JP6060027B2 - Cutting tool and design method thereof - Google Patents

Description

  The present invention cuts a work material with a cutting edge that rotates about an axis and is provided on a peripheral surface, and the unequal pitch unequal lead end mill in which the cutting edge is formed with unequal pitch and unequal leads. The present invention also relates to a cutting tool such as an unequal pitch unequal lead mill and a design method thereof.

  As shown in FIG. 7A, the general end mill 100 has a configuration in which the cutting edges 101 are distributed at a uniform pitch in the circumferential direction (rotation direction) and the pitch angle φ is 90 °. In the case of this end mill 100, there is a drawback that self-excited chatter vibration is likely to occur.

  Therefore, in order to suppress the occurrence of the self-excited chatter vibration, as shown in FIG. 7B, the pitch angles φ of the adjacent cutting edges 111 in the circumferential direction are made different so that the cutting edges 111 are distributed at unequal pitches. A pitch end mill 110 has been proposed (see, for example, Patent Document 1).

JP 2006-198767 A

  However, the unequal pitch end mill has an effect of suppressing the occurrence of chatter vibration because the distribution position is fixed at a constant distribution position even if the distribution position of the cutting edges is unequal pitch in the circumferential direction. There is a drawback that the range of conditions in which can be expressed is narrow.

  Therefore, in order to widen the above condition range, an unequal pitch unequal lead end mill shown in FIG. 8 (a view seen from a direction orthogonal to the axial direction of the tool) has been proposed. In this unequal pitch unequal lead end mill, the twist angle (lead angle) of the cutting edge in the unequal pitch end mill is set such that one of the adjacent cutting edges in the circumferential direction is θ1, and the other is θ2 different from θ1 (≠ θ1). By adopting this configuration, the interval (pitch angle) between the cutting edges varies depending on the position of the cutting edge in the axial direction, so that it is possible to widen the condition range in which the chatter vibration suppressing effect can be exhibited. In FIG. 8, a solid line inclined by θ1 or θ2 with respect to the axis (dashed line) represents a ridgeline of the cutting edge.

  However, although the above-mentioned unequal pitch unequal lead end mill is effective in suppressing self-excited chatter vibration, the cutting force is increased or decreased by distributing the tool cutting edges to the unequal pitch, and the cutting resistance is increased or decreased. As a forced vibration, machining vibration (forced chatter vibration) during machining may occur.

  The machining vibration is generated as follows. That is, as shown in FIG. 9 (a), in the equal pitch end mill, the shape and size of the cutting force generated by the cutting of each cutting edge is theoretically equal, so that machining vibration does not occur. As shown in FIG. 4, in an unequal pitch unequal lead end mill with different cutting edge intervals, cutting resistance increases with a cutting edge X having a large interval from the preceding cutting edge, and conversely, the interval from the preceding cutting edge increases. Since the cutting force decreases with the narrow cutting edge Y, the variation (difference) in the cutting force acts as a new excitation force, and forcible chatter vibration occurs as machining vibration during machining.

  SUMMARY OF THE INVENTION The present invention has been made to solve such problems of the prior art, and an object of the present invention is to provide a cutting tool capable of preventing the occurrence of forced chatter vibration and a design method thereof.

The cutting tool design method according to the present invention includes a pair of first cutting edges and second cutting edges at symmetrical positions with an axis centered on a peripheral surface, and the adjacent first cutting edges and second cutting edges. Inequalities that are alternately arranged at unequal pitches with different intervals between the cutting edges preceding in the rotation direction and the lead angles of the first cutting edge and the second cutting edge with respect to the axis are different. A cutting tool design method in which each cutting edge is provided as a lead, wherein the lead angle of the first cutting edge is θ1, the lead angle of the second cutting edge is θ2, the pitch angle of the first cutting edge is φ1, The pitch angle of the second cutting edge is φ2, the rake angle of the second cutting edge is α2, the tool diameter is D, and a plurality of distances within the range from the front end to the rear end of the cutting edge in the axial direction. The cutting resistance of the first cutting edge with respect to the cutting resistance of the second cutting edge is expressed by the following equation (1). The ratio B is calculated, and the cutting resistance ratio A2 of the second cutting edge at the rake angle α2 of the second cutting edge is calculated by the following equation (2) before or after the calculation of the ratio B of the cutting resistance. Then, the calculated cutting force ratio A2 is divided by each of the cutting force ratios B to obtain a divided value A2 / B, and the plurality of values when the divided value A2 / B is obtained by the following equation (3): Determining a rake angle α1 of the first cutting edge at each of the distances;
B = {L (tan θ2−tan θ1) + Dφ1π / 360}
/ {L (tan θ1−tan θ2) + Dφ2π / 360} (1)
However, L is the distance from the tip of the cutting edge in the axial direction.
A2 = exp (−k · α2) (2)
A2 / B = exp (−k · α1) (3)
However, k is a coefficient.

  Subsequently, calculating a rake angle curve α1 ′ of the first cutting edge continuously connecting all the rake angles α1 based on the rake angles α1 of all the first cutting edges obtained. It is characterized by.

  Here, the step of determining the rake angle α1 of the first cutting edge at each of a plurality of distances determines the rake angle α1 of the first cutting edge for one of the plurality of distances, and then Sequentially determining the rake angle α1 of the first cutting edge for each of the other ones.

  In the case of the cutting tool design method of the present invention, the distance from the cutting edge tip is based on the rake angle α1 of the first cutting edge at a plurality of positions, and the first cutting edge rake continuously from the cutting tool tip. An angle curve α1 ′ can be obtained, and by setting the rake angle of the first cutting edge based on the calculated curve α1 ′, the cutting resistances of the first cutting edge and the second cutting edge are the same at each distance. It is possible to prevent the occurrence of forced chatter vibration.

  In the cutting tool of the present invention, a pair of first cutting edges and second cutting edges are arranged in symmetrical positions with an axis centered on the peripheral surface, and each of the adjacent first cutting edges and second cutting edges in the rotation direction. It is alternately arranged with unequal pitches with different intervals from the preceding cutting edge, and unequal leads with different lead angles with respect to the axis of the first cutting edge and the second cutting edge, It is a cutting tool provided with each cutting edge, Comprising: The rake angle of the 1st cutting edge and the 2nd cutting edge is designed using the design method of the said cutting tool, It is characterized by the above-mentioned.

  Even in the cutting tool of the present invention, the rake angle curve α1 ′ of the continuous first cutting edge from the cutting edge tip to the cutting edge rear end calculated by the above-described cutting tool design method is used. Since the rake angle of the first cutting edge is set based on this, it becomes possible to make the cutting resistances of the first cutting edge and the second cutting edge the same, and to prevent the occurrence of forced chatter vibration. it can.

  In the case of the present invention, based on the rake angle α1 of the first cutting edge at a plurality of positions at a distance from the cutting edge tip, the continuous first cutting edge from the cutting edge tip to the trailing edge of the cutting tool is determined. A rake angle curve α1 ′ can be obtained, and by setting the rake angle of the first cutting edge based on the calculated curve α1 ′, the cutting resistances of the first cutting edge and the second cutting edge are the same at each distance. It is possible to prevent the occurrence of forced chatter vibration.

It is an expanded view of the cutting edge of the unequal pitch unequal lead end mill tool contained in the cutting tool of the present invention. It is a figure which shows the relationship between the cutting resistance ratio and the rake angle used as the basis of this invention. It is explanatory drawing of the rake angle designed by the design method of this invention. It is a figure which shows the relationship between the cutting resistance ratio and the rake angle in the case of cast iron type material. It is a figure which shows the relationship between the cutting resistance ratio in the case of a stainless steel material, and a rake angle. It is a figure which shows the relationship between the cutting resistance ratio in the case of carbon steel type material, and a rake angle. (A) is sectional drawing of an equal pitch end mill, (b) is sectional drawing of an unequal pitch end mill. It is a schematic diagram (front view) of the cutting edge of an unequal pitch unequal lead end mill tool. (A) is a relational diagram between cutting resistance and tool rotation angle in an equal pitch end mill, and (b) is a relational diagram between cutting resistance and tool rotation angle in an unequal pitch end mill.

  The present invention makes it possible to prevent the occurrence of forced chatter vibration in a cutting tool such as an unequal pitch unequal lead end mill or an unequal pitch unequal lead mill.

(Principle of cutting tool design method in the present invention)
FIG. 1 is a development view of cutting edges of an unequal pitch unequal lead end mill. The horizontal axis indicates the circumferential position around the axis, and the vertical axis indicates the axial distance (L) from the tool tip of the cutting edge. I'm taking it.

  This cutting tool is a four-blade end mill, and as the four cutting edges, a pair of first cutting edges are arranged symmetrically with respect to the axis, and a pair of second cutting edges are arranged on the axis. The first cutting edge, the second cutting edge, the first cutting edge, and the second cutting edge are arranged in this order around the axis, which are arranged symmetrically with respect to the center. Here, the pitch angle of the first cutting edge is φ1, the pitch angle of the second cutting edge is φ2 (≠ φ1), the lead angle of the first cutting edge is θ1, and the lead angle of the second cutting edge is θ2 (≠ θ1). The pitch angle of the first cutting edge here means the angle around the axis between the first cutting edge and the second cutting edge preceding the first cutting edge. The pitch angle of the second cutting edge means an angle around the axis between the second cutting edge and the first cutting edge preceding the second cutting edge.

  In this cutting tool, the interval W between adjacent cutting edges changes according to the axial distance (L) of the cutting edges.

  Here, the ratio B of the cutting resistance of the first cutting edge of the lead angle θ1 to the cutting resistance of the second cutting edge of the lead angle θ2 is expressed as the following equation (1) as a function of the axial distance (L). Is done.

B = {L (tan θ2−tan θ1) + Dφ1π / 360}
/ {L (tan θ1-tan θ2) + Dφ2π / 360} (1)
Where D is the diameter of the cutting tool.

  As understood from the equation (1), in the unequal pitch unequal lead end mill, the cutting resistance ratio B changes with the change in the axial distance (L) of the cutting edge. Therefore, in order to suppress the change in the cutting resistance ratio B and prevent the occurrence of forced chatter vibration, the cutting resistance is set to the reciprocal of Formula (1) at each of the axial distances (L) of the cutting edge. It is necessary to change

  This change in cutting force can be achieved by using a cutting resistance ratio A having a certain relationship with the rake angle α, obtained by the applicant of the present application by performing a cutting experiment described later.

  FIG. 2 is a diagram showing the relationship between the cutting resistance ratio A and the rake angle α, where the horizontal axis represents the rake angle α and the vertical axis represents the cutting resistance ratio A. The rake angle α is an angle of the rake face of the cutting edge 2 with respect to a line segment (radial line segment) F passing through the axis O of the cutting tool 1 as shown in FIG.

  FIG. 2 is a diagram obtained by conducting a cutting experiment on a representative grade of aluminum alloy. The cutting resistance ratio A is based on the value obtained when the rake angle is 0 degree with respect to the resultant force of the tangential force and the normal force of the cutting force measured during the cutting process. The solid line indicates the average value of the cutting force obtained by the experiment.

  The experimental conditions are as follows. The tool rotation speed was 2000 rpm, the feed rate was 150 mm / min, the axial cut was 5 mm, the radial cut was 2 mm, the tool diameter was 10 mm, and the number of blades was 4. In the experiment, two types of end mills having a twist angle of 30 degrees and 50 degrees were used, and the influence of the twist angle was also considered. The work material type was A5052 (JIS), and the lubricant was EC50 (5%) manufactured by Yushiro Chemical. In the experiment, a dynamometer (9263A) manufactured by Nippon Kistler was used for measurement of cutting resistance. Moreover, the tool made the carbide end mill.

  As understood from FIG. 2, the cutting resistance ratio A decreases as the rake angle α increases. Therefore, by changing the rake angle α continuously and appropriately in accordance with the change in the axial distance (L) of the cutting edge, the equation (1) is obtained for each of the axial distances (L) of the cutting edge described above. A reciprocal cutting resistance can be realized.

  The average value of the cutting resistance ratio A indicated by the solid line is expressed by the following equation (2) (that is, k = 0.0245).

Cutting resistance ratio A = exp (−0.0245α) (2)
The rake angle α can be accurately obtained by using the equation (2). And it becomes possible to prevent generation | occurrence | production of a forced chatter vibration by manufacturing the cutting tool which has the blade edge of this calculated | required rake angle (alpha) over the full length (the whole axial direction).

(Contents of cutting tool design method in this embodiment)
Below, the design method of the cutting tool in this embodiment is demonstrated concretely.

  Table 1 summarizes various conditions in Example 1 and the conventional example.

実施例１では第２切れ刃のすくい角α２を５度、第１切れ刃のすくい角α１を、本発明を適用して求めた角度（＊の部分）とした。なお、従来例では第１切れ刃のすくい角α１および第２切れ刃のすくい角α２をそれぞれ１０度と一定値にした。また、表１中の実施例１でピッチ角度につき、１１０−７０−１１０−７０度と記載しているが、これは、（第１切れ刃のピッチ角度）−（第２切れ刃のピッチ角度）−（第１切れ刃のピッチ角度）−（第２切れ刃のピッチ角度）ということを表している。このことは、従来例の各ピッチ角度についても同様であり、また、すくい角およびリード角についても同様です。

In Example 1, the rake angle α2 of the second cutting edge was 5 degrees, and the rake angle α1 of the first cutting edge was an angle (part indicated by *) obtained by applying the present invention. In the conventional example, the rake angle α1 of the first cutting edge and the rake angle α2 of the second cutting edge are set to constant values of 10 degrees, respectively. Moreover, although it describes as 110-70-110-70 degree | times per pitch angle in Example 1 in Table 1, this is (pitch angle of 1st cutting edge)-(pitch angle of 2nd cutting edge). )-(Pitch angle of the first cutting edge)-(pitch angle of the second cutting edge). The same applies to each pitch angle in the conventional example, and the same applies to the rake angle and lead angle.

  Other conditions were as follows. That is, the axial cut, the radial cut, the tool diameter (diameter), the number of blades, the blade length, and the lubricant are all the same in Example 1 and the conventional example, and are 5 mm, 2 mm, 10 mm, 4, 30 mm, respectively. EC50 (5%) manufactured by Yushiro Chemical was used. The tool rotation speed was 5000 rpm for Example 1 and 2000 rpm for the conventional example. The feed rate was 150 mm / min for the conventional example, and 500 mm / min for Example 1. Regarding the pitch angle, in the conventional example, the pitch angle φ1 of the first cutting edge is set to 100 degrees, the pitch angle φ2 of the second cutting edge is set to 80 degrees, and in Example 1, the pitch angle φ1 of the first cutting edge is set to 110 degrees. The pitch angle φ2 of the second cutting edge was set to 70 degrees. Regarding the lead angle, in the conventional example, the lead angle θ1 of the first cutting edge is 30 degrees and the lead angle θ2 of the second cutting edge is 31 degrees. In Example 1, the lead angle θ1 of the first cutting edge is 30 degrees. The lead angle θ2 of the second cutting edge was set to 35 degrees. The work material type was S45C (JIS) for the conventional example, and A5052 (JIS) for Example 1.

Example 1
First, the design contents of the rake angle α in the first embodiment will be described.

  In the unequal lead unequal pitch end mill of Example 1, since the rake angle α2 of the second cutting edge is 5 degrees, the cutting resistance ratio A2 of the second cutting edge is 0.885 from the following equation (3). Become.

Cutting resistance ratio A2 = exp (−0.0245α2) (3)
On the other hand, the cutting resistance ratio B at the position of the cutting edge tip (L = 0) of the tool is φ1 = 110 degrees, φ2 = 70 degrees, θ1 = 30 degrees, θ2 = 35 degrees, and from the above equation (1), B = 110/70 = 1.57 times. For this reason, it is necessary to reduce the cutting resistance ratio A1 of the first cutting edge to 1 / 1.57≈0.64 times (= 1 / B). The calculation of the cutting resistance ratio B may be performed prior to the calculation of the cutting resistance ratio A2 of the second cutting edge. The same applies to the following.

From the above, it cutting resistance ratio A1 of the first cutting edge is 0.885 × 0.6 37 (= A2 / B) = 0.56 4, sets the first cutting blade rake angle α1 It turns out that it is necessary.

Therefore, by the cutting resistance ratio A1 = 0.56 4 of the first cutting edge and the following equation (4), when determined by calculating back the rake angle α1 of the first cutting blade, the tip of the first cutting edge (L = 0 The rake angle α1 at the position of 5 degrees.

Cutting resistance ratio A1 = exp (−0.0245α1) (4)
Next, the calculation is performed in the same manner as described above for L = 10 mm. That is, the cutting resistance ratio B is 10 2 in the diameter (D) of the tool, φ1 = 110 degrees, φ2 = 70 degrees, θ1 = 30 degrees, θ2 = 35 degrees, and the formula (1) is 2.2 2 since the times, the cutting resistance ratio A1 of the first cutting edge, it is necessary to reduce the 1 / 2.2 2 ≒ 0.45 times reversed.

  From this, it can be seen that it is necessary to set the first cutting edge at the rake angle α1 at which the cutting resistance ratio A1 of the first cutting edge is 0.885 × 0.45 = 0.398.

Therefore, when the cutting resistance ratio A1 = 0.398 of the first cutting edge and the rake angle α1 of the first cutting edge are obtained by back calculation according to the equation (4), the rake at the position of L = 10 mm of the first cutting edge is obtained. The angle α1 is 37.5 degrees.

Subsequently, in the case of L = 20 mm, for the case L = 30 mm of the (cutting edge rear), by performing the same manner operation, the rake angle at the position of L = 20 mm of the first cutting blade α1 is 53 become .8 degrees, rake angle at the rear end position of L = 30 mm of the first cutting blade α1 becomes 74.5 degrees.

Finally, the rake angle α1 of each first cutting edge when L = 0 mm, 10 mm, 20 mm, and 30 mm. By performing interpolation based on 5 degrees, 37.5 degrees, 53.8 degrees, and 74.5 degrees, a curve α1 ′ of the rake angle of the first cutting edge continuously connected over the entire length of the blade length of 30 mm is obtained. The cutting edge shape is designed. In addition, as said curve (alpha) 1 ', what was connected continuously and smoothly is preferable.

  Note that the interpolation can be theoretically interpolated with an exponential function expressed by equation (4).

  In the cutting tool according to Example 1 manufactured based on the cutting edge shape designed as described above, the cutting resistances of the first cutting edge and the second cutting edge can be made the same at each distance. Thus, it is possible to prevent the occurrence of forced chatter vibration.

  On the other hand, in the unequal lead unequal pitch end mill of the conventional example, since the rake angle α is designed to be a constant 10 degrees regardless of the distance L from the tip, self-excited vibration does not occur. Machining vibration due to unequal division occurred inside, and the machining sound increased.

  When processing is performed using the cutting tool according to the first embodiment, it is considered that high-speed processing, high-efficiency processing, and the like can be performed in addition to further increase in the amount of cutting.

(Example 2)
In Example 1, the rake angle α of the cutting edge was obtained when an aluminum alloy (specifically, A5052 (JIS)) was used as the work material type. In Example 2, the rake angle α was obtained for a cast iron material. Using the relationship between the cutting resistance ratio A and the rake angle α, the rake angle α1 of the first cutting edge is obtained.

FIG. 4 is a diagram obtained by conducting a cutting experiment on a representative grade of cast iron material. As can be seen from this diagram, between the cutting force A and the rake angle α, the following equation (5)
Cutting resistance ratio A = exp (−0.0122α) (5)
(Ie, k = 0.0122). The cutting resistance ratio A is based on the value when the rake angle is 0 degree with respect to the resultant force of the tangential force and the normal force of the cutting force measured during the cutting process. The solid line in the figure shows the average value of cutting resistance obtained by experiment.

  The experimental conditions of the cutting experiment are as shown in Table 2. That is, the tool rotation speed was 2000 rpm, the feed rate was 150 mm / min, the axial cut was 5 mm, the radial cut was 2 mm, the tool diameter was 10 mm, and the number of blades was 4. In the experiment, two types of end mills having a twist angle of 30 degrees and 50 degrees were used, and the influence of the twist angle was also considered. As the work material type, FCD-S, FCD400, FC300 (JIS) were used, and the lubricant was EC50 (5%) manufactured by Yushiro Chemical. A dynamometer (9263A) manufactured by Nippon Kisler was used for the measurement of cutting resistance. Moreover, the tool made the carbide end mill.

実験に用いた工具は、第２切れ刃のすくい角α２を１０度とし、第１切れ刃のすくい角α１を、式（１）及び式（５）を適用して求めた角度（＊の部分）とした。すなわち、工具の軸方向距離Ｌ＝０，１０，２０，３０の場所での切削抵抗の比Ｂを式（１）から導出し、式（５）を用いて第２切れ刃のすくい角α２（＝１０）から切削抵抗比Ａ２を算出し、以下の式（６）
Ａ２／Ｂ＝ｅｘｐ（−０．０１２２α１）・・・（６）
を用いて第１切れ刃のすくい角α１を各Ｌに対して導出した。

The tool used for the experiment was such that the rake angle α2 of the second cutting edge was 10 degrees, and the rake angle α1 of the first cutting edge was obtained by applying the equations (1) and (5) (part of * ). That is, the cutting resistance ratio B at the location of the axial distance L = 0, 10, 20, 30 of the tool is derived from the equation (1), and the rake angle α2 (2) of the second cutting edge using the equation (5). = 10) The cutting resistance ratio A2 is calculated from the following equation (6)
A2 / B = exp (−0.0122α1) (6)
Was used to derive the rake angle α1 of the first cutting edge for each L.

  In the cutting tool according to the second embodiment, it becomes possible to make the cutting resistances of the first cutting edge and the second cutting edge the same at each portion where the distance L in the axial direction is different, and forced chatter vibration. Can be prevented.

Example 3
In Example 3, the rake angle α1 of the first cutting edge is obtained using the relationship between the cutting resistance ratio A and the rake angle α when a stainless steel material is used as the work material type. As the stainless steel material, 13Cr-3.8Ni, SUS630, 15-5PH, and SUS304 (JIS) were used.

FIG. 5 is a diagram obtained by conducting a cutting experiment on representative grades of stainless steel materials. As can be seen from this diagram, between the cutting force A and the rake angle α, the following equation (7)
Cutting resistance ratio A = exp (−0.0077α) (7)
(Ie, k = 0.777). The cutting resistance ratio A is based on the value when the rake angle is 0 degree with respect to the resultant force of the tangential force and the normal force of the cutting force measured during the cutting process. The solid line in the figure shows the average value of cutting resistance obtained by experiment. The experimental conditions for the cutting experiment are the same as the experimental conditions for the cutting experiment described in Example 2.

The tool used in the experiment is such that the rake angle α2 of the second cutting edge is 10 degrees, and the rake angle α1 of the first cutting edge is obtained by applying the equations (1) and (7) (part of * ). That is, the cutting resistance ratio B at the location of the axial distance L = 0, 10, 20, 30 of the tool is derived from the equation (1), and the rake angle α2 (2) of the second cutting edge using the equation (7). = 10) The cutting resistance ratio A2 is calculated from the following equation (8)
A2 / B = exp (−0.0077α1) (8)
Was used to derive the rake angle α1 of the first cutting edge for each L.

  In the cutting tool according to the third embodiment, it becomes possible to make the cutting resistances of the first cutting edge and the second cutting edge the same at each portion where the distance L in the axial direction is different, and forced chatter vibration. Can be prevented.

Example 4
In Example 4, the rake angle α1 of the first cutting edge is obtained using the relationship between the cutting resistance ratio A and the rake angle α when a carbon steel material is used as the work material type. SCW480, SCM440, S45C, S25C, and SACM645 (JIS) were used as the carbon steel material.

FIG. 6 is a diagram obtained by conducting a cutting experiment on representative grades of carbon steel materials. As can be seen from this diagram, between the cutting force A and the rake angle α, the following equation (9)
Cutting resistance ratio A = exp (−0.0188α) (9)
(Ie, k = 0.188). The cutting resistance ratio A is based on the value when the rake angle is 0 degree with respect to the resultant force of the tangential force and the normal force of the cutting force measured during the cutting process. The solid line in the figure shows the average value of cutting resistance obtained by experiment. The experimental conditions for the cutting experiment are the same as the experimental conditions for the cutting experiment described in Example 2.

The tool used in the experiment is such that the rake angle α2 of the second cutting edge is 10 degrees, and the rake angle α1 of the first cutting edge is obtained by applying the equations (1) and (9) (part of * ). That is, the cutting resistance ratio B at the location of the axial distance L = 0, 10, 20, 30 of the tool is derived from the equation (1), and the rake angle α2 (2) of the second cutting edge using the equation (9). = 10) The cutting resistance ratio A2 is calculated from the following equation (10)
A2 / B = exp (−0.0188α1) (10)
Was used to derive the rake angle α1 of the first cutting edge for each L.

  In the cutting tool according to the fourth embodiment, it is possible to make the cutting resistances of the first cutting edge and the second cutting edge the same at each portion where the distance L in the axial direction is different, forcing chatter vibration. Can be prevented.

  Note that, in the above-described Patent Document 1, it is disclosed that, in a cutting tool having an unequal pitch, the rake angle is uniquely increased as the pitch angle is increased. However, when this disclosure is applied to cutting tools with unequal pitch and unequal leads, the cutting resistances of cutting edges moving back and forth in the circumferential direction cannot be made equal. More specifically, in the unequal pitch unequal lead cutting tool shown in FIG. 5, the distance c1 between the cutting edges 121 and 122 is larger than the distance c2 between the cutting edges 121 and 122 at the position C in the axial direction. This is because at the position D, the distance d1 between the cutting edges 121 and 122 is smaller than the distance d2 between the cutting edges 121 and 122, and the distance between the cutting edges is reversed depending on the position in the axial direction.

  In the embodiment described above, an example in which the rake angle α2 of the second cutting edge is made constant and the rake angle α1 of the first cutting edge is calculated has been described, but the present invention is not limited thereto, and the second Of course, the calculation can be performed by changing the rake angle α2 of the cutting edge and calculating the rake angle α1 of the first cutting edge.

  In the above-described embodiment, an example is described in which the rake angle α2 of the second cutting edge is made constant and the rake angle α1 of the first cutting edge is calculated, but the present invention is not limited to this, The same can be applied to the case where the rake angle α1 of the first cutting edge is made constant or changed, and the rake angle α2 of the second cutting edge is calculated.

Claims (2)

A pair of first cutting edges and second cutting edges at symmetrical positions with an axial center on the peripheral surface, and each of the adjacent first cutting edges and second cutting edges in advance in the rotational direction Each of the cutting edges was provided with unequal leads with different lead angles with respect to the axis of the first cutting edge and the second cutting edge, which were alternately arranged at unequal pitches with different intervals. A cutting tool design method,
The lead angle of the first cutting edge is θ1, the lead angle of the second cutting edge is θ2, the pitch angle of the first cutting edge is φ1, the pitch angle of the second cutting edge is φ2, the rake angle of the second cutting edge is α2, The first cutting edge with respect to the cutting resistance of the second cutting edge according to the following formula (1) for a plurality of distances within the range from the leading edge to the trailing edge of the cutting edge in the axial direction, where the tool diameter is D The cutting resistance ratio B is calculated, and before or after the calculation of the cutting resistance ratio B, the cutting resistance of the second cutting edge when the rake angle α2 of the second cutting edge is obtained by the following equation (2): The ratio A2 is calculated, and the calculated cutting force ratio A2 is divided by each of the cutting force ratios B to obtain a divided value A2 / B. The following equation (3) is used to obtain the divided value A2 / B. Obtaining a rake angle α1 of the first cutting edge at each of the plurality of distances;
B = {L (tan θ2−tan θ1) + Dφ1π / 360}
/ {L (tan θ1−tan θ2) + Dφ2π / 360} (1)
However, L is the distance from the tip of the cutting edge in the axial direction.
A2 = exp (−k · α2) (2)
A2 / B = exp (−k · α1) (3)
However, k is a coefficient.
Subsequently, calculating a rake angle curve α1 ′ of the first cutting edge continuously connecting all the rake angles α1 based on the rake angles α1 of all the first cutting edges obtained. A cutting tool design method characterized by the above.   A pair of first cutting edge and second cutting edge in a symmetrical position with the axis centered on the peripheral surface, and the distance between the adjacent first cutting edge and second cutting edge in the rotational direction. Each of the cutting edges was provided with unequal leads with different lead angles with respect to the axial centers of the first cutting edge and the second cutting edge. A cutting tool, wherein the rake angle of the first cutting edge and the rake angle of the second cutting edge are designed using the cutting tool design method according to claim 1.

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