CN106584206A - Normal correction method for hole making of automatic drilling and riveting machine - Google Patents
Normal correction method for hole making of automatic drilling and riveting machine Download PDFInfo
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- CN106584206A CN106584206A CN201611025556.1A CN201611025556A CN106584206A CN 106584206 A CN106584206 A CN 106584206A CN 201611025556 A CN201611025556 A CN 201611025556A CN 106584206 A CN106584206 A CN 106584206A
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- laser displacement
- drift angle
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23Q—DETAILS, COMPONENTS, OR ACCESSORIES FOR MACHINE TOOLS, e.g. ARRANGEMENTS FOR COPYING OR CONTROLLING; MACHINE TOOLS IN GENERAL CHARACTERISED BY THE CONSTRUCTION OF PARTICULAR DETAILS OR COMPONENTS; COMBINATIONS OR ASSOCIATIONS OF METAL-WORKING MACHINES, NOT DIRECTED TO A PARTICULAR RESULT
- B23Q15/00—Automatic control or regulation of feed movement, cutting velocity or position of tool or work
- B23Q15/20—Automatic control or regulation of feed movement, cutting velocity or position of tool or work before or after the tool acts upon the workpiece
- B23Q15/22—Control or regulation of position of tool or workpiece
- B23Q15/26—Control or regulation of position of tool or workpiece of angular position
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
- B21J—FORGING; HAMMERING; PRESSING METAL; RIVETING; FORGE FURNACES
- B21J15/00—Riveting
- B21J15/10—Riveting machines
- B21J15/28—Control devices specially adapted to riveting machines not restricted to one of the preceding subgroups
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- Mechanical Engineering (AREA)
- Machine Tool Sensing Apparatuses (AREA)
Abstract
The invention discloses a normal correction method for hole making of an automatic drilling and riveting machine. According to the method, based on reading numbers of four laser displacement sensors, a three-point method or a four-point method is firstly adopted for calculating the direction deviation between the normal direction of a to-be-machined hole position on the surface of an aircraft panel and the axis of a tool, then the target posture of the drilling and riveting machine is calculated based on the deviation and the current posture of the drilling and riveting machine; and hole making normal correction of the drilling and riveting machine is achieved through motion of the drilling and riveting machine. By means of the method, the hole making normal deviation of the automatic drilling and riveting machine can be corrected to be within 0.1 degree, and the calculation process is simplified while the hole making normal correction precision is guaranteed.
Description
Technical field
The invention belongs to riveting field is bored in aircraft digital assembly automation, it is related to a kind of drilling normal direction of automatic drill riveter and repaiies
Correction method.
Background technology
In aircraft assembling, riveting remains main method of attachment.Traditional hand riveting's labor condition is poor, production effect
Rate is low, and riveting quality depends critically upon the experience and technology of workman, it is difficult to meet the requirement of aircraft assembling.The mechanization of riveting and
Automatization, is the inexorable trend of riveting technology development.In terms of automatic Drilling/Riveting, external research and application to correlation technique is
More ripe, such as the equipment supplier such as EI, GEMCOR, BROETJE have developed respective automatic drill riveter, and successful Application respectively
In the numeric terminal of Multiple Type aircraft;And the aircratfsman and scientific research institutions of the country also began to independently grind in recent years
From dynamic boring and riveting machine, to improve the quality and efficiency of boring riveting.
Automatic drill riveter during drilling, due to aircraft target ship assembling manufacturing error and automatic drill riveter position error
Impact, certain deviation can be produced at the hole position to be processed of aircraft target ship surface between normal direction and tool axis direction.Normal direction is inclined
Difference is excessive, will directly affect drilling machining accuracy and aircraft assembling quality, while reducing cutting-tool's used life, it is seen that boring
It is very important to the detection and amendment of Norma l deviation during riveting.Currently have scholar to propose various methods to correct drilling
When Norma l deviation, such as document " parallel institution normal direction adjustment algorithm based on 3-PRS in aircraft assembling, Zou Jihua, Zhou Wanyong,
Han Xianguo. China Mechanical Engineering, 2011,22 (5), 557-560 " and document " aviation drilling robot ending vertical degree intelligence tune
Section method, public cyclopentadienyl shake, Yuan Peijiang, Wang Tianmiao, etc. BJ University of Aeronautics & Astronautics's journal, 2012,38 (10), 1400-1404 ".This
A little methods can be effectively reduced Norma l deviation during drilling, but calculate complex, realize that process is difficult.
The content of the invention
In order to meet the requirement during aircraft target ship drilling to vertical precision, the present invention proposes a kind of automatic drill riveter
Drilling normal direction modification method, the method not only can guarantee that drilling machining accuracy but also can simplify calculating process.
The method using capital equipment be four laser displacement sensors on boring and riveting machine presser feet, boring and riveting machine work
At presser feet end face center, four laser displacement sensors are evenly distributed on the axle centered on presser feet axis to tool establishment of coordinate system
On the face of cylinder, and the line of two neighboring laser displacement sensor is parallel with tool coordinates system X-axis or Y-axis respectively.
A kind of drilling normal direction modification method of automatic drill riveter, specifically includes following steps:
(1) boring and riveting machine is moved at hole position to be processed;
(2) read the reading of four laser displacement sensors;
(3) reading according to laser displacement sensor, calculates the drift angle α that automatic drill riveter is rotated around tool coordinates system X-axis
With the drift angle β rotated around tool coordinates system Y-axis;
(4) the drilling Norma l deviation θ angles of automatic drill riveter according to drift angle α and drift angle β, are calculated;
(5) whether θ angles are judged less than 0.1 °, if it is not, execution step (6), if so, terminates amendment;
(6) current drilling axial direction according to automatic drill riveter, drift angle α and drift angle β, calculate the target system of automatic drill riveter
Hole axle to, and by automatic drill riveter motion adjustment drilling axis direction, then branch to step (2).
In step (3), the calculation procedure of drift angle α and drift angle β is:
(3-1) whether effectively to judge the reading of four laser displacement sensors, if the reading of four laser displacement sensors
Number is effective, execution step (3-2), if the reading of three laser displacement sensors is effectively, execution step (3-3), if few
Effective, the execution step (3-4) in the reading of three laser displacement sensors;
(3-2) valid reading according to four laser displacement sensors, is calculated drift angle α and drift angle β using four-point method;
(3-3) valid reading according to three laser displacement sensors, is calculated drift angle α and drift angle β using line-of-sight course;
(3-4) report an error process.
In step (3-1), when the hot spot of laser displacement sensor beats the surface near hole hole position to be processed, without beating
To in machined hole or outside workpiece, then it is assumed that the reading of the laser displacement sensor is effective, otherwise it is assumed that the laser displacement is passed
The reading of sensor is invalid.
In step (3-2), the calculation procedure of described four-point method is:
(3-2-1) direction coefficient with reference to four laser displacement sensors calculate respectively its arrive surface of the work it is vertical away from
From;
(3-2-2) laser displacement sensor of calculating instrument coordinate system X-axis side two to surface of the work vertical dimension
One meansigma methodss, and two laser displacement sensors of calculating instrument coordinate system X-axis opposite side are to the second of surface of the work vertical dimension
Meansigma methodss;
(3-2-3) according to the first meansigma methodss, the distance meter of the symmetrical hot spot of the second meansigma methodss and tool coordinates system X-axis both sides
Calculation obtains drift angle α;
(3-2-4) laser displacement sensor of calculating instrument coordinate system Y-axis side two to surface of the work vertical dimension
Three meansigma methodss, and two laser displacement sensors of Y-axis opposite side are calculated to the 4th meansigma methodss of surface of the work vertical dimension;
(3-2-5) according to the 3rd meansigma methodss, the distance meter of the symmetrical hot spot of the 4th meansigma methodss and tool coordinates system Y-axis both sides
Calculation obtains drift angle β.
In step (3-3), the calculation procedure of described line-of-sight course is:
(3-3-1) direction coefficient with reference to three laser displacement sensors calculate respectively its arrive surface of the work it is vertical away from
From;
(3-3-2) according to monosymmetric two laser displacement sensors of tool coordinates system X-axis to the vertical of surface of the work
The distance of distance and the two laser displacement sensor hot spots calculates drift angle α;
(3-3-3) according to monosymmetric two laser displacement sensors of tool coordinates system Y-axis to the vertical of surface of the work
The distance of distance and the two laser displacement sensor hot spots calculates drift angle β.
The caliberating device that the acquisition of the direction coefficient of four laser displacement sensors is used is:
The scaling board is provided with installing hole and fabrication hole;
The mounting hole site is in scaling board center;
The fabrication hole is the hole of multigroup arrangement that is square, and per group includes four holes, and each hole position is in square summit,
The square center for being centrally located at scaling board, every group of fabrication hole constitutes the different square length of side, center superposition and the length of side is parallel.
Preferably, described fabrication hole is three groups, three square length of sides of fabrication hole composition are different, center superposition and
The length of side is parallel.
The method that four laser displacement sensor direction coefficients are obtained using the caliberating device specifically includes following steps:
A, scaling board is installed on main shaft by plug, main shaft will be locked after scaling board adjustment level;
B, main shaft are moved along direction of feed, and the position for adjusting four laser displacement sensors is respectively aligned to its four hot spots
Four fabrication holes of scaling board one of which, fix four laser displacement sensors and to record four fabrication holes constituted square
The length of side;
C, main shaft continue to move along direction of feed, make scaling board be adjacent to presser feet end face, and four laser displacement sensors are read
Number zero setting;
D, main shaft move to first position along direction of feed, record the reading l of four laser displacement sensors respectively11、
l21、l31And l41;
E, main shaft continue to move to the second position, record the reading l of four laser displacement sensors respectively12、l22、l32With
l42;
F, according to reading l11、l21、l31、l41、l12、l22、l32And l42, calculate the direction of four laser displacement sensors
Coefficient:
Wherein, L is the distance between first position and second position.
In step (4), the computational methods at described automatic Drilling/Riveting mechanism hole Norma l deviation θ angles are:
In step (6), the calculation procedure of described automatic drill riveter targeted attitude is:
(6-1) read the current drilling axis direction N of automatic zhuan rivetersc:
Nc=[Ncx Ncy Ncz]T
(6-2) attitude misalignment matrix Δ R is calculated according to drift angle α and drift angle β:
(6-3) the target drilling axis direction N of Zi Dong zhuan riveters is calculated according to following formula Jit:
Nt=Δ R × Nc。
The advantage of the drilling normal direction modification method of automatic drill riveter of the present invention:
(1) the drilling Norma l deviation of automatic drill riveter can be adapted within 0.1 °;
(2) while drilling normal direction amendment precision is ensured, simplify calculating process;
(3) direction coefficient of laser displacement sensor in the calculating of Norma l deviation, is employed, sensor and knife has been taken into account
The installation of tool diameter parallel and the situation of angled installation;
(4) in the calculating of Norma l deviation, two methods of line-of-sight course and four-point method are employed, has taken into account three and four and swashed
The effective situation of Optical displacement sensor reading.
Description of the drawings
Fig. 1 is the distribution schematic diagram of laser displacement sensor in the present invention on boring and riveting machine;
Fig. 2 is the schematic flow sheet of drilling modification method of the present invention;
Fig. 3 is that automatic drill riveter calculates schematic diagram around tool coordinates system X-axis rotation drift angle α;
Fig. 4 is that automatic drill riveter calculates schematic diagram around tool coordinates system Y-axis rotation drift angle β.
Specific embodiment
In order to more specifically describe the present invention, below in conjunction with the accompanying drawings and specific embodiment is to technical scheme
It is described in detail.
As shown in figure 1, the inventive method using capital equipment be four laser on automatic drill riveter presser feet
Displacement transducer, respectively laser displacement sensor S1, laser displacement sensor S2, laser displacement sensor S3 and laser displacement
Sensor S4, automatic drill riveter tool coordinates system OXYZSet up at presser feet end face center, four laser displacement sensors uniformly divide
Cloth is on the face of cylinder of axle centered on presser feet axis, and the line of two neighboring laser displacement sensor is sat with instrument respectively
Mark system X-axis or Y-axis are parallel.
As shown in Fig. 2 the drilling normal direction modification method of automatic drill riveter of the present invention comprises the steps:
Step 1, boring and riveting machine are moved at hole position to be processed.
Step 2, reads the reading l of four laser displacement sensors1For 18.383mm, l2For 17.652mm, l3For
17.408mm and l4For 17.687mm.
Step 3, according to the reading of laser displacement sensor, calculate automatic drill riveter around tool coordinates system X-axis rotate it is inclined
The angle α and drift angle β around the rotation of tool coordinates system Y-axis;
In this step, when the hot spot of laser displacement sensor beats the surface near hole hole position to be processed, without getting to
In machined hole or outside workpiece, then it is assumed that the reading of the laser displacement sensor is effective, otherwise it is assumed that the laser displacement is sensed
The reading of device is invalid.
If the reading of four laser displacement sensors is effective, drift angle α and drift angle β is calculated using four-point method, specifically
Method is as follows:
As shown in figure 3, first, laser displacement sensor is calculated respectively with reference to the direction coefficient of four laser displacement sensors
To the vertical dimension l ' of surface of the work1、l′2、l′3With l '4;Specific formula for calculation is as follows:
l′1=l1×c1=18.383 × 0.8636=15.876mm
l′2=l2×c2=17.652 × 0.8637=15.246mm
l′3=l3×c3=17.408 × 0.8665=15.084mm
l′4=l4×c4=17.687 × 0.8576=15.168mm
Wherein, c1、c2、c3And c4The respectively direction coefficient of four laser displacement sensors;
The caliberating device that the acquisition of the direction coefficient of four laser displacement sensors is used is:
The scaling board is provided with installing hole and fabrication hole;
The mounting hole site is in scaling board center;
The fabrication hole is the hole of three groups of arrangements that are square, and per group includes four holes, and each hole position is in square summit,
The square center for being centrally located at scaling board, every group of fabrication hole constitutes the different square length of side, center superposition and the length of side is parallel.
The method that four laser displacement sensor direction coefficients are obtained using the caliberating device specifically includes following steps:
A, scaling board is installed on main shaft by plug, main shaft will be locked after scaling board adjustment level;
B, main shaft are moved along direction of feed, and the position for adjusting four laser displacement sensors is respectively aligned to its four hot spots
Four fabrication holes of scaling board one of which, fix four laser displacement sensors and to record four fabrication holes constituted square
The length of side;
C, main shaft continue to move along direction of feed, make scaling board be adjacent to presser feet end face, and four laser displacement sensors are read
Number zero setting;
D, main shaft move to first position along direction of feed, record the reading l of four laser displacement sensors respectively11For
20.661mm, l21For 22.192mm, l31For 21.537mm and l41For 21.330mm;
E, main shaft continue to move to the second position, record the reading l of four laser displacement sensors respectively12For
43.819mm, l22For 45.348mm, l32For 44.618mm and l42For 44.651mm;
F, according to reading l11、l21、l31、l41、l12、l22、l32And l42, calculate the direction of four laser displacement sensors
Coefficient:
Wherein, L is the distance between first position and second position, the present embodiment L=20mm.
Then, laser displacement sensor S1 and laser displacement sensor S2 is calculated to the meansigma methodss of surface of the work vertical dimension
l′12, and laser displacement sensor S3 and laser displacement sensor S4 to the meansigma methodss l ' of surface of the work vertical dimension34, specifically
Computing formula is as follows:
Next, calculating drift angle α, specific formula for calculation is as follows:
Wherein, dyFor boring and riveting machine presser feet end face it is parallel with surface of the work when, laser displacement sensor S1 and laser displacement are passed
Hot spot distance or the hot spot distance between laser displacement sensor S2 and laser displacement sensor S3 between sensor S4, this enforcement
In example, dy=53mm;
As shown in figure 4, calculating laser displacement sensor S1 and laser displacement sensor S4 to surface of the work vertical dimension
Meansigma methodss l '14, and laser displacement sensor S2 and laser displacement sensor S3 is to the meansigma methodss of surface of the work vertical dimension
l′23, specific formula for calculation is as follows:
Finally, calculate drift angle β as follows:
Wherein, dxFor boring and riveting machine presser feet end face it is parallel with surface of the work when, laser displacement sensor S1 and laser displacement are passed
Hot spot distance or the hot spot distance between laser displacement sensor S3 and laser displacement sensor S4 between sensor S2, this enforcement
In example, dx=53mm.
If the reading of three laser displacement sensors is effective, drift angle α and drift angle β is calculated using line-of-sight course, specifically
Method is as follows:
Assume the effective laser displacement sensor of three readings be laser displacement sensor S1, laser displacement sensor S2 and
Laser displacement sensor S3, first, calculates laser displacement sensor respectively to the vertical dimension l ' of surface of the work1、l′2With l '3,
Specific formula for calculation is as follows:
l′1=l1×c1=15.876mm
l2'=l2×c2=15.246mm
l′3=l3×c3=15.084mm
Then, drift angle α is calculated, specific formula for calculation is as follows:
Wherein, dyFor boring and riveting machine presser feet end face it is parallel with surface of the work when, laser displacement sensor S2 and laser displacement are passed
Hot spot distance between sensor S3, in the present embodiment, dy=53mm;
Finally, drift angle β is calculated, specific formula for calculation is as follows:
Wherein, dxFor boring and riveting machine presser feet end face it is parallel with surface of the work when, laser displacement sensor S1 and laser displacement are passed
Hot spot distance between sensor S2, in the present embodiment, dx=53mm.
Step 4, according to drift angle α and drift angle β, calculates the drilling Norma l deviation θ angles of automatic drill riveter, by taking four-point method as an example:
Step 5, judges that amendment, whether less than 0.1 °, is if so, terminated, if it is not, execution step 6 in θ angles.
Step 6, the current pose, drift angle α and drift angle β according to automatic drill riveter calculate the target appearance of automatic drill riveter
State, and the direction of the motion adjustment drilling axis by automatic drill riveter, then branch to step 2.
The calculation procedure of automatic drill riveter targeted attitude is:
First, read the current drilling axis direction N of automatic zhuan rivetersc:
Nc=[0.003245 0.052664 0.998607]T
Then, attitude misalignment matrix Δ R is calculated according to drift angle α and drift angle β:
Finally, the target drilling axis direction N of Zi Dong zhuan riveters is calculated according to following formula Jit:
Nt=Δ R × Nc=[- 0.003121 0.060854 0.998140]T。
Drilling is carried out by above method, calculating process can either be simplified and be ensure that machining accuracy again.
Above-described specific embodiment has been described in detail to technical scheme and beneficial effect, Ying Li
Solution is to the foregoing is only presently most preferred embodiment of the invention, is not limited to the present invention, all principle models in the present invention
Interior done any modification, supplement and equivalent etc. are enclosed, be should be included within the scope of the present invention.
Claims (9)
1. a kind of drilling normal direction modification method of automatic drill riveter, specifically includes following steps:
(1) boring and riveting machine is moved at hole position to be processed;
(2) read the reading of four laser displacement sensors;
(3) reading according to laser displacement sensor, calculate the drift angle α that rotates around tool coordinates system X-axis of automatic drill riveter and around
The drift angle β of tool coordinates system Y-axis rotation;
(4) the drilling Norma l deviation θ angles of automatic drill riveter according to drift angle α and drift angle β, are calculated;
(5) whether θ angles are judged less than 0.1 °, if it is not, execution step (6), if so, terminates amendment;
(6) current drilling axial direction according to automatic drill riveter, drift angle α and drift angle β, calculate the target drilling axle of automatic drill riveter
To, and the direction of the motion adjustment drilling axis by automatic drill riveter, then branch to step (2).
2. the drilling normal direction modification method of automatic drill riveter according to claim 1, it is characterised in that:In step (3), institute
The drift angle α for stating and the calculation procedure of drift angle β are:
(3-1) whether effectively to judge the reading of four laser displacement sensors, if the reading of four laser displacement sensors is equal
Effectively, execution step (3-2), if the reading of three laser displacement sensors is effectively, execution step (3-3), if fewer than three
The reading of individual laser displacement sensor is effective, execution step (3-4);
(3-2) valid reading according to four laser displacement sensors, is calculated drift angle α and drift angle β using four-point method;
(3-3) valid reading according to three laser displacement sensors, is calculated drift angle α and drift angle β using line-of-sight course;
(3-4) report an error process.
3. the drilling normal direction modification method of automatic drill riveter according to claim 2, it is characterised in that:In step (3-2),
The calculation procedure of described four-point method is:
(3-2-1) direction coefficient with reference to four laser displacement sensors calculates its vertical dimension for arriving surface of the work respectively;
(3-2-2) laser displacement sensor of calculating instrument coordinate system X-axis side two is to the first flat of surface of the work vertical dimension
Average, and two laser displacement sensors of calculating instrument coordinate system X-axis opposite side are to the second average of surface of the work vertical dimension
Value;
(3-2-3) calculated according to the distance of the first meansigma methodss, the symmetrical hot spot of the second meansigma methodss and tool coordinates system X-axis both sides
To drift angle α;
(3-2-4) laser displacement sensor of calculating instrument coordinate system Y-axis side two is to the 3rd flat of surface of the work vertical dimension
Average, and two laser displacement sensors of Y-axis opposite side are calculated to the 4th meansigma methodss of surface of the work vertical dimension;
(3-2-5) calculated according to the distance of the 3rd meansigma methodss, the symmetrical hot spot of the 4th meansigma methodss and tool coordinates system Y-axis both sides
To drift angle β.
4. the drilling normal direction modification method of automatic drill riveter according to claim 2, it is characterised in that:In step (3-3),
The calculation procedure of described line-of-sight course is:
(3-3-1) direction coefficient with reference to three laser displacement sensors calculates its vertical dimension for arriving surface of the work respectively;
(3-3-2) vertical dimension according to monosymmetric two laser displacement sensors of tool coordinates system X-axis to surface of the work
And the distance of the two laser displacement sensor hot spots calculates drift angle α;
(3-3-3) vertical dimension according to monosymmetric two laser displacement sensors of tool coordinates system Y-axis to surface of the work
And the distance of the two laser displacement sensor hot spots calculates drift angle β.
5. the drilling normal direction modification method of automatic drill riveter according to claim 1, it is characterised in that:In step (4), institute
The computational methods at the automatic Drilling/Riveting mechanism hole Norma l deviation θ angles stated are:
6. the drilling normal direction modification method of automatic drill riveter according to claim 1, it is characterised in that:In step (6), institute
The calculation procedure of the automatic drill riveter targeted attitude stated is:
(6-1) read the current drilling axis direction N of automatic zhuan rivetersc:
Nc=[Ncx Ncy Ncz]T
(6-2) attitude misalignment matrix Δ R is calculated according to drift angle α and drift angle β:
(6-3) the target drilling axis direction N of Zi Dong zhuan riveters is calculated according to following formula Jit:
Nt=Δ R × Nc。
7. according to claim 3 or 4 automatic drill riveter drilling normal direction modification method, it is characterised in that:Four laser positions
The caliberating device that the acquisition of the direction coefficient of displacement sensor is adopted for:
The scaling board is provided with installing hole and fabrication hole;
The mounting hole site is in scaling board center;
The fabrication hole is the hole of multigroup arrangement that is square, and per group includes four holes, and each hole position is in square summit, square
The center of scaling board is centrally located at, every group of fabrication hole constitutes the different square length of side, center superposition and the length of side is parallel.
8. the drilling normal direction modification method of automatic drill riveter according to claim 7, it is characterised in that:Described fabrication hole is
Three groups, three square length of sides of fabrication hole composition are different, the center superposition and length of side is parallel.
9. the drilling normal direction modification method of automatic drill riveter according to claim 8, it is characterised in that:Using the caliberating device
The method for obtaining four laser displacement sensor direction coefficients specifically includes following steps:
A, scaling board is installed on main shaft by plug, main shaft will be locked after scaling board adjustment level;
B, main shaft are moved along direction of feed, and the position for adjusting four laser displacement sensors makes its four hot spots be respectively aligned to demarcate
Four fabrication holes of plate one of which, fix four laser displacement sensors and record the constituted square side of four fabrication holes
It is long;
C, main shaft continue to move along direction of feed, make scaling board be adjacent to presser feet end face, and four laser displacement sensor readings are put
Zero;
D, main shaft move to first position along direction of feed, record the reading l of four laser displacement sensors respectively11、l21、l31
And l41;
E, main shaft continue to move to the second position, record the reading l of four laser displacement sensors respectively12、l22、l32And l42;
F, according to reading l11、l21、l31、l41、l12、l22、l32And l42, calculate the direction coefficient of four laser displacement sensors:
Wherein, L is the distance between first position and second position.
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