JP2000005915A - Ball end mill cutting method and milling machine controller - Google Patents

Abstract

(57) [Summary] PROBLEM TO BE SOLVED: To provide a smell for cutting a die or the like by a ball end mill.
Tool inclination angle without trial and error by cutting test
Can be set, greatly improving the accuracy of the finished dimensions.
That. SOLUTION: The milling machine control device 3 of the present invention comprises a CA
By inputting numerical values from the D / CAM processing device 2 etc.,
Angle of inclination β at which the acting bending moment is suppressed _f, Β
_pIs determined by numerical calculation, and the NC milling machine 4
Set the tool inclination angle properly. In the above numerical calculation,
Angle of inclination β_fAnd left-right inclination angle β_pInitial settings
And the bending mode on the tool
Calculate the estimated value corresponding to the
Angle of inclination β until_f, Β_pReset and the above estimation
Repeat, β_f, Β_pIs calculated. When cutting
The bending moment on the tool is reduced, and the tool does not bend
Therefore, the accuracy is greatly improved.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to the technical field of a milling machine, and more particularly, to the technical field of a milling machine for performing plunge cutting by using a ball end mill. INDUSTRIAL APPLICABILITY The present invention is suitable for cutting a deep bottom forging die in which the hardness of the ball end mill is liable to increase the deflection of the ball end mill but demands a high dimensional accuracy, particularly for a cold forging made of a high hardness material. Ideal for cutting dies.

[0002]

2. Description of the Related Art An example of the prior art is disclosed in Japanese Patent Publication No.
No. 724,583 discloses a cutting method using a milling machine in which a tool (milling cutter) is inclined, although a ball end mill is not illustrated. Conventionally known cutting methods using a ball end mill (referred to as a tool) with a milling machine include vertical cutting in which the tool is set upright on the surface to be cut of the work and tool for cutting the surface to be cut of the work. There is inclined cutting that is performed by inclining. Figure 1 for inclined cutting
As shown in the figure, plunge cut (piercing cut, β _f <0) performed by tilting the tool so that the tip of the tool protrudes in the tool feed direction, and reverse cut (β _f > 0) performed by tilting the tool in the opposite direction ). Fig. 2
As shown in FIG. 5, plunge cutting (piercing cutting, β _p <0) performed by tilting the tool so that the tip of the tool protrudes in the pick feed direction, and reverse cutting (β _p > 0) performed by tilting the tool in the opposite direction ).

[0003] It is conventionally known that, when plunge cutting is performed with an appropriate inclination angle set, the deflection of the tool during cutting is reduced, and the dimensional accuracy of the finished surface cut by a ball end mill is improved.

[0004]

However, means for calculating in advance prior to cutting how to set the inclination angle (β _f , β _p ) of the ball end mill to obtain higher dimensional accuracy of the finished surface. There was no. Therefore, if an attempt is made to set an appropriate inclination angle, a cutting test is performed by changing the inclination angle of the ball end mill many times.
Since there was no other means than searching for the proper tilt angle after trial and error, finding the proper tilt angle required a great deal of cost and time. Further, if the inclination angle of the ball end mill was appropriately set depending on the can and experience, the improvement of the cutting dimension accuracy could be expected only at most about 10%, and the dramatic improvement of the cutting dimension accuracy could not be obtained.

Accordingly, the present invention provides a cutting method using a ball end mill and a milling machine control device which can set an appropriate tool inclination angle without trial and error by a cutting test and can greatly improve the precision of a finished cut size. Issues to be solved.

[0006]

Means for Solving the Problems [Background to the Invention] As described above, the inventors consider the reason why the dimensional accuracy of the finished surface is improved by plunge cutting as follows. That is, in normal vertical cutting, as shown in FIG. 3, the difference between the chip cross-sectional area A on one side of the cutter of the ball end mill and the chip cross-sectional area B on the other side is large. Therefore, a large bending moment acts on the ball end mill, and the deflection of the ball end mill increases. Conversely, in plunge cutting in which the tool inclination angle is set at an appropriate angle, as shown in FIG. 4, the chip cross-sectional area A on one side of the cutter of the ball end mill and the chip cross-sectional area B on the other side are different. They are almost equivalent. Therefore, with proper plunge cutting,
Since the bending moment acting on the ball end mill is smaller than in vertical cutting, and the deflection of the ball end mill is suppressed, the cutting dimensional accuracy is improved.

[0007] Therefore, if the inventors can estimate the force such as cutting resistance acting on the tool at the time of cutting by numerical calculation, and can estimate the bending moment acting on the ball end mill, the tool inclination angle is re-set. It was discovered that the bending moment could be reduced to near zero by repeating the estimation several times. However, in order to estimate the cutting force acting on the tool at the time of cutting by numerical calculation, a complicated mathematical operation including a coordinate transformation and handling a three-dimensional shape is required. Therefore, the inventors have determined a mathematical formula for estimating the cutting force, established a calculation method, and confirmed the effect by an actual cutting test. The present invention shown in the following means and examples has been invented after such development efforts.

[Invention of Method] (First Means) A first means of the present invention relates to performing a plunge cut (piercing cut) by inclining a ball end mill with respect to the surface of a work in a milling machine in a front-rear direction and a left-right direction with respect to a feed direction. Before cutting, the set values of the front-rear inclination angle and the left-right inclination angle of the rotation axis of the ball end mill are initially set, and the estimated value corresponding to the front-rear bending moment applied in the front-rear direction of the rotation axis of the ball end mill And an estimated value corresponding to the lateral bending moment applied in the lateral direction of the rotation axis, and repeatedly performing the resetting and the estimation of the set value until both the estimated values are equal to or less than a predetermined value. An appropriate value of the two angles is calculated, and cutting is performed after setting the inclination angle of the ball end mill of the milling machine with the appropriate value. This is a cutting method using a ball end mill.

In this means, prior to the actual plunge cutting by the ball end mill, the appropriate values of the front-back inclination angle β _f (β _f <0) and the left-right inclination angle β _p (β _p <0) of the rotation axis of the ball end mill are provided. Is calculated. That is, first, the front-rear inclination angle β _f and the left-right inclination angle β _p of the rotation axis of the ball end mill are appropriately initialized, an estimated value corresponding to the front-rear bending moment applied in the front-rear direction of the rotation axis of the ball end mill, and the same rotation axis And an estimated value corresponding to the lateral bending moment applied in the lateral direction. Here, each estimated value corresponding to each bending moment need not be a value obtained by estimating the bending moment itself, but may be an estimated value proportional to the bending moment. Thereafter, the two inclination angles β _f and β _p are reset from the initial values, and the estimated values corresponding to the two bending moments are estimated again, and the estimated values proportional to both the bending moments are obtained again. In this way, the calculation of each estimated value proportional to both bending moments is repeated by resetting both inclination angles β _f and β _p, and the absolute value of each estimated value proportional to both bending moments is sufficiently reduced to zero. The calculation is repeated until the value becomes equal to or less than a predetermined value that is determined to be close.

As a result, the proper values of the two inclination angles β _f and β _p at which the absolute values of the respective estimated values proportional to the two bending moments are sufficiently close to zero are obtained, and the inclination of the ball end mill is adjusted in accordance with the proper values. Cutting is performed by a milling machine with an angle set. In the cutting performed by the ball end mill performed in this manner, the bending moment acting on the ball end mill is largely suppressed, so that the bending deformation of the ball end mill is largely suppressed, and the finished dimensional accuracy of the cut is greatly improved.

Therefore, according to the cutting method using the ball end mill of the present means, it is possible to set appropriate tool inclination angles β _f and β _p without trial and error by a cutting test.
There is an effect that it is possible to greatly improve the precision of the finished cutting dimensions. In addition, a method of estimating each estimated value proportional to both bending moments is exemplified in the following second means to fourth means, but other estimation methods can be used. For example, taking into account not only the cutting force acting in the tangential direction of the turning surface of the cutter but also the action of the force pushing or pulling the cutter in the turning radius direction, the action of the reaction force generated at the time of cutting, etc. Each of the above estimated values can be estimated more precisely.

In this means, the bending moment acting on the ball end mill is divided into two, that is, the front-rear direction and the left-right direction, and each is approached to zero. It need not be limited to This is because if the bending moment is zero in any two directions that are not parallel to each other, the bending moment in all directions is zero, which is equivalent to the bending moment in the left-right direction and the front-back direction being zero. .

(Second Means) The second means according to the first means, wherein the estimated value corresponding to the bending moment in the front-rear direction is obtained by calculating a cross-sectional area of a chip on the right side of the rotation axis of the ball end mill. The estimated value corresponding to the left and right bending moment is estimated from the difference between the chip cross-sectional area at the left and the chip cross-sectional area at the front and the chip cross-sectional area at the rear of the rotation axis of the ball end mill. This is a cutting method using a ball end mill estimated based on the difference between

In this means, it is assumed that the estimated value corresponding to the bending moment acting in the predetermined direction is proportional to the difference between the chip cross-sectional areas in both directions orthogonal to the predetermined direction. Therefore, since the chip cross-sectional area is obtained only by performing the integration, there is no need to perform the double integration, and the amount of calculation can be reduced. Therefore, according to this means, there is an effect that the effect of the first means can be almost achieved with a relatively small amount of calculation.

It is to be noted that the distance of the chip cross section from the tool rotation axis is taken into account when integrating each minute area, and the area moment formed by the chip cross section around the tool rotation axis is calculated. Can be. If the area moment calculated in this way is replaced with a mere chip cross-sectional area, the bending moment calculation accuracy of the present means can be much improved without increasing the calculation amount much.

(Third Means) In the third means according to the first means, the estimated value corresponding to the bending moment in the front-rear direction is obtained by calculating a chip volume on a right half surface of the rotating shaft of the ball end mill and a left chip volume. Estimated from the difference between the chip volume on the half surface and the estimated value corresponding to the lateral bending moment, the difference between the chip volume on the front surface of the rotary shaft of the ball end mill and the chip volume on the rear surface is calculated. This is a cutting method using a ball end mill estimated by

According to this means, the estimated value corresponding to the bending moment acting in the predetermined direction is proportional to the difference between the chip volume on the right half surface and the chip volume on the left half surface from the predetermined direction. Standing on assumptions. Therefore, it is necessary to perform double integration in order to obtain the chip volume, but the amount of calculation does not need to be so large in view of the current processing capacity of the computer.

Therefore, according to this means, there is an effect that the effect of the first means can be almost achieved with a moderate amount of calculation. (Fourth Means) A fourth means according to the first means, wherein the estimated values corresponding to the front-rear bending moment and the left-right bending moment are each orthogonal to a chip cross-sectional area generated by the ball end mill. This is a cutting method using a ball end mill, which is estimated as an integral value of the longitudinal component force and the lateral component force of the cutting force acting on the entire circumference of the rotating shaft.

In this means, the dominant component of the reaction force acting on the ball end mill from the work is the cutting resistance,
It is assumed that the cutting force acts in a direction tangential to the outer peripheral surface of the cutter orthogonally to the chip cross section, and the magnitude of the cutting force is proportional to the chip cross section. Then, both estimated values corresponding to the longitudinal bending moment and the lateral bending moment are estimated as integral values of the longitudinal force component and the lateral force component of the cutting force over the entire circumference of the rotating shaft. That is, this means is modeled most precisely from the second means to the fourth means, and both estimated values corresponding to the front-back bending moment and the left-right bending moment are precisely estimated.

Therefore, according to this means, the two inclination angles β _f and β _p for suppressing the bending moment acting on the tool to near zero can be obtained most accurately, and the effect of the above-mentioned first means is the same as that of the above-mentioned first means. There is an effect that it is exerted even better than the second means and the third means. [Apparatus Invention] (Fifth Means) A fifth means of the present invention performs plunge cutting (piercing cutting) by inclining a ball end mill with respect to the surface of a work in a front-rear direction and a left-right direction with respect to a feeding direction at predetermined inclination angles. This is a milling machine control device for setting the inclination angle of the rotation axis of the ball end mill to an appropriate value for a milling machine capable of performing such operations. The feature of the present means is that at least input means for inputting input values corresponding to the tool radius and the number of cutter blades of the ball end mill and desired pick feed, cutting depth, feed speed and tool rotation speed, Corresponding to the longitudinal bending moment applied in the longitudinal direction of the rotation axis of the ball end mill, based on the value, the initial value of the inclination angle of the ball end mill appropriately set, and the integration step width appropriately set. Estimating means for estimating an estimated value to be calculated and an estimated value corresponding to a lateral bending moment applied in the left-right direction of the rotation axis; and until the absolute values of the estimated values obtained by the estimating means become equal to or less than a predetermined value. Convergence means for adjusting the set values of both the front and rear inclination angles and the left and right inclination angles of the rotation axis of the end mill, repeating the estimation, and thereby calculating the appropriate values of both angles Is to have an output means for outputting the proper values of both the angle calculated by said converging means, in the milling machine in a format compatible with the tool inclination angle setting means of the milling machine.

In the present means, the input means firstly inputs at least input values corresponding to the tool radius and the number of cutter blades of the ball end mill and the desired pick feed, cutting depth, feed speed and tool rotational speed. It is input to the milling machine controller of the means. Next, by estimation means,
Based on these input values, appropriately set initial values of the inclination angles β _f , β _p of the ball end mill, and an appropriately set integration step width, the longitudinal direction of the rotation axis of the ball end mill is determined. An estimated value corresponding to the front-back bending moment and an estimated value corresponding to the left-right bending moment in the left-right direction of the rotating shaft are estimated.

Further, by the convergence means, the estimation means
Until the absolute value of the two estimated values becomes
Of the front-rear tilt angle and the left-right tilt angle of the
Set value β of both angles_f, Β_pAnd repeat the above estimation
And then both angles β_f, Β_pThe appropriate value of is calculated
You. Finally, the convergence means calculates by the convergence means.
Appropriate value β of both issued angles _f, Β_pBut milling machine
Output to milling machine in a format suitable for tool inclination angle setting means
Is done. Then, the inclination angle of the rotation axis of the ball end mill
Is the most appropriate value β_f, Β_pIs set to plunge
Bending Moment Generated on Ball End Mill When Cutting
And the deflection of the ball end mill is suppressed.
Leads to. As a result, trial-and-error
Even if it is not returned, the finished dimensions of the ball end mill
The effect is obtained that the accuracy of the method is greatly improved.

Therefore, according to the milling machine control device of the present means, the proper inclination angles β _f and β _p of the ball end mill can be set without trial and error by a cutting test, and the accuracy of the finished cut dimensions is greatly improved. There is. In the milling machine control device of the present means, it is assumed that the present means is implemented even when humans intervene in input / output and the like.
In other words, in extreme terms, the milling machine control device of the present means may be a stand-alone personal computer or workstation in which a program corresponding to each of the above means is incorporated. Of course, the input value is automatically input to the present means from the CAD / CAM database built in the host control computer, and the appropriate values of the inclination angles β _f and β _p output from the present means are automatically calculated. It is most desirable that the information be transmitted to and received from the control panel of the milling machine. In this way, automation is advanced and labor is saved, and in addition to the effect of improving the accuracy of the cut finish dimensions of this means,
The labor saving effect of this means is further improved.

(Sixth means) The sixth means of the present invention is the fifth means according to the fifth means, wherein the convergence means adjusts the set values β _f and β _{p of the} angles by a numerical value based on an inclination method. It is a milling machine control device that automatically adjusts by the solution method. In this means, the set values β _f and β _p of the inclination angle of the ball end mill are automatically adjusted by the convergence means having a built-in inclination method. Appropriate value of inclination angle β
_{f, β p} can be obtained quickly and precisely.

Therefore, according to this means, in addition to the effect of the fifth means described above, the appropriate values β _f and β _{p of} the inclination angles can be quickly and precisely determined without requiring any manpower for adjustment and convergence of the inclination angles. There is an effect that is required. If the input / output and the initial value setting, and the setting of the step size and the convergence condition, etc. are also automated, the milling machine control device of this means automatically operates without any manual operation.
Further labor saving becomes possible.

[0026]

DESCRIPTION OF THE PREFERRED EMBODIMENTS Embodiments of a cutting method and a milling machine control device using a ball end mill according to the present invention will be clearly and fully described in the following examples so that those skilled in the art can understand the present invention. Before describing the embodiments, the meaning of each symbol used in the formulas and the definition of the coordinate system will be clarified with reference to the drawings, and the formulas will be derived so that the formulas can be used. .

[Definition of Formula] (Definition of Tool Coordinate System) As shown in FIG. 5A, the tool coordinate system fixed to the ball end mill has a hemispherical surface having a radius R formed by a cutter at the tip of the ball end mill. Is a right-handed, non-rotating coordinate system that moves with the ball end mill with the coordinate origin at the center point of. The z-axis of the tool coordinate system is set to point in the direction of the main axis so as to coincide with the center axis of the ball end mill. The y-axis of the tool coordinate system is set in a direction coinciding with the feed direction when the ball end mill stands upright (β _f = β _p = 0). The x-axis of the tool coordinate system is
Similarly, the ball end mill is set upright in a direction corresponding to the pick feed direction. However, as described above, the tool coordinate system is a non-rotating coordinate system only when the inclination angles β _f and β _p of the ball end mill are constant, and if the inclination angle changes for any reason, The tool coordinate system also rotates and moves in the same manner as the ball end mill.

The cutting edge angular position k is, as shown in FIG. 5B, an angular position from the negative direction of the z-axis of the tool coordinate system, that is, from the tip end direction of the ball end mill. On the other hand, as shown in FIG. 5 (c), the rotation angle position φ of the cutting edge of the ball end mill is clockwise (tool rotation direction) as viewed from the z axis from the negative direction of the x axis of the tool coordinate system. It is assumed that the angular position around the z-axis is measured. However, in the embodiment described later, since the rotation angle position φ is to be measured from the positive direction of the x axis of the tool coordinate system, the starting point of the rotation angle position φ (φ
= 0) is to be understood as temporary.

Therefore, the arbitrary cutting edge position P at the radius R is, as shown in FIG. 5A again, a plane including the z-axis defined by the rotation angle position φ (0 ≦ φ ≦ 2π). , The cutting edge angle position k (0 ≦ k ≦
The position raised by (π / 2) is defined as a combination of the rotation angle position φ and the cutting edge angle position k. next,
As shown in FIGS. 6 (a) and 6 (b), the shape of the chips generated per cutting edge (cutter) during cutting by the ball end mill is shifted in the feeding direction by the feed amount f _z per cutting edge. It has a substantially triangular shape formed between the two spheres that are going on. The upper surface of the swarf is a part of the upper surface of the cut surface of the workpiece, and the left end surface of the swarf is a part of the groove-shaped surface to be formed at the time of the previous cutting.

Here, as shown in FIG.
Cutting edge angle position k corresponding to the upper end of the chip at the degree position φ
_aAnd the cutting blade angular position k at the lower end of the chip_eIs a tool
Inclination angle β = [β_f, Β_p]^TAnd the rotation angle position φ
Defined as a number. In addition, actually shaving the chips
Effective cutting edge angle k which is the angle range of the cutting edge_cIs k_aWhen
k_e(K_c= K_a-K_e). here
The ball end mill has a plunge cut with an inclination angle.
(Β_f<0, β_p<0) so the lower end of the chips
Cutting edge angle position k corresponding to the part_eIs always zero and the effective
Blade angle k_cIs k _aIs equal to Note that along the cutting edge angle position k
The effective cutting edge length s is the inclination angle β _f, Β_psmell
Effective cutting edge angle k which is a function of the rotational angle position φ_cSought
Then s = R · k_cEasily sought.

Further, as shown in FIG. 6 (d), the range of the rotational angular position φ of the chips at a predetermined cutting edge angle position _{k (k e ≦ k ≦ k} a) , the rotational angle position at the time of cut Range from φ _e to rotation angle position φ _a at the end of cutting (φ _e ≦ φ ≦ φ _a )
It is. Rotation angle φ during actual cutting during this time
_c (0 ≦ φ _c ) is obtained by φ _c = φ _a −φ _e . The effective cutting length l along the rotation angle position φ
_c is l if the rotation angle φ _c during actual cutting, which is a function of the cutting edge angle position k at the inclination angles β _f and β _p , is determined.
_c = R · sin (k) · φ _c is easily obtained.

(Definition of Cutting Surface) The effective cutting vector K that defines the direction of the triaxial component of the reaction force acting on each cutting edge point of the ball end mill from the workpiece as the work material is k _e = 0. k _c = k _a , and the following equation 1 is expressed in the tool coordinate system.
Is represented by a vector.

[0033]

(Equation 1)

Here, the x-axis component and the y-axis component in the tool coordinate system in the above equation 1 are components corresponding to the reaction force due to the cutting resistance as the reaction force perpendicular to the chip cross-sectional area cut by the cutting edge. It is. On the other hand, the z-axis component in Equation 1 indicates a component corresponding to a reaction force generated when the cutting edge is pressed against the workpiece by plunge cutting. x-axis component and y
Regarding the fact that the vector sum of the cutting force of the axis component is proportional to sin (k _c ) and the z-axis component is proportional to cos (k _c ), although no clear explanation is given theoretically,
Experience has shown that these values are generally taken.
Since the component in the z-axis direction does not generate a bending moment in the ball end mill, if only the relationship between the x-axis component and the y-axis component is correctly grasped, the error in the z-axis direction component in the subsequent mathematical expression development will be described. Is acceptable. As an aside, those skilled in the art are accustomed to saying that cutting force includes the z-axis component.

The inclination angle β _{f in} the tool feed direction during inclined cutting including plunge cutting is defined as an in-plane inclination including two directions of a normal direction extending in the vertical direction of the work surface and the tool feed direction. Shall be. Further, the inclination angle beta _p of the pick feed direction, shall be defined as the slope in a plane containing a line with the inclination angle beta _p direction pick feed direction. That is, the tool coordinate system is rotated from the workpiece coordinate system by the tilt angle β _{f in the} tool feed direction, and then tilted by the tilt angle β _p from the coordinate system tilted by the tilt angle β _f toward the pick feed direction. Things. Then, the rotation matrix D at that time is represented as a matrix having elements shown in the following Expression 2.

[0036]

(Equation 2)

Therefore, the effective cutting vector K expressed in the tool coordinate system is converted into the cutting action vector Kc of the ball end mill at the time of inclined cutting in the work coordinate system by the following equation ₍ 3).

[0038]

(Equation 3)

Next, in order to determine various parameters at the time of cutting, a geometric vector notation of a non-cut portion of the work is performed. At this time, in order to determine the tool rotation angle phi _c during cutting, it intended to cover the fan-shaped cutting surface as a kind of envelope. Then, as shown in FIG. 7B, the cut surface is defined by a curved surface and a curved portion, in particular, as shown in FIG. 7B. The curved surface formed between the corners where two of the three fan-shaped line segments intersect with each other is a generating surface generated by the cutting edge of the ball end mill, and is close to a spherical surface, but one of the cutting edges. Since there is an amount of feed per tooth f _z , a quadratic surface slightly deviating from the spherical surface is formed.

Here, a vector in the tool feed direction is defined as f, a unit vector on the y-axis in the workpiece coordinate system, and a unit vector in a direction perpendicular to a plane on which the workpiece is cut is defined as n.
Assuming that the feed direction is parallel to the work surface, the following equation 4 holds.

[0041]

(Equation 4)

By solving the three-dimensional simultaneous partial differential equation, the effective cutting edge angle k _c for determining the shape of the work surface of the workpiece can be expressed as an arbitrary rotation angle position φ (φ _e ≦ φ ≦ φ _a ) as follows: Can be obtained from Equation 5.

[0043]

(Equation 5)

Conversely, the rotation angle φ during actual cutting is_cIs
Cutting edge angle position k (k_e= 0 k k_a) Function
Can also be obtained numerically. This relationship is illustrated in the diagram.
As shown in Fig. 8, the characteristic
Since it can be illustrated as a graph showing the movement,
If the same graph is created based on the above Equation 5,
Rotation angle φ during actual cutting_c As a function of the cutting edge angular position k
You can also ask. However, FIG. 8 facilitates understanding.
Cutting but not plunge cutting
The reverse cut is illustrated. Soy sauce
The cutting edge angle position k at the lowest position of actual cutting_eOr notch
K that sometimes occurs _eThe lowest value of k_minIs non-zero
Or rotation angle φ during actual cutting_c= Not 360 °
FIG. 8 is a graph showing a unique behavior different from plunge cutting.
Has become.

First, the boundary curves of FIGS.
Cutting edge angle k ₁₂ to produce the (fan shape 2) is fan-shaped F (phi
_c ) and the rotation angle φ _c during actual cutting, FIG.
(B) As the (x, z) curve viewed from the arrow A in the following equation (6)
Is represented by

[0046]

(Equation 6)

Here, the vector K _c (k ₁₂ ) is a cutting action vector at the cutting edge angle k ₁₂ = k _max -k _min , and p is a pick feed [mm]. Next, FIGS. 7 and 8
Boundary curve - similarly cutting edge angle k ₂₃ to produce a value of the z-axis at A arrow in FIG. 7 (b) is a constant line is expressed by an equation 7.

[0048]

(Equation 7)

Here, a vector K _c (k ₂₃ ) is a cutting action vector at the cutting edge angle k ₂₃ , t is a cutting depth [mm] of the ball end mill from the work surface, and R
Is the radius [mm] of the cutting edge of the ball end mill.

Finally, the boundary curves in FIGS.
Cutting edge angle k for generating (fan shape 1) ₁₃Is a three-dimensional curve and
Then, it is expressed by the following Expression 8.

[0051]

(Equation 8)

Where the vector K_c(K₁₃) Is the cutting edge angle
the cutting action vector at k13, the vector K
_c(Φ_c, K_c) Is the effective cutting edge angle k_c= K_a-K_e= K_a−
0 = k_a, Rotation angle φ during actual cutting_c= Φ_a−φ_e= 360
This is the cutting action vector in degrees. Also, f _zIs a cutting blade
It is a feed amount per mm [mm / tooth].

Each parameter calculated as above is
Cutting from the start of cutting of the cutting edge of the ball end mill to the end
Obtained by time (more accurate because of the plunge cut
Is formed while the cutting blade makes one round)
The behavior of is shown. This characteristic behavior is plunge cut
In the case of reverse cut instead, as shown in FIG.
Although it has a relatively simple shape,
In this case, chips are cut out continuously, so as shown in FIG.
Thus, it is formed in a spiral shape. The thickness of the chips is
Of the mill (the rotation angle at the start of cutting)
Position φ_eAnd the rotation angle position φ at the start of idle cutting_a)When,
Two cutting edge angle positions (the cutting edge at the lowest cutting edge position during actual cutting)
Angular position k_eAnd the cutting edge angle at the highest position of the cutting edge during actual cutting
Degree position k _a) Is calculated within the range. In addition, plunge
Usually φ in cut_e= 0 °, φ_a= 360 °
Rotation angle during actual cutting φ_cIs φ_c= Φ_a−φ_e= 360
°.

[0054] In the same manner as the equation 8, a three-dimensional curved surface creation surface by cutting enclosed by boundary curves of Figure 7 --- is the effective cutting edge angle kc and the rotation angle phi _c in real cutting parameters ( It is expressed by the following equation 9 as a parameter.

[0055]

(Equation 9)

(Chip cross-sectional area) Predetermined rotation angle position φ (φ
_e ≦ φ ≦ φ _a ) and the cutting edge angular position k (k _e ≦ k ≦
The chip thickness h in k _a ) is the tool inclination angle β _f , β _p
Is calculated numerically as a function of the rotation angle position φ and the cutting edge angle position k. Between the cuts cutting blades at a rotational angular position phi = phi _e until the cutting edge is round, only tool feed f _z per sheet number × cutting of the cutting edge, because the ball end mill is fed, analysis Chip thickness h (k, φ)
Was difficult to seek. Therefore, the chip thickness h
(K, φ) is numerically obtained by a numerical analysis tool having a three-dimensional model. The parameters included at this time are the inclination angles β _f and β _p , the radius R of the cutting edge of the ball end mill, and the number of cutting edges. i, the tool feed amount f _z per cutting edge, the cutting depth t, and the pick feed p.

Thus, the chip thickness h (k, φ) is again
As shown in FIG. 6 (c), the inclination angle β _f, Β_pEtc.
Data as shown in FIG. 6 (c).
The chip cross-sectional area A (φ) at the rotation angle position φ of
It is calculated by 0.

[0058]

(Equation 10)

Here, the value of the above equation (10) is calculated by a computer by numerical calculation including numerical integration. The value of k _e is the case of plunge-cut (to be considered open angle of the cutting edge) is always zero, the value of k _a is a function of the angular position φ of the cutting-specific behavior of FIG. 8 It can be determined from the graph shown. Further, since h (k, φ) also changes depending on the inclination angles β _f and β _p , the inclination angle β
_f and β _p are also added as independent variables, and h (k, φ, β _f ,
β _p ). Regarding the independent variable of the chip thickness h, the same applies to the following equation.

The area moment MA, which is the primary moment formed by the chip cross-sectional area A (φ) around the axis of rotation of the tool,
(Φ) is calculated by numerical calculation according to the following equation (11).

[0061]

[Equation 11]

Here, the bending moment around the rotation axis of the tool due to the cutting resistance acting on the cutting edge during cutting is expressed by the above equation (11).
Is considered to occur in proportion to the area moment represented by the following expression, so the area moment MA (φ) has a significant significance.

(Chip volume) By integrating the chip cross-sectional area A (φ) with respect to φ, it is possible to obtain the volume V of the chips to be cut out while one cutting blade makes one round according to the following equation (12).

[0064]

(Equation 12)

The volume moment MV, which is the primary moment formed by the chip volume V around the tool rotation axis, is obtained by numerical calculation according to the following equation (13).

[0066]

(Equation 13)

Here, it is considered that the reaction torque generated around the tool rotation axis due to the cutting resistance acting during cutting is proportional to the volume moment expressed by the above equation (13). (Component force of cutting force) As described above, the bending moment around the tool rotation axis due to the cutting force acting on the cutting edge during cutting is the area moment MA (φ) expressed by the above equation (11).
It is considered to be proportional to Therefore, the area moment M
By multiplying A (φ) by sinφ or cosφ and integrating with respect to the rotational angle position φ, a value proportional to the bending moment in the left-right direction or the front-back direction of the ball end mill with respect to the feed direction can be calculated. That is, a value Fp proportional to the bending moment in the left-right direction
Is obtained by multiplying the area moment MA (φ) by sinφ and integrating the result with respect to the rotational angle position φ, by the following Expression 14. Similarly, the value Ff proportional to the bending moment in the front-rear direction is the area moment MA
By multiplying (φ) by cos φ and integrating with respect to the rotation angle position φ, it can be obtained by the following equation 15.

[0068]

[Equation 14]

[0069]

(Equation 15)

(Restriction of Inclination Angle) In the above description, the cutting edge has been described as if it were at the center (k = 0) of the tip of the ball end mill. An opening without a cutting edge is formed at the center of the tip. That is, as shown in FIG.
Since there is an opening with a diameter L and a half apex angle α at the tip of the ball end mill, and no cutting edge is formed in the opening,
No cutting is performed at the portion corresponding to the opening while the cutting blade makes one round. Therefore, as shown in FIG. 9 again, a substantially circular hole-shaped defective portion corresponding to the tool opening is formed in the center of the chip. However, the portion left uncut at the central portion of the cutting chips is cut on the inner peripheral side of the opening portion of the cutting blade sent thereafter, so that it does not remain on the work as it is.

In FIG. 10, the opening is greatly exaggerated. However, in order to secure the cutting portion A corresponding to the cutting portion B to offset the bending moment, the opening is formed from the surface of the work. There is a restriction that the ball end mill must not be tilted until it protrudes. Then, the vertical distance ab from the cutting bottom of the ball end mill to the upper end of the opening is:
Since it must be smaller than the cutting depth t, there is a constraint expressed by the following equation (16).

[0072]

T> ab = R ｛1-cos (−β _f +
α)｝ However, the half apex angle α of the opening portion is sin ⁻¹ (L / 2R). As a result, the inclination angle β _f in the feed direction is subject to the constraint shown in the following Expression 17 in addition to the constraint of plunge cutting.

[0073]

0 <−β _f <cos ⁻¹ (1-t / R) -α Similarly, the inclination angle β _p in the pick feed direction is −β
_{In the} range where _f is relatively small, there is approximately a constraint shown in the following Expression 18 in addition to the constraint of plunge cut.

[0074]

0 <−β _p <cos ⁻¹ (1-t / R) −α Therefore, the inclination angles β _f , β of the ball end mill
_p needs to be set within the range of constraints that satisfy both Equation 17 and Equation 18 from the initial value to the appropriate value. [Embodiment 1] (Cutting Method by Ball End Mill of Embodiment 1) The cutting method by a ball end mill as Embodiment 1 of the present invention is a method in which a ball end mill is moved forward and backward and left and right with respect to the surface of a work in a milling machine with respect to a feed direction. It is used when performing plunge cutting (piercing cutting) by tilting. That is, in the cutting method using the ball end mill of the present embodiment, before cutting, the appropriate values of the inclination angles β _f and β _p of the ball end mill are calculated by numerical calculation,
Cutting is performed after setting the inclination angle of the ball end mill of the milling machine with the appropriate value.

In calculating the appropriate values of the inclination angles β _f and β _p , first, the set values of both the front-back inclination angle β _f and the left-right inclination angle β _p of the rotation axis of the ball end mill are initially set. Then, an estimated value corresponding to the front-rear bending moment applied in the front-rear direction of the rotation axis of the ball end mill and an estimated value corresponding to the left-right bending moment applied in the left-right direction of the rotation axis are estimated by numerical calculation. next,
Until the absolute value of the estimated value corresponding to both bending moments becomes equal to or less than a predetermined value, resetting of the set values β _f and β _p and estimation of the estimated value corresponding to both moments by the same numerical calculation are repeatedly performed. . As a result, the inclination angle β _f , which suppresses the absolute value of the estimated value corresponding to both moments to a predetermined value or less,
Since β _p is calculated, the inclination angles β _f and β _p are set to appropriate values.

The above-described cutting method using the ball end mill of this embodiment will be described more specifically below. Unlike the above description, as shown in FIG. 11, the positive direction of the x-axis in the pick feed direction of the tool coordinate system is set as the starting point (φ _c = 0) of the rotation angle φ _c during actual cutting, and φ _c is set. It is defined as the same clockwise increasing angle as the direction of rotation of the tool. Similarly, the rotation angle position φ also starts from the positive direction of the x-axis in the pick feed direction of the tool coordinate system, and φ is defined as an angle that increases in the same clockwise direction as the rotation direction of the tool. And
Specific calculations are performed according to the flowcharts shown in FIGS.

First, when the operation is started at the beginning of FIG. 12, each input value (R, f _z , t, p; defined but see “Description of Signs”) and , The inclination angle β _f ,
It is assumed that the initial value of β _p has already been input or set. In the execution step (a), the range in which the inclination angles β _f and β _p can be set is set by the above Expressions 17 and 18. Next, in the execution step (b), the rotation angle φ _c during the actual cutting is defined as described above (may be defined before the start of the calculation).

[0078] Then, in executing step (c), the initial value beta _f of the inclination angle, with respect to beta _p, according to the number 6 above, boundary curve - cutting edge angle k ₁₂ for generating is calculated. Similarly, in executing step (d), according to the number 7 of the aforementioned boundary curve - cutting edge angle k ₁₂ is calculated to generate, in execution step (e), according to the number 8 described above, boundary curve - generating a cutting edge angle k ₁₃ is calculated.

[0079] Then, phi in execution step (f), a cutting edge angle position k _e in cutting edge angle position ka and the lowest position at the highest position in the actual cutting, are subdivided in a predetermined segment ( 0
≦ φ ≦ 2π). As described above, the eigen behavior model or the three-dimensional numerical model corresponding to the graph of FIG. 8 is automatically generated by the computer.

Then, the process proceeds to the latter half of the flowchart shown in FIG. 13, and in order to obtain the inclination angle β _f in the tool feed direction, numerical integration is performed at an appropriate integration interval in accordance with the following equation (19). Volume A (f) 0 →
π and the pseudo volume A (f) π → 2π of the front part are obtained in advance.

[0081]

[Equation 19]

Here, f in parentheses is a suffix indicating the feed direction (feed direction). The reason that the pseudo volume is not called the volume or the cross-sectional area is that it is double-integrated at the cutting edge angle position k and the rotation angle position φ, but is different from the normal volume calculated by the aforementioned equation (12). This is because it has a dimension of area and is different from the cross-sectional area. However, since only Rsink is missing in the integrand for the volume of the above equation 12,
It was essentially considered to be a pseudo volume and was called pseudo volume.

Pseudo volume A at the rear with respect to the tool feed direction
(F) The difference between 0 → π and the pseudo volume A (f) π → 2π at the front is a value roughly proportional to the bending moment for bending the ball end mill in the left-right direction (pick feed direction) orthogonal to the feed direction. . Therefore, the front pseudo volume A (f)
Abs (f) = | A (f) 0 → π−A (f) π → 2π | The absolute value of the difference between 0 → π and the pseudo volume A (f) π → 2π at the rear
Is determined to be sufficiently small, it means that the bending moment in the left-right direction is substantially suppressed to around zero.

This determination is made in the next determination step (h).
Will be Abs (f) ≡ is determined in this step.
| A (f) 0 → π−A (f) π → 2π | ≦ ε (sufficiently small
Is a positive judgment value). Judgment step
If No is determined in (h), the bending moment in the left-right direction
Right has not yet been sufficiently suppressed,
Feed direction which has a dominant direction bending moment
Angle of inclination β_fIs reset properly and the execution
Return to step (c). Conversely, in the judgment step (h), the judgment is Yes.
When set, the bending moment in the left-right direction is sufficiently suppressed.
The bending moment in the left-right direction.
Dominant feed direction tilt angle β _fSet value
Is determined to be an appropriate value.

When the appropriate value of the inclination angle β _f is temporarily set in this way, in the next execution step (i), in order to obtain the inclination angle β _p in the pick feed direction, an appropriate value is obtained according to the following equation (20). Numerical integration is performed at integration intervals.

[0086]

(Equation 20)

By the numerical calculation of the above Expression 20, the pseudo volume A (p) π / 2 → 3π / 2 at the rear in the pick feed direction.
And the pseudo volume A (p) 3π / 2 → π / 2 at the front. In the above Expression 20, p in parentheses is a suffix indicating the pick feed direction, and the integral range 3π / 2 → π /
2 is equivalent to 3π / 2 → 5π / 2.

Here, with respect to the pick feed direction, the pseudo volume A (p) π / 2 → 3π / 2 at the rear and the pseudo volume A at the front
(P) The difference from 3π / 2 → π / 2 is a value that is approximately proportional to the bending moment in the front-rear direction of bending the ball end mill in the tool feed direction orthogonal to the pick feed direction. Therefore, the pseudo volume A at the rear with respect to the pick feed direction
(P) π / 2 → 3π / 2 and pseudo volume A (p) 3π / 2 → π in front
/ 2 Absolute value Abs (p) = | A (p) π / 2 → 3π /
If it is determined that 2-A (p) 3π / 2 → π / 2 | is sufficiently small, it means that the bending moment in the front-rear direction is substantially suppressed to around zero.

This determination is made in the next determination step (j). What is determined in this step is Abs (p) =
| A (p) π / 2 → 3π / 2−A (p) 3π / 2 → π / 2 | ≦ ε
(A sufficiently small positive judgment value). If No is determined in the determination step (j), it means that the bending moment in the front-rear direction has not yet been sufficiently suppressed, and therefore the inclination angle β in the pick feed direction which has a dominant influence on the bending moment in the front-rear direction. _p is appropriately reset, and the process returns to the execution step (c) again. Conversely, if the determination in step (j) is Yes, the bending moment in the front-rear direction is sufficiently suppressed, and the inclination angle in the pick feed direction, which has a dominant influence on the bending moment in the front-rear direction. The set value of β _p is determined to be an appropriate value.

At this stage, since the inclination angle β _{f in the} feed direction has already been determined to be an appropriate value in the above-mentioned step (h), an appropriate value (optimum value) for both inclination angles β _f and β _p. Has been obtained. Therefore, if it is determined as Yes in the determination step (j), the set values of both the inclination angles β _f and β _p at that stage are output as appropriate values, and the inclination angle of the ball end mill of the milling machine is set. The actual cutting will be started.

(Numerical Example and Effect of First Embodiment) After actually performing calculations in accordance with the above-mentioned flowcharts (see FIGS. 12 and 13), cutting by a ball end mill with a milling machine was tested. So report the results. The ball end mill used at that time had a radius of the cutting blade portion of R = 5 mm and a two-blade having an opening having a diameter L = 0.3 mm at the center of rotation at the tip.
Milling machine setting, pick feed is p = 0.3m
m, the cutting depth was t = 0.3 mm, the tool feed amount per cutting edge was f _z = 0.135 mm / tooth, and the tool protrusion length was 10 times the tool diameter.

First, in the execution step (a), based on Equations (17) and (18), -18 ° <β _f <0 ° and −1 ° with respect to both inclination angles β _f and β _p of the ball end mill.
A restriction of 8 ° <β _p <0 ° was obtained. Therefore, as initial values of the two inclination angles β _f and β _p , β _f = −5 °,
β _p = −10 ° was set. Then, in executing step (b), defined rotational angle phi _c in real cutting is performed.

Then, based on the above conditions, in execution steps (c) to (e), the boundary curves of the three sides of the chips are obtained, and subsequently in execution step (f), the cutting edge angular position at the highest position is obtained. k _a and cutting edge angle position k _e at the lowest position has been determined. Next, in the execution step (g), the rear pseudo volume A (f) 0 → π and the front pseudo volume A
(F) π → 2π was obtained as follows according to the above-mentioned equation (19). The rear pseudo volume A (f) 0 → π = 0.063 mm ² .The front pseudo volume A (f) π → 2π = 0.101 mm ^{2. In the} following determination step (h), the rear pseudo volume and the front pseudo volume are determined. Assuming that the absolute value of the difference from the volume is 0.05 mm ² or less as the convergence condition (ε = 0.05 mm ² ), the convergence determination is No. Since the front pseudo volume at this state is much larger than the rear pseudo volume, so as to increase the rear pseudo volume reduces the front pseudo volume to suppress the difference between, deeply the feed direction of the inclination angle beta _f, beta _f =
Reset as -7 °.

In the execution step (g), which is repeated from the execution step (c), the rear pseudo volume and the front pseudo volume are calculated as follows. The rear pseudo volume A (f) 0 → π = 0.083 mm ² .The front pseudo volume A (f) π → 2π = 0.081 mm ^{2. In the} subsequent determination step (h), the rear pseudo volume and the front pseudo volume are determined. Since the absolute value of the difference from the volume is 0.05 mm ² or less, the convergence determination was Yes, so that the inclination angle β _{f in} the feed direction is considered to have converged properly, and the next execution step (i Proceed to).

Next, in the execution step (i), the rear pseudo volume A (p) π / 2 → 3π / 2 and the front pseudo volume A (p) 3π / 2 → π / 2 in the pick feed direction are calculated as described above. It was obtained as follows according to Equation 20. Rear pseudo volume A (p) π / 2 → 3π / 2 = 0.054 mm ² Front pseudo volume A (p) 3π / 2 → π / 2 = 0.109 mm ^{2 In the} following determination step (j), Assuming that the absolute value of the difference between the rear pseudo volume and the front pseudo volume is 0.05 mm ² or less, as the convergence condition (ε = 0.05 mm ² ), the convergence determination is No. Since the front pseudo volume at this state is much larger than the rear pseudo volume, so as to suppress the difference between them to increase the rear pseudo volume reduces the front pseudo volume, deep inclination angle beta _p of pick-feed direction, Reset as β _p = −13 °.

Then, when the process is repeated from the execution step (c) again, the judgment step (h) is also judged as Yes, so that the operation proceeds to the execution step (i). In the execution step (i), the rear pseudo volume and the front pseudo volume in the pick feed direction were calculated as follows. Rear pseudo volume A (p) π / 2 → 3π / 2 = 0.077 mm ² Front pseudo volume A (p) 3π / 2 → π / 2 = 0.092 mm ^{2 With} this value, in the determination step (j) since it is determined as No again to further deepen the inclination angle beta _p of pick feed direction, and reset the β _p = -14 °. Then, when the calculation was performed again from the step (c), the following calculation was performed in the execution step (i). Rear pseudo volume A (p) π / 2 → 3π / 2 = 0.087 mm ² Front pseudo volume A (p) 3π / 2 → π / 2 = 0.082 mm ^{2 In the} following determination step (j), since the absolute value of the difference between the rear pseudo volume and said front pseudo volume is 0.05 mm ^2, the convergence determination so came out with Yes, will assume that properly converge the inclination angle beta _p of the pick-feed direction Was. As a result, as the optimum inclination angles, β _f = −7 ° and β _p = −
14 ° was required.

To prove the effect of the above calculation results,
A cutting test was actually performed to measure the dimensional accuracy, and compared with the dimensional accuracy of the comparative example. At this time, the material of the work (work material) was SKD11, and its hardness was HRC60. The dimensional errors of the machined surfaces are summarized in Table 1 below.

[0098]

[Table 1] Dimensional error As is clear from Table 1 above, according to the cutting method using the ball end mill in the present example, the dimensional accuracy was improved by slightly more than an order of magnitude compared to the vertical cutting in Comparative Example 1, and The improvement of the dimensional accuracy of less than one order of magnitude was also obtained with respect to the initial value set for. That is, in comparison with the vertical cutting in Comparative Example 1, the plunge cutting in which the inclination angle is appropriately set in Comparative Example 2 can be expected to reduce only a dimensional error of about several percent, whereas the plunge cutting according to the present embodiment can reduce the dimensional error. There is an effect that a dimensional error of about one digit can be reduced.

As common knowledge of those skilled in the art of processing such as cutting,
To improve the dimensional accuracy by an order of magnitude, the cost of the machine tool and the number of man-hours required for the work are increased by several times, and it is necessary to endure a significant increase in cost. However, according to the present invention, as the minimum equipment, it is sufficient to have a program for executing the calculation method of this embodiment (see FIGS. 12 and 13) and one personal computer capable of calculating the program.

Therefore, according to the cutting method using the ball end mill of this embodiment, there is an effect that the cutting accuracy can be improved by about one digit with a very small increase in cost. Moreover, the cutting method using the ball end mill of the present embodiment is suitable for cutting a forging die having a deep bottom shape, which has high hardness and tends to increase the deflection of the ball end mill, but requires strict precision in finished dimensions. In particular,
Ideal for cutting cold forging dies made of high hardness materials.

(Milling Machine Control Apparatus of First Embodiment) The present invention has been described so far from the viewpoint of a method invention, but from now on, it will be described as an apparatus invention. As shown in FIG. 14, a milling machine control device according to the first embodiment of the present invention receives an input from numerical data generated by a CAD / CAM processing device 2 and adds a tilt angle of a ball end mill to a control plate 4 of an NC milling machine 4. Is a device that outputs an appropriate value of The milling machine control device 3 of the present embodiment is of a real prototype level used for experimenting the numerical examples described above, and the input and output of the milling machine control device 3 are performed manually by an operator. I have.

Since the CAD / CAM processing device 2 sets the processing conditions and the like based on the storage device 1 of the product drawing, the tool radius R, the feed amount f _z per cutting edge, the pick feed p, the cutting depth, Input values such as t are set by the CAD / CAM processing device 2. In the present embodiment, these input values are read by the operator from the output of the CAD / CAM processing device 2 and input to the milling machine control device 3 of the present embodiment from the keyboard. The milling machine control device 3 is a computer that stores a program that embodies the above-described numerical calculation algorithm, and has a function of calculating the optimal inclination angles β _f and β _p of the ball end mill. The appropriate values β _f and β _p of the two inclination angles obtained by the milling machine control device 3 are read by the operator from the display on the display, and are input to the control panel 5 of the NC milling machine 4 by input means such as a keyboard. At this time, the appropriate values β _f and β _p of both inclination angles are converted into values suitable for the ab two-axis control unit 52 of the control panel 5 and input. However, if the two axes ab are the same axis system as the coordinate axis system of the inclination angles β _f and β _p , the above conversion is not necessary. The NC milling machine 4 includes the CAD / CAM processing device 2 and the milling machine control device 3 as described above.
The drive unit 6 is controlled by the control panel 5 which is input from the controller and performs plunge cutting by a ball end mill.

That is, the milling machine control device 3 of this embodiment can perform plunge cutting (piercing cutting) by inclining the ball end mill with respect to the surface of the work in the front-rear direction and the left-right direction with respect to the feed direction at predetermined inclination angles. This is an apparatus for setting the inclination angles β _f and β _p of the rotation axis of the ball end mill to appropriate values with respect to the possible NC milling machine 4.

This apparatus has at least input means, estimation means, convergence means and output means. The input means is specifically a keyboard and an input program. At least, the tool radius R and the number of cutter blades of the ball end mill, the desired pick feed p, the cutting depth t,
It has a function of inputting input values corresponding to the feed speed and the tool rotation speed.

The estimating means is, specifically, an arithmetic unit. The input value, appropriately set initial values of the inclination angles β _f and β _p of the ball end mill, and appropriately set integration step size And an estimated value corresponding to the longitudinal bending moment acting in the longitudinal direction of the rotation axis of the ball end mill based on
It has a function of estimating an estimated value corresponding to a lateral bending moment applied in the lateral direction of the rotating shaft. The estimating means performs the execution step (g) of the above-described flowchart (see FIG. 13).
And execution step (i).

The convergence means is specifically an arithmetic unit. However, the forward and backward inclination angles β _f and the left and right inclination angles β _f of the rotation axis of the ball end mill are kept until the above-mentioned estimated values obtained by the above-mentioned estimation means become equal to or less than predetermined values. _It has a function of adjusting the set values of both angles of _p and repeating the above estimation, thereby calculating appropriate values of both angles β _f and β _p . The convergence means corresponds to the judging step (h) and the judging step (j) in the above-described flowchart (see FIG. 13) and a function of appropriately resetting the inclination angles β _f and β _p . That is, the convergence means
Inclination angle beta _f, performed until the convergence determination of beta _p, having an inclination angle beta _f until convergence, reconfigure the beta _p function to repeat the operation on the operation means. In this means at the prototype level, the function of properly resetting the inclination angles β _f and β _p relied on the judgment of the operator in the initial state, but originally a numerical value based on the inclination method as described later It should be programmed so that the tilt angles β _f and β _p are automatically reset by the solution method.

The output means is a display in the present means at the stage of trial production. The appropriate values β _f and β _p of the two inclination angles calculated by the convergence means are used to set the tool inclination angle of the control panel 5 of the NC milling machine 4. Ab biaxial control unit 52 as a means
And has a function of outputting to the control panel 5 of the NC milling machine 4 in a format suitable for. Milling machine control device 3 of the present embodiment
Is configured as described above, it exhibits an operation equivalent to the above-described cutting method using the ball end mill of the present embodiment, and as a result, it can exhibit the same effect as the above-described effect.

That is, according to the milling machine control device 3 of this embodiment, there is an effect that the cutting accuracy can be improved by about one digit at a relatively small cost. Further, the milling machine control device 3 of the present embodiment is suitable for cutting a forging die having a deep bottom shape, which has a high hardness and tends to have a large deflection of a ball end mill, but has a severe requirement for finished dimensional accuracy. Ideal for cutting cold forging dies made of hard materials.

(Modification 1 of Embodiment 1) As Modification 1 of this embodiment, it is possible to implement a milling machine control device 3 that automates input / output operations and operation of convergence means. In this modification, an input value appropriately set from the CAD / CAM processing device 2 is automatically input to the milling machine control device 3 online, and if there is an insufficient input, a display prompting the input is displayed. The correct input value is replenished from the keyboard. The appropriate values β _f and β _p of the inclination angles obtained as a result of the numerical calculation are converted into numerical data suitable for the a-axis and the b-axis for inclining the ball end mill of the NC milling machine 4, and are transmitted from the milling machine control device 3 to the NC milling machine. 4 is automatically output online to the control panel 5.

Further, in this modification, the convergence means has a function in the program for automatically adjusting the set values of the inclination angles β _f and β _p by a numerical solution based on the inclination method. I have. That is, moderate small angle (e.g. 0.1 °) value corresponding to only the inclination angle beta _f or beta staggered _p bending moment is calculated, which corresponds to a partial differential value of a value corresponding to a bending moment due to the inclination angle The tilt is calculated and the correct correction is made to the tilt angle to automatically reset the tilt angle. Therefore, since an operator is not required for operating the convergence means, the convergence calculation is performed more quickly. Further, by setting the allowable range (ie, ε) of the value corresponding to the bending moment to be narrower, it becomes possible to more accurately obtain the appropriate values β _f and β _p of the inclination angle.

The inventors have already developed a milling machine control device 3 having such a convergence means and are operating it on a trial basis. The milling machine control device 3 is a high-performance personal computer in terms of hardware, and incorporates a CAD tool having a three-dimensional modeling function as software. Therefore, according to the milling machine control device 3, a function of performing a numerical operation with a graphic display of a three-dimensional numerical model is obtained, and a three-dimensional grasp of a virtual cutting situation, a created surface by cutting, and a shape of a chip is obtained. Has the effect that it becomes easier for the operator.

Therefore, according to the present modification, the above-described actual
In addition to the effect of the first embodiment, the inclination angle β _f, Β_pThe appropriate value of
Since labor savings including man-hours until calculation are advanced,
Mistakes can be prevented and labor costs can be reduced.
There is an effect that. (Modification 2 of Embodiment 1) Modification 2 of Embodiment 1
Instead of the pseudo volume by the above equations 19 and 20
Therefore, the volume in the correct meaning based on the above equation 12
To calculate the bending moment by
is there.

That is, in this modified embodiment, the estimated value corresponding to the bending moment in the feed direction is estimated from the difference between the chip volume on the first half and the chip volume on the second half of the rotation axis of the ball end mill. , The inclination angle β _{f in the} feed direction is reset based on the difference. The estimated value corresponding to the bending moment is calculated from the difference between the chip volume on the right half of the rotation axis of the ball end mill and the chip volume on the left half, and the inclination in the pick feed direction is calculated based on the difference. The angle β _p is reset.

Therefore, according to the present modification, the inclination angles β _f and β _p are adjusted based on the chip volume calculation more practically than in the first embodiment, so that a higher finished dimensional accuracy can be achieved. There is an effect that it can be obtained. (Modification 3 of Embodiment 1) As Modification 3 of the present embodiment, a cutting method using a ball end mill for performing convergence judgment by making the pseudo volume of Embodiment 1 or the volume of Modification 2 described above dimensionless is described. It is possible.

In this modification, the tool radius R included in the pseudo volume or volume of the chips is divided by the same tool radius R to make it non-dimensional (it is not necessary to apply R from the beginning), and the chip thickness is reduced. h (k, φ) is divided by the feed amount f _z per cutting edge to make it non-dimensional. If the pseudo volume or volume of the chips is dimensionless, even if cutting conditions such as the tool radius R and the feed rate f _z per cutting edge change, the dimensionless pseudo volume or volume is reduced. There is less need to adjust the determination value ε that determines the range of the equivalence determination.

Therefore, according to the present modified embodiment, the number of setting inputs by the operator is reduced when the above-described first embodiment and the first and second modified embodiments are implemented, so that there is an effect that the labor can be further saved. Embodiment 2 (Cutting Method by Ball End Mill of Embodiment 2) The cutting method by a ball end mill as Embodiment 2 of the present invention is similar to that of Embodiment 1 except that the pseudo volume of This is a simple method of suppressing a bending moment by suppressing a difference in cross-sectional area. The chip cross-sectional area at an arbitrary rotation angle position φ can be easily obtained only by performing a single integration with respect to the cutting edge angle position k according to the above equation (10).

That is, in the cutting method using the ball end mill of this embodiment, the estimated value corresponding to the bending moment in the front-rear direction with respect to the feed direction is the chip cross-sectional area A (0 °) on the right side of the rotation axis of the ball end mill. And the chip cross-sectional area A (180 °) on the left. The estimated value corresponding to the bending moment in the left-right direction with respect to the feed direction is the chip cross-sectional area A (270 °) in front of the rotation axis of the ball end mill and the chip cross-sectional area A (90 °) behind. Is estimated with the difference from

Therefore, the inclination angle β _{p in the} left-right direction with respect to the feed direction is appropriate as long as the bending moment in the front-rear direction is sufficiently suppressed if the difference between the left and right chip cross-sectional areas in the feed direction converges to zero. The value is determined. Similarly, the inclination angle β _{f in the} front-rear direction with respect to the feed direction is determined to be an appropriate value on the assumption that the bending moment in the left-right direction is sufficiently suppressed if the difference in the cross-sectional area of the chips before and after the feed direction converges to zero. Is done.

Therefore, according to the cutting method using the ball end mill of the present embodiment, the amount of calculation is drastically reduced while obtaining the effect of improving the finishing dimensional accuracy according to the first embodiment. Therefore, the present embodiment can be implemented by a cheaper combination of hardware and software, so that there is an effect that the cost can be reduced as compared with the first embodiment. In this embodiment, the corresponding milling machine control device 3 can be implemented as in the first embodiment.

(Modification 1 of Embodiment 2) As Modification 1 of the present embodiment, the chip cross-sectional area A calculated by Expression 10 is used.
Instead of taking the difference of (φ), the difference of the area moment MA (φ) of the chip cross-sectional area calculated by the above equation 11 is taken, and the inclination angles β _f and β _p are converged to appropriate values. Implementation is possible. Since the cutting force acting on the ball end mill is governed by the area moment MA (φ) of the chip cross-sectional area rather than the chip cross-sectional area A (φ), in this modification, the bending moment is estimated from the second embodiment. And the convergence values of the inclination angles β _f and β _p become more accurate.

Therefore, according to the present modification, the proper values of the inclination angles β _f and β _p for which convergence has been determined become more accurate, and
There is an effect that the finished dimensional accuracy is improved as compared with the second embodiment only by slightly increasing the calculation amount as compared with the second embodiment. (Other Modifications of Embodiment 2) For this embodiment,
Modifications corresponding to Modifications 1 and 3 of Embodiment 1 described above can be performed, and the same function and effect can be obtained.

[Embodiment 3] (Cutting Method by Ball End Mill of Embodiment 3) The cutting method by the ball end mill as the embodiment 3 of the present invention uses the above-mentioned formulas 14 and 15 to calculate the cutting distance in the lateral direction with respect to the feed direction. This is a full-scale method of calculating a value Fp proportional to the force and a value Ff proportional to the component force in the front-back direction.

That is, in the cutting method using the ball end mill of the present embodiment, both estimated values corresponding to the lateral bending moment and the longitudinal bending moment in the feed direction are estimated by Expressions 14 and 15. That is, both estimated values are respectively integrated values Fp and Ff of the cutting force generated by the ball end mill and acting perpendicularly to the cross-sectional area of the chip and acting on the entire circumference of the rotating shaft of the component force in the left-right direction and the force component in the front-rear direction. And Equation 15: Since the left-right component force and the front-rear component force of the cutting force are most accurately reflected on the integral values Fp and Ff calculated by Equations 14 and 15, if the integral values Fp and Ff are suppressed to near zero, The bending moments in the left-right direction and the front-rear direction are also very precisely suppressed to near zero.

Therefore, the convergence values of the inclination angles β _f , β _p for suppressing the integrated values Fp, Ff calculated by the equations (14) and (15) to near zero, respectively, are quite precisely the bending moments in the left-right direction and the front-back direction. Is an appropriate value for suppressing the value near zero. Therefore, according to the cutting method using the ball end mill of the present embodiment, it is possible to perform the cutting process in which the finishing dimensional accuracy is further improved than in the first embodiment only by increasing the calculation amount to several times the calculation amount of the first embodiment. Has the effect of becoming

In this embodiment, the corresponding milling machine control device 3 can be implemented similarly to the first embodiment. (Modification 1 of Embodiment 3) As Modification 1 of the present embodiment, the values Ff and Fp corresponding to both bending moments are suppressed simultaneously by resetting both the inclination angles β _f and β _p at the same time. It is possible to implement a method of quickly converging the two inclination angles β _f and β _p to appropriate values.

That is, the value F corresponding to the bending moment
For the purpose of simultaneously reducing both f and Fp, the sum of squares P≡Ff ² + Fp ² of Ff and Fp is adopted as the evaluation function P, and both inclination angles β _f and β _p are converged by the steepest descent method. it can. At this time, based on the evaluation function P calculated by changing the inclination angles β _f and β _p by minute angles,
The mutually perpendicular slopes corresponding to ∂P / ∂β _f and ∂P / ∂β _p are calculated, and both variables β _f and β _p are converged to an appropriate value in parallel by the steepest descent method. Therefore, the number of repetitive operations can be reduced, and the amount of operations can be reduced as compared with the third embodiment.

Therefore, according to the present modification, there is an effect that the amount of calculation can be reduced and the calculation time can be reduced as compared with the third embodiment, while maintaining the excellent effects of the third embodiment. Therefore, if the assumptions made in modeling the cutting force are sufficiently correct, it is probably reasonable to assume that this variant is the best mode of the present invention.

(Various Modifications of the Third Embodiment) Modifications corresponding to the first and third modifications of the first embodiment described above can be implemented in this embodiment, and the same operation and effect can be obtained. .

[Brief description of the drawings]

FIG. 1 is a perspective view showing a typical example of a plunge cut.

FIG. 2 is a perspective view showing another typical example of plunge cutting.

FIG. 3 is a schematic view showing a cross-sectional area of a chip in vertical cutting.

FIG. 4 is a schematic diagram showing a chip cross-sectional area in plunge cutting.

FIG. 5 is a set diagram showing the definition of an angle in a tool coordinate system. (A) A perspective view showing a rotation angle position φ and a cutting edge angle position k. (B) A perspective view showing a definition of a cutting edge angle position k. Perspective view showing the definition of the rotation angle position φ

FIG. 6 is a set diagram showing the shape of a chip for calculating the volume of the chip and the like. (A) A perspective view showing a ball end mill and a work. (B) A perspective view schematically showing a shape of a chip. ) Schematic diagram showing an example of the chip cross-sectional area. (D) Schematic diagram showing another example of the chip cross-sectional area.

7A and 7B are perspective views showing a cutting depth t and a pick feed p; and FIG. 7B is a perspective view showing a shape of a cutting surface created by cutting. Sectional view showing the shape of the creation surface of

FIG. 8 is a graph showing the intrinsic behavior of cutting by a ball end mill.

FIG. 9 is a perspective view showing a shape of a chip for one round by one cutting blade.

FIG. 10 is a cross-sectional view schematically showing an opening portion of a blade end of a ball end mill.

FIG. 11 is a schematic diagram showing a definition of a tool rotation angle φ _{c in} the first embodiment.

FIG. 12 is a flowchart illustrating the first half of the tilt angle setting logic according to the first embodiment.

FIG. 13 is a flowchart illustrating the second half of the tilt angle setting logic according to the first embodiment.

FIG. 14 is a block diagram showing an arrangement of a milling machine control device as the first embodiment;

[Explanation of symbols]

β _f : The angle of inclination of the ball end mill in the feed direction (β _f
<0) β _p : inclination angle of the ball end mill in the pick feed direction (β _p <0) β: inclination angle vector of the ball end mill (β = [β
^{_{f, β p] T) R}} : Cutter radius of the ball end mill [mm] f _z: cutter (cutting blade) tool feed per one [mm /
tooth] t: Depth of cut [mm] p: Pick feed [m
m] k: cutting edge angle positions k _c: the effective cutting edge angle _{(k c = k a -k e} ) k a: cutting edge angle position k _e at the highest position in the actual cutting: Lowest position during actual cutting Φ: Rotation angle position of the cutting edge of the ball end mill φ _c : Rotation angle during actual cutting (φ _c = φ _a- φ _e ) φ _a : Rotation angle position at the end of cutting φ _e : Infeed H, h (k, φ): Chip thickness l _c : Effective cutting length s: Effective cutting edge length α: Opening angle (half apex angle) L: Opening diameter 1: Product Storage device for drawings (storage device for numerical data by CAD) 2: CAD / CAM processing device 3: Milling machine control device (device of the present invention) 4: NC milling machine 5: NC milling machine control board 51: xyz three-axis control unit 52 : Ab two-axis control unit 6: NC milling machine drive unit

 ──────────────────────────────────────────────────続 き Continuing on the front page (72) Inventor Kunio Naito 41 Toyota Chuo R & D Co., Ltd., No. 41, Nagachutecho, Aichi-gun Toyota Motor Co., Ltd. (72) Inventor ▲ Takahisa Yasuhisa 1 Toyota Town, Toyota City, Aichi Prefecture Toyota Motor Co., Ltd. F-term (reference) 3C022 AA09 AA10 KK02 KK06 QQ00

Claims (6)

[Claims] In a milling machine, when a ball end mill is tilted in a front-rear direction and a left-right direction with respect to a feeding direction with respect to a surface of a workpiece, plunge cutting (piercing cutting) is performed, and before and after the cutting, the rotating shaft of the ball end mill is tilted back and forth. Initialize the setting values of both the angle and the left and right tilt angle,
An estimated value corresponding to the longitudinal bending moment applied in the front-rear direction of the rotation axis of the ball end mill and an estimated value corresponding to the left-right bending moment applied in the left-right direction of the rotation axis are calculated, and both the estimated values are predetermined values. The resetting of the set value and the estimation are repeated until the following values are obtained, the proper values of the two angles are calculated, and the cutting is performed after setting the inclination angle of the ball end mill of the milling machine with the proper values. A cutting method using a ball end mill. 2. An estimated value corresponding to the front-rear bending moment is estimated based on a difference between a chip cross-sectional area on the right side and a chip cross-sectional area on the left side of the rotation axis of the ball end mill. The cutting method using the ball end mill according to claim 1, wherein the estimated value corresponding to the bending moment is estimated based on a difference between a chip cross-sectional area in front of the rotation axis of the ball end mill and a chip cross-sectional area in rear of the ball end mill. . 3. An estimated value corresponding to the front-rear bending moment is estimated from a difference between a chip volume on a right half surface and a chip volume on a left half surface of the rotating shaft of the ball end mill, The cutting method using the ball end mill according to claim 1, wherein the estimated value corresponding to (1) is estimated based on a difference between a chip volume on a front half surface of the rotary shaft of the ball end mill and a chip volume on a rear half surface of the ball end mill. 4. The front-rear bending moment and the left-right bending moment correspond to the front-rear component force and the left-right direction of the cutting force generated by the ball end mill and acting orthogonally to the chip cross-sectional area. The cutting method using a ball end mill according to claim 1, wherein the component force is estimated as an integrated value of the entire circumference of the rotation axis. 5. A ball end mill for a milling machine capable of performing plunge cutting (piercing cutting) by inclining a ball end mill with respect to a surface of a workpiece in a front-rear direction and a left-right direction with respect to a feed direction, respectively. A milling machine control device for setting a tilt angle of a rotating shaft to an appropriate value, at least, a tool radius and the number of cutter blades of the ball end mill, a desired pick feed, a cutting depth,
Input means for inputting input values corresponding to the feed speed and the tool rotation speed; the input values, the initial values of the inclination angles of the ball end mill appropriately set, and the integration step width appropriately set Based on the estimated value corresponding to the longitudinal bending moment applied in the front-rear direction of the rotation axis of the ball end mill, and estimation means for estimating the estimated value corresponding to the left-right bending moment applied in the left-right direction of the rotation axis, Until both the estimated values by the estimating means are equal to or less than a predetermined value,
A convergence means for adjusting the set values of both the front-rear inclination angle and the left-right inclination angle of the rotation axis of the ball end mill, repeating the estimation, and thereby calculating an appropriate value of the two angles; The appropriate values of the two angles are
Output means for outputting to the milling machine in a format suitable for the tool inclination angle setting means of the milling machine. 6. The milling machine control device according to claim 5, wherein said convergence means automatically adjusts the set values of the angles by a numerical solution based on a tilt method.