CN109240214B - Contour error estimation and visualization method for multi-axis numerical control machining - Google Patents
Contour error estimation and visualization method for multi-axis numerical control machining Download PDFInfo
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- G05B19/41—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by interpolation, e.g. the computation of intermediate points between programmed end points to define the path to be followed and the rate of travel along that path
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Abstract
The invention discloses a contour error estimation and visualization method for multi-axis numerical control machining, which comprises two parts, namely a contour error estimation method and a contour error visualization method: the contour error estimation method is composed of contour error estimation based on three-dimensional linear spline interpolation and positive and negative discrimination of contour error based on a cutter curved surface, the contour error visualization method associates the contour error with another parameter to make a visualization graph, the visualization graph comprises a contour error curve of stroke calibration, a contour error multiplied magnification graph and a contour error chromatogram display graph, the position of an actual track of a relative space position of an actual track relative to an ideal curved surface can be effectively displayed, the contour error is visually displayed by utilizing three graphs, the contour error estimation method and the contour error visualization method are provided, and measurement data of the ideal track and the actual track of a machine tool are converted into a contour error display image which comprehensively displays various items of information of the contour error and has good readability, so that the visualization, the clarity and the analysis are visual and convenient.
Description
Technical Field
The invention belongs to the technical field of multi-axis numerical control machining precision, and particularly relates to a contour error estimation and visualization method for multi-axis numerical control machining.
Background
The multi-axis numerical control machining refers to the linkage machining which can control a plurality of motion axes simultaneously to obtain various complex curved surfaces, and is a core component of the modern mechanical manufacturing technology. In multi-axis numerical control machining, servo control systems of all axes are difficult to synchronize, and the servo control systems are one of main causes of inaccurate machining profiles. The contour error is generally defined as the shortest distance from the actual processing track to the ideal processing track in the processing process, and can effectively reflect the matching degree of the servo control systems of all axes. Therefore, the method has important significance for guaranteeing and improving numerical control machining precision by estimating and displaying the contour error in the multi-axis numerical control machining.
At present, the research of machine tools and hydraulic pressure, 1999(6), 59-61, (b) Cheng M Y, Lee C.motion control for controlling-Following Tasks Based on Real-Time control error timing, IEEE Transactions on Industrial Electronics,2007,54(3) 1686-; and estimating a projection point of the actual position point on the contour curve according to the current feeding speed, and taking the distance from the current position point to a connecting line of the projection point and the target point as an estimated value of the contour error. Most of the current research on contour error estimation aims at plane contour errors, and multi-axis numerical control machining generally needs to consider contour errors in three-dimensional space. In addition, the contour error calculated by the conventional contour error estimation method is usually an absolute value and cannot reflect the spatial position relationship between the actual trajectory and the ideal trajectory.
For the method for displaying the contour error, related research is less, no unified standard exists at present, and a common mode is to display various items of information of the contour error through local amplification display of the whole contour and a contour error curve calibrated by time respectively. However, this display method has two problems: under the conditions of high-speed machining, large command rotation angle or unsmooth transition, because the speed fluctuation is large, the display of the contour error information by using the time as the contour error curve of the abscissa is incomplete and unintuitive, the corresponding relation can not be formed with the position of the actual contour, and the relevance and the logicality are lacked among all parts of the method; the locally enlarged contour display can only display error conditions in a very local range, so that the overall contour error condition is difficult to observe, and the comparison of the contours before and after compensation or improvement and the improvement effect of the contour error are inconvenient to measure.
Disclosure of Invention
The invention aims to provide a contour error estimation and visualization method for multi-axis numerical control machining, which can add contour errors in three-dimensional space for precise calculation aiming at multi-axis numerical control machining, and simultaneously visually display the contour errors by reflecting the spatial position relationship between the actual track and the ideal track of a cutter through the signs of the contour errors.
The embodiment of the invention is realized by the following steps:
a contour error estimation and visualization method for multi-axis numerical control machining comprises a contour error estimation method and comprises the following steps:
s1, judging the space track of the cutter, executing S2 if the space track is a linear track, and executing S3 if the space track is a curved track;
s2, calculating the distance from the actual straight line position of the cutter point to the ideal straight line position, wherein the calculation result is a contour error, and executing S4;
s3, interpolating the curve track into a straight line segment by using a linear spline interpolation method, calculating the straight line by two coordinates with similar positions on the ideal curve, approximately taking the contour error as the distance from the tool point to the straight line segment, and returning to S2 to calculate the contour error;
and S4, determining the signs of the contour errors, wherein the signs are positive and negative respectively when the actual track is positioned on the first side and the second side of the ideal curved surface, and judging through the contour error expression.
In a preferred embodiment of the present invention, in the above S4, the profile error expression is:
wherein epsilon is a contour error,
is a normal vector of the ideal location point,
is an ideal positionA vector of points to the point of the actual position,
and
the point where the product of (a) and (b) is 0 does not exist, and the ideal contour position point corresponding to the actual contour position is such that
And
the product of (a) is greater than or less than 0.
In the preferred embodiment of the present invention, the above mentioned
And said
Are respectively:
wherein (x)0，y0，z0) Is the ideal position of the point, (x ', y ', z ') is the actual position of the point,
the ideal curved surface F (x, y, z) is 0 in (x)0，y0，z0) The normal vector of (a) is,
is the ideal position (x) of the tool nose point0，y0，z0) Distance to the actual position (x ', y ', z ').
In a preferred embodiment of the present invention, the method for estimating and visualizing the contour error for multi-axis numerical control machining includes a method for visualizing the contour error S5: and associating the contour error in the step S4 with the display parameter, and visually displaying the display parameter through a relational graph of the contour error and the display parameter.
In a preferred embodiment of the present invention, the display parameters include a stroke distance, the profile error is associated with the stroke distance of the actual point, different corresponding relationships between the stroke distance and the profile error are formed, and a display diagram of the profile error and the stroke distance is generated.
In a preferred embodiment of the present invention, the display parameters include a multiple, the contour error is multiplied by the multiple to be amplified, and then the multiplied contour error is added to the ideal locus point position to be used as an actual locus point, so as to make a three-dimensional coordinate graph of the ideal locus and the actual locus.
In a preferred embodiment of the present invention, the display parameters include a color spectrum, different colors are used to represent the positive and negative of the profile error, different depths of the colors are used to represent the profile errors with different sizes, and after the three-dimensional coordinates of the actual trajectory are made, the profile error color spectrum display is made on the trajectory curve using different colors.
In a preferred embodiment of the present invention, the relationship between the travel distance and the profile error is expressed as:
wherein s is the travel of the point of the tool tip, v is the moving speed of the point of the tool tip, t is the moving time of the point of the tool tip, and t isnowThe total time of the movement of the tool nose point.
In a preferred embodiment of the present invention, the actual position of the point after the contour error amplification is set to (x ', y ', z '):
wherein (x)0，y0，z0) The ideal position of the tool point is n is a multiplying coefficient.
In a preferred embodiment of the present invention, the expression of the profile error in S2 is as follows:
wherein, epsilon is a contour error, A, B, C, D is a coefficient of 0 of a straight line Ax + By + Cz + D, and the actual point position is (x ', y ', z ').
The invention has the beneficial effects that:
the invention converts a three-dimensional curve track into a linear track through linear spline interpolation, accurately calculates the contour error of the space track of the cutter, defines the positive and negative of the contour error through the positive and negative judgment of a vector product in the contour error estimation process, effectively displays the position of the actual track relative to an ideal curved surface at the relative space position of the actual track through the contour error, intuitively displays the contour error by utilizing three figures, provides a contour error estimation method and a contour error visualization method, converts the measurement data of the ideal track and the actual track of the machine tool into a contour error display image which comprehensively displays various information of the contour error and has good readability, and the visualization figure is more intuitive and clear.
Drawings
To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are required to be used in the embodiments will be briefly described below, and it should be understood that the following drawings only illustrate some embodiments of the present invention and therefore should not be considered as limiting the scope.
FIG. 1 is a schematic diagram of the steps of the contour error estimation and visualization method for multi-axis numerical control machining according to the present invention;
FIG. 2 is a schematic view of a trajectory of a point of a tool tip according to the present invention;
FIG. 3 is a schematic diagram of the three-dimensional curve estimated profile error of the present invention;
FIG. 4 is a schematic diagram of the positive and negative determination of the profile error of the present invention;
FIG. 5 is a graph of profile error versus travel distance in accordance with the present invention;
FIG. 6 is a multiplied, magnified view of the profile error of the present invention;
FIG. 7 is a graphical representation of the profile error of the present invention;
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. The components of embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.
Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
First embodiment
Referring to fig. 1, the present embodiment provides a method for estimating and visualizing a contour error for multi-axis numerical control machining, which includes two parts, namely, a contour error estimation method and a contour error visualization method: the contour error estimation method is composed of contour error estimation based on three-dimensional linear spline interpolation and positive and negative discrimination of contour error based on a cutter curved surface, and the contour error visualization method relates the contour error with another parameter to make a visualization graph which comprises a contour error curve of stroke calibration, a contour error multiplied magnification and a contour error chromatogram display graph.
The contour error estimation method (S1-S4) and the contour error visualization method S5 comprise the following steps:
s1, judging the space track of the cutter, executing S2 if the space track is a linear track, and executing S3 if the space track is a curved track;
s2, calculating the distance from the actual straight line position of the cutter point to the ideal straight line position, wherein the calculation result is a contour error, and executing S4;
s3, interpolating the curve track into a straight line segment by using a linear spline interpolation method, calculating the straight line by two coordinates with similar positions on the ideal curve, approximately taking the contour error as the distance from the tool point to the straight line segment, and returning to S2 to calculate the contour error;
s4, determining signs of the contour error, wherein the signs are positive and negative respectively when the actual track is positioned on the first side and the second side of the ideal curved surface, and judging through the contour error expression;
and S5, associating the contour error in the S4 with the display parameters, and carrying out visual display through a relational graph of the contour error and the display parameters.
Referring to fig. 2, the spatial trajectory of the tool is determined, and if the spatial trajectory is a linear trajectory, i.e., the spatial trajectory is a straight line segment, a profile error epsilon under a three-dimensional spatial linear trajectory command is defined, and a distance from an actual position to an ideal trajectory is defined, the profile error is calculated by setting an equation of the straight line segment of the ideal trajectory closest to the ideal trajectory as:
Ax+By+Cz+D＝0
the shortest distance from the actual knifepoint position to the straight-line segment track of the ideal track can be calculated as a profile error epsilon:
where ∈ is a profile error, and A, B, C, D are coefficients of which straight lines Ax + By + Cz + D are 0, respectively, (x ', y ', z ') is an actual position of the tool tip point.
It can be seen that for a spatially linear trajectory, the contour error can be directly solved by definition.
Referring to fig. 3, if the trajectory of the tool nose point is a space curve, a three-dimensional linear spline is used for interpolation estimation of an absolute value of a profile error, generally speaking, the ideal trajectory of the tool is a curve, and the profile error of the curve trajectory is estimated, and an ideal trajectory equation needs to be solved or approximately solved by means of analytic solution, interpolation, fitting and the like.
The invention relates to a contour error estimation and visualization method for multi-axis numerical control machining, which expands a common plane contour error estimation method based on linear spline interpolation into a three-dimensional space and interpolates an ideal track into a straight line segment.
By simulation, number of machinesAnd obtaining three-dimensional point position data of the actual track according to collection or part measurement, dividing the ideal track into straight line segments by a three-dimensional spline interpolation method, and converting the contour error estimation of the curved track into the contour error of the straight line track. For the calculation of the straight-line segment contour error, an equation of the interpolation straight-line segment of the ideal track with the nearest distance is set, a two-dimensional curve is taken as an example, and coordinates of two ideal position points with the nearest distance to an actual position point are set as (x)1，y1) And (x)2，y2) Then, the expression of the straight line between two points is:
where z and f (x, y) are straight lines passing through the coordinates of two points at the ideal position.
The distance from the actual point to the straight line segment is approximate to the contour error, and the contour error estimation of the curve track can be converted into the contour error of the straight line track in a linear spline interpolation mode. The invention expands the common plane contour error estimation method based on linear spline interpolation into a three-dimensional space, interpolates an ideal track into a straight line segment, and returns to the step S2 to estimate the contour error by using a calculation method of which the track is a linear straight line.
The shortest distance from the actual knifepoint position to the straight-line segment track of the ideal track can be calculated as a profile error epsilon:
where ∈ is a profile error, and A, B are coefficients in which the straight line Ax + By + D is 0, respectively, and (x ', y') is an actual position of the tool tip point.
The absolute value of the contour error can be obtained through the contour error estimation based on the linear spline interpolation method, and the spatial position relation between the ideal track and the actual track cannot be expressed. If the running contour error detection track is regarded as a side milling action, the inaccuracy of a curved surface generally has two conditions of under-cut and over-cut, the damage degree of the over-cut and the under-cut to the blank is different, whether the part with the contour error needs to be scrapped or reworked cannot be determined only through the absolute value of the contour error, the corresponding machine tool debugging and production scheduling are also different, the under-cut and the over-cut phenomena of the contour cannot be distinguished only by using the absolute value of the contour error as the contour error, and the machine tool debugging and the production scheduling in the actual processing cannot be well guided. Therefore, the positive or negative of the contour error needs to be determined by the positive or negative determination of the contour error based on the curved surface of the tool.
Defining the positive and negative of the contour error: referring to the definition of over-cut and under-cut, the curved surface formed by the tool according to the ideal position and posture motion is set as a reference, when the actual track is positioned on one side of the curved surface, the contour error is defined to be positive, the other side of the curved surface is defined to be negative, and the judgment of the positive and negative of the contour error can be calculated in the following mode.
Referring to fig. 4, a curved surface formed by the tool moving along the ideal path and the posture is taken as a boundary, two sides of the curved surface are respectively a first side and a second side, the profile error of the first side of the curved surface is set to be positive, the second side of the curved surface is set to be negative, the actual position of the tool nose point is set to be (x ', y', z '), and the corresponding ideal position of the tool is set to be (x', y ', z')0，y0，z0) The curved surface F (x, y, z) formed by the tool moving according to the ideal position and posture is 0 at (x)0，y0，z0) Is a normal vector of
Then, the positive and negative of the contour error epsilon can be judged as:
wherein epsilon is a contour error,
is a normal vector of the ideal location point,
a vector of ideal location points to actual location points,
and
the point where the product of (a) and (b) is 0 does not exist, and the ideal contour position point corresponding to the actual contour position is such that
And
the product of (a) is greater than or less than 0.
The positive direction of the contour error of the S-shaped track is set according to the method, the positive and negative judgment can be carried out on the contour error of the track obtained by the previous calculation, namely, the absolute value of the contour error is calculated through three-dimensional linear spline interpolation, and then the positive and negative judgment of the contour error is determined through a contour error positive and negative judgment method based on the cutter curved surface, so that an accurate and complete information contour error estimation result can be obtained.
Next, the contour error is visualized.
The contour error visualization method comprises three parts: and (3) displaying a profile error curve, a profile error multiplied by an enlarged image and a profile error chromatogram by using the stroke calibration.
Compared with a profile error curve taking the machining time as an abscissa axis, the profile error curve calibrated by the travel of the tool nose point can more accurately reflect the change trend of the profile error. Integrating the moving speed v of the tool nose point to obtain the stroke s of the tool nose point:
wherein s is the travel of the point of the tool tip, v is the moving speed of the point of the tool tip, t is the moving time of the point of the tool tip, and t isnowThe total time of the movement of the tool nose point.
Referring to fig. 5, a profile error stroke distance relationship diagram is plotted by taking a tool nose point stroke s as an abscissa and a corresponding profile error epsilon value as an ordinate, so as to obtain a stroke calibration profile error curve; by using the stroke of the tool point and the contour error at the corresponding moment, a contour error curve calibrated by the stroke can be obtained, the problem of information loss of the contour error curve using time as an abscissa axis is solved, and important information such as the fluctuation condition of the contour error, the general trend, the position of an error peak value and the like can be reflected.
The conventional common contour error visualization method adopts a local error amplification mode to display an actual contour, cannot display the tendency of the contour on the whole, and is difficult to visually observe the whole condition of the contour error.
Drawing a profile error multiplication graph, and calculating to obtain an actual track after error multiplication: the ideal position of the tool nose point of the machine tool is set as (x)0，y0，z0) The actual position is (x, y, z), and the error multiplied actual position (x ', y ', z ') is:
where n is a multiplication factor that can be adjusted according to the order of the contour error, typically set to 100, 400, or 1000.
Referring to FIG. 6, the contour error is multiplied by the enlarged view to draw the ideal tool path (x)0，y0，z0) The error multiplied by the three-dimensional space map of the amplified trajectory (x ', y ', z ') can be used to obtain the contour error multiplied by the amplified map. And displaying information such as error distribution, error peak position, spatial relation with an ideal profile and the like of the actual profile in a profile error multiplication graph mode.
The currently common outline error visualization method is weak in logicality and relevance, the reflection of an error peak value and a sensitive area is not visual, and the readability is poor. Therefore, a contour display method which is convenient for overall observation is needed on the basis of contour error curves and contour chromatographic line display.
Referring to fig. 7, a contour error chromatogram display diagram shows the trajectory of a tool through a chromatogram, i.e. a display method for drawing a curved surface or a curve by using a changing color and displaying information with more than one dimension in the graph0，y0，z0) And coloring, wherein the contour error is colored red in a regular manner, the contour error is colored blue in a negative manner, the color is darker as the absolute value of the error is larger, the corresponding relation between the color and the error value is marked on the side surface of the image through a color code, a contour error chromatographic display graph can be obtained, a large amount of information such as error distribution, error peak position, spatial relation with an ideal contour, error mean value and order of magnitude can be displayed clearly and visually, and the information such as the peak value of the contour error can correspond to a contour error curve and a contour error multiplication graph.
The invention has the following advantages:
1. the positive and negative of the contour error are defined in the process of contour error estimation, the positive and negative of the contour error can be marked in the process of contour error display, and the relative spatial position of the actual track can be effectively displayed;
2. the range, the position, the peak value and other information of the error area can be visually displayed by using the contour error curve taking the stroke as the abscissa, and the peak value of the contour error and the position of the sensitive area in the actual track can be better displayed;
3. aiming at the problem that the outline error cannot be integrally observed and compared in a local outline amplifying mode, the chromatogram and the error multiplication graph are used for visualizing the outline error, and various information of the outline error can be displayed more intuitively and comprehensively on the whole.
4. Through the contour error chromatogram, the corresponding relation between the color and the error value is marked on the side surface of the image through a color code, so that a contour error chromatogram display picture can be obtained, and a large amount of information such as error distribution, error peak position, spatial relation with an ideal contour, error mean value, order of magnitude and the like can be displayed clearly and visually.
The method comprises the steps of converting a three-dimensional curve track into a linear track through linear spline interpolation, accurately calculating the contour error of a space track of a cutter, judging the position of an actual track relative to an ideal curved surface through the positive and negative of a vector product, visually displaying the contour error by utilizing three figures, providing a contour error estimation method and a contour error visualization method, and converting measured data of the ideal track and the actual track of the machine tool into a contour error display image which comprehensively displays various information of the contour error and has good readability.
This description describes examples of embodiments of the invention, and is not intended to illustrate and describe all possible forms of the invention. It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Those skilled in the art can make various other specific changes and combinations based on the teachings of the present invention without departing from the spirit of the invention, and these changes and combinations are within the scope of the invention.
Claims (8)
1. A contour error estimation and visualization method for multi-axis numerical control machining is characterized by comprising a contour error estimation method, and the method comprises the following steps:
s1, judging the space track of the cutter, executing S2 if the space track is a linear track, and executing S3 if the space track is a curved track;
s2, calculating the distance from the actual straight line position of the cutter point to the ideal straight line position, wherein the calculation result is a contour error, and executing S4;
s3, interpolating the curve track into a straight line segment by using a linear spline interpolation method, calculating the straight line by two coordinates with similar positions on the ideal curve, approximately taking the contour error as the distance from the tool point to the straight line segment, and returning to S2 to calculate the contour error;
s4, determining signs of the contour error, wherein the signs are positive and negative respectively when the actual track is positioned on the first side and the second side of the ideal curved surface, and judging through a contour error expression, wherein the contour error expression is as follows:
wherein epsilon is a contour error,
is a normal vector of the ideal location point,
is a vector of ideal to actual location points, the
And said
Are respectively:
wherein (x)0，y0，z0) Is the ideal position of the point, (x ', y ', z ') is the actual position of the point,
the ideal curved surface F (x, y, z) is 0 in (x)0，y0，z0) The normal vector of (a) is,
is the ideal position (x) of the tool nose point0，y0，z0) Distance to the actual position (x ', y ', z ').
2. The method for estimating and visualizing the profile error for multi-axis numerical control machining according to claim 1, wherein the method comprises a profile error visualization method S5: and associating the contour error in the S4 with a display parameter, and performing visual display through a relational graph of the contour error and the display parameter.
3. The method for estimating and visualizing the profile error for multi-axis numerical control machining according to claim 2, wherein the display parameters comprise a travel distance, the profile error is associated with the travel distance of an actual point, different corresponding relationships between the travel distance and the profile error are formed, and a display diagram of the profile error and the travel distance is made.
4. The method for estimating and visualizing the contour error for multi-axis numerical control machining according to claim 2, wherein the display parameters include a multiple, the contour error is multiplied by the multiple to be amplified, the multiplied contour error is added to the position of the ideal track point to serve as an actual track point, and a three-dimensional coordinate graph of the ideal track and the actual track is formed.
5. The method for estimating and visualizing the profile error facing the multi-axis numerical control machining as claimed in claim 2, wherein the display parameters comprise a color spectrum, different colors are used for representing the positive and negative of the profile error, different depths of the colors are used for representing the profile errors with different sizes, and after the three-dimensional coordinates of the actual trajectory are made, a profile error color spectrum display graph is made on the trajectory curve by using different colors.
6. The method for estimating and visualizing the profile error of multi-axis numerical control machining according to claim 3, wherein the relational expression of the travel distance and the profile error is as follows:
wherein s is the travel of the point of the tool tip, v is the moving speed of the point of the tool tip, t is the moving time of the point of the tool tip, and t isnowThe total time of the movement of the tool nose point.
7. The method for estimating and visualizing the contour error for multi-axis NC machining according to claim 4, wherein the actual position of the point after the contour error is amplified is set as (x ', y ', z '):
wherein (x)0，y0，z0) The ideal position of the tool point is n is a multiplying coefficient.
8. The method for estimating and visualizing the profile error of multi-axis numerical control machining according to claim 1, wherein the expression of the profile error in S2 is as follows:
wherein, epsilon is a contour error, A, B, C, D is a coefficient of 0 of a straight line Ax + By + Cz + D, and the actual point position is (x ', y ', z ').
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| CN102591257A (en) * | 2012-02-27 | 2012-07-18 | 山东理工大学 | Parameter curve cutter path oriented numerical control system contour error control method |
| CN107479497A (en) * | 2017-09-11 | 2017-12-15 | 大连理工大学 | A kind of five-axis robot track profile errors two close cycles compensation method |
| CN107544430A (en) * | 2017-09-20 | 2018-01-05 | 华中科技大学 | A kind of profile errors evaluation method of three axis numerically controlled machine |
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| CN102591257A (en) * | 2012-02-27 | 2012-07-18 | 山东理工大学 | Parameter curve cutter path oriented numerical control system contour error control method |
| CN107479497A (en) * | 2017-09-11 | 2017-12-15 | 大连理工大学 | A kind of five-axis robot track profile errors two close cycles compensation method |
| CN107544430A (en) * | 2017-09-20 | 2018-01-05 | 华中科技大学 | A kind of profile errors evaluation method of three axis numerically controlled machine |
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