Vibration simulation device and machining shape simulation device

Abstract

Provided is a vibration simulation device capable of highly accurately predicting vibration at a machining point in generative gear cutting. A vibration simulation device (1) for vibration between a tool and a workpiece in generative gear cutting for generating a gear by cutting a workpiece by means of a tool comprises: a shape defining unit (120) that defines a tool shape and a workpiece shape on the basis of analysis conditions including tool specifications, workpiece specifications, and machining conditions; an interference region computation unit (130) that computes an interference region between the tool and the workpiece during generative gear cutting on the basis of the tool shape, the workpiece shape, and the relative movement trajectory of the tool and the workpiece; a cutting force computation unit (140) that computes the cutting force to be applied when the tool removes the interference region from the workpiece; a dynamic characteristic calculation unit (150) that calculates relative dynamic characteristics between the tool and the workpiece or individual dynamic characteristics thereof on the basis of the analysis conditions; and a vibration computation unit (160) that computes relative vibration between the tool and the workpiece on the basis of the cutting force and the relative dynamic characteristics.

Description

Vibration simulation device and machining shape simulation device

[0001] The present invention relates to a vibration simulation device and 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] The present disclosure has been made in consideration of the above circumstances, and aims to provide a vibration simulation device that can predict vibrations at a machining point in gear generating cutting with high accuracy.

[0007] One aspect of the present disclosure is a vibration simulation device for simulating vibration between a tool and a workpiece in gear generating cutting processing in which a workpiece is cut with a tool to create a gear, the vibration simulation device having: a shape definition unit that defines a tool shape and a workpiece shape based on analysis conditions including tool specifications, workpiece specifications, processing conditions, and dynamic characteristics; 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 relative movement trajectories 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 calculation unit that calculates a 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.

[0008] In one aspect of the vibration simulation device of the present disclosure, first, an interference area between the tool and workpiece during gear-generating cutting is calculated based on the tool shape and workpiece shape specified under analysis conditions and the relative movement trajectory between the tool and workpiece, and then a cutting force to remove the interference area is calculated. Then, relative dynamic characteristics or individual dynamic characteristics between the tool and workpiece are calculated 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.

[0009] As described above, according to the above aspect, it is possible to provide a vibration simulation device that can predict vibrations at a machining point in gear generating cutting with high accuracy.

[0010] 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. 19 is a diagram showing a final machining position by each definition point P(k). FIG. 20 is a diagram showing the calculation results of each component of the cutting force. FIG. 21 is a diagram showing a prediction result by the vibration simulation device of this embodiment. FIG. 22 is a diagram showing a prediction result by the machining shape simulation device of this embodiment. FIG. 23 is another diagram showing a prediction result by the machining shape simulation device of this embodiment. FIG. 24 is a diagram showing a prediction result by the machining shape simulation device of a comparative example. FIG. 25 is a conceptual diagram comparing the prediction result by the machining shape simulation device of this embodiment with the prediction result of the comparative example. FIG. 26 is another conceptual diagram comparing the prediction result by the machining shape simulation device of this embodiment with the prediction result of the comparative example.

[0011] 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 inner or outer peripheral surface of the workpiece 20 using a tool that is a hob cutter.

[0012] 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.

[0013] 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.

[0014] 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.

[0015] 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.

[0016] 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 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 Zw direction, or the workpiece 20 may be moved in the direction opposite to the Zw direction. In other words, at least one of the tool 10 and the workpiece 20 is moved so that the tool 10 moves in the Zw direction relative to the workpiece 20.

[0017] 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, a gear 21 is 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 gear 21 has been machined partway into the workpiece 20, but by continuing the above operation, the gear 21 will be formed over the entire axial length of the workpiece 20.

[0018] 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.

[0019] 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.

[0020]

[0021] 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 each tool blade 11 and each tooth groove 22 is geometrically in the same cutting state.

[0022] 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.

[0023] 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.

[0024] 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).

[0025] 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.

[0026] 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 acquisition unit 110, a shape definition unit 120, 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 and a machining result prediction unit 190.

[0027] 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, and (4-8) explanation of machining result prediction processing.

[0028] 4-1. Shape Definition Processing The shape definition processing will be described with reference to the analysis condition acquisition unit 110 and the shape definition unit 120 in FIG. 1. First, the analysis condition acquisition 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 also include other information. The analysis conditions can be acquired by the analysis condition acquisition unit 110 by a user inputting 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).

[0029] 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 acquiring 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 approximate shape 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.

[0030] 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).

[0031] 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.

[0032] 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.

[0033] 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.

[0034] 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.

[0035] 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).

[0036] 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.

[0037] 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.

[0038] 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.

[0039] 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.

[0040] 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).

[0041] 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).

[0042] 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.

[0043] 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).

[0044] 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)).

[0045] 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.

[0046] 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).

[0047] 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.

[0048] 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.

[0049] 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).

[0050]

[0051] 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.

[0052] 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.

[0053] Here, the cutting depth calculation process will be described with reference to the intersection calculation unit 133, removal length calculation unit 134, and final processing position extraction unit 135 in FIG.

[0054] 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.

[0055] 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 ).

[0056] 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).

[0057] 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.

[0058] 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.

[0059] 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.

[0060] 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.

[0061] 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.

[0062] 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:

[0063]

[0064] Here, the unit vector is defined as in equation (4).

[0065]

[0066] 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).

[0067]

[0068] 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).

[0069]

[0070] 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).

[0071]

[0072] 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.

[0073] 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.

[0074] 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.

[0075] 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. 2). In this embodiment, the transfer function processing unit 161 outputs displacement, velocity, and acceleration.

[0076] 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.

[0077] 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.

[0078] 4-7. 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 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. 2). That is, the positions of the tool 10 and the workpiece 20 are updated to update the relative position between them, and the shape obtained by removing the interference region is used as the updated workpiece shape. 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. 2).

[0079] When machining is completed (Yes in S7 in FIG. 2), the output unit 170 outputs the calculation result of the vibration calculation unit 160 (S8 in FIG. 2). Each time the output unit 170 is updated by the update unit 180, it outputs the calculation result based on the update information. The output result of the output unit 170 is shown in FIG. 21(a), for example, and the vibration amplitude with transfer function correction is relatively close to the actually measured value, confirming that calculation can be performed with high accuracy.

[0080] 4-8. Prediction of Machining Result Next, the prediction of the machining result 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 updated based on the interference region updated by the update unit 180 is predicted as the shape of the workpiece 20 after machining.

[0081] When the machining shape simulation device 100 predicted machining results under normal conditions where chatter vibrations do not occur during machining and under abnormal conditions where chatter vibrations occur during machining, it predicted that the tooth flank shape would have small irregularities under the normal conditions as shown in Figure 22(a), and that the tooth flank shape would have large irregularities under the abnormal conditions as shown in Figure 22(b). This shows that the occurrence of chatter vibrations during machining is reflected in the prediction results, and that highly accurate predictions are possible.

[0082] Furthermore, as shown in Figure 23(a), under normal conditions, the tooth trace form error (difference between maximum and minimum) and the tooth profile form error (difference between maximum and minimum) are both relatively small, but as shown in Figure 23(b), under abnormal conditions, the tooth trace form error and tooth profile form error are larger than under normal conditions.On the other hand, in the comparative example in which the thrust force is not taken into account in the calculation of the cutting force, the prediction results under normal and abnormal conditions were equivalent, as shown in Figures 24(a) and 24(b).

[0083] When the prediction results of the Example and the Comparative Example were compared, as shown in Figure 25, the tooth trace form error showed a difference between normal and abnormal conditions in the prediction results of the Example, but no difference between normal and abnormal conditions in the prediction results of the Comparative Example. Furthermore, as shown in Figure 26, the tooth profile form error showed results similar to those of the tooth trace form error. These findings demonstrate that the prediction results of the Example exhibit higher prediction accuracy than the Comparative Example.

[0084] 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 specified 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 calculated 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.

[0085] As described above, according to this embodiment, it is possible to provide a vibration simulation device 1 that can predict vibrations at a machining point in gear generating cutting with high accuracy.

[0086] Furthermore, this embodiment includes an updating unit 180 that updates the relative position between the tool 10 and the workpiece 20 and the shape of the workpiece based on the interference region calculated by the interference region calculation unit 130 and the relative vibration calculated by the vibration calculation unit 160. The present embodiment also includes an output unit 170 that outputs the relative vibration repeatedly calculated by the interference region calculation unit 130, cutting force calculation unit 140, and vibration calculation unit 160 based on the update results by the updating unit 180. This makes it possible to predict and output the relative vibration with high accuracy.

[0087] In this embodiment, the cutting force calculation unit 140 calculates at least the principal force Fc and the thrust force Ft based on cutting theory during gear generating cutting, and calculates the cutting force FH based on the principal force Fc and the thrust force Ft. As a result, the cutting force FH is calculated based on the thrust force Ft in addition to the principal force Fc, improving the calculation accuracy of the cutting force FH and enabling the relative vibration to be predicted with high accuracy.

[0088] In this embodiment, the shape determining unit 120 defines the boundary between the rake face 11b and the flanks 11a and 11c of the tool 10 as a plurality of point clouds in the shape of the tool 10, and defines the machined portion in the shape of the workpiece 20 as a reference cylindrical surface having the central axis Zw of the workpiece 20 as its central axis and a plurality of pins 26 of specified lengths erected on the reference cylindrical surface in a normal direction. The orientation of the pins 26 is toward the center of the reference cylindrical surface when machining the inner peripheral surface of the workpiece 20, and toward the outside from the center of the reference cylindrical surface when machining the outer peripheral surface of the workpiece 20. The interference region calculating unit 130 calculates the intersections of each pin 26 with an infinitesimal line segment trajectory, which indicates the trajectory of an infinitesimal line segment connecting two adjacent definition points P and P1 in the point cloud from a predetermined first time position to a predetermined second time position, and calculates the interference region as the region of each pin 26 that is located inward of the intersection point on the tool 10. Furthermore, when the infinitesimal line segment moves from the position at the first time to the position at the second time, the cutting force calculation unit 140 calculates at least the principal force Fc(i) and the thrust force Ft(i) based on cutting theory as the cutting force FH, divides the principal force Fc(i) and the thrust force Ft(i) into components in the three orthogonal axis directions, adds up the principal force Fc(i) and the thrust force Ft(i) for each component, and then adds up the components in the three orthogonal axis directions over the entire region for each component. This improves the calculation accuracy of the cutting force.

[0089] In this embodiment, the vibration calculation unit 160 includes a transfer function processing unit 161 that calculates the relative vibration using a transfer function based on the cutting force and the relative dynamic characteristics, and a restoring action calculation unit 162 that calculates the restoring action that increases nonlinearly with an increase in the amplitude of the relative vibration. This corrects the transfer function or the cutting force FH, thereby preventing the calculated relative vibration from diverging, and enabling the relative vibration to be calculated with high precision.

[0090] In addition, in this embodiment, the machining shape simulation device 100 includes the vibration simulation device 1, and a machining result prediction unit 190 that predicts the machining result of the workpiece 20 based on the output result of the vibration simulation device 1 that is based on the relative vibration repeatedly calculated by the interference region calculation unit 130, the cutting force calculation unit 140, and the vibration calculation unit 160. As a result, when predicting the machining result of the workpiece 20, the output result of the vibration simulation device 1 is reflected, and therefore, the prediction accuracy can be improved.

[0091] 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.

[0092] 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 vibration simulation device for the interaction between a tool and a workpiece in gear-generating cutting processes, in which gears are created by cutting a workpiece with a tool, The above workpiece is supported so as to be rotatable around its central axis. The above tool has multiple tool blades formed as protrusions on its outer circumference and is supported so as to be rotatable around its central axis. The above-mentioned tool blade has a rake face on the end face in the extending direction of the tool blade, and relief faces on the side surface and radial outer surface of the tool blade in the extending direction. The central axis of the above tool intersects with the central axis of the above workpiece at an angle. The gear-generating cutting process described above involves synchronizing the rotation of the tool with the rotation of the workpiece, and moving at least one of the tool and the workpiece so that the tool moves relative to the workpiece in the direction of the workpiece's central axis, thereby causing the multiple tool blades included in the multiple tool blades to simultaneously participate in cutting the multiple tooth grooves included in the gear formed on the workpiece, thereby creating a gear on the inner or outer surface of the workpiece. A shape defining unit that defines the tool shape and workpiece shape based on analysis conditions including tool specifications, workpiece specifications, and machining conditions, An interference region calculation unit calculates the interference region between the tool and the workpiece during the gear-generating cutting process based on the tool shape, the workpiece shape, and the relative movement trajectory of the tool and the workpiece. A cutting force calculation unit that calculates the cutting force when the above tool removes the interference region from the above workpiece, A dynamic characteristics calculation unit that calculates the relative dynamic characteristics between the tool and the workpiece based on the above analysis conditions, A vibration calculation unit that calculates the relative vibration between the tool and the workpiece based on the above cutting force and the above relative dynamic characteristics, An update unit updates the relative position between the tool and the workpiece and the shape of the workpiece based on the interference region calculated by the interference region calculation unit and the relative vibration calculated by the vibration calculation unit. An output unit outputs the relative vibration that has been repeatedly calculated by the interference region calculation unit, the cutting force calculation unit, and the vibration calculation unit based on the update results from the above update unit, It has, The above-mentioned shape defining part defines the boundary between the rake face and the flank face of the tool as a group of points in the shape of the tool, and defines the workpiece shape as a workpiece part by a reference cylindrical surface with the central axis of the workpiece as its central axis and a group of pins of a specified length erected on the reference cylindrical surface in the direction normal to the surface. The above interference region calculation unit calculates the intersection points of each pin with the infinitesimal line segment trajectory, which represents the trajectory of an infinitesimal line segment connecting two adjacent defined points in the point cloud from a predetermined first time position to a predetermined second time position, and calculates the region where each pin is located inside the tool beyond the intersection point as the interference region. The above cutting force calculation unit calculates, as the cutting force, at least a principal force and a back force for each inter-definition point region, which is the region of two adjacent definition points among the multiple point clouds that define the boundary based on cutting theory, when the minute line segment moves from the position at the first time to the position at the second time, divides the principal force and the back force into components in the orthogonal three-axis direction, sums the principal force and the back force for each component, and then sums the components in the orthogonal three-axis direction for each component in the entire region of the inter-definition point region. The vibration calculation unit includes a transfer function processing unit that calculates the relative vibration using a transfer function based on the cutting force and the relative dynamic characteristics, and a restoring action calculation unit that calculates a restoring action that increases nonlinearly with increasing amplitude of the relative vibration by correcting the transfer function used in the transfer function processing unit or the cutting force input to the transfer function processing unit based on at least one of the displacement, velocity, and acceleration output by the transfer function processing unit. Vibration simulation device.

2. A vibration simulation apparatus according to claim 1, The system includes an interference region calculation unit, a cutting force calculation unit, and a vibration calculation unit, and a machining result prediction unit that predicts the machining result of the workpiece based on the output results of the vibration simulation device, which are based on the relative vibrations that are repeatedly calculated by the vibration calculation unit. A machine shape simulation device for gear generation cutting.