CN107631738B - Method for identifying imbalance of gyro flywheel couple - Google Patents
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Abstract
The invention discloses a method for identifying unbalance of a gyro flywheel couple, and relates to a method for identifying unbalance of a gyro flywheel couple. The method aims to solve the problems that the existing classical influence coefficient method can generate partial non-solution conditions and the difference between different solutions is large. The invention comprises the following steps: firstly, adding even unbalance type trial weights to N phases of a rotor, acquiring rotor roll angle data under the condition of identifying the rotating speed, and obtaining roll angle-frequency multiplication amplitude phi corresponding to the N phases of the trial weights added according to the roll angle datak(ii) a Secondly, the roll angle-frequency multiplication amplitude value corresponding to the N phase adding trial weights obtained in the step one is phikIdentifying original even unbalance of the gyrowheel rotor by adopting a least square estimation algorithm based on an amplitude influence coefficient method or a least square estimation algorithm based on an amplitude and phase influence coefficient method; and thirdly, correcting the even unbalance of the gyro flywheel according to the identification result of the original even unbalance of the gyro flywheel rotor obtained in the second step. The invention is used for the field of dynamic balance of rotating machinery.
Description
Technical Field
The invention relates to the field of dynamic balance of rotating machinery, in particular to a gyro flywheel pair unbalance identification method.
Background
The miniaturization of the spacecraft has become a main hotspot and inevitable trend of space technology development by combining the characteristics of light weight, small volume, low cost, short development period, easy technology updating, high functional density, rapidness, flexibility, good maneuverability and the like. The attitude control system is one of the most important subsystems of the spacecraft, is a main contributor to the mass, the volume, the cost, the power consumption and the like of the tiny spacecraft, and the light weight realization and the multifunctional integration of the attitude control system are important means for promoting the development of the tiny spacecraft.
A gyro flywheel is a novel attitude control and attitude sensing device, integrates the functions of a variable-speed double-frame control moment gyro and a dynamic tuning gyro, and simultaneously realizes three-dimensional moment output and two-dimensional attitude angular rate measurement by controlling the angular momentum amplitude and the direction of a mechanical rotating body. The device improves the integration level and efficiency of the spacecraft attitude control system, reduces the volume, the quality, the power consumption and the cost of the spacecraft attitude control system, and is an important way for realizing the research of the micro spacecraft attitude control technology.
Due to the limitations of the processing technology and the assembly level, the mass distribution of the rotor of the gyro flywheel is not uniform, and vibration can be caused during high-speed rotation. The rotor tilts along the equatorial axis at the same frequency as the rotating speed due to the even unbalance of the gyro flywheel, so that the moment output precision and the attitude sensitive precision of the gyro flywheel are reduced, the normal work of a gyro flywheel system is influenced, and the system is unstable or even damaged in severe cases. Therefore, realizing high-precision dynamic unbalance identification and adjustment is a key technical problem which needs to be solved in gyro flywheel research.
When the gyro flywheel even unbalance is identified by using a classical influence coefficient method (the patent name is: an even unbalance identification method based on gyro flywheel moment coil current, the patent number is 201710556832.5), under the condition of a closed loop of a gyro flywheel tilting control loop, the even unbalance is solved by solving a simultaneous equation set by using a moment coil current signal, but the situation of no solution may exist according to the difference selected by the simultaneous equation set.
Disclosure of Invention
The invention aims to solve the problems that the existing classical influence coefficient method can generate partial non-solution conditions and the difference between different solutions is large, and provides a gyro-flywheel even imbalance identification method.
A gyro flywheel pair unbalance identification method comprises the following steps:
step one, adding even unbalance type trial weights to N phases of a rotor, acquiring rotor roll angle data under the condition of identifying the rotating speed, and obtaining roll angle-frequency multiplication amplitude phi corresponding to the N phases of the trial weights added according to the roll angle datak；
Step two, obtaining the product by utilizing the step oneThe tilt angle-frequency multiplication amplitude corresponding to the N phase adding trial weights is phikIdentifying original even unbalance of the gyrowheel rotor by adopting a least square estimation algorithm based on an amplitude influence coefficient method or a least square estimation algorithm based on an amplitude and phase influence coefficient method;
and step three, correcting the even unbalance of the gyro flywheel according to the original even unbalance identification result of the gyro flywheel rotor obtained in the step two.
The invention has the beneficial effects that:
the method can realize identification and correction of even unbalance of the gyro flywheel, effectively improve the mass distribution of the gyro flywheel rotor, reduce the first frequency multiplication amplitude of the tilt angle of the gyro flywheel rotor from 0.0232 degrees to 0.0022 degrees, and has obvious correction effect when the even unbalance correction amplitude of the gyro flywheel is 90.4 percent, as shown in figure 4. Therefore, moment noise of the gyro flywheel can be effectively reduced, and the running stability of the rotor is improved, so that the moment output precision and the attitude measurement precision of the rotor are improved.
Aiming at the defects of a classical influence coefficient method (the patent name is: an even unbalance identification method based on gyro flywheel moment coil current), the invention adopts a roll angle signal under the open-loop condition of a roll control loop to directly reflect the vibration caused by even unbalance, but not the moment coil current under the closed-loop condition of the roll control loop to indirectly reflect the vibration caused by even unbalance; meanwhile, the existence and reasonableness of the knowledge are guaranteed by using an improved influence coefficient method based on least square.
According to the invention, even unbalance calculation is carried out by linear least square fitting by utilizing a rotor tilt angle signal and adopting an improved influence coefficient method based on least square under the open loop condition of a gyro flywheel tilt control loop, so that the existence of the solution can be ensured. The effect of identifying the original even unbalance of the gyro flywheel by using the improved influence coefficient method based on least square is shown in the table I, and the table I can know that the identification can be realized by using more than three groups of data and the identification result has little difference.
The effect pair of the original even unbalance of the gyrorotor is identified by using an improved influence coefficient method (the invention) based on least square and a classical influence coefficient method (the patent name is: an even unbalance identification method based on gyrorotor moment coil current), for example, as shown in the second table, the second table shows that the identification result of the improved influence coefficient method based on least square is stable, and no solution exists.
In conclusion, the improved influence coefficient method based on the least square is more suitable for identifying the even unbalance of the gyro flywheel.
TABLE I improved influence coefficient method identification result (3600r/min) based on least squares
TABLE II comparison of identification results (3600r/min) using two algorithms
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a diagram showing the repeatability of the gyro flywheel tilt angle-frequency doubling amplitude varying with the rotation speed;
FIG. 3 is a graph showing the variation of the roll angle-doubling amplitude with the trial weight added phase for different trial weight phases;
FIG. 4 is a comparison graph of a gyro flywheel rotor tilt angle-frequency multiplication amplitude before and after identification and correction by using the identification algorithm of the present invention under the open loop condition of the tilt control loop.
Detailed Description
The first embodiment is as follows: as shown in fig. 1, a method for identifying an imbalance of a gyro-flywheel couple includes the following steps:
the specific process of determining the identification rotating speed of the even unbalance amount by the early preparation work is as follows:
1) selecting a test rotating speed of omega within the range of the working rotating speed of the gyro flywheeli，i＝1,2,…,n；
2) When testing the rotation speed omegaiAfter the operation is stable, the gyro flywheel works in an open loop state of a tilting control loop, the data of the tilting angle of a rotor of the gyro flywheel within 10 seconds are recorded, and the step is repeatedly executed for 5 times;
3) calculating the roll angle data acquired in the step 2) by adopting fast Fourier transform to obtain a test rotating speed omega for 5 timesiCorresponding roll angle-frequency multiplication amplitude is phiijJ-1, 2, …,5, as shown in fig. 2.
4) According to 5 times of tilting angle, namely frequency multiplication amplitude phiijMethod for determining identification rotating speed omega of gyro flywheel rotor along with repeatability of rotating speed change curveT。
Step one, adding even unbalance type trial weights to N phases of a rotor, acquiring rotor roll angle data under the condition of identifying the rotating speed, and obtaining roll angle-frequency multiplication amplitude phi corresponding to the N phases of the trial weights added according to the roll angle datak；
Step two, the roll angle-frequency multiplication amplitude value corresponding to the N phase adding trial weights obtained in the step one is phikIdentifying original even unbalance of the gyrowheel rotor by adopting a least square estimation algorithm based on an amplitude influence coefficient method or a least square estimation algorithm based on an amplitude and phase influence coefficient method;
and step three, correcting the even unbalance of the gyro flywheel according to the original even unbalance identification result of the gyro flywheel rotor obtained in the step two.
The method can realize identification and correction of even unbalance of the gyro flywheel, effectively improve the mass distribution of the gyro flywheel rotor, reduce the first frequency multiplication amplitude of the tilt angle of the gyro flywheel rotor from 0.0232 degrees to 0.0022 degrees, and has obvious correction effect when the even unbalance correction amplitude of the gyro flywheel is 90.4 percent, as shown in figure 4. Therefore, moment noise of the gyro flywheel can be effectively reduced, and the running stability of the rotor is improved, so that the moment output precision and the attitude measurement precision of the rotor are improved.
Aiming at the defects of a classical influence coefficient method (the patent name is: an even unbalance identification method based on gyro flywheel moment coil current), the invention adopts a roll angle signal under the open-loop condition of a roll control loop to directly reflect the vibration caused by even unbalance, but not the moment coil current under the closed-loop condition of the roll control loop to indirectly reflect the vibration caused by even unbalance; meanwhile, the existence and reasonableness of the knowledge are guaranteed by using an improved influence coefficient method based on least square.
The second embodiment is as follows: the first difference between the present embodiment and the specific embodiment is: in the first step, even unbalance type trial weights are added to N phases of the rotor, rotor roll angle data are collected under the condition of identifying the rotating speed, and roll angle-frequency multiplication amplitude phi corresponding to the N phases of the phase adding trial weights is obtained according to the roll angle datakThe specific process comprises the following steps:
one step, when no test weight is added, the gyro flywheel rotor is enabled to identify the rotating speed omegaTStably running, recording gyroscopic flywheel rotor roll angle data within 10 seconds under the open loop condition of a roll control loop, and calculating the rotor roll angle by adopting fast Fourier transform to obtain an initial roll angle-frequency multiplication amplitude phi0；
Step one, two, in the phase theta of the gyro flywheel rotorkWhere k is 1,2, …, N, N is not less than 3, N is the number of positions to which trial weights are added, and the added mass is mkIs in even unbalance form (namely, the mass m is respectively added at the symmetrical positions of the upper surface and the lower surface of the rotorkTrial weight of/2);
step three, when the gyro flywheel rotor identifies the rotating speed omegaTWhen the gyroscope flywheel rotor stably runs, recording gyroscopic flywheel rotor roll angle data within 10 seconds under the open-loop condition of a roll control loop;
step four, calculating the inclination angle of the rotor by adopting fast Fourier transform to obtain the inclination angle-frequency multiplication amplitude phi corresponding to N phase adding trial weightsk。
Other steps and parameters are the same as those in the first embodiment.
The third concrete implementation mode: the present embodiment differs from the first or second embodiment in that: what is needed isIn the second step, the N phase adding trial weights obtained in the first step are used, and the corresponding roll angle-frequency multiplication amplitude is phikThe specific process of identifying the original even unbalance of the gyrorotor rotor by adopting a least square estimation algorithm based on an amplitude influence coefficient method or a least square estimation algorithm based on an amplitude and phase influence coefficient method is as follows:
step two, firstly: the phase and amplitude of the original even unbalance of the gyro flywheel are assumed to be theta0And U0The equivalent mass of the original even unbalance amount on the test weight surface (the plane added with the test weight) is m0. Based on an influence coefficient method, the relation between the roll angle and the even unbalance when the N phases of the rotor are subjected to the test weight in the form of adding the even unbalance is expressed in a complex form as follows:
wherein C is1,C2For the influence coefficient, theta, of the gyro flywheel prototype to be correctedC1,θC2Are respectively C1And C2A corresponding phase; u shapekFor added even unbalance, phikAnd thetaφkRepresenting the roll angle-frequency multiplication amplitude and phase when the test weight in the form of even unbalance is added to the N phases; e denotes the base of the natural logarithm, i denotes the unit of an imaginary number, eixX is θ, cosx + isinxφk,θC1,θU,θC2,θ0Or thetak。
Rewriting formula (1) to the following form:
the formula (2) is arranged as Axk＝bkIn the form of (a), wherein,
wherein A is a parameter matrix, xk、bkIs an intermediate variable;
according to least squares, by sum of squares of residuals
The minimum is the standard, the parameter matrix A can be estimated, and the inclination angle can meet the requirement when no test weight is added
An optimal solution of the original even imbalance can be estimated with amplitude and phase m respectively0And theta0。
Step two: the specific process of the least square estimation algorithm based on the amplitude influence coefficient method or the least square estimation algorithm based on the amplitude and phase influence coefficient method is as follows:
(1) the least square estimation algorithm based on the amplitude influence coefficient method comprises the following steps: that is, equation (1) is expressed in scalar form as:
the sum of the squared residuals is then expressed as:
according to the least square method, more than or equal to three groups of experimental data mk，θkAnd phikCarry-in (7) to identify m with minimum sum of squared residuals as the criterion0And theta0；
(2) The least square estimation algorithm based on the amplitude and phase influence coefficient method is as follows: that is, equation (1) is expressed in scalar form as:
wherein theta ismTo add the mth phase, θ, of the trial weight in even-unbalanced formnTo add the nth phase of the trial weight in even unbalance form, k, m, N is 1,2, …, N ≧ 3, the sum of the squares of the residuals is expressed as:
wherein the content of the first and second substances,
wherein EkError of the system of equations, Ek TIs EkTransposing;
according to the least square method, the experimental data phi when no test weight is added0And thetaφ0And experimental data m of two groups or morek，θk，φk，θφkWith equations (9) and (10), the parameters are estimated using the residual sum of squares, J, as a criterion
According to
Identification m0And theta0(estimate the optimal solution of the original even imbalance amplitude and phase, i.e., m0And theta0)。
Other steps and parameters are the same as those in the first or second embodiment.
The fourth concrete implementation mode: the difference between this embodiment mode and one of the first to third embodiment modes is: the specific process of correcting the even unbalance of the gyro flywheel according to the identification result of the original even unbalance of the gyro flywheel rotor obtained in the step two in the step three is as follows:
phase θ on trial weight surface0The added mass at the +180 DEG position is m0And balancing the balance weight in an even unbalance mode to finish the correction. Enabling the gyro flywheel rotor to identify the rotation speed omegaTAnd (4) stably running, recording a tilting angle-frequency multiplication amplitude of the gyro flywheel within 10 seconds under the condition of open loop of a tilting control loop, and verifying the even unbalance identification and correction effect by comparing the tilting angle-frequency multiplication amplitude with the correction forward tilting angle-frequency multiplication amplitude.
Other steps and parameters are the same as those in one of the first to third embodiments.
The following examples were used to demonstrate the beneficial effects of the present invention:
the first embodiment is as follows:
the method comprises the following steps: even unbalance type test weights with the mass of 0.5g are added at the positions of 0 degree, 60 degrees, 120 degrees, 180 degrees, 240 degrees, 300 degrees and 360 degrees of a test weight plane of the gyrorotor flywheel rotor respectively. And when the gyroduower rotor stably runs at the identification rotating speed of 3600r/min, recording the roll angle data of the gyroduower rotor within 10 seconds under the open-loop condition of the roll control loop. Calculating the tilt angle of the rotor by adopting fast Fourier transform to obtain tilt angle-frequency multiplication amplitudes phi corresponding to different trial weight phases1,φ2,φ3,φ4,φ5,φ6,φ7. The variation of the rotor roll angle-doubled frequency amplitude with the phase of the added trial weight is shown in fig. 3.
Step two: according to the least square estimation algorithm based on the amplitude, the relationship between the tilt angle of the gyro flywheel rotor and the even imbalance under different test weight conditions expressed in a scalar form is shown as a formula (6), the sum of squares of the residual errors is shown as a formula (7), the minimum sum of squares of the residual errors is used as a standard, seven groups of experimental data are used for obtaining that the phase of the original even imbalance is 265 degrees, and the equivalent mass of the original even imbalance on the test weight surface is 0.518 g.
Step three: the correction is completed by adding a weight in the form of an even unbalance with a mass of 0.518g at phase 85 °. After correction, when the gyrowheel rotor stably runs at the rotating speed of 3600r/min, the data of the roll angle of the gyrowheel rotor within 10 seconds under the open-loop condition of the roll control loop are recorded, the roll angle of the rotor is calculated by adopting fast Fourier transform, the frequency doubling amplitude of the roll angle before and after correction is compared, and the even unbalance identification and correction effect is verified, as shown in fig. 4, the frequency doubling amplitude of the roll angle is reduced from 0.0232 degrees to 0.0022 degrees.
The present invention is capable of other embodiments and its several details are capable of modifications in various obvious respects, all without departing from the spirit and scope of the present invention.
Claims (2)
1. A gyro flywheel pair imbalance identification method is characterized by comprising the following steps: the gyro flywheel pair unbalance identification method comprises the following steps:
step one, adding even unbalance type trial weights to N phases of a rotor, acquiring rotor roll angle data under the condition of identifying the rotating speed, and obtaining roll angle-frequency multiplication amplitude phi corresponding to the N phases of the trial weights added according to the roll angle datak(ii) a The specific process is as follows:
one step, when no test weight is added, the gyro flywheel rotor is enabled to identify the rotating speed omegaTStably running, recording gyroscopic flywheel rotor roll angle data within 10 seconds under the open loop condition of a roll control loop, and calculating the rotor roll angle by adopting fast Fourier transform to obtain an initial roll angle-frequency multiplication amplitude phi0；
Step one, two, in the phase theta of the gyro flywheel rotorkWhere k is 1,2, …, N, N is not less than 3, and the added mass is mkA trial weight in the form of an even imbalance of (c);
step three, when the gyro flywheel rotor identifies the rotating speed omegaTWhen the gyroscope flywheel rotor stably runs, recording gyroscopic flywheel rotor roll angle data within 10 seconds under the open-loop condition of a roll control loop;
step four, calculating the inclination angle of the rotor by adopting fast Fourier transform to obtain the inclination angle-frequency multiplication amplitude phi corresponding to N phase adding trial weightsk；
Step two, the roll angle-frequency multiplication amplitude value corresponding to the N phase adding trial weights obtained in the step one is phikUsing a baseIdentifying original even unbalance of the gyro flywheel rotor by a least square estimation algorithm of an amplitude influence coefficient method or a least square estimation algorithm based on the amplitude and phase influence coefficient method; the specific process is as follows:
step two, firstly: the phase and amplitude of the original even unbalance of the gyro flywheel are assumed to be theta0And U0The equivalent mass of the original even unbalance on the test weight surface is m0(ii) a Based on an influence coefficient method, the relation between the roll angle and the even unbalance when the N phases of the rotor are subjected to the test weight in the form of adding the even unbalance is expressed in a complex form as follows:
wherein C is1,C2For the influence coefficient, theta, of the gyro flywheel prototype to be correctedC1,θC2Are respectively C1And C2A corresponding phase; u shapekFor added even unbalance, phikAnd thetaφkRepresenting the roll angle-frequency multiplication amplitude and phase when the test weight in the form of even unbalance is added to the N phases;
rewriting formula (1) to the following form:
the formula (2) is arranged as Axk＝bkIn the form of (a), wherein,
wherein A is a parameter matrix, xk、bkIs an intermediate variable;
step two: the specific process of the least square estimation algorithm based on the amplitude influence coefficient method or the least square estimation algorithm based on the amplitude and phase influence coefficient method is as follows:
(1) the least square estimation algorithm based on the amplitude influence coefficient method comprises the following steps: that is, equation (1) is expressed in scalar form as:
the sum of the squared residuals is then expressed as:
more than or equal to three groups of experimental data mk，θkAnd phikSubstituting into equation (7), and identifying m with minimum sum of squared residuals as the standard0And theta0；
(2) The least square estimation algorithm based on the amplitude and phase influence coefficient method is as follows: that is, equation (1) is expressed in scalar form as:
wherein theta ismTo add the mth phase, θ, of the trial weight in even-unbalanced formnTo add the nth phase of the trial weight in even imbalance, the sum of the squared residuals is expressed as:
wherein the content of the first and second substances,
wherein EkError of the system of equations, Ek TIs EkTransposing;
the experimental data phi when no test weight is added0And thetaφ0And more than or equal to two sets of experimental data mk，θk，φk，θφkWith equations (9) and (10), the parameters are estimated using the residual sum of squares, J, as a criterion
According to
Identification m0And theta0；
And step three, correcting the even unbalance of the gyro flywheel according to the original even unbalance identification result of the gyro flywheel rotor obtained in the step two.
2. The method for identifying the imbalance of the gyrometer according to claim 1, wherein: the specific process of correcting the even unbalance of the gyro flywheel according to the identification result of the original even unbalance of the gyro flywheel rotor obtained in the step two in the step three is as follows:
phase θ on trial weight surface0The added mass at the +180 DEG position is m0And balancing the balance weight in an even unbalance mode to finish the correction.
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| CN109143861B (en) * | 2018-09-07 | 2021-06-29 | 哈尔滨工业大学 | Active vibration suppression method for variable speed tilting momentum wheel system based on torquer |
| CN109211215B (en) * | 2018-10-26 | 2022-03-18 | 哈尔滨工业大学 | Three-degree-of-freedom flexible support rotor tilting vibration control method |
| CN110702315A (en) * | 2019-06-06 | 2020-01-17 | 上海航天控制技术研究所 | On-orbit estimation method and device for static imbalance characteristic of large-inertia rotating part |
| CN111578966B (en) * | 2020-04-09 | 2021-07-16 | 哈尔滨工程大学 | Hemisphere harmonic oscillator characteristic parameter identification method based on LMS algorithm |
| CN113029436B (en) * | 2021-03-01 | 2023-10-20 | 大唐东北电力试验研究院有限公司 | Method for dynamically balancing long shaft of three-cylinder two-exhaust 200MW steam turbine generator assembly |
| CN113156987B (en) * | 2021-04-15 | 2022-05-31 | 哈尔滨工业大学 | Spacecraft actuating mechanism combining double-frame shear type moment gyroscope and flywheel and control method thereof |
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