CN103425811A - Identification method of equivalent inertia and equivalent damping of feeding system of numerical control machine tool - Google Patents

Abstract

The invention relates to an identification method of equivalent inertia and equivalent damping of a feeding system of a numerical control machine tool. The identification method comprises establishing a simplified second order dynamics model of the feeding system and calculating to obtain a difference equation of the simplified second order dynamics model; performing continuous and effective motivation on the feeding system of the numerical control machine tool through G code displacement signals and meanwhile obtaining current signal and motor rotating speed signal data of a feeding servo motor; obtaining the equivalent inertia and the equivalent damping of the feeding system of the numerical control machine tool from the difference equation according to the least square method after the current signal and rotating speed signal data are brought into the difference equation. The identification method mainly solves the problem of dynamic parameter identification during dynamic modeling of the numerical control machine tool. According to the identification method of the equivalent inertia and the equivalent damping of the feeding system of the numerical control machine tool, the inertia and the damping of the system can be identified in the closed-loop state of the machine tool accurately, the accurate modeling of a servo system of the machine tool can be achieved, and the technical basis can be provided for achievement of high accuracy and high efficiency machining control of the numerical control machine tool.

Description

The equivalent inertia of NC machine tool feed system and the discrimination method of equivalent damping

Technical field

The present invention relates to the discrimination method of a kind of NC machine tool feed system equivalent inertia and equivalent damping, particularly utilize the G code displacement signal continuously and effectively to encourage NC machine tool feed system, using current of electric data and the motor speed data discrimination method as parameter.

Background technology

At a high speed, accurate, be efficiently the direction of Modern NC Machine Tool development, but the dynamic perfromance of feed system has important impact to precision and the efficiency of high-speed machine tool.The commercial digital control system of the top grade of controlling for closed-loop, suitable feed system is controlled parameter and is depended on Mechanic system parameter.Inappropriate control parameter not only can make feed system larger tracking error occur, also there will be the vibration of mechanical system when serious, causes the degradation of crudy even to cause device damage, thereby affects crudy and working (machining) efficiency.Based on this, obtain the dynamic parameter of feed systems such as equivalent inertia and equivalent damping, realize the modeling of feed system, carry out the Research on Dynamic Characteristic of feed system, realize the control of high-speed machine tool high precision, be the prerequisite that realizes high speed, precision, highly-efficient processing.In addition, the numerically-controlled machine in production, realize that Open-loop Identification is very difficult, and best bet is closed-loop identification, and adopting suitable pumping signal is the key of carrying out closed-loop identification, requires the excitation that pumping signal can continuous and effective to the system of institute's identification.Be subject to the open restriction of numerically-controlled machine, to the input signal of numerically-controlled machine digital control system kinematic axis, except position signalling, other signal is all very difficult.

Summary of the invention

According to this situation, the present invention proposes a kind of discrimination method to NC machine tool feed system equivalent inertia and equivalent damping, during the method has solved and produced, lathe is difficult to the difficult problem of open loop closed loop, can accurately pick out equivalent inertia and equivalent damping accordingly, the method proposed is Machine Tool Feeding System dynamic modeling accurately, and the working (machining) efficiency and the crudy that improve numerically-controlled machine are significant.

The discrimination method of a kind of NC machine tool feed system equivalent inertia and equivalent damping is characterized in that having:

The 1st step, set up the feed system second order kinetic model of simplifying and calculate its difference equation;

The 2nd step, continuously and effectively encourage NC machine tool feed system by the G code displacement signal, and obtain current signal and the motor speed signal data of feed servo motor simultaneously;

The 3rd step, by the data of current signal and tach signal, after bringing difference equation into, draw equivalent inertia and the equivalent damping of NC machine tool feed system from difference equation according to least square method.

In the 1st step, feed system second order kinetic model and difference equation draw by following process above:

At first, take motor shaft as research object, according to the relevant control theory, set up the differential equation:

${\mathrm{iK}}_t=J_e\stackrel{\·}{\mathrm{\ω}}+B_e\mathrm{\ω}+T_e---\left(1\right)$

Wherein, K _tFor motor torque constant, J _eFor equivalent inertia, B _mFor equivalent damping, ω is motor angular velocity, and i is current of electric

Then, the differential equation (1) is rewritten into to equation (2):

$K_t(i-T_e/K_t)=J_e\stackrel{\·}{\mathrm{\ω}}+B_e\mathrm{\ω}---\left(2\right)$

Then, by both sides Laplace transformation computing, described equation (2) is deformed into to equation (3):

$W\left(s\right)=\frac{b}{a}\×\frac{a}{s+a}[I\left(s\right)-T_e\left(s\right)/K_t]---\left(3\right)$

Wherein, W, I is respectively the Laplace transformation form of ω, i, and a=B _e/ J _e, b=K _t/ J _e

Then, with T _sFor the sampling period, to equation (3) discretize, draw difference equation (4):

$\mathrm{\ω}(k+1)=e^{-a{T}_s}\mathrm{\ω}\left(k\right)+\frac{b}{a}(1-e^{-a{T}_s})[i\left(k\right)-T_e\left(k\right)/K_t]---\left(4\right)$

Then, the T of moment of friction will be derived from _e(k)/K _tBe equivalent to interference current, suppose that with ω interference current in the same way be d _f ⁺, the reverse interference electric current is d _f ^-, the two all can be seen as the function of ω, now T _eCan be write as:

$T_e\left(\mathrm{\ω}\left(k\right)\right)=P_V\left(\mathrm{\ω}\left(k\right)\right)\·{d_f}^{+}+N_V\left(\mathrm{\ω}\left(k\right)\right)\·{d_f}^{-}$

Wherein, P _V(ω (k)), N _V(ω (k)) is respectively for describing d _f ⁺, d _f ^-The function of direction is defined by following formula:

$P_V\left(\mathrm{\&omega;}\left(k\right)\right)=\left\{\begin{array}{cc}0& \mathrm{\&omega;}\left(k\right)<\mathrm{\&Omega;}\\ 1& \mathrm{\&omega;}\left(k\right)\&GreaterEqual;\mathrm{\&Omega;}\end{array}\right.,N_V\left(\mathrm{\&omega;}\left(k\right)\right)=\left\{\begin{array}{cc}0& \mathrm{\&omega;}\left(k\right)>-\mathrm{\&Omega;}\\ -1& \mathrm{\&omega;}\left(k\right)\&le;-\mathrm{\&Omega;}\end{array}\right.$

Wherein, Ω is the threshold values of judging velocity reversal, according to difference equation (4), draws difference equation (5)

${\mathrm{\&omega;}}_m(k+1)=[\mathrm{\&omega;}\left(k\right)i\left(k\right)-P_V\left(\mathrm{\&omega;}\left(k\right)\right)-N_V\left(\mathrm{\&omega;}\left(k\right)\right)]$

${[e^{-a{T}_s}b(1-e^{-a{T}_s})/\mathrm{ab}(1-e^{-a{T}_s}){d_f}^{+}/\mathrm{ab}(1-e^{-a{T}_s})d_f-/a]}^T---\left(5\right)$

In above-mentioned the 2nd step, by the G code displacement signal, NC machine tool feed system continuously and effectively being encouraged is according to following process implementation:

At first, required pumping signal u is comprised of the second displacement curve of the constant duration of the different acceleration of m section, and m<10, every section quafric curve acceleration respectively:

a ₀K,a ₁K,...,a _iK,...,a _mK

Wherein K is the scale factor constant

Then, regulation forms whole displacement excitation curve by the little straight-line segment of n section constant duration, and n > > m.

Wherein, every little straight-line segment time interval is T _s, be the discrete minimum interval of curve, get the integral multiple of machine tool position controller control cycle.

Then, obtain the speed command v of the little straight-line segment of k section _kWith displacement commands y _k:

$v_k=\underset{i=0}{\overset{k}{\mathrm{\&Sigma;}}}{a}_{\mathrm{ij}}{T}_s$

$u_k=\underset{i=0}{\overset{k}{\mathrm{\&Sigma;}}}{v}_i{T}_s$

Wherein, described a _IjRefer to that the little straight-line segment of i section institute is in j section quafric curve section.

In above-mentioned the 3rd step, by the data of current signal and tach signal, after bringing difference equation into, draw equivalent inertia and the equivalent damping of NC machine tool feed system from difference equation according to least square method, by following process implementation:

At first define following equation for difference equation (5):

Y ⁰=[ω(2)ω(3)...ω(N)] ^T

${\mathrm{\&Phi;}}^0=\left[\begin{array}{cccc}\mathrm{\&omega;}\left(1\right)& i\left(1\right)& -P_V\left(\mathrm{\&omega;}\left(1\right)\right)& -N_V\left(\mathrm{\&omega;}\left(1\right)\right)\\ \mathrm{\&omega;}\left(2\right)& i\left(2\right)& -P_V\left(\mathrm{\&omega;}\left(2\right)\right)& -N_V\left(\mathrm{\&omega;}\left(2\right)\right)\\ ...& ...& ...& ...\\ \mathrm{\&omega;}(N-1)& i(N-1)& -P_V\left(\mathrm{\&omega;}(N-1)\right)& -N_V\left(\mathrm{\&omega;}(N-1)\right)\end{array}\right]$

${\mathrm{\&theta;}}^0={[e^{-a{T}_s}b(1-e^{-a{T}_s})/\mathrm{ab}(1-e^{-a{T}_s}){d_f}^{+}/\mathrm{ab}(1-e^{-a{T}_s}){d_f}^{-}/a]}^T$

Then, according to the least squares identification theoretical method, draw θ ⁰The optimal estimation vector:

$\widehat{{\mathrm{\&theta;}}^0}={\left({\left({\mathrm{\&Phi;}}^0\right)}^T{\mathrm{\&Phi;}}^0\right)}^{-1}{\left({\mathrm{\&Phi;}}^0\right)}^T{Y}^0---\left(6\right)$

Wherein, ω (2), ω (3) ... ω (N) is the 2nd, 3 ... the motor shaft angular velocity in N sampling period,

I (1), i (2) ... i (N-1) is respectively the 1st, 2 ... the current of electric in N-1 sampling period,

Then, define and be used for respectively describing d _f ⁺, d _f ^-The function P of direction _V(ω (k)), N _V(ω (k)):

$P_V\left(\mathrm{\&omega;}\left(k\right)\right)=\left\{\begin{array}{cc}0& \mathrm{\&omega;}\left(k\right)<\mathrm{\&Omega;}\\ 1& \mathrm{\&omega;}\left(k\right)\&GreaterEqual;\mathrm{\&Omega;}\end{array}\right.,N_V\left(\mathrm{\&omega;}\left(k\right)\right)=\left\{\begin{array}{cc}0& \mathrm{\&omega;}\left(k\right)>-\mathrm{\&Omega;}\\ -1& \mathrm{\&omega;}\left(k\right)\&le;-\mathrm{\&Omega;}\end{array}\right.$

Wherein, Ω is the threshold values that defines the axle zero angle speed of servomotor.

Thus, draw the NC machine tool feed system equivalent inertia:

J _e=K _t/b，

Thus, draw equivalent damping:

B _e=aJ _e

Wherein, $a=-1n\left(\widehat{{\mathrm{\&theta;}}^0}\left(1\right)\right)/T_s,b=a\widehat{{\mathrm{\&theta;}}^0}\left(2\right)/(1-e^{-a{T}_s})$

Representative respectively

The 1st, 2 row components of vector

Carrying out identification when test, first get less scale factor K, then strengthen gradually, when tending towards stability, the result of identification stops experiment, get experimental result value after final as identification result.

Invention effect and effect

The present invention is by utilizing G code can the dynamic continuance of feed system effectively be encouraged, and then the discrimination method proposed, and accurately picks out equivalent inertia and equivalent damping, thereby can overcome the difficult problem that the numerically-controlled machine in production is difficult to Open-loop Identification and effectively encourages;

Provide simple and practical discrimination method accurately to obtain equivalent inertia and equivalent damping, thereby can provide technical foundation for NC machine tool feed system power system modeling accurately;

Can provide foundation for improving the crudy of numerically-controlled machine in high-speed, high precision processing and the solution of working (machining) efficiency problem.

The accompanying drawing explanation:

Fig. 1 is the identification principle figure in embodiment

Fig. 2 is electric current, the tach signal data of the identification in embodiment

Fig. 3 is the NC machine tool feed system kinetic model of the simplification in embodiment

(a) be time, accelerating curve

(b) be time, rate curve

(c) be time, displacement curve

Fig. 4 is the example of empirical curve as a result of the identification in embodiment

(a) be the identification result of equivalent inertia

(b) be the identification result of equivalent damping

Embodiment:

The experimental technique that the NC machine tool feed system equivalent inertia provided in present embodiment and equivalent damping carry out identification comprises the following steps:

The 1st step: set up the feed system second order kinetic model of simplifying and calculate its difference equation.

Fig. 1 is the identification principle figure in embodiment, as shown in Figure 1:

At first, take motor shaft as research object, according to the relevant control theory, set up the differential equation:

${\mathrm{iK}}_t=J_e\stackrel{\&CenterDot;}{\mathrm{\&omega;}}+B_e\mathrm{\&omega;}+T_e---\left(1\right)$

Wherein, K _tFor motor torque constant, J _eFor equivalent inertia, B _mFor equivalent damping, ω is motor angular velocity, and i is current of electric

Fig. 2 is electric current, the tach signal data of the identification in embodiment.As shown in Figure 2, when determining the axis servomotor of identification, for the tach signal ω of the needed current i of the identification of J, B and motor, the external interface provided by servo-driver obtains.

Then, the differential equation (1) is rewritten into to equation (2):

$K_t(i-T_e/K_t)=J_e\stackrel{\&CenterDot;}{\mathrm{\&omega;}}+B_e\mathrm{\&omega;}---\left(2\right)$

Then, by both sides Laplace transformation computing, described equation (2) is deformed into to equation (3):

$W\left(s\right)=\frac{b}{a}\&times;\frac{a}{s+a}[I\left(s\right)-T_e\left(s\right)/K_t]---\left(3\right)$

Wherein, W, I is respectively the Laplace transformation form of ω, i, and a=B _e/ J _e, b=K _t/ J _e

Then, with T _sFor the sampling period, to equation (3) discretize, draw difference equation (4):

$\mathrm{\&omega;}(k+1)=e^{-a{T}_s}\mathrm{\&omega;}\left(k\right)+\frac{b}{a}(1-e^{-a{T}_s})[i\left(k\right)-T_e\left(k\right)/K_t]---\left(4\right)$

Then, the T of moment of friction will be derived from _e(k)/K _tBe equivalent to interference current, suppose that with ω interference current in the same way be d _f ⁺, the reverse interference electric current is d _f ^-, the two all can be seen as the function of ω, now T _eCan be write as:

$T_e\left(\mathrm{\&omega;}\left(k\right)\right)=P_V\left(\mathrm{\&omega;}\left(k\right)\right)\&CenterDot;{d_f}^{+}+N_V\left(\mathrm{\&omega;}\left(k\right)\right)\&CenterDot;{d_f}^{-}$

Wherein, P _V(ω (k)), N _V(ω (k)) is respectively for describing d _f ⁺, d _f ^-The function of direction is defined by following formula:

$P_V\left(\mathrm{\&omega;}\left(k\right)\right)=\left\{\begin{array}{cc}0& \mathrm{\&omega;}\left(k\right)<\mathrm{\&Omega;}\\ 1& \mathrm{\&omega;}\left(k\right)\&GreaterEqual;\mathrm{\&Omega;}\end{array}\right.,N_V\left(\mathrm{\&omega;}\left(k\right)\right)=\left\{\begin{array}{cc}0& \mathrm{\&omega;}\left(k\right)>-\mathrm{\&Omega;}\\ -1& \mathrm{\&omega;}\left(k\right)\&le;-\mathrm{\&Omega;}\end{array}\right.$

Wherein, Ω is the threshold values of judging velocity reversal, according to difference equation (4), draws difference equation (5)

${\mathrm{\&omega;}}_m(k+1)=[\mathrm{\&omega;}\left(k\right)i\left(k\right)-P_V\left(\mathrm{\&omega;}\left(k\right)\right)-N_V\left(\mathrm{\&omega;}\left(k\right)\right)]$

${[e^{-a{T}_s}b(1-e^{-a{T}_s})/\mathrm{ab}(1-e^{-a{T}_s}){d_f}^{+}/\mathrm{ab}(1-e^{-a{T}_s})d_f-/a]}^T---\left(5\right)$

The 2nd step of the NC machine tool feed system equivalent inertia that the present embodiment is related and the discrimination method of equivalent damping: by the G code displacement signal, NC machine tool feed system continuously and effectively being encouraged is according to following process implementation:

Input signal is input to the numerically-controlled machine positioner.

Fig. 3 (a) is time, accelerating curve.As shown in Fig. 3 (a)

Required pumping signal u is comprised of the second displacement curve of the constant duration of the different acceleration of m section, and m<10, every section quafric curve acceleration respectively:

a ₀K, _a1K,...,a _iK,...,a _mK

Wherein K is the scale factor constant

Then, regulation forms whole displacement excitation curve by the little straight-line segment of n section constant duration, and n > > m

Wherein, every little straight-line segment time interval is T _s, be the discrete minimum interval of curve, get the integral multiple of machine tool position controller control cycle

Then, obtain the speed command v of the little straight-line segment of k section _kWith displacement commands y _k:

$v_k=\underset{i=0}{\overset{k}{\mathrm{\&Sigma;}}}{a}_{\mathrm{ij}}{T}_s$

$u_k=\underset{i=0}{\overset{k}{\mathrm{\&Sigma;}}}{v}_i{T}_s$

Wherein, described a _IjRefer to that the little straight-line segment of i section institute is in j section quafric curve section

The 3rd step: by the data of current signal and tach signal, after bringing difference equation into, draw equivalent inertia and the equivalent damping of NC machine tool feed system from difference equation according to least square method, by following process implementation

At first define following equation for difference equation (5):

Y ⁰=[ω(2)ω(3)...ω(N)] ^T

${\mathrm{\&Phi;}}^0=\left[\begin{array}{cccc}\mathrm{\&omega;}\left(1\right)& i\left(1\right)& -P_V\left(\mathrm{\&omega;}\left(1\right)\right)& -N_V\left(\mathrm{\&omega;}\left(1\right)\right)\\ \mathrm{\&omega;}\left(2\right)& i\left(2\right)& -P_V\left(\mathrm{\&omega;}\left(2\right)\right)& -N_V\left(\mathrm{\&omega;}\left(2\right)\right)\\ ...& ...& ...& ...\\ \mathrm{\&omega;}(N-1)& i(N-1)& -P_V\left(\mathrm{\&omega;}(N-1)\right)& -N_V\left(\mathrm{\&omega;}(N-1)\right)\end{array}\right]$

${\mathrm{\&theta;}}^0={[e^{-a{T}_s}b(1-e^{-a{T}_s})/\mathrm{ab}(1-e^{-a{T}_s}){d_f}^{+}/\mathrm{ab}(1-e^{-a{T}_s}){d_f}^{-}/a]}^T$

Then, according to the least squares identification theoretical method, draw θ ⁰The optimal estimation vector:

$\widehat{{\mathrm{\&theta;}}^0}={\left({\left({\mathrm{\&Phi;}}^0\right)}^T{\mathrm{\&Phi;}}^0\right)}^{-1}{\left({\mathrm{\&Phi;}}^0\right)}^T{Y}^0---\left(6\right)$

Wherein, ω (2), ω (3) ... ω (N) is the 2nd, 3 ... the motor shaft angular velocity in N sampling period,

I (1), i (2) ... i (N-1) is respectively the 1st, 2 ... the current of electric in N-1 sampling period,

Then, define and be used for respectively describing d _f ⁺, d _f ^-The function P of direction _V(ω (k)), N _V(ω (k)):

$P_V\left(\mathrm{\&omega;}\left(k\right)\right)=\left\{\begin{array}{cc}0& \mathrm{\&omega;}\left(k\right)<\mathrm{\&Omega;}\\ 1& \mathrm{\&omega;}\left(k\right)\&GreaterEqual;\mathrm{\&Omega;}\end{array}\right.,N_V\left(\mathrm{\&omega;}\left(k\right)\right)=\left\{\begin{array}{cc}0& \mathrm{\&omega;}\left(k\right)>-\mathrm{\&Omega;}\\ -1& \mathrm{\&omega;}\left(k\right)\&le;-\mathrm{\&Omega;}\end{array}\right.$

Wherein, Ω is the threshold values that defines the axle zero angle speed of servomotor

Thus, draw the NC machine tool feed system equivalent inertia

J _e=K _t/b，

Thus, draw equivalent damping

B _e=aJ _e

Wherein, $a=-1n\left(\widehat{{\mathrm{\&theta;}}^0}\left(1\right)\right)/T_s,b=a\widehat{{\mathrm{\&theta;}}^0}\left(2\right)/(1-e^{-a{T}_s})$

Wherein,

Representative respectively The 1st, 2 row components of vector,

Fig. 4 (a) is the result of the equivalent inertia identification in embodiment;

Fig. 4 (b) is the result of the equivalent damping identification in embodiment.

When carrying out the identification test, first get less scale factor K, then strengthen gradually, when tending towards stability, the result of identification stops experiment, get final experimental result value as identification result, as shown in Figure 4.

Finally, the present invention not only is only limited to embodiment, based on aim of the present invention, can carry out various variations, these is not got rid of from scope of the present invention.

Claims (4)

1. the discrimination method of a NC machine tool feed system equivalent inertia and equivalent damping is characterized in that having:

The 1st step, set up the feed system second order kinetic model of simplifying and calculate its difference equation;

The 2nd step, continuously and effectively encourage NC machine tool feed system by the G code displacement signal, and draw current signal data and the motor speed signal data of feed servo motor simultaneously;

The 3rd step, by described current signal data and described tach signal data, after bringing described difference equation into, draw equivalent inertia and the equivalent damping of NC machine tool feed system from described difference equation according to least square method.

2. the discrimination method of NC machine tool feed system equivalent inertia according to claim 1 and equivalent damping is characterized in that:

In described the 1st step, described feed system second order kinetic model and described difference equation draw by following process:

At first, according to the relevant control theory, take motor shaft as research object, set up the differential equation:

Wherein, K _tFor motor torque constant, J _eFor equivalent inertia, B _mFor equivalent damping, ω is motor angular velocity, and i is current of electric,

Then, the described differential equation is rewritten into to equation (2):

Then, by both sides Laplace transformation computing, described equation (2) is deformed into to equation (3):

$W\left(s\right)=\frac{b}{a}?\frac{a}{s+a}[I\left(s\right)T_e\left(s\right)/K_t]---\left(3\right)$

Wherein, W, I is respectively the Laplace transformation form of ω, i, and a=B _e/ J _e, b=K _t/ J _e,

Then, with T _SFor the sampling period, to described equation (3) discretize, draw difference equation (4):

$\mathrm{\&omega;}(k+1)=e^{{-\mathrm{aT}}_s}\mathrm{\&omega;}\left(k\right)+\frac{b}{a}(1-e^{{-\mathrm{aT}}_s})[i\left(k\right)-T_e\left(k\right)/K_t]---\left(4\right)$

Then, the T of moment of friction will be derived from _e(k)/K _tBe equivalent to interference current, suppose that with ω interference current in the same way be d _f ⁺, the reverse interference electric current is d _f ^-, the two all can be seen as the function of ω, now T _eCan be write as:

T _e(ω(k))=P _V(ω(k))?d _f ⁺N _V(ω(k))□d _f ^-

Wherein, P _V(ω (k)), N _V(ω (k)) is respectively for describing d _f ⁺, d _f ^-The function of direction is defined by following formula:

$N_v\left(\mathrm{\&omega;}\left(k\right)\right)=\begin{array}{ccc}0& \mathrm{\&omega;}\left(k\right)>& -W\\ -1& \mathrm{\&omega;}\left(k\right)?& W\end{array}$

Wherein, W is the threshold values of judging velocity reversal, according to described difference equation (4), draws difference equation (5),

${\mathrm{\&omega;}}_m(k+1)=[\mathrm{\&omega;}\left(k\right)i\left(k\right)-P_V\left(\mathrm{\&omega;}\left(k\right)\right)-N_V\left(\mathrm{\&omega;}\left(k\right)\right)]$

3. the discrimination method of NC machine tool feed system equivalent inertia according to claim 1 and equivalent damping is characterized in that:

In described the 2nd step, by the G code displacement signal, NC machine tool feed system continuously and effectively being encouraged is according to following process implementation:

At first, required pumping signal u is comprised of the second displacement curve of the constant duration of the different acceleration of m section, and m<10, every section quafric curve acceleration respectively:

a ₀K,α ₁K,…,α _iK,…,a _mK

Wherein K is the scale factor constant,

Then, regulation forms whole displacement excitation curve by the little straight-line segment of n section constant duration, and n > > m,

Wherein, every little straight-line segment time interval is T _s, be the discrete minimum interval of curve, get the integral multiple of machine tool position controller control cycle,

Then, obtain the speed command v of the little straight-line segment of k section _kWith displacement commands y _k:

$v_k=\underset{i=0}{\overset{k}{\mathrm{\&Sigma;}}}{a}_{\mathrm{ij}}{T}_s$

$u_k=\underset{i=0}{\overset{k}{\mathrm{\&Sigma;}}}{v}_i{T}_s$

Wherein, described a _IjRefer to that the little straight-line segment of i section institute is in j section quafric curve section.

4. the discrimination method of NC machine tool feed system equivalent inertia according to claim 1 and equivalent damping is characterized in that:

In described the 3rd step, after bringing described current signal data and described tach signal data into described difference equation, according to least square method, from described difference equation, draw described equivalent inertia and equivalent damping, by following process implementation:

At first, define following equation for described difference equation (5):

Then, according to the least squares identification theoretical method, draw the optimal estimation vector of described θ 0:

$\widehat{{\mathrm{\&theta;}}^0}={\left({\left({\mathrm{\&Phi;}}^0\right)}^T{\mathrm{\&Phi;}}^0\right)}^{-1}{\left({\mathrm{\&Phi;}}^0\right)}^T{Y}^0---\left(6\right)$

Wherein, ω (2), ω (3),

The 2nd, 3 ... the motor shaft angular velocity in N sampling period,

Wherein, i (1), i (2),

Respectively the 1st, 2 ... the current of electric in N-1 sampling period,

Then, define and be used for respectively describing d _f ⁺, d _f ^-The function P of direction _V(ω (k)), N _V(ω (k)):

$N_v\left(\mathrm{\&omega;}\left(k\right)\right)=\begin{array}{ccc}0& \mathrm{\&omega;}\left(k\right)>& -W\\ -1& \mathrm{\&omega;}\left(k\right)?& W\end{array}$

Wherein, W is the threshold values that defines the axle zero angle speed of described servomotor.

Thus, draw the NC machine tool feed system equivalent inertia:

J _e=K _t/b，

Thus, draw equivalent damping:

B _e=aJ _e

Wherein, $a=-\ln \left(\widehat{{\mathrm{\&theta;}}^{\text{0}}}\left(1\right)\right)/T_s,$ $b=a\widehat{{\mathrm{\&theta;}}^0}\left(2\right)/(1-e^{{-\mathrm{aT}}_s});$

Representative respectively

The 1st, 2 row components of vector.

Images