CN113759830B - Linear path numerical control machining feed speed control method based on equivalent acceleration - Google Patents
Linear path numerical control machining feed speed control method based on equivalent acceleration Download PDFInfo
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Abstract
The invention discloses a linear path numerical control machining feed speed control method based on equivalent acceleration. Numerical control machining is carried out along a linear path, an inflection point on the linear path is used as a path turning point, and a sampling interval is intercepted and sampled to generate an input position sequence by taking the inflection point as a starting point; inputting the input position sequence into a differential equation of a numerical control machining servo system, and solving by using a discrete system digital analysis method to obtain an output position sequence; obtaining an acceleration sequence through second-order difference, and obtaining the equivalent acceleration of a sampling interval through filtering processing; and processing to obtain a feed speed constraint value at the turning point of the path according to the equivalent acceleration and a given upper limit of the normal acceleration, and further constraining the numerical control machining feed speed to realize control. The method has good stability, the obtained constraint value of the feeding speed is more reasonable and stable, and the efficiency and the quality of numerical control machining can be effectively improved.
Description
Technical Field
The invention relates to a feeding speed control method in the field of multi-axis numerical control machining and manufacturing of free-form surfaces, in particular to a feeding speed control method at a corner of a continuous small line segment path.
Background
In the numerical control machining manufacturing, the magnitude of the feeding speed plays a decisive role in the machining efficiency and quality, and too low a speed can increase the machining time, and too high a speed can cause larger profile errors and impact and vibration of a machine tool, so that the machining quality is influenced. The continuous small-line-segment path is widely used for describing a multi-axis numerical control high-speed high-precision machining path, and has the advantages of good universality and simple calculation. But also has the defects that the feeding speed direction has sudden change at the corner of the adjacent line segment, the length of the line segment is shortest and is only a few micrometers, and the like, and the defects bring difficulty to the realization of high-speed and high-precision numerical control machining.
The main method for solving the above problems is to reasonably control the feeding speed at the corner of the path of the continuous small line segments, which has become a necessary and important technology for numerical control machining of free-form surfaces.
Two methods for controlling the feeding speed at the corner of a path of a continuous small line segment are mainly used, namely an angle constraint method and a curvature constraint method.
The angle constraint method firstly obtains the angle of the turning angle, and then substitutes the turning angle into the calculation model to obtain the feed speed constraint value. The angle constraint method has a good effect on a region with a long line segment in a machining path, but has the problem that the obtained feed speed constraint value is too large and unstable for a continuous small line segment path.
The curvature constraint method firstly approximately obtains the curvature radius of the continuous small line segment path, and then obtains the constraint value of the feeding speed according to the curvature radius. The curvature constraint method can obtain better results for continuous small line segment paths with shorter line segments and small line segment length and direction changes, but the feed speed constraint value obtained by the curvature constraint method is not reasonable for continuous small line segment paths with larger length and direction changes and longer line segments.
In other studies, researchers have restricted the feeding speed of a line segment path according to the limitations of acceleration, following error, contour error, cutting force and the like of each axis in numerical control machining; or the line segment path is fitted into a parameter curve firstly, and then the fitted curve is subjected to feeding speed planning, but the stability and the real-time performance of the feeding speed control methods are all to be improved.
Disclosure of Invention
In order to overcome the defects of the existing feed speed control methods, the invention provides a linear path numerical control machining feed speed control method based on equivalent acceleration. The method can be applied to a multi-axis numerical control system, and can be used for restraining the feeding speed at the corners of the continuous small line segment path so as to effectively control the feeding speed of the linear path numerical control machining. The method has good stability, the obtained constraint value of the feeding speed is more reasonable and stable, and the efficiency and the quality of numerical control machining can be effectively improved.
In order to achieve the technical purpose, the feed speed constraint value in numerical control processing is obtained by processing a series of steps such as path position point sampling, discrete processing track point prediction, acceleration filtering processing and the like, and the specific technical scheme is as follows:
the numerical control processing is carried out along a linear path, the linear path is a broken line, a plurality of input interpolation points distributed at intervals exist on the linear path, an inflection point on the linear path is used as a path turning point O, and then:
s1: taking a path turning point O of a speed constraint value to be solved as a starting point, respectively taking a distance along two directions of a linear path, and then jointly forming a sampling interval, and sampling in the sampling interval to generate an input position sequence P;
s2: inputting the input position sequence P into a differential equation of a numerical control machining servo system, and solving by using a discrete system digital analysis method to obtain an output position sequence Q;
s3: carrying out second order difference calculation on the output position sequence Q to obtain an acceleration sequence A corresponding to the output position sequence Q, and carrying out filtering processing on the acceleration sequence A by adopting a digital filter to obtain the equivalent acceleration of a sampling interval
S4: according to equivalent acceleration
And a given upper limit A of normal acceleration n Processing to obtain a feed rate constraint value F at the desired turning point O O By restricting the value F at the feed speed O And (4) controlling the numerical control machining feeding speed in a constrained manner.
The differential equation of the numerical control machining servo system is specifically as follows:
q(i)＝a 0 ·p(i)+a 1 ·p(i-1)+a 2 ·p(i-2)-b 0 ·q(i-1)-b 1 ·q(i-2)
where i denotes the number of sampling points, i =0，1，2，…，a 0 、a 1 、a 2 Values of coefficients representing the input sequence in the difference equation, b 0 、b 1 Expressing the coefficient value of an output sequence in the difference equation, and solving the coefficient value through an observation matrix in the following text; p (i) represents an input coordinate value of a sampling point with a number i, and q (i) represents an output coordinate value of a sampling point with a number i;
and setting the following initial conditions, satisfying the following relationship:
q(-2)＝q(-1)＝p(-2)＝p(-1)＝p(0)
wherein p (0) is an input coordinate value of a sampling point having a sequence number of 0, p (-1) represents an input coordinate value of a sampling point having a sequence number of-1, p (-2) represents an input coordinate value of a sampling point having a sequence number of-2, and values of p (-1) and p (-2) are obtained by adding two sampling points before the first sampling point. q (-1) represents the output coordinate value of the sampling point with the sequence number-1, and q (-2) represents the output coordinate value of the sampling point with the sequence number-2.
When the feed speed constraint value at the turning point O of the path is solved, the problem is converted into the equivalent acceleration of the solution sampling interval
In S4, the feed speed constraint value F at the turning point O of the path is obtained by processing according to the following formula O ：
Wherein, F a The reference instruction feed speed at the turning point O of the path is shown, and the numerical control machining is carried out according to the reference instruction feed speed F a The processing is performed along a linear path.
The numerical control machining servo system is a servo motor of each motion axis of the machine tool.
Compared with the prior art, the invention has the beneficial effects that:
the feeding speed control method is insensitive to the characteristics of the length of a line segment on a path, the size of a corner and the like, so that the feeding speed control method has better stability; the feeding speed of the numerical control machining path obtained by the method is more reasonable and stable, and the efficiency and the quality of multi-axis numerical control machining can be improved.
Drawings
In order to more clearly illustrate the technical solution of the present invention, the drawings used in the specific implementation method will be briefly described below.
FIG. 1 is a flow chart of the main implementation steps of the present invention;
FIG. 2 is a schematic diagram of the main implementation steps of the present invention;
FIG. 3 is a schematic diagram of the three-axis CNC machining servo system functions and control architecture;
FIG. 4 is a schematic diagram of a solving process for an X-axis acceleration sequence;
FIG. 5 is a schematic diagram of a Hanning window function;
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the following describes the implementation and performance analysis of the present invention in detail with reference to the accompanying drawings and examples.
The method adopts methods such as path position point sampling, discrete processing track point prediction, acceleration filtering processing and the like to calculate the feed speed constraint value in the numerical control processing process, and refer to fig. 1 and fig. 2.
The following three-axis numerical control machining of a continuous small line segment path is taken as an example to sequentially perform detailed implementation description on four steps:
firstly, because the processing processes of track point prediction, acceleration filtering and the like are performed based on discrete digital signals, an original line segment path needs to be sampled to generate a discrete input position sequence P.
Firstly, analyzing a numerical control G code file, sequentially recording segment paths therein, and respectively traversing the segment paths in a forward direction and a reverse direction by taking a path turning point O of a current speed constraint value to be solved as a starting point until the accumulated traversal distances in the two directions reach a target value. And finally, taking the two-way traversed line segment path as a sampling interval, and taking N sampling points for the two-way traversed line segment path, thereby generating an input position sequence P as follows:
P＝{P x ，P y ，P z }＝{(p x (i)，p y (i)，p z (i))|i＝0，…，N-1}
wherein, P x Indicating the sequence of input positions of the X-axis, P y Indicating the sequence of input positions of the Y axis, P z Indicating the input position sequence of the Z-axis, i indicating the number of sample points, p x (i) X-axis input coordinate values, p, representing sample points numbered i y (i) Input coordinate value of Y-axis, p, representing sampling points of serial number i z (i) And inputting a coordinate value of a Z axis of the sampling point with the serial number i, wherein N is the total number of the sampling points, and the coordinate value is obtained by solving the length of the window function in the following text.
And step two, because the position output of the servo system lags behind the instruction input, the actual processing track and the original line section path have difference, and the corresponding feeding speed and acceleration have certain deviation. Therefore, the method of discrete system digital analysis can be used for predicting the 'actual processing track' of the original line segment path after the original line segment path is acted by the servo system. Performing equivalent acceleration based on predicted position information
The obtained feed speed constraint value is more accurate to output.
The function and control structure of the three-axis NC machining servo system is shown in FIG. 3, H x (s)，H y (s)，H z (s) is a transfer function of X-axis, Y-axis, Z-axis, which can be approximated as a second order constant discrete system. Taking X-axis as an example, let its input sequence P x Is { p x (i) I =0, \ 8230;, N-1}, corresponding output sequence Q x Is { q x (i) I =0, \ 8230;, N-1}, the differential equation of the corresponding numerical control machining servo system can be expressed as:
q x (i)＝a 0 ·p x (i)+a 1 ·p x (i-1)+a 2 ·p x (i-2)-b 0 ·q x (i-1)-b 1 ·q x (i-2)
where i denotes the number of the sample point, i =0,1,2, ..., a 0 、a 1 、a 2 Coefficient value representing input sequence in difference equation, b 0 、b 1 Expressing the coefficient value of the output sequence in the difference equation, and solving the coefficient value through an observation matrix in the following text; q. q.s x (i) X-axis output coordinate values, q, representing sample points of sequence number i x (i-1) the X-axis of the sampling point with the sequence number of i-1 outputs a coordinate value, and so on.
When i =0, q x (-2)、q x (-1)、p x (-2)、p x (-1)、p x (0) Satisfying q as a boundary condition of the difference equation x (-2)＝q x (-1)＝p x (-2)＝p x (-1)＝p x (0) Wherein p is x (0) The coordinate value is input for the X axis with the number 0.
Interpolation period T of numerical control system s For a sampling period, collecting N groups of samples from input and output position points of the sampling period to obtain an output vector q:
observation matrix phi of
The coefficient vector r is
r＝[b 0 b 1 a 0 a 1 a 2 ] T ＝(Φ t Φ) -1 Φ T
The input position sequence P of the X axis x Substituting into the differential equation corresponding to the three-axis numerical control machining servo system to obtain the output position sequence Q of the X axis x . Similarly, the output position sequence Q of the Y axis and the Z axis can be obtained y 、Q z Therefore, an output position sequence Q which is output by the three-axis numerical control machining servo system and is closer to the real situation is obtained as follows:
Q＝{Q x ，Q y ，Q z }＝{(q x (i)，q y (i)，q z (i))|i＝0，…，N-1}
wherein q is x (i) X-axis output coordinate value, q, representing sample point of sequence number i y (i) Output coordinate value of Y axis representing sampling point with serial number i, q z (i) The Z-axis representing the sampling point with index i outputs a coordinate value.
Thirdly, based on the obtained output position sequence, carrying out equivalent acceleration
And (4) solving. As shown in fig. 4, taking the X-axis as an example, the X-axis component Q of Q is considered x Calculating the difference to obtain the speed sequence V of the X axis x Comprises the following steps:
wherein M is 1 A coefficient matrix representing an equation;
further, velocity sequence V for said X-axis x The difference calculation is carried out to obtain the acceleration sequence A of the X axis x Comprises the following steps:
similarly, the acceleration sequence A of the Y axis and the Z axis can be obtained y 、A z So as to obtain an acceleration sequence A corresponding to the output position sequence Q:
A＝{A x ，A y ，A z }＝{(a x (i)，a y (i)，a z (i))|i＝0，…，N-1}
wherein, a x (i) X-axis acceleration values, a, representing sampling points of sequence number i y (i) Y-axis acceleration values, alpha, representing sampling points of sequence number i z (i) And represents the Z-axis acceleration value of the sample point with the index i.
In finding the X-axisAcceleration sequence A of x Then, in order to eliminate the high frequency acceleration signal therein and reduce the influence of the error introduced by the difference calculation on the output result, the FIR digital low pass filter based on the Hanning window shown in fig. 5 is used to perform the filtering process shown in the following formula, thereby obtaining the equivalent acceleration
Is greater than or equal to the X-axis component->
Where h (i) is the impulse response of the FIR low-pass filter, h d (i) For the unit impulse response of an ideal low-pass filter, w (i) is an expression of a Hanning window function, i is an arbitrary integer, and ω is c To the cut-off frequency, τ is the group delay,
and N is the length of the window function, namely the number N of the sampling points.
The value of N can be obtained by the transition bandwidth formula of the window function:
wherein f is s ，f pass ，f stop Respectively the sampling frequency, the passband cut-off frequency and the stopband start frequency of the FIR low-pass filter.
And finally, carrying out discrete Fourier transform on the filter to obtain an amplitude-frequency response value delta of the filter so as to verify whether the filtering performance of the filter meets the design requirement. E.g. delta is greater than the stop band of the systemAttenuation delta stop Then the filter meets the design requirements; otherwise it is necessary to increase the length N of the window function or to replace the window function to redesign the filter.
In conclusion, a filter processing formula of the X-axis equivalent acceleration at the path turning point O is obtained:
the acceleration sequence A of the X axis x Substituting the above formula to obtain the equivalent acceleration of the X axis
Comprises the following steps:
recording the coefficients in the above formula
Is m 2 。
Similarly, the equivalent accelerations of the Y and Z axes at the point O are obtained as follows:
thus, the resultant acceleration at point O is found to be:
the predicted value of the acceleration at the turning point O of the path to be obtained, that is, the equivalent acceleration corresponding to the sampling interval containing the point O
And step four, solving the feed speed constraint value at the turning point O of the path.
In numerical control machining of a continuous small-line-segment path, a reference command feed speed F in the vicinity of a point O a Is a constant value, so its tangential acceleration is 0, its equivalent acceleration
I.e. normal acceleration, then:
in the formula, ρ v Is the equivalent radius of curvature of the path of the continuous small line segments.
And set at another feed speed F O Numerically controlling and processing the continuous small line segment path to make its normal acceleration just equal to its maximum allowable value A n Then, there are:
wherein, F O I.e. the constraint value of the feeding speed at the turning point O of the path, which is:
the constraint speed of each corner on the continuous small line segment path can be obtained according to the formula, so that the numerical control machining feeding speed of the continuous small line segment path can be reasonably and effectively controlled. The speed control method is matched with the traditional look-ahead and interpolation method for use, so that the three-axis numerical control machining of the continuous small line segment path can be realized.
The invention innovatively combines the position point sampling method, the discrete system digital analysis method, the acceleration filtering processing method and other methods for use, and can effectively and reasonably calculate the feed speed constraint value in the numerical control machining process. And because the invention has stronger universality in principle, the speed control method can be widely applied to numerical control processing of various linear paths. The invention has been carried out multiple times of simulation verification and test verification, which proves the feasibility and effectiveness of the method of the invention and realizes the purpose of the invention: the speed control algorithm runs stably, and the feeding speed is reasonable in the numerical control machining process. Compared with the conventional angular constraint method and other speed control methods, the method disclosed by the invention can improve the processing quality of the surface of the workpiece, can also improve the processing efficiency and shorten the processing time, and is favorable for promoting the application of the continuous small line segment path in high-speed and high-precision numerical control processing.
The above content is a specific embodiment of the present invention for three-axis numerical control machining, and it should not be understood that the specific implementation of the present invention is limited to this embodiment, and the present invention is also applicable to four-axis, five-axis, and other multi-axis numerical control machining scenarios. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of the invention, and such equivalent modifications or substitutions are included in the scope of the present application.
Claims (2)
1. A linear path numerical control machining feed speed control method based on equivalent acceleration is characterized by comprising the following steps: the method comprises the following steps:
the numerical control processing is carried out along a linear path, the linear path is a broken line, an inflection point on the linear path is used as a path turning point O, and then:
s1: taking a path turning point O of a speed constraint value to be solved as a starting point, respectively taking a distance along two directions of a linear path, and then jointly forming a sampling interval, and sampling in the sampling interval to generate an input position sequence P;
s2: inputting the input position sequence P into a differential equation of a numerical control machining servo system, and solving by using a discrete system digital analysis method to obtain an output position sequence Q;
s3: carrying out second order difference calculation on the output position sequence Q to obtain an acceleration sequence A corresponding to the output position sequence Q, and carrying out filtering processing on the acceleration sequence A by adopting a digital filter to obtain the equivalent acceleration of a sampling interval
The step S3 is specifically: first, the X-axis component Q in the output position sequence Q is corrected x Carrying out difference calculation to obtain the speed sequence V of the X axis x Comprises the following steps:
wherein M is 1 A coefficient matrix representing an equation;
velocity sequence V for the X-axis x The difference calculation is carried out to obtain the acceleration sequence A of the X axis x Comprises the following steps:
then, the acceleration sequence A of the Y axis and the Z axis is obtained y 、A z So as to obtain an acceleration sequence A corresponding to the output position sequence Q:
A＝{A x ,A y ,A z }＝{(a x (i),a y (i),a z (i))|i＝0,…,N-1}
wherein, a x (i) X-axis acceleration values, a, representing sampling points of sequence number i y (i) Y-axis acceleration values, a, representing sampling points of sequence number i z (i) A Z-axis acceleration value representing a sampling point with a sequence number i;
determining the acceleration sequence A of the X axis ( Then, the equivalent acceleration is obtained by performing a filtering process shown in the following equation using an FIR digital low-pass filter of a Hanning window
X-axis component +>
Where h (i) is the impulse response of the FIR low-pass filter, h d (i) For the unit impulse response of an ideal low-pass filter, w (i) is an expression of a Hanning window function, i is an arbitrary integer, and ω is c To the cut-off frequency, τ is the group delay,
n is the length of the window function, namely the number N of the sampling points;
the value of N is obtained by the transition bandwidth formula of the window function:
wherein f is s ,f pass ,f stop Respectively the sampling frequency, the passband cut-off frequency and the stopband starting frequency of the FIR low-pass filter;
finally, carrying out discrete Fourier transform on the filter to obtain an amplitude-frequency response value delta of the filter so as to verify whether the filtering performance of the filter meets the design requirement; if the value of delta is greater than the stop band attenuation delta of the system stop Then the filter meets the design requirements; otherwise, the length N of the window function needs to be increased or the window function needs to be replaced to redesign the filter;
obtaining a filtering processing formula of the X-axis equivalent acceleration at the path turning point O:
the acceleration sequence A of the X axis x Substituting the above formula to obtain the equivalent acceleration of the X axis
Comprises the following steps:
recording the coefficients in the above formula
Is m 2 ；
The equivalent accelerations of the Y and Z axes at the point O are respectively obtained as:
the resulting acceleration at point O is finally obtained as:
the predicted value of the acceleration at the turning point O of the path to be obtained, that is, the equivalent acceleration corresponding to the sampling interval containing the point O
/>
S4: according to equivalent acceleration
And a given upper limit A of normal acceleration n Processing to obtain a feed rate constraint value F at the found path turning point O O By restricting the value F at the feed speed O Controlling the numerical control machining feeding speed in a constrained manner;
in the step S4, the feed rate constraint value F at the turning point O of the path is obtained by processing according to the following formula O ：
Wherein, F a Indicating the reference command feed speed at the turning point O of the path.
2. The linear path numerical control machining feed speed control method based on the equivalent acceleration as claimed in claim 1, characterized in that: the differential equation of the numerical control machining servo system is specifically as follows:
q(i)＝a 0 ·p(i)+a 1 ·p(i-1)+a 2 ·p(i-2)-b 0 ·q(i-1)-b 1 ·q(i-2)
where i denotes the number of the sampling points, i =0,1,2, \ 8230;, a 0 、a 1 、a C Values of coefficients representing the input sequence in the difference equation, b 0 、b 1 Expressing the coefficient value of the output sequence in the difference equation, and solving the coefficient value through an observation matrix in the following text; p (i) represents an input coordinate value of a sampling point with a number i, and q (i) represents an output coordinate value of a sampling point with a number i;
interpolation period T of numerical control system s For a sampling period, collecting N groups of samples from input and output position points of the sampling period to obtain an output vector q:
the observation matrix phi is
Coefficient vector r is r = [ b = 0 b 1 a 0 a 1 a C ] T ＝(Φ T Φ) -1 Φ T
And setting the following initial conditions, satisfying the following relationship: q (-2) = q (-1) = p (-2) = p (-1) = p (0).
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| CN113759830B (en) * | 2021-09-02 | 2023-04-18 | 浙江大学 | Linear path numerical control machining feed speed control method based on equivalent acceleration |
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| CN101211177A (en) * | 2006-12-29 | 2008-07-02 | 中国科学院沈阳计算技术研究所有限公司 | Filter technique based numerical control system acceleration and deceleration control method |
| TWI688844B (en) * | 2018-12-19 | 2020-03-21 | 國立臺北科技大學 | Control device and method for controlling machine |
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