CN114218718B - S-shaped track flexible vibration suppression reliability analysis method - Google Patents

S-shaped track flexible vibration suppression reliability analysis method Download PDF

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CN114218718B
CN114218718B CN202210161197.1A CN202210161197A CN114218718B CN 114218718 B CN114218718 B CN 114218718B CN 202210161197 A CN202210161197 A CN 202210161197A CN 114218718 B CN114218718 B CN 114218718B
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shaped track
vibration suppression
flexible
current
function
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CN114218718A (en
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韩旭
陶友瑞
李本旺
胡俊宇
赵赢
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Chongqing Kairui Robot Technology Co ltd
Hebei University of Technology
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Chongqing Dexin Robot Detection Center Co ltd
Hebei University of Technology
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    • G06F2119/02—Reliability analysis or reliability optimisation; Failure analysis, e.g. worst case scenario performance, failure mode and effects analysis [FMEA]

Abstract

The application discloses a method for analyzing S-shaped track flexible vibration suppression reliability, which comprises the following steps: acquiring an acceleration following error sample function of each rotor of the linear servo motors in the sample under the current S-shaped track design method; establishing a mover acceleration interval process variable function; establishing a mover acceleration interval process variable function and attenuation amplitude of residual vibration suppression attenuation energy of the current S-shaped track flexible vibration suppression systemP I (ω n ) The mapping model of (2); calculating the rotor acceleration following error of the current motor sample to meet the design index P of the current S-shaped track flexible vibration suppression system*Degree of reliability ofP(ii) a And when the judgment reliability P is higher, evaluating that the reliability of the current motor sample is higher. The method provides a diagnosis basis for the diagnosis of the motor performance, namely the residual vibration suppression effect of the motor on the current S-shaped track flexible vibration suppression system, and is more convenient and efficient compared with the traditional diagnosis method.

Description

S-shaped track flexible vibration suppression reliability analysis method
Technical Field
The present disclosure relates generally to a reliability analysis method, and more particularly, to a reliability analysis method for suppressing flexible vibration with an S-shaped track.
Background
With the vigorous development of the precision machining industry in China, the linear motor servo system with high speed, high precision and moving performance is widely applied to the semiconductor automation industry. It is worth noting that a flexible link is ubiquitous in a mechanical device for connecting an end actuator and a linear motor mover. Therefore, when the positioning movement is carried out, the tail end actuating mechanism is easy to generate the phenomenon of low-frequency vibration, namely the residual vibration phenomenon of the flexible servo system. Therefore, the vibration suppression problem of the flexible servo system is researched, and the method has important significance for developing a high-performance motion platform.
Based on the motion model shown in fig. 1, the mover in the linear servo motor system moves from point a (time t is 0) to point B at a constant speed, and when the mover reaches point B (time t is t)f) Then, the rotor stops moving, but the flexible tail end has residual vibration; in the industry, in order to suppress residual vibration of the flexible tail end, an S-shaped motion track is designed for the rotor, and theoretically, based on the S-shaped motion track, after the rotor stops, the flexible tail end is in a static state after the rotor stops moving.
The conventional track vibration suppression reliability assessment method has the following premises: it is contemplated that the servo system can follow the reference signal exactly as it is. Due to the influence of various external factors and the limitation of the bandwidth of the servo loop, the result obtained on the premise is ideal, and even has no reference significance under some poor working conditions.
After the S-shaped track of the linear motor servo system is designed, motors in different batches have different rotor displacement following performances, different following performances can generate different influences on the residual vibration suppression effect, and some motors with poor following performances can not be directly suitable for the current S-shaped track planning method.
Disclosure of Invention
In view of the above-mentioned drawbacks or deficiencies in the prior art, it is desirable to provide a sigmoid trajectory flexible vibration suppression reliability analysis method.
In a first aspect, the present application provides a method for analyzing the reliability of suppressing flexible vibration of a sigmoid track, the method comprising the following steps:
acquiring an acceleration following error sample function of each rotor of the linear servo motor in the sample under the current S-shaped track design method, as shown in a formula (13):
Figure GDA0003572076400000021
Figure GDA0003572076400000022
the acceleration is input acceleration of a linear servo motor in S-shaped track motion;
Figure GDA0003572076400000023
the actual acceleration of the rotor in the S-shaped track motion;
establishing a mover acceleration interval process variable function according to a formula (2):
Figure GDA0003572076400000024
fU e(t) is the upper boundary function of the mover acceleration interval process variable function, fD e(t) is a lower boundary function of a mover acceleration interval process variable function; the upper boundary function and the lower boundary function envelop all acceleration following error sample functions; the mover acceleration interval process variable function has a median function fM e(t) and a radius r;
establishing a mover acceleration interval process variable function and a residual vibration suppression attenuation energy attenuation amplitude P of the current S-shaped track flexible vibration suppression systemI(ωn) The mapping model of (2);
calculating the rotor acceleration following error of the motor in the sample according to the formula (9) to meet the design index P*Reliability P of (d):
Figure GDA0003572076400000025
wherein P is*A design index for suppressing attenuation energy attenuation amplitude for residual vibration;
ωnthe standard resonance frequency of the flexible tail end in the current S-shaped track flexible vibration suppression system is obtained;
PI(ωn) The attenuation amplitude of the residual vibration energy, P, of the flexible tip of the current S-shaped track flexible vibration suppression system when the flexible tip has a standard resonance frequencyI(ωn) Is an interval variable; pD(ωn) Is PI(ωn) Lower boundary function of PU(ωn) Is PI(ωn) The upper boundary function of (1);
when the judgment reliability P is larger, evaluating that the current motor sample meets the design index P of the current S-shaped track flexible vibration suppression system*The higher the reliability of (c).
According to the technical scheme provided by the embodiment of the application, the method further comprises the following steps:
dividing the acceleration interval of the rotor into process variable functions
Figure GDA00035720764000000310
The median function, the autocorrelation function and the radius are input into a non-random vibration analysis model to obtain the displacement response x of the flexible tail endI e(t)；
Establishing a mover acceleration interval process variable function and a residual vibration suppression and attenuation energy attenuation amplitude P of the current S-shaped track flexible vibration suppression system according to the following formula (8), formula (7) and formula (6)I(ωn) The mapping model of (2):
PI(ωn)＝1-EN(wn),PI(ωn)∈1 (8)
Figure GDA0003572076400000031
Figure GDA0003572076400000032
EN(ωn) When the flexible tail end has the standard resonance frequency, the normalized residual vibration energy of the current S-shaped track flexible vibration suppression system is obtained;
ES residual(ωn) When the flexible tail end has the standard resonance frequency, the residual vibration energy stored in the flexible tail end is stored when the S-shaped track motion of the current S-shaped track flexible vibration suppression system is finished;
ET residual(ωn) When the flexible tail end has standard resonance frequency, the S-shaped track flexible vibration suppression system with the largest jerk is used for storing residual vibration energy at the flexible tail end when the S-shaped track motion is finished;
wherein m iseMass of the flexible tip; k is the equivalent spring rate of the flexible tip.
According to the technical scheme provided by the embodiment of the application, the mover acceleration interval process variable function of the current S-shaped track flexible vibration system
Figure GDA00035720764000000311
The autocorrelation function of (a) is calculated according to the following formula (3) and formula (4):
Figure GDA0003572076400000033
Figure GDA0003572076400000034
Figure GDA0003572076400000035
as a function of process variable of mover acceleration interval at time ti
Figure GDA0003572076400000036
The quadratic root of the radius;
Figure GDA0003572076400000037
is a process variable function of the rotor acceleration interval at the time ti
Figure GDA0003572076400000038
The quadratic root of the radius;
Figure GDA0003572076400000039
τ is an autocorrelation coefficient ti-tj.
According to the technical scheme provided by the embodiment of the application, the method further comprises the following steps:
setting allowable standard V for acquiring normalized residual vibration energy of current S-shaped track flexible vibration suppression systemtol；
Determining an allowable perturbation interval [ omega ] of a resonant frequency of the flexible tip according to the following formula (10)n U,ωn D]；
EN(wn)≤Vtol (10)
Determining the robustness W of the current motor sample to the resonant frequency of the current S-shaped track flexible vibration suppression system through formula (11) and formula (12):
Figure GDA0003572076400000041
WI＝(ωn U-ωn D)/ωn (12)
wherein W*Designing indexes for the robustness of the resonant frequency of the flexible tail end in a set flexible vibration suppression system;
WIfor the resonant frequency robustness of the compliant tip in current S-track compliant vibration suppression systems, WIIs an interval variable;
determining resonant frequency robustnessWhen W is larger, evaluating that the current motor sample meets the design index W of the current S-shaped track flexible vibration suppression system*The higher the reliability of (c).
In the scheme, the displacement following error in the linear motor servo system is used as an uncertainty factor, and the displacement following error is embodied through the rotor acceleration interval process variable function, so that the rotor acceleration interval process variable function and S-shaped track flexible vibration suppression attenuation energy attenuation amplitude PI(ωn) Establishing a mapping model, and calculating that the current motor sample meets the design index P through a formula (9)*The residual vibration suppression effect of the motor sample is diagnosed according to the reliability P, and because uncertainty variables are considered, the evaluation on the residual vibration suppression effect is more practical and more accurate; meanwhile, a diagnosis basis is provided for the diagnosis of the performance of the motors, namely the residual vibration suppression effect of the motors on the current S-shaped track flexible vibration suppression system, and compared with the traditional diagnosis method, the method is more convenient and efficient.
In a further preferred scheme of the scheme, the allowable perturbation range of the resonant frequency is calculated under the condition that the robustness W of the resonant frequency meets a certain residual vibration attenuation amplitude, the reliability of the linear servo motor performance on the current S-shaped track planning and various design indexes can be further evaluated comprehensively by further evaluating the robustness W of the resonant frequency of the current motor performance on the flexible tail end and the reliability and the robustness W of the resonant frequency, and the accuracy of the whole motor performance diagnosis model is high.
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Other features, objects and advantages of the present application will become more apparent upon reading of the following detailed description of non-limiting embodiments thereof, made with reference to the accompanying drawings in which:
FIG. 1 is a relationship between a linear servo motor drive control system and a flexible link equivalent dual mass spring damping system.
FIG. 2 is a schematic diagram showing the corresponding relationship among rotor jerk, acceleration, speed and displacement during the S-shaped track process in the linear servo motor driving and controlling system;
FIG. 3 is a diagram of a process variable function corresponding to the acceleration following error interval of the linear servo motor in FIG. 2;
FIG. 4 is a schematic diagram of an allowed perturbation interval of resonant frequencies.
Detailed Description
The present application will be described in further detail with reference to the following drawings and examples. It is to be understood that the specific embodiments described herein are merely illustrative of the relevant invention and not restrictive of the invention. It should be noted that, for convenience of description, only the portions related to the present invention are shown in the drawings.
It should be noted that the embodiments and features of the embodiments in the present application may be combined with each other without conflict. The present application will be described in detail below with reference to the embodiments with reference to the attached drawings.
In the linear motor servo system, the S-shaped motion track is designed based on the output displacement x of the rotorbEqual to the reference displacement x input by the system to the linear motor servo systemrefIn fact, in the linear motor servo system, the actual output displacement x of the moverbNot in accordance with the reference displacement xrefEqual, actual output displacement xbWill follow the shift reference instruction xrefWith a following error between them; both have the relationship shown in the following formula (14):
e(t)＝xb(t)-xref(t) (14)
e (t) is a displacement following error of the mover.
Referring to fig. 1, the relation between a linear servo motor driving and controlling system and a flexible link equivalent dual-mass spring damping system is shown. Wherein xrefGiving an input displacement reference instruction to a linear servo motor driving and controlling system; e is the servo following error; gcIs a feedback controller; t isdDisturbance for the outside world; gPA motor rotor dynamic model is obtained; x is the number ofbActually outputting displacement for the rotor; m isbThe rotor mass is; m iseMass of the flexible tip; x is the number ofeDisplacement of the flexible tip relative to the mover; b is the coefficient of viscous damping force received by the rotor; and c is the coulomb friction coefficient received by the rotor. For an equivalent spring damping structure, k isAn equivalent spring rate; d is the equivalent spring damping coefficient.
In general, due to the high frequency component of the acceleration signal during the motion of the mover, a residual vibration phenomenon may occur at the flexible tip when the motion is stopped.
The residual vibration suppression trajectory planning strategy commonly used in linear servo systems is a sigmoid trajectory, as shown in fig. 2. Taking a typical exercise parameter plan as an example, the sigmoid trajectory can be determined by the following five exercise parameters: displacement reference instruction xrefTarget velocity vrefTime t of uniform accelerationjTime of uniform acceleration taAt constant speed tv. Wherein, [ x ]ref,vref]Given by the actual process, i.e. requiring the tail end of the actuator to move from point A to point B at a constant speed, and tj，ta，tv]And for the variables to be designed, the flexible tail end is accelerated and decelerated through reasonable planning. Wherein when [ tj，ta]Determination of the value of (a), tvThe value of (c) is then determined. t is tfIs the termination time of the S-shaped track motion.
Generally, for a weak damping flexible servo system, when the formula (1) is satisfied, the zero residual vibration at the tail end of the flexible servo system when the positioning motion is completed can be realized, and the S-shaped track has stronger robustness to the perturbation of model parameters. The model parameters include the resonant frequency and the damping ratio of the flexible tail end, and the damping ratio is particularly small, so that the scheme is not considered, and therefore, in the scheme, the model parameters only refer to the resonant frequency of the flexible tail end, namely the natural frequency of the flexible tail end.
Figure GDA0003572076400000061
N is above+Representing a positive integer.
Because the design method does not consider uncertain variables, the adaptability and the reliability of the design to different linear servo motor systems are difficult to guarantee.
Assuming a current sigmoid-track compliant vibration suppression system, toA determined S-shaped track design scheme is provided, namely three design variables [ tj，ta，tv]It has been given that the control performance of the current linear servo motor samples is evaluated for the flexible vibration suppression reliability of the current sigmoid trajectory design by:
s1, acquiring an acceleration following error sample function of each linear servo motor rotor in the sample under the current S-shaped track design method, as shown in formula (13):
Figure GDA0003572076400000062
Figure GDA0003572076400000063
the acceleration is input acceleration of a linear servo motor in S-shaped track motion;
Figure GDA0003572076400000064
the actual acceleration of the rotor in the S-shaped track motion;
t is time;
in the servo motor system, the rotor displacement following error can be accessed at any time, namely the formula (14) can be obtained at any time, so that the linear servo motor rotor acceleration following error can be generated at any time;
s2, establishing a mover acceleration interval process variable function according to the formula (2):
Figure GDA0003572076400000071
as shown in FIG. 3, fU e(t) is the upper boundary function of the process variable function of the acceleration interval of the rotor, fD e(t) is a lower boundary function of a mover acceleration interval process variable function; the upper boundary function and the lower boundary function envelop all acceleration following error sample functions; the process variable function of the rotor acceleration interval has a median valueFunction fM e(t) and a radius r;
s3, extracting second-order differential inter-process variable of acceleration following error of linear servo motor
Figure GDA0003572076400000072
R belongs to R; r is a real number. In this example: the following error radius r is given equal to 0.1.
It has r ∈ [0,1 ]; as shown in fig. 4, the parameter r is obtained by finding the data of the sample function that deviates farthest from the median function and differencing.
S4, calculating a second-order differential interval process variable function of the acceleration following error of the linear servo motor according to the following formula (3)
Figure GDA00035720764000000710
The autocorrelation function of. In this embodiment, the superscript symbol "I" indicates that the variable is an interval process variable;
Figure GDA0003572076400000073
Figure GDA0003572076400000074
as a function of process variable of mover acceleration interval at time ti
Figure GDA0003572076400000075
The quadratic root of the radius; in this example: the autocorrelation coefficient is determined according to the following formula (4):
Figure GDA0003572076400000076
Figure GDA0003572076400000077
τ ═ ti-tj is the autocorrelation coefficient.
S5 process for dividing acceleration of rotorFunction of variables
Figure GDA0003572076400000078
Inputting the median function, the autocorrelation function and the radius of the vibration into a non-random vibration analysis model;
obtaining the displacement response x of the flexible terminalI e(t)；
The nonrandom vibration analysis method is a mature prior art, and the detailed calculation process is not repeated herein, and in the nonrandom vibration analysis method, the displacement response x of the flexible terminal is calculated mainly by the following formula (5)I e(t)：
Figure GDA0003572076400000079
H(t-τ1) For a single degree of freedom vibration system at time t-tau1Displacement response after being excited by unit pulse; t is tfThe time is counted from the time of the S-shaped track motion and the time when the S-shaped track motion is finished.
S6, calculating the residual vibration energy stored in the flexible tail end when the flexible tail end has the standard resonance frequency and the motion of the current S-shaped track flexible vibration suppression system in the S-shaped track is finished according to the following formula (6);
for the sake of convenience of distinction, the residual vibration energy at this time is denoted as ES residual(ωn)；
Figure GDA0003572076400000081
S7, calculating residual vibration energy stored at the flexible tail end when the flexible tail end has the standard resonance frequency and the S-shaped track flexible vibration suppression system with the maximum jerk is at the end of S-shaped track motion according to the formula (6);
for the sake of convenience of distinction, the residual vibration energy at this time is denoted as ET residual(ωn)；
S8 calculating the Flexible tip havingAt the standard resonant frequency, the normalized residual vibration energy E of the current S-shaped track flexible vibration suppression systemN(ωn)；
Figure GDA0003572076400000082
S9, calculating the attenuation amplitude P of the residual vibration energy of the flexible tail end of the current S-shaped track flexible vibration suppression system when the flexible tail end has the standard resonance frequency according to the formula (8)I(ωn)，PI(ωn) Is an interval variable;
PI(ωn)＝1-EN(wn),PI(ωn)∈1 (8)
s10, obtaining design index P of attenuation amplitude of residual vibration suppression attenuation energy*(ii) a Calculating the rotor acceleration following error of the motor in the sample according to the following formula (9) to meet the design index P*Reliability P of (d):
Figure GDA0003572076400000083
ωnthe standard resonance frequency of the flexible tail end in the current S-shaped track flexible vibration suppression system is obtained;
PD(ωn) Is PI(ωn) Lower boundary function of PU(ωn) Is PI(ωn) The upper boundary function of (1).
The steps are that a rotor acceleration interval process variable function and a residual vibration suppression attenuation energy attenuation amplitude P of the current S-shaped track flexible vibration suppression system are establishedI(ωn) The mapping model of (2);
s10, when the judgment reliability P is larger, evaluating that the current motor sample meets the design index P of the current S-shaped track flexible vibration suppression system*The higher the reliability of (c).
In the scheme, the displacement following error in the linear motor servo system is taken as an uncertainty factor, and a rotor is addedThe speed interval process variable function reflects displacement following errors, so that the mover acceleration interval process variable function and S-shaped track flexible vibration suppression attenuation energy attenuation amplitude PI(ωn) Establishing a mapping model, and calculating that the current motor sample meets the design index P through a formula (9)*The reliability P is used for diagnosing the residual vibration suppression effect of the motor sample, a diagnosis basis is provided for the diagnosis of the motor performance, namely the residual vibration suppression effect of the batch of motors on the current S-shaped track flexible vibration suppression system, and compared with the traditional diagnosis method, the method is more convenient and efficient.
Example 2
In this embodiment, on the basis of the embodiment, after the step s9, the reliability of the current design solution is further evaluated by the following steps:
s11, obtaining a set allowable standard V of the normalized residual vibration energy of the current S-shaped track flexible vibration suppression systemtol；
S12, determining the allowable perturbation interval [ omega ] of the resonant frequency of the flexible end according to the following formula (10)n U,ωn D]：
EN(wn)≤Vtol (10)
Referring to FIG. 4, in the present embodiment, a set allowable criterion V is giventol0.05, with (ω)n U/ωn)-(ωn D/ωn) 0.28 represents the size of the allowed perturbation interval of the resonance frequency.
S13, determining the resonant frequency robustness W of the current motor sample in the current S-shaped track flexible vibration suppression system through the formula (11) and the formula (12):
Figure GDA0003572076400000091
WI＝(ωn U-ωn D)/ωn (12)；
wherein W*Suppressing resonant frequencies of compliant tips in systems for set compliant vibrationDesign indexes of rate robustness;
WIfor the resonant frequency robustness of the compliant tip in current S-track compliant vibration suppression systems, WIIs an interval variable;
s14, when the robustness W of the resonance frequency is judged to be larger, the current motor sample is evaluated to meet the design index W of the current S-shaped track flexible vibration suppression system*The higher the reliability of (c).
In the embodiment, the robustness W of the resonant frequency meets the allowed perturbation range of the resonant frequency under a certain residual vibration attenuation amplitude, the reliability of the performance of the linear servo motor on the current S-shaped track planning and various design indexes can be further evaluated by further evaluating the robustness W of the performance of the current motor on the resonant frequency of the flexible tail end and comprehensively evaluating the reliability and the robustness W of the resonant frequency, and the whole motor diagnosis model is accurate and efficient.
The above description is only a preferred embodiment of the application and is illustrative of the principles of the technology employed. It will be appreciated by a person skilled in the art that the scope of the invention as referred to in the present application is not limited to the embodiments with a specific combination of the above-mentioned features, but also covers other embodiments with any combination of the above-mentioned features or their equivalents without departing from the inventive concept. For example, the above features may be replaced with (but not limited to) features having similar functions disclosed in the present application.

Claims (3)

1. A method for analyzing S-shaped track flexible vibration suppression reliability is characterized by comprising the following steps:
acquiring an acceleration following error sample function of each rotor of the linear servo motor in the sample under the current S-shaped track design method, as shown in a formula (13):
Figure FDA0003572076390000011
Figure FDA0003572076390000012
the acceleration is input acceleration of a linear servo motor in S-shaped track motion;
Figure FDA0003572076390000013
the actual acceleration of the rotor in the S-shaped track motion;
establishing a mover acceleration interval process variable function according to a formula (2):
Figure FDA0003572076390000014
fU e(t) is the upper boundary function of the process variable function of the acceleration interval of the rotor, fD e(t) is a lower boundary function of a mover acceleration interval process variable function; the upper boundary function and the lower boundary function envelop all acceleration following error sample functions; the mover acceleration interval process variable function has a median function fM e(t) and radius r;
establishing a mover acceleration interval process variable function and a residual vibration suppression attenuation energy attenuation amplitude P of the current S-shaped track flexible vibration suppression systemI(ωn) The mapping model of (2);
calculating the rotor acceleration following error of the motor in the sample according to the formula (9) to meet the design index P*Reliability P:
Figure FDA0003572076390000015
wherein P is*A design index for restraining attenuation energy attenuation amplitude of residual vibration;
ωnthe standard resonance frequency of the flexible tail end in the current S-shaped track flexible vibration suppression system is obtained;
PI(ωn) When the flexible tip has a standard resonance frequency, the presentResidual vibration energy attenuation amplitude, P, of flexible tail end of S-shaped track flexible vibration suppression systemI(ωn) Is an interval variable; pD(ωn) Is PI(ωn) Lower boundary function of PU(ωn) Is PI(ωn) The upper boundary function of (1);
when the judgment reliability P is larger, evaluating that the current motor sample meets the design index P of the current S-shaped track flexible vibration suppression system*The higher the reliability of (2);
dividing the acceleration interval of the rotor into process variable functions
Figure FDA0003572076390000016
Inputting the median function, the autocorrelation function and the radius into a non-random vibration analysis model to obtain the displacement response x of the flexible tail endI e(t)；
Establishing a mover acceleration interval process variable function and a residual vibration suppression and attenuation energy attenuation amplitude P of the current S-shaped track flexible vibration suppression system according to the following formula (8), formula (7) and formula (6)I(ωn) The mapping model of (2):
PI(ωn)＝1-EN(wn),PI(ωn)∈1 (8)
Figure FDA0003572076390000021
Figure FDA0003572076390000022
EN(ωn) When the flexible tail end has the standard resonance frequency, normalizing residual vibration energy of the current S-shaped track flexible vibration suppression system;
ES residual(ωn) When the flexible tail end has the standard resonant frequency, the flexible tail end is stored when the S-shaped track flexible vibration suppression system finishes the motion of the S-shaped trackThe residual vibrational energy of (a);
ET residual(ωn) When the flexible tail end has standard resonance frequency, the S-shaped track flexible vibration suppression system with the largest jerk is used for storing residual vibration energy at the flexible tail end when the S-shaped track motion is finished;
wherein m iseMass of the flexible tip; k is the equivalent spring rate of the flexible tip.
2. The S-shaped track flexible vibration suppression reliability analysis method according to claim 1, wherein a mover acceleration interval process variable function of a current S-shaped track flexible vibration system
Figure FDA0003572076390000023
The autocorrelation function (c) is calculated according to the following equations (3) and (4):
Figure FDA0003572076390000024
Figure FDA0003572076390000025
Figure FDA0003572076390000026
as a function of process variable of rotor acceleration interval at time ti
Figure FDA0003572076390000027
The quadratic root of the radius;
Figure FDA0003572076390000028
as a function of process variable of acceleration interval of rotor at time tj
Figure FDA0003572076390000029
Quadratic of radiusA root;
Figure FDA00035720763900000210
τ ═ ti-tj is the autocorrelation coefficient.
3. The S-shaped track flexible vibration suppression reliability analysis method according to claim 2, further comprising the steps of:
obtaining a set allowable standard V of normalized residual vibration energy of a current S-shaped track flexible vibration suppression systemtol；
Determining an allowable perturbation interval [ omega ] of a resonant frequency of the flexible tip according to the following formula (10)n U,ωn D]；
EN(wn)≤Vt9l (10)
Determining the resonant frequency robustness W of the current motor sample to the current S-shaped track flexible vibration suppression system through formula (11) and formula (12):
Figure FDA0003572076390000031
WI＝(ωn U-ωn D)/ωn (12)
wherein W*Designing indexes for the robustness of the resonant frequency of the flexible tail end in a set flexible vibration suppression system;
WIfor the resonant frequency robustness of the compliant tip in current S-track compliant vibration suppression systems, WIIs an interval variable;
when the robustness W of the resonant frequency is judged to be larger, the current motor sample is evaluated to meet the design index W of the current S-shaped track flexible vibration suppression system*The higher the reliability of (c).
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