Machining shape simulation device

Abstract

Provided is a vibration simulation device (1) for simulation of vibration between a tool (10) and a workpiece (20) in gear generation cutting, the vibration simulation device (1) comprising a shape defining unit (120) that defines a tool shape and a workpiece shape, an interference region calculation unit (130) that calculates an interference region between the tool (10) and the workpiece (20) during processing on the basis of the tool (10) and the relative movement trajectory of the workpiece (20), a cutting force calculation unit (140) that calculates a cutting force during removal of the interference region from the workpiece (20) by the tool (10), a movement characteristic defining unit (150) that defines relative movement characteristics or individual movement characteristics between the tool and workpiece, a vibration calculation unit (160) that calculates relative vibration between the tool and workpiece on the basis of the cutting force and the relative movement characteristics, a frequency analysis unit (191) that performs frequency analysis on the vibration calculation result or the cutting force calculation result, a vibration occurrence evaluation unit (192) that evaluates the state of occurrence of relative vibration on the basis of the frequency analysis result of the frequency analysis unit (191), and a vibration state display unit (193) that displays the evaluation result.

Description

Machining shape simulation device

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

[0002] A known gear machining method is the gear skiving method described in Patent Document 1. This gear skiving method uses a machining tool having multiple tool blades on its outer periphery, with the central axis of the machining tool at an angle with respect to an axis parallel to the central axis of the workpiece, and while the workpiece and the machining tool are rotated synchronously, the machining tool is advanced in a straight line in the direction of the central axis of the workpiece to perform cutting.

[0003] Patent Document 2 describes a gear cutting simulation device for gear skiving. This gear cutting simulation device makes it possible to grasp the amount of cutting force acting on which part of the cutting tool blade, and this can be used to determine cutting conditions such as the cutting depth and feed rate of the cutting tool, enabling the design of an appropriate gear cutting device.

[0004] JP 2012-45687 A JP 2014-237185 A

[0005] In gear-generating cutting processes such as gear skiving, in addition to static behaviors such as displacements caused by the average machining load between the tool and the workpiece at the cutting point and the relative static stiffness between the tool and the workpiece, dynamic behaviors caused by fluctuations in the machining load between the tool and the workpiece and the relative dynamic characteristics between the tool and the workpiece, i.e., vibrations such as forced vibrations and self-excited vibrations, occur. However, conventional gear cutting simulations do not adequately take such vibrations into account, which is one of the factors that causes a discrepancy between the actual cutting results and the predicted results by simulation, reducing the prediction accuracy. Therefore, to improve the prediction accuracy of gear-generating cutting processes, it is necessary to accurately predict vibrations at the cutting point. However, accurate prediction of such vibrations in gear-generating cutting processes has not been achieved to date, which poses a challenge to improving the prediction accuracy of gear-generating cutting processes.

[0006] Furthermore, even if the results of gear generating cutting are predicted, they cannot be used effectively unless they are properly displayed to the user. Therefore, there is room for improvement in the display of predicted results.

[0007] Furthermore, even if the machining results predicted while taking vibration into full consideration as described above satisfy the desired gear accuracy, if the cutting resistance generated by machining is concentrated in a very small area on the cutting edge of the machining tool, the cutting edge of the tool may be damaged, making machining based on the prediction impossible. Therefore, to determine whether the predicted machining results are possible, it is necessary to consider the cutting conditions of the tool's cutting edge. However, conventional gear machining simulations do not provide an appropriate display of the predicted cutting conditions to the user, and the user must rely on the experience of an expert to determine whether machining is possible. Therefore, there is room for improvement in the display of the predicted cutting conditions, which is the basis for determining whether machining is possible.

[0008] The present disclosure has been made in consideration of the above circumstances, and aims to provide a machining shape simulation device that can predict vibrations at the machining point in gear generating cutting with high accuracy, improves the display of the prediction results, and makes it easy to determine whether machining is possible.

[0009] One aspect of the present disclosure is a machined shape simulation device that simulates the machined shape of a gear based on relative vibration between a tool and a workpiece in gear generating cutting processing in which a workpiece is cut with a tool to generate a gear, the device comprising: a shape defining unit that defines a tool shape and a workpiece shape based on analysis conditions including tool specifications, workpiece specifications, and processing conditions; a cutting edge model storage unit that stores model data of a cutting edge shape for the tool shape; an interference area calculation unit that calculates an interference area between the tool and the workpiece during gear generating cutting processing based on the tool shape, the workpiece shape, and a relative movement trajectory of the tool and the workpiece; a cutting force calculation unit that calculates a cutting force when the tool removes the interference area from the workpiece; a dynamic characteristic definition unit that defines relative dynamic characteristics 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. a frequency analysis unit that performs frequency analysis on the calculation results of the vibration calculation unit or the calculation results of the cutting force calculation unit; a vibration generation evaluation unit that evaluates the generation state of the relative vibration based on the frequency analysis result of the frequency analysis unit; a vibration state display unit that displays the evaluation result of the vibration generation evaluation unit; a cutting edge state extraction unit that extracts cutting edge state extraction data during processing in a plurality of evaluation regions of the cutting edge shape based on at least the calculation result of the interference region calculation unit; an evaluation item input unit that inputs evaluation items in the cutting edge state extraction data; and a cutting edge state display unit that displays the evaluation items of the cutting edge state extraction data in the evaluation region together with the cutting edge shape.

[0010] In one aspect of the present disclosure, a machining shape simulation device first calculates an interference area between the tool and workpiece during gear-generating cutting based on the tool shape and workpiece shape defined based on analysis conditions and the relative movement trajectory between the tool and workpiece, and then calculates a cutting force to remove the interference area. Then, relative dynamic characteristics or individual dynamic characteristics between the tool and workpiece are defined based on the analysis conditions, and the relative vibration between the tool and workpiece is calculated based on the cutting force and the dynamic characteristics. This makes it possible to predict vibration at the machining point during gear-generating cutting with high accuracy.

[0011] Furthermore, the state of occurrence of relative vibration is evaluated based on the calculation results of the vibration calculation unit or the calculation results of the cutting force calculation unit, based on the frequency analysis results of the frequency analysis unit, and the evaluation result is displayed. By displaying the evaluation result in this way, the display content of the prediction result is improved so that the user can make effective use of the prediction result.

[0012] Furthermore, because gear-generating cutting involves cutting curved tooth flanks, the predicted results of the machined shape tend to be more complex than when machining flat surfaces, such as with an end mill, making it difficult for users to understand the predicted results. However, as described above, improvements have been made to the display of predicted results, allowing users to effectively utilize the predicted results of the machined shape and chatter vibrations in gear-generating cutting, which cuts curved tooth flanks.

[0013] In addition, by displaying the cutting edge shape of the tool along with the cutting edge condition extraction data for the evaluation item, even an unexperienced user can determine whether or not the cutting edge of the tool will be damaged, making it easier to determine whether the predicted machining results are possible.

[0014] As described above, according to the above aspect, it is possible to provide a machining shape simulation device that can predict vibrations at a machining point in gear generating cutting with high accuracy and improves the display content of the prediction results.

[0015] 1 is a functional block diagram of a vibration simulation device and a machining shape simulation device of this embodiment. FIG. 2 is a flow diagram explaining how to use the vibration simulation device and the machining shape simulation device of this embodiment. FIG. 3 is a functional block diagram (procedure) of the rake angle calculation unit of FIG. 1. FIG. 4 is a perspective view showing the basic operation of gear machining. FIG. 5 is a partial cross-sectional schematic view of the machining tool of FIG. 4. FIG. 6 is a diagram explaining the operation of gear skiving, showing the relative position of a workpiece and a machining tool, projected onto the Xw, Zw plane (viewed from the Yw direction). FIG. 7 is a diagram explaining the operation of gear skiving, showing the relative position of a workpiece and a machining tool, projected onto the Xw, Yw plane (viewed from the Zw direction). FIG. 8 is a diagram showing the process from the start to the end of cutting of a tooth groove with a tool blade. FIG. 9 is a perspective view of a tool blade showing definition points in the definition point determination unit of FIG. 1. FIG. 10 is a diagram showing a cutting depth vector L(i), a vector between definition points B(i), and a plane G(i). FIG. 11 is a diagram showing a blade surface normal vector N(i). FIG. 12 is a diagram showing a projection normal vector Ng(i). FIG. 13 is a diagram showing a projected rake angle αg(i). 14 is a diagram showing a portion of one tooth groove that is removed in one feed in the tooth groove direction of one tool blade. FIG. 15 is a diagram showing the relationship between the tool rotation angle and the rake angle in the cutting of FIG. 13. FIG. 16 is a diagram showing a two-dimensional cutting model. FIG. 17 is a diagram showing a reference state of a model of a workpiece. FIG. 18 is a diagram showing a model of a workpiece and a model of a machining tool. FIG. 19 is a diagram showing a model of a workpiece in a state where the pin length has been changed. FIG. 20 is a diagram showing a final machining position by each definition point P(k). FIG. 21 is a diagram showing the calculation results of each component of the cutting force. FIG. 22 is a diagram showing a prediction result by the vibration simulation device of this embodiment. FIG. 23 is a diagram showing a first prediction result of tooth flank quality evaluation by the machined shape simulation device of this embodiment. FIG. 24 is a diagram showing a second prediction result of tooth flank quality evaluation by the machined shape simulation device of this embodiment. FIG. 25 is a diagram showing a third prediction result of tooth flank quality evaluation by the machined shape simulation device of this embodiment. FIG. 26 is a diagram showing a first prediction result of chatter vibration evaluation by the machined shape simulation device of this embodiment. FIG. 27 is a diagram showing a second prediction result of chatter vibration evaluation by the machined shape simulation device of this embodiment. FIG. 28 is a diagram showing a third prediction result of chatter vibration evaluation by the machined shape simulation device of this embodiment.(a) A conceptual diagram showing a model of cutting edge shape, and (b) a conceptual diagram when selecting an evaluation item, in the cutting edge condition display unit of this embodiment. (a) A conceptual diagram showing a model of cutting edge shape and evaluation items, and (b) a conceptual diagram displaying the values ​​of evaluation items in evaluation regions, in the cutting edge condition display unit of this embodiment. (a) A conceptual diagram showing evaluation items in all evaluation regions, and (b) a conceptual diagram displaying the maximum values ​​of evaluation items in all evaluation regions, in the cutting edge condition display unit of this embodiment. Conceptual diagram showing time series data and evaluation items, in the cutting edge condition display unit of this embodiment. Conceptual diagram showing values ​​at specific times in the time series data and specific values ​​of evaluation items, in the cutting edge condition display unit of this embodiment.

[0016] 1. Basic Operations of Gear-Generating Cutting First, the basic operations of gear-generating cutting to which the machining shape simulation device 100 (see FIG. 1) equipped with the vibration simulation device 1 of this embodiment is applied will be described with reference to FIGS. 4 and 5. 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.

[0017] 4, 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.

[0018] As shown in Figures 4 and 5, 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.

[0019] 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.

[0020] 4, 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. 6A). In other words, the central axes Zt and Zw of the tool 10 are not parallel to each other.

[0021] 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 4. 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.

[0022] 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 4. Note that Figure 4 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.

[0023] 2. 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.

[0024] 3. 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 now be described. As shown in FIGS. 6A and 6B , 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 incorporated 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.

[0025]

[0026] 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 4) of a gear 21 formed on the inner periphery of the workpiece 20, but typically each tool blade 11 and each tooth groove 22 is geometrically in the same cutting state.

[0027] 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 equation (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. 7, 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.

[0028] 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 of the tool blade 11 involved in cutting.

[0029] 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. 8. This allows two-dimensional processing for each region ΔP(i, i+1).

[0030] That is, for each region ΔP(i, i+1), a two-dimensional cutting model is used to calculate the rake angle α(i) and calculate 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 of 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. In this embodiment 1, unless otherwise specified, the physical quantity in "vibration" and "relative vibration" is displacement, but this is not limited to this and may also be acceleration or velocity. This will be explained in detail below.

[0031] 4. 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 setting unit 110, a shape defining unit 120, an interference region calculation unit 130, a cutting force calculation unit 140, a dynamic characteristic defining unit 150, a vibration calculation unit 160, an output unit 170, and an update unit 175. The machining shape simulation device 100 includes a vibration simulation device 1, a tooth surface property evaluation unit 180, a chatter vibration evaluation unit 190, a display condition setting unit 200, an integrated display unit 201, and a cutting edge state evaluation unit 210.

[0032] Here, in explaining the vibration simulation device 1 and the machining shape simulation device 100, the following will be explained in the following order, with reference to the flow diagram of FIG. 2 showing the usage mode of the machining shape simulation device 100: (4-1) Explanation of shape definition processing, (4-2) Explanation of rake angle calculation processing, (4-3) Explanation of two-dimensional cutting model, (4-4) Explanation of cutting depth calculation processing, (4-5) Explanation of cutting force calculation processing, (4-6) Explanation of relative vibration calculation processing, (4-7) Explanation of information update and calculation result output, (4-8) Explanation of tooth surface property evaluation, (4-9) Explanation of chatter vibration evaluation, and (4-10) Explanation of cutting edge state evaluation.

[0033] 4-1. Shape Definition Processing The shape definition processing will be described with reference to the analysis condition setting unit 110 and the shape definition unit 120 in FIG. 1. First, the analysis condition setting unit 110 acquires analysis conditions required for simulation in the vibration simulation device 1 and the machining shape simulation device 100 (step S1 in FIG. 2). 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 in a gear generating cutting device (not shown). The analysis conditions may have a predetermined analysis range and may also include other information. The analysis condition setting unit 110 can acquire the analysis conditions by having the user input some or all of the analysis conditions, or by retrieving some or all of the analysis conditions pre-stored in a storage unit (not shown).

[0034] The shape defining unit 120 defines the shapes of the tool 10 and the workpiece 20 based on the analysis conditions acquired by the analysis condition setting unit 110 (step S2 in FIG. 2 ). In this embodiment, the shapes of the tool 10 and the workpiece 20 are defined by a point cloud consisting of a plurality of points located on the surfaces of the tool 10 and the workpiece 20. Specifically, as shown in FIG. 8 , in the tool 10, 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) are defined 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, an approximation of the boundary line on the tool blade 11 is obtained. Here, although 13 definition points P(1) to P(13) are shown in FIG. 8 , 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.

[0035] Here, the terminology used in the following processing regarding the tool blade 11 will be explained with reference to FIG. 8 . 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).

[0036] As shown in FIG. 16 , the workpiece 20 is represented by placing pins 26 of a specified length at specified intervals on a reference plane and creating triangular patches 27 at the tips of the pins. However, since the workpiece 20 is cylindrical, the reference plane is a cylindrical surface whose central axis is the central axis Zw of the workpiece 20. The shape of the workpiece 20 is defined by placing pins 26 of a specified length at specified intervals on the reference cylindrical surface, parallel to the normal direction to the reference cylindrical surface. The pins 26 are oriented toward the center of the reference cylindrical surface when machining the inner peripheral surface, and toward the outside from the center of the reference cylindrical surface when machining the outer peripheral surface. Note that in FIGS. 16 to 18 , the reference cylindrical surface is represented as a plane for convenience.

[0037] 4-2. 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. For each inter-definition point area ΔP(i, i+1), the cutting-in vector calculation unit 131 calculates 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, the direction in which the entire inter-definition point area ΔP(i, i+1) moves is not easily calculated.

[0038] Therefore, as shown in Fig. 9, 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.

[0039] 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. 3.

[0040] The calculation of the rake angle α(i) will be described below with reference to Fig. 3 and Figs. 9 to 12. First, as shown in Fig. 3, the cutting vector L(i) is calculated by the cutting vector calculation unit 131 as described above (reference numeral S31 in Fig. 3), and then the inter-definition point vector B(i) is calculated (S32 in Fig. 3). 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. 9. Here, the midpoint Pc(i, i+1) is located at the middle position of the inter-definition point vector B(i).

[0041] 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. 3). The plane G(i) is as shown in FIG. 9.

[0042] 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.

[0043] 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.

[0044] 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. 3). 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. 10, 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.

[0045] As shown in Figure 10, 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).

[0046] 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. 3).

[0047] 11, plane G(i) and plane Q(i) are not necessarily the same plane. Therefore, although the blade surface normal vector N(i) is located on plane Q(i), it is not necessarily located 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.

[0048] 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. 3). The projected rake angle αg(i) is as shown in FIG. 12. Here, since the projected rake angle αg(i) is calculated on the plane G(i), it differs from the actual rake angle α(i).

[0049] 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)).

[0050] 13 , 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.

[0051] 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. 14, 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. 8), the cutting edge of the tool blade 11 (solid line in the figure, definition points P(5)-P(9) in Fig. 8), and the right cutting surface of the tool blade 11 (dash line in the figure, definition points P(10)-P(13) in Fig. 8) in the range from the start of cutting (tool rotation angle σs) to the end of cutting (tool rotation angle σe).

[0052] Each line segment representing the rake angle αg(i) is a set of values ​​at the midpoint Pc(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.

[0053] Next, a two-dimensional cutting model based on two-dimensional cutting theory will be described with reference to Fig. 15. Fig. 15 shows the cutting model on the plane G(i) described above. In Fig. 15, a workpiece 20 is cut by the tool blade 11 of a tool 10.

[0054] 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. 15. Here, the principal force Fc(i) and thrust force Ft(i) at the relevant portion are respectively expressed as in equation (2).

[0055]

[0056] 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.

[0057] 4-4. 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. 17 to 19.

[0058] Here, the cutting depth calculation process will be described with reference to the intersection calculation unit 133, removal length calculation unit 134, and final machining position extraction unit 135 in FIG.

[0059] 17 , 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 shape defining unit 120 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 intersections of each pin 26 representing the workpiece 20 and the trajectory plane 11p of the tool blade 11 are calculated.

[0060] If the intersection calculation unit 133 finds an intersection, the removal length calculation unit 134 changes the length of each pin 26 representing the workpiece 20, as shown in Fig. 18 . 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 the cut shape is stored. At this time, the removal length calculation unit 134 stores the removal length of each pin 26. This removal length of the pin 26 corresponds to the cutting amount 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. 2 ).

[0061] 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. 19 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).

[0062] 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 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.

[0063] The cutting depth d1(i) in the two-dimensional cutting model corresponds to the average of the cutting depth (corresponding to the radial 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.

[0064] 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-in amount at each definition point P(k), and further calculates the cutting-in amount d1(i) at the midpoint Pc(i, i+1). The intersection calculation unit 133 calculates the intersection between each pin 26 representing the workpiece 20 and the locus plane 11p of the tool blade 11 within the range from the start of cutting one tooth groove 22 with one tool blade 11 to the end of cutting. Then, each time the cutting of one tooth groove 22 with one tool blade 11 is repeatedly performed from the start of cutting to the end of cutting, the shape of the workpiece 20 is updated and the intersection between each pin 26 representing the workpiece 20 and the locus plane 11p of the tool blade 11 is calculated.

[0065] 4-5. 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 explained with reference to FIG. 1 regarding the cutting force calculation unit 140.

[0066] 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. 15 (S4 in Fig. 2). 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.

[0067] 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:

[0068]

[0069] Here, the unit vector is defined as in equation (4).

[0070]

[0071] 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).

[0072]

[0073] 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).

[0074]

[0075] 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).

[0076]

[0077] 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 20, for example, and are close to the measured values, confirming that the calculation results are highly accurate.

[0078] 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 characteristics defining unit 150, the vibration calculating unit 160, and the output unit 170 in FIG.

[0079] First, the dynamic characteristic defining unit 150 defines the relative dynamic characteristic or individual dynamic characteristic between the tool 10 and the workpiece 20. In this embodiment, the defining is based on information acquired by the analysis condition setting unit 110. For example, the analysis condition setting unit 110 can define the dynamic characteristic as the defining result of the dynamic characteristic defining unit 150 based on information acquired by a hammering test or the like. Note that the relative dynamic characteristic can be defined based on individually calculated values ​​of the tool 10 and the workpiece 20. 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.

[0080] 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 defined by the dynamic characteristics defining unit 150 and the cutting force FH (S5 in FIG. 2). In this embodiment, the transfer function processing unit 161 outputs displacement, velocity, and acceleration.

[0081] 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.

[0082] As shown in Figure 21, 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.

[0083] 4-7. Information Update and Output of Calculation Results Next, information update by the update unit 175 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 175 and output by the output unit 170. In addition, the calculation results of the cutting force calculation unit 140 are also output by the output unit 170. The update unit 175 updates the relative position between the tool 10 and the workpiece 20 and the workpiece shape based on the interference area calculated by the interference area calculation unit 130 and the relative vibration calculated by the vibration calculation unit 160 (S6 in FIG. 2). That is, the positions of the tool 10 and the workpiece 20 are updated to update the relative positions between them, and the shape with the interference area removed is used as the updated workpiece shape. Then, based on the updated information, the interference area calculation unit 130 calculates the interference area, the cutting force calculation unit 140 calculates the cutting force, and the vibration calculation unit 160 calculates the relative vibration (No in S7 of Figure 2), until the processing of the workpiece 20 is completed, and the vibration simulation results are calculated.

[0084] When the processing is completed (Yes in S7 in FIG. 2), the output unit 170 outputs the calculation result of the vibration calculation unit 160. The output result of the output unit 170 is shown in FIG. 21, for example, and the vibration displacement with transfer function correction is relatively close to the actually measured value, confirming that calculation can be performed with high accuracy.

[0085] 4-8. Tooth Flank Property Evaluation Next, a description will be given of tooth flank property evaluation using the machining shape simulation device 100 shown in Fig. 1. In the first embodiment, the tooth flank property evaluation and chatter vibration evaluation, which will be described later, are processed in parallel.

[0086] Prior to the tooth flank characteristic evaluation, display conditions are set by the display condition setting unit 200 shown in Fig. 1 (step S8 in Fig. 2). The display conditions can set conditions related to display such as the tooth trace direction range, tooth profile direction range, and error range to be displayed in the predicted tooth flank shape display unit 182 shown in Fig. 1, the number and tooth trace direction positions of tooth profiles to be displayed in the predicted tooth profile shape display unit 184, and the frequency range and amplitude range to be displayed in the vibration state display unit 193.

[0087] The tooth flank property evaluation is processed in the following order: First, in step S9 of Fig. 2, the workpiece shape recorded by the machining result prediction unit 181 of the tooth flank property evaluation unit 180 is updated based on the output result of the output unit 170 using the shape of the machined workpiece 20 last updated by the update unit 175 shown in Fig. 1. Then, in step S10 of Fig. 2, the predicted tooth flank shape, predicted tooth trace shape, and predicted tooth profile shape are displayed.

[0088] The predicted tooth flank form is displayed based on the display conditions set by the predicted tooth flank form display unit 182. The predicted tooth flank form is displayed as a contour diagram, for example, as shown in Figures 22(a), 23(a), and 24(a), with the tooth trace direction and tooth profile direction as the display axes, and includes data on the difference from the reference surface. In this embodiment 1, an involute tooth profile is used as the reference surface, and the difference from the involute tooth profile is displayed as the error. In other words, the predicted tooth flank form displayed by the predicted tooth flank form display unit 182 is a contour diagram showing the error with the tooth trace direction and tooth profile direction as the display axes.

[0089] The predicted tooth trace form is displayed by the predicted tooth trace form display unit 183 based on the display conditions set by the display condition setting unit 200. The predicted tooth trace form is displayed as a scatter diagram of a cross section at a predetermined tooth profile direction position, as a relationship with an error, which is the difference from the involute tooth profile in the tooth trace direction, as shown in Figures 22(b), 23(b), and 24(b), for example.

[0090] The predicted tooth profile is displayed by the predicted tooth profile display unit 184 based on the display conditions set by the display condition setting unit 200. For example, the predicted tooth profile is shown as a scatter diagram of a cross section at a predetermined position in the tooth trace direction, showing the difference from the involute tooth profile in the tooth profile direction as a relationship with the error, as shown in Figures 22(c), 23(c), and 24(c).

[0091] The display contents of the display units 182 to 184 in step S10 are laid out and displayed on a single screen by the integrated display unit 201 shown in Fig. 1 in the display modes shown in Figs. 22 to 24, respectively. Although not shown, the integrated display unit 201 may display various types of gear accuracy numerical data, such as total tooth profile error and total tooth trace error, calculated in advance by the machining result prediction unit 181 based on the workpiece shape, along with the display contents shown in Figs. 22 to 24. If the workpiece is a helical gear, the layout may also display the cross-sectional shape along the meshing progression line. Furthermore, the layout may also display the results of Fourier frequency analysis of the cross-sectional shape along the meshing progression line as a gear noise evaluation index.

[0092] 22 to 24 are examples of predicted machining results under normal conditions in which no chatter vibration occurs during machining, a first abnormal condition in which relatively small chatter vibration occurs during machining, and a second abnormal condition in which relatively large chatter vibration occurs during machining. Under the normal conditions, errors in the tooth flank shape, tooth trace shape, and tooth profile shape are predicted to be small, as shown in Figures 22(a) to (c), under the first abnormal condition, errors in the tooth flank shape, tooth trace shape, and tooth profile shape are predicted to be slightly larger than under normal conditions, as shown in Figures 23(a) to (c), and under the second abnormal condition, errors in the tooth flank shape, tooth trace shape, and tooth profile shape are predicted to be significantly larger than under normal conditions, as shown in Figures 24(a) to (c).

[0093] It was confirmed that the prediction reflected the presence or absence of chatter vibration and the degree of chatter vibration. Therefore, it is understood that by using the prediction results of the machining shape simulation device 100, it is possible to predict with high accuracy the occurrence of chatter vibration during machining even when the prediction results of the tooth flank shape are used.

[0094] 4-9. Chatter Vibration Evaluation Meanwhile, chatter vibration evaluation in step S11 shown in FIG. 2 is performed by the chatter vibration evaluation unit 190 shown in FIG. 1. In the chatter vibration evaluation unit 190, the frequency analysis unit 191 acquires time-series relative vibration from the calculation results of the vibration calculation unit 160 output by the output unit 170, or acquires time-series cutting force, which is the calculation result of the cutting force calculation unit 140. Thereafter, in step S12, the frequency analysis unit 191 performs calculation by frequency analysis. Note that in the first embodiment, the physical quantity of the relative vibration output by the output unit 170 is displacement, but acceleration or velocity may also be used. Furthermore, the frequency analysis in the frequency analysis unit 191 can be performed by short-time Fourier transform, fast Fourier transform, wavelet transform, or the like. In the first embodiment, the time-series relative vibration is calculated by short-time Fourier transform.

[0095] Then, in step S13 of FIG. 2, the vibration generation state is evaluated by the vibration generation evaluation unit 192 shown in FIG. 1, and the results are created as a contour diagram in which the display range is set based on the display conditions set by the display condition setting unit 200, and the display axes are frequency and machining time, and the amplitude of displacement is represented by a color map such as a grayscale. The contour diagram is then displayed by the vibration state display unit 193. The frequency range displayed in the contour diagram is a frequency range that includes the cutting edge passing frequency component and the chatter vibration frequency component, which will be described later. Note that the display axis of the contour diagram displayed by the vibration state display unit 193 may be tooth trace direction position instead of machining time. Furthermore, the contour diagram displayed by the vibration state display unit 193 may be displayed on a single screen together with the display units 182 to 184 of the tooth surface characteristic evaluation unit 180, laid out by the integrated display unit 201 shown in FIG. 1.

[0096] 25 to 27 are examples of contour diagrams that display the evaluation results of chatter vibration evaluation of time-series relative vibration predicted under normal conditions in which no chatter vibration occurs during machining, a first abnormal condition in which relatively small chatter vibration occurs during machining, and a second abnormal condition in which relatively large chatter vibration occurs during machining.

[0097] In the contour diagram shown in Figure 25, only the cutting edge passing frequency component is detected from the start to the end of machining, and no chatter vibration frequency component is detected, indicating that chatter vibration does not occur during machining. The cutting edge passing frequency is a value calculated by multiplying the tool rotation frequency by the number of tool teeth. The fact that the main frequency component of vibrations generated during machining is only this cutting edge passing frequency component indicates the occurrence of so-called forced vibrations that occur directly when the tool teeth contact the workpiece. Furthermore, the chatter vibration frequency is a frequency near the natural frequency of the dynamic stiffness between the tool and the workpiece, and varies depending on the machining conditions input into the vibration simulation device 1. While Figures 25 to 27 show frequencies higher than the cutting edge passing frequency, it can also be lower than the cutting edge passing frequency.

[0098] On the other hand, the contour diagram shown in Figure 26 detects the cutting edge passing frequency component from the start to the end of machining, and furthermore, the chatter vibration frequency component is detected at a relatively small displacement amplitude, indicating that small chatter vibration occurs during machining. Also, the contour diagram shown in Figure 27 detects only the cutting edge passing frequency component from the start to the end of machining, and furthermore, the chatter vibration frequency component is detected at a relatively large displacement amplitude, indicating that large chatter vibration occurs during machining. Note that the frequency components detected around the chatter vibration frequency component are sidebands of chatter vibration, which arise due to the intermittent nature of cutting.

[0099] Although not shown, it was confirmed that when the cutting force calculated by the cutting force calculation unit 140 was obtained in step S11 shown in FIG. 2 and chatter vibration evaluation was performed by the processing of steps S12 and S13, a contour diagram similar to that obtained when the above-mentioned relative vibration was used was obtained.

[0100] As described above, it has been confirmed that the contour diagrams shown in Fig. 25, Fig. 26 and Fig. 27 reflect the presence or absence of chatter vibration and the degree of chatter vibration. Therefore, it is understood that the occurrence of chatter vibration during machining can be predicted with high accuracy by performing the chatter vibration evaluation using the machining shape simulation device 100.

[0101] 4-10. Cutting Edge Condition Evaluation Furthermore, the cutting edge condition evaluation by the cutting edge condition evaluation unit 210 shown in Fig. 1 is performed in steps S14 to S16 in parallel with steps S4 to S6 shown in Fig. 2. First, in step S14, the cutting edge condition extraction unit 212 in the cutting edge condition evaluation unit 210 shown in Fig. 1 extracts cutting edge condition extraction data during machining in multiple evaluation regions of the cutting edge shape stored in the cutting edge model storage unit 211 based on at least the calculation results of the interference region calculation unit 130.

[0102] In this embodiment, the cutting edge model storage unit 211 stores model data of the cutting edge shape in the shape of the tool 10 defined by the shape defining unit 120. The multiple evaluation areas in the cutting edge shape stored in the cutting edge model storage unit 211 are stored as a point cloud in which each point represents an evaluation area, and for example, the evaluation area of ​​a cross section orthogonal to the tooth trace direction at an arbitrary position in the cutting edge shape is made up of a point cloud displayed on the cutting edge state display unit 214 (described later), as shown in Fig. 28(a), and each point represents an evaluation area.

[0103] Next, proceeding to step S15, the evaluation items in the cutting edge state extraction data are input to the evaluation item input unit 213 in the cutting edge state evaluation unit 210 shown in Fig. 1. The evaluation items include cutting resistance, and can further include at least one of the depth of cut, rake angle, and surface pressure.

[0104] The cutting resistance, which is an evaluation item in the cutting edge condition extraction data, is the maximum value or integrated value of the cutting resistance during machining at a point in the evaluation area of ​​the cutting edge. The cutting resistance is calculated by the cutting edge condition extraction unit 212 based on at least the calculation results of the vibration calculation unit 160 and the cutting force calculation unit 140.

[0105] The cutting depth, which is an evaluation item in the cutting edge condition extraction data, is the maximum value of the cutting depth during machining at a point that is the evaluation area of ​​the cutting edge. The rake angle, which is an evaluation item, is the minimum value of the cutting depth during machining at a point that is the evaluation area of ​​the cutting edge. The cutting depth and rake angle are calculated by the cutting edge condition extraction unit 212 based on at least the calculation results of the interference area calculation unit 130.

[0106] The surface pressure, which is an evaluation item in the cutting edge condition extraction data, is the maximum value of the surface pressure generated at a point in the evaluation area of ​​the cutting edge during machining. The surface pressure is calculated by the cutting edge condition extraction unit 212 based on at least the calculation result of the cutting force calculation unit 140.

[0107] The user of the machining shape simulation device 100 can input the evaluation items into the evaluation item input unit 213 in step S15. In this embodiment, the user can do this by operating the input terminal as follows. First, as shown in FIG. 28A , the cutting edge state display unit 214 (described later) displays input fields for the user to input evaluation items into the evaluation item input unit 213. Then, the user can select the evaluation item input unit 213 by hovering the pointer over it using the input terminal on the cutting edge state display unit 214, thereby displaying a pull-down menu 213a listing the evaluation items as shown in FIG. 28A . The user can input the desired evaluation item into the evaluation item input unit 213 by hovering the pointer over the desired evaluation item in the pull-down menu 213a using the input terminal. In this embodiment, in the example shown in FIG. 29A , cutting resistance (maximum value) is input as the evaluation item into the evaluation item input unit 213.

[0108] Then, the process proceeds to step S16, where the cutting edge condition display unit 214 displays the evaluation items of the cutting edge condition extraction data in the evaluation area along with the cutting edge shape. In the example shown in FIG. 29(b), the cutting resistance (maximum value) in the evaluation area of ​​the cutting edge shape selected by the user is displayed in the portion indicated by reference numeral 213b. The user can visually confirm the maximum cutting resistance indicated by reference numeral 213b, allowing even non-experts to easily determine whether or not damage will occur to the cutting edge of the tool. Similarly, if the integrated value of cutting resistance is entered instead of the cutting resistance (maximum value) as the evaluation item, the integrated value of cutting resistance can be visually confirmed, allowing even non-experts to easily determine whether or not damage will occur to the cutting edge of the tool. In this embodiment, the cutting edge condition display unit 214 is separate from the integrated display unit 201, but it may be integrated with the integrated display unit 201.

[0109] The cutting edge condition display unit 214 may also display the entire evaluation region of the cutting edge shape in a display format set based on the value of the cutting edge condition extraction data for the evaluation item. For example, in the example shown in FIG. 30( a), the evaluation region indicated by reference numeral 213d shows evaluation regions where the cutting resistance is equal to or greater than a predetermined reference value as an evaluation item with a filled circle, and the evaluation region indicated by reference numeral 213c shows evaluation regions where the cutting resistance is less than the predetermined reference value with a hollow circle. Alternatively to the example shown in FIG. 30( a), the evaluation region indicated by reference numeral 213e shows evaluation regions where the cutting resistance is maximum as an evaluation item with a filled triangle, and evaluation regions where the cutting resistance is less than the maximum value with a filled dot. Although not shown, evaluation regions where the integrated value of cutting resistance is maximum as an evaluation item may be shown by a filled circle, and evaluation regions where the integrated value is less than the maximum value with a filled dot. In either case, the maximum or integrated value of cutting resistance can be visually confirmed, allowing even non-experts to easily determine whether or not damage will occur to the cutting edge of the tool. The display format may be a display format in which the color is changed instead of a black or white display format.

[0110] The cutting edge condition display unit 214 can also display time-series data along with the cutting edge shape and evaluation items. In the example shown in FIGS. 31 and 32 , as shown in FIG. 31 , the display item 215a of the time-series data 215 can be selected from a pull-down menu (not shown), and time-series data 216 of cutting force is displayed. The time-series data of cutting force can be obtained based on the calculation results of the cutting force calculation unit 140 shown in FIG. 1 . Then, as shown in FIG. 32 , a user sets an arbitrary time t1 in the time setting unit 215b, and the time t1 is clearly indicated in the time-series data 215. Furthermore, the cutting edge shape at time t1 and the depth of cut value 213b are displayed on the XY coordinate plane 216 as evaluation items of the cutting edge condition extraction data in the evaluation area. In this case, the user can visually recognize the value indicated by the symbol 213b, and even an unskilled user can easily determine whether or not damage will occur to the cutting edge of the tool.

[0111] 5. Effects The vibration simulation device 1 of this embodiment first calculates an interference area between the tool 10 and workpiece 20 during gear-generating cutting based on the tool shape and workpiece shape defined based on the analysis conditions and the relative movement trajectory between the tool 10 and workpiece 20, and then calculates a cutting force to remove the interference area. Then, the relative dynamic characteristics or individual dynamic characteristics between the tool 10 and workpiece 20 are defined based on the analysis conditions, and the relative vibration between the tool 10 and workpiece 20 is calculated based on the cutting force and the dynamic characteristics. This makes it possible to predict vibrations at the processing point during gear-generating cutting with high accuracy.

[0112] Furthermore, the state of occurrence of relative vibration is evaluated based on the calculation results of the vibration calculation unit 160 or the calculation results of the cutting force calculation unit 140 based on the frequency analysis results of the frequency analysis unit 191, and the evaluation result is displayed. By displaying the evaluation result in this way, the display content of the prediction result is improved so that the user can effectively use the prediction result.

[0113] Furthermore, because the gear-generating cutting process in this embodiment involves cutting curved tooth flanks, the predicted results of the machined shape tend to be more complex than when machining flat surfaces, such as with an end mill, making it difficult for the user to understand the predicted results. However, as described above, the display of the predicted results has been improved, allowing the user to effectively utilize the predicted results of the machined shape and chatter vibration in gear-generating cutting, which cuts curved tooth flanks.

[0114] Furthermore, by displaying the cutting edge shape of the tool 10 along with the cutting edge condition extraction data for the evaluation item, even an unexperienced user can determine whether or not the cutting edge of the tool 10 will be damaged, making it easier to determine whether the predicted machining results can be achieved.

[0115] Furthermore, in this embodiment 1, there are provided a predicted tooth flank shape display unit 182 which displays a predicted tooth flank shape including data on the difference from a reference surface, with the tooth trace direction and tooth profile direction as display axes, based on the prediction result of the machining result prediction unit 181, a predicted tooth trace shape display unit 183 which displays a predicted tooth flank shape at a predetermined tooth profile direction position, with the tooth trace direction position and the difference from the reference surface as display axes, and a predicted tooth profile shape display unit 184 which displays a predicted tooth flank shape at a predetermined tooth trace direction position, with the tooth profile direction position and the difference from the reference surface as display axes, and an integrated display unit 201 which displays the display contents of the predicted tooth flank shape display unit 182, the predicted tooth trace shape display unit 183, and the predicted tooth profile shape display unit 184 at predetermined positions on one screen. This makes it easier for the user to intuitively grasp the tooth flank shape, tooth trace shape, and tooth profile shape, and the display contents of the prediction results have been improved so that the user can effectively utilize the prediction results.

[0116] In addition, in this embodiment 1, the integrated display unit 201 can display the display contents of the vibration state display unit 193 at a predetermined position on the single screen. This makes it easier for the user to grasp the vibration state as well as the tooth flank shape, tooth trace shape, and tooth profile shape, and the display contents of the prediction results are improved so that the user can effectively use the prediction results.

[0117] Moreover, in the first embodiment, a display condition setting unit 200 is further provided for setting the display content to be displayed on the integrated display unit 201. This makes it possible to improve the display content of the prediction results so that the user can effectively utilize the prediction results.

[0118] In addition, in the first embodiment, the frequency analysis unit 191 outputs, as the frequency analysis result, a contour diagram obtained by short-time Fourier transform of the time-series data of the calculation result of the vibration calculation unit 160 or the calculation result of the cutting force calculation unit 140. This makes it easier for the user to understand the vibration state.

[0119] Furthermore, in the first embodiment, the frequency analysis unit 191 may output a scatter diagram obtained by fast Fourier transform as the frequency analysis result, instead of performing short-time Fourier transform on the time-series data of the calculation result of the vibration calculation unit 160 or the calculation result of the cutting force calculation unit 140. Even in this case, the user can grasp the vibration state, and the same effect as in the first embodiment can be achieved.

[0120] Furthermore, in the first embodiment, the vibration occurrence evaluation unit 192 evaluates the occurrence state of relative vibration based on the detection results of the cutting edge passing frequency component and the chatter vibration frequency component in the frequency analysis result of the frequency analysis unit 191. This makes it possible to predict with high accuracy whether chatter vibration will occur.

[0121] In addition, in the present embodiment, the vibration state display unit 193 displays the frequency analysis results of the frequency analysis unit 191 in a frequency range including the cutting edge passing frequency component and the chatter vibration frequency component, with the machining time and frequency as display axes, thereby enabling the user to accurately grasp the vibration state.

[0122] In the first embodiment, the cutting edge state extraction data includes, as an evaluation item, at least the surface pressure calculated based on the calculation result of the cutting force calculation unit 140. This makes it possible to easily determine whether or not the cutting edge of the tool 10 will be damaged.

[0123] In the first embodiment, the cutting edge state extraction data includes, as an evaluation item, at least the cutting resistance calculated based on the calculation results of the vibration calculation unit 160 and the cutting force calculation unit 140. This makes it possible to easily determine whether or not damage to the cutting edge of the tool 10 will occur.

[0124] In the first embodiment, the cutting edge state extraction data includes, as evaluation items, at least the rake angle or the cutting depth calculated based on the calculation result of the interference region calculation unit 130. This makes it possible to easily determine whether or not the cutting edge of the tool 10 will be damaged.

[0125] In this embodiment, the cutting edge condition display unit 214 displays the cutting edge condition extraction data for the evaluation items in the selected evaluation area among the evaluation areas of the cutting edge shape, thereby enabling the user to easily determine whether or not any area of ​​the cutting edge of the tool 10 is likely to be damaged.

[0126] In this embodiment, the cutting edge condition display unit 214 can display the entire evaluation region of the cutting edge shape in a display format set based on the value of the cutting edge condition extraction data for the evaluation item, which makes it easier for the user to visually recognize the cutting edge condition extraction data and more easily determine whether or not damage will occur in any region of the cutting edge of the tool 10.

[0127] In this embodiment, the cutting edge condition display unit 214 can display, in a specific display format, the area within the evaluation area of ​​the cutting edge shape where the cutting edge condition extraction data is at its maximum or minimum value or the area where the integrated value of the cutting edge condition extraction data is at its maximum value. This makes it easier for the user to visually identify the area where the cutting resistance is at its maximum or minimum value or the area where the integrated value of the cutting resistance is at its maximum value, and makes it easier to determine whether or not damage will occur in any area of ​​the cutting edge of the tool 10.

[0128] Furthermore, the machining shape simulation device 100 of this embodiment is configured to calculate cutting edge state extraction data during machining in a plurality of evaluation regions in the cutting edge shape based on at least the calculation results of the interference region calculation unit 130 using the cutting edge state extraction unit 212, display the cutting edge shape on the cutting edge state display unit 214 based on the model data stored in the cutting edge model storage unit 211, and display the evaluation items in the cutting edge state extraction data inputted to the evaluation item input unit 213 for the evaluation region of the selected cutting edge shape on the cutting edge state display unit 214. This allows the user of the machining shape simulation device 100 to determine whether or not breakage or the like will occur in any region of the cutting edge of the tool 10, and to easily determine whether or not breakage or the like will occur in the tool 10.

[0129] As described above, according to the above-described one aspect, it is possible to provide a machining shape simulation device 100 that can predict vibrations at the machining point in gear generating cutting with high accuracy, improves the display content of the prediction results, and makes it easy to determine whether machining is possible.

[0130] In this embodiment 1, the tooth surface characteristics evaluation and chatter vibration evaluation are performed after the completion of machining. Alternatively, the tooth surface characteristics evaluation may be performed each time the workpiece shape is updated, and the chatter vibration evaluation may be performed each time the relative vibration or cutting force is calculated.

[0131] 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 machined shape simulation device that simulates the machined shape of a gear based on the relative vibration between a tool and a workpiece in gear-generating cutting, in which a workpiece is cut with a tool to create a gear, comprising: a shape definition unit that defines the tool shape and the workpiece shape based on analysis conditions including tool specifications, workpiece specifications, and cutting conditions; a cutting edge model storage unit that stores model data of the cutting edge shape of the tool shape; an interference area calculation unit that calculates the interference area between the tool and the workpiece during gear-generating cutting, based on the tool shape, the workpiece shape, and the relative movement trajectories of the tool and the workpiece; a cutting force calculation unit that calculates the cutting force when the tool removes the interference area from the workpiece; a dynamic characteristic definition unit that defines the relative dynamic characteristics 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 characteristics. a frequency analysis unit that performs frequency analysis on the calculation results of the vibration calculation unit or the calculation results of the cutting force calculation unit; a vibration generation evaluation unit that evaluates the generation state of the relative vibration based on the frequency analysis result of the frequency analysis unit; a vibration state display unit that displays the evaluation result of the vibration generation evaluation unit; a cutting edge state extraction unit that extracts cutting edge state extraction data during machining in a plurality of evaluation regions of the cutting edge shape based on at least the calculation result of the interference region calculation unit; an evaluation item input unit that inputs evaluation items in the cutting edge state extraction data; and a cutting edge state display unit that displays the evaluation items of the cutting edge state extraction data in the evaluation region together with the cutting edge shape.

2. A machining shape simulation device as set forth in claim 1, comprising: a predicted tooth flank shape display unit which displays a predicted tooth flank shape including data relating to the difference from a reference surface, based on the prediction result of said machining result prediction unit, with the tooth trace direction and tooth profile direction as display axes; a predicted tooth trace shape display unit which displays a predicted tooth flank shape at a predetermined tooth profile direction position, with the tooth trace direction position and the difference from the reference surface as display axes; a predicted tooth profile shape display unit which displays the predicted tooth flank shape at a predetermined tooth trace direction position, with the tooth profile direction position and the difference from the reference surface as display axes; and an integrated display unit which displays the display contents of said predicted tooth flank shape display unit, said predicted tooth trace shape display unit and said predicted tooth profile shape display unit at predetermined positions on a single screen.

3. The machining shape simulation device according to claim 2, wherein said integrated display unit displays the display contents of said vibration state display unit at a predetermined position on said single screen.

4. The machining shape simulation device according to claim 3, further comprising a display condition setting section for setting the display contents to be displayed on said integrated display section.

5. A machining shape simulation device according to any one of claims 1 to 4, wherein the frequency analysis unit outputs, as the frequency analysis result, a contour diagram obtained by performing a short-time Fourier transform on the time-series data of the calculation results of the vibration calculation unit or the calculation results of the cutting force calculation unit.

6. A machining shape simulation device according to any one of claims 1 to 4, wherein the frequency analysis unit outputs, as the frequency analysis result, a scatter diagram obtained by fast Fourier transforming time series data of the calculation results of the vibration calculation unit or the calculation results of the cutting force calculation unit.

7. A machining shape simulation device according to any one of claims 1 to 4, wherein the vibration generation evaluation unit evaluates the generation state of the relative vibration based on the detection results of the frequency analysis result of the frequency analysis unit, the cutting edge passing frequency component calculated based on the specifications of the tool, and the chatter vibration frequency component calculated based on the determination result of the dynamic characteristic determination unit.

8. The machining shape simulation device described in claim 7, wherein the vibration state display unit displays the frequency analysis results of the frequency analysis unit in a frequency range including the cutting edge passing frequency component and the frequency component of the chatter vibration, with machining time and frequency as display axes.

9. A machining shape simulation device according to any one of claims 1 to 4, wherein the cutting edge condition extraction data includes, as an evaluation item, at least a surface pressure calculated based on the calculation results of the cutting force calculation unit.

10. A machining shape simulation device according to any one of claims 1 to 4, wherein the cutting edge condition extraction data includes, as evaluation items, cutting resistance calculated based on at least the calculation results of the vibration calculation unit and the calculation results of the cutting force calculation unit.

11. A machining shape simulation device according to any one of claims 1 to 4, wherein the cutting edge condition extraction data includes, as an evaluation item, at least the rake angle or cutting depth calculated based on the calculation results of the interference area calculation unit.

12. A machining shape simulation device described in any one of claims 1 to 4, wherein the cutting edge condition display unit displays the cutting edge condition extraction data for the evaluation item in a selected evaluation area from among the evaluation areas of the cutting edge shape.

13. A machining shape simulation device described in any one of claims 1 to 4, wherein the cutting edge condition display unit displays the cutting edge shape in the entire evaluation area in a display format set based on the value of the cutting edge condition extraction data for the evaluation item.

14. A machining shape simulation device according to any one of claims 1 to 4, wherein the cutting edge condition display unit displays in a specific display format the area within the evaluation area of the cutting edge shape where the cutting edge condition extraction data has a maximum or minimum value, or the area where the integrated value of the cutting edge condition extraction data has a maximum value.

15. A machining shape simulation device as described in any one of claims 1 to 4, configured such that the cutting edge state extraction unit extracts the cutting edge state extraction data based on at least the calculation results of the interference area calculation unit, the cutting edge state display unit displays the cutting edge shape based on the model data stored in the cutting edge model storage unit, and the cutting edge state display unit displays the evaluation items in the cutting edge state extraction data inputted into the evaluation item input unit for the evaluation area of the selected cutting edge shape.

Images