WO2008001835A1

WO2008001835A1 - Processing apparatus and method of controlling processing apparatus

Info

Publication number: WO2008001835A1
Application number: PCT/JP2007/062968
Authority: WO
Inventors: Takahiro Kunugi; Atsushi Ogihara; Jun Furukawa
Original assignee: Thk Co., Ltd.
Priority date: 2006-06-28
Filing date: 2007-06-28
Publication date: 2008-01-03
Also published as: JP5113747B2; JPWO2008001835A1

Abstract

A method of controlling a processing apparatus capable of processing workpieces, such as grind stones, into a variety of shapes. The processing apparatus has an X-axis movement mechanism (9) capable of moving a tool (8) relative to a workpiece (7) into the X-axis direction in a two-dimensional plane (P), a Y-axis movement mechanism (10) capable of moving the tool in the Y-axis direction in the two-dimensional plane (P), and a θ-axis rotation mechanism (20) capable of rotating the tool (8) in the two-dimensional plane about the end (8a) of the tool (8) in contact with the workpiece. A controller of the processing apparatus designs a locus curve along which the tool (8) is moved and the attitude of the tool during the movement, controls the X-axis movement mechanism (9) and the Y-axis movement mechanism (10) to move the tool (8) along the locus curve, and controls the θ-axis rotating mechanism (20) to change the attitude of the tool (8) in the two-dimensional plane (P).

Description

Specification

Processing apparatus and control method of processing apparatus

Technical field

TECHNICAL FIELD [0001] The present invention relates to a machining apparatus that moves a tool relative to a workpiece and cares for a force article and a method for controlling the machining apparatus.

Background art

A processing apparatus removes unnecessary portions of a workpiece by cutting, grinding, or other methods, and forms the workpiece into a required processing shape. The track of the relative movement of the tool with respect to the workpiece is transferred to the force!

[0003] As a type of processing device, a dresser device that forms the outer shape of a mortar with a dresser is known (Patent Document 1). As shown in FIG. 27, a turret 1 as a workpiece is driven to rotate about an axis 2. The outer periphery of the grindstone 1 is formed by a rotary dresser 3 as a tool. The rotary dresser 3 rotates and swivels around a vertical line with a radius R.

FIG. 28 is a cross-sectional view taken along line AA in FIG. Vertical line 4 passes through the center of curvature of the arc-shaped molding surface of turret 1. When the rotary dresser 3 is swung around the vertical line 4, the trajectory of the swivel movement of the mouth dresser 3 is transferred to the turret 1. In this dresser apparatus, as shown in FIG. 29, a rotary dresser 3 having a tapered portion 3a at the outer edge is used, and a wall surface 3b of the tapered portion 3a is brought into contact with a straight portion of the grindstone 1 so that an arc portion of the grindstone is obtained. Form a molding surface that combines the straight part with!

[0005] Patent Document 1: Japanese Patent Laid-Open No. 49-50589 (see page 2, Fig. 1 to Fig. 3)

Disclosure of the invention

Problems to be solved by the invention

[0006] However, in the conventional dresser device, only an arc shape with a constant radius of curvature can be formed, and the degree of freedom of the shape of the forming surface is small. Even if the turning radius of the rotary dresser is adjusted to form an arc surface with different curvature radii, the molding surface can be formed into a combination of multiple arcs with different curvature centers or multiple curvature radii can be combined. Set arc It is difficult to form a combined shape. In particular, as shown in Fig. 30, a boulder with an arc-shaped center of curvature on both the outside and inside of the molding surface, with the molding surface of the boulder as the boundary (circular arcs Rl and R2 are inside the molding surface) It is impossible to mold the center of curvature in the arc part R3 and R4).

[0007] Also, in the conventional dresser device, although it can be said that a molding surface combining an arc portion and a linear portion can be formed, the shape of the molding surface depends on the shape of the taper portion of the rotary dresser, so There is a limit to the degree of freedom.

In other words, in the conventional dresser device, the trajectory of the movement of the dresser transferred to the boulder is mechanically controlled, so that the boulder cannot be covered in various shapes! /.

Accordingly, an object of the present invention is to provide a method for controlling a machining apparatus and a machining apparatus capable of machining a workpiece into various shapes.

Means for solving the problem

[0010] Hereinafter, the present invention will be described.

In order to solve the above-mentioned problem, the invention described in claim 1 is a method for controlling a machining apparatus for machining a workpiece by moving the tool relative to the workpiece, and the tool is described above. An X-axis moving mechanism that can move relative to the workpiece in the X-axis direction in the two-dimensional plane (P), and the tool perpendicular to the X-axis in the two-dimensional plane with respect to the workpiece. A Y-axis moving mechanism that can be moved relatively in the Y-axis direction, and a tool that rotates in the two-dimensional plane (P) around the tip of the tool that contacts the workpiece. A trajectory curve of the tool corresponding to the machining shape in the two-dimensional plane (P) of the workpiece (which may include a straight line). ) And design the posture of the tool on the locus curve. A trajectory control step of controlling the X-axis moving mechanism and the Y-axis moving mechanism to move the tool relative to the workpiece along the trajectory curve, and the Θ-axis rotating mechanism. And a posture control step of controlling and changing the posture of the tool on the trajectory curve in the two-dimensional plane.

[0011] In the invention according to claim 2, in the trajectory 'attitude design step, the clothoid in which the tangential direction angle is given by a quadratic expression having a curve length according to the method for controlling a machining apparatus according to claim 1 Song The trajectory curve of the tool is designed using a line, and the normal direction angle of the trajectory curve is calculated in at least a part of the trajectory curve, and based on the normal direction angle! The posture of the tool is designed.

[0012] The invention according to claim 3 is the method of controlling a machining apparatus according to claim 1 or 2, wherein, in the trajectory 'posture design step, one end of a trajectory curve that is symmetrical about the symmetry axis. The tool is moved from the point to the axis of symmetry, and then the tool is moved to the other end of the locus curve, and then the tool is moved from the other end of the locus curve to the axis of symmetry. The trajectory curve is designed so as to make it happen.

[0013] The invention according to claim 4 is the method of controlling a machining apparatus according to claim 2, wherein the workpiece is a gun that rotates around an axis line arranged in the two-dimensional plane (P). The tool is a dresser, and the processing device is a dresser device that forms the outer shape of the turret with the dresser. In the trajectory 'posture design step, at least In some sections, the dresser posture is designed so that the center line of the dresser faces the normal direction of the trajectory curve.

[0014] The invention according to claim 5 is the method of controlling a processing apparatus according to claim 4, wherein the dresser includes a flat surface and a corner portion having a predetermined width at the tip that contacts the turret. In the trajectory / posture design step, the dresser posture is set so that the center line of the dresser faces the normal direction of the trajectory curve in at least a part of the section on the trajectory curve. Design, thereby bringing the flat surface of the dresser into contact with the grindstone, and in other sections on the trajectory curve, the dresser's posture is such that the center line of the dresser is other than the normal direction of the trajectory curve. It is designed to face, whereby the corner portion of the dresser is brought into contact with the grindstone.

[0015] The invention according to claim 6 is the method for controlling a processing apparatus according to claim 4 or 5, wherein the turret is a gothic search groove having a circular arc of a cross section of a ball screw or a linear guide. Used to grind the ball rolling groove of the shape, and in the locus' attitude design process, in order to obtain the turret capable of adjusting the contact angle (α) of the ball screw or linear guide, the symmetry axis is centered. The bilaterally symmetric trajectory curve can be divided into two left and right with the symmetry axis as a boundary, and each of the divided pair of trajectory curves is symmetric. It is characterized by being able to shift the shaft by force.

[0016] The invention according to claim 7 is the method for controlling a machining apparatus according to any one of claims 4 to 6, wherein the turret grinds a ball rolling groove of a ball screw or a linear guide. In the trajectory 'posture design step, the trajectory curve that is symmetric about the axis of symmetry can be shifted in the axial direction of the axis of symmetry in order to adjust the cut amount of the dresser. And

[0017] The invention according to claim 8 is a machining apparatus for moving the tool relative to the workpiece to calcare the workpiece, wherein the tool is moved to the workpiece in a two-dimensional plane ( An X-axis moving mechanism capable of relatively moving in the X-axis direction in (P), and a relative to the Y-axis direction perpendicular to the X-axis in the two-dimensional plane (P) with respect to the workpiece. A Y-axis moving mechanism that can be moved in an automatic manner, and a Θ-axis rotating mechanism that can rotate the tool in the two-dimensional plane (P) around the tip of the tool that contacts the workpiece. Designing a trajectory curve of the tool (which may include a straight line) corresponding to the machining shape of the workpiece in the two-dimensional plane (P), and determining the posture of the tool on the trajectory curve Design and control the X-axis moving mechanism and the Y-axis moving mechanism to The tool is moved relative to the workpiece along a trajectory curve corresponding to a machining shape in a two-dimensional plane (P), and the Θ-axis rotation mechanism is controlled to control the two-dimensional plane. And a control device for changing the posture of the tool on the trajectory curve in (P).

[0018] The invention according to claim 9 is the processing apparatus according to claim 8, wherein the control device uses a clothoid curve in which a tangential direction angle is given by a quadratic expression having a curve length. Designing a trajectory curve, calculating a normal direction angle of the trajectory curve in at least a part of the trajectory curve, and designing the posture of the tool based on the normal direction angle It is characterized by.

The invention's effect

[0019] According to the invention described in claim 1, since the X-axis moving mechanism and the Y-axis moving mechanism move the tool along the designed trajectory curve, the workpiece can have various shapes in a two-dimensional plane. Can be processed. In addition, the Θ axis rotation mechanism changes the tool posture on the trajectory curve. Therefore, the tool can be directed in the optimum direction according to the machining shape. Here, since the tool rotates in a two-dimensional plane around the tip that contacts the workpiece, even if the posture of the tool is changed, the position of the tip of the tool that contacts the workpiece does not change. Therefore, changes in the posture of the tool will not affect the shape of the workpiece! ,.

[0020] According to the invention described in claim 2, since the two-dimensional clothoid curve in which the tangential direction angle is given by the quadratic expression of the curve length is used for the locus curve, the normal direction angle on the locus curve is It can be calculated easily.

[0021] According to the invention described in claim 3, the shape of the symmetrical workpiece can be stabilized.

[0022] According to the invention of claim 4, the dresser wear can be reduced by orienting the dresser in the normal direction with respect to the processed shape of the turret, and the wear of the dresser varies. Can be reduced.

[0023] According to the invention of claim 5, even if the center of curvature of the trajectory curve is closer to the dresser than the trajectory curve and the radius of curvature of the trajectory curve is smaller than the width of the dresser, the dresser is The shape of the turret can be shaped to match the trajectory curve that does not pass through the turret.

[0024] According to the invention of claim 6, a grindstone capable of adjusting the contact angle between the ball and the ball rolling groove can be formed.

[0025] According to the invention of claim 7, the amount of dresser cut into the turret can be adjusted.

[0026] According to the invention described in claim 8, since the tool can be moved along the designed trajectory curve by the X-axis moving mechanism and the Y-axis moving mechanism, the workpiece can be moved in a two-dimensional plane. It can be processed into various shapes. Also, the Θ-axis rotation mechanism can change the posture of the tool on the trajectory curve, so that the tool can be directed in the optimum direction according to the machining shape. Here, since the tool rotates in a two-dimensional plane around the tip that contacts the workpiece, the position of the tip of the tool that contacts the workpiece does not change even if the posture of the tool is changed. Therefore, the change in the posture of the tool does not affect the shape of the workpiece.

[0027] According to the invention of claim 9, the trajectory curve is given by a quadratic expression in which the tangential direction angle is a curve length. Since the obtained two-dimensional clothoid curve is used, the normal direction angle on the trajectory curve can be easily calculated.

Brief Description of Drawings

FIG. 1 is a side view showing a processing apparatus according to a first embodiment of the present invention.

[Figure 2] Top view of the dresser

[Fig. 3] Perspective view showing a ball screw ground by a grindstone

[Fig. 4] Perspective view showing a linear guide ground by a grindstone

[Figure 5] Diagram showing the machining shape of the turret in the horizontal plane

[Fig.6] A figure showing the dresser's trajectory 'posture that moves along the grinding wheel shape

圆 7] Block diagram of the control device

[Figure 8] Diagram showing a tabular motion table

[Figure 9] Flowchart executed by Motion Designer

[Fig.10] Trajectory design screen displayed on computer display device

[Fig. 11] Diagram showing another example of the locus / posture of the dresser moving along the processed shape of the turret

[Figure 12] Conceptual diagram of the trajectory design method for obtaining a grindstone with adjustable contact angle

FIG. 13 is a diagram showing the cross-sectional shape of a grindstone with an adjusted contact angle

圆 14] Conceptual diagram of trajectory design method for adjusting dresser cutting depth

圆 15] Diagram showing an example of the dresser posture designed so that the dresser posture is in the normal direction of the trajectory curve

圆 16] Diagram showing an example where the width of the flat surface at the tip of the dresser is larger than the radius of curvature of the small-diameter arc portion of the locus curve

[Figure 17] Figure showing the arc portion of the dresser that has been cut too much

圆 18] Diagram showing an example of the dresser posture designed so that the dresser posture is not in the normal direction of the trajectory curve

圆 19] Diagram showing the arc portion of the dresser cut smoothly

[Figure 20] Motion 'Flowchart executed by the operator

[Fig.21] Diagram showing basic clothoid curve

[Fig.22] Flowchart of the program executed by the interpolation method using clothoid curve [FIG. 23] Schematic diagram for explaining the method for obtaining the initial value of the tangential direction angle.

[Figure 24] Schematic diagram for explaining the three-point arc method

FIG. 25 is a side view of the machining apparatus according to the second embodiment of the present invention viewed from the X-axis direction.

FIG. 26 is a side view of the machining apparatus according to the second embodiment of the present invention viewed from the Y-axis direction.

[Fig.27] Side view of conventional dresser device

[Fig.28] A diagram showing a method for forming a turret using a conventional dresser (cross-sectional view taken along line A-A in Fig. 27)

FIG. 29 is a diagram showing a method for forming a turret using a conventional dresser.

FIG. 30 is a view showing a turret shape that cannot be formed by a conventional dresser device.

BEST MODE FOR CARRYING OUT THE INVENTION

FIG. 1 shows a processing apparatus according to the first embodiment of the present invention. In this processing apparatus, the outer peripheral surface of the grindstone 7 as a workpiece is formed by a dresser as a tool. The turret 7 is mounted on the heating device so as to be rotatable about its axis 7a, and is not shown in the figure! The axis 7a of the turret 7 is located in the two-dimensional plane, for example, the horizontal plane P. At the time of processing, the turret 7 installed with the dresser force separated also is moved in the y direction in the figure by being directed toward the dresser 8 by a turret Y-axis moving device (not shown).

[0030] A dresser 8 is disposed in a horizontal plane P including the axis 7a of the grindstone 7. The dresser 8 can be moved in the X-axis direction (direction perpendicular to the paper surface) in the horizontal plane by the X-axis moving mechanism 9 and can be moved in the Y-axis direction orthogonal to the X-axis in the horizontal plane by the Y-axis moving mechanism 10. The dresser 8 can be rotated in the horizontal plane by the Θ-axis rotation mechanism 20.

[0031] On the base 11 of the processing apparatus, a Y-axis moving mechanism 10 that moves the Y-axis table 17 in the Y-axis direction by means of ball screw mechanisms 14 and 16 is attached. The rotation of the Y-axis servo motor 12 is transmitted to the screw shaft 14 via the worm gear 13. Here, when the worm gear 13 having a small speed ratio is used, the amount of movement of the Y-axis table 17 relative to the amount of rotation of the Y-axis servomotor 12 can be reduced, and the Y-axis table 17 can be moved with high accuracy. The screw shaft 14 is rotatably supported on the base 11 via a bearing 15. A ball screw nut 16 is screwed onto the screw shaft 14. A Y-axis table 17 is coupled to the upper surface of the ball screw nut 16. The Y-axis table 17 is supported on the base through a linear guide so as to be slidable in the Y-axis direction. Note that the base 11 of the processing apparatus is moved in the Y-axis direction within a horizontal plane by a slide mechanism 19 such as an air cylinder. The slide mechanism 19 moves the dresser to the machining position or separates the machining position force.

An X-axis moving mechanism 9 is attached on the Y-axis table 17. The X-axis moving mechanism 9 also moves the X-axis table 21 in the X-axis direction by the ball screw mechanism. The rotation of the X-axis servo motor is transmitted to the screw shaft 22 via the worm gear. The screw shaft 22 is rotatably supported on the Y-axis table 17 via a bearing. A ball screw nut 23 is screwed onto the screw shaft 22. An X-axis table 21 is coupled to the upper surface of the ball screw nut 23. The Y-axis table 21 is supported on the Y-axis table 17 via the linear guide 24 so as to be slidable in the Y-axis direction.

A Θ-axis rotation mechanism 20 is attached on the X-axis table 21. A column 26 is coupled on the X-axis table 21. In the column 26, a Θ axis 27 extending in the vertical direction is rotatably supported via a bearing 28. The axis 27a of the Θ axis 27 points in the vertical direction and is orthogonal to the horizontal plane P. The Θ shaft 27 extends downward from the portion supported by the bearing 28, and a dresser 8 is attached to the lower end thereof. The upper end of the Θ axis 27 is suspended from the support portion by the bearing 28, and the lower end of the Θ axis 27 is not supported. In order to avoid interference with the turret 7, the 0-axis 27 is inclined obliquely from the upper end to the lower end. The axis 27a of the zero axis 27 is the center of rotation of the dresser 8 in the horizontal plane P. The position of the dresser 8 is adjusted so that the tip 8a of the dresser 8 is positioned on the axis 27a of the Θ axis 27. The dresser 8 is fixed to the Θ axis 27 mm by a set screw 29.

A Θ-axis servo motor 29 is coupled to the column 26. The rotation of the Θ-axis servomotor 29 is transmitted to the Θ-axis 27 through the reduction gear 30 and the worm gear 31. By interposing the reduction gear 30 and the worm gear 31, the dresser 8 can be rotated with high accuracy.

FIG. 2 shows a plan view of the dresser 8. The dresser 8 consists of a diamond tool that grinds the grinding wheel 7. The dresser 8 is moved in the X-axis direction in the horizontal plane P by the X-axis moving mechanism 9 described above, and is moved in the Y-axis direction by the Y-axis moving mechanism 10. Then, the Θ-axis rotating mechanism 20 is rotated in the horizontal plane P around the tip 8a.

[0037] The dresser 8 is a single stone dresser in which a diamond with a sharp tip 8a is embedded. Alternatively, a prismatic dresser in which a prismatic diamond having a flat surface is embedded in the tip 8a may be used, or a disc-shaped rotary dresser may be used. The disk-type rotor lead dresser is a rotary dresser that is driven to rotate about the axis of the disk. In FIG. 2, a prismatic dresser is shown as an example. Therefore, the dresser 8 has a flat surface 8b having a predetermined width and a corner 8c at the tip 8a.

The grindstone 7 formed by the dresser 8 is used for grinding the ball screw 31 shown in FIG. 3 and the ball rolling groove of the linear guide shown in FIG. The ball screw 31 has a ball 34 inserted between the ball rolling groove 32a of the screw shaft 32 and the ball rolling groove 33a of the nut 33, and a return path 35 is provided in the nut 33 so that the ball 34 can circulate. It is. The guide 40 is used to guide the moving body in a linear motion, and the ball rolling groove 36a of the track rail 36 that extends linearly and the bowl-shaped moving block that moves along the track rail 36. A ball 38 is inserted between the ball rolling groove 37a of 37 and a return path 39 is provided in the moving block 37 so that the ball 38 can circulate. These ball screws 31 and linear guides 40 【Cow! / Tetsuteoraki, Bonole rolling groove 32a, 33a, 36a, 37a cross-sectional shape ・ When formed into a circular arch groove shape with a single arc force In some cases, it is formed in a Gothic arch groove shape consisting of two arcs.

FIG. 5 shows an example of a processed shape in the horizontal plane of the grindstone 7 formed by the dresser 8. The Karoe shape in the horizontal plane of the grindstone 7 is made to match the cross-sectional shape of the ball rolling grooves 32a, 33a, 36a, 37a. In this example, the processed shape in the horizontal plane P of the turret 7 is set to the Gothic arch groove shape in accordance with the ball rolling grooves 32a, 33a, 36a, and 37a of the Gothicarch groove. That is, the processing shape of the turret 7 has an arc portion 41 composed of two arcs Rl and R2, and the curvature radii of the two arcs Rl and R2 are equal. The center of curvature of the arc R1 and the center of curvature of the arc portion R2 are separated by a distance L. Straight portions 42 are provided on both sides of the arc portion 41. At the connecting portion between the arc portion 41 and the linear portion 42, an arc portion 43 such as a small-diameter arc R3, R4 is provided. The centers of curvature of the arcs Rl and R2 and the centers of curvature of the arcs R3 and R4 are on the inside and outside of the turret 7 with the molding surface of the grindstone 7 as a boundary.

[0040] As shown in FIG. 6, the locus and posture of the dresser 8 in the horizontal plane P are controlled, and the grindstone 7 is formed into a processed shape. Specifically, the X-axis moving mechanism 9 and the Y-axis moving mechanism 10 are By controlling, the dresser 8 is moved along the locus curve 44 in the horizontal plane P (corresponding to the processing shape of the grindstone), and the Θ-axis rotation mechanism 20 is controlled to change the locus curve 44 in the horizontal plane P Change the dresser 8 posture.

A control device for the dresser device will be described. FIG. 7 shows a configuration diagram of the control device 55.

The hardware of the control device 55 consists of a computer 56 (left side of the dotted line in the figure) such as a personal computer in which the software up to the creation of the motion 'table 51 is installed, and the motion' table 51 is read and the X, Υ, It consists of a motor control device 57 (right side from the dotted line in the figure) that incorporates a motion 'operator 54 to operate the Θ axis. The computer 56 of the control device 55 creates a motion table 51 that describes the displacement values of each motion axis by taking the time axis in the row direction and the X, Υ, and Θ axes of the dresser device in the column direction. On the basis of the Yong table 51, the motor control device 57 of the control device 55 controls each axis of the dresser device. A signal command from the motion 'table 51 and the motion' editor 53 is transmitted between the computer 56 and the motor control device 57.

[0042] The software of the control device 55 is a motion to create a motion 'table 51

'Designer 52 and multiple motions'' Motion to edit table 51 'Editor 53 (sequencer) and motion to operate X, Υ, and Θ axis servo motors in response to these command inputs' Operator Consists of 54 and

[0043] First, the motion 'table 51 will be described. Giving the position and / or attitude of dresser 8 as a function of time is called motion. As shown in FIG. 8, the motion 'table 51 describes the absolute value or incremental value of the displacement of each axis with the time axis in the row direction and each operation axis (servo motor) in the column direction. The absolute value is an absolute value relative to the reference value, and the incremental value is a value that increments at each time interval. In Fig. 8, the force for which the absolute value is described does not necessarily start from zero.

[0044] The motion 'table 51 is sent to a robot or the like in CSV (Comma Separated Value) format data, for example. Since motion 'table 51 is tabular data with vertical columns and horizontal rows, it is converted to a single column using the CSV method so that it can be sent via serial communication. Specifically, for example, the table data has 0, 0, 5 rows from the upper left, 1, 2, 5, rows , 3, 6, 5, ideology, ヽぅ fununi に Converted to IJ data.

A flow chart executed by the motion designer 52 for creating the motion table 51 will be described with reference to FIG.

[0046] <Track and Posture Design (S 1)>

When the dresser 8 moves, the contact point of the tip of the dresser 8 with the turret 7 (hereinafter referred to as the tool point) temporally moves on a continuous trajectory curve (which may include a straight line) drawn in a plane. You can think of it as moving. The position of the tool point is represented by coordinates (x, y), and the posture of the dresser 8 is represented by, for example, a rotation angle with respect to the x and y axes. Regardless of the complexity of the movement, the tool point trajectory is continuously connected without interruption. The first stage of motion control is to design the trajectory curve of the dresser 8 and the posture of the dresser 8.

FIG. 10 shows a trajectory design screen displayed on the display device of the computer 56. First, the operator inputs, for example, the XY coordinates of six point sequences P1 to P6 to the computer 56 in correspondence with the machining shape of the turret 7 shown in FIG. Input means such as a keyboard and a mouse can be used for input. P1 → P2 is the section corresponding to the straight part 42 of the machining shape, P2 → P3 → P4 is the section corresponding to the small circular arc part 43 of the cage shape, and P4 → P5 → P6 is the section. This section corresponds to the arcuate portion 41 having a large diameter. When the operator inputs a point sequence, the computer designs a locus curve 60 that interpolates the point sequence P1 to P6. The designed locus curve 60 is displayed on the display device. In this embodiment, a clothoid curve is used in designing the locus curve 60. In a clothoid curve, the tangential angle of the curve is given continuously as a function of the curve length. Therefore, the continuity of movement is maintained. An interpolation method using this clothoid curve will be described later. After designing the trajectory curve 60 interpolated from P1 to P6, the computer 56 inverts the trajectory curve 60 around the symmetry axis 59 on the workpiece origin to obtain a symmetrical trajectory curve 44 as shown in FIG. design.

As shown in FIG. 6, the computer 56 designs the trajectory curve 44 and also the posture of the dresser 8. In this embodiment, in designing the posture, the posture of the dresser 8 is designed so that the center line 8d of the dresser 8 faces the normal direction of the locus curve 44 in all sections on the locus curve 44. Directing the normal direction reduces the wear on the dresser 8 and This is to reduce the variation in wear in each part of the support 8. The clothoid curve is given a tangential angle, so the normal direction of the curve can be calculated simply by rotating the given tangential angle by 90 degrees. When a clothoid curve is used, as shown in FIG. 9, the position E of the dresser 8 is also given, and the posture E of the dresser 8 is also given as a function of the curve length s.

[0049] As shown in FIG. 6, when the dresser 8 is moved along the locus curve 44 from one end 44a of the symmetrical locus curve 44 to the other end 44b, the machining time is shortened. You can. However, this method tends to cause variations in the shapes of the arcs R1 and R2. Therefore, as shown in FIG. 11, the dresser 8 is moved from one end 44a of the locus curve 44 to the symmetry axis 59, and then the dresser 8 is moved to the other end 44b of the locus curve 44. Thereafter, the dresser 8 may be moved from the other end 44 b of the trajectory curve 44 to the symmetry axis 59. Designing the trajectory curve in this way takes some machining time but stabilizes the shapes of arcs R1 and R2.

FIG. 12 shows a conceptual diagram of a trajectory design method for obtaining the grindstone 7 that can adjust the contact angle of the ball screw 31 or the linear guide 40. As shown in FIG. 12, the computer 56 creates divided trajectory curves (1) and (2) obtained by dividing the trajectory curve 44 into left and right with the symmetry axis as a boundary. The operator inputs the offset of the segmented trajectory curves (1) and (2) on the input screen shown in FIG. The computer 56 shifts each of the pair of divided trajectory curves 45 in the X direction toward the symmetry axis 59 by the specified offset amount. The radius of curvature of arcs Rl and R2 is not changed.

[0051] As shown in FIG. 13, the contact angles α 1, α 2 are the ball screw 31 or the inner diameter of the Bonole 34, 38 of the linear guide 40, the point, the ridge, and the Bonole rolling groove 32a, 33a, The angle between the line 46 that connects 36a and 37a and the line that connects the symmetrical axis 59 of the symmetric Bonolet rolling grooves 32a, 33a, 36a, and 37a. Here, the shape of the whetstone 7 and the cross-sectional shape of the ball rolling grooves 32a, 33a, 36a, 37a are the same, so the cross-sectional shape of the ball rolling grooves 32a, 33a, 36a, 37a is changed to the cross-sectional shape of the grindstone 7. Instead, contact angles 1 and 2 are shown. By changing the offset amount, the contact angles α 1 and α 2 can be adjusted. For example, the contact angle ex 1 can be increased as the contact angle oc 2.

FIG. 14 is a conceptual diagram of a trajectory design method for adjusting the cutting amount of the dresser 8. After grinding the ball rolling grooves 32a, 33a, 36a, 37a with the grindstone 7, the grindstone 7 may be re-formed with the dresser 8. In this case, it is necessary to mold the turret with a slightly deeper cut than the previously molded shape. The operator inputs the shift amount for each divided trajectory curve (1X2) on the input screen shown in FIG. As shown in FIG. 14, the commutator 56 has a trajectory curve 44 (consisting of split trajectory curves (1) and (2)) designed symmetrically about the symmetry axis 59 by the specified shift amount. Is shifted in the direction of the symmetry axis 59 (in the Y direction). Thereby, the worn turret 7 can be cut by a predetermined cut amount.

As shown in FIG. 15, in the trajectory 'posture design method, the posture of the dresser 8 is designed so that the posture of the dresser 8 faces the normal direction of the trajectories 41 to 43. However, as shown in FIG. 16, when a prismatic dresser is used for the dresser 8, the tip of the dresser 8 has a flat surface 8b having a predetermined width and a corner 8c. If the width W1 of the flat surface of the dresser 8 tip is larger than the radius of curvature R3 of the small-diameter arc 43 of the locus curve 44, even if the tip of the dresser 8 is moved along the locus curve, the tip of the dresser 8 The corner 8c goes over the turret 7 In this case, as shown in FIG. 17, the arc portion 43 of the molded dresser 8 has a shape that is excessively cut.

In order to solve this problem, in the present embodiment, as shown in FIG. 18, the corner of the dresser 8 is replaced with the turret 7 until the straight arc portion 43 reaches the arc portion 43 having a small diameter. Design the posture of the dresser 8 so that it makes contact. That is, the center line 8d of the dresser 8 is directed in a direction other than the normal direction of the locus curve 44. When the boundary between the small-diameter arc portion 43 and the large-diameter arc portion 41 is reached, the posture design is switched, and the dresser 8 is designed so that the posture of the dresser 8 faces the normal direction of the locus curve 44. Thereby, the flat surface 8b of the dresser 8 is brought into contact with the turret 7. FIG. 19 shows the shape of the grindstone 7 formed by such a trajectory 'posture design. It can be seen that a smooth shape can be obtained even in the arc part 43 with a small diameter.

[0055] When a single stone dresser with a sharp tip is used as the dresser 8, the posture should be designed so as to be in the normal direction of the trajectory curve in all sections where it is not necessary to switch the posture. However, it is necessary to pay attention to wear of the sharp tip.

[0056] <Fitting of motion curve (S2)>

As shown in Figure 9, the second stage of motion control is a tool moving on the designed trajectory curve. The point's speed is to determine the acceleration. The time function of the tool point on the trajectory curve is determined by determining the speed'acceleration of the tool point. The operator

In the screen shown in FIG. 10, the speed of the dresser 8 is input. The computer 56 determines the tool point speed'acceleration so that the dresser 8 can be moved at the specified speed. In this embodiment, a curve with good characteristics adopted in the cam mechanism is adopted, and this is provided as a universal cam curve with variable parameters. The position and orientation defined in the Cartesian space (real space) constitutes a group of continuous curves. Fit a motion curve to each curve and specify acceleration / deceleration. Cartesian space is a three-dimensional coordinate system created using three axes x, y, and z that are orthogonal to each other at the original point, and can represent not only the position of the tool point but also the posture.

[0057] <Time division (S3)>

Since the locus and motion are fixed, the tool point position and orientation are given as a function of time t. Thus, when the time t is given at minute time intervals, the displacement of the tool point with respect to each time can be obtained. For example, an appropriate value of 2 ms (milliseconds) or less is selected as the time interval.

By the above procedure, the position and orientation of the tool point with respect to time t in the Cartesian coordinate system (real space) are calculated. There are (x, y, θ) as variables.

[0059] <Inverse mechanism solution (S5)>

Next, the rotation angle of each axis necessary to give the position and orientation of the tool point is obtained. This process is generally called Inverse Kinematics. The inverse mechanism solution is to obtain the rotation angle θ 1 to Θ 3 of the axial space from the position “attitude” of the actual space. Since the reverse mechanism solution is unique to each processing device, prepare a solution for each processing device.

[0060] <Calculation of each axis servo motor displacement by axis coordinate system (S6)>

Find the inverse mechanism solution for each time-divided tool point, and use this as an integer for the displacement pulse of each axis servo motor. When not using pulse control, use the minimum resolution unit (resolution) of each axis displacement, and obtain it as integer data equivalent to the number of pulses.

[0061] <Create motion table (S7)> The absolute value or incremental value of each axial displacement thus obtained is stored in the computer memory as the table data of the aforementioned motion table 51.

[0062] The motion 'editor 53 shown in Fig. 7 will be described. The motion “editor 53” is used to edit a plurality of motion “tables 51”. For example, the usage of the created motion “table 51” is set in order. Specifically, for example, if the motion 'table 51 is A, B, C, the order is set as B when A ends, C when B ends, and B and C together when A ends Or run. It is close to a sequencer in the sense that it gives a sequence of operations. The motion 'editor 53' may be externally installed with the motion 'designer 52, typically a force built into the computer.

[0063] Next, the motion 'operator 54 incorporated in the motor control device 57 will be described. Motion 'operator 54 is commonly referred to as a servomechanism (ie, an automatic feedback control system for mechanical motion). Here we call the 'motion' operator for general purposes. The motion 'operator 54 reads the motion' table 51 created by the motion 'designer 52 via communication etc., distributes the input data to each axis, determines the synchronization between each axis, and the servo motor of each axis To control. That is, the motion 'operator 54 controls the X-axis servo motor and the Y-axis servo motor based on the motion' table 51 to move the dresser 8 along the locus curve 44. At the same time, the Θ-axis servo motor is controlled to change the posture of the dresser 8 in the horizontal plane.

Hereinafter, a procedure executed by the motion operator 54 will be described in detail with reference to FIG.

There are several ways to send motion 'table 51 data from computer 56 to motor controller 57. The first method uses a high-speed communication line as the transmission medium. As the high-speed communication line, Ethernet (registered trademark) (R), USB, IEEE 1394, etc. can be used. Depending on the conditions, a wireless or low-speed communication line can be used. The second method is to read data by connecting a bus directly. If the computer and motor controller are not separated, they can be used. The third method uses a portable memory medium. Transport using CD, DVD, memory card, etc. [0065] <Load motion table (S2)>

Since each communication method has its own protocol, the motion table 51 is read according to that protocol.

[0066] <Distribution of input data to each axis (S3)>

Since the motion table 51 is usually created for multiple axes, it needs to be distributed to each axis. There is also a method of compulsorily distributing using a hub etc. (a method of distributing a line of data to the drivers of each axis in order on the delivery side), but usually only the data related to each axis is received on the receiving side Like that. If there is a memory on the receiving side, for example, the vertical axis data shown in Fig. 8 is received as X-axis data, the data in the next column is received as Y-axis data, and the Θ-axis data is further received. The next column data can be received.

[0067] <Synchronization, sequence control (S4)>

In order to move several axes all at once, it is necessary to send some synchronization signal. For example, when trying to draw an arc with tool points, the X-axis servo motor and the Y-axis servo motor must be powered together. By sending the synchronization signal to the servo driver, each axis servo motor will move together. It is desirable to send the synchronization signal once at time-divided time intervals.

[0068] In order to take a sequence with various input / output signals of the dresser device, the motion editor 53! / 編集 needs to edit the motion table 51 by the sequencer. For example, when the limit switch is activated, the tool point may be stopped, or when the temperature is measured with a sensor and the temperature rises, the tool point may be slowed down. In such a case, if there is an input signal from the sensor, the motion table 51 is edited by the motion editor 53 or the sequencer.

Whether each axis servo motor moves following the motion command is the role of the servo driver and each axis servo motor. In this embodiment, return the feedback signal to the computer 56 for creating the motion table! The motion 'table creation computer 56 never enters the servo loop. [0070] As described above, the X-axis moving mechanism 9 and the Y-axis moving mechanism 10 are controlled to move the dresser 8 along the locus curve 44 (matching the processing shape of the turret) in the horizontal plane, and Θ By controlling the shaft rotating mechanism 20, it becomes possible to change the posture of the dresser 8 of the trajectory curve 44 in the horizontal plane Ρ.

[0071] Hereinafter, an interpolation method using a clothoid curve will be described in detail.

To achieve interpolation in general

1. Determine the interpolation formula.

2. Determine the auxiliary variable.

3. Determine the step and calculate the coordinates sequentially.

There are three stages: 2. A reverse solution is required in 2. A forward solution is required in 3.

[0072] The basic theory of clothoid curves and clothoid segments will be briefly described. First, definitions of related terms including the clothoid curve will be shown.

Position P = x + j-y

Arc length s (variable (actual displacement measured along curve length)), h (constant (total length of clothoid curve)) Definition of tangential direction angle ej (φ) ≡dp / ds (position vector is differentiated by arc length) Unit vector) Curvature definition φ'≡ (1φΖΐ3 Differentiated by arc length of tangential angle

Definition of shrinkage φ〃≡d '/ ds Curvature derivative by arc length

Definition of straight line d φ Zds≡ 0 Curve with constant tangential angle is straight line

Definition of circle 1φ b ds≡0 Curve with constant curvature is a circle (including a straight line)

Definition of clothoid (1φ "Zds≡0 shrinkage constant curve is clothoid (including circle)

Clothoid basic formula: obtained by sequentially integrating the defining formula. φ '= φ' 0+ φ s

φ = 0+ '0 · 5 + 2-s ^ (Tangential direction is given by a quadratic expression of curve length)

P = J Θΐ (0+ O-s + "/ 2-s' ^, 2) ds (1)

FIG. 21 shows a basic clothoid curve, and the solid line in FIG. 21 shows a curve when φ 0 = φ′0 = 0, φ ″ = π / 2. -This is called Yu's spiral, and the broken line in the figure shows the curve when φ〃 = 1 πΖ 2. Cs and Sn are known as Fresnel integrals.

It should be noted that the following description method is adopted in this specification as expression of the mathematical expression. I division symbol

^ Exponentiation

i = [v] Example of fractional truncation [0. 5] = 0 one [one 0.5.] = 1

a.. b Integration interval or cumulative interval from a to b

a --- Cumulative interval from a to infinity

ej () = e ^ ') = cos φ + j' sin φ 2D single vector

[0075] A clothoid segment is obtained by cutting out a part of a clothoid curve in the same way as cutting out an arc from a circle. Determine the start point Ρ0 and end point P1 with the above basic formula, and perform definite integration with the arc length from 0 to h. In addition, the section is made dimensionless as (S = 0..1), the bending angle φν = φ'0'h as the arc component of the angle change, and the reduced angle as the clothoid component () U = φ〃Ζ2. 2 and define. The basic formula of clothoid segment is from (1)

Pl = PO + h-ej (O) J ej (v -S + φη -S ^ ds

S = 0..1 (2)

[0076] The shape of the clothoid segment is determined only by the bending angle φV and the contraction angle φu, the size is h, the position is P0, and the direction is φ0. The arc length h, the curvature angle φ V, and the contraction angle φ u are collectively referred to as interval parameters. Lines, circles and clothoids are separate figures. A straight line is infinite and has a direction, a circle is infinite and large, a clothoid is infinite in length, its existence range is finite, and has both direction and size. By the definition above, the line segment is a subset of an arc, and the arc is a subset of a clothoid segment. As described above, the method of obtaining the end point and the tangential direction angle by giving the start point, the tangential direction angle, and the interval parameter is called a forward solution. On the other hand, the method of obtaining the interval parameter by giving the start and end positions and the tangential angle is called the inverse solution.

[0077] FIG. 22 shows a flowchart of a program executed by the interpolation method using a clothoid curve. The control method according to the present embodiment interpolates P1 to P6 point sequences given in advance using clothoid segments calculated by a computer. In the interpolation method using a clothoid curve, first, each coordinate P (X, y) of the above point sequence is input (step 1).

Next, the tangential direction angle φ at each point is obtained (step 2). Tangent angle Φ is the top Indicates the direction of each tangent at each point, and is represented by the angle formed by the tangent to the reference line. The tangential angle φ obtained in the second step is temporary except for the end points.

[0079] Next, interval parameters in all intervals are obtained (step 3). The interval parameter is composed of the arc length h, the bending angle φ ν, and the contraction angle φ u. The interval auxiliary variable can be obtained at high speed by solving the inverse solution of “Crosoid's reduced angle polynomial” by the following first calculation process to fifth calculation process. In other words, the chord length and directional angle are calculated from the difference in position between the start point and end point (first calculation process), and the coefficient of the differential force contraction polynomial of the tangential direction angle between the start point and end point is calculated ( (Second calculation process), calculate the contraction angle by solving the contraction polynomial of y by Newton's method (third calculation process), and calculate the arc length using the contraction angle and the contraction polynomial of X (Calculation process), a curvature angle is calculated from the difference in tangential direction angle and the contraction angle (fifth calculation process). Note that the third arithmetic processing is performed by using a joint approximation formula for the inverse Newton method.

[0080] Next, the process proceeds to step 4 to obtain curvature difference evaluation values at intermediate points excluding both ends of each point, and mark the maximum point of these curvature difference evaluation values (step 41). It is determined whether or not the curvature difference evaluation value is within the allowable range (step 42) .If the curvature difference evaluation value is within the allowable range, step 4 is terminated. The tangential direction angle was corrected (Step 43), the interval parameters of the two sections before and after the maximum point were recalculated (Step 44), and the curvature difference evaluation values at the maximum point and the three points before and after were recalculated. After (Step 41), return to Step 42 and repeat.

As a result, the curvature difference evaluation values at all points can be finally reduced to a predetermined tolerance or less.

[0081] In the subsequent fifth step, the division auxiliary variable suitable for the product-sum operation is calculated by dividing the interval auxiliary variable obtained in the fourth step as described above. Then, the position is sequentially obtained based on these division assist variables. This makes it possible to obtain an optimum position command for interpolating between the point sequences.

As a specific interpolation method, as shown in the flowchart of FIG. 22, first, the point sequence Pi (xi, yi) to be interpolated (where i is 0, 1, 2,..., N) Enter (first step).

[0083] Next, in the second step, an initial value of the tangential direction angle φ i at each point Pi is obtained. The An example of the solution means in this step is shown below. As shown in Fig. 23, three consecutive points are selected, and the tangential angles φΑ, Β, φ at each point of the arc passing through these three points (A, B, C in Fig. 24). Ask for. If the angle of each side of the triangle ff a + b = c is 0 a, Θ b, 0 c, the vertex angle α is

a = Θ c— Θ a

β = π— 6b + Θ a

γ = Θ b-Θ c

The tangent direction at each point of the arc passing through the three points is equal to the circumference angle and the chordal arc angle, so Α = Θ a- γ = Θ a- Θ b + Θ c

Β = Θ b- α = Θ b- Θ c + Θ a

Given in.

[0084] According to the theory as described above, the tangential angle φ at each point is sequentially obtained. In the present specification, the above-described solution is referred to as “three-point arc”. φΒ can be calculated for (n-1) points from i = 1 to n-1. For i = 0 and i = n endpoints, force may be entered separately. Simply, φA at i = l is set to i = 0, and 0C at i = n—1 is set to i = n. You may use it.

[0085] Next, the process proceeds to the third step, and interval parameters for each interval are obtained. The interval auxiliary variable is composed of the arc length h of the curve connecting the two points, the curvature φν, and the reduction angle 〖. The following “Crosoid reduced-angle polynomial expression” is used to obtain interval parameters at high speed.

Pl = P0 + h-∑cn [n] -ej (n [n])-φηη η = 0 ... (4)

Coefficient size cn [n] = ∑cnm [m] m = 0 ...

Where cnm [m] = w ^/ ½Z (2m + l)! / n (4m + 4k + 2)

k = l..n

w = —v 2

ν = (1-0) / 2

Coefficient direction φη [η] = (φ0 + φ1— η · π) Ζ2

The proof of this formula is not detailed, but in the basic formula (2) of the clothoid segment, the variable is replaced by T = —l. , Binomial expanded It is obtained by integrating later. String length for the reverse solution! :, Deformed using the direction angle of the string Θ, and scalar decomposition

r / h = ∑χη [η] · u η n = 0 ...

0 = ∑ yn [n] · u n n = 0 ...

xn [n] = cn [n] · cos (φ n [n]) n = 0 ...

yn [n] = cn [n] · sin (φ n [n]) n = 0 ...

φη = (0+ 1-η · π) / 2-θ. Use these formulas to solve the inverse solution as follows:

<ο

[0086] First, the chord angle Θ and length r are obtained from the difference between the starting position (P0 = x0 + j'y0) and the arriving position (Pl = xl + j'yl). ).

Θ = a-tan ((yl -y0) / (xl -χθ))

r = x'cos Θ + ysin θ

[0087] Next, from the starting tangential direction angle φ 0, the arrival tangential direction angle φ 1 and the chord angle Θ, the initial calculation 4

w = — (φΐ—φ 0) ^ 2/4

cnm [0] = 1

cnm [m] = cnm [m— 1] * wZ 2m / (2m + 1J

m = L.mmax cnm [mmax] <h / x

Calculate Next, start the following equation 5 starting from n = 0 and repeat until cn [nmax] becomes δ Zr.

cn [n] = ∑cnm m = 0..mmax

yn [n] = cn [n] 氺 sin φ n

cnm [m] = cnm [m― 1 / (4m + 4n + 2)

m = 0..mmax

φ n = φ n— π Z2

This is the second calculation process. [0088] Next, the reduction factor polynomial yyn [n φ n = 0 n = 0..nmax of y

Is solved by -Euton method to obtain φ u (third operation processing). In other words, the appropriate φ u is

Er = ∑yn [n], φ u n n = 0..nmax

If the allowable error δ> | Er |, the third calculation process is completed. Otherwise, φ u = φ u—Ery ∑, in'yn [n ”'φ u (η— 1)}

η = L.nmax

Then calculate Er again.

[0089] Next, using the reduced polynomial of X

h = rZ∑ {xn [n φ n} n = 0..nmax is obtained (fourth operation process).

[0090] Finally, the curvature angle is calculated (fifth calculation process).

ν = φ 1— u0— u

[0091] Newton's method has a second-order convergence, so it is very efficient. Since the nature of the coefficient, it does not diverge. The speed is further increased by specifying the desired φν, () U region. Note that the solution according to Step 3 in FIG. 22 is referred to as “rotating reverse solution”. The above “rotation” means a clothoid curve. The convolution solution is also used in the next step 44.

[0092] It is the selection of an appropriate initial value that determines the efficiency of the Newton method. The following “Clothoid joint approximation formula” provides a highly accurate initial value. Although the proof of this equation is not described in detail, when this equation is expanded to a polynomial of reduction rate and compared with (4), it completely matches from the 0th order to the 2nd order, and the differential power of the coefficient of the 3rd order term ¾iZl2600 A small thing is powerful.

Pl = PO + h-ej ((O + l) / 2)-{a + b-ej (-k- u)} (5)

k = 2 * cn [2] / cn [l]

b = cn [l] / k

a = cn [0] -b

The error is evaluated by h 'φ 3 Z12600. For example, if the h force OOOmm, is lrad, the error is 8 μm or less. Deformation using the length r and angle Θ of the string, and scalar decomposition, = (0+ 1) / 2- Θ

r / h ^ a'cos φ + b'cos (() ―] ί · φ u) 0 ^ a · sin + b 'sin (φ―) ί · φ u)

So,

φ {a 'sin (a' sin φ Zb) + φ} / k

Gives a very good! / ヽ approximation.

[0093] Further, the process proceeds to the fourth step. In step 41 constituting step 4, the curvature difference evaluation value at each intermediate point is obtained by the following equation. If the curvature of section 0 at midpoint 1 is φ '10 and the curvature of section 1 is φ '11,

('10-'11) 1ι0 · Μ / 2

This is V, which is the geometric mean of the position error when the opposite curvature is adopted for each. Because it is the dimension of the position, the judgment of accuracy is wrong.

[0094] Then, in this step 41, the maximum point is marked. In the next step 42, the absolute value of this value at the maximum point is compared with the given allowable value. If the maximum point is less than the allowable value, the fourth step is completed. If the maximum point is larger than the allowable value in this step 42, the process proceeds to the next step 43 to correct the tangential direction angle at the maximum point. The correction angle is (φ '10 —φ '11) -sqrt (h0-hl) Z8, which is the value obtained by dividing the curvature difference evaluation value by the geometric mean of the arc lengths on both sides and 4. As a result, it turns out that the difference in curvature at the maximum point is almost zero. /

[0095] Further, in step 44, the same solution (rotating reverse solution) as in step 3 is executed only twice, and interval parameters in the interval before and after the maximum point are obtained.

[0096] Further, returning to step 41, the same equation as the process of step 41 is executed only three times to calculate the curvature difference evaluation value between the maximum point and the front and back points, and then step 42 is performed again. Thus, step 4 consisting of steps 41 to 44 is repeated until the evaluation value falls within the allowable range in the determination of step 43.

[0097] Next, the process proceeds to step 51, where the starting point and the tangential direction angle (x0, y0, φ0), the interval parameter (h, ν,

() U) Determine the step assist variables (du, dv, dx, dy, vx, vy, ux, uy). Seriously calculate the harm ij number n. Here, an example of a case where the latter stage has a straight line function is taken. If there is only a natural point function, divide more, and if there is an arc function, divide it less. If there is a clothoid function, n = l and no division is required. The number of divisions is the approximate straight line (string) and Determine the difference from the original curve (arc) to be within the required error δ. If the part with large curvature is short and the part with small length is long and divided with variable length, the number of divisions is minimized. For simplicity of calculation, “equal arc length division” is adopted. Therefore, φ'max, which is the larger of φ'Ο or φ'1, is assumed to be a curvature, and an arc with an arc length h is assumed, and the error when this is divided into n parts is evaluated.

[0098] where

If you use

φ 'max = (I φ 1− φ 0 | + 1 φ u |) Zh.

δ = {1— cos (φ 'max * h. / n / 2)} /' max

cos0 = 1- Θ "2/2! + θ" 4/4! ... because

δ <= φ 'max * (hZn 2Z8

If you use one [one a] as the integer round-up symbol,

n = — [― h * sqrt ('max / δ / 8)]

It is.

[0099] The auxiliary variable (division auxiliary variable) of the subdivided section may be calculated as follows using dh = hZn. du, ux and uy are constants.

du = φ uZ n 2

ux = cos (du)

uy = sin (du)

dv, vx, vy, dx, dy are initial values of variables.

dv = φ O / 2 * dh + du / 2

vx = cos (dv)

vy = sin (dv)

dx = dh water cos (0O + dv)

dy = dh water sin (0O + dv)

[0100] Finally, in step 52, the division assist variable is incremented to obtain sequential positions. x = x + dx water vyZdv (7)

y = y + dx water vy / dv

w = dx * νχ— dy * vy

dy = dx * vy + dy * vx

dx = w

dv = dv + du

w = vx * ux— vy * uy

vy = vx * uy + vy * ux

vx = ww

w = dx * vx— dy * vy

dy = dx * vy + dy * vx

Repeat dx = w.

[0101] The original (3) stepped by 6 sums (differences) and 8 products, whereas 9 sums

(Difference) and 14 products (quotient). The amount of computation is almost doubled, but the accuracy is improved by orders of magnitude. Taking into account the ratio of the arc length and chord length of the section, switching the curvature at the end by halving the section, and switching the tangential direction at the center of the section is not improving the accuracy. .

[0102] In this way, all sections are sequentially interpolated with clothoid segments. By using the trajectory control method according to this embodiment configured as described above, an optimal clothoid curve can be obtained easily and at high speed, and interpolation control that meets the required level can be performed.

[0103] In addition, when interpolating the point sequence determined by the theoretical formula force and calculation, the tangential direction angle at each point is calculated at the same time, and the second and fourth steps can be passed. it can. Further, when the curvature continuity is not required, the fourth step can be passed. Furthermore, when the calculation accuracy may be low, the joint approximation formula can be used from the beginning instead of the third step. At this time, cn [n] can also calculate the trigonometric force as follows, regardless of the series formula of (4).

-w / 6 <= δ

cn [0] = l Otherwise, cn [0] = sin (v) / v

When w "2/840 <= δ

cn [l] = (l + w / 10) / 6

Otherwise, cn [l] = (cos (v) -cn [0]) / w / 2

-w "3/498960 <= when δ

cn [2] = (l + (l + w / 36) * w / 14) / 60

Otherwise, cn [2] = (cn [0] — 6 * cn [l]) / w / 4

25 and 26 show a second embodiment of the processing apparatus. Fig. 25 shows a side view of the processing device as seen from the X-axis direction, and Fig. 26 shows a rear view of the processing device as seen from the Y-axis direction. In the processing apparatus of this embodiment, similarly to the first embodiment, the X-axis moving mechanism 9 that moves the dresser 8 in the X-axis direction in the horizontal plane and the Y-axis moving mechanism 10 that moves in the Y-axis direction are provided. Prepare. Then, a Θ-axis rotation mechanism 20 that rotates the dresser 8 in the Θ-axis direction within a horizontal plane is provided.

[0105] The machining apparatus of the second embodiment differs from the machining apparatus of the first embodiment in that the X-axis moving mechanism 9, the Y-axis moving mechanism 10, the Θ-axis rotating mechanism 20, and the grindstone 7 are both vertical surfaces. A tilt mechanism 61 is provided for tilting the inside. The tilt mechanism 61 includes an electric motor 62, a worm 63 that is rotationally driven by the electric motor 62, and a worm gear 64 that meshes with the worm 63. The tilt mechanism 61 is automatically controlled. An operator manually operates the electric motor 62 to obtain a predetermined inclination angle.

[0106] When grinding a ball screw, a dresser device is provided on the same base as the grinding device. The grindstone 7 is tilted according to the lead angle of the screw. In the processing apparatus of the second embodiment, since the tilt mechanism 61 is provided, the tilted grindstone 7 can be formed.

[0107] The present invention is not limited to the above-described embodiment, and various modifications can be made without departing from the scope of the present invention. For example, the movement of the tool relative to the workpiece in the two-dimensional plane is relative. The X axis movement mechanism and the Y axis movement mechanism may move the workpiece instead of the tool. The work piece is not limited to a turret, and the tool is not limited to a dresser. This specification is based on Japanese Patent Application No. 2006-178496 filed on Jun. 28, 2006. All this content is included here.

Claims

The scope of the claims

[1] A method for controlling a machining apparatus that moves a tool relative to a workpiece to check a force,

An X-axis moving mechanism capable of moving the tool relative to the workpiece in the X-axis direction in a two-dimensional plane; and the tool on the X-axis in the two-dimensional plane with respect to the workpiece. The Y-axis moving mechanism that can be moved relatively in the orthogonal Y-axis direction, and the tool can be rotated in the two-dimensional plane around the tip of the tool that contacts the calorie object. Using a processing apparatus having a Θ-axis rotation mechanism,

The trajectory curve of the tool (which may include a straight line) corresponding to the machining shape of the workpiece in the two-dimensional plane is designed, and the posture of the tool on the trajectory curve is designed. Locus and posture design process,

A trajectory control step of controlling the X-axis moving mechanism and the Y-axis moving mechanism to move the tool relative to the workpiece along the trajectory curve;

And a posture control step of changing the posture of the tool on the trajectory curve in the two-dimensional plane by controlling the Θ-axis rotation mechanism.

[2] In the locus / posture design process,

The locus curve of the tool is designed using a clothoid curve whose tangential direction angle is given by a quadratic expression of the curve length, and

2. The machining according to claim 1, wherein a normal direction angle of the trajectory curve is calculated in at least a part of the trajectory curve, and a posture of the tool is designed based on the normal direction angle. Control method of the device.

[3] In the locus / posture design process,

The tool is moved from one end of a symmetrical trajectory curve around the axis of symmetry to the axis of symmetry, and then the tool is moved to the other end of the trajectory curve, and then The method of controlling a machining apparatus according to claim 1, wherein the trajectory curve is designed so that the tool is moved from the other end of the trajectory curve to the axis of symmetry.

[4] The workpiece is a grindstone that rotates around an axis arranged in the two-dimensional plane,

The tool is a dresser;

The processing device is a dresser device that forms an outer shape of the grindstone with the dresser. In the locus / posture design step, a centerline of the dresser is the centerline of the dresser in the at least a part of the locus curve. 3. The method for controlling a machining apparatus according to claim 2, wherein the posture of the dresser is designed so as to face a normal direction of a locus curve.

[5] The dresser has a flat surface and a corner of a predetermined width at the tip that contacts the turret,

In the locus / posture design step, in the at least a part of the locus curve,

The dresser posture is designed so that the center line of the dresser faces the normal direction of the trajectory curve, thereby bringing the flat surface of the dresser into contact with the grindstone,

In other sections on the locus curve, the dresser's posture is designed so that the center line of the dresser faces in a direction other than the normal direction of the locus curve, so that the corner portion of the dresser is placed on the turret 5. The method for controlling a processing apparatus according to claim 4, wherein contact is made.

[6] The turret is used to grind a ball rolling groove of a gothic groove groove shape having a circular arc force with a cross section of a ball screw or a linear guide,

In the locus and posture design process,

In order to obtain the turret that can adjust the contact angle of the ball screw or the linear guide, the trajectory curve that is symmetric about the symmetry axis can be divided into two parts left and right with the symmetry axis as a boundary. 6. The method for controlling a machining apparatus according to claim 4, wherein each of the paired divided trajectory curves can be shifted by being directed toward the symmetry axis.

[7] The turret is used for grinding a ball screw or a ball rolling groove of a linear guide.

In the locus and posture design process,

In order to adjust the cut-in amount of the dresser, it is The trajectory curve can be shifted in the axial direction of the symmetry axis.

4 or 6, and the processing method control method described in any of the above.

[8] A processing apparatus for moving a tool relative to a workpiece to check a force object, wherein the tool is relative to the workpiece in the X-axis direction in a two-dimensional plane. An X-axis moving mechanism that can be moved automatically,

A Y-axis moving mechanism capable of moving the tool relative to the additive in the Y-axis direction perpendicular to the X-axis in the two-dimensional plane;

A Θ-axis rotation mechanism capable of rotating the tool in the two-dimensional plane around the tip of the tool that contacts the workpiece;

The tool trajectory curve (including straight lines) corresponding to the machining shape of the workpiece in the two-dimensional plane is designed, and the posture of the tool on the trajectory curve is designed, and the X axis The tool is moved along the trajectory curve (which may include a straight line) corresponding to the machining shape of the workpiece in the two-dimensional plane by controlling the moving mechanism and the Y-axis moving mechanism. And a control device that controls the Θ axis rotation mechanism to change the posture of the tool on the trajectory curve in the two-dimensional plane. Processing equipment.

[9] The control device designs the trajectory curve of the tool using a clothoid curve in which a tangential direction angle is given by a quadratic expression of a curve length, and at least in a section on the trajectory curve, 9. The machining apparatus according to claim 8, wherein the normal direction angle of the locus curve is calculated, and the posture of the tool is designed based on the normal direction angle.