CN113778021B - Triaxial linkage numerical control system for processing saxophone whistle piece - Google Patents
Triaxial linkage numerical control system for processing saxophone whistle piece Download PDFInfo
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Abstract
The invention discloses a triaxial linkage numerical control system for processing saxophone whistle pieces, which comprises a processing machine tool, wherein an automatic pushing and feeding mechanism, a clamping and processing movement mechanism, a processing mechanism and an ordered receiving mechanism are arranged on the processing machine tool, and an engineering computer for controlling the automatic pushing and feeding mechanism, the clamping and processing movement mechanism, the processing mechanism and the ordered receiving mechanism is arranged on the processing machine tool, wherein a numerical control system is arranged in the engineering computer; the engineering computer controls the automatic pushing and feeding mechanism to send saxophone whistle blanks into the clamping and processing movement mechanism for positioning according to the numerical control system, then the rear control processing mechanism processes saxophone whistle on the clamping and processing movement mechanism, and after the processing is finished, the saxophone whistle blanks of the clamping and processing movement mechanism are sent into the ordered receiving mechanism for ordered receiving. The automatic feeding and processing device for the saxophone whistle piece can automatically feed and process and receive the saxophone whistle piece, and effectively improves the production efficiency of the saxophone whistle piece.
Description
Technical Field
The invention belongs to the technical field of saxophone whistle pieces, and particularly relates to a triaxial linkage numerical control system for processing saxophone whistle pieces.
Background
Music is free from national borders and folk art development, so that the development of the music is gradually internationalized, more saxophone lovers are started to emerge in China, and along with the increasing popularization of saxophone stringed instruments, the requirements of flute-head accessories matched with the music are gradually increased. The whistle piece is called to the sound fitting of installing on the flute head, and it produces vibration through the drainage and moves the sound, and the flute head just is equivalent to the oscillator, and various pronunciation demands can be satisfied to different model whistle pieces, like midrange, high pitch and inferior midrange etc. all have own exclusive model whistle piece.
The tubular instruments such as saxophone enter the life of people, the required amount of whistle pieces for drainage on a blowing nozzle of the tubular instruments is increased rapidly, the high-precision irregular surface of the whistle pieces is dealt with, and a systematic mature processing control system is temporarily absent in China, so that an automatic processing system of the whistle pieces needs to be established urgently. Therefore, we propose a three-axis linkage numerical control system for processing saxophone whistle pieces.
Disclosure of Invention
In order to solve the technical problems, the invention provides the following technical scheme:
the invention discloses a triaxial linkage numerical control system for processing saxophone chips, which comprises a processing machine tool, wherein the processing machine tool is provided with an automatic pushing and feeding mechanism, a clamping and processing movement mechanism, a processing mechanism and an ordered receiving mechanism, and is provided with an engineering computer for controlling the automatic pushing and feeding mechanism, the clamping and processing movement mechanism, the processing mechanism and the ordered receiving mechanism, wherein the engineering computer is internally provided with a numerical control system; the engineering computer controls the automatic pushing and feeding mechanism to send saxophone whistle blanks into the clamping and processing movement mechanism for positioning according to the numerical control system, then controls the processing mechanism to process the saxophone whistle on the clamping and processing movement mechanism, and sends the saxophone whistle to the ordered receiving mechanism for ordered receiving after the processing is completed;
the numerical control system comprises a monitoring module, the monitoring module monitors the feeding state of the automatic feeding mechanism and the clamping state of the clamping processing movement mechanism respectively, when the feeding state of the automatic feeding mechanism and the clamping state of the clamping processing movement mechanism are normal, the processing work is carried out, and otherwise, the machine is stopped for maintenance.
As a preferable technical scheme of the invention, the numerical control system comprises a central application module, wherein the central application module comprises an initialization module, a detection module, a man-machine interface module, a motion control module, a parameter setting module and a data generation module;
the initialization module is used for initializing variables and position parameters; the motor shafts are used for ensuring that the motor shafts enter a correct processing preparation state and position after being started;
the detection module comprises sensors for detecting motor shafts in all mechanisms;
the man-machine interface module comprises an operation panel module, a state information bar module and a menu toolbar module; the status information bar module is used for dynamically displaying the status of the system; the state dynamic state of the system comprises the servo state of each motor shaft, the motion state of each motor shaft, the state of a sensor in the system and the alarm state of each motor shaft;
the motion control module comprises an automatic processing module, a start-stop control module and an automatic zeroing module for zeroing all motor shafts;
the parameter setting module comprises a processing cutter parameter setting module, an origin parameter setting module for setting a clamping processing movement mechanism and a movement parameter setting module;
the data generation module comprises a data input and storage module, a data algorithm fitting module and a data modification and display module; the data input and storage module is used for inputting and storing the original data of the saxophone sheet curved surface, the data algorithm fitting module is used for fitting the original data of the saxophone sheet curved surface to form processing data, and the data modification and display module is used for modifying and displaying the processing data.
As a preferred technical scheme of the invention, the central application module comprises a motion display module, wherein the motion display module is used for displaying motion parameters of each motor shaft.
As a preferable technical scheme of the invention, the automatic zeroing module performs zeroing on each motor shaft, namely, firstly, initializing to ensure that each motor shaft enters a correct processing preparation state and position after being started, and then setting motion parameters, wherein the motion parameters comprise search distance, speed and smoothing time; and then each motor shaft moves to drive the platform to move until an origin switch arranged in each mechanism is triggered, and the movement is stopped, so that the motor shafts complete zero-returning work.
As a preferable technical scheme of the invention, the algorithm fitting method of the data algorithm fitting module comprises the following steps,
step 1, firstly, obtaining original data of a saxophone whistle piece curved surface through an original model, and further obtaining a curve of the saxophone whistle piece curved surface;
step 2, recovering to obtain an original curve surface model through point cloud obtained by grid division of the saxophone whistle piece surface, fitting by using an interpolation approximation method to obtain an interpolation curve of the original curve surface model, and further obtaining an interpolation curve of the original curve surface model;
step 3, performing curve fitting analysis on the interpolation curve by using a linear regression model polynomial base pair to obtain a fitting curve, and further obtaining a preliminary curved surface;
and 4, performing surface fitting on the preliminary curved surface by a singular value decomposition method to obtain a final fitted curved surface.
In a preferred embodiment of the present invention, the method for performing curve fitting analysis on the interpolation curve in the step 3 by using the polynomial basis of the linear regression model is that,
establishing a linear regression model y=w' x+e, wherein e is an error, w is a parameter coefficient to be calculated and represents the relation of a plurality of factors existing in the model, and if a plurality of independent variables exist, the expression is f (x) =w T x+b＝w 1 x 1 +w 2 x 2 +...+w n x n +b,
Wherein, x is a parameter such as (x 1, x2, x3, …, xi, …, xn), i is different values representing different parameter values, wherein w= (w 1, w2, w3, …, wn), after calculating w and b, the relation between the parameters can be represented by a linear model;
solving the linear model by using a least square method, optimizing w and b model parameters,
the expression of the expression is that,
where w and b are represented by w and b, respectively, b is a scalar representing the optimum error value, there are,
let the above equation be zero, perform optimal solution w and b, and calculate:
performing matrix calculation, X represents the existing data set, each row represents a sample, the size of which is n (m+1), and J represents (w, b), then
Y＝(y 1 ，y 2 ，...，y n ) T ，
Then there is J * ＝argmin(Y-XJ) T (Y-XJ)，
The optimal solution of J can be obtained by solving the partial derivative of J and making the partial derivative zero,
J * ＝(X T X) -1 X T and Y, further obtaining an optimal linear regression model.
Numbering the original data of the curved surface of the saxophone whistle piece to be X i I=1, 2,3, …, n, and the data are ordered, resulting in a curve f (x) where all points appear, referred to as an interpolation curve; and pass through X ij The curved surface of i=1, 2,3, …, n, j=1, 2,3, …, n is called an interpolated curved surface f (u, v), and the parameters u and v are the coordinates of the curved surface parameters.
As a preferred technical solution of the present invention,
the method for performing surface fitting on the preliminary curved surface based on the singular value decomposition method in the step 4 is that a real matrix with M being m×n and the rank being R is provided, and then an M-order orthogonal matrix U and an n-order orthogonal matrix I exist, so that the following requirements are met
M＝UDI T ，
Wherein D is an m x n order matrix,
wherein sigma i I=1, 2, …, R, is the singular value of matrix M,
assuming that given measurement data points Pi (xi, yi, zi), (i=1, 2,3, … M, j=1, 2,3, … n), then m=a ij ＝z ij M-dimensional vector u k For data points (x i ，(u k ) i ) I=1, 2, …, m, a curve function u can be obtained by curve fitting k (x) K=1, 2, …, R. Similarly, for n-dimensional vector I k Data points (y) i ，(I k ) j ) J=1, 2, …, n, a curve fitting function I can also be obtained k (y), k＝1,2,…,R；
Wherein the formula (5-23) is rewritable as
From the above, it can be deduced
Where i=1, 2, …, m, j=1, 2, …, n. The binary surface function can be expressed as
As a preferred technical solution of the present invention, the verification analysis is performed on the finally obtained fitted curved surface in the step 4, and the method of the verification analysis is to construct a bezier curve, where the bezier curve is constructed based on a Bernstein polynomial, and the n-th Bernstein polynomial is represented as follows:
wherein t is [0,1 ]]，I=1, 2,3, …, n. The constructed nth order parametric curve segment is expressed as
In the formula, u is E [0,1 ]],p i Is used to control the vertices of the feature polygons,
given n+1 control vertices p i (i=0, 1,2, …, n), weight w i (i=0, 1,2, …, n), the rational bezier curve expression for n times is as follows
Wherein,is an n-th order Bernstein basis function, and is typically expressed in terms of an unorganized Bezier curve definition
A set of control points p on a given plane i (i=0, 1,2,3, …), the T-Bezier curve expression for the three times is as follows
Wherein,
b 0 (t)＝(1-γsint)(1-sint) 2 ，
b 1 (t)＝sint(1-sint)(2+γ-γsint),
b 2 (t)＝cost(1-cost)(2+γ-γcost)，
b 3 (t)＝(1-γcost)(1-cost) 2 ；
wherein the method comprises the steps ofγ∈[0，1]. The beneficial effects of the invention are as follows:
1. this kind of saxophone whistle processing is with triaxial linkage numerical control system, wherein the engineering computer is according to numerical control system control automatic pushing materials feeding mechanism with the saxophone whistle blank send into centre gripping processing motion in and fix a position, then back control processing mechanism carries out the processing with the saxophone whistle on the centre gripping processing motion, send into the ordered receipts material in the order receiving mechanism with the saxophone whistle of centre gripping processing motion after the processing is accomplished, thereby accomplish autoloading, processing and the receipts material to the saxophone whistle, effectively improved the production efficiency of saxophone whistle.
2. The three-axis linkage numerical control system for processing the saxophone whistle piece can monitor each production link by arranging the initialization module, the detection module, the man-machine interface module, the motion control module, the parameter setting module and the data generation module, so that safe and orderly production and processing work is ensured.
3. The data algorithm fitting module in the triaxial linkage numerical control system for processing the saxophone reed fits the saxophone reed curved surface through a set specific fitting method, so that the processed saxophone reed curved surface can better fit the actual requirement.
Drawings
The accompanying drawings are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate the invention and together with the embodiments of the invention, serve to explain the invention. In the drawings:
FIG. 1 is a schematic diagram of a three-axis linkage numerical control system for processing saxophone tabs;
FIG. 2 is a system block diagram of a numerical control system of a three-axis linkage numerical control system for processing saxophone chips according to the present invention;
FIG. 3 is a zero-return flow chart of an automatic zero-return module of the three-axis linkage numerical control system for processing saxophone tabs;
FIG. 4 is a control flow chart of a three-axis linkage numerical control system for processing saxophone tabs according to the present invention;
FIG. 5 is a graph showing the effect of a linear regression model polynomial basis fitting of a three-axis linkage numerical control system for saxophone tab processing according to the present invention;
FIG. 6 is a graph of the effect of surface fitting by a singular value decomposition method of a three-axis linkage numerical control system for saxophone tab processing according to the present invention;
FIG. 7 is a graph showing a vertex change contrast of a Bezier curve of a three-axis-linkage numerical control system for processing saxophone sheets according to the present invention;
FIG. 8 is a three-time T-Bezier plot of a three-axis linked numerical control system for processing saxophone tabs according to the present invention.
Detailed Description
The preferred embodiments of the present invention will be described below with reference to the accompanying drawings, it being understood that the preferred embodiments described herein are for illustration and explanation of the present invention only, and are not intended to limit the present invention.
Examples: as shown in fig. 1, the triaxial linkage numerical control system for saxophone sheet processing comprises a processing machine tool 1, wherein an automatic pushing and feeding mechanism 2, a clamping and processing movement mechanism 3, a processing mechanism 4 and an ordered receiving mechanism 5 are arranged on the processing machine tool 1, an engineering computer 6 for controlling the automatic pushing and feeding mechanism 2, the clamping and processing movement mechanism 3, the processing mechanism 4 and the ordered receiving mechanism 5 is arranged on the processing machine tool, and a numerical control system is arranged in the engineering computer 6;
as shown in fig. 4, the engineering computer 6 controls the automatic pushing and feeding mechanism 2 to send saxophone tab blanks into the clamping and processing movement mechanism 3 for positioning according to the numerical control system, then controls the processing mechanism 4 to process the saxophone tabs on the clamping and processing movement mechanism 3, and sends the saxophone tabs of the clamping and processing movement mechanism 3 into the ordered receiving mechanism 5 for ordered receiving after the processing is completed; the automatic feeding, processing and receiving of the saxophone whistle piece are completed, and the production efficiency of the saxophone whistle piece is effectively improved.
The air cylinder 1 in the automatic pushing and feeding mechanism pushes out the whistle piece blank from the storage cartridge clip, the blank is waited for being sent to the automatic processing platform by the air cylinder 2, and is sent to the clamping and processing movement mechanism 3, then the air cylinder 3 in the clamping and processing movement mechanism 3 clamps the whistle piece blank to prevent shaking in the processing process, the model parameters are preconfigured in the loading software, and the automatic process is started. The cutter shaft can not be opened by a processing main shaft, particularly, if the cylinder 2 is not retracted, collision of the cutter shaft is likely to be caused, hardware is damaged, and even safety is endangered, so that in-place and return detection of each cylinder is very important, and once the cutter shaft is abnormal, the machine tool is required to be stopped to remove the abnormality, and then the machine tool is restored to process.
The numerical control system comprises a monitoring module, the monitoring module monitors the feeding state of the automatic feeding mechanism and the clamping state of the clamping processing movement mechanism respectively, when the feeding state of the automatic feeding mechanism and the clamping state of the clamping processing movement mechanism are normal, the processing work is carried out, otherwise, the machine is stopped for maintenance, and the production safety is higher.
As shown in fig. 2, the numerical control system comprises a central application module, wherein the central application module comprises an initialization module, a detection module, a man-machine interface module, a motion control module, a parameter setting module and a data generation module;
the initialization module is used for initializing variables and position parameters; the motor shafts are used for ensuring that the motor shafts enter a correct processing preparation state and position after being started;
the detection module comprises sensors for detecting motor shafts in all mechanisms;
the man-machine interface module comprises an operation panel module, a state information bar module and a menu toolbar module; the status information bar module is used for dynamically displaying the status of the system; the state dynamic state of the system comprises the servo state of each motor shaft, the motion state of each motor shaft, the state of a sensor in the system and the alarm state of each motor shaft;
the servo state of each motor shaft is that whether each motor shaft is correctly enabled determines whether the motor can be started or not, namely, the first step of starting the motor must ensure the normal enabling state, if any one shaft is enabled abnormally in software, the processing cannot be started, and the coordination linkage of each shaft can be ensured only by eliminating the abnormality after stopping the machine.
Motion state of each shaft: if each shaft is in a motion state, the corresponding indicator lamp turns green, and whether the problem of error in matching of a certain shaft occurs or not can be observed for positioning analysis; status of sensors in the system: the system mainly comprises positive and negative limit switches (proximity sensors) and an origin switch corresponding to all the shafts, position limitation is needed to be added to all the shafts when automatic processing of whistle pieces is carried out, hardware damage caused by abnormal software operation is prevented, maintenance cost is increased, the interface display of the sensors is carried out, once the system goes wrong, the shaft to which the vertical horse is positioned triggers limit, further investigation of software and hardware problems is carried out, and the origin switch is needed to be matched when all the shafts are started or are initialized after the system is abnormal, and the zero position of all the shafts is positioned by the sensors.
Alarm state of each shaft motor: the motor overload alarm device is used for monitoring whether an overload or an unknown error such as an encoder communication problem occurs or not to alarm, an operator can clearly observe the occurrence of the abnormality through the alarm prompt control, the situation can be generally checked through the alarm error prompt of the driver, and the machine can be restarted after the error is cleared, so that the motor can normally run.
The motion control module comprises an automatic processing module, a start-stop control module and an automatic zeroing module for zeroing all motor shafts;
the parameter setting module comprises a processing cutter parameter setting module, an origin parameter setting module for setting a clamping processing movement mechanism and a movement parameter setting module;
and the processing cutter parameter setting module is used for modifying, storing and reading processing parameters. In the left parameter set, the positions of the tool and the wood block on the platform are mainly set. The method mainly aims at the replacement of the cutter shaft or the damage condition of the backing plate, the machining relative position is determined according to the sizes of the replaced wood blocks and the cutter, and the fact that the surface size of the whistle piece cannot deviate too much is ensured in sequence, so that the parameter of the part is required to be measured accurately. The middle group is a processing origin information parameter of each shaft, and is mainly used for determining the relative distance between the processing ready state position of each shaft and the origin of each shaft, wherein the relative position is expressed by pulse quantity, and the processing back parameter is used for correcting the error of hardware installation, and processing is ensured to be started from the thinnest tail end of the whistle piece before the first step of processing. The last part of bamboo chip parameter group is to ensure the model of the whistle chip, and the system is used for processing the whistle chip curved surface of various models, and the basic sizes of the whistle chips of different models are set by configuring the parameters.
The data generation module comprises a data input and storage module, a data algorithm fitting module and a data modification and display module; the data input and storage module is used for inputting and storing the original data of the saxophone sheet curved surface, the data algorithm fitting module is used for fitting the original data of the saxophone sheet curved surface to form processing data, and the data modification and display module is used for modifying and displaying the processing data.
The center application module comprises a motion display module, and the motion display module is used for displaying motion parameters of all motor shafts.
As shown in fig. 3, the automatic zeroing module performs zeroing on each motor shaft, namely, firstly, initializing to ensure that each motor shaft enters a correct processing preparation state and position after being started, and then setting motion parameters, wherein the motion parameters comprise a search distance, a speed and a smooth time; and then each motor shaft moves to drive the platform to move until an origin switch arranged in each mechanism is triggered, and the movement is stopped, so that the motor shafts complete zero-returning work.
In the invention, in the process of multiple experimental debugging, the zeroing motion is found to have pulse errors sometimes, and particularly in the Z direction, the thinnest end of the processed whistle piece is only 0.2 millimeter, so that a small amount of pulse deviation can cause great deviation of the processing size. Even directly trigger the limit switch in the Z direction, therefore, a method for increasing the pulse equivalence ratio is adopted, and the conversion ratio of pulse quantity to millimeter is 2000:1, so that the loss of a small quantity of pulse quantity can be ensured without causing great dimensional deviation.
And judging whether each shaft correctly returns to the zero point or not, and prompting by using sensor hardware to alarm. The guide screws and the sliding rails are arranged on the shafts, the rotary motion of the shafts is converted into the translational motion of the sliding rail platforms, and the state display interface can monitor the running state of each platform and mainly realize signal change monitoring on limit switches at two ends of each sliding rail platform. When the machine tool motion is abnormal and the system is reset, whether each shaft is correctly returned to the original point switch position is detected. And a machine tool operator can make a judgment in real time through the observation of the interface monitoring module, and whether the system operates normally or not.
The invention can set the height of the prepared wood block and the left-right swinging angle, clamp and relax the wood block by the cylinder control button, and the R-axis center line correction button starts the automatic cutting wood block for correction. The method for correcting the midline is that a whistle piece blank is clamped firstly by a left-right swing cutting method, a cushion block arranged on a processing platform is processed after a spindle motor is started, the whistle piece blank swings left and right by a fixed same angle, a straight line is cut out, and finally the cushion block forms a straight line which is the center of a rotating shaft.
Firstly, data fitting is carried out according to a corresponding fitting interpolation algorithm, the rotation angle and the height change value required by switching between every two points are calculated according to fitted data, after the reasonable change amount of each axis on each micro segment is ensured, a PT data button is clicked and stored, PT data of different processing modes can be stored in a local engineering catalog for model loading and calling.
The center application module further comprises an auxiliary function module, wherein the auxiliary function module is used for debugging the platform movement and debugging the feeding cartridge clips and the receiving cartridge clips in the automatic pushing and feeding mechanism 2 and the ordered receiving mechanism 5.
The algorithm fitting method of the data algorithm fitting module comprises the following steps,
step 1, firstly, obtaining original data of a saxophone whistle piece curved surface through an original model, and further obtaining a curve of the saxophone whistle piece curved surface;
step 2, recovering to obtain an original curve surface model through point cloud obtained by grid division of the saxophone whistle piece surface, fitting by using an interpolation approximation method to obtain an interpolation curve of the original curve surface model, and further obtaining an interpolation curve of the original curve surface model;
step 3, performing curve fitting analysis on the interpolation curve by using a linear regression model polynomial base pair to obtain a fitting curve, and further obtaining a preliminary curved surface;
and 4, performing surface fitting on the preliminary curved surface by a singular value decomposition method to obtain a final fitted curved surface.
In practical engineering, the accuracy of the data points obtained by us cannot be guaranteed, and if the obtained data points are directly used for directly constructing a curved surface and a curve, the deviation is great, and the obtained curved surface is of no significance. The approximation of the data points aims to solve the problem, a corresponding curve or curved surface is constructed by adopting a method, and the approximation curve or curved surface can be obtained by ensuring that the error between the approximation curve or curved surface and the measured data points is minimum under a certain constraint condition.
The method for fitting the interpolation curve of the original curve surface model by using the interpolation approximation method in the step 2 is that,
numbering the original data of the curved surface of the saxophone whistle piece to be X i I=1, 2,3, …, n, and the data are ordered, resulting in a curve f (x) where all points appear, referred to as an interpolation curve; and pass through X ij The curved surface of i=1, 2,3, …, n, j=1, 2,3, …, n is called an interpolated curved surface f (u, v), and the parameters u and v are the coordinates of the curved surface parameters.
The invention adopts the linear regression model polynomial base commonly used in statistical analysis to carry out curve fitting analysis, because compared with other models, the linear model has fewer measurement data points, the statistical characteristics are easy to obtain, and compared with the nonlinear model, the linear regression model is simpler to analyze and solve parameter variables to obtain a linear equation.
The method for performing curve fitting analysis on the interpolation curve by using the linear regression model polynomial base in the step 3 is that,
establishing a linear regression model y=w' x+e, wherein e is an error, w is a parameter coefficient to be calculated and represents the relation of a plurality of factors existing in the model, and if a plurality of independent variables exist, the expression is as follows
f(x)＝w T x+b＝w 1 x 1 +w 2 x 2 +...+w n x n +b ,
Wherein, x is a parameter such as (x 1, x2, x3, …, xi, …, xn), i is different values representing different parameter values, wherein w= (w 1, w2, w3, …, wn), after calculating w and b, the relation between the parameters can be represented by a linear model;
solving the linear model by using a least square method, optimizing w and b model parameters,
the expression of the expression is that,
where w and b are represented by w and b, respectively, b is a scalar representing the optimum error value, there are,
let the above equation be zero, perform optimal solution w and b, and calculate:
performing matrix calculation, X represents the existing data set, each row represents a sample, the size of which is n (m+1), and J represents (w, b), then
Y＝(y 1 ，y 2 ，...，y n ) T
Then there is J * ＝argmin(Y-XJ) T (Y-XJ)，
The optimal solution of J can be obtained by solving the partial derivative of J and making the partial derivative zero,
J * ＝(X T X) -1 X T and Y, further obtaining an optimal linear regression model. And (3) carrying out fitting analysis on the curve on the saxophone whistle piece curved surface by utilizing a linear model, firstly taking 10 intersecting lines at equal intervals along the Y direction of the whistle piece width direction, taking 9 measuring points at equal intervals on each intersecting line, fitting according to the data value obtained by modeling the whistle piece in the previous section, and respectively trying for fitting of secondary and tertiary curves. Considering that only the data fitting in the width direction is performed, the effect of the measured data in the length direction may be changed, so that the characteristics of the whole curve are not met, therefore, the data point fitting in the length direction needs to be performed again, 9 curves are cut in the length direction, 10 data points are taken from each curve, and the fitting attempt is still performed. And finally, observing the fitting effect for a plurality of times, and finding that the whole fitting curved surface effect is optimal when the fitting direction is along the width direction for the last time, wherein the fitting data points in the width direction and the length direction are more in accordance with the real model. The effect after fitting is shown in fig. 5.
The invention adopts a method based on singular value decomposition technology to carry out surface fitting attempt. The singular value decomposition method can be used for excavating important information in the matrix, so that a relation mode between local and whole is obtained, and the matrix can be subjected to dimension reduction analysis, so that the method is a reliable orthogonal matrix decomposition method.
The method for performing surface fitting on the preliminary curved surface based on the singular value decomposition method in the step 4 is that a real matrix with M being m×n and the rank being R is provided, and then an M-order orthogonal matrix U and an n-order orthogonal matrix I exist, so that the following requirements are met
M＝UDI T ，
Wherein D is an m x n order matrix,
wherein sigma i I=1, 2, …, R, is the singular value of matrix M,
assuming that given measurement data points Pi (xi, yi, zi), (i=1, 2,3, … M, j=1, 2,3, … n), then m=a ij ＝z ij M-dimensional vector u k For data points (x i ，(u k ) i ) I=1, 2, …, m, a curve function u can be obtained by curve fitting k (x) K=1, 2, …, R. Similarly, for n-dimensional vector I k Data points (y) i ，(I k ) j ) J=1, 2, …, n, a curve fitting function I can also be obtained k (y), k＝1,2,…,R。
Wherein the formula (5-23) is rewritable as
From the above, it can be deduced
Where i=1, 2, …, m, j=1, 2, …, n. The binary surface function can be expressed as
When the original graph of the curve is not known, the curve fitting is performed by using the singular value decomposition method, and a relatively ideal effect can be obtained, and the fitting effect is shown in the following figure 6.
In the automatic processing system of the irregular curved surface of the whistle piece, the invention also needs to construct a Bezier curve for interpolation analysis to carry out experimental verification,
and (3) performing verification analysis on the finally obtained fitting curved surface in the step (4), wherein the verification analysis method is to construct a Bezier curve, and the Bezier curve is constructed based on a Bernstein polynomial, wherein the Bernstein polynomial is expressed as follows:
wherein t is [0,1 ]]，I=1, 2,3, …, n. The constructed nth order parametric curve segment is expressed as
In the formula, u is E [0,1 ]], p i Is used to control the vertices of a feature polygon, which may be referred to as an n-degree Bezier curve, where the Bezier polygon is defined as a straight line p i The fold lines n formed by the successive connection are deformed, also called control polygons.
As shown in FIG. 7, only the control vertex p is varied 1 Different Bezier curves can be obtained and must be tangent to the first and last control points and the first and last line segments.
The bezier curve is known to have the advantages of simple shape, easy prediction and the like, but the bezier curve also has biplanarity, the curve generated by the method is difficult to adjust local shape characteristics of the bezier curve, and the bezier curve can only be approximately simulated and cannot be accurately expressed for some quadratic curves. On the premise of controlling the vertex to be unchanged, the rational Bezier curve can accurately represent the conical curve and can modify the curve shape in the whole range, so that the study of the rational Bezier curve is also indispensable.
Among these are the nature of the Bezier curve. Convex hull nature: the convex hull formed by the control vertexes must contain the constructed rational Bezier curve. Degradation shrinkage: the number of points at which the control polygon intersects a certain straight line must be not less than the number of points at which the bezier curve intersects the same straight line. Geometric invariance: no factors other than control vertices can interfere with the change in the curve.
Given n+1 control vertices p i (i=0, 1,2, …, n), weight w i (i=0, 1,2, …, n), the rational bezier curve expression for n times is as follows
Wherein,is an n-th order Bernstein basis function, and is typically expressed in terms of an unorganized Bezier curve definition
A set of control points p on a given plane i (i=0, 1,2,3, …), the T-Bezier curve expression for the three times is as follows
Wherein,
b 0 (t)＝(1-γsint)(1-sint) 2 ，
b 1 (t)＝sint(1-sint)(2+γ-γsint),
b 2 (t)＝cost(1-cost)(2+γ-γcost)，
b 3 (t)＝(1-γcost)(1-cost) 2 the method comprises the steps of carrying out a first treatment on the surface of the Wherein the method comprises the steps ofγ∈[0，1]. Let γ=1, p 0 P 1 、P 1 P 2 、P 2 P 3 Length is respectively l 0 、l 1 、l 2 The unit vector is denoted as T 0 、T 1 、T 2 Satisfies the following formula
P i+1 -P i -T i l i ，
Wherein. i takes on values of 0,1 and 2. Let T be 0 And T is 1 The turning angle is theta 1 ，T 1 And T is 2 The turning angle is theta 2 The slope of the P (t) curve at the end point can be deduced
As shown in FIG. 8, a three-time T-Bezier plot, P in the figure 0 、P 1 、P 3 And P 4 The curve is the three times T-Bezier curve fitted. The curve closer to the control polygon is obtained by the 4 dominant points in the figure, so that in the whistle piece curved surface automatic processing system, the T-Bezier curve can be adopted for fitting, the curve closer to the real curved surface characteristic is obtained, and the automatic processing is convenient.
Finally, it should be noted that: the foregoing description is only a preferred embodiment of the present invention, and the present invention is not limited thereto, but it is to be understood that modifications and equivalents of some of the technical features described in the foregoing embodiments may be made by those skilled in the art, although the present invention has been described in detail with reference to the foregoing embodiments. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (6)
1. A three-axis linkage numerical control system for processing saxophone whistle sheets is characterized in that: the automatic pushing and feeding mechanism (2), the clamping and processing movement mechanism (3), the processing mechanism (4) and the ordered receiving mechanism (5) are arranged on the processing machine tool (1), and an engineering computer (6) for controlling the automatic pushing and feeding mechanism (2), the clamping and processing movement mechanism (3), the processing mechanism (4) and the ordered receiving mechanism (5) is arranged on the processing machine tool, wherein a numerical control system is arranged in the engineering computer (6); the engineering computer (6) controls the automatic pushing and feeding mechanism (2) to send saxophone whistle blanks into the clamping and processing movement mechanism (3) for positioning according to the numerical control system, then controls the processing mechanism (4) to process the saxophone whistle on the clamping and processing movement mechanism (3), and sends the saxophone whistle to the ordered receiving mechanism (5) for ordered receiving after the processing is completed;
the numerical control system comprises a monitoring module, wherein the monitoring module monitors the feeding state of the automatic feeding mechanism and the clamping state of the clamping processing movement mechanism respectively, when the feeding state of the automatic feeding mechanism and the clamping state of the clamping processing movement mechanism are normal, the processing work is carried out, otherwise, the machine is stopped for maintenance;
the numerical control system comprises a central application module, wherein the central application module comprises an initialization module, a detection module, a man-machine interface module, a motion control module, a parameter setting module and a data generation module;
the initialization module is used for initializing variables and position parameters; the motor shafts are used for ensuring that the motor shafts enter a correct processing preparation state and position after being started;
the detection module comprises sensors for detecting motor shafts in all mechanisms;
the man-machine interface module comprises an operation panel module, a state information bar module and a menu toolbar module; the status information bar module is used for dynamically displaying the status of the system; the state dynamic state of the system comprises the servo state of each motor shaft, the motion state of each motor shaft, the state of a sensor in the system and the alarm state of each motor shaft;
the motion control module comprises an automatic processing module, a start-stop control module and an automatic zeroing module for zeroing all motor shafts;
the parameter setting module comprises a processing cutter parameter setting module, an origin parameter setting module for setting a clamping processing movement mechanism and a movement parameter setting module;
the data generation module comprises a data input and storage module, a data algorithm fitting module and a data modification and display module; the data input and storage module is used for inputting and storing the original data of the saxophone sheet curved surface, the data algorithm fitting module is used for fitting the original data of the saxophone sheet curved surface to form processing data, and the data modification and display module is used for modifying and displaying the processing data;
the algorithm fitting method of the data algorithm fitting module comprises the following steps,
step 1, firstly, obtaining original data of a saxophone whistle piece curved surface through an original model, and further obtaining a curve of the saxophone whistle piece curved surface;
step 2, recovering to obtain an original curve surface model through point cloud obtained by grid division of the saxophone whistle piece surface, fitting by using an interpolation approximation method to obtain an interpolation curve of the original curve surface model, and further obtaining an interpolation curve of the original curve surface model;
step 3, performing curve fitting analysis on the interpolation curve by using a linear regression model polynomial base pair to obtain a fitting curve, and further obtaining a preliminary curved surface;
step 4, performing surface fitting on the preliminary curved surface by a singular value decomposition method to obtain a final fitted curved surface;
the method for performing curve fitting analysis on the interpolation curve by using the linear regression model polynomial base in the step 3 is that,
establishing a linear regression model y=w' x+e, wherein e is an error, w is a parameter coefficient to be calculated and represents the relation of a plurality of factors existing in the model, and if a plurality of independent variables exist, the expression is as follows
Wherein, x is a parameter such as (x 1, x2, x3, …, xi, …, xn), i is different values representing different parameter values, wherein w= (w 1, w2, w3, …, wn), after calculating w and b, the relation between the parameters can be represented by a linear model;
solving the linear model by using a least square method, optimizing w and b model parameters, wherein the expression is as follows,
,
where w and b are represented by w and b, respectively, b is a scalar representing the optimum error value, there are,
let the above equation be zero, perform optimal solution w and b, and calculate:
performing matrix calculation, X represents the existing data set, each row represents a sample, the size of which is n (m+1), and J represents (w, b), then
Then there is
The optimal solution of J can be obtained by solving the partial derivative of J and making the partial derivative zero,
and obtaining an optimal linear regression model.
2. The three-axis linkage numerical control system for saxophone sheet processing according to claim 1, wherein the central application module comprises a motion display module for displaying motion parameters of each motor shaft.
3. The three-axis linkage numerical control system for processing saxophone chips according to claim 1, wherein the automatic zeroing module performs zeroing on each motor shaft, and the method comprises the steps of firstly initializing to ensure that each motor shaft enters a correct processing preparation state and position after being started up, and then setting motion parameters, wherein the motion parameters comprise a search distance, a speed and a smooth time; and then each motor shaft moves to drive the platform to move until an origin switch arranged in each mechanism is triggered, and the movement is stopped, so that the motor shafts complete zero-returning work.
4. The three-axis linkage numerical control system for saxophone sheet processing according to claim 1, wherein the method for fitting the interpolation curve of the original curve surface model by using the interpolation approximation method in the step 2 is that,
numbering the original data of the curved surface of the saxophone whistle piece to beI=1, 2,3, …, n, and the data are ordered, resulting in a curve f (x) where all points appear, referred to as an interpolation curve; while passing->The curved surface of i=1, 2,3, …, n, j=1, 2,3, …, n is called an interpolated curved surface f (u, v), and the parameters u and v are the coordinates of the curved surface parameters.
5. The three-axis linkage numerical control system for saxophone sheet processing according to claim 1, wherein the method of performing surface fitting on the preliminary curved surface by singular value decomposition in the step 4 is that a real matrix with m×n matrix and R rank is provided, and then M-order orthogonal matrix U, n-order orthogonal matrix I exist, satisfying the following conditions
Wherein D is an m x n order matrix,
wherein the method comprises the steps ofI=1, 2, …, R, is the singular value of matrix M,
assuming that the measurement data points Pi (xi, yi, zi), (i=1, 2,3, … m, j=1, 2,3, … n) are given
M＝M-dimensional vector u k For data points (x i ，(u k ) i ) I=1, 2, …, m, a curve function u can be obtained by curve fitting k (x) K=1, 2, …, R; similarly, for n-dimensional vector I k Data points (y) i ，(I k ) j ) J=1, 2, …, n, a curve fitting function I can also be obtained k (y),k＝1,2,…,R；
Wherein the formula (5-23) is rewritable as
From the above, it can be deduced
Where i=1, 2, …, m, j=1, 2, …, n; the binary surface function can be expressed as
6. The three-axis linkage numerical control system for saxophone sheet processing according to claim 1, wherein in the step 4, verification analysis is performed on the finally obtained fitting curved surface, and the method of verification analysis is to construct a bezier curve, wherein the bezier curve is constructed based on a Bernstein polynomial, and n-th Bernstein polynomial is represented as follows:
wherein t is [0,1 ]]，The constructed nth order parametric curve segment is expressed as
In the formula, u is E [0,1 ]],p i Is used to control the vertices of the feature polygons,
given n+1 control vertices p i (i=0, 1,2, …, n), weight w i (i=0, 1,2, …, n), the rational bezier curve expression for n times is as follows
Wherein,is an n-th order Bernstein basis function, and is typically expressed in terms of an unorganized Bezier curve definition
A set of control points p on a given plane i (i=0, 1,2,3, …), the T-Bezier curve expression for the three times is as follows
Wherein,
b 0 (t)＝(1-γsint)(1-sint) 2 ，
b 1 (t)＝sint(1-sint)(2+γ-γsint)，
b 2 (t)＝cost(1-cost)(2+γ-γcost)，
b3(t)＝(1-γcost)(1-cost)2；
wherein the method comprises the steps ofγ∈[0，1]。
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