CN111123834B - Method for evaluating electromechanical coupling strength of linear motor feeding system - Google Patents

Method for evaluating electromechanical coupling strength of linear motor feeding system Download PDF

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CN111123834B
CN111123834B CN201911370978.6A CN201911370978A CN111123834B CN 111123834 B CN111123834 B CN 111123834B CN 201911370978 A CN201911370978 A CN 201911370978A CN 111123834 B CN111123834 B CN 111123834B
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coupling
electromechanical coupling
electromechanical
feeding system
strength
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杨晓君
赵万华
刘辉
吕盾
张俊
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Xian Jiaotong University
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    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/18—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form
    • G05B19/404—Numerical control [NC], i.e. automatically operating machines, in particular machine tools, e.g. in a manufacturing environment, so as to execute positioning, movement or co-ordinated operations by means of programme data in numerical form characterised by control arrangements for compensation, e.g. for backlash, overshoot, tool offset, tool wear, temperature, machine construction errors, load, inertia
    • G—PHYSICS
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    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
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Abstract

The invention provides a method for evaluating the electromechanical coupling strength of a linear motor feeding system, which comprises the following steps: step 1, establishing an electromechanical coupling equation according to the servo drive output characteristic and the mechanical system dynamic characteristic of a linear motor feeding system; step 2, extracting electromechanical coupling terms according to the electromechanical coupling equation obtained in the step 1, and respectively calculating the coupling strength of the single coupling loop and the coupling strength of the whole feeding system according to the extracted electromechanical coupling terms; step 3, establishing a criterion table of electromechanical coupling strength levels of the linear motor feeding system according to the coupling strength of the single electromechanical coupling item relative to the linear motor feeding system obtained in the step 2, and evaluating the coupling strength of various electromechanical coupling phenomena; the coupling strength of various electromechanical coupling phenomena in the direct-drive feeding system can be accurately and effectively judged, the contribution rates of different coupling loops to the total coupling strength can be rapidly discussed, and the method has important guiding significance for rapid tracing of the motion error of the linear motor feeding system and implementation of an optimization control method.

Description

Method for evaluating electromechanical coupling strength of linear motor feeding system
Technical Field
The invention belongs to the field of performance analysis and optimization of numerical control machines, and particularly relates to an electromechanical coupling strength evaluation method for a linear motor feeding system.
Background
The linear motor feeding system has the advantages of large thrust, high speed and precision, good dynamic response and the like, and has wide application prospect in the fields of high-speed and high-precision numerical control machines and the like. However, in a high-grade numerical control machine tool, compared with a traditional ball screw feeding system, a linear motor feeding system is not widely applied, and the performance advantages of the linear motor feeding system are not fully exerted and utilized. Besides the cost, the problems of complex motion error cause, high control difficulty and the like of the linear motor feeding system are main problems restricting the application of the linear motor feeding system.
All intermediate mechanical links of the permanent magnet synchronous linear motor feeding system are eliminated, the motor is directly connected with the driving part, and a complex electromechanical coupling phenomenon exists between the servo driving system and the mechanical system, so that the motion stability of the system is influenced, complex and variable motion errors are caused, and the motion performance of the system and the final machining precision of parts are deteriorated. In the current research work on a linear motor feeding system, the coupling effect problem between a driving system and a mechanical system is not analyzed and researched by the system, the nature of electromechanical coupling of the system is difficult to be integrally mastered by sporadic research work on the coupling problem, particularly, a coupling strength evaluation method for the coupling problem is lacked, the coupling strength of various coupling problems cannot be evaluated, the leading problem is difficult to master when structure optimization and control compensation are carried out, and the optimization compensation effect is influenced.
Disclosure of Invention
The invention aims to provide an electromechanical coupling strength evaluation method for a linear motor feeding system, which solves the problems that the existing coupling strength evaluation method for coupling problems is lacked, the coupling strength of various coupling problems cannot be evaluated, the leading problem is difficult to master during structure optimization and control compensation, and the optimization compensation effect is influenced.
In order to achieve the purpose, the invention adopts the technical scheme that:
the invention provides a method for evaluating the electromechanical coupling strength of a linear motor feeding system, which comprises the following steps:
step 1, establishing an electromechanical coupling equation according to the servo drive output characteristic and the mechanical system dynamic characteristic of a linear motor feeding system;
step 2, extracting electromechanical coupling terms according to the electromechanical coupling equation obtained in the step 1, and respectively calculating the coupling strength of the single coupling loop and the coupling strength of the whole feeding system according to the extracted electromechanical coupling terms;
and 3, establishing an electromechanical coupling strength level criterion table of the linear motor feeding system according to the coupling strength of the single electromechanical coupling item relative to the linear motor feeding system obtained in the step 2, and evaluating the coupling strength of various electromechanical coupling phenomena.
Preferably, in step 1, the electromechanical coupling equation obtained by establishing is:
Figure BDA0002339639260000021
wherein, X0Being mechanical systemsNominal movement, XrFor the vibrational response of mechanical systems, sio,mio,ssM denotes the state variables and system parameters of the servo system and the mechanical system, respectively, F0In order to be the nominal output of the driving motor,
Figure BDA0002339639260000022
respectively, first and second derivatives of X, X0For nominal movement of mechanical systems, XrFor mechanical system vibration, F is motor output, FoutFor external interference, pkineticFor mechanical system dynamics, pgeometryAs regards the parameters of the mechanical geometry,
Figure BDA0002339639260000023
is an electromechanical coupling term.
Preferably, in step 2, the coupling strength of the single coupling loop is calculated by the following specific method:
Figure BDA0002339639260000024
wherein the content of the first and second substances,
Figure BDA0002339639260000025
denotes the power spectral density, F [ deg. ] of each coupling term]Representing the Fourier transform, TiRepresents a coupling term time period; pFThe power spectral density of the overall thrust of the motor is represented, T represents the time period of the overall thrust, and i represents the number of coupling terms.
Preferably, in step 2, the coupling strength of the whole feeding system is calculated by the following specific method:
Figure BDA0002339639260000031
wherein the content of the first and second substances,
Figure BDA0002339639260000032
denotes the power spectral density, F [ deg. ] of each coupling term]Which represents the fourier transform of the signal,Tirepresents a coupling term time period; pFThe power spectral density of the overall thrust of the motor is represented, T represents the time period of the overall thrust, and i represents the number of coupling terms.
Preferably, the coupling strength of various electromechanical coupling phenomena is evaluated, and the specific judgment basis is as follows:
when the electromechanical coupling factor delta is larger than 10%, the coupling level is strong coupling, and the corresponding electromechanical coupling problem must be considered in practical analysis;
when the electromechanical coupling factor is 5% < delta < 10%, the coupling level is moderate coupling, and whether the corresponding electromechanical coupling problem is considered or not is judged according to the actual working condition requirement;
when the electromechanical coupling factor is 1% < delta < 5%, the coupling level is sub-weak coupling, and the corresponding electromechanical coupling problem is generally not considered;
when the electromechanical coupling factor delta is less than 1%, the coupling level is weak coupling, and the corresponding electromechanical coupling problem is ignored;
wherein the electromechanical coupling factor Delta is the coupling strength Delta of the single coupling loopciOr coupling strength delta of the entire feed systemc。
Compared with the prior art, the invention adopts the technical scheme that:
the invention provides an electromechanical coupling strength evaluation method for a linear motor feeding system, which aims at solving the problem of complex electromechanical coupling related to multiple loops and multiple parameters in a direct-drive linear motor feeding system, provides a coupling strength evaluation index and establishes a coupling strength grade judgment basis. The coupling strength method provided by the invention can be used for accurately and effectively judging the coupling strength of various electromechanical coupling phenomena in a direct-drive feeding system, can be used for rapidly discussing the contribution rate of different coupling loops to the total coupling strength, has important guiding significance for rapidly tracing the motion error of the linear motor feeding system and implementing an optimization control method, and has important value and significance for realizing the popularization and application of linear motor feeding in a high-speed high-precision numerical control machine tool.
Drawings
FIG. 1 is a schematic view of a linear motor feed system;
FIG. 2 is a principal vibration pattern of a linear motor feed system mechanical system;
FIG. 3 is a schematic diagram of the electromechanical coupling phenomenon of the linear motor feed system;
fig. 4 is a criterion of electromechanical coupling strength level of the linear motor feeding system.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
As shown in fig. 1 to 4, the method for evaluating the electromechanical coupling strength of the linear motor feeding system provided by the invention comprises the following steps:
step one, analyzing an electromechanical coupling action relation between a servo drive output characteristic and a mechanical system dynamic characteristic of a linear motor feeding system according to the servo drive output characteristic and the mechanical system dynamic characteristic of the linear motor feeding system, and establishing an electromechanical coupling equation, namely:
Figure BDA0002339639260000041
wherein, X0Nominal movement of mechanical systems, XrFor the vibrational response of mechanical systems, sio,mio,ssM denotes the state variables and system parameters of the servo system and the mechanical system, respectively, F0In order to be the nominal output of the driving motor,
Figure BDA0002339639260000042
respectively, first and second derivatives of X, X0For nominal movement of mechanical systems, XrFor mechanical system vibration, F is motor output, FoutFor external interference, pkineticFor mechanical system dynamics, pgeometryAs regards the parameters of the mechanical geometry,
Figure BDA0002339639260000043
is an electromechanical coupling term.
Step two, extracting an electromechanical coupling term according to the coupling equation obtained in the step one, introducing a single electromechanical coupling factor, and calculating the coupling strength of the single coupling loop:
Figure BDA0002339639260000044
introducing a system coupling factor, and calculating the coupling strength of the whole feeding system:
Figure BDA0002339639260000051
wherein the content of the first and second substances,
Figure BDA0002339639260000052
denotes the power spectral density, F [ deg. ] of each coupling term]Representing the Fourier transform, TiRepresents a coupling term time period; pFThe power spectral density of the overall thrust of the motor is represented, T represents the time period of the overall thrust, and i represents the number of coupling terms.
Step three, according to the calculation result of the step two, establishing an electromechanical coupling strength level criterion table of the linear motor feeding system, and evaluating the coupling strength of various electromechanical coupling phenomena, wherein the specific judgment basis is as follows:
when the electromechanical coupling factor delta is larger than 10%, the coupling level is strong coupling, and the corresponding electromechanical coupling problem must be considered in practical analysis;
when the electromechanical coupling factor is 5% < delta < 10%, the coupling level is moderate coupling, and whether the corresponding electromechanical coupling problem is considered or not is judged according to the actual working condition requirement;
when the electromechanical coupling factor is 1% < delta < 5%, the coupling level is sub-weak coupling, and the corresponding electromechanical coupling problem is generally not considered;
when the electromechanical coupling factor Δ < 1%, the coupling level is weak coupling, and the corresponding electromechanical coupling problem is negligible.
Wherein the electromechanical coupling factor Delta is the coupling strength Delta of the single coupling loopciOr coupling strength delta of the entire feed systemc。
Examples
A high-speed five-axis vertical machining center driven by a self-built linear motor is used as an analysis case, an x axis is selected as a test object, and the test object moves back and forth within a full stroke at a feed speed of 15 m/min. The method comprises the steps of utilizing a laser interferometer to respectively test the feeding displacement and torsional oscillation of a feeding system in the motion process, and utilizing a numerical control system with collection software to collect thrust data in the motion process. The method comprises the following specific steps:
1) the servo drive output characteristics of the linear motor feeding system were obtained through experimental tests, as shown in table 1. The main vibration modes of the mechanical system are shown in fig. 2.
TABLE 1 Linear motor feed system servo drive output thrust frequency spectrum characteristic
Figure BDA0002339639260000061
By analyzing the output thrust characteristics of the servo drive and the vibration characteristics of a mechanical system, four types of electromechanical coupling problems are found, namely electromechanical coupling caused by thrust harmonics, counter electromotive force harmonics, air gap fluctuation and encoder errors, and the coupling process is shown in figure 3.
The analysis establishes an electromechanical coupling equation according to the electromechanical coupling action relationship between the two, namely
Figure BDA0002339639260000062
Wherein, X0Nominal movement of mechanical systems, XrFor the vibrational response of mechanical systems, sio,mio,ssM denotes the state variables and system parameters of the servo system and the mechanical system, respectively, F0In order to be the nominal output of the driving motor,
Figure BDA0002339639260000063
respectively, first and second derivatives of X, X0For nominal movement of mechanical systems, XrFor mechanical system vibration, F is motor output, FoutFor external interference, pkineticFor mechanical system dynamics, pgeometryAs regards the parameters of the mechanical geometry,
Figure BDA0002339639260000064
is an electromechanical coupling term.
2) Extracting an electromechanical coupling term according to the coupling equation obtained in the first step, introducing a single electromechanical coupling factor to calculate the coupling strength of the single coupling loop, and obtaining a result shown in table 2:
Figure BDA0002339639260000071
TABLE 2 Single electromechanical coupling factor of various electromechanical coupling terms of linear motor feeding system
Figure BDA0002339639260000072
By introducing a system coupling factor, the coupling strength of the entire feed system is calculated, i.e.
Figure BDA0002339639260000073
Wherein the content of the first and second substances,
Figure BDA0002339639260000074
denotes the power spectral density, F [ deg. ] of each coupling term]Representing the Fourier transform, TiRepresents a coupling term time period; pFThe power spectral density of the overall thrust of the motor is represented, T represents the time period of the overall thrust, and i represents the number of coupling terms.
3) And establishing an electromechanical coupling strength level criterion table of the linear motor feeding system according to the calculation result of the step two, and evaluating the coupling strength of various electromechanical coupling phenomena as shown in figure 4.
As can be seen from table 2, the electromechanical coupling phenomenon in the linear motor feeding system is mainly the thrust harmonic coupling term, and is moderate coupling, mainly due to the coupling caused by the end force. The feedback error coupling term is a sub-weak coupling term. The external force coupling term and the air gap fluctuation coupling term are weak coupling terms. Although a single coupling term is not prominent, a strong coupling of the entire feeding system is caused due to the presence of multiple coupling factors.

Claims (1)

1. The method for evaluating the electromechanical coupling strength of the linear motor feeding system is characterized by comprising the following steps of:
step 1, establishing an electromechanical coupling equation according to the servo drive output characteristic and the mechanical system dynamic characteristic of a linear motor feeding system;
step 2, extracting electromechanical coupling terms according to the electromechanical coupling equation obtained in the step 1, and respectively calculating the coupling strength of the single coupling loop and the coupling strength of the whole feeding system according to the extracted electromechanical coupling terms;
step 3, establishing an electromechanical coupling strength level criterion table of the linear motor feeding system according to the coupling strength of the single electromechanical coupling item relative to the linear motor feeding system obtained in the step 2, and evaluating the coupling strength of various electromechanical coupling phenomena;
in step 1, the electromechanical coupling equation is established as follows:
Figure FDA0003020978060000011
wherein the content of the first and second substances,
Figure FDA0003020978060000012
first and second derivatives of X, respectively; (ii) a sio,mio,ss,msRespectively representing state variables and system parameters of a servo system and a mechanical system; f is the motor output; f0Is the nominal output of the driving motor; foutIs an external disturbance; x0Nominal motion of the mechanical system; xrVibrating for a mechanical system; p is a radical ofkineticFor mechanical system dynamics, pgeometryAs regards the parameters of the mechanical geometry,
Figure FDA0003020978060000013
is an electromechanical coupling term;
in step 2, calculating the coupling strength of a single coupling loop, the specific method is as follows:
Figure FDA0003020978060000014
wherein the content of the first and second substances,
Figure FDA0003020978060000015
representing the Fourier transform, TiRepresents a coupling term time period; pFThe power spectral density of the overall thrust of the motor is represented, T represents the time period of the overall thrust, and i represents the number of coupling terms;
Figure FDA0003020978060000016
representing the power spectral density of each coupling term;
in step 2, calculating the coupling strength of the whole feeding system, the specific method is as follows:
Figure FDA0003020978060000021
evaluating the coupling strength of various electromechanical coupling phenomena, wherein the specific judgment basis is as follows:
when the electromechanical coupling factor delta is more than 10 percent, the coupling level is strong coupling, and the corresponding electromechanical coupling problem must be considered in practical analysis;
when the electromechanical coupling factor is more than 5% and less than 10%, the coupling level is moderate coupling, and whether the corresponding electromechanical coupling problem is considered or not is judged according to the actual working condition requirement;
when the electromechanical coupling factor is more than 1% and less than 5%, the coupling level is sub-weak coupling, and the corresponding electromechanical coupling problem is generally not considered;
when the electromechanical coupling factor delta is less than 1%, the coupling level is weak coupling, and the corresponding electromechanical coupling problem is ignored;
wherein the electromechanical coupling factor Delta is the coupling strength Delta of the single coupling loopciOr coupling strength delta of the entire feed systemc。
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