Hole processing tool and its design, manufacturing and evaluation methods

Abstract

We provide a simple method for evaluating the results of simulations based on the Matsuzaki-Liu model. A hole drilling tool for forming holes with multiple cutting edges, in which when each cutting edge is applied to the characteristic equation of the Matsuzaki-Liu model, the integer value closest to the imaginary part of the quasi-static characteristic root s, which is the characteristic root at frequency ω = 0, is defined as N0, and the maximum real part of the quasi-static characteristic root s that satisfies 3≦N0≦2n+1 (n is the number of cutting edges) is defined as the maximum real part σ MAX When this is the case, the maximum real part Rσ of the standard hole drilling tool MAXX for which the maximum real part Tσ MAX is within a predetermined threshold.

Description

[Technical field]

[0001] The present invention relates to a hole-making tool and a method for designing, manufacturing and evaluating the same. The hole-making tool is preferably used for, for example, reaming, as well as for general hole-making such as end milling and drilling. [Background technology]

[0002] For example, one of the causes of the deterioration of the hole machining accuracy in reaming is the polygonal shape of the machined hole. A solution to this problem is proposed in Non-Patent Document 1. In this non-patent document 1, the mechanism of the polygonal hole phenomenon in reaming is considered to be a self-excited vibration phenomenon caused by time delay. A characteristic equation based on the so-called Matsuzaki-Liu model is proposed. Based on the characteristic root, a simulation is performed for the arrangement of cutting edges that can suppress the self-excited vibration in a reamer (hole drilling tool). A demonstration test was conducted on a reamer that was evaluated in the simulation as being capable of suppressing self-excited vibration, and it was found that it was able to machine holes with high roundness. [Prior art documents] [Patent documents]

[0003] [Non-Patent Document 1] "Fundamental Study on the Phenomenon of Hole Diversification in Reaming", Transactions of the Japan Society of Mechanical Engineers, Vol. 83, No. 852, 2017 DISCLOSURE OF THEINVENTION [Problem to be solved by the invention]

[0004] In the simulation described in Non-Patent Document 1, the angle arrangement of the cutting edges of the reamer to be evaluated is substituted into the characteristic equation of the Matsuzaki-Liu model and analyzed, and the vibration frequency and its characteristic root are made to correspond to each corner, assuming that a hole having a diagonal to 13-sided polygon is formed, and a chart is created. The obtained chart is then evaluated to determine whether the angle arrangement of the cutting edges to be evaluated is good or bad. Please refer to Figures 4 and 5 for examples of the charts shown in Non-Patent Document 1. More specifically, the maximum value (real part) of the characteristic root is observed for the charts of 2 to 13 sides obtained as a result of the simulation. It is considered that the influence of polygons whose maximum value of the characteristic root exceeds zero is manifested during reaming. The larger the value of the characteristic root, the stronger the influence becomes. Therefore, all charts of 2 to 13 sides are thoroughly observed, and the arrangement of cutting edge angles where the value of each characteristic root is below zero or close to zero is judged to be a good product. In other words, the above evaluation process had to be carried out one by one for each row of cutting edge angles to be evaluated, which was time-consuming. [Means for solving the problem]

[0005] Therefore, the present inventors have investigated a method for easily evaluating the results of a simulation based on the Matsuzaki-Liu model. As a result, I noticed that all the curves in the charts in Figures 4 and 5 were gentle. Therefore, I thought that the value when the frequency ω is set to zero (the value on the vertical axis in the chart) reflected the maximum value. Furthermore, when the frequency ω is set to zero, the characteristic equation of the Matsuzaki-Liu model is simplified (terms including ω can be ignored), and the calculation speed is also improved.

[0006] In this way, the characteristic root when the frequency ω = 0 is named the quasi-static characteristic root. This quasi-static characteristic root is determined for all corners by calculation, and the maximum value among them is used to evaluate the quality of the arrangement of the cutting edge angles being evaluated. However, to judge the quality of a product solely from the numerical value obtained by calculation (the characteristic root at frequency ω=0), the person making the judgment must be highly skilled. In addition, it is difficult to objectively grasp the degree of quality.

[0007] Therefore, the inventors have investigated the criteria for evaluating the value of the quasi-static characteristic root. As a result of the investigation, the maximum value of the real part of the quasi-static characteristic root σ MAX We focused on the maximum real part Rσ of the cutting edges arranged at a certain angle. MAX Based on this, the maximum real part Tσ of the angle sequence of the cutting edge to be evaluated is MAX We decided to compare the following: In particular, when the cutting edge angles are arranged at equal intervals, the maximum real part Rσ MAX and the maximum real part Tσ of the evaluation object MAX It was found that there was a strong correlation between the difference in roundness and the test results, where the test results refer to the roundness when an actual reaming operation was performed using a reamer equipped with the evaluated cutting edge angle arrangement.

[0008] In the example, a reamer (6 teeth) is used as an example, and the cutting edges are set at equal intervals as the reference hole drilling tool. The maximum real part Rσ of the quasi-static characteristic root is calculated. MAX was calculated using the characteristic equation of the Matsuzaki-Liu model. In addition, the maximum real part Tσ of the quasi-static characteristic root of the evaluation object (with various cutting edge angle arrangements) MAX was calculated in the same way. Then, the difference between the two (maximum real part Tσ MAX -Maximum real part Rσ MAX The difference is called the Quasi-static Characteristic Root (QCR). On the other hand, reaming was carried out using the reference hole-drilling tool and the evaluation target hole-drilling tool, and the roundness of the resulting holes was measured. The relationship between the measured circularity and the above-mentioned QCR value is shown in FIG. The results in Figure 8 show that there is a high correlation between the QCR value and roundness.

[0009] Based on the above findings, the first aspect of the present invention is defined as follows: A hole processing tool for forming a hole having multiple cutting edges, When each cutting edge is fitted to the characteristic equation of the Matsuzaki-Liu model, the integer value closest to the imaginary part of the quasi-static characteristic root s, which is the characteristic root at frequency ω = 0, is defined as N0. The maximum real part of the quasi-static characteristic root s that satisfies 3≦N0≦2n+1 (n is the number of cutting edges) is the maximum real part σ MAX When Maximum real part Rσ of the reference hole drilling tool MAX For the maximum real part Tσ MAX is within a predetermined threshold value. The hole drilling tool of the first aspect thus defined is the maximum real part Rσ of the reference hole drilling tool. MAX For the maximum real part Tσ MAX is within a predetermined threshold range, it is possible to ensure high roundness when drilling holes, as can be seen from the relationship in FIG. Furthermore, according to the hole-drilling tool of the first aspect thus defined, the maximum real part is evaluated in comparison with the reference hole-drilling tool, so that the evaluation is objective.

[0010] The second aspect of the present invention is defined as follows: A hole drilling tool as defined in a first aspect, wherein in the characteristic equation, a quasi-static characteristic root corresponds to a 2-13 polygon; The reference hole processing tool has cutting edges arranged at equal intervals, The maximum real part Tσ of the target hole drilling tool MAX and the maximum real part Rσ of the reference hole drilling tool MAX The absolute value of the difference between and is 0.075 or more. However, Tσ MAX ≦Rσ MAX

[0011] The hole-drilling tool of the second aspect defined in this manner more specifically reflects the results of FIG. 8, and by using a hole-drilling tool having such characteristics, a high degree of circularity can be ensured in the drilled hole. The reason for limiting the quasi-static characteristic root to 13 or less sides is that a shape exceeding 13 sides is close to a circle, and even if this occurs, it will not have a significant effect on actual drilling. On the other hand, when 14 or more sides are reflected, if the maximum real part of the quasi-static characteristic root obtained there becomes large, there is a risk that the QCR value will become large, even though it will have almost no effect on actual drilling.

[0012] The third aspect of the present invention is defined as follows: In the hole drilling tool defined in the second aspect, the maximum real part Tσ of the target hole drilling tool MAX and the maximum real part Rσ of the reference hole drilling tool MAX The absolute value of the difference between is 0.10 or more. The hole-drilling tool defined in the third aspect thus defined is a more specific reflection of the results of FIG. 8, and by using a hole-drilling tool having such characteristics, a higher degree of roundness can be ensured for the hole to be drilled.

[0013] The fourth aspect of the present invention is defined as follows: In the hole drilling tool defined in the second aspect, the maximum real part Tσ of the target hole drilling tool MAX and the maximum real part Rσ of the reference hole drilling tool MAX The absolute value of the difference between is 0.125 or more. The hole-drilling tool of the fourth aspect defined in this manner further reflects the results of FIG. 8, and by using a hole-drilling tool having such characteristics, a higher degree of roundness can be ensured for the hole to be drilled.

[0014] The fifth aspect of the present invention is defined as follows: In the hole-drilling tools defined in any one of the second to fourth items, the number n of cutting edges is six. The fifth aspect of the hole-drilling tool defined in this manner further reflects the results of FIG. 8, and by using a hole-drilling tool having such characteristics, a higher degree of circularity can be ensured for the holes that are drilled.

[0015] The sixth aspect of the present invention is defined as follows: In the hole-cutting tool specified in the second to fifth aspects, between cutting edge i (i is a natural number) and the cutting edge i+1 adjacent thereto in the counter-rotation direction The parting angle αi+1 and the parting angle αi+2 between the cutting edge i+1 and the cutting edge i+2 adjacent thereto in the counter-rotational direction are expressed in the circumferential direction of the hole drilling tool. The margin width tmi or land width ti of the cutting edge i and the margin width tmi+1 or land width ti+1 of the cutting edge i+1 are The hole processing tool The magnitude relationship matches when viewed in the circumferential direction.

[0016] According to the hole-cutting tool defined in the sixth aspect thus defined, the width of the cutting edge in contact with the workpiece (margin width, land width) is changed. The change corresponds to the angle (partition angle) of the adjacent cutting edges. That is, the larger the parting angle, the greater the load on the cutting edge downstream in the direction of rotation that contacts the workpiece. Therefore, wear of that part is likely to progress. Therefore, if the parting angle becomes larger, the width of the cutting edge in contact with the workpiece is correspondingly increased to suppress the progress of wear and thereby prevent uneven distribution of wear.

[0017] The seventh aspect of the present invention is defined as follows: In the hole drilling tool according to the sixth aspect, the ratio of the split angles is (α2:α3:……:αn+1) and the margin width The hole drilling tool in the circumferential direction The margin width ratio (tm1:tm2:...:tmn) when viewed from the above, or the land width The entire circumference of the hole processing portion The land width ratio (t1:t2: . . . :tn) when viewed from the top is the same as that of the bottom.

[0018] The eighth aspect of the present invention is defined as follows: In the hole-drilling tool defined in the sixth or seventh aspect, a marginal portion of the cutting edge is coated with a hard coating. According to the hole drilling tool of the eighth aspect defined as above, uneven distribution of wear can be prevented while reducing the amount of hard coating material used. The hole drilling tool described above is suitably used for reaming (ninth aspect). [Brief description of the drawings]

[0019] [Figure 1] FIG. 1 is a photograph showing a reamer, which is an example of a hole-making tool according to the present invention. [Diagram 2] Figure 2 is a schematic diagram showing the basic parameters of the Matsuzaki-Liu model applied to a hole-making tool with six cutting edges. [Diagram 3] Figure 3 is a schematic diagram showing the analytical principle of the Matsuzaki-Liu model. [Figure 4] FIG. 4 shows the analysis results for a hole-making tool with equally spaced cutting edges, with the horizontal axis of each chart showing frequency and the vertical axis showing characteristic roots. [Diagram 5] FIG. 5 shows the analysis results of a hole-making tool with cutting edges spaced apart from one another, with the horizontal axis of each chart showing frequency and the vertical axis showing characteristic roots. [Figure 6] FIG. 6 shows the relationship between the number of revolutions and the roundness obtained when holes were drilled using the hole drilling tools of Comparative Examples 1 and 2 and Examples 1 to 6 of the present invention. [Figure 7] FIG. 7 shows the relationship between the number of revolutions and the roundness obtained when holes were drilled using the hole drilling tools according to Examples 7 to 12 of the present invention. [Figure 8] FIG. 8 is a graph showing the relationship between the QCR value and the average circularity in the examples and comparative examples. [Figure 9] FIG. 9 is a conceptual diagram showing the division angles of the cutting edges of a hole-making tool. [Figure 10] FIG. 10 is an explanatory diagram in mechanical terms of the hole drilling tool. [Figure 11] Figure 11 shows the relationship between the maximum real part σMAX of the quasi-static characteristic root and the average roundness. [Figure 12] FIG. 12 shows the relationship between the real part of the characteristic root and the rotation speed for Comparative Examples 1 and 2 and Examples 1 and 2. [Figure 13] FIG. 13 shows the relationship between the real part of the maximum characteristic root and the number of polygons. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0020] First, we explain the Matsuzaki-Liu model. FIG. 1 is a photograph showing a hole-making tool (reamer) used in reaming. In general reaming, the workpiece is fixed and the reamer rotates, but in order to clarify the basic characteristics, we will use a simpler analysis model in which the tool is fixed and the workpiece rotates. In addition, a pilot hole is drilled in the workpiece, and in normal cutting conditions where cutting is performed without the tool vibrating, the center of the pilot hole and the axis center of the reamer are assumed to be aligned. Figure 2 shows an analytical model of reaming with six cutting edges. The figure shows the reamer viewed from the front of the cutting edge, with the reamer not rotating and the workpiece rotating clockwise at angular velocity ω. The reamer and spindle are considered to move as a single unit, with only translational motion within the plane being considered, and rotational motion and bending and twisting of the reamer being ignored. For simplicity, the reamer and spindle are also considered to be isotropically supported by a spring and dashpot. A coordinate system 0-xy is fixed in space with the center of the pilot hole as the origin, and the coordinates of the central axis of the reamer are (x, y). The number of teeth of the reamer is n, and one cutting edge is placed in the positive direction of the x-axis. Starting from this cutting edge, cutting edges i (i=1, 2, …, n) are placed in the opposite direction to the rotation direction of the workpiece. ;Blades on x-axis: 1 ) and number the cutting edge i With cutting edge i+1 The angle is α i+1 In addition, α 1 =0rad It is considered that cutting force and contact force act on each cutting edge. It is assumed that cutting is performed only at the axial tip of the reamer, and the principal and thrust components of the cutting force act on the cutting part. In addition, normal force and frictional force due to contact with the machined hole are taken into consideration for parts other than the axial tip of the cutting edge.

[0021] Figure 3 shows the relationship between the cutting edges and the machined hole in the case of a six-blade reaming tool. This figure shows the surface of the machined hole developed, with the horizontal axis representing the axial position and the vertical axis representing the circumferential angle. In this figure, the cutting edges are shown as horizontal solid lines, and the left end represents the axial tip. The workpiece is fed while rotating relative to the cutting edges, but in the figure, the rotation is represented by a vertical downward movement and the feed is represented by a horizontal rightward movement, so the workpiece moves downward and to the right along the diagonal direction shown by the dotted line. Therefore, cutting is performed at the axial tip of the cutting edges shown by the red lines, and the rest of the cutting edge comes into contact with the part cut by the previous cutting edge, in order. Since cutting is performed simultaneously by all cutting edges, the axial length cut by a certain cutting edge is the length fed until the part cut by the previous cutting edge reaches it, as shown in Figure 3. Therefore, if the feed per revolution of the workpiece is δ, the axial length of the part cut by cutting edge i is δ i becomes:

number

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[0022] Assume the solution of equation 7 is as follows:

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[0023] The results of analyzing the equation of motion for such a model are shown in the chart of Figure 4 (equally divided blades) and the chart of Figure 5 (unequally divided blades).

[0024] In this invention, since the quasi-static characteristic root with frequency ω=0 is used, the characteristic equation of the Matsuzaki-Liu model can be summarized as follows:

number

[0025] The parameters used in analyzing the equation of motion are the arrangement angle of the cutting edge (α j ) are as follows: Kcd / K =1.0 kd / K =1.0 b=0.01 m=0.10 m =1 Here, m is an integer value and the others are dimensionless quantities.

[0026] The results of analyzing the equation of motion for each of the examples and comparative examples shown are shown in Table 1. [Table 1]

[0027] In Table 1, the maximum characteristic root indicates the maximum value of the characteristic root (real part) at all frequencies and in the 2- to 13-gon shapes. To obtain this value, it is necessary to calculate the amount of data required to draw numerous charts as shown in Figures 4 and 5. On the other hand, the maximum real part of the quasi-static characteristic root σ MAX N0 is the integer value closest to the imaginary part of the quasi-static characteristic root s, which is the characteristic root at frequency ω=0, and it refers to the largest real part of the quasi-static characteristic root s that satisfies 3≦N0≦13. The maximum real part σ of the quasi-static characteristic root s MAX The calculations (values ​​on the vertical axis of each chart) only need to be performed when the frequency ω = 0. Furthermore, the equation of motion is simplified at frequency ω = 0, so the burden on calculations is greatly reduced. Therefore, it is possible to evaluate a large number of targets with the same load on the computer. The QCR value is the maximum real part Rσ of the quasi-static characteristic root of Comparative Example 1 (equally divided cutting edges). MAX and the maximum real part Tσ of the quasi-static characteristic root of other examples and comparative examples MAX This shows the difference between

[0028] For each of the Examples and Comparative Examples, a reaming test was carried out so as to meet the analysis conditions. The basic test conditions were as follows (adjusted according to the material and the type of reamer device): About Reamers Diameter of bottom of groove: φ5.2mm Groove depth: 1.4mm Groove radius: R0.05~R0.3mm Land width: Depends on separation angle Margin width: 0.5mm Material: Cemented carbide Hard coating material: nitrides such as TiN, TiAlN, TiSiN, and AlCrN Hard coating target: Reamer all around Work material Material: FC250 (gray cast iron) Outer diameter: φ8 (outer diameter of reamer = 7.98) Pilot hole diameter: φ7.5 (outer diameter of pilot hole drill) Length: Pilot hole depth 26, reaming depth 24 Drilling Conditions Rotation speed: 2000~6000rpm Advance speed: Feed rate 200~600mm / min Cutting speed (circumferential speed at φ8) 50~15m / min Cutting oil: Soluble type water-soluble cutting oil Inner diameter measurement conditions Measuring device: TAYLOR HOBSON Talyrond 365 Measurement position: The first surface is the point 0.5 to 1 mm into a 24 mm deep reamed hole from the surface, and the roundness of a total of 12 surfaces is measured at 2 mm intervals in the depth direction.

[0029] The test results of the example and the comparative example are shown in FIG. 6 and FIG. In each of the charts in FIG. 6 and FIG. 7, the vertical axis indicates the roundness, and the horizontal axis indicates the rotation speed of the reamer. The average roundness in Table 1 shows the average of the roundness in each chart in Figure 6 and Figure 7. Extremely out-of-roundness values ​​are excluded when calculating the average value. This is to eliminate errors caused by the drive unit of the reamer device.

[0030] Fig. 8 shows the relationship between the QCR value and the average circularity in Table 1. In Table 1, the two data on the right side show the comparative examples, and the other data show the examples. 8, it can be seen that the average circularity is high when the absolute value of the QCR value is 0.075 or more. Furthermore, the absolute value is preferably 0.10 or more. More preferably, the absolute value is 0.125 or more. In addition to the reamers of Comparative Examples 1 and 2 in Table 1, various reamers have been proposed and sold in the past. Some of them may accidentally have a QCR value that exceeds each of the above thresholds. However, the QCR value proposed in this specification is a completely new concept by the present inventors in evaluating the performance of a reamer, and such accidental conventional reamers do not disclose the concept at all. Therefore, even if such a reamer existed before the filing of this application, the present invention is not considered to lose its novelty. And, if such a reamer existed before the filing of this application, it will be excluded from the claims covering the hole drilling tool.

[0031] From Table 1, the reamers with the cutting edge angles and arrangements shown in each example show excellent characteristics (roundness). It is believed that the same performance, i.e., the reproducibility of roundness, can be obtained even if the cutting edges are changed by ±3 degrees in the cutting edge angle arrangement of each example. In particular, the reamers having the cutting edge angle arrangements shown in Examples 10 and 11 exhibit excellent characteristics (roundness). With such an arrangement of cutting edges, it is believed that the same performance, i.e., reproducibility of roundness, can be obtained even if each cutting edge is changed by ±5 degrees. Therefore, another aspect of the present invention can be defined as follows: A reamer having six cutting edges, the angles of the cutting edges being 35 to 45 degrees, 75 to 85 degrees, 55 to 65 degrees, 50 to 60 degrees, 30 to 40 degrees, and 85 to 95 degrees, respectively. Further, reamers having angles of 45 to 55 degrees, 25 to 35 degrees, 95 to 105 degrees, 65 to 75 degrees, 65 to 75 degrees, and 35 to 45 degrees, respectively.

[0032] Figure 9 shows a schematic diagram of the disassembly angle of each cutting edge of a reamer, and Figure 10 shows a schematic diagram of the cutting edge shape of a reamer. When machining with a reamer, the larger the parting angle, the greater the load on the cutting edge on the rear side in the rotation direction. This load accelerates the wear of the cutting edges. If the wear rate of each cutting edge of the reamer varies, it becomes difficult to maintain a high degree of roundness and reduces durability. Therefore, in order to prevent variation in wear of each cutting edge and ensure the rigidity of each cutting edge, it is preferable to adjust the width of the part of the cutting edge that comes into contact with the workpiece (the width of the land part (land width) or the width of the margin part (margin width)) according to the spacing between the cutting edges (division angle).

[0033] More specifically, the relationship in magnitude of the dividing angle αi between cutting edge i and the adjacent cutting edge i+1 in the counter-rotational direction when viewed around the entire circumference of the processing tool is matched with the relationship in magnitude of the margin width tmi+1 and / or land width ti+1 of cutting edge i+1 when viewed around the entire circumference of the processing tool. Furthermore, the ratio of the division angle αi when viewed around the entire circumference of the processing tool (α1:α2: ...:αn) is made to coincide with the ratio of the margin width when viewed around the entire circumference of the processing tool (tm2:tm3: ...:tmn:tm1) and / or the ratio of the land width when viewed around the entire circumference of the processing tool (t2:t3: ...:tn:tm1).

[0034] Other experimental results by the present inventors are shown in FIGS. Figure 11 shows the relationship between the maximum real part σMAX of the quasi-static characteristic root and the average roundness. From this figure, it can be seen that the maximum real part σMAX of the quasi-static characteristic root itself can be an index showing the characteristics of the hole drilling tool. Comparing this with FIG. 8, it can be seen that the QCR value more clearly indicates the characteristics.

[0035] FIG. 12 shows the relationship between the real part of the characteristic root of the characteristic equation of the Matsuzaki-Liu model and the rotation speed for Comparative Examples 1 and 2 and Examples 1 and 2. FIG. 13 similarly shows the relationship between the real part of the maximum characteristic root and the number of polygons.

[0036] The present invention is not limited to the above-mentioned aspects and embodiments. Various modifications that do not deviate from the scope of the claims and that can be easily conceived by a person skilled in the art are also included in the present invention.

Claims

1. A hole processing tool for forming a hole having multiple cutting edges, When each cutting edge is fitted to the equation of motion of the Matsuzaki-Liu model, the integer value closest to the imaginary part of the quasi-static characteristic root s, which is the characteristic root at the vibration frequency ω = 0, is determined as N. ０ year, Here, the Matsuzaki-Liu model is expressed as follows: [0010] 3≦N ０ The maximum real part of the quasi-static characteristic root s that satisfies ≦2n+1 (n is the number of cutting edges) is the maximum real part σ MAX When Maximum real part Rσ of the reference hole drilling tool ＭＡＸ For the maximum real part Tσ ＭＡＸ is within a predetermined threshold range, The quasi-static characteristic root corresponds to a standard hole drilling tool having a 2 to 13 polygonal shape, The reference hole processing tool has the cutting edges arranged at equal pitches, The range of the threshold value is the maximum real part Tσ of the target hole drilling tool. ＭＡＸ and the maximum real part Rσ of the reference hole drilling tool ＭＡＸ The absolute value of the difference between T and Tσ is 0.075 or more. ＭＡＸ ≦Rσ ＭＡＸ A hole processing tool.

2. The hole drilling tool according to claim 1, wherein the absolute value of the difference is 0.10 or more.

3. The hole drilling tool according to claim 1 , wherein the absolute value of the difference is 0.125 or more.

4. The hole drilling tool according to any one of claims 1 to 3, wherein the number n of cutting edges is 6.

5. 5. A hole drilling tool according to claim 1, wherein the relationship in magnitude between a dividing angle αi+1 between a cutting edge i (i is a natural number) and an adjacent cutting edge i+1 in the counter-rotational direction and a dividing angle αi+2 between said cutting edge i+1 and an adjacent cutting edge i+2 in the counter-rotational direction when viewed in the circumferential direction of the hole drilling tool coincides with the relationship in magnitude between a margin width tmi or a land width ti of said cutting edge i and a margin width tmi+1 or a land width ti+1 of said cutting edge i+1 when viewed in the circumferential direction of the hole drilling tool.

6. The hole drilling tool according to claim 5, wherein the ratio of the division angles (α2:α3:...:αn+1) coincides with the ratio of the margin widths when viewed in the circumferential direction of the hole drilling tool (tm1:tm2:...:tmn) or the ratio of the land widths when viewed in the circumferential direction of the hole drilling portion (t1:t2:...:tn).

7. The hole-making tool according to claim 5 or 6, wherein a marginal portion of the cutting edge is coated with a hard coating.

8. The hole drilling tool according to any one of claims 1 to 7, which is used for reaming.

9. A method for designing a hole processing tool for forming a hole having a plurality of cutting edges, comprising the steps of: The multiple cutting edges having angles arbitrarily selected as the target processing tool are fitted to the characteristic equation of the Matsuzaki-Liu model to obtain the integer value N closest to the imaginary part of the quasi-static characteristic root s, which is the characteristic root at frequency ω = 0. ０ Identify Here, the Matsuzaki-Liu model is expressed as follows: [0025] 3≦N ０ The maximum real part σ, which is the maximum real part of the quasi-static characteristic root s that satisfies ≦2n+1 (n is the number of cutting edges), ＭＡＸ Identify Maximum real part Rσ of the reference hole drilling tool ＭＡＸ For the maximum real part Tσ ＭＡＸ In a method for designing a hole drilling tool, the target drilling tool is selected, The quasi-static characteristic root corresponds to the reference hole drilling tool having a 2 to 13 polygonal shape, The reference hole processing tool has cutting edges arranged at equal intervals, The range of the threshold value is the maximum real part Tσ of the target hole drilling tool. ＭＡＸ and the maximum real part Rσ of the reference hole drilling tool ＭＡＸ The absolute value of the difference between Tσ and Tσ is 0.075, 0.10, or 0.125 or more. ＭＡＸ ≦Rσ ＭＡＸ A method for designing a hole drilling tool.

10. A method for manufacturing a hole drilling tool, comprising the steps of: manufacturing a hole drilling tool based on a design obtained by the design method according to claim 9;

11. A method for evaluating a hole processing tool for forming a hole having multiple cutting edges, comprising: The cutting edges of the tool to be evaluated are fitted to the characteristic equation of the Matsuzaki-Liu model to find the integer value N closest to the imaginary part of the quasi-static characteristic root s, which is the characteristic root at angular velocity ω = 0. ０ Identify Here, the Matsuzaki-Liu model is expressed as follows: [0030] 3≦N ０ The maximum real part σ of the quasi-static characteristic root s that satisfies ≦2n+1 (n is the number of cutting edges) ＭＡＸ Identify Maximum real part Rσ of the reference hole drilling tool ＭＡＸ For the maximum real part Tσ ＭＡＸ In the evaluation method for a hole drilling tool, a target tool is determined to be a good product when the value of the threshold value is within a predetermined threshold value. The quasi-static characteristic root corresponds to the reference hole drilling tool having a 2 to 13 polygonal shape, The reference hole processing tool has cutting edges arranged at equal intervals, The range of the threshold value is the maximum real part Tσ of the target hole drilling tool. ＭＡＸ and the maximum real part Rσ of the reference hole drilling tool ＭＡＸ The absolute value of the difference between Tσ and Tσ is 0.075, 0.10, or 0.125 or more. ＭＡＸ ≦Rσ ＭＡＸ A method for evaluating hole-making tools.

12. A method for evaluating a hole processing tool for forming a hole having multiple cutting edges, comprising: The multiple cutting edges of the evaluation target tool are fitted to the characteristic equation of the Matsuzaki-Liu model, and the integer value N closest to the imaginary part of the quasi-static characteristic root s, which is the characteristic root at angular velocity ω = 0, is obtained. ０ Identify Here, the Matsuzaki-Liu model is expressed as follows: [0045] 3≦N ０ The maximum real part σ, which is the maximum real part of the quasi-static characteristic root s that satisfies ≦2n+1 (n is the number of cutting edges), ＭＡＸ Identify and evaluate methods.

13. A reamer having six cutting edges, the angles of the cutting edges being 35 to 45 degrees, 75 to 85 degrees, 55 to 65 degrees, 50 to 60 degrees, 30 to 40 degrees, and 85 to 95 degrees, respectively.

14. The reamer has six cutting edges, and the angles of the cutting edges are set to 45 to 55 degrees, 25 to 35 degrees, 95 to 105 degrees, 65 to 75 degrees, and 35 to 45 degrees, in that order.

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