CN105656449B - A kind of electric spark voltage across poles signal processing method based on kalman filter - Google Patents

Abstract

The present invention relates to a kind of method of processing the electric spark inter-electrode voltage signal based on the Kalman filter. It is assumed that the inter-electrode voltage is generated by white noise through a linear filter. On the basis of this assumption, the Yule-Walker innovation gain matrix is used By processing the collected inter-electrode voltage signal, a transfer function from white noise to inter-electrode voltage can be obtained, and then the transfer function is converted into the state equation required for designing a Kalman filter. The invention can greatly reduce the noise interference in the collected inter-electrode voltage signal, thereby avoiding the influence of the noise on the servo movement in the electric discharge machining process, reducing some unnecessary back and forth movements of the servo shaft, and improving the efficiency of the electric discharge machining .

Description

A Kalman Filter-Based Processing Method for EDM Interpolar Voltage Signal

technical field

The invention relates to electric spark process control, belongs to the technical field of special processing, in particular to a design method of a Kaman filter used for electric spark inter-electrode voltage detection.

Background technique

EDM is a process of removing material from a workpiece by a series of spark discharges between the workpiece and the electrode. EDM is widely used in molds, aerospace, medical equipment and other fields. Compared with traditional milling, EDM has many differences. For example, the speed of electric discharge machining is different from the given speed feed in milling. It determines whether the machining direction is forward or backward according to the measured inter-electrode state, and according to the current measured inter-electrode voltage and the set servo voltage. The difference determines the forward or backward speed, so the speed of EDM is determined by the state between poles. Because the inter-electrode voltage determines the direction and speed of the servo axis, it is very important to detect and estimate the inter-electrode voltage. At present, the most commonly used inter-electrode voltage detection methods are the average voltage method and the sliding average voltage method, which is to calculate the sliding average voltage for the inter-electrode voltage from the past few cycles to the current sampling cycle. The calculated results are consistent with the preset servo voltages are compared as shown in Figure 1.

The Chinese invention patent application with publication number 101791728A "Non-contact inter-electrode voltage detection method and circuit design for electrostatic induction micro-EDM" proposes a non-contact inter-electrode voltage detection method for electrostatic induction micro-EDM. The method used is used to detect the inter-electrode voltage, but it is generally realized by hardware. Moreover, this method still cannot solve the problem of noise interference in the inter-electrode voltage signal. In order to detect the follow-up steps, the present invention assumes that the inter-electrode voltage is generated by white noise through a linear filter. On the basis of this assumption, a Kalman filter model is established to perform Kalman filter processing on the inter-electrode voltage signal to reduce the signal noise interference, thus it is completely different from the content of the present invention.

Due to the strong electric field and magnetic field interference generated during EDM, the collected inter-electrode voltage contains strong noise interference. In this case, using a Kalman filter is a good choice. Because the Kalman filter is an optimal linear filter, the estimation error of the signal can be considered as white noise. The design of the Kalman filter is based on the state equation of the system and the autocovariance matrix of the signal, and the design can only be carried out with these information. But for EDM, both the state equation and the autocovariance matrix must be derived from the collected inter-electrode voltage.

Contents of the invention

In order to overcome the above-mentioned deficiencies in the prior art, the present invention provides a method for processing electric spark inter-electrode voltage signals based on a Kalman filter, which can greatly reduce the noise interference in the collected inter-electrode voltage signals, and avoid affecting the electric spark due to noise. The servo movement during the spark machining process reduces unnecessary back and forth movement of the servo axis and improves the efficiency of EDM.

Technical solution of the present invention is as follows:

A method for processing electrical spark inter-electrode voltage signals based on a Kalman filter, the method comprising the following steps:

Step 1: Real-time acquisition of the inter-electrode voltage signal, and then transmitted to the numerical control system for subsequent calculation of transfer function, state equation and steady-state gain;

Step 2: Assuming that the inter-electrode voltage is generated by white noise through a linear filter, the transfer function between the white noise and the inter-electrode voltage is established, and the transfer function is converted into a normative controllable state equation;

Step 3: Calculate the autocovariance matrix between the measurement noise and the process noise and the cross-covariance matrix between the two from the state equation and the white noise variance, and then obtain the steady-state gain between the inter-electrode voltage and the estimated voltage ;

Step 4: Design a Kalman filter according to the state equation and covariance matrix;

Step 5: Use the Kalman filter model to process the inter-electrode voltage signal. The filtered inter-electrode voltage is used as the feedback signal of the servo controller, which can greatly reduce the noise in the inter-electrode voltage signal, thereby reducing unnecessary servo axis movement , Improve processing efficiency and serve processing. Unnecessary servo axis movement means that due to noise interference, the voltage signal that can be processed normally is less than the minimum threshold value set by the current servo movement, which causes the CNC system to think that the current short circuit causes the servo axis to retreat, or exceeds the maximum threshold value As a result, the CNC system thinks that the current is open, causing the servo axis to overshoot.

Principle of the present invention is as follows:

The present invention assumes that the inter-electrode voltage is generated by white noise through a linear filter. On the basis of this assumption, the Yule-Walker autocovariance method is used to process the collected inter-electrode voltage signal, and it can be obtained from white noise to the pole-to-electrode voltage signal. A transfer function of the voltage between. This transfer function is transformed into an equation of state. The transfer function between white noise and inter-electrode voltage can be expressed as

Here q ^-1 is the time shift operator, e(k) is white noise, a _i , i=1...n is the coefficient on the denominator, b ₀ is a constant that makes the steady-state gain 1, y(k) is voltage between poles. In order to obtain Equation (1), the Yule-Walker autocovariance method is used to solve the coefficients, as follows:

where r(k) is the autocovariance when the time offset is k, and the value of k ranges from 0 to M. Equation (2) can be expressed in a more compact matrix form

Rc=r (3)

where R is the autocovariance matrix, so the coefficient vector c can be obtained

c=R ^-1 r (4) The relationship between coefficient vector c and coefficient vector a can be expressed as

c=[c ₁ ,c ₂ ,…,c _M ]=[-a ₁ ,-a ₂ ,…,-a _M ] (5)

Now that we have the transfer equation, we want to test the assumption that the input signal is white noise. According to the transfer function between white noise and inter-electrode voltage signal, the inverse function of the transfer function from white noise to inter-electrode voltage can be used To detect whether the input e(k) of the transfer function is white noise. e(k) can be given by

Get it. White noise can be judged by the following conditions:

According to the transfer function equation (1), using the standard controllable form, the state equation can be obtained

y(k)=[(b ₁ -b ₀ a ₁ )(b ₂ -b ₀ a ₂ )…(b _n -b ₀ a _n )]x(k)+Hw(k)+v(k)

where w(k) is the process noise and v(k) is the measurement noise. Equation (8) can be expressed in a more compact matrix form:

x(k+1)=Ax(k)+Gw(k)

y(k)=Cx(k)+Hw(k)+v(k) (9)

in,

C=[(b ₁ -b ₀ a ₁ )(b ₂ -b ₀ a ₂ )...(b _n -b ₀ a _n )], H=b ₀ .

Process noise w(k), measurement noise v(k) and white noise e(k) can be expressed as

w(k)=e(k) (10)

v(k)=e(k) (11)

In the design of the Kalman filter, two autocovariance matrices and a cross-covariance matrix are needed. In order to facilitate the derivation of the variance matrix, the compound process noise is first defined and composite measurement noise

With compound process noise and composite measurement noise The state equation can be written as

According to the state equation (14), the autocovariance matrix of the composite process noise can be derived

The autocovariance matrix of the composite measurement noise can be obtained by the following formula:

compound process noise and composite measurement noise The cross-covariance matrix between can be expressed as:

The three variance matrices Q(k), R(k) and N(k) used are defined as

Q(k)=E(w(k)w ^T (k)) (18)

R(k)=E(v(k) ^vT (k)) (19)

N(k)=E(w(k) ^vT (k)) (20)

After having the state equation and the information of the three variance matrices, the Kalman filter can be designed. Post-event state vector ex ante state a correction of .

where M(k) is the innovation gain matrix, is the prediction error. L(k) is the Kaman gain matrix.

The state estimation error matrix is required in the calculation, which can be expressed as:

After the transient state process has passed, P(k) enters a steady state. In order to reduce the amount of real-time calculation, the steady state P can be applied during EDM. Steady state P can be calculated by the following formula

P(1|0)=pI (27)

Among them, P(1|0) is the initial value of P, I is the identity matrix, and p is a constant, which can be 100.

During the EDM process, the measured inter-electrode voltage will be filtered by a Kalman filter. In order to keep the range of the processed filtered voltage value and the collected original voltage within the same reading range, it is necessary to obtain the signal from the original signal y(k) to the filtered signal The steady-state gain between. This is asking for Afterwards, it can be multiplied by an inverse of the steady-state gain, thus keeping the input and output voltages of the Kalman filter in the same range of values.

from y(k) to Steady state gain of

The state equation is expressed as follows:

Applying z-transformation to equations (29) to (31), we can get

therefore The transfer function between them is:

in: So substitute z=1 into The transfer function between, you can get from y(k) to Steady state gain of

Compared with the existing technology, there is strong noise interference in the original inter-electrode voltage signal diagram. In this case, it cannot reflect the actual state of the current processing. It is possible that the original normal processing voltage signal is less than The minimum threshold value set by the current servo motion causes the CNC system to think that the current processing is short-circuited, resulting in a short-circuit retreat of the servo axis, or exceeds the maximum threshold and causes the CNC system to consider the current processing to be open, causing the servo axis to overshoot and affect normal processing. The invention can greatly reduce the noise interference in the collected inter-electrode voltage signal, thereby avoiding the influence of the noise on the servo movement in the electric discharge machining process, reducing some unnecessary back and forth movements of the servo shaft, and improving the efficiency of the electric discharge machining .

Description of drawings

Fig. 1 is a servo control diagram of gap voltage detection in the present invention.

Fig. 2 is a schematic diagram of the implementation platform of the present invention.

Fig. 3 is a graph of inter-electrode voltage signal acquisition in a specific embodiment of the present invention, wherein graph (a) is an unprocessed original graph, graph (b) is a Kalman filter.

Fig. 4 is a comparison chart of processing rates of different processing methods for inter-electrode voltage signals in the same embodiment of processing a hole with a depth of 10 mm.

Detailed ways

The specific embodiment of the present invention is carried out on the HE 70 EDM machine produced by Shanghai Hanba Electromechanical Co., Ltd. The schematic diagram of the platform is shown in Figure 2. The motion control of the entire machine tool is realized by the PMAC motion control card. The real-time sampling period set by the PC is 2ms, and the servo period of the PMAC motion control card is 0.88ms. The PC and the PMCA motion control card are realized through the DPRAM module on the PMAC motion control card. The inter-electrode voltage signal is collected through the ACC-28A card connected to the PMAC control card, and is transmitted to the PC in real time through the DPRAM module.

Example:

First assume that the inter-electrode voltage is generated by white noise through a linear filter, establish the transfer function of white noise and inter-electrode voltage, and obtain the relevant parameters in formula (1), see Table 1 for details:

Table 1 The dynamic model sampling period of the gap voltage is 2ms

Then use the Kalman filter based on the above model to process a small hole with a depth of 10mm, and conduct a comparative experiment with the moving average filter. The experiment uses a Ф10 rod-shaped graphite electrode, and the workpiece is tool steel. The processing conditions are as shown in Table 2 below:

Table 2 Small hole processing experimental parameters

servo voltage peak current Pulse Width pulse interval Lifting time Lifting cycle 49V 28A 60μs 40μs 1s 5s

Described moving average filter is defined as following processing to the inter-electrode voltage signal that PMAC sampling period gathers:

Among them, u(k) is the sampling signal of the current sampling period.

In the specific embodiment, the effect of the Kalman filter is shown in Figure 3. There is strong noise interference in the original inter-electrode voltage signal diagram. In this case, it cannot reflect the actual state of the current processing, and it may be caused by noise interference. If the voltage signal is less than the minimum threshold value set by the current servo motion, unnecessary short-circuit retreat will occur, or if it exceeds the maximum threshold value, the CNC system will think that the current circuit is open, causing overshoot and affecting normal processing.

Shown in table 3 of concrete processing result:

Table 3 Comparison of processing results of two filtering methods

where the backoff time ratio is defined as follows:

Among them, T _retract is the retracting time, and T _total is the total processing time including lifting the tool.

It can be seen from Table 3 that regardless of the processing time or the retraction time ratio, the results obtained by using the Kaman filter are better than the moving average filter. The specific speed comparison chart from 1mm to 10mm is shown in Figure 4. And as far as the processing effect is concerned, the three processings using the sliding average filter all produce carbon deposits, while the three processings using the Kaman filter do not produce carbon deposits, that is, the processing stability of the Kaman filter is better than that of the sliding average filter.

The preferred specific embodiments of the present invention have been described in detail above. Those skilled in the art should understand that many modifications and changes can be made according to the concept of the present invention without departing from the scope of the present invention. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention by changing materials or characteristics on the basis of the prior art should be within the scope of protection defined by the claims.

Claims (2)

1. A method for processing an interelectrode voltage signal based on a Kalman filter is characterized by comprising the following steps:

the method comprises the following steps: acquiring an interelectrode voltage signal in real time and transmitting the interelectrode voltage signal to a numerical control system;

step two: assuming that the interelectrode voltage is generated by white noise through a linear filter, establishing a transfer function between the white noise and the interelectrode voltage, and converting the transfer function into a standard controllable equation of state;

the transfer function between the white noise and the interelectrode voltage is expressed as:

<mrow> <mover> <mi>G</mi> <mo>~</mo> </mover> <mrow> <mo>(</mo> <msup> <mi>q</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mi>y</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mi>e</mi> <mrow> <mo>(</mo> <mi>k</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <msub> <mi>b</mi> <mn>0</mn> </msub> <mrow> <mn>1</mn> <mo>+</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <msup> <mi>q</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>+</mo> <mo>...</mo> <mo>+</mo> <msub> <mi>a</mi> <mi>n</mi> </msub> <msup> <mi>q</mi> <mrow> <mo>-</mo> <mi>n</mi> </mrow> </msup> </mrow> </mfrac> </mrow>

in the formula, q^-1Is a time-shift operator, e (k) is white noise, a_iI is 1 … n, b is a coefficient on the denominator₀Is a constant that gives a steady state gain of 1, and y (k) is the filtered white noise;

the transfer function adopts Yule-Walker autocovariance to solve the coefficient, and the formula is as follows:

wherein r (k) is the autocovariance at time offset k, k ranging from 0 to M;

step three: solving an autocovariance matrix between the measurement noise and the process noise and a cross covariance matrix between the measurement noise and the process noise by using a state equation and a white noise variance so as to obtain a steady gain between the interelectrode voltage and the estimated voltage;

step four: designing a Kalman filter according to a state equation and a covariance matrix;

step five: and processing the interelectrode voltage signal by using a Kalman filter model, wherein the filtered interelectrode voltage is used as a feedback signal of the servo controller.

2. The method for processing the electric spark interpolar voltage signal based on the kalman filter of claim 1, wherein the step one collects the interpolar voltage by an ACC-28A card and transmits the collected interpolar voltage to a numerical control system in real time by a DPRAM module of a PMAC.