CN109446470B - Non-contact detection-based die wear prediction method for spiral bevel gear machining - Google Patents

Non-contact detection-based die wear prediction method for spiral bevel gear machining Download PDF

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CN109446470B
CN109446470B CN201811367351.0A CN201811367351A CN109446470B CN 109446470 B CN109446470 B CN 109446470B CN 201811367351 A CN201811367351 A CN 201811367351A CN 109446470 B CN109446470 B CN 109446470B
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displacement sensor
laser displacement
bevel gear
die
spiral bevel
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CN109446470A (en
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姚斌
马晓帆
卢杰
蔡志钦
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Xiamen University
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
    • B21K—MAKING FORGED OR PRESSED METAL PRODUCTS, e.g. HORSE-SHOES, RIVETS, BOLTS OR WHEELS
    • B21K1/00—Making machine elements
    • B21K1/28—Making machine elements wheels; discs
    • B21K1/30—Making machine elements wheels; discs with gear-teeth
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
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    • G06F18/2411—Classification techniques relating to the classification model, e.g. parametric or non-parametric approaches based on the proximity to a decision surface, e.g. support vector machines

Abstract

A non-contact detection-based die wear prediction method for spiral bevel gear machining relates to spiral bevel gear machining. Establishing a mathematical model of introducing an installation inclination angle error of the laser displacement sensor under any installation pose; correcting the installation inclination angle of the laser displacement sensor, completing a calibration experiment on detection items of the arc-tooth bevel gear, and establishing an object plane inclination angle error compensation model; establishing a relation model of the abrasion loss of the forging die and the number of forging pieces by using an improved support vector machine algorithm; and predicting the abrasion degree of the die for processing the spiral bevel gear by using an algorithm of a self-iterative support vector machine. The method is characterized in that the relationship between the abrasion degree of a forging die and the number of forging pieces is established by precisely measuring the detection items of the spiral bevel gear and using a self-iterative support vector machine prediction algorithm, so that the abrasion of the die for processing the spiral bevel gear is detected and predicted.

Description

Non-contact detection-based die wear prediction method for spiral bevel gear machining
Technical Field
The invention relates to spiral bevel gear machining, in particular to a mold wear prediction method for spiral bevel gear machining based on non-contact detection.
Background
In the forging process, the precision forging forming is a novel process with less or no cutting. The gear finish forging is a gear manufacturing technology which directly obtains complete gear teeth through precision forging and can be used without or with only little finish machining on the tooth surface. The finish forged gear has the advantages of good mechanical properties, high material utilization rate, less environmental pollution and the like, and is gradually widely adopted. However, in the forging process, when the situation that the forged piece is unqualified due to abrasion of the die occurs, the situation is not easy to be noticed in time, and a large number of unqualified workpieces are generated successively. Therefore, the abrasion degree of the forging die can be timely and accurately judged, and the method is of great importance to product control cost and quality and efficiency improvement.
There are many types of gears that can be finish forged, including circular tooth bevel gears. In order to ensure the quality of the spiral bevel gear, various parameters of the spiral bevel gear need to be detected after finish forging. The existing gear process detection comprises manual contact detection and laser detection. The traditional contact type measurement is inconvenient to operate and low in efficiency, and subjective errors of inspectors exist. The laser detection technology is widely used, has the advantages of high measurement precision, strong anti-interference capability, simple structure, flexible use and the like, and makes it possible for the laser triangulation distance measuring sensor to realize high-precision measurement of complex curved surface profile. According to the principle of laser triangulation distance measurement, the error factors measured by the laser triangulation method mainly include: 1) imaging system errors, mainly affected by lateral magnification and objective lens distortion; 2) data processing errors and system installation errors; 3) environmental factor errors such as temperature and humidity; 4) errors introduced by changes in the characteristics of the surface being measured; mainly comprises displacement value deviation errors caused by error factors such as the color, the roughness and the measured inclination angle of a measured surface. For the existing laser displacement sensor, environmental factors such as data processing errors, system installation errors, objective lens distortion rate, temperature and humidity and the like are controlled highly. Therefore, the main error factor affecting the precision of laser triangulation is the error introduced by the change of the characteristics of the measured surface.
The prior art patent search finds that the application number is CN107167078A, the name of the invention is: a multi-degree-of-freedom laser displacement sensor system and a spiral bevel gear measuring method are disclosed in the Chinese patent application. The invention provides a mechanism device for measuring a spiral bevel gear with multiple degrees of freedom, which ensures that data acquired by a sensor is complete and effective by adjusting and fixing the rotation pose of a sensor bracket. However, this method has the following problems: (1) errors caused by the characteristic change of the measured surface are not considered, and the errors comprise installation inclination angle errors and object plane inclination angle errors; (2) the device needs to be adjusted for each measurement, and the operation steps are complicated; (3) the method is only used for monitoring the quality of the current spiral bevel gear, and the wear condition of the die is not fed back by utilizing the relationship between the spiral bevel gear and the forging die.
In conclusion, the object plane with a complex detected tooth profile must measure the inclination angle error, including the installation inclination angle error and the measurement inclination angle error, so that the quality condition of the gear cannot be objectively reflected, and the production cost cannot be controlled. The wear condition of the die cannot be reflected correctly, and if the worn die is continuously used for forging and pressing the gear, a large amount of unqualified products are produced. Therefore, accurate measurement of gear parameters is of great importance for accurate reflection and prediction of the forging die wear condition.
Disclosure of Invention
The invention aims to provide a non-contact detection-based die wear prediction method for processing a spiral bevel gear, which can solve the problem of precision detection of the spiral bevel gear.
The invention comprises the following steps:
1) establishing a mathematical model of introducing an installation inclination angle error of the laser displacement sensor under any installation pose;
2) correcting the installation inclination angle of the laser displacement sensor, completing a calibration experiment on detection items of the arc-tooth bevel gear, and establishing an object plane inclination angle error compensation model;
3) establishing a relation model of the abrasion loss of the forging die and the number of forging pieces by using an improved support vector machine algorithm;
4) and predicting the abrasion degree of the die for processing the spiral bevel gear by using an algorithm of a self-iterative support vector machine.
In the step 1), the laser displacement sensor measures at any installation pose, an installation inclination angle error is necessarily introduced into a measurement result, and the installation pose of the laser displacement sensor needs to be calibrated; the calibration process can be as follows: the method comprises the following steps of installing a laser displacement sensor on a Z axis of a three-coordinate measuring instrument, converting a measured value of the laser displacement sensor from a self coordinate system to a reference coordinate system, and establishing the following three coordinate systems:
(1) a machine tool coordinate system O-XYZ of the measuring machine, wherein the coordinate system takes the 0 position of a Y-axis grating ruler of the machine tool as an original point, and the directions of 3 coordinate axes are respectively consistent with the directions of 3 guide rails of the measuring machine;
(2) measuring coordinate system o of laser displacement sensors-xsyszsThe coordinate system takes a point on the laser displacement sensor, the measured value of which is 0, as an origin, and the directions of 3 coordinate axes are respectively consistent with the directions of XYZ axes;
(3) machine coordinate system oM-xMyMzMThe coordinate system is established in the state that the measuring machine returns to 0, the point of the laser displacement sensor with the measured value of 0 is taken as the origin, and the directions of 3 coordinate axes are respectively consistent with the direction of X, Y, Z axes;
measured value of laser displacement sensor from os-xsyszsTo oM-xMyMzMHas a coordinate conversion order of os-xsyszs→oM-xMyMzMExpressed in homogeneous coordinates as:
Figure GDA0002474951350000031
in the formula (1), [ x ]SySzS]TFor laser displacement sensors at os-xsyszsMeasured value in s coordinate system, laser beam at os-xsyszsThe unit vector is (l, m, n) and the length is d (the unit vector can be directly read from a laser displacement sensor); r1 and T1 are each os-xsyszsRelative to oM-xMyMzMThe rotation matrix and the translation matrix of (a); t1 represents the value x for the raster valueM0,yM0,zM0：
Figure GDA0002474951350000032
The laser displacement sensor is positioned at o through a formula (2)s-xsyszsConversion of the measured value of (A) to (o)M-xMyMzMPerforming the following steps;
the plane equation for the calibration plane α is set to:
Ax+By+Cz+D＝0 (3)
(A, B, C) is the normal vector of plane α.
Assuming that the intersection point of the laser and the plane α is P1, the value of the laser displacement sensor is d1, and the grating reading is (x)M1,yM1,zM1) Then, combining formula (2) and formula (3) gives:
A(xM1+ld1)+B(yM1+md1)+C(zM1+nd1)+D＝0 (4)
when the laser displacement sensor is moved by Δ X along the-X direction, where Δ X is the grating variation value of the grating along the X direction, the intersection point of the laser displacement sensor and the plane α becomes P2, the laser beam is emittedThe value is d2, the grating reading is xM1-Δx,yM1,zM1And then:
A(xM1+ld2-Δx)+B(yM1+md2)+C(zM1+nd2)+D＝0 (5)
subtracting the equations (4) and (5) to obtain:
Figure GDA0002474951350000033
similarly, moving Δ Y along the-Y direction and Δ Z along the-Z direction, respectively, results in:
Figure GDA0002474951350000041
wherein, U is constant Al + Bm + Cn, and the result is obtained after simplification:
lΔdx/Δx+mΔdy/Δy+nΔdz/Δz＝0 (8)
let a1＝Δdx/Δx、b1＝Δdy/Δy、c1＝ΔdzAnd/Δ z, then:
a1l+b1m+c1n＝0 (9)
and because:
l2+m2+n2＝1 (10)
then, the values of the unit direction vectors (l, m, n) of the laser beams of the laser displacement sensor can be obtained through the formulas (8) to (10), and in the calibration process, PN is a normal vector of the measured surface and is a known value; assuming that the unit vector of incident light at any installation angle is EP ═ l, m, n, the inclination angle of the point P is:
Figure GDA0002474951350000042
the α that is obtained at this time is the installation inclination angle of the laser displacement sensor.
In the step 1), the pose of the laser displacement sensor is adjusted and corrected, and the installation inclination angle α is corrected.
In the step of2) In the above, the specific method for completing the calibration experiment of the detection item of the arc-tooth bevel gear and establishing the object plane tilt angle error compensation model may be: firstly, an inclination error calibration experiment is built according to the inclination angle of the object plane of the spiral bevel gear: installing a sine gauge on the measuring platform, and calibrating a correct inclination angle by adjusting the height of the sine gauge; on an O-XYZ coordinate system, AB is the length of the sine gauge, BC represents the height of the standard gauge block, and the inclination angle of the sine gauge
Figure GDA0002474951350000043
This can be achieved by adjusting the height of the standard gauge block, in △ ABC:
BC＝AB·sinφ (12)
the calibration experiment of the detection items of the arc-tooth bevel gear, namely the object plane inclination error calibration experiment, is completed, and the experiment specifically comprises the following steps:
(1) the object plane inclination error correction experimental device consists of a numerical control machining center, a laser displacement sensor, a laser interferometer, a sine gauge and a standard gauge block; the laser displacement sensor is arranged on a Z axis of the numerical control machining center, the sine gauge is arranged on a workbench right below the laser displacement sensor, the laser interferometer light path component is fixed on the Z axis and the workbench through a magnetic meter frame, and the Z axis can move under the control of a numerical control system;
(2) correcting the installation inclination angle of the laser displacement sensor before the start of the experiment, ensuring that a laser beam is vertically incident, adjusting the position of an interferometer light path component, ensuring that the light path does not deviate and the laser interferometer can accurately read in the process of moving along the Z axis, and building a required inclination angle error correction experiment according to the content of a spiral bevel gear detection item;
(3) when an experiment is started, a computer program of a coordinate system controls a Z-axis carrying sensor to move up and down, the numerical values of a laser displacement sensor and a laser interferometer are recorded within the effective measurement range (-10 mm) of the laser displacement sensor every time the Z-axis carrying sensor moves 0.1mm, and the difference value of the numerical values is the error value of the laser displacement sensor;
after the calibration experiment is completed, establishing an object plane inclination angle error compensation model, and fitting the measurement depth error under a certain inclination angle by using a least square method to obtain the relation between the measurement depth and the measurement error;
after the error compensation model is established, in the actual detection process of the spiral bevel gear, an interpolation method is applied to obtain a compensation result, and the quality condition of the gear is judged according to the result of each parameter after compensation.
In the step 3), after the arc-tooth bevel gear is precisely measured by using the error compensation model, establishing a relation model of the abrasion loss of the forging die and the number of forging pieces by using an improved support vector machine algorithm;
according to the above-mentioned method, using
Figure GDA0002474951350000051
Denotes the test item, in κ1,κ2,κ3.., the measured value of each test item is shown, and the number of forged gears of the die is shown by N. Assuming that the nth gear is detected, based on the above parameters, the following mapping relationship can be established:
Figure GDA0002474951350000052
is provided with
Figure GDA0002474951350000053
Setting [123.. n ] for all parameters of n gears before die forging]The number of gears forged and pressed by the corresponding grinding tool;
the experimental data are divided into training data and prediction data, and the detection data are trained by using an improved support vector machine algorithm. Different from the traditional support vector machine prediction algorithm, the improved support vector machine regression prediction algorithm introduces relaxation factors;
let niFor predicting the number of gears forged by the spiral bevel gear die to reach a certain abrasion degree, the corresponding parameter values of each detection item are as follows:
Figure GDA0002474951350000054
mifor actually forging gears with dies of the same degree of wearThe number of the detection items is as follows:
Figure GDA0002474951350000061
then:
＝|pre-rea| (16)
if not less than ξ (ξ is the relaxation factor setting), indicating that the accuracy of the sample parameter for predicting the die wear is poor, the values of pre are replaced by the values of rea, and correspondingly, miSubstitution of niRetraining the sample data; therefore, relaxation factors are introduced into the traditional support vector machine algorithm, and the accuracy of prediction is improved.
In the step 4), in the step of predicting the wear degree of the die for processing the spiral bevel gear by using the self-iterative support vector machine algorithm, the wear degree of the spiral bevel gear comprises die wear early warning and die wear repairing states which are respectively SwAnd SrAnd (4) showing. According to the gear detection item parameter prediction, when the two states are reached, the number of the gears forged by the die is NpwAnd NprRepresents; the number of the gears actually processed by the current die is NrIf N is presentr≤NpwContinuously using the die for processing; n is a radical ofpw＜Nr≤NprPreparing to replace the die, and ensuring the processing efficiency; n is a radical ofr＞NprAnd replacing the new die and repairing the old die.
Establishing a mathematical model of introducing an installation inclination error of the laser displacement sensor under any measurement pose, and correcting the installation inclination; and (3) obtaining the influence rule of the object plane inclination angle on the measurement precision by combining experimental analysis, finishing the accurate calibration of the detection item of the arc-tooth bevel gear under the influence of the factor, and establishing an error compensation model. The method is characterized in that the relationship between the abrasion degree of a forging die and the number of forging pieces is established by precisely measuring the detection items of the spiral bevel gear and using a self-iterative support vector machine prediction algorithm, so that the abrasion of the die for processing the spiral bevel gear is detected and predicted.
Drawings
FIG. 1 is a flow chart of an embodiment of the present invention.
Fig. 2 is a schematic diagram of a machine tool coordinate system of the measuring machine, a measuring coordinate system of the laser displacement sensor and a machine coordinate system.
FIG. 3 is a schematic diagram of a calibration process of the installation pose of the laser displacement sensor.
Fig. 4 is a schematic diagram for solving the installation inclination angle of the laser displacement sensor.
FIG. 5 is a schematic diagram of a spiral bevel gear test item.
FIG. 6 is a calibration curve of the tilt angle of the object plane.
Detailed Description
The following examples will further illustrate the present invention with reference to the accompanying drawings.
Referring to fig. 1 and 2, an embodiment method of the present invention includes the steps of:
the method comprises the following steps: establishing a mathematical model of introducing an installation inclination angle error of the laser displacement sensor under any installation pose;
step two: correcting the installation inclination angle of the laser displacement sensor, completing a calibration experiment on detection items of the arc-tooth bevel gear, and establishing an object plane inclination angle error compensation model;
step three: establishing a relation model of the abrasion loss of the forging die and the number of forging pieces by using an improved support vector machine algorithm;
according to the step one, under any installation pose of the laser displacement sensor, the measurement result must introduce installation inclination angle errors, so that the installation pose of the laser displacement sensor needs to be calibrated.
The calibration process is as follows: the method comprises the following steps of installing a laser displacement sensor on a Z axis of a three-coordinate measuring instrument, converting the measured value of the laser displacement sensor from a self coordinate system to a reference coordinate system, and establishing the following three coordinate systems in the process:
1) and the machine tool coordinate system of the measuring machine is O-XYZ. The coordinate system takes the position 0 of a Y-axis grating ruler of the machine tool as an original point, and the directions of 3 coordinate axes are respectively consistent with the directions of 3 guide rails of the measuring machine;
2) measuring coordinate system o of laser displacement sensors-xsyszs. The coordinate system takes a point with a measurement value of 0 on the laser displacement sensor as an origin and has 3 coordinate axesThe directions are respectively consistent with the directions of XYZ axes;
3) machine coordinate system oM-xMyMzM. The coordinate system is established in the state that the measuring machine returns to 0, the point of the laser displacement sensor with the measured value of 0 is taken as the origin, and the directions of 3 coordinate axes are respectively consistent with the directions of X, Y, Z axes.
Measured value of laser displacement sensor from os-xsyszsTo oM-xMyMzMHas a coordinate conversion order of os-xsyszs→oM-xMyMzM. Expressed in homogeneous coordinates as:
Figure GDA0002474951350000071
wherein [ x ]SySzS]TFor laser displacement sensors at os-xsyszsThe measurement in s-coordinate system, unit vector of laser beam in osxsyszs is (l, m, n), length is d (can be read directly from laser displacement sensor); r1 and T1 are each os-xsyszsRelative to oM-xMyMzMThe rotation matrix and the translation matrix of (a); t1 represents the value x for the raster valueM0,yM0,zM0。
Figure GDA0002474951350000072
The laser displacement sensor is positioned at o through the above formulas-xsyszsConversion of the measured value of (A) to (o)M-xMyMzMIn (1).
Set the plane equation of the calibration plane α to
Ax+By+Cz+D＝0 (19)
(A, B, C) is the normal vector of plane α.
The simplified process of l, m, n calibration is shown in FIG. 3, assuming that the intersection point of the laser with plane α is P1, the value of the laser is d1, and the grating reading is (x)M1,yM1,zM1) Then, combining equation (18) and equation (19) yields:
A(xM1+ld1)+B(yM1+md1)+C(zM1+nd1)+D＝0 (20)
when the laser displacement sensor is moved by Δ X along the-X direction, where Δ X is the raster variation value of the raster along the X direction, the intersection point of the laser displacement sensor and the plane α becomes P2, the laser value is d2, and the raster reading is XM1-Δx,yM1,zM1Then, then
A(xM1+ld2-Δx)+B(yM1+md2)+C(zM1+nd2)+D＝0
(21)
Subtracting the equations (20) and (21) to obtain:
Figure GDA0002474951350000081
similarly, moving Δ Y along the-Y direction and Δ Z along the-Z direction, respectively, results in:
Figure GDA0002474951350000082
wherein, U is constant Al + Bm + Cn, and the following is obtained after simplification:
lΔdx/Δx+mΔdy/Δy+nΔdz/Δz＝0
(24)
let a1＝Δdx/Δx、b1＝Δdy/Δy、c1＝ΔdzAnd/Δ z, then:
a1l+b1m+c1n＝0
(25)
and because:
l2+m2+n2＝1
(26)
then, the unit direction vector (l, m, n) of the laser beam of the laser displacement sensor can be obtained by the equations (24) to (26). As shown in fig. 4, PN is a normal vector of the measured surface and is a known value. Assuming that the unit vector of incident light at any installation angle is EP ═ l, m, n, the inclination angle of the point P is:
Figure GDA0002474951350000091
and adjusting and correcting the pose of the laser displacement sensor and correcting the installation inclination α.
According to the non-contact precision detection-based die wear prediction method for processing the spiral bevel gear, after the installation inclination angle of the laser displacement sensor is corrected, a calibration experiment of the detection item of the spiral bevel gear is completed, and an object plane inclination angle error compensation model is established.
The spiral bevel gear has a plurality of detection items, and the invention is only explained for one detection item, but is not limited to the detection item. As shown in FIG. 5, the chordal tooth thickness of the spiral bevel gear is measured at three normal sections 1a, 1b and 1c from the small end in the tooth width direction, respectively. As can be seen from the figure, the tilt error of the object plane must be introduced in the detection process.
And completing a calibration experiment on the detection item of the arc-tooth bevel gear, and establishing an object plane inclination angle error compensation model. Firstly, an inclination error calibration experiment is built according to the inclination angle of the object plane of the spiral bevel gear: installing a sine gauge on the measuring platform, and calibrating a correct inclination angle by adjusting the height of the sine gauge, as shown in fig. 4, on an O-XYZ coordinate system, AB is the length of the sine gauge, BC represents the height of a standard gauge block, and then the inclination angle of the sine gauge is determined
Figure GDA0002474951350000092
This can be achieved by adjusting the height of the standard gauge block, i.e. in △ ABC:
BC＝AB·sinφ (28)
the calibration experiment of the detection items of the arc-tooth bevel gear, namely the object plane inclination error calibration experiment, is completed, and the experiment specifically comprises the following steps:
1) the object plane inclination error correction experimental device consists of a numerical control machining center, a laser displacement sensor, a laser interferometer, a sine gauge and a standard gauge block. The laser displacement sensor is installed on the Z axis of the numerical control machining center, and the sine gauge is placed on the workbench right below the laser displacement sensor. The laser interferometer light path component is fixed on the Z axis and the workbench through a magnetic meter frame. The Z axis can be controlled by a numerical control system to move.
2) Before the experiment begins, the posture of the laser sensor needs to be accurately adjusted to ensure that the laser beam vertically enters. The position of the interferometer optics assembly is then adjusted to ensure that the optics path does not drift and that the laser interferometer can read accurately during movement along the Z-axis. According to the content of the detection items, the experiment establishes an error correction experiment with an inclination angle of A error:
A＝90°-B (29)
where B is the face cone angle of the spiral bevel gear.
3) When the experiment is started, the computer program of the coordinate system controls the Z-axis carrying sensor to move up and down, and the numerical values of the laser displacement sensor and the laser interferometer are recorded within the effective measurement range (-10 mm) of the laser displacement sensor every time the Z-axis carrying sensor moves 0.1 mm. And (4) collating the experimental data, and obtaining the measurement data of 200 groups of laser displacement sensors and laser interferometers in total through experiments, wherein the difference value of the measurement data is the error value of the laser displacement sensor.
And after the calibration experiment is completed, establishing an object plane inclination angle error compensation model. And fitting the measurement depth error under the determined inclination angle by using a least square method, wherein the influence of the measurement depth on the measurement error is in a linear relation under the condition that the conical surface angle is determined. The calibration curve of the object plane tilt angle is shown in fig. 6.
After the error compensation model is established, an interpolation method is applied to the actual detection process of the spiral bevel gear to obtain a compensation result. And judging the quality condition of the gear according to the compensated parameter results.
After the arc-tooth bevel gear is precisely measured by using the error compensation model, a relation model of the abrasion loss of the forging die and the number of forging pieces is established by using an improved support vector machine algorithm.
According to the above-mentioned method, using
Figure GDA0002474951350000101
Denotes the test item, in κ1,κ2,κ3..The measured value of each test item is represented, and the number of die forged gears is represented by N. Assuming that the nth gear is detected, based on the above parameters, the following mapping relationship can be established:
Figure GDA0002474951350000102
is provided with
Figure GDA0002474951350000103
Setting [123.. n ] for all parameters of n gears before die forging]The number of the gears forged and pressed by the corresponding grinding tool.
Experimental data is divided into training data and prediction data, and detection data is trained by using an improved support vector machine algorithm. Unlike traditional support vector machine prediction algorithms, the improved support vector machine regression prediction algorithm introduces relaxation factors.
Let niFor predicting the number of gears forged by the spiral bevel gear die to reach a certain abrasion degree, the corresponding parameter values of each detection item are as follows:
Figure GDA0002474951350000104
mithe number of the actually forged gears is that the corresponding parameter values of each detection item are as follows:
Figure GDA0002474951350000111
then:
＝|pre-rea|(33)
if not less than ξ (ξ is the relaxation factor setting), indicating that the accuracy of the sample parameter for predicting the die wear is poor, the values of pre are replaced by the values of rea, and correspondingly, miSubstitution of niAnd retraining the sample data. Therefore, relaxation factors are introduced into the traditional support vector machine algorithm, and the accuracy of prediction is improved.
Predicting arc teeth by using self-iterative support vector machine algorithmWear degree of a die for processing the bevel gear. The wear degree of the spiral bevel gear comprises a die wear early warning state and a die wear repairing state which are respectively SwAnd SrAnd (4) showing. According to the gear detection item parameter prediction, when the two states are reached, the number of the gears forged by the die is NpwAnd NprAnd (4) showing. The number of the gears actually processed by the current die is NrIf: n is a radical ofr≤NpwContinuously using the die for processing; n is a radical ofpw＜Nr≤NprPreparing to replace the die, and ensuring the processing efficiency; n is a radical ofr＞NprAnd replacing the new die and repairing the old die.

Claims (6)

1. The method for predicting the abrasion of the die for processing the spiral bevel gear based on non-contact detection is characterized by comprising the following steps of:
1) establishing a mathematical model of introducing an installation inclination angle error of the laser displacement sensor under any installation pose;
2) correcting the installation inclination angle of the laser displacement sensor, completing a calibration experiment on detection items of the arc-tooth bevel gear, and establishing an object plane inclination angle error compensation model;
3) establishing a relation model of the abrasion loss of the forging die and the number of forging pieces by using an improved support vector machine algorithm; after the arc-tooth bevel gear is precisely measured by using the error compensation model, a relation model of the abrasion loss of a forging die and the number of forging pieces is established by using an improved support vector machine algorithm, and the method specifically comprises the following steps: by using
Figure FDA0002524330660000011
Denotes the test item, in κ1,κ2,κ3.., representing the measured value of each detection item, and representing the number of the forged gears of the die by N; assuming that the nth gear is detected, the following mapping relationship is established according to the parameters:
Figure FDA0002524330660000012
is provided with
Figure FDA0002524330660000013
Setting [123.. n ] for all parameters of n gears before die forging]The number of gears forged and pressed by the corresponding grinding tool;
dividing experimental data into training data and prediction data, and training detection data by using an improved support vector machine algorithm; different from the traditional support vector machine prediction algorithm, the improved support vector machine regression prediction algorithm introduces relaxation factors;
let niFor predicting the number of gears forged by the spiral bevel gear die to reach a certain abrasion degree, the corresponding parameter values of each detection item are as follows:
Figure FDA0002524330660000014
mithe number of the actually forged gears is that the corresponding parameter values of each detection item are as follows:
Figure FDA0002524330660000015
then:
＝|pre-rea| (16)
if the value is more than or equal to ξ, the accuracy of the sample parameter for predicting the die wear is poor, wherein ξ is a set value of a relaxation factor, and the values of rea are used for replacing the values of pre, and correspondingly, miSubstitution of niRetraining the sample data; therefore, relaxation factors are introduced into the traditional support vector machine algorithm, and the accuracy of prediction is improved;
4) and predicting the abrasion degree of the die for processing the spiral bevel gear by using an algorithm of a self-iterative support vector machine.
2. The method for predicting the wear of the die for processing the spiral bevel gear according to claim 1, wherein in the step 1), the laser displacement sensor is used for measuring at any installation pose, and an installation inclination error is necessarily introduced into a measurement result, so that the installation pose of the laser displacement sensor is calibrated.
3. The method for predicting the wear of a die for spiral bevel gear machining based on non-contact detection as claimed in claim 2, wherein said calibration process comprises: the method comprises the following steps of installing a laser displacement sensor on a Z axis of a three-coordinate measuring instrument, converting a measured value of the laser displacement sensor from a self coordinate system to a reference coordinate system, and establishing the following three coordinate systems:
(1) a machine tool coordinate system O-XYZ of the measuring machine, wherein the coordinate system takes the 0 position of a Y-axis grating ruler of the machine tool as an original point, and the directions of 3 coordinate axes are respectively consistent with the directions of 3 guide rails of the measuring machine;
(2) measuring coordinate system o of laser displacement sensors-xsyszsThe coordinate system takes a point on the laser displacement sensor, the measured value of which is 0, as an origin, and the directions of 3 coordinate axes are respectively consistent with the directions of XYZ axes;
(3) machine coordinate system oM-xMyMzMThe coordinate system is established in the state that the measuring machine returns to 0, the point of the laser displacement sensor with the measured value of 0 is taken as the origin, and the directions of 3 coordinate axes are respectively consistent with the direction of X, Y, Z axes;
measured value of laser displacement sensor from os-xsyszsTo oM-xMyMzMHas a coordinate conversion order of os-xsyszs→oM-xMyMzMExpressed in homogeneous coordinates as:
Figure FDA0002524330660000021
in the formula (1), [ x ]SySzS]TFor laser displacement sensors at os-xsyszsMeasured value in s coordinate system, laser beam at os-xsyszsThe unit vector is (l, m, n) and the length is d, and the unit vector is directly read from the laser displacement sensor; r1 and T1 are eachos-xsyszsRelative to oM-xMyMzMThe rotation matrix and the translation matrix of (a); t1 represents the value x for the raster valueM0,yM0,zM0：
Figure FDA0002524330660000022
The laser displacement sensor is positioned at o through a formula (2)s-xsyszsConversion of the measured value of (A) to (o)M-xMyMzMPerforming the following steps;
the plane equation for the calibration plane α is set to:
Ax+By+Cz+D＝0 (3)
(A, B, C) is the normal vector of plane α;
assuming that the intersection point of the laser and the plane α is P1, the value of the laser displacement sensor is d1, and the grating reading is (x)M1,yM1,zM1) Combining formula (2) and formula (3) to obtain:
A(xM1+ld1)+B(yM1+md1)+C(zM1+nd1)+D＝0 (4)
when the laser displacement sensor moves along the X direction by delta X, wherein delta X is the grating change value of the grating along the X direction, the intersection point of the laser displacement sensor and the plane α is changed into P2, the numerical value of the laser is d2, and the grating reading is XM1-Δx,yM1,zM1And then:
A(xM1+ld2-Δx)+B(yM1+md2)+C(zM1+nd2)+D＝0 (5)
subtracting the equations (4) and (5) to obtain:
Figure FDA0002524330660000031
similarly, respectively moving Δ Y along the-Y direction and Δ Z along the-Z direction results in:
Figure FDA0002524330660000032
wherein, U is constant Al + Bm + Cn, and the result is obtained after simplification:
lΔdx/Δx+mΔdy/Δy+nΔdz/Δz＝0 (8)
let a1＝Δdx/Δx、b1＝Δdy/Δy、c1＝ΔdzAnd/Δ z, then:
a1l+b1m+c1n＝0 (9)
and because:
l2+m2+n2＝1 (10)
obtaining the value of the unit direction vector (l, m, n) of the laser beam of the laser displacement sensor by the formulas (8) to (10), wherein PN is the normal vector of the measured surface and is a known value in the calibration process; assuming that the unit vector of incident light at any installation angle is EP ═ l, m, n, the inclination angle of the point P is:
Figure FDA0002524330660000041
the α that is obtained at this time is the installation inclination angle of the laser displacement sensor.
4. The method for predicting the wear of the die for processing the spiral bevel gear according to claim 1, wherein in the step 1), when the mathematical model of the error of the installation inclination angle introduced by the laser displacement sensor at any installation posture is established, the posture of the laser displacement sensor is adjusted and corrected, and the installation inclination angle is corrected.
5. The method for predicting the wear of the die for processing the spiral bevel gear based on the non-contact detection as claimed in claim 1, wherein in the step 2), the specific method for completing the calibration experiment of the detection item of the spiral bevel gear and establishing the object plane inclination angle error compensation model comprises the following steps: firstly, the inclination is determined according to the object plane of the spiral bevel gearAngle building dip error calibration experiment: installing a sine gauge on the measuring platform, and calibrating a correct inclination angle by adjusting the height of the sine gauge; on an O-XYZ coordinate system, AB is the length of the sine gauge, BC represents the height of the standard gauge block, and the inclination angle of the sine gauge
Figure FDA0002524330660000042
Obtained by adjusting the height of the standard gauge block, in △ ABC:
BC＝AB·sinφ (12)
the calibration experiment of the detection items of the arc-tooth bevel gear, namely the object plane inclination error calibration experiment, is completed, and the experiment specifically comprises the following steps:
(1) the object plane inclination error correction experimental device consists of a numerical control machining center, a laser displacement sensor, a laser interferometer, a sine gauge and a standard gauge block; the laser displacement sensor is arranged on a Z axis of the numerical control machining center, the sine gauge is arranged on a workbench right below the laser displacement sensor, the laser interferometer light path component is fixed on the Z axis and the workbench through a magnetic meter frame, and the Z axis can move under the control of a numerical control system;
(2) correcting the installation inclination angle of the laser displacement sensor before the start of the experiment, ensuring that a laser beam is vertically incident, adjusting the position of an interferometer light path component, ensuring that the light path does not deviate and the laser interferometer can accurately read in the process of moving along the Z axis, and building a required inclination angle error correction experiment according to the content of a spiral bevel gear detection item;
(3) when an experiment is started, a computer program of a coordinate system controls a Z-axis carrying sensor to move up and down, the numerical values of a laser displacement sensor and a laser interferometer are recorded within the effective measurement range (-10 mm) of the laser displacement sensor every time the Z-axis carrying sensor moves 0.1mm, and the difference value of the numerical values is the error value of the laser displacement sensor;
after the calibration experiment is completed, establishing an object plane inclination angle error compensation model, and fitting the measurement depth error under a certain inclination angle by using a least square method to obtain the relation between the measurement depth and the measurement error;
after the error compensation model is established, in the actual detection process of the spiral bevel gear, an interpolation method is applied to obtain a compensation result, and the quality condition of the gear is judged according to the result of each parameter after compensation.
6. The method for predicting wear of a mold for machining a spiral bevel gear according to claim 1, wherein in step 4), the self-iterative support vector machine algorithm is used to predict the wear of the mold for machining the spiral bevel gear, and the wear of the spiral bevel gear includes a mold wear warning and a mold wear repairing state, which are respectively SwAnd SrRepresents; according to the gear detection item parameter prediction, when the two states are reached, the number of the gears forged by the die is NpwAnd NprRepresents; the number of the gears actually processed by the current die is NrIf N is presentr≤NpwContinuously using the die for processing; n is a radical ofpw＜Nr≤NprPreparing to replace the die, and ensuring the processing efficiency; n is a radical ofr＞NprAnd replacing the new die and repairing the old die.
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