Rotor unbalance rapid adjustment method based on Kalman filtering

Abstract

The invention discloses a rotor unbalance rapid adjustment method based on Kalman filtering, and belongs to the technical field of rotor dynamic balance. According to the method, a rotor rotating speed signal is obtained through a magnetic encoder, and a piezoelectric vibration sensor is triggered to collect a radial vibration signal. In the aspect of signal processing, a zero phase shift filter is adopted to remove noise interference, and an initial phase and an amplitude are extracted by using FFT (Fast Fourier Transform). And calculating a rotating speed change rate based on the sliding time window, and judging whether the rotor is in a steady-state or transient-state working condition. Under the transient working condition, a state space model containing amplitude, phase and rotating speed is constructed, and unbalance adjustment parameters are predicted through Kalman filtering recursion; and under a steady-state working condition, accurately calculating a correction parameter by adopting a least square method. In addition, a least square fitting model based on a sine function is constructed, amplitude estimation is optimized, and the unbalance calculation precision is improved. According to the invention, the unbalance of the rotor can be quickly and accurately adjusted, and the stability and the service life of a rotating system are improved.

Description

Technical Field:

[0001] The present invention belongs to the technical field of rotor dynamic balancing, and particularly relates to a method for quickly adjusting rotor imbalance based on Kalman filtering, which is especially applicable to real-time monitoring and dynamic correction of the imbalance of a rotor system under variable speed conditions. Background Art:

[0002] With the continuous improvement of the requirements for the operating accuracy and stability of rotating machinery in modern industry, the imbalance problem of the rotor system has increasingly become a key factor affecting the performance and service life of equipment. Traditional imbalance adjustment techniques mainly rely on analyzing and compensating vibration signals under stable speed conditions. These methods can solve the imbalance problem well under fixed working conditions, but when the equipment is in a variable speed or transient state, due to the sudden change in speed and the significant increase in the complexity of vibration signals, traditional methods often have a lag in response and insufficient filtering accuracy, making it difficult to capture the initial phase and amplitude of vibration signals in real time, resulting in unsatisfactory imbalance adjustment effects.

[0003] In practical applications, during the start-up, acceleration, deceleration, or load change process of the rotor, its vibration signal is often affected by environmental noise, DC offset, and other interferences. In the prior art, traditional filtering and frequency domain analysis means are mostly used to process the collected vibration signals, but this method is prone to phase distortion and cannot accurately reflect the coupling effect of speed changes on the vibration amplitude and phase, thus affecting the accurate estimation of the imbalance. In addition, the adjustment strategy based on a single state estimation method has limitations in dealing with the rapid changes under dynamic working conditions and cannot simultaneously meet the adjustment requirements under transient and steady-state working conditions.

[0004] To solve the above technical problems, the present invention proposes a method for quickly adjusting rotor imbalance based on Kalman filtering. According to the collected signal, a zero-phase shift filter is used to preprocess the vibration signal, filtering out noise interference and DC offset irrelevant to the imbalance, and the initial phase and amplitude of the signal are extracted through FFT transformation, providing accurate input parameters for constructing a state space model including amplitude, phase, and speed. The data fed back by the magnetic encoder is used to determine whether the current working condition is in a steady state or a transient state, so as to select a suitable algorithm path for subsequent signal processing. Under transient working conditions, based on this state space model, Kalman filtering is used to recursively predict the imbalance adjustment parameters to achieve rapid response and real-time compensation for the imbalance; while under steady-state working conditions, the least squares method is used for accurate calculation to further optimize the accuracy of imbalance correction. Finally, a complex model of the imbalance vibration response and the imbalance is constructed, and the correction amount is calculated according to the influence coefficient method to ensure the overall accuracy and stability of the adjustment process. Summary of the Invention:

[0005] To solve the above problems, the object of the present invention is to relate to a rapid rotor imbalance adjustment method based on Kalman filtering, which is particularly applicable to the dynamic balance adjustment of a rotor under variable speed conditions, and is used to realize the real-time monitoring and dynamic correction of the unbalance amount of the rotor system during sudden speed change or speed change process, and improve the stability and safety of the rotor system under complex operating conditions.

[0006] S1. Obtain the rotational speed signal of the rotor during operation through a magnetic encoder built in the rotating device, and trigger a piezoelectric vibration sensor to collect the radial vibration signal of the rotor based on the rotational speed signal.

[0007] S2. Process the vibration signal using a zero-phase shift filter (the purpose is to obtain a zero-phase shift filter), filter out the noise interference components and DC offset unrelated to the unbalance amount, obtain the processed signal, and extract the initial phase and amplitude of the signal using FFT transformation.

[0008] S3. Determine whether the current unbalance rotational speed state is in a stable state or a variable speed instantaneous state (stable operating state).

[0009] S4. Under transient conditions, construct a state space model including amplitude, phase, and rotational speed, recursively predict the unbalance adjustment parameters through Kalman filtering, and output them to the actuator in real time.

[0010] S5. Under steady-state conditions, use the recursive least squares method with a forgetting factor to accurately calculate the unbalance correction parameters.

[0011] S6. According to the unbalance response of the rotor at different rotational speeds and operating conditions, guide the formulation of the correction strategy to achieve rapid adjustment of the rotor unbalance.

[0012] In S1, the rotational speed signal of the rotor during operation is collected through a magnetic encoder built in the rotating device, and the pulse signal of the magnetic encoder is used as the trigger source. The piezoelectric vibration sensor is driven by the DAQ system (using the PFI pin and the hardware timing trigger mode, and the sampling rate is set to 32 times the rotational speed fundamental frequency) to synchronously collect the radial vibration signal of the rotor, and the vibration signal subset x(n) is obtained.

[0013] In S2, the vibration signal x(n) is preprocessed using a zero-phase shift filter, and the process is as follows:

[0014] S21. Sequentially filter the vibration signal subset x(n) to obtain x1(n), that is, x1(n) = x(n) · h(n), where h(n) is the unit impulse response sequence of the selected filter.

[0015] S22. Reverse x1(n) to obtain the reverse sequence x2(n), that is, x2(n) = x1(N - 1 - n), where N is the number of points of the original input sequence.

[0016] S23 performs the same filtering process on x2(n) to obtain the response sequence x3(n), that is, x3(n) = x2(n)·h(n);

[0017] S24 reverses x3(n) to obtain the final filtered output signal x4(n), that is, the vibration signal with zero phase shift, that is, x4(n) = x3(N - 1 - n);

[0018] Perform FFT transformation on the obtained vibration signal with zero phase shift, and extract its amplitude and initial phase;

[0019] S3 calculates the rotational speed change rate based on a sliding time window and dynamically sets the discrimination threshold. By comparing the continuous relationship between the rotational speed change rate and the set threshold, it is judged whether the current rotational speed state is in a steady - state operation or a variable - speed transient state, providing a basis for selecting an appropriate method for subsequent signal processing.

[0020] S4 Under transient operating conditions, construct a state vector containing vibration amplitude, phase, and rotational speed, and establish a state - transition equation and an observation equation according to the actual system characteristics, where:

[0021] S41 Construct a state vector containing amplitude, phase, and rotational speed Among them, A k is the vibration amplitude at the current moment;

[0022] is the vibration phase angle;

[0023] n k is the rotor rotational speed;

[0024] S42 Construct a state equation as follows:

[0025] State equation: x k = Cx k-1 + Du k + w k (1) Among them, x k represents the true value at time k;

[0026] C represents the state - transition matrix, k A ,k φ are the coupling coefficients of rotational speed change to amplitude and phase respectively, and are calibrated according to experiments and finite - element simulations;

[0027] x k-1 represents the true value at time k - 1;

[0028] D represents the control - input matrix, b A is the amplitude - adjustment efficiency coefficient;

[0029] u k represents the externally applied adjustment command / balance head compensation torque at time k;

[0030] w k represents the random disturbance during the state transition process at time k;

[0031] S43 Construct the observation equation as follows:

[0032] Observation equation: y k = Hx k + v k (2) where y k represents the observed value obtained by the sensor;

[0033] H represents the observation matrix;

[0034] v k represents the observation noise, mainly sensor error, environmental interference, etc., and the covariance matrix is

[0035] S44 According to the state estimate value output by the Kalman filter, respectively obtain the amplitude and phase A and

[0036] In S5, construct a least - squares fitting model with a sine function as the basis function to estimate the amplitude of the pre - processed vibration signal. The fitting function is as follows:

[0037]

[0038] At this time, according to the principle of the least - squares method, there is one and only one A and such that the sum of the squares of the differences in the numerical distances between y3(n) and Y is the smallest, that is, the solution function is:

[0039]

[0040] Respectively take the partial derivatives of the amplitude A, set its partial derivative equation to 0, and solve for A, to obtain the amplitude and phase of the unbalance.

[0041] 7. Construct a complex relationship model between the vibration response and the unbalance, and the relationship is as follows:

[0042] V = A·e jφ (5)

[0043] where j is the imaginary unit;

[0044] V is the complex relationship expression of the unbalance;

[0045] 8. By analyzing the unbalance response of the rotor under different rotational speeds and operating conditions, a mapping relationship between the unbalance amount and the correction amount is established, thereby guiding the formulation of the correction strategy and realizing the rapid adjustment of rotor unbalance.

[0046] Through the comprehensive utilization of magnetic encoder triggered sampling, zero-phase shift filtering, FFT signal analysis, state space modeling, and Kalman filter recursive prediction, and combined with the least squares method, the present invention realizes the rapid and accurate prediction and correction of the rotor unbalance amount under transient and steady-state operating conditions respectively. This method not only improves the dynamic balance adjustment accuracy and response speed of the rotor system under variable rotational speed conditions, but also enhances the system's safety and maintenance convenience through the fault tracing function, providing an efficient and reliable solution for practical industrial applications. Description of the Drawings:

[0047] Figure 1 , Flowchart of the rapid rotor unbalance adjustment method; Detailed Embodiments:

[0048] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the detailed embodiments. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0049] S1. Obtain the rotational speed signal of the rotor during operation through a magnetic encoder built in the rotating device, and trigger a piezoelectric vibration sensor to collect the radial vibration signal of the rotor based on the rotational speed signal;

[0050] S2. Process the vibration signal using a zero-phase shift filter (the purpose is to obtain a zero-phase shift filter), filter out the noise interference components and DC offset irrelevant to the unbalance amount, obtain the processed signal, and extract the initial phase and amplitude of the signal using FFT transformation;

[0051] S3. Determine whether the current unbalance rotational speed state is in a stable state or a variable-speed instantaneous state stable operation state;

[0052] S4. Under transient operating conditions, construct a state space model including amplitude, phase, and rotational speed, recursively predict the unbalance amount adjustment parameters through Kalman filtering, and output them to the actuator in real time;

[0053] S5. Under steady-state operating conditions, accurately calculate the unbalance amount correction parameters using the least squares method;

[0054] S6. According to the unbalance response of the rotor under different rotational speeds and operating conditions, guide the formulation of the correction strategy and realize the rapid adjustment of rotor unbalance;

[0055] In S1, a magnetic encoder is installed in the rotor system to measure the rotational speed of the rotor at 1800 rpm, the angular velocity is 188.4 rad / s, the fundamental frequency is 30 Hz. The PFI pin of the DAQ is used to receive the magnetic encoder pulse signal, and the hardware timing trigger mode is configured to ensure that the vibration signal sampling rate meets 32 times the rotational speed fundamental frequency, that is, f s = 960 Hz, to obtain a complete synchronous sampling signal. The radial vibration signal of the rotor is collected by a piezoelectric vibration sensor to form a signal sequence x(n);

[0056] In S2, a zero-phase shift filter is used to remove the DC offset and high-frequency noise interference unrelated to the unbalance. The steps are as follows:

[0057] In S21, the vibration signal subset x(n) is sequentially filtered to obtain x1(n), that is, x1(n) = x(n)·h(n), where h(n) is the unit impulse response sequence of the selected filter;

[0058] In S22, x1(n) is reversed to obtain the reversed sequence x2(n), that is, x2(n) = x1(N - 1 - n), and N is the number of points of the original input sequence;

[0059] In S23, x2(n) is subjected to the same filtering process to obtain the response sequence x3(n), that is, x3(n) = x2(n)·h(n);

[0060] In S24, x3(n) is reversed to obtain the final filtered output signal x4(n), that is, the vibration signal with zero phase shift, that is, x4(n) = x3(N - 1 - n);

[0061] The FFT transformation is performed on the obtained vibration signal with zero phase shift, and its amplitude and initial phase are extracted, which are 10 and 30° respectively;

[0062] In S3, the rotational speed change rate dn / dt is calculated based on a sliding time window to be 2.5 r / s 2 and 5 r / s 2 , the discrimination threshold θ is dynamically set to 4.2. According to the continuous relationship between the rotational speed change rate and the threshold, the operating condition state is determined as transient or steady state. The sliding time window length T is 1 s, and the discrimination threshold is θ. Steady state determination requires |dn / dt| ≤ θ and continuous for 3T. According to the determination basis, when the rotational speed change rate is 5 rad / s 2 , it is in a steady state, and when the rotational speed change rate is 2.5 r / s 2 , it is in a transient state;

[0063] In the case of transient operation of the rotor, a fast rotor unbalance adjustment method based on Kalman filtering, characterized in that the construction of the state space model in S4 includes the following steps:

[0064] S41 constructs a state vector including amplitude, phase, and rotational speed i.e., [10μm, 30°, 1800] T

[0065] where A k is the vibration amplitude at the current moment;

[0066] is the vibration phase angle;

[0067] n k is the rotational speed of the rotor;

[0068] S42 constructs a state equation as follows:

[0069] State equation: x k = Cx k-1 + Du k + w k (1)

[0070] where x k represents the true value at time k, which can be calculated as [11.1μm, 30.05°, 1810] T ;

[0071] C represents the state transition matrix, k A and k φ are the coupling coefficients of rotational speed change on amplitude and phase respectively, which are calibrated according to experiments and finite element simulations, and are

[0072] x k-1 represents the true value at time k - 1, which is [10μm, 30°, 1800] T ;

[0073] D represents the control input matrix, b A is the amplitude adjustment efficiency coefficient, which is

[0074] u k represents the adjustment command / external balance head compensation torque applied at time k, which is 5N·m;

[0075] w k represents the random disturbance during the state transition at time k, which is 1800rpm;

[0076] S43 constructs an observation equation as follows:

[0077] Observation equation: y k = Hx k + vk (2)

[0078] Among them, y k represents the observed value obtained by the sensor, that is, [11.1μm, 30.05°, 1810] T ;

[0079] H represents the observation matrix, which is

[0080] v k represents the observation noise, mainly sensor error, environmental interference, etc., and the covariance matrix is Assume the noise is 0;

[0081] Based on the state estimation value output by the Kalman filter, the amplitude and phase are obtained respectively, and their values are 11.1 and 30.05°;

[0082] When the rotor is operating in a steady state, a least-squares fitting model with a sine function as the basis function is constructed to estimate the amplitude of the preprocessed vibration signal. The fitting function is as follows:

[0083]

[0084] At this time, according to the principle of the least-squares method, there is one and only one A and such that the sum of the squares of the differences in the numerical distances between y3(n) and Y is the smallest, that is, the function to be solved is:

[0085]

[0086] Respectively take the partial derivatives of the amplitude A, let its partial derivative equation be 0, and solve for A, The amplitude and phase of the unbalance amount are obtained as 8.5 and 45° respectively.

[0087] 7. Construct a complex relationship model between the vibration response and the unbalance amount, and the relationship is as follows:

[0088]

[0089] Among them, j is the imaginary unit;

[0090] V is the complex relationship expression of the unbalance amount;

[0091] Based on the amplitude and phase of 11.1 and 30.05° obtained by using the Kalman filter under transient conditions, the complex relationship model between its vibration response and the unbalance amount is V = 11.1e j·30.05° .

[0092] Based on the least squares fitting under steady-state conditions, its amplitude and phase are 8.5 and 45° respectively, and the complex relationship model between its vibration response and unbalance is V = 8.5e j·45° .

[0093] 8. By analyzing the unbalance response of the rotor at different speeds and operating conditions, a mapping relationship between the unbalance and the correction amount is established, thereby guiding the formulation of the correction strategy and realizing the rapid adjustment of rotor unbalance.

[0094] The above is the preferred embodiment of the present invention. It should be pointed out that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. A method for rapid rotor imbalance adjustment based on Kalman filtering, characterized in that: The steps include: S1. Obtain the speed signal of the rotor during operation through the magnetic encoder built into the rotating device, and trigger the piezoelectric vibration sensor to collect the radial vibration signal of the rotor based on the speed signal; S2. The vibration signal is processed by a zero phase shift filter (the purpose is to obtain a zero phase shift filter) to filter out the noise interference component and DC offset that are not related to the imbalance amount, obtain the processed signal, and extract the initial phase and amplitude of the signal by FFT transformation; S3. Determine whether the current unbalanced speed state is in a stable state or a variable speed instantaneous state stable operation state; S4. Under transient conditions, a state space model including amplitude, phase, and speed is constructed, and the imbalance adjustment parameters are recursively predicted through Kalman filtering, and output to the actuator in real time; S5. Under steady-state conditions, the least square method is used to accurately calculate the unbalance correction parameters; S6. According to the imbalance response of the rotor at different speeds and working conditions, guide the formulation of correction strategies to achieve rapid adjustment of rotor imbalance.

2. The rotor imbalance rapid adjustment method based on Kalman filtering according to claim 1 is characterized in that: The way in which the magnetic encoder triggers the piezoelectric vibration sensor in S1 is: use the pulse signal of the magnetic encoder as the external trigger source, input it through the PFI pin of DAQ, configure the hardware timing trigger mode of DAQ, set the trigger edge to the rising edge, and calculate the vibration signal sampling rate according to the magnetic encoder pulse frequency. The sampling rate is 32 times the base frequency of the speed to achieve complete synchronous sampling and obtain the vibration signal subset x(n).

3. The rotor imbalance rapid adjustment method based on Kalman filtering according to claim 1 is characterized in that: The process of processing the vibration signal x(n) by the zero phase shift filter in S2 is as follows: S21 sequentially filters the vibration signal subset x(n) to obtain x1(n), that is, x1(n)=x(n)·h(n), where h(n) is the unit impulse response sequence of the selected filter; S22 reverses x1(n) to obtain the reverse sequence x2(n), that is, x2(n) = x1(N-1-n), where N is the number of points in the original input sequence; S23 performs the same filtering process on x2(n) to obtain a response sequence x3(n), that is, x3(n)=x2(n)·h(n); S24 inverts x3(n) to obtain a final filtered output signal x4(n), i.e., a vibration signal with zero phase shift, i.e., x4(n)=x3(N-1-n); Perform FFT transformation on the vibration signal with zero phase shift, and extract its amplitude and initial phase.

4. The rotor imbalance rapid adjustment method based on Kalman filtering according to claim 1 is characterized in that: In S3, the speed change rate dn / dt is calculated based on the sliding time window, and the discrimination threshold θ is dynamically set. The operating state is judged as transient or steady according to the continuous relationship between the speed change rate and the threshold. The sliding time window length T and the discrimination threshold θ are used. The steady-state judgment must satisfy |dn / dt|≤θ and last for 3T.

5. The rotor imbalance rapid adjustment method based on Kalman filtering according to claim 1, characterized in that: The construction of the state space model described in S4 includes the following steps: S41 constructs a state vector containing amplitude, phase, and speed Among them, A k is the vibration amplitude at the current moment; is the vibration phase angle; n k is the rotor speed; S42 constructs the state equation as follows: Equation of state: x k =Cx k-1 +Du k +w k (1) Where x k represents the true value at time k; C represents the state transfer matrix, k A ,k φ are the coupling coefficients of speed change to amplitude and phase, respectively, which are calibrated according to experiments and finite element simulations; x k-1 Represents the true value at time k-1; D represents the control input matrix, b A is the amplitude adjustment efficiency coefficient; u k represents the externally applied adjustment command / balancing head compensation torque at time k; w k represents the random disturbance in the state transition process at time k; S43 constructs the observation equation as follows: Observation equation: y k =Hx k +v k (2) Where y k Represents the observation value obtained by the sensor; H represents the observation matrix; v k represents the observation noise, which is mainly sensor error, environmental interference, etc. The covariance matrix is S44 obtains the amplitude A and phase A respectively based on the state estimation value output by the Kalman filter.

6. The Kalman filter rotor imbalance rapid adjustment method according to claim 1, characterized in that: In S5, a least square fitting model with a sine function as the basis function is constructed to estimate the amplitude of the preprocessed vibration signal. The fitting function is as follows: At this time, according to the principle of least squares method, there is only one A and The sum of the squares of the differences between the numerical distances of y3(n) and Y is minimized, that is, the solution function is: The amplitude A, Find the partial derivative and set its partial derivative equation to 0, solve A, The magnitude and phase of the unbalanced quantity are obtained.

7. The Kalman filter rotor imbalance rapid adjustment method according to claim 1, characterized in that: In S6, a complex relationship model between vibration response and imbalance is constructed, and the relationship is as follows: V=A·e jφ (5) Where, j is the imaginary unit; V is the complex relationship expression of the unbalanced quantity.

8. The Kalman filter rotor imbalance rapid adjustment method according to claim 1, characterized in that: In S6, the unbalanced response of the rotor under different speeds and working conditions is analyzed, and the mapping relationship between the unbalanced amount and the correction amount is established, thereby guiding the formulation of the correction strategy and achieving rapid adjustment of the rotor imbalance.

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