Modeling method of mechanical analytical model for drum-stationary blade rub-impact of aero-engine

Abstract

The invention relates to a modeling method of a mechanical analysis model for drum-stationary blade rub-impact of an aero-engine. The modeling method comprises the following steps: step 1, calculating projection positions of rub-impact points when rub-impact faults occur to inner rings of a drum and a stationary blade; 2, calculating the intrusion amount of a rub-impact point when the rub-impact fault occurs; and 3, simulating the normal rub-impact force of the rub-impact point by adopting a linear rub-impact force model, and simulating the tangential rub-impact force of the rub-impact point by adopting the Coulomb friction law. According to the mechanical analysis model established by the method, flexible contact deformation caused by collision and friction of the drum and the stator is fully considered, the dynamic characteristic simulation accuracy of rotor-stator rub-impact of the aero-engine can be effectively improved, and theoretical support can be provided for dynamic design of an aero-engine power rotor system.

Description

Technical Field

[0001] The invention belongs to the technical field of mechanical analytical models and relates to a modeling method of a mechanical analytical model of an aircraft engine drum-stationary blade friction. Background Art

[0002] The drum is a typical rotating thin-walled part in the rotor system of an aircraft engine. It is light in weight and is very easy to vibrate and deform. Once a friction failure occurs, it will be extremely dangerous. In view of the friction dynamic characteristics between a rotating cylindrical shell such as a drum and a stator, Qin Chaoye's team at Tsinghua University used a semi-analytical method to establish a dynamic model of a rotating cylindrical shell and studied the dynamic characteristics when a friction failure occurred between the cylindrical shell and the stator. Cao Dengqing's team at Harbin Institute of Technology simplified the shaft into an elastic support for the inner hole of the wheel disc, established a dynamic model of the shaft-disk-drum through a semi-analytical method, and compared the dynamic characteristics of the wheel disc-casing friction and drum-casing friction. The above two existing analyses of the dynamic characteristics of drum-stator friction are based on semi-analytical dynamic models, which cannot simulate the point friction, local friction, and full-circle friction of a real aircraft engine drum. The problem of rotor-stator flexible deformation cannot be considered. Summary of the invention

[0003] In order to solve the above technical problems, the purpose of the present invention is to provide a modeling method of a mechanical analytical model of aircraft engine drum-stator friction, which can simulate the friction conditions of a real aircraft engine drum and effectively solve the problem that the current friction model cannot take into account the flexible deformation of the rotor and stator.

[0004] The present invention provides a modeling method for a mechanical analytical model of an aircraft engine drum-stationary blade friction, comprising:

[0005] Step 1: Calculate the projection position of the friction point when the drum and the inner ring of the stationary blade have a friction failure;

[0006] Step 2: Calculate the intrusion amount of the friction point when the friction fault occurs;

[0007] Step 3: Use Coulomb's friction law to simulate the tangential friction force at the friction point, and use the linear friction force model to simulate the normal friction force at the friction point.

[0008] The analytical model established by the modeling method of the mechanical analytical model of the aircraft engine drum-stationary blade friction of the present invention has the following main advantages compared with the current domestic friction force model:

[0009] (1) The mechanical analytical model of the present invention fully considers the flexible contact deformation caused by the drum and the stator during the collision and friction process, which can effectively improve the simulation accuracy of the dynamic characteristics of the aircraft engine rotor-stator friction, and can provide theoretical support for the dynamic design of the aircraft engine rotor system.

[0010] (2) The mechanical analytical model of the present invention simulates the point friction, local friction and full-circle friction between the drum and the stator, and can provide a mechanical model with a modified reliable spectrum for the existing aircraft engine rotor-stator friction simulation model, making the simulation closer to the actual working conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 It is a flow chart of a modeling method of a mechanical analytical model of an aircraft engine drum-stationary blade friction according to the present invention;

[0012] Figure 2 It is a schematic diagram of the static state of the friction model;

[0013] Figure 3 It is a schematic diagram of the rotational collision of the friction model. DETAILED DESCRIPTION

[0014] like Figure 1 As shown, a modeling method of a mechanical analytical model of an aircraft engine drum-stationary blade friction of the present invention comprises:

[0015] Step 1: Calculate the projection position of the friction point when the drum and the inner ring of the stationary blade have a friction failure. The step 1 is specifically as follows:

[0016] like Figure 2 and 3 As shown in the figure, the parts that collide are the drum and the inner ring of the casing. When the system is in a static state, the center O of the inner ring i The center of the drum is located at O, which coincides with the origin of the coordinate system. However, the rotor system always has factors such as imbalance and installation error. The eccentricity of its axis is e, and the drum and the inner ring are prone to friction failure during rotation. At this time, the rotor axis will deviate from its original position, and the inner ring will also deviate from its original position due to the impact force of the rotor and the unbalanced force transmitted to the casing by the rotor.

[0017] Step 1.1: Assume that a point A on the drum rubs against the inner ring of the stationary blade, and the two adjacent nodes on both sides of point A on the inner ring are B and C respectively. The coordinate positions of points A, B, and C after the rotational rubbing are expressed as:

[0018]

[0019] Among them, X A is the horizontal coordinate of the friction point A, Y A is the ordinate of the friction point A; B is the horizontal coordinate of point B on the inner ring, Y B is the ordinate of point B on the inner ring; X C is the horizontal coordinate of point C on the inner ring, Y Cis the ordinate of point C on the inner ring; e is the installation misalignment error of the drum; u A 、v A are the vibration displacements of point A in the X and Y directions respectively; u B 、v B are the vibration displacements of point B in the X and Y directions respectively; u C 、v C are the vibration displacements of point C in the X and Y directions respectively; R dr With R in Represent the radius of the drum and the inner ring respectively; α is the sum of the rotation angle and the phase angle of the friction point A on the drum, that is, α = ωt + α0; β B , β C They are the phase angles corresponding to points B and C on the inner ring respectively.

[0020] Step 1.2: Project the friction point A onto BC to get the projection point Coordinates:

[0021]

[0022] in, The projection point The horizontal axis of The projection point The vertical coordinate of .

[0023] Step 2: Calculate the intrusion amount of the friction point when the friction fault occurs. Step 2 is specifically as follows:

[0024] Step 2.1: Whether the friction fault occurs needs to be judged using the gap function, such as Figure 3 As shown. Establish the gap function of the intrusion amount of the rubbing point:

[0025]

[0026] Among them, C r is the vector product of the inner ring and the drum friction point, when c r When <0, it means that there is friction failure between the drum and the inner ring. r When ≥0, it indicates that there is no friction fault between the drum and the inner ring.

[0027] Step 2.2: Calculate the vector product C of the inner ring and the drum friction point according to the following formula r :

[0028]

[0029] Among them, r BC,n is the normal vector of points B and C on the inner ring where friction occurs; it is calculated through the coordinates of points B and C:

[0030]

[0031] Step 3: Coulomb's friction law is used to simulate the tangential friction force of the friction point, and a linear friction force model is used to simulate the normal friction force of the friction point. Step 3 is specifically as follows:

[0032] Step 3.1: Calculate the velocity of point A by taking the first-order partial derivative of the position of point A with respect to time.

[0033]

[0034] Step 3.2: By Calculate the first-order partial derivative of the point position with respect to time and calculate Point speed

[0035]

[0036] Step 3.3: Calculate the value of point A and The projection of the velocity of a point on the BC tangent direction:

[0037]

[0038]

[0039] in, is the projection of the velocity of point A on the tangent direction of BC, for The projection of the velocity of a point on the tangent direction of BC.

[0040] r BCt is the tangent vector of the friction point A on the inner ring, calculated according to the following formula:

[0041]

[0042] Step 3.4: When the drum rubs against the inner ring, the rotor may produce two types of vortex motion, positive precession and reverse precession, which may cause the absolute velocity direction of node A on the drum to be different in the Cartesian coordinate system, thus causing the difference between point A and Therefore, in order to consider the tangential friction force of the drum under different motion states, by judging the relative speed of point A and The relationship between the projections of the velocity of the point on the BC tangent direction is used to calculate the direction function of the tangential friction force sgn(H):

[0043]

[0044] Among them, r BC is the direction vector along the BC direction.

[0045] Step 3.5: Normal friction force F on the drum n and tangential friction force F t The size is expressed as:

[0046]

[0047] Among them, k r is the friction stiffness, which can be calculated by applying a constant force on the flexible casing and dividing it by the corresponding deformation; μ is the friction coefficient.

[0048] Step 3.6: In the Cartesian coordinate system, decompose the tangential friction force and the normal friction force into the X and Y directions, and the friction force on point A is expressed as:

[0049]

[0050] in, is the component of the friction force on point A in the X direction, A

[0051] The component of the friction force on the point in the Y direction is, is the projection of the normal vector of points B and C on the inner ring where friction occurs in the X direction, It is the projection of the normal vector of points B and C on the inner ring where friction occurs in the Y direction.

[0052] Step 3.7: When point A on the drum is subjected to friction, the inner ring is subjected to an equal and opposite friction. When point A is between points B and C, interpolation is required. Then the friction force on points B and C on the inner ring is expressed as:

[0053]

[0054] in, is the component of the friction force on point B in the X direction, is the component of the friction force on point B in the Y direction, is the component of the friction force on point C in the X direction, is the component of the friction force on point C in the Y direction.

[0055] The above description is only a preferred embodiment of the present invention and is not intended to limit the concept of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for modeling a mechanical analytical model of aeroengine drum-stator friction, characterized in that: include: Step 1: Calculate the projection position of the friction point when the drum and the inner ring of the stator blade have a friction failure; Step 2: Calculate the intrusion amount of the friction point when the friction failure occurs; Step 3: Use Coulomb's friction law to simulate the tangential friction force at the friction point, and use the linear friction force model to simulate the normal friction force at the friction point.

2. The modeling method of the mechanical analytical model of the aircraft engine drum-stationary blade friction according to claim 1 is characterized in that: The step 1 is specifically as follows: Step 1.1: Assume that a point A on the drum rubs against the inner ring of the stationary blade, and the two nodes on the inner ring adjacent to point A on both sides are B and C respectively. The coordinate positions of points A, B, and C after the rotational rubbing are expressed as: Among them, X A is the horizontal coordinate of the friction point A, Y A is the ordinate of the friction point A; B is the horizontal coordinate of point B on the inner ring, Y B is the ordinate of point B on the inner ring; X C is the horizontal coordinate of point C on the inner ring, Y C is the ordinate of point C on the inner ring; e is the installation misalignment error of the drum; u A 、v A are the vibration displacements of point A in the X and Y directions respectively; u B 、v B are the vibration displacements of point B in the X and Y directions respectively; u C 、v C are the vibration displacements of point C in the X and Y directions respectively; R dr With R in Represent the radius of the drum and the inner ring respectively; α is the sum of the rotation angle and the phase angle of the friction point A on the drum, that is, α = ωt + α0; β B , β C They are the phase angles corresponding to points B and C on the inner ring respectively; Step 1.2: Project the friction point A onto BC to obtain the coordinates of the projected point A: in, The projection point The horizontal axis of is the ordinate of the projection point A.

3. The modeling method of the mechanical analytical model of the aircraft engine drum-stationary blade friction according to claim 1 is characterized in that: The step 2 is specifically as follows: Step 2.1: Establish the gap function of the intrusion amount of the rubbing point: Among them, C r is the vector product of the inner ring and the drum friction point, when c r When <0, it means that there is friction failure between the drum and the inner ring. r When ≥0, it means there is no friction fault between the drum and the inner ring; Step 2.2: Calculate the vector product C of the inner ring and the drum friction point according to the following formula r : Among them, r BC,n is the normal vector of points B and C on the inner ring where friction occurs; it is calculated through the coordinates of points B and C:

4. The modeling method of the mechanical analytical model of the aircraft engine drum-stationary blade friction according to claim 3 is characterized in that: The step 3 is specifically as follows: Step 3.1: Calculate the velocity of point A by taking the first-order partial derivative of the position of point A with respect to time. Step 3.2: By Calculate the first-order partial derivative of the point position with respect to time and calculate Point speed Step 3.3: Calculate the value of point A and The projection of the velocity of a point on the BC tangent direction: is the projection of the velocity of point A on the tangent direction of BC, for The projection of the velocity of the point on the tangent direction of BC; r BC,t is the tangent vector of the friction point A on the inner ring, calculated according to the following formula: Step 3.4: In order to consider the tangential friction force of the drum under different motion states, by judging the The relationship between the projections of the velocity of the point on the BC tangent direction is used to calculate the direction function of the tangential friction force sgn(H): Among them, r BC is the direction vector along the BC direction; Step 3.5: Normal friction force F on the drum n and tangential friction force F t The size is expressed as: Among them, k r is the friction stiffness, which can be calculated by applying a constant force on the flexible casing and dividing it by the corresponding deformation; μ is the friction coefficient; Step 3.6: In the Cartesian coordinate system, decompose the tangential friction force and the normal friction force into the X and Y directions, and the friction force on point A is expressed as: in, is the component of the friction force on point A in the X direction, is the component of the friction force on point A in the Y direction, is the projection of the normal vector of points B and C on the inner ring where friction occurs in the X direction, is the projection of the normal vector of points B and C on the inner ring where friction occurs in the Y direction; Step 3.7: When point A on the drum is subjected to friction, the inner ring is subjected to an equal and opposite friction. When point A is between points B and C, interpolation is required. Then the friction force on points B and C on the inner ring is expressed as: in, is the component of the friction force on point B in the X direction, is the component of the friction force on point B in the Y direction, is the component of the friction force on point C in the X direction, is the component of the friction force on point C in the Y direction.

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