JP4517156B2 - Method for calculating uneven shape of cutting surface in milling and processing control method for uneven shape - Google Patents

Description

  The present invention is a technique for calculating the fine unevenness generated on the work surface when milling using a metal working machine of a milling machine from the setting of the work surface and the cutting edge of the tool and the cutting process conditions, The present invention relates to a processing control technique for obtaining a cutting processing condition to obtain a target uneven shape.

  Conventionally, milling has lower processing accuracy than beam processing or photolithographic process, but processing efficiency is said to be good. In this milling, a fine uneven shape left uncut occurs on the surface to be processed. It has been considered difficult to control the uneven shape.

  The conventional CAM system for curved surface processing includes information on the processing range, processing method (reciprocal cutting, contour cutting, etc.), ball end mill radius, processing accuracy, and target curved surface (hereinafter referred to as the user's interactive input). The movement path of the ball end mill is calculated based on the target curved surface. The workpiece shape after cutting along this movement path is obtained by subtracting the sweep 3D model representing the tool movement trajectory shape from the 3D model representing the shape of the workpiece before cutting using the collective calculation function of the 3D modeling system. calculate.

At this time, there are a method based on the dexel expression and a method based on the voxel expression for the solid model representing the shape of the workpiece.

With this conventional technology, when the end mill is fed at high speed with respect to the rotation of the tool for the purpose of shortening the cutting time or using the uneven shape generated on the workpiece surface as a function, The shape of the workpiece after cutting could not be predicted well.
In addition, the method of performing interference calculation between a solid model tool and a work piece by piece has a problem that it takes time for calculation instead of accuracy.

Japanese Laid-Open Patent Publication No. 2001-198718 discloses a method of cutting a curved surface with high accuracy in milling. This cutting method is performed by moving a milling tool having a circular cutting edge rotation locus in a predetermined tool feed direction in a state in which the rotation axis is inclined with respect to the normal of the machining surface at each cutting point. The surface of the workpiece is cut by a cutting blade that passes through the tool feed direction side region of the blade rotation axis locus. However, even if the large shape / dimension of the machined surface after cutting is controlled, the shape of the uncut unevenness cannot be accurately calculated. Moreover, the uneven shape could not be controlled.
JP 2001-198718 A

  The problem to be solved by the present invention is to solve these conventional problems, and to calculate the shape of the uncut unevenness of the cutting surface from the cutting conditions accurately and quickly, and to determine the shape of the uncut unevenness It is an object of the present invention to provide a method for accurately calculating the shape of the remaining unevenness on the cut surface in milling, and a method for controlling the uneven shape / dimension, which can be controlled to have a predetermined shape / size.

The configuration of the present invention that solves this problem is as follows.
1) Set the workpiece surface shape of the workpiece and the cutting edge shape of the milling tool, introduce an auxiliary curved surface that intersects the workpiece surface, and cut the line of intersection between the auxiliary curved surface and the workpiece surface A workpiece formed by milling by setting a point trajectory and setting the cutting point speed, tool rotation speed, tool posture, and cutting start rotation angle of the tool to the cutting point trajectory. This is a method for calculating the fine uneven shape of the processed surface at a high speed, and the uncut height in the calculation process by the computer software comprising the following steps a to e after the following first and second setting steps. To calculate the uneven shape of the cutting surface in milling, the first setting process: on the work surface of the workpiece surrounded by the closed curve Is set with parameters m and n Setting process input to the computer Second setting process: The tool cross section curve and cutting edge curve of the tool with reference to the tool origin on the rotation axis of the tool, the parameter w indicating the position on the tool cross section curve and cutting edge curve Setting process calculation process to be set and input to the computer: Calculation process step by computer software consisting of steps i to e A: Set a plurality of auxiliary curved surfaces intersecting the work surface, The intersection line can be used as a cutting point locus, and the locus of the cutting point in the real space and the locus of the cutting point in the parameter space of the work surface can be described with the parameter u indicating the position of the cutting point. Step b): Set the cutting point speed and tool rotation speed discretely with respect to the cutting point trajectory, set the cutting start rotation angle, Steps for continuously setting the tool inclination angle and tool rotation angle with respect to parameter u Step C: Deriving a curved surface by moving the cutting edge with parameters u and w, and the tool origin position and tool axis as CL data Step of deriving vector with parameter u D: Step of arranging multiple virtual lines on the work surface by aligning them at a predetermined pitch in the pick feed direction E: Curved surface created by movement of virtual lines and tool cutting edge The position of the uncut height is calculated for each cutting edge of the tool, and the position of the minimum uncut height is obtained from the calculated remaining height positions. Step 2) to determine unremoved height 2) The calculated uneven shape calculated by the method for calculating the uneven shape of the cut surface in the milling process of 1) and the target uneven surface. The cutting control conditions are changed so that the comparison becomes small compared with the shape, and a satisfactory cutting processing condition is obtained. The processing control method 3) of the concave and convex shape on the processing surface of the milling processing is obtained in 2) above. Further, the present invention is a machining control method for the concave and convex shape of a milling work surface by outputting a tool origin position and a tool axis vector, which are CL data of satisfactory cutting conditions, and using them as control data for a milling machine.

  In the present invention, the shape of the surface to be machined, the shape of the tool, and the auxiliary curved surface are introduced to determine the locus of the cutting point. By giving the cutting conditions, it is possible to easily and quickly calculate the uncut shape of the cut surface of the cut surface, and it can be used to determine whether the cutting conditions are good or bad. In addition, it is possible to easily determine the shape of the tool, the locus of the cutting point, and the cutting processing condition for making the uncut shape of the uncut shape predetermined.

  The shape of the work surface is set by a CAD device, the setting of the tool shape is input by a tool setting device, the setting is input to a processing computer, and the computer software (program) calculates in steps i to e. It is what is done.

  Hereinafter, the calculation of the present invention will be specifically described.

  In the present invention, by setting the shape of the tool, the locus of the cutting point on the work surface of the workpiece and the cutting conditions, and placing a virtual line on the work surface, The concavo-convex shape of the cut surface is calculated from the intersection with the virtual line.

  The procedure of the embodiment of the method for calculating the uneven shape of the cut surface of the present invention is shown in FIG. FIG. 2 shows the program steps of the uneven shape calculation process. Furthermore, it is determined whether the calculated uneven shape is the target uneven shape, and if it is not the target, the uneven shape is calculated in the same manner by changing the tool shape / cutting point trajectory and cutting conditions. judge. If the determination result is good, the setting / cutting condition data is converted into NC data, and the NC processing device is operated on the actual workpiece (workpiece) to process the required uneven shape on the workpiece surface.

FIG. 1 is a process explanatory diagram showing the process of the present embodiment. Reference numeral 1 denotes a first setting process for setting the surface shape to be processed by a CAD apparatus. Reference numeral 2 denotes a second setting step for setting the tool shape with the tool setting device. Reference numeral 3 denotes a calculation process for setting cutting processing conditions and calculating uneven shape data on the processing surface using software (program) of a computer. Reference numeral 4 denotes an evaluation process for comparison with a target value by a determination device. 5 is a process of calculating NC data. Reference numeral 10 denotes a milling NC processing apparatus.
FIG. 2 is a flowchart of a program for calculating uneven shape data.

Hereinafter, each process will be described sequentially. The notation on the drawings and the formulas and formulas will be described.
Capital letter: Indicates a coordinate system.
Bold: indicates a vector or a point.
Lower right subscript _p : Cutting point trajectory number Lower right subscript _q : Cutting point speed and tool rotation number lower right subscript _k : Cutting blade number Lower right subscript _j : Pick Number of virtual line in feed direction Subscript _{x, y, z} : The following Table 1 and Table 2 showing elements of vectors or points are used in the description, claims, variables, symbols, mathematical formulas and drawings. It is a control table which shows the correspondence in which a term means the same thing.

As a tool used for milling of the present invention, a hard tool such as a diamond tool is used. In addition, use a workpiece with good cutting properties such as free-cutting brass.

(First setting process)
The workpiece surface shape wp (m, n) of the workpiece surrounded by the closed curve is input using a CAD device. Here, m and n are parameters representing the position of the work surface.

(Second setting process)
Next, a method for setting the tool shape using a tool setting device (not shown) will be described with reference to FIG. In general CAD / CAM, there is no such way to set the tool shape.
First, the tool cross section curve tp (w) is set as in the following equation. Also, set the number of teeth enum and the twist ψ _k (w) (k = 1L enum) of the cutting edge curve around the tool axis. Here, w is a parameter indicating the position on the tool cross section curve and the cutting edge curve, and k is the number of the cutting edge.

上記の設定から工具断面曲線の単位接線ベクトル tt(w) 、工具断面曲線の単位法線ベクトル tn(w) を下記の式から導出する。

From the above settings, the unit tangent vector tt (w) of the tool section curve and the unit normal vector tn (w) of the tool section curve are derived from the following equations.

次に、切削点のパラメータ w_c(β) を、下記の式を解くことによって導出する。ここで、 β は工具の傾斜角である。よって、切削点 tp(β) 、切削点における単位接線ベクトル tt(β) 、切削点における単位法線ベクトル tn(β) は下記の式となる。

Next, the cutting point parameter w _c (β) is derived by solving the following equation. Where β is the tilt angle of the tool. Therefore, the cutting point tp (β), the unit tangent vector tt (β) at the cutting point, and the unit normal vector tn (β) at the cutting point are as follows.

次に、切れ刃曲線 ep_k(w) を下記の式から導出する。

Next, the cutting edge curve ep _k (w) is derived from the following equation.

(Calculation process)
(Step i)
Next, a method for setting the locus of the cutting point will be described with reference to FIG.
If the number of trajectories of the cutting point is pnum, pnum auxiliary curved surfaces ip _p are created, and by calculating the intersection line of the auxiliary curved surfaces ip _p and the work surface wp (m, n), pnum real space The cutting point trajectory cp _p (u) and the cutting point trajectory up _p (u) in the parameter space of the work surface are calculated.
Here, u is a parameter indicating the position of the cutting point, p is the number of the locus of the cutting point, and p = 1, 2, L pnum.

(Step B)
Next, a method of setting other cutting conditions will be described with reference to FIG.
First, the tool turning angle α _p (u) and the tool inclination angle β _p (u) are set in the locus cp _p (u) of the cutting point.

Next, the cutting point speed fp _p (u), the cutting point speed f _{p, q} and the tool rotation speed φ _{p, q} and the tool cutting start rotation angle △ θ _p are set, and the tool rotation angle θ _p (u) is derived from the following equation.
Here, qdiv _p is the number of divisions of the locus cp _p (u) of the cutting point. Q is the number of the cutting point speed and the rotation speed of the tool, and q = 1, 2, L qdiv _p . Further, the range of the cutting point speed f _{p, q} and the rotation speed φ _{p, q} is up _{, q-1} < u <up _{, q} .

(Step C)
Next, referring to FIG. 5, a method for deriving a curved surface m ep _{p, k} (u, w) that can be obtained by moving the tool cutting edge, a tool origin p _p (u) that is CL data, a tool axis direction vector a _p The derivation method of (u) is explained.

First, the following vector is derived. Where wn (m, n) is the unit normal vector of the machined surface, cn _p (u) is the unit normal vector of the machined surface on the locus of the cutting point, and cf _p (u) is The unit tangent vector of the locus of the cutting point, cb _p (u) is the unit vector where cf _p (u) and cn _p (u) are orthogonal.

Next, the tool coordinate system T _p (u), the tool origin p _p (u), and the tool axis direction vector a _p (u) are derived from the following equations.

Next, the curved surface m ep _{p, k} (u, w) generated by the movement of the tool cutting edge is derived from the following equation.

(Step D)
Next, a virtual line arrangement method will be described with reference to FIG.

First, set the number of divisions jdiv in the pick feed direction. Next, the number pc (1 <pc <pnum) of the locus of the cutting point that becomes the center of the uneven shape of the work surface is set. Next, the parameter uc _pc of the locus cp _pc (u) of the cutting point is set.

Next, a plane jp is calculated which passes through the point cp _pc (uc _pc ) where the virtual line of the locus of the cutting point is located, and which is normal to the tangent vector cf _pc (uc _pc ) at that point.

Next, the intersection point between the plane jp and the locus cp _pc−1 (u) of the cutting point is calculated, and u _pc−1 is calculated. Similarly, the parameter u _{pc + 1} is also calculated.

The position (m _j , n _j ) of the virtual line is calculated as follows. Where j is the virtual line number.

Next, the virtual line lp _j (d) is defined as follows. Here, d is the uncut height position.

(Stepho)
Next, a method for calculating the uneven shape will be described. Curved m ep _p can by movement of the cutting edge and imaginary line _{lp j (d), k (} u, w) by calculating the intersection of an imaginary line lp _j (d) of the uncut height of the candidate d _{j, p, k} (k = 1L enum) and (p = pc-1, pc, pc + 1) can be calculated, and the smallest of these is the uncut height d _j of the virtual line lp _j (d).
(1), (2) and (3) show the method of calculating the intersection.

(1) Intersection calculation method using Newton-Raphson method The intersection can be calculated by applying the Newton-Raphson method to the following nonlinear simultaneous equations. The explanation of the Newton-Raphson method is omitted. Here, the method for determining the initial values ds, us, and ws used in the Newton-Raphson method will be described.

First, the initial value ds is calculated from the following equation.

次に、初期値 us は、切れ刃上の切削点と被加工面上の切削点とが一致するようにするために、 θk＝θ_p(u) を、 u についてニュートン・ラプソン法で解いた解とする。ここで、 θk は下記の式であり、 Round[θ] は θ を四捨五入する関数である。この方程式を解くための初期値は、仮想線 lp_j(d) を配置する際に用いたパラメータ uc_pc である。

Next, the initial value us is obtained by solving θk = θ _p (u) for u with the Newton-Raphson method so that the cutting point on the cutting edge and the cutting point on the work surface coincide. Let it be a solution. Here, θk is the following equation, and Round [θ] is a function that rounds off θ. The initial value for solving this equation is the parameter uc _pc used to place the virtual line lp _j (d).

例外的に、工具断面曲線が楕円であり、工具中心付近で切削を行う際には、この us では、想定した範囲内に削り残し高さの候補 d_j,p,k を算出できないことがある。その場合、 us を少しずらすことになる。
次に、初期値 ws は下記の式から算出する。

Exceptionally, when the tool cross-section curve is an ellipse and cutting is performed near the center of the tool, this us may not be able to calculate the candidate remaining height d _{j, p, k} within the assumed range. . In that case, we will shift us a little.
Next, the initial value ws is calculated from the following equation.

例外的に、工具断面曲線が楕円であり、工具中心付近で切削を行う際には、下記の式を w についてニュートン・ラプソン法で解いた解を ws とする。この方程式を解くための初期値は w_c（β_p(us)） である。また、 p,ｑ は u_p,q-1 < u < u_p,q を満たす番号である。

Exceptionally, the tool section curve is an ellipse, and when cutting near the center of the tool, ws is a solution obtained by solving the following equation for w using the Newton-Raphson method. The initial value for solving this equation is w _c (β _p (us)). P and q are numbers satisfying u _{p, q-1} < u <up _{, q} .

(2) An intersection calculation method by approximating a curved surface formed by moving the cutting edge as a set of triangles.
The intersection point can be calculated by approximating the curved surface formed by the movement of the cutting edge as a set of triangles. A description of a method for approximating a curved surface as a set of triangles and a method for calculating the intersection of a triangle and a straight line will be omitted. Here, a method of determining the parameter ranges [uss, uee] and [wss, wee] of the curved surface that can be generated by moving the cutting edge will be described.

First, uss is a solution obtained by solving θ _p (u) = θ (uc _pc ) + ε for u by the Newton-Raphson method. Here, ε is a set value that is an angle increment. The initial value for solving this equation is the parameter uc _pc used to place the virtual line lp _j (d). The same is true for uee.

Next, wss is a solution obtained by solving Equation 16 or Equation 17 for w. Here, zv is a set value that is the distance in the normal direction of the processing surface from the cutting point, and xv is a setting value that is the distance in the direction normal to the normal direction of the processing surface from the cutting point. The initial value for solving this equation is w _c (β (uc _pc )) using the parameter uc _pc used when placing the virtual line lp _j (d). The same applies to wee.

ただし、 w の最小値、方程式の解が最大値が決まっており、上記の、最小値、最大値の範囲外になるとき、 wss、wee はそれぞれその最小値、最大値となる。

However, when the minimum value of w and the maximum value of the solution of the equation are determined, and wss and wee are outside the range of the minimum and maximum values described above, wss and wee are the minimum and maximum values, respectively.

  (3) A method in which a curved surface formed by moving the cutting edge is approximated as a set of triangles to obtain intersection points, and the intersection points are set to initial values ds, us, ws, and the Newton-Raphson method is performed.

(Evaluation process 4)
Next, from the concavo-convex shape calculated as shown in FIG. 7, the tool cross section curve tp (w), the twist of the cutting edge curve around the tool axis ψ _k (w), the locus of the cutting point cp _p (u), the tool turning The angle α _p (u), tool inclination angle β _p (u), cutting point speed f _{p, q} , tool rotation speed φ _{p, q} , tool cutting start phase angle △ θ _p We will improve.

(NC data calculation process 5)
NC is calculated from the tool origin p _p (u), the tool axis direction vector a _p (u), the cutting point speed f _{p, q} and the tool rotation speed φ _{p, q} . At this time, the feed speed set by the NC is not the speed of the cutting point of the cutting point but the speed of the tool origin. Therefore, the cutting point speed is converted into the tool origin speed.

When the rotation of the tool can be controlled, cutting is performed by controlling the rotation of the tool. When the rotation of the tool cannot be controlled, the orientation of the spindle is performed before cutting in each tool path, and the rotation of the tool is controlled in a pseudo manner by setting the initial rotation angle of the tool to zero.

Examples of the method for forming the uneven shape of the surface to be cut according to the present invention include the following, and the present invention is useful for a method for processing the product.
(1) To control the frictional force, the fine uneven shape is controlled.
(2) Provide fine irregularities to ensure lubricating oil at the sliding part.
(3) In order to control optical functions required for the surface such as reflection, diffraction, appearance, and gloss, fine irregularities are controlled.
(4) Provide fine irregularities on the surface to improve heat transfer characteristics and control boundary layer flow.
(5) Provide decorative irregularities on the surface.
(6) Provide fine irregularities on the mold to improve the release characteristics.
(7) The quality of regenerative medicine is improved by controlling the fine irregularities on the surface of the implant inserted into the body.
(8) Provide fine water ruggedness that has a strong water repellency and has a purifying action such that solid particles such as dust hardly adhere.
(9) To control the surface adhesion phenomenon, fine irregularities are controlled.
(10) The efficiency can be improved by using fine unevenness as a resonator and applying it to the surface of the radiator.
(11) It can be used to determine cutting conditions for reducing the uncut height of the workpiece surface.

It is process explanatory drawing of an Example. It is a flowchart figure of the program of the calculation process of uneven | corrugated shape data. It is explanatory drawing of the setting of the tool shape of the 2nd setting process of an Example. It is explanatory drawing of the setting of the locus | trajectory of the cutting point of the 3rd setting process of an Example, and cutting conditions. It is explanatory drawing of the derivation | leading-out method of the curved surface made by the movement of the cutting blade of an Example. It is explanatory drawing of the arrangement | positioning method of the virtual line on the to-be-processed surface of an Example. It is explanatory drawing which shows the difference in the uneven | corrugated shape of the to-be-processed surface by the kind of tool of an Example.

Explanation of symbols

1 1st setting process 2 2nd setting process 3 Calculation process of uneven shape data 4 Evaluation process 5 NC data calculation process 10 Milling NC processing equipment

Claims (3)

Set the work surface shape of the workpiece and the cutting edge shape of the milling tool, introduce an auxiliary curved surface that intersects the work surface, and set the intersection line of the auxiliary curved surface and the work surface to the cutting point Set the cutting point speed, the rotation speed of the tool, the posture of the tool, and the cutting condition of the cutting start rotation angle of the tool in the locus of the cutting point, and the workpiece coverage formed by milling. This is a method to calculate the fine uneven shape of the machined surface at high speed, and calculate the uncut height after the following first and second setting steps in the calculation process by the computer software consisting of the following steps (i) to (e). Then, a method for calculating the uneven shape of the cut surface in milling, in which the uncut height is defined as a fine uneven shape on the surface to be processed.
1st setting process: Setting process where the position on the work surface of the workpiece surrounded by the closed curve is set with parameters m, n and input to the computer 2nd setting process: Tool origin on the rotation axis of the tool Setting process calculation process for setting the tool cross section curve and the cutting edge curve of the tool as a reference with the parameter w indicating the position on the tool cross section curve and the cutting edge curve and inputting it to the computer: A computer comprising steps i to e Steps of calculation using the software: A: Set a plurality of auxiliary curved surfaces intersecting the work surface, calculate the intersection line between the work surface and the auxiliary curved surface, and use this intersection line as the locus of the cutting point to cut in the real space Steps that allow the locus of the point and the locus of the cutting point in the parameter space of the work surface to be described by the parameter u indicating the position of the cutting point Step B: For the locus of the cutting point Steps for setting the cutting point speed and the tool rotation speed discretely, setting the cutting start rotation angle, and continuously setting the tool turning angle, tool tilt angle and tool rotation angle with respect to the parameter u : Deriving a curved surface generated by moving the cutting edge with parameters u and w, and deriving the tool origin position and tool axis vector as CL data with parameter u Step d: Multiple virtual lines on the work surface Steps of arranging and aligning at a predetermined pitch in the pick-feed direction Step E: Calculate the position of uncut height as the intersection of the virtual line and the curved surface formed by the movement of the tool cutting edge, and calculate the position of the uncut height A step of obtaining the minimum uncut height position from the obtained uncut height position for each cutting edge of the tool and setting the uncut height as the uncut height position.   Compared with the uneven shape calculated by the method of calculating the uneven shape of the cutting surface in the milling process of claim 1 and the target shape of the target unevenness, the cutting conditions are changed so that the comparison becomes small, A machining control method for irregularities on the milling surface to obtain satisfactory cutting conditions.   A machining control method for the uneven shape of a milling work surface by outputting the tool origin position and the tool axis vector, which are CL data of the satisfactory machining conditions obtained in claim 2, as control data for the milling machine. .

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