CN104647132A - Active control method of milling chatter vibration based on electric spindle of magnetic suspension bearing - Google Patents

Abstract

The invention discloses an active control method of milling chatter vibration based on an electric spindle of a magnetic suspension bearing. The method comprises the following steps: collecting a current displacement signal generated when the electric spindle has the milling chatter vibration; obtaining a state vector Q(t) formed by the displacement of the electric spindle and the speed; obtaining harmonic displacement which is shown as the formula in the description according to the electric spindle displacement [Fx Fy]T and a trigonometric function column vector phi(t); obtaining a first self-adaptive weight coefficient which is shown as the formula in the description and a second self-adaptive weight coefficient which is shown as the formula in the description; obtaining a first self-adaptive rate K1 and a second self-adaptive rate K2 according to the harmonic displacement h(t), the first self-adaptive weight coefficient lambda1 and a second self-adaptive weight coefficient lambda2; obtaining self-adaptive control current which is shown as the formula in the description according to the first self-adaptive rate K1, the second self-adaptive rate K2 and the harmonic displacement h(t); and applying the self-adaptive control current Qc(t) on a radial magnetic suspension bearing and generating corresponding magnetic field force so as to restrain the chatter vibration of the spindle. Through the active control method, the chatter vibration in the milling process is eliminated, thereby ensuring the processing quality and improving the processing efficiency.

Description

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

Technical field

The invention belongs to Computerized Numerical Control processing technology field, more specifically, relate to a kind of milling parameter Active Control Method based on magnetic suspension bearing electric chief axis.

Background technology

In complex-curved class part five-shaft numerical control processing Flutter Suppression, conventional method is based on Passive Control, these class methods are by regulating the technological parameters such as the speed of mainshaft, tool feeding cycle, maximum cutting-in, cutter length, angle between teeth, make system works in the below of salient angle effect point, thus obtain higher rotating speed and cutting-in under the prerequisite ensureing milling stability.Although passive control methods design and installation is simple, the stable region that it can adjust is very little, limited to the improvement of closed loop power.Therefore the control device changing the intrinsic dynamic characteristic of main axle unit must be adopted to suppress flutter, and this control device is namely based on the active control technology of magnetic suspension bearing electric chief axis.

The thought of magnetic suspension bearing electric chief axis active control technology is by configuring magnetic suspension bearing brake and sensor in spindle motor unit proper site, utilize the effect of FEEDBACK CONTROL, the overall dynamics performance of closed-loop system is changed, thus the closed-loop stabilization region of effective extension system, therefrom find the point that performance is more excellent, improve maximum metal milling rate.Active control technology has the ability of radical change system dynamics behavior, and therefore it suppresses the ability of flutter to be better than Passive Control technology far away.

Through the retrieval to existing document, find that there is following prior art: application number is 201310475810.8, publication No. is CN 103769945A, name is called " vibration suppressing method and lathe ", this technology is by changing the speed of mainshaft to reach the effect suppressing flutter, belong to Passive Control, also limited for the ability improving working (machining) efficiency.

Summary of the invention

For the defect of prior art, the object of the present invention is to provide a kind of milling parameter Active Control Method based on magnetic suspension bearing electric chief axis, be intended to solve the workpiece surface quality caused because of self-excitation chatter phenomenon in existing Digit Control Machine Tool Milling Process decline, the problem that milling efficiency is low.

The invention provides a kind of milling parameter Active Control Method based on magnetic suspension bearing electric chief axis, comprise the steps:

(1) when electro spindle generation milling parameter, the current displacement signal of electro spindle is gathered;

(2), after filter and amplification and differential process being carried out to described current displacement signal, the state vector Q (t) be made up of electro spindle displacement and speed is obtained; Described state vector Q (t) is the column vector of 4 dimensions;

(3) electro spindle displacement [F is obtained according to described state vector Q (t) _xf _y] ^t=C _q[Q (t-T/N)-Q (t)];

Wherein $C_q=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\end{array}\right],$ The electro spindle displacement that Q (t-T/N) is the t-T/N moment and the state vector that speed is formed, T represents main shaft swing circle, and N represents the number of teeth of milling cutter, the electro spindle displacement F in x direction _xwith the electro spindle displacement F in y direction _yare all vectors of 1 dimension, the subscript T of vector represents the transposition to vector;

(4) Fourier transformation is carried out to each element in cutting force dynamic matrix K (t), obtain cutting force harmonic wave dynamic matrix K _α(t), and according to cutting force harmonic wave dynamic matrix K _αt () obtains harmonic wave

Wherein cutting force harmonic wave dynamic matrix K _α(t) for each element in cutting force dynamic matrix K (t) carry out Fourier expansion front 2 α+1 item parts and, ω=2 π N/T is harmonic frequency, and α is the suitable positive integer chosen;

(5) according to described electro spindle displacement [F _xf _y] ^twith described trigonometric function column vector obtain harmonic displacement wherein harmonic displacement h (t) is 4 α+2 dimensional vectors;

(6) according to state displacement term coefficient matrix A and Lyapunov Equation Χ A+A ^tΧ=-I obtains symmetric positive definite matrix Χ, obtains state weight coefficient [Λ according to symmetric positive definite matrix Χ ₁Λ ₂]=XB, according to state weight coefficient [Λ ₁Λ ₂] and described state vector Q (t) obtain the first self adaptation weight coefficient with the second self adaptation weight coefficient

Wherein, I is the unit matrix that 4 row 4 arrange, Λ _ifour dimensional vectors, λ _ithe vector of one dimension, i=1,2;

(7) according to described harmonic displacement h (t), described first self adaptation weight coefficient λ ₁with described second self adaptation weight coefficient λ ₂obtain the first adaptive rate with the second adaptive rate

Wherein, the first adaptive change rate second adaptive change rate Φ ₁and Φ ₂be respectively the symmetric positive definite matrix on two 4 α+2 rank of getting arbitrarily, the first adaptive rate with the second adaptive rate be 4 α+2 dimensional vectors;

(8) according to described first adaptive rate described second adaptive rate and described harmonic displacement h (t) obtains Self Adaptive Control electric current wherein Q _ct () is 2 dimensional vectors;

(9) by described 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.

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

Further, described Cutting Force Coefficient matrix B is: $B=\left[\begin{array}{cc}0& 0\\ 0& 0\\ 1/m& 0\\ 0& 1/m\end{array}\right],$ M is the modal mass of milling cutter system architecture.

Further, described 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 φ _jt () represents the anglec of rotation of a jth cutter tooth of milling cutter, K _tand K _rrepresent Cutting Force Coefficient, g _j(φ _j(t)) and S (t) represent screening function and trigonometric function battle array respectively, expression formula is: $S\left(t\right)=\left[\begin{array}{cc}\cos {\mathrm{\φ}}_j\left(t\right)& \sin {\mathrm{\φ}}_j\left(t\right)\\ -\sin {\mathrm{\φ}}_j\left(t\right)& \cos {\mathrm{\φ}}_j\left(t\right)\end{array}\right];$ Wherein φ _sand φ _erepresent the incision of cutter tooth opposite piece respectively and cut out angle.

Further, described cutting force dynamic matrix K (t) take T/N as the periodic function matrix in cycle, i.e. K (t+T/N)=K (t), and then Fourier transformation can be carried out to each element in cutting force dynamic matrix K (t).

Further, it is larger that described positive integer α chooses, and approximate is more accurate, but computation complexity is larger.

Further, described 4 α+2 rank symmetric positive definite matrix Φ ₁and Φ ₂, can be taken as when α=1: ${\mathrm{\Φ}}_1={\mathrm{\Φ}}_2=\left[\begin{array}{cccccc}1& & & & & \\ & 2& & & & \\ & & 2& & & \\ & & & 1& & \\ & & & & 2& \\ & & & & & 2\end{array}\right]*{10}^{11}.$

By the above technical scheme that the present invention conceives, compared with prior art, this technical scheme utilizes this feature of cutting force dynamic matrix cyclically-varying, employing Fourier space is similar to, design the self-adjusting Self Adaptive Control electric current along with main shaft change in displacement, and then suppress flutter by the intrinsic dynamic characteristic of magnetic suspension bearing change main axle unit, the beneficial effect carrying out Milling Process when axial cutting-in is larger and whole milling process still can be kept stable can be obtained, thus while ensure that workpiece surface quality, also improve milling efficiency.

Accompanying drawing explanation

Fig. 1 is milling Stability diagram, and transverse axis represents rotating speed size, and unit is rev/min; The longitudinal axis represents axial cutting-in size, and unit is millimeter;

Fig. 2 is closed loop control framework schematic diagram;

Fig. 3 is the agent structure schematic diagram of Milling Process Active Flutter Suppression System;

In figure, the implication of each label is as follows: 1 is milling cutter; 2 is handle of a knife; 3 is magnetic suspension bearing rotor displacement Autonomous test parts; 4 is radial magnetic bearing; 5 is magnetic suspension bearing rotor displacement Autonomous test parts; 6 is radial magnetic bearing; 7 is power amplifier; 8 is power amplifier; 9 is magnetically suspended bearing; 10 is PC; 11 is wave filter; 12 is workbench; 13 is workpiece.

Detailed description of the invention

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.

Below in conjunction with accompanying drawing, the specific embodiment of the present invention is described further.It should be noted that at this, the explanation for these embodiments understands the present invention for helping, but does not form limitation of the 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.

In actual Milling Process, to the speed of mainshaft Ω specified arbitrarily, when axial cutting-in b is very little, dynamic cutting force F _tt () is very little on the impact of whole milling process, namely whole milling process is all stable, but now milling efficiency is very low, does not meet our requirement; So wish that larger axial cutting-in is to obtain higher milling efficiency, but along with the increase of axial cutting-in b, whole system can be subject to dynamic cutting force F _tthe impact of (t), the instability therefore become, produces chatter phenomenon, have impact on the crudy of workpiece; As shown in Figure 1, transverse axis represents the size of speed of mainshaft Ω, and the longitudinal axis represents the size of axial cutting-in b, with solid-line curve in scheming for boundary, represent stability region (flutter not occurring) below curve, above curve, represent unstable region (generation flutter).

The present invention, in order to improve milling efficiency and ensure workpiece processing quality, the basis of Dynamic Model of Milling Process proposes a kind of milling parameter Active Control Method based on magnetic suspension bearing electric chief axis; Specifically comprise the following steps:

(1) set up milling dynamics equation, milling dynamics equation arranged and carries out state space transformation, obtaining state space equation;

(2) according to the milling dynamics equation set up, design Self Adaptive Control electric current Q _c(t).

More specifically, in step (), when main shaft is static, obtain the modal mass m of milling cutter system architecture, the dampingratioζ of milling cutter system architecture and the intrinsic pi ω of milling cutter system architecture by identification _n, the milling cutter system architecture modal parameter obtained when recycling main shaft is static replaces modal parameter during main shaft rotation milling, and then set up corresponding 2DOF system model to describe the vibration of main shaft, the spindle vibration model of acquisition is:

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

Wherein q ₁(t) and q ₂t () is the displacement in main shaft two frees degree.

Further, go out Cutting Force Coefficient by milling Experimental Identification, carry out dynamic cutting force F _t(t) modeling; In conjunction with the cutting force COEFFICIENT K that identification obtains _twith normal direction Cutting Force Coefficient K _r, the dynamic cutting force model of foundation is $F_t\left(t\right)={\mathrm{bf}}_{z}K\left(t\right)\left[\begin{array}{c}1\\ 0\end{array}\right]+\mathrm{bK}\left(t\right)\left[\begin{array}{c}{q}_1(t-T/N)-q_1\left(t\right)\\ q_2(t-T/N)-q_2\left(t\right)\end{array}\right],$ Wherein b represents axial cutting-in, f _zrepresent every cutter tooth amount of feeding, T represents main shaft swing circle, and N represents the number of teeth of milling cutter, $K\left(t\right)=\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{g}_j\left({\mathrm{\φ}}_j\left(t\right)\right)S\left(t\right){\left[K_t{K}_r\right]}^T\left[\sin {\mathrm{\φ}}_j\left(t\right)\cos {\mathrm{\φ}}_j\left(t\right)\right]$ Be cutting force dynamic matrix, cutting force dynamic matrix K (t) take T/N as the periodic function matrix in cycle, i.e. K (t+T/N)=K (t), φ _jt () represents the anglec of rotation of a jth cutter tooth of milling cutter, the subscript T of vector represents the transposition (lower same) to vector, g _j(φ _j(t)) and S (t) represent screening function and trigonometric function battle array respectively, expression formula is:

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

Wherein φ _sand φ _erepresent the incision of cutter tooth opposite piece respectively and cut out angle.

And then can described in establishment step () milling dynamics equation be:

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

And state space equation is as follows described in step ():

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

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

Order,

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

Then above-mentioned formula 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, represent state velocity, A represents state displacement term coefficient matrix, and B represents Cutting Force Coefficient matrix, C _qrepresent hangover state displacement term coefficient matrix.

In step (two), Self Adaptive Control electric current Q _ct the design process of () is as follows:

(1) Fourier transformation is carried out to each element in cutting force dynamic matrix K (t), obtain cutting force harmonic wave dynamic matrix K _α(t), and according to cutting force harmonic wave dynamic matrix K _αt () obtains harmonic wave

Wherein cutting force harmonic wave dynamic matrix K _α(t) for each element in cutting force dynamic matrix K (t) carry out Fourier expansion front 2 α+1 item parts and, expression formula is: the constant vector that 2 unknown α+1 tie up can be set to; ω=2 π N/T is harmonic frequency, and α is the suitable positive integer chosen, and α is larger, and approximate is more accurate, but computation complexity is larger.At this, we choose α=2, can set further harmonic displacement as wherein electro spindle displacement [F _xf _y] ^t=C _q[Q (t-T/N)-Q (t)], the electro spindle displacement F in x direction _xwith the electro spindle displacement F in y direction _yare all vectors of 1 dimension, x direction and y direction are perpendicular in the plane of main shaft, and x direction is mutually vertical with y direction, and h (t) is 4 α+2 dimensional vectors.

(2) according to state displacement term coefficient matrix A and Lyapunov Equation Χ A+A ^tΧ=-I obtains symmetric positive definite matrix Χ, obtains state weight coefficient [Λ according to symmetric positive definite matrix Χ ₁Λ ₂]=XB, according to state weight coefficient [Λ ₁Λ ₂] and described state vector Q (t) obtain the first self adaptation weight coefficient with the second self adaptation weight coefficient wherein I is the unit matrix that 4 row 4 arrange, Λ ₁and Λ ₂all four dimensional vectors, λ _ithe vector of one dimension, i=1,2.

(3) the first adaptive rate is designed with the second adaptive rate get arbitrarily two 4 α+2 rank symmetric positive definite matrixs, use Φ respectively at this ₁and Φ ₂represent, then make the first adaptive change rate be second adaptive change rate is again by separating the adaptive change rate of differential equation form, the first adaptive rate can be obtained with the second adaptive rate wherein the first adaptive rate with the second adaptive rate be 4 α+2 dimensional vectors.

(4) according to the first adaptive rate second adaptive rate and harmonic displacement h (t) obtains Self Adaptive Control electric current Q _c(t), its expression formula is: wherein Q _ct () is 2 dimensional vectors.

Further, the Self Adaptive Control electric current Q will calculated _ct () is multiplied by corresponding magnetic suspension bearing electric chief axis COEFFICIENT K _amb, the size obtaining the power that magnetic suspension bearing produces is: F _a(t)=K _ambq _c(t), thus the closed-loop control system (as shown in Figure 2) that formation one is stable, namely $\stackrel{\·}{Q}\left(t\right)=\mathrm{AQ}\left(t\right)+\mathrm{bB}\{f_{z}K\left(t\right){\left[1\begin{array}{cc}& \end{array}0\right]}^T+K\left(t\right)C_q[Q(t-T/N)-Q\left(t\right)\left]\right\}+F_a\left(t\right),$ Wherein K _amb4 row 2 column matrix.

Secondly, the online ACTIVE CONTROL based on Milling Process active flutter surppression device is carried out according to the Self Adaptive Control electric current of design; As shown in Figure 3, the critical piece needed for online ACTIVE CONTROL is made up of magnetic suspension bearing milling electro spindle, magnetic suspension bearing rotor displacement Autonomous test parts, magnetically suspended bearing, signal APU four major part; Wherein, magnetic suspension bearing milling electro spindle comprises the spindle units such as two radial magnetic bearings 4 and 6, cutter 1, handle of a knife 2; Magnetic suspension bearing rotor displacement Autonomous test parts comprise band-pass circuit, one-level amplifying circuit, differential detection circuit, demodulator circuit, low-pass filter circuit etc., mainly integrated in the drawings 3 and 5 in; Magnetically suspended bearing is an integrated manipulator 9 based on DSP; Signal APU comprises wave filter 11, power amplifier 7 and 8, A/D and D/A signaling conversion circuit.Above-mentioned parts are adopted to realize the online active flutter surppression of Digit Control Machine Tool Milling Process, its process is: spindle motor carry its tools 1 rotates and carries out Milling Process to workpiece 13, in the process when axial cutting-in b is larger, very easily there is flutter, our chatter phenomenon by producing in magnetic suspension bearing rotor displacement Autonomous test parts 3 and 5 Real-Time Monitoring process; When detecting that chatter phenomenon occurs, magnetic suspension bearing rotor displacement Autonomous test parts 3 and 5 amplify through power amplifier 8 after vibration signal being passed to wave filter 11, then magnetically suspended bearing 9 is passed to by A/D conversion, and in PC10, show this vibration signal, vibratory output size is brought into the Self Adaptive Control electric current Q of offline design above simultaneously _ct () calculates Self Adaptive Control electric current Q in PC10 _cthe size of (t), the Self Adaptive Control electric current Q finally will calculated _ct output signal that () obtains after magnetically suspended bearing 9 processes is processed through power amplifier 7 after being changed by D/A, be converted into current signal, act on radial magnetic bearing 4 and 6, produce the flutter of corresponding magnetic field force to main shaft to suppress, ensure that the stability of Milling Process accordingly.Point curve wherein in the visible Fig. 1 of closed-loop control simulated effect, the stability region that the stability region that this closed loop point curve is formed is formed much larger than open loop solid-line curve, namely when axial cutting-in is larger, closed-loop system is also stable, and then improves working (machining) efficiency.

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 (6)

1., based on a milling parameter Active Control Method for magnetic suspension bearing electric chief axis, it is characterized in that, comprise the steps:

(1) current displacement signal during electro spindle generation milling parameter is gathered;

(2), after filter and amplification and differential process being carried out to described current displacement signal, the state vector Q (t) be made up of electro spindle displacement and speed is obtained;

(3) electro spindle displacement [F is obtained according to described state vector Q (t) _xf _y] ^t=C _q[Q (t-T/N)-Q (t)];

Wherein $C_q=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\end{array}\right],$ The electro spindle displacement that Q (t-T/N) is the t-T/N moment and the state vector that speed is formed, T represents main shaft swing circle, and N represents the number of teeth of milling cutter, F _xfor the electro spindle displacement in x direction, F _yfor the electro spindle displacement in y direction, subscript T represents the transposition to vector;

(4) Fourier transformation is carried out to each element in cutting force dynamic matrix K (t), obtain cutting force harmonic wave dynamic matrix K _α(t), and according to cutting force harmonic wave dynamic matrix K _αt () obtains trigonometric function column vector

Wherein cutting force harmonic wave dynamic matrix K _α(t) for each element in cutting force dynamic matrix K (t) carry out Fourier expansion front 2 α+1 item parts and, ω=2 π N/T is harmonic frequency, and α is positive integer;

(5) according to described electro spindle displacement [F _xf _y] ^twith described trigonometric function column vector obtain harmonic displacement

(6) according to state displacement term coefficient matrix A and Lyapunov Equation Χ A+A ^tΧ=-I obtains symmetric positive definite matrix Χ, obtains state weight coefficient [Λ according to symmetric positive definite matrix Χ ₁Λ ₂]=XB, according to state weight coefficient [Λ ₁Λ ₂] and described state vector Q (t) obtain the first self adaptation weight coefficient with the second self adaptation weight coefficient

(7) according to described harmonic displacement h (t), described first self adaptation weight coefficient λ ₁with described second self adaptation weight coefficient λ ₂obtain the first adaptive rate with the second adaptive rate

Wherein, the first adaptive change rate second adaptive change rate Φ ₁and Φ ₂be respectively the symmetric positive definite matrix on two 4 α+2 rank of getting arbitrarily, the first adaptive rate with the second adaptive rate be 4 α+2 dimensional vectors;

(8) according to described first adaptive rate described second adaptive rate and described harmonic displacement h (t) obtains Self Adaptive Control electric current (9) by described 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.

2. milling parameter Active Control Method as claimed in claim 1, it is characterized in that, described state displacement term coefficient matrix A is:

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

3. milling parameter Active Control Method as claimed in claim 1, it is characterized in that, described Cutting Force Coefficient matrix B is: $B=\left[\begin{array}{cc}0& 0\\ 0& 0\\ 1/m& 0\\ 0& 1/m\end{array}\right],$ M is the modal mass of milling cutter system architecture.

4. milling parameter Active Control Method as claimed in claim 1, it is characterized in that, described cutting force dynamic matrix is: $K\left(t\right)=\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{g}_j\left({\mathrm{\φ}}_j\left(t\right)\right)S\left(t\right){\left[\begin{array}{cc}{K}_t& K_r\end{array}\right]}^T\left[\begin{array}{cc}{\sin \mathrm{\φ}}_j\left(t\right)& {\cos \mathrm{\φ}}_j\left(t\right)\end{array}\right];$

Wherein φ _jt () represents the anglec of rotation of a jth cutter tooth of milling cutter, K _tand K _rrepresent Cutting Force Coefficient, g _j(φ _j(t)) and S (t) represent screening function and trigonometric function battle array respectively; $S\left(t\right)=\left[\begin{array}{cc}{\cos \mathrm{\φ}}_j\left(t\right)& {\sin \mathrm{\φ}}_j\left(t\right)\\ -{\sin \mathrm{\φ}}_j\left(t\right)& {\cos \mathrm{\φ}}_j\left(t\right)\end{array}\right];$ φ _sand φ _erepresent the incision of cutter tooth opposite piece respectively and cut out angle.

5. milling parameter Active Control Method as claimed in claim 1, is characterized in that, described cutting force dynamic matrix K (t) take T/N as the periodic function matrix in cycle, K (t+T/N)=K (t).

6. milling parameter Active Control Method as claimed in claim 1, is characterized in that, described 4 α+2 rank symmetric positive definite matrix Φ ₁and Φ ₂, when α=1, ${\mathrm{\Φ}}_1={\mathrm{\Φ}}_2=\left[\begin{array}{cccccc}1& & & & & \\ & 2& & & & \\ & & 2& & & \\ & & & 1& & \\ & & & & 2& \\ & & & & & 2\end{array}\right]*{10}^{11}.$