CN105425720A - Method for recognizing kinetic parameter of machine tool based on current signal - Google Patents

Abstract

The method discloses a method for recognizing a kinetic parameter of a machine tool based on a current signal. The application of the machine tool causes the changes of the dynamic characteristics of the machine tool, thereby affecting the machining precision and performance of the machine tool. The conventional machine tool kinetic study mainly focuses on the study of the dynamic characteristics of the machine tool through employing vibration sensors installed independently for obtaining vibration signals, thereby causing the high testing cost. Therefore, the invention proposes the method for recognizing kinetic parameter of machine tool through a motor current signal obtained at an excitation state. Because the condition is a full-closed-loop condition, the motor current signal has a dynamic response process of input and output. The method processes a preprocessed current signal through employing a least square complex exponential algorithm, and recognizes a kinetic parameter of a feeding system, so as to achieve the quick recognition of the kinetic parameter of the machine tool. When the method is used for recognizing the kinetic parameter of the machine tool, the method saves time and labor, is simple and quick in recognition, and is high in efficiency.

Description

A kind of method based on current signal identification lathe kinetic parameter

Technical field

The invention belongs to numerically-controlled machine dynamics research field, more specifically, relate to a kind of numerically-controlled machine kinetic parameter Fast Identification Method.

Background technology

The common method of current research lathe vibration characteristics directly replaces complete machine dynamics by the dynamics at point of a knife point place.The method thinks that the rigidity of machine tool structure is far longer than the rigidity of cutter, and machine tool structure can be regarded as rigid body, therefore only needs the dynamics considering point of a knife point place.Altintas obtains the kinetic parameter at machine tool cusp place by power hammer tap test, and utilizes kinetic parameter to carry out cutting stability analysis.Kamalzade carries out motion-activated to the ball screw that scrambler is equipped with at two ends, achieves the identification of ball screw axis and torsion mode parameter, and contrasts with Analysis Mode parameter, achieve more consistent result;

Tradition obtains the research of Machine Tool Modal parameter mainly by directly picking up the vibration signal of vibration transducer, and installation is inconvenient, testing cost is too high; Simultaneously owing to mainly passing through to the research of Machine Tool Dynamics the vibration signal directly picking up vibration transducer, installation is inconvenient and testing cost is too high; As time goes on can there is the change in physical significance in Machine Tool Feeding System, affects the dynamics of lathe, therefore needs a kind of quick and convenient low cost to obtain the method for machine power mathematic(al) parameter, to study the instantaneous operating conditions of lathe.

Kinetic parameter of the present invention, refers to lathe natural frequency and damping ratio.

Summary of the invention

For prior art Problems existing, the present invention proposes a kind of can the kinetic parameter method of acquisition Machine Tool Feeding System real-time, by obtaining the current signal of Machine Tool Feeding System, pre-service is carried out to it, pre-service is carried out to the current signal after obtaining, used by pretreated current signal least square complex exponential algorithm to process it, Fast Identification goes out the kinetic parameter of lathe.

For achieving the above object, the present invention proposes a kind of method based on current signal identification lathe kinetic parameter, it is characterized in that, comprise the steps:

(1) start lathe, perform pseudo random code, Active spurring is carried out to feed shaft, makes its random motion, realize lathe autoexcitation, thus evoke the kinetic parameter of lathe; Described dynamic mathematic(al) parameter, refers to lathe natural frequency and damping ratio;

(2) current sensor is utilized to be obtained from the motor current signal of foment lower feeding axle;

(3) root-mean-square value is got to the current signal obtained, carry out high-pass filtering pre-service; Used by pre-service after-current signal least square complex exponential algorithm to process it, pick out the kinetic parameter of lathe; Concrete steps make Fourier analysis to the current signal obtained, and obtains limit s _r, then obtain natural frequency ω by following formula _rand dampingratioζ _r:

$\left\{\begin{array}{c}{\mathrm{\ω}}_r=\left|s_r\right|\\ {\mathrm{\ξ}}_r=\sqrt{\frac{1}{1+{\left(\frac{\mathrm{Im}\left(R_r\right)}{\mathrm{Re}\left(R_r\right)}\right)}^2}}\end{array}\right.$

Wherein, R _r=s _rΔ t, Δ t is sampling time interval.

The derivation of calculating formula is as follows:

If cause the expression formula of P point displacement frequency response function to be by q point power in a system:

$H_{pq}\left(j\mathrm{\ω}\right)=\underset{r=1}{\overset{N}{\Σ}}(\frac{A_{rpq}}{jw-s_r}+\frac{A_{rpq}^{*}}{jw-s_r^{*}})$

A in formula _rpqfor the corresponding residual of r rank mode, relevant with Mode Shape; N is the number of degrees of freedom, of system; J is imaginary symbols; * conjugation is represented; s _rfor frequency response function r rank mode limit, relevant with model frequency and damping ratio.

Above formula is simplified, and makes A _r+N=A _r ^*, S _r+N=S _r ^*, can obtain:

namely P point displacement frequency response function is caused by q point power.

Carry out inverse FFT to above formula, obtaining system response function h (t) is:

$h\left(t\right)=Re\left(\underset{r=1}{\overset{2N}{\Σ}}{A}_r{e}^{s_{r}t}\right)$

Because the response function of actual measurement is time discrete time series, if time series t _k=k Δ t, Δ t are the time intervals of sampling, and k is sampling ordinal number, and above formula can be expressed as:

$h\left(t\right)=h\left(k\mathrm{\Δ}t\right)=\underset{r=1}{\overset{2N}{\Σ}}{A}_r{e}^{s_{r}t}=\underset{r=1}{\overset{2N}{\Σ}}{A}_r{e}^{s_{r}k\mathrm{\Δ}t}=\underset{r=1}{\overset{2N}{\Σ}}{A}_r{V}_r^k,(k=0,1,2,3,\mathrm{....}L)$

In formula, L+1 is the data length of the impulse response function of measured signal, and the general sampling time is longer, so L+1 is more much bigger than 2N.

Wherein then its system of equations form is:

$\left\{\begin{array}{c}{h}_0=\underset{r=1}{\overset{2N}{\Σ}}{A}_r{V}_r^0=A_1+A_2+...+A_{2N}\\ h_1=\underset{r=1}{\overset{2N}{\Σ}}{A}_r{V}_r^1=A_1{V}_1+A_2{V}_2+...+A_{2N}{V}_{2N}\\ h_2=\underset{r=1}{\overset{2N}{\Σ}}{A}_r{V}_r^2=A_1{V}_1^2+A_2{V}_2^2+...+A_{2N}{V}_{2N}^2\\ .\\ .\\ h_L=\underset{r=1}{\overset{2N}{\Σ}}{A}_r{V}_r^L=A_1{V}_1^L+A_2{V}_2^L+...+A_{2N}{V}_{2N}^L\end{array}\right.$

Vr is regarded as a root with the polynomial equation on the 2N rank of real coefficient (autoregressive coefficient), namely

$\underset{k=0}{\overset{2N}{\Σ}}{\mathrm{\β}}_k{V}^k=\underset{r=1}{\overset{N}{\Π}}(V-V_r)(V-V_r^{*})=0$

Can be found out by above formula, β _2N=1, respectively β is multiplied by the equal sign both sides of the formula in (3.4) _k, and add up, can obtain:

$\underset{k=0}{\overset{2N}{\Σ}}{\mathrm{\β}}_k{h}_k=\underset{k=0}{\overset{2N}{\Σ}}{\mathrm{\β}}_k\underset{r=1}{\overset{2N}{\Σ}}{A}_r{V}_r^k=\underset{r=1}{\overset{2N}{\Σ}}{A}_r\underset{k=0}{\overset{2N}{\Σ}}{\mathrm{\β}}_k{V}_r^k$

Again because then

For calculating autoregressive coefficient β _k, need structure system of equations, offset a Δ t mode backward by during each peek, successively from actual measurement h _kin get 2N+1 data, substitute into above formula, form a prescription journey as follows:

Autoregressive coefficient β is calculated with this _k, system of equations is as follows:

$\left\{\begin{array}{c}\underset{k=0}{\overset{2N-1}{\Σ}}{\mathrm{\β}}_k{h}_k={\mathrm{\β}}_0{h}_0+{\mathrm{\β}}_1{h}_1+...+{\mathrm{\β}}_{2N-1}{h}_{2N-1}=-h_{2N}\\ \underset{k=0}{\overset{2N-1}{\Σ}}{\mathrm{\β}}_k{h}_{k+1}={\mathrm{\β}}_0{h}_1+{\mathrm{\β}}_1{h}_2+...+{\mathrm{\β}}_{2N-1}{h}_{2N}=-h_{2N+1}\\ .\\ .\\ .\\ \underset{k=0}{\overset{2N-1}{\Σ}}{\mathrm{\β}}_k{h}_{k+M-1}={\mathrm{\β}}_0{h}_{M-1}+{\mathrm{\β}}_1{h}_M+...+{\mathrm{\β}}_{2N-1}{h}_{L-1}=-h_L\end{array}\right.$

Wherein M=L-2N

Then this solution of equation:

{β}＝([h] ^T[h]) ^-1([h] ^T{h'})

By try to achieve { β } and increase an element β _2N=1, then:

$\underset{k=0}{\overset{2N}{\Σ}}{\mathrm{\β}}_k{V}^k={\mathrm{\β}}_0+{\mathrm{\β}}_{1}V+{\mathrm{\β}}_2{V}^2+...+{\mathrm{\β}}_{2N-1}{V}^{2N-1}+V^{2N}=0$

Try to achieve by factor beta _kthe root of a polynomial of composition, then can obtain frequencies omega _rwith damping ratio ξ _r:

$\left\{\begin{array}{c}{R}_r=\ln V_r=s_r\mathrm{\Δ}t\\ {\mathrm{\ω}}_r=\frac{\left|R_r\right|}{\mathrm{\Δ}t}=\left|s_r\right|\\ {\mathrm{\ξ}}_r=\sqrt{\frac{1}{1+{\left(\frac{\mathrm{Im}\left(R_r\right)}{\mathrm{Re}\left(R_r\right)}\right)}^2}}\end{array}\right.$

The Fast Identification Method of the machine power mathematic(al) parameter that the present invention proposes, it is by directly obtaining the current signal of servomotor, least square complex exponential algorithm is used to process it, obtain the kinetic parameter of feed system, realize the object of Fast Identification numerically-controlled machine kinetic parameter with this, it is time saving and energy saving to have, and differentiates simple and quick, efficiency advantages of higher, can be used for the on-line monitoring of the assembly quality of NC machine tool feed system.

Accompanying drawing explanation

Fig. 1 is the concrete implementing procedure figure of a kind of method based on current signal identification lathe kinetic parameter of the present invention;

Fig. 2 is the schematic diagram based on current signal identification lathe kinetic parameter;

Fig. 3 is that the time-frequency of vibration signal and the current signal obtained under autoexcitation condition contrasts;

Fig. 4 is the specific embodiment based on current signal identification lathe kinetic parameter.

Embodiment

In order to make object of the present invention, technical scheme and advantage clearly understand, below in conjunction with drawings and Examples, the present invention is further elaborated.Should be appreciated that specific embodiment described herein only in order to explain the present invention, be not intended to limit the present invention.In addition, if below in described each embodiment of the present invention involved technical characteristic do not form conflict each other and just can mutually combine.

Described be a kind of embodiment of the present invention, a kind of dynamic method based on current signal identification lathe below, the method specifically comprises:

(1) collection of motor current signal:

First signals collecting platform building is good, to the motor suspension Hall current sensor of tested kinematic axis, PCB vibration transducer is fitted in feed screw nut vice division chief simultaneously, by Belgian LMS Acquisition Instrument, this is a signals collecting instrument, by this kind of acquisition instrument, the vibration transducer fitting in nut vice division chief is connected by signal wire with current sensor, guarantee to obtain accurately the motor current signal of waiting to encourage feed shaft, the fundamental purpose obtaining vibration signal is the accuracy of the current signal identification result by the acquisition of vibration signal verificating current sensor, as described in Figure 1.Secondly impact generation excitation by applying repeatedly acceleration and deceleration to the worktable of numerically-controlled machine, make it meet the condition of work of pseudo-random excitation, realize the excitation to numerically-controlled machine.According to the motivational techniques to lathe, use matlab to make it generate G code, by the G code generated, import in numerically-controlled machine, the table feed motion of domination number controlled machine, thus produce excitation; Under utilizing acquisition instrument to gather stimulus movement, numerically-controlled machine is energized feed shaft motor response current signal.

(2) process of signal:

Used by current signal operational modal analysis theoretical, namely only have the Modal Analysis Theory under the condition exporting or encourage the unknown.Modal parameter natural frequency and the damping ratio of work of numerical control machine can be obtained.The kinetic parameter of lathe is picked out by using least square complex exponential algorithm to current signal, least square complex exponential is also known as Prony polynomial method, least square complex exponential only uses the impulse response data of a measuring point when identifying model frequency and damping ratios, its basic thought is to comprise complex frequency to be identified in the transform factor.Structure Prony polynomial expression, makes equal the value of the transform factor its zero point.Like this, transform will be solved factor converting for solving the polynomial coefficient of Prony.In order to solve this group coefficient, the autoregressive model of structure impulse response data sequence, autoregressive coefficient and the polynomial coefficient of Prony, by sampling in different starting point, obtain the system of linear equations about autoregressive coefficient, the solution of autoregressive coefficient can be obtained, so Prony root of polynomial can be tried to achieve by least square method.In this way, the natural frequency in the kinetic parameter of Fast Identification lathe and damping ratio is achieved.

Each step above-mentioned as shown in Figure 1.

Its root-mean-square value (RMS) is asked by the three-phase current signal obtaining motor, by carrying out high-pass filtering pre-service to current signal, filtering is lower than the interfering frequency within 10HZ, use work by least square complex exponential algorithm to it, the kinetic parameter of identification lathe, described current signal mainly gathers the three-phase current signal of feed motion axle by current Hall sensor.

Select the reason of the kinetic parameter of current signal identification lathe as follows:

The translation of slide unit in feed system, is be applied to leading screw by the rotary motion of motor, is converted to the translation of slide unit; The moment that motor produces is used for the action executing of feed system, overcomes the friction of motor bearings, the friction of guide rail, cutting moment.

As shown in Figure 2, the electric current that motor exports is respectively i _u, i _v, i _wfor motor three-phase alternating current, I _rMSfor the root-mean-square value of three-phase current its concrete corresponding relation is: T _m(t)=FR'=K _ti _q; electric current is converted to equivalent action moment of torsion, is converted to the acting force acted on slide unit to be to it |: { F}=K _t/ R'{I _rms; When lathe is when being subject to external forces, its kinetics relation is as follows, [M], [C], and [K] is the structure matrix of lathe, represents quality, damping ratio rigidity respectively; { x} is displacement, speed respectively.The function of time of acceleration, from above-mentioned relation, contains the kinetic parameter information of lathe, F: Motor torque is converted to the power acted on feeding system structure in its current signal; Kt: motor torque constant; Iq: armature supply; Tm: motor torque; R ': the reduction coefficient between power and motor force square;

Current signal its both as the input signal of feed system, again as the output signal of this system, the in real time duty of reflection lathe, current signal does work to feed system as input signal under high frequency effect, controls the telemechanical back and forth of slide unit.

It can thus be appreciated that act on the power of feed system slide unit and armature electric current is a kind of linear corresponding relation, as shown in Figure 3, it is the contrast of the time-domain and frequency-domain of current signal and the vibration signal obtained under lathe is energized effect, can be looked by figure, the current signal obtained has good consistance in time domain, and the frequency domain information that simultaneously two kinds of signals are contained has the consistance of height; Therefore a kind of new identification lathe dynamic method is proposed in this article, when having encouraged the natural frequency of lathe, micrometric displacement signal on its microcosmic reacts on feed system by grating scale sensor as input signal, control the fluctuation of current signal, therefore the kinetic parameter information of lathe is contained in current signal, be the machine power mathematic(al) parameter picked out at vibration signal and current signal as shown in Figure 4, two kinds have good anastomose property.

Therefore, select the method for current signal identification lathe kinetic parameter can well the kinetic parameter of identification lathe.

The inventive method can go out the kinetic parameter of lathe by Fast Identification, does not need complicated sensor installation, adapts to site environment.

Those skilled in the art will readily understand; the foregoing is only preferred embodiment of the present invention; not in order to limit the present invention, all any amendments done within the spirit and principles in the present invention, equivalent replacement and improvement etc., all should be included within protection scope of the present invention.

Claims (1)

1., based on a method for current signal identification lathe kinetic parameter, it is characterized in that, comprise the steps:

(1) start lathe, perform pseudo random code, Active spurring is carried out to feed shaft, makes its random motion, realize lathe autoexcitation, thus evoke the kinetic parameter of lathe;

(2) current sensor is utilized to be obtained from the motor current signal of foment lower feeding axle;

(3) root-mean-square value is got to the current signal obtained, carry out high-pass filtering pre-service, filtering low-frequency disturbance; Used by pre-service after-current signal least square complex exponential algorithm to process it, pick out the kinetic parameter of lathe, concrete steps are:

(3.1) Fourier analysis is done to the current signal obtained, obtain frequency response function r rank mode limit s _r;

(3.2) natural frequency ω is obtained by following formula _rand dampingratioζ _r:

$\left\{\begin{array}{c}{\mathrm{\ω}}_r=\left|s_r\right|\\ {\mathrm{\ξ}}_r=\sqrt{\frac{1}{1+{\left(\frac{\mathrm{Im}\left(R_r\right)}{\mathrm{Re}\left(R_r\right)}\right)}^2}}\end{array}\right.$

Wherein, R _r=s _rΔ t, Δ t are sampling time interval.