Calculation method of specific cutting force, creation method of stability limit diagram, device that calculates specific cutting force, and device that creates stable limit diagram

Abstract

To provide a specific cutting force in which an actual characteristic in processing is reflected more.SOLUTION: In a calculation method of a specific cutting force, a specific cutting force of a tool is calculated on the basis of a weighted sum of a first specific cutting force and a second specific cutting force. The first specific cutting force is obtained from a first cutting force received by a first portion that contacts a workpiece in the tool used in the cutting processing, the first portion having a first rake angle. The second specific cutting force is obtained from a second cutting force received by a second portion that contacts the workpiece in the tool used in the cutting processing, the second portion not having the first rake angle.SELECTED DRAWING: Figure 2

Description

[Technical field]

[0001] The present disclosure relates to a method for calculating a specific cutting resistance, a method for creating a stability limit diagram, an apparatus for calculating a specific cutting resistance, and an apparatus for creating a stability limit diagram. [Background technology]

[0002] Conventionally, there exists a technique for determining the occurrence of chatter vibration when a rotating tool is used to perform cutting processing with a machine tool, using a stability limit diagram (see Patent Documents 1 and 2). In creating the stability limit diagram in Patent Document 1, the mass coefficient, damping coefficient, and rigidity included in the transfer function expressing the vibration characteristics of the spindle system of the machine tool including the tool, as well as the specific cutting resistance of the tool are used. In determining the transfer function of the spindle system, a vibration detector is attached to the tool, and an impact is applied with a hammer to the tool attached to the spindle system of the machine tool, and the residual vibration of the tool is measured. Then, the transfer function that best reproduces the residual vibration is identified. Meanwhile, the value published by the tool manufacturer for each tool is used as the specific cutting resistance. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] JP 2013-43240 A [Patent Document 2] JP 2007-222981 A [Patent Document 3] JP 2018-158432 A Summary of the Invention [Problem to be solved by the invention]

[0004] However, the actual specific cutting resistance of a tool varies depending on the machining conditions. For this reason, if the values ​​of the specific cutting resistance announced by each tool manufacturer are used as is, it may not be possible to create a stability limit diagram that accurately reflects the characteristics of the actual spindle system when machining. If the stability limit diagram does not accurately reflect the characteristics of the actual spindle system, chatter vibration may occur in cutting even if the rotation speed and the cutting depth are set using the stability limit diagram. This problem is not limited to the creation of a stability limit diagram, but also exists when various studies on cutting are performed using the specific cutting resistance of a tool. [Means for solving the problem]

[0005] The present disclosure can be realized in the following forms.

[0006] (1) According to one embodiment of the present disclosure, there is provided a method for calculating a specific cutting resistance of a tool used in cutting processing, in which the specific cutting resistance of the tool is calculated based on a weighted sum of a first specific cutting resistance obtained from a first cutting resistance received by a first portion of the tool used in the cutting processing that comes into contact with a workpiece and has a first rake angle, and a second specific cutting resistance obtained from a second cutting resistance received by a second portion of the tool used in the cutting processing that comes into contact with the workpiece and does not have the first rake angle. In this embodiment, the specific cutting resistance of a tool is calculated by considering not only the first cutting resistance received by the first portion of the tool that is in contact with the workpiece and has the first rake angle, but also the second cutting resistance received by the second portion of the tool that is in contact with the workpiece and does not have the first rake angle. Therefore, it is possible to calculate a specific cutting resistance that better reflects the characteristics of the tool in actual machining, compared to the value of the specific cutting resistance announced by the manufacturer. In addition, by adjusting the weights in the weighted sum in accordance with the actual machining state, it is possible to calculate a specific cutting resistance that better reflects the characteristics of the tool in the actual machining. (2) In the method for calculating the specific cutting resistance of the above embodiment, in calculating the weighted sum, a weight assigned to the first specific cutting resistance is 1, and a weight assigned to the second specific cutting resistance is a value obtained by dividing a cutting cross-sectional area of ​​the second portion in the cutting process by a sum of a cutting cross-sectional area of ​​the first portion and a cutting cross-sectional area of ​​the second portion in the cutting process. In this manner, it is possible to calculate a specific cutting resistance that is suitable for actual cutting in many cases. (3) In the method for calculating the specific cutting resistance of the above embodiment, a value prepared in advance for each material of the workpiece may be used as the first specific cutting resistance and the second specific cutting resistance. By adopting such an embodiment, it is possible to calculate a specific cutting resistance that reflects the characteristics of the material of the workpiece in actual machining. (4) In the method for calculating the specific cutting resistance of the above embodiment, the first specific cutting resistance and the second specific cutting resistance may be calculated by two-dimensional cutting theory or plasticity analysis prior to calculating the specific cutting resistance of the tool. By adopting such an embodiment, it is possible to calculate a specific cutting resistance that better reflects the characteristics of the tool and workpiece in actual machining. (5) According to another aspect of the present disclosure, there is provided a method for creating a stability limit diagram in cutting processing, in which the stability limit diagram in the cutting processing is created using the specific cutting resistance calculated by the method of the above aspect. In this manner, a stability limit diagram can be created that sufficiently accurately reflects the characteristics of the actual tool when performing cutting. (6) According to another aspect of the present disclosure, there is provided an apparatus that calculates a specific cutting resistance of a tool based on a weighted sum of a first specific cutting resistance obtained from a first cutting resistance experienced by a first portion of a tool used for cutting processing that comes into contact with a workpiece and has a first rake angle, and a second specific cutting resistance obtained from a second cutting resistance experienced by a second portion of the tool used for the cutting processing that comes into contact with the workpiece and does not have the first rake angle. (7) In the device of the above aspect, the specific cutting resistance may be used to create a stability limit diagram for the cutting process. The present disclosure can be realized in various forms other than the specific cutting resistance calculation method, the stability limit diagram creation method, and the device for implementing those methods, for example, the control method for the device, a computer program for implementing that control method, a non-transitory recording medium on which that computer program is recorded, etc. [Brief description of the drawings]

[0007] [Figure 1] FIG. 1 is a block diagram showing a system 1 for creating a stability limit diagram. [Diagram 2] 4 is a flowchart showing a process performed when the system 1 creates a stability limit diagram. [Diagram 3] FIG. 2 is an explanatory diagram showing the relationship between a tool 100 and a workpiece WP in cutting processing. [Figure 4] 1 is an enlarged view showing a portion removed from a workpiece WP by a tool 100 during cutting. [Diagram 5] FIG. 2 is an explanatory diagram illustrating a schematic relationship between a tool 100 and a workpiece WP in cutting processing. [Figure 6] 6 is an explanatory diagram showing a concept of dividing the cutting shown in FIG. 5 into cutting by a first portion 110 of the tool 100 and cutting by a second portion 120 of the tool 100. FIG. [Figure 7] 10 is an explanatory diagram showing the relationship between a cutting cross-sectional area Acc1 of a first portion 110 and a cutting cross-sectional area Acc2 of a second portion 120. FIG. [Figure 8] 1 is a graph showing a compliance curve Cc1 indicating the response characteristics of a main shaft system. [Figure 9] 1 is a diagram showing a stability limit diagram in cutting processing using the tool 100. FIG. [Figure 10] 1 is a graph showing the value of the specific cutting resistance k0s of the tool 100. [Figure 11] FIG. 13 is a diagram showing an analysis of machining of a workpiece WP2 by a second tool 102 using the finite element method. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0008] A. First embodiment: A1. System Hardware Configuration: FIG. 1 is a block diagram showing a system 1 that creates a stability limit diagram. The system 1 can perform cutting processing on a workpiece WP. The system 1 can calculate a specific cutting resistance of a tool in cutting processing of the workpiece WP. Furthermore, the system 1 can create a stability limit diagram in cutting processing of the workpiece WP. The system 1 includes a tool 100, a cutting device 200, and an NC (Numerically Control) control device 900.

[0009] The tool 100 is replaceably attached to a cutting device 200 (see the middle left part of FIG. 1). The tool 100 is rotated by the cutting device 200 to cut a workpiece WP.

[0010] The cutting device 200 is numerically controlled by an NC control device 900, and performs cutting processing on a workpiece WP with a tool 100 (see the left part of FIG. 1). The cutting device 200 includes a holding unit 210, a cutting unit 220, and a bed 280.

[0011] The holder 210 is provided on a bed 280. The holder 210 can hold a workpiece WP. The holder 210 can move the workpiece WP in the X-axis direction on the bed 280. In FIG. 1, an X-axis, a Y-axis, and a Z-axis that are perpendicular to each other are shown. The X-axis, the Y-axis, and the Z-axis shown in other figures respectively correspond to the X-axis, the Y-axis, and the Z-axis shown in FIG. 1.

[0012] The cutting unit 220 is provided on a bed 280. The tool 100 is replaceably attached to the cutting unit 220, and the cutting unit 220 can rotate the tool 100. The cutting unit 220 can move the tool 100 in the Y-axis direction and the Z-axis direction on the bed 280. The cutting unit 220 includes a column 224 and a main shaft unit 225.

[0013] Column 224 is provided on bed 280. Column 224 can move in the Z-axis direction on bed 280. The movement of column 224 is indicated by arrow Az in FIG. 1. Column 224 supports main shaft portion 225. Column 224 can move main shaft portion 225 in the Y-axis direction. The movement of main shaft portion 225 is indicated by arrow Ay in FIG. 1.

[0014] The main shaft portion 225 is provided on the column 224. The tool 100 is replaceably attached to the main shaft portion 225, and the main shaft portion 225 can rotate the tool 100. The main shaft portion 225 includes a spindle 225s and a drive motor 225m. The tool 100 is replaceably attached to the spindle 225s. The spindle 225s is rotated by the rotation output of the drive motor 225m. As a result, the tool 100 is rotated by the rotation output of the drive motor 225m.

[0015] The cutting device 200 performs cutting processing to cut the workpiece WP into any shape by moving the tool 100 in the Y-axis and Z-axis directions using the cutting unit 220 and moving the workpiece WP in the X-axis direction using the holding unit 210.

[0016] The NC control device 900 numerically controls the cutting device 200 (see the upper right part of FIG. 1). The NC control device 900 is a computer equipped with a display 970 functioning as an output device and a keyboard 980 functioning as an input device. The NC control device 900 further includes a CPU 910 which is a processor, a RAM 950, and a ROM 960.

[0017] The RAM 950 includes a main memory which is a semiconductor memory and a hard disk which is an auxiliary storage device. The ROM 960 stores a database 962 and computer programs. The CPU 910 loads the computer programs stored in the ROM 960 into the main memory and executes them to realize various functions such as numerical control of the cutting of the workpiece WP, calculation of the specific cutting resistance of the tool in the cutting of the workpiece WP, and creation of a stability limit diagram in the cutting of the workpiece WP.

[0018] The database 962 stored in the ROM 960 is referenced in calculating the specific cutting resistance of the tool in cutting the workpiece WP. The database 962 will be described later.

[0019] A2. System processing: FIG. 2 is a flowchart showing the process when the system 1 creates a stability limit diagram. The process of FIG. 2 realizes a method for creating a stability limit diagram in cutting. In step S100, a first specific cutting resistance k1 and a second specific cutting resistance k2 are acquired. Specifically, first, information representing the type of the tool 100 and information representing the material of the workpiece WP are input to the NC control device 900 via the keyboard 980 (see the lower right part of FIG. 1). The CPU 910 of the NC control device 900 acquires the first specific cutting resistance k1 and the second specific cutting resistance k2 by referring to the database 962 stored in the ROM 960 based on the information representing the type of the tool 100 and the information representing the material of the workpiece WP. The first specific cutting resistance k1 and the second specific cutting resistance k2 will be described below.

[0020] Fig. 3 is an explanatory diagram showing the relationship between the tool 100 and the workpiece WP in cutting. In Fig. 3, the X-axis direction is the direction in which the tool 100 is fed relative to the workpiece WP by the holder 210 (see the lower right part of Fig. 1). The Z-axis direction is the direction in which the tool 100 is cut by the column 224. The velocity vector of the main motion in cutting in this embodiment is along the Y-axis direction. The part indicated with the symbol Acc0 is the part removed from the workpiece WP by the tool 100.

[0021] 4 is an enlarged view showing a portion removed from the workpiece WP by the tool 100 in cutting. In FIG. 4, the feed amount is indicated by Fd. The cutting depth is indicated by Dp. The cutting cross-sectional area of ​​the portion removed from the workpiece WP by the tool 100 is indicated by Acc0.

[0022] FIG. 5 is an explanatory diagram showing a schematic relationship between the tool 100 and the workpiece WP in cutting. FIG. 5 shows the tool 100 and the workpiece WP in a state seen from a direction 90 degrees different from that in FIG. 3 and FIG. 4. In cutting, the tool 100 used in cutting has a first portion 110 that mainly comes into contact with the workpiece WP (see the upper center part of FIG. 5). The first portion 110 is a so-called "rake face." The first portion 110 has a first rake angle Φr1 with respect to the workpiece WP. The cutting resistance that the first portion 110 receives from the workpiece WP is shown in FIG. 5 as a principal force CF11 and a thrust force CF12 of the first cutting resistance CF1.

[0023] In the cutting process, the tool 100 used in the cutting process further has a second portion 120 that contacts the workpiece WP and does not have the first rake angle Φr1 (see the lower center part of FIG. 5). The second portion 120 includes a ridge portion of the tip of the tool 100 that cuts into the workpiece WP. However, in FIG. 5, which is a schematic diagram, the second portion 120 is shown enlarged and in a plan view. In FIG. 5, the rake angle of the second portion 120 is shown as a second rake angle Φr2.

[0024] The second portion 120 may be substantially flat or may be curved. The process of providing the cutting edge of the tool 100 with the substantially flat second portion 120 in advance is called "chamfer honing". The process of providing the cutting edge of the tool 100 with the curved second portion 120 in advance is called "round honing". The second portion 120 may become large as a result of the cutting edge being worn down when the tool 100 is used for cutting. The cutting resistance that the second portion 120 receives from the workpiece WP is shown in FIG. 5 as a principal force CF21 and a thrust force CF22 of the second cutting resistance CF2.

[0025] FIG. 6 is an explanatory diagram showing the concept of dividing the cutting shown in FIG. 5 into cutting by the first part 110 of the tool 100 and cutting by the second part 120 of the tool 100. The diagram shown in the left part of FIG. 6 is substantially the same as FIG. 5. In this embodiment, the tool 100 is divided into a virtual first tool 101 having only the first part 110 as a surface in contact with the workpiece, and a virtual second tool 102 having only the second part 120 as a surface in contact with the workpiece (see the right and center parts of FIG. 6). In FIG. 6, the workpiece cut by the virtual first tool 101 is shown as workpiece WP1. In FIG. 6, the workpiece cut by the virtual second tool 102 is shown as workpiece WP2.

[0026] The specific cutting resistance obtained from the thrust force CF12 of the first cutting resistance CF1 is called the first specific cutting resistance k1. Specifically, the first specific cutting resistance k1 is obtained by the following formula. k1 = CF12 / Acc1 (1)

[0027] In formula (1), Acc1 is the cutting cross-sectional area Acc1 of the first portion 110. In this specification, the cutting cross-sectional area is the area occupied by the portion of the workpiece removed by cutting with each part of the tool when projected onto a plane perpendicular to the velocity vector of the main motion in the cutting process.

[0028] Fig. 7 is an explanatory diagram showing the relationship between the cutting cross-sectional area Acc1 of the first portion 110 and the cutting cross-sectional area Acc2 of the second portion 120. In Fig. 7, the portion surrounded by the tool path Tpp in the previous cutting, the surface Swp of the workpiece WP, and the tool path Tpc in the current cutting is the portion removed from the workpiece WP by the tool 100 in the current cutting. The area of ​​the portion removed from the workpiece WP by the tool 100 in the current cutting is, in other words, the cutting cross-sectional area Acc0 of the entire tool 100.

[0029] To facilitate understanding of the technology, the second portion 120 is shown enlarged in the schematic diagram of Fig. 6. However, in reality, the cutting cross-sectional area Acc2 of the second portion 120 is significantly smaller than the cutting cross-sectional area Acc1 of the first portion 110. Although the degree of enlargement is smaller than in Figs. 5 and 6, Fig. 7 also shows the second portion 120 larger than it actually is.

[0030] The specific cutting resistance obtained from the thrust force CF22 of the second cutting resistance CF2 is called the second specific cutting resistance k2. Specifically, the second specific cutting resistance k2 is obtained by the following formula. k2 = CF22 / Acc2 (2)

[0031] The values ​​of the first specific cutting resistance k1 and the second specific cutting resistance k2 vary depending on the machining conditions of the cutting process. The machining conditions include the feed rate and the depth of cut, as well as the type of tool and the material of the workpiece. The values ​​of the first specific cutting resistance k1 and the second specific cutting resistance k2 can be obtained by experiment or simulation. A database 962 stored in the ROM 960 stores the values ​​of the first specific cutting resistance k1 and the second specific cutting resistance k2 for each combination of the type of tool and the material of the workpiece (see the middle right part of FIG. 1). More specifically, the database 962 stores the values ​​of the first specific cutting resistance k1 and the second specific cutting resistance k2 for each combination of the type of tool, the material of the workpiece, the feed rate and the depth of cut.

[0032] 2, the CPU 910 of the NC control device 900 acquires the first specific cutting resistance k1 and the second specific cutting resistance k2 by referring to the database 962 stored in the ROM 960 based on the information representing the type of the tool 100, the information representing the material of the workpiece WP, the feed amount, and the cutting depth. That is, in this embodiment, values ​​prepared in advance for each material of the workpiece WP are used as the first specific cutting resistance k1 and the second specific cutting resistance k2.

[0033] By carrying out such processing, the specific cutting resistance k0 that reflects the material characteristics of the workpiece WP in actual machining can be calculated with minimal processing time in step S200, which will be described later.

[0034] In step S200, the CPU 910 of the NC control device 900 calculates the specific cutting resistance k0 of the tool 100 used in the cutting process based on the first specific cutting resistance k1 and the second specific cutting resistance k2. More specifically, the specific cutting resistance k0 is calculated based on a weighted sum of the first specific cutting resistance k1 and the second specific cutting resistance k2.

[0035] By carrying out such processing, the specific cutting resistance k0 of one tool 100 is calculated by taking into consideration not only the main first cutting resistance CF1 received by the first portion 110 in contact with the workpiece WP and having the first rake angle Φr1, but also the second cutting resistance CF2 received by the second portion 120 in contact with the workpiece WP and not having the first rake angle Φr1. Therefore, it is possible to calculate a specific cutting resistance k0 that better reflects the characteristics of the tool 100 in actual machining, compared to the value of the specific cutting resistance announced by the manufacturer.

[0036] Moreover, by adjusting the weights in the weighted sum in accordance with the actual machining state, it is possible to calculate a specific cutting resistance k0 that better reflects the characteristics of the tool 100 in the actual machining.

[0037] The calculation formula for the specific cutting resistance k0 used in step S200 is the following formula (3). k0 = k1 + (Acc2 / Acc0)×k2 ··· (3) Acc0 = Acc1 + Acc2 (4)

[0038] In the calculation of the weighted sum by the above formula (3), the weight assigned to the first specific cutting resistance k1 is 1. In the calculation of the weighted sum by the above formula (3), the weight assigned to the second specific cutting resistance k2 is a value obtained by dividing the cutting cross-sectional area Acc2 of the second portion 120 in the cutting process by the sum Acc0 of the cutting cross-sectional areas Acc1 and Acc2 of the first portion 110 and the second portion 120 in the cutting process. The cutting cross-sectional areas Acc0 and Acc2 are calculated by the CPU 910 based on the information indicating the type of tool 100 input in step S100 and the cutting conditions such as the feed rate and the cutting depth (see FIG. 4).

[0039] By carrying out such processing, the specific cutting resistances k1, k2 of the respective parts are reflected in the specific cutting resistance k0 of the entire tool in accordance with the ratio of the areas of the parts removed by cutting by the respective parts 110, 120 of the tool when projected onto a plane perpendicular to the velocity vector of the main motion. As a result, it is possible to calculate a specific cutting resistance k0 that is suitable for actual cutting in many cases.

[0040] The method for calculating the specific cutting resistance k0 of the tool 100 used in cutting is realized by the processing of steps S100 and S200 in Fig. 2. In Fig. 2, the method for calculating the specific cutting resistance k0 of the tool 100 used in cutting is indicated as M1 (see the upper left part of Fig. 2). The specific cutting resistance k0 is calculated for various combinations of the cutting depth Dp and the feed rate Fd by the processing M1. The functional part of the CPU 910 that calculates the specific cutting resistance k0 of the tool 100 used in cutting is indicated in Fig. 1 as a specific cutting resistance calculation part 912 (see the upper right part of Fig. 1).

[0041] 2, a transfer function of vibration of the peripheral configuration of the tool 100 attached to the cutting device 200 is obtained. A vibration system including the tool 100 and the peripheral configuration of the cutting device 200 of the tool 100 is referred to as a "spindle system" in this specification.

[0042] A user of the system 1 attaches a vibration sensor to either the tool 100 or the spindle system. Then, the user of the system 1 applies an impact with a hammer to either the tool 100 or the spindle system. Thereafter, the vibration sensor measures the residual vibration of the spindle system. The detection result of the vibration sensor is transmitted to the CPU 910 of the NC control device 900. As a result, the CPU 910 of the NC control device 900 can obtain the frequency response characteristics of the spindle system.

[0043] FIG. 8 is a graph showing a compliance curve Cc1 indicating the response characteristics of the spindle system. The horizontal axis of FIG. 8 represents frequency. The graph of FIG. 8 is a double logarithmic graph. The CPU 910 of the NC control device 900 determines a transfer function G of the spindle system so as to best match the maximum peak Pk portion of the compliance curve Cc1. The transfer function G of the spindle system is shown below. G = 1 / (ms 2 +cs+k) ··· (5)

[0044] In equation (5), m is the mass coefficient, c is the damping coefficient, and k is the stiffness. The response characteristics of the transfer function G of the spindle system determined in step S300 are shown by a solid line in FIG.

[0045] In step S400 of FIG. 2, the CPU 910 of the NC control device 900 creates a stability limit diagram Dsl for cutting processing using the tool 100, using the specific cutting resistance k0 calculated in steps S100 and S200, and the damping coefficient m, damping coefficient c, and stiffness k of the transfer function G calculated in step S300.

[0046] The trajectory of the blade of the tool 100 in cutting can be calculated based on the above parameters. The trajectory of the blade of the tool 100 is not constant with respect to the workpiece WP, but is wavy. If there is a large phase difference between the wave of the blade trajectory in the current cutting and the wave of the blade trajectory in the previous cutting, it can be determined that chatter vibration is occurring. Based on such a determination, the presence or absence of chatter vibration is determined for various combinations of the tool rotation speed V and the cutting depth Dp.

[0047] The CPU 910 of the NC control device 900 displays the created stability limit diagram Dsl on a display 970 (see the lower right part of FIG. 1). A functional part of the CPU 910 that creates a stability limit diagram for cutting processing using the tool 100 is shown in FIG. 1 as a stability limit diagram creation part 913 (see the upper right part of FIG. 1).

[0048] FIG. 9 is a stability limit diagram Dsl in cutting using the tool 100. The horizontal axis of the stability limit diagram Dsl in FIG. 9 is the rotation speed V of the tool. The vertical axis of the stability limit diagram Dsl in FIG. 9 is the cutting depth Dp (see the right part of FIG. 4). The area below the limit curve LC in the stability limit diagram Dsl is the stable region Rs. The area above the limit curve LC in the stability limit diagram Dsl is the vibration generation region Rcv. When cutting is performed with a combination of the rotation speed V and cutting depth Dp included in the stable region Rs, it is predicted that chatter vibration will not occur in the spindle system. When cutting is performed with a combination of the rotation speed V and cutting depth Dp included in the vibration generation region Rcv, it is predicted that chatter vibration will occur in the spindle system.

[0049] A user of the system 1 selects a combination of the rotation speed V and the depth of cut Dp included in the stable region Rs as the combination of the rotation speed and the depth of cut Dp used in the cutting process based on the stability limit diagram Dsl. Then, the user performs the cutting process using the tool 100 in the cutting device 200 with the selected combination of the rotation speed V and the depth of cut Dp. As a result, the cutting process can be performed without chatter vibration.

[0050] In this embodiment, the stability limit diagram Dsl in the cutting process is created using the specific cutting resistance k0 calculated based on the weighted sum of the first specific cutting resistance k1 and the second specific cutting resistance k2 in step S200. Therefore, it is possible to create a stability limit diagram Dsl that sufficiently accurately reflects the characteristics of the actual tool 100 when performing cutting process, compared to a stability limit diagram created using a specific cutting resistance determined by considering only the main cutting resistance.

[0051] A3. Study on specific cutting resistance: The inventors of the technique disclosed herein conducted a study by simulation of the specific cutting resistance of the tool calculated by the process of step S200 in Fig. 2. Specifically, the inventors of the technique disclosed herein conducted a simulation of the specific cutting resistance of the tool 100 for various sizes of the cutting cross-sectional area Acc2 of the second portion 120. Then, the specific cutting resistance k0s of the tool 100 was obtained for various sizes of the cutting cross-sectional area Acc2.

[0052] Fig. 10 is a graph showing the value of the specific cutting resistance k0s of the tool 100 obtained as a result of the simulation. In Fig. 10, the horizontal axis is the ratio of the cutting cross-sectional area Acc2 of the second portion 120 to the cutting cross-sectional area Acc0 of the entire tool 100, that is, (Acc2 / Acc0) (see formula (3)). From Fig. 10, it can be seen that in the simulation, the value of the specific cutting resistance k0s of the tool 100 is generally in a linear relationship with (Acc2 / Acc0). In Fig. 10, the straight line showing the tendency of the specific cutting resistance k0s with respect to (Acc2 / Acc0) is indicated by the dashed line Lt.

[0053] The results shown in Fig. 10 confirm that the calculation formula (3) for the specific cutting resistance k0 is correct. In Fig. 10, the point where the extension of the dashed line Lt, which shows the trend of the specific cutting resistance k0s value, intersects with the vertical axis of the graph, that is, the point where (Acc2 / Acc0) = 0, is the first specific cutting resistance k1 in formula (3).

[0054] FIG. 11 is a diagram showing an analysis of machining of a workpiece WP2 by the second tool 102 using the finite element method. Assuming that the tool 100 has a chamfer honed cutting edge, a model 102m of the second tool 102 was created as a virtual second tool 102 having only the second portion 120 (see the center part of FIG. 6). In FIG. 11, a model of the workpiece WP2 cut by the virtual second tool 102 is shown as WP2m. As a result of the analysis, a value almost equivalent to the gradient of the dashed line Lt showing the trend of the specific cutting resistance k0s in FIG. 10 was obtained, which confirmed that the calculation formula (3) of the specific cutting resistance k0 is correct.

[0055] B. Other embodiments: B1. Alternative embodiment 1: (1) In the above embodiment, when calculating the transfer function of the vibration of the spindle system, a vibration sensor is attached to either the tool 100 or the spindle system (see the middle left part of FIG. 1). Then, the residual vibration of the spindle system is measured by the vibration sensor. However, the measurement of the residual vibration of the spindle system may be performed by a non-contact sensor.

[0056] (2) In the schematic diagram of Fig. 5 used in the above embodiment, the first rake angle Φr1 and the second rake angle Φr2 are inclined to the same side with respect to the ZX plane. However, the first rake angle Φr1 and the second rake angle Φr2 may be inclined to different sides with respect to the ZX plane. In such a case, the first rake angle Φr1 and the second rake angle Φr2 have values ​​with different signs.

[0057] (3) In the above embodiment, the transfer function of the vibration of the main shaft system is expressed by the formula (5). That is, the main shaft system is expressed as a first-order lag element. However, the main shaft system may be expressed as a second-order lag element.

[0058] (4) In the above embodiment, the CPU 910 of the NC control device 900 creates a stability limit diagram Dsl by using the specific cutting resistance k0 calculated in step S200 and the damping coefficient m, damping coefficient c, and stiffness k of the transfer function G calculated in step S300 (see step S400 in FIG. 2). However, depending on the vibration characteristics of the spindle system, the stability limit diagram may be created without using one or two of the damping coefficient m, damping coefficient c, and stiffness k.

[0059] B2. Alternative embodiment 2: In the above embodiment, in calculating the specific cutting resistance k0, the weight assigned to the first specific cutting resistance k1 is 1 (see formula (3) above). In calculating the specific cutting resistance k0, the weight assigned to the second specific cutting resistance k2 is (Acc2 / Acc0) (see formula (3) above). However, the weight assigned to the first specific cutting resistance k1 and the weight assigned to the second specific cutting resistance k2 may be other values. The weight of the weighted sum when calculating the specific cutting resistance may be adjusted according to the actual machining state.

[0060] For example, when Acc2 is sufficiently small relative to Acc0, the weight assigned to the second specific cutting resistance k2 may be (Acc2 / Acc1). The weight assigned to the second specific cutting resistance k2 may also be a function of the time the tool has been used for cutting. The weight assigned to the first specific cutting resistance k1 may also be a constant minus the weight assigned to the second specific cutting resistance k2.

[0061] For example, the second specific cutting resistance k2 may be a value obtained as follows. k2 = CF22 / CL2 (6)

[0062] In formula (6), CL2 is the length of the portion of the tool path Tpc in the current cutting among the contours that define the portion to be removed from the workpiece WP by the tool 100 in the cutting process (see FIG. 7). In this case, the calculation formula for the specific cutting resistance k0 is given by the following formula (7). k0 = k1 + (CL2 / Acc0)×k2 ··· (7)

[0063] B3. Alternative embodiment 3: In the above embodiment, the CPU 910 of the NC control device 900 acquires the first specific cutting resistance k1 and the second specific cutting resistance k2 by referring to the database 962 stored in the ROM 960 based on the information indicating the type of the tool 100 and the information indicating the material of the workpiece WP (see S100 in FIG. 2). That is, in the above embodiment, values ​​prepared in advance for each material of the workpiece WP are used as the first specific cutting resistance k1 and the second specific cutting resistance k2.

[0064] However, the first specific cutting resistance k1 and the second specific cutting resistance k2 may be calculated by two-dimensional cutting theory, taking into account the actual cutting conditions, prior to the calculation of the specific cutting resistance k0 of the tool 100. The "two-dimensional cutting theory" is a theory for analyzing two-dimensional cutting, i.e., cutting in which chips are generated two-dimensionally. In two-dimensional cutting, a single straight cutting edge is placed perpendicular to the cutting speed, the cutting thickness is constant along the cutting edge, and deformation occurs uniformly in any plane perpendicular to the cutting edge.

[0065] Furthermore, the first specific cutting resistance k1 and the second specific cutting resistance k2 may be calculated by plastic analysis in consideration of the actual cutting conditions prior to the calculation of the specific cutting resistance k0 of the tool 100. The finite element method can be adopted as the method of plastic analysis (see FIG. 11). Furthermore, the particle method can also be adopted as the method of plastic analysis. When assuming a tool 100 with chamfer honing applied to the cutting edge, the finite element method can be adopted. On the other hand, when assuming a tool 100 with round honing applied to the cutting edge, the particle method can be adopted.

[0066] In calculating the first specific cutting resistance k1 and the second specific cutting resistance k2, various parameters of the tool 100 and the workpiece WP in actual machining, as well as the cutting device 200, are used. In such an embodiment, it is possible to calculate the specific cutting resistance k0 that better reflects the machining conditions including the characteristics of the tool 100 and the workpiece WP in actual machining.

[0067] B4. Alternative embodiment 4: 2, the CPU 910 of the NC control device 900 uses the specific cutting resistance k0 calculated in step S200 and the damping coefficient m, damping coefficient c, and stiffness k of the transfer function G calculated in step S300 to create a stability limit diagram Dsl in cutting using the tool 100. However, the calculated specific cutting resistance k0 may be used for other purposes without being limited to the creation of a stability limit diagram.

[0068] For example, the cutting resistance, i.e., the cutting force F, can be obtained by the following equation (8). F = k1×Acc1 + k2×Acc2 (8) F = k0 × Acc0

[0069] 2, if the first specific cutting resistance k1, the second specific cutting resistance k2, and the cutting cross-sectional area Acc0 of the entire tool 100 are obtained, then the cutting cross-sectional area Acc2 of the second portion 120 can be obtained by measuring the cutting force F. Therefore, the size of the second portion 120 at the tip of the tool 100, i.e., the degree of wear of the tool 100, can be known from the measured value of the cutting force F.

[0070] Moreover, by measuring the cutting force F, k2×Acc2, i.e., the second cutting resistance CF2 received by the second portion 120, can be obtained. As a result, the stress received by each portion of the second portion 120 can be calculated based on the information on the shape of the tool 100. Therefore, the tool 100 can be replaced before the stress increases to such an extent that the second portion 120 of the tool 100 is damaged. The same process can be performed for the first portion 110 of the tool 100.

[0071] The present disclosure is not limited to the above-mentioned embodiment, and can be realized in various configurations without departing from the spirit of the present disclosure. For example, the technical features of the embodiments corresponding to the technical features in each aspect described in the Summary of the Invention can be appropriately replaced or combined to solve some or all of the above-mentioned problems or to achieve some or all of the above-mentioned effects. Furthermore, if a technical feature is not described as essential in this specification, it can be appropriately deleted. [Explanation of symbols]

[0072] 1...system, 100...tool, 101...first tool, 102...second tool, 102m...model of second tool, 110...first part, 120...second part, 200...cutting device, 210...holding part, 220...cutting part, 224...column, 225...main shaft part, 225m...driving motor, 225s...spindle, 280...bed, 900...NC control device, 910...CPU, 950...RAM, 960...ROM, 9 62...database, 970...display, 980...keyboard, Acc0...cutting cross-sectional area of ​​entire tool, Acc1...cutting cross-sectional area of ​​first part, Acc2...cutting cross-sectional area of ​​second part, Ay...arrow indicating movement of spindle part 225, Az...arrow indicating movement of column 224, BF...thrust force, CF1...first cutting resistance, CF11...principal force of first cutting resistance, CF12...thrust force of first cutting resistance, CF2...second cutting resistance, CF21...principal force of second cutting resistance, CF22...thrust force of second cutting resistance, Cc1...compliance curve, Dp...cutting depth, Dsl...stability limit diagram, Fd...feed rate, G...transfer function, LC...limit curve, Lt...dashed line indicating trend of specific cutting resistance k0s, M1...calculation method of specific cutting resistance k0, Pk...maximum peak of compliance curve Cc1, Rcv...vibration generation area, Rs...stable area, Swp...surface of workpiece, Tpc...current tool path, Tpp...previous tool path, V...rotational speed of tool, WP...workpiece, WP1...workpiece cut by first tool 101, WP2...workpiece cut by second tool 102, WP2m...model of workpiece cut by second tool 102, c...damping coefficient, k...rigidity, k0s...specific cutting resistance, m...damping coefficient, Φr1...first rake angle, Φr2...second rake angle

Claims

1. A method for calculating a specific cutting resistance of a tool used in cutting processing, comprising the steps of: a first specific cutting resistance obtained from a first cutting resistance received by a first portion of the tool used in the cutting process, the first portion contacting a workpiece and having a first rake angle; a second specific cutting resistance obtained from a second cutting resistance received by a second portion of the tool used in the cutting process that comes into contact with the workpiece and does not have the first rake angle; and calculating a specific cutting resistance of the tool based on a weighted sum of the above.

2. 2. The method for calculating a specific cutting resistance according to claim 1, When calculating the weighted sum, The weight given to the first specific cutting resistance is 1; a weight assigned to the second specific cutting resistance is a value obtained by dividing a cutting cross-sectional area of ​​the second portion in the cutting process by a sum of a cutting cross-sectional area of ​​the first portion and a cutting cross-sectional area of ​​the second portion in the cutting process.

3. 3. The method for calculating the specific cutting resistance according to claim 2, A method for calculating a specific cutting resistance, wherein values ​​prepared in advance for each material of the workpiece are used as the first specific cutting resistance and the second specific cutting resistance.

4. 3. The method for calculating the specific cutting resistance according to claim 2, a cutting resistance calculating method for calculating a specific cutting resistance of the tool, the first specific cutting resistance and the second specific cutting resistance being calculated by a two-dimensional cutting theory or a plasticity analysis prior to calculating the specific cutting resistance of the tool;

5. A method for creating a stability limit diagram in cutting processing, comprising the steps of: A method for creating a stability limit diagram, comprising the steps of: creating the stability limit diagram in the cutting process by using the specific cutting resistance calculated by the method according to any one of claims 1 to 4.

6. 1. An apparatus comprising: a first specific cutting resistance obtained from a first cutting resistance received by a first portion of a tool used in a cutting process, the first portion contacting a workpiece and having a first rake angle; a second specific cutting resistance obtained from a second cutting resistance received by a second portion of the tool used in the cutting process that comes into contact with the workpiece and does not have the first rake angle; and calculating a specific cutting resistance of the tool based on a weighted sum of the above.

7. 7. The apparatus of claim 6, An apparatus for generating a stability limit diagram for the cutting process using the specific cutting resistance.

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