CN104647132B - A kind of milling parameter Active Control Method based on magnetic suspension bearing electric chief axis - Google Patents

Abstract

The invention discloses a kind of milling parameter Active Control Method based on magnetic suspension bearing electric chief axis, comprise the steps: current displacement signal when gathering electro spindle generation milling parameter; Obtain the state vector Q (t) be made up of electro spindle displacement and speed; According to electro spindle displacement [F _xf _y] ^twith trigonometric function column vector obtain harmonic displacement obtain the first self adaptation weight coefficient with the second self adaptation weight coefficient according to harmonic displacement h (t), the first self adaptation weight coefficient λ ₁with the second self adaptation weight coefficient λ ₂obtain the first adaptive rate with the second adaptive rate according to the first adaptive rate second adaptive rate and harmonic displacement h (t) obtains Self Adaptive Control electric current by Self Adaptive Control electric current Q _ct () acts on radial magnetic bearing, and produce corresponding magnetic field force, thus realizes suppressing the flutter of main shaft.The present invention eliminates the flutter produced in milling process, and then ensure that crudy and improve working (machining) efficiency.

Description

Milling flutter active control method based on magnetic suspension bearing electric spindle

Technical Field

The invention belongs to the technical field of numerical control machining, and particularly relates to a milling flutter active control method based on an electric spindle of a magnetic suspension bearing.

Background

In the aspect of five-axis numerical control machining chatter suppression of complex curved surface parts, a traditional method mainly adopts passive control, and the method enables a system to work below a salient angle effect point by adjusting technological parameters such as main shaft rotating speed, cutter feeding period, maximum cutting depth, cutter length and tooth space angle, so that high rotating speed and cutting depth are obtained on the premise of ensuring milling stability. Although the passive control method is simple in design and installation, the adjustable stability interval is small, and improvement on closed-loop dynamics is limited. Therefore, it is necessary to adopt a control means for changing the inherent dynamic characteristics of the spindle unit, i.e., an active control technique based on the electromagnetic spindle of the magnetic bearing, to suppress chattering vibration.

The active control technology of the electric spindle of the magnetic suspension bearing has the idea that the magnetic suspension bearing brake and the sensor are arranged at the proper position of the electric spindle unit, and the whole dynamic performance of a closed-loop system is changed by utilizing the feedback control effect, so that the closed-loop stable area of the system is effectively expanded, the point with better performance is found, and the maximum metal milling rate is improved. The active control technique has the capability of fundamentally changing the dynamic behavior of the system, so that the capability of suppressing chattering vibration is far stronger than that of the passive control technique.

Through the search of the prior documents, the following prior arts are found: the technology, which is called a vibration suppression method and a machine tool with application number 201310475810.8 and publication number CN103769945A, achieves the effect of suppressing chatter vibration by changing the rotation speed of a main shaft, belongs to passive control, and has limited capability of improving the machining efficiency.

Disclosure of Invention

Aiming at the defects of the prior art, the invention aims to provide a milling chatter active control method based on a magnetic suspension bearing electric spindle, and aims to solve the problems of reduced workpiece surface quality and low milling efficiency caused by a self-excitation chatter phenomenon in the milling process of the conventional numerical control machine tool.

The invention provides a milling flutter active control method based on a magnetic suspension bearing electric spindle, which comprises the following steps:

(1) collecting a current displacement signal of the motorized spindle when the motorized spindle generates milling vibration;

(2) after filtering, amplifying and differentiating the current displacement signal, obtaining a state vector Q (t) formed by the displacement and the speed of the electric spindle; the state vector q (t) is a 4-dimensional column vector;

(3) obtaining an electrical spindle displacement [ F ] from the state vector Q (t)_xF_y]^T＝C_q[Q(t-T/N)-Q(t)]；

Wherein $C_q=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\end{array}\right],$ Q (T-T/N) is a state vector formed by the electric spindle displacement and the speed at the time of T-T/N, T represents the rotation period of the spindle, N represents the number of cutter teeth of the milling cutter, and the electric spindle displacement F in the x direction_xAnd electric spindle displacement F in the y direction_yAll are 1-dimensional vectors, and the superscript T of the vector represents the transposition of the vector;

(4) fourier transform is carried out on each element in the cutting force dynamic matrix K (t) to obtain a cutting force harmonic dynamic matrix K_α(t) and harmonic dynamic matrix K according to cutting force_α(t) obtaining harmonics

Wherein the cutting force harmonic dynamic matrix K_α(T) the sum of the first 2 α +1 terms of fourier series expansion for each element in the cutting force dynamic matrix k (T), where ω is 2 π N/T is the harmonic frequency, α is a selected appropriate positive integer;

(5) according to the electric spindle displacement [ F ]_xF_y]^TAnd the trigonometric function column vectorObtaining harmonic shiftWherein the harmonic shift h (t) is a 4 α +2 dimensional column vector;

(6) according to the state displacement term coefficient matrix A and the Lyapunov equation beta A + A^Tbeta-I, a symmetric positive definite matrix beta is obtained, and a state weight coefficient [ Λ ] is obtained from the symmetric positive definite matrix beta₁Λ₂]XB, according to a state weight coefficient [ Λ₁Λ₂]And the state vector Q (t) obtains a first adaptive weight coefficientAnd a second adaptive weight coefficient

Where I is a 4-row 4-column identity matrix, Λ_iIs a four-dimensional column vector, λ_iIs a one-dimensional vector, i is 1, 2;

(7) according to the harmonic displacement h (t), the first adaptive weight coefficient lambda₁And said second adaptive weight coefficient lambda₂Obtaining a first adaptation rateAnd a second adaptation rate

Wherein the first adaptive rate of changeSecond adaptive rate of changeΦ₁And phi₂Two symmetric positive definite matrices of order 4 α +2, first adaptation rate, taken arbitrarily, respectivelyAnd a second adaptation rateAre 4 α + 2-dimensional column vectors;

(8) according to the first adaptive rateThe second adaptation rateAnd the harmonic displacement h (t) is obtained as an adaptive control currentWherein Q_c(t) is a 2-dimensional column vector;

(9) controlling the current Q adaptively_cAnd (t) acting on the radial magnetic suspension bearing and generating corresponding magnetic field force, thereby realizing the suppression of the main shaft flutter.

Further, the state displacement term coefficient matrix a is: $A=\left[\begin{array}{cccc}0& 0& 1& 0\\ 0& 0& 0& 1\\ -{{\mathrm{\ω}}_n}^2& 0& -2\mathrm{\ζ}{\mathrm{\ω}}_n& 0\\ 0& -{{\mathrm{\ω}}_n}^2& 0& -2\mathrm{\ζ}{\mathrm{\ω}}_n\end{array}\right],$ zeta is the damping ratio, omega, of the milling cutter system structure_nIs the natural frequency of the milling cutter system structure.

Further, the cutting force coefficient matrix B is: $B=\left[\begin{array}{cc}0& 0\\ 0& 0\\ 1/m& 0\\ 0& 1/m\end{array}\right],$ and m is the modal quality of the milling cutter system structure.

Further, the cutting force dynamic matrix is: $K\left(t\right)=\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{g}_j\left({\mathrm{\φ}}_j\left(t\right)\right)S\left(t\right){\left[K_t{K}_r\right]}^T\left[\sin {\mathrm{\φ}}_j\left(t\right)\cos {\mathrm{\φ}}_j\left(t\right)\right];$ wherein phi_j(t) represents the rotation angle of the jth tooth of the milling cutter, K_tAnd K_rDenotes the coefficient of cutting force, g_j(φ_j(t)) and S (t) respectively represent a screening function and a trigonometric function matrix, and the expression is as follows: $S\left(t\right)=\left[\begin{array}{cc}\cos {\mathrm{\φ}}_j\left(t\right)& \sin {\mathrm{\φ}}_j\left(t\right)\\ -\sin {\mathrm{\φ}}_j\left(t\right)& \cos {\mathrm{\φ}}_j\left(t\right)\end{array}\right];$ wherein phi_sAnd phi_eRepresenting the cutting and cutting angles of the cutter teeth relative to the workpiece, respectively.

Further, the cutting force dynamic matrix K (T) is a periodic function matrix with a period of T/N, that is, K (T + T/N) ═ K (T), and each element in the cutting force dynamic matrix K (T) may be fourier-transformed.

Further, the larger the positive integer α is chosen, the more accurate the approximation, but the more complex the calculation.

Further, the 4 α +2 order symmetric positive definite matrix Φ₁And phi₂When α is equal to 1, the following may be taken: ${\mathrm{\Φ}}_1={\mathrm{\Φ}}_2=\left[\begin{array}{cccccc}1& & & & & \\ & 2& & & & \\ & & 2& & & \\ & & & 1& & \\ & & & & 2& \\ & & & & & 2\end{array}\right]*{10}^{11}.$

compared with the prior art, the technical scheme provided by the invention utilizes the characteristic that the cutting force dynamic matrix periodically changes, adopts Fourier series approximation, designs the self-adaptive control current automatically adjusted along with the displacement change of the spindle, further changes the inherent dynamic characteristic of the spindle unit through the magnetic suspension bearing to inhibit flutter, can obtain the beneficial effect that the whole milling process can still be kept stable when the milling is carried out under the condition of large axial cutting depth, and further improves the milling efficiency while ensuring the surface quality of a workpiece.

Drawings

FIG. 1 is a graph of milling stability region with the horizontal axis showing the magnitude of the rotation speed in revolutions per minute; the vertical axis represents the axial depth of cut in millimeters;

FIG. 2 is a schematic diagram of a closed-loop control model;

FIG. 3 is a schematic structural diagram of a main body of the milling chatter active suppression system;

the meanings of the reference symbols in the figures are as follows: 1 is a milling cutter; 2 is a knife handle; 3, a magnetic suspension bearing rotor displacement self-detection component; 4 is a radial magnetic suspension bearing; 5, a magnetic suspension bearing rotor displacement self-detection component; 6 is a radial magnetic suspension bearing; 7 is a power amplifier; 8 is a power amplifier; 9 is a magnetic suspension bearing controller; 10 is PC; 11 is a filter; 12 is a workbench; and 13 is a workpiece.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

The following further describes embodiments of the present invention with reference to the drawings. It should be noted that the description of the embodiments is provided to help understanding of the present invention, but the present invention is not limited thereto. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

In the actual milling process, when the axial cutting depth b is very small, the dynamic cutting force F is applied to any specified main shaft rotating speed omega_t(t) the influence on the whole milling process is small, namely the whole milling process is stable, but the milling efficiency is low at the moment and does not meet the requirements of people; a larger axial cut is desired to obtain a higher milling efficiency, but as the axial cut b increases, the whole system is subjected to dynamic cutting forces F_t(t), thus becoming unstable, generating chattering phenomena, affecting the processing quality of the workpiece; as shown in fig. 1, the horizontal axis represents the magnitude of the spindle rotation speed Ω, the vertical axis represents the magnitude of the axial cutting depth b, the solid curve in the figure is used as a boundary, the lower part of the curve represents a stable region (no chatter vibration occurs), and the upper part of the curve represents an unstable region (chatter vibration occurs).

In order to improve the milling efficiency and ensure the processing quality of a workpiece, the invention provides a milling flutter active control method based on a magnetic suspension bearing electric spindle on the basis of a dynamic model in the milling process; the method specifically comprises the following steps:

establishing a milling kinetic equation, arranging the milling kinetic equation and carrying out state space transformation to obtain a state space equation;

(II) designing self-adaptive control current Q according to the established milling kinetic equation_c(t)。

More specifically, in the step (one), when the main shaft is static, the modal mass m of the milling cutter system structure, the damping ratio zeta of the milling cutter system structure and the inherent circumferential ratio omega of the milling cutter system structure are obtained through identification_nAnd then, replacing modal parameters during the rotation milling of the main shaft with the structural modal parameters of the milling cutter system obtained when the main shaft is static, and then establishing a corresponding 2-degree-of-freedom system model to describe the vibration of the main shaft, wherein the obtained main shaft vibration model is as follows:

$\left[\begin{array}{c}m{\stackrel{\·\·}{q}}_1\left(t\right)\\ m{\stackrel{\·\·}{q}}_2\left(t\right)\end{array}\right]+\left[\begin{array}{cc}2\mathrm{\ζ}{\mathrm{\ω}}_n& 0\\ 0& 2\mathrm{\ζ}{\mathrm{\ω}}_n\end{array}\right]\left[\begin{array}{c}{\stackrel{\·}{q}}_1\left(t\right)\\ {\stackrel{\·}{q}}_2\left(t\right)\end{array}\right]+\left[\begin{array}{cc}{\mathrm{\ω}}^2& 0\\ 0& {\mathrm{\ω}}^2\end{array}\right]\left[\begin{array}{c}{q}_1\left(t\right)\\ q_2\left(t\right)\end{array}\right]=0$

wherein q is₁(t) and q₂(t) is the amount of displacement in two degrees of freedom of the principal axis.

Further, the coefficient of the cutting force is identified through a milling experiment, and the dynamic cutting force F is carried out_t(t) modeling; tangential cutting force coefficient K obtained by combining identification_tAnd coefficient of normal cutting force K_rThe dynamic cutting force model is established as $F_t\left(t\right)={\mathrm{bf}}_{z}K\left(t\right)\left[\begin{array}{c}1\\ 0\end{array}\right]+\mathrm{bK}\left(t\right)\left[\begin{array}{c}{q}_1(t-T/N)-q_1\left(t\right)\\ q_2(t-T/N)-q_2\left(t\right)\end{array}\right],$ Wherein b denotes axial cutting depth, f_zShowing the feed amount of each cutter tooth, T showing the rotation period of the main shaft, N showing the number of cutter teeth of the milling cutter, $K\left(t\right)=\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{g}_j\left({\mathrm{\φ}}_j\left(t\right)\right)S\left(t\right){\left[K_t{K}_r\right]}^T\left[\sin {\mathrm{\φ}}_j\left(t\right)\cos {\mathrm{\φ}}_j\left(t\right)\right]$ is dynamic of cutting forceThe matrix, cutting force dynamic matrix K (T), is a periodic function matrix with T/N as period, i.e. K (T + T/N) ═ K (T), phi_j(T) represents the rotation angle of the jth tooth of the milling cutter, the superscript T of the vector represents the transposition of the vector (the same applies below), g_j(φ_j(t)) and S (t) respectively represent a screening function and a trigonometric function matrix, and the expression is as follows:

$S\left(t\right)=\left[\begin{array}{cc}\cos {\mathrm{\φ}}_j\left(t\right)& \sin {\mathrm{\φ}}_j\left(t\right)\\ -\sin {\mathrm{\φ}}_j\left(t\right)& \cos {\mathrm{\φ}}_j\left(t\right)\end{array}\right]$

wherein phi_sAnd phi_eRespectively representing cutter teethThe cut-in and cut-out angles with respect to the workpiece.

Further, the milling kinetic equation in the step (one) can be established as follows:

$\left[\begin{array}{c}m{\stackrel{\·\·}{q}}_1\left(t\right)\\ m{\stackrel{\·\·}{q}}_2\left(t\right)\end{array}\right]+\left[\begin{array}{cc}2\mathrm{\ζ}{\mathrm{\ω}}_n& 0\\ 0& 2\mathrm{\ζ}{\mathrm{\ω}}_n\end{array}\right]\left[\begin{array}{c}{\stackrel{\·}{q}}_1\left(t\right)\\ {\stackrel{\·}{q}}_2\left(t\right)\end{array}\right]+\left[\begin{array}{cc}{{\mathrm{\ω}}_n}^2& 0\\ 0& {{\mathrm{\ω}}_n}^2\end{array}\right]\left[\begin{array}{c}{q}_1\left(t\right)\\ q_2\left(t\right)\end{array}\right]={\mathrm{bf}}_{z}K\left(t\right)\left[\begin{array}{c}1\\ 0\end{array}\right]+\mathrm{bK}\left(t\right)\left[\begin{array}{c}{q}_1(t-T/N)-q_1\left(t\right)\\ q_2(t-T/N)-q_2\left(t\right)\end{array}\right]$

and the state space equation in step (one) is as follows:

$\left[\begin{array}{c}{\stackrel{\·}{q}}_1\left(t\right)\\ {\stackrel{\·}{q}}_2\left(t\right)\\ {\stackrel{\·\·}{q}}_1\left(t\right)\\ {\stackrel{\·\·}{q}}_2\left(t\right)\end{array}\right]=\left[\begin{array}{cccc}0& 0& 1& 0\\ 0& 0& 0& 1\\ -{{\mathrm{\ω}}_n}^2& 0& -2\mathrm{\ζ}{\mathrm{\ω}}_n& 0\\ 0& -{{\mathrm{\ω}}_n}^2& 0& -2\mathrm{\ζ}{\mathrm{\ω}}_n\end{array}\right]\left[\begin{array}{c}{q}_1\left(t\right)\\ q_2\left(t\right)\\ {\stackrel{\·}{q}}_1\left(t\right)\\ {\stackrel{\·}{q}}_2\left(t\right)\end{array}\right]+$

$b\left[\begin{array}{cc}0& 0\\ 0& 0\\ 1/m& 0\\ 0& 1/m\end{array}\right]f_{z}K\left(t\right)\{\left[\begin{array}{c}1\\ 0\end{array}\right]+K\left(t\right)\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\end{array}\right]\left[\begin{array}{c}{q}_1(t-T/N-q_1\left(t\right)\\ q_2(t-T/N)-q_2\left(t\right)\\ {\stackrel{\·}{q}}_1(t-T/N)-{\stackrel{\·}{q}}_1\left(t\right)\\ {\stackrel{\·}{q}}_2(t-T/N)-{\stackrel{\·}{q}}_2\left(t\right)\end{array}\right]\}$

in order to ensure that the water-soluble organic acid,

$Q\left(t\right)\left[\begin{array}{c}{q}_1\left(t\right)\\ q_2\left(t\right)\\ {\stackrel{\·}{q}}_1\left(t\right)\\ {\stackrel{\·}{q}}_2\left(t\right)\end{array}\right],A=\left[\begin{array}{cccc}0& 0& 1& 0\\ 0& 0& 0& 1\\ -{{\mathrm{\ω}}_n}^2& 0& -2\mathrm{\ζ}{\mathrm{\ω}}_n& 0\\ 0& -{{\mathrm{\ω}}_n}^2& 0& -2\mathrm{\ζ}{\mathrm{\ω}}_n\end{array}\right],B=\left[\begin{array}{cc}0& 0\\ 0& 0\\ 1/m& 0\\ 0& 1/m\end{array}\right]$

the above equation state space equation becomes:

$\stackrel{\·}{Q}\left(t\right)=\mathrm{AQ}\left(t\right)+\mathrm{bB}{\{f}_{z}K\left(t\right){\left[1\begin{array}{cc}& \end{array}0\right]}^T+K\left(t\right)C_q[Q(t-T/N)-Q\left(t\right)]\}$

wherein,representing the state velocity, A representing the state displacement term coefficient matrix, B representing the cutting force coefficient matrix, C_qRepresenting a time-lag state shift term coefficient matrix.

In the second step, the current Q is controlled adaptively_cThe design process of (t) is as follows:

(1) fourier transform is carried out on each element in the cutting force dynamic matrix K (t) to obtain a cutting force harmonic dynamic matrix K_α(t) and harmonic dynamic matrix K according to cutting force_α(t) obtaining harmonics

Wherein the cutting force harmonic dynamic matrix K_α(t) the sum of the first 2 α +1 terms of the fourier series expansion for each element in the cutting force dynamics matrix k (t), where: an unknown constant vector of 2 α +1 dimensions may be set, ω ═ 2 π N/T is the harmonic frequency, α is a suitable positive integer selected, the larger α, the more precise the approximation, but the more complex the calculation, here we select α ═ 2, and further may set the harmonic shift to 2Wherein the electric principal axis is displaced [ F ]_xF_y]^T＝C_q[Q(t-T/N)-Q(t)]Electric spindle displacement F in the x-direction_xAnd electric spindle displacement F in the y direction_yAre each 1-dimensional vectors, the x-direction and the y-direction are in a plane perpendicular to the principal axis, and the x-direction and the y-direction are perpendicular to each other, and h (t) is a 4 α + 2-dimensional column vector.

(2) According to the state displacement term coefficient matrix A and the Lyapunov equation beta A + A^Tbeta-I, a symmetric positive definite matrix beta is obtained, and a state weight coefficient [ Λ ] is obtained from the symmetric positive definite matrix beta₁Λ₂]XB, according to a state weight coefficient [ Λ₁Λ₂]And the state vector Q (t) obtains a first adaptive weight coefficientAnd a second adaptive weight coefficientWhere I is an identity matrix of 4 rows and 4 columns, Λ₁And Λ₂Are all four-dimensional column vectors, λ_iIs a one-dimensional vector, i is 1, 2.

(3) Designing a first adaptation rateAnd a second adaptation rateTwo arbitrary positive definite matrixes of 4 α +2 order symmetry are taken, where phi is used₁And phi₂Then let the first adaptive change rate beThe second adaptive rate of change isThen, by solving the adaptive change rate in the form of differential equation, the first adaptive rate can be obtainedAnd a second adaptation rateWherein the first adaptation rateAnd a second adaptation rateAre 4 α +2 dimensional column vectors.

(4) According to a first adaptation rateSecond rate of adaptationAnd harmonic shift h (t) obtaining an adaptive control current Q_c(t), the expression of which is:wherein Q_cAnd (t) is a 2-dimensional column vector.

Further, the calculated adaptive control current Q_c(t) multiplying the corresponding coefficient K of the electric spindle of the magnetic suspension bearing_ambAnd obtaining the force generated by the magnetic suspension bearing as follows: f_a(t)＝K_amb·Q_c(t) to form a stable closed loop control system (as shown in FIG. 2), i.e. $\stackrel{\·}{Q}\left(t\right)=\mathrm{AQ}\left(t\right)+\mathrm{bB}\{f_{z}K\left(t\right){\left[1\begin{array}{cc}& \end{array}0\right]}^T+K\left(t\right)C_q[Q(t-T/N)-Q\left(t\right)\left]\right\}+F_a\left(t\right),$ Wherein K_ambIs a 4 row 2 column matrix.

Secondly, performing online active control based on a milling flutter active suppression device according to the designed adaptive control current; as shown in figure 3, the main components required by the online active control are a magnetic suspension bearing milling electric spindle, a magnetic suspension bearing rotor displacement self-detection component and a magnetThe suspension bearing controller and the signal auxiliary processing part are formed; the magnetic suspension bearing milling electric spindle comprises two radial magnetic suspension bearings 4 and 6, a cutter 1, a cutter handle 2 and other spindle parts; the magnetic suspension bearing rotor displacement self-detection component comprises a band-pass circuit, a primary amplification circuit, a differential detection circuit, a demodulation circuit, a low-pass filter circuit and the like, and is mainly integrated in 3 and 5 in the figure; the magnetic suspension bearing controller is an integrated controller 9 based on DSP; the signal auxiliary processing part includes a filter 11, power amplifiers 7 and 8, and a/D and D/a signal conversion circuits. The components are adopted to realize the online flutter active suppression of the milling of the numerical control machine tool, and the process is as follows: the spindle motor drives the cutter 1 to rotate to mill a workpiece 13, and when the axial cutting depth b is large in the process, chatter vibration is easy to occur, and the chatter vibration phenomenon generated in the machining process is monitored in real time through the magnetic suspension bearing rotor displacement self-detection parts 3 and 5; when the flutter phenomenon is detected, the magnetic suspension bearing rotor displacement self-detection parts 3 and 5 transmit vibration signals to a filter 11, then the vibration signals are amplified by a power amplifier 8 and then transmitted to a magnetic suspension bearing controller 9 through A/D conversion, the vibration signals are displayed in a PC10, and meanwhile, the vibration quantity is brought into the self-adaptive control current Q designed off line in the prior art_c(t) calculating the adaptive control current Q in PC10_c(t) and finally the calculated adaptive control current Q_c(t) the output signal obtained after being processed by the magnetic bearing controller 9 is converted into a current signal through D/A conversion and then processed by the power amplifier 7, the current signal acts on the radial magnetic bearings 4 and 6, and the corresponding magnetic field force is generated to restrain the vibration of the main shaft, so that the stability of milling is correspondingly ensured. The closed-loop control simulation effect can be shown as a point curve in fig. 1, a stable region formed by the closed-loop point curve is far larger than a stable region formed by an open-loop solid curve, namely, when the axial cutting depth is larger, a closed-loop system is also stable, and further the processing efficiency is improved.

It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (6)

1. A milling flutter active control method based on a magnetic suspension bearing electric spindle is characterized by comprising the following steps:

(1) acquiring a current displacement signal when milling flutter occurs to the spindle;

(2) after filtering, amplifying and differentiating the current displacement signal, obtaining a state vector Q (t) formed by the displacement and the speed of the electric spindle;

(3) obtaining an electrical spindle displacement [ F ] from the state vector Q (t)_xF_y]^T＝C_q[Q(t-T/N)-Q(t)]；

Wherein $C_q=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\end{array}\right],$ Q (T-T/N) is a state vector formed by the displacement and the speed of the electric spindle at the time of T-T/N, T represents the rotation period of the spindle, N represents the number of cutter teeth of the milling cutter, F_xIs the displacement of the electric main shaft in the x direction, F_yFor the electric spindle displacement in the y direction, superscript T represents the transpose of the vector;

(4) fourier transform is carried out on each element in the cutting force dynamic matrix K (t) to obtain a cutting force harmonic dynamic matrix K_α(t) and harmonic dynamic matrix K according to cutting force_α(t) obtaining a trigonometric function sequence vector

Wherein the cutting force harmonic dynamic matrix K_α(T) the sum of the first 2 α +1 terms, where the fourier series expansion is performed for each element in the cutting force dynamic matrix k (T), ω -2 π N/T is the harmonic frequency, α is a positive integer;

(5) according to the electric spindle displacement [ F ]_xF_y]^TAnd the trigonometric function column vectorObtaining harmonic shift

(6) According to the state displacement term coefficient matrix A and the Lyapunov equation beta A + A^Tbeta-I, a symmetric positive definite matrix beta is obtained, and a state weight coefficient [ Λ ] is obtained from the symmetric positive definite matrix beta₁Λ₂]XB, according to a state weight coefficient [ Λ₁Λ₂]And the state vector Q (t) obtains a first adaptive weight coefficientAnd a second adaptive weight coefficientB is a cutting force coefficient matrix;

(7) according to the harmonic displacement h (t), the first adaptive weight coefficient lambda₁And said second adaptive weight coefficient lambda₂Obtaining a first adaptation rateAnd a second adaptation rate

Wherein the first adaptive rate of changeSecond adaptive rate of changeΦ₁And phi₂Two symmetric positive definite matrices of order 4 α +2, first adaptation rate, taken arbitrarily, respectivelyAnd a second adaptation rateAre 4 α + 2-dimensional column vectors;

(8) according to the first adaptive rateThe second adaptation rateAnd the harmonic displacement h (t) is obtained as an adaptive control current(9) Controlling the current Q adaptively_cAnd (t) acting on the radial magnetic suspension bearing and generating corresponding magnetic field force, thereby realizing the suppression of the main shaft flutter.

2. The active milling chattering control method according to claim 1, wherein the state displacement term coefficient matrix a is:

$A=\left[\begin{array}{cccc}0& 0& 1& 0\\ 0& 0& 0& 1\\ -{{\mathrm{\ω}}_n}^2& 0& -2{\mathrm{\ζ\ω}}_n& 0\\ 0& -{{\mathrm{\ω}}_n}^2& 0& -2{\mathrm{\ζ\ω}}_n\end{array}\right],$ zeta is the damping ratio, omega, of the milling cutter system structure_nIs the natural frequency of the milling cutter system structure.

3. The active milling chatter control method of claim 1, wherein the cutting force coefficient matrix B is: $B=\left[\begin{array}{cc}0& 0\\ 0& 0\\ 1/m& 0\\ 0& 1/m\end{array}\right],$ and m is the modal quality of the milling cutter system structure.

4. The active milling chatter control method of claim 1, wherein the cutting force dynamic matrix is: $K\left(t\right)=\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{g}_j\left({\mathrm{\φ}}_j\left(t\right)\right)S\left(t\right){\left[\begin{array}{cc}{K}_t& K_r\end{array}\right]}^T\left[\begin{array}{cc}{\mathrm{sin\φ}}_j\left(t\right)& {\mathrm{cos\φ}}_j\left(t\right)\end{array}\right];$

wherein phi_j(t) represents the rotation angle of the jth tooth of the milling cutter, K_tAnd K_rDenotes the coefficient of cutting force, g_j(φ_j(t)) and s (t) represent the screening function and the trigonometric function matrix, respectively; $S\left(t\right)=\left[\begin{array}{cc}{\mathrm{cos\φ}}_j\left(t\right)& {\mathrm{sin\φ}}_j\left(t\right)\\ -{\mathrm{sin\φ}}_j\left(t\right)& {\mathrm{cos\φ}}_j\left(t\right)\end{array}\right];$ φ_sand phi_eRepresenting the cutting and cutting angles of the cutter teeth relative to the workpiece, respectively.

5. The active milling chatter control method of claim 1, wherein the cutting force dynamic matrix K (T) is a periodic function matrix with a period of T/N, and K (T + T/N) is K (T).

6. The active milling chattering control method of claim 1, wherein the positive definite matrix Φ of order 4 α +2 symmetry₁And phi₂When α is equal to 1, the device will, ${\mathrm{\Φ}}_1={\mathrm{\Φ}}_2=\left[\begin{array}{cccccc}1& & & & & \\ & 2& & & & \\ & & 2& & & \\ & & & 1& & \\ & & & & 2& \\ & & & & & 2\end{array}\right]*{10}^{11}.$