JP2016155215A - Work-piece machining method and work-piece machining system - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a work-piece machining method and a work-piece machining system capable of suppressing chattering vibration when a high-hardness work-piece is machined by an end mill.SOLUTION: A work-piece machining system 10 includes a machine tool 20 and an end mill 30. The end mill 30 is fitted to a spindle 26 of the machine tool 20. The end mill 30 is an unequal reed end mill provided with four sheets of cutting blades. The machine tool 20 relatively moves a work-piece 40 and the end mill 30 which rotates together with the spindle 26 and, thereby, cuts the work-piece 40. The work-piece 40 is cut on condition that a value of a/Δa gets 0.354 or more. The value of ais stability limit cut [mm] of an equal pitch end mill when the equal pitch end mill cuts the work-piece 40 in place of the end mill 30. Δa is an interval [mm] in the axial direction of a reproduction effect offset lines adjacent to each other in a reproduction effect offset diagram of the end mill 30.SELECTED DRAWING: Figure 1

Description

  The present invention relates to a workpiece machining method and a workpiece machining system.

  It is known that when a difficult-to-cut material formed from stainless steel or the like is processed as an workpiece by an end mill, chatter vibration is likely to occur, and the surface properties of the cut workpiece are deteriorated. It is also known that when chatter vibration occurs during cutting, the tool life of the end mill is reduced. For example, Non-Patent Document 1 discloses a machining method for cutting a workpiece formed from SUS304 with an unequal lead end mill as a workpiece machining method for suppressing chatter vibration when machining a workpiece with an end mill.

Yuuji Takagi, Yoshihiko Kimura "Examination of Unequal Lead End Mill for Chatter Vibration Suppression"

  For example, when a high-hardness workpiece that has been subjected to a hardening process such as a quenching process is processed by the above-described workpiece processing method, chatter vibration may occur due to the specific cutting resistance of the high-hardness material. In this case, the surface properties of the high-hardness workpiece cut by the end mill deteriorate. Therefore, it may be difficult to finish with an end mill so that a high-hardness workpiece becomes a highly accurate sliding part such as a cam.

  An object of the present invention is to provide a workpiece machining method and a workpiece machining system capable of suppressing chatter vibration when machining a high hardness workpiece with an end mill.

A workpiece machining method according to a first aspect of the present invention is a workpiece machining method for cutting a workpiece by relatively moving an end mill mounted on a rotating spindle of a machine tool and a high hardness workpiece. The end mill includes a plurality of cutting edges twisted with respect to the axial direction of the end mill and arranged in the circumferential direction of the end mill, and the plurality of cutting edges include two cutting edges having different twist angles. In the condition that the value of the formula (1) shown below is 0.165 or more,
a _lim / Δa (1)
(A _lim : axial stability limit cut [mm] of the equi-pitch end mill when the equi-pitch end mill cuts the workpiece, Δa: adjacent regeneration in the regeneration effect offset diagram of the unequal lead end mill The effect canceling line is spaced in the axial direction [mm]) and the workpiece is cut. According to the first aspect, the effect of suppressing chatter vibration is enhanced by cutting the workpiece under the condition that the value of the expression (1) is 0.165 or more. Therefore, the workpiece machining method can suppress chatter vibration when a high-hardness workpiece is cut with an end mill.

  In the workpiece machining method, the workpiece may be cut under a condition that the value of the expression (1) is 0.354 or more. In this case, the chatter vibration suppressing effect is further enhanced. Therefore, the workpiece machining method can further suppress chatter vibration.

A workpiece machining system according to a second aspect of the present invention includes a machine tool having a main shaft and an end mill that can be mounted on the main shaft. The workpiece machining system has a relatively high hardness and the end mill mounted on the rotating main shaft. A workpiece machining system for cutting the workpiece by moving the workpiece, wherein the end mill includes a plurality of cutting edges that are twisted with respect to an axial direction of the end mill and arranged in a circumferential direction of the end mill, The cutting edge is an unequal lead end mill including two cutting edges having different twist angles, and the machine tool includes the workpiece and the unequal lead end mill mounted on the rotating spindle. In a condition that the relative movement and the value of the formula (1) shown below is 0.165 or more,
a _lim / Δa (1)
(A _lim : axial stability limit cut [mm] of the equal pitch end mill when the equal pitch end mill cuts the workpiece, Δa: adjacent to each other in the non-uniform lead end mill regeneration effect offset diagram A distance between the regenerative effect canceling lines in the axial direction [mm]), and cutting the workpiece. According to the 2nd aspect, there can exist an effect similar to the workpiece | work processing method of a 1st aspect.

A workpiece machining method according to a third aspect of the present invention is a workpiece machining method for cutting a workpiece by relatively moving an end mill mounted on a rotating spindle of a machine tool and a high hardness workpiece. The end mill includes a plurality of cutting edges twisted with respect to an axial direction of the end mill and arranged in a circumferential direction of the end mill, and the plurality of cutting edges include two cutting edges having different twist angles. In the unequal lead end mill included, the condition that the cutting angle range Q in the radial direction of the unequal lead end mill is within 0.095 [rad], and the value of equation (2) shown below is 9 .401 × 10 ⁻³ or more,
(Ω _c : natural angular frequency [rad / s] of the unequal lead end mill, E: Young's modulus [GPa] of the material forming the unequal lead end mill, β ₁ , β ₂ : the two cutting edges The twist angle [deg], n: rotational speed of the unequal lead end mill [min ⁻¹ ], H: hardness of the workpiece [HV], N: the number of the plurality of cutting edges, D: the unequal lead End mill tool diameter [mm], l: protrusion length of the unequal lead end mill [mm]) The workpiece is cut. According to the third aspect, the cutting angle range Q in the radial direction of the unequal lead end mill is 0.095 [rad] or less, and the value of the formula (2) is 9.401 × 10 ⁻³ or more. The workpiece is cut. When the workpiece is cut, the chatter vibration suppression effect is enhanced. Therefore, the workpiece machining method can suppress chatter vibration when a high-hardness workpiece is cut with an end mill.

The said workpiece | work processing method may cut the said workpiece | work on the conditions from which the value of said Formula (2) becomes 20.205 * 10 < ^-3 > or more. In this case, the workpiece machining method can further enhance the chatter vibration suppressing effect.

In the workpiece machining method, the twist angles of the two cutting edges may be different from each other by 2 ° or more. In this case, the value of tan β ₂ -tan β ₁ in equation (2) increases. Therefore, even if n, H, N, and Q increase, the value of equation (2) tends to be 9.401 × 10 ⁻³ or more. Therefore, the workpiece machining method can cut the workpiece while suppressing chatter vibration even under conditions where n, H, N, and Q are increased.

A workpiece machining system according to a fourth aspect of the present invention includes a machine tool having a main shaft, an end mill that can be mounted on the main shaft, a high-hardness workpiece, and the end mill that is mounted on the rotating main shaft. A workpiece processing system for cutting the workpiece by relatively moving, wherein the end mill includes a plurality of cutting edges twisted with respect to an axial direction of the end mill and arranged in a circumferential direction of the end mill. The cutting edge is an unequal lead end mill including two cutting edges having different twist angles, and the machine tool includes the workpiece and the unequal lead end mill mounted on the rotating spindle. Are moved relative to each other, and the cutting angle range Q in the radial direction of the unequal lead end mill is within 0.095 [rad], and is shown below. The value of the expression (2) that is in a condition to be 9.401 × ^{10 -3} or more,
(Ω _c : natural angular frequency [rad / s] of the unequal lead end mill, E: Young's modulus [GPa] of the material forming the unequal lead end mill, β ₁ , β ₂ : the two cutting edges The twist angle [deg], n: rotational speed of the unequal lead end mill [min ⁻¹ ], H: hardness of the workpiece [HV], N: the number of the plurality of cutting edges, D: the unequal lead End mill tool diameter [mm], l: protrusion length of the unequal lead end mill [mm]) The workpiece is cut. According to the 4th aspect, there can exist an effect similar to the workpiece processing method of a 3rd aspect.

1 is a perspective view of a workpiece processing system 10. FIG. 1 is an overall view of an end mill 30. FIG. It is explanatory drawing of the vibration mode which exists when the end mill 30 cuts the workpiece | work 40. FIG. It is a conceptual diagram of the end mill 30 and the workpiece | work 40 of FIG.3 (b). It is a reproduction effect cancellation diagram of end mill 5. It is a figure which shows the positional relationship of the end mill 5 and the workpiece 50. FIG. It is explanatory drawing which shows the mechanism by which a reproduction effect is canceled. FIG. 6 is a diagram illustrating a difference between an axial position from a point A to a point C in FIG. 5 and a phase delay of a cutting edge of the end mill 5. It is a figure which shows the specification of the end mills 1-6. It is a figure which shows the pitch angle and the twist angle in each front-end | tip of the end mills 5 and 6. FIG. It is a three-view figure of workpiece 50A, 50B. It is a figure which shows the dimension W1, W2 corresponding to each of workpiece 50A, 50B. It is a figure which shows the conditions of cutting experiment. It is explanatory drawing which shows the processing machine 100 used for the cutting experiment. It is a figure which shows the presence or absence of chatter vibration in the cutting which used the end mills 1 and 2. FIG. It is a figure which shows the presence or absence of the chatter vibration in the cutting process using the end mills 3 and 4. FIG. It is a figure which shows the presence or absence of chatter vibration in the cutting which used the end mills 5 and 6. FIG. It is a figure which shows the processed surface 55 of the workpiece 50B to which the cutting process was given. It is explanatory drawing which shows the processing machine 200 and dynamometer 256 used for the measurement of specific cutting resistance.

<1. Outline of Work Machining System 10>
The outline | summary of the workpiece processing system 10 which is one Embodiment of this invention is demonstrated. The workpiece machining system 10 is a workpiece machining system that cuts the workpiece 40 while suppressing chatter vibration. One example of chatter vibration is self-excited chatter vibration. Self-excited chatter vibration is disclosed by a well-known document (for example, Eiji Shamoto “Generation mechanism and suppression of chatter vibration in machining”, Electric Steel / Daido Special Steel Technique Vol. 82, No. 2). Self-excited chatter vibration is vibration that occurs when a closed loop exists in the cutting process that feeds back and expands the vibration. Self-excited chatter vibration includes mode coupling type self-excited chatter vibration and regenerative type self-excited chatter vibration. The mode coupling type self-excited chatter vibration is generated when the vibration modes in two directions (for example, two directions orthogonal to each other in the radial direction of the tool) have resonance frequencies close to each other. . In the regenerative self-excited chatter vibration, the vibration that occurred when the tool was cut one revolution before (one blade before when it is a multi-blade tool) remains as the undulation on the work surface of the workpiece, leaving the vibration as the undulation. Is regenerated as a variation in the cut thickness in the current cutting. For this reason, a closed loop is formed in which the cutting force of the tool fluctuates to generate vibration again. When the loop gain increases, vibration generated by some kind of growth grows and regenerative self-excited chatter vibration occurs.

<2. Configuration of Workpiece Processing System 10>
The configuration of the workpiece machining system 10 will be described with reference to FIGS. In the following description, the upper, lower, right diagonally downward, left diagonally upward, left diagonally downward, and right diagonally upward of FIG. 1 are respectively referred to as the upward, downward, rightward, leftward, forward, and forward of the workpiece processing system 10, respectively. It will be backward. The left-right direction, the front-rear direction, and the up-down direction of the workpiece machining system 10 are an X-axis direction, a Y-axis direction, and a Z-axis direction, respectively.

  The workpiece machining system 10 includes a machine tool 20 and an end mill 30. The machine tool 20 is a machine that rotates the end mill 30 mounted on the main shaft 26 at a high speed, moves the workpiece 40 mounted on the work table 21, and performs a cutting process on the workpiece 40.

  The structure of the machine tool 20 will be described with reference to FIG. The machine tool 20 includes a base 22, a column 25, a spindle head 27, a spindle 26, a work table 21, and a control box 24. The base 22 is a metal substantially rectangular parallelepiped base. The column 25 is a prism that extends upward from the base 22. The spindle head 27 is provided so as to be movable in the Z-axis direction along the front surface of the column 25. The spindle head 27 moves when a Z-axis motor (not shown) is driven. The spindle head 27 supports the spindle 26 rotatably inside. The main shaft 26 has a mounting hole at the lower end. The end mill 30 is attached to the attachment hole via a tool holder. The spindle head 27 is provided with a spindle motor (not shown). The main shaft 26 rotates by driving the main shaft motor. The work table 21 is provided in the upper center of the base 22. The work table 21 is movable in the X-axis direction and the Y-axis direction by an X-axis motor (not shown), a Y-axis motor (not shown), and a guide mechanism (not shown).

  The control box 24 stores a numerical control device (not shown). The numerical control device controls the X-axis motor, the Y-axis motor, and the Z-axis motor based on the NC program, so that the work 40 held on the work table 21 and the end mill 30 mounted on the main shaft 26 are relative to each other. Move.

  The end mill 30 will be described with reference to FIG. The end mill 30 of the present embodiment is an unequal lead end mill having four cutting edges 33, and the protruding length from the main shaft 26 is 36 mm. For example, the end mill 30 of the present embodiment has a tool diameter (diameter) of 8 mm and a length of 70 mm. The four cutting edges 33 are formed within a range of at least 15 mm from the tip of the end mill 30. The four cutting edges 33 are twisted with respect to the axial direction of the end mill 30 and are arranged side by side in the circumferential direction of the end mill 30.

  The four cutting edges 33 include two cutting edges 33 having different twist angles (lead angles). In the end mill 30 of the present embodiment, for example, the twist angle of two of the four cutting edges 33 is 40 °, and the twist angle of the other two cutting edges 33 is 45 °. . For example, the four cutting edges 33 in the present embodiment are alternately arranged along the circumferential direction of the end mill 30 with cutting edges 33 having a twist angle of 40 ° and cutting edges 33 having a twist angle of 45 °.

  Hereinafter, of the cutting edges 33 provided in the end mill 30, the difference in twist angle between two cutting edges 33 having different twist angles is simply referred to as “angle difference of twist angles”. The difference in the twist angle of the end mill 30 in this embodiment is 5 °. The difference in twist angle of the end mill 30 may be 2 ° or more, and preferably 5 ° or more. When the difference in twist angle is 2 ° or more, the workpiece machining system 10 can exhibit an effect of suppressing chatter vibration when the workpiece 40 is cut.

  The number of cutting edges 33 provided in the end mill 30 may be two or more. For example, when the number of cutting edges 33 is four, each cutting edge 33 faces the other one cutting edge 33 with the axis of the end mill 30 interposed therebetween. Therefore, the rotation of the end mill 30 that rotates with the main shaft 26 is easily stabilized. In addition, since the number of the cutting edges 33 is four, the workpiece 40 is cut by the cutting edge 33 during one rotation of the end mill 30 as compared with the case where the number of the cutting edges is two or three. The number of times increases. Thereby, the end mill 30 can cut the workpiece 40 efficiently in a short time. Furthermore, when the number of the cutting edges 33 is four, the end mill 30 in which the difference in twist angle is 2 ° or more is easier to manufacture than in the case of five or more.

  With reference to FIG. 1, the workpiece | work 40 made into the cutting object by the workpiece | work processing system 10 is demonstrated. The workpiece 40 is a high hardness workpiece. The high-hardness workpiece is a workpiece having a hardness of 210 HV or more and 1000 HV or less. An example of a workpiece having a hardness of 210 HV or more and 1000 HV or less is a hardened steel. The material of the hardened steel is, for example, SK105, S45C, or SUJ3. The workpiece 40 of this embodiment is a hardened steel whose material is SK105. The hardness of the workpiece 40 is, for example, 697HV (60HRC).

<3. Machining Method in Work Machining System 10>
With reference to FIG. 1, the processing method of the workpiece | work 40 in the workpiece | work processing system 10 is demonstrated. The end mill 30 is mounted in a mounting hole (not shown) of the main shaft 26 via a tool holder, and the work 40 is attached to the work table 21 via a mounting jig (not shown). The machine tool 20 drives a Z-axis motor (not shown) to adjust the height of the end mill 30. The machine tool 20 drives a spindle motor (not shown) and rotates the spindle 26. The end mill 30 rotates with the main shaft 26. As an example, the rotation speed of the end mill 30 of this embodiment is 6000 [min ⁻¹ ].

  The machine tool 20 drives an X-axis motor and a Y-axis motor (not shown), adjusts the position of the workpiece 40, and then drives an X-axis motor (not shown) to move the workpiece 40 along the X-axis direction. . The workpiece 40 moves relative to the rotating end mill 30. The machine tool 20 cuts the workpiece 40 with four rotating cutting edges 33. The cutting depth d [mm] of the workpiece 40 in the axial direction of the end mill 30 is not limited, but is preferably 6 mm or less. In other words, when the tool diameter of the end mill 30 is D [mm], it is preferable that the workpiece 40 is cut under the condition that d / D is 0.75 (= 6/8) or less. In the present embodiment, the machine tool 20 cuts the workpiece 40 by setting the cutting depth in the axial direction of the end mill 30 to 6 mm.

  At the same time, the machine tool 20 cuts the workpiece 40 with a low depth of cut in the radial direction of the end mill 30. The cutting with a low cutting amount is a cutting with a very small cutting amount δ [mm] in the radial direction of the end mill 30 (see FIG. 3B), for example, finishing. More specifically, the low cutting amount cutting is a cutting in which the radial cutting amount δ [mm] (hereinafter sometimes simply referred to as the cutting amount δ) is 0.018 mm or less, preferably cutting. This is a cutting in which the insertion amount δ is 0.012 mm or less.

  The workpiece 40 moves in the X-axis direction while being cut with a low depth of cut in the radial direction of the end mill 30. Thereby, the machine tool 20 performs cutting on the workpiece 40.

  With reference to FIG. 3B and FIG. 4, the cutting amount δ [mm] and the cutting angle range Q [rad] in the radial direction of the end mill 30 (hereinafter sometimes simply referred to as the cutting angle range Q) and The relationship will be described. FIG. 3 is a schematic view of the end mill 30 and the workpiece 40 when viewed along the axial direction of the end mill 30. FIG. 4 is a further simplified view of the end mill 30 and the workpiece 40 shown in FIG. In FIG. 4, illustration of the four cutting edges 33 of the end mill 30 is omitted.

The cutting angle range Q is determined when the rotation angle at the position where each cutting edge 33 (see FIG. 3) cuts the workpiece 40 most in the radial direction of the end mill 30 (point M shown in FIG. 4) is 0 °. Reference numeral 33 denotes an engagement angle for cutting the surface of the workpiece 40. The cutting angle range Q is obtained by Expression (3).
Q = cos ⁻¹ ((D−2δ) / D) (3)
According to Equation (3), when the cutting depth δ is 0.018 mm, the cutting angle range Q is 0.09490 [rad], and when the cutting depth δ is 0.012 mm, the cutting angle range Q is 0.077748 [rad]. Accordingly, the low cutting amount cutting is cutting in which the cutting angle range Q is 0.095 [rad] or less, and preferably corresponds to cutting in which the cutting angle range Q is 0.078 [rad] or less. .

  With reference to FIG. 3, the effect by which the machine tool 20 cuts the workpiece | work 40 with the low cutting amount in the radial direction of the end mill 30 is demonstrated. The end mill 30 may be mounted on the machine tool 20 in a state of protruding from the main shaft 26 so that the main shaft 26 (see FIG. 1) and the above-described mounting jig (not shown) do not interfere during cutting. is there. The end mill 30 that protrudes long from the main shaft 26 is likely to be less rigid than the workpiece 40. Therefore, when the cutting depth δ in the radial direction is large, vibration modes having resonance frequencies close to each other exist in the two radial directions of the end mill 30 (see FIG. 3A), so The chatter vibration is likely to occur. However, as shown in FIG. 3B, since the cutting amount in the radial direction of the end mill 30 is extremely small, the cutting process by the end mill 30 is approximately approximated to a cutting process in one direction. Therefore, the mode coupling type self-excited chatter vibration is difficult to grow. Therefore, the workpiece machining system 10 can cut the workpiece 40 while suppressing the mode coupling type self-excited chatter vibration.

  The effect of the machine tool 20 cutting the workpiece 40 with the end mill 30 having a torsion angle difference of 5 ° will be described. When the specific cutting resistance is large because the hardness of the workpiece 40 is high, or when the axial direction cutting of the end mill 30 is large, regenerative self-excited chatter vibration is generated even if the cutting amount in the radial direction of the end mill 30 is extremely small. It becomes a problem. However, the end mill 30 having a torsional angle difference of 5 ° has a high effect of suppressing regenerative self-excited chatter vibration, as verified by evaluation in Examples 1 and 2 described later. Therefore, the workpiece machining system 10 can cut the workpiece 40 while suppressing regenerative self-excited chatter vibration.

The workpiece machining system 10 cuts the workpiece 40 by the end mill 30 under the condition that the value of the expression (1) shown below is 0.354 or more.
a _lim / Δa (1)
Here, a _lim is an axial stability limit cut [mm] of the equal pitch end mill when an equal pitch end mill (not shown) cuts the workpiece 40 instead of the end mill 30. The stability limit cut is an amount of cut in the axial direction when the end mill to be cut can suppress chatter vibration regardless of the rotation speed in cutting using a general end mill. The stability limit cut a _lim is a so-called unconditional stability limit. Δa is an interval [mm] at which adjacent reproduction effect cancellation lines on a reproduction effect cancellation diagram, which will be described later, are separated from each other in the axial direction of the end mill (that is, the vertical axis direction of the reproduction effect cancellation diagram). That is, Δa is the offset line interval.

In the present embodiment, a _lim is 1.415 [mm], and Δa is 3.997 [mm]. As will be described later, Expression (1) is a new expression related to the present invention, and is an expression used when it is determined whether chatter vibration can be suppressed. The workpiece machining system 10 can suppress chatter vibration by cutting the workpiece 40 under the condition that the value of the expression (1) is 0.354 or more.

As will be described later, Expression (1) can be replaced with Expression (2). The expression (2) is a new expression related to the present invention similar to the expression (1), and is an expression used when it is determined whether chatter vibration can be suppressed.
Here, ω _c is the natural angular frequency [rad / s] of the end mill 30. E represents the Young's modulus of the material forming the end mill 30 as E [GPa]. β ₁ and β ₂ [deg] are twist angles of the cutting edge of the end mill 30. n [min ⁻¹ ] is the rotation speed of the end mill 30. H [HV] is the hardness of the workpiece 40. N is the number of cutting edges of the end mill 30. Q [rad] is a cutting angle range in the radial direction of the end mill 30. D [mm] is the tool diameter of the end mill 30. l [mm] is the protruding length of the end mill 30.

In this embodiment, ω _c is 7816π [rad / s] obtained by multiplying 3908 Hz, which is the maximum negative real part frequency of the end mill 30, by 2π. E is 604 [GPa]. β ₁ and β ₂ are 45 ° and 40 °, respectively. n is 6000 min ⁻¹ . H is 697 HV. N is four. Q is 0.077748 [rad]. D is 8 mm. l is 36 mm. Therefore, the value of Expression (2) is 20.205 × 10 ⁻³ . The workpiece machining system 10 can suppress chatter vibration by cutting the workpiece 40 under the condition that the value of the expression (2) is 20.205 × 10 ⁻³ .

<4. Various evaluations>
Hereinafter, the evaluation performed in order to identify the processing conditions for suppressing the regenerative self-excited chatter vibration will be described. In Example 1, the reproduction effect cancellation diagram was created so that the conditions of the end mill that can suppress the regenerative self-excited chatter vibration were specified. In Example 2, a cutting experiment was performed using a plurality of end mills including the end mill specified in Example 1. In Example 3, a cutting experiment was performed using a standard end mill in order to specify the cutting angle range Q for suppressing regenerative self-excited chatter vibration. In the cutting experiment conducted in Examples 2 and 3, it was evaluated whether chatter vibration was suppressed.

Example 1
With reference to FIGS. 5 to 9, evaluation using the reproduction effect cancellation diagram will be described. The regenerative effect canceling line is a straight line indicating the rotational speed at which the regenerative self-excited chatter vibration is suppressed on the graph showing the relationship between the rotational speed of the end mill and the axial cutting amount of the end mill. By creating the regenerative effect cancellation diagram, the mechanism for suppressing the regenerative chatter vibration is qualitatively understood, and the conditions of the end mill for suppressing the regenerative chatter vibration are specified.

A reproduction effect cancellation diagram will be described. The condition that the regenerative self-excited chatter vibration is suppressed by the unequal pitch end mill is expressed by the following equation (4) depending on the chatter vibration frequency, the unequal pitch angle difference, and the tool rotation speed.
n [min ⁻¹ ] is the tool rotation number, θ ₁ and θ ₂ [rad] are the pitch angles, f _c [Hz] is the chatter vibration frequency, and m is an arbitrary integer.

In this evaluation, for the sake of simplicity, the maximum negative real part frequency is used instead of the chatter vibration frequency. The maximum negative real part frequency is identified when the end mill tip is subjected to impulse excitation. For example, the maximum negative real part frequency of a 6-flute end mill is 3741 Hz, and the maximum negative real part frequency of a 4-blade end mill is 3908 Hz. However, it is known that the frequency of the actual regenerative self-excited chatter vibration does not always coincide with the maximum negative real part frequency and is in the vicinity of the maximum negative real part frequency. If the pitch angle of the end mill is θ ₁ , θ ₂ , θ ₃ ,... Along the circumferential direction, θ ₁ = θ ₃ , θ ₂ = θ ₄ , θ ₁ + θ ₂ = π in the four-flute end mill. [rad] is a, a 6-blade end _{mill, θ 1 = θ 3 = θ} 5, θ 2 = θ 4 = θ 6, are _{θ 1 + θ 2 = 2π /} 3 [rad].

  In this evaluation, among the end mills 1 to 6 shown in FIG. The end mills 1 and 2 are equal pitch end mills, the end mills 3 and 4 are unequal pitch end mills, and the end mills 5 and 6 are unequal lead end mills.

The pitch angle difference of the end mill 3 which is a six-blade unequal pitch end mill is 3 °. Regarding the end mill 3, 3741 min ⁻¹ is obtained when m = 0 as the rotational speed at which the regenerative self-excited chatter vibration is suppressed based on the equation (4). The reproduction effect offset line for the end mill 3 is indicated by an arrow in FIG.

The pitch angle difference of the end mill 4 which is a four-blade unequal pitch end mill is 4.6 °. For the end mill 4, based on the equation (4), as the rotation speed of self-excited chatter vibration of the reproduction type is suppressed, 1997Min ^-1 is obtained in the case of m = 1, is 5992Min ^-1 in the case of m = 0 can get. The regenerative effect cancellation line for the end mill 4 is indicated by an arrow in FIG.

Consider expanding the conditions for suppressing the regeneration effect to the case of unequal lead end mills. Regeneration effect is attributed to the vibration marks one blade before a cut thickness variation in chatter vibration frequency f _c. FIG. 5 illustrates an example of an end mill 5 (see FIG. 9) that is a four-blade unequal lead end mill. The difference in twist angle of the end mill 5 is 1 ° (45 ° / 44 °). Cutting edges located at a position of 7.7 mm from the tip of the end mill 5 have an equal pitch. Hereinafter, as shown in FIG. 6, a case is considered in which the end mill 5 cuts the workpiece 50 in a state where the tip of the end mill 5 is positioned 1 mm below a workpiece 50 described later. Further, the cutting depth d (see FIG. 6) in the axial direction of the end mill is referred to as an axial position d. First, the pitch angle theta ₁ of the cutting edge in the axial position d of the end _mill, is assigned to theta _2, the the maximum negative real portion of the case of four blade end mill 3908Hz is assigned to chatter vibration frequency f _c, Based on the equation (4), a tool rotation speed n capable of suppressing the regeneration effect is obtained. In FIG. 5, the relationship obtained based on Expression (4) with respect to the axial position d and the tool rotation speed n is indicated by a broken line.

  Next, consider the effect of the pitch angle gradually changing due to unequal leads. At a specific rotational speed, the pitch angle difference is an optimum value satisfying the expression (4) at the axial position on the broken line in FIG. 5, and the reproduction effect is canceled out. At axial positions slightly above and below the broken line, the reproduction effect is not completely canceled and a slight reproduction effect occurs. However, the reproduction effect that occurs above the broken line and the reproduction effect that occurs below the broken line have opposite phases. Therefore, the two reproduction effects cancel each other out in a range of heights that are equal in the vertical direction from the broken line. Therefore, the reproduction effect disappears. For example, at point B in FIG. 5, the reproduction effect at each blade cancels out. The reproduction effect remaining in the range from the point B to the point A is canceled by the antiphase reproduction effect generated in the range from the point B to the point C. Therefore, the axial effect indicated by the point A suppresses the regeneration effect as a whole tool.

With reference to FIG. 7, the cancellation of the reproduction effect will be specifically described. 7 (a), (b), and (c) are shown in the left diagram, in which the plurality of cutting edges are out of phase at the axial positions of points A, B, and C at the rotational speed of 6000 min ⁻¹ shown in FIG. A state in which machining is performed with vibration is schematically shown. FIG. 7 shows a schematic diagram of a two-blade end mill for ease of explanation. The right diagram of FIG. 7 shows wave removing, which is a component that the vibration of the previous blade regenerates, and wave cutting, which is the vibration component of the current blade, in each cutting, and each cutting is performed with the same wave cutting phase. Has been redrawn. Wave cutting basically does not make the machining system unstable because it does not involve a phase delay. On the other hand, wave removing is accompanied by a phase lag and causes unstable regenerative self-excited chatter vibration. The pitch angle difference Δθ _B (= θ _B2 −θ _B1 ) of the point B on the straight line of m = −1 in FIG. 3 is expressed as f _c = 3908 [Hz] and n = 6000 [min in Equation (4). ⁻¹ ] and m = −1 are obtained. That is, Δθ _B = (1 + 2m) π × n / (60f _c ) = − π × 6000 / (60 × 3908) = − 0.08039 [rad]. The axial position d _B of the point B is d _B = 7.7-1-(− Δθ _B ) × 2 / (1−tan 44 °) = 2.014 [mm]. Regarding the pitch angle θ _B1 of the second blade relative to the first blade and the pitch angle θ _B2 of the first blade relative to the second blade, θ _B2 = (2π + Δθ from θ _B2 + θ _B1 = 2π [rad]. _B ) /2=3.101 [rad] and [theta] _B1 = [theta] _B2 + [Delta] [theta] _B = 3.182 [rad].

Consider the phase delay φ _B1 of the second blade relative to the first blade and the phase delay φ _B2 of the first blade relative to the second blade. As shown in the left diagram of FIG. _{6 (b), φ B1 =} θ B1 × 60 / n × f c = 3.182 × 60/6000 × 3908-2π × 19 = 4.964 [rad] becomes, phi _B2 = Θ _B2 × 60 / n × f _c = 3.11 × 60/6000 × 3908-2π × 19 = 1.822 [rad]. In a normal equi-pitch end mill, since these phase lags are equal, the reproduction effect is strengthened. In this study, the difference in phase lag between φ _B1 and φ _B2 is Δφ _B = φ _B1 −φ _B2 = Since it is π [rad], the wave removing of the first blade and the wave removing of the second blade cancel each other and the reproduction effect is eliminated.

Next, the axial positions d _A and d _{C at} the points A and C and the pitch angle differences Δθ _A and Δθ _C will be examined. d _A , d _C , Δθ _A , and Δθ _C are values necessary for calculating the phase lag at points A and C. The distances from the point B are the same in the axial positions of the points A and C (see FIG. 5). Therefore, d _A = d _B × 2 = 2.014 × 2 = 4.028 [mm] and d _C = 0 [mm]. The pitch angle difference between point A and point C is Δθ _A = (d _A −6.7) × (1−tan 44 °) /2=−0.04583 [rad], and Δθ _C = (d _C −6). 7) × (1-tan44 °) /2=−0.1149 [rad].

Similarly to the point B, the difference Δφ _A in the phase delay of the vibration due to the pitch angle difference Δθ _A at the point _A is calculated. From Δθ _A = −0.04583 [rad], each pitch angle of the point A becomes θ _A2 = (2π + Δθ _A ) /2=3.119 [rad], and θ _A1 = θ _A2 −Δθ _A = 3.165. [Rad]. Regarding the phase delay φ _A1 of the second blade relative to the first blade and the phase delay φ _A2 of the first blade relative to the second blade, as shown in FIG. 7A, φ _A1 = θ _{A1 × 60 / n × f c} = 3.119 × 60/6000 × 3908-2π × 19 = 4.289 [rad] _{becomes, φ A2 = θ A2 × 60} / n × f c = 3.165 × 60 / 6000 × 3908-2π × 19 = 2.497 [rad]. The difference in phase delay between φ _A1 and φ _A2 is Δφ _A = φ _A1 −φ _A2 = 1.791 = π−1.350 [rad].

Finally, to calculate the difference [Delta] [phi _C phase delay of chatter vibration due to the pitch angle difference [Delta] [theta] _C of the blade at point C. From Δθ _C = −0.1149 [rad], for each pitch angle of point C, θ _C2 = (2π + Δθ _C ) /2=3.084 [rad], and θ _C1 = θ _C2 + Δθ _C = 3.199. [Rad]. Regarding the phase delay φ _C1 of the second blade relative to the first blade and the phase delay φ _C2 of the first blade relative to the second blade, as shown in FIG. 7C, φ _C1 = θ _{C1 × 60 / n × f c} = 3.199 × 60/6000 × 3908-2π × 19 = 5.639 [rad] _{becomes, φ C2 = θ C2 × 60} / n × f c = 3.084 × 60 / It is 6000 * 3908-2 (pi) * 19 = 1.147 [rad]. The difference in phase lag between φ _C1 and φ _C2 is Δφ _C = φ _C1 −φ _C2 = 4.492 = π + 1.350 [rad].

From the above calculation results, the difference in phase delay between the wave removing of the first blade and the wave removing of the second blade at point A is Δφ _A = π−1.350 [rad]. On the other hand, the difference in phase lag between the wave removing of the first blade and the wave removing of the second blade at point C is Δφ _C = π + 1.350 [rad]. It is understood that the point A and the point C have the same value, both positive and negative, across π [rad], and the reproduction effects at the points A and C cancel each other out. FIG. 8 shows the relationship between the axial position from point A to point C and the phase delay difference Δφ between the wave removing of the first blade and the wave removing of the second blade. As shown in FIG. 8, the phase lag difference Δφ in the range from point A to point B and the phase lag difference Δφ in the range from point C to point B are also located at the same distance across point B. Thus, it is understood that the reproduction effect is offset and disappears. Therefore, a solid line (solid line passing through point A and point J) obtained by doubling the axial cut indicated by a dotted line of m = −1 in FIG. 5 has a reproduction effect below and above the dotted line passing through point B. It becomes the reversal effect offset line to be offset. Similarly, a solid line (solid line passing through the points D and I) obtained by doubling the axial cut indicated by the dotted line of m = −2 is a reproduction effect cancellation line in which the reproduction effect is canceled above and below the dotted line. It becomes. Further, considering the point G in FIG. 5, the reproduction effects from the point G to the point H and from the point I to the point H, which are vertically symmetrical with respect to the dotted line of m = −1, cancel each other. Furthermore, since the point I is on the reproduction effect cancellation line, the reproduction effect below the point I is canceled out. Therefore, the solid line passing through the point G and the point J is a reproduction effect cancellation line.

  The unequal pitch end mill has an effect of suppressing regenerative self-excited chatter vibration near a specific rotational speed. On the other hand, the unequal lead end mill has an effect of suppressing regenerative self-excited chatter vibration under conditions near the regenerative effect cancellation line (relationship between a specific rotational speed and axial cutting). In the unequal lead end mill, even if the position is in the axial direction not on the reproduction effect cancellation line, only the reproduction effect corresponding to the distance from the closest cancellation line remains. Therefore, it is expected that the unequal lead end mill is effective in suppressing regenerative self-excited chatter vibration under a wide range of processing conditions. Furthermore, if the reproduction effect canceling lines are dense due to an increase in the difference in twist angle, a higher suppression effect is expected. From this evaluation, it can be specified that the end mill 6 can exhibit a high effect of suppressing chatter vibration.

(Example 2)
Chatter vibration evaluation will be described with reference to FIGS. In this evaluation, a cutting experiment using the end mills 1 to 6 was performed, and whether or not chatter vibration occurred was evaluated. Thereby, it is verified whether the end mill 6 can suppress chatter vibration in actual cutting.

  With reference to FIG.9 and FIG.10, the end mills 1-6 used for a cutting experiment are demonstrated. The end mills 1 to 6 are cemented carbide end mills. The external dimensions of the end mills 1 to 6 are the same as those of the end mill 30 (see FIG. 2). The end mills 1 to 6 are the same as commercially available end mills except that they do not have a bottom blade and the specifications shown in FIG.

  The end mills 1 and 2 are standard end mills in which the twist angle of the cutting edge is 45 °. The end mill 1 includes six cutting edges so that the pitch angle is 60 °. The end mill 2 includes four cutting edges so that the pitch angle is 90 °. The end mills 3 and 4 are unequal pitch end mills in which the twist angle of the cutting edge is 45 °. The end mill 3 includes six cutting edges so that the pitch angles are alternately 58.5 ° and 61.5 ° along the circumferential direction. The end mill 4 includes four cutting edges so that the pitch angles are alternately 87.7 ° and 92.3 ° along the circumferential direction. The end mill 5 is a conventional four-blade unequal lead end mill. The end mill 5 includes cutting edges having a twist angle of 45 ° and cutting edges having a twist angle of 44 ° alternately along the circumferential direction (see FIG. 10A). The four cutting edges of the end mill 5 are arranged at an equal pitch at a position 7.7 mm from the tip. The pitch angle at the tip of the end mill 5 is alternately 86.2 ° and 93.8 ° along the circumferential direction (see FIG. 10A). The end mill 6 is a four-blade unequal lead end mill having an extremely large twist angle difference. The end mill 6 includes a cutting edge having a twist angle of 40 ° and a cutting edge having a twist angle of 45 ° alternately along the circumferential direction (see FIG. 10B). The four cutting edges of the end mill 6 are arranged at an equal pitch at a position 7.7 mm from the tip. The pitch angle at the tip of the end mill 6 is 72.3 ° and 107.8 ° alternately along the circumferential direction (see FIG. 10B).

  The workpieces 50A and 50B, which are workpieces used in the cutting experiment, will be described with reference to FIGS. The workpieces 50A and 50B have the same specifications except for the dimensions W1 and W2 shown in FIG. FIG. 12 shows the dimensions W1 and W2 of the workpieces 50A and 50B, respectively. Hereinafter, the workpieces 50A and 50B may be collectively referred to as a workpiece 50 (see FIG. 6). The workpiece 50 is a hardened steel whose material is SK105. The hardness of the workpiece 50 is 60 HRC (697 HV).

  A cutting experiment method will be described. The end mills 1 to 6 rotate at a set predetermined number of revolutions and perform cutting on the respective machining surfaces 55 of the workpieces 50A and 50B. The end mills 1 to 6 cut the workpiece 50 in a state where the tip is positioned 1.0 mm below the workpiece 50 (see FIG. 6). As shown in FIG. 11, the respective machining surfaces 55 of the workpieces 50 </ b> A and 50 </ b> B are cut from the right end of the drawing to the left end of the drawing (in the direction of arrow A). Since the amount of cut in the axial direction of the end mills 1 to 6 varies in the range of 0.5 to 6.5 mm and 6.5 to 12.5 mm, the chatter vibration stability limit is easily evaluated. The rotation speeds of the end mills 1 to 6 are set in various patterns. The workpieces 50A and 50B are used for each set number of rotations.

  The conditions of the cutting experiment will be described with reference to FIG. The machining targeted in the cutting experiment is a side finishing for hardened steel. The cutting depth δ in the radial direction of the end mills 1 to 6 is 0.012 mm. The maximum chip thickness of the end mills 1 to 6 is 0.002 mm. Since the cutting depth δ in the radial direction and the maximum chip thickness are extremely small, the chip amount is extremely small. For this reason, even if the flutes of the end mills 1 to 6 are shallow and the chip pocket is small, there is no problem in cutting. In the end mill 6, the groove bottom diameter (the distance from the bottom of the other flute opposite to the bottom of one flute) is 85% of the tool diameter (see FIG. 10B). This makes it possible to manufacture an unequal lead end mill having a portion where the angle difference of the twist angle is as large as 5 degrees and the pitch angle is minimized, and the tool rigidity of the end mill 6 is also improved. Note that the groove bottom diameter of a normal unequal lead end mill is about 70% of the tool diameter. Further, since the cutting depth δ in the radial direction of the end mills 1 to 6 is 0.012 mm, the cutting angle range Q in the radial direction of the end mills 1 to 6 is 0.07748 [rad].

  As shown in FIG. 14, a processing machine 100 used in a cutting experiment is a vertical machining center in which a main shaft 101 extends in the vertical direction. During the cutting process, the rotation period signal is measured by the optical sensor 51, and chatter vibrations in the radial direction and the feed direction of the end mills 1 to 6 are measured by the eddy current displacement sensors 52 and 53. Cutting resistance is measured by the dynamometer 56. The optical sensor 51 is a digital fiber sensor FS-V31M manufactured by Keyence Corporation. The eddy current type displacement sensors 52 and 53 are high resolution gap sensors AEC-5706PS manufactured by Electronic Applications Co., Ltd. The dynamometer 56 is manufactured by Kistler Instrument Corp. This is a three-component dynamometer 9257B made by the manufacturer. In addition, in FIG. 14, the end mill 6 is illustrated as an example among the end mills 1-6.

  The end mills 1 to 6 are attached to the main shaft 101 of the processing machine 100 via a tool holder 103. The protruding lengths of the end mills 1 to 6 are 36 mm and are constant. An impulse test is performed before and after cutting to confirm the resonance frequency. In the impulse test, an impulse hammer (not shown) and an optical displacement meter (not shown) are used. Impulse hammers are available from PCB Piezotronics Inc. 086D80 manufactured by Sensor Signal Conditioner Model 480E09. The optical displacement meter is ST-3711 manufactured by Iwatsu Tsushinki Co., Ltd.

  A method for evaluating the presence or absence of chatter vibration will be described. During cutting and idling of the spindle 101, the vibration displacement of the shaft portions of the end mills 1 to 6 is measured by the eddy current displacement sensors 52 and 53 and analyzed as follows to determine whether chatter vibration exists. Is made. First, the trigger signal detected by the optical sensor 51 is used, and the displacement data during idling of the spindle 101 at the same rotational position is subtracted from the displacement data during cutting detected by the eddy current displacement sensors 52 and 53. . Thereby, the run-out of the shaft portion and the shape error component are removed from the displacement data during cutting detected by the eddy current displacement sensors 52 and 53. Next, the displacement data from which the shaft runout and the shape error component are removed is converted into the frequency domain by FFT. The displacement data converted into the frequency domain by the FFT is multiplied by the displacement magnification of the tip of the end mills 1 to 6 with respect to the shaft, thereby estimating the amount of displacement of each tip of the end mills 1 to 6. The displacement magnifications of the end portions of the end mills 1 to 6 are obtained from the vibration mode displacement distribution obtained by the impulse test before cutting. The presence / absence of chatter vibration is evaluated based on the maximum value of the frequency components of the displacements of the end portions of the end mills 1 to 6 that do not coincide with an integral multiple of the spindle rotation frequency. In this evaluation, in each of the end mills 1 to 6, it is determined that chatter vibration has occurred when the vibration displacement component at the tip portion is 2 μm or more, and it is determined that chatter vibration has not occurred when the vibration displacement component is less than 1 μm. The

  The determination result of chatter vibration will be described with reference to FIGS. In each of FIGS. 15 to 17, “×” indicates that the maximum value of the vibration displacement component at any of the end portions of the end mills 1 to 6 is 2 μm or more, and “Δ” is 1 μm or more and less than 2 μm. “◯” indicates that it was less than 1 μm, and “−” indicates that there is no measurement data. FIGS. 15A and 15B show the evaluation results of chatter vibration in a cutting experiment using the end mills 1 and 2, respectively. FIGS. 16A and 16B show the evaluation results of chatter vibration in a cutting experiment using the end mills 3 and 4, respectively. FIGS. 17A and 17B are evaluation results of chatter vibration in a cutting experiment using the end mills 5 and 6, respectively. Note that the solid line indicated by the arrow in FIG. 16 and the solid line indicated on the graph of FIG. 17 are both reproduction effect cancellation lines.

  As shown in FIG. 15 (a), chatter vibrations occurred in almost all conditions including the condition that the axial depth of cut was 1 mm in the cutting of the end mill 1. On the other hand, as shown in FIG. 15 (b), when the end mill 2 was cut, chatter vibration was less generated in the low-speed / low-axis direction cutting region than the end mill 1. On the other hand, chatter vibration occurred in a wide area on the high-speed / high-axis cutting side.

  As shown in FIGS. 16A and 16B, in the cutting process of the end mills 3 and 4, chatter vibration was not generated in the vicinity of the specific rotation speed indicated by the regenerative effect cancellation line, but chatter vibration was generated. There was an area.

  As shown in FIG. 17A, chatter vibration was generated in the cutting process of the end mill 5 at a specific rotational speed and axial cutting conditions. On the other hand, as shown in FIG. 17 (b), in the cutting process of the end mill 6, no chatter vibration was generated in all conditions under which the cutting process was performed. That is, it was verified that the end mill 6 has a great effect of suppressing chatter vibration. The reason why the end mill 6 has a high effect of suppressing chatter vibration is considered to be that there are dense reproduction effect canceling lines. Further, in the region where the axial cutting depth d of the end mill 6 was 6 mm or less, there was no region where the vibration component was 1 μm or more and less than 2 μm. That is, in the end mill 6, it was confirmed that chatter vibration is further suppressed in a region where d / D is 0.75 or less.

In the cutting process of the end mill 3 (see FIG. 16A), the chatter vibration frequency measured during the cutting process at the rotation speed of 3800 min ⁻¹ was 4495 Hz. Since the maximum negative real portion frequency specified by the impulse test is 3741Hz, the actual regeneration effect nulling condition of the end mill 3 is considered to have shifted to the vicinity of the rotational speed 4495Min ^-1 from 3741min ^-1. In the cutting process of the end mill 4 (see FIG. 16B), the chatter vibration frequency measured during the cutting process at the rotational speed of 6000 min ⁻¹ was 4375 Hz. Since the maximum negative real portion frequency specified by the impulse test is 3908Hz, the actual regeneration effect nulling condition of the end mill 4 is shifted from 1997Min ^-1 and 5992Min ^-1 around 2236Min ^-1 and 6708Min ^-1 it is conceivable that.

The same applies to FIG. 17A showing the result of the end mill 5. Even on the reproduction effect cancellation line, chatter vibration occurred at, for example, a rotational speed of 4000 min ⁻¹ . The regenerative effect cancellation line is created based on the maximum negative real part frequency of 3908 Hz previously identified by impulse excitation, whereas the chatter vibration frequency measured during cutting at a rotational speed of 4000 min ⁻¹ is 4625 Hz. It was. Therefore, it is considered that the actual reproduction effect cancellation condition is shifted in the upper right direction (high-speed rotation / high cutting direction) with respect to the reproduction effect cancellation line depicted in FIG.

FIG. 18 shows an example of the processed surface 55 of the workpiece 50B that has been subjected to cutting. FIG. 18A shows the machined surface 55 cut by the end mill 2 under the conditions of a rotational speed of 7000 min ⁻¹ and an axial depth of cut of 6.5 mm to 12.5 mm. FIG. 18B shows the machined surface 55 cut by the end mill 6 under the conditions of a rotational speed of 6750 min ⁻¹ and an axial depth of cut of 6.5 mm to 12.5 mm. On the machined surface 55 cut by the end mill 2 that is a standard end mill, chatter vibration is generated in the axial direction of the end mill 2. On the other hand, chatter vibration does not occur at all on the machined surface 55 cut by the end mill 6. This result coincides with the evaluation result of chatter vibration shown in FIGS. 15 (b) and 17 (b).

  From the above evaluation, it became clear that the end mill 6 suppresses regenerative self-excited chatter vibration at all the axial cutting depths set in this evaluation. When the end mill 6 has an axial depth of cut of 6 mm or less (d / D is 0.75 or less), no vibration of 1 μm or more and less than 2 μm was generated. It became clear that self-excited chatter vibration could be further suppressed. The fact that the end mill 6 suppresses the regenerative self-excited chatter vibration in a wide range is understood by the presence of the regenerative effect canceling line. If the difference in the twist angle of the end mill 6 is larger than 5 °, the regenerative effect canceling line exists more densely, and it is considered that regenerative self-excited chatter vibration is suppressed. On the other hand, as the rotation speed of the end mill 6 increases, the interval between the reproduction effect cancellation lines increases. Therefore, it is considered that chatter vibration occurs when the end mill 6 performs cutting under conditions exceeding the maximum value of the rotation speed set in this evaluation.

  In addition, even if the cutting amount in the radial direction is extremely small under the conditions set in this evaluation, chatter vibration may occur in many conditions set in this evaluation in the end mills 1 and 2 that are normal end mills. It became clear. Further, it has been clarified that the end mills 3 and 4 which are unequal pitch end mills have a chatter vibration suppressing effect in the vicinity of a specific rotational speed. Further, it has been clarified that the end mill 5, which is a conventional unequal lead end mill, has an effect of suppressing chatter vibration in the vicinity of a condition satisfying a relationship between a specific rotational speed and an axial cut.

(Example 3)
Next, evaluation of chatter vibration using the end mill 2 will be described. In this evaluation, it was determined whether chatter vibration occurred when a workpiece (not shown) was cut by the end mill 2. The conditions of the cutting experiment of this evaluation will be described. In the cutting experiment, a workpiece (not shown) having a substantially rectangular work surface was used. The material and hardness of the workpiece are the same as those of the workpieces 50A and 50B of the second embodiment. The rotation speed of the end mill 2 is 6000 [min ⁻¹ ]. The cutting depth d in the axial direction of the end mill 2 is 8 [mm]. The cutting depth δ in the radial direction of the end mill 2 is 0.020 [mm]. That is, the cutting angle range Q in the radial direction of the end mill 2 is 0.1000 [rad]. Other conditions of the cutting experiment are the same as in Example 2.

  The results of the cutting experiment will be described. When the end mill 2 cuts the workpiece, chatter vibration occurred. Accordingly, even when the above-described cutting is performed using an unequal lead end mill instead of the end mill 2, chatter vibration is considered to occur under the condition that the radial cutting depth δ is 0.020 mm. In Example 2 described above, chatter vibration did not occur on the condition that the cutting depth δ in the radial direction of the end mill 6 was 0.012 mm. Accordingly, chatter vibration is less likely to occur when the radial cutting depth δ of the unequal lead end mill is 0.018 mm or less, and chatter vibration is less likely to occur when the cutting depth δ is 0.012 mm or less. Conceivable. When the cutting depth δ in the radial direction is 0.018 mm, the cutting angle range Q is 0.09490 [rad], and when the cutting depth δ is 0.012 mm, the cutting angle range Q is 0. 07748 [rad]. Accordingly, in cutting using an unequal lead end mill, when the cutting angle range Q is 0.095 [rad] or less, chatter vibration is less likely to occur, and the cutting angle range Q is 0.078 [ rad] or less, it is considered that chatter vibration is less likely to occur.

  From the above evaluation, it has been clarified that the condition that the unequal lead end mill can cut a high-hardness workpiece while suppressing chatter vibration is a condition that the cutting angle range Q is 0.095 [rad] or less. . Further, it has been clarified that chatter vibration is less likely to occur under the condition where the cutting angle range Q is 0.078 [rad] or less.

<5. Study on generalization of machining conditions to suppress chatter vibration>
As confirmed by (Example 2), in the cutting process in which the end mill 6 is used, chatter vibration is suppressed regardless of the axial cutting depth of the end mill 6. Further, in the end mill 5, chatter vibration is suppressed in the vicinity of a specific rotational speed and an axial cut. Therefore, it was studied to generalize the processing conditions for suppressing chatter vibration based on the processing conditions of the cutting processing in which the end mills 5 and 6 are used. The generalization of the processing conditions is realized by using any one of the above formulas (1) and (2).

<5-1. Generalization of machining conditions using equation (1)>
First, the cancellation line interval Δa [mm] in the reproduction effect cancellation diagram of a general unequal lead end mill (hereinafter simply referred to as unequal lead end mill) will be described. The plurality of cutting edges provided in the unequal lead end mill include two cutting edges having different twist angles. Let the twist angles of the two cutting edges be β ₁ and β ₂ [deg], respectively. A pitch angle difference Δθ [rad] (hereinafter simply referred to as “a” [mm] apart from the equal pitch position where the plurality of cutting edges provided in the unequal lead end mill have an equal pitch from each other along the axial direction of the unequal lead end mill. The pitch angle difference Δθ is obtained by the equation (5).
Δθ = 2a (tan β ₂ -tan β ₁ ) / D (5)
Hereinafter, the distance from the equal pitch position to the position spaced a [mm] along the axial direction of the unequal lead end mill is referred to as the axial distance a [mm].

Expression (6) is obtained by substituting Expression (5) into Expression (4).
120f _c (tan β ₂ −tan β ₁ ) a / (nD) = (1 + 2m) π (6)
When Expression (6) is transformed, Expression (7) is obtained.
Therefore, the offset line interval Δa [mm] is obtained by the equation (8).
In the cutting process using the end mill 6 of (Example 2), the offset line interval Δa [mm] under the condition that the rotational speed is 6000 min ⁻¹ is obtained by Expression (9).

From FIG. 17B, it can be confirmed that the offset line interval Δa when the end mill 6 performs the cutting process under the condition that the rotational speed is 6000 min ⁻¹ and the value obtained by the equation (9) are approximate to each other. It can also be confirmed that chatter vibration does not occur at an interval that approximates the value obtained by equation (9).

In the cutting process using the end mill 5 of Example 2, the offset line spacing Δa under the condition that the rotational speed is 2750 min ⁻¹ is obtained by Expression (10).
17A, it can be confirmed that the offset line interval Δa when the end mill 5 performs the cutting process under the condition that the rotation speed is 2750 min ⁻¹ and the value obtained by the expression (10) are approximate to each other. Further, it can be confirmed that chatter vibration is generated at an interval that approximates the value obtained by Expression (10). However, in the cutting of the end mill 5 where the rotational speed is 2750 min ⁻¹ , there is only one “x” indicating the occurrence of chatter vibration, so the offset line spacing Δa is slightly smaller than the value obtained by the equation (10). If the value is small, chatter vibration is considered not to occur. Therefore, it can be considered that the processing conditions under which the end mill 5 performs the cutting with the rotation speed of 2750 min ⁻¹ are the critical processing conditions for switching from the processing conditions in which chatter vibration is generated to the processing conditions in which chatter vibration is suppressed. it can.

Next, consideration will be given to the stability limit cutting a _lim of the equal pitch end mill in the cutting process in which the equal pitch end mill is used. The stability limit cut a _lim of the equal pitch end mill is obtained by the equation (11).
a _lim = -1 / (2K _f G (ω _c )) (11)
In Equation (11), K _f [N / mm ² ] is the specific cutting resistance, G [mm / N] is the real part of the transfer function of the workpiece machining system equipped with the equal pitch end mill, and ω _c [ rad / s] is the natural angular frequency of the end mill.

The a _lim of the end mill 2 that is a four-blade equal pitch end mill used in (Example 2) is K _f = 2350 N / mm ² and G = −2.948 × 10 ⁻³ mm / By substituting N and adding 5.1% as the duty ratio, it is obtained as shown in Expression (12).
A method for measuring K _f (= 2350 [N / mm ² ]) will be described later. G (= −2.948 × 10 ⁻³ [mm / N]) is determined by an impulse test. The duty ratio is the ratio of the rotation angle that the end mill 2 rotates while cutting the workpiece 50 that is a workpiece with four cutting edges to the rotation angle of one rotation of the end mill 2 (that is, 360 °). is there.

Consider Equation (1), which is an equation obtained by dividing the left side of Equation (11) by the cancellation line interval Δa. By dividing the left side of equation (11) by the offset line spacing Δa and further substituting ω _c = 2πf _c , equation (13) is obtained.
By using the expression (13), under the condition that the rotation speed is n _max [min ⁻¹ ] or less, the machining conditions for suppressing chatter vibration regardless of the axial cutting and the rotation speed of the unequal lead end mill are: Identified.

It will be considered to apply the condition for cutting the end mill 6 at a rotational speed of 6000 min ⁻¹ in Example 2 to Equation (13). In this case, Expression (14) is obtained by Expression (9) and Expression (12).
a _lim /Δa=1.415/3.997=0.354 Equation (14)
Next, in (Example 2), it is considered to apply the condition for cutting the end mill 5 at a rotation speed of 2750 min ⁻¹ to the equation (13). In this case, Expression (15) is obtained by Expression (10) and Expression (12).
a _lim /Δa=1.415/8.591=0.165 (15)

As described above, occurrence of chatter vibration is suppressed under the machining conditions in which the end mill 6 is machined at a rotational speed of 6000 min ⁻¹ . The condition for cutting the end mill 5 at a rotation speed of 2750 min ⁻¹ is regarded as a boundary machining condition for suppressing chatter vibration. Therefore, chatter vibration is suppressed when the value of Expression (13) (that is, Expression (1)) is 0.165 or more, and chatter vibration is further suppressed when the value of Expression (13) is 0.354 or more. It is thought that it is done.

Here, a numerical value of 0.165 or 0.354 is considered. First, the axial cut on the cancellation line cancels out the reproduction effect completely, and chatter vibration does not occur. The most likely occurrence is in the case of an axial cut, which is the midpoint between the cancellation line and the cancellation line. At that time, the reproduction effect is completely canceled in the axial cut range up to the cancellation line, but the reproduction effect occurs in the axial cut range above it, and the axial range is 0.5 times Δa. . However, even within this range, the reproduction effect is offset to some extent. On the other hand, a _lim indicates the stability limit when the reproduction effect is not canceled out at all. From the above, when a _lim is 0.165 to 0.354 times smaller than 0.5 times Δa, a stable condition can be obtained in any axial cutting. Theoretically, the reproduction effect is canceled by half at the midpoint, so it is considered to be 0.25 times, and it can be said that the experimental results agree well with this. Since the theoretical consideration and the evaluation result are in good agreement, there is no need for further evaluation, and Equation (1) is an equation for determining whether or not chatter vibration can be suppressed. It is understood that it is useful.

Referring to FIG. 19, a description will be given of a measuring method of the specific cutting force K _f which is substituted in the equation (12). Hereinafter, the front-rear direction, the left-right direction, and the up-down direction in FIG. 19 are respectively referred to as an X-axis direction, a Y-axis direction, and a Z-axis direction. The measurement of the specific cutting force _{K f,} machine 200, the workpiece 250, and the end mill 260 is used. The processing machine 200 is a vertical machining center in which a main shaft 201 extends in the vertical direction. A workpiece 250 is fixed to the main shaft 201. The workpiece 250 has a hollow disk shape. The material and hardness of the workpiece 250 are the same as those of the workpiece 40 (see FIG. 1).

  A dynamometer 256 is installed on the work table 210 of the processing machine 200. An end mill 260 is fixed to the dynamometer 256 via a vise 230. The end mill 260 is an end mill in which the twist angles of the cutting edges are all equal, that is, a standard end mill. The axial direction of the end mill 260 coincides with the Z-axis direction.

  The processing machine 200 executes positioning of the end mill 260 and the workpiece 250 in the X-axis direction and the Z-axis direction. The processing machine 200 moves the end mill 260 in the Y-axis direction by moving the work table 210, and performs cutting on the workpiece 250 that is rotated by the main shaft 201. The cutting speed is about 150 [m / min], and the feed speed in the Y-axis direction is 0.0004 [mm / rev] to 0.0062 [mm / rev]. The lubricating oil used when cutting is performed is the same as in (Example 2) (see FIG. 13). The specific cutting resistance Kf is measured by a dynamometer 256.

<5-2. Generalization using Equation (2)>
Next, generalization using equation (2) will be discussed. The unequal lead end mill mounted on the processing machine 100 can be regarded as a mandrel whose one end is completely fixed. The calculation formula for obtaining the resonance frequency f _c [Hz] of the mandrel whose one end is completely fixed is a well-known document (for example, “New Mechanical Engineering Handbook” edited by the New Mechanical Engineering Handbook Editorial Committee, published by Rigaku Corporation). “Chapter 6, Shaft / Key and Shaft Coupling” of “Part 2 Mechanical Design”). Resonance frequency _{f c} of the unequal lead end mill is determined by equation (16).
In equation (16), λ is a dimensionless constant determined by the support conditions of the unequal lead end mill, and E [kg / mm ² ] is the longitudinal elastic modulus (Young's modulus) of the material forming the unequal lead end mill. , Ρ [kg / mm ³ ] is the density of the unequal lead end mill, A [mm ² ] is the cross sectional area of the unequal lead end mill, and I [mm ⁴ ] is the cross sectional second moment of the unequal lead end mill. The cross-sectional secondary moment I of an unequal lead end mill regarded as a mandrel is obtained by equation (17).
I = πD ^4/64 ···· formula (17)

When a load W directed in a direction orthogonal to the axis of the unequal lead end mill is applied to the tip of the unequal lead end mill, the maximum deflection y _max [mm] of the unequal lead end mill is obtained by Expression (18).
y _max = Wl ³ / (3EI)... formula (18)
The compliance y _max / W, which is the reciprocal of the dynamic stiffness of the unequal lead end mill, is obtained by equation (19).
And stability limit cut b _lim [mm] of each cutting edge of an unequal lead end mill is calculated | required by Formula (20).
Here, considering the number N of cutting edges and the cutting angle range Q [rad], a cutting force equal to the number of cutting edges is applied to the unequal lead end mill during one revolution of the unequal lead end mill. While the blade cuts the cutting angle range Q, the cutting force is continuously applied to the unequal lead end mill. For this reason, N and Q are inversely proportional to the stability limit cut. Therefore, the stability limit cut is expressed by equation (21).
Equation (8), by _{ω c = 2πf c, a lim} / Δa is represented by the formula (22).
By omitting the constant in equation (22), equation (23) is obtained.
Furthermore, the work of the hardness H [HV] than that proportional to _{k f,} equation (23) is rewritten into equation (24).
That is, it can be seen that the expression (2) is an expression corresponding to the expression (1) and is a mathematical expression suitable for specifying the processing conditions for suppressing chatter vibration. Here, the Young's modulus E is a value of “stress σ / strain ε”, and its unit is N / mm ² (1 × 10 ⁻⁹ GPa). On the other hand, Vickers hardness H [HV] is a value of “test load F / surface area S of dent due to indenter”, and the unit is generally indicated as HV, but it is kgf / mm ² (9.8 N / mm ² ). is there. The unit of the cut angle range Q is [rad], and the unit of the equation (23) is made dimensionless.

When the condition for cutting the end mill 6 in (Example 2) at a rotational speed of 6000 min ⁻¹ is applied to the expression (2), the expression (25) is obtained.
Further, when the condition for cutting the end mill 5 in (Example 2) at a rotational speed of 2750 min ⁻¹ is applied to the expression (2), the expression (26) is obtained.

As described above, chatter vibration is suppressed under the condition of Expression (25). Further, the condition of Expression (26) can be regarded as a boundary condition for switching from the condition for generating chatter vibration to the condition for suppressing chatter vibration. Therefore, when the value of the expression (2) becomes 9.401 × ^{10 -3} or more, chatter vibration is suppressed, the value of the expression (2) is 20.205 × ^{10 -3} or more, chatter vibrations are further suppressed It is thought.

  Formula (2) is a mathematical formula derived on the assumption that one end of the end mill is completely fixed and a load is applied only to the tip. Therefore, Expression (1) is an expression that can more accurately determine whether chatter vibration can be suppressed than Expression (2).

<6. Main actions and effects of this embodiment>
As described above, the workpiece machining system 10 cuts the workpiece 40 with the end mill 30 under the condition that the value of the expression (1) is 0.165 or more. Thereby, the suppression effect of chatter vibration increases. Therefore, the workpiece machining system 10 can suppress chatter vibration when the workpiece 40 is cut by the end mill 30. Since chatter vibration is suppressed even if the amount of cut in the axial direction of the end mill 30 is increased, the workpiece machining system 10 efficiently performs a finishing process that makes the machining surface of the workpiece 40 a good surface roughness in a short time. it can.

  The workpiece machining system 10 cuts the workpiece 40 with the end mill 30 under the condition that the value of the expression (1) is 0.354 or more. Thereby, since the vibration suppression effect further increases, the workpiece machining system 10 can further suppress chatter vibration.

The end mill 30 cuts the workpiece 40 with a low depth of cut in the radial direction. That is, the workpiece machining system 10 cuts the workpiece 40 under the condition that the cutting angle range Q is within 0.095 [rad]. Thereby, the cutting process by the end mill 30 is approximately approximated to a cutting process in one direction, and the mode coupling type self-excited chatter vibration hardly grows. Moreover, the workpiece machining system 10 cuts the workpiece 40 under the condition that the value of the expression (2) is 9.401 × 10 ⁻³ or more. When the workpiece 40 is cut, the regenerative self-excited chatter vibration suppressing effect is enhanced. Therefore, the workpiece machining system 10 can suppress chatter vibration when the workpiece 40 is cut by the end mill 30.

Further, when the workpiece machining system 10 cuts the workpiece 40 under the condition that the value of the expression (2) is 20.205 × 10 ⁻³ or more, the effect of suppressing the regenerative self-excited chatter vibration is further enhanced. Therefore, the workpiece machining system 10 can further suppress chatter vibration when the workpiece 40 is cut by the end mill 30.

The end mill 30 is an unequal lead end mill in which the difference in torsion angle is 5 °. Since the difference in the twist angle of the end mill 30 is 2 ° or more, the value of tan β ₂ -tan β ₁ in the equation (2) increases. Therefore, even if n, H, N, and Q increase, the value of equation (2) tends to be 9.401 × 10 ⁻³ or more. Therefore, the workpiece machining system 10 can cut the workpiece 40 while suppressing chatter vibration even under conditions where n, H, N, and Q are increased. The workpiece machining system 10 can be applied to a wider range of machining conditions than when the difference in twist angle is less than 2 °.

  Moreover, the workpiece machining system 10 cuts the workpiece 40 under the condition that d / D is 0.75 or less. Thereby, when the workpiece 40 is cut, chatter vibration is further suppressed over the axial direction of the end mill 30.

  In addition, this invention is not limited to said embodiment, A various change is possible. The machine tool 20 may move the end mill 30 in the X-axis direction instead of moving the work table 21 to which the workpiece 40 is attached in the X-axis direction.

  Further, instead of the angle difference of the twist angle of the end mill 30 being 5 °, for example, among the four cutting edges 33, the angle difference of the twisting angle of the two cutting edges 33 is 7 °, and the remaining two sheets The angle difference of the twist angle of the cutting edge 33 may be 10 °.

Further, the twist angles of the four cutting edges 33 may all be different from each other, or only the twist angle of one cutting edge 33 may be different from the twisting angles of the other three cutting edges 33. When there are three or more types of twist angles of the cutting edge 33, there are a plurality of combinations of the cutting edges 33 that offset the regeneration effect. In this case, | tanβ ₂ −tanβ ₁ | in the formula (2) is defined as | tanβ _i −tanβ _(i−1) | with two cutting edges 33 adjacent to each other along the circumferential direction of the end mill 30 as a set. Should be replaced. | Tan β _i −tan β _(i−1) | is a value defined by each combination of the plurality of cutting edges 33, and is a value proportional to the pitch difference of the cutting edges 33. When | tan β _i −tan β _(i−1) | in each group is equal, a high canceling effect is obtained. In addition, even if | tan β _i −tan β _(i−1) | in each combination is not completely equal, a certain amount of canceling effect can be obtained.

  Further, along the circumferential direction of the end mill 30, two cutting edges having a twist angle of 40 ° instead of the cutting edges 33 having a twist angle of 40 ° and the cutting edges 33 having a twist angle of 45 ° alternately arranged. 33 may be adjacent along the circumferential direction of the end mill 30. In this case, the two cutting edges 33 having a twist angle of 45 ° are also adjacent to each other along the circumferential direction of the end mill 30.

DESCRIPTION OF SYMBOLS 10 Work processing system 20 Machine tool 26 Spindle 30 End mill 40 Work 33 Cutting edge

Claims (7)

A work machining method for cutting the workpiece by relatively moving an end mill mounted on a rotating spindle of a machine tool and a high-hardness workpiece,
The end mill includes a plurality of cutting edges twisted with respect to the axial direction of the end mill and arranged in the circumferential direction of the end mill, and the plurality of cutting edges do not include two cutting edges having different twist angles. An equal lead end mill,
Under the condition that the value of the formula (1) shown below is 0.165 or more,
a _lim / Δa (1)
(A _lim : axial stability limit cut [mm] of the equi-pitch end mill when the equi-pitch end mill cuts the workpiece.
Δa: spacing in the axial direction [mm] between adjacent reproduction effect cancellation lines in the reproduction effect cancellation diagram of the unequal lead end mill)
A workpiece machining method comprising cutting the workpiece.   The workpiece machining method according to claim 1, wherein the workpiece is cut under a condition that the value of the expression (1) is 0.354 or more. A workpiece comprising a machine tool having a spindle and an end mill that can be mounted on the spindle, and cutting the workpiece by relatively moving a high-hardness workpiece and the end mill mounted on the rotating spindle. A processing system,
The end mill includes a plurality of cutting edges twisted with respect to the axial direction of the end mill and arranged in the circumferential direction of the end mill, and the plurality of cutting edges do not include two cutting edges having different twist angles. An equal lead end mill,
The machine tool relatively moves the workpiece and the unequal lead end mill mounted on the rotating main spindle, and the value of the following expression (1) is 0.165 or more so,
a _lim / Δa (1)
(A _lim : axial stability limit cut [mm] of the equi-pitch end mill when the equi-pitch end mill cuts the workpiece.
Δa: spacing in the axial direction [mm] between adjacent reproduction effect cancellation lines in the reproduction effect cancellation diagram of the unequal lead end mill)
A workpiece machining system for cutting the workpiece. A work machining method for cutting the workpiece by relatively moving an end mill mounted on a rotating spindle of a machine tool and a high-hardness workpiece,
The end mill includes a plurality of cutting edges twisted with respect to the axial direction of the end mill and arranged in the circumferential direction of the end mill, and the plurality of cutting edges do not include two cutting edges having different twist angles. An equal lead end mill,
The condition that the cutting angle range Q in the radial direction of the unequal lead end mill is within 0.095 [rad], and the condition that the value of the expression (2) shown below is 9.401 × 10 ⁻³ or more. so,
(Ω _c : natural angular frequency [rad / s] of the unequal lead end mill
E: Young's modulus [GPa] of the material forming the unequal lead end mill
β ₁ , β ₂ : the twist angle [deg] of the two cutting edges
n: Number of rotations of the unequal lead end mill [min ⁻¹ ]
H: Hardness of the workpiece [HV]
N: Number of the plurality of cutting edges D: Tool diameter [mm] of the unequal lead end mill
l: protrusion length [mm] of the unequal lead end mill
A workpiece machining method comprising cutting the workpiece. The workpiece machining method according to claim 4, wherein the workpiece is cut under a condition that the value of the expression (2) is 20.205 × 10 ⁻³ or more.   The work machining method according to claim 4 or 5, wherein the twist angles of the two cutting edges are different from each other by 2 ° or more. A workpiece comprising a machine tool having a spindle and an end mill that can be mounted on the spindle, and cutting the workpiece by relatively moving a high-hardness workpiece and the end mill mounted on the rotating spindle. A processing system,
The end mill includes a plurality of cutting edges twisted with respect to the axial direction of the end mill and arranged in the circumferential direction of the end mill, and the plurality of cutting edges do not include two cutting edges having different twist angles. An equal lead end mill,
The machine tool relatively moves the workpiece and the unequal lead end mill mounted on the rotating main shaft, and a cutting angle range Q in the radial direction of the unequal lead end mill is 0.095 [rad]. ] And a condition that the value of the formula (2) shown below is 9.401 × 10 ⁻³ or more,
(Ω _c : natural angular frequency [rad / s] of the unequal lead end mill
E: Young's modulus [GPa] of the material forming the unequal lead end mill
β ₁ , β ₂ : the twist angle [deg] of the two cutting edges
n: Number of rotations of the unequal lead end mill [min ⁻¹ ]
H: Hardness of the workpiece [HV]
N: Number of the plurality of cutting edges D: Tool diameter [mm] of the unequal lead end mill
l: protrusion length [mm] of the unequal lead end mill
A workpiece machining system for cutting the workpiece.