CN112015142A - NURBS-based small segment processing method - Google Patents
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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 small segment processing method based on NURBS, which relates to the technical field of automatic control, and solves the problems of complex processing and frequent start and stop in processing due to large number of small segments by carrying out NURBS curve fitting on the small segments by adopting a global approximation algorithm, filtering and removing redundant points in data points and carrying out characteristic segmentation, thereby improving the processing speed; and performing speed planning on the fitted NURBS curve by adopting an S-curve-based acceleration and deceleration algorithm, performing interpolation operation by using a Taylor algorithm, processing the calculated feeding speed, and replacing the speed at the initial moment by using the speed corresponding to the intermediate moment in each interpolation period, so that the speed error after dispersion is reduced, the motion speed of each axis is smoothed, and the interpolation precision is improved.
Description
Technical Field
The invention relates to the technical field of automatic control, in particular to a small line segment processing method based on NURBS.
Background
Most of tool tracks of numerical control machining are free curves and have complex shapes, in the traditional machining mode, a large number of tiny segment track points are obtained through CAM software processing, then a linear arc instruction is called for machining (for example, a speed curve planning method of a small segment suitable for a numerical control device tool, the publication number is CN108303952A), but the problems of low machining efficiency, poor machining quality and the like are caused by the fact that a machine tool needs to be started and stopped frequently and gets out of bed to shake. Because the non-uniform ratio B-spline curve can accurately represent a free curve or a curved surface, the part processing quality and efficiency can be greatly improved (such as a spatial free curve fitting method based on the NURBS, the publication number is CN 106959666A; such as a numerical control system, a device with a storage function and a NURBS curve interpolation method, the publication number is CN 109416529A). The small line segments have a large number of data points, but are not distinguished, some line segments mixed in the middle do not need to be fitted, and the speed error can be increased after the fitting; the direct use of the NURBS curve interpolated speed alone may increase the discretized speed error.
In view of the above, a new technical solution is urgently needed to solve the above problems.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a small segment processing method based on NURBS, which carries out NURBS curve fitting on small segments by adopting a global approximation algorithm, filters and removes redundant points in data points, carries out characteristic segmentation, solves the problems of complex processing and frequent start and stop during processing due to large quantity of small segments, and further improves the processing speed; and performing speed planning on the fitted NURBS curve by adopting an S-curve-based acceleration and deceleration algorithm, performing interpolation operation by using a Taylor algorithm, processing the calculated feeding speed, and replacing the speed at the initial moment by using the speed corresponding to the intermediate moment in each interpolation period, so that the speed error after dispersion is reduced, the motion speed of each axis is smoothed, and the interpolation precision is improved.
In order to achieve the above object, the present invention provides the following technical solutions:
a small line segment processing method based on NURBS comprises the following steps:
the method comprises the following steps of (1) obtaining position information data of small line segment points, and obtaining micro line segments through characteristic segmentation;
step (2) carrying out NURBS curve fitting on the tiny line segments in the step (1) by adopting a global approximation algorithm to obtain a NURBS curve;
segmenting the NURBS curve through a curvature maximum point, and calculating a speed constraint value corresponding to the curvature maximum point;
step (4) solving the arc length of each segment of the NURBS curve in the step (3) through a self-adaptive Simpson algorithm, and carrying out prospective verification on the speed constraint value;
step (5) obtaining a continuous curve of the feeding speed through S curve acceleration and deceleration planning according to the arc length in the step (4) and the speed constraint value after the forward-looking verification; and replacing the initial speed with the speed corresponding to the intermediate time in each interpolation period to obtain the speed of a single interpolation period, continuously calculating the position of the next interpolation point by using a Taylor algorithm, and continuing the next step.
Step (6) judging whether the curve of the section is the last interpolation section; if not, returning to the step (5) to operate the next section of curve; if yes, the process is ended.
Preferably, the step (1) is specifically: acquiring position information data of small line segments, filtering and removing redundant points in data points, carrying out feature segmentation, firstly setting a maximum threshold value of angle change between adjacent line segments, classifying the maximum threshold value, and dividing the small line segments into two types: the line fitting method comprises a long straight line segment and a curve to be fitted, wherein the curve to be fitted is a tiny line segment.
Preferably, the step (2) is specifically: set the tiny line segment data point to Q0，Q1，…QmThe weight value omegaiFixed at 1, the parameter values of the data points are calculated using a chord length parameterization method
PiIs a control point, N is the number of control points, m > N, Ni，p(u) is a p-th order B-spline basis function, then the expression of the NURBS curve is:
the chord length d of the discrete points can be calculated by using chord length parameterization, and the parameter value can be calculated
From the parameter values, a node vector u is determinedi(ii) a The data points are approximated under the least square meaning by a least square curve approximation method, each control point value P can be solved, and if the tool position deviation and the bow height error do not meet the requirements, the fitting curve needs to be adjusted; after the control point is obtained, whether the tool position deviation is smaller than a set value or not needs to be judged, if not, the control point needs to be added or the node vector needs to be obtained again until the requirement is met, whether the bow height error is smaller than the set value or not needs to be judged after the tool position deviation meets the requirement, if not, the node vector needs to be inserted to reduce the bow height error, and finally, a NURBS curve fitted by the micro-segment points can be obtained.
Preferably, the step (3) is specifically: calculating parameter values
Curvature k (u) ofi) Calculating the parameter value at the maximum value of the curvature according to the curvature, and segmenting at the maximum value to obtain a node vector Uk_i，Uk_i+1]K denotes the kth NURBS curve and i denotes the ith segment of the kth NURBS curve.
Advantageous effects
According to the small segment processing method based on the NURBS, provided by the invention, the small segment is subjected to NURBS curve fitting by adopting a global approximation algorithm, redundant points in data points are filtered and removed, and characteristic segmentation is carried out, so that the problems of complex processing and frequent start and stop during processing due to large number of small segments are solved, and the smoothness and the processing speed of a speed curve are further improved; the fitted NURBS curve is subjected to speed planning by adopting an S-curve-based acceleration and deceleration algorithm, interpolation operation is carried out by utilizing a Taylor algorithm, the calculated feeding speed is processed, the speed corresponding to the middle moment in each interpolation period is used for replacing the speed at the initial moment, the discrete speed error is reduced, the movement speed of each axis is smoothed, and the interpolation precision is effectively improved.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the structures shown in the drawings without creative efforts.
FIG. 1 is a flow chart of a NURBS-based small segment processing method according to the present invention;
FIG. 2 is a NURBS curve fitting flow chart of a NURBS-based small segment processing method according to the present invention;
FIG. 3 is a NURBS curve fitting interpolation simulation diagram of a NURBS-based small segment processing method according to the present invention;
fig. 4 is a speed-time simulation diagram of a NURBS-based small segment processing method according to the present invention.
Detailed Description
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 only a part of the embodiments of the present invention, and not all of the embodiments. 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.
As shown in fig. 1, a method for processing small line segments based on NURBS includes the following steps:
the method comprises the following steps of (1) obtaining position information data of small line segment points, and obtaining micro line segments through characteristic segmentation;
step (2) carrying out NURBS curve fitting on the tiny line segments in the step (1) by adopting a global approximation algorithm to obtain a NURBS curve;
segmenting the NURBS curve through a curvature maximum point, and calculating a speed constraint value corresponding to the curvature maximum point;
step (4) solving the arc length of each segment of the NURBS curve in the step (3) through a self-adaptive Simpson algorithm, and carrying out prospective verification on the speed constraint value;
step (5) obtaining a continuous curve of the feeding speed through S curve acceleration and deceleration planning; and replacing the initial speed with the speed corresponding to the intermediate time in each interpolation period to obtain the speed of a single interpolation period, continuously calculating the position of the next interpolation point by using a Taylor algorithm, and continuing the next step.
Step (6) judging whether the curve of the section is the last interpolation section; if not, returning to the step (5) to operate the next section of curve; if yes, the process is ended.
Specifically, the step (1) specifically comprises: acquiring position information data of small segment points, filtering and removing data redundant points which do not need NURBS fitting in the data points, carrying out feature segmentation, firstly setting a maximum threshold value of angle change between adjacent segments, classifying the maximum threshold value, and dividing the small segment points into two types: the scheme does not process points of the long straight line segment and only fits the points NURBS of the tiny line segment.
As shown in fig. 2, the NURBS curve fitting process in step (2) specifically includes: set the tiny line segment data point to Q0，Q1，…QmAfter obtaining, the weight omegaiFixed at 1, the parameter values of the data points are calculated using a chord length parameterization method
PiIs a control point, N is the number of control points, m > N, Ni，p(u) is a p-th order B-spline basis function, then the expression of the NURBS curve is:
the chord length d of the discrete points can be calculated by using chord length parameterization, and the parameter value can be calculated
From the parameter values, a node vector u is determinedi(ii) a The data points are approximated under the least square meaning by a least square curve approximation method, each control point value P can be solved, and if the tool position deviation and the bow height error do not meet the requirements, the fitting curve needs to be adjusted; after the control point is obtained, whether the tool position deviation is smaller than a set value or not needs to be judged, if not, the control point needs to be added or the node vector needs to be obtained again until the requirement is met, whether the bow height error is smaller than the set value or not needs to be judged after the tool position deviation meets the requirement, if not, the node vector needs to be inserted to reduce the bow height error, and finally, a NURBS curve fitted by the micro-segment points can be obtained.
Calculating parameter values
Curvature k (u) ofi) Calculating the parameter value at the maximum value of the curvature according to the curvature, and segmenting at the maximum value to obtain a node vector Uk_i，Uk_i+1]K denotes the kth NURBS curve and i denotes the ith segment of the kth NURBS curve.
Solving the arc length of each section of curve to be l by utilizing an adaptive Simpson algorithmk_iThe speed of the end point of each section of curve is limited by the bow height error, the normal speed, the normal acceleration and the maximum feeding speed input by a user, and the maximum allowable speed limited by the path length of the front section and the rear section is determined by utilizing bidirectional scanning; to this end, the curve segment and endpoint velocities have all been determined.
In the acceleration and deceleration and interpolation module, only S-shaped acceleration and deceleration planning and interpolation are needed to be carried out on the current section, and due to integral multiple influence of the interpolation period of the current section, the previous section can be compensated by the path of the next section, so that the speed and acceleration continuity is approximately maintained in the transition section, and a continuous speed curve can be obtained.
In order to reduce the speed error after dispersion, the speed corresponding to the intermediate time in the interpolation period is used for the feeding speed corresponding to the interpolation point, then the parameter value corresponding to the next interpolation point can be calculated by the Taylor expansion formula, and the next interpolation position point (x) can be calculated by the NURBS curve parameter valuei+1，yi+1，zi+1)。
As shown in fig. 3 and 4, after the interpolation of the current segment is completed, it is determined whether the current segment is the last segment of the kth curve; if not, continuing the acceleration and deceleration planning of the next section of S curve; if yes, the curve interpolation of the (k + 1) th curve is carried out until the interpolation is completed.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.
Claims (4)
1. A small line segment processing method based on NURBS is characterized in that: comprises that
The method comprises the following steps of (1) obtaining position information data of small line segment points, and obtaining micro line segments through characteristic segmentation;
step (2) carrying out NURBS curve fitting on the tiny line segments in the step (1) by adopting a global approximation algorithm to obtain a NURBS curve;
segmenting the NURBS curve through a curvature maximum point, and calculating a speed constraint value corresponding to the curvature maximum point;
step (4) solving the arc length of each segment of the NURBS curve in the step (3) through a self-adaptive Simpson algorithm, and carrying out prospective verification on the speed constraint value;
step (5) obtaining a continuous curve of the feeding speed through S curve acceleration and deceleration planning; and replacing the initial speed with the speed corresponding to the intermediate time in each interpolation period to obtain the speed of a single interpolation period, continuously calculating the position of the next interpolation point by using a Taylor algorithm, and continuing the next step.
Step (6) judging whether the curve of the section is the last interpolation section; if not, returning to the step (5) to operate the next section of curve; if yes, the process is ended.
2. The NURBS-based small segment processing method according to claim 1, wherein: the step (1) is specifically as follows: acquiring position information data of small line segments, filtering and removing redundant points in data points, carrying out feature segmentation, firstly setting a maximum threshold value of angle change between adjacent line segments, classifying the maximum threshold value, and dividing the small line segments into two types: the line fitting method comprises a long straight line segment and a curve to be fitted, wherein the curve to be fitted is a tiny line segment.
3. The NURBS-based small segment processing method according to claim 1, wherein: the step (2) is specifically as follows: set the tiny line segment data point to Q0，Q1，…QmThe weight value omegaiFixed at 1, the parameter values of the data points are calculated using a chord length parameterization method
PiIs a control point, N is the number of control points, m > N, Ni，p(u) is a p-th order B-spline basis function, then the expression of the NURBS curve is:
the chord length d of the discrete points can be calculated by using chord length parameterization, and the parameter value can be calculated
From the parameter values, a node vector u is determinedi(ii) a The data points are approximated by least square curve approximation method in the least square sense, and each control point value P can be obtained if the tool position deviation and bow height error are not equalIf the requirements are met, the fitting curve needs to be adjusted; after the control point is obtained, whether the tool position deviation is smaller than a set value or not needs to be judged, if not, the control point needs to be added or the node vector needs to be obtained again until the requirement is met, whether the bow height error is smaller than the set value or not needs to be judged after the tool position deviation meets the requirement, if not, the node vector needs to be inserted to reduce the bow height error, and finally, a NURBS curve fitted by the micro-segment points can be obtained.
4. The NURBS-based small segment processing method according to claim 1, wherein: the step (3) is specifically as follows: calculating parameter values
Curvature k (u) ofi) Calculating the parameter value at the maximum value of the curvature according to the curvature, and segmenting at the maximum value to obtain a node vector Uk_i，Uk_i+1]K denotes the kth NURBS curve and i denotes the ith segment of the kth NURBS curve.
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| CN117270455B (en) * | 2023-11-20 | 2024-03-15 | 成都飞机工业（集团）有限责任公司 | Digital filtering-based groove cavity milling tool path optimization method |
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