JPWO2008001835A1 - Processing apparatus and control method of processing apparatus - Google Patents

Abstract

Provided is a control method of a processing apparatus capable of processing a workpiece such as a grindstone into various shapes. The processing apparatus can move the tool 8 in the X-axis direction in the two-dimensional plane P with respect to the workpiece 7 and the X-axis moving mechanism 9 that can move the tool 8 in the Y-axis direction in the two-dimensional plane P. A Y-axis moving mechanism 10 and a θ-axis rotating mechanism 20 capable of rotating the tool 8 in a two-dimensional plane around the tip 8a of the tool 8 that contacts the workpiece. The control device of the processing apparatus designs a trajectory curve / posture in which the tool 8 moves, controls the X-axis moving mechanism 9 and the Y-axis moving mechanism 10, moves the tool 8 along the trajectory curve, and θ The posture of the tool 8 in the two-dimensional plane P is changed by controlling the shaft rotation mechanism 20.

Description

  The present invention relates to a processing apparatus for processing a workpiece by moving a tool relative to the workpiece and a control method for the processing apparatus.

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

  As one type of processing apparatus, a dresser apparatus that forms an outer shape of a grindstone with a dresser is known (Patent Document 1). As shown in FIG. 27, the grindstone 1 as a workpiece is driven to rotate about the 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 while maintaining a distance of radius R.

  FIG. 28 shows a cross-sectional view taken along line AA of FIG. The vertical line 4 passes through the center of curvature of the arc-shaped molding surface of the grindstone 1. When the rotary dresser 3 is swiveled around the vertical line 4, the trajectory of the swivel movement of the rotary dresser 3 is transferred to the grindstone 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 linear portion of the grindstone 1, thereby A molding surface is formed by combining straight portions.

JP 49-50589 (refer to page 2, FIGS. 1 to 3)

  However, in the conventional dresser device, only an arc shape with a constant curvature radius 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 circular arc surfaces with different curvature radii, the molding surface can be formed into a combination of multiple circular arcs with different curvature centers, or multiple curvature radii can be combined. It is difficult to form a shape combining arcs. In particular, as shown in FIG. 30, a grindstone having an arc-shaped curvature center on both the outside and inside of the molding surface, with the molding surface of the grindstone as a boundary (arc portions R1 and R2 have a center of curvature on the inside of the molding surface. The arc portions R3 and R4 have a center of curvature outside the molding surface).

  In addition, in the conventional dresser device, although it is possible to form a molding surface that combines an arc portion and a straight portion, the shape of the molding surface depends on the shape of the taper portion of the rotary dresser, so the degree of freedom in shape There are limitations.

  In other words, in the conventional dresser device, since the locus of movement of the dresser transferred to the grindstone is mechanically controlled, the grindstone cannot be processed into various shapes.

  Then, an object of this invention is to provide the control method and processing apparatus of the processing apparatus which can process a workpiece into various shapes.

The present invention will be described below.
In order to solve the above-mentioned problem, the invention according to claim 1 is a control method of a processing apparatus for processing a workpiece by moving a tool relative to the workpiece, wherein the tool is moved to the workpiece. An X-axis moving mechanism capable of relatively moving in the X-axis direction in the two-dimensional plane (P) with respect to the workpiece, and the tool perpendicular to the X-axis in the two-dimensional plane with respect to the workpiece A Y-axis moving mechanism capable of relatively moving in the axial direction, and a θ-axis capable of rotating the tool in the two-dimensional plane (P) around the tip of the tool contacting the workpiece And using a processing device having a rotation mechanism, and designing a trajectory curve of the tool (which may include a straight line) corresponding to the processing shape in the two-dimensional plane (P) of the workpiece, A trajectory / posture design engineer for designing the posture of the tool on the trajectory 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 controlling the θ-axis rotating mechanism. And a posture control step of changing the posture of the tool on the locus curve in the two-dimensional plane.

  According to a second aspect of the present invention, in the trajectory / posture design step, in the method for controlling a machining apparatus according to the first aspect, the tool is obtained by using a clothoid curve in which a tangential direction angle is given by a quadratic expression having a curve length. And 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. Features.

  According to a third aspect of the present invention, in the method for controlling a machining apparatus according to the first or second aspect, in the trajectory / posture design step, the trajectory curve is symmetric with respect to one end of a trajectory curve centered on a symmetry axis. Moving the tool to the axis of symmetry, then moving the tool to the other end of the trajectory curve, and then moving the tool from the other end of the trajectory curve to the axis of symmetry The trajectory curve is designed.

  The invention according to claim 4 is the method for controlling the machining apparatus according to claim 2, wherein the workpiece is a grindstone that rotates around an axis 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 grindstone with the dresser, and in the trajectory / posture design step, in the at least part of the section on the trajectory curve, The posture of the dresser is designed so that the center line of the dresser faces the normal direction of the locus curve.

  According to a fifth aspect of the present invention, in the method for controlling a processing apparatus according to the fourth aspect, the dresser has a flat surface and a corner portion having a predetermined width at the tip that contacts the grindstone, In the trajectory / posture design step, the dresser's posture is designed so that the centerline of the dresser is directed in the normal direction of the trajectory curve in the at least part of the section on the trajectory curve. In the other section on the locus curve, the dresser is designed so that the center line of the dresser faces other than the normal direction of the locus curve. The corner portion of the dresser is brought into contact with the grindstone.

  A sixth aspect of the present invention is the method of controlling a machining apparatus according to the fourth or fifth aspect, wherein the grindstone is a ball screw or a linear guide of a Gothic arch groove-shaped ball rolling having two arcs in cross section. Used to grind grooves, and in the locus / posture design process, the locus that is symmetric about the axis of symmetry is obtained in order to obtain the grindstone that can adjust the contact angle (α) of the ball screw or linear guide. The curve can be divided into right and left parts with the symmetry axis as a boundary, and each of the pair of divided locus curves can be shifted toward the symmetry axis.

  The invention according to claim 7 is the method of controlling a processing apparatus according to any one of claims 4 to 6, wherein the grindstone is used for grinding a ball rolling groove of a ball screw or a linear guide, In the trajectory / posture design step, the trajectory curve that is symmetrical about the axis of symmetry can be shifted in the axial direction of the axis of symmetry in order to adjust the cutting amount of the dresser.

  Invention of Claim 8 is a processing apparatus which processes a workpiece by moving a tool relatively with respect to a workpiece, Comprising: The said tool is in a two-dimensional plane (P) with respect to the said workpiece. An X-axis moving mechanism capable of relatively moving in the X-axis direction, and moving the tool relative to the workpiece in the Y-axis direction perpendicular to the X-axis in the two-dimensional plane (P) A Y-axis moving mechanism capable of rotating the tool in the two-dimensional plane (P) around the tip of the tool that contacts the workpiece; The tool trajectory curve (which may include a straight line) corresponding to the machining shape in the two-dimensional plane (P) is designed, and the posture of the tool on the trajectory curve is designed, and the X The two-dimensional plane (P) of the workpiece is controlled by controlling the axis moving mechanism and the Y axis moving mechanism. ) In the two-dimensional plane (P) by moving the tool relative to the workpiece along a locus curve corresponding to the machining shape in And a control device that changes the posture of the tool on the locus curve.

  According to a ninth aspect of the present invention, in the processing apparatus according to the eighth aspect, the control device designs the trajectory curve of the tool using a clothoid curve given by a quadratic expression whose tangential direction angle is a curve length. In addition, the normal direction angle of the trajectory curve is calculated in at least a part of the trajectory curve, and the posture of the tool is designed based on the normal direction angle.

  According to the first aspect of the present invention, since the X-axis moving mechanism and the Y-axis moving mechanism move the tool along the designed locus curve, the workpiece is processed into various shapes in a two-dimensional plane. be able to. Further, since the posture of the tool on the locus curve can be changed by the θ-axis rotation mechanism, the tool can be directed in an 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, the change in the posture of the tool does not affect the shape of the workpiece.

  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 trajectory curve, the normal direction angle on the trajectory curve can be easily calculated. .

  According to the third aspect of the invention, the shape of the symmetrical workpiece can be stabilized.

  According to the fourth aspect of the present invention, the dresser is oriented in the normal direction with respect to the processing shape of the grindstone, so that the wear of the dresser can be reduced and the variation in the wear of the dresser can be reduced. it can.

  According to the invention described in claim 5, even if the center of curvature of the trajectory curve is closer to the dresser side than the trajectory curve and the radius of curvature of the trajectory curve is smaller than the width of the dresser, the dresser gets over the grindstone. The shape of the grindstone matched to the trajectory curve can be formed.

  According to invention of Claim 6, the grindstone which can adjust the contact angle of a ball | bowl and a ball rolling groove | channel can be shape | molded.

  According to invention of Claim 7, the cutting amount of the dresser to a grindstone can be adjusted.

  According to the eighth aspect of the present invention, the tool can be moved along the designed trajectory curve by the X-axis moving mechanism and the Y-axis moving mechanism, so that the workpiece can be variously shaped in a two-dimensional plane. Can be processed. Further, since the posture of the tool on the locus curve can be changed by the θ-axis rotation mechanism, the tool can be directed in an 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, the change in the posture of the tool does not affect the shape of the workpiece.

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

The side view which shows the processing apparatus in 1st embodiment of this invention. Top view of the dresser A perspective view showing a ball screw ground by a grindstone The perspective view which shows the linear guide ground with a grindstone The figure which shows the processing shape in the horizontal surface of a grindstone The figure which shows the locus and posture of the dresser moving along the processing shape of the grindstone Block diagram of control device Diagram showing a tabular motion table Flowchart executed by Motion Designer Trajectory design screen displayed on computer display The figure which shows the other example of the locus | trajectory and attitude | position of a dresser which moves along the processing shape of a grindstone Conceptual diagram of the trajectory design method for obtaining a grindstone with adjustable contact angle The figure which shows the cross-sectional shape of the grindstone which adjusted the contact angle Conceptual diagram of trajectory design method for adjusting dresser cutting depth The figure which shows the example which designed the posture of the dresser so that the posture of the dresser faces the normal direction of the locus curve The figure which shows the example whose width | variety of the flat surface of a dresser tip is larger than the curvature radius of the small diameter circular arc part of a locus curve Figure showing the arc of the dresser that has been cut too much The figure which shows the example which designed the posture of the dresser so that the posture of the dresser faces other than the normal direction of the trajectory curve The figure which shows the circular arc part of the dresser which was cut smoothly Flow chart executed by the motion operator Diagram showing basic clothoid curve Flow chart of program executed by interpolation method using clothoid curve Schematic for explaining how to get the initial value of the tangential angle Schematic for explaining the three-point arc method The side view seen from the X-axis direction of the processing apparatus of the second embodiment of the present invention The side view seen from the Y-axis direction of the processing apparatus of the second embodiment of the present invention Side view of a conventional dresser device The figure which shows the shaping | molding method of the grindstone by the conventional dresser (AA sectional view taken on the line of FIG. 27) The figure which shows the shaping method of the grindstone with the conventional dresser The figure which shows the shape of the grindstone which cannot be shape | molded with the conventional dresser apparatus.

  FIG. 1 shows a processing apparatus in a 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 grindstone 7 is provided in the processing device so as to be rotatable around its axis 7a, and is rotated by a grindstone driving device (not shown). The axis 7a of the grindstone 7 is located in a two-dimensional plane, for example, the horizontal plane P. At the time of processing, the grindstone 7 set apart from the dresser is moved in the y direction in the figure toward the dresser 8 by a grindstone Y-axis moving device (not shown).

  A dresser 8 is disposed in the horizontal plane P including the axis 7 a 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 movement mechanism 9, and can be moved in the Y-axis direction orthogonal to the X-axis in the horizontal plane by the Y-axis movement mechanism 10. The dresser 8 can be rotated in the horizontal plane by the θ-axis rotation mechanism 20.

  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 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 movement amount of the Y-axis table 17 with respect to the rotation amount 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 via a linear guide so as to be slidable in the Y-axis direction.

  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 processing position or moves it away from the processing position.

  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 a 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 a linear guide 24 so as to be slidable in the Y-axis direction.

  A θ-axis rotating mechanism 20 is attached on the X-axis table 21. A column 26 is coupled on the X-axis table 21. A θ axis 27 extending in the vertical direction is rotatably supported on the column 26 via a bearing 28. The axis 27a of the θ axis 27 faces 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 the dresser 8 is attached to the lower end thereof. The upper end portion of the θ-axis 27 is suspended from the support portion by the bearing 28, and the lower end portion of the θ-axis 27 is not supported. In order to avoid interference with the grindstone 7, the θ-axis 27 is inclined obliquely from the upper end to the lower end. The axis 27a of the θ axis 27 becomes the rotation center of the dresser 8 in the horizontal plane P. The position of the dresser 8 is adjusted such 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 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 is composed of a diamond tool for grinding the grindstone 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.

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

  The grindstone 7 formed by the dresser 8 is used to grind 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 a ball rolling groove 32a of a screw shaft 32 and a ball rolling groove 33a of a nut 33, and a return path 35 is provided in the nut 33 so that the ball 34 can circulate. It is. The linear guide 40 is used to guide the moving body in a linear motion, and includes a ball rolling groove 36 a of the track rail 36 that extends linearly and a bowl-shaped moving block 37 that moves along the track rail 36. A ball 38 is inserted between the ball rolling groove 37a and a return path 39 is provided in the moving block 37 so that the ball 38 can circulate. In the ball screw 31 and the linear guide 40, the ball rolling grooves 32a, 33a, 36a, and 37a may have a circular arch groove shape formed of a single circular arc or two circular arcs. It may be formed in a Gothic arch groove shape.

  FIG. 5 shows an example of a processed shape in the horizontal plane P of the grindstone 7 formed by the dresser 8. The processing shape of the grindstone 7 in the horizontal plane P is matched with the cross-sectional shape of the ball rolling grooves 32a, 33a, 36a, 37a. In this example, the processing shape in the horizontal plane P of the grindstone 7 is set to the Gothic arch groove shape according to the ball rolling grooves 32a, 33a, 36a, and 37a of the Gothic arch groove. That is, the processing shape of the grindstone 7 has an arc portion 41 composed of two arcs R1, R2, and the curvature radii of the two arcs R1, 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. Linear portions 42 are provided on both sides of the arc portion 41. An arc portion 43 made of small-diameter arcs R3 and R4 is provided at a connection portion between the arc portion 41 and the linear portion 42. The centers of curvature of the arcs R1 and R2 and the centers of curvature of the arcs R3 and R4 are on the inside and outside of the grindstone 7 with the molding surface of the grindstone 7 as a boundary.

  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 controlled to move the dresser 8 along the locus curve 44 (matching the processing shape of the grindstone) in the horizontal plane P and rotate the θ axis. The mechanism 20 is controlled to change the posture of the dresser 8 of the trajectory curve 44 in the horizontal plane P.

  A control device of the dresser device will be described. FIG. 7 shows a configuration diagram of the control device 55. The hardware of the control device 55 includes a computer 56 such as a personal computer in which software up to the creation of the motion table 51 is installed (left side of the dotted line in the figure), and the X, Y, θ axes of the dresser device by reading the motion table 51. And a motor control device 57 (on the right side of the dotted line in the figure) in which a motion operator 54 is installed. The computer 56 of the control device 55 creates a motion table 51 that describes the displacement values of the respective operation axes by taking the time axis in the row direction and the X, Y, and θ axes of the dresser device in the column direction. Based on the table 51, the motor control device 57 of the control device 55 controls each axis of the dresser device. Signal commands from the motion table 51 and the motion editor 53 are transmitted between the computer 56 and the motor control device 57.

  The software of the control device 55 includes a motion designer 52 for creating the motion table 51, a motion editor 53 (sequencer) for editing the plurality of motion tables 51, and receiving these command inputs, , Y, and θ-axis servo motors, and a motion operator 54 for operating the servo motors.

  First, the motion table 51 will be described. Giving the position and / or orientation of the dresser 8 as a function of time is called motion. As shown in FIG. 8, the motion table 51 describes the absolute value or the 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 with respect to the reference value, and the incremental value is a value that is incremented at each time interval. Although the absolute value is described in FIG. 8, it does not necessarily start from 0.

  The motion table 51 is sent to a robot or the like as CSV (Comma Separated Value) data, for example. Since the motion table 51 is tabular data having vertical columns and horizontal rows, it is converted into a single column of data using the CSV method so that it can be transmitted by serial communication. Specifically, for example, the table data is converted into a single column of data from the upper left, such as 0, 0, 5 rows, 1, 2, 5, rows, 3, 6, 5, rows. The

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

<Design of locus / posture (S1)>
When the dresser 8 moves, the point of contact with the grindstone 7 at the tip of the dresser 8 (hereinafter referred to as a tool point) moves temporally on a continuous locus curve (which may include a straight line) drawn in a plane. Then you can think. 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. In any complicated 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 to design 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, XY coordinates of six point sequences P1 to P6 to the computer 56 in correspondence with the machining shape of the grindstone 7 shown in FIG. Input means such as a keyboard and a mouse can be used for input. P1 → P2 is a section corresponding to the straight portion 42 of the machining shape, P2 → P3 → P4 is a section corresponding to the small-diameter arc portion 43 of the machining shape, and P4 → P5 → P6 is a large machining shape. This is a section corresponding to the circular arc portion 41 of the diameter. When the operator inputs a point sequence, the computer designs a trajectory curve 60 obtained by interpolating the point sequences P1 to P6. The designed locus curve 60 is displayed on the display device. In the present 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 obtained by interpolating P1 to P6, the computer 56 inverts the trajectory curve 60 about the symmetry axis 59 on the workpiece origin, so that 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 8 d of the dresser 8 faces the normal direction of the locus curve 44 in all sections on the locus curve 44. The reason for directing the normal direction is to reduce the wear of the dresser 8 and to reduce the variation in wear in each part of the dresser 8. Since the tangential direction angle is given in the clothoid curve, the normal direction of the curve can be calculated only by rotating the given tangential direction angle by 90 degrees. When the clothoid curve is used, the posture E of the dresser 8 as well as the position P of the dresser 8 is given as a function of the curve length s, as shown in FIG.

  As shown in FIG. 6, when the dresser 8 is moved along the locus curve 44 from one end 44a to the other end 44b of the symmetrical locus curve 44, the machining time can be shortened. 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 trajectory curve 44 to the symmetry axis 59, and then the dresser 8 is moved to the other end 44b of the trajectory curve 44. The dresser 8 may be moved from the other end 44b of the locus curve 44 to the axis of symmetry 59. When the trajectory curve is designed in this way, it takes a little processing time, but the shapes of the arcs R1 and R2 are stabilized.

  FIG. 12 is 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) by dividing the trajectory curve 44 into left and right with the symmetry axis as a boundary. The operator inputs the offset amount of the divided 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 designated offset amount. The curvature radii of the arcs R1 and R2 are not changed.

  As shown in FIG. 13, the contact angles α1, α2 are lines connecting the center point O of the balls 34, 38 of the ball screw 31 or the linear guide 40 and the ball rolling grooves 32a, 33a, 36a, 37a. 46 and a line connecting the symmetrical ball rolling grooves 32 a, 33 a, 36 a, and 37 a with symmetrical axes 59. Here, since the processing shape of the grindstone 7 and the cross-sectional shape of the ball rolling grooves 32a, 33a, 36a, 37a coincide, 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 α1 and α2 are shown. By changing the offset amount, the contact angles α1 and α2 can be adjusted. For example, the contact angle α1 can be increased like the contact angle α2.

  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 32 a, 33 a, 36 a, and 37 a with the grindstone 7, the grindstone 7 may be formed again with the dresser 8. In this case, it is necessary to form the grindstone with a slightly deeper cut than the previously formed processed shape. The operator inputs the shift amount for each of the divided trajectory curves (1) and (2) on the input screen shown in FIG. As shown in FIG. 14, the computer 56 generates a trajectory curve 44 (consisting of divided trajectory curves (1) and (2)) designed symmetrically about the symmetry axis 59 by the designated shift amount. Shift in the direction of the symmetry axis 59 (in the Y direction). Thereby, the worn grindstone 7 can be cut by a predetermined cut amount.

  As shown in FIG. 15, in the locus / 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 trails 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 portion 8c. If the width W1 of the flat surface at the tip of the dresser 8 is larger than the radius of curvature R3 of the small-diameter arc portion 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 corners 8c go around the grindstone 7. If it becomes like this, as FIG. 17 shows, it will become a shape where the circular arc part 43 of the shape | molded dresser 8 was shaved too much.

  In order to solve this problem, in the present embodiment, as shown in FIG. 18, the corner of the dresser 8 is brought into contact with the grindstone 7 until reaching the arc portion 43 having a small diameter from the straight portion 42. The posture of the dresser 8 is designed. In other words, the center line 8 d 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 grindstone 7. FIG. 19 shows the shape of the grindstone 7 formed by such a locus / posture design. It can be seen that a smooth shape can be obtained even in the small-diameter arc portion 43.

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

<Fitting of motion curve (S2)>
As shown in FIG. 9, the second stage of motion control is to determine the speed / acceleration of the tool point moving on the designed trajectory curve. How the tool point moves as a function of time on the trajectory curve is determined by determining the speed and acceleration of the tool point. The operator inputs the speed of the dresser 8 on the screen shown in FIG. The computer 56 determines the speed and acceleration of the tool point so that the dresser 8 can be moved at a designated speed. In the present embodiment, a curve with good characteristics adopted in the cam mechanism is adopted, and this is provided as a variable cam universal cam curve. The positions and postures defined in the Cartesian space (real space) constitute a continuous curve group. Fit a motion curve to each curve and specify acceleration / deceleration. The Cartesian space is a three-dimensional coordinate system created using three axes x, y, and z that are orthogonal to each other at the origin, and can represent not only the position of the tool point but also the posture.

<Time division (S3)>
Since the trajectory and motion are determined, the position / orientation of the tool point is given as a function of time t. Thereby, when the time t is given at a minute time interval, 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.

<Calculation of the position and orientation of the dresser 8 using the Cartesian coordinate system (S4)>
With 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. Variables include (x, y, θ).

<Reverse mechanism solution (S5)>
Next, the rotation angle of each axis necessary to give the position / posture of the tool point is obtained. This process is generally called Inverse Kinematics. The reverse mechanism solution is to obtain the rotation angles θ1 to θ3 of the axial space from the position / posture of the actual space. Since the reverse mechanism solution is unique to each processing apparatus, a solution is prepared for each processing apparatus.

<Calculation of each axis servo motor displacement by axis coordinate system (S6)>
An inverse mechanism solution is obtained for each time-divided tool point, and this is converted into an integer as a displacement pulse of each axis servo motor. When the pulse control is not used, the data is obtained as integerized data corresponding to the number of pulses using the minimum resolution unit (resolution) of each axial displacement.

<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 motion table 51 described above.

  The motion editor 53 shown in FIG. 7 will be described. The motion editor 53 edits a plurality of motion tables 51, and for example, sets the order of use of the created motion tables 51. Specifically, for example, if the motion table 51 is A, B, and C, the order is set as B when A is over, C when B is over, or B and C together when A is over. Run it. It is close to a sequencer in the sense of giving a sequence of operations. The motion editor 53 is generally built in the computer together with the motion designer 52, but may be placed outside.

  Next, the motion operator 54 incorporated in the motor control device 57 will be described. The motion operator 54 is commonly referred to as a servomechanism (ie, an automatic feedback control system for mechanical movement). Here, a motion operator is called for generalization. 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 determines the servo motor for each axis. 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, the procedure executed by the motion operator 54 will be described in detail with reference to FIG.
<Communication (S1)>
There are several ways to send motion table 51 data from the computer 56 to the motor controller 57. The first method uses a high-speed communication line as a transmission medium. As a high-speed communication line, Ethernet (registered trademark) (R), USB, IEEE 1394, or the like can be used. Further, depending on conditions, a wireless or low-speed communication line can be used. The second method is a method of reading data by directly connecting a bus or the like. If the computer and the motor control device are not separated, it can be adopted. The third method uses a portable memory medium. Transport using CD, DVD, memory card, etc.

<Read motion table (S2)>
Since each communication method has its own protocol, the motion table 51 is read according to that protocol.

<Distribution of input data to each axis (S3)>
Since the motion table 51 is usually created for a plurality of axes, it must be distributed for each axis. There is also a method of compulsorily distributing using a hub etc. (a method of distributing one row of data to the drivers of each axis in order on the delivery side), but normally only receiving data related to each axis on the receiving side To do. If there is a memory on the receiving side, for example, the vertical column of data shown in FIG. 8 is received as X-axis data, the next column of data is received as Y-axis data, and the next data is received as θ-axis data. Can receive column data.

<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 moved together. By sending the synchronization signal to the servo driver, the servo motors for each axis move together. It is desirable that the synchronization signal is always sent once at time-divided time intervals.

  In order to take a sequence with various input / output signals of the dresser device, it is necessary to edit the motion table 51 by the motion editor 53 or the sequencer. For example, there are cases where the tool point is stopped when the limit switch is activated, or the temperature of the tool point is measured by a sensor, and the speed of the tool point may be decreased when the temperature becomes high. 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.

<Each axis driver and each axis servo motor (S5, S6)>
Whether or not each axis servo motor moves following the motion command is the role of the servo driver and each axis servo motor. In this embodiment, the feedback signal is not returned to the computer 56 for creating the motion table. The computer 56 for creating the motion table never enters the servo loop.

  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 grindstone) in the horizontal plane P, and the θ-axis rotating mechanism 20. Can be controlled to change the posture of the dresser 8 of the trajectory curve 44 in the horizontal plane P.

The interpolation method using a clothoid curve will be described in detail below.
To implement interpolation in general: Determine the interpolation formula.
2. Determine the auxiliary variable.
3. Decide the step and calculate the coordinates sequentially.
There are three stages. And the reverse solution is 3. A forward solution is required.

Briefly explain the basic theory of clothoid curves and clothoid segments. 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 the curve length)), h (constant (total length of clothoid curve))
Definition of tangential direction angle ej (φ) ≡dp / ds (unit vector obtained by differentiating position vector by arc length)
Definition of curvature φ'≡dφ / ds Definition of differential shrinkage by arc length of tangential angle φ "≡dφ '/ ds Definition of differential line by arc length of curvature dφ / ds≡0 Curve with constant tangential angle is a straight line Definition of circle dφ '/ ds≡0 A curve with constant curvature is a circle (including a straight line)
Definition of clothoid dφ "/ ds≡0 Curve with constant shrinkage is clothoid (including circle)
Clothoid basic formula: Obtained by sequentially integrating the defining formula. φ '= φ'0 + φ "· s
φ = φ0 + φ'0 · s + φ "/ 2 · s ^ 2 (Tangential direction is given by a quadratic expression of the curve length)
P = ∫ej (φ0 + φ'0 · s + φ "/ 2 · s ^ 2) ds (1)

  FIG. 21 shows a basic clothoid curve, and the solid line in the figure shows a curve when φ0 = φ′0 = 0 and φ ″ = π / 2. This curve is called a Cornu spiral. The broken line in the figure shows a curve when φ ″ = − π / 2. Cs and Sn are known as Fresnel integrals.

In this specification, the following description method is adopted as expression of the mathematical expression.
/ Division symbol
^ Power symbol i = [v] Decimal part truncation Example [0.5] = 0-[-0.5] = 1
a. . b Integration interval from a to b or cumulative interval a ... Cumulative interval from a to infinity ej (φ) = e ^ (j · φ) = cosφ + j · sinφ Two-dimensional unit vector

The clothoid segment is obtained by cutting a part of a clothoid curve in the same manner as cutting a line segment from a straight line and an arc from a circle. The starting point P0 and the ending point P1 are determined by the above basic formula, and the arc length is set from 0 to h to perform definite integration. Further, the section is made dimensionless as (S = 0.0.1), the bending angle φv = φ′0 · h as the arc component of the angle change, and the contraction angle φu = φ ″ / 2 · h as the clothoid component. The basic formula of clothoid segment is φ'1 = (φv + 2 · φu) / h from (1)
φ1 = φ0 + φv + φu
P1 = P0 + h · ej (φ0) · ∫ej (φv · S + φu · S ^ 2) ds
S = 0.1 (2)

  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 bending angle φv, and the contraction angle φu are collectively referred to as an interval auxiliary variable. Lines, circles and clothoids are separate figures. A straight line is infinite and has a direction, a circle is finite and has a size, a clothoid has an infinite length, an existence range is finite, and has a 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, a method for obtaining the interval auxiliary variable by giving the positions of the start point and end point and the tangential direction angle is called an inverse solution.

FIG. 22 shows a flowchart of a program executed by an interpolation method using a clothoid curve. The control method according to the present embodiment interpolates P1 to P6 given in advance using a clothoid segment calculated by a computer. In the interpolation method using a clothoid curve, first, the coordinates P _i (x _i , y _i ) of the point sequence are input (step 1).

Next, a tangential angle φ _i at each point is obtained (step 2). The tangential direction angle φ _i indicates the direction of the tangent at each of the above points, and is represented by an angle φ _i formed by the tangent to the reference line. The tangential direction angle φ _{i obtained in} the second step is provisional except for the end points.

  Next, interval parameters in all intervals are obtained (step 3). The interval auxiliary variable is constituted by an arc length h, a bending angle φv, and a contraction angle φu. The interval auxiliary variable can be obtained at high speed by solving the inverse solution of the “clothoid contraction polynomial” by the procedure consisting of the following first calculation process to fifth calculation process. That is, the chord length and the directional angle are calculated from the difference in position between the start point and the end point (first calculation process), and the coefficient of the reduced angle polynomial is calculated from the difference in the tangential direction angle between the start point and the end point ( (Second calculation process), a reduction angle polynomial of y is solved by Newton's method to calculate a reduction angle (third calculation process), and an arc length is calculated using the above reduction angle and the reduction angle polynomial of x (fourth calculation process). Arithmetic operation), and the curvature angle is calculated from the difference in tangential direction angle and the contraction angle (fifth arithmetic processing). In addition, about the said 3rd calculation process, a joint approximation formula can also be used for Newton's method reverse solution.

Next, the process proceeds to step 4 where a curvature difference evaluation value at an intermediate point excluding both ends of each point is obtained, the maximum point of these curvature difference evaluation values is marked (step 41), and the curvature difference evaluation value of the maximum point is determined. Is determined to be within the allowable range (step 42), and if the curvature difference evaluation value is within the allowable range, step 4 is terminated. Otherwise, the tangential direction angle of the maximum point is corrected. (Step 43), recalculate the interval parameters of the two sections before and after the maximum point (step 44), recalculate the curvature difference evaluation values at the three points of the maximum point and the front and back points (step 41), Return to 42 and repeat.
As a result, the curvature difference evaluation values at all points can be finally made equal to or less than the tolerance given in advance.

  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. And a position is calculated | required sequentially based on these division | segmentation auxiliary variables. Thereby, an optimum position command for interpolating between the point sequences can be obtained.

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

Next, in the second step, an initial value of the tangential direction angle φi at each point Pi is obtained. An example of the solution means in this step is shown below. As shown in FIG. 23, three consecutive points are selected, and tangential angles φA, φB, and φC at the respective points of the arc passing through these three points (A, B, and C in FIG. 24) are obtained. If the angles of each side of the triangle a + b = c are θa, θb, and θc, the vertex angle α is
α = θc−θa
β = π−θb + θa
γ = θb−θc
The tangential direction at each point of the arc passing through the three points is equal to the circumference angle and the chord arc angle.
φA = θa−γ = θa−θb + θc
φB = θb−α = θb−θc + θa
φC = θc−β + π = θc−θa + θb
Given in.

  Based on 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”. φB can be calculated for (n−1) points from i = 1 to n−1. The end points of i = 0 and i = n may be input separately, but simply, φA at i = 1 is set to i = 0, and φC at i = n−1 is set to i = n. You may use it.

Subsequently, it progresses to a 3rd process and the area auxiliary variable of each area is calculated | required. The interval auxiliary variable is constituted by an arc length h, a curvature angle φv, and a contraction angle φu of a curve connecting two points. In order to obtain the interval parameter at high speed, the following “Crosoid reduced-angle polynomial expression” is used.
P1 = P0 + h · Σcn [n] · ej (φn [n]) · φu ^ n n = 0 ... (4)
Coefficient size cn [n] = Σcnm [m] m = 0 ...
Here, cnm [m] = w ^ m / (2m + 1)! / Π (4m + 4k + 2)
k = 1..n
w = -v ^ 2
v = (φ1−φ0) / 2
Coefficient direction φn [n] = (φ0 + φ1-n · π) / 2
The proof of this formula will not be described in detail, but in the basic formula (2) of the clothoid segment, the variable is replaced with T = −1.1 instead of S = 0.0.1 to make it swingless dimensionless. It is obtained by integrating after expanding the terms. For inverse solution, transform using string length r and string direction angle θ, and then scalar decomposition, r / h = Σxn [n] · φu ^ n n = 0 ...
0 = Σyn [n] ・ φu ^ n n = 0 ...
xn [n] = cn [n] .cos (ψn [n]) n = 0 ...
yn [n] = cn [n] · sin (ψn [n]) n = 0 ...
ψn = (φ0 + φ1−n · π) / 2−θ. Use these formulas to solve the inverse solution in the following procedure.

First, the chord angle θ and the length r are obtained from the difference between the departure position (P0 = x0 + j · y0) and the arrival position (P1 = x1 + j · y1) (first calculation process).
θ = a · tan ((y1−y0) / (x1−x0))
r = x · cos θ + y · sin θ

Next, from the starting tangential direction angle φ0, the arriving tangential direction angle φ1 and the chord angle θ, the initial calculation 4 formula ψn = (φ0 + φ1) / 2−θ
w =-(φ1-φ0) ^ 2/4
cnm [0] = 1
cnm [m] = cnm [m-1] * w / 2m / (2m + 1)
m = 1..mmax cnm [mmax] <δ / r
Calculate Next, the following five equations are repeated starting from n = 0 until cn [nmax] <δ / r.
cn [n] = Σcnm m = 0..mmax
xn [n] = cn [n] * cos ψn
yn [n] = cn [n] * sin ψn
cnm [m] = cnm [m-1] / (4m + 4n + 2)
m = 0..mmax
ψn = ψn−π / 2
This is the second calculation process.

Next, the contraction polynomial of y Σyn [n] · φu ^ n = 0 n = 0..nmax
Is obtained by Newton's method to obtain φu (third operation processing). That is, with an appropriate φu as an initial value, Er = Σyn [n] · φu ^ n n = 0.
If the allowable error δ> | Er |, the third calculation process is completed. Otherwise, φu = φu−Er / Σ {n · yn [n] · φu ^ (n−1)}
n = 1..nmax
Then, Er is calculated again.

Next, h is calculated using h = r / Σ {xn [n] · φu ^ n} n = 0..nmax using a reduction factor polynomial of x (fourth arithmetic processing).

Finally, the curvature angle is calculated (fifth calculation process).
φv = φ1−φu0−φu

  Newton's method is very efficient because of second-order convergence. Since the coefficient is good, it does not diverge. By specifying the required φv and φu regions, the speed can be further increased. Note that the solution according to step 3 in FIG. 22 is referred to as a “rotating reverse solution”. The above “rotation” means a clothoid curve. The convolution inverse solution is also used in the next step 44.

It is the selection of an appropriate initial value that determines the efficiency of the Newton method. According to the following “clothoid joint approximation formula”, a highly accurate initial value can be obtained. 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 second order, and the difference in the coefficient of the third order term is h / 12600. You can see that it is smaller.
P1≈P0 + h · ej ((φ0 + φ1) / 2) · {a + b · ej (−k · φu)} (5)
k = 2 * cn [2] / cn [1]
b = cn [1] / k
a = cn [0] -b
The error is evaluated by h · φu ^ 3/12600. For example, if h is 1000 mm and φu is 1 rad, the error is 8 μm or less. When the string length r and angle θ are used for deformation and scalar decomposition, ψ = (φ0 + φ1) / 2−θ where r / h≈a · cosψ + b · cos (ψ−k · φu)
0 ≒ a ・ sinψ + b ・ sin (ψ-k ・ φu)
So,
φu≈ {a · sin (a · sinψ / b) + ψ} / k
Gives a very good approximation.

Further, the process proceeds to the fourth step. In step 41 constituting step 4, the curvature difference evaluation value of 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,
(Φ'10-φ'11) ・ h0 ・ h1 / 2
This is a geometric mean of position errors when the opposite curvature is adopted for each. Since it is the dimension of position, it is easy to judge accuracy.

  In 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 a given allowable value. If the maximum point is equal to or smaller than the allowable value, the fourth step is completed. If the maximum point is larger than the allowable value in 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 · h1) / 8, which is a 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, the curvature difference at the maximum point is almost zero, but it is known that the curvature at the front and rear points does not resonate much.

  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.

  Further, returning to the above step 41, the same formula as the process of step 41 is executed only three times, the curvature difference evaluation values of the maximum point and the front and rear points are calculated, and then step 42 is performed again. In this way, Step 4 including Steps 41 to 44 is repeated until the evaluation value falls within the allowable range in the determination of Step 43.

  Next, the process proceeds to step 51, where a starting auxiliary variable (du, dv, dx, dy, vx, vy, tangential direction angle (x0, y0, φ0), interval auxiliary variable (h, φv, φu)) is determined. ux, uy). First, the division number n is calculated. Here, an example of a case where the latter stage has a straight line function is taken. Of course, if there is only a point function, divide more, and if there is an arc function, divide it less. If there is a clothoid function, n = 1 and no division is necessary. The number of divisions is determined so that the difference between the approximate straight line (string) and the original curve (arc) is within the required error δ. When the curvature is large, the length is short, and when the curvature is long, the number of divisions is minimized by dividing the variable length. Therefore, the larger φ′max of the absolute values of φ′0 or φ′1 is defined as a curvature, and an arc having an arc length h is assumed, and an error when this is divided into n is evaluated.

here,
φ'0 = (φ1-φ0-φu) / h
φ'1 = (φ1−φ0 + φu) / h
If φ is used, φ′max = (| φ1−φ0 | + | φu |) / h.
δ = {1-cos (φ′max * h / n / 2)} / φ′max
cosθ = 1-θ ^ 2/2! + Θ ^ 4/4! Since δ <= φ'max * (h / n) ^ 2/8
If you use-[-a] as an integer round-up symbol,
n = − [− h * sqrt (φ′max / δ / 8)]
It is.

The auxiliary variable (division auxiliary variable) of the subdivided section may be calculated as follows using dh = h / n. du, ux, ui are constants.
du = φu / n ^ 2
ux = cos (du)
uy = sin (du)
dv, vx, vy, dx, dy are initial values of variables.
dv = φ'0 / 2 * dh + du / 2
vx = cos (dv)
vy = sin (dv)
dx = dh * cos (φ0 + dv)
dy = dh * sin (φ0 + dv)

Finally, in step 52, the division assist variable is incremented to obtain sequential positions.
x = x + dx * vy / dv (7)
y = y + dx * vy / dv
w = dx * vx-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.

  The original (3) is stepped by 6 sums (differences) and 8 products, whereas it is stepped by 9 sums (differences) and 14 products (quotients). 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 in the section, switching the curvature at the end by halving the section, and switching the tangential direction at the center of the section contributes to improving accuracy.

  In this way, all the 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 corresponding to the required level can be performed.

In addition, when interpolating a point sequence determined by calculation from a theoretical formula, the tangential direction angle at each point can be calculated at the same time, and the second and fourth steps can be passed. 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 be calculated from a trigonometric function as follows, regardless of the series formula of (4).
Cn [0] = 1 when −w / 6 <= δ
Otherwise, cn [0] = sin (v) / v
When w ^ 2/840 <= δ, cn [1] = (1 + w / 10) / 6
Otherwise, cn [1] = (cos (v) −cn [0]) / w / 2
Cn [2] = (1+ (1 + w / 36) * w / 14) / 60 when −w ^ 3/498960 <= δ
Otherwise, cn [2] = (cn [0] -6 * cn [1]) / w / 4

  25 and 26 show a second embodiment of the processing apparatus. FIG. 25 shows a side view of the processing apparatus viewed from the X-axis direction, and FIG. 26 shows a rear view of the processing apparatus viewed from the Y-axis direction. Similarly to the first embodiment, the processing apparatus of this embodiment also includes an X-axis movement mechanism 9 that moves the dresser 8 in the X-axis direction in the horizontal plane, and a Y-axis movement mechanism 10 that moves in the Y-axis direction. . Then, a θ-axis rotating mechanism 20 that rotates the dresser 8 in the θ-axis direction within a horizontal plane is provided.

  Unlike the processing apparatus of the first embodiment, the processing apparatus of the second embodiment tilts the X-axis movement mechanism 9, the Y-axis movement mechanism 10, the θ-axis rotation mechanism 20, and the grindstone 7 all within the vertical plane. An inclination mechanism 61 is provided. 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 not automatically controlled. An operator manually operates the electric motor 62 to obtain a predetermined inclination angle.

  When grinding a ball screw, a dresser device is provided on the same base as the grinding device. And the grindstone 7 is inclined 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.

  The present invention is not limited to the above-described embodiment, and can be variously modified without changing the gist of the present invention. For example, the movement of the tool relative to the workpiece in the two-dimensional plane may be relative, and the X-axis movement mechanism and the Y-axis movement mechanism may move the workpiece instead of the tool. Further, the workpiece is not limited to a grindstone, and the tool is not limited to a dresser.

  The present specification is based on Japanese Patent Application No. 2006-17896 filed on Jun. 28, 2006. All this content is included here.

[0002]
It is difficult to form a combined shape. In particular, as shown in FIG. 30, a grindstone having an arc-shaped curvature center on both the outside and inside of the molding surface, with the molding surface of the grindstone serving as a boundary (arc portions R1 and R2 have a center of curvature inside the molding surface. The arc portions R3 and R4 have a center of curvature outside the molding surface).
[0007]
In addition, in the conventional dresser device, although it is possible to form a molding surface that combines an arc portion and a straight portion, the shape of the molding surface depends on the shape of the taper portion of the rotary dresser, so the degree of freedom in shape There are limitations.
[0008]
In other words, in the conventional dresser device, since the locus of movement of the dresser transferred to the grindstone is mechanically controlled, the grindstone cannot be processed into various shapes.
[0009]
Then, an object of this invention is to provide the control method and processing apparatus of the processing apparatus which can process a workpiece into various shapes.
Means for Solving the Problems [0010]
The present invention will be described below.
In order to solve the above-mentioned problem, the invention according to claim 1 is a control method of a processing apparatus for processing a workpiece by moving a tool relative to the workpiece, wherein the tool is moved to the workpiece. An X-axis moving mechanism capable of moving relative to the X-axis direction in the two-dimensional plane (P) with respect to the workpiece, and the tool perpendicular to the X-axis in the two-dimensional plane with respect to the workpiece A Y-axis moving mechanism capable of relatively moving in the axial direction, and a θ-axis capable of rotating the tool in the two-dimensional plane (P) around the tip of the tool contacting the workpiece And a processing device having a rotation mechanism, and using a clothoid curve given by a quadratic equation whose tangential direction angle is a curve length, the workpiece is made to correspond to the machining shape in the two-dimensional plane (P). Design tool trajectory curves (may include straight lines) And a trajectory / posture design step of 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 on the trajectory curve based on the normal direction angle. 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 controlling the θ-axis rotating mechanism. And a posture control step of changing the posture of the tool on the trajectory curve in the two-dimensional plane.
[0011]

[0003]
[0012]
According to a third aspect of the present invention, in the method for controlling a machining apparatus according to the first aspect, in the trajectory / posture design step, the symmetry axis extends from one end of a left-right symmetric trajectory curve about the symmetry axis. Moving the tool up, and then moving the tool to the other end of the trajectory curve, and then moving the tool from the other end of the trajectory curve to the axis of symmetry. A trajectory curve is designed.
[0013]
Invention of Claim 4 is the grindstone which rotates around the axis line arrange | positioned in the said two-dimensional plane (P) in the control method of the processing apparatus of Claim 1, The tool is a dresser, and the processing device is a dresser device that forms the outer shape of the grindstone with the dresser, and in the trajectory / posture design step, in the at least part of the section on the trajectory curve, The posture of the dresser is designed so that the center line of the dresser faces the normal direction of the locus curve.
[0014]
According to a fifth aspect of the present invention, in the method for controlling a processing apparatus according to the fourth aspect, the dresser has a flat surface and a corner portion having a predetermined width at the tip that contacts the grindstone, In the trajectory / posture design step, the dresser's posture is designed so that the centerline of the dresser is directed in the normal direction of the trajectory curve in the at least part of the section on the trajectory curve. In the other section on the locus curve, the dresser is designed so that the center line of the dresser faces other than the normal direction of the locus curve. The corner portion of the dresser is brought into contact with the grindstone.
[0015]
A sixth aspect of the present invention is the method of controlling a machining apparatus according to the fourth or fifth aspect, wherein the grindstone is a ball screw or a linear guide of a Gothic arch groove-shaped ball rolling having two arcs in cross section. The trajectory used for grinding a groove, and in the trajectory / posture design process, the trajectory that is symmetrical about the axis of symmetry in order to obtain the grindstone that can adjust the contact angle (α) of the ball screw or linear guide. The curve can be divided into left and right with the symmetry axis as a boundary, and each of the pair of divided locus curves is symmetrical

[0004]
It can be shifted toward the axis.
[0016]
The invention according to claim 7 is the method of controlling a processing apparatus according to any one of claims 4 to 6, wherein the grindstone is used for grinding a ball rolling groove of a ball screw or a linear guide, In the trajectory / posture design step, the trajectory curve that is symmetrical about the axis of symmetry can be shifted in the axial direction of the axis of symmetry in order to adjust the cutting amount of the dresser.
[0017]
The invention according to claim 8 is a processing apparatus for processing a workpiece by moving the tool relative to the workpiece, the tool being in a two-dimensional plane (P) with respect to the workpiece. An X-axis moving mechanism that can be moved relatively in the X-axis direction, and the tool is moved relative to the workpiece in the Y-axis direction perpendicular to the X-axis in the two-dimensional plane (P). A Y-axis moving mechanism capable of rotating, a θ-axis rotating mechanism capable of rotating the tool in the two-dimensional plane (P) around the tip of the tool contacting the workpiece, and a tangential angle Designing the trajectory curve of the tool (which may include straight lines) corresponding to the machining shape of the workpiece in the two-dimensional plane (P) using a clothoid curve given by a quadratic expression of the curve length And at least in some sections on the trajectory curve The normal direction angle of the trajectory curve is calculated, the posture of the tool on the trajectory curve is designed based on the normal direction angle, the X-axis moving mechanism and the Y-axis moving mechanism are controlled, and the machining Moving the tool relative to the workpiece along a trajectory curve corresponding to a machining shape in the two-dimensional plane (P) of the workpiece, and controlling the θ-axis rotation mechanism, And a control device that changes a posture of the tool on the locus curve in a two-dimensional plane (P).
[0018]
Effects of the Invention [0019]
According to the first aspect of the present invention, since the X-axis moving mechanism and the Y-axis moving mechanism move the tool along the designed locus curve, the workpiece is processed into various shapes in a two-dimensional plane. be able to. In addition, the θ-axis rotation mechanism changes the tool posture on the locus curve.

[0005]
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, the change in the posture of the tool does not affect the shape of the workpiece.
[0020]
Further, since a two-dimensional clothoid curve in which the tangential direction angle is given by a quadratic expression of the curve length is used for the trajectory curve, the normal direction angle on the trajectory curve can be easily calculated.
[0021]
According to the third aspect of the invention, the shape of the symmetrical workpiece can be stabilized.
[0022]
According to the fourth aspect of the present invention, the dresser is oriented in the normal direction with respect to the processing shape of the grindstone, so that the wear of the dresser can be reduced and the variation in the wear of the dresser can be reduced. it can.
[0023]
According to the invention described in claim 5, even if the center of curvature of the trajectory curve is closer to the dresser side than the trajectory curve and the radius of curvature of the trajectory curve is smaller than the width of the dresser, the dresser gets over the grindstone. The shape of the grindstone matched to the trajectory curve can be formed.
[0024]
According to invention of Claim 6, the grindstone which can adjust the contact angle of a ball | bowl and a ball rolling groove | channel can be shape | molded.
[0025]
According to invention of Claim 7, the cutting amount of the dresser to a grindstone can be adjusted.
[0026]
According to the eighth aspect of the present invention, the tool can be moved along the designed trajectory curve by the X-axis moving mechanism and the Y-axis moving mechanism, so that the workpiece can be variously shaped in a two-dimensional plane. Can be processed. Further, since the posture of the tool on the locus curve can be changed by the θ-axis rotation mechanism, the tool can be directed in an 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, the change in the posture of the tool does not affect the shape of the workpiece.
[0027]
The trajectory curve is given by a quadratic expression whose tangential angle is the curve length.

Claims (9)

A method for controlling a processing apparatus for processing a workpiece by moving a tool relative to the workpiece,
An X-axis movement 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. A Y-axis moving mechanism that can be moved relatively in the orthogonal Y-axis direction, and a θ-axis that can rotate the tool in the two-dimensional plane around the tip of the tool that contacts the workpiece Using a processing device having a rotation mechanism,
A trajectory for designing the tool trajectory curve (which may include a straight line) corresponding to the machining shape of the workpiece in the two-dimensional plane and designing the posture of the tool on the trajectory curve Attitude 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 rotating mechanism. In the locus / posture design process,
Designing the trajectory curve of the tool using a clothoid curve whose tangential angle is given by a quadratic expression of the curve length;
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 the posture of the tool is designed based on the normal direction angle. Control method of the device. In the locus / posture design process,
The tool is moved from one end of a left-right symmetrical trajectory curve about the symmetry axis to the symmetry axis, and then the tool is moved to the other end of the trajectory curve, and then the trajectory curve 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 tool to the axis of symmetry. 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 the outer shape of the grindstone with the dresser,
In the trajectory / posture design step, the posture of the dresser is designed so that a center line of the dresser faces a normal direction of the trajectory curve in the at least part of the section on the trajectory curve. The method for controlling a machining apparatus according to claim 2. The dresser has a flat surface having a predetermined width and a corner at the tip that contacts the grindstone,
In the locus / posture design step, in the at least part of the section on the locus curve,
Design the posture of the dresser 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,
The posture of the dresser is designed so that the center line of the dresser faces in a direction other than the normal direction of the locus curve in another section on the locus curve, and thereby the corner portion of the dresser contacts the grindstone. The method for controlling a machining apparatus according to claim 4, wherein: The grindstone is used for grinding a ball rolling groove in the shape of a Gothic arch groove having a cross section of two arcs of a ball screw or a linear guide,
In the locus / posture design process,
In order to obtain the grindstone 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 pair of divided trajectory curves can be shifted toward the symmetry axis. The grindstone is used for grinding a ball screw or a ball rolling groove of a linear guide,
In the locus / posture design process,
7. The trajectory curve that is symmetric about a symmetry axis can be shifted in the axial direction of the symmetry axis in order to adjust the cutting amount of the dresser. Control method of processing equipment. A processing device for processing a workpiece by moving a tool relative to the workpiece,
An X-axis moving mechanism capable of moving the tool relative to the workpiece in the X-axis direction within a two-dimensional plane;
A Y-axis moving mechanism capable of moving the tool relative to the workpiece in the Y-axis direction orthogonal 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 a straight line) corresponding to the machining shape of the workpiece in the two-dimensional plane is designed, the posture of the tool on the trajectory curve is designed, and the X-axis moving mechanism And controlling the Y-axis moving mechanism to move the tool relative to the workpiece along a trajectory curve (which may include a straight line) corresponding to the machining shape of the workpiece in the two-dimensional plane. 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.   The control device designs the trajectory curve of the tool using a clothoid curve whose tangential direction angle is given by a quadratic expression of a curve length, and at least a part of the trajectory curve on the trajectory curve. The machining apparatus according to claim 8, wherein a normal direction angle is calculated, and the posture of the tool is designed based on the normal direction angle.

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