Vibration simulation device and machining shape simulation device

Abstract

A vibration simulation device (1) for vibration between a tool (10) and a workpiece (20) during gear-making cutting, in which a gear is produced by cutting the workpiece (20) with the tool (10), comprises: a shape definition unit (120) configured to define a tool shape and a workpiece shape based on analysis conditions that include tool specifications, workpiece specifications, and machining conditions; a superposition region calculation unit (130) configured to calculate a superposition region between the tool (10) and the workpiece (20) during gear-making cutting based on the tool shape, the workpiece shape, and a relative motion path between the tool (10) and the workpiece (20);a cutting force calculation unit (140) configured to calculate a cutting force of the tool (10) to remove the superimposed region from the workpiece (20); a dynamic property calculation unit (150) configured to calculate relative dynamic properties or individual dynamic properties between the tool (10) and the workpiece (20) based on the analysis conditions; and a vibration calculation unit (160) configured to calculate a relative vibration between the tool and the workpiece based on the cutting force and the relative dynamic properties.

Description

TECHNICAL AREA

[0001] The present invention relates to a vibration simulation device and a machining shape simulation device. STATE OF THE ART

[0002] A gear-cutting method described in patent document 1 is known. This gear-cutting method uses a machining tool having a plurality of cutting edges on its outer circumference. When the central axis of the machining tool is set at an angle with respect to an axis parallel to the central axis of a workpiece, and when the workpiece and the machining tool are rotated synchronously, the machining tool is moved directly in the direction of the central axis of the workpiece to perform a cutting action.

[0003] Patent document 2 describes a gear cutting simulation device for gear skiving. This device makes it possible to determine the cutting force acting on each part of the cutting edge of the machining tool. This information can be used to determine machining conditions such as cutting depth and feed rate, thus enabling the design of a suitable gear cutting device. DOCUMENTS ACCORDING TO THE STATE OF TECHNOLOGY PATENT DOCUMENTS Patent document 1: Japanese unexamined patent application publication no. 2012-45687 (JP 2012 - 45 687 A) Patent document 2: Japanese unexamined patent application publication no. 2014-237185 (JP 2014 - 237 185 A) SUMMARY OF THE INVENTION Problem to be solved by the invention

[0004] In gear-generating cutting processes such as gear skiving, static behavior occurs, such as misalignment, caused by an average machining load generated between a tool and a workpiece at a machining point and a relative static strength between the tool and the workpiece, and dynamic behavior occurs, caused by fluctuations in the machining load generated between the tool and the workpiece and relative dynamic properties between the tool and the workpiece, i.e., vibrations such as forced vibration and self-excited vibration.However, conventional gear cutting simulations do not fully account for such vibrations, which is one of the factors that causes a discrepancy between actual cutting results and the results predicted by the simulations, thus reducing prediction accuracy. To improve the predictive accuracy of gear cutting results, it is necessary to predict the vibrations at the machining point with high accuracy. However, such vibrations have not been predicted with high accuracy in gear cutting. This is a challenge in improving the predictive accuracy of gear cutting.

[0005] The present disclosure was made in view of such circumstances, and one of its objectives is to provide a vibration simulation device that can predict vibrations at a machining point during gear manufacturing cutting with high accuracy. Means to solve the problem

[0006] One embodiment of the present disclosure is a vibration simulation device for vibration between a tool and a workpiece during gear-making machining, in which a gear is produced by cutting the workpiece with the tool. The vibration simulation device comprises: a shape definition unit configured to define a tool shape and a workpiece shape based on analysis conditions that include tool specifications, workpiece specifications, and machining conditions; a superposition region calculation unit configured to calculate a superposition region between the tool and the workpiece during gear-making machining based on the tool shape, the workpiece shape, and a relative motion path between the tool and the workpiece;a cutting force calculation unit configured to calculate a cutting force of the tool for removing the superimposed region from the workpiece; a dynamic property calculation unit configured to calculate relative dynamic properties or individual dynamic properties between the tool and the workpiece based on the analysis conditions; and a vibration calculation unit configured to calculate a relative vibration between the tool and the workpiece based on the cutting force and the relative dynamic properties. Effects of the invention

[0007] The vibration simulation device, according to the embodiment of the present disclosure, first calculates the superposition region between the tool and the workpiece during gear-making cutting, based on the tool and workpiece shapes defined by the analysis conditions and the relative path of motion between the tool and the workpiece. It then calculates the cutting force required to remove the superposition region. The vibration simulation device then calculates the relative dynamic properties, or the individual dynamic properties, between the tool and the workpiece based on the analysis conditions, and calculates the relative vibrations between the tool and the workpiece based on the cutting force and the dynamic properties. Thus, it is possible to predict vibrations at the machining point during gear-making cutting with high accuracy.

[0008] As described above, it is possible, according to the above-described design, to provide a vibration simulation device that can predict vibrations at the machining point during gear manufacturing cutting with high accuracy. BRIEF DESCRIPTION OF THE DRAWINGS Fig. Figure 1 shows a functional block diagram of a vibration simulation device and a machining shape simulation device according to an exemplary embodiment. Fig. Figure 2 shows a flowchart illustrating how the vibration simulation device and the machining shape simulation device are used according to the exemplary embodiment. Fig. Figure 3 shows a functional block diagram (a sequence) of a rake angle refraction unit according to Fig. 1. Fig. Figure 4 shows a perspective view illustrating a basic process of gear cutting. Fig. Figure 5 shows a schematic partial section view of a machining tool according to Fig. 4. Fig. Figure 6A shows a representation illustrating a gear skiving process, showing relative positions of a workpiece and the machining tool projected onto an Xw, Zw plane (as viewed in a Yw direction). Fig. Figure 6B shows a representation illustrating the process of gear skiving, with the relative positions of the workpiece and the machining tool projected onto an Xw, Yw plane (as viewed in a Zw direction). Fig. Figure 7 shows a representation illustrating a process from the start of cutting a tooth space with a tool cutting edge to the end of the cutting. Fig. Figure 8 shows a perspective view of the tool cutting edge, with definition points in a definition point determination unit in Fig. 1 are shown. Fig. Figure 9 shows a representation illustrating a cutting vector L(i), an intermediate definition point vector B(i) and a plane G(i). Fig. Figure 10 shows a representation illustrating an intersection surface normal vector N(i). Fig. Figure 11 shows a representation illustrating a projected normal vector Ng(i). Fig. Figure 12 shows a representation illustrating a projected rake angle ag(i). Fig. Figure 13 shows a representation illustrating a section that is removed in a (single) tooth space by a (single) feed of a (single) tool cutting edge in one tooth space direction. Fig. Figure 14 shows a diagram illustrating the relationship between a tool rotation angle and a rake angle during cutting in Fig. 13 illustrated. Fig. Figure 15 shows a representation illustrating a two-dimensional cutting model. Fig. Figure 16 shows a reference state of a model of the workpiece. Fig. Figure 17 shows the model of the workpiece and a model of the machining tool. Fig. Figure 18 shows the model of the workpiece with varying pin lengths. Fig. Figure 19 shows a representation illustrating a final processing position at each definition point P(k). Fig. Figure 20 shows a representation illustrating calculation results of components of a cutting force. Fig. Figure 21 shows a representation illustrating prediction results obtained by the vibration simulation device according to the embodiment. Fig. Figure 22 shows a representation illustrating prediction results obtained by the machining form simulation device according to the exemplary embodiment. Fig. Figure 23 shows another illustration demonstrating prediction results obtained by the machining form simulation device according to the exemplary embodiment. Fig. Figure 24 shows a representation illustrating prediction results obtained by a machining form simulation device according to a comparative example. Fig. Figure 25 shows a conceptual representation of a comparison between the prediction results obtained by the machining form simulation device according to the exemplary embodiment and the prediction results in the comparison examples. Fig. Figure 26 shows a further conceptual representation of a comparison between the prediction results obtained by the machining form simulation device according to the embodiment and the prediction results in the comparison example. METHODS OF IMPLEMENTING THE INVENTION 1. Basic process of gear manufacturing cutting

[0009] First, the basic process of gear manufacturing cutting, in which a machining form simulation device 100 (see Fig. 1) is applied with a vibration simulation device 1 according to an exemplary embodiment, with reference to Fig. 4 and Fig. 5 described. The present embodiment illustrates an example in which the gear-forming cutting is a gear-forming operation for forming a gear 21 on an inner circumferential surface of a workpiece 20 using a tool 10, which is a skiving tool. However, the present invention can also be applied to a case in which the gear-forming cutting is a gear-forming operation for cutting a gear on the outer circumferential surface of the workpiece 20. The present invention can also be applied to a case in which the gear-forming cutting is a milling operation for cutting a gear on the inner circumferential surface or the outer circumferential surface of the workpiece 20 using a tool, which is a hob cutter or gear cutter.

[0010] As it is in Fig. As shown in Figure 4, the workpiece 20 is formed in a ring shape, and the gear 21 is formed on its inner circumferential surface. The workpiece 20 is rotatably supported about its central axis Zw. This means that the workpiece 20 is rotatable about a C-axis.

[0011] As it is in Fig. 4 and Fig. As shown in Figure 5, the tool 10 has a plurality of cutting edges 21 on its outer circumference and is supported such that it is rotatable about a central axis Zt of the tool 10. That is, the tool 10 is rotatable about a U-axis. Each cutting edge 11 is formed as a projecting edge. Each cutting edge 11 has side surfaces 11a in the extension direction of the cutting edge 11, an end surface 11b in the extension direction, and a radially outer surface 11c. In the gear-making cutting process, the end surface 11b serves as a rake face, and the side surface 11a and the radially outer surface 11c serve as clearance faces. In particular, the side surface 11a serves as a side clearance face, and the radially outer surface 11c serves as an end clearance face.

[0012] According to the present embodiment, the cutting edge 11 has a helix angle γ1 with respect to the central axis Zt of the tool 10. However, the cutting edge 11 can be configured such that the helix angle γ1 is zero. The radially outer surface 11c of the cutting edge 11 is inclined with respect to the central axis Zt. That is, the circumscribing surface of the cutting edge 11 is conical. An inclination angle ξb of the radially outer surface 11c of the cutting edge 11 corresponds to a rake angle during cutting. The end surface 11b of the cutting edge 11 is inclined at an angle ξa with respect to a plane that is orthogonal to the central axis Zt. The inclination angle ξa of the end surface 11b of the cutting edge 11 corresponds to a rake angle during cutting. Although not shown, the side surface 11a of the cutting edge 11 has a side clearance angle.

[0013] As it is in Fig. As shown in Figure 4, the central axis Zt of the tool 10 has an angle with respect to an axis that is parallel to the central axis Zw of the workpiece 20, i.e. it has a crossing angle (cutting angle) θ (see Figure 4). Fig. 6A). This means that the central axes Zt and Zw of the two are not parallel.

[0014] In this state, the tool 10 is moved in the direction of the central axis Zw of the workpiece 20 relative to the workpiece 20, as indicated by the wide arrow in Fig. As specified in 4, the rotation of the tool 10 and the rotation of the workpiece 20 are synchronized. The tool 10 can be moved in the intermediate direction, or the workpiece 20 can be moved in a direction opposite to the intermediate direction. This means that the workpiece 10 and / or the workpiece 20 is moved such that the tool 10 moves in the intermediate direction relative to the workpiece 20.

[0015] Since the central axis Zt of the tool 10 and the central axis Zw of the workpiece 20 have the 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. Then the gear 21 is formed on the inner rotating surface of the workpiece 20, as shown in Fig. 4 is shown. Fig. Figure 4 shows a state in which the gear 21 is partially cut into the workpiece 20. The gear 21 is formed over the entire axial length of the workpiece 20 by continuing the process described above. 2. Gear-making cutting device

[0016] For example, a (not shown) five-axis machining center can be used as a gear-making cutting device to carry out the gear-making cutting process according to the present embodiment. That is, a device can be used that can move the tool 10 and the workpiece 20 straight ahead in three axes that are orthogonal to each other, rotate the tool 10 and the workpiece 20 about their axes (U-axis rotation, C-axis rotation), and tilt the central axis Ct of the tool 10 and the central axis Cw of the workpiece 20. 3. Overview of the vibration simulation device 1 and the machining form simulation device 100

[0017] An overview of the vibration simulation device 1 and the machining geometry simulation device 100 according to the present embodiment of the present invention is described below. As described in Fig. 6A and Fig. As shown in Figure 6B, during gear skiving, the tool 10 is advanced in the direction of the central axis Zw of the workpiece 20, while the workpiece 20 and the tool 10 are rotated synchronously (U-axis rotation, C-axis rotation). A rotation angle η of the workpiece 20 and a rotation angle σ of the tool 10 (the tool cutting edges 11) (hereinafter referred to as the "tool rotation angle σ") are related by the following equation (1). Jw is the number of teeth of the gear 21, Jt is the number of teeth of the tool cutting edges 11, and δ is a correction angle. The machining form simulation device 100 can be integrated into a control device of the gear-making cutting device. The machining form simulation device 100 can be an embedded system such as a PLC (Programmable Logic Controller) or a CNC (Computer Numerical Control) device, or it can be a personal computer or a server. [Equation 1] η=(Jw / Jt)σ+δ

[0018] In gear skiving, the multitude of cutting edges 11 formed on the outer circumference of the tool 10 are used simultaneously to cut a multitude of tooth spaces 22 (see Fig. 4) of the gear 21 involved, which are formed on the inner circular surface of the workpiece 20, and each tool cutting edge 11 and each tooth space 22 are geometrically in the same cutting state.

[0019] Therefore, according to the present embodiment, the machining form simulation device 100 performs an analysis by rotating the tool 10 by a small angle, i.e., by slightly increasing the tool rotation angle σ in expression (1), focusing on the rotation of a tool cutting edge 11 in a tooth space 22. If the focus is also on the feed of a tool cutting edge 11 in a (single) tooth space 22, the area from the start of cutting by a (single) tool cutting edge 11 to the end of cutting is clearly defined. That is, as shown in the sequence of (a), (b), and (c) in Fig. As shown in Figure 7, the cutting edge 11 starts cutting the tooth space 22 at a tool rotation angle σs, progresses to a tool rotation angle σ = 0 and ends cutting the tooth space 22 at a tool rotation angle σe.

[0020] Thus, the cutting state of a (single) tool cutting edge 11 can be analyzed in detail in a shorter time than before. The tool cutting edge properties required for a correct design of the tool 10, i.e., the rake angle of the tool cutting edge 11 and the cutting force of the tool cutting edges 11 simultaneously involved in cutting, can be easily calculated.

[0021] As described above, the shape of the cutting edge 11 of the tool 10 is very complex. As will be described in detail later, as in Fig. As shown in Figure 8, the boundary between the end surface 11b (clamping surface) of the tool cutting edge 11 and each of the side surfaces 11a and the radially outer surface 11c (clearance surfaces) is divided into a plurality of regions ΔP(i, i+1). Thus, two-dimensional processing can be carried out for each region ΔP(i, i+1).

[0022] This means that for each region ΔP(i, i+1), a rake angle α(i) is calculated using a two-dimensional cutting model, and a cutting force FH(i) is calculated. The calculated cutting force FH(i) is then used to calculate a cutting force FH in all regions. A relative vibration between the tool 10 and the workpiece 20 is calculated using the cutting force FH(i) and the dynamic properties of the tool 10 and the workpiece 20. A detailed description follows. 4. Details of the vibration simulation device 1 and the machining form simulation device 100

[0023] The vibration simulation device 1 and the machining form simulation device 100 are described below. The vibration simulation device 1 and the machining form simulation device 100 are configured by one or more processors and memory devices. As described in Fig. As shown in Figure 1, the vibration simulation device 1 comprises an analysis condition procurement unit 110, a shape definition unit 120, a superposition region calculation unit 130, a cutting force calculation unit 140, a dynamic property calculation unit 150, a vibration calculation unit 160, an output unit 170, and an update unit 180. The machining shape simulation device 100 comprises the vibration simulation device 1 and a machining result prediction unit 190.

[0024] The vibration simulation device 1 and the machining form simulation device 100 are described below with reference to the flowchart of Fig. 2, which shows how the machining form simulation device 100 is used, a description in the sequence (4-1) of a form definition process, (4-2) of a rake angle calculation process, (4-3) of the two-dimensional cutting model, (4-4) of a cutting depth calculation process, (4-5) of a cutting force calculation process, (4-6) of a relative vibration calculation process, (4-7) of an information update and an output of calculation results, and (4-8) of a machining result prediction process. 4-1. Form definition process

[0025] For the shape definition process, the analysis condition procurement unit 110 and the shape definition unit (120) are required according to Fig. 1 described. First, the analysis condition procurement unit 110 procures analysis conditions that are required for simulations in the vibration simulation device 1 and the machining form simulation device 100 (step S1 in Fig. 2) The analysis conditions include tool specifications, which are the specifications of tool 10, workpiece specifications, which are the specifications of workpiece 20, and machining conditions in the (not shown) gear-making cutting device. The analysis conditions may include other information. The analysis condition retrieval unit 110 can retrieve the analysis conditions by a user entering some or all of the analysis conditions, or by retrieving some or all of the analysis conditions pre-stored in a (not shown) memory unit.

[0026] The shape definition unit 120 defines the shapes of the tool 10 and the workpiece 20 based on the analysis conditions procured by the analysis condition procurement unit 110 (step S2 in Fig. 2) According to the present embodiment, the shapes of the tool 10 and the workpiece 20 are defined by point clouds consisting of a plurality of points located on the surfaces of the tool 10 and the workpiece 20. In particular, the tool 10, as shown in Fig. As shown in Figure 8, the boundary between the end surface 11b (clamping surface) of each tool blade 11 and each of the side surfaces 11a of the radially outer surface 11c (free surfaces) is defined as a plurality of definition points P(k). That is, an approximate shape of the boundary of the tool blade 11 is obtained by connecting the definition points P(k) (where k = 1 to n, where n is a natural number) with straight lines. Fig. Figure 8 shows 13 definition points P(1) to P(13), however, the number of definition points P(k) can be freely set. If only the tooth flanks of the gear 21 and not the underside are machined, the multitude of definition points P(k) can only be defined at the boundary between the end surface 11b, which is the rake face, and the side surface 11a, which is the side clearance face, and not at the boundary between the end surface 11b and the radially outer surface 11c, which is the front clearance face.

[0027] The terminology to be used in the following processes with regard to the tool blade 11 is defined with reference to Fig. Section 8 describes the following. A region between two adjacent definition points P(i) and P(i+1) is called an intermediate definition region ΔP(i, i+1). For example, a region between the definition points P(1) and P(2) is ΔP(1, 2). A midpoint between the two adjacent definition points P(i) and P(i+1) is called Pc(i, i+1). For example, a midpoint between the definition points P(1) and P(2) is Pc(1, 2).

[0028] With respect to workpiece 20, a machining target section of 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, as shown in Fig. Figure 16 shows that, since the workpiece 20 has a cylindrical shape, the cylindrical surface, which has a central axis corresponding to the central axis Zw of the workpiece 20, serves as the reference plane. The pins 26 of specified length, which are parallel to a direction normal to the cylindrical reference surface, are aligned at specified intervals on the cylindrical reference surface. The orientation of the pins 26 is set towards the center of the cylindrical reference surface when the inner circumferential surface is machined, and outwards from the center of the cylindrical reference surface when the outer circumferential surface is machined. In this way, the shape of the workpiece 20 is defined. Fig. Figures 16 to 18 show the cylindrical reference surface as a plane for ease of illustration. 4-2. Rake angle calculation process

[0029] Below, a cutting vector calculation unit 131 and a rake angle calculation unit 132 are described for the rake angle calculation process, which are in the superposition region calculation unit 130 according to Fig. The cutting vector calculation unit 131 calculates a cutting vector L(i) for each intermediate definition point region ΔP(i, i+1), which causes the intermediate definition point region ΔP(i, i+1) to move in the cutting direction while the tool 10 rotates from a rotation angle σ1 at a first time to a rotation angle σ2 at a second time. However, the direction in which the entire intermediate definition point region ΔP(i, i+1) moves is not easy to calculate.

[0030] Therefore, as it is in Fig. Figure 9 shows that a vector Lc(i) of the center point Pc(i, i+1) between two adjacent definition points P(i), P(i+1) moving in the cutting direction is calculated as the cutting vector L(i). With the center point Pc(i, i+1), the vector of motion of this point can be easily and reliably calculated.

[0031] The rake angle calculation unit 132 calculates a rake angle α(i) based on the cutting vector L(i). The rake angle α(i) is a rake angle when the workpiece 20 is cut in each intermediate definition point region ΔP(i, i+1). The rake angle calculation unit 132 calculates the rake angle α(i) by a Fig. 3. The process shown.

[0032] The calculation of the rake angle α(i) is described below with reference to Fig. 3 and 9 to 12 are described. First, as is described in Fig. As shown in Figure 3, the cutting vector L(i) is calculated by the cutting vector calculation unit 131, as described above (reference symbol S31 in Figure 3). Fig. 3), and then an intermediate definition point vector B(i) is calculated (S32 in Fig. 3) The intermediate definition point vector B(i) is a vector that connects two adjacent definition points P(i), P(i+1), as described in Fig. Figure 9 shows the center point Pc(i, i+1) at the middle position on the intermediate definition point vector B(i).

[0033] Next, a plane G(i) having the cutting vector L(i), calculated by the cutting vector calculation unit 131 and orthogonal to the intermediate definition point vector B(i), is calculated on the basis of the cutting vector L(i) and the intermediate definition point vector B(i) (reference symbol S33 in Fig. 3) The plane G(i) is in Fig. 9 shown.

[0034] To define the plane G(i), a plane definition normal vector C(i) is used. This means that the plane definition normal vector C(i) is a vector that passes through the center point Pc(i, i+1) and is orthogonal to the intersection vector L(i) and the intermediate definition point vector B(i). Therefore, the plane G(i) can be defined as a plane that passes through the center point Pc(i, i+1) and has the intersection vector L(i) as well as the plane definition normal vector C(i).

[0035] The purpose of calculating the plane G(i) is to use the two-dimensional cutting model based on a two-dimensional cutting theory, as described above. That is, a cutting force FH(i) on the plane G(i) is calculated by applying the two-dimensional cutting model to the plane G(i).

[0036] Next, a normal vector N(i) (hereinafter referred to as the "cutting surface normal vector") of the tool cutting edge 11 at the center point Pc(i, i +1) is calculated (reference symbol S34 in Fig. 3) The normal vector of the cutting surface N(i) cannot be obtained by simply taking the two adjacent points of definition P(i), P(i + 1). Therefore, as described in Fig. Figure 10 shows that three or more adjacent definition points P(k) are used, including the definition points P(i) and P(i+1). In this case, three definition points P(i-1), P(i), and P(i+1) are used.

[0037] As it is in Fig. As shown in Figure 10, a plane Q(i) passing through the three definition points P(i-1), P(i), and P(i+1) is determined. On the plane Q(i), a vector passing through the midpoint Pc(i, i+1) and orthogonal to the intermediate definition point vector B(i) is defined as the normal vector of the intersection surface N(i).

[0038] After the plane G(i) and the cutting surface normal vector N(i) have been calculated, a projected normal vector Ng(i), which is a projection of the cutting surface normal vector N(i) onto the plane G(i), is calculated (reference symbol S35 in Fig. 3).

[0039] As it is in Fig. As shown in Figure 11, the plane G(i) and the plane Q(i) are not necessarily the same plane. Therefore, the normal vector of the intersection surface N(i) lies on the plane Q(i), but not necessarily on the plane G(i). Therefore, as described above, the normal vector of the intersection surface N(i) is projected onto the plane G(i) to obtain the projected normal vector Ng(i) on the plane G(i).

[0040] Then a projected rake angle αg(i), which is an angle between the projected normal vector Ng(i) and the cutting vector L(i) on the plane G(i), is calculated (reference symbol S36 in Fig. 3) The projected rake angle ag(i) is in Fig. Figure 12 shows that the projected rake angle ag(i) is calculated on the plane G(i) and therefore differs from the actual rake angle α(i).

[0041] For the use of the two-dimensional cutting model on the plane G(i), the projected rake angle ag(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)).

[0042] As it is in Fig. As shown in Figure 13, a (single) feed of a (single) cutting edge 11 in a (single) tooth space 22 in the tooth space direction (arrow direction) removes, for example, a section 23, indicated by cross-hatching in the figure, as an overlap region. This means that the cutting edge 11 rotates as the feed advances. If the tool rotation angle σ is σs, the cutting edge 11 is at a cutting start position (a position indicated in the figure by the long dashed line interrupted by two short dashes). If the tool rotation angle σ is σa, σb, or σc, the cutting edge 11 is at a section where the removed section (the overlap region) 23 overlaps the long dashed line interrupted by a short dash in the figure.When the tool rotation angle σ σe, the tool cutting edge 11 is at a cutting end position (a position indicated in the figure by a long dashed line interrupted by two short dashes).

[0043] The rake angle ag(i) is determined in the region from the start of cutting by a tool cutting edge 11 in a tooth space 22 to the end of the cutting. For example, as shown in Fig. Figure 14 shows the rake angle ag(i) in relation to the tool rotation angle σ for each of the left cutting surfaces of the tool cutting edge 11 (dashed line in the figure, definition points P(1) to P(4) in Fig. 8), the cutting edge of the tool cutting edge 11 (solid lines in the figure, definition points P(5) to P(9) in Fig. 8) and the right cutting surface of the tool cutting edge 11 (long dashed lines interrupted by a short line in the figure, definition points P(10) to P(13) in Fig. 8) in the area from the start of cutting (tool rotation angle σs) to the end of cutting (tool rotation angle σe).

[0044] Each line segment specifying the rake angle ag(i) is a set of values ​​at the midpoint P(i, i + 1) of the cutting edge 11. When the tool rotation angle σ 0, the cutting edge 11 reaches the center of the tooth space 22 in the tooth space direction (the same applies to the following figures). At a location where the specified rake angle ag(i) is negative, the cutting depth and cutting force increase locally. Therefore, the specifications of the cutting edge 11 are modified such that the rake angle ag(i) is not negative. 4-3. Two-dimensional cutting model

[0045] Below is the two-dimensional cutting model based on two-dimensional cutting theory with reference to Fig. 15 described. Fig. Figure 15 shows the cutting model on the plane G(i) described above. Fig. 15 the workpiece 20 is cut by the cutting edge 11 of the tool 10.

[0046] On the plane G(i), the rake face of the cutting edge 11 is the end face 11b, the side clearance face is the side face 11a, and the front clearance face is the radially outer face 11c. The rake angle is αg(i). The depth of cut is d1(i), and the shear angle is φ(i). The cutting vector of the cutting edge 11 is L(i), and the normal vector of the cutting edge 11 is Ng(i). The cutting vector L(i) corresponds to a principal force Fc(i) in the two-dimensional cutting model, and a shear force Ft(i) is defined in Fig. 15 shown. The main force Fc(i) and the shear force Ft(i) at this section are given by equation (2). [Equation 2] {Fc(i)=τsAcos(β−αg(i))sinϕ(i) cos(ϕ(i)+β−αg(i))Ft(i)=τsAsin(β−αg(i))sinϕ(i) cos(ϕ(i)+β−αg(i)) τs: Shear stress A: Cutting cross-sectional area αg(i): rake angle β: Angle of friction of the rake faces φ(i): Shear angle

[0047] In equation (2), τs is the shear stress and is obtained beforehand based on a target material, etc. The cutting cross-sectional area A can be expressed as the product of B(i), which is the distance between two adjacent definition points P(i) and P(i+1), and the cutting depth d1(i) in the intermediate definition point region ΔP(i, i+1). The cutting depth d1(i) is the average of a cutting depth (corresponding to a radial depth) at definition point P(i) and a cutting depth at definition point P(i+1). φ(i) is the shear angle and can be obtained from known engineering information. αg(i) is the projected rake angle, which has been described above. β is the rake face friction angle and is determined empirically. As described above, it can be understood that the two-dimensional cutting model can be applied by calculating the rake angle ag(i) on the plane G(i).The present invention can be applied to a case in which a three-dimensional cutting model is used instead of the two-dimensional cutting model in the same way as in the case of the two-dimensional model. 4-4. Cutting depth calculation process

[0048] In the two-dimensional cutting model described above, the cutting force FH(i) can be obtained if the cutting depth d1(i) can be determined. If the immediately preceding shape of workpiece 20 and the shape of workpiece 20 in the current cutting process are known, the cutting depth d1(i) can be obtained from the difference between the two. A detailed description follows below with reference to Fig. 17 to 19.

[0049] For the cutting depth calculation process, a crossing point calculation unit 133, a removal length calculation unit 134 and a final machining position extraction unit 135 are used in Fig. 1. will be described.

[0050] In the intersection point calculation unit 133, it is assumed that the tool cutting edge 11 moves relative to the workpiece 20, using the shape of the workpiece 20 defined by the shape definition unit 120, when the tool rotation angle σ increases slightly from σ1 to σ2, and an infinitesimal line segment motion path of the tool cutting edge 11 of the tool 10 is used, as described in Fig. Figure 17 shows that, according to the present embodiment, the infinitesimal line segment motion path of a boundary 11s between the end face 11b, which is the rake face, and each of the side faces 11a and the radially outer face 11c, which are the clearance faces, from a position 11s1 at the first time when the tool rotation angle σ is σ1, to a position 11s2 at the second time when the tool rotation angle σ increases slightly to σ2, is defined by a path plane 11p using triangular patches. A crossing point (intersection point) between each pin 26, which represents the workpiece 20, and the path plane 11p of the cutting tool 11 is calculated by relative movement of the cutting tool 11.

[0051] When the intersection point calculation unit 133 finds an intersection point, the removal length calculation unit 134 changes the length of each pin 26 representing the workpiece 20, as shown in Fig. Figure 18 shows that a portion of the workpiece 20 is cut by the tool cutting edge 11 when the tool rotation angle σ increases slightly from σ1 to σ2, and the shape is stored after cutting. The removal length calculation unit 134 stores the removal length of each pin 26. The removal length of the pin 26 corresponds to a cutting depth when the tool rotation angle σ increases slightly from σ1 to σ2 (when the first time has elapsed until the second time), and the overlap region between the tool 10 and the workpiece 20 is calculated (S3 in Figure 18). Fig. 2).

[0052] The final machining position extraction unit 135 extracts the final machining positions of the definition points P(k), which represent the tool cutting edge 11, while the tool rotation angle σ increases slightly from σ1 to σ2. Fig. Figure 19 shows the points to which the definition points P(k) move while the rotation angle σ increases slightly from σ1 to σ2. The open circles indicate the final machining positions of the definition points P(k), and the black circles indicate positions other than the final machining positions of the definition points P(k).

[0053] This means that the final machining positions of the definition points P(k) correspond to the positions of the definition points P(k) at the tool rotation angle σ2. If these positions are known, the cutting depth at each definition point P(k) can be calculated based on the final machining position and the immediately preceding shape of the workpiece 20. This means that the change in the shape of the workpiece 20 can be detected while the tool rotation angle σ increases slightly from σ1 to σ2.

[0054] The cutting depth d1(i) in the two-dimensional cutting model corresponds to the average of the cutting depth (which corresponds to the radial depth) at the definition point P(i) and the cutting depth at the definition point P(i+1). This means that the cutting depth at each definition point P(k) can be obtained, and therefore the cutting depth d1(i) at the midpoint Pc (i, i+1) can be calculated.

[0055] In this way, the final machining position extraction unit 135 calculates the final machining positions of the definition points P(k), calculates the cutting depth at each definition point P(k), and further calculates the cutting depth d1(i) at the midpoint Pc(i, i + 1). The intersection point calculation unit 133 calculates the intersection point between each pin 26, representing the workpiece 20, and the path plane 11p of the tool cutting edge 11 in the area from the start of cutting a (single) tooth space 22 with a (single) tool cutting edge 11 to the end of the cutting. Each time the cutting of a tooth space 22 with a tool cutting edge 11 is repeatedly performed from start to end, the shape of the workpiece 20 is updated, and the intersection point between each pin 26, representing the workpiece 20, and the path plane 11p of the tool cutting edge 11 is calculated. 4-5. Cutting force calculation process

[0056] The following describes a process for calculating the cutting force FH(i) in each region ΔP(i, i +1) using the two-dimensional cutting model. For this process, the cutting force calculation unit 140 is used according to... Fig. 1 described.

[0057] The cutting force calculation unit 140 according to Fig. 1 calculates the cutting force FH(i) in each region ΔP (i, i +1) using the in Fig. 15 two-dimensional cutting model shown (S4 in Fig. 2) The cutting force FH(i) can be calculated by dividing the principal force Fc(i) and the shear force Ft(i) in the equation (2) described above into Xw-direction components, Yw-direction components and Zw-direction components in the directions of the three orthogonal axes of the workpiece 20 and by adding the components in each direction.

[0058] This means that the principal force Fc(i) and the thrust force Ft(i) are subdivided into the Xw directional components, the Yw directional components and the Zw directional components, as described below. [Equation 3] {Fc(i)=(Fcx(i), Fcy(i), Fcz(i))Ft(i)=(Ftx(i), Fty(i), Ftz(i))

[0059] A unit vector is defined as in equation (4). [Equation 4] v(i)→=(vx(i), vy(i), vz(i))(vx(i)2+vy(i)2+vz(i)2=1)

[0060] Components Fcx(i), Fcy(i), Fcz(i) of the main force Fc(i) and components Ftx(i), Fty(i), Ftz(i) of the shear force Ft(i) are given by the following equation (5). [Equation 5] {Fcx(i)=Fc(i)⋅vx(i)Fcy(i)=Fc(i)⋅vy(i)Fcz(i)=Fc(i)⋅vz(i)Ftx(i)=Ft(i)⋅vx(i)Fty(i)=Ft(i)⋅vy(i)Ftz(i)=Ft(i)⋅vz(i)

[0061] Components FHx(i), FHy(i), FHz(i) of the cutting force FH(i) are given by an equation (6) using the components of the main force Fc(i) and the shear force Ft(i). [Equation 6] {FHx(i)=Fc(i)⋅vx(i)+Ft(i)⋅vx(i)FHy(i)=Fc(i)⋅vy(i)+Ft(i)⋅vy(i)FHz(i)=Fc(i)⋅vz(i)+Ft(i)⋅vz(i)

[0062] Since the cutting force FH in all regions is the sum of the cutting forces FH(i) in the regions ΔP(i, i +1), the components FHx, FHy, FHz of the cutting force FH are given by equation (7). [Equation 7] {FHx(i)=∑(Fc(i)⋅vx(i)+Ft(i)⋅vx(i))FHy(i)=∑(Fc(i)⋅vy(i)+Ft(i)⋅vy(i))FHz(i)=∑(Fc(i)⋅vz(i)+Ft(i)⋅vz(i))

[0063] The cutting force FH in all regions can be calculated based on equation (7). For example, the calculation results of the components of the cutting force FH in Fig. 20 are shown, and are close to the actual measured values, thus confirming that these are highly accurate calculation results. 4-6. Relative vibration calculation process

[0064] The following describes a procedure for calculating the relative vibration between tool 10 and workpiece 20. The dynamic property calculation unit 150, the vibration calculation unit 160, and the output unit 170 are used for the calculation of the relative vibration according to... Fig. 1 described.

[0065] First, the dynamic property calculation unit 150 calculates relative dynamic properties or individual dynamic properties between the tool 10 and the workpiece 20. According to the present embodiment, the calculation is performed based on information obtained by the analysis condition acquisition unit 110. For example, the dynamic properties can be calculated based on information obtained by the analysis condition acquisition unit 110 through a hammering test, etc. The relative dynamic properties can be calculated based on the tool 10 and the workpiece 20, which are calculated individually. If the dynamic properties of the workpiece 20 can be ignored, the dynamic properties of the tool 10 can be used as the relative dynamic properties.

[0066] The vibration calculation unit 160 comprises a transfer function processing unit 161 and a recovery action calculation unit 162. The transfer function processing unit 161 calculates a relative vibration between the tool 10 and the workpiece 20 based on a transfer function using the relative dynamic properties calculated by the dynamic property calculation unit 150 and the cutting force FH (S5 in Fig. 2) According to the present embodiment, the transfer function processing unit 161 outputs an offset, a velocity, and an acceleration.

[0067] The recovery action calculation unit 162 determines a recovery action that increases non-linearly relative to an increase in the amplitude of the relative vibration calculated by the transfer function processing unit 161. According to the present embodiment, the transfer function to be used in the transfer function processing unit 161, or the cutting force FH to be input into the transfer function processing unit 161, is corrected based on the offset, velocity, and / or acceleration output by the transfer function processing unit 161. The recovery action calculation unit 162 is designed, for example, to reflect the effect of vibration suppression by process damping when the workpiece 20 is cut with the tool 10.

[0068] As it is in Fig. As shown in Figure 21, if no correction is made by the recovery action calculation unit 162, the offset resulting from the calculation by the vibration calculation unit 160 will diverge over time, but this divergence will be suppressed by correcting the transfer function or the cutting force FH by the recovery action calculation unit 162. 4-7. Information update and output of calculation results

[0069] The following describes an information update by update unit 180 and an output by output unit 170. First, the calculation results of the transfer function processing unit 161 are output to update unit 180 and then output from output unit 170. Update unit 180 updates the relative positions of tool 10 and workpiece 20 and the workpiece shape based on the superposition region calculated by superposition region calculation unit 130 and the relative vibration calculated by vibration calculation unit 160 (S6 in Fig. 2) This means that the positions of tool 10 and workpiece 20 are updated to reflect their relative positions, and the shape in which the overlay region is removed is set as the updated workpiece shape. Based on the updated information, the overlay region calculation unit 130 repeatedly calculates the overlay region, the cutting force calculation unit 140 repeatedly calculates the cutting force, and the vibration calculation unit 160 repeatedly calculates the relative vibration until the machining of workpiece 20 is complete (No in S7 in Fig. 2).

[0070] When the processing is complete (Yes in S7 in Fig. 2), output unit 170 outputs the calculation results of vibration calculation unit 160 (S8 in Fig. 2) Each time the update unit 180 performs an update, the output unit 170 outputs the calculation results based on the updated information. The results output by the output unit 170 are, for example, in Fig. 21(a) shown, and the vibration amplitude with transfer function correction is relatively close to the actually measured value, confirming that the calculation can be performed with high accuracy. 4-8. Processing result prediction

[0071] Below is a machining result prediction by the machining form simulation device 100, which is in Fig. As shown in Figure 1, the machining form simulation device 100 describes the shape of the workpiece 20 being machined, as predicted by the machining result prediction unit 190 based on the update result of the update unit 180. Specifically, the workpiece shape that is updated based on the superimposed region updated by the update unit 180 is predicted as the shape of the workpiece 20 being machined.

[0072] The machining form simulation device 100 predicted machining results under normal conditions, in which no chatter vibration occurred during machining, and under abnormal conditions, in which vibration occurred during machining. Under normal conditions, it predicted that the tooth flank shape would exhibit small irregularities, as seen in Fig. 22(a). Under the abnormal conditions, it was predicted that the tooth flank shape would exhibit large irregularities, as shown in Fig. Figure 22(b) shows that the occurrence of a chatter vibration during processing is reflected in the prediction results, thus confirming that a highly accurate prediction can be made.

[0073] As it is in Fig. As shown in Figure 23(a), under normal conditions both the tooth flank line shape variation (difference between maximum and minimum) and the tooth profile variation (difference between maximum and minimum) are relatively small. As shown in Figure 23(a), Fig. As shown in Figure 23(b), under abnormal conditions the tooth flank line shape variation and the tooth profile variation are greater than those under normal conditions. In a comparative example where the shear force was not considered in the calculation of the cutting force, the prediction results were equivalent under normal and abnormal conditions, as shown in Figure 23(b). Fig. 24(a) and Fig. 24(b) is shown.

[0074] When the prediction results according to the exemplary implementation and according to the comparative example were compared, it shows how it works in Fig. As shown in Figure 25, the tooth flank line shape variation showed a difference between the normal and abnormal conditions in the prediction results according to the embodiment, but did not show a difference between the normal and abnormal conditions in the prediction results of the comparison example. As shown in Fig.As shown in Figure 26, the tooth profile variation also showed the same results as the tooth flank line shape variation. Based on the above, it was found that the prediction results according to the exemplary embodiment show a higher prediction accuracy than according to the comparison example. 5. Functions and effects

[0075] The vibration simulation device 1, according to the present embodiment, first calculates the superposition region between the tool 10 and the workpiece 20 during gear manufacturing cutting, based on the tool and workpiece shapes defined by the analysis conditions, and the relative path of motion between the tool 10 and the workpiece 20. It then calculates the cutting force required to remove the superposition region. The vibration simulation device 1 then calculates the relative dynamic properties, or the individual dynamic properties, between the tool 10 and the workpiece 20 based on the analysis conditions and calculates the relative vibration between the tool 10 and the workpiece 20 based on the cutting force and the dynamic properties. Thus, it is possible to predict vibrations at the machining point during gear manufacturing cutting with high accuracy.

[0076] As described above, according to the present embodiment it is possible to provide a vibration simulation device 1 which can predict vibrations at the machining point during gear manufacturing cutting with high accuracy.

[0077] According to the present embodiment, the update unit 180 is provided, which updates the relative positions of the tool 10 and the workpiece 20 and the workpiece shape based on the superposition region calculated by the superposition region calculation unit 130 and the relative vibration calculated by the vibration calculation unit 160. According to the present embodiment, the output unit 170 is provided, which outputs the relative vibration, which is repeatedly calculated by the superposition region calculation unit 130, the cutting force calculation unit 140, and the vibration calculation unit 160 based on the update results obtained by the update unit 180. Thus, the relative vibration can be predicted and output with high accuracy.

[0078] According to the present embodiment, the cutting force calculation unit 140 calculates at least the main force Fc and the thrust force Ft based on the cutting theory in the gear manufacturing cutting process and calculates the cutting force FH based on the main force Fc and the thrust force Ft. Therefore, the cutting force FH is calculated based on the thrust force Ft in addition to the main force Fc. Thus, the calculation accuracy of the cutting force FH can be improved, and the relative vibration can be predicted with high accuracy.

[0079] According to the present embodiment, the shape definition unit 120 defines the boundary between the rake face 11b and the clearance face 11a, 11c of the tool 10 in the shape of the tool 10 as a point cloud consisting of a plurality of points, and defines the machining target section in the shape of the workpiece 20 by a cylindrical reference surface having a central axis corresponding to the central axis Zw of the workpiece 20, and the plurality of pins 26 of specified length erected in the normal direction on the cylindrical reference surface. The orientation of the pin 26 is set towards the center of the cylindrical reference surface when the inner circumferential surface of the workpiece 20 is machined, and is set outwards from the center of the cylindrical reference surface when the outer circumferential surface of the workpiece 20 is machined.The overlay region calculation unit 130 calculates the intersection point between each of the pins 26 and the infinitesimal line segment path, which is a path of an infinitesimal line segment connecting the two adjacent definition points P, P1 in the point cloud from a position at a predetermined first time to a position at a second time, and as the overlay region calculates a region in which each of the pins 26 is located within the tool 10 from the intersection point.When calculating the cutting force FH, the cutting force calculation unit 140 calculates the principal force Fc(i) and / or the shear force Ft(i) based on a cutting theory. As the infinitesimal line segment moves from the position at the first time to the position at the second time, the principal force Fc(i) and the shear force Ft(i) are divided into components in the directions of three orthogonal axes. The principal force Fc(i) and the shear force Ft(i) are added for each type of component, and then the components in the directions of the three orthogonal axes are added together in all regions for each type of component. This improves the calculation accuracy of the cutting force.

[0080] According to the present embodiment, the vibration calculation unit 160 comprises the transfer function processing unit 161, which calculates the relative vibration using the transfer function based on the cutting force and the relative dynamic properties, and the recovery action calculation unit 162, which determines the recovery action, which increases non-linearly with an increase in the amplitude of the relative vibration. Therefore, the transfer function or the cutting force FH is corrected, thereby suppressing the divergence of the calculated relative vibration. Thus, the relative vibration can be calculated with high accuracy.

[0081] According to the present embodiment, the machining form simulation device 100 comprises the vibration simulation device 1 and the machining result prediction unit 190, which predicts the machining result of the workpiece 20 based on the output result from the vibration simulation device 1. This output result is based on relative vibrations repeatedly calculated by the superposition region calculation unit 130, the cutting force calculation unit 140, and the vibration calculation unit 160. Therefore, when predicting the machining result of the workpiece 20, the output result from the vibration simulation device 1 is reflected. Thus, the prediction accuracy can be improved.

[0082] According to the present embodiment, the cutting force is calculated based on the principal force Fc and the shear force Ft using a two-dimensional cutting model based on two-dimensional cutting theory. When calculating the cutting force in three dimensions, a three-dimensional cutting model based on three-dimensional cutting theory can be improved to include the feed force in addition to the principal force Fc and the shear force Ft.

[0083] The present disclosure is not limited to the embodiment described above and can be applied to various embodiments without deviating from the idea of ​​the present disclosure. QUOTES INCLUDED IN THE DESCRIPTION

[0000] This list of documents cited by the applicant was automatically generated and is included solely for the reader's convenience. The list is not part of the German patent or utility model application. The DPMA accepts no liability for any errors or omissions. Cited patent literature

[0000] JP 2012-45687

[0003] JP 2012 - 45 687 A

[0003] JP 2014-237185

[0003] JP 2014 - 237 185 A

[0003]

Claims

[1] Vibration simulation device for vibration between a tool and a workpiece during gear-making cutting, in which a gear is produced by cutting the workpiece with the tool, wherein the vibration simulation device comprises: a shape definition unit that is configured to define a tool shape and a workpiece shape based on analysis conditions that include tool specifications, workpiece specifications, and machining conditions. an overlap region calculation unit that is configured to calculate an overlap region between the tool and the workpiece during gear manufacturing cutting based on the tool shape, the workpiece shape, and a relative path of motion between the tool and the workpiece. a cutting force calculation unit that is configured to calculate a cutting force of the tool for removing the overburden region from the workpiece, a dynamic property calculation unit configured to calculate relative dynamic properties or individual dynamic properties between the tool and the workpiece based on the analysis conditions, and A vibration calculation unit configured to calculate a relative vibration between the tool and the workpiece based on the cutting force and the relative dynamic properties. [2] Vibration simulation device according to claim 1, further comprising: an update unit configured to update the relative positions of the tool and workpiece and the workpiece shape based on the superposition region calculated by the superposition region calculation unit and the relative vibration calculated by the vibration calculation unit, and an output unit that is configured to output the relative vibration based on the update results obtained by the update unit, which is repeatedly calculated by the superposition region calculation unit, the cutting force calculation unit, and the vibration calculation unit. [3] Vibration simulation device according to claim 1 or 2, wherein the cutting force calculation unit is configured to calculate a principal force and a thrust force based on a cutting theory in the gear generating cutting edges, and to calculate the cutting force based on the principal force and the thrust force. [4] Vibration simulation device according to claim 1 or 2, wherein: The shape definition unit is configured to define a boundary between a rake face and a clearance face of the tool in a shape of the tool as a point cloud of a plurality of points, and to define a machining target position in a shape of the workpiece by means of a cylindrical reference surface having a central axis corresponding to a central axis of the workpiece and a plurality of pins of a specified length erected in a normal direction on the cylindrical reference surface. The overlay region calculation unit is configured to calculate an intersection point between each of the pins and an infinitesimal line segment path, which is a path of an infinitesimal line segment connecting two adjacent definition points in the point cloud from a position at a predetermined first time to a position at a second time, and as the overlay region to calculate a region in which each of the pins is located within the tool from the intersection point, and The cutting force calculation unit is configured to calculate the cutting force as a principal force and / or a shear force based on a cutting theory when the infinitesimal line segment moves from the position at the first time to the position at the second time, to divide the principal force and the shear force into components in directions of three orthogonal axes, to add the principal force and the shear force for each type of component, and then to add the components in the directions of the three orthogonal axes in all regions for each type of component. [5] Vibration simulation device according to claim 1 or 2, wherein the vibration calculation unit comprises a transfer function processing unit configured to calculate the relative vibration using a transfer function based on the cutting force and the relative dynamic properties, and a recovery action calculation unit configured to determine a recovery action that increases non-linearly relative to an increase in the amplitude of the relative vibration. [6] Machining shape simulation device for a gear manufacturing cutting process, wherein the machining shape simulation device comprises: a vibration simulation device according to claim 1 or 2, and a processing result prediction unit configured to predict a machining result of the workpiece based on a vibration simulation result that exhibits the relative vibration repeatedly calculated by the superposition region calculation unit, the cutting force calculation unit, and the vibration calculation unit.

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