CN113759830B - Linear path numerical control machining feed speed control method based on equivalent acceleration - Google Patents

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

Feed speed control method for linear path CNC machining based on equivalent acceleration

Technical Field

The invention relates to a feed speed control method in the field of multi-axis numerical control machining of free-form surfaces, and in particular to a feed speed control method at a corner of a continuous small line segment path.

Background Art

In CNC machining, the feed speed plays a decisive role in machining efficiency and quality. If the speed is too low, it will increase the machining time, and if it is too high, it will cause large contour errors and shock and vibration of the machine tool, affecting the machining quality. Continuous small line segment paths are widely used to describe multi-axis CNC high-speed and high-precision machining paths, with the advantages of good versatility and simple calculation. However, there are also disadvantages such as sudden changes in the feed speed direction at the corners of adjacent line segments and the shortest line segment length of only a few microns. These disadvantages have brought difficulties to the realization of high-speed and high-precision CNC machining.

The most important way to solve the above problems is to reasonably control the feed speed at the corners of the continuous small line segment path, which has become a necessary and important technology for free-form surface CNC machining.

There are two main methods for controlling the feed speed at the corners of continuous small line segment paths, namely the angle constraint method and the curvature constraint method.

The angle constraint method first obtains the angle of the corner, and then substitutes it into the calculation model to obtain the feed rate constraint value. The angle constraint method has a good effect on the area with long line segments in the processing path, but for the continuous small line segment path, the feed rate constraint value obtained is too large and unstable.

The curvature constraint method first approximates the curvature radius of the continuous small line segment path, and then obtains the feed speed constraint value based on the curvature radius. The curvature constraint method can achieve good results for continuous small line segment paths with short segments and small changes in segment length and direction, but for continuous small line segment paths with large changes in length and direction and containing long segments, the feed speed constraint value obtained by the curvature constraint method is not reasonable.

In some other studies, scholars constrained the feed speed of the line segment path according to the limitations of each axis acceleration, following error, contour error and cutting force in CNC machining; or first fit the line segment path into a parametric curve, and then planned the feed speed for the fitting curve, but the stability and real-time performance of these feed speed control methods need to be improved.

Summary of the invention

In order to overcome the shortcomings of some existing feed speed control methods mentioned above, the present invention provides a linear path CNC machining feed speed control method based on equivalent acceleration. It can be applied to a multi-axis CNC system to constrain the feed speed at the corner of a continuous small line segment path to achieve effective control of the linear path CNC machining feed speed. The method of the present invention has good stability, and the obtained feed speed constraint value is more reasonable and stable, which can effectively improve the efficiency and quality of CNC machining.

In order to achieve the above technical objectives, the present invention processes the feed speed constraint value during CNC machining through a series of steps such as path position point sampling, discrete machining trajectory point prediction and acceleration filtering processing. The specific technical scheme is as follows:

CNC machining is performed along a linear path. The linear path is a broken line. There are many input interpolation points distributed at intervals on the linear path. The inflection point on the linear path is used as the path turning point O. Then:

S1: Starting from the turning point O of the path where the speed constraint value is to be determined, a distance is taken in each direction along the linear path to form a sampling interval, and sampling is performed in the sampling interval to generate an input position sequence P;

S2: Input the input position sequence P into the differential equation of the CNC machining servo system, and use the discrete system digital analysis method to solve it to obtain the output position sequence Q;

S3: Perform second-order difference calculation on the output position sequence Q to obtain the acceleration sequence A corresponding to the output position sequence Q, and use a digital filter to filter the acceleration sequence A to obtain the equivalent acceleration of the sampling interval.

和给定的法向加速度上限A_n，处理获得所求路径转折点O处的进给速度约束值F_O，以进给速度约束值F_O对数控加工进给速度进行约束实现控制。S4: According to the equivalent acceleration

and the given upper limit of normal acceleration _An , the feed speed constraint value F _O at the turning point O of the desired path is obtained, and the feed speed constraint value F _O is used to constrain the feed speed of the numerical control machining to realize control.

The differential equation of the numerical control machining servo system is specifically:

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)

Wherein, i represents the serial number of the sampling point, i=0, 1, 2, ..., _a0 , _a1 , _a2 represent the coefficient values of the input sequence in the difference equation, _b0 , _b1 represent the coefficient values of the output sequence in the difference equation, which will be obtained through the observation matrix later; p(i) represents the input coordinate value of the sampling point with serial number i, and q(i) represents the output coordinate value of the sampling point with serial number i;

And set the following initial conditions to satisfy the following relationship:

q(-2)＝q(-1)＝p(-2)＝p(-1)＝p(0)

Among them, p(0) is the input coordinate value of the sampling point with sequence number 0, p(-1) is the input coordinate value of the sampling point with sequence number -1, and p(-2) is the input coordinate value of the sampling point with sequence number -2. The values of p(-1) and p(-2) are obtained by adding two sampling points before the first sampling point. q(-1) is the output coordinate value of the sampling point with sequence number -1, and q(-2) is the output coordinate value of the sampling point with sequence number -2.

When solving the feeding speed constraint value at the turning point O of the path, the present invention converts the problem into solving the equivalent acceleration of the sampling interval.

In S4, the feed speed constraint value F _O at the path turning point O is obtained according to the following formula:

Wherein, _Fa represents the reference command feed speed at the turning point O of the path, and the CNC machining is performed along the linear path according to the reference command feed speed _Fa .

The numerical control machining servo system is specifically a servo motor for each motion axis of the machine tool.

Compared with the prior art, the present invention has the following beneficial effects:

The feed speed control method of the present invention is insensitive to characteristics such as the length of the line segment on the path and the size of the corner, so it has better stability; the feed speed of the CNC machining path obtained by this method is more reasonable and stable, and can improve the efficiency and quality of multi-axis CNC machining.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to more clearly illustrate the technical solution of the present invention, the following briefly introduces the drawings used in the specific implementation method.

FIG1 is a flow chart of the main implementation steps of the present invention;

FIG2 is a schematic diagram of the main implementation steps of the present invention;

FIG3 is a schematic diagram of the function and control structure of a three-axis CNC machining servo system;

FIG4 is a schematic diagram of the solution process of the X-axis acceleration sequence;

FIG5 is a schematic diagram of a Hanning window function;

DETAILED DESCRIPTION

In order to make the purpose, technical solutions and advantages of the present invention more clear, the implementation process and performance analysis of the present invention are further described in detail below in conjunction with the accompanying drawings and embodiments.

The present invention adopts path position point sampling, discrete machining trajectory point prediction and acceleration filtering processing methods to calculate the feed speed constraint value in the numerical control machining process, see Figures 1 and 2.

The following takes the three-axis CNC machining of continuous small line segment paths as an example to explain the implementation of the four steps in detail:

Step 1: Since the processing processes such as machining trajectory point prediction and acceleration filtering of the present invention are all based on discrete digital signals, it is necessary to first sample the original line segment path to generate a discrete input position sequence P.

First, parse the CNC G code file and record the line segment path in turn. Then, take the turning point O of the path where the current speed constraint value is to be calculated as the starting point, and traverse the line segment path in the forward and reverse directions respectively until the cumulative traversal distance in both directions reaches the target value. Finally, take the line segment path traversed in both directions as the sampling interval, take N sampling points, and generate the 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}

Among them, _Px represents the input position sequence of the X-axis, _Py represents the input position sequence of the Y-axis, _Pz represents the input position sequence of the Z-axis, i represents the sequence number of the sampling point, _px (i) represents the X-axis input coordinate value of the sampling point with sequence number i, _py (i) represents the Y-axis input coordinate value of the sampling point with sequence number i, _pz (i) represents the Z-axis input coordinate value of the sampling point with sequence number i, and N is the total number of sampling points, which will be obtained by solving the length of the window function later.

的求解，输出求得的进给速度约束值将更加准确。Step 2: Since the position output of the servo system will lag behind the command input, there will be a difference between the actual processing trajectory and the original line segment path, resulting in a certain deviation in the corresponding feed speed and acceleration. Therefore, the discrete system digital analysis method can be used to predict the "actual processing trajectory" of the original line segment path after the servo system is applied. Equivalent acceleration is calculated based on the predicted position information.

The solution of the feed rate constraint will be more accurate.

The function and control structure of the three-axis CNC machining servo system are shown in Figure 3. _Hx (s), _Hy (s), and _Hz (s) are the transfer functions of the X-axis, Y-axis, and Z-axis, which can be approximated as a second-order steady-state discrete system. Taking the X-axis as an example, assuming that its input sequence _Px is { _px (i)|i＝0, ..., N-1}, and the corresponding output sequence _Qx is { _qx (i)|i＝0, ..., N-1}, the differential equation of the corresponding CNC 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)

Wherein, i represents the serial number of the sampling point, i=0, 1, 2,…, _a0 , _a1 , _a2 represent the coefficient values of the input sequence in the difference equation, _b0 , _b1 represent the coefficient values of the output sequence in the difference equation, which will be obtained through the observation matrix later; _qx (i) represents the X-axis output coordinate value of the sampling point with serial number i, _qx (i-1) represents the X-axis output coordinate value of the sampling point with serial number i-1, and so on.

When i=0, _qx (-2), _qx (-1), _px (-2), _px (-1), and _px (0) are the boundary conditions of the difference equation, satisfying _qx (-2)= _qx (-1)= _px (-2)= _px (-1)= _px (0), where _px (0) is the X-axis input coordinate value with serial number 0.

Taking the interpolation period _Ts of the numerical control system as the sampling period, N groups of samples are collected from the position points of its input and output, and its output vector q is obtained as:

The observation matrix Φ is

The coefficient vector r is

r＝[b ₀ b ₁ a ₀ a ₁ a ₂ ] ^T = (Φ ^t Φ) ^-1 Φ ^T

Substituting the input position sequence P _x of the X axis into the differential equation corresponding to the three-axis CNC machining servo system can obtain the output position sequence Q _x of the X axis. Similarly, the output position sequences Q _y and Q _z of the Y axis and Z axis can be obtained, thereby obtaining the output position sequence Q of the three-axis CNC machining servo system that is closer to the actual situation as follows:

Q={Q _x , Q _y , Q _z }={(q _x (i), q _y (i), q _z (i))|i=0,...,N-1}

Among them, _qx (i) represents the X-axis output coordinate value of the sampling point with sequence number i, _qy (i) represents the Y-axis output coordinate value of the sampling point with sequence number i, and _qz (i) represents the Z-axis output coordinate value of the sampling point with sequence number i.

的求解。如图4所示，以X轴为例，对Q中的X轴分量Q_x进行差分计算，求得X轴的速度序列V_x为：Step 3: Based on the output position sequence obtained above, perform the equivalent acceleration

As shown in Figure 4, taking the X-axis as an example, the X-axis component Q _x in Q is differentially calculated to obtain the velocity sequence V _x of the X-axis:

Among them, M ₁ represents the coefficient matrix of the equation;

Furthermore, by performing differential calculation on the velocity sequence _Vx of the X-axis, the acceleration sequence _Ax of the X-axis can be obtained as follows:

Similarly, the acceleration sequences A _y and A _z of the Y and Z axes can be obtained, thereby obtaining the acceleration sequence A corresponding to the output position sequence Q:

A={A _x , A _y , _Az }={(a _x (i), a _y (i), a _z (i))|i=0,...,N-1}

Wherein, a _x (i) represents the X-axis acceleration value of the sampling point with sequence number i, a _y (i) represents the Y-axis acceleration value of the sampling point with sequence number i, and α _z (i) represents the Z-axis acceleration value of the sampling point with sequence number i.

的X轴分量

After obtaining the acceleration sequence _Ax of the X axis, in order to eliminate the high-frequency acceleration signal and reduce the influence of the error introduced by the differential calculation on the output result, the FIR digital low-pass filter based on the Hanning window shown in Figure 5 can be used to perform the filtering process shown in the following formula to obtain the equivalent acceleration

The X-axis component

N为窗函数的长度，即所述的采样点的个数N。Where h(i) is the impulse response of the FIR low-pass filter, _hd (i) is the unit impulse response of the ideal low-pass filter, w(i) is the expression of the Hanning window function, i is an arbitrary integer, _ωc is the cutoff frequency, τ is the group delay,

N is the length of the window function, that is, the number of sampling points N.

The value of N can be obtained from the transition bandwidth formula of the window function:

Among them, _fs , _fpass , and _fstop are the sampling frequency, passband cutoff frequency, and stopband start frequency of the FIR low-pass filter respectively.

Finally, the filter is subjected to discrete Fourier transform to obtain its amplitude-frequency response value δ to verify whether its filtering performance meets the design requirements. If the value of δ is greater than the system's stopband attenuation δ _stop , then the filter meets the design requirements; otherwise, the length of the window function N needs to be increased or the window function needs to be replaced to redesign the filter.

In summary, the filtering formula for the X-axis equivalent acceleration at the turning point O of the path is obtained:

为：Substituting the acceleration sequence _Ax of the X axis into the above formula, we can get the equivalent acceleration of the X axis:

for:

为m₂。Note the coefficients in the above formula

is m ₂ .

Similarly, the equivalent accelerations of the Y and Z axes at point O are:

Therefore, the resultant acceleration at point O is:

This is the predicted acceleration value at the turning point O of the path to be determined, that is, the equivalent acceleration corresponding to the sampling interval containing point O

Step 4: Solve the feed rate constraint value at the turning point O of the path.

即为法向加速度，则有：In the CNC machining of continuous small line segments, the reference command feed speed _Fa near point O is a constant value, so its tangential acceleration is 0, and its equivalent acceleration is

is the normal acceleration, then:

Where ρ _v is the equivalent curvature radius of the continuous small line segment path.

And suppose that this continuous small line segment path is processed by CNC with another feed speed F _O so that its normal acceleration is just equal to its maximum allowable value _An , then:

Among them, F _O is the feed rate constraint value at the turning point O of the path, and its value is:

According to the above formula, the constraint speed at each corner of the continuous small line segment path can be obtained, so that the CNC machining feed speed of the continuous small line segment path can be reasonably and effectively controlled. The speed control method of the present invention is used in conjunction with the traditional look-ahead and interpolation method to realize three-axis CNC machining of the continuous small line segment path.

The present invention innovatively combines position point sampling, discrete system digital analysis methods and acceleration filtering processing methods, which can effectively and reasonably calculate the feed speed constraint value in the CNC machining process. And because the present invention has strong universality in principle, the speed control method can be extended to various types of linear path CNC machining. The present invention has been verified by simulation and test for many times, which have proved the feasibility and effectiveness of the method of the present invention, and achieved the purpose of the invention: the speed control algorithm runs stably and the feed speed is reasonable during CNC machining. Compared with the existing speed control methods such as the angle constraint method, the method of the present invention can improve the surface machining quality of the workpiece while also improving the machining efficiency and shortening the machining time, which helps to promote the application of continuous small line segment paths in high-speed and high-precision CNC machining.

The above content is a specific embodiment of the present invention for three-axis CNC machining. It cannot be determined that the specific implementation of the present invention is limited to this embodiment. The present invention is also applicable to multi-axis CNC machining scenarios such as four-axis and five-axis. Technical personnel familiar with the field can also make various equivalent modifications or substitutions without violating the creative spirit of the present invention, and these equivalent modifications or substitutions are all included in the scope of this application.

Claims (2)

1. A linear path CNC machining feed speed control method based on equivalent acceleration, characterized in that the method comprises the following steps: CNC machining is performed along a linear path, which is a broken line. The inflection point on the linear path is taken as the path turning point O. Then: S1: Starting from the turning point O of the path where the speed constraint value is to be determined, a distance is taken in each direction along the linear path to form a sampling interval, and sampling is performed in the sampling interval to generate an input position sequence P; S2: Input the input position sequence P into the differential equation of the CNC machining servo system, and use the discrete system digital analysis method to solve it to obtain the output position sequence Q; S3: Perform second-order difference calculation on the output position sequence Q to obtain the acceleration sequence A corresponding to the output position sequence Q, and use a digital filter to filter the acceleration sequence A to obtain the equivalent acceleration of the sampling interval.

The step S3 is specifically as follows: first, the X-axis component Q _x in the output position sequence Q is differentially calculated to obtain the X-axis velocity sequence V _x :

Among them, M ₁ represents the coefficient matrix of the equation; By performing differential calculation on the velocity sequence _Vx of the X-axis, the acceleration sequence _Ax of the X-axis can be obtained as follows:

Then, the acceleration sequences A _y and A _z of the Y and Z axes are obtained, thereby obtaining the 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) represents the X-axis acceleration value of the sampling point with sequence number i, a _y (i) represents the Y-axis acceleration value of the sampling point with sequence number i, and a _z (i) represents the Z-axis acceleration value of the sampling point with sequence number i; The acceleration sequence A of the X axis is obtained ₍ afterwards, the FIR digital low-pass filter of the Hanning window is used to perform the filtering process shown in the following formula to obtain the equivalent acceleration

The X-axis component

Where h(i) is the impulse response of the FIR low-pass filter, _hd (i) is the unit impulse response of the ideal low-pass filter, w(i) is the expression of the Hanning window function, i is an arbitrary integer, _ωc is the cutoff frequency, τ is the group delay,

N is the length of the window function, that is, the number of sampling points N; The value of N is obtained from the transition bandwidth formula of the window function:

Among them, _fs , _fpass , and _fstop are the sampling frequency, passband cutoff frequency, and stopband start frequency of the FIR low-pass filter respectively; Finally, the filter is subjected to discrete Fourier transform to obtain its amplitude-frequency response value δ to verify whether its filtering performance meets the design requirements; if the value of δ is greater than the system's stopband attenuation δ _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; The filtering formula for the X-axis equivalent acceleration at the turning point O of the path is obtained:

Substituting the acceleration sequence _Ax of the X axis into the above formula, we can get the equivalent acceleration of the X axis:

for:

Note the coefficients in the above formula

is m ₂ ; The equivalent accelerations of the Y and Z axes at point O are:

Finally, the resultant acceleration at point O is:

This is the predicted acceleration value at the turning point O of the path to be determined, that is, the equivalent acceleration corresponding to the sampling interval containing point O

S4: According to the equivalent acceleration

and the given upper limit of normal acceleration _An , the feed speed constraint value F _O at the turning point O of the desired path is obtained, and the feed speed constraint value F _O is used to constrain the feed speed of the CNC machining to realize control; In S4, the feed speed constraint value F _O at the path turning point O is obtained according to the following formula:

Wherein, _Fa represents the reference command feed speed at the turning point O of the path. 2. According to the method for controlling the feed speed of linear path CNC machining based on equivalent acceleration in claim 1, it is characterized in that the differential equation of the CNC machining servo system is specifically: 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) Wherein, i represents the serial number of the sampling point, i＝0,1,2,…, a ₀ , a ₁ , a _C represent the coefficient values of the input sequence in the difference equation, b ₀ , b ₁ represent the coefficient values of the output sequence in the difference equation, which will be obtained through the observation matrix later; p(i) represents the input coordinate value of the sampling point with serial number i, and q(i) represents the output coordinate value of the sampling point with serial number i; Taking the interpolation period _Ts of the numerical control system as the sampling period, N groups of samples are collected from the position points of its input and output, and its output vector q is obtained as:

The measurement matrix Φ is

The coefficient vector r is r=[b ₀ b ₁ a ₀ a ₁ a _C ] ^T = (Φ ^T Φ) ^-1 Φ ^T And the following initial conditions are set to satisfy the following relationship: q(-2)=q(-1)=p(-2)=p(-1)=p(0).

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