CN108107734A - A kind of permanent magnetic linear synchronous motor feed system mechanical-electric coupling modeling method - Google Patents
A kind of permanent magnetic linear synchronous motor feed system mechanical-electric coupling modeling method Download PDFInfo
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Abstract
The present invention provides a kind of permanent magnetic linear synchronous motor feed system mechanical-electric coupling modeling method, comprises the following steps：1. utilize spectrum signature of the electromagnetic energy method analysis with calculating permanent magnetic linear synchronous motor servo thrust output；2. establish permanent magnetic linear synchronous motor feed system mechanical kinetics model using Lagrange's equation；3. analyze the interactively that intercouples between permanent magnetic linear synchronous motor feed system servo-drive and mechanical system；4. according to the interactively that intercouples between servo-drive and mechanical system, permanent magnetic linear synchronous motor feed system various factors coupling electromechanical Coupling Model is established.The present invention can quickly and effectively in analysis system all kinds of coupled problems essential laws.Influence size of all kinds of mechanical-electric couplings of evaluation fast and reliable simultaneously to system motion stationarity.It further supplements due to new change caused by mechanical-electric coupling problem, the perfect integrated modelling approach of complex electromechanical systems.
Description
Technical field
The present invention relates to High Speed NC Machine Tools Dynamic Performance Analysis fields, are specially a kind of permanent magnetic linear synchronous motor feeding
System mechanical-electric coupling modeling method.
Background technology
In recent years, as the efficient height of digital control processing is refined the increasingly raising of demand, permanent-magnetism linear motor feed system is with it
The advantages that outstanding high thrust, high speed, high acceleration and high-precision, before there is wide application in high-grade, digitally controlled machine tools
Scape.The Zero-drive Chain structure of Linear motor feeding system uniqueness so that motor thrust directly acts on mechanical system, and external interference
Etc. mechanical oscillation caused by factors also directly react on motor.Relation is intercoupled between servo-drive and mechanical system more
Step up it is close, have become influence Linear motor feeding system robust motion an important factor for.Especially it is applied to numerical control
The Linear motor feeding system of lathe, mechanical system and nonideal single inertia system, are influenced by each dynamic engaging portion characteristic, are had
There is multistage Oscillatory mode shape, the coupled relation between system can be aggravated, deteriorate system motion precision.
It researchs and analyses at present in work, due to ignoring the dynamic characteristic of mechanical system, permanent magnetic linear synchronous motor feeding system
Mechanical-electric coupling problem in system obtains the deep analysis and research of system not yet.And influenced by many factors, servo is driven
It is dynamic between mechanical system there is not a kind of mechanical-electric coupling phenomenon, also exist between each coupling circuit and influence each other, increase
The difficulty researched and analysed.How the modeling of system is carried out to mechanical-electric coupling problem with analyzing for further controlling and changing
The influence of kind coupling has great importance.
The content of the invention
For problems of the prior art, the present invention provides a kind of permanent magnetic linear synchronous motor feed system electromechanics coupling
Modeling method is closed, can parsing characterization quickly and effectively be carried out to a few quasi-representative mechanical-electric coupling phenomenons present in system, is disclosed
The essential laws of coupling, at the same can quantitative description its influence to system motion stationarity, for commenting for mechanical-electric coupling problem
Valency and control, which improve, to have great importance.
The present invention is to be achieved through the following technical solutions：
A kind of permanent magnetic linear synchronous motor feed system mechanical-electric coupling modeling method, comprises the following steps：
Step 1 analyzes the frequency spectrum spy with calculating permanent magnetic linear synchronous motor servo thrust output using electromagnetic energy method
Sign；
Step 2 establishes permanent magnetic linear synchronous motor feed system mechanical kinetics model using Lagrange's equation；
Step 3, the feed system mechanical kinetics mould of servo thrust output spectrum signature and step 2 based on step 1
Type, from mechanical oscillation caused by the variation of linear motor air gap, thrust harmonic wave caused by mechanical torsional oscillation and mechanical twisting vibration
Three aspects of influence to grating scale feedback signal, analyze permanent magnetic linear synchronous motor feed system servo-drive and mechanical system
Between the interactively that intercouples；
Step 4 according to the interactively that intercouples between the servo-drive and mechanical system obtained in step 3, is built
Vertical permanent magnetic linear synchronous motor feed system various factors coupling electromechanical Coupling Model is as follows,
Wherein, F is permanent magnetic linear synchronous motor thrust, and k=a, b, c represent a, b, c three-phase of electrical-coil；ElkAnd Emk
Respectively the armature back-emf of three-phase coil and unloaded back-emf, ikFor servo three-phase current, v is motor movement speed；F0' be
Consider the motor name thrust of air gap variation, Fr' original thrust the harmonic wave of motor changed for consideration air gap, FgTo consider that air gap becomes
The new thrust harmonic components changed, xiIt is command signal, xoFor output signal of displacement, Gp(s) letter is passed for position ring control, s is micro-
Divide operator, Gv(s) letter, K are passed for speed ring controlAFor electric current loop equieffective ratio gain, KFFor motor thrust constant, FmFor motor
The nominal thrust of output, FrFor motor output harmonic wave power, GmF (s) be mechanical system direction of feed model, Gmi(s) for machinery other
Directional dynamics model；△ δ are that mechanical twisting vibrates the encoder errors generated, Ge(s) it is encoder errors and mechanical twisting
Biography letter between vibration；xδ0To consider the feedback signal of encoder errors.
Preferably, in step 1, according to the structure composition of driving circuit, considering driving circuit, to include dead zone humorous
All kinds of non-linear factors and electric machine structure of ripple, modulation harmonic wave and counter electromotive force harmonic wave include slot effect, end effect
Should be with all kinds of non-linear factors of magnetic linkage harmonic wave, using electromagnetic energy method, the frequency spectrum for calculating permanent magnetic linear synchronous motor thrust F is special
Sign is as follows,
F=∑s (Elk+Emk)·ik/v。
Preferably, in step 2, ignore the flexibility of workbench, take workbench along three axis and the fortune around three axis
It moves, i.e. { x, y, z, θx, θy, θz}TFor generalized coordinates；Ignore the effect of intercoupling between each vibration shape, utilize Lagrange's equation
The mechanical kinetics equation of Linear motor feeding system is established,
Wherein, X=[x y z θx θy θz]TFor worktable displacement,The respectively single order of X, second dervative, M,
C, K are respectively mass matrix, damping matrix and stiffness matrix, and F is external force matrix.
Preferably, when considering that linear motor air gap changes caused by being vibrated due to mechanical twisting in step 3, introduce opposite
Permeance function describes influence of the mechanical twisting vibration to motor gas-gap magnetic field, and utilizes electromagnetic energy method, and consideration gas is calculated
The motor thrust output of gap variation,
F=F '0+F′r+Fg。
Preferably, caused by considering thrust harmonic wave in step 3 during mechanical oscillation, establish based on PID three close-loop control models,
Wherein, position ring is controlled using P, and speed ring is controlled using PI, and electric current loop is equivalent to proportional gain, the motor that step 1 is obtained
Thrust output is introduced in the form of interference；By the dynamic characteristic in other directions of the mechanical system in addition to direction of feed respectively etc.
It imitates and introduces model for relatively independent two-order oscillation system, the parameters in model are obtained by Experimental Identification, it is final to establish
The electromechanical integrated model of system under the effect of thrust harmonic wave,
[(xi-x0)·Gp(s)-x0·s]·Gv(s)·KA·KF=F '0
(F′0+F′r+Fg)·Gmf(s)+∑(F′0+F′r+Fg)·Gmi(s)=x0。
Preferably, when influence of the mechanical twisting vibration to grating scale feedback signal is considered in step 3, based on grating scale work
Make principle, the encoder errors that mechanical twisting vibration generates be calculated,
Δ δ=∑ (F0′+Fr′+Fg)·Gmi(s)·Ge(s),
And obtained encoder feedback error is introduced into feedback control loop, obtain considering the feedback letter of encoder errors
Number,
xδ0=x0+Δδ。
Compared with prior art, the present invention has technique effect beneficial below：
The present invention is for the typical mechanical-electric coupling phenomenon of three classes present in system, it is proposed that permanent magnetic linear synchronous motor into
Give system mechanical-electric coupling modeling method, can quickly and effectively in analysis system all kinds of coupled problems essential laws.Profit simultaneously
System displacement fluctuation caused by can accurately calculating all kinds of mechanical-electric coupling problems with modeling method proposed by the present invention, quickly may be used
Influence size of all kinds of mechanical-electric couplings of evaluation leaned on to system motion stationarity.The present invention is on the basis of traditional integrated modelling approach
On, it further supplements due to new change caused by mechanical-electric coupling problem, the perfect integrated modelling approach of complex electromechanical systems,
It traces to the source for the kinematic error of Linear motor feeding system, the analysis and optimization of mechanical-electric coupling problem, which improves, has important meaning
Justice.
Description of the drawings
Fig. 1 is the schematic diagram of permanent magnetic linear synchronous motor feeding system structure described in present example.
Fig. 2 is permanent magnetic linear synchronous motor feed system electromechanical Coupling Model of the present invention.
Fig. 3 is the thrust result of spectrum analysis of experimental bench motor described in present example.
Fig. 4 is the result of spectrum analysis of experimental bench displacement fluctuation described in present example.
In figure：1 is workbench；2 be line slideway and sliding block；3 be grating scale scale；4 be grating ruler reading head；5 be electricity
Motor-driven son；6 be motor stator；7 be lathe bed.
Specific embodiment
With reference to specific embodiment, the present invention is described in further detail, it is described be explanation of the invention and
It is not to limit.
A kind of permanent magnetic linear synchronous motor feed system mechanical-electric coupling modeling method of the present invention considers servo-drive spy
The interactively that intercouples of property, mechanical dynamics property and the two, establishes electromechanical Coupling Model.Specifically include following step
Suddenly：
Step 1 considers all kinds of non-linear factor (such as dead zone harmonic wave, modulation harmonic wave and anti-electricity in driving circuit
Kinetic potential harmonic wave etc.) and electric machine structure non-linear factor (such as slot effect, end effect, magnetic linkage harmonic wave), utilize electromagnetic energy
Amount method calculates permanent magnetic linear synchronous motor thrust spectrum signature, i.e.,
F=∑s (Elk+Emk)·ik/v
Wherein, k=a, b, c represent a, b, c three-phase of electrical-coil；ElkAnd EmkThe armature of respectively three-phase coil is anti-electric
Gesture and unloaded back-emf；ikFor servo three-phase current；V is motor movement speed.
Step 2 ignores the flexibility of workbench, takes workbench along three axis and the movement around three axis, i.e., and x, y,
Z, θx, θy, θz}TFor generalized coordinates.Ignore the effect of intercoupling between each vibration shape, straight-line electric is established using Lagrange's equation
The mechanical kinetics equation of machine feed system, i.e.,
Wherein, X=[x y z θx θy θz]TFor worktable displacement,The respectively single order of X, second dervative, M, C,
K is respectively mass matrix, damping matrix and stiffness matrix, and F is external force matrix.
Step 3 considers that linear motor air gap changes caused by being vibrated due to mechanical twisting, introduces relative magnetic permeability letter first
Number description mechanical twisting vibrates the influence to motor gas-gap magnetic field, and is calculated using electromagnetic energy method and considers air gap variation
Motor thrust output, i.e.,
F=F '0+F′r+Fg
Wherein, F '0To consider the motor name thrust of air gap variation, F 'rTo consider that the original thrust of motor of air gap variation is humorous
Ripple, FgTo consider the new thrust harmonic components of air gap variation.
Secondly, mechanical oscillation caused by considering thrust harmonic wave is established based on PID three close-loop control models, wherein, position ring is adopted
It is controlled with P, speed ring is controlled using PI, and electric current loop is equivalent to proportional gain, the motor thrust output that step 1 is obtained, with dry
The form disturbed introduces；Mechanical system is equivalent to relatively independent two-order oscillation system and introduces model, is obtained by Experimental Identification
Parameters in model finally establish the electromechanical integrated model of the system under the effect of thrust harmonic wave, i.e.,
[(xi-x0)·Gp(s)-x0·s]·Gv(s)·KA·KF=F '0
(F′0+F′r+Fg)·Gmf(s)+∑(F′0+F′r+Fg)·Gmi(s)=x0
Wherein, xiIt is command signal, xoFor output signal of displacement, Gp(s) letter being passed for position ring control, s is differential operator,
Gv(s) letter, K are passed for speed ring controlAFor electric current loop equieffective ratio gain, KFFor motor thrust constant, FmName is exported for motor
Thrust, FrFor motor output harmonic wave power, GmF (s) be mechanical system direction of feed model, Gmi(s) it is other mechanical direction power
Learn model.
Additionally, it is contemplated that mechanical twisting vibrates the influence to grating scale feedback signal, based on grating scale operation principle, calculate
The encoder errors generated to mechanical twisting vibration, i.e.,
Δ δ=∑ (F '0+F′r+Fg)·Gmi(s)·Ge(s)
Wherein, Ge(s) be encoder errors and mechanical twisting vibration between biography letter.
Obtained encoder feedback error is introduced into feedback control loop, obtains considering the feedback letter of encoder errors
Number, i.e.,
xδ0=x0+Δδ
Step 4, the interaction relationship between the servo-drive and mechanical system that are obtained based on step 3, establishes permanent magnetism
Linear synchronous motor feed system various factors coupling electromechanical Coupling Model, i.e.,
Specifically, permanent magnetic linear synchronous motor feed system is as shown in Figure 1, the uniaxial linear motor feeding experiment of selection one
Platform is test cases, and displacement signal is acquired by laser interferometer, sample frequency 10KHz.Motor thrust is carried by servo
Monitoring of software is acquired, sample frequency 1KHz.In experiment test, feed speed 20m/min.It is as follows：
1) all kinds of non-linear factor (such as dead zone harmonic wave, modulation harmonic wave and counter electromotive force in driving circuit are considered
Harmonic wave etc.) and electric machine structure non-linear factor (such as slot effect, end effect, magnetic linkage harmonic wave), using electromagnetic energy method,
Permanent magnetic linear synchronous motor thrust spectrum signature is calculated, i.e.,
F=∑s (Elk+Emk)·ik/ v=F0+Fr+Fc+Fe+Fq+FL (1)
Wherein F0It is motor name thrust, FrIt is motor ripple thrust, FcIt is Slot force, FeIt is End Force, FqIt is ripple tooth socket coupling
With joint efforts, FLIt is inductance asymmetry HARMONIC FORCE.
2) ignore the flexibility of workbench, take workbench along three axis and the movement around three axis, i.e. { x, y, z, θx,
θy, θz}TFor generalized coordinates.Ignore the effect of intercoupling between each vibration shape, using Lagrange's equation establish linear motor into
To the mechanical kinetics equation of system, i.e.,
Wherein, wherein：X=[x y z θx θy θz]TFor worktable displacement,Respectively the single order of X, second order are led
Number, M, C, K are respectively mass matrix, damping matrix and stiffness matrix, and F is external force matrix.
In the test cases, mechanical structure is simple, and the coupling between each mode of machinery can be ignored.In addition,
Since workbench y is to very high to intrinsic frequency with z, and the damping in the two directions is larger, and oscillatory response amplitude is relatively low, point
It can be not considered in analysis feed system Self excitation Response.Therefore in subsequent analysis Main Analysis workbench in the vibration of direction of feed
And the twisting vibration around each axis.
3) first, consider that linear motor air gap changes caused by being vibrated due to mechanical twisting, introduces relative magnetic permeability function and retouches
Influence of the mechanical twisting vibration to motor gas-gap magnetic field is stated, and the motor for considering air gap variation is calculated using electromagnetic energy method
Thrust output, i.e.,
F=F '0+F′r+Fg (3)
Wherein, F '0To consider the motor name thrust of air gap variation, F 'rTo consider the original thrust harmonic wave of motor of air gap variation,
FgTo consider the new thrust harmonic components of air gap variation.
Due in present case, mechanical twisting oscillation amplitude very little, therefore motor name thrust caused by it and original thrust
Harmonic wave varies less, and when analyzing influence of the air gap fluctuation to feed system robust motion, only considers what air gap variation generated
New motor thrust harmonic wave.
Secondly, mechanical oscillation caused by considering thrust harmonic wave is established based on PID three close-loop control models, and wherein position ring is adopted
It is controlled with P, speed ring is controlled using PI, and electric current loop is equivalent to proportional gain, the motor thrust output that step 1 is obtained, with dry
The form disturbed introduces；Mechanical system direction of feed is equivalent to single inertia system, and the torsional oscillation in three directions of mechanical system is equivalent
Model is introduced for relatively independent two-order oscillation system, the parameters in model are obtained by Experimental Identification, final establish pushes away
The electromechanical integrated model of system under the effect of power harmonic wave, i.e.,
[(xi-x0)·Gp(s)-x0·s]·Gv(s)·KA·KF=F '0 (4)
(F′0+F′r+Fg)·Gmf(s)+∑(F′0+F′r+Fg)·Gmi(s)=x0 (5)
Wherein, xiIt is command signal, xoFor output signal of displacement, Gp(s) letter is passed for position ring control, s is differential operator, Gv(s)
It is controlled for speed ring and passes letter, KAFor electric current loop equieffective ratio gain, KFFor motor thrust constant, FmNominal thrust is exported for motor,
FrFor motor output harmonic wave power, GmF (s) be mechanical system direction of feed model, Gmi(s) it is other mechanical directional dynamics moulds
Type.
Additionally, it is contemplated that mechanical twisting vibrates the influence to grating scale feedback signal, based on grating scale operation principle, calculate
The encoder errors generated to mechanical twisting vibration, i.e.,
Δ δ=∑ (F '0+F′r+Fg)·Gmi(s)·Ge(s) (6)
Wherein, Ge(s) be encoder errors and mechanical twisting vibration between biography letter.
Obtained encoder feedback error is introduced into feedback control loop, obtains considering the feedback letter of encoder errors
Number, i.e.,
xδ0=x0+Δδ (7)
4) the comprehensive model being previously obtained, establishes permanent magnetic linear synchronous motor feed system various factors coupling mechanical-electric coupling mould
Type is as shown in Fig. 2, i.e.
In Fig. 2, xiFor command signal, xoIt exports and responds for system, KpFor position loop gain, KvFor speed ring gain, TvFor
The speed ring time of integration, KFFor thrust constant, FrFor thrust harmonic wave caused by encoder errors, m is driving load, Jx,Jy,JzFor
The rotary inertia in three directions of mechanical system, Cθx,Cθy,CθzFor the damping of three torsional oscillations of mechanical system, Kθx,Kθy,KθzFor
The torsion stiffness of mechanical three torsional oscillations；My,Mp,MrFor equieffective ratio coefficient of the motor thrust on three torsional directions；
Sy,Sp,SrFor the ratio conversion factor between three torsional oscillations and feeding displacement fluctuation；Gp(s),Gy(s) and Gr(s) it is respectively
Transmission function between mechanical three direction torsional oscillations and encoder errors.
5) choose the obtained thrust of experiment test and displacement fluctuation data steady-state process same section, carries out spectrum analysis,
As a result as shown in Figure 3 and Figure 4.In Fig. 3, the deviation of digitized representation theoretical calculation and measured result in thrust frequency spectrum bracket；
In Fig. 4, bracket inner digital represents the frequency and amplitude of corresponding points.It, will for main thrust harmonic components according to Fig. 3 and Fig. 4
The theoretical calculation displacement fluctuation result that integrated model obtains is compared with experiment test displacement fluctuation result, as a result such as 1 institute of table
Show.
Theoretical calculation and the experimental results comparison of 1 displacement fluctuation of table
It can be obtained by Fig. 3, Fig. 4 and table 1, a variety of mechanical-electric coupling phenomenons are implicitly present in Linear motor feeding system, are made
The stable state displacement fluctuation that can not ignore into system.The wherein maximum deviation of displacement fluctuation the calculated results and measured result is
5.3%, it was confirmed that the accuracy and reliability of electromechanical Coupling Model result of calculation.
Claims (6)
1. a kind of permanent magnetic linear synchronous motor feed system mechanical-electric coupling modeling method, which is characterized in that comprise the following steps：
Step 1 analyzes the spectrum signature with calculating permanent magnetic linear synchronous motor servo thrust output using electromagnetic energy method；
Step 2 establishes permanent magnetic linear synchronous motor feed system mechanical kinetics model using Lagrange's equation；
Step 3, the feed system mechanical kinetics model of servo thrust output spectrum signature and step 2 based on step 1,
From mechanical oscillation caused by the variation of linear motor air gap, thrust harmonic wave caused by mechanical torsional oscillation and mechanical twisting vibration to light
Three aspects of influence of grid ruler feedback signal, are analyzed between permanent magnetic linear synchronous motor feed system servo-drive and mechanical system
The interactively that intercouples；
Step 4 according to the interactively that intercouples between the servo-drive and mechanical system obtained in step 3, is established forever
Magnetic-synchro Linear motor feeding system various factors coupling electromechanical Coupling Model is as follows,
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<msubsup>
<mi>F</mi>
<mn>0</mn>
<mo>&prime;</mo>
</msubsup>
<mo>+</mo>
<msubsup>
<mi>F</mi>
<mi>r</mi>
<mo>&prime;</mo>
</msubsup>
<mo>+</mo>
<msub>
<mi>F</mi>
<mi>g</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>&CenterDot;</mo>
<msub>
<mi>G</mi>
<mrow>
<mi>m</mi>
<mi>i</mi>
</mrow>
</msub>
<mrow>
<mo>(</mo>
<mi>s</mi>
<mo>)</mo>
</mrow>
<mo>&CenterDot;</mo>
<msub>
<mi>G</mi>
<mi>e</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>s</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>x</mi>
<mrow>
<mi>&delta;</mi>
<mn>0</mn>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mi>x</mi>
<mn>0</mn>
</msub>
<mo>+</mo>
<mi>&Delta;</mi>
<mi>&delta;</mi>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>;</mo>
</mrow>
Wherein, F is permanent magnetic linear synchronous motor thrust, and k=a, b, c represent a, b, c three-phase of electrical-coil；ElkAnd EmkRespectively
For the armature back-emf of three-phase coil and unloaded back-emf, ikFor servo three-phase current, v is motor movement speed；F0' it is to consider
The motor name thrust of air gap variation, Fr' original thrust the harmonic wave of motor changed for consideration air gap, FgTo consider air gap variation
New thrust harmonic components, xiIt is command signal, xoFor output signal of displacement, Gp(s) letter is passed for position ring control, s calculates for differential
Son, Gv(s) letter, K are passed for speed ring controlAFor electric current loop equieffective ratio gain, KFFor motor thrust constant, FmIt is exported for motor
Nominal thrust, FrFor motor output harmonic wave power, GmF (s) be mechanical system direction of feed model, Gmi(s) it is other mechanical directions
Kinetic model；△ δ are that mechanical twisting vibrates the encoder errors generated, Ge(s) it is that encoder errors are vibrated with mechanical twisting
Between biography letter；xδ0To consider the feedback signal of encoder errors.
2. a kind of permanent magnetic linear synchronous motor feed system mechanical-electric coupling modeling method according to claim 1, feature
It is, in step 1, according to the structure composition of driving circuit, considering driving circuit includes dead zone harmonic wave, modulation harmonic wave
And all kinds of non-linear factors and electric machine structure of counter electromotive force harmonic wave include slot effect, end effect and magnetic linkage harmonic wave
All kinds of non-linear factors, using electromagnetic energy method, it is as follows to calculate the spectrum signature of permanent magnetic linear synchronous motor thrust F,
F=∑s (Elk+Emk)·ik/v。
3. a kind of permanent magnetic linear synchronous motor feed system mechanical-electric coupling modeling method according to claim 1, feature
Be, in step 2, ignore the flexibility of workbench, take workbench along three axis and the movement around three axis, i.e., x, y, z,
θx, θy, θz}TFor generalized coordinates；Ignore the effect of intercoupling between each vibration shape, linear motor is established using Lagrange's equation
The mechanical kinetics equation of feed system,
<mrow>
<mi>M</mi>
<mover>
<mi>X</mi>
<mo>&CenterDot;&CenterDot;</mo>
</mover>
<mo>+</mo>
<mi>C</mi>
<mover>
<mi>X</mi>
<mo>&CenterDot;</mo>
</mover>
<mo>+</mo>
<mi>K</mi>
<mi>X</mi>
<mo>=</mo>
<mi>F</mi>
</mrow>
Wherein, X=[x y z θx θy θz]TFor worktable displacement,The respectively single order of X, second dervative, M, C, K points
Not Wei mass matrix, damping matrix and stiffness matrix, F be external force matrix.
4. a kind of permanent magnetic linear synchronous motor feed system mechanical-electric coupling modeling method according to claim 1, feature
It is, when considering that linear motor air gap changes caused by being vibrated due to mechanical twisting in step 3, introduces relative magnetic permeability function and retouch
Influence of the mechanical twisting vibration to motor gas-gap magnetic field is stated, and utilizes electromagnetic energy method, the electricity for considering air gap variation is calculated
Machine thrust output,
F=F0′+Fr′+Fg。
5. a kind of permanent magnetic linear synchronous motor feed system mechanical-electric coupling modeling method according to claim 1, feature
It is, caused by considering thrust harmonic wave in step 3 during mechanical oscillation, establishes based on PID three close-loop control models, wherein, position ring
It being controlled using P, speed ring is controlled using PI, and electric current loop is equivalent to proportional gain, the motor thrust output that step 1 is obtained, with
The form of interference introduces；The dynamic characteristic in other directions of the mechanical system in addition to direction of feed is equivalent to respectively relatively independent
Two-order oscillation system introduce model, the parameters in model are obtained by Experimental Identification, finally establish thrust harmonic wave effect
Under system electromechanical integrated model,
[(xi-x0)·Gp(s)-x0·s]·Gv(s)·KA·KF=F0′
(F0′+Fr′+Fg)·Gmf(s)+∑(F0′+Fr′+Fg)·Gmi(s)=x0。
6. a kind of permanent magnetic linear synchronous motor feed system mechanical-electric coupling modeling method according to claim 1, feature
It is, when influence of the mechanical twisting vibration to grating scale feedback signal is considered in step 3, based on grating scale operation principle, calculates
The encoder errors that mechanical twisting vibration generates are obtained,
Δ δ=∑ (F0′+Fr′+Fg)·Gmi(s)·Ge(s),
And obtained encoder feedback error is introduced into feedback control loop, obtain considering the feedback signal of encoder errors,
xδ0=x0+Δδ。
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| CN111123834A (en) * | 2019-12-26 | 2020-05-08 | 西安交通大学 | Method for evaluating electromechanical coupling strength of linear motor feeding system |
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