Complete machine model transient response calculation method with gap support

Abstract

The invention discloses a transient response calculation method for a complete machine model with a gap support. The method comprises the following steps that SS1, whole machine nonlinear modeling of a rotor-bearing-casing system is carried out, linear component modeling of a whole machine structure and nonlinear modeling of a gap bearing are included, linear component modeling of the whole machine structure comprises rotor modeling, casing modeling, linear bearing modeling and installation section modeling, and linear component modeling of the whole machine structure comprises linear component modeling of the rotor-bearing-casing system and linear component modeling of the gap bearing; the non-linear modeling of the gap support comprises non-linear modeling considering friction influence and contact influence, and a whole machine non-linear rotor dynamic model is constructed; step SS2, response calculation of a Newmark method based on variable step size control is carried out; and step SS3, extracting transient responses of each node of the rotor, the support and the casing. According to the method provided by the invention, the fit clearance between the rotor journal and the bearing inner ring and the influence of the casing are considered at the same time, the transient response of the rotor-bearing-casing system is calculated, the vibration characteristics of the whole machine with the clearance bearing are analyzed, and support is provided for the structural design of an engine.

Description

Technical Field

[0001] The invention relates to a transient response calculation method for a whole machine model with clearance support, and belongs to the field of engine dynamics simulation. Background Art

[0002] Turbine engines are an important power equipment in the field of aerospace. Structurally, they are usually assembled from a rotor, a support, and a casing system. The rotor generally adopts a two-point or three-point support scheme, and is supported on the load-bearing casing through two or three bearings and other structures. In order to improve assembly efficiency, in structural design, a clearance fit can be used between the inner ring of the bearing and the rotor journal. The clearance fit makes the bearing installation more convenient, but during the operation of the rotor, there are collisions and frictions between the rotor journal and the inner ring of the bearing, which introduces nonlinear factors to the whole system, making the rotor dynamics simulation of the whole model very difficult. Therefore, it is necessary to establish an effective transient response calculation method to perform rotor dynamics simulation of the whole model of the rotor-support-casing system with clearance support.

[0003] In the current research work, considering the influence of the clearance between the inner ring of the bearing, a transient response calculation method of the rotor-support system has been established, which can calculate the transient response of the rotor-support system. However, the influence of the casing is ignored, and the transient response of the rotor-support-casing system cannot be fully calculated and analyzed. In the established transient response calculation method of the rotor-support-casing system, the influence of the clearance between the rotor journal and the inner ring of the bearing is not considered. Therefore, it is very necessary to consider the clearance between the rotor journal and the inner ring of the bearing and the influence of the casing at the same time, and to establish a transient response calculation method for the rotor-support-casing system, which can better reflect the vibration characteristics of the whole machine and provide support for the overall structural design of the engine. Summary of the invention

[0004] The purpose of the present invention is to overcome the technical defects of the prior art, solve the above-mentioned technical problems, and propose a transient response calculation method for a whole machine model with gap support.

[0005] The present invention specifically adopts the following technical scheme: The present invention proposes a method for calculating the transient response of a whole machine model with a gap support. By establishing a finite element model of linear components (including rotors, linear supports, casings, mounting sections, etc.) in the whole machine structure based on the finite element method, and combining the linear component model and the gap support nonlinear model, a rotor-support-casing system whole machine model with gap support nonlinearity is constructed. Then, the Newmark method based on variable step-size control is used to calculate the nonlinear rotor dynamics transient response of the whole machine model. Finally, the transient responses of key nodes such as the rotor, support, casing, etc. are extracted from the calculation results. The specific modeling and calculation methods of each part are described in detail below.

[0006] (1) Finite element modeling of linear components in the rotor-support-casing system

[0007] In the finite element model of the rotor-support-casing system, the wheel disc can be treated as a concentrated mass, which effectively reduces the degree of freedom of the model and improves the calculation efficiency of the model. The disc unit mainly considers the inertia and gyroscopic effects, and its unit mass matrix and gyroscopic matrix are respectively

[0008]

[0009] Among them, m d is the mass of the disk, I d is the diameter moment of inertia, I p Polar moment of inertia.

[0010] The shaft element adopts Timoshenko beam element, considering inertia, shear and gyroscopic effects. It has two nodes and only considers transverse bending vibration. It needs to use 8 coordinates to describe

[0011] [u1,v1,θ1,ψ1,u2,v2,θ2,ψ2](3)

[0012] Among them, u1, v1, θ1, ψ1 are the horizontal translation displacement, vertical translation displacement, rotation around the horizontal axis and rotation around the vertical axis of the first node respectively; u2, v2, θ2, ψ2 are the horizontal translation displacement, vertical translation displacement, rotation around the horizontal axis and rotation around the vertical axis of the second node respectively.

[0013] The mass matrix, stiffness matrix and gyro matrix of the general circular cross-section shaft element are

[0014]

[0015] in,

[0016] The casing is also modeled using beam elements, but the gyroscopic effect does not need to be considered.

[0017] For linear support components, the forces acting on the support in the x and y directions can be expressed as

[0018]

[0019] (2) Nonlinear modeling of gap support

[0020] Considering the contact and friction effects of the gap support, the actual nonlinear force F nl is the radial pressure F n and tangential friction f t The superposition of:

[0021] F nl=F n cosθ+f t sinθ (8)

[0022] Among them, the radial pressure F n for

[0023]

[0024] Tangential friction force f t for

[0025]

[0026] Among them, k bn The nonlinear parameters are contact stiffness, c bn contact damping and μ is the friction coefficient.

[0027] (3) Newmak method based on variable step size control

[0028] The vibration differential equation of the nonlinear system at time t+Δt is:

[0029]

[0030] Among them, the nonlinear force f nl (t+Δt) has a complex nonlinear representation, but through appropriate equation relationships, it can always be expressed as the displacement u(t+Δt) and velocity u(t+Δt) at the current moment t+Δt. With acceleration The function of these three. Combined with the classic Newmark formula, the speed is expressed by u(t+Δt) With acceleration Nonlinear force f nl (t+Δt) can be expressed as a function f of the displacement u(t+Δt) nl (t+Δt)=f nl (u(t+Δt)). Based on this, the algebraic equation of the nonlinear system is constructed:

[0031]

[0032] Note that both sides of the equation contain the unknown u(t+Δt), and the function f nl The form of (u(t+Δt)) is complex, so a nonlinear equation solver needs to be introduced for iterative solution. For example, the equation can be directly solved iteratively by the Newton-Raphson method.

[0033] If the displacement u(t0) and velocity at the initial time t0 are known With acceleration value By repeating the calculation according to the above steps, the displacement, velocity and acceleration values ​​at any time that satisfy the vibration differential equation of the nonlinear system can be integrated.

[0034] The Newmark method is used for adaptive step-size control. For nonlinear systems, adaptive step-size control based on the number of iterative solutions is used to accelerate convergence and improve computational efficiency.

[0035] When the Newmark family algorithm for nonlinear systems is used for calculation, there must be an iterative step of calculation using the Newton-Raphson method. Therefore, adaptive step size control can be performed according to the number of iterations. The steps are as follows:

[0036] 1) If there is no solution, proceed as follows: The solution step length of the current point is too long, so reduce the solution step length of the current step.

[0037]

[0038] 2) If there is a solution, but the number of iterations is too small, then: the step size can be increased appropriately, but at the same time, the step size must be controlled not to exceed the set maximum step size, so as not to make the step size too large and affect the calculation accuracy of the next point.

[0039]

[0040] 3) If there is a solution and the number of iterations is appropriate, proceed to: keep the step size unchanged for the next point.

[0041] Beneficial effects achieved by the present invention: The present invention proposes a method for calculating the transient response of a whole machine model with a clearance support. Based on the finite element method, a finite element model of linear components (including rotors, linear supports, casings, mounting sections, etc.) in the whole machine structure is established. The linear component model and the clearance support nonlinear model are combined to construct a whole machine model of a rotor-support-casing system with clearance support nonlinearity. Then, the Newmark method based on variable step-size control is used to calculate the nonlinear rotor dynamics transient response of the whole machine model. Finally, the transient responses of key nodes such as the rotor, support, and casing are extracted from the calculation results. The method proposed by the present invention simultaneously considers the clearance between the rotor journal and the inner ring of the bearing and the influence of the casing, calculates the transient response of the rotor-support-casing system, analyzes the vibration characteristics of the whole machine with clearance support, and provides support for engine structure design. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 are the axis units of the two planes in the local coordinate system.

[0043] Figure 2 It is a one-dimensional beam unit model of an axis of an engine complete system embodiment of the present invention.

[0044] Figure 3It is a one-dimensional beam unit model of a first-stage fan disk and a second-stage turbine disk of an engine complete system embodiment of the present invention.

[0045] Figure 4 It is a schematic diagram of the support position of an engine complete system embodiment of the present invention.

[0046] Figure 5 It is a schematic diagram of a one-dimensional beam unit model of a casing of an engine complete system embodiment of the present invention.

[0047] Figure 6 It is a schematic diagram of a one-dimensional beam unit model of an engine system embodiment of the present invention.

[0048] Figure 7 It is a transient response diagram of an engine complete system embodiment of the present invention at different speeds in experimental tests and simulation tests.

[0049] Figure 8 It is a spectrum characteristic diagram of an engine complete system embodiment of the present invention under test and simulation test at resonant speed.

[0050] Fig. 9 It is a three-dimensional spectrum characteristic diagram of an engine complete system embodiment of the present invention under different speeds of test and simulation tests.

[0051] Fig.10 It is a flow chart of a method for calculating transient response of a whole machine model with gap support according to the present invention. DETAILED DESCRIPTION

[0052] The present invention will be further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and cannot be used to limit the protection scope of the present invention.

[0053] The process of the transient response calculation method of the whole machine model with gap support proposed by the present invention is as follows: Fig.10 As shown. Based on the finite element method, a finite element model of the linear components (including rotors, linear supports, casings, mounting nodes, etc.) in the whole machine structure is established. Combining the linear component model and the gap support nonlinear model, a rotor-support-casing system whole machine model with gap support nonlinearity is constructed. Then, the Newmark method based on variable step-size control is used to calculate the nonlinear rotor dynamics transient response of the whole machine model. Finally, the transient responses of key nodes such as the rotor, support, casing, etc. are extracted from the calculation results. The specific modeling and calculation methods of each part are detailed below.

[0054] like Fig.10 As shown, the present invention proposes a method for calculating transient response of a whole machine model with clearance support, comprising the following steps:

[0055] Step SS1: nonlinear modeling of the whole machine of the rotor-support-casing system, including linear component modeling of the whole machine structure and nonlinear modeling of the clearance support. The linear component modeling of the whole machine structure includes rotor modeling, casing modeling, linear support modeling, and mounting section modeling. The nonlinear modeling of the clearance support includes nonlinear modeling considering friction effect and contact effect, and constructing a nonlinear rotor dynamics model of the whole machine.

[0056] Step SS2: Response calculation based on Newmark method with variable step size control;

[0057] Step SS3: Extract the transient response of each node of the rotor, support, and casing.

[0058] The linear component modeling of the whole machine structure in step SS1 includes: finite element modeling of linear components in the rotor-support-casing system, specifically including: in the finite element model of the rotor-support-casing system, the wheel disc is treated as a concentrated mass, and the disc unit mainly considers inertia and gyroscopic effects, and its unit mass matrix and gyroscopic matrix are respectively

[0059]

[0060] Where m d is the mass of the disk, I d is the diameter moment of inertia, I p Polar moment of inertia.

[0061] The linear component modeling of the whole machine structure in step SS1 includes: Figure 1 As shown, the shaft unit adopts Timoshenko beam unit, considering inertia, shear and gyroscopic effects, has two nodes, and only considers transverse bending vibration. It needs to be described by 8 coordinates, namely:

[0062] [u1,v1,θ1,ψ1,u2,v2,θ2,ψ2](3)

[0063] Among them, u1, v1, θ1, ψ1 are the horizontal translation displacement, vertical translation displacement, rotation around the horizontal axis and rotation around the vertical axis of the first node respectively; u2, v2, θ2, ψ2 are the horizontal translation displacement, vertical translation displacement, rotation around the horizontal axis and rotation around the vertical axis of the second node respectively.

[0064] The linear component modeling of the whole machine structure in step SS1 also includes: the mass matrix, stiffness matrix and gyro matrix of the general circular cross-section shaft unit are respectively

[0065]

[0066]

[0067] in,

[0068] The receiver is also modeled using beam elements, but the gyroscopic effect does not need to be considered;

[0069] For linear support components, the forces acting on the support in the x and y directions are expressed as

[0070]

[0071] Among them, f x 、f y are the forces acting on the support in the x and y directions respectively.

[0072] The nonlinear modeling of the gap support in step SS1 considers the contact and friction effects of the gap support, and its actual nonlinear force F nl is the radial pressure F n and tangential friction f t The superposition of:

[0073] F nl =F n cosθ+f t sinθ (8)

[0074] Among them, the radial pressure F n for

[0075]

[0076] Tangential friction force f t for

[0077]

[0078] Among them, k bn The nonlinear parameters are contact stiffness, c bn is the contact damping and μ is the friction coefficient.

[0079] The step SS2 includes: based on the Newmak method of variable step size control, the vibration differential equation of the nonlinear system at time t+Δt is:

[0080]

[0081] Among them, the nonlinear force f nl (t+Δt) has a complex nonlinear representation, but through appropriate equation relationships, it can always be expressed as the displacement u(t+Δt) and velocity u(t+Δt) at the current moment t+Δt. With acceleration The function of these three; combined with the classic Newmark formula, the speed is expressed by u(t+Δt) With acceleration Nonlinear force f nl (t+Δt) is expressed as a function of displacement u(t+Δt) nl (t+Δt)=f nl (u(t+Δt)); Based on this, the algebraic equation of the nonlinear system is constructed:

[0082]

[0083] Note that both sides of the equation contain the unknown u(t+Δt), and the function f nl The form of (u(t+Δt)) is complex, so a nonlinear equation solver needs to be introduced for iterative solution.

[0084] The step SS2 further comprises: directly iterating and solving the algebraic equations of the nonlinear system by means of the Newton-Raphson method.

[0085] The step SS2 also includes: performing adaptive step length control using the Newmark method. For nonlinear systems, adaptive step length control based on the number of iterative solutions is used. When the Newmark algorithm for nonlinear systems is used for calculation, there must be an iterative step of calculating using the Newton-Raphson method. Therefore, adaptive step length control is performed according to the number of iterations. The steps are as follows:

[0086] 1) If there is no solution, proceed as follows: The solution step length of the current point is too long, so reduce the solution step length of the current step.

[0087]

[0088] 2) If there is a solution, but the number of iterations is too small, then: increase the step size appropriately, but at the same time, control the step size not to exceed the set maximum step size, so as not to make the step size too large and affect the calculation accuracy of the next point;

[0089]

[0090] 3) If there is a solution and the number of iterations is appropriate, proceed to: keep the step size unchanged for the next point.

[0091] The step SS3 also includes: if the displacement u(t0) and the velocity at the initial time t0 are known

[0092] With acceleration value By repeating the calculation according to step SS2, the displacement, velocity and acceleration values ​​at any time that satisfy the vibration differential equation of the nonlinear system can be obtained through integration.

[0093] A specific implementation method is described by taking a certain engine system as an example.

[0094] (1) Rotor modeling

[0095] The rotor shaft has a variable cross-section. The geometric parameters of 40 key points on the rotor shaft are extracted to describe the rotor shaft. The rotor one-dimensional beam unit model is established as follows: Figure 2 shown.

[0096] (2) Disk unit modeling

[0097] The first-stage fan disk and the second-stage turbine disk are not uniform disks. They can be equivalent to disks with equal moment of inertia, mass and density. The one-dimensional beam element model of the first-stage fan disk and the second-stage turbine disk is established as follows: Figure 3 As shown, the node where the first-stage fan disk is located is node 3, and the nodes where the first-stage and second-stage turbine disks are located are nodes 39 and 40.

[0098] (3) Support modeling

[0099] For the support stiffness K xx , K yy When the support stiffness K is equal, the left and right stiffness of the support are equal and are isotropic. xx , K yy When they are not equal, the support is anisotropic. Different support types will have a great impact on the rotor dynamics. The stiffness matrix and damping matrix of the support are as follows:

[0100]

[0101] In the whole machine system, there are 3 supports, support position 1 is located at the fan stator casing, support position 2 is located at the combustion chamber casing, and support position 3 is located at the combustion chamber casing. Figure 4 shown.

[0102] (5) Receiver Modeling

[0103] The casing is built using variable cross-section beam elements. The one-dimensional beam element model of the casing is as follows: Figure 5 shown.

[0104] (6) Machine modeling

[0105] Considering the nonlinearity of the support at pivot point 3, the one-dimensional model of the whole machine is as follows: Figure 6 shown.

[0106] (7) Calculation of nonlinear response of the whole machine

[0107] The response calculation of the whole machine nonlinear model is performed, and the transient response is as follows: Figure 7 The spectrum analysis of the transient response of the whole machine is shown as follows. Figure 8 As shown in the figure, it can be found that it contains 1, 2, and 3 frequency response components. By calculating and analyzing the whole machine response at multiple speeds, the waterfall diagram of the whole machine nonlinear model can be obtained as shown in the figure below: Fig. 9 shown.

[0108] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0109] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 These computer program instructions can also be stored in a computer-readable memory that can guide a computer or other programmable data processing device to work in a specific way, so that the instructions stored in the computer-readable memory produce a product including an instruction device, which implements the functions specified in the process. Figure 1 A process or multiple processes and / or boxes Figure 1 These computer program instructions can also be loaded onto a computer or other programmable data processing device, so that a series of operation steps are executed on the computer or other programmable device to produce a computer-implemented process, so that the instructions executed on the computer or other programmable device provide for implementing the process in the process. Figure 1 A process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0110] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the relevant field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A method for calculating transient response of a whole machine model with clearance support, characterized in that: The steps include: Step SS1: nonlinear modeling of the whole machine of the rotor-support-casing system, including linear component modeling of the whole machine structure and nonlinear modeling of the clearance support. The linear component modeling of the whole machine structure includes rotor modeling, casing modeling, linear support modeling, and mounting section modeling. The nonlinear modeling of the clearance support includes nonlinear modeling considering friction effect and contact effect, and constructing a nonlinear rotor dynamics model of the whole machine. Step SS2: Response calculation based on Newmark method with variable step size control; Step SS3: Extract the transient response of each node of the rotor, support, and casing.

2. The method for calculating transient response of a whole machine model with clearance support according to claim 1, characterized in that: The linear component modeling of the whole machine structure in step SS1 includes: finite element modeling of linear components in the rotor-support-casing system, specifically including: in the finite element model of the rotor-support-casing system, the wheel disc is treated as a concentrated mass, and the disc unit mainly considers inertia and gyroscopic effects, and its unit mass matrix and gyroscopic matrix are respectively Where m d is the mass of the disk, I d is the diameter moment of inertia, I p Polar moment of inertia.

3. The method for calculating transient response of a whole machine model with clearance support according to claim 1, characterized in that: The linear component modeling of the whole machine structure in step SS1 includes: the shaft unit adopts Timoshenko beam unit, considers inertia, shear and gyroscopic effects, has two nodes, only considers lateral bending vibration, and needs to be described by 8 coordinates, namely: [u1,v1,θ1,ψ1,u2,v2,θ2,ψ2](3) Among them, u1, v1, θ1, ψ1 are the horizontal translation displacement, vertical translation displacement, rotation around the horizontal axis and rotation around the vertical axis of the first node respectively; u2, v2, θ2, ψ2 are the horizontal translation displacement, vertical translation displacement, rotation around the horizontal axis and rotation around the vertical axis of the second node respectively.

4. The method for calculating transient response of a whole machine model with clearance support according to claim 3 is characterized in that: The linear component modeling of the whole machine structure in step SS1 also includes: the mass matrix, stiffness matrix and gyro matrix of the general circular cross-section shaft unit are respectively in, The receiver is also modeled using beam elements, but the gyroscopic effect does not need to be considered; For linear support components, the forces acting on the support in the x and y directions are expressed as Among them, f x 、f y are the forces acting on the support in the x and y directions respectively.

5. The method for calculating transient response of a whole machine model with clearance support according to claim 1, characterized in that: The nonlinear modeling of the gap support in step SS1 considers the contact and friction effects of the gap support, and its actual nonlinear force F nl is the radial pressure F n and tangential friction f t The superposition of: F nl =F n cosθ+f t sinθ (8) Among them, the radial pressure F n for Tangential friction force f t for Among them, k bn The nonlinear parameters are contact stiffness, c bn is the contact damping and μ is the friction coefficient.

6. The method for calculating transient response of a whole machine model with clearance support according to claim 1, characterized in that: The step SS2 includes: based on the Newmak method of variable step size control, the vibration differential equation of the nonlinear system at time t+Δt is: Among them, the nonlinear force f nl (t+Δt) has a complex nonlinear representation, but through appropriate equation relationships, it can always be expressed as the displacement u(t+Δt) and velocity u(t+Δt) at the current moment t+Δt. With acceleration The function of these three; combined with the classic Newmark formula, the speed is expressed by u(t+Δt) With acceleration Nonlinear force f nl (t+Δt) is expressed as a function of displacement u(t+Δt) nl (t+Δt)=f nl (u(t+Δt)); Based on this, the algebraic equation of the nonlinear system is constructed: Note that both sides of the equation contain the unknown u(t+Δt), and the function f nl The form of (u(t+Δt)) is complex, so a nonlinear equation solver needs to be introduced for iterative solution.

7. The method for calculating transient response of a whole machine model with clearance support according to claim 6, characterized in that: The step SS2 further comprises: directly iterating and solving the algebraic equations of the nonlinear system by means of the Newton-Raphson method.

8. The method for calculating transient response of a whole machine model with clearance support according to claim 7, characterized in that: The step SS2 also includes: performing adaptive step length control using the Newmark method. For nonlinear systems, adaptive step length control based on the number of iterative solutions is used. When the Newmark algorithm for nonlinear systems is used for calculation, there must be an iterative step of calculating using the Newton-Raphson method. Therefore, adaptive step length control is performed according to the number of iterations. The steps are as follows: 1) If there is no solution, proceed as follows: The solution step length of the current point is too long, so reduce the solution step length of the current step. 2) If there is a solution, but the number of iterations is too small, then: increase the step size appropriately, but at the same time, control the step size not to exceed the set maximum step size, so as not to make the step size too large and affect the calculation accuracy of the next point; 3) If there is a solution and the number of iterations is appropriate, proceed to: keep the step size unchanged for the next point.

9. The method for calculating transient response of a whole machine model with clearance support according to claim 7, characterized in that: The step SS3 also includes: if the displacement u(t0) and the velocity at the initial time t0 are known With acceleration value By repeating the calculation according to step SS2, the displacement, velocity and acceleration values ​​at any time that satisfy the vibration differential equation of the nonlinear system can be obtained through integration.

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