JP3685776B2 - Large workpiece automatic finishing method and apparatus - Google Patents

Description

[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a surface finishing method and apparatus, and more particularly to a finishing method and apparatus for a large casting product having a complicated curved surface shape such as a large turbine blade.
[0002]
[Prior art]
Conventionally, a finishing process requiring high accuracy of a workpiece having a large and complicated curved surface shape such as a large turbine blade has been manually performed. In manual finishing work, there are many ways to finish the work surface by bringing the surface of the work into line contact with a belt-type finishing device. Finishing the work by alternately repeating grinding work and work finish status check work by gauge alignment. Yes.
[0003]
The work finish state is checked by using the reference gauge created for each reference cross section, and the work of aligning the work surface with the reference gauge for each reference cross section is repeated many times according to the progress of grinding. It has become.
In addition, it is necessary to adjust the next grinding process against the reference gauge, and quickly and accurately measure which part has how much finishing allowance, and optimal grinding conditions such as workpiece position / posture and machining force It takes considerable skill to select.
Furthermore, when a large workpiece is targeted, the physical burden on the operator is large.
For this reason, automation of finishing work is strongly demanded.
[0004]
However, in order to automate the finishing work of large workpieces, three-dimensional positioning and posture determination between a heavy workpiece and a processing tool must be performed with high accuracy. In particular, in order to automatically finish turbine blades with complex curved surfaces such as irregularities and twists, an advanced machining positioning device that has appropriate rigidity and can be positioned accurately and does not change position during machining is required. is there. Further, since the positioning mechanism and its operation data are complicated, an arithmetic device having an advanced operation control function and an advanced arithmetic function is required.
Therefore, since the production cost and the maintenance cost when introducing the automation equipment provided with such an apparatus become large, it is hardly put into practical use at present.
[0005]
[Problems to be solved by the invention]
Therefore, the problem to be solved by the present invention is a method and a method for performing high-precision automatic finishing on a workpiece having a large and complicated shape such as a turbine blade by a simpler apparatus configuration and simpler operation control. It is providing the apparatus which implements.
[0006]
[Means for Solving the Problems]
In order to solve the above problems, the automatic finishing method of the present invention measures the cross-sectional shape of the workpiece to be finished, calculates the difference between the cross-sectional shape obtained by measurement and the design value of the work finish shape, and sets it as the required machining amount. The method further comprises a workpiece position adjusting step for aligning the workpiece so that the required machining amount existing on the workpiece surface is distributed and equalized over the entire workpiece surface.
[0007]
According to the automatic finishing method of the present invention, from the information on the required machining amount obtained by aligning the design shape and the measurement shape that should be the final shape of the workpiece, in the direction in which the machining tool matches the final shape surface of the workpiece. Since the operation of the processing tool is controlled, the control algorithm relating to the workpiece position and orientation and the processing tool position adjustment is simple, and the change depending on the situation is reduced, and the processing amount and the control amount calculation load can be reduced.
In addition, since the position and orientation of the workpiece with respect to the processing tool can be adjusted so that the processing amount is evenly distributed, the number of times of grinding processing is reduced and the processing efficiency is improved.
[0008]
In the workpiece position adjusting step, first and second feature points are set on the contour of the design shape, and first corresponding feature points corresponding to the first feature point of the design shape are set on the measured contour of the workpiece cross-sectional shape. And determining a second corresponding feature point separated from the first corresponding feature point by a distance between the first feature point and the second feature point on the contour of the measurement cross-sectional shape, and determining the first feature point as the first corresponding feature point. Are placed so that the straight line connecting the first corresponding feature point and the second corresponding feature point overlaps the straight line connecting the first feature point and the second feature point, and the design shape is moved in a direction perpendicular to the straight line. Thus, the required machining amount can be equalized by disposing the deviation between the design shape and the measured cross-sectional shape, that is, the position where the surplus of the measured cross-sectional shape is dispersed and equalized over the entire circumference.
[0009]
When equalization is not enough, move the design shape in the direction perpendicular to the straight line as above and move the design shape in the direction perpendicular to the straight line after moving the position of the first corresponding feature point along the contour of the measurement cross-sectional shape. It is possible to evaluate the surplus dispersion state at the position to be converted, repeat the evaluation of the surplus dispersion state by moving the first corresponding feature point, and find the position where the surplus is most averaged. it can.
The average of the surplus can be obtained by a high-level calculation such as the least square mean value of the deviation over the entire circumference of the contour, but the surplus is the most at the point where the difference between the maximum value and the minimum value is minimum. Even if the processing is simplified by assuming that the positions are averaged, there is no problem in finishing.
[0010]
When calculating the amount of surplus, it is preferable to measure in the direction normal to the design shape contour. This is because when the grinding tool is pressed perpendicularly to the workpiece surface for processing, the calculated required processing amount matches the processing direction of the grinding tool. However, when the design shape is determined as a parallel plane with an appropriate interval, the calculation is simplified if the workpiece cross-sectional shape is measured in the plane and the amount of surplus is calculated in the direction perpendicular to the design shape contour. .
By using the procedure of the present invention, the required machining amount can be equalized quickly and always in the same procedure using simple logic.
[0011]
In addition, the finishing tool has a relief mechanism that can escape in a predetermined direction and generate a pressing force corresponding to the amount of relief, so that the original position when the machining tool does not escape is on the surface of the finished shape of the workpiece. It is preferable to perform finishing so as to be positioned.
If the finishing tool is equipped with a relief mechanism so that the processing tool is fixed and the position and orientation of the workpiece surface are adjusted, for example, the surface position of the final shape of the workpiece is set at the position before the machining tool escapes. Since it is sufficient to operate so as to match, it is not necessary to form different data again each time the grinding process is repeated, and the operation amount data of the positioning device is simplified.
[0012]
Also, if the required amount of machining is large, the pressing force will increase. If the required amount of processing is zero, the pressing force will be zero according to the required amount of processing. Therefore, even if there is a large or small difference in the equalized required machining amount, it can be absorbed, and even if there is a part that matches the design shape before it is finished, that part will not be ground, so it will be finished in the correct shape be able to.
Also, even when performing multiple finishes that differ from rough grinding to final finish grinding, once the processing positioning operation amount is calculated for the workpiece, by relatively simple operation amount correction for each grinding tool, These finishing processes can be performed sequentially, and automation of these finishing processes is also easy.
[0013]
In order to carry out the finishing method, the automatic finishing apparatus of the present invention includes a processing positioning device, a grinding device, a workpiece shape measuring device, a data storage device, and a control device. Among these, the processing positioning device grips the workpiece at the tip and adjusts the position and posture of the workpiece in accordance with instructions from the control device. In addition, the grinding device includes a finishing tool at the tip for grinding the surface by hitting the surface of the workpiece. The finishing tool can be moved in a predetermined direction, and the pressing force of the finishing tool can be adjusted according to the amount of movement. The workpiece shape measuring device measures the outer shape of the workpiece, and the data storage device stores the final finished shape of the workpiece. Further, the control device compares the outer shape of the workpiece and the final finished shape, searches for a position where the deviation is distributed over the entire workpiece surface and equalized, and instructs the machining positioning device to adjust the position and posture of the workpiece.
[0014]
The machining positioning device can adjust the position and orientation of the workpiece so that the working surface of the finishing tool hits from the normal direction of the workpiece surface whenever the three orthogonal axes and the three rotation axes can be driven. However, in the apparatus of the present invention, since it is premised that the workpiece surface is brought into line contact with the finishing tool, it is not necessary to rotate the workpiece axis during machining. It is possible to have five degrees of freedom of the axis and the two rotation axes. If the number of operating axes is reduced by reducing the degree of freedom of the device, the rigidity of the device is improved, so that the positioning accuracy of each axis is improved, and the device manufacturing cost and the maintenance cost can be reduced to make an economical device. .
[0015]
The relief mechanism of the grinding apparatus can be constituted by a uniaxial linear motion mechanism equipped with a portion that supports the finishing tool. The single-axis linear motion mechanism moves the finishing tool in a direction that changes the distance to the workpiece surface. Further, the finishing tool may be provided with a force sensor for measuring the pressing force so that the feedback control of the movement amount can be performed.
The finishing tool may be a grinding belt, supported by a plurality of rollers, and rotated by a belt rotation motor.
In addition, a plurality of grinding devices can be provided so that a grinding device for applying a workpiece can be selected by the work positioning device, so that any finishing state can be achieved, and the finishing state can be improved sequentially from rough finishing to final finishing. You may do it.
[0016]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, the finishing apparatus for large workpieces of the present invention will be described in detail with reference to the drawings based on one embodiment.
FIG. 1 is a configuration diagram of the automatic finishing apparatus of this embodiment.
The automatic finishing device 1 of the present embodiment includes a machining positioning device 2, a belt-type finishing tool 31, a force-controlled grinding device 3 having a pressing force control mechanism, a workpiece shape measuring device 4, a data storage device 5, and controls these. The control device 6 is provided.
[0017]
The processing positioning device 2 grips the workpiece 7 with the gripping member 21 at the tip and presses it against the finishing tool 31, and includes a translation mechanism having three degrees of freedom of the X axis, the Y axis, and the Z axis, and a vertical Z axis in the figure. It has two rotation axes, a θ rotation axis around and an α rotation axis around the X axis parallel to the paper surface. Therefore, if the workpiece 7 is set with careful attention to the axial direction while being sandwiched in the longitudinal direction, the finishing tool 31 can be brought into substantially vertical contact with the surface at an arbitrary surface position.
The θ rotation axis is used to align the surface inclination with the finished tool surface in accordance with the curved surface shape of the workpiece.
[0018]
The force-controlled grinding device 3 includes a belt-type finishing tool 31, a roller 32 that stretches the grinding belt of the finishing tool, a motor 33 that rotates the belt, and a force sensor 34 that measures the pressing force applied to the finishing tool 31. These are equipped with a uniaxial linear motion mechanism 35 that moves them in a uniaxial direction.
The number of finish grindings and the grinding thickness at the time of grinding are determined according to the deviation between the measured shape and the design shape, that is, the surplus amount of the workpiece, the workpiece material, the type of tool, the usage status of the tool, and the like.
[0019]
The finishing tool 31 includes a force sensor 34 and a feedback control mechanism that adjusts the driving amount by taking in the detection output of the force sensor. FIG. 2 is a block diagram illustrating this feedback control mechanism.
When there is a portion Δ that requires machining on the surface of the workpiece 7 on which the tool 31 acts, the uniaxial linear motion mechanism 35 moves the machining device backward by an amount that is not obstructed by the necessary machining portion Δ and cannot escape. The digging amount is determined based on the positional deviation amount Δ between the tool position and the final target position at this time, and a pressing force corresponding to this is calculated to generate a pressing force command value. The single-axis linear motion mechanism is configured so that the pressing force actually generated by the tool 31 is detected by the force sensor 34 and compared with the pressing force command value so as to generate an appropriate pressing force based on the force deviation between the two. A drive signal for correcting the position of 35 is generated, and the uniaxial linear motion mechanism 35 is driven to dig a predetermined amount under a predetermined pressing force.
When the finishing process is repeatedly performed and finally the target position is reached and the required machining amount becomes zero, the pressing force command value also becomes zero, so that the workpiece is not cut beyond the target position.
[0020]
As the workpiece shape measuring device 4, various types of outer shape measuring devices can be used, but in this embodiment, a measuring device using a laser displacement meter is used.
The laser displacement meter is fixed to the beam, and the cross-sectional shape of the workpiece is measured while the workpiece gripped by the machining positioning device 2 is moved below the laser displacement meter.
The data storage device 5 particularly stores the design shape of the workpiece. Also, parameter values used for determining the processing conditions may be stored here.
[0021]
FIG. 3 is a flowchart showing the processing procedure of automatic finishing in the present embodiment.
First, the shape of the workpiece 7 attached to the machining positioning device 2 of the automatic finishing device 1 is measured by the workpiece shape measuring device 4 (S11), and the design shape data of the workpiece stored in the data storage device 5 is read out. Then, the final shape of the workpiece 7 in a state in which the workpiece 7 is fixed to the gripping member 21 of the processing positioning device 2 is determined by aligning the measured shape data with each other (S12).
[0022]
FIG. 4 is a conceptual diagram for explaining the concept of alignment between the measurement shape and the design shape, FIG. 5 is a procedure diagram for explaining the alignment procedure, and FIG. 6 is a flowchart of the alignment procedure.
The workpiece 7 processed in the present embodiment is, for example, a turbine nozzle. The turbine nozzle has a plurality of vertical cross-sectional shapes stored at appropriate intervals in the longitudinal direction in the data storage device 5 as design cross-sectional shapes in the product.
The workpiece 7 is attached to the gripping member 21 so that the longitudinal direction of the workpiece 7 is the X-axis direction. And the cross-sectional shape of a workpiece | work is measured in the location corresponded to the position of each reference | standard cross section D1-Dn which determined the design cross section, and cross-sectional shape before a process is acquired.
[0023]
Among the measured cross sections, an appropriate reference cross section D is selected (S21), and the measurement shape and the design shape are aligned on the cross section (S22).
The positioning of the design shape F and the measurement shape M is performed using feature points on the outline of the cross-sectional shape, as will be described with reference to FIG.
First, two feature points P on the contour of the design cross-sectional shape F are extracted and used. As an example of the feature points, here, in consideration of the characteristics of the contour shape of the finished object, the concave inflection point is the first feature point P1, and the end point is the second feature point P2 (FIG. 5 ( a)).
[0024]
Next, in the measurement cross-sectional shape M, an appropriate point corresponding to the first feature point is selected as the first candidate point Q1, and the contour is separated by the same distance as the distance L between the first feature point P1 and the second feature point P2. The second candidate point Q2 is taken at the upper position (FIG. 5B).
The first feature point P1 and the second feature point P2 are aligned with the first candidate point Q1 and the second candidate point Q2, respectively, and the design sectional shape F is superimposed on the measured sectional shape M (FIG. 5C).
[0025]
The design cross-sectional shape F is shifted in the direction perpendicular to the straight line connecting the candidate points Q1 and Q2 (FIG. 5D) to quantitatively determine the distribution of surplus space between the design cross-sectional shape F and the measured cross-sectional shape M. Evaluate and ensure that the surplus is averaged over the entire contour.
Further, the distribution state of surplus can be evaluated by a well-known statistical method such as a mean square value over the entire contour and a difference between the minimum value and the maximum value.
[0026]
Further, the first candidate point Q1 is moved by an appropriate amount along the contour of the measurement cross-sectional shape M, the second candidate point Q2 is determined by the above method (FIG. 5 (e)), and the feature point is superimposed on the candidate point. The design cross-sectional shape F is shifted by an appropriate amount in a direction perpendicular to the straight line connecting the candidate points so that the surplus amount is equalized, and the surplus amount distribution state is quantitatively evaluated.
While moving little by little in this manner, the design cross-sectional shape F is arranged by searching the position where the surplus amount is most evenly distributed within the measured cross-sectional shape M (FIG. 5 (f)) (S23). At this time, the design sectional shape F must be arranged so as to be included in the measured sectional shape M.
[0027]
Next, the surplus distribution in another reference cross section when the design cross-sectional shape F is arranged at the above position is calculated, and the surplus distribution state of the entire workpiece is evaluated.
Furthermore, the reference section D is changed to another one, the same procedure is repeated, and the surplus amount distribution state of the entire workpiece when the design cross-sectional shape F is arranged at the position where the surplus amount is equalized in the reference section. The position where the surplus amount is equalized is determined as the position of the final design cross-sectional shape F (S25). At this time, the design cross-sectional shape F must be arranged so as to be included in the measurement cross-sectional shape M over the entire workpiece.
[0028]
The contour of the design cross-sectional shape F in the measured cross-sectional shape M determined in this way becomes the finished product outer shape, and the calculated surplus becomes the necessary processing amount in the finish grinding (S13). The required machining amount at an intermediate position not included in each reference cross section can be obtained by interpolation from the necessary machining amounts in each reference cross section.
Since the finishing tool 31 is arranged so that the rotation axis of the finishing tool 31 is parallel to the machining surface, the surplus thickness Δ is in a direction perpendicular to the contour of the design sectional shape F in the reference section as shown in FIG. It is preferable to evaluate. The required machining amount can be expressed by a vector having a direction of a perpendicular line set on the contour of the design cross-sectional shape F and having a distance to the measurement cross-sectional shape M as a length.
[0029]
When determining the position of the design cross-sectional shape in the initially selected reference cross-section D, the surplus amount distribution in other reference cross-sections is evaluated at the same time, and the position where the surplus distribution of the entire workpiece is most equalized is optimal. You may make it be a position. In this case, although the amount of calculation may increase, optimization is performed not for one reference cross section but for the entire workpiece, so that an arrangement can be made such that the surplus distribution of the entire workpiece is more even.
Also, instead of repeating the same calculation for each reference cross section, the vicinity of the design cross section shape position obtained in one reference cross section is perturbed to search for the position where the surplus distribution of the entire workpiece is most even. May be. In this method, the amount of calculation is reduced, and a relatively appropriate position can be quickly determined.
[0030]
Based on the calculated required machining amount, positioning operation data of the machining positioning device 2 at each machining position is calculated (S14).
The force-control grinding device 3 includes a mechanism 35 that escapes in a direction opposite to the direction in which the processing tool 31 is pressed, and is further controlled by the pressing force control device so that the processing pressing force corresponds to the escape amount. Moreover, the measurement shape of the workpiece | work in the state hold | gripped by the process positioning apparatus and the final finishing shape in a measurement shape are given by the said procedure.
Therefore, the workpiece gripped by the machining positioning device 2 is made to face the machining surface of the machining tool 31 of the force-controlled grinding device 3 in which the perpendicular line in the contour of the design cross-sectional shape set in the workpiece is fixed and added. The position and posture of the work 7 are adjusted so that the tool 31 and the final finished shape surface come into contact with each other.
[0031]
For example, for each processing position, the inclination of the perpendicular is the inclination α of the rotation axis of the gripping member 21, and the coordinates in the X, Y, and Z directions are determined so that the contour of the design cross-sectional shape F contacts the processing tool 31.
When finishing using a belt-type grinding apparatus using a belt having a width, the working surface of the finishing tool 31 and the work 7 are in line contact with each other. Therefore, when the finished surface has a curved surface in the longitudinal direction. It is necessary to adjust the orientation of the gripped work 7 so that the surface of the work 7 is parallel to the working surface of the processing tool 31 so that there is no step on the surface.
[0032]
FIG. 8 is a diagram for explaining an adjustment amount calculation method when the θ-axis is used.
The direction of the surface at the point P1t in the reference cross section D of the design cross-sectional shape M is the point P2t at which the plane S including the perpendicular n standing at the point P1t and perpendicular to the reference cross-section intersects the design cross-sectional shape in the adjacent reference cross section. The inclination θ of the straight line P1tP2t connecting the points P1t can be set. If the inclination θ of the straight line is processed as an operation amount of the rotation axis θ around the Z axis, no step is generated.
In this manner, the workpiece positioning operation can be performed with five degrees of freedom of the three orthogonal axes of XYZ, the rotation axis α axis around the X axis, and the rotation axis θ axis around the Z axis.
[0033]
Next, data such as workpiece material, tool type, usage status, etc. are read from the storage device, and based on the previously calculated required machining amount, the pressing force command value of the force-controlled grinding device 3 at each machining position, finishing Processing conditions such as the number of processing repetitions are calculated (S15).
In accordance with the position / orientation command value of the machining positioning device 2 determined in this way and the machining conditions of the force-controlled grinding device 3, the workpiece 7 is rotated once around the axis while being applied to the machining tool 31. Next, the work 7 is shifted in the longitudinal direction by a step width smaller than the width of the work tool 31 so that the work tool 31 hits a new processed portion of the work 7 and finished in the same way. In this way, the finishing process is performed over the entire circumference of the workpiece 7 by repeating the grinding process while shifting by a predetermined step size.
When the force control grinding device 3 is configured so that the pressing force is zero when the required processing amount is zero, the pressing force is applied even if the grinding tool 31 hits a portion where there is no surplus during finishing. Because there is no, it is not dug more than the design cross-sectional shape.
[0034]
Further, the finishing process over the entire circumference is repeated by the number of times calculated previously (S16).
After machining, the external shape of the workpiece 7 is measured again using the workpiece shape measuring device 4 (S17), the surplus amount is calculated (S18), and the surplus amount is within the required machining accuracy. Confirm (S19).
When the amount of surplus is not within the predetermined range, the processing conditions are calculated again for the new surplus state, and the finish is repeated until the shape of the work 7 becomes the final finish shape to finish the work.
The apparatus of the present embodiment can also be applied when automating finishing operations of other types of large-sized members such as turbine blades and propellers.
[0035]
Note that a mechanism of the rotational motion θ around the Z axis may be mounted on the grinding apparatus 3. By reducing the number of operation axes of the processing positioning device 2 to four, the rigidity can be further improved and the processing accuracy can be improved.
Further, in the embodiment, the processing positioning device and the force control type grinding device are provided correspondingly one by one. For example, as shown in FIG. 9, a plurality of processing tools each equipped with different processing tools from rough finishing to final finishing are mounted. These grinding finishing apparatuses may be installed side by side, and the machining positioning apparatus may be moved to appropriately select the finishing degree for machining. Further, as shown in FIG. 10, a plurality of grinding devices may be arranged so as to surround the processing positioning device so that the processing positioning device can rotate so that the workpiece can be applied to different grinding devices.
In the apparatus configured as described above, since the relative positional relationship is common between the machining positioning device and each grinding device, each axis movement amount of the machining positioning device is related to the amount of movement with respect to one grinding device. Since it suffices to make corrections, it is very easy to calculate the amount of motion.
[0036]
【The invention's effect】
As described above, by using the automatic finishing method or the automatic finishing apparatus of the present invention, it is possible to automate the finishing process of a large casting product having a complicated curved surface shape such as a large turbine blade.
[Brief description of the drawings]
FIG. 1 is a configuration diagram of an automatic finishing apparatus according to an embodiment of the present invention.
FIG. 2 is a block diagram for explaining a feedback control mechanism in the force-controlled grinding apparatus of the present embodiment.
FIG. 3 is a flowchart showing a processing procedure of automatic finishing in the present embodiment.
FIG. 4 is a conceptual diagram for explaining alignment between a measurement shape and a design shape in the present embodiment.
FIG. 5 is a flowchart for explaining a positioning procedure in the present embodiment.
FIG. 6 is a flowchart showing the alignment procedure in this embodiment.
FIG. 7 is a diagram illustrating a method for calculating a required machining amount in the present embodiment.
FIG. 8 is a diagram illustrating a θ-axis motion amount calculation method in the present embodiment.
FIG. 9 is a layout diagram in the case where a plurality of grinding apparatuses are arranged on a straight line in the present embodiment.
FIG. 10 is a layout view in the case where a plurality of grinding apparatuses are arranged on the circumference in the present embodiment.
[Explanation of symbols]
DESCRIPTION OF SYMBOLS 1 Automatic finishing device 2 Processing positioning device 21 Gripping member 3 Force control type grinding device 31 Finishing tool 32 Roller 33 Motor 34 Force sensor 35 Uniaxial linear motion mechanism 4 Work shape measuring device 5 Data storage device 6 Control device 7 Workpiece

Claims (2)

  Measure the cross-sectional shape of the workpiece to be finished, calculate the deviation when the measured cross-sectional shape and the design value of the workpiece finish shape are overlapped, and set it as the required machining amount. An automatic finishing method for a large workpiece, comprising a workpiece position adjusting step for aligning the workpiece so as to be distributed and equalized, wherein the calculation of the required machining amount and the workpiece in the workpiece position adjusting step are performed. The first and second feature points are set at appropriate positions on the contour of the design shape, and the first feature of the design shape on the contour of the measured cross-sectional shape of the workpiece is set as the procedure for dispersing the entire surface. The first corresponding feature point is determined at an appropriate position corresponding to the point, and the second corresponding feature point is separated from the first corresponding feature point by the distance between the first feature point and the second feature point on the outline of the measurement cross-sectional shape. To detect the first feature point Overlaying the corresponding feature point, the straight line connecting the first corresponding feature point and the second corresponding feature point is arranged so as to overlap the straight line connecting the first feature point and the second feature point. By moving the design shape to evaluate the dispersion state of the surplus, and further moving the first corresponding feature point and repeating the evaluation of the surplus dispersion state, the deviation between the design shape and the cross-sectional shape of the measurement is all around. An automatic finishing method characterized in that it is performed by selecting and arranging positions that are distributed and more equalized.   The finishing tool is allowed to escape in a predetermined one-axis direction, and a larger pressing force is generated as the escape amount increases, and the position when the processing tool does not escape is located on the surface of the finished shape of the workpiece. The automatic finishing method according to claim 1, wherein the automatic finishing method is operated.

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