A method and system for suppressing unbalanced vibration of a magnetic bearing

Abstract

The present invention discloses a method and system for suppressing unbalanced vibration of a magnetic bearing, belonging to the technical field of active control of magnetic bearings. During static suspension, self-learning is first performed, and X-axis and Y-axis position angle instructions of different frequencies that change according to the sine and cosine laws are injected to obtain X-axis and Y-axis position responses of corresponding frequencies within the full speed range, thereby obtaining transfer functions containing phase angle and amplitude information under different frequency bands; when the rotor rotates at high speed, the position responses of the X-axis and Y-axis are measured in real time, and their running trajectories are described in a vector representation manner, and the current rotational angular velocity is calculated in real time; a feedforward current is constructed and injected through the transfer function and the rotational angular velocity calculated in real time, and a disturbance suppression coefficient is introduced at the same time to achieve different degrees of unbalanced vibration suppression. This method is applicable to the movement of bearing rotors at high speeds, can smoothly cross the critical speed, and achieve effective suppression of unbalanced vibration.

Description

Technical Field

[0001] The present invention belongs to the technical field of active control of magnetic bearings, and more specifically, relates to a method and system for suppressing unbalanced vibration of a magnetic bearing. Background Art

[0002] Active magnetic bearings (AMBs) utilize electromagnetic force generated by energizing the windings to levitate the rotor, thus avoiding the mechanical contact of traditional bearings. They are a high-performance, novel support method. Because they lack mechanical friction, the bearing rotor can operate at high speeds, offering advantages such as long life, low loss, no lubrication requirements, and zero pollution. They have found widespread application in fields such as energy storage and aerospace.

[0003] Ideally, when a magnetic bearing rotates, the rotor's geometric center and center of gravity align, resulting in stable, fixed rotation. However, machining precision is limited, and inaccurate rotor dynamic balancing can cause the rotor's center of gravity to shift from its geometric center, leading to unbalanced vibration. If this vibration is not suppressed, it can endanger system safety and result in significant economic losses.

[0004] Currently, there are two main methods for suppressing unbalanced vibration in magnetically levitated rotors: zero-displacement control and zero-current control. The zero-displacement control method adds a current of equal magnitude and opposite direction to the controller output current, thereby offsetting the unbalanced force and minimizing the displacement of the magnetic bearing rotor. The zero-current control method eliminates the current component in the controller output current that has the same frequency as the rotor speed, causing the magnetic bearing rotor to rotate about its inertia axis, achieving minimum electromagnetic force control.

[0005] Zero-current control strategies often employ specific algorithms to extract the phase of the rotor's co-frequency vibration displacement signal and compensate for it, thereby suppressing unbalanced vibration. Currently, adaptive notch filters using the least mean square (LMS) algorithm have been widely researched and applied for unbalanced vibration compensation control. However, this algorithm is generally applicable to vibration control at constant speed and is limited to low-speed operating conditions. The phase-variable adaptive LMS notch filter described in Chinese patent CN202110102615.5 can achieve system stability across the entire speed range, but it only selects specific phase offset angles within certain speed ranges to suppress unbalanced vibration by compensating for the phase, without achieving continuous phase compensation. Furthermore, the influence of the control amplitude is not considered, making it difficult to achieve ideal unbalanced vibration suppression. Furthermore, the design and implementation of the LMS notch filter and its adaptive algorithm are complex, requiring complex frequency domain calculations, which reduces system reliability, hinders practical control, and increases actual costs. Furthermore, traditional displacement vibration suppression methods generally require speed information, meaning a speed sensor must be installed. However, for magnetic bearing systems that are not suitable for speed sensors, there is currently no reliable solution for displacement vibration suppression.

[0006] Therefore, it is necessary to propose a method for suppressing the unbalanced vibration of the magnetic bearing rotor that does not require a speed sensor and is more practical in engineering. It can not only achieve stable operation of the magnetic bearing rotor under the full speed range, but also take into account the simplicity, reliability and easy control of the system. Summary of the Invention

[0007] In response to the defects of the prior art, the purpose of the present invention is to provide a method for controlling the unbalanced vibration of a magnetic bearing, aiming to solve the problem of unbalanced vibration of the magnetic bearing rotor within the full speed range. At the same time, it also provides a speed measurement method that does not require a sensor, which can achieve stability control and imbalance suppression of the magnetic bearing.

[0008] To achieve the above objectives, the present invention provides the following technical solutions:

[0009] A method for suppressing unbalanced vibration in a magnetic bearing without a speed sensor uses a vector to represent the trajectory of the geometric center of the bearing rotor at high speed, which can be normalized to the X-axis and Y-axis, with the amplitude representing the vibration amplitude. The method includes the following steps:

[0010] (1) In static suspension, the X-axis and Y-axis position angle given signals x are injected with an angular frequency of ω1 and a sine-cosine law. * (t), y *(t), after outputting the control current of the winding according to the conventional PID control method, the X-axis and Y-axis position responses x1(t) and y1(t) at the corresponding angular frequency ω1 are obtained, thereby obtaining the transfer function containing the phase angle and amplitude information related to the control system transfer function at the angular frequency ω1.

[0011] (2) In the entire speed range, let ω1 start from a relatively small angular frequency and increase it with a certain integer value Δω. i According to step (1), the corresponding frequency response process transfer function is obtained The frequency response process transfer function G in the entire speed range is obtained by linear interpolation method. x (s), G y (s).

[0012] (3) When the bearing rotor rotates at high speed, the current angular velocity ω is calculated in real time using trigonometric functions based on the vector representation of the trajectory using the position responses x(t) and y(t) measured by the displacement sensor on the X and Y axes, respectively. This method does not require a speed or position sensor to be installed on the rotor shaft to obtain the real-time rotor speed.

[0013] (4) According to the frequency response process transfer function G under the current rotation angular velocity ω x (jω), G y (jω) and the position response of the displacement sensor x(t), y(t), by introducing the disturbance suppression coefficient α, the feedforward current i is constructed qkx 、i qky injection, the current output of the controller is: in represents the output current before suppression, represents the output current after suppression; the introduction of the feedforward current suppresses the harmonics of the control current and reduces its amplitude, thereby suppressing the unbalanced vibration of the bearing rotor. In the above technical solution, the trajectory of the geometric center of the bearing rotor is represented by a vector and can be decomposed into X-axis and Y-axis components. The amplitude of this vector represents the amplitude of the unbalanced vibration, and its angle θ with the X-axis represents the phase angle of the rotor geometric center, and its derivative is the rotational angular velocity ω.

[0014] In the above technical solution, step (1) is performed as follows: by injecting the X-axis and Y-axis position angle given signals x which are the same as the rotational speed frequency ω1 in the suspended state * (t) = X0cosω1t, y *(t) = Y0sinω1t (X0, Y0 are constants), simulate the running trajectory of the bearing rotor under unbalanced force, and measure the X-axis and Y-axis position responses x1(t) and y1(t) through the displacement sensor. The transfer function value at frequency ω1 is obtained through frequency domain calculation:

[0015]

[0016] In the above technical solution, step (3) is performed as follows: the running trajectory of the bearing rotor geometric center under unbalanced vibration is approximately a circle. Through the vector representation method in step (1), the position response can be made as follows: x(t) = cosωt = cosθ, y(t) = sinωt = sinθ, then According to the rule that the vibration frequency of the bearing rotor is the same as the speed, the speed of the bearing rotor can be calculated in real time using the following formula:

[0017]

[0018] Where θ(n) is the phase angle at the current sampling moment, θ(n-1) is the phase angle at the previous sampling moment, and T is the sampling period. This method can obtain the real-time rotor speed without installing a speed or position sensor.

[0019] In the above technical solution, the feedforward current i in step (4) qkx 、i qky The construction method is carried out as follows: According to the frequency response process transfer function G obtained in step (2), x (s), G y (s) and the rotation angular velocity ω obtained in step (3), construct the feedforward current i qkx 、i qky As shown below:

[0020]

[0021] In order to avoid direct calculation in the frequency domain, take Δ x =180°-∠G x (jω), Δ y =180°-∠G y (jω), substitute Δ x , Δ y After that, we can get i qkx 、i qky The expression in the time domain is:

[0022]

[0023] Where P is the proportional control coefficient, x(t) and y(t) are the position responses measured by the sensor, and α is the disturbance suppression coefficient, which generally ranges from 1 to 10.

[0024] In summary, the present invention first uses the vector circle representation method to describe the running trajectory of the geometric center under unbalanced force, and the actual speed of the rotating shaft can be measured in real time according to the response of the displacement sensor; then, a self-learning process is first performed during static suspension, and position angle given signals of different frequencies are injected, and the frequency response process transfer function is obtained according to the actual response; then, a feedforward current at the corresponding frequency is constructed according to the measured speed and process transfer function, and after being injected into the controller, compensation for the unbalanced force can be achieved, which can effectively suppress the unbalanced vibration of the magnetic bearing rotor at all speeds.

[0025] The present invention also provides an unbalanced vibration suppression system for a magnetic bearing, comprising: a computer-readable storage medium and a processor;

[0026] The computer-readable storage medium is used to store executable instructions;

[0027] The processor is configured to read the executable instructions stored in the computer-readable storage medium and execute the above-mentioned method for suppressing unbalanced vibration of the magnetic bearing.

[0028] Compared with the prior art, the above technical solutions conceived by the present invention can achieve the following beneficial effects:

[0029] 1. The control method provided by the present invention does not require the installation of a speed measurement sensor. The actual speed can be obtained by simply measuring the position response results of the X-axis and Y-axis, expressing them through trajectory circle vectors, solving the phase, and performing differential processing, thereby reducing costs and the complexity of the control system.

[0030] 2. The control method provided by the present invention does not rely on the design parameters of the magnetic bearing rotor. The corresponding feedforward current can be constructed only through the frequency response process transfer function during static suspension. It is universal and easy to operate. At the same time, the harmonics and amplitude of the compensated control current are reduced, which is beneficial to improving the stability of the system.

[0031] 3. The control method provided by the present invention does not depend on the operating speed of the magnetic bearing rotor. By fitting the frequency response process transfer function of multiple measurement points, it can achieve unbalanced vibration suppression within the full speed range and improve the stability and reliability of the system.

[0032] 4. The control method provided by the present invention does not require a complex frequency domain calculation process. The time domain expression of the feedforward current can be directly constructed through a simple phase angle transformation, which greatly simplifies the calculation process and is more conducive to actual engineering control. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 is a system flow chart of the control method of the present invention;

[0034] Figure 2 This is a control principle diagram of the magnetic bearing-rotor system of the present invention;

[0035] Figure 3 This is a schematic diagram showing the vector representation of the geometric center trajectory of the magnetic levitation rotor of the present invention;

[0036] Figure 4 The schematic diagram of the transfer function solution of the frequency response process of the present invention;

[0037] Figure 5 This is the speed solving principle diagram of the present invention;

[0038] Figure 6 The magnetic bearing rotor system in the embodiment;

[0039] Figure 7 This is a comparison diagram between the calculated rotation speed and the actual rotation speed in the embodiment;

[0040] Figure 8 This is a comparison diagram of the controller output current before and after suppression in the embodiment;

[0041] Figure 9 This is a diagram showing the effect of suppressing the unbalanced vibration of the magnetic bearing rotor in the embodiment. DETAILED DESCRIPTION

[0042] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely for explaining the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0043] The present invention proposes a method for suppressing unbalanced vibration of a magnetic bearing without a speed sensor. The system flow chart is as follows: Figure 1 As shown in the control principle diagram Figure 2 As shown, the vector diagram of the magnetic suspension rotor geometric center running trajectory is as follows Figure 3 As shown in the figure, the positions of the displacement sensors are specified as X-axis and Y-axis respectively. Then the position of the geometric center of the rotor at a certain moment can be represented by a vector, whose amplitude represents the vibration amplitude, and the angle θ with the X-axis is the phase, x s and y s The result measured by the sensor.

[0044] The specific steps include:

[0045] (1) According to the above-mentioned X-axis and Y-axis, during static suspension, the X-axis and Y-axis position angle given signals x with an angular frequency of ω1 and a change in the sine and cosine law are injected. *(t) = X0cosω1t, y * (t) = Y0sinω1t (X0, Y0 are constants), simulate the running trajectory of the bearing rotor under unbalanced force, and obtain the X-axis and Y-axis position responses x1(t) and y1(t) at the corresponding angular frequency ω1 through the displacement sensor, so as to obtain the transfer function containing the phase angle and amplitude information related to the control system transfer function at the angular frequency ω1 through frequency domain calculation. The principle of solving the frequency response process transfer function is as follows Figure 4 The calculation formula is as follows:

[0046]

[0047] (2) In the entire speed range, let ω1 start from a relatively small angular frequency and increase it with a certain integer value Δω. i According to step (1), the corresponding frequency response process transfer function is obtained The frequency response process transfer function G in the entire speed range is obtained by linear interpolation method. x (s), G y (s).

[0048] (3) When the bearing rotor rotates at high speed, according to the rotor geometric center running trajectory vector representation method, the position responses of the X-axis and Y-axis measured by the displacement sensor can be x(t) = cosωt = cosθ, y(t) = sinωt = sinθ, then The principle of speed calculation is as follows Figure 5 As shown, according to the rule that the vibration frequency of the bearing rotor is the same as the speed, the speed ω of the bearing rotor can be calculated in real time by the following formula:

[0049]

[0050] Where θ(n) is the phase angle at the current sampling moment, θ(n-1) is the phase angle at the previous sampling moment, and T is the sampling period. This method can obtain the real-time rotor speed without installing a speed or position sensor.

[0051] (4) The frequency response process transfer function G obtained according to step (2) x (s), G y (s) and the position response of the displacement sensor x(t), y(t), by introducing the disturbance suppression coefficient α, the feedforward current i can be constructed qkx 、i qky , the current output of the controller is: in represents the output current before the suppression algorithm is added, Indicates the output current after the suppression algorithm is added.

[0052] Feedforward current i qkx 、i qky The construction method is as follows: According to the frequency response process transfer function G obtained in step 2 x (s), G y (s) and the rotation angular velocity ω obtained in step (3), take Δ x =180°-∠G x (jω), Δ y =180°-∠G y (jω), construct the feedforward current i qkx 、i qky As shown below:

[0053]

[0054] In order to avoid direct calculation in the frequency domain, substitute Δ x , Δ y , we can get i qkx 、i qky The expression in the time domain is:

[0055]

[0056] Where P is the proportional control coefficient, x(t) and y(t) are the position responses measured by the sensor, and α is the disturbance suppression coefficient, which generally ranges from 1 to 10.

[0057] According to steps (1) to (4), Figure 6 The unbalanced vibration control method of the magnetic bearing rotor system is shown in Table 1.

[0058] Table 1

[0059]

[0060]

[0061] By using the control method of the present invention, the comparison between the speed calculated by the vector representation method and the actual speed can be obtained. Figure 7 As shown in the figure, it can be seen that the theoretical calculation results are consistent with the actual values. Figure 8 This is a comparison chart of the controller output current before and after the unbalanced vibration suppression method is added. The figure clearly shows that after adding the algorithm, the amplitude of the output current is significantly reduced from 6A to 1.5A, which is beneficial to the stability of the system. Figure 9The unbalanced vibration suppression method is added to the vibration displacement in the Y-axis direction. The figure clearly shows that before the suppression algorithm is added, the maximum vibration displacement is 12μm. After the suppression algorithm is added, the maximum vibration displacement is 5μm, which is a decrease of 58.3% compared with the previous figure, which has a good unbalanced vibration suppression effect.

[0062] It will be easily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for suppressing unbalanced vibration of a magnetic bearing, wherein the running trajectory of the geometric center of the bearing rotor is represented by a vector and unified into the X-axis and Y-axis; characterized in that: The following steps are involved: (1) Introduce the self-learning process: In static suspension, inject the X-axis and Y-axis position angle given signal x with an angular frequency of ω1 and a sine and cosine law. * (t), y * (t), the X-axis and Y-axis position responses x1(t) and y1(t) at the corresponding angular frequency ω1 are obtained, thereby obtaining the transfer function containing phase angle and amplitude information at the angular frequency ω1 (2) During the self-learning process, within the entire speed range, let ω1 start from the preset value and increase continuously by integer value Δω. i According to step (1), the corresponding frequency response process transfer function is obtained The frequency response process transfer function G in the entire speed range is obtained by linear interpolation method. x (s), G y (s); (3) When the bearing rotor rotates at high speed, the position responses x(t) and y(t) of the rotor's trajectory are measured respectively, and the current rotation angular velocity ω is calculated in real time through trigonometric operations; (4) According to the frequency response process transfer function G under the current rotation angular velocity ω x (jω), G y (jω) and position response x(t), y(t), by introducing the disturbance suppression coefficient α, the feedforward current i is constructed qkx 、i qky , the introduction of feedforward current suppresses the amplitude of control current, thereby achieving the suppression of unbalanced vibration of bearing rotor.

2. The method for suppressing unbalanced vibration of a magnetic bearing according to claim 1, characterized in that: The trajectory of the geometric center of the bearing rotor is represented by a vector and decomposed into X-axis and Y-axis components. The amplitude of the vector represents the amplitude of the unbalanced vibration, and the angle θ between it and the X-axis represents the phase angle of the geometric center of the rotor. Its derivative is the rotational angular velocity ω of the rotor shaft.

3. The method for suppressing unbalanced vibration of a magnetic bearing according to claim 1, characterized in that: Step (1) is performed as follows: In the static suspension state, the X-axis and Y-axis position angle given signals x are injected with the same rotational speed frequency ω1. * (t) = X0cosω1t, y * (t) = Y0sinω1t, simulate the running trajectory of the bearing rotor under unbalanced force, and measure the X-axis and Y-axis position responses x1(t) and y1(t) through the displacement sensor. The transfer function value at frequency ω1 is obtained through frequency domain calculation: Among them, X0 and Y0 are fixed values.

4. The method for suppressing unbalanced vibration of a magnetic bearing according to claim 1, characterized in that: Step (3) is performed as follows: Let the position response be: x(t) = cosωt = cosθ, y(t) = sinωt = sinθ, then According to the rule that the vibration frequency of the bearing rotor is the same as the speed, the speed of the bearing rotor can be calculated in real time using the following formula: Where θ(n) is the phase angle at the current sampling moment, θ(n-1) is the phase angle at the previous sampling moment, and T is the sampling period. This method can obtain the real-time speed of the rotor without installing a speed or position sensor.

5. The method for suppressing unbalanced vibration of a magnetic bearing according to claim 1, characterized in that: The feedforward current i in step (4) qkx 、i qky The construction method is carried out as follows: According to the frequency response process transfer function G obtained in step (2), x (s), G y (s) and the rotation angular velocity ω obtained in step (3), construct the feedforward current i qkx 、i qky As shown below: Take Δ x =180°-∠G x (jω), Δ y =180°-∠G y (jω), we get i qkx 、i qky The expression in the time domain is: Where P is the proportional control coefficient, and x(t) and y(t) are the position responses measured by the sensor.

6. The method for suppressing unbalanced vibration of a magnetic bearing according to claim 5, characterized in that: The control current output is: in represents the output current before suppression, Indicates the output current after suppression.

7. An unbalanced vibration suppression system for a magnetic bearing, characterized in that: include: Computer-readable storage media and processor; The computer-readable storage medium is used to store executable instructions; The processor is configured to read the executable instructions stored in the computer-readable storage medium and execute the method for suppressing unbalanced vibration of a magnetic bearing according to any one of claims 1 to 6.

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