Dynamic calculation method for high-speed double-span rotor connection structure

Abstract

The invention discloses a dynamic calculation method for a high-speed double-span rotor connection structure. The dynamic calculation method comprises the steps that a double-span rotor-spline-coupler three-dimensional finite element model based on a thin layer unit is established; establishing a spline connection structure rigidity loss analysis equivalent model; calculating to obtain different connection structure states, equivalent stiffness and system critical rotating speed characteristic relations; carrying out optimization design on the spline connection structure according to a calculation result; establishing a coupling rigidity calculation model; establishing a coupling mass / rigidity-double-span rotor system critical rotating speed calculation model, and calculating to obtain a coupling mass / rigidity and system critical rotating speed characteristic relationship; performing optimization design on the coupling structure according to a calculation result; and the overall structure of the double-span rotor is optimized. The influence rule of the spline connection structure and the coupler connection structure on the critical rotating speed of the double-span rotor system can be disclosed, and theoretical support and a design method are provided for structural design of the double-span rotor system connected through the coupler.

Description

Technical Field

[0001] The present invention relates to the technical field of liquid rocket engine dynamics design, and in particular to a dynamics calculation method for a high-speed double-span rotor connection structure. Background Art

[0002] Multi-span rotor systems connected by flexible metal couplings are widely used in rotating machinery across various industries. Flexible couplings primarily facilitate speed and power transmission between the drive and load devices, as well as compensation for rotor misalignment during high-speed operation. In the field of liquid rocket engines, as engines develop toward higher speeds and higher reliability, the requirements for cryogenic, high-speed rotation systems are increasing. High-speed rotation systems generally employ a dual-span rotor structure consisting of a high-speed drive, coupling, and cryogenic test device. These dual-span rotors are designed as rigid rotors (operating at speeds below the first-order critical speed).

[0003] When the driving shaft and the driven shaft are connected to form a multi-span rotor system through a coupling, the entire unit shaft system has its own dynamic characteristics, which are both related to and different from the critical speed of each single rotor. For the rotor system, the system is usually no longer continuous through pre-tightening assembly or spline torque transmission, which reduces the local stiffness of the structure and complicates the dynamic modeling of the rotor system. Although a lot of results have been achieved in the past research on double-span rotors and equivalent contact, there is currently a lack of research on the influence of spline connection structure, coupling structure characteristics, etc. on the critical speed characteristics of double-span rotor systems, making it impossible to accurately carry out double-span rotor dynamic design and performance evaluation. Therefore, in order to study the dynamic characteristics of the double-span rotor system after connection through a coupling, it is necessary to establish a model for the high-speed double-span rotor connection structure and the analysis of the dynamic characteristics of the double-span rotor to provide theoretical support for the high-speed double-span rotor structure design and engineering application. Summary of the Invention

[0004] The technical problem solved by the present invention is to overcome the shortcomings of the existing technology, provide an equivalent stiffness calculation method for a high-speed double-span rotor connection structure and a dynamic calculation method for the double-span rotor equivalent connection, and provide theoretical support for the structural design of the double-span rotor system.

[0005] The solution of the present invention is:

[0006] A method for calculating the dynamics of a high-speed double-span rotor connection structure includes:

[0007] Establish a three-dimensional finite element model of a double-span rotor-spline-coupling based on thin-layer elements;

[0008] Establish an equivalent model for spline connection structure stiffness loss analysis;

[0009] Calculate and obtain the relationship between different connection structure states and system critical speed characteristics;

[0010] Optimize the design of the spline connection structure according to the calculation results;

[0011] Establish a calculation model for the stiffness of the coupling;

[0012] Establish a calculation model for the critical speed of the double-span rotor system with the mass / stiffness of the coupling, and calculate the relationship between the mass / stiffness of the coupling and the critical speed characteristics of the system;

[0013] Optimize the design of the coupling structure according to the calculation results;

[0014] Optimize the overall structure of the double-span rotor.

[0015] Preferably, establish a three-dimensional finite element model of the double-span rotor-spline-coupling based on thin-layer elements, and the method is as follows:

[0016] Establish a three-dimensional finite element model of the double-span rotor-spline-coupling;

[0017] Establish a first equivalent contact thin layer at the mating contact part between the coupling and the shaft shoulders at both ends of the rotor;

[0018] Establish a second equivalent contact thin layer at the contact part between the rotor and the spline of the coupling;

[0019] Establish a third equivalent contact thin layer at the contact part between the coupling pressing plate and the coupling;

[0020] Establish a fourth equivalent contact thin layer at the contact part between the coupling pressing plate and the bolt;

[0021] The first equivalent contact thin layer, the second equivalent contact thin layer, the third equivalent contact thin layer, and the fourth equivalent contact thin layer are all simulated by 8-node hexahedron solid thin-layer elements.

[0022] Preferably, establish an equivalent model for analyzing the stiffness loss of the spline structure, and the method is as follows:

[0023] In the three-dimensional finite element model of the double-span rotor-spline-coupling based on thin-layer elements, intercept a section of the main shaft, and the intercepted length is the length L2 of the spline mating section + the non-mating section L1;

[0024] The calculation model for the equivalent stiffness of the spline mating section includes the equivalent stiffness model of the spline connection structure and the stiffness calculation model of the bolt flange contact surface; the equivalent stiffness model of the spline connection structure includes the spline contact model A, the integral binding contact model B, and the thin-layer element contact finite element stiffness calculation model C; the stiffness calculation model of the bolt flange contact surface includes the flange stiffness calculation model D, the stiffness calculation model E based on the full-contact thin-layer element, the integral binding flange model F, and the pre-tightening friction contact model G;

[0025] The boundary load application during simulation of spline contact model A, integral binding contact model B, and thin-layer unit contact finite element stiffness calculation model C is divided into two steps: i. Applying the overall speed n and spindle torque T; ii. Applying the external load on the intercepted spindle end face;

[0026] The boundary load application for the flange stiffness calculation model D, the stiffness calculation model E based on full-contact thin-layer elements, the integrated binding flange model F, and the preloaded friction contact model G is divided into two steps: i. Applying the bolt preload force F0 and the rotational speed n; ii. Applying an external load to the intercepted spindle end face;

[0027] In the above A, B, C, D, E, F, and G, when the i-th model is simulated, an external load F is applied to the spindle end face. i , obtain the average displacement value X of the main axis section of the corresponding model i , calculate the equivalent stiffness value k of the i-th model according to the formula i , k i =F i / X i , i=A, B, C, D, E, F, G.

[0028] Preferably, in the equivalent stiffness model of the spline connection structure,

[0029] Spline contact model A is as follows: the second equivalent contact thin layer is replaced by the real spline connection structure, and the contact is set as friction contact;

[0030] The integral bonding contact model B is as follows: the second equivalent contact layer is removed, the inner diameter of the coupling and the outer diameter of the rotor are made consistent and in direct contact, and the bonding contact is set;

[0031] The thin layer unit contact finite element stiffness calculation model C retains the second equivalent contact thin layer, and the second equivalent contact thin layer is set to be in bound contact with the coupling and the rotor.

[0032] Preferably, in the bolt flange contact surface stiffness calculation model,

[0033] The flange stiffness calculation model D retains the first equivalent contact thin layer, the third equivalent contact thin layer, and the fourth equivalent contact thin layer;

[0034] The stiffness calculation model E of the thin layer element based on full contact retains the first equivalent contact thin layer, the second equivalent contact thin layer, the third equivalent contact thin layer, and the fourth equivalent contact thin layer;

[0035] The integrated binding flange model F removes the first equivalent contact layer, the second equivalent contact layer, the third equivalent contact layer, and the fourth equivalent contact layer, so that the two end surfaces of the coupling are in direct contact with the rotor and the coupling pressure plate respectively, and the bolts are in direct contact with the coupling pressure plate;

[0036] The contacts of the models D, E, and F are all set as bonded contacts;

[0037] For the pre-tightening friction contact model G, on the basis of the integral bonded flange model F, except that the bolts and the bolt holes of the rotor are set as bonded contacts, the remaining parts are all set as friction contacts.

[0038] Preferably, the relationship between different connection structure states and the critical speed characteristics of the system is calculated as follows:

[0039] Using the equivalent model for analyzing the stiffness loss of the spline structure, set the value of the elastic modulus E as the equivalent contact thin layer elastic modulus for the dynamic calculation of the double-span rotor;

[0040] Carry out dynamic simulation calculations to obtain the relationship between different connection structure states and the critical speed characteristics of the double-span rotor. The influencing factors of the connection structure state include bolt pre-tightening force and spindle torque.

[0041] Preferably, the elastic modulus E of the first equivalent contact thin layer, the second equivalent contact thin layer, the third equivalent contact thin layer, and the fourth equivalent contact thin layer is determined as follows:

[0042] Obtain the average displacement X of the i-th model through simulation calculations. In this process, continuously change the elastic modulus of the equivalent contact thin layer. When the average displacement values X of the i-th model and the j-th model are the same, at this time, the equivalent stiffness of the i-th model and the j-th model is consistent, and the numerical value of the elastic modulus of the equivalent contact thin layer taken at this time is the elastic modulus numerical value of this model.

[0043] Preferably, optimize the design of the spline connection structure according to the calculation results, including:

[0044] According to the calculation results and combined with the actual working conditions, optimize the reference diameter, number of teeth of the spline, size of the bolts, and pre-tightening force of the connection, and finally obtain the spline connection structure with the optimal dynamic performance.

[0045] Preferably, the method for establishing the coupling stiffness calculation model is as follows:

[0046] Establish a three-dimensional model of the coupling, import it into the finite element software, set the boundary conditions, and obtain the coupling stiffness calculation model;

[0047] Set the left end face of the coupling as face A and the right end face of the coupling as face B. Apply a fixed constraint on face A and apply a radial displacement XX on the right end face. Extract the support reaction force F on face A under the boundary condition of the radial displacement XX on face B n ;

[0048] Apply a bending angle Q on the right end face and extract the support reaction moment M on face A under the boundary condition of the bending angle Q on face B;

[0049] The radial stiffness K of the coupling is r , angular stiffness K m for:

[0050] K r =F n / XX

[0051] K m =M / Q.

[0052] Preferably, the coupling mass / stiffness-double-span rotor system critical speed calculation model includes a coupling stiffness-double-span rotor system critical speed calculation model and a coupling mass-double-span rotor system critical speed calculation model;

[0053] Among them, a coupling stiffness-double-span rotor system critical speed calculation model is established to calculate the characteristic relationship between coupling stiffness and system critical speed. The method is as follows:

[0054] A coupling model with different stiffnesses is established using the coupling stiffness calculation model. These models are then assembled with the rotors at both ends to form a double-span rotor system connected by couplings with different stiffnesses, i.e., a coupling stiffness-double-span rotor system critical speed calculation model. Finite element software is then used to perform critical speed calculations to obtain the critical speed of the double-span rotor system connected by couplings with different stiffnesses.

[0055] There are two types of coupling mass-double-span rotor system critical speed calculation models. The first one is to establish couplings of different masses and couple them with the rotors at both ends while keeping the coupling stiffness unchanged, and calculate the critical speed of the double-span rotor system connected by couplings of different masses. The second one is to set an additional mass m on the coupling while keeping the total mass and stiffness of the coupling unchanged, and couple the coupling with the rotors at both ends. By changing the axial position of the additional mass m, the critical speed of the double-span rotor system under different additional mass positions of the coupling is calculated.

[0056] The beneficial effects of the present invention compared with the prior art are:

[0057] This paper uses an equivalent contact thin-layer element method, taking into account the stiffness loss of the coupling and spline structures, to provide a detailed analysis of the impact of the spline and coupling structures on the critical speed of the system. The proposed calculation method reveals the influence of the spline and coupling structures on the critical speed of a two-span rotor system, providing theoretical support and design methods for the structural design of a two-span rotor system connected by a coupling. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 The calculation method flow of the double-span rotor connection structure dynamics;

[0059] Figure 2It is the equivalent contact model of the rotor - coupling thin layer element;

[0060] Figure 3 It is the mechanical model for the equivalent stiffness analysis of the spline connection structure;

[0061] Figure 4 The boundary conditions for the coupling stiffness calculation. Specific implementation manners

[0062] To make the objectives, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present application without creative efforts shall fall within the scope of protection of the present application.

[0063] Embodiment:

[0064] As Figure 1 shown, the dynamic calculation method for the double - span rotor connection structure provided by the embodiment of the present invention includes the following steps:

[0065] S1: Establish a three - dimensional finite element model of the double - span rotor - spline - coupling based on thin layer elements;

[0066] S2: Establish an equivalent model for the stiffness loss analysis of the spline connection structure;

[0067] S3: Calculate and obtain the relationship between different connection structure states, equivalent stiffness and the critical speed characteristics of the system;

[0068] S4: Optimize the design of the spline connection structure according to the calculation results;

[0069] S5: Establish a coupling stiffness calculation model;

[0070] S6: Establish a calculation model for the critical speed of the coupling mass / stiffness - double - span rotor system;

[0071] S7: Calculate and obtain the relationship between the coupling mass / stiffness and the critical speed characteristics of the system;

[0072] S8: Optimize the design of the coupling structure;

[0073] S9: Optimize the overall structure of the double - span rotor;

[0074] Step S1 is specifically as follows: 3D models of mating components such as the coupling 4 and the rotor 1 are established respectively by 3D modeling software, and equivalent contact thin layers ①2, ②3, ③5, and ④7 are established respectively between the shoulder contact parts of the coupling 4 and the two ends of the rotor 1, the spline contact parts of the rotor 1 and the coupling 4, the contact parts of the coupling pressure plate 6 and the coupling 4, and the contact parts of the coupling pressure plate 6 and the bolt 8, specifically as Figure 2 shown.

[0075] The equivalent contact thin layers ①2, ②3, ③5, and ④7 are all simulated by 8-node hexahedron solid thin layer elements, and their dimensional parameters include thickness d, length l1, and width l2. Then the proportionality coefficient of the thin layer element thickness should satisfy

[0076] R = max(l1, l2) / d = 10 - 100

[0077] Step S2 is specifically as follows: Establish a mechanical analysis model of the local part of the main shaft and the spline mating section of the coupling as Figure 3 shown. Figure 3 In it, 41 is the simplified structure of the coupling. The total length of the intercepted local model is the spline mating end length L2 + the non-mating section L1, and both L1 and L2 are fixed values. Among them, the coupling is simplified to a cylindrical rotating body, the outer circular surface is the W surface, which is set as fixed; the cross-section of the intercepted main shaft is the U surface, and an external load F is set on the U surface. By calculation, the average displacement X of the U surface in the direction of the radial load F is obtained, and the equivalent stiffness of the spline mating section structure is defined as

[0078] K h = F / X

[0079] The calculation models of the equivalent stiffness of the spline mating section structure are divided into the equivalent stiffness model of the spline connection structure and the stiffness calculation model of the bolt flange contact surface. There are a total of 7 specific contact calculation models, namely the spline contact model A, the one-piece binding contact model B, the thin layer element contact finite element stiffness calculation model C, the flange stiffness calculation model D, the stiffness calculation model E based on the thin layer element of full contact, the one-piece binding flange model F, and the pre-tightening friction contact model G.

[0080] There are 3 types of the equivalent stiffness models of the spline connection structure, namely the spline contact model A, the one-piece binding contact model B, and the thin layer element contact finite element stiffness calculation model C. Several models are all in Figure 3On the basis of the coupling model, thin layer ①2, bolt 8, coupling pressure plate 6, and thin layer ③5 are removed, leaving a gap between the coupling 4 and the rotor 1. Among them, the spline contact A model is to replace the equivalent contact thin layer ② with a real spline connection structure, and the contact is set as frictional contact with a friction coefficient of 0.15; the spline contact B model is to remove thin layer ②3, make the inner circular hole diameter of the coupling 4 the same as the outer circular surface diameter of the rotor 1 and directly contact, and set it as bonded contact; the spline contact C model is to retain thin layer ②3, and thin layer ②3 is set as bonded contact with both the coupling 4 and the rotor 1.

[0081] When simulating the boundary loads of the above A, B, and C models, it is divided into two steps: First, apply the overall rotational speed n and the spindle torque T; Second, apply the external load F to the spindle end face.

[0082] There are 4 calculation models for the bolt flange contact surface stiffness, namely the flange stiffness calculation model D, the stiffness calculation model E based on the thin layer element of full contact, the integral bonded flange model F, and the pre-tightening frictional contact model G.

[0083] The flange stiffness calculation model D based on the thin layer element sets Figure 3 thin layer ①2, thin layer ③5, and thin layer ④7 in Figure 3 ; the stiffness calculation model E based on the thin layer element of full contact sets Figure 3 all thin layer ①2, thin layer ②3, thin layer ③5, and thin layer ④7 in

[0084] ; the integral bonded flange model F removes all of ①2, thin layer ②3, thin layer ③5, and thin layer ④7 in

[0085] so that the two end faces of the coupling 4 are in direct contact with the rotor 1 and the coupling pressure plate 6 respectively, and the bolt 8 is in direct contact with the coupling pressure plate 6. The contacts of the flange stiffness calculation models D, E, and F are all set as bonded contact.

[0086] The 7 contact calculation models of A, B, C, D, E, F, and G can obtain the average displacement values X1, X2, X3, X4, X5, X6, X7 of the spindle cross-section U and the equivalent stiffness values k1, k2, k3, k4, k5, k6, k7 of different models through finite element simulation calculation, as shown in Table 1 specifically. For the determination of the elastic modulus E of thin layer ①2, thin layer ②3, thin layer ③5, and thin layer ④7, the corresponding average displacement X of the model can be calculated. When the average displacement values X of the two calculated models are the same, the elastic modulus value of the thin layer element can be consistent with the boundary conditions of the compared calculation model at this time.

[0087] Table 1 Summary of Different Models

[0088]

[0089] Step S3 is specifically as follows: Through step S2, the elastic modulus E of the corresponding equivalent contact thin layer under different connection structure states, different bolt pre-tightening forces F0, or different spindle torques T is calculated. Then, the value of the elastic modulus E is set as the elastic modulus of the contact thin layer for the dynamic calculation of the double-span rotor, and dynamic simulation calculation is carried out to obtain the influence of different connection structure states, different bolt pre-tightening forces F0, or different spindle torques T on the critical speed characteristics of the double-span rotor.

[0090] For example: The determination method of the thin layer ②3 is to continuously change the value of the elastic modulus of the thin layer ②3, and calculate and compare model C with model A, and model C with model B respectively. When the equivalent stiffness of the two compared models is the same, the value of the elastic modulus of the thin layer ②3 can be determined; The determination methods of the thin layer ①2, thin layer ③5, and thin layer ④7 are to continuously change the elastic moduli of the thin layer ①2, thin layer ③5, and thin layer ④7, and calculate and compare model D with model F, and model D with model G respectively. When the equivalent stiffness of the two compared models is the same, the elastic moduli of the thin layer ①2, thin layer ③5, and thin layer ④7 can be determined.

[0091] Step S4 is specifically as follows: According to the critical speed calculation results of step S3, combined with the actual working conditions, optimize the reference diameter, number of teeth, etc. of the spline, and optimize the design of the size of the bolt and the pre-tightening force of the connection, and finally obtain the spline connection structure with the best dynamic performance.

[0092] Step S5 is specifically as follows: Establish a three-dimensional model of the coupling, import it into ansys, set the boundary conditions, and the schematic diagram of the coupling stiffness calculation model is as Figure 4 shown. Among them, the left end face of the coupling is set as surface A, and the right end face of the coupling is set as surface B. Apply a Fixd fixed constraint on surface A, apply a radial displacement XX and a bending angle Q on the right end face respectively, and then extract the support reaction force F on surface A under the boundary condition of the radial displacement XX on surface B n, the support reaction moment M of the A side under the boundary condition of the bending angle Q of the B side, then the radial stiffness and angular stiffness of the coupling are:

[0093] K r = F n / XX

[0094] K m = M / Q

[0095] In the preferred embodiment provided by the present invention, step S6 is specifically: the coupling stiffness - double - span rotor system critical speed calculation model is to establish coupling models with different stiffnesses through the coupling stiffness calculation model in step S5, and assemble them with the two - end rotors to form a double - span rotor system connected by couplings with different stiffnesses, and then carry out critical speed calculation through ansys to obtain the critical speeds of the double - span rotor systems connected by couplings with different stiffnesses.

[0096] The coupling mass - double - span rotor system critical speed calculation model is divided into two types. The first type is to establish couplings with different masses and couple them with the two - end rotors while keeping the coupling stiffness unchanged; the second type is to set an additional mass m on the coupling while keeping the total mass and stiffness of the coupling unchanged, and couple the coupling with the two - end rotors. By changing the axial position of the additional mass m, the influence of the additional mass position on the system critical speed can be analyzed.

[0097] In the preferred embodiment provided by the present invention, step S7 is specifically: according to the double - span rotor mass / stiffness - double - span rotor system critical speed calculation model established in step S6, the influence of the coupling stiffness, mass, and mass distribution on the system critical speed is obtained through simulation calculation.

[0098] In the preferred embodiment provided by the present invention, step S8 is specifically: according to the models established in S5 - S7 and the analysis results, optimize the coupling structure to obtain a coupling structure with better dynamic performance.

[0099] In the preferred embodiment provided by the present invention, step S9 is specifically: based on the models established in S1 - S8, the analysis results, etc., optimize the design of the weak links of the overall structure after the double - span rotors are coupled.

[0100] The parts not detailed in the present invention belong to the common general knowledge of those skilled in the art.

Claims

1. A dynamic calculation method for the connection structure of a high-speed double-span rotor, characterized in that, Including: Establish a three-dimensional finite element model of a double-span rotor-spline-coupling based on thin-layer elements; Establish an equivalent model for analyzing the stiffness loss of the spline connection structure; Calculate the relationship between different connection structure states and the critical speed characteristics of the system; Optimize the design of the spline connection structure according to the calculation results; Establish a stiffness calculation model for the coupling; Establish a calculation model for the critical speed of the coupling mass / stiffness-double-span rotor system, and calculate the relationship between the coupling mass / stiffness and the critical speed characteristics of the system; Optimize the design of the coupling structure according to the calculation results; Optimize the overall structure of the double-span rotor.

2. The dynamic calculation method of a high-speed double-span rotor connection structure according to claim 1, wherein, The method for establishing a three-dimensional finite element model of a double-span rotor-spline-coupling based on thin-layer elements is as follows: Establish a three-dimensional finite element model of a double-span rotor-spline-coupling; Establish a first equivalent contact thin layer at the mating contact part between the coupling and the shoulder of the two end rotors; Establish a second equivalent contact thin layer at the contact part between the rotor and the spline of the coupling; Establish a third equivalent contact thin layer at the contact part between the coupling pressing plate and the coupling; Establish a fourth equivalent contact thin layer at the contact part between the coupling pressing plate and the bolt; The first equivalent contact thin layer, the second equivalent contact thin layer, the third equivalent contact thin layer, and the fourth equivalent contact thin layer are all simulated by 8-node hexahedral solid thin-layer elements.

3. A dynamic calculation method for a high-speed double-span rotor connection structure according to claim 1, characterized in that The method for establishing an equivalent model for analyzing the stiffness loss of the spline structure is as follows: In the three-dimensional finite element model of a double-span rotor-spline-coupling based on thin-layer elements, intercept a section of the main shaft, and the intercepted length is the length L2 of the spline mating section + the non-mating section L1; The calculation model for the equivalent stiffness of the spline mating section includes an equivalent stiffness model of the spline connection structure and a stiffness calculation model for the bolt flange contact surface; the equivalent stiffness model of the spline connection structure includes a spline contact model A, an integrated binding contact model B, and a thin-layer element contact finite element stiffness calculation model C; the stiffness calculation model for the bolt flange contact surface includes a flange stiffness calculation model D, a stiffness calculation model E of a thin-layer element based on full contact, an integrated binding flange model F, and a pre-tightening friction contact model G; When simulating the spline contact model A, the integrated binding contact model B, and the thin-layer element contact finite element stiffness calculation model C, the boundary load application is divided into two steps: i. Apply the overall rotational speed n and the main shaft torque T; ii. Apply an external load to the end face of the intercepted main shaft; When simulating the flange stiffness calculation model D, the stiffness calculation model E of a thin-layer element based on full contact, the integrated binding flange model F, and the pre-tightening friction contact model G, the boundary load application is divided into two steps: i. Apply the bolt pre-tightening force F0 and the rotational speed n; ii. Apply an external load to the end face of the intercepted main shaft; Among the above A, B, C, D, E, F, and G, when the i-th model is simulated and calculated, an external load F is applied to the spindle end face i , and the average displacement value X of the spindle cross-section of the corresponding model is obtained i . According to the formula, the equivalent stiffness value k of the i-th model is calculated i , k i = F i / X i , where i = A, B, C, D, E, F, G 4. A dynamic calculation method for a high-speed double-span rotor connection structure according to claim 3, characterized in that In the equivalent stiffness model of the spline connection structure, The spline contact model A is: replace the second equivalent contact thin layer with a real spline connection structure, and set the contact as friction contact; The integrated binding contact model B is: remove the second equivalent contact thin layer, make the inner circular hole diameter of the coupling the same as the outer circular surface diameter of the rotor and directly contact, and set it as binding contact; The thin-layer element contact finite element stiffness calculation model C is to retain the second equivalent contact thin layer, and set the second equivalent contact thin layer to be in binding contact with both the coupling and the rotor.

5. A dynamic calculation method for a high-speed double-span rotor connection structure according to claim 3, characterized in that In the stiffness calculation model for the bolt flange contact surface, The flange stiffness calculation model D retains the first equivalent contact thin layer, the third equivalent contact thin layer, and the fourth equivalent contact thin layer; The stiffness calculation model E based on the thin layer element with full contact retains the first equivalent contact thin layer, the second equivalent contact thin layer, the third equivalent contact thin layer, and the fourth equivalent contact thin layer; The integral binding flange model F removes the first equivalent contact thin layer, the second equivalent contact thin layer, the third equivalent contact thin layer, and the fourth equivalent contact thin layer, making the two end faces of the coupling directly contact the rotor and the coupling pressure plate respectively, and the bolts directly contact the coupling pressure plate; The contacts of the models D, E, and F are all set as binding contacts; For the pre-tightening friction contact model G, on the basis of the integral binding flange model F, except that the bolts and the bolt holes of the rotor are set as binding contacts, the rest of the parts are set as friction contacts.

6. A dynamic calculation method for a high-speed double-span rotor connection structure according to claim 1, characterized in that Calculate the relationship between different connection structure states and the critical speed characteristics of the system as follows: Using the equivalent model for analyzing the stiffness loss of the spline structure, set the value of the elastic modulus E as the elastic modulus of the equivalent contact thin layer for the dynamic calculation of the double-span rotor; Carry out dynamic simulation calculations to obtain the relationship between different connection structure states and the critical speed characteristics of the double-span rotor. The influencing factors of the connection structure state include the bolt pre-tightening force and the spindle torque.

7. A dynamic calculation method for a high-speed double-span rotor connection structure according to claim 6, characterized in that The elastic modulus E of the first equivalent contact thin layer, the second equivalent contact thin layer, the third equivalent contact thin layer, and the fourth equivalent contact thin layer is determined as follows: Obtain the average displacement X of the i-th model through simulation calculations. During this process, continuously change the elastic modulus of the equivalent contact thin layer. When the average displacement values X of the i-th model and the j-th model are the same, the equivalent stiffness of the i-th model and the j-th model is consistent at this time, and the numerical value of the elastic modulus of the equivalent contact thin layer taken at this time is the elastic modulus numerical value of this model.

8. A dynamic calculation method for a high-speed double-span rotor connection structure according to claim 1, characterized in that Optimize the design of the spline connection structure according to the calculation results, including: According to the calculation results and combined with the actual working conditions, optimize the reference diameter, number of teeth of the spline, the size of the bolts, and the pre-tightening force of the connection, and finally obtain the spline connection structure with the best dynamic performance.

9. A dynamic calculation method for a high-speed double-span rotor connection structure according to claim 1, characterized in that, The method for establishing the coupling stiffness calculation model is as follows: Establish a three-dimensional model of the coupling, import it into the finite element software, set the boundary conditions, and obtain the coupling stiffness calculation model; The left end face of the coupling is designated as face A, and the right end face of the coupling is designated as face B. A fixed constraint is applied to face A, and a radial displacement XX is applied to the right end face. The support reaction force F of face A under the boundary condition of the radial displacement XX of face B is extracted. n ; Apply the bending angle Q to the right end face, and extract the support reaction moment M of the A surface under the boundary condition of the bending angle Q of the B surface; Then the radial stiffness K of the coupling r , and the angular stiffness K m are as follows: K r = F n / XX K m = M / Q.

10. A dynamic calculation method for a high-speed double-span rotor connection structure according to claim 1, characterized in that, The coupling mass / stiffness - critical speed calculation model of the double-span rotor system includes the coupling stiffness - critical speed calculation model of the double-span rotor system and the coupling mass - critical speed calculation model of the double-span rotor system; Among them, to establish the coupling stiffness - critical speed calculation model of the double-span rotor system and calculate the relationship between the coupling stiffness and the critical speed characteristics of the system, the method is as follows: Establish coupling models with different stiffnesses through the coupling stiffness calculation model, and assemble them with the two end rotors to form a double-span rotor system connected by couplings with different stiffnesses, that is, the coupling stiffness - critical speed calculation model of the double-span rotor system; then carry out critical speed calculations through the finite element software to obtain the critical speeds of the double-span rotor systems connected by couplings with different stiffnesses; The critical speed calculation model of the coupling mass - double - span rotor system is divided into two types. The first type is to establish couplings with different masses while keeping the coupling stiffness unchanged, and couple them with the two - end rotors. Based on this, the critical speeds of the double - span rotor systems connected by couplings with different masses are calculated. The second type is to set an additional mass m on the coupling while keeping the total mass and stiffness of the coupling unchanged, and couple the coupling with the two - end rotors. By changing the axial position of the additional mass m, the critical speeds of the double - span rotor system at different positions of the additional mass of the coupling are calculated.

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