Blade arrival time accurate simulation method based on blade tip timing principle

Abstract

The application provides a blade arrival time accurate simulation method based on a blade tip timing principle, comprising the following steps: (1) establishing a blade tip timing sensor model based on sensor circumferential and axial layout information; (2) carrying out static force and modal analysis based on a finite element analysis method, and establishing a rotating blade model; (3) continuously processing blade tip finite element discrete nodes of the rotating blade model; (4) establishing a blade arrival time model based on the sensor and the rotating blade model, judging the position relationship between the sensor and the blade from the axial and circumferential directions, and iteratively solving the blade arrival time. The application considers the influence of the axial position change on the simulation model in the blade movement process by simulating the working process of the blade tip timing test system, the result is not dependent on the finite element grid density, and a more accurate blade arrival time can be obtained.

Description

Technical Field

[0001] This invention belongs to the field of vibration testing technology for rotating blades of aerospace engines, and specifically relates to a method for accurately simulating the arrival time of blades based on the blade tip timing principle. Background Technology

[0002] High-cycle fatigue failure of rotor blades due to vibration is a bottleneck problem restricting the development and service of aero-engines in my country. Advanced aero-engines, due to increased aerodynamic loads, reduced structural mechanical damping, and the use of lightweight structures, exhibit even more pronounced vibration issues. To ensure the safety and reliability of the engine, vibration testing of the blades is necessary. Under extreme service environments of high temperature, high pressure, and high speed, traditional strain gauge methods suffer from low strain gauge survival rates and complex lead-wire / slip ring transmission, limiting the measurement of strain at only a limited number of locations on a limited number of blades. Tip-timed testing technology, due to its non-contact nature and ability to monitor the vibration of the entire stage of the blade throughout its entire lifecycle, has become the most promising vibration testing method. However, tip-timed sampling signals are time pulse signals and cannot be directly used for vibration analysis. To understand the vibration characteristics of the blades, corresponding vibration parameter identification algorithms need to be developed.

[0003] When initially evaluating vibration parameter identification algorithms, numerical simulation models are typically used to obtain blade tip timing data, mainly including virtual signal models, lumped parameter models, and finite element models. Virtual signal and lumped parameter models cannot reflect the geometric features and true dynamic characteristics of the blade / disk structure, often resulting in high accuracy in simulation models but significant errors in practical applications. Finite element models, as a more complete numerical method, can reflect the detailed features and complex vibration modes of the blade / disk structure. However, existing methods, on the one hand, determine the blade arrival time only through the circumferential positional relationship between the blade and the blade tip timing sensor, without considering the axial positional changes of the blade and sensor due to deformation, which is inconsistent with the actual blade tip timing test process; on the other hand, the simulation results heavily depend on the finite element mesh density. If the mesh is sparse, only one node can be captured during blade movement, introducing errors into the simulation of blade arrival time. Summary of the Invention

[0004] To overcome the shortcomings of existing technologies, this invention provides a precise simulation method for blade arrival time based on the blade tip timing principle. This method is a blade arrival time simulation method that does not depend on the finite element mesh density and considers the axial position changes during blade movement. It constructs a blade tip timing simulation model that can simulate the working process of the blade tip timing test system and reflect the changes of sensor measuring points during blade movement, thus serving and supporting the blade tip timing vibration test technology for aero-engines.

[0005] To achieve the above objectives, the technical solution adopted by the present invention to solve the above technical problems is as follows:

[0006] A precise simulation method for blade arrival time based on the blade tip timing principle is proposed. This method utilizes the finite element method to simulate the operation of a blade tip timing test system, constructing a blade tip timing sensor model, a rotating blade model, and a blade arrival time model. Polynomial curve fitting is performed on the discrete nodes of the blade tip finite element model to achieve mesh density independence processing of the simulation model and continuous processing of the rotating blade model. The relative positional relationship between the blade and the sensor is determined from both axial and circumferential dimensions to achieve an accurate solution for the blade arrival time. The specific steps include:

[0007] Step (1): Based on the axial and circumferential layout information of the sensor, establish the blade tip timing sensor model;

[0008] Step (2): Based on the finite element method, static and modal analyses are performed to establish a rotating blade model, utilizing the initial position u of the blade. ori Static deformation u sta Vibration displacement u vib The rotational variation represents the circumferential and axial coordinates of the rotating blade at different times;

[0009] Step (3): Perform polynomial curve fitting on the circumferential and axial coordinates of the blade tip finite element nodes at different times obtained in step (2) to realize the continuous processing of the rotating blade model.

[0010] Step (4): Based on the blade tip timing sensor model and the continuously processed rotating blade model in steps (1), (2) and (3), determine the relative positional relationship between the sensor and the blade tip curve in the axial and circumferential directions at different times, and establish the blade arrival time model accordingly. The time that meets the sensor measurement accuracy requirements is the blade arrival time.

[0011] Further, in step (1), the circumferential and axial coordinates of the nth sensor are respectively expressed as... Where ρ is the casing radius, θ n For the circumferential angle of the sensor, For circumferential installation error, S n Let ΔP be the axial coordinate of the sensor. nz This refers to axial installation error.

[0012] Further, in step (2), the nodal coordinates, static deformation, modal displacement, modal displacement scaling factor, and rotational speed of the blade finite element mesh are used as inputs. Considering the coordinate changes caused by rotation, static deformation, and vibration, a rotating blade model is established. The circumferential and axial coordinates of the blade at time t are respectively expressed as... and U(z,t)=u ori (z)+u sta (z)+u vib (z,t), where uori As the initial position, u sta For static deformation, u vib The value represents the vibration displacement, ρ is the casing radius, Ω is the rotor angular frequency, and mod is the remainder sign. Let u be the circumferential vibration displacement of the blade at time t. vib (z,t) represents the axial vibration displacement of the blade at time t.

[0013] Further, in step (3), the finite element discrete nodes of the blade tip section in the rotating blade model are equivalent to curves, and polynomial curve fitting is performed on the axial and circumferential coordinates of the nodes, expressed as: in, and U z These are the circumferential and axial coordinates of the blade tip node, a0~a n represents the polynomial fitting parameters, and n represents the polynomial order.

[0014] Further, in step (4), using the blade tip timing sensor model and the rotating blade model, the upper and lower bounds [t1, t2] of the blade arrival time measured by the nth sensor and its intermediate time t3 are determined; the relative positional relationship between the sensor and the blade tip fitting curve at time t3 is calculated, and the upper and lower bounds [t1, t2] of the blade arrival time are corrected accordingly; the parameters of the sensor and the rotating blade model are iteratively updated until the positional difference between the two meets the measurement accuracy requirements of the sensor in the circumferential and axial directions, i.e. P nz -U z (t)|<Tol(z), where, and P nz Let be the circumferential and axial coordinates of the nth sensor. and U z (t) represents the circumferential and axial coordinates of the leaf tip fitting curve at time t, respectively. Tol(z) represents the circumferential and axial measurement accuracy of the sensor.

[0015] The advantages of this invention compared to existing technologies are:

[0016] (1) This invention can make full use of the finite element analysis method of blade / disk structure to improve the accuracy of the simulation model of rotating blade;

[0017] (2) The rotating blade model established in this invention processes the discrete nodes of the finite element at the blade tip into a continuous form, so that the simulation results do not depend on the mesh density, and can accurately capture the intersection of the sensor and the blade tip section, thereby improving the accuracy of the blade arrival time calculation.

[0018] (3) The blade arrival time model established by this invention takes into account the axial and circumferential positional relationship between the sensor and the blade tip section. The blade arrival time is determined by the measurement accuracy in both directions, which is more in line with the real situation. Attached Figure Description

[0019] Figure 1 The overall flowchart for the timing simulation model of the leaf tip;

[0020] Figure 2 This is a flowchart of the blade arrival time model. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be 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 illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0022] The technical solution of the blade arrival time accurate simulation method based on the blade tip timing principle of the present invention will be further described below with reference to the accompanying drawings. All angles involved are in radians.

[0023] like Figure 1 As shown, the precise simulation method for blade arrival time based on the blade tip timing principle of the present invention specifically includes the following steps:

[0024] Step 1: Establish the blade tip timing sensor model. Assuming the blade tip timing test system contains N sensors, using the sensor's axial coordinate S, circumferential angle θ, casing radius ρ, and installation error as inputs, establish the circumferential and axial coordinate representation of the blade tip timing sensor model, i.e.:

[0025]

[0026] P n (z)=S n +ΔP nz , n=1,2,…,N (2)

[0027] In the formula, Let P be the circumferential coordinate of the nth sensor. n (z) represents the axial coordinate of the nth sensor, ΔP nz Let n be the axial installation error of the nth sensor. Let be the circumferential installation error of the nth sensor.

[0028] Step 2: Establish the rotating blade model. The blade coordinates start from the initial position u. ori Static deformation u staVibration displacement u vib The determination is made from four parts: rotational change, etc. The specific steps are as follows:

[0029] ① Conduct finite element static and modal analyses. Using the finite element mesh model of the blade, boundary conditions, material parameters, and rotational speed as inputs, and considering geometric nonlinearity, rotational softening, and stress stiffening effects under centrifugal and aerodynamic loads, perform static analysis to obtain the static deformation u of the blade. sta Based on this, modal analysis with prestress was performed to obtain the natural vibration frequency and modal displacement of the blade.

[0030] ② Regarding the resonance state, which is of great concern in engineering, a modal displacement scaling factor is introduced to convert the modal displacement into vibration displacement u corresponding to different amplitudes. vib The expression is:

[0031]

[0032] In the formula, Let t represent the circumferential and axial vibration displacements of the blade at time t, and μ be the modal displacement scaling factor. Let f represent the circumferential and axial modal displacements, and f be the natural vibration frequency of the blade.

[0033] ③ Establish rotating blade models at different times. The axial coordinates of the blade can be represented as:

[0034] U(z,t)=u ori (z)+u sta (z)+u vib (z,t) (4)

[0035] In the formula, U(z,t) is the axial coordinate of the blade at time t, u ori (z) and u sta (z) represents the axial coordinates and axial static deformation of the blade finite element node, respectively. vib (z,t) represents the axial vibration displacement of the blade at time t, which is determined by step ②.

[0036] The circumferential coordinates of the blade can be represented as:

[0037]

[0038] In the formula, Let be the circumferential coordinate of the blade at time t. and These represent the circumferential coordinates and circumferential static deformation of the blade's finite element nodes, respectively. Let t be the circumferential vibration displacement of the blade at time t, determined by step ②, where ρ is the casing radius, Ω is the rotor rotation angular frequency, and mod is the remainder sign.

[0039] Step 3: Perform continuous processing on the discrete nodes at the blade tip. A polynomial is used to fit the finite element nodes at the blade tip in the clockwise direction of rotation. The clockwise direction of rotation for the compressor is the blade head side, and for the turbine, it is the blade back side. The fitted curve can be expressed as:

[0040]

[0041] In the formula, and U z These are the circumferential and axial coordinates of the blade tip node, a0~a n represents the polynomial fitting parameters, and n represents the polynomial order.

[0042] Step 4: Establish the blade arrival time model. Using the tip-timed sensor model and the continuously processed rotating blade model, determine the relative positional relationship between the sensor and the tip fitting curve at different times until the time that meets the measurement accuracy requirements is found; this time is the blade arrival time. The calculation process is as follows: Figure 2 As shown. The specific steps are as follows:

[0043] ① Determine the upper and lower bounds [t1, t2] of the arrival time of the blade corresponding to the nth sensor and its intermediate time t3, expressed as:

[0044]

[0045]

[0046]

[0047] In the formula, Δθ is the circumferential angle of the sensor relative to the blade being measured, Ω is the angular frequency of the rotor rotation, and ρ is the radius of the casing. and These represent the maximum static deformation and maximum vibration displacement at the blade tip node, respectively.

[0048] ② Determine the relative positional relationship between the sensor and the fitted curve at the blade tip. Calculate the polynomial of the blade tip curve at time t3 based on the calculation in step 3. Based on this, the circumferential coordinates of the points on the tip fitting curve that are the same as the axial coordinates of the nth sensor are calculated. The expression is:

[0049]

[0050] In the formula, a0~a n P represents the polynomial fitting parameters of the leaf tip curve at time t3. nz Let be the axial coordinate of the nth sensor.

[0051] Then, determine the leaf tip node. With the nth sensor The positional relationship between them. If This indicates that the blades are ahead of the sensor, and vice versa.

[0052] ③ Iteratively solve for the blade arrival time. Based on the positional relationship in step ②, correct the upper and lower bounds of the blade arrival time. If the blade is ahead of the sensor, assign t3 to the upper bound t2 of the arrival time in the next cycle, i.e., t3 = t2. Otherwise, let t3 = t1. At this point, we can obtain the new upper and lower bounds of the blade arrival time [t1, t2] and its intermediate time t3.

[0053] The tip timing sensor and the rotating blade model are iteratively updated until their positions meet the sensor's measurement accuracy requirements. The time t at this point is the arrival time of the blade, expressed as:

[0054]

[0055] |P nz -U z (t)|<Tol(z) (12)

[0056] In the formula, and P nz Let be the circumferential and axial coordinates of the nth sensor. and U z (t) represents the circumferential and axial coordinates of the leaf tip fitting curve at time t, respectively. Tol(z) represents the circumferential and axial measurement accuracy of the sensor.

[0057] The above embodiments are provided for the purpose of describing the present invention only, and are not intended to limit the scope of the invention. The scope of the invention is defined by the appended claims. Various equivalent substitutions and modifications made without departing from the spirit and principles of the invention should be covered within the scope of the invention.

Claims

1. A method for accurately simulating the arrival time of a blade based on the tip timing principle, characterized in that, The working process of a blade tip timing test system is simulated using the finite element method. A blade tip timing sensor model, a rotating blade model, and a blade arrival time model are constructed. Polynomial curve fitting is performed on the discrete nodes of the blade tip finite element model to achieve mesh density independence in the simulation model. The relative positional relationship between the blade and the sensor is determined from both axial and circumferential dimensions to achieve an accurate solution for the blade arrival time. The specific steps include: Step (1): Based on the axial and circumferential layout information of the sensor, establish the blade tip timing sensor model; Step (2): Based on the finite element method, static and modal analyses are performed to establish a rotating blade model, utilizing the initial position u of the blade. ori Static deformation u sta Vibration displacement u vib The rotational variation represents the circumferential and axial coordinates of the rotating blade at different times; Step (3): Perform polynomial curve fitting on the circumferential and axial coordinates of the blade tip finite element nodes at different times obtained in step (2) to realize the continuous processing of the rotating blade model. Step (4): Based on the blade tip timing sensor model and the continuously processed rotating blade model in steps (1), (2) and (3), determine the relative positional relationship between the sensor and the blade tip curve in the axial and circumferential directions at different times, and establish the blade arrival time model accordingly. The time that meets the sensor measurement accuracy requirements is the blade arrival time.

2. The method for accurately simulating blade arrival time based on the blade tip timing principle according to claim 1, characterized in that, In step (1), the circumferential coordinates of the nth sensor are represented as follows: The axial coordinate is represented as P n (z)=S n +ΔP nz Where ρ is the casing radius, θ n For the circumferential angle of the sensor, For circumferential installation error, S n Let ΔP be the axial coordinate of the sensor. nz This refers to axial installation error.

3. The method for accurately simulating blade arrival time based on the blade tip timing principle according to claim 2, characterized in that, In step (2), the nodal coordinates, static deformation, modal displacement, modal displacement scaling factor, and rotational speed of the blade finite element mesh are used as inputs. Considering the coordinate changes caused by rotation, static deformation, and vibration, a rotating blade model is established. The circumferential coordinates of the blade at time t are expressed as follows: The axial coordinate is represented as U(z,t)=u ori (z)+u sta (z)+u vib (z,t), where u ori As the initial position, u sta For static deformation, u vib The value represents the vibration displacement, ρ is the casing radius, Ω is the rotor angular frequency, and mod is the remainder sign. Let u be the circumferential vibration displacement of the blade at time t. vib (z,t) represents the axial vibration displacement of the blade at time t.

4. The method for accurately simulating blade arrival time based on the tip timing principle according to claim 3, characterized in that, In step (3), the finite element discrete nodes of the blade tip section in the rotating blade model are represented as curves, and polynomial curve fitting is performed on the axial and circumferential coordinates of the nodes, expressed as: in, and U z These are the circumferential and axial coordinates of the blade tip node, a0~a n represents the polynomial fitting parameters, and n represents the polynomial order.

5. The method for accurately simulating blade arrival time based on the tip timing principle according to claim 4, characterized in that, In step (4), the upper and lower bounds [t1, t2] of the blade arrival time measured by the nth sensor and the intermediate time t3 are determined using the blade tip timing sensor model and the rotating blade model; the relative positional relationship between the sensor and the blade tip fitting curve at time t3 is calculated, and the upper and lower bounds [t1, t2] of the blade arrival time are corrected accordingly; the parameters of the sensor and the rotating blade model are iteratively updated until the positional difference between the two meets the measurement accuracy requirements of the sensor in the circumferential and axial directions, i.e. |P nz -U z (t)|<Tol(z), where, and P nz Let be the circumferential and axial coordinates of the nth sensor. and U z (t) represents the circumferential and axial coordinates of the leaf tip fitting curve at time t, respectively. Tol(z) represents the circumferential and axial measurement accuracy of the sensor.

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