CN102059573A - Modeling method for dual-driving synchronous electromechanical coupling characteristic of walking beam type gantry machine tool - Google Patents

Abstract

The invention discloses a modeling method for the dual-driving synchronous electromechanical coupling characteristic of a walking beam type gantry machine tool and solves the problems that the mechanical characteristics of a coupling part of the walking beam type gantry machine tool are decoupled and modeled. The modeling method is characterized in that the factor that the load of the gantry machine tool moves on a cross beam is considered and the problems that the speed of the dual-driving two-shaft coupling part is decoupled with force can be solved. According to the modeling method disclosed by the invention, the actual conditions of the mechanical characteristics for the dual-driving two shafts during synchronous movement can be accurately reflected and main factors for influencing the asynchronous error of two shafts can be disclosed; and the modeling method provides theoretical basis for measures for reducing the dual-driving asynchronous error.

Description

The two modeling methods of driving synchronous electromechanical coupling characteristics of movable beam type Longmen machine tool

Technical field

The present invention relates to a kind of modeling method, be specifically related to the two modeling methods of driving synchronous electromechanical coupling characteristics of a kind of movable beam type Longmen machine tool.

Background technology

The header portion of movable beam type Longmen machine tool (or two columns) is advanced by bi-motor, the common driving of mariages thick stick, and this kind portal frame structure is because electric parameter, the suffered frictional force mechanical couplings effects inconsistent and two between centers of diaxon have produced two asynchronous errors of driving diaxon, this error not only can make frame for movement produce distortion, also can reduce the exercise performance of system significantly, therefore, reduce the main key technology that two asynchronous errors of driving diaxon become the movable beam type Longmen machine tool.

Two frictional force and mechanical couplings of driving diaxon are the two nonsynchronous principal elements of diaxon of driving of influence, for realizing two Synchronization Control of driving diaxon, reduce the diaxon synchronous error, need set up and accurately to describe two Mathematical Modelings of driving Synchronization Control, describe out frictional force and mechanical couplings to two influences of driving synchronous error, the key of setting up this model promptly is to realize two decoupling zeros of driving diaxon speed and power.

In the Mathematical Modeling of a feed shaft of the common driving of existing bi-motor, what have simply is a second-order system with the transmission system equivalence, adopt the parameter of the method establishment model of System Discrimination, though can be with two mechanical couplings partly decoupleds that drive, but the operation principle that can not reflect control system, though what have sets up out single shaft transmission model according to theory analysis, but do not set up the control model part of diaxon tool mechanical couplings, promptly do not consider the suffered frictional force difference of diaxon, and diaxon is because the influence of the interaction force that mechanical couplings produces, therefore a kind of method of coupling unit being carried out decoupling zero based on theory analysis is proposed, and be applied to two drive the synchro system modeling, have very important significance.

Summary of the invention

The object of the present invention is to provide the two modeling methods of driving synchronous electromechanical coupling characteristics of a kind of movable beam type Longmen machine tool, can set up out two Synchronization Control models that drive, and then realize driving the synchronous accurate control of diaxon two based on theory based on the method.

For achieving the above object, the technical solution used in the present invention is:

Step 1: adopt the single shaft modeling method to set up two transmission system models that drive diaxon, obtain first driving force F ₁With second driving force F ₂

Step 2: with the first driving force F that obtains in the step 1 ₁With second driving force F ₂For input, set up the mechanical couplings model according to two mechanical properties of driving synchronization structure

Employing is carried out the decoupling zero that theoretic force analysis is realized diaxon power and speed to two common coupling units that drive of two motors that drive, and sets up out the mechanical couplings model of diaxon, and the formula of diaxon mechanical couplings is as follows:

(F ₁-F _f1)+(F ₂-F _f2)＝Ma (11)

y＝∫∫adt (12)

L ₁＝∫v _xdt (13)

L ₂＝L-L ₁ (14)

(F ₁-F _f1)L ₁-(F ₂-f _f2)L ₂＝J _MBα (15)

y ₁≈y+L ₁α (16)

${\mathrm{<figure-callout\; id="1"\; label="v"\; filenames="HDA0000031602820000032.png"\; state="\{\{state\}\}">v</figure-callout>}}_1=\frac{{\mathrm{<figure-callout\; id="1"\; label="dy"\; filenames="HDA0000031602820000032.png"\; state="\{\{state\}\}">dy</figure-callout>}}_1}{\mathrm{dt}}---\left(17\right)$

y ₂≈y-L ₂α (18)

${\mathrm{<figure-callout\; id="2"\; label="v"\; filenames="HDA0000031602820000032.png"\; state="\{\{state\}\}">v</figure-callout>}}_2=\frac{{\mathrm{<figure-callout\; id="2"\; label="dy"\; filenames="HDA0000031602820000032.png"\; state="\{\{state\}\}">dy</figure-callout>}}_2}{\mathrm{dt}}---\left(19\right)$

Diff＝y ₁-y ₂ (20)

F wherein ₁Be first driving force, f _F1Be first suffered frictional force, F ₂Be second driving force, f _F2Be second suffered frictional force, M is the crossbeam quality, and a is the barycenter acceleration of coupling unit, L ₁Be the distance of main shaft portion apart from driving shaft, L ₂Be the distance of main shaft portion distance from driving shaft, L is two distances of driving two between centers, and y is a crossbeam barycenter institute moving displacement, v _xBe the speed of load movement on the crossbeam, y ₁Driving shaft institute moving displacement, y ₂Be driven shaft institute moving displacement, Diff is the synchronous error v of diaxon ₁Be first speed, v ₁Be second speed, α is that the common mechanical part that drives is owing to the deflection angle that stressed difference produced, J _MBThe inertia that is produced with respect to the mass axis motion of coupling unit for whole mechanical couplings part;

According to the feed speed of the diaxon of separating decoupling, adopt frictional force model and identified parameters, calculate the frictional force of diaxon, realize the stressed decoupling zero of diaxon, diaxon frictional force is calculated as follows:

${\mathrm{<figure-callout\; id="1"\; label="f\; f"\; filenames="HDA0000031602820000032.png"\; state="\{\{state\}\}">f</figure-callout>}}_f={\mathrm{<figure-callout\; id="1"\; label="F\; c"\; filenames="HDA0000031602820000032.png"\; state="\{\{state\}\}">F</figure-callout>}}_c+(F_{s1}-F_{c1})e^{-{\left({v/v}_{s1}\right)}^{\mathrm{\&delta;}1}}+\mathrm{<figure-callout\; id="1"\; label="delta"\; filenames="HDA0000031602820000032.png"\; state="\{\{state\}\}">delta</figure-callout>}1\&CenterDot;v1---\left(21\right)$

${\mathrm{<figure-callout\; id="2"\; label="f\; f"\; filenames="HDA0000031602820000032.png"\; state="\{\{state\}\}">f</figure-callout>}}_f={\mathrm{<figure-callout\; id="2"\; label="F\; c"\; filenames="HDA0000031602820000032.png"\; state="\{\{state\}\}">F</figure-callout>}}_c+(F_{s2}-F_{c2})e^{-{\left({v/v}_{s2}\right)}^{\mathrm{\&delta;}2}}+\mathrm{<figure-callout\; id="2"\; label="delta"\; filenames="HDA0000031602820000032.png"\; state="\{\{state\}\}">delta</figure-callout>}2\&CenterDot;v2---\left(22\right)$

F wherein _F1Be first suffered frictional force, f _F2Be second suffered frictional force, F _S1Be first maximum static friction force, F _S2Be second maximum static friction force, F _C1Be first Coulomb friction power, F _C2Be second Coulomb friction power, v _S1Be the critical speed that first frictional force changes, v _S2It is the critical speed that second frictional force changes, δ 1 is that first beam warp is tested constant, δ 2 is that second beam warp is tested constant, delta1 is first viscous friction coefficient, delta2 is second viscous friction coefficient, draw the frictional force of diaxon according to formula (21) (22), finish the emulation of model in the substitution model.

In two foundation of driving the Synchronization Control model, mainly be the frictional force difference of diaxon and the common stressed difference in part (as crossbeam) two ends that drives of diaxon, and then the displacement that has produced these part two ends is inconsistent, caused the position deflection, and this position deflection has further caused diaxon to pull mutually, the coupling unit two ends are stressed more inconsistent, further caused the asynchronous of diaxon.Therefore setting up diaxon mechanical couplings model is the key of setting up accurate model, is the basis of the asynchronous error of analyzing influence, also is emphasis summary of the invention of the present invention.

The present invention loads under the prerequisite of moving on the crossbeam in consideration, by the decoupling zeros calculating that the force analysis at coupling unit two ends has been realized drive diaxon speed to two, simultaneously according to specific frictional force model, the actual speed that decoupling is separated in utilization calculates two frictional force of driving diaxon, and this frictional force factor is to influence one of single shaft control precision principal element.

The present invention integrates by two single shaft control model and the mechanical couplings models that drive diaxon that will set up respectively, has realized twoly driving diaxon speed and stressed decoupling zero, has set up twin shaft and has controlled model.Wherein the single shaft control model is output as the driving thrust that acts on workbench, and by will two driving the output substitution mechanical couplings model of diaxon single shaft control model separately, realization is two drives diaxon speed and stressed decoupling zero, finishes the foundation of twin shaft control model.

The present invention is based on theory analysis and realized the decoupling zero of diaxon coupling part component and speed, can on control principle, realize the synchronous error quantitative Analysis of Factors.

Considered to load on the factor of moving on the crossbeam in the decoupling method among the present invention, the quantitative analysis that in the time of can realizing the two-axle interlocking operation synchronous error is influenced.

Modeling method in according to the present invention is set up the control model, is convenient to realize, and is simple and clear, for theoretical foundation has been made in the proposition that the measure that reduces synchronous error is provided.

Description of drawings

The two Synchronization Control model framework charts that drive of Fig. 1;

Fig. 2 single axis table driving-chain analysis chart;

Fig. 3 Stribeck curve map;

Fig. 4 diaxon frictional force model curve figure;

Fig. 5 crossbeam force analysis figure;

Fig. 6 crossbeam moving displacement figure;

Lathe each several part composition diagram in Fig. 7 example;

Fig. 8 emulation and result of the test figure.

The specific embodiment

Driving the Synchronization Control model below in conjunction with complete two of accompanying drawing and of being built is described in further detail implementation method of the present invention.

Among the present invention, because bi-motor drives coupling unit jointly and does unidirectional feed motion, the each several part of its transmission system is formed with the single shaft feed system does not have too big difference, major different is two mechanical couplings effects of driving between moving component of diaxon muck in driving and the diaxon, therefore can utilize the analysis of single shaft feed system and modeling method to set up diaxon control model.At first set up the feed system transmission model of single shaft, consider two mechanical couplings parts of driving diaxon then, and then set up two control models that drive.Another pith of setting up model is the establishment of each parameter in the model, three planer-type milling machine lathes with a Dual-motors Driving trabeation in the instantiation are example, shown in the lathe each several part composition diagram in Fig. 7 example: workbench 1 is motionless, prop up crane span structure by first column 2 and second column 3, main spindle box (Z axle) can (X-axis) direction move on crossbeam 4, crossbeam 4 (X-axis) can move back and forth on the guide rail of being made up of Dual-motors Driving (Y-axis and V axle), in view of the above, set up the control model of Dual-motors Driving tool mechanical couplings workbench.

Drive the each several part module that the Synchronization Control model framework chart is depicted as institute's simulation model as Fig. 1 is two, model is drawn together with the lower part: driving shaft positioner (11), driven shaft positioner (21), driving shaft speed ring (12), driven shaft speed ring (22), driving shaft electric current loop (13), driven shaft electric current loop (23), driving shaft leading screw (14), driven shaft leading screw (24), driving shaft frictional force model (15), driven shaft frictional force model (25), diaxon mechanical couplings model (5).Be positioned at the driving shaft positioner (11) of digital control system inside, the speed command signal that driven shaft positioner (21) produces is given the driving shaft speed ring (12) of main driven shaft AC servo motor, driven shaft speed ring (22), then through driving shaft electric current loop (13), driven shaft electric current loop (23) produces Torque Control output, simultaneously by the detected rate signal of motor code-disc as driving shaft speed ring (12), the speed feedback of driven shaft speed ring (22) is carried out speed closed loop control, the moment of torsion output that is produced by motor offers driving shaft leading screw (14) respectively, driven shaft leading screw (24) rotatablely moves and promotes the main driven shaft workbench, and then diaxon speed is carried out decoupling zero by diaxon mechanical couplings model (5), set up driving shaft frictional force model (15), driven shaft frictional force model (25) feeds back to the position feedback of diaxon simultaneously and does position closed loop control in the digital control system.

1, sets up the control model of single shaft

1) foundation of mechanical drive department sub-model

A two motor, leading screw, workbench that drive in the diaxon are example (another axle is consistent with it).By Analysis of Transmission to single shaft control part and mechanical part, shown in Fig. 2 single axis table driving-chain analysis chart, the transmission relationship model formula that then can get mechanical part by principle of moment balance as the formula (1),

$\left\{\begin{array}{c}{T}_m=(J_m+J_s)\frac{{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HDA0000031602820000032.png"\; state="\{\{state\}\}">d</figure-callout>}}^2{\mathrm{\&theta;}}_{\mathrm{<figure-callout\; id="2"\; label="m\; dt"\; filenames="HDA0000031602820000032.png"\; state="\{\{state\}\}">m</figure-callout>}}}{{\mathrm{dt}}^{}}+T_M\\ T_M=K_s({\mathrm{\&theta;}}_m-{\mathrm{\&theta;}}_M)\\ F_M=\frac{2\mathrm{\&pi;}}{L_0}{T}_M\\ F_M-f_f=\mathrm{Ma}\\ f_f=\mathrm{\&mu;}\left(v\right)\end{array}\right.---\left(1\right)$

Wherein: T _mBe the output torque of motor, T _MBe the load torque of leading screw, J _mBe rotor rotary inertia, J _sBe the rotary inertia of leading screw, K _sBe the torsional rigidity of leading screw, θ _mBe rotor corner, θ _MFor leading screw contacts corner with workbench, f _fBe the frictional force of leading screw and driver part, F _MBe the driving force of leading screw to workbench, L _oBe the leading screw helical pitch, a is the acceleration of workbench, and M is the quality of driver part, and μ (v) is friction model, specifically sees the part of setting up of diaxon control model.J _m, L _o, M, μ (v) be the parameter that need determine at instantiation.J wherein _m, L _oMotor and leading screw specification according to concrete use obtain, and M obtains J by the quality of evaluation work platform _s, K _sCan obtain by formula (2):

$\left\{\begin{array}{c}{J}_S=\frac{{\mathrm{\&pi;r}}^2{\mathrm{<figure-callout\; id="0"\; label="L"\; filenames="HDA0000031602820000041.png"\; state="\{\{state\}\}">L</figure-callout>}}_0\mathrm{\&rho;}{\mathrm{<figure-callout\; id="2"\; label="D"\; filenames="HDA0000031602820000032.png"\; state="\{\{state\}\}">D</figure-callout>}}^2}{8}\\ K_s=\frac{{\mathrm{\&pi;GD}}^4}{32({\mathrm{<figure-callout\; id="0"\; label="L"\; filenames="HDA0000031602820000041.png"\; state="\{\{state\}\}">L</figure-callout>}}_0+y)}\end{array}\right.---\left(2\right)$

Wherein r is that leading screw radius, L are that leading screw length, ρ are the density of material of leading screw, and D is that diameter, the G of leading screw is that leading screw material shear modulus, y are the actual displacement that diaxon is passed by.According to concrete example, each parameter is: r=0.025 (m), L=2.670 (m), ρ=7800 (kg/m ³), G=8.24 * 10 ¹⁰(N/m ²)

It is as follows to obtain parameter thus:

J _m＝125×10 ^-4(kg·m ²)，L _o＝10(mm)，M＝1355kg，J _s＝127.72×10 ^-4(kg·m ²)

2) foundation of control section model

Feed drive system among the present invention adopts AC servo drive system and permagnetic synchronous motor.Permagnetic synchronous motor adopts rotor flux linkage orientation control (i _d=0), by the electromagnetic relationship of motor, the motor mathematical model that can obtain adopting the d-q axle to fasten is shown below:

$\left\{\begin{array}{c}{T}_m=K_t{i}_q\\ E_f=\mathrm{p\&omega;}{\mathrm{\&psi;}}_f=K_e\mathrm{\&omega;}\\ u_q-E_f={\mathrm{Ri}}_q+L_q\frac{{\mathrm{di}}_q}{\mathrm{<figure-callout\; id="2"\; label="dt\; J\; d"\; filenames="HDA0000031602820000032.png"\; state="\{\{state\}\}">dt</figure-callout>}}& \\ J\frac{d^{}}{}\frac{{}^2{\mathrm{\&theta;}}_m}{{\mathrm{<figure-callout\; id="2"\; label="dt"\; filenames="HDA0000031602820000032.png"\; state="\{\{state\}\}">dt</figure-callout>}}^2}=K_t{i}_q-T_M-B_m\frac{{\mathrm{d\&theta;}}_m}{\mathrm{dt}}\\ B_m=\frac{K_t{K}_e}{R}\end{array}\right.---\left(3\right)$

T wherein _mBe motor output torque, K _tBe motor torque constant, i _qBe stator current q shaft current, L _qBe stator winding q axle inductance, R is a stator resistance, E _fBe the counter electromotive force of motor, K _eBe the back electromotive force constant of motor, ω is the angular speed of motor, B _mEquivalent damping coefficient for motor.B _m, R, K _q, K _t, K _eBe the parameter that to determine at instantiation.K wherein _tCan obtain according to the selected rating of electric machine, and Several Parameters can obtain by following formula in addition;

$\left\{\begin{array}{c}R=\frac{(U_e\&CenterDot;I_e-P_e)}{2\&CenterDot;I_e^2}\left(\mathrm{\&Omega;}\right)\\ K_e=\sqrt{\frac{2}{3}}\&CenterDot;\frac{30\&CenterDot;(U_e-R\&CenterDot;I_e)}{n_e\&CenterDot;\mathrm{\&pi;}}(\mathrm{Vs}/\mathrm{rad})\\ L_q=\frac{30\&CenterDot;U_e}{2.5\&CenterDot;p\&CenterDot;\mathrm{\&pi;}\&CenterDot;n_e\&CenterDot;I_e}\end{array}\right.---\left(4\right)$

U wherein _e, I _e, n _e, P _e, P is rated voltage, rated current, rated speed, rated power, the number of pole-pairs of motor.

The used parameter of electric machine of the present invention is U _e=200 (V), I _e=54.7 (Arms), n _e=1500 (r/min), P _e=7.5 (KW), p=8.Then can try to achieve each parameter is:

K _t＝0.93(N·m/Arms)、R＝0.545(Ω)、K _e＝0.8843(Vs/rad)、L _q＝0.0132(H)

Servo-drive is typical three ring control structures: i.e. position ring, speed ring, electric current loop, controlling unit in this invention adopts digital control system to adopt speed control connection mode, positioner is arranged in digital control system, speed control and current controller are all in servo-drive system, wherein current controller adopts PI (proportional integral) control, speed control adopts PI control, positioner adopts P (ratio) control, for eliminating the vibration clutter in the command signal, a torque command wave filter, K have been added in the electric current loop front according to concrete servo-driver _PpBe position ring gain, K _PvBe speed ring gain, T _vBe speed ring integration time constant, T _fBe torque command time constant filter, K _PiBe current loop gain, T _iThe electric current loop integration time constant,

Be conversion coefficient, K _Pp, K _Pv, T _v, T _f, K _Pi, T _i, K is the parameter that need determine at concrete example, each parameter is among the present invention: K _Pp=2, K _Pv=100, T _v=0.01 (s), T _f=0.5ms, K _Pi=3000, T _i=57.2ms, K=0.0016.

2, two foundation of driving two shaft models

Two control section, motor parts of driving in two shaft models all adopt consistent parameter, so the parameter of parameters in the emulation and single shaft model, for distinguishing diaxon, driving shaft adopts and is designated as 1 parameter name down, and driven shaft adopts and is designated as 2 parameter name down.Set up two keys of driving diaxon Synchronization Control model and be the foundation of frictional force model and mechanical couplings part, thus below make labor at these two parts.

(1) the speed characteristics decoupling zero of diaxon mechanical couplings part

Existing mechanical couplings when two main distinctions of driving Synchronization Control model and single feeding model are that two motors drive crossbeam jointly.And this mechanical couplings is to set up two keys of driving the Synchronization Control model for producing the key factor of synchronous error so set up the mechanical couplings model.This mechanical couplings effect can be analyzed by analyzing common the stressed of part-crossbeam that drives of two motors, and shown in Fig. 5 crossbeam force analysis figure, crossbeam is respectively in the power that the contact portion place with leading screw is subjected to: the driving force (F of motor ₁, F ₂), the frictional force (f of crossbeam and leading screw part ₁, f ₂), normal pressure (N ₁, N ₂).The crossbeam barycenter produces displacement (y forward under the acting in conjunction of the driving force of two motors and frictional force ₁, y ₂), and the stressed difference at crossbeam two ends has caused the torsional movement of crossbeam, and that this torsional movement of crossbeam has produced the displacement at crossbeam two ends is inconsistent, and therefore the crossbeam motion that departs from ideal position can set up following mechanical couplings model shown in Fig. 6 crossbeam moving displacement figure:

$\left\{\begin{array}{c}(F_1-f_1)+(F_2-f_2)=\mathrm{Ma}\\ y=\&Integral;\&Integral;\mathrm{<figure-callout\; id="1"\; label="adt\; L"\; filenames="HDA0000031602820000032.png"\; state="\{\{state\}\}">adt</figure-callout>}& \\ L_{}{}_1=\&Integral;v_x\mathrm{<figure-callout\; id="2"\; label="dt\; L"\; filenames="HDA0000031602820000032.png"\; state="\{\{state\}\}">dt</figure-callout>}& \\ L_{}{}_2=L-L_1\\ (F_1-f_1)L_1-(F_2-f_2){\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HDA0000031602820000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_2=J_{\mathrm{MB}}\mathrm{\&alpha;}\\ {\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="HDA0000031602820000032.png"\; state="\{\{state\}\}">y</figure-callout>}}_1\&ap;y+{\mathrm{<figure-callout\; id="1"\; label="L"\; filenames="HDA0000031602820000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_1\mathrm{\&alpha;}\\ {\mathrm{<figure-callout\; id="1"\; label="v"\; filenames="HDA0000031602820000032.png"\; state="\{\{state\}\}">v</figure-callout>}}_1=\frac{{\mathrm{<figure-callout\; id="1"\; label="dy"\; filenames="HDA0000031602820000032.png"\; state="\{\{state\}\}">dy</figure-callout>}}_1}{\mathrm{<figure-callout\; id="2"\; label="dt\; y"\; filenames="HDA0000031602820000032.png"\; state="\{\{state\}\}">dt</figure-callout>}}& \\ y_{}{}_2\&ap;y-{\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HDA0000031602820000032.png"\; state="\{\{state\}\}">L</figure-callout>}}_2\mathrm{\&alpha;}\\ {\mathrm{<figure-callout\; id="2"\; label="v"\; filenames="HDA0000031602820000032.png"\; state="\{\{state\}\}">v</figure-callout>}}_2=\frac{{\mathrm{<figure-callout\; id="2"\; label="dy"\; filenames="HDA0000031602820000032.png"\; state="\{\{state\}\}">dy</figure-callout>}}_2}{\mathrm{dt}}\\ \mathrm{Diff}=y_1-y_2\end{array}\right.---\left(1\right)$

F wherein ₁Be first driving force, f _F1Be first suffered frictional force, F ₂Be second driving force, f _F2Be second suffered frictional force, M is the crossbeam quality, and a is the barycenter acceleration of coupling unit, L ₁Be the distance of main shaft portion apart from driving shaft, L ₂Be the distance of main shaft portion distance from driving shaft, L is two distances of driving two between centers, and y is a crossbeam barycenter institute moving displacement, v _xBe the speed of load movement on the crossbeam, y ₁Driving shaft institute moving displacement, y ₂Be driven shaft institute moving displacement, Diff is the synchronous error v of diaxon ₁Be first speed, v ₁Be second speed, α is that the common mechanical part that drives is owing to the deflection angle that stressed difference produced, J _MBThe inertia that is produced with respect to the mass axis motion of coupling unit for whole mechanical couplings part.F wherein ₁, F ₂Determine f by motor and speed thereof ₁, f ₂Determine that by the suffered frictional force in axle two ends specifically see the part that the frictional force model is set up, M is 1355kg for the crossbeam quality, do not consider main shaft factor when crossbeam moves back and forth during emulation, main shaft is placed in the middle of the crossbeam, L is then arranged ₁=L ₂=0.9m by setting up the mechanical model of lathe, has calculated crossbeam and the main shaft inertia J with respect to the crossbeam gravity axis in Solidworks _MB=1111 (kgm ²), so far, two all parameters of driving in the Synchronization Control model are established and are finished each parameter name and size in parameters such as following table 1 simulation model.

Each parameter name and size in table 1 simulation model

(2) two decoupling zeros of driving diaxon frictional force are calculated

The foundation of the frictional force model of mechanical part is to set up whole machine driven system model and control system model based, adopts the Stribeck friction model among the present invention, its expression formula as the formula (2):

$f\left(v\right)=F_c+(F_s-F_c)e^{-{(v/v_s)}^{\mathrm{\&delta;}}}+\mathrm{delta}\&CenterDot;v---\left(2\right)$

Wherein: F _sBe maximum static friction force, F _cBe Coulomb friction power, v _sBe the Stribeck critical speed, δ is an empirical, and delta is the viscous friction coefficient.Shown in the curve table diagrammatic sketch 3Stribeck curve map of friction model, this model has parameter than other models to be determined easily, and can be than the advantage of complete expression frictional force with the velocity variations process.

In the instantiation,, set up out the relation of frictional force and speed, establish out F by the nonlinear function match by measuring the frictional force under the friction speed _c, F _s, v _s, the isoparametric value of δ, delta, and then set up out the frictional force model.And directly measure the difficult realization of frictional force, pass through the indirect method of measurement among the present invention, promptly by measuring the frictional force that the moment of torsion on the leading screw comes evaluation work platform and guide rail under the certain speed.By formula (3)

F-f＝Ma (3)

As can be known, driving force F and frictional resistance are in poised state when a=0.Therefore can obtain the size of friction torque indirectly by the driving torque of measuring leading screw.And then obtain the size of frictional force and coefficient of friction.Adopted among the present invention and servo-driver is crossed RS232 with the computer expert be connected, utilized the method for the parameter estimator software of servo-driver, directly read and preserved the moment of torsion output valve of motor.The torque value of measuring each speed all is to begin to measure after crossbeam operates steadily, sample frequency is 25HZ, sampling time is 8s, in these 8 seconds, there is the torque value of minor fluctuations to average with least square method, this mean value as the Motor torque output valve under this speed, during the lathe operation, two two motors that drive are measured simultaneously, and utilize Matlab software to sampled data is carried out the nonlinear function match, can obtain frictional force model fitting result such as Fig. 4 diaxon frictional force model curve figure of diaxon

F _s1＝135.8730(N) F _s2＝202.1862(N)

F _c1＝42.2739(N) F _c2＝173.4290(N)

delt1＝0.0085 delt2＝0.0052

v _s1＝91.2534mm/min v _s2＝289.5762mm/min

Adopt Matlab/Simulink to carry out model emulation according to above-mentioned modeling method, the each several part model is built out respectively, then model is packaged into: subsystems such as position ring controller, speed ring controller, current loop controller, ball-screw model, frictional force model, mechanical couplings model.Then these subsystems are connected, the parameter that adopts is the emulation of finishing system model.Command signal employing displacement is the signal on slope in the emulation, the slope of ramp signal is 0.1, having represented feed speed is 0.1m/s, that is 6000mm/min, since in actual tests by time delay, the number of winning the confidence 0.05s start-up time constantly, in order to verify simulation model, the lathe crossbeam at the uniform velocity advances with the speed of 6000mm/min in the actual experiment, simultaneously utilize VC++ to write the reading software of data such as twin shaft velocity of displacement based on digital control system in open type, read and store the diaxon velocity of displacement data that feed back to by lathe grating chi, and obtain the offset deviation of diaxon, compare with the simulation result model, show by Fig. 8 emulation and result of the test figure (a) result, after wherein rate curve shows walking 100mm, the speed responsive state that tends towards stability substantially, so gathered the synchronous error of lathe in the reality with the feed speed walking 100mm of 6000mm/min, and with simulation result relatively, shown in Fig. 8 emulation and result of the test figure (b).The synchronous error of simulation result and result of the test are identical substantially, have proved the correctness of model, have illustrated that also the difference of diaxon frictional force and diaxon mechanical couplings are the principal element that produces the diaxon synchronous error.

More than show and describe basic principle of the present invention and principal character, those skilled in the art should understand, and the present invention is not subjected to the restriction of above-mentioned example; every according to content of the present invention; according to method of the present invention, do some improvement and variation, all drop into the scope of protection of the invention.

Claims (1)

1. two modeling methods of driving synchronous electromechanical coupling characteristics of movable beam type Longmen machine tool is characterized in that:

Step 1: adopt the single shaft modeling method to set up two transmission system models that drive diaxon, obtain first driving force F ₁With second driving force F ₂

Step 2: with the first driving force F that obtains in the step 1 ₁With second driving force F ₂For input, set up the mechanical couplings model according to two mechanical properties of driving synchronization structure

Employing is carried out the decoupling zero that theoretic force analysis is realized diaxon power and speed to two common coupling units that drive of two motors that drive, and sets up out the mechanical couplings model of diaxon, and the formula of diaxon mechanical couplings is as follows:

(F ₁-f _f1)+(F ₂-f _f2)＝Ma (11)

y＝∫∫adt (12)

L1＝∫v _xdt (13)

L ₂＝L-L ₁ (14)

(F ₁-f _f1)L ₁-(F ₂-f _f2)L ₂＝J _MBα (15)

y ₁≈y+L ₁α (16)

$v_1=\frac{{\mathrm{dy}}_1}{\mathrm{dt}}---\left(17\right)$

y ₂≈y-L ₂α (18)

$v_2=\frac{{\mathrm{dy}}_2}{\mathrm{dt}}---\left(19\right)$

Diff＝y ₁-y ₂ (20)

F wherein ₁Be first driving force, f _F1Be first suffered frictional force, F ₂Be second driving force, f _F2Be second suffered frictional force, M is the crossbeam quality, and a is the barycenter acceleration of coupling unit, L ₁Be the distance of main shaft portion apart from driving shaft, L ₂Be the distance of main shaft portion distance from driving shaft, L is two distances of driving two between centers, and y is a crossbeam barycenter institute moving displacement, v _xBe the speed of load movement on the crossbeam, y ₁Driving shaft institute moving displacement, y ₂Be driven shaft institute moving displacement, Diff is the synchronous error v of diaxon ₁Be first speed, v ₁Be second speed, α is that the common mechanical part that drives is owing to the deflection angle that stressed difference produced, J _MBThe inertia that is produced with respect to the mass axis motion of coupling unit for whole mechanical couplings part;

According to the feed speed of the diaxon of separating decoupling, adopt frictional force model and identified parameters, calculate the frictional force of diaxon, realize the stressed decoupling zero of diaxon, diaxon frictional force is calculated as follows:

$f_{f1}=F_{c1}+(F_{s1}-F_{c1})e^{-{(v/v_{s1})}^{\mathrm{\&delta;}1}}+\mathrm{delta}1\&CenterDot;v1---\left(21\right)$

$f_{f2}=F_{c2}+(F_{s2}-F_{c2})e^{-{(v/v_{s2})}^{\mathrm{\&delta;}2}}+\mathrm{delta}2\&CenterDot;v2---\left(22\right)$

F wherein _F1Be first suffered frictional force, f _F2Be second suffered frictional force, F _S1Be first maximum static friction force, F _S2Be second maximum static friction force, F _C1Be first Coulomb friction power, F _C2Be second Coulomb friction power, v _S1Be the critical speed that first frictional force changes, v _S2It is the critical speed that second frictional force changes, δ 1 is that first beam warp is tested constant, δ 2 is that second beam warp is tested constant, delta1 is first viscous friction coefficient, delta2 is second viscous friction coefficient, draw the frictional force of diaxon according to formula (21) (22), finish the emulation of model in the substitution model.

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