CN110308701A - A kind of direct-drive high-speed feed system kinematic accuracy prediction technique considering thrust harmonic characterisitic - Google Patents
A kind of direct-drive high-speed feed system kinematic accuracy prediction technique considering thrust harmonic characterisitic Download PDFInfo
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Abstract
A kind of direct-drive high-speed feed system kinematic accuracy prediction technique considering thrust harmonic characterisitic provided by the invention, the following steps are included: step 1, according to the direct-drive high-speed feed system kinematic accuracy analysis model for considering thrust harmonic characterisitic, system interference transmission function is obtained；Step 2, the system interference transmission function obtained according to step 1 extract characteristic equation；Step 3 brings real system parameter in characteristic equation obtained in step 2 into, obtains the root of characteristic equation, differentiates to the root of characteristic equation；Step 4, according to differentiating as a result, the system interference transmission function G obtained using step 1 in step 3r(s), by inverse Laplace transformation, the system motion precision under single thrust harmonic wave effect is obtained；Step 5 repeats step 4, obtains the direct-drive high-speed feed system kinematic accuracy of all thrust harmonic waves；Linear motor pushing force fluctuation problem in traditional analysis is extended directly into the kinematic accuracy of final feed system by the present invention, for further evaluating influence degree of the force oscillation phenomenon of linear motor in practical numerically-controlled machine tool with important directive significance.
Description
Technical field
The invention belongs to motor drivens and control field, and in particular to it is a kind of consider thrust harmonic characterisitic direct-drive high-speed into
System motion accuracy prediction method is given, the occasions such as high speed and super precision numerically-controlled machine tool are suitable for.
Background technique
Permanent magnetic linear synchronous motor feed system realizes feeding Zero-drive Chain, feeds system compared to more traditional ball-screw
System, has many advantages, such as that thrust is big, speed is high and precision is good, has a wide range of applications in various fields such as high speed and super precision numerically-controlled machine tools
Prospect.However Zero-drive Chain structure also have the shortcomings that it is numerous, wherein most distinct issues are due to driving circuit and electric machine structure
Force oscillation caused by non-linear.For force oscillation, domestic and foreign scholars have carried out a large amount of research work, surround electric machine structure
Optimization proposes a variety of methods with control backoff algorithm, has important value and significance for improving force oscillation.
Direct-drive high-speed feed system eliminates all intermediate mechanical transmission links, and thrust harmonic wave directly acts on mechanical system
System is difficult force oscillation caused by thoroughly eliminating all kinds of factors although have passed through structure optimization and control compensation.Compared to biography
System Ball-screw Drive Systems, thrust harmonic wave still have more significant impact to system motion precision.Traditional thrust is humorous
Wave analysis and calculation method, only in permanent magnetic linear synchronous motor itself, there is no influenced to expand to feed system
Final kinematic accuracy.Although the system output that can be obtained under the effect of thrust harmonic wave is rung by means of some numerical simulation softwares
It answers, but this method calculates the internal mechanism time-consuming, analysis result is acted on without method interpretation thrust harmonic wave, is not easy to discuss different
Affecting laws of the different frequency thrust harmonic wave to system motion precision under SERVO CONTROL parameter and load, it is difficult to quickly and effectively divide
Analyse the sensitive parameter that thrust harmonic wave influences.If a kind of direct-drive high-speed of quick accurate consideration thrust harmonic characterisitic can be established
Feed system kinematic accuracy Analytic Calculation Method, for advanced optimizing servo parameter and building control compensation policy with important
Value and significance.
Summary of the invention
The purpose of the present invention is to provide a kind of direct-drive high-speed feed system kinematic accuracy for considering thrust harmonic characterisitic is pre-
There is time-consuming, be difficult in survey method, the thrust frequency analysis and calculation method for solving direct-drive high-speed feed system in the prior art
The problem of sensitive parameter that quickly and effectively analysis thrust harmonic wave influences.
In order to achieve the above object, the technical solution adopted by the present invention is that:
A kind of direct-drive high-speed feed system kinematic accuracy prediction technique considering thrust harmonic characterisitic provided by the invention, packet
Include following steps:
Step 1, according to consider thrust harmonic characterisitic direct-drive high-speed feed system kinematic accuracy analysis model, be
System disturbance transfer function；
Step 2, the system interference transmission function obtained according to step 1 extract characteristic equation；
Step 3 brings real system parameter in characteristic equation obtained in step 2 into, obtains the root of characteristic equation, right
The root of characteristic equation is differentiated；
Step 4, according to differentiating as a result, the system interference transmission function G obtained using step 1 in step 3r(s),
By inverse Laplace transformation, the system motion precision under single thrust harmonic wave effect is obtained；
Step 5 repeats step 4, obtains the direct-drive high-speed feed system kinematic accuracy of all thrust harmonic waves.
Preferably, in step 1, system interference transmission function Gr(s) expression formula are as follows:
Wherein, GrIt (s) is system interference transmission function, s is Laplace operator, xoIt (s) is system output response, Ftr
It (s) is motor thrust harmonic wave, KpFor position ring proportional gain, KvFor velocity loop proportional gain, TvFor the speed ring time of integration, KA
For electric current loop equieffective ratio gain, KFFor motor thrust constant, m is driving load quality.
Preferably, in step 2, the expression formula of characteristic equation are as follows:
as3+bs2+ cs+d=0
Wherein, a=m, b=KvKF, c=KvKF/Tv+KFKvKp, d=KpKvKF/Tv。
Preferably, in step 3, the specific method differentiated to the root of characteristic equation is:
Work as D=b2When -3ac < 0, characteristic equation has a real root and two conjugation imaginary roots；
Work as D=b2- 3ac > 0, andWhen, characteristic equation has a real root and two conjugate radicals
Root；
Work as D=b2- 3ac > 0, andWhen, there are three real roots for characteristic equation.
Preferably, in step 4, the expression formula of the system motion precision under single thrust harmonic wave effect are as follows:
xtr0(t)=L-1[Gr(s)·Ftr(s)]
Wherein, L-1Indicate inverse Laplace transformation, FtrIt (s) is the complex field form of thrust harmonic wave.
Preferably, in step 5, the expression formula of the direct-drive high-speed feed system kinematic accuracy of all thrust harmonic waves are as follows:
Compared with prior art, the beneficial effects of the present invention are:
A kind of direct-drive high-speed feed system kinematic accuracy prediction technique considering thrust harmonic characterisitic provided by the invention, leads to
The kinematic accuracy that the linear motor pushing force fluctuation problem in traditional analysis is extended directly into final feed system is crossed, for into one
Influence degree of the force oscillation phenomenon of step evaluation linear motor in practical numerically-controlled machine tool has important directive significance.And
The calculation method can accurately obtain the direct-drive high-speed feed system movement output response under multifrequency thrust harmonic disturbance effect
Analytic solutions, different servo control parameter can be easily discussed using calculated result and load lower different frequency thrust harmonic wave pair
The affecting laws of system motion precision can effectively analyze the sensitive parameter of thrust harmonic wave influence, particularly with further excellent
Changing servo parameter and building control compensation policy has important value and significance.
Detailed description of the invention
Fig. 1 is direct-drive high-speed feed system kinematic accuracy analysis model；
Fig. 2 is the direct-drive high-speed feed system robust motion test result for considering the effect of thrust harmonic wave.
Specific embodiment
With reference to the accompanying drawing, the present invention is described in more detail.
A kind of direct-drive high-speed feed system kinematic accuracy prediction technique considering thrust harmonic characterisitic provided by the invention, packet
Include following steps:
Step 1 establishes the direct-drive high-speed feed system kinematic accuracy analysis model for considering thrust harmonic characterisitic, is
Unite disturbance transfer function Gr(s), i.e.,
Wherein, GrIt (s) is system interference transmission function, s is Laplace operator, xoIt (s) is system output response, Ftr
It (s) is motor thrust harmonic wave, KpFor position ring proportional gain, KvFor velocity loop proportional gain, TvFor the speed ring time of integration, KA
For electric current loop equieffective ratio gain, KFFor motor thrust constant, m is driving load quality.
Consider thrust harmonic wave direct-drive high-speed feed system kinematic accuracy analysis model, specifically include position ring, speed ring,
Electric current loop, linear motor and driving part and feedback element, position ring are controlled using ratio, and speed ring uses proportional integration control
System, electric current loop are equivalent to proportional gain, and the thrust harmonic wave that linear motor generates introduces model, mechanical system etc. in the form interfered
Effect is single inertia system, and closed feedback loop gain is 1.
Step 2: the transmission function obtained according to step 1 extracts characteristic equation, i.e.,
as3+bs2+ cs+d=0
Wherein: a=m, b=KvKF, c=KvKF/Tv+KFKvKp, d=KpKvKF/Tv
Real system parameter is brought into characteristic equation obtained in step 2, the root of characteristic equation is obtained, to feature side
The root of journey is differentiated；
Wherein, real system parameter includes position ring proportional gain, velocity loop proportional gain and the time of integration, motor thrust
Constant and system drive load.
The specific method differentiated to the case where root of characteristic equation is:
Work as D=b2When -3ac < 0, characteristic equation has a real root and two conjugation imaginary roots；
Work as D=b2- 3ac > 0, andWhen, characteristic equation has a real root and two conjugate radicals
Root；
Work as D=b2- 3ac > 0, andWhen, there are three real roots for characteristic equation.
Step 3: the case where the characteristic equation root obtained according to step 2, the disturbance transfer function obtained using step 1,
By inverse Laplace transformation, the system motion precision under single thrust harmonic wave effect is obtained, i.e.,
xtr0(t)=L-1[Gr(s)·Ftr(s)]
Step 4: step 3 is repeated, obtains the direct-drive high-speed feed system kinematic accuracy of all thrust harmonic waves, i.e.,
Embodiment
The present embodiment selects certain to feed experimental bench, the experimental bench maximum feed speed equipped with straight the uniaxial of feed system that drive
For 30m/min, peak acceleration 1g.Specific step is as follows:
Step 1: the direct-drive high-speed feed system kinematic accuracy analysis model for considering thrust harmonic characterisitic is established, such as attached drawing 1
It is shown, specifically include position ring, speed ring, electric current loop, linear motor, driving part and feedback element, wherein position ring uses
Ratio control；Speed ring uses proportional plus integral control；Electric current loop is equivalent to proportional gain；Linear motor generate thrust harmonic wave with
The form of interference introduces model；Mechanical system is equivalent to single inertia system, and closed feedback loop gain is 1.
According to the kinematic accuracy analysis model of foundation, system interference transmission function is obtained, i.e.,
Wherein, GrIt (s) is system interference transmission function, s is Laplace operator, xoIt (s) is system output response, Ftr
It (s) is motor thrust harmonic wave, KpFor position ring proportional gain, KvFor velocity loop proportional gain, TvFor the speed ring time of integration, KA
For electric current loop equieffective ratio gain, KFFor motor thrust constant, m is driving load quality.
Step 2: the transmission function obtained according to step 1 extracts characteristic equation, i.e.,
as3+bs2+ cs+d=0
Wherein, a=m, b=KvKF, c=KvKF/Tv+KFKvKp, d=KpKvKF/Tv
Real system parameter is brought into characteristic equation obtained in step 2, the root of characteristic equation is obtained, to feature side
The root of journey is differentiated；
Wherein, real system parameter includes position ring proportional gain, velocity loop proportional gain and the time of integration, motor thrust
Constant and system drive load.
The specific method differentiated to the case where root of characteristic equation is:
Work as D=b2When -3ac < 0, characteristic equation has a real root and two conjugation imaginary roots；
Work as D=b2- 3ac > 0, andWhen, characteristic equation has a real root and two conjugate radicals
Root；
Work as D=b2- 3ac > 0, andWhen, there are three real roots for characteristic equation.
Step 3: assuming that the thrust harmonic wave in linear motor is multiple periodic sinusoidal forms, final output is rung
It should be the superposition of multiple harmonic waves.In order to simplify calculating process, one of them are selected, i.e.,
Corresponding Laplace transform are as follows:
The disturbance transfer function obtained using step 1 obtains the movement essence of the complex field under single thrust harmonic wave effect
Degree, i.e.,
The case where characteristic equation root obtained according to step 2, by inverse Laplace transformation, obtain single thrust harmonic wave
System motion precision under effect, i.e.,
System motion precision when characteristic equation has a real root and two conjugation imaginary roots, under single thrust harmonic wave effect
Are as follows:
When there are three system motion precision when real root, under single thrust harmonic wave effect for characteristic equation are as follows:
In formula, items are that coefficient can be obtained by inverse Laplace transformation, s1,s2,s3Respectively three of characteristic equation
Root.
Step 4: step 3 is repeated, the direct-drive high-speed feed system kinematic accuracy for considering all thrust harmonic waves is obtained, that is, works as
When characteristic equation has a real root and two conjugation imaginary roots, the system motion precision of all thrust harmonic waves is considered are as follows:
When characteristic equation is there are three real root, the system motion precision of all thrust harmonic waves is considered are as follows:
High-speed direct-drive kinematic system actual motion precision is tested using laser interferometer, uses frequency for 1KHz,
Feed speed is 20m/min.
The stable state displacement fluctuation error term in kinematic accuracy is extracted, Fourier transformation is carried out to it, compares different frequencies respectively
Experimental results and the calculated results under rate, as shown in Fig. 2；By attached drawing 2 it is found that the theory of systematic steady state displacement fluctuation
It is only 4% with experimental result maximum deviation, it was demonstrated that the accuracy and reliability of calculation method proposed by the invention.
Claims (6)
1. a kind of direct-drive high-speed feed system kinematic accuracy prediction technique for considering thrust harmonic characterisitic, which is characterized in that including
Following steps:
It is dry to obtain system according to the direct-drive high-speed feed system kinematic accuracy analysis model for considering thrust harmonic characterisitic for step 1
Disturb transmission function；
Step 2, the system interference transmission function obtained according to step 1 extract characteristic equation；
Step 3 brings real system parameter in characteristic equation obtained in step 2 into, the root of characteristic equation is obtained, to feature
Equation root is differentiated；
Step 4, according to differentiating as a result, the system interference transmission function obtained using step 1, passes through La Pula in step 3
This inverse transformation obtains the system motion precision under single thrust harmonic wave effect；
Step 5 repeats step 4, obtains the direct-drive high-speed feed system kinematic accuracy of all thrust harmonic waves.
2. a kind of direct-drive high-speed feed system kinematic accuracy prediction side for considering thrust harmonic characterisitic according to claim 1
Method, which is characterized in that in step 1, system interference transmission function Gr(s) expression formula are as follows:
Wherein, GrIt (s) is system interference transmission function, s is Laplace operator, xoIt (s) is system output response, FtrIt (s) is electricity
Machine thrust harmonic wave, KpFor position ring proportional gain, KvFor velocity loop proportional gain, TvFor the speed ring time of integration, KAFor electric current loop
Equieffective ratio gain, KFFor motor thrust constant, m is driving load quality.
3. a kind of direct-drive high-speed feed system kinematic accuracy prediction side for considering thrust harmonic characterisitic according to claim 1
Method, which is characterized in that in step 2, the expression formula of characteristic equation are as follows:
as3+bs2+ cs+d=0
Wherein, a=m, b=KvKF, c=KvKF/Tv+KFKvKp, d=KpKvKF/Tv。
4. a kind of direct-drive high-speed feed system kinematic accuracy prediction side for considering thrust harmonic characterisitic according to claim 1
Method, which is characterized in that in step 3, the specific method differentiated to the root of characteristic equation is:
Work as D=b2When -3ac < 0, characteristic equation has a real root and two conjugation imaginary roots；
Work as D=b2- 3ac > 0, andWhen, characteristic equation has a real root and two conjugation imaginary roots；
Work as D=b2- 3ac > 0, andWhen, there are three real roots for characteristic equation.
5. a kind of direct-drive high-speed feed system kinematic accuracy prediction side for considering thrust harmonic characterisitic according to claim 1
Method, which is characterized in that in step 4, the expression formula of the system motion precision under single thrust harmonic wave effect are as follows:
xtr0(t)=L-1[Gr(s)·Ftr(s)]
Wherein, L-1Indicate inverse Laplace transformation, FtrIt (s) is the complex field form of thrust harmonic wave.
6. a kind of direct-drive high-speed feed system kinematic accuracy prediction side for considering thrust harmonic characterisitic according to claim 1
Method, which is characterized in that the direct-drive high-speed feed system kinematic accuracy in step 5, under all thrust harmonic wave effects are as follows:
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