial distance R of the cylindrical coordinate system lattice in which the workpiece shape is represented, it is possible to increase the data density of the tooth flanks while maintaining a low data density of the tooth tips and tooth roots in the workpiece shape model, thereby reducing the calculation load while satisfying requirements for improved gear performance and prediction accuracy of machining results.

[0011] As described above, according to the above-described one aspect, it is possible to provide a machining shape simulation device that can achieve both improved prediction accuracy of gear performance and machining results in gear generating cutting and reduced calculation load.

[0012] 10 is a functional block diagram of the machining shape simulation device of the present embodiment. FIG. 11 is a conceptual diagram of a cylindrical coordinate system grid and a workpiece shape model of the present embodiment. FIG. 12 is a conceptual diagram of a workpiece shape model in a polar coordinate system of the present embodiment. FIG. 13 is a partial enlarged view of FIG. 3. FIG. 14 is a partial enlarged view of a workpiece shape model in a polar coordinate system in a modified embodiment. FIG. 15 is a flow diagram explaining how to use the vibration simulation device and the machining shape simulation device of the present embodiment. FIG. 16 is a functional block diagram (procedure) of the rake angle calculation unit of FIG. 1. FIG. 17 is a perspective view showing the basic operation of gear machining. FIG. 18 is a partial sectional schematic view of the machining tool of FIG. 1. FIG. 19 is a diagram explaining the operation of gear skiving, showing the relative positions of the workpiece and the machining tool, projected onto the Xw, Zw plane (viewed from the Yw direction). FIG. 19 is a diagram explaining the operation of gear skiving, showing the relative positions of the workpiece and the machining tool, projected onto the Xw, Yw plane (viewed from the Zw direction). FIG. 19 is a diagram showing the process from the start to the end of cutting of the tool blade relative to the tooth groove. FIG. 19 is a perspective view of the tool blade showing the definition points in the definition point determination unit of FIG. 1. 18 is a diagram showing the cutting depth vector L(i), the inter-definition point vector B(i), and the plane G(i). FIG. 19 is a diagram showing the blade surface normal vector N(i). FIG. 20 is a diagram showing the projection normal vector Ng(i). FIG. 21 is a diagram showing the projected rake angle αg(i). FIG. 22 is a diagram showing the portion of one tool blade in one tooth groove that is removed in one feed in the tooth groove direction. FIG. 23 is a diagram showing the relationship between the tool rotation angle and the rake angle in the cutting of FIG. 17. FIG. 24 is a diagram showing a two-dimensional cutting model. FIG. 25 is a diagram showing the reference state of the workpiece shape model. FIG. 26 is a diagram showing a workpiece shape model and a machining tool shape model. FIG. 27 is a diagram showing the workpiece shape model in a state where the azimuth angle has been changed. FIG. 28 is a diagram showing the final machining position by each definition point P(k). FIG. 29 is a diagram showing the calculation results of each component of the cutting force. FIG. 29 is a diagram showing the prediction results by the vibration simulation device of the present embodiment.

[0013] 1. Definition of Workpiece Shape Model The definition of a workpiece shape model to which gear-generating cutting is applied, which is the target of application of the machining shape simulation device 100 (see FIG. 1) in this embodiment, will be described with reference to FIGS. 1 to 4.

[0014] In this embodiment, first, a required value for the prediction accuracy of the machining result is acquired by the analysis condition acquisition unit 110 shown in FIG. 1 . The required value for the prediction accuracy of the machining result can be arbitrarily set by the user, or may be a preset value. Next, based on the required value for prediction accuracy, the cylindrical coordinate system lattice definition unit 111 defines a cylindrical coordinate system lattice, as shown in FIG. 2 , which is composed of a radial distance R component, an axial coordinate Z component, and an azimuth angle θ component, and in which a lattice pitch Pr of the radial distance R is set based on the required value for prediction accuracy. Each Z coordinate plane in the cylindrical coordinate system lattice shown in FIG. 2 can be represented as a polar coordinate system composed of a radial distance R component and an azimuth angle θ component, and a polar coordinate system with a Z coordinate component Z1 is represented as shown in FIG. 3 .

[0015] In this embodiment, as shown in Figures 3 and 4, the grating pitch Pr of the radial distance R is set to an equal interval. However, this is not limited to this, and the grating pitch Pr of the radial distance R may be set to an unequal interval. For example, as in a modified embodiment shown in Figure 5, in the tooth flank portions Wmc1 and Wmc2, the grating pitch Pr1 at the center of the tooth flank portions Wmc1 and Wmc2 may be made small, and the grating pitch Pr2 near the tooth tip Wa and near the tooth root Wb may be made large. In either case, the range of the radial distance R is set to a range from the tooth tip Wa to the tooth root Wb of the gear to be generated on the workpiece 20.

[0016] Furthermore, in this embodiment, the cylindrical coordinate system lattice definition unit 111 sets the cylindrical coordinate system lattice so that the lattice points of the cylindrical coordinate system lattice are located at positions that are the targets of prediction accuracy verification by the prediction accuracy verification unit 191, which will be described later. Verification of prediction accuracy will be described in detail later.

[0017] Next, the workpiece shape model defining unit 120 defines a workpiece shape model in a cylindrical coordinate system lattice based on analysis conditions including tool specifications, workpiece specifications, and machining conditions, so that the axial direction of the gear to be generated is parallel to the direction of the axial coordinate Z, as shown in FIGS. 2 to 4 . In this embodiment, the axial direction of the gear to be generated coincides with the direction of the axial coordinate Z, and the origin O shown in FIG. 3 coincides with the center of the cross section of the workpiece 20 at the Z-axis coordinate component Z1. As described above, this workpiece shape model is defined as an "RZ-θ system model" and is defined by specifying the azimuth angle θ with respect to the radial distance R and the axial coordinate Z. Note that in the workpiece shape model shown in the cylindrical coordinate system lattice, two lattice points are obtained for each tooth groove for one radial distance R: one on one tooth flank and one on the other tooth flank. Therefore, in a polar coordinate system of radial distance R and azimuth angle θ, the number of lattice points in the workpiece shape model is the number of teeth × 2 × the number of radial distances R.

[0018] For example, as shown in FIG. 4, in the workpiece shape model, in a polar coordinate system of a radial distance R and an azimuth angle θ in a Z-axis coordinate component Z1, in the m-th tooth groove among the plurality of tooth grooves formed on the workpiece 20, the lattice point Wm11 of one tooth flank portion Wmc1 with respect to the radial distance r1 is ｍ ｒ１、１ is specified, and the lattice point Wm21 of the other tooth surface portion Wmc2 has an azimuth angle θ ｍ ｒ１、２ Similarly, for radial distances r2 to r5, lattice points Wm12, Wm13, Wm14, and Wm15 of one tooth surface portion Wmc1 are designated by an azimuth angle θ ｍ ｒ２、１ , θ ｍ ｒ３、１ , θ ｍ ｒ４、１ , θ ｍ ｒ５、１ is specified, and the lattice points Wm22, Wm23, Wm24, and Wm25 of the other tooth surface portion Wmc2 are set at an azimuth angle θ ｍ ｒ２、２ , θ ｍ ｒ３、２ , θ ｍ ｒ４、２ , θ ｍ ｒ５、２is specified. In the tooth tip Wa and tooth bottom Wb, no lattice points exist except at the junctions with the tooth flanks Wmc1 and Wmc2. In all tooth spaces, an azimuth angle θ is similarly specified for the radial distances r1 to r5 of the lattice points. Furthermore, an azimuth angle θ is specified for the radial distances r1 to r5 of the lattice points for all Z-axis coordinate components in the cylindrical coordinate system. As a result, the workpiece shape model shown in FIG. 2 is defined. The defined workpiece shape model is stored in a storage unit (not shown).

[0019] In this embodiment, the central axis of the gear to be generated coincides with the direction of the axial coordinate Z, and the origin O shown in Fig. 3 coincides with the center of the cross section of the workpiece 20 at the Z-axis coordinate component Z1. Alternatively, the axial direction of the gear to be generated may coincide with the direction of the axial coordinate Z, but the central axis of the gear may be at a position different from the axial coordinate Z. In this case, the workpiece shape model can be specified so that lattice points exist not only in the tooth flanks Wmc1 and Wmc2 but also in the tooth tip Wa and tooth bottom Wb in areas other than the junctions with the tooth flanks Wmc1 and Wmc2.

[0020] 2. Basic Operations of Gear-Generating Cutting Next, the basic operations of gear-generating cutting to which the machining shape simulation device 100 (see FIG. 1) in this embodiment is applied will be described with reference to FIGS. 8 and 9. Here, in this embodiment, an example is given in which the gear-generating cutting is skiving, in which a gear 21 is formed on the inner peripheral surface of a workpiece 20 using a tool 10 that is a skiving cutter. However, this is also applicable to skiving, in which a gear is machined on the outer peripheral surface of the workpiece 20. It is also applicable to hobbing, in which a gear is machined on the outer peripheral surface of the workpiece 20 using a tool that is a hob cutter.

[0021] 8, the workpiece 20 is formed in an annular shape, and a gear 21 is formed on its inner peripheral surface. The workpiece 20 is supported so as to be rotatable about its central axis Zw. In other words, the workpiece 20 is rotatable about the C-axis.

[0022] As shown in Figures 8 and 9, the tool 10 has a plurality of tool blades 11 on its outer periphery and is supported rotatably around the central axis Zt of the tool 10. In other words, the tool 10 is rotatable around a U axis. Each tool blade 11 is formed as a ridge. Each tool blade 11 has a side surface 11a in the extension direction of the tool blade 11, an end surface 11b in the extension direction, and a radial outer surface 11c. In gear generating cutting, the end surface 11b serves as a rake face, and the side surface 11a and the radial outer surface 11c serve as flanks. In particular, the side surface 11a serves as a side flank, and the radial outer surface 11c serves as a front flank.

[0023] In this embodiment, the tool blade 11 has a helix angle γ1 with respect to the central axis Zt of the tool 10. However, the tool blade 11 may be formed so that the helix angle γ1 is zero. The radial outer surface 11c of the tool blade 11 is inclined with respect to the central axis Zt. That is, the circumscribing surface of the tool blade 11 is formed in a conical shape. The inclination angle ξb of the radial outer surface 11c of the tool blade 11 corresponds to the clearance angle in cutting. The end face 11b of the tool blade 11 is inclined by an angle ξa with respect to a plane perpendicular to the central axis Zt. The inclination angle ξa of the end face 11b of the tool blade 11 corresponds to the rake angle in cutting. Although not shown, the side surface 11a of the tool blade 11 has a side clearance angle, and the edge angle of the end face 11b of the tool blade 11 is zero.

[0024] 8, the central axis Zt of the tool 10 is at an angle with respect to an axis parallel to the central axis Zw of the workpiece 20, i.e., at an intersection angle θ (see FIG. 10A). In other words, the central axes Zt and Zw of the tool 10 are not parallel to each other.

[0025] In this state, while synchronizing the rotation of the tool 10 and the rotation of the workpiece 20, the tool 10 is moved straight relative to the workpiece 20 in the direction indicated by the arrow f, which is opposite and parallel to the direction of the central axis Zw of the workpiece 20, as shown by the thick arrow in Figure 8. Note that the tool 10 may be moved in the direction f, or the workpiece 20 may be moved in the direction opposite to the direction f. In other words, at least one of the tool 10 and the workpiece 20 is moved so that the tool 10 moves in the direction f relative to the workpiece 20.

[0026] Because the central axis Zt of the tool 10 and the central axis Zw of the workpiece 20 form an intersection angle θ, a relative velocity is generated between the tool 10 and the workpiece 20 at the machining point. As a result, the workpiece 20 is cut. As a result, tooth grooves 22 of the gear 21 are formed on the inner peripheral surface of the workpiece 20, as shown in Figure 8. Note that Figure 8 shows a state in which the tooth grooves 22 have been machined partway into the workpiece 20, but by continuing the above operation, the tooth grooves 22 will be formed over the entire axial length of the workpiece 20.

[0027] 3. Gear-generating cutting device A gear-generating cutting device for carrying out the gear-generating cutting method of this embodiment may be, for example, a 5-axis machining center (not shown). That is, a device may be used that can relatively move the tool 10 and the workpiece 20 linearly in three mutually orthogonal axis directions, rotate the tool 10 and the workpiece 20 about their respective axes (U-axis rotation, C-axis rotation), and tilt the central axis Zt of the tool 10 and the central axis Zw of the workpiece 20.

[0028] 4. Overview of the Vibration Simulation Device 1 and the Machined Shape Simulation Device 100 An overview of the vibration simulation device 1 and the machined shape simulation device 100 according to an embodiment of the present invention will be described. As shown in FIGS. 10A and 10B , in gear skiving, the workpiece 20 and the tool 10 are rotated synchronously (U-axis rotation, C-axis rotation) while the tool 10 is fed in the direction of the center axis Zw of the workpiece 20. At this time, the rotation angle η of the workpiece 20 and the rotation angle σ of the tool 10 (tool blade 11) (hereinafter referred to as the "tool rotation angle σ") are related by the following equation (1). Here, Jw is the number of teeth of the gear 21, Jt is the number of teeth of the tool blade 11, and δ is the correction angle. The machined shape simulation device 100 may be built into the control device of a gear generating cutting device. The machining shape simulation device 100 may also be an embedded system such as a PLC (Programmable Logic Controller) or a CNC (Computer Numerical Control) device, or may also be a personal computer or a server.

[0029]

[0030] In gear skiving, multiple tool blades 11 formed on the outer periphery of the tool 10 are simultaneously involved in cutting multiple tooth grooves 22 (see Figure 8) of a gear 21 formed on the inner periphery of the workpiece 20, but each tool blade 11 and each tooth groove 22 is geometrically in the same cutting state.

[0031] Therefore, the machining shape simulation device 100 of this embodiment focuses on the rotation of one tool blade 11 in one tooth space 22, and performs analysis by rotating the tool 10 by a small angle, that is, by slightly increasing the tool rotation angle σ in formula (1). Furthermore, by focusing on the feed of one tool blade 11 in one tooth space 22, the range from the start of cutting to the end of cutting of one tool blade 11 becomes clear. That is, as shown in the order of (a), (b), and (c) in Fig. 11, the tool blade 11 starts cutting the tooth space 22 at a tool rotation angle σs, passes through a tool rotation angle σ = 0, and ends cutting the tooth space 22 at a tool rotation angle σe.

[0032] This allows for more detailed analysis of the cutting state of one tool blade 11 in a shorter time than conventional methods, and also makes it possible to easily calculate the tool blade characteristics required for proper design of the tool 10, i.e., the rake angle of the tool blade 11 and the cutting force exerted by the tool blade 11 involved in cutting.

[0033] As described above, the shape of the tool blade 11 of the tool 10 is very complex. Therefore, as will be described in detail later, the boundary lines between the end face 11b (rake face) of the tool blade 11 and the side face 11a and radial outer face 11c (flank face) are divided into a plurality of regions ΔP(i, i+1) as shown in Fig. 12. This allows two-dimensional processing for each region ΔP(i, i+1).

[0034] That is, for each region ΔP(i, i+1), a two-dimensional cutting model is used to calculate the rake angle α(i) and compute the cutting force FH(i). Then, the calculated cutting force FH(i) is used to calculate the cutting force FH for the entire region. Furthermore, the relative vibration between the tool 10 and the workpiece 20 is calculated using the cutting force FH(i) and the dynamic characteristics of the tool 10 and the workpiece 20. This will be explained in detail below.

[0035] 5. Details of the Vibration Simulation Device 1 and the Machining Shape Simulation Device 100 The vibration simulation device 1 and the machining shape simulation device 100 will be described. The vibration simulation device 1 and the machining shape simulation device 100 are configured with one or more arithmetic processing devices and storage devices, and as shown in Fig. 1, the vibration simulation device 1 includes an analysis condition acquisition unit 110, a cylindrical coordinate system lattice definition unit 111, a workpiece shape model definition unit 120, a tool shape model definition unit 121, an interference region calculation unit 130, a cutting force calculation unit 140, a dynamic characteristic calculation unit 150, a vibration calculation unit 160, an output unit 170, and an update unit 180. The machining shape simulation device 100 includes the vibration simulation device 1, a machining result prediction unit 190, and a prediction accuracy verification unit 191.

[0036] Here, in explaining the machining shape simulation device 100, the following will be described in the following order, with reference to the flow diagram of FIG. 6 showing the usage mode of the machining shape simulation device 100: (5-1) explanation of the process for defining the workpiece shape model and the tool shape model, (5-2) explanation of the process for calculating the rake angle, (5-3) explanation of the two-dimensional cutting model, (5-4) explanation of the process for calculating the cutting depth, (5-5) explanation of the process for calculating the cutting force, (5-6) explanation of the process for calculating the relative vibration, (5-7) explanation of the update of information and the output of the calculation results, and (5-8) explanation of the process for predicting the machining result and verifying the prediction results.

[0037] 5-1. Processing for defining workpiece shape model and tool shape model In the processing for defining the workpiece shape model, the analysis conditions are acquired by the analysis condition acquisition unit 110 as described above (step S1 in FIG. 6), and then the cylindrical coordinate system lattice definition unit 111 and the workpiece shape model definition unit 120 define the workpiece shape model (step S2a in FIG. 6). As a result, the shape of the workpiece 20 is defined by a point cloud consisting of a plurality of points (lattice points) located on the surface of the workpiece shape model.

[0038] The analysis conditions include tool specifications, which are the specifications of the tool 10, workpiece specifications, which are the specifications of the workpiece 20, and machining conditions for a gear generating cutting device (not shown). The analysis conditions may also include other information. The analysis conditions acquired by the analysis condition acquisition unit 110 can be acquired by the user inputting some or all of the analysis conditions, or by retrieving some or all of the analysis conditions stored in advance in a storage unit (not shown).

[0039] The tool shape model definition process is performed by the tool shape model definition unit 121 based on the analysis conditions acquired by the analysis condition acquisition unit 110 (step S2b in FIG. 6 ). In this embodiment, the shape of the tool 10 is defined by a point cloud consisting of a plurality of points located on the surface of the tool shape model. Specifically, as shown in FIG. 12 , the tool 10 defines the boundary lines between the end face 11b (rake face) of each tool blade 11 and the side face 11a and radial outer surface 11c (flank face) as a plurality of definition points P(k). In other words, by connecting the plurality of definition points P(k) (where k = 1 to n, n is a natural number) with straight lines, the shape of the boundary line of the tool blade 11 is approximated. Here, although FIG. 12 shows 13 definition points P(1) to P(13), the number of definition points P(k) can be freely set. In addition, when machining only the tooth surface of the gear 21 and not the tooth bottom, the multiple definition points P(k) can be defined only on the boundary line between the end face 11b, which is the rake surface, and the side surface 11a, which is the side relief surface, and not on the boundary line between the end face 11b and the radial outer surface 11c, which is the front relief surface.

[0040] Here, the terminology used in the following processing regarding the tool blade 11 will be explained with reference to FIG. 12 . The area between two adjacent definition points P(i) and P(i+1) is referred to as the inter-definition point area ΔP(i, i+1). For example, the area between definition points P(1) and P(2) is ΔP(1, 2). Furthermore, the midpoint between two adjacent definition points P(i) and P(i+1) is referred to as Pc(i, i+1). For example, the midpoint between definition points P(1) and P(2) is Pc(1, 2).

[0041] For a workpiece 20 represented by a cylindrical coordinate system lattice, the processed portion of the workpiece 20 is represented by specifying an azimuth angle θ with respect to a radial distance R and an axial coordinate Z using an RZ-θ system model 26, as shown in FIG.

[0042] 5-2. Rake Angle Calculation Process Next, the rake angle calculation process will be described with reference to the cutting-in vector calculation unit 131 and the rake angle calculation unit 132 included in the interference area calculation unit 130 in Fig. 1. The cutting-in vector calculation unit 131 calculates, for each inter-definition point area ΔP(i, i+1), a cutting-in vector L(i) along which the inter-definition point area ΔP(i, i+1) moves in the cutting direction while the tool 10 rotates from the rotation angle σ1, which is the first time, to the rotation angle σ2, which is the second time. However, it is not easy to calculate the direction in which the entire inter-definition point area ΔP(i, i+1) moves.

[0043] Therefore, as shown in Fig. 13, the vector Lc(i) along which the midpoint Pc(i, i+1) of two adjacent definition points P(i) and P(i+1) moves in the cutting direction is calculated as the cutting vector L(i). In this way, by using the midpoint Pc(i, i+1), the vector along which the point moves can be calculated easily and reliably.

[0044] The rake angle calculation unit 132 calculates the rake angle α(i) based on the cutting vector L(i). The rake angle α(i) is the rake angle when cutting the workpiece 20 using each inter-definition point area ΔP(i, i+1). The rake angle calculation unit 132 calculates the rake angle α(i) according to the procedure shown in FIG. 7.

[0045] The calculation of the rake angle α(i) will be described below with reference to Fig. 7 and Figs. 13 to 16. First, as shown in Fig. 7, the cutting vector L(i) is calculated by the cutting vector calculation unit 131 as described above (reference numeral S31 in Fig. 7), and then the inter-definition point vector B(i) is calculated (S32 in Fig. 7). The inter-definition point vector B(i) is a vector connecting two adjacent definition points P(i) and P(i+1), as shown in Fig. 13. Here, the midpoint Pc(i, i+1) is located at the middle position of the inter-definition point vector B(i).

[0046] Next, based on the incision vector L(i) calculated by the incision vector calculation unit 131 and the inter-definition point vector B(i), a plane G(i) that includes the incision vector L(i) and is perpendicular to the inter-definition point vector B(i) is calculated (reference numeral S33 in FIG. 7). The plane G(i) is as shown in FIG.

[0047] Here, a normal vector C(i) for defining the plane is used to define the plane G(i). That is, the normal vector C(i) for defining the plane is a vector that passes through the midpoint Pc(i, i+1) and is perpendicular to the incision vector L(i) and the inter-definition point vector B(i). Therefore, the plane G(i) can be defined as a plane that passes through the midpoint Pc(i, i+1) and includes the incision vector L(i) and the normal vector C(i) for defining the plane.

[0048] The purpose of calculating this plane G(i) is to use a two-dimensional cutting model based on two-dimensional cutting theory, as described above. In other words, by applying the two-dimensional cutting model to the plane G(i), the cutting force FH(i) on the plane G(i) is calculated.

[0049] Next, a normal vector N(i) (hereinafter referred to as the "blade surface normal vector") of the tool blade 11 at the midpoint Pc(i, i+1) is calculated (reference numeral S34 in FIG. 7). Here, the blade surface normal vector N(i) cannot be obtained by simply determining two adjacent definition points P(i) and P(i+1). Therefore, as shown in FIG. 14, three or more adjacent definition points P(k) including the definition points P(i) and P(i+1) are used. Here, three definition points P(i-1), P(i), and P(i+1) are used.

[0050] As shown in Figure 14, a plane Q(i) is determined that passes through three definition points P(i-1), P(i), and P(i+1). Then, on the plane Q(i), a vector that passes through the midpoint Pc(i, i+1) and is perpendicular to the vector B(i) between the definition points is defined as the blade surface normal vector N(i).

[0051] Next, after calculating the plane G(i) and the blade surface normal vector N(i), a projection normal vector Ng(i) obtained by projecting the blade surface normal vector N(i) onto the plane G(i) is calculated (reference number S35 in FIG. 7).

[0052] 15, plane G(i) and plane Q(i) are not necessarily the same plane. Therefore, the blade surface normal vector N(i) is located on plane Q(i), but not necessarily on plane G(i). Therefore, as described above, by projecting the blade surface normal vector N(i) onto plane G(i), the projected normal vector Ng(i) located on plane G(i) is obtained.

[0053] Next, the projected rake angle αg(i), which is the angle between the projected normal vector Ng(i) and the cutting vector L(i) on the plane G(i), is calculated (reference numeral S36 in FIG. 7). The projected rake angle αg(i) is as shown in FIG. 16. Here, since the projected rake angle αg(i) is calculated on the plane G(i), it differs from the actual rake angle α(i).

[0054] However, in order to use the two-dimensional cutting model on the plane G(i), the projected rake angle αg(i) is estimated as the rake angle α(i). In this way, the rake angle calculation unit 132 calculates the rake angle α(i) (=projected rake angle αg(i)).

[0055] 17 , in one feed of one tool blade 11 in one tooth groove 22 in the tooth groove direction (direction of the arrow in the figure), for example, a portion 23 shown by the hatched line in the figure becomes an interference region and is removed. That is, the tool blade 11 rotates as the feed proceeds, and is located at the cutting start position (position shown by the two-dot chain line in the figure) when the tool rotation angle σ is σs, is located at the portion where the removed portion (interference region) 23 and the one-dot chain line in the figure overlap when the tool rotation angle σ is σa, σb, or σc, and is located at the cutting end position (position shown by the two-dot chain line in the figure) when the tool rotation angle σ is σe.

[0056] The rake angle αg(i) can be found in the range from the start of cutting to the end of cutting for one tool blade 11 in one tooth groove 22. For example, as shown in Fig. 18, the rake angle αg(i) relative to the tool rotation angle σ can be found for each of the left cutting surface of the tool blade 11 (broken line in the figure, definition points P(1)-P(4) in Fig. 12), the cutting edge of the tool blade 11 (solid line in the figure, definition points P(5)-P(9) in Fig. 12), and the right cutting surface of the tool blade 11 (dash line in the figure, definition points P(10)-P(13) in Fig. 12) in the range from the start of cutting (tool rotation angle σs) to the end of cutting (tool rotation angle σe).

[0057] Each line segment representing the rake angle αg(i) is a set of values ​​at the midpoint P(i, i+1) of the tool blade 11. When the tool rotation angle σ is 0, this is when the tool blade 11 reaches the center of the tooth groove 22 in the tooth groove direction (the same applies to the following figures). At locations where the calculated rake angle αg(i) is negative, the cutting depth increases and the cutting force increases locally, so the specifications of the tool blade 11 are changed so that the rake angle αg(i) does not become negative.

[0058] Next, a two-dimensional cutting model based on two-dimensional cutting theory will be described with reference to Fig. 19. Fig. 19 shows the cutting model on the plane G(i) described above. In Fig. 19, a workpiece 20 is cut by the tool blade 11 of a tool 10.

[0059] Here, in plane G(i), the rake face of the tool blade 11 is the end face 11b, the side relief face is the side surface 11a, and the front relief face is the radial outer surface 11c. The rake angle is αg(i). The cutting amount is d1(i), and the shear angle is φ(i). At this time, the cutting vector by the tool blade 11 is L(i), and the normal vector of the tool blade 11 is Ng(i). The cutting vector L(i) corresponds to the principal force Fc(i) in the two-dimensional cutting model, and the thrust force Ft(i) is illustrated as shown in FIG. 19. Here, the principal force Fc(i) and thrust force Ft(i) at the relevant portion are respectively expressed as in equation (2).

[0060]

[0061] In equation (2), τs is the shear stress and is obtained in advance based on the target material, etc. The cutting cross-sectional area A can be expressed as the product of b(i), the distance between two adjacent definition points P(i) and P(i+1), and the cutting depth d1(i) of the area between the definition points ΔP(i, i+1). The cutting depth d1(i) corresponds to the average of the cutting depth (corresponding to the radial depth) at definition point P(i) and the cutting depth at definition point P(i+1). φ(i) is the shear angle, which can be obtained from publicly known technical information. αg(i) is the projected rake angle mentioned above. β is the rake face friction angle, which is determined empirically. As described above, it can be seen that the two-dimensional cutting model can be applied by calculating the rake angle αg(i) on plane G(i). The same application as the two-dimensional model can be applied when a three-dimensional cutting model is used instead of the two-dimensional cutting model.

[0062] 5-4. Cut-in Amount Calculation Processing In the above two-dimensional cutting model, if the cut-in amount d1(i) can be obtained, the cutting force FH(i) can be obtained. If the shape of the workpiece 20 immediately before and the shape of the workpiece 20 when cutting this time are known, the cut-in amount d1(i) can be obtained from the difference between the two. This will be described in detail below with reference to FIGS. 21 to 23.

[0063] Here, the cutting depth calculation process will be described with reference to the intersection calculation unit 133, the removal area calculation unit 134, and the final machining position extraction unit 135 in FIG.

[0064] 21 , the intersection calculation unit 133 considers the case where the tool blade 11 moves relative to the workpiece 20 using the shape of the workpiece 20 and the infinitesimal line segment movement trajectory of the tool blade 11 of the tool 10 when the tool rotation angle σ defined by the tool shape model definition unit 121 slightly increases from σ1 to σ2. In this embodiment, the infinitesimal line segment movement trajectory from when the boundary 11s between the end face 11b (the rake face) and the side face 11a and radial outer surface 11c (the flank face) is at a first time position 11s1 where the tool rotation angle σ is σ1 to a second time position 11s2 where the tool rotation angle σ slightly increases to σ2 is defined by a trajectory plane 11p using a triangular patch. Then, by moving the tool blade 11 relatively, the intersection of the RZ-θ system model 26 representing the workpiece 20 and the trajectory plane 11p of the tool blade 11 is calculated.

[0065] If the intersection calculation unit 133 finds an intersection, the removal area calculation unit 134 changes the shape of the RZ-θ system model 26 representing the workpiece 20, as shown in Fig. 22. That is, a portion of the workpiece 20 is cut by the tool blade 11 when the tool rotation angle σ increases slightly from σ1 to σ2, and this portion is stored as the shape after cutting. At this time, the removal area calculation unit 134 stores the removal area removed from the RZ-θ system model 26. The azimuth angle θ corresponding to this removal area corresponds to the amount of cut when the tool rotation angle σ increases slightly from σ1 to σ2 (when the first time point has elapsed until the second time point), and the interference area between the tool 10 and the workpiece 20 is calculated (S3 in Fig. 6).

[0066] The final machining position extraction unit 135 extracts the final machining positions of each definition point P(k) representing the tool blade 11 while the tool rotation angle σ slightly increases from σ1 to σ2. Here, Fig. 23 plots the points to which each definition point P(k) moves while the tool rotation angle σ slightly increases from σ1 to σ2. An open circle indicates the final machining position of each definition point P(k), and a black circle indicates a position other than the final machining position of each definition point P(k).

[0067] In other words, the final machining position of each definition point P(k) corresponds to the position of each definition point P(k) at tool rotation angle σ2. If these positions are known, the cutting depth at each definition point P(k) can be calculated from the azimuth angle θ of the final machining position and the shape of the workpiece 20 immediately before. In other words, it is possible to grasp the change in shape of the workpiece 20 while the tool rotation angle σ increases slightly from σ1 to σ2.

[0068] The cutting depth d1(i) in the two-dimensional cutting model corresponds to the average of the cutting depth at the definition point P(i) and the cutting depth at the definition point P(i+1). In other words, since the cutting depth at each definition point P(k) can be obtained, the cutting depth d1(i) at the midpoint Pc(i, i+1) can be calculated.

[0069] In this way, the final machining position extraction unit 135 calculates the final machining position based on each definition point P(k), calculates the cutting amount at each definition point P(k), and further calculates the cutting amount d1(i) at the midpoint Pc(i, i+1). The intersection calculation unit 133 calculates the intersection between the RZ-θ system model 26 representing the workpiece 20 and the trajectory plane 11p of the tool blade 11 within the range from the start to the end of cutting of one tooth groove 22 by one tool blade 11. Then, each time the cutting of one tooth groove 22 by one tool blade 11 is repeatedly executed from the start to the end of cutting, the shape of the workpiece 20 is updated and the intersection between the RZ-θ system model 26 representing the workpiece 20 and the trajectory plane 11p of the tool blade 11 is calculated.

[0070] 5-5. Cutting Force Calculation Process Next, the calculation process of the cutting force FH(i) for each region ΔP(i, i+1) using the two-dimensional cutting model will be described. This process will be described with reference to FIG. 1 with respect to the cutting force calculation unit 140.

[0071] The cutting force calculation unit 140 in Fig. 1 calculates the cutting force FH(i) for each region ΔP(i, i+1) using the two-dimensional cutting model shown in Fig. 19 (S4 in Fig. 6). This cutting force FH(i) can be calculated by dividing the principal force Fc(i) and thrust force Ft(i) in the above-mentioned formula (2) into components in the Xw direction, the Yw direction, and the Zw direction, which are the three orthogonal axial directions of the workpiece 20, and then adding up the components in each direction.

[0072] That is, the principal force Fc(i) and thrust force Ft(i) are divided into Xw direction, Yw direction, and Zw direction components and are expressed as follows:

[0073]

[0074] Here, the unit vector is defined as in equation (4).

[0075]

[0076] Then, the components Fcx(i), Fcy(i), Fcz(i) of the principal force Fc(i) and the components Ftx(i), Fty(i), Ftz(i) of the thrust force Ft(i) are expressed by the following equation (5).

[0077]

[0078] The components FHx(i), FHy(i), and FHz(i) of the cutting force FH(i) are expressed as in equation (6) using the components of the principal force Fc(i) and the thrust force Ft(i).

[0079]

[0080] The cutting force FH in the entire region is the sum of the cutting forces FH(i) in each region ΔP(i, i+1), and therefore each component FHx, FHy, and FHz of the cutting force FH is expressed as in equation (7).

[0081]

[0082] The cutting force FH in the entire region can be calculated based on the formula (7). The calculation results of each component of the cutting force FH are shown in Figure 24, for example, and are close to the measured values, confirming that the calculation results are highly accurate.

[0083] Next, a description will be given of a process for calculating the relative vibration between the tool 10 and the workpiece 20. The process for calculating the relative vibration will be described with reference to the dynamic characteristic calculation unit 150, the vibration calculation unit 160, and the output unit 170 in FIG.

[0084] First, the dynamic characteristic calculation unit 150 calculates the relative dynamic characteristic or individual dynamic characteristic between the tool 10 and the workpiece 20. In this embodiment, the calculation is performed based on information acquired by the analysis condition acquisition unit 110. For example, the analysis condition acquisition unit 110 can calculate the dynamic characteristic based on information acquired by a hammering test or the like. The relative dynamic characteristic can be calculated based on the tool 10 and the workpiece 20 that are calculated individually. Furthermore, if the dynamic characteristic of the workpiece 20 can be ignored, the dynamic characteristic of the tool 10 can be used as the relative dynamic characteristic.

[0085] The vibration calculation unit 160 includes a transfer function processing unit 161 and a restoring action calculation unit 162. The transfer function processing unit 161 calculates the relative vibration between the tool 10 and the workpiece 20 based on a transfer function from the relative dynamic characteristics calculated by the dynamic characteristics calculation unit 150 and the cutting force FH (S5 in FIG. 6). In this embodiment, the transfer function processing unit 161 outputs displacement, velocity, and acceleration.

[0086] The restoring action calculation unit 162 calculates a restoring action that increases nonlinearly with an increase in the amplitude of the relative vibration calculated by the transfer function processing unit 161. In this embodiment, the transfer function used in the transfer function processing unit 161 or the cutting force FH input to the transfer function processing unit 161 is corrected based on at least one of the displacement, velocity, and acceleration output by the transfer function processing unit 161. The restoring action calculation unit 162 is appropriately designed, for example, to reflect the effect of vibration suppression by process damping when cutting the workpiece 20 with the tool 10.

[0087] As shown in Figure 25, if no correction is made by the restoring action calculation unit 162, the displacement calculated by the vibration calculation unit 160 will diverge over time, but this divergence is suppressed by correcting the transfer function or cutting force FH by the restoring action calculation unit 162.

[0088] 5-7. Information Update and Output of Calculation Results Next, information update by the update unit 180 and output by the output unit 170 will be described. First, the calculation results of the transfer function processing unit 161 are input to the update unit 180 and output from the output unit 170. The update unit 180 updates the relative position between the tool 10 and the workpiece 20 and the workpiece shape model based on the interference region calculated by the interference region calculation unit 130 and the relative vibration calculated by the vibration calculation unit 160 (S6 in FIG. 6). That is, the positions of the tool 10 and the workpiece 20 are updated to update the relative position between them, and the shape from which the interference region has been removed is used as the updated workpiece shape model. Then, based on the updated information, the interference region calculation unit 130 calculates the interference region, the cutting force calculation unit 140 calculates the cutting force, and the vibration calculation unit 160 calculates the relative vibration, repeating this process until machining of the workpiece 20 is completed (No in S7 in FIG. 6).

[0089] When the processing is completed (Yes in S7 in FIG. 6), the output unit 170 outputs the calculation result of the vibration calculation unit 160 (S8 in FIG. 6). Each time the output unit 170 is updated by the update unit 180, the output unit 170 outputs the calculation result based on the update information.

[0090] 5-8. Prediction of machining shape and verification of prediction result Next, prediction of machining shape by the machining shape simulation device 100 shown in Fig. 1 will be described. In the machining shape simulation device 100, the machining result prediction unit 190 predicts the shape of the workpiece 20 after machining based on the update result of the update unit 180. Specifically, the workpiece shape model updated based on the interference region updated by the update unit 180 is predicted as the shape of the workpiece 20 after machining.

[0091] Next, verification of the prediction result by the prediction accuracy verification unit 191 shown in FIG. 1 will be described. The prediction accuracy verification unit 191 verifies the prediction accuracy by comparing the machined shape predicted by the machining result prediction unit 190 with the target shape. The prediction accuracy is verified by comparing a specific reference position in the target shape with a corresponding position in the predicted shape, which is the prediction result, that corresponds to the reference position. The reference position can be set at any position on the tooth flank portions Wmc1 and Wmc2, and multiple reference positions can be set. Then, as described above, the cylindrical coordinate system lattice definition unit 111 sets a cylindrical coordinate system lattice so that the lattice points of the cylindrical coordinate system lattice are located at target positions for verifying the prediction accuracy of the machined shape.

[0092] 6. Actions and Effects Next, the actions and effects of the machining shape simulation device 100 of this embodiment will be described in detail. The machining shape simulation device 100 of this embodiment defines a cylindrical coordinate system lattice in which the lattice pitch of the radial distance R is set to a predetermined value, and uses an RZ-θ system model, which is a workpiece shape model defined by specifying an azimuth angle θ with respect to the radial distance R and the axial coordinate Z of the lattice pitch set in the cylindrical coordinate system. In the RZ-θ system model, by reducing the lattice pitch of the radial distance R of the cylindrical coordinate system lattice in which the workpiece shape model is represented, it is possible to increase the data density of the tooth flanks Wmc1 and Wmc2 while maintaining a low data density of the tooth tip Wa and tooth root Wb in the workpiece shape model, and therefore it is possible to reduce the calculation load while improving the prediction accuracy of gear performance and machining results.

[0093] Furthermore, in this embodiment, the tool 10 is provided with a cutting force calculation unit 140 that calculates the cutting force when removing the interference area from the workpiece 20, and the machining result prediction unit 190 predicts the machining result of the workpiece 20 based on the calculation results of the interference area calculation unit 130 and the cutting force calculation unit 140. In this way, by predicting the machining result of the workpiece 20 using the calculation result of the cutting force in addition to the calculation result of the interference area, it is possible to further improve the prediction accuracy of gear performance and machining results.

[0094] This embodiment also includes a dynamic characteristic calculation unit 150 that calculates the relative dynamic characteristic or individual dynamic characteristics between the tool 10 and the workpiece 20 based on the analysis conditions, and a vibration calculation unit 160 that calculates the relative vibration between the tool 10 and the workpiece 20 based on the cutting force and the relative dynamic characteristic. The machining result prediction unit 190 predicts the machining result of the workpiece 20 based on the vibration simulation result consisting of the relative vibration repeatedly calculated by the interference region calculation unit 130, the cutting force calculation unit 140, and the vibration calculation unit 160. This makes it possible to improve the prediction accuracy of gear performance and machining results while reducing the calculation load.

[0095] Furthermore, in this embodiment, the workpiece shape model defining unit 120 defines the workpiece shape model so that the axial direction of the gear generated in the workpiece shape coincides with the axial coordinate Z. This makes it easier to densely allocate grid points to the tooth flanks while keeping the number of grid points at the tooth tip and tooth root in a cylindrical coordinate system grid. In other words, the data density at the tooth flanks can be further increased while maintaining a low data density at the tooth tip and tooth root, thereby further improving the prediction accuracy of gear performance and machining results while reducing the calculation load.

[0096] The workpiece shape model defining unit 120 may define the workpiece shape model so that the axial direction of the gear generated in the workpiece shape is at a position different from the axial coordinate Z. In this case, lattice points can also be positioned at the tooth tip and tooth bottom, so that when there is a need to also improve the prediction accuracy of the shapes of the tooth tip and tooth bottom, this requirement can be met.

[0097] In this embodiment, the cylindrical coordinate system lattice defining unit 111 sets the radial distance R in the cylindrical coordinate system lattice to the range from the tooth tip Wa to the tooth root Wb of the gear to be generated. This makes it possible to further increase the data density of the tooth flanks Wmc1 and Wmc2 while maintaining a low data density of the tooth tip Wa and tooth root Wb on the workpiece shape, thereby further improving the prediction accuracy of gear performance and machining results while reducing the calculation load.

[0098] In this embodiment, the grating pitch Pr of the radial distance R is set to be equal across the entire tooth flanks Wmc1 and Wmc2, thereby improving the prediction accuracy of the shape of the entire tooth flanks.

[0099] On the other hand, as in the modified embodiment, the grating pitch Pr of the radial distance R may be set so that the grating pitch is smaller at the center of the tooth depth in the tooth flank portions Wmc1 and Wmc2 and larger near the tooth bottom and the tooth tip. In this case, it is possible to particularly improve the prediction accuracy of the shapes near the centers of the tooth depth of the tooth flank portions Wmc1 and Wmc2, which is more important, while reducing the calculation load for other portions, thereby further achieving both improved prediction accuracy and reduced calculation load.

[0100] In addition, in the first embodiment, the grating pitch Pr of the radial distance R is set based on the required value of the prediction accuracy of the machining shape. This makes it possible to reduce the calculation load while setting the grating pitch Pr so as to satisfy the required value of the prediction accuracy of the machining shape.

[0101] Furthermore, this embodiment includes a prediction accuracy verification unit 191 that compares a specific reference position in the target shape of cutting with a corresponding position in the predicted shape in the prediction result of the machining result prediction unit 190, which corresponds to the reference position. The cylindrical coordinate system lattice definition unit 111 sets a cylindrical coordinate system lattice so that lattice points of the cylindrical coordinate system lattice are located at target positions for verification of the prediction accuracy of the machining shape. This eliminates the need for interpolation between lattice points when verifying the prediction accuracy, thereby improving the accuracy of verification of the prediction accuracy.

[0102] As described above, according to this embodiment and its modifications, it is possible to provide a machining shape simulation device that can improve the prediction accuracy of gear performance and machining results in gear generating cutting while reducing the calculation load.

[0103] In this embodiment, the cutting force is calculated based on the principal force Fc and the thrust force Ft using a two-dimensional cutting model based on two-dimensional cutting theory. However, when calculating the cutting force in three dimensions, a three-dimensional cutting model based on three-dimensional cutting theory may be used to take into account the feed force in addition to the principal force Fc and the thrust force Ft.

[0104] The present disclosure is not limited to the above-described embodiments, and can be applied to various embodiments without departing from the spirit of the present disclosure.

Claims

1. A machining shape simulation device for predicting a machined shape in gear-generating cutting, in which a workpiece is cut with a tool to create a gear, comprising: a cylindrical coordinate system lattice definition unit that defines a cylindrical coordinate system lattice consisting of a radial distance R component, an axial coordinate Z component, and an azimuth angle θ component, with the lattice pitch of the radial distance R set to a predetermined value; a workpiece shape model definition unit that defines a workpiece shape model in the cylindrical coordinate system lattice, based on analysis conditions including tool specifications, workpiece specifications, and machining conditions, such that the axial direction of the gear to be generated is parallel to the direction of the axial coordinate Z, and the azimuth angle θ is specified for the radial distance R and axial coordinate Z of the set lattice pitch; a tool shape model definition unit that defines a tool shape model based on the analysis conditions; and an interference region calculation unit that calculates an interference region between the tool shape model and the workpiece shape model during gear-generating cutting, based on the workpiece shape model, the tool shape model, and the relative movement trajectories of the tool and the workpiece. a machining result prediction unit that predicts a machining result of the workpiece based on a calculation result of the interference region calculation unit.

2. A machining shape simulation device as described in claim 1, further comprising a cutting force calculation unit that calculates the cutting force when the tool removes the interference area from the workpiece, and the machining result prediction unit predicts the machining result of the workpiece based on the calculation results of the interference area calculation unit and the cutting force calculation unit.

3. A machining shape simulation device according to claim 2, comprising: a dynamic characteristic calculation unit that calculates the relative dynamic characteristic or individual dynamic characteristics between the tool and the workpiece based on the analysis conditions; and a vibration calculation unit that calculates the relative vibration between the tool and the workpiece based on the cutting force and the relative dynamic characteristic, wherein the machining result prediction unit predicts the machining result of the workpiece based on a vibration simulation result consisting of the relative vibration repeatedly calculated by the interference area calculation unit, the cutting force calculation unit and the vibration calculation unit.

4. A machining shape simulation device according to any one of claims 1 to 3, wherein the workpiece shape model definition unit defines the workpiece shape model so that the central axis of the gear generated in the workpiece coincides with the axis coordinate Z.

5. A machining shape simulation device according to any one of claims 1 to 3, wherein the workpiece shape model definition unit defines the workpiece shape model so that the central axis of the gear generated in the workpiece is at a position different from the axis coordinate Z.

6. A machining shape simulation device according to any one of claims 1 to 3, wherein the cylindrical coordinate system lattice definition unit sets the radial distance R in the cylindrical coordinate system lattice to a range from the tip to the root of the gear to be generated.

7. A machining shape simulation device according to any one of claims 1 to 3, wherein the grating pitch is set at equal intervals over the entire tooth surface.

8. A machining shape simulation device according to any one of claims 1 to 3, wherein the lattice pitch is set so that it is smaller at the center of the tooth depth in the tooth flank portion and larger near the tooth bottom and tooth tip.

9. The machining shape simulation device according to any one of claims 1 to 3, wherein the grid pitch is set based on a required value for prediction accuracy of the machining shape.

10. A machining shape simulation device according to any one of claims 1 to 3, further comprising a prediction accuracy verification unit that verifies the prediction accuracy of the prediction result of the machining result prediction unit by comparing a specific reference position in the target shape of the cutting process with a corresponding position in the predicted shape in the prediction result of the machining result prediction unit that corresponds to the reference position, and wherein the cylindrical coordinate system grid definition unit defines the cylindrical coordinate system grid so that lattice points of the cylindrical coordinate system grid are located at target positions for verification of the prediction accuracy of the machining shape.

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