An analysis method for torsional vibration stability of a low-pressure rotor of an aero-engine

Abstract

The present disclosure is an analysis method for the torsional vibration stability of a low-pressure rotor of an aero-engine, comprising: establishing a torsional vibration model of the low-pressure rotor of the aero-engine; constructing a torsional vibration matrix equation of the low-pressure rotor; substituting the amplitude and frequency of the exciting torque into the matrix equation to obtain a forced torsional vibration matrix equation containing damping; respectively establishing control functions taking the rotational speeds of the low-pressure turbine and the fan rotor as feedback rotational speed signals of the control system, and substituting them into the forced torsional vibration matrix equation containing damping to obtain corresponding control equations; and using the Routh stability criterion to determine the positive and negative of the real parts of the characteristic roots of the two control equations to determine the torsional vibration stability of the low-pressure rotor. The present embodiment respectively establishes two rotational speed feedback control equations, clearly distinguishes the influence of the feedback signals on the system damping, and locates the root cause of instability; and the Routh stability criterion is used for determination, the criterion is clear and the conclusion is reliable, and the torsional vibration stability of the low-pressure rotor can be quickly determined.

Description

Technical Field

[0001] This invention relates to the field of aero-engine dynamics analysis technology, and in particular to an analysis method for the torsional vibration stability of a low-pressure rotor of an aero-engine. Background Technology

[0002] In reality, aero-engine rotor systems exhibit complex bending-torsional coupled vibrations, meaning that lateral and torsional vibrations interact. Torsional vibration can cause both lateral and axial vibrations, potentially leading to lateral instability. Conversely, lateral vibration can also induce torsional vibration, particularly in flexible rotors with slender shafts, where the bending-torsional coupling is stronger. Currently, torsional vibration is often neglected in the dynamic analysis and design of aero-engine rotors. This is primarily due to: ① the relatively short shafts and large diameters and wall thicknesses of older engine rotors, preventing their torsional natural frequencies from falling within the operating speed range; ② the significant damping provided by fluids to rotor torsional vibration; ③ the sensor measuring rotor speed is typically installed near the nodes of the torsional mode. When the speed signal is used as control feedback, it does not cause torsional instability; ④ the control system's adjustment frequency does not coincide with the rotor's torsional natural frequency; and ⑤ there is no situation where the rotor's torsional natural frequency coincides with a critical speed. Furthermore, failures caused by rotor torsional vibration are relatively rare in actual aero-engine operation, hence the lack of sufficient attention and in-depth research on this issue.

[0003] With the diversification of flight missions, the requirements for overall engine performance and thrust-to-weight ratio are constantly increasing, and the characteristics of variable operating conditions are becoming more prominent. Modern aero-engine low-pressure rotors generally have slender shafts and flexible connection structures, with the low-pressure turbine and fan rotors located at opposite ends of the shaft. This means that the rotor's first-order torsional natural frequency falls within the operating speed range. The airflow-induced dynamic load that triggers torsional vibration is always present, and it is the mainstream excitation; that is, the airflow fluctuations in the mainstream channel generate fluctuating torques, forming the excitation torque for rotor torsional vibration, leading to rotor torsional resonance or forced torsional vibration. The excitation torque is not a single-frequency dynamic load; it generally contains several frequency components. Therefore, the possibility of causing rotor torsional resonance is relatively high. Since the excitation originates from the mainstream channel, the excitation torque is often relatively large, and even if torsional resonance is not triggered, forced vibration may still be quite intense. However, there is currently a lack of relevant analytical methods for rotor torsional vibration stability. Therefore, in-depth research and verification of rotor torsional vibration are urgently needed to provide a theoretical basis for improving engine rotor dynamics design methods and fault diagnosis.

[0004] It should be noted that this section is intended to provide background or context for the technical solutions of this disclosure as set forth in the claims. The description herein does not constitute an admission that it is prior art simply because it is included in this section. Summary of the Invention

[0005] The purpose of this invention is to provide an analytical method for the torsional vibration stability of a low-pressure rotor of an aero-engine, thereby overcoming, to at least to some extent, one or more problems caused by the limitations and defects of related technologies.

[0006] This invention provides a method for analyzing the torsional vibration stability of a low-pressure rotor in an aero-engine, comprising the following steps: S1. Establish a torsional vibration model of the low-pressure rotor of an aero-engine. The torsional vibration model simplifies the low-pressure rotor into a rigid low-pressure turbine and a rigid fan rotor connected at both ends of a non-inertia elastic shaft. S2, Construct the torsional vibration matrix equation of the low-pressure rotor based on the torsional vibration model; S3. Substitute the amplitude and frequency of the excitation torque acting on the low-pressure turbine and fan rotor into the torsional vibration matrix equation of the low-pressure rotor to obtain the damped forced torsional vibration matrix equation. S4. Establish control functions with low-pressure turbine speed and fan rotor speed as feedback speed signals of the control system, respectively. Substitute the control functions into the damped forced torsional vibration matrix equation to obtain the corresponding control equations. S5. The Holwitz stability criterion is used to determine the sign of the real part of the characteristic root of the two control equations. If the real part of the characteristic root is negative, the torsional vibration of the low-pressure rotor is stable; if the real part of the characteristic root is positive, the torsional vibration of the low-pressure rotor is unstable.

[0007] In this invention, in S2, the torsional vibration matrix equation of the low-pressure rotor is expressed as follows:

[0008] in, The polar rotational inertia of the low-pressure turbine; This represents the polar rotational inertia of the fan rotor; The rotation angle of the low-pressure turbine. This refers to the angular acceleration of the low-pressure turbine. The rotation angle of the fan rotor. This refers to the angular acceleration of the fan rotor. For the torsional stiffness of the low-pressure rotor; This refers to the excitation torque acting on the low-pressure turbine; This is the excitation torque acting on the fan rotor.

[0009] In this invention, in S3, the damped forced torsional vibration matrix equation is expressed as follows:

[0010] in, This represents the aerodynamic damping coefficient of the low-pressure turbine. This represents the aerodynamic damping coefficient of the fan rotor; The amplitude of the excitation torque acting on the low-pressure turbine; The amplitude of the excitation torque acting on the fan rotor; j The imaginary unit; The excitation frequency; t For time; The rotational speed of the low-pressure turbine; This represents the rotational speed of the fan rotor.

[0011] In this invention, the control function in S4 is represented as follows:

[0012] in, For pneumatic control torque; For gain; The governing equations are expressed as follows:

[0013] Specifically, when the low-pressure turbine speed is used as the feedback speed signal for the control system, for When the fan rotor speed is used as the feedback speed signal for the control system, for .

[0014] In this invention, in step S5, when the low-pressure turbine speed is used as the feedback speed signal of the control system, the Holwitz stability criterion is used to determine that the real part of the characteristic root of the corresponding control equation is negative, and the torsional vibration of the low-pressure rotor is stable; when the fan rotor speed is used as the feedback speed signal of the control system, the Holwitz stability criterion is used to determine that the real part of the characteristic root of the corresponding control equation is positive, and the torsional vibration of the low-pressure rotor is unstable.

[0015] In this invention, the modal transformation of the damped forced torsional vibration matrix equation is performed to obtain the low-pressure rotor modal damping ratio. When the low-pressure rotor modal damping ratio is greater than or equal to 5%, the torsional resonance of the low-pressure rotor can be suppressed.

[0016] In this invention, modal transformation is performed on the forced torsional vibration matrix equation with damping to obtain the low-pressure turbine damping coefficient and the fan rotor damping coefficient. When both satisfy the following formula, the torsional vibration peak value of the low-pressure rotor can be suppressed:

[0017] in, The modal damping ratio; This refers to the torsional stiffness of the low-pressure rotor.

[0018] The technical solution provided by this invention may include the following beneficial effects: This invention discloses a method for analyzing the torsional vibration stability of a low-pressure rotor in an aero-engine. It employs a simplified modeling approach using an inertia-free elastic shaft and rigid bodies at both ends, enabling independent analysis of the torsional vibration of the low-pressure rotor without considering bending-torsional coupling or high-pressure rotor coupling. This method offers high modeling efficiency, low computational complexity, and strong engineering applicability. Two speed feedback control equations are established to clearly distinguish the impact of feedback signals on system damping and pinpoint the root cause of instability. The Holwitz stability criterion is used for determination, providing a clear and reliable criterion that allows for rapid assessment of the stability of the low-pressure rotor's torsional vibration. Attached Figure Description

[0019] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure. It is obvious that the drawings described below are merely some embodiments of this disclosure, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0020] Figure 1 A flowchart illustrating the analysis method for the torsional vibration stability of a low-pressure rotor of an aero-engine in an exemplary embodiment of this disclosure; Figure 2 This illustrates a torsional vibration model of a low-pressure rotor in an exemplary embodiment of this disclosure; Figure 3 This diagram illustrates the analysis flowchart for suppressing peak torsional vibration in a low-pressure rotor system according to an exemplary embodiment of this disclosure. Figure 4 This invention illustrates a fan rotor front end speed measuring device in an exemplary embodiment of the present disclosure; Figure 5 A flowchart illustrating the torsional vibration stability analysis of a low-pressure rotor system in an exemplary embodiment of this disclosure is shown. Detailed Implementation

[0021] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that this disclosure will be more comprehensive and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0022] Furthermore, the accompanying drawings are merely illustrative diagrams of embodiments of this disclosure and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities.

[0023] This example implementation first provides a method for analyzing the torsional vibration stability of a low-pressure rotor in an aero-engine. Please refer to [reference needed]. Figure 1 This method may include: S1-S5, as follows: S1. Establish a torsional vibration model of the low-pressure rotor of an aero-engine. The torsional vibration model simplifies the low-pressure rotor into a rigid low-pressure turbine and a rigid fan rotor connected at both ends of a non-inertia elastic shaft. S2, Construct the torsional vibration matrix equation of the low-pressure rotor based on the torsional vibration model; S3. Substitute the amplitude and frequency of the excitation torque acting on the low-pressure turbine and fan rotor into the torsional vibration matrix equation of the low-pressure rotor to obtain the damped forced torsional vibration matrix equation. S4. Establish control functions with low-pressure turbine speed and fan rotor speed as feedback speed signals of the control system, respectively. Substitute the control functions into the damped forced torsional vibration matrix equation to obtain the corresponding control equations. S5. The Holwitz stability criterion is used to determine the sign of the real part of the characteristic root of the two control equations. If the real part of the characteristic root is negative, the torsional vibration of the low-pressure rotor is stable; if the real part of the characteristic root is positive, the torsional vibration of the low-pressure rotor is unstable.

[0024] In this embodiment, a simplified modeling method using an inertia-free elastic shaft and rigid bodies at both ends is adopted, which can independently analyze the torsional vibration of the low-pressure rotor without considering bending-torsional coupling and high-pressure rotor coupling. This method has high modeling efficiency, low computational load, and strong engineering applicability. Two speed feedback control equations are established to clearly distinguish the influence of feedback signals on system damping and locate the root cause of instability. The Holwitz stability criterion is used for judgment, which is clear and reliable, and can quickly determine whether the torsional vibration of the low-pressure rotor is stable.

[0025] The specific process of each step in the above embodiments will be described below.

[0026] S1. When analyzing the torsional vibration of an aero-engine, the torsional natural frequency of the high-pressure rotor is usually high, much higher than the operating speed. Therefore, the torsional vibration of the low-pressure rotor needs to be given special attention. In this application, when analyzing the torsional vibration of the low-pressure rotor, a torsional vibration model of the low-pressure rotor is first established. This model simplifies the low-pressure rotor into a rigid low-pressure turbine and a rigid fan rotor connected to opposite ends of a non-inertia elastic shaft. Figure 2 As shown.

[0027] In addition, when analyzing the torsional vibration of the low-pressure rotor, this application defines the rigid body torsional vibration (in phase) as the 0th order mode, and focuses on the first order mode, namely the anti-phase vibration mode of the fan rotor and the low-pressure turbine.

[0028] S2, First, based on the torsional vibration model, establish the differential equation for rotor torsional vibration, as shown below: (1.1) (1.2) In the formula, The polar rotational inertia of the low-pressure turbine; This represents the polar rotational inertia of the fan rotor; The rotation angle of the low-pressure turbine. This refers to the angular acceleration of the low-pressure turbine. The rotation angle of the fan rotor. This refers to the angular acceleration of the fan rotor. For the torsional stiffness of the low-pressure rotor; This refers to the excitation torque acting on the low-pressure turbine; This is the excitation torque acting on the fan rotor.

[0029] Equations (1.1) and (1.2) can be combined into matrix form, which is the matrix equation for the torsional vibration of the low-pressure rotor, as follows: (1.3) Assume the solution to equation (1.3) is: (1.4) In the formula, This refers to the rotational amplitude of the low-pressure turbine. This represents the rotational angle amplitude of the fan rotor; j The imaginary unit; This is the torsional vibration frequency of the low-pressure rotor; t For time.

[0030] Substituting the above solution into the homogeneous equation corresponding to equation (1.3), we obtain the following equation: (1.5) The characteristic equation is obtained from the coefficient determinant: (1.6) The 0th order natural frequency is obtained by solving. for: (1.7) It can be seen that the low-pressure rotor exhibits rigid body rotation but no torsional vibration.

[0031] The first natural frequency is obtained by solving. for: (1.8) The angle magnitude of the fan rotor can be obtained from equation (1.5): (1.9) Equation (1.9) shows that when the low-pressure rotor is... During resonance, the low-pressure turbine and the fan rotor experience torsional vibration in opposite phase.

[0032] S3, any fluctuations in the main flow of the engine will generate dynamic loads that excite torsional vibration of the low-pressure rotor. In addition to the structural characteristics of the low-pressure rotor, the key factors affecting the forced torsional vibration of the low-pressure rotor are the characteristics of the excitation load, including amplitude, frequency and damping characteristics.

[0033] On the one hand, under normal circumstances, the structural damping of torsional vibration of a low-pressure rotor is very small. However, during the torsional vibration process of a low-pressure rotor, due to the change in rotational speed, both the fan rotor and the low-pressure turbine will be subjected to strong airflow. This aerodynamic force provides significant damping for the torsional vibration of the low-pressure rotor and is a key factor in suppressing torsional vibration of the low-pressure rotor.

[0034] On the other hand, any fluctuation in airflow will cause fluctuations in aerodynamic forces. As the main force for work, fluctuations in tangential force will generate fluctuating torque, thereby exciting torsional vibration of the low-pressure rotor. For example, unstable intake, combustion oscillations, airflow wakes, and other unsteady flows will all cause fluctuations in the main flow, generating fluctuating torque with relatively large amplitudes, thus exciting torsional vibration of the low-pressure rotor. Generally, the dynamic load generated by airflow is not a simple harmonic wave, but contains several frequency components. When the frequency of any of these components coincides with the torsional natural frequency of the low-pressure rotor, torsional resonance will occur in the low-pressure rotor. Even without resonance, strong forced vibration may occur. Therefore, avoiding large torsional vibrations in the low-pressure rotor is not easy. This is a problem that was not considered in previous engine designs.

[0035] For simplicity, this application analyzes only one component. The excitation torques applied to the fan rotor and low-pressure turbine by the device are as follows: (1.10) In the formula, The amplitude of the excitation torque acting on the low-pressure turbine. The amplitude of the excitation torque acting on the fan rotor. The excitation frequency is denoted as .

[0036] When solving for forced torsional vibration of a rotor, damping needs to be considered. Assume the torsional damping of the low-pressure turbine and fan rotors is linear aerodynamic damping, with damping coefficients of [missing values]. and .

[0037] Substituting equation (1.10) and the damping coefficient into equation (1.3), we get: (1.11) in, This refers to the rotational speed of the low-pressure turbine (specifically, the angular velocity of the low-pressure turbine). This refers to the rotational speed of the fan rotor (specifically, the angular velocity of the fan rotor).

[0038] The response obtained is: (1.12) in, It has no actual physical meaning; its reference is given in formulas (1.13) or (1.14).

[0039] In equation (1.12): (1.13) or: (1.14) when When, i.e., excitation frequency With the first-order torsional natural frequency When they overlap, The value is used This is represented as follows: (1.15) Due to the presence of damping, the peak value at resonance is suppressed. However, when hour, The resonance peak value is infinite.

[0040] As mentioned earlier, the excitation torque amplitude and It is generally caused by the main fluctuations in engine power, and is often quite large. Even As can be seen from equation (1.12), when the excitation torque amplitude and When the amplitude is large, the amplitude of forced vibration will also be very prominent.

[0041] To further analyze the effect of damping, a modal transformation is performed on equation (1.11), yielding: (1.16) In the formula, the coefficient vector is the low-pressure rotor torsional vibration mode vector. This represents the modal response of the low-pressure rotor.

[0042] Find the first and second derivatives of equation (1.16) and substitute them into equation (1.11). Then, multiply both sides of the resulting equation. Divide again The modal equations are obtained as follows: (1.17) In the formula, and They are The first and second derivatives, let ,but, Let be the modal damping coefficient, and we have: (1.18) Assume a torsional natural frequency is constructed using a low-pressure turbine. The virtual rotor, Let the modal damping ratio of the virtual rotor corresponding to the low-pressure turbine be: (1.19) Assume a fan rotor is used to construct a torsional natural frequency of... The virtual rotor, Let the modal damping ratio of the virtual rotor corresponding to the fan rotor be: (1.20) use and This is to facilitate the estimation of the maximum aerodynamic damping of the low-pressure rotor, which can be calculated separately using aerodynamic principles. and And then find and .

[0043] Further order: (1.21) In the formula, This is the low-pressure rotor modal damping ratio.

[0044] From equation (1.21), we can obtain: (1.22) From equation (1.18), we can obtain: (1.23) This yields the upper bound of the first-order modal damping ratio of the low-pressure rotor. Therefore, when designing the control system, it is necessary to ensure that the negative damping provided by the control system to the torsional vibration of the low-voltage rotor is always less than this upper limit, and to leave sufficient margin, for example, 20%.

[0045] Solving equation (1.17), the modal response of the low-pressure rotor is obtained as follows: (1.24) In the formula, This represents the phase difference.

[0046] Dimensionless processing of equation (1.24) yields: (1.25) Low-pressure rotor modal damping ratio Reaching 5% or higher will effectively suppress low-pressure rotor torsional resonance.

[0047] As shown in equation (1.18), the aerodynamic damping coefficients of the fan rotor and the low-pressure turbine must satisfy the following equation (1.26). Only then can it reach more than 5%.

[0048] (1.26) In summary, when the low-pressure rotor of an engine is subjected to forced vibration, to effectively suppress the torsional vibration peak of the rotor system, the aerodynamic damping of the low-pressure turbine and fan rotors should satisfy equation (1.26). Otherwise, the torsional vibration peak of the rotor system will be difficult to suppress. In conclusion, the analysis process for whether the torsional vibration peak can be effectively suppressed is as follows: Figure 3 As shown.

[0049] In S4, the engine control system typically uses engine speed as a feedback signal to control the engine's state. During control, valves are used to adjust the fuel supply, changing the combustion heat energy in the combustion chamber, ultimately altering the aerodynamic torque of the gas-driven low-pressure turbine, and thus regulating the engine speed. This is a complex nonlinear process, and currently, there is no precise model to describe it.

[0050] To qualitatively analyze the impact of the control system on the torsional vibration stability of the low-pressure rotor, a specific engine setting state was selected as the analysis baseline. In this state, the set rotational speed of the low-pressure rotor was... The corresponding aerodynamic torque is If the low-pressure rotor speed is maintained at the set speed... Then the aerodynamic torque remains constant. If the low-pressure rotor experiences torsional vibration under these conditions, the control system adjusts the fuel supply to the combustion chamber. By changing the total gas pressure, this alters the drive torque of the low-pressure turbine, thereby controlling the low-pressure rotor speed towards the set speed. Therefore, the speed signal must be used as a feedback signal for the control system.

[0051] Linearizing the control process in the vicinity of the above state, i.e., the pneumatic control torque is proportional to the rotational speed, can be described by the following control function: (1.27) In the formula, For pneumatic control torque, q For gain, The speed is used as feedback. When the low-pressure turbine speed is used as the feedback speed signal for the control system... for When the fan rotor speed is used as the feedback speed signal for the control system, for The pneumatic control torque acts on the low-pressure turbine. Its function is to adjust the pneumatic control torque to 0 when the current speed is at the set target speed. When the speed fluctuates, the pneumatic control torque is adjusted to maintain the low-pressure rotor speed at a set value. In fact, adjusting the pneumatic control torque can hardly guarantee that the low-pressure rotor speed will always be maintained at the set speed; it can only control the speed fluctuation within a certain range.

[0052] Currently, two locations are set up in different engines to measure the low-pressure rotor speed: (1) In some engines, a speed measuring wheel is set near the No. 2 support. The voltage pulse of the high tooth is measured by an electromagnetic sensor, thereby obtaining the speed of the fan rotor.

[0053] (2) In other engines, due to limitations such as structure and sensor leads, a speed measuring rotor is driven by the inner teeth of the front journal of the fan rotor. A speed measuring sound wheel is installed at the end of the speed measuring rotor, such as... Figure 4 As shown, the fan rotor speed is obtained by measuring the voltage pulse at the high-speed teeth using an electromagnetic sensor.

[0054] Typically, the rotational speed of the low-pressure turbine is not directly measured in an engine. However, this application divides the torsional vibration stability analysis into two cases to compare the rotational speeds of the low-pressure turbine and the fan rotor: (1) Directly measure the speed of the low-pressure turbine and use it as the speed signal to be fed back to the control system; (2) Directly measure the speed of the fan rotor and use it as the speed signal to be fed back to the control system.

[0055] The two situations described above will be explained in detail below.

[0056] 1. The speed of the low-pressure turbine is used as the feedback speed signal. Assuming the speed signal fed back to the control system is the speed of the low-pressure turbine, then its corresponding control function is: (1.28) Substituting into equation (1.11), we obtain the corresponding governing equations as follows: (1.29) After rearranging and combining the terms, we get: (1.30) As can be seen from (1.30), the aerodynamic control torque increases the damping of the low-pressure turbine.

[0057] Let the solution to the governing equation (1.29) be: (1.31) In the formula, These are the characteristic roots of the governing equation (1.29).

[0058] Substituting the solution (1.31) into equation (1.30), we get: (1.32) The characteristic equation is then obtained as follows: (1.33) When the characteristic roots of characteristic equation (1.33) When the characteristic root is zero, it indicates that the low-pressure rotor has no torsional vibration, so the case where the characteristic root is zero is not considered.

[0059] Divide both sides of the characteristic equation (1.33) ,get: (1.34) (1.34) can be simplified to a polynomial in standard form as follows: (1.35) Assume characteristic roots It has the following form: (1.36) The stability of torsional vibration of the low-pressure rotor is determined by the real part of the characteristic root. The sign determines the outcome: (1) Then the low-pressure rotor will become unstable due to torsional vibration. (2) Then the low-pressure rotor vibration system is stable.

[0060] Determine using the Holwitz stability criterion The sign of the sign is calculated as follows: Calculate the coefficient determinant separately: (1.37) (1.38) (1.39) (1.40) In the formula, , , Let represent the first, second, and third order principal minors constructed from the coefficients of the characteristic equation (1.35), respectively. , , , They represent the characteristic roots respectively. The constant term, coefficient of the linear term, coefficient of the quadratic term, and coefficient of the cubic term in the characteristic equation.

[0061] According to the Holwitz stability criterion, the real part of the characteristic roots That is, the real part of the characteristic root is always less than zero. Therefore, the torsional vibration of the low-pressure rotor will not become unstable and is damped.

[0062] Assuming the aerodynamic damping coefficient is 0, that is The determinant above is still greater than 0. This indicates that when the low-pressure turbine speed is used as the control feedback signal, the aerodynamic control torque provides torsional damping for the rotor, improving the rotor's stability against torsional vibration.

[0063] 2. The fan rotor speed is used as the feedback speed signal. When the fan rotor speed is selected as the speed signal fed back to the control system, the corresponding control function is: (1.41) Substituting into equation (1.11), we obtain the corresponding governing equations as follows: (1.42) After rearranging and combining the terms, we get: (1.43) As can be seen, the damping matrix in the equation contains cross terms. q .

[0064] Let the solution to the governing equation (1.42) be: (1.44) Substituting the solution (1.44) into equation (1.43), we get: (1.45) The characteristic equation is then obtained as follows: (1.46) These are the characteristic roots of the characteristic equation (1.46).

[0065] Similarly, when the characteristic roots of the characteristic equation (1.46) When , it indicates no vibration.

[0066] when Then we have: (1.47) Equation (1.47) can be written as a standard polynomial as follows: (1.48) Assume characteristic roots It has the following form: (1.49) The stability of rotor torsional vibration is analyzed using the Holwitz stability criterion, as follows: (1.50) (1.51) (1.52) (1.53) In the formula, here, , , Let represent the first, second, and third-order principal minors constructed from the coefficients of the characteristic equation, respectively. , , , They represent the characteristic roots respectively. The constant term, coefficient of the linear term, coefficient of the quadratic term, and coefficient of the cubic term in the characteristic equation.

[0067] Assuming the aerodynamic damping is 0, that is, when hour, ; Therefore, the real part of the characteristic root is , i.e., characteristic roots It is always greater than zero. This indicates that when the fan rotor speed is used as the control feedback signal, the aerodynamic control torque provides negative damping for rotor torsional vibration, reducing the rotor's stability against torsional vibration.

[0068] Therefore, in S5, when the low-pressure turbine speed is used as the feedback speed signal of the control system, the Holwitz stability criterion is used to determine that the real part of the characteristic root of the corresponding control equation is negative, and the torsional vibration of the low-pressure rotor is stable; when the fan rotor speed is used as the feedback speed signal of the control system, the Holwitz stability criterion is used to determine that the real part of the characteristic root of the corresponding control equation is positive, and the torsional vibration of the low-pressure rotor is unstable.

[0069] The stability conditions and the mechanism of torsional vibration instability are explained below.

[0070] (1.54) (1.55) Only when equation (1.54) or equation (1.55) holds true will we have , The real part of the characteristic roots Only then will the rotor be stable. Because The second term in equation (1.54) can be ignored. Assume the fan rotor damping coefficient... With low-pressure turbine damping coefficient If they are the same, then they can be assumed to be the system's torsional vibration damping. Thus, the stability condition for the low-pressure rotor is obtained: (1.56) The above conditional equations indicate that the torsional vibration of the low-pressure rotor will not become unstable only when the aerodynamic damping of the low-pressure rotor is sufficiently large to satisfy the aforementioned stability conditions. However, it is difficult for aerodynamic damping to meet these stability conditions. Therefore, the risk of torsional vibration instability of the low-pressure rotor due to control torque is significant.

[0071] In summary, the process for analyzing the torsional vibration stability of the low-pressure rotor of an aero-engine is as follows: Figure 5 As shown.

[0072] The mechanism of torsional vibration instability in the low-pressure rotor of an aero-engine is as follows: the feedback signal used for control is the fan rotor speed, while the regulating aerodynamic torque acts on the low-pressure turbine. The torsional vibration of the low-pressure turbine and the fan rotor are out of phase. During torsional vibration, the fan rotor speed increases, and the low-pressure turbine speed decreases; conversely, the fan rotor speed decreases, and the low-pressure turbine speed increases. When torsional vibration increases the fan rotor speed, the control system determines that the low-pressure turbine speed is also increasing, and thus reduces the aerodynamic torque. This reduction in regulating aerodynamic torque further reduces the low-pressure turbine speed; that is, during 1 / 4 of the torsional vibration cycle, the regulating aerodynamic torque does positive work, inputting energy into the torsional vibration. After 1 / 2 of the torsional vibration cycle, the fan rotor speed decreases, and the low-pressure turbine speed increases. Based on the decreased fan rotor speed, the control system increases the regulating aerodynamic torque, causing the low-pressure turbine speed to increase further, continuing to input energy into the torsional vibration. This cycle repeats continuously, with the regulating aerodynamic torque continuously inputting energy into the torsional vibration of the low-pressure rotor, causing its amplitude to increase continuously, leading to torsional vibration instability. Because it continuously receives excitation energy from the main channel, this torsional vibration instability can be extremely severe. If emergency measures are not taken in time, it can often lead to serious malfunctions or even shaft breakage. Therefore, it must be given special attention.

[0073] Therefore, torsional vibration should be considered in the design and control of low-pressure rotors for aero-engines. The following three aspects can be considered for the design and control of rotor torsional vibration: (1) When designing rotor dynamics, the torsional vibration characteristics of the rotor should be calculated. At the same time, the torsional vibration excitation load sources and load spectrum that may occur under working conditions should be analyzed to avoid rotor torsional resonance.

[0074] (2) When designing engine performance, the damping coefficients of the low-pressure turbine and fan rotor should be calculated. and Furthermore, by combining structural and torsional vibration dynamics design, the following can be obtained: and . It should not be less than 10%. When calculating, at least 3 states can be selected, such as slow, intermediate and maximum states.

[0075] (3) The aerodynamic torque adjustment generally acts on the low-pressure turbine. The control system should use the low-pressure turbine speed signal as the feedback signal, or install the speed sensor near the node of the torsional vibration mode, for example, near the No. 2 support point, to avoid torsional vibration instability of the rotor system. Currently, several engine models have speed sensors installed at the front end of the fan rotor to measure the rotor speed. If this speed signal is used as the control feedback signal to adjust the aerodynamic torque, there is a risk of torsional vibration instability of the low-pressure rotor.

[0076] In addition, to avoid torsional resonance or torsional instability in the rotor system, special consideration must be given to the coupling between the control system and the rotor torsional vibration.

[0077] This invention can determine whether there is a risk of torsional vibration instability by obtaining a few simple parameters of the low-pressure rotor system of an aero-engine.

[0078] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

[0079] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. In addition, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0080] Other embodiments of the invention will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of the invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein. The specification and examples are to be considered exemplary only, and the true scope and spirit of the invention are indicated by the appended claims.

Claims

1. A method for analyzing the torsional vibration stability of a low-pressure rotor of an aero-engine, characterized in that, Includes the following steps: S1. Establish a torsional vibration model of the low-pressure rotor of an aero-engine. The torsional vibration model simplifies the low-pressure rotor into a rigid low-pressure turbine and a rigid fan rotor connected at both ends of a non-inertia elastic shaft. S2, Construct the torsional vibration matrix equation of the low-pressure rotor based on the torsional vibration model; S3. Substitute the amplitude and frequency of the excitation torque acting on the low-pressure turbine and fan rotor into the torsional vibration matrix equation of the low-pressure rotor to obtain the damped forced torsional vibration matrix equation. S4. Establish control functions with low-pressure turbine speed and fan rotor speed as feedback speed signals of the control system, respectively. Substitute the control functions into the damped forced torsional vibration matrix equation to obtain the corresponding control equations. S5. The Holwitz stability criterion is used to determine the sign of the real part of the characteristic root of the two control equations. If the real part of the characteristic root is negative, the torsional vibration of the low-pressure rotor is stable; if the real part of the characteristic root is positive, the torsional vibration of the low-pressure rotor is unstable.

2. The method for analyzing the torsional vibration stability of a low-pressure rotor of an aero-engine according to claim 1, characterized in that, In S2, the torsional vibration matrix equation of the low-pressure rotor is expressed as follows: in, The polar rotational inertia of the low-pressure turbine; This represents the polar rotational inertia of the fan rotor; The rotation angle of the low-pressure turbine. This refers to the angular acceleration of the low-pressure turbine. The rotation angle of the fan rotor. This refers to the angular acceleration of the fan rotor. For the torsional stiffness of the low-pressure rotor; This refers to the excitation torque acting on the low-pressure turbine; This is the excitation torque acting on the fan rotor.

3. The method for analyzing the torsional vibration stability of a low-pressure rotor of an aero-engine according to claim 2, characterized in that, In S3, the damped forced torsional vibration matrix equation is expressed as follows: in, This represents the aerodynamic damping coefficient of the low-pressure turbine. This represents the aerodynamic damping coefficient of the fan rotor; The amplitude of the excitation torque acting on the low-pressure turbine; The amplitude of the excitation torque acting on the fan rotor; j The imaginary unit; The excitation frequency; t For time; The rotational speed of the low-pressure turbine; This represents the rotational speed of the fan rotor.

4. The method for analyzing the torsional vibration stability of a low-pressure rotor of an aero-engine according to claim 3, characterized in that, In S4, the control function is expressed as follows: in, For pneumatic control torque; For gain; The governing equations are expressed as follows: Specifically, when the low-pressure turbine speed is used as the feedback speed signal for the control system, for When the fan rotor speed is used as the feedback speed signal for the control system, for .

5. The method for analyzing the torsional vibration stability of a low-pressure rotor of an aero-engine according to claim 4, characterized in that, In S5, when the low-pressure turbine speed is used as the feedback speed signal of the control system, the Holwitz stability criterion is used to determine that the real part of the characteristic root of the corresponding control equation is negative, and the torsional vibration of the low-pressure rotor is stable; when the fan rotor speed is used as the feedback speed signal of the control system, the Holwitz stability criterion is used to determine that the real part of the characteristic root of the corresponding control equation is positive, and the torsional vibration of the low-pressure rotor is unstable.

6. The method for analyzing the torsional vibration stability of a low-pressure rotor of an aero-engine according to claim 5, characterized in that, Modal transformation is performed on the matrix equation of the forced torsional vibration with damping to obtain the modal damping ratio of the low-pressure rotor. When the modal damping ratio of the low-pressure rotor is greater than or equal to 5%, the torsional resonance of the low-pressure rotor can be suppressed.

7. The method for analyzing the torsional vibration stability of a low-pressure rotor of an aero-engine according to claim 6, characterized in that, Modal transformation is performed on the matrix equation of the damped forced torsional vibration to obtain the damping coefficients of the low-pressure turbine and the fan rotor. When both satisfy the following equation, the peak torsional vibration of the low-pressure rotor can be suppressed: in, The modal damping ratio; This refers to the torsional stiffness of the low-pressure rotor.

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