CN115096261B - Method for measuring inclination of forging based on improved elliptic fitting optimization algorithm - Google Patents
Method for measuring inclination of forging based on improved elliptic fitting optimization algorithm Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C9/00—Measuring inclination, e.g. by clinometers, by levels
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/26—Measuring arrangements characterised by the use of optical techniques for measuring angles or tapers; for testing the alignment of axes
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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
- G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
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- 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
- G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
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- G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- G06N3/00—Computing arrangements based on biological models
- G06N3/004—Artificial life, i.e. computing arrangements simulating life
- G06N3/006—Artificial life, i.e. computing arrangements simulating life based on simulated virtual individual or collective life forms, e.g. social simulations or particle swarm optimisation [PSO]
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Abstract
The invention relates to a method for measuring inclination of a forging piece based on an improved ellipse fitting optimization algorithm, which belongs to the technical field of detection of critical geometric quantity of the forging piece and comprises the steps of collecting distance data, carrying out coordinate transformation, screening sample points, fitting an ellipse by using a PSO algorithm through an orthogonal geometric distance model, fitting a central axis of the forging piece on a three-dimensional space by using a fitting ellipse center, and calculating the inclination. According to the method, the sample points are selected through the random division areas, the interference of the abnormal value clusters on the fitting result is eliminated through the weighted quantile screening, and the calculation force is saved; the problem of high curvature deviation can be eliminated by constructing an orthogonal geometric distance residual model, and a better approximation effect can be obtained; fitting ellipse through improved PSO algorithm to obtain fitting ellipse with higher accuracy and stability; the measurement errors in the range of-3 degrees to 3 degrees are smaller than 0.05 degrees, and the measurement requirement of the inclination of the forging is met.
Description
Technical Field
The invention relates to a method for measuring inclination of a forging piece based on an improved elliptic fitting optimization algorithm, and belongs to the technical field of detection of key geometric quantities of the forging piece.
Background
The parts produced by the forging technology are widely applied to a plurality of fields of metallurgy, aerospace, weapon equipment, transportation and the like, wherein long shaft forgings are commonly used for rotating shafts or connecting shafts of rotating mechanisms, such as ship propeller shafts, nuclear power half-speed rotors and the like, and ring forgings are commonly used for rotating parts or fixed parts, such as vehicle and ship hubs, evaporation tank bases and the like. Upsetting and punching are important procedures of columnar or annular forgings in the forging process, and the position and the posture between an upsetting rod or a perforating needle and a forging blank can have great influence on the machining quality.
At present, the optical technology is widely applied to the geometric quantity measurement of forgings and can be divided into a machine vision method and a laser scanning method. For the machine vision method, on one hand, the side image of the forging piece can be directly obtained through a CCD, and the size of the forging piece is determined after image processing, however, the method is easily influenced by measuring environmental noise; on the other hand, a linear laser image projected onto the surface of the forging piece can be obtained by utilizing a CCD, and the document Spectral selective and difference imaging laser triangulation measurement system for on line measurement of large hot workpieces in precision open die forging obtains the cross section of the workpiece by green strip laser projected onto the surface of the workpiece, so that the diameter of the forging piece is solved; the method comprises the steps of firstly obtaining a green strip laser image and then fitting by using multi-section point cloud data to obtain a circumferential curve of the thermal state cylinder forging piece. For the laser scanning method, the laser range finder can be driven by the rotary platform or the servo motor to acquire point cloud data, and then the three-dimensional image of the measured piece is reconstructed by the point cloud data. Although the application of the above detection technique has been studied on forging size measurement, the measurement study on forging inclination is still in the beginning stage.
Disclosure of Invention
The invention aims to provide a method for measuring the inclination of a forging piece based on an improved ellipse fitting optimization algorithm, which is characterized in that the visualization of the profile of a measured section is realized by coordinate transformation, a sample point is screened by combining a random method, a geometric parameter model of a fitting ellipse is solved by using a PSO algorithm, a three-dimensional linear equation of a central shaft of the forging piece is obtained from a central point of the fitting ellipse, and the inclination angle of the forging piece is calculated from the linear equation. The influence of the abnormal value on measurement is avoided, the calculation efficiency and the accuracy are improved, and the inclination of the forging piece is measured more conveniently, rapidly and accurately.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows:
a method for measuring inclination of forging based on an improved elliptic fitting optimization algorithm comprises the following steps:
step 1: controlling the stepping motor to move to drive the spiral screw rod, so that the rotation axis of the measured forging piece is aligned with the rotating shaft, and the laser range finder reaches the measuring position;
step 2: the computer drives the laser range finder and the servo motor to start simultaneously, and the dynamic distance di between the laser range finder and the surface of the measured forging piece is measured;
step 3: the system device of the control computer carries out coordinate transformation and sample point screening on the distance information, and carries out ellipse fitting on the screened points after eliminating the influence of abnormal values, and the specific steps are as follows:
step 31: the angle of each turn of the laser range finder is recorded as theta 0 The angle theta rotated by the laser range finder at a certain position is k theta 0 K represents a kth point swept by the laser rangefinder, and a position coordinate (x k ,y k ) Namely, the coordinates of the profile sample points of the measured forging are as follows:
x k ＝(L-d)·cosθ
y k ＝(L-d)·sinθ
wherein: l represents the distance from the laser range finder to the rotation center, and d represents the distance from the laser range finder to the surface of the measured forging piece;
step 32: carrying out random area division on the sample points of the measured cross section profile of the measured forging piece obtained in the step 31, wherein each time is divided into 6 areas uniformly, randomly selecting one sample point from each area, carrying out direct algebraic fitting on the selected sample points, and an elliptic equation represented by the direct algebraic fitting is as follows:
Ax 2 +Bxy+Cy 2 +Dx+Ey+F＝0
traversing all sample points, constructing an orthogonal geometric distance residual error model, carrying out weighted quantile screening according to the model, and storing sample points corresponding to orthogonal geometric residual errors meeting the conditions;
step 33: according to the definition of the orthogonal geometric distance residual model in the step 32, the problem of the target ellipse parameter is converted into the problem of solving the nonlinear objective function, the minimum orthogonal geometric distance residual between the fitting ellipse and the sample point selected in the step 32 is set as the objective function, and the ellipse is represented by a model vector u, specifically:
u＝(x c y c a b α) t
wherein: (x) c ,y c ) Is an ellipse center, a is a long axis, b is a short axis, and alpha is an included angle between the long axis a and an X positive half axis; the constraint conditions are satisfied:
C1:a,b∈R +
C2:b≤a
C3:θ c ∈[0,π)
C4:x c ,y c ∈R
solving an objective function by using a particle swarm optimization algorithm, wherein a model vector u corresponding to the objective function is a fitting ellipse parameter;
step 4: fitting the central axis of the measured forging by the centers of all cross sections, and finally solving the inclination angle of the forging by a central axis equation, wherein the inclination angle is specifically as follows:
where (a, b, c) is the coordinates of a known point on a straight line, and (m, n, l) is the direction vector of a spatial straight line, and the slope of the projection equation of the three-dimensional straight line on the XOZ (YOZ) plane can be calculated as the corresponding X, Y tilt angle.
The technical scheme of the invention is further improved as follows: the algebraic fitting method in the step 32 is as follows: from the formula
To determine each coefficient and then, according to the extremum principle, to minimize F (a, B, C, D, E, F), there must be
Wherein, let the vector λ= [ A, B, C, D, E, F] t Representing the ellipse parameters.
The technical scheme of the invention is further improved as follows: the process of establishing the elliptic orthogonal geometric distance residual model in the step 32 is as follows:
starting from the geometric equation of a general ellipse with a half major axis length a, a half minor axis length b, a direction angle α (angle between major axis and X axis of ellipse), a center (X c ,y c ) The geometric representation of the elliptic equation is specifically:
to reduce the amount of computation required to calculate the intersection point, a new local coordinate system (O-XY) is built in the fitted coordinate system (O-XY), and the transformation relationship between the two coordinate systems is represented by a rotation matrix and a translation vector:
wherein X in the translation vector c ,Y c Representing the center coordinates of the ellipse under the fitting coordinate system, wherein the parameters are provided by iterative initial values;
in the local coordinate system, the equation for an ellipse is expressed as:
the tangent equation at the intersection point is expressed as:
from this, the orthographic geometric residual model can be written as:
the technical scheme of the invention is further improved as follows: the sample point screening method in the step 32 is as follows:
screening the sample points in the step 32 by using a weighted quantile method, traversing the sample points, and recording the square sum G (u) of the orthogonal geometric residuals corresponding to each group of sample points in an array num_index, wherein the square sum G (u) is expressed as:
where X represents the coordinates of the data point in the fitted coordinate system and f represents a nonlinear function that obtains the orthogonal distance of the data point to the ellipse.
These values were arranged from small to large, and note that the values after arrangement were:
G (1) ≤G (2) ≤...≤G (m)
wherein G is (k) Represents the corresponding G value of the kth group;
to pre-calculate p only finds k, letThen x (m) ＜ξ p ＜x (k+1) When an abnormal value occurs, the p quantile of the selected point does not change, resulting in inaccurate thresholds and poor quality of the selected point. In order to extract the quality of the selected points, the influence of abnormal values on the bad fitting effect is reduced, and a weight function is added on the basis of the highest percentile, wherein the weight function is expressed as:
ξ p ＝(mp-k)(w' k+1 ·x (k+1) -w' k ·x (k) )+w' k ·x (k)
where the sum of the squares of the weighted algebraic distances is expressed as:
wherein, alpha represents a weight coefficient, and the decision formula is specifically as follows:
storing G (u) corresponding to the sample points in all the steps 32 in an array best_elipse_par to satisfy G (u) < ζ p Sample point coordinates of the conditions.
The technical scheme of the invention is further improved as follows: the objective function establishment method in the step 33 is as follows:
according to the definition of the geometric fitting algorithm on the error distance, the problem of solving the target ellipse parameters for the sample points of the pair of data best_elipses_par is converted into the problem of solving a nonlinear objective function, specifically:
where X represents the coordinates of the data point in the fitted coordinate system, f represents a nonlinear function that obtains the orthogonal distance of the data point to the ellipse, u represents the parameters of the equation of the ellipse to be solved, and min represents the objective function, i.e., the minimum value of G (u) to be solved.
The technical scheme of the invention is further improved as follows: the ellipse objective function min can calculate an ellipse vector u by the particle swarm optimization algorithm in the step 33; in the PSO algorithm, each particle can update its velocity and position:
wherein i is a particle index; j is a dimension index; p is p best And g best The adaptive values of (a) are the inertial weights and acceleration coefficients of the variables; k is the current iteration number; c 1 And c 2 Is an acceleration constant; r is (r) 1 And r 2 Is in accordance with [0,1 ]]Random numbers distributed even in the range; w is an inertial weight coefficient that has the ability to trade off global and local search capabilities, the values of which are shown below:
updating the position x and velocity v of the particles continues until the required minimum mismatch is reached. The criteria for stopping updating both values is based on the maximum number of iterations or required calculation accuracy.
By adopting the technical scheme, the invention has the following technical effects:
the invention provides a forging inclination measuring method based on an improved optimization algorithm fitting ellipse, which comprises the steps of constructing a measuring device consisting of a measured forging, a laser range finder, an inclination sensor and the like, performing multiple processing on measured distance data, converting the measured distance data into a forging central axis in a three-dimensional space, obtaining the inclination of the forging, and obviously eliminating error interference of an abnormal value cluster; the established X, Y directional measurement calibration curve can eliminate systematic errors, the forge pieces in different inclination states are measured, and after the measurement results are corrected by using a calibration equation, the measurement errors in the range of-3 degrees to 3 degrees are smaller than 0.05 degrees, so that the measurement requirements of the inclination of the forge pieces can be met.
Drawings
FIG. 1 is a diagram of a laser ranging and detection driving experiment device of the present invention;
FIG. 2 is a graph comparing fitting results after outlier cluster presence and rejection;
FIG. 3 is a G (u) convergence curve of a PSO algorithm fit ellipse;
FIG. 4 is a graph showing the data processing results when the Y-direction is inclined by 3.0;
fig. 5 is a system error curve.
The device comprises a measured forging piece 1, a gradient-adjustable platform 2, an objective table 3, an objective table 4, a stepping motor 5, a spiral screw rod 6, a fixed support 7, a rotating shaft 8, a servo motor 9, a reduction gearbox 10, a base 11, an adjustable support leg 12, a laser range finder 13 and a computer.
Detailed Description
The invention is further described in detail below with reference to the attached drawings and specific examples:
a forge piece inclination amount measuring method based on an improved optimization algorithm fitting ellipse comprises the steps of carrying out surrounding measurement on a forge piece by utilizing a laser displacement sensor to obtain forge piece cross section distance information, and carrying out outlier discrimination and elimination on acquired distance data based on a regression analysis method; and carrying out coordinate transformation and direct least square fitting on the data from which the abnormal values are removed, fitting the central axis of the forging by the centers of the cross sections, and finally solving the inclination angle of the forging by a central axis equation.
The laser ranging and detection driving experimental device is shown in fig. 1, and is an experimental device of the method for measuring the inclination of the forging based on the improved elliptic fitting optimization algorithm.
The laser ranging and detection driving experimental device comprises a laser detection device and a detection driving device, wherein the laser detection device comprises: the inclination adjustable platform 2, the objective table 3, the base 10, the adjustable support 11, the laser range finder 12 and the computer 13. The detection driving device includes: the device comprises a stepping motor 4, a spiral screw 5, a rotating shaft 7, a servo motor 8, a reduction gearbox 9 and a fixed support 6.
The working process of the laser ranging and detecting driving device is as follows:
the adjustable support leg 11 is adjusted to keep the whole measuring system horizontal, the measured forging 1 is fixed on the inclination adjustable platform 2, the stepping motor 4 drives the spiral screw 5 to move the measuring pose and calibrate the experimental system, and the laser range finder 12 is aligned to the rotation axis of the rotating shaft 7; the servo motor 8 and the reduction gearbox 9 drive the rotating shaft 7 to rotate continuously by 360 degrees, at the moment, the measured forging 1 rotates along with the rotation, and the laser range finder 12 detects the distance between the measured forging 1 and the surface of a cross section of the measured forging 1 rotating by a circle; the inclination angle state of the measured forging 1 is changed by the adjustable inclination platform 2, the XY inclination angle in the state is recorded, and the distance of the surface of the section of the measured forging 1 rotating by one circle is measured again by the laser range finder 12. The measured distance data are transmitted to the computer 13, and the system device of the computer 13 adopts visual studio, industrial control software and Matlab to jointly program, wherein the Matlab is mainly used for processing the data.
The measured forging 1 is cylindrical, the diameter is 200mm, and the height is 240mm; the inclination angle of the inclination adjustable platform 2 is adjusted by a fine adjustment screw rod positioned at the left side position, and the adjustment range is +/-3 degrees; the inclination angle is measured by an electronic inclinometer, the biaxial measurement resolution of the electronic inclinometer is 0.01 degrees, and the biaxial measurement precision is 0.05 degrees; the servo motor 8 is connected with the reduction gearbox 9, an output shaft of the reduction gearbox 9 drives the fixed support 6 connected through the rotating shaft 7, a driving pulse signal of the servo motor 8 is supplied by the S7-200PLC, the laser range finder 12 is fixed, and the measured forge piece 1 rotates to finish surrounding measurement; the effective stroke and the positioning precision of the spiral screw 5 are respectively 200mm and 0.03mm; the screw rod 5 is driven by a 42 step motor 4, driving pulse signals are supplied by an STM32 singlechip, and data acquisition and processing are completed by using software written in C#.
A method for measuring inclination of forging based on an improved elliptic fitting optimization algorithm comprises the following specific steps:
step 1: the stepping motor 4 is controlled to move to drive the spiral screw rod 5, so that the rotation axis of the measured forging piece 1 is aligned with the rotating shaft 7, and the laser range finder 12 reaches the measuring position.
Step 2: the computer 13 drives the laser range finder 12 and the servo motor 8 to start simultaneously, and the dynamic distance di between the laser range finder 12 and the surface of the measured forging piece 1 is measured;
step 3: the system device of the control computer carries out coordinate transformation and sample point screening on the distance information, and carries out ellipse fitting on the screened points after eliminating the influence of abnormal values, and the specific steps are as follows:
step 31: the angle of each turn of the laser rangefinder 12 is denoted as θ based on the principle of polar to rectangular conversion 0 The angle θ through which the laser rangefinder 12 rotates at a certain position is kθ 0 K represents the kth point swept by the laser rangefinder 12, the position coordinates of the kth point (x k ,y k ) Namely, the coordinates of the profile sample points of the measured forging are as follows:
wherein: l represents the distance of the laser rangefinder from the centre of rotation, which is related to the length of the rotating arm in the measurement system, in experiments a known amount, d represents the distance of the laser rangefinder from the surface of the forging, in experiments measured;
step 32: carrying out random area division on the sample points of the measured cross section profile of the measured forging piece obtained in the step 31, randomly and uniformly dividing the sample points into 6 areas each time, randomly selecting one sample point from each area, carrying out direct algebraic fitting on the selected sample points, constructing an orthogonal set distance residual model, carrying out weighted quantile screening on the sample points according to the model, and expressing an elliptic equation by the direct algebraic fitting as follows:
Ax 2 +Bxy+Cy 2 +Dx+Ey+F＝0 (2)
the algebraic fit evaluation function is determined as:
to determine each coefficient and then, according to the extremum principle, to minimize F (a, B, C, D, E, F), there must be
Wherein, let the vector λ= [ A, B, C, D, E, F] t Representing the ellipse parameters.
Elliptic orthogonal geometric distance residual model: starting from the geometric equation of a general ellipse with a half major axis length a, a half minor axis length b, a direction angle α (angle between major axis and X axis of ellipse), a center (X c ,y c ) The geometric representation of the elliptic equation is specifically:
to reduce the amount of computation required to find the intersection point, a new local coordinate system (O-XY) is built in the fitted coordinate system (O-XY). The transformation relation of the two coordinate systems is represented by a rotation matrix and a translation vector:
wherein X in the translation vector c ,Y c The circle center coordinates of the ellipse under the fitting coordinate system are represented, and the parameters are provided by iterative initial values.
In the local coordinate system, the equation for an ellipse is expressed as:
the tangent equation at the intersection point is expressed as:
from this, the orthographic geometric residual model can be written as:
weighting and dividing number screening is carried out according to an orthogonal geometric distance residual error model, sample points are traversed, and the square sum G (u) of the orthogonal geometric residual errors corresponding to each group of sample points is recorded in an array num_index, and is expressed as:
where X represents the coordinates of the data point in the fitted coordinate system and f represents a nonlinear function that obtains the orthogonal distance of the data point to the ellipse.
These values were arranged from small to large, and note that the values after arrangement were:
G (1) ≤G (2) ≤...≤G (m) (11)
wherein G is (k) Representing the corresponding G value of the kth group.
To pre-calculate p only finds k, letThen x (m) ＜ξ p ＜x (k+1) When an abnormal value occurs, the p quantile of the selected point does not change, resulting in inaccurate thresholds and poor quality of the selected point. In order to extract the quality of the selected points, the influence of abnormal values on the bad fitting effect is reduced, and a weight function is added on the basis of the highest percentile, wherein the weight function is expressed as:
ξ p ＝(mp-k)(w' k+1 ·x (k+1) -w' k ·x (k) )+w' k ·x (k) (12)
where the sum of the squares of the weighted algebraic distances is expressed as:
wherein, alpha represents a weight coefficient, and the decision formula is specifically as follows:
storing G (u) corresponding to the sample points in all the steps 32 in an array best_elipse_par to satisfy G (u) < ζ p Sample point coordinates of the conditions.
Step 33: and carrying out ellipse fitting based on a particle swarm optimization algorithm on the sample points of the array best_elipse_par.
According to the definition of the orthogonal geometry distance residual model in step 32, the problem of the target ellipse parameter is converted into the problem of solving the nonlinear target function, specifically:
where X represents the coordinates of the data point in the fitted coordinate system, f represents a nonlinear function that obtains the orthogonal distance of the data point to the ellipse, u represents the parameters of the equation of the ellipse to be solved, and min represents the objective function, i.e., the minimum value of G (u) to be solved.
The ellipse is characterized by a model vector u, specifically:
u＝(x c y c a b α) t (16)
wherein: (x) c ,y c ) Is the center of the ellipse, a is the long axis, b is the short axis, and alpha is the included angle between the long axis a and the positive half axis of X. The constraint conditions are satisfied:
and solving an ellipse by using the PSO algorithm to obtain an ellipse objective function min. In the PSO algorithm, each particle can update its velocity and position:
wherein i is a particle index; j is a dimension index; p is p best And g best The adaptive values of (a) are the inertial weights and acceleration coefficients of the variables; k is the current iteration number; c 1 And c 2 Is an acceleration constant; r is (r) 1 And r 2 Is in accordance with [0,1 ]]Random numbers distributed even in range. w is an inertial weight coefficient that has the ability to trade off global and local search capabilities. The values are as follows:
updating the position x and velocity v of the particles continues until the required minimum mismatch is reached. The criteria for stopping updating both values is based on the maximum number of iterations or required calculation accuracy.
Step 4: fitting the center of each cross section to obtain the central axis of the forging 1 to be measured, and finally solving the inclination angle of the forging by a central axis equation, wherein the inclination angle is specifically as follows:
where (a, b, c) is the coordinates of a known point on a straight line, and (m, n, l) is the direction vector of a spatial straight line, and the slope of the projection equation of the three-dimensional straight line on the XOZ (YOZ) plane can be calculated as the corresponding X, Y tilt angle.
And the platform is adjusted to enable the workpiece to generate inclination angles at the same time in the XY direction, and systematic error compensation is carried out on the measurement results, wherein the measurement results of the workpiece at different inclination angles are shown in Table 1.
Table 1 inclination measurement results
From the data analysis of table 1, it can be obtained that the measurement results of 6 groups of different inclinations are analyzed, the maximum measurement error is 0.04 degrees, the average measurement error is less than 0.03 degrees, and the measurement results show that the measurement method provided herein can realize accurate measurement of the inclination angle in the range of 0-3 degrees.
The traditional least square ellipse fitting technology looks at the equal weight of all sample points, larger errors can occur when abnormal value clusters exist in the measured forge piece, iteration optimizing performance is not achieved, larger deviation can occur in an ellipse fitting result, and accordingly inclination measurement is inaccurate. The method provided by the invention eliminates the abnormal value clusters by using a weighted quantile method, and the pair of the ellipse fitting result and the traditional method is shown in figure 2, so that the method is fully proved to effectively eliminate the influence of the abnormal value clusters and improve the fitting precision.
According to the forging inclination measuring method based on the improved optimization algorithm fitting ellipse, an iteration curve of G (u) is shown in fig. 3, and the fact that the value of G (u) reaches convergence at the 35 th generation is shown in the figure. The workpiece is fixed on an inclination adjustable platform, the measurement results of the workpiece inclined by 0.00 degrees in the X direction and 3.00 degrees in the Y direction are shown in fig. 4, 8 different-height cross section measurement conditions and the center positions of the cross sections are shown in the drawing, the vertical distances between adjacent cross sections are 16mm, the space coordinates of a plurality of ellipse major axis center points in the vertical direction are obtained, and finally the forging central axis is obtained through fitting. Because of systematic errors in the measuring device, the workpiece is first measured at different angles of inclination to determine the calibration equation. Adjusting the platform to different inclinations according to the indication of the electronic inclinometer, so that different postures of the workpiece are generated; firstly, the inclination of a workpiece in the X (Y) direction is 0.00 degrees, then, different inclination angles are set in the Y (X) direction for measurement, the measurement range is-3 degrees to 3 degrees, the interval is 1 degree, the measurement results in the X direction and the Y direction are shown as figure 5, the measurement values are fitted by using a primary function, and the fitting result shows good linearity.
The above examples are only illustrative of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention, and various modifications and improvements made by those skilled in the art to the technical solution of the present invention should fall within the scope of protection defined by the claims of the present invention without departing from the spirit of the present invention.
Claims (3)
1. The method for measuring the inclination of the forging based on the improved elliptic fitting optimization algorithm is characterized by comprising the following steps of: the experimental device used by the method comprises a laser ranging experimental device and a detection driving experimental device, wherein the laser ranging experimental device comprises: inclination adjustable platform (2), objective table (3), base (10), adjustable stabilizer blade (11), laser range finder (12) and computer (13), detect drive experimental apparatus includes: step motor (4), screw (5), pivot (7), servo motor (8), reducing gear box (9) and fixed bolster (6), measured forging (1) are fixed on gradient adjustable platform (2), include the following step:
step 1: aligning the rotation axis of the measured forging piece with the rotating shaft, and enabling the laser range finder to reach a measuring position;
step 2: the computer drives the laser range finder and the servo motor to start simultaneously, and the dynamic distance between the laser range finder and the surface of the measured forging piece is measured;
step 3: the system device of the control computer carries out coordinate transformation and sample point screening on the distance information, and carries out ellipse fitting on the screened points after eliminating the influence of abnormal values, and the specific steps are as follows:
step 31: the angle of each turn of the laser range finder is recorded as theta 0 The angle theta rotated by the laser range finder at a certain position is k theta 0 K represents a kth point swept by the laser rangefinder, and a position coordinate (x k ,y k ) Namely, the coordinates of the profile sample points of the measured forging are as follows:
x k ＝(L-d)·cosθ
y k ＝(L-d)·sinθ
wherein: l represents the distance from the laser range finder to the rotation center, and d represents the distance from the laser range finder to the surface of the measured forging piece;
step 32: carrying out random area division on the sample points of the measured cross section profile of the measured forging piece obtained in the step 31, wherein each time is divided into 6 areas uniformly, randomly selecting one sample point from each area, carrying out direct algebraic fitting on the selected sample points, and an elliptic equation represented by the direct algebraic fitting is as follows:
Ax 2 +Bxy+Cy 2 +Dx+Ey+F＝0
constructing an orthogonal geometric distance residual error model, carrying out weighted quantile screening on sample points according to the model, traversing all the sample points, and storing the sample points corresponding to the orthogonal geometric residual errors meeting the conditions;
step 33: performing ellipse fitting based on a particle swarm optimization algorithm on the stored sample points, and according to the definition of the orthogonal geometric distance residual error model in the step 32, converting the problem of the target ellipse parameter into the problem of solving a nonlinear objective function, setting the minimum orthogonal geometric distance residual error between the fitting ellipse and the sample point selected in the step 32 as the objective function, wherein the ellipse is represented by a model vector u, and specifically comprises:
u＝(x c y c a’b’α) t
wherein: (x) c ,y c ) Is an ellipse center, a ' is a long axis, b ' is a short axis, and alpha is an included angle between the long axis a ' and an X positive half axis; the constraint conditions are satisfied:
C1：a’,b’∈R +
C2：b’≤a’
C3：α∈[0,π)
C4：x c ，y c ∈R
solving an objective 2 function by using a particle swarm optimization algorithm, wherein a model vector u corresponding to the objective function is a fitting ellipse parameter;
step 4: controlling a stepping motor to move to drive a spiral screw rod to obtain 8 cross section measurement conditions with different heights, calculating the center point of each cross section, fitting the center of each cross section to obtain the central axis of the measured forging, and finally solving the inclination angle of the forging by a central axis equation, wherein the vertical distance between adjacent cross sections is 16mm, and the inclination angle is specifically as follows:
wherein, (a, b, c) is the coordinate of a known point on the central axis, and (m, n, l) is the inclination angle of the central axis towards X, Y, which is calculated by the slope of the projection equation of the central axis on the XOZ plane and the YOZ plane.
2. The method for measuring inclination of forging based on improved elliptic fitting optimization algorithm according to claim 1, wherein the algebraic fitting method in the step 32 is as follows: from the formula
To determine each coefficient and then, according to the extremum principle, to minimize F (a, B, C, D, E, F), there must be。
3. The method for measuring the inclination of a forging based on the improved elliptic fitting optimization algorithm according to claim 1, wherein the elliptic orthogonal geometric distance residual model building process in the step 32 is as follows:
starting from the geometric equation of a general ellipse, a ' of the ellipse is the major axis, b ' is the minor axis, the direction angle α is the angle between the major axis a ' of the ellipse and the positive half axis of X, and the center (X c ,y c ) The geometric representation of the elliptic equation is specifically:
to reduce the amount of computation required to calculate the intersection point, a new local coordinate system (O-XY) is built in the fitted coordinate system (O-XY), and the transformation relationship between the two coordinate systems is represented by a rotation matrix and a translation vector:
wherein X in the translation vector c ,Y c Representing the center coordinates of the ellipse under the fitting coordinate system, wherein the parameters are provided by iterative initial values;
in the local coordinate system, the equation for an ellipse is expressed as:
the tangent equation at the intersection point is expressed as:
from this, the orthographic geometric distance residual model can be written as:
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