Gear shape machining system

Abstract

To provide a gear shape machining system capable of highly accurately predicting vibration of a machining point in a gear generation cutting process and highly accurately machining a workpiece into an ideal machined shape.SOLUTION: A gear shape machining system 1 for performing a gear generation cutting process comprises: an interference region calculation unit 130 that calculates an interference region between a tool and a workpiece; a cutting force calculation unit 140 that calculates a cutting force for removing the interference region; a dynamic characteristic defining unit 150 that defines relative dynamic characteristics between the tool and the workpiece; a vibration calculation unit 160 that calculates relative vibration between the tool and the workpiece; a machining result prediction unit 190 that predicts a machining result of the workpiece on the basis of a vibration simulation result of the interference region calculation unit 130, the cutting force calculation unit 140, and the vibration calculation unit 160; a wavy waveform extraction unit 191 that extracts a wavy waveform on a tooth-form direction formed on a tooth surface on the basis of the machining result prediction; and a tool correction amount calculation unit 193 that calculates a correction amount of an edge shape of the tool on the basis of the wavy waveform.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to a gear shape machining system. [Background technology]

[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, and cuts the workpiece by moving the machining tool in a straight line in the direction of the workpiece's central axis while rotating the workpiece and the machining tool synchronously, with the central axis of the machining tool at an angle to an axis parallel to the central axis of the workpiece.

[0003] Patent Document 2 describes a gear cutting simulation device for gear skiving. This gear cutting simulation device makes it possible to determine 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. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Japanese Patent Application Laid-Open No. 2012-45687 [Patent Document 2] Japanese Patent Application Laid-Open No. 2014-237185 Summary of the Invention [Problem to be solved by the invention]

[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 and the relative static stiffness between the tool and the workpiece at the cutting point, 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 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, posing a challenge to improving the prediction accuracy of gear-generating cutting processes. Furthermore, when there is a large shape error between the predicted shape obtained by gear-generating cutting and the ideal machined shape, adjusting machine settings and optimizing cutting conditions alone may not be enough to compensate for the shape error.

[0006] The present invention has been made in view of the above circumstances, and aims to provide a gear shape machining system that can accurately predict vibrations at the machining point during gear generating cutting, while machining a workpiece into an ideal machining shape with high precision. [Means for solving the problem]

[0007] One aspect of the present invention is A gear shape machining system that performs gear generating cutting, which performs cutting on a workpiece with a tool to generate a gear, comprising: a shape defining unit that defines a tool shape and a workpiece shape based on analysis conditions including tool specifications, workpiece specifications, and machining conditions; an interference area calculation unit that calculates an interference area between the tool and the workpiece during gear generating cutting, 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 region from the workpiece; a dynamic characteristic defining unit that defines a relative dynamic characteristic between the tool and the workpiece based on the analysis conditions; 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 machining result prediction unit that predicts a machining result of the workpiece based on a vibration simulation result including the relative vibration repeatedly calculated by the interference region calculation unit, the cutting force calculation unit, and the vibration calculation unit; a waviness waveform extraction unit that extracts a waviness waveform in a tooth profile direction formed on the tooth surface of the gear based on the prediction result of the processing result prediction unit; a tool correction amount calculation unit that calculates a correction amount for the cutting edge shape of the tool based on the undulation waveform; The gear shape machining system has: [Effects of the Invention]

[0008] In one aspect of the gear shape machining system, the interference area between the tool and workpiece during gear-generating cutting is first calculated based on the tool shape and workpiece shape defined based on the analysis conditions and the relative movement trajectory between the tool and workpiece, and a cutting force to remove the interference area is then calculated. Then, the 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 allows for highly accurate prediction of vibration at the machining point during gear-generating cutting. Then, based on the prediction result, the waviness waveform formed on the tooth flank in the tooth profile direction is extracted, and a correction amount for the tool cutting edge shape is calculated based on the waviness waveform. By using a tool whose cutting edge shape has been corrected based on the correction amount, the workpiece can be machined to an ideal machined shape with high accuracy.

[0009] As described above, according to the above aspect, it is possible to provide a gear shape machining system that can accurately predict vibrations at the machining point during gear generating cutting, and can accurately machine a workpiece into an ideal machining shape. [Brief explanation of the drawings]

[0010] [Figure 1] FIG. 1 is a functional block diagram of a gear shape machining system according to an embodiment of the present invention. [Figure 2] FIG. 1 is a flow chart illustrating a mode of use of the gear shape machining system of the present embodiment. [Figure 3] FIG. 2 is a functional block diagram (procedure) of a rake angle calculation unit in FIG. 1. [Figure 4] FIG. 1 is a perspective view showing the basic operation of gear machining. [Figure 5] 5 is a partial cross-sectional schematic view of the machining tool of FIG. 4. [Figure 6A] This is a diagram explaining the operation of gear skiving, showing the relative positions of the workpiece and the machining tool, projected onto the Xw, Zw plane (viewed from the Yw direction). [Figure 6B] This is a diagram explaining the operation of gear skiving, showing the relative positions of the workpiece and the machining tool, projected onto the Xw, Yw plane (viewed from the Zw direction). [Figure 7] 10A and 10B are diagrams illustrating the process from the start of cutting to the end of cutting in the tooth groove of the tool blade. [Figure 8] 2 is a perspective view of a tool blade showing definition points in the definition point determination unit of FIG. 1. FIG. [Figure 9] FIG. 10 is a diagram showing a cut vector L(i), a vector between definition points B(i), and a plane G(i). [Figure 10] FIG. 10 is a diagram showing a blade surface normal vector N(i). [Figure 11] FIG. 10 is a diagram showing a projection normal vector Ng(i). [Figure 12] FIG. 10 is a diagram showing the projected rake angle αg(i). [Figure 13] FIG. 10 is a diagram showing the portion removed in one tooth groove by one feed of one tool blade in the tooth groove direction. [Figure 14] FIG. 14 is a diagram showing the relationship between the tool rotation angle and the rake angle in the cutting of FIG. [Figure 15] FIG. 1 is a diagram showing a two-dimensional cutting model. [Figure 16] 1 shows the reference state of a model of the workpiece. [Figure 17] A model of the workpiece and a model of the machining tool are shown. [Figure 18] 10 shows a model of the workpiece with the pin length changed. [Figure 19] FIG. 10 is a diagram showing the final machining position according to each definition point P(k). [Figure 20] FIG. 10 is a diagram showing the calculation results of each component of the cutting force. [Figure 21] FIG. 10 is a diagram showing the results of calculation of relative vibration between a tool and a workpiece. [Figure 22] FIG. 10 is a diagram showing the results of prediction of tooth flank characteristics by the gear shape machining system of the present embodiment. [Figure 23] FIG. 1(a) is an enlarged view of a portion of a gear, and FIG. 1(b) is a conceptual diagram showing multiple machining point trajectories on the tooth surface. [Figure 24] 5A and 5B are conceptual diagrams showing errors in each processing point locus in the present embodiment. [Figure 25] 10A and 10B are conceptual diagrams showing changes in the cutting edge shape of a tool before and after correction in this embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0011] 1. Basic operations of gear cutting First, the basic operation of gear generating cutting in the gear shape machining system 1 of this embodiment will be described with reference to Figures 4 and 5. Here, in this embodiment, an example is given of a case where 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 a case where the gear generating cutting is skiving, in which a gear is machined on the outer peripheral surface of the workpiece 20. It is also applicable to a case where the gear generating cutting is hobbing, in which a gear is machined on the 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 FIGS. 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, and the edge angle of the end face 11b of the tool blade 11 is zero.

[0015] As shown in Figure 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 Figure 6A). In other words, the central axes Zt and Zw of the two are not parallel. .

[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 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 Fig. 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.

[0017] Since 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 Fig. 4. Note that Fig. 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.

[0018] 2. Gear generating cutting equipment 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 around 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 Gear Shape Machining System 1 An overview of a gear shape machining system 1 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 central axis Zw of the workpiece 20. 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") at this time 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 gear shape machining system 1 may be built into the control device of a gear generating cutting device. The gear shape machining system 1 may also be an embedded system such as a programmable logic controller (PLC) or computer numerical control (CNC) device, or may be a personal computer or server.

[0020]

number

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

[0022] Therefore, the gear shape machining system 1 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, i.e., 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 for one tool blade 11 becomes clear. That is, as shown in the order of (a), (b), and (c) in Figure 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 detailed analysis of the cutting state of one tool blade 11 in a shorter time than before. It also makes it possible to easily calculate the tool blade characteristics required for proper design of the tool 10, namely, the rake angle of the tool blade 11 and the cutting force of 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 multiple 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 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 the first embodiment, 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.

[0026] 4. Details of Gear Shape Machining System 1 The gear shape machining system 1 is composed of one or more arithmetic processing devices and memory devices, and as shown in FIG. 1 , is equipped with an analysis condition setting unit 110, a shape determination unit 120, an interference region calculation unit 130, a cutting force calculation unit 140, a dynamic characteristic determination unit 150, a vibration calculation unit 160, an output unit 170, an update unit 180, a machining result prediction unit 190, a waviness waveform extraction unit 191, a tooth flank shape modification amount calculation unit 192, and a tool compensation amount calculation unit 193.

[0027] Here, in explaining the gear shape machining system 1, while referring to the flow diagram showing the usage mode of the gear shape machining system 1 shown in Figure 2, the following will be explained in the following order: (4-1) explanation of the shape determination process, (4-2) explanation of the rake angle calculation process, (4-3) explanation of the two-dimensional cutting model, (4-4) explanation of the cutting depth calculation process, (4-5) explanation of the cutting force calculation process, (4-6) explanation of the relative vibration calculation process, (4-7) explanation of information update and output of calculation results, (4-8) explanation of the machining result prediction process, and (4-9) explanation of the tool shape correction process.

[0028] 4-1. Shape definition processing The shape determination process will be described with reference to the analysis condition setting unit 110 and the shape determination unit 120 in FIG. 1. First, the analysis condition setting unit 110 acquires the analysis conditions required for the simulation in the gear shape machining system 1 (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 for a gear generating cutting machine (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 memory 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 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, in the tool 10, as shown in FIG. 8, 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 of 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 cutting 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. Because 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 parallel to the normal direction of the reference cylindrical surface at specified intervals on 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 of the reference cylindrical surface when machining the outer peripheral surface. 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. The cutting-in vector calculation unit 131 calculates, for each inter-definition point area ΔP(i, i+1), a cutting-in vector L(i) along which the inter-definition point area ΔP(i, i+1) moves in the cutting direction while the tool 10 rotates from a rotation angle σ1, which is a first time, to a rotation angle σ2, which is a second time. However, it is not easy to calculate the direction in which the entire inter-definition point area ΔP(i, i+1) moves.

[0033] Therefore, as shown in Fig. 9, the vector Lc(i) along which the midpoint Pc(i, i+1) between 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). Here, the calculation of the rake angle α(i) by the rake angle calculation unit 132 is performed according to the procedure shown in FIG.

[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 midpoint 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.

[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 vector between the definition points 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 the 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, the 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) passing through three definition points P(i-1), P(i), and P(i+1) is determined. Then, on the plane Q(i), a vector passing through the midpoint Pc(i, i+1) and 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), the 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) is determined within 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 determined separately for 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) within 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] 4-3. 2D cutting model Next, a two-dimensional cutting model based on two-dimensional cutting theory will be described with reference to Fig. 15. Fig. 15 shows a cutting model on the plane G(i) described above. In Fig. 15, a workpiece 20 is cut by a tool blade 11 of a tool 10.

[0049] Here, in plane G(i), the rake face of tool blade 11 is end face 11b, the side relief face is side face 11a, and the front relief face is radial outer face 11c. The rake angle is αg(i). The cutting depth is d1(i), and the shear angle is φ(i). At this time, the cutting vector by tool blade 11 is L(i), and the normal vector of 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]

number

[0051] In equation (2), τs is the shear stress, which is determined 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 depth of cut d1(i) of the area between the definition points ΔP(i, i+1). The depth of cut d1(i) corresponds to the average of the depth of cut (corresponding to the radial depth) at definition point P(i) and the depth of cut 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, calculating the rake angle αg(i) on plane G(i) allows the application of a two-dimensional cutting model. The same application as for the two-dimensional model can be applied to a three-dimensional cutting model instead of the two-dimensional cutting model.

[0052] 4-4. Cutting depth calculation process In the above two-dimensional cutting model, if the cutting depth 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 cutting depth d1(i) can be obtained from the difference between the two. This will be explained in detail below with reference to Figures 17 to 19.

[0053] Here, the cutting amount calculation process will be explained with respect 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 point 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 cutting with the tool blade 11 when the tool rotation angle σ increases slightly from σ1 to σ2, and this shape after cutting 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 to 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 position 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 the 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 amount at each definition point P(k), and further calculates the cutting amount d1(i) at the midpoint Pc(i, i+1). The intersection calculation unit 133 calculates the intersection between each pin 26 representing the workpiece 20 and the trajectory plane 11p of the tool blade 11 within the range from the start to the end of cutting of one tooth groove 22 by one tool blade 11. Then, each time the cutting of one tooth groove 22 by one tool blade 11 is repeatedly performed from the start 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 trajectory 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) will be described using a two-dimensional cutting model. This process will be described 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, Yw direction, and 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]

number

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

[0065]

number

[0066] Then, the components Fcx(i), Fcy(i), and Fcz(i) of the principal force Fc(i) and the components Ftx(i), Fty(i), and Ftz(i) of the thrust force Ft(i) are expressed by the following equation (5).

[0067]

number

[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]

number

[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]

number

[0072] The cutting force FH in the entire region can be calculated based on equation (7). The calculation results for 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] 4-6. Relative vibration calculation processing Next, a description will be given of a procedure for calculating the relative vibration between the tool 10 and the workpiece 20. The procedure 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.

[0074] 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 calculation is performed based on information acquired by the analysis condition setting unit 110. For example, the analysis condition setting unit 110 can calculate the dynamic characteristic based on information acquired by a hammering test or the like. The relative dynamic characteristic can be defined 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 defined by the dynamic characteristics definition 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 FIG. 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 the correction of the transfer function or cutting force FH by the restoring action calculation unit 162 suppresses this divergence.

[0078] 4-7. Information update and calculation result output Next, the information update by the update unit 180 and the output by the output unit 170 will be described. First, the calculation result of the transfer function processing unit 161 is input to the update unit 180 and output by 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 relative position between the tool 10 and the workpiece 20 is updated by updating the positions of the tool 10 and the workpiece 20, and the shape obtained by removing the interference region is defined 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 (No in S7 in FIG. 2). Repeated calculations by the interference region calculation unit 130, the cutting force calculation unit 140, and the vibration calculation unit 160 provide a vibration simulation result consisting of the relative vibration as a calculation result.

[0079] When machining is completed (Yes in S7 of FIG. 2), the output unit 170 outputs the calculation result of the vibration calculation unit 160, and the machining result is predicted by the machining result prediction unit 190 as described below (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 calculation result output by the output unit 170 is shown in FIG. 21, for example, and is relatively close to the actual measured value for vibration displacement with transfer function correction, confirming that calculation can be performed with high accuracy.

[0080] 4-8. Prediction of machining results Next, a description will be given of the processing result prediction process performed by the gear shape machining system 1 shown in Fig. 1. In the gear shape machining system 1, the processing result prediction unit 190 predicts the shape of the workpiece 20 after machining based on the update result of the update unit 180 (S8 in Fig. 2). Specifically, the workpiece shape is predicted as the shape of the workpiece 20 after machining based on the interference area updated by the update unit 180.

[0081] The gear shape machining system 1 predicted the machining results under normal conditions where no chatter vibration occurs during machining and under abnormal conditions where chatter vibration occurs during machining. Under the normal conditions, the tooth flank shape was predicted to have small irregularities, as shown in Figure 22(a), and under the abnormal conditions, the tooth flank shape was predicted to have large irregularities, as shown in Figure 22(b).

[0082] 4-9. Tool shape correction processing Next, we will explain the correction process of the tool shape by the gear shape machining system 1 shown in Fig. 1. In the gear shape machining system 1, the machining result prediction unit 190 extracts the waviness waveform in the tooth profile direction formed on the tooth flank 210 by the waviness waveform extraction unit 191 shown in Fig. 1 from the prediction result under normal conditions where no chatter vibration occurs (S9 in Fig. 2).

[0083] Extraction of the waviness waveform is performed as follows: As an example, first, as shown in Fig. 23(a), in the predicted shape of the left tooth flank 211 of a pair of tooth flanks 210 in one tooth groove 22 formed on the inner peripheral surface of the workpiece 20, when the machining point in the gear generating process proceeds in a direction inclined with respect to the tooth trace direction as shown in Fig. 23(b), a plurality of machining point loci including a first machining point locus Pt1, a second machining point locus Pt2, a third machining point locus Pt3, a fourth machining point locus Pt4, and a fifth machining point locus Pt5 are formed sequentially. 24(a) to 24(e), the waviness waveform extraction unit 191 extracts a waviness waveform Ptx (thick line portion in FIG. 23(a)) that is parallel to the tooth trace direction and has waviness in the tooth profile direction, including recessed portions Pa and protruding portions Pb, for each of the machining point trajectories Pt1 to Pt5, as a shape that includes an error from the involute shape that is the target tooth profile shape, from the predicted shape of the machining result prediction unit 190. Note that a waviness waveform Ptx is also extracted for the right tooth flank 212, similar to the left tooth flank 211.

[0084] Next, the tooth flank shape modification amount calculation unit 192 shown in Fig. 1 calculates the modification amount S of the tooth profile on the tooth flank 210 of the workpiece 20 (S10 in Fig. 2). As shown in Figs. 24(a) to (e), the waviness waveform extracted by the waviness waveform extraction unit 191 has a shape that roughly follows a sine curve, so the tooth flank shape modification amount calculation unit 192 calculates the tooth profile modification amount S for modifying the tooth flank 210 (left tooth flank 211 and right tooth flank 212) into an involute shape, which is the target tooth profile shape, based on the approximation formula shown in Equation (8) below. Similarly, for the right tooth flank 212, the tooth profile modification amount S for modifying the tooth profile to an involute shape, which is the target tooth profile shape, is calculated based on the approximation formula shown in Equation (8) below.

[0085]

number

[0086] 1 calculates a correction amount for the cutting edge shape of the tool 10 based on the waviness waveform (S11 in FIG. 2). In this embodiment, the tool correction amount calculation unit 193 calculates the cutting edge shape of the tool 10 based on the tooth flank shape modification amount S calculated by the tooth flank shape modification amount calculation unit 192 based on the waviness waveform. That is, by performing a back calculation from the tooth profile modification amount S, it is possible to calculate a tool shape capable of machining the workpiece 20 into an involute tooth profile. As a result, by applying the correction amount to the shape of the cutting edge of the tool 10 shown in FIG. 25(a), the shape of the cutting edge of the tool 10 after correction becomes a shape Qtx having a waveform in reverse phase to the waviness waveform Ptx (see FIG. 23(a)) extracted by the waviness waveform extraction unit 191, as shown in FIG. 25(b).

[0087] Therefore, by machining with the corrected tool 10 shown in Figure 25(b), the waviness formed on the tooth flank 210 of the workpiece 20 is canceled out, making it possible to form with high precision the target tooth flank shape, an involute shape.The grinding wheel shape for forming the corrected tool shape of the tool 10 can be found by back-calculating from the corrected tool shape.By forming the tool using this grinding wheel shape, it is possible to machine the workpiece 20 into an involute tooth shape.

[0088] If the waviness phase differs during actual machining, it is possible to reduce the error by adjusting the waviness phase according to the machining conditions (depth of cut).

[0089] 5. Effects In the gear shape machining system 1 of this embodiment, first, an interference area between the tool 10 and the workpiece 20 during gear-generating cutting is calculated based on the tool shape and workpiece shape defined based on the analysis conditions and the relative movement trajectory between the tool 10 and the workpiece 20, and a cutting force to remove the interference area is calculated. Then, the relative dynamic characteristics or individual dynamic characteristics between the tool 10 and the workpiece 20 are calculated based on the analysis conditions, and the relative vibration between the tool 10 and the workpiece 20 is calculated based on the cutting force and the dynamic characteristics. This allows for highly accurate prediction of vibration at the machining point during gear-generating cutting. Then, based on the predicted machining result, a waviness waveform in the tooth profile direction formed on the tooth flank 210 is extracted, and a correction amount for the cutting edge shape of the tool 10 is calculated based on the waviness waveform. By using the tool 10 whose cutting edge shape has been corrected based on the correction amount, the workpiece 20 can be machined to an ideal machined shape with high accuracy.

[0090] As described above, according to this embodiment, it is possible to provide a gear shape machining system that can accurately predict vibrations at the machining point during gear generating cutting and machine the workpiece 20 into an ideal machining shape with high precision.

[0091] Furthermore, this embodiment includes a tooth flank shape modification amount calculation unit 192 that calculates the tooth profile shape modification amount S of the workpiece 20 based on the waviness waveform. Then, a tool correction amount calculation unit 193 calculates the correction amount of the cutting edge shape of the tool 10 by back-calculating the tooth profile shape modification amount S calculated by the tooth flank shape modification amount calculation unit 192. This makes it possible to further eliminate waviness that has been formed on the tooth flank 210 of the workpiece 20 in the predicted shape.

[0092] In this embodiment, the tooth flank shape modification amount calculation unit 192 calculates the tooth profile shape modification amount S based on a relational expression expressed as S=A×sin(θ+φ), where S is the tooth profile shape modification amount, A is the shape amplitude of the waviness waveform, φ is the relative phase between the tool 10 and the workpiece 20, and θ is the rotation angle of the tool 10. This makes it possible to easily calculate the tooth profile shape modification amount S.

[0093] In this embodiment, the tool 10 is a gear skiving cutter having a plurality of tool blades 11 formed in a ridge on its outer periphery, supported rotatably around its central axis, and having a rake face 11b on an end face of the tool blade 11 in the extension direction thereof, and having relief faces 11a, 11c on a side face of the tool blade 11 in the extension direction and on a radially outer face thereof, and the central axis Zt of the tool 10 forms an intersecting angle with the central axis Zw of the workpiece 20. The gear generating cutting process is performed by moving at least one of the tool 10 and the workpiece 20 so that the tool 10 moves in the central axis direction of the workpiece 20 relative to the workpiece 20 while synchronizing the rotation of the tool 10 with the rotation of the previous workpiece, thereby causing the multiple tool blades 11 included in the tool 10 to simultaneously participate in cutting a plurality of tooth grooves 22 included in a gear formed in the workpiece 20, thereby generating a gear on the inner or outer peripheral surface of the workpiece 20. This allows the gear to be formed on the workpiece 20 with high precision.

[0094] In this embodiment, a cylindrical surface having the central axis Zw of the workpiece 20 as the central axis is used as a reference surface, and the shape of the workpiece 20 is defined based on the lengths of the pins 26 erected on the reference cylindrical surface at specified intervals in a direction parallel to the normal direction to the reference cylindrical surface, and each calculation is performed based on this. However, without being limited to this, the shape of the workpiece 20 may be defined by specifying the radial distance R of the lattice pitch set in the cylindrical coordinate system and the azimuth angle θ with respect to the axial coordinate Z, and each calculation may be performed based on this.

[0095] 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. [Explanation of symbols]

[0096] 1. Gear shape processing system 10...Tools 11...Tool blade 11a...Side surface (side relief) 11b...End face (rake face) 11c...Side (front relief) 20...Workpiece 21...Gear 210...tooth surface 211...Left tooth surface 212...Right tooth surface 22...Tooth groove 23...Removed part (interference area) 110...Analysis condition setting section 120...shape determining section 130...Interference area calculation unit 140...Cutting force calculation section 150...Dynamic characteristic definition section 160...Vibration calculation section 170...Output section 180...Update section 190...Processing result prediction unit 191...Wave waveform extraction section 192...Tooth surface shape modification amount calculation unit 193...Tool compensation amount calculation section

Claims

1. A gear shape machining system that performs gear generating cutting, which performs cutting on a workpiece with a tool to generate a gear, comprising: a shape defining unit that defines a tool shape and a workpiece shape based on analysis conditions including tool specifications, workpiece specifications, and machining conditions; an interference area calculation unit that calculates an interference area between the tool and the workpiece during gear generating cutting, 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 region from the workpiece; a dynamic characteristic defining unit that defines a relative dynamic characteristic between the tool and the workpiece based on the analysis conditions; 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 machining result prediction unit that predicts a machining result of the workpiece based on a vibration simulation result including the relative vibration repeatedly calculated by the interference region calculation unit, the cutting force calculation unit, and the vibration calculation unit; a waviness waveform extraction unit that extracts a waviness waveform in a tooth profile direction formed on the tooth surface of the gear based on the prediction result of the processing result prediction unit; a tool correction amount calculation unit that calculates a correction amount for the cutting edge shape of the tool based on the undulation waveform; A gear shape machining system having the above structure.

2. a tooth surface shape modification amount calculation unit that calculates a tooth surface shape modification amount of the workpiece based on the waviness waveform, 2. The gear shape machining system according to claim 1, wherein the tool compensation amount calculation unit calculates the compensation amount by back-calculating the tooth profile modification amount calculated by the tooth flank shape modification amount calculation unit.

3. 3. The gear shape machining system according to claim 2, wherein the tooth flank shape modification amount calculation unit calculates the tooth profile shape modification amount based on a relational expression expressed as S = A × sin(θ + φ), where S is the tooth profile shape modification amount, A is the shape amplitude of the waviness waveform, φ is the relative phase between the tool and the workpiece, and θ is the rotation angle of the tool.

4. The tool is a gear skiving cutter having a plurality of tool blades formed in a ridge on the outer periphery of the tool, being supported rotatably around the central axis of the tool, and the tool blades having a rake surface on an end surface in an extension direction of the tool blades, and having relief surfaces on a side surface in the extension direction of the tool blades and on a radially outer surface, a central axis of the tool has an intersecting angle with a central axis of the workpiece; 3. The gear shape machining system according to claim 1 or 2, wherein the gear generating cutting process involves moving at least one of the tool and the workpiece so that the tool moves in the direction of the central axis of the workpiece relative to the workpiece while synchronizing the rotation of the tool with the rotation of the workpiece, thereby causing a plurality of tool blades included in the plurality of tool blades to simultaneously participate in cutting a plurality of tooth grooves included in a gear formed in the workpiece, thereby generating a gear on the inner or outer peripheral surface of the workpiece.

Images