JP2009083295A - Scribing device and method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a scribing device capable of forming a scribed line conforming to a programmed curved line on a surface of a workpiece. <P>SOLUTION: This scribing device includes a cutter wheel 11 for carving a scribed line on a surface of workpiece 17, a holder 31 for holding the cutter wheel 11 to allow its rotation around a central line of rotation, a traveling mechanism for moving the cutter wheel 11 for the workpiece 17 relatively so that the cutter wheel 11 rolls on the surface of the workpiece 17, a rotary mechanism for letting the cutter wheel 11 and the holder 31 turn around a vertical line L2 crossing the surface of workpiece 17 orthogonally, and a controller for controlling an angle of turn of the cutter wheel 11 around the vertical line L2. A contact point where the cutter wheel 11 and the workpiece 17 come into contact mutually is positioned on the vertical line L2. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention relates to a scribing apparatus and a scribing method for scribing a scribe line on a thin plate-shaped workpiece made of a brittle material such as glass or semiconductor.

  When a thin plate-shaped workpiece made of a brittle material is cut, a scribe line as a mark is engraved on the surface of the workpiece in advance. When the work is bent along the scribe line, the crack on the front surface reaches the back surface, and the work is cut.

  The scribing method for scribing the scribe line on the workpiece is either by pressing a disk-shaped cutter wheel against the surface of the workpiece and rolling the cutter wheel on the workpiece surface while applying pressure, or by further cutting the cutter wheel while rolling the cutter wheel. A method of vibrating is known. When the cutter wheel is vibrated, deep vertical cracks can be formed on the surface of the workpiece, thereby enabling full cut.

  Whether the cutter wheel is oriented in the direction of travel of the cutter wheel has a significant effect on cutting quality. If it is assumed that the cutter wheel is inclined with respect to the traveling direction of the cutter wheel, an excessive force is applied to the cutter wheel during scribing, and the cutting quality of the workpiece is deteriorated.

In order to make the inclination of the cutter wheel coincide with the traveling direction of the cutter wheel, as shown in FIG. 13, a scribe head incorporating a turning mechanism (swing mechanism) 4 for turning the cutter wheel 1 in a horizontal plane is known. (For example, refer to Patent Document 1). A holder 2 that holds the cutter wheel 1 is supported by a bearing 3 so as to be rotatable around a vertical axis 2a. The holder 2 holds the cutter wheel 1 so that it can roll on the surface of the workpiece 5. When forming a slack line on the surface of the work 5, the cutter wheel 1 can freely rotate around the vertical axis 2a of the holder 2. For this reason, the inclination of the cutter wheel 1 passively follows the traveling direction of the cutter wheel 1 as if it were a caster of a chair.
JP 2007-118355 A

  In a scribing device using a conventional swing mechanism, when the cutter wheel 1 is moved along a programmed curve such as an arc, the swing angle of the cutter wheel 1 is arbitrarily changed. The position of the wheel 1 cannot be controlled. For this reason, the position of the rotating shaft 2a of the holder 2 is moved along a programmed curve.

  However, as shown in FIG. 14, even if the rotation axis 2 a of the holder 2 is moved along the programmed curve 6, the cutter wheel 1 passes through the inside of the curve. That is, a scribe line 7 deviated from the programmed curve 6 is formed on the surface of the workpiece.

  SUMMARY An advantage of some aspects of the invention is that it provides a scribing apparatus and a scrubbing method capable of forming a programmed scribe line on the surface of a workpiece.

  The present invention will be described below.

  In order to solve the above-mentioned problem, the invention according to claim 1 is characterized in that the cutter wheel that engraves a scribe line on the surface of a workpiece and the cutter wheel so that the cutter wheel can rotate around its rotation center line. A holder for holding, a moving mechanism for moving the cutter wheel relative to the workpiece so that the cutter wheel can roll on the surface of the workpiece, and the cutter wheel orthogonal to the surface of the workpiece. A scribing mechanism comprising: a rotating mechanism for turning around a vertical line; and a control device for controlling a turning angle of the cutter wheel around the vertical line, wherein the contact point between the cutter wheel and the workpiece is located on the vertical line. Device.

  The invention according to claim 2 is the scribing device according to claim 1, wherein the control device is configured so that the cutter wheel faces a tangential direction of a scribe line formed on a surface of the workpiece. The turning angle around the vertical line is controlled.

  According to a third aspect of the present invention, in the scribing device according to the second aspect, the control device designs a locus using a clothoid curve having a tangential direction angle given by a quadratic expression having a curve length, and the locus. Calculating the tangential direction angle, operating the moving mechanism based on the trajectory, controlling the position of the cutter wheel on the surface of the workpiece, operating the rotating mechanism based on the tangential direction angle, The turning angle of the cutter wheel around the vertical line is controlled.

  The invention according to claim 4 is a scribing method in which a scribe line is engraved on the workpiece while the cutter wheel is brought into contact with the surface of the workpiece and the cutter wheel is rolled on the surface of the workpiece. In this scribing method, the cutter wheel is relatively moved along the surface of the workpiece while rotating the cutter wheel around a vertical line passing through a contact point between the cutter wheel and the workpiece while being orthogonal to each other.

  According to the first aspect of the present invention, even if the cutter wheel is turned around the vertical line, the position of the contact point between the cutter wheel and the workpiece does not change. Accordingly, a programmed scribe line can be formed on the surface of the workpiece.

  According to the invention described in claim 2, since the cutter wheel faces the tangential direction of the scribe line, the resistance applied to the cutter wheel can be minimized. Therefore, it is possible to form a scribe line with little damage such as chipping in the work.

  According to the third aspect of the present invention, since the locus is designed using the clothoid curve whose tangential direction angle is given by the quadratic expression of the curve length, the tangential direction of the locus can be easily calculated.

  According to the fourth aspect of the present invention, even if the cutter wheel is turned around a vertical line, the position of the contact point between the cutter wheel and the workpiece does not change. Accordingly, a programmed scribe line can be formed on the surface of the workpiece.

  A scribing apparatus according to an embodiment of the present invention will be described below with reference to the accompanying drawings. FIG. 1 shows a vertical sectional view of a scribing device.

  The scribe device engraves a scribe line on a thin plate-like workpiece 17 made of a brittle material such as glass or semiconductor. The scribe line is a propagation of a vertical crack, and is used as a mark when the workpiece 17 is divided. The workpiece 17 is sucked and held on the table 16 of the scribe device. The cutter wheel 11 rolls on the surface of the workpiece 17 while being pressed against the surface of the workpiece 17. As the cutter wheel 11 rolls and moves on the surface of the workpiece 17, a scribe line is engraved on the surface of the workpiece 17. The cutter wheel 11 is held by the holder 31 so as to be able to rotate around its rotation axis.

  FIG. 2 shows a detailed view of the cutter wheel 11. The cutter wheel 11 is formed in a disk shape and has a sharp ridge line 11a on the outer peripheral portion thereof. The ridge line 11 a of the cutter wheel 11 becomes a blade that bites into the workpiece 17. A through hole 11 b into which the axle 31 a of the holder 31 is inserted is opened at the center of the cutter wheel 11. The cutter wheel 11 rotates around the axle 31 a of the holder 31. The rotation center line L1 of the cutter wheel 11 is parallel to the surface of the workpiece 17 and faces the horizontal direction.

  In this embodiment, in order to form a deep vertical crack in the workpiece 17, the cutter wheel 11 is vibrated in the vertical direction. As shown in FIG. 1, the holder 31 is attached to the scribe head 12. The scribe head 12 vibrates the cutter wheel 11 in the vertical direction. The cylindrical housing 18 of the scribe head 12 is provided with a piezoelectric element (piezo actuator) that generates distortion when an external voltage is applied, for example, as the vibrator 19. An electric wire 20 is connected to the piezoelectric element. When the voltage applied to the piezoelectric element is changed at a predetermined frequency, the piezoelectric element expands and contracts periodically. Vibration is generated by the periodic expansion and contraction of the piezoelectric element. A magnetic material such as a magnetostrictive element that causes distortion in the magnetic material when a magnetic field is applied may be used.

  A receiving portion 21 is provided in close contact with the upper side of the vibrator 19, and a vibration transmission shaft 22 is provided in close contact with the lower end portion. The vibration of the vibrator 19 is transmitted to the vibration transmission shaft 22. The disc spring 27 causes the vibration of the vibration transmission shaft 22 to follow the vibration of the vibrator 19. The vibration of the vibration transmission shaft 22 is guided to the slide bearing 29. The receiving portion 21 is accommodated in the housing 18 and receives a reaction of vibration.

  The receiving portion 21 is rotatably supported by a rotary bearing 23 provided in the housing. The vibration transmission shaft 22 is rotatably supported by a rotary bearing 26 provided in the housing. The rotation center lines of the receiving portion 21 and the vibration transmission shaft 22 are perpendicular to the workpiece 17. For this reason, the cutter wheel 11 and the holder 31 can turn around the vertical line L2.

  The rotation mechanism 30 turns the cutter wheel 11 and the holder 31 around the vertical line L2. A gear is processed at the upper end of the receiving portion 21. The output shaft of the θ-axis servomotor 28 is attached with a pulley with a gear processed. A belt 25 is stretched between the gear of the receiving portion 21 and the output shaft of the θ-axis servomotor 28. By rotating the output shaft of the θ-axis servomotor 28, the receiving portion 21 can be rotated, and consequently the cutter wheel 11 can be rotated. The driver of the θ-axis servo motor 28 controls the rotation angle of the θ-axis servo motor 28 together with a computer such as a host computer that generates an angle command. In addition to the winding transmission mechanism such as the belt 25, various power transmission mechanisms such as a gear mechanism may be used.

  The moving mechanism 13 moves the scribe head 12 in the X and / or Y direction within a two-dimensional plane on the surface of the workpiece 17. The moving mechanism 13 includes an X-axis moving mechanism that moves the scribe head in the X-axis direction and a Y-axis moving mechanism that moves the scribe head in the Y-axis direction. The X-axis and Y-axis moving mechanism is composed of an X-axis and Y-axis servomotor, and a motion conversion means such as a ball screw mechanism that converts the rotational motion of the X-axis and Y-axis servomotor into the linear motion of the scribe head 12. Is done. The moving mechanism 13 may move the table 16 instead of moving the scribe head 12.

  The scribe head 12 is guided by the linear guide 15 so as to be slidable in the vertical direction with respect to the base 14. After the scribe head 12 is lowered until the cutter wheel 11 comes into contact with the upper surface of the workpiece 17, the moving mechanism 13 moves the scribe head 12 along the surface of the workpiece 17. Roll and move on a two-dimensional plane. A scribe line is cut on the surface of the workpiece 17 by the rolling motion of the cutter wheel 11. Note that the scribe head 12 may be pressed against the surface of the workpiece 17 by a pressurizing means such as an air cylinder.

  FIG. 3 shows the positional relationship between the vertical line L <b> 2 and the cutter wheel 11. The contact point P between the cutter wheel 11 and the workpiece 17 is on the vertical line L2 so that the position of the contact point P between the cutter wheel 11 and the workpiece 17 does not change even when the cutter wheel 11 turns in a horizontal plane. The vertical line L2 also intersects with the rotation center line L1 of the cutter wheel 11.

  FIG. 4 shows a conceptual diagram of the cutter wheel 11 moving on the designed trajectory 34. The control device designs the trajectory 34 of the scribe line to be formed on the surface of the workpiece 17 using a clothoid curve whose tangential direction angle is given by a quadratic expression having a curve length. Then, the trajectory 34 is designed, and the tangential direction angle 35 of the trajectory 34 is calculated. Next, the control device operates the moving mechanism 13 based on the designed trajectory 34, and controls the position of the cutter wheel 11 so that the designed scribe line trajectory 34 is formed on the surface of the workpiece 17. At the same time, the rotation mechanism 30 is operated based on the tangential direction angle 35 to control the posture of the cutter wheel 11, that is, the turning angle around the vertical line so that the cutter wheel 11 faces the tangential direction. By controlling in this way, the inclination of the cutter wheel 11 follows the traveling direction of the cutter wheel 11, so that an excessive force is not applied from the cutter wheel 11 to the workpiece 17, and a scribe line with few cracks and chips is formed. Can do.

  The configuration of the control device will be described in detail below. FIG. 5 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 incorporated (on the left side of the dotted line in the figure) and the X, Y, θ axes of the scribe device by reading the motion table 51. It comprises a driver 57 (on the right side of the dotted line in the figure) incorporating a motion operator 54 for operating the servo motor.

  The computer 56 creates a motion table 51 in which displacement values of the respective operation axes are described by taking the time axis in the row direction and the X, Y, and θ axes of the scribe device in the column direction. Based on the motion table 51, the driver 57 controls each axis of the scribe device. Signal commands from the motion table 51 and the motion editor 53 are transmitted between the computer 56 and the driver 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 attitude of the cutter wheel 11 as a function of time is called motion. As shown in FIG. 6, the motion table 51 describes the time axis in the row direction and each operation axis (servo motor) in the column direction as an absolute value or an incremental value of the displacement of each axis. 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. 7, it does not necessarily start from zero.

  The motion table 51 is, for example, CSV (Comma Separated Value) data. 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 cutter wheel 11 rolls on the surface of the workpiece 17, the contact point between the tip of the cutter wheel 11 and the workpiece 17 (hereinafter referred to as a tool point) is a continuous locus drawn in a plane (may include a straight line). You can think of it moving over time. The position of the tool point is represented by coordinates (x, y), and the posture of the cutter wheel 11 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 of the cutter wheel 11 and to design the posture of the cutter wheel 11.

  The operator inputs the XY coordinates of a plurality of point sequences to the computer 56 in correspondence with the scribe lines formed on the surface of the workpiece 17. Input means such as a keyboard and a mouse are used for input. When the operator inputs a point sequence, the computer designs a locus 60 obtained by interpolating the point sequence. In the present embodiment, a clothoid curve is used in designing the locus 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.

  As shown in FIG. 4, the computer 56 designs the trajectory 34 and also the posture of the cutter wheel 11. In this embodiment, in designing the posture, the posture of the cutter wheel 11 is designed so that the traveling direction of the cutter wheel 11 faces the tangential direction of the locus 34 in all sections on the locus 34. In the clothoid curve, since the tangential direction angle is given, the tangential direction angle can be easily calculated. When the clothoid curve is used, the posture E of the cutter wheel 11 is given as a function of the curve length s as well as the position P of the cutter wheel 11 as shown in FIG.

<Fitting of motion curve (S2)>
As shown in FIG. 7, the second stage of motion control is to determine the speed / acceleration of the tool point moving on the designed trajectory. How the tool point moves as a function of time on the trajectory is determined by determining the speed and acceleration of the tool point. The operator inputs the speed of the cutter wheel 11. The computer 56 determines the speed and acceleration of the tool point so that the cutter wheel 11 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 cutter wheel 11 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 scribe device, a solution is prepared separately for each scribe device.

<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.

  A motion editor 53 shown in FIG. 5 edits a plurality of motion tables 51. For example, the usage of the created motion tables 51 is set in order. 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 driver 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 cutter wheel 11 along the locus 34. At the same time, the θ-axis servo motor is controlled to change the posture of the cutter wheel 11 in the horizontal plane.

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

<Communication (S1)>
There are several methods for sending data of the motion table 51 from the computer 56 to the driver 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 driver 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 data shown in FIG. 6 is received as the x-axis data, the next column data is received as the y-axis data, and the next data as the θ-axis data is further received. Can receive column data.

<Synchronization, sequence operation (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 scribe 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 servo 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 cutter wheel 11 along the locus in the horizontal plane, and the θ-axis rotating mechanism 30 is controlled to change the locus in the horizontal plane P. It is possible to change the posture of the cutter wheel 11 on 34.

  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. 9 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. 10 shows a flowchart of a program executed by an interpolation method using a clothoid curve. The control method according to the present embodiment interpolates a given point sequence 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 (S1).

Next, a tangential angle φ _i at each point is obtained (S2). The tangential direction angle φ indicates the direction of the tangent at each of the above points, and is represented by the angle φ formed by the tangent to the reference line. The tangential angle φ obtained in the second step is provisional except for the end points.

  Next, interval parameters in all intervals are obtained (S3). 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 S4, 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 (S41), and the curvature difference evaluation value of the maximum point is allowed. It is determined whether or not it is within the range, and if the curvature difference evaluation value is within this allowable range, S4 is terminated (S42), otherwise, the tangential direction angle of the maximum point is corrected (S43). Then, the section auxiliary variables of the two sections before and after the maximum point are recalculated (S44), and the curvature difference evaluation values at the three points of the maximum point and the front and back points are recalculated (S41), and the process returns to S42 and is repeated.

  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 section 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. 10, 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 stroke, 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. 11, three consecutive points are selected, and tangential direction angles φA, φB, and φC at the respective points of the arc passing through these three points (A, B, and C in FIG. 12) 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 (3)
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.

Next, the process proceeds to the third process, and section parameters for each section are obtained. 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..nmax
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 S3 in FIG. 10 is referred to as a “rotation reverse solution”. The above “rotation” means a clothoid curve. The convolution reverse solution is also used in the next step S44.

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.

Furthermore, proceed to the fourth process. In step S41 constituting step S4, 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 S41, the maximum point is marked. In the next step S42, the absolute value of this value at the maximum point is compared with a 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 step S42, the process proceeds to the next step S43, and the tangential direction angle at the maximum point is corrected. 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 S44, the same solution (rotating reverse solution) as in step S3 is executed only twice, and interval parameters in the interval before and after the maximum point are obtained.

  Further, returning to step S41, the same equation as the process of step S41 is executed only three times to calculate the curvature difference evaluation value between the maximum point and the front and rear points, and then step S42 is performed again. In this way, step S4 including the steps from step S41 to step S44 is repeated until the evaluation value falls within the allowable range in the determination in step S43.

  Next, proceeding to step S51, from the starting point, the tangential direction angle (x0, y0, φ0), and the interval auxiliary variables (h, φv, φu), the step auxiliary variables (du, dv, dx, dy, vx, vy, 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 can be minimized by dividing the variable length. However, for the sake of simplicity of calculation, “equal arc length division” is adopted. 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 S52, the division assist variable is incremented to obtain sequential positions.
x = x + dx * vy / dv
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. (7)

  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 strokes can be passed. Further, when the curvature continuity is not required, the fourth stroke 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 stroke. 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

  Note that 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 scribing device does not have to vibrate the cutter wheel when rolling the cutter wheel on the surface of the workpiece. The scribe line formed on the surface of the workpiece by the cutter wheel is not limited to an arc having a constant curvature, but can be formed in various shapes such as a curve with a changing curvature and a combination of a straight line and an arc.

1 is a vertical sectional view of a scribing apparatus according to an embodiment of the present invention. Detailed view of cutter wheel ((a) shows a front view and (b) shows a side view) Side view showing the positional relationship between the vertical line and the cutter wheel Conceptual diagram of the cutter wheel moving on the designed trajectory Block diagram of control device Diagram showing a tabular motion table Flowchart executed by Motion Designer 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 Side view showing a conventional scribing device (including a partial vertical sectional view) Diagram showing deviation between programmed curve and scribe line actually formed (conventional example)

Explanation of symbols

DESCRIPTION OF SYMBOLS 11 ... Cutter wheel 13 ... Movement mechanism 17 ... Work piece 28 ... (theta) axis servomotor (rotation mechanism)
29 ... Slide bearing (rotary / reciprocating bearing)
DESCRIPTION OF SYMBOLS 30 ... Rotation mechanism 31 ... Holder 34 ... Trajectory 35 ... Tangent direction angle 55 ... Control apparatus L1 ... Rotation center line L2 ... Vertical line P ... Contact point of cutter wheel and workpiece | work

Claims (4)

A cutter wheel that engraves scribe lines on the surface of the workpiece,
A holder for holding the cutter wheel so that the cutter wheel can rotate around its rotation center line;
A moving mechanism for moving the cutter wheel relative to the workpiece so that the cutter wheel can roll on the surface of the workpiece;
A rotation mechanism for turning the cutter wheel around a vertical line perpendicular to the surface of the workpiece;
A control device for controlling a turning angle of the cutter wheel around the vertical line,
A scribing device in which a contact point between the cutter wheel and the workpiece is located on the vertical line.   The control device controls a turning angle of the cutter wheel around the vertical line so that the cutter wheel faces a tangential direction of a scribe line formed on the surface of the workpiece. The scribing device described in 1. The control device designs a trajectory using a clothoid curve in which a tangential direction angle is given by a quadratic expression of a curve length, calculates a tangential direction angle of the trajectory,
The moving mechanism is operated based on the trajectory, the position of the cutter wheel on the surface of the workpiece is controlled, the rotation mechanism is operated based on the tangential direction angle, and the vertical line of the cutter wheel is controlled. The scribing device according to claim 2, wherein the turning angle of the rotation is controlled. In a scribing method in which a cutter wheel is brought into contact with the surface of the workpiece and the cutter wheel is rolled on the surface of the workpiece, while scribing a scribe line on the workpiece,
A scribe that moves the cutter wheel relatively along the surface of the workpiece while rotating the cutter wheel around a vertical line that passes through a contact point between the cutter wheel and the workpiece and is orthogonal to the surface of the workpiece. Method.

Images