A modal optimization design method for a dual-rotor system with intermediate bearings

Abstract

The application discloses a kind of modal optimization design methods of double-rotor system with intermediate bearing, without considering critical speed and its margin range, all modes of double-rotor system with intermediate bearing in high pressure excitation and low pressure excitation in whole speed range are optimized, all modes are evaluated using the modal tolerance evaluation function constructed in the application, the maximum of optimization objective function constructed in the application is pursued using genetic algorithm, and the final optimization result can be output after each order modal tolerance evaluation function is greater than 0.8, which makes each order mode after the modal optimization design of double-rotor system with intermediate bearing can meet the requirement of tolerance resonance, can run at critical speed, so that double-rotor system can run at any speed, without following "critical speed margin" rule, improve the high mobility of aeroengine, provide reference and thought for the design of next generation aeroengine.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of aero-engines, in particular to a modal optimization design method for a double-rotor system with an intermediate bearing. BACKGROUND

[0002] The main configuration of modern aero-engines is a double-rotor system with an intermediate bearing, which includes a low-pressure rotor and a high-pressure rotor. Due to the errors that cannot be completely eliminated in the production and assembly process, there are unbalance amounts on the low-pressure rotor and the high-pressure rotor caused by these errors. During the operation of the aero-engine, the unbalance amounts on the low-pressure rotor and the high-pressure rotor will generate unbalanced excitation forces, which means that the double-rotor system simultaneously exists low-pressure excitation sources and high-pressure excitation sources. No matter the low-pressure excitation sources or the high-pressure excitation sources, they will excite the vibration of the entire double-rotor system of the aero-engine through the intermediate bearing, therefore, the critical speeds of the double-rotor system include two types of critical speeds, i.e., the critical speeds of the low-pressure excitation modes and the critical speeds of the high-pressure excitation modes. For civil aero-engines, higher safety and economy are the goals pursued, therefore, they are stably operated in a small high-efficiency speed range most of the time, and in the design of the structure of the double-rotor civil engine with an intermediate bearing, the critical speeds are adjusted to avoid the high-efficiency speed range, i.e., the "critical speed margin" criterion is always applicable. However, for military aero-engines, the continuous pursuit of high performance and high thrust-to-weight ratio makes the double-rotor system with an intermediate bearing more flexible, the critical speeds in the speed range are more, and the high maneuverability requirement of military aircraft requires the aero-engine to work in a wide speed range, it is difficult to design a military aero-engine that meets the requirements according to the "critical speed margin" criterion. Therefore, an optimization design method for the double-rotor system with an intermediate bearing is urgently needed, which can allow the aero-engine to work at the critical speed and its neighborhood.

[0003] In the article "Improvement Design of Vibration Characteristics of a Certain Type of Gas Turbine [J]. Aviation Engine, 2010, 36(01): 7-9." by Feng Guoqian, in order to improve the safety of a certain type of gas turbine, the critical speed of the gas turbine rotor is improved, and the method is to improve the critical speed margin. The optimization object in the article is a single-rotor ground machine, and the rated speed also has only one speed, and the optimization design according to the "critical speed margin" criterion can improve the vibration characteristics, but for the double-rotor system with an intermediate bearing which has more critical speeds and the aero-engine which has a wider working speed range, the "critical speed margin" criterion is obviously no longer applicable.

[0004] Liao Mingfu proposed a design method of aero-engine rotor structure dynamics in the invention patent with the publication number CN103912315B, which takes the margin between the modal of the elastic supported rotor and the modal of the absolutely rigid supported rotor as the optimization parameter design method, ensuring the performance of the damper. Li Yan proposed a double rotor design method to avoid the dynamic critical following phenomenon in the invention with the publication number CN111310288A, which considers the inertia parameters of the blade disc of the double rotor system and the relationship between the high pressure rotor and the low pressure rotor, and proposes a double rotor design method to avoid the dynamic critical following phenomenon. The above two design methods provide a new design idea for ensuring the safety of the rotor system, but the consideration factors are single, only from the damper performance or the avoidance of critical following phenomenon, and the problem of how to safely operate the double rotor system with intermediate bearing under the condition of being unable to avoid the critical speed is not solved.

[0005] Liao Mingfu first proposed the design concept of "tolerable modal" in the book "Rotor Dynamics" (Xi'an, Northwest Industrial University Press, published in November 2015), which allows the rotor to work at the critical speed without leaving a margin for the critical speed, but the book only takes the "critical speed margin" optimization design method without the "critical speed margin" constraint as the double rotor system optimization design method under the "tolerable modal", without considering the influence of unbalance and the condition of damper performance, and without considering the safety of intermediate bearing, which is imperfect.

[0006] Zhao Lu carried out tolerable modal optimization design for rigid high pressure rotor system in the article "Aero-engine high pressure rotor 'tolerable modal' design and experimental verification[J]. Propulsion Technology, 2022, 43(02): 324-336." Huang Jiangbo carried out tolerable modal optimization design for flexible low pressure rotor system in the article "Aero-engine low pressure rotor system 'tolerable modal' design and experimental verification[J]. Journal of Aerospace Power, 2022, 37(05): 964-979." The above two designs are carried out for single rotor system, which can provide reference for the tolerable modal optimization design of double rotor system with intermediate bearing, but the double rotor system is more complex than the single rotor system, and the coupling effect of the intermediate bearing makes the double rotor system different from the simple superposition of two single rotor systems. Therefore, the tolerable modal optimization design method of the double rotor system with intermediate bearing needs to be established.

[0007] The existing double rotor system optimization design method with intermediate bearing has the above-mentioned deficiencies, which restricts the structural dynamics design of the double rotor aero-engine. SUMMARY

[0008] In order to overcome the problems of the existing technology, such as the applicability of the critical speed margin criterion is smaller and smaller, the modal optimization design method is imperfect, and the modal optimization design method for the dual-rotor system is not proposed, the application provides a modal optimization design method for a dual-rotor system with an intermediate bearing.

[0009] The dual-rotor system with the intermediate bearing is composed of a low-pressure rotor system, a high-pressure rotor system and a fourth intermediate support, wherein the low-pressure rotor system comprises a low-pressure fan disc, a low-pressure turbine disc, a low-pressure rotor shaft, a first elastic support, a second rigid support and a fifth elastic support, and the high-pressure rotor system comprises a high-pressure compressor disc, a high-pressure turbine disc, a high-pressure rotor shaft and a third elastic support.

[0010] The low-pressure fan disc and the low-pressure turbine disc are respectively sleeved on both ends of the low-pressure rotor shaft, and the first elastic support and the second rigid support are sequentially arranged between the low-pressure fan disc and the low-pressure turbine disc; the fifth elastic support is located on the outer side of the low-pressure turbine disc and at the end of the low-pressure rotor shaft.

[0011] The high-pressure rotor shaft is sleeved on the low-pressure rotor shaft, and the outer circumferential surface of the end of the high-pressure rotor shaft close to the low-pressure fan disc is supported by the third elastic support, and the inner circumferential surface of the end of the high-pressure rotor shaft close to the low-pressure turbine disc is supported by the fourth intermediate support.

[0011] The application is characterized in that,

[0012] The specific process is as follows:

[0013] Step 1, determining the input conditions of the optimization design.

[0014] The input conditions of the optimization design comprise the finite element node positions of a one-dimensional finite element model of the dual-rotor system with the intermediate bearing, material parameters and the speed control law of the dual-rotor system with the intermediate bearing.

[0015] The element type of the one-dimensional finite element model is linear, and each finite element node is distributed along the axial direction of the low-pressure rotor shaft and the axial direction of the high-pressure rotor shaft in the dual-rotor system with the intermediate bearing.

[0016] Each finite element node comprises the tenth finite element node, the eleventh finite element node, the twelfth finite element node, the thirteenth finite element node and the fourteenth finite element node distributed on the high-pressure rotor shaft, and the first finite element node, the second finite element node, the third finite element node, the fourth finite element node, the fifth finite element node, the sixth finite element node, the seventh finite element node, the eighth finite element node and the ninth finite element node distributed on the low-pressure rotor shaft.

[0017] The specific position of each finite element node is:

[0018] The tenth finite element node, the eleventh finite element node, the twelfth finite element node, the thirteenth finite element node and the fourteenth finite element node are distributed on the high-pressure rotor shaft, wherein the tenth finite element node is located at the end face of the high-pressure rotor shaft near the low-pressure fan disc, and the tenth finite element node corresponds to the axis of the third elastic support; the fourteenth finite element node is located at the end face of the high-pressure rotor shaft near the low-pressure turbine disc, and the fourteenth finite element node corresponds to the axis of the fourth intermediate support; the position of the eleventh finite element node corresponds to the axial symmetry plane of the high-pressure compressor disc; the position of the thirteenth finite element node corresponds to the axial symmetry plane of the high-pressure turbine disc; the twelfth finite element node is located at the midpoint between the eleventh finite element node and the thirteenth finite element node.

[0019] The first finite element node, the second finite element node, the third finite element node, the fourth finite element node, the seventh finite element node, the eighth finite element node and the ninth finite element node are distributed on the low-pressure rotor shaft. The first finite element node is located at the end face of the low-pressure rotor shaft near the low-pressure fan disc, and the first finite element node corresponds to the outer end face of the low-pressure fan disc; the ninth finite element node is located at the end face of the low-pressure rotor shaft near the low-pressure turbine disc, and the ninth finite element node corresponds to the axis of the fifth elastic support; the eighth finite element node corresponds to the axial symmetry plane of the low-pressure turbine disc; the seventh finite element node is located on the side of the inner end face of the low-pressure turbine disc, and corresponds to the axis of the fourth intermediate support. The second finite element node, the third finite element node and the fourth finite element node are respectively located between the inner end face of the low-pressure fan disc and the end face of the adjacent high-pressure rotor shaft, and the second finite element node corresponds to the axis of the second rigid support, the third finite element node corresponds to the axis of the second rigid support, and the fourth finite element node corresponds to the axis of the third elastic support. When the distance between the fourth finite element node and the seventh finite element node is 1 / 4 of the total length of the low-pressure rotor shaft, the fifth finite element node and the sixth finite element node are arranged between the fourth finite element node and the seventh finite element node, and the distance between the fifth finite element node and the sixth finite element node is 1 / 8-1 / 10 of the total length of the low-pressure rotor shaft.

[0020] The material parameters are the density, the elastic modulus and the Poisson's ratio of the material of the double-rotor system with intermediate bearings, the density of the material is 8304 kg / m 3 , the elastic modulus is 2.069×10 11 N / m 2 , and the Poisson's ratio is 0.3.

[0021] The speed control law of the belt intermediate bearing dual-rotor system satisfies the following relationship: h and the speed of the low-pressure rotor Ω L .

[0022] The speed control law of the belt intermediate bearing dual-rotor system satisfies the following relationship:

[0023] Ω h =-1.5Ω L (28)

[0024] In formula (28), Ω L is the speed of the low-pressure rotor, and has a value range of 0-20000 r / min, Ω h is the speed of the high-pressure rotor, and has a value range of -30000-0 r / min, wherein the negative sign indicates that the high-pressure rotor rotates in the opposite direction to the low-pressure rotor.

[0025] At this point, all the input conditions for the optimized design are obtained, including the finite element node positions of the one-dimensional finite element model of the belt intermediate bearing dual-rotor system, the material parameters, and the speed control law of the belt intermediate bearing dual-rotor system.

[0026] Step 2, determine the independent variables of the optimized design.

[0027] The independent variables of the optimized design include: the length, outer radius, and inner radius of each shaft element on the high-pressure rotor shaft of the belt intermediate bearing dual-rotor system; the length, outer radius, and inner radius of each shaft element on the low-pressure rotor shaft; the mass, polar moment of inertia, and polar moment of inertia of each disc; the stiffness and damping of each support; and the stiffness and damping of each support. The discs include low-pressure fan discs, high-pressure compressor discs, high-pressure turbine discs, and low-pressure turbine discs. The supports include the fifth elastic support, the fourth intermediate support, the third elastic support, the second rigid support, and the first elastic support. Among them:

[0028] The shaft element is a shaft segment between each two adjacent finite element nodes in the one-dimensional finite element model of the belt intermediate bearing dual-rotor system.

[0029] Step 3, determine the constraint conditions of the optimized design.

[0030] The constraint conditions of the optimized design include: the value range of the independent variables of the optimized design determined in step 2, the rigid support modal constraint, and the blade disc inertia parameter constraint. The rigid support modal constraint is a constraint condition for avoiding the occurrence of a rotor modal with absolute rigidity of the support of the belt intermediate bearing dual-rotor system under the speed control law. The blade disc inertia parameter constraint is a constraint condition for avoiding the dynamic critical following phenomenon of the belt intermediate bearing dual-rotor system.

[0031] The specific process of determining the constraint conditions of the optimized design is:

[0032] ⅠDetermination of the value range of the independent variable:

[0033] The shaft element independent variable is the length of the distance between adjacent finite element nodes on each low-pressure rotor shaft, the inner radius of the low-pressure rotor shaft, and the outer radius of the low-pressure rotor shaft; the length of the distance between adjacent finite element nodes on each high-pressure rotor shaft, the inner radius of the high-pressure rotor shaft, and the outer radius of the high-pressure rotor shaft; the parameters of each disc; and the parameters of each support.

[0034] The determined value range of each shaft element independent variable is:

[0035] ⅰThe length of the distance between adjacent finite element nodes:

[0036] The length of the distance between the first finite element node and the second finite element node is 40.00-60.00 mm; the length of the distance between the second finite element node and the third finite element node is 40.00-60.00 mm; the length of the distance between the third finite element node and the fourth finite element node is 40.00-60.00 mm; the length of the distance between the fourth finite element node and the fifth finite element node is 70.00-110.00 mm; the length of the distance between the fifth finite element node and the sixth finite element node is 60.00-90.00 mm; the length of the distance between the sixth finite element node and the seventh finite element node is 60.00-90.00 mm; the length of the distance between the seventh finite element node and the eighth finite element node is 40.00-60.00; the length of the distance between the eighth finite element node and the ninth finite element node is 40.00-60.00; the length of the distance between the tenth finite element node and the eleventh finite element node is 40.00-60.00; the length of the distance between the eleventh finite element node and the twelfth finite element node is 60.00-90.00; the length of the distance between the twelfth finite element node and the thirteenth finite element node is 60.00-90.00; and the length of the distance between the thirteenth finite element node and the fourteenth finite element node is 60.00-90.00.

[0037] ⅱThe value range of the inner radius of the low-pressure rotor shaft is 5.00-8.00 mm, and the value range of the outer radius is 13.00-17.00 mm; the value range of the inner radius of the high-pressure rotor shaft is 515.00-24.00 mm, and the value range of the outer radius is 22.00-28.00 mm;

[0038] ⅲThe disc parameters are the mass, polar moment of inertia, and moment of inertia with respect to diameter of each disc; the discs are low-pressure fan discs, low-pressure turbine discs, high-pressure compressor discs, and high-pressure turbine discs; and the determined value ranges of the disc parameters are:

[0039] The mass of the low-pressure fan disk is 4.00-6.00 / kg, the polar moment of inertia is 240.00-280.00 / 10 -4 kg·m 2 , and the moment of inertia about the diameter is 120.00-140.00 / 10 -4 kg·m 2 .

[0040] The mass of the low-pressure turbine disk is 4.00-6.00 / kg, the polar moment of inertia is 240.00-280.00 / 10 -4 kg·m 2 , and the moment of inertia about the diameter is 120.00-140.00 / 10 -4 kg·m 2 .

[0041] The mass of the high-pressure compressor disk is 2.00-4.00 / kg, the polar moment of inertia is 90.00-180.00 / 10 -4 kg·m 2 , and the moment of inertia about the diameter is 45.00-90.000 / 10 -4 kg·m 2 .

[0042] The mass of the high-pressure turbine disk is 2.00-4.00 / kg, the polar moment of inertia is 90.00-180.00 / 10 -4 kg·m 2 , and the moment of inertia about the diameter is 45.00-90.000 / 10 -4 kg·m 2 .

[0043] The parameters of each support include the stiffness and damping of each support; the each support is a first elastic support, a second rigid support, a third elastic support, a fourth intermediate support and a fifth elastic support.

[0044] The determined parameter value range of each support is respectively:

[0045] The stiffness of the first elastic support is 5x10 5 -1x10 7 / N·m -1 , and the damping is 2000 / N·s·m -1 .

[0046] The stiffness of the second rigid support is 1x10 7 -5x10 9 / N·m -1 , and the damping is 300 / N·s·m -1 .

[0047] The stiffness of the third elastic support is 5x105 ~1x10 7 / N·m -1 , damping is 1000 / N·s·m -1 ;

[0048] The stiffness of the fourth intermediate support is 1x10 7 ~5x10 9 / N·m -1 , damping is 300 / N·s·m -1 ;

[0049] The stiffness of the fifth elastic support is 5x10 5 ~1x10 7 / N·m -1 , damping is 2000 / N·s·m -1 .

[0050] The rigid support modal constraint determined in II is:

[0051]

[0052] In equation (29):

[0053]

[0054] In equations (29) and (30), ω Lcri is any order low pressure excitation critical speed in the working range of the adopted double rotor system with intermediate bearing, and are the low pressure excitation first order and the low pressure excitation second order of the rigid support critical speed of the adopted double rotor system with intermediate bearing. In equation (30), the value 0.9 represents the lower bound of the constraint, and the value 1.1 represents the upper bound of the constraint.

[0055] The low pressure excitation critical speed is obtained by bringing the input conditions in step 1 and the independent variables in step 2 into the finite element. The rigid support critical speed is obtained by bringing the input conditions in step 1, the independent variables in step 2 except the support stiffness, and all support stiffnesses of the double rotor system with intermediate bearing being 1x10 8 N / m into the finite element.

[0056] In equation (31), ω hcrg is any order high pressure excitation critical speed in the working range of the adopted double rotor system with intermediate bearing, and are the high pressure excitation first order and the high pressure excitation second order of the rigid support critical speed of the double rotor system with intermediate bearing; the high pressure excitation critical speed is obtained by bringing the input conditions of the optimization design in step 1 and the independent variables of the optimization design in step 2 into the finite element.

[0057] III. Determine the disc inertia parameter constraints as:

[0058] min(f(ξ L ),f(ξ h ))>0 (32)

[0059] In equation (32), for the counter-rotating dual-rotor:

[0060]

[0061] In equation (33), the ξ L is the ratio of the polar moment of inertia to the diametral moment of inertia of any disc on the low-pressure rotor of the dual-rotor system with intermediate bearing as described in step 2, and the ξ h is the ratio of the polar moment of inertia to the diametral moment of inertia of any disc on the high-pressure rotor of the dual-rotor system with intermediate bearing as described in step 2. In equation (33), the value 0.95 represents the lower constraint, and the value 1.05 represents the upper constraint.

[0062] IV. Determine the optimization objective of the optimization design.

[0063] The optimization objective of the optimization design is:

[0064]

[0065] In equation (34), m is the number of low-pressure excited modes of the dual-rotor system with intermediate bearing in the working range, which is obtained by bringing the input conditions described in step 1 and the independent variables described in step 2 into the finite element, and n is the number of high-pressure excited modes of the dual-rotor system with intermediate bearing in the working range, which is obtained by bringing the input conditions described in step 1 and the independent variables described in step 2 into the finite element, ζ Li is the optimization weight of the i-th low-pressure excited mode, ζ hg is the optimization weight of the g-th high-pressure excited mode, f Lito is the modal tolerability evaluation function of the i-th low-pressure excited mode of the dual-rotor system with intermediate bearing, and f hgto is the modal tolerability evaluation function of the g-th high-pressure excited mode of the dual-rotor system with intermediate bearing.

[0066] Determine the values of the initial optimization weights of all modes; the initial optimization weights of all modes are all taken as 1.

[0067] The expression of the modal tolerability evaluation function f Lito of the i-th low-pressure excited mode of the dual-rotor system with intermediate bearing in equation (34) is as follows:

[0068]

[0069] In equation (35), f a total strain energy ratio of the elastic supports for the i-th order mode excited by the low pressure, the total strain energy ratio of the elastic supports being a sum of strain energy ratios of the first elastic support, the third elastic support and the fifth elastic support, a strain energy ratio evaluation function of the intermediate supports for the i-th order mode excited by the low pressure, an unbalance influence factor for the i-th order mode excited by the low pressure.

[0070] the total strain energy ratio of the elastic supports for the i-th order mode excited by the low pressure in the formula (35) The expression is:

[0071]

[0072] In the formula (36), a total strain energy of the elastic supports for the i-th order mode excited by the low pressure, a total strain energy of the rigid supports for the i-th order mode excited by the low pressure, a strain energy of the intermediate supports for the i-th order mode excited by the low pressure, and are strain energies of the high pressure rotor shaft and the low pressure rotor shaft respectively under the i-th order mode excited by the low pressure.

[0073] The intermediate supports are intermediate supports. The elastic supports are the first elastic support, the third elastic support and the fifth elastic support. The rigid supports are the second rigid supports.

[0074] the total strain energy of the elastic supports for the i-th order mode excited by the low pressure in the formula (36) The expression is as follows:

[0075]

[0076] In the formula (37), W is the number of the elastic supports of the finite element model of the double-rotor system with intermediate bearings in step 1, and is 3. is the stiffness of the a-th elastic support, a=1, is the stiffness of the first elastic support; a=2, is the stiffness of the third elastic support; a=3, is the stiffness of the fifth elastic support.r Li,eb,a represents a normalized displacement at the a-th elastic support in the i-th order mode excited by the low pressure; a=1, Li,eb,1 represents a normalized displacement at the first elastic support in the i-th order mode excited by the low pressure; a=2, Li,eb,2 represents a normalized displacement at the third elastic support in the i-th order mode excited by the low pressure; a=3, Li,eb,3normalized displacement at the fifth elastic support in the i-th mode shape of the low pressure excited system; the normalized displacement, is obtained by bringing the input conditions of step 1 and the independent variables of step 2 into the finite element method using the finite element calculation method of the prior art.

[0077] the total strain energy of the rigid support in the i-th mode shape of the low pressure excited system of formula (36) The expression of is as follows:

[0078]

[0079] Z in formula (38) is the number of rigid supports of the finite element model of the double rotor system with intermediate bearing mentioned in step 1, which is 1; is the stiffness of the second rigid support; r Li,rb,b normalized displacement at the second rigid support in the i-th mode shape of the low pressure excited system.

[0080] the strain energy of the intermediate support in the i-th mode shape of the low pressure excited system of formula (36) The expression of is as follows:

[0081]

[0082] S in formula (39) in is the stiffness of the intermediate support, r Li,in is the normalized displacement at the intermediate support.

[0083] the strain energy of the high pressure rotor shaft in the i-th mode shape of the low pressure excited system of formula (36) The expression is as follows:

[0084]

[0085] Φ in formula (40) Li is the i-th mode shape vector of the low pressure excited system, which is obtained by bringing the input conditions of step 1 and the independent variables of step 2 into the finite element method using the finite element calculation method. S HP is the stiffness matrix of the high pressure rotor shaft, which is obtained by bringing the input conditions of step 1 and the independent variables of step 2 into the finite element method using the finite element calculation method.

[0086] the strain energy of the low pressure rotor shaft in the i-th mode shape of the low pressure excited system of formula (36) The expression is as follows:

[0087]

[0088] S in formula (41) LP is the stiffness matrix of the low pressure rotor shaft, which is obtained by bringing the input conditions of step 1 and the independent variables of step 2 into the finite element method using the finite element calculation method.

[0089] The intermediate support strain energy evaluation function of the low-pressure excited i-th order mode of formula (35) The expression is as follows:

[0090]

[0091] In formula (42), σ in The intermediate support strain energy ratio limit value is 1%. The intermediate support strain energy ratio of the low-pressure excited i-th order mode is as follows:

[0092]

[0093] The unbalance influence factor of the low-pressure excited i-th order mode of formula (35) The expression is as follows:

[0094]

[0095] In formula (44), M is the number of low-pressure rotor finite element nodes of the finite element model of the double-rotor system with an intermediate bearing in step 1, which is 9, r L (i, k) represents the normalized displacement of the low-pressure rotor at the k-th finite element node in the low-pressure excited i-th order mode shape.a i,k represents the unbalance weight coefficient at the k-th finite element node in the low-pressure excited i-th order mode shape, and the value range is [0, 1]; when there is a common unbalance on the finite element node, the unbalance weight coefficient of the finite element node is 1; when the finite element node can achieve high-precision dynamic balancing, the unbalance weight coefficient of the finite element node is 0; the values of the first and ninth finite element nodes are 0, and the values of the remaining low-pressure rotor finite element nodes are 1.

[0096] The modal tolerability evaluation function f of the high-pressure excited g-th order mode of the double-rotor system with an intermediate bearing of formula (34) hgto The expression is as follows:

[0097]

[0098] In formula (45), The total elastic support strain energy ratio of the high-pressure excited g-th order mode is The intermediate support strain energy ratio evaluation function of the high-pressure excited g-th order mode is The unbalance influence factor of the high-pressure excited g-th order mode.

[0099] The total elastic support strain energy ratio of the high-pressure excited g-th order mode of formula (45) The expression is as follows:

[0100]

[0101] in formula (46), is the total strain energy of the elastic support of the g-th mode of high-pressure excitation, is the total strain energy of the rigid support of the g-th mode of high-pressure excitation, is the strain energy of the intermediate support of the g-th mode of high-pressure excitation, and are the strain energies of the high-pressure rotor shaft and the low-pressure rotor shaft under the g-th mode of high-pressure excitation, respectively.

[0102] The intermediate support is an intermediate support. The elastic support is a first elastic support, a third elastic support, a fifth elastic support. The rigid support is a second rigid support.

[0103] The expression of the total strain energy of the elastic support of the g-th mode of high-pressure excitation in formula (46) is as follows:

[0104]

[0105] r h,beg,a in formula (20) represents the normalized displacement at the a-th elastic support in the g-th mode of high-pressure excitation, r hg,eb,1 in formula (20) represents the normalized displacement at the first elastic support in the i-th mode of high-pressure excitation, r hg,eb,2 in formula (20) represents the normalized displacement at the third elastic support in the i-th mode of high-pressure excitation, r hg,eb,3 in formula (20) represents the normalized displacement at the fifth elastic support in the i-th mode of high-pressure excitation;

[0106] The expression of the total strain energy of the rigid support of the g-th mode of high-pressure excitation in formula (46) is as follows:

[0107]

[0108] r hg,rb,b in formula (48) represents the normalized displacement at the second rigid support in the g-th mode of high-pressure excitation.

[0109] The expression of the strain energy of the intermediate support of the g-th mode of high-pressure excitation in formula (46) is as follows:

[0110]

[0111] r hg,in is the normalized displacement at the intermediate support.

[0112] The strain energy of the high-pressure rotor shaft under the g-th mode of high-pressure excitation in formula (46) The expression is as follows:

[0113]

[0114] Φ in formula (50) hg is the high-pressure excited g-th order modal shape vector, which is obtained by bringing the input conditions described in step 1 and the independent variables described in step 2 into finite elements through a finite element calculation method.

[0115] The strain energy of the low-pressure rotor shaft under the high-pressure excited g-th order modal described in formula (46) The expression is as follows:

[0116]

[0117] The intermediate support strain energy evaluation function of the high-pressure excited g-th order modal described in formula (51) The expression is as follows:

[0118]

[0119] Φ in formula (52) is the intermediate support strain energy ratio of the high-pressure excited g-th order modal, and the expression is as follows:

[0120]

[0121] The imbalance influence factor of the high-pressure excited g-th order modal described in formula (53) The expression is as follows:

[0122]

[0123] In formula (54), N is the number of high-pressure rotor finite element nodes of the finite element model of the double-rotor system with an intermediate bearing described in step 1, and is 5. h (g, k) represents the normalized displacement of the high-pressure rotor at the jth finite element node in the high-pressure excited g-th order modal shape. g,k represents the imbalance weight coefficient at the jth finite element node in the high-pressure excited g-th order modal shape, and the value range is [0, 1]; when there is a frequently occurring imbalance on the finite element node, the imbalance weight coefficient of the finite element node is 1; when the finite element node can achieve high-precision dynamic balancing, the imbalance weight coefficient of the finite element node is 0; the value of all high-pressure rotor finite element nodes is 1.

[0124] Step 5, determining genetic algorithm parameters

[0125] The genetic algorithm parameters include the number of generations, the number of populations, the number of population individuals, the migration rate, the generation gap, the crossover probability, and the mutation probability.

[0126] The determined genetic algorithm parameters are: genetic generation number 80, population number 5, population individual 50, migration rate 0.2, generation gap 0.9, crossover probability 0.7, and mutation probability 0.1.

[0127] Step 6, optimization design is performed.

[0128] The optimization design is performed according to the input condition in step 1, the independent variable in step 2, the constraint condition in step 3, the optimization objective in step 4, and the genetic algorithm parameters in step 5, and the specific process is as follows:

[0129] Step I, a large number of initial populations are randomly generated from the independent variable in step 2 in the value range in step 3;

[0130] Step II, the initial population and the input condition in step 1 are brought into the finite element by using the finite element calculation method in the prior art, and it is judged whether the rigid support modal constraint and the blade inertia parameter constraint in step 3 are satisfied, if the constraints are satisfied, the optimization is continued, and if the constraints are not satisfied, step I is repeated until the constraints are satisfied.

[0131] Step III, the initial population and the input condition in step 1 are brought into the finite element by using the finite element calculation method in the prior art, and the optimization objective of the optimization design in step 4 is calculated.

[0132] Step IV, the independent variable is constantly updated by the genetic algorithm.

[0133] The independent variable in step 2 is constantly updated by the genetic algorithm, and the updated independent variable and the input condition in step 1 are respectively brought into the finite element, and it is judged whether the rigid support modal constraint and the blade inertia parameter constraint in step 3 are satisfied. If the constraints are satisfied, the updated independent variable and the input condition in step 1 are brought into the finite element by using the finite element calculation method in the prior art, the optimization objective of the optimization design in step 4 is calculated, and based on the genetic algorithm, the independent variable in step 2 that makes the optimization objective maximum is found. If the constraints are not satisfied, the independent variable in step 2 is constantly updated by the genetic algorithm. When the following conditions are satisfied, the optimization is ended and the optimization result of the independent variable in step 2 is output: the genetic algorithm running generation number exceeds the genetic generation number in step 5, or the optimization objective function in step 4 is greater than 0.99.

[0134] Step 7, the optimization result is verified.

[0135] The method for checking the optimization result is: using the finite element calculation method in the prior art, the optimization result in the fourth step and the input condition in the first step are brought into the finite element to obtain the modal tolerance evaluation function of each mode of the low-pressure excitation and the modal tolerance evaluation function of each mode of the high-pressure excitation of the double-rotor system with the intermediate bearing in the fourth step; if the modal tolerance evaluation function of each mode obtained is all greater than or equal to 0.8, the optimization result in the fifth step is the optimal result of the tolerance mode optimization design of the double-rotor system with the intermediate bearing; if there is a mode with the modal tolerance evaluation function less than 0.8, the optimization weight in the third step is adjusted, the genetic generation number in the fifth step is adjusted, and the first step is repeated to re-optimize until the modal tolerance evaluation function of each mode obtained is all greater than or equal to 0.8.

[0136] The adjustment method of the optimization weight is: for the mode with the modal tolerance evaluation function less than 0.8, the weight of the mode is increased by 150% on the basis of the weight in the previous time, and the weight of the remaining modes is unchanged.

[0137] The adjustment method of the genetic generation number is: the genetic generation number in the fifth step is increased by 120%.

[0138] After the double-rotor system with the intermediate bearing is subjected to the tolerance mode optimization design, the following results are obtained:

[0139] The optimization parameters of the shaft elements are determined as follows:

[0140] i The distance length between the adjacent finite element nodes in each shaft element, the sum of the inner radius and the outer radius of the high-pressure rotor shaft, and the sum of the inner radius and the outer radius of the low-pressure rotor shaft are as follows:

[0141] The distance length between the first finite element node and the second finite element node is 45.97 mm; the inner radius is 6.72 mm; and the outer radius is 15.63 mm;

[0142] The distance length between the second finite element node and the third finite element node is 59.39 mm; the inner radius is 7.57 mm; and the outer radius is 5.96 mm;

[0143] The distance length between the third finite element node and the fourth finite element node is 40.64 mm; the inner radius is 6.58 mm; and the outer radius is 14.76 mm;

[0144] The distance length between the fourth finite element node and the fifth finite element node is 106.68 mm; the inner radius is 7.25 mm; and the outer radius is 113.88 mm;

[0145] The distance length between the fifth finite element node and the sixth finite element node is 78.71 mm; the inner radius is 5.90 mm; and the outer radius is 16.44 mm;

[0146] The length of the distance between the sixth finite element node and the seventh finite element node is 82.28 mm; the inner radius is 6.37 mm; and the outer radius is 13.88 mm;

[0147] The length of the distance between the seventh finite element node and the eighth finite element node is 56.94 mm; the inner radius is 7.12 mm; and the outer radius is 15.79 mm;

[0148] The length of the distance between the eighth finite element node and the ninth finite element node is 48.39 mm; the inner radius is 6.90 mm; and the outer radius is 15.13 mm;

[0149] The length of the distance between the tenth finite element node and the eleventh finite element node is 40.89 mm; the inner radius is 20.57 mm; and the outer radius is 24.71 mm;

[0150] The length of the distance between the eleventh finite element node and the twelfth finite element node is 65.83 mm; the inner radius is 20.88 mm; and the outer radius is 26.88 mm;

[0151] The length of the distance between the twelfth finite element node and the thirteenth finite element node is 74.99 mm; the inner radius is 18.72 mm; and the outer radius is 22.93 mm;

[0152] The length of the distance between the thirteenth finite element node and the fourteenth finite element node is 58.56 mm; the inner radius is 19.90 mm; and the outer radius is 27.18 mm.

[0153] The determined optimal value of the disc parameter is:

[0154] The mass of the low-pressure fan disc is 4.62 / kg, the polar moment of inertia is 255.96 / 10 -4 kg·m 2 , and the moment of inertia about the diameter is 127.98 / 10 -4 kg·m 2 ;

[0155] The mass of the low-pressure turbine disc is 4.04 / kg, the polar moment of inertia is 195.460 / 10 -4 kg·m 2 , and the moment of inertia about the diameter is 97.73 / 10 -4 kg·m 2 ;

[0156] The mass of the high-pressure compressor disc is 3.66 / kg, the polar moment of inertia is 161.56 / 10 -4 kg·m 2 , and the moment of inertia about the diameter is 80.72 / 10 -4 kg·m 2 ;

[0157] The mass of the high-pressure turbine disk is 2.31 / kg, and the polar moment of inertia is 98.67 / 10 -4 kg·m 2 The moment of inertia with respect to the diameter is 49.33 / 10 -4 kg·m 2 .

[0158] The determined parameter value ranges of the respective supports are as follows:

[0159] The stiffness of the first elastic support is 4.66×10 6 / N·m -1 , and the damping is 2000 / N·s·m -1 ;

[0160] The stiffness of the second rigid support is 7.23×10 7 / N·m -1 , and the damping is 300 / N·s·m -1 ;

[0161] The stiffness of the third elastic support is 5.00×10 5 / N·m -1 , and the damping is 1000 / N·s·m -1 ;

[0162] The stiffness of the fourth intermediate support is 5.21×10 7 / N·m -1 , and the damping is 300 / N·s·m -1 ;

[0163] The stiffness of the fifth elastic support is 9.06×10 6 / N·m -1 , and the damping is 2000 / N·s·m -1 .

[0164] The modal tolerability evaluation functions of the respective modes are as follows:

[0165] The tolerability evaluation function of the first mode excited by the low-pressure is 0.98;

[0166] The tolerability evaluation function of the second mode excited by the low-pressure is 0.85;

[0167] The tolerability evaluation function of the third mode excited by the low-pressure is 0.92;

[0168] The tolerability evaluation function of the first mode excited by the high-pressure is 0.99;

[0169] The tolerability evaluation function of the second mode excited by the high-pressure is 0.87;

[0170] The admissibility evaluation function of the third order mode excited by high pressure is 0.91.

[0171] Up to now, the admissible mode optimization design of the double-rotor system with intermediate bearing is completed.

[0172] Compared with the prior art, the present application has the following beneficial effects:

[0173] The admissible mode optimization design method of the double-rotor system with intermediate bearing established by the present application aims at the main problems in the prior art, such as the applicability of the "critical speed margin" criterion is getting smaller and smaller, the admissible mode optimization design method is imperfect, and the admissible mode optimization design method for the double-rotor system with intermediate bearing is not available:

[0174] 1. The admissible mode optimization design method of the double-rotor system with intermediate bearing does not consider the critical speed and its margin range, and optimizes all modes of the double-rotor system with intermediate bearing under high pressure excitation and low pressure excitation in the whole speed range. The mode admissibility evaluation function constructed by the present application is used to evaluate all modes, and the genetic algorithm is used to pursue the maximum value of the optimization objective function constructed by the present application. The final optimization result can be output only after the admissibility evaluation function of each order mode is greater than 0.8. This makes each order mode meet the requirement of tolerating resonance after the admissible mode optimization design of the double-rotor system with intermediate bearing, and the double-rotor system can run at the critical speed, so that the double-rotor system can run at any speed, and the high mobility of the aero-engine is ensured.

[0175] Table 1 is the calculation results of the admissibility evaluation function of each order mode of the double-rotor experimental device with intermediate bearing after admissible mode optimization design and the continuous running time at the critical speed.

[0176] Table 1 is the calculation results of the admissibility evaluation function of each order mode of the double-rotor experimental device with intermediate bearing after admissible mode optimization design and the continuous running time at the critical speed.

[0177]

[0178]

[0179] As can be seen from Table 1, the admissibility evaluation function of each order mode of the double-rotor experimental device with intermediate bearing after admissible mode optimization design is above 0.8; the double-rotor experimental device with intermediate bearing is continuously running at each order critical speed for at least 3790s, which fully proves that it can tolerate resonance at the critical speed, and the resonance at the critical speed is the worst working condition of the engine, which also proves that the double-rotor system can run at any speed.

[0180] 2. In the constraint condition of the allowable modal optimization design method of the double-rotor system with intermediate bearing, based on the existing design method of the rotor structure dynamics of the aero-engine for the single-rotor system, the rigid support modal constraint condition for the double-rotor system with intermediate bearing is established, a margin is set between the critical speed of the double-rotor system with intermediate bearing under the elastic support condition and the critical speed of the double-rotor system with intermediate bearing under the rigid support condition, and the damper failure caused by the similarity of the modal of the double-rotor system with intermediate bearing under the elastic support condition and the modal of the double-rotor system with intermediate bearing under the rigid support condition is avoided; based on the existing double-rotor design method which only considers a single factor to avoid the dynamic critical following phenomenon, the blade disc inertia parameter constraint condition for the double-rotor system with intermediate bearing is established, a margin is set between the polar moment of inertia and the polar moment of inertia of the blade disc diameter, and the critical following phenomenon caused by the equality of the two is avoided. The modal tolerance evaluation function constructed by the application comprehensively considers the elastic support total strain energy proportion, the intermediate support strain energy proportion evaluation function and the modal imbalance influence factor, wherein the elastic support total strain energy proportion reflects the proportion of the total strain energy of the elastic support in the total strain energy of the double-rotor system with intermediate bearing, the damper is installed at the elastic support, the strain energy at the elastic support is dissipated through the damper, the higher the elastic support total strain energy proportion, the more energy dissipated by the damper, and the safer the double-rotor system with intermediate bearing; the intermediate support strain energy proportion evaluation function adopts the “one vote veto system” to protect the safety of the intermediate bearing, and the reason is that the intermediate support strain energy proportion reflects the proportion of the intermediate support strain energy in the total strain energy of the double-rotor system with intermediate bearing, when the intermediate support strain energy proportion exceeds the limit value, the intermediate bearing is easily damaged, therefore, considering the intermediate support strain energy proportion evaluation function in the modal tolerance evaluation function can effectively protect the safety of the intermediate bearing; the modal imbalance influence factor reflects the sensitivity of the double-rotor system with intermediate bearing to the imbalance, the larger the modal imbalance influence factor, the more sensitive the double-rotor system with intermediate bearing to the imbalance, and the smaller the tolerable imbalance. The optimization design target of the application is composed of the modal tolerance evaluation function combined with the optimization weight, and the optimization design needs to meet the constraint condition established by the application, therefore, in the allowable modal optimization design of the double-rotor system with intermediate bearing, the damper effectiveness, the blade disc inertia parameter coupling, the damper damping effect, the intermediate bearing safety and the imbalance sensitivity are considered at the same time, the constraint condition established by the application and the modal tolerance evaluation function constructed by the application are associated, and the allowable modal optimization design method is more perfect.

[0181] 3, The application describes in detail the input conditions, independent variables, constraint conditions, optimization objectives, genetic algorithm parameters and optimization design process of the modal optimization design of the double-rotor system with intermediate bearings, and systematically establishes the modal optimization design method of the double-rotor system with intermediate bearings. The modal optimization design method of the double-rotor system with intermediate bearings enables the double-rotor aero-engine to work in the full speed range, without following the "critical speed margin" principle, improves the maneuverability of the fighter, and provides a reference and idea for the design of the next generation of aero-engines.

[0182] Figure 3 After the double-rotor system with intermediate bearings is designed by the modal optimization design method and the "critical speed margin" principle respectively, the vibration response calculation results at the intermediate bearings are compared. Figure 3 It can be seen that the vibration response curve 27 of the double-rotor system with intermediate bearings designed by the "critical speed margin" principle has exceeded 80 μm, and some curves are above the 40 μm vibration response mark 28, so the engine cannot stay in the speed range where the vibration response at the intermediate bearing exceeds 40 μm for a long time, which means that the double-rotor system with intermediate bearings designed by the "critical speed margin" principle cannot work at any speed in the full speed range for a long time, and needs to avoid some speeds; and the vibration response curve 29 of the double-rotor system with intermediate bearings designed by the modal optimization design method does not exceed the 40 μm vibration response mark 28 in the full speed range, which means that the double-rotor system with intermediate bearings designed by the modal optimization design method can stay at any speed in the full speed range without deliberately avoiding some speeds, which improves the maneuverability of the fighter.

[0183] After solving the above key problems, the method of the application is applied to the structural dynamics design stage of the double-rotor system with intermediate bearings, which is a process running through the dynamics design of the double-rotor system of the aero-engine, and has important engineering application value for the structural dynamics design of the double-rotor aero-engine. BRIEF DESCRIPTION OF DRAWINGS

[0184] Figure 1 It is a flow chart of the modal optimization design of the double-rotor system with intermediate bearings.

[0185] Figure 2 It is a structural schematic diagram of the double-rotor system with intermediate bearings.

[0186] Figure 3 It is a comparison diagram of vibration response calculation results.

[0187] Figure 4 It is a flow chart of the application.

[0188] In the diagram: 1. Low-pressure fan disk; 2. Low-pressure rotor shaft; 3. High-pressure rotor shaft; 4. High-pressure compressor disk; 5. High-pressure turbine disk; 6. Low-pressure turbine disk; 7. Centerline; 8. Fifth elastic support; 9. Fourth intermediate support; 10. Third elastic support; 11. Second rigid support; 12. First elastic support; 13. First finite element node; 14. Second finite element node; 15. Third finite element node; 16. Fourth finite element node; 17. Fifth finite element node; 18. Sixth finite element node; 19. Seventh finite element node. 20. Eighth finite element node; 21. Ninth finite element node; 22. Tenth finite element node; 23. Eleventh finite element node; 24. Twelfth finite element node; 25. Thirteenth finite element node; 26. Fourteenth finite element node; 27. Vibration response curve at the intermediate bearing of a dual rotor system with intermediate bearing designed according to the "critical speed margin" criterion; 28. 40μm vibration response marker line; 29. ​​Vibration response curve at the intermediate bearing of a dual rotor system with intermediate bearing designed using the accommodative modal optimization design method. Detailed Implementation

[0189] This implementation example demonstrates an acceptable modal optimization design method for a certain type of dual-rotor system with intermediate bearings.

[0190] The dual-rotor system with intermediate bearings described herein is a conventional dual-rotor system with intermediate bearings. A schematic diagram of the dual-rotor system with intermediate bearings used in this embodiment is shown below. Figure 2 As shown. The dual-rotor system with intermediate bearings consists of a low-pressure rotor system, a high-pressure rotor system, and a fourth intermediate support 9. The low-pressure rotor system includes a low-pressure fan disk 1, a low-pressure turbine disk 6, a low-pressure rotor shaft 2, a first elastic support 12, a second rigid support 11, and a fifth elastic support 8. The high-pressure rotor system includes a high-pressure compressor disk 4, a high-pressure turbine disk 5, a high-pressure rotor shaft 3, and a third elastic support 10. The low-pressure fan disk 1 and the low-pressure turbine disk 6 are respectively mounted at both ends of the low-pressure rotor shaft 2. The first elastic support 12 and the second rigid support 11 are sequentially located between the low-pressure fan disk 1 and the low-pressure turbine disk 6. The fifth elastic support 8 is located outside the low-pressure turbine disk and at the end of the low-pressure rotor shaft.

[0191] The high-pressure rotor shaft 3 is mounted on the low-pressure rotor shaft. The outer circumferential surface of the high-pressure rotor shaft near the low-pressure fan disk 1 is supported by a third elastic support 10, and the inner circumferential surface of the high-pressure rotor shaft near the low-pressure turbine disk 6 is supported by a fourth intermediate support 9. A high-pressure compressor disk 4 and a high-pressure turbine disk 5 are mounted on the outer circumference of the high-pressure rotor shaft 3, with the high-pressure compressor disk close to the low-pressure fan disk 1 and the high-pressure turbine disk close to the end of the low-pressure turbine disk 6.

[0192] The specific process is as follows:

[0193] Step 1, determining the input conditions of the optimization design.

[0194] The input conditions of the optimization design include the finite element node positions of a one-dimensional finite element model of the belt intermediate bearing double-rotor system, material parameters, and the rotating speed control law of the belt intermediate bearing double-rotor system.

[0195] The element type of the one-dimensional finite element model is linear, and each finite element node is distributed along the axial direction of the low-pressure rotor shaft and the axial direction of the high-pressure rotor shaft in the belt intermediate bearing double-rotor system; the position of each finite element node is determined by the method proposed by Liao Mingfu in the chapter of finite element method in the textbook “Rotor Dynamics” published by Northwest Industrial University Press.

[0196] In this embodiment, to determine the axial positions of the axial finite element nodes of the one-dimensional finite element model in the structure of the belt intermediate bearing double-rotor system, fourteen finite element nodes are marked in the structural diagram of the belt intermediate bearing double-rotor system, as shown in Figure 2 Each finite element node is located on the low-pressure rotor shaft 2 and the high-pressure rotor shaft 3. The specific positions of each finite element node are as follows:

[0197] The tenth finite element node 22, the eleventh finite element node 23, the twelfth finite element node 24, the thirteenth finite element node 25, and the fourteenth finite element node 26 are distributed on the high-pressure rotor shaft 3. The tenth finite element node is located at the end face of the high-pressure rotor shaft close to the low-pressure fan disc 1, and the tenth finite element node 22 corresponds to the axis of the third elastic support 10. The fourteenth finite element node 26 is located at the end face of the high-pressure rotor shaft close to the low-pressure turbine disc 6, and the fourteenth finite element node corresponds to the axis of the fourth intermediate support 9. The position of the eleventh finite element node 23 corresponds to the axial symmetry plane of the high-pressure compressor disc 4. The position of the thirteenth finite element node corresponds to the axial symmetry plane of the high-pressure turbine disc 5. The twelfth finite element node 24 is located at the midpoint between the eleventh finite element node and the thirteenth finite element node.

[0198] The first finite element node 13, the second finite element node 14, the third finite element node 15, the fourth finite element node 16, the seventh finite element node 19, the eighth finite element node 20 and the ninth finite element node 21 are distributed on the low-pressure rotor shaft 2. The first finite element node 13 is located at the end face of the low-pressure rotor shaft having the low-pressure fan disc 1 at one end, and the first finite element node corresponds to the outer end face of the low-pressure fan disc; the ninth finite element node 21 is located at the end face of the low-pressure rotor shaft having the low-pressure turbine disc 6 at one end, and the ninth finite element node corresponds to the axis of the fifth elastic support 8; the eighth finite element node 20 corresponds to the axial symmetry plane of the low-pressure turbine disc; the seventh finite element node 19 is located at the side of the inner end face of the low-pressure turbine disc 1, and corresponds to the axis of the fourth intermediate support 9. The second finite element node 14, the third finite element node 15 and the fourth finite element node 16 are respectively located between the inner end face of the low-pressure fan disc 1 and the end face of the adjacent high-pressure rotor shaft 3, and the second finite element node corresponds to the axis of the second rigid support 12, the third finite element node corresponds to the axis of the second rigid support 11, and the fourth finite element node corresponds to the axis of the third elastic support 10. When the spacing between the fourth finite element node 16 and the seventh finite element node 19 is 1 / 4 of the total length of the low-pressure rotor shaft, the fifth finite element node 17 and the sixth finite element node 18 are arranged between the fourth finite element node and the seventh finite element node, and the distance between the fifth finite element node and the sixth finite element node is 1 / 8-1 / 10 of the total length of the low-pressure rotor shaft.

[0199] The material parameters include the density, the elastic modulus and the Poisson's ratio of the material of the intermediate bearing double-rotor system, in the embodiment, the density of the material is 8304 kg / m 3 , the elastic modulus is 2.069×10 11 N / m 2 , and the Poisson's ratio is 0.3.

[0200] The speed control law of the intermediate bearing double-rotor system satisfies the control law between the speed Ω h of the high-pressure rotor and the speed Ω L of the low-pressure rotor, which is determined by consulting the "Aero-engine Design Manual".

[0201] The high-pressure rotor and the low-pressure rotor are counter-rotating in the embodiment.

[0202] The speed control law of the intermediate bearing double-rotor system satisfies the following relationship:

[0203] Ω h =-1.5Ω L (28)

[0204] Ω L is the rotating speed of the low pressure rotor, whose value range is 0-20000, unit is r / min, Ω h is the rotating speed of the high pressure rotor, whose value range is -30000-0, unit is r / min, wherein the negative sign indicates that the high pressure rotor rotates in the opposite direction to the low pressure rotor.

[0205] At this point, all the input conditions of the optimized design are obtained, including the finite element node positions of the one-dimensional finite element model of the double rotor system with intermediate bearing, the material parameters, and the rotating speed control law of the double rotor system with intermediate bearing.

[0206] Step 2, determine the independent variables of the optimized design.

[0207] The independent variables of the optimized design include the length, outer radius, and inner radius of each shaft element on the high pressure rotor shaft of the double rotor system with intermediate bearing; the length, outer radius, and inner radius of each shaft element on the low pressure rotor shaft; the mass, polar moment of inertia, and polar moment of inertia of each disc, including the low pressure fan disc 1, the high pressure compressor disc 4, the high pressure turbine disc 5, and the low pressure turbine disc 6; the stiffness and damping of each support, including the fifth elastic support 8, the fourth intermediate support 9, the third elastic support 10, the second rigid support 11, and the first elastic support 12. Among them:

[0208] The shaft element is the shaft segment between each two adjacent finite element nodes in the one-dimensional finite element model of the double rotor system with intermediate bearing.

[0209] Step 3, determine the constraint conditions of the optimized design.

[0210] The constraint conditions of the optimized design include the value range of the independent variables determined in step 2, the rigid support modal constraint, and the blade disc inertia parameter constraint. The rigid support modal constraint is a constraint condition to avoid the occurrence of a rotor modal with absolute rigidity of the support of the double rotor system with intermediate bearing under the rotating speed control law; the blade disc inertia parameter constraint is a constraint condition to avoid the dynamic critical following phenomenon of the double rotor system with intermediate bearing.

[0211] The specific process of determining the constraint conditions of the optimized design is as follows:

[0212] I. Determine the value range of the independent variables:

[0213] The value range of the independent variables is the limiting range in the variable optimization process using the genetic algorithm, i.e., the independent variables only change within the value range in the genetic algorithm optimization process. The determination principle of the value range of the independent variables is to ensure that the structural strength, weight, and space of the double rotor system with intermediate bearing meet the requirements of the "Aeroengine Design Manual".

[0214] The value ranges of the design-optimized independent variables in this embodiment are shown in Table 2, Table 3, and Table 4:

[0215] Table 2 shows the value ranges of the independent variables of the shaft elements determined

[0216] Shaft element Length / mm Inner radius / mm Outer radius / mm First finite element node ~ Second finite element node 40.00～60.00 5.00～8.00 13.00～17.00 Second finite element node ~ Third finite element node 40.00～60.00 5.00～8.00 13.00～17.00 Third finite element node to Fourth finite element node 40.00～60.00 5.00～8.00 13.00～17.00 Fourth finite element node ~ Fifth finite element node 70.00～110.00 5.00～8.00 13.00～17.00 Fifth finite element node ~ Sixth finite element node 60.00～90.00 5.00～8.00 13.00～17.00 Sixth finite element node ~ Seventh finite element node 60.00～90.00 5.00～8.00 13.00～17.00 Seventh finite element node ~ Eighth finite element node 40.00～60.00 5.00～8.00 13.00～17.00 Eighth finite element node ~ to Ninth finite element node 40.00～60.00 5.00～8.00 13.00～17.00 Tenth finite element node ~ Eleventh finite element node 40.00～60.00 15.00～24.00 22.00～28.00 Eleventh finite element node ~ Twelfth finite element node 60.00～90.00 15.00～24.00 22.00～28.00 Twelfth finite element node ~ Thirteenth finite element node 60.00～90.00 15.00～24.00 22.00～28.00 Thirteenth finite element node ~ Fourteenth finite element node 40.00～60.00 15.00～24.00 22.00～28.00

[0217] Disc Mass / kg Polar moment of inertia / 10-4kg·m2 Moment of inertia to diameter / 10-4kg·m2 Low pressure fan disc 4.00～6.00 240.00～280.00 120.00～140.00 Low pressure turbine disc 4.00～6.00 240.00～280.00 120.00～140.00 High pressure compressor disc 2.00～4.00 90.00～180.00 45.00～90.00 High pressure turbine disc 2.00～4.00 90.00～180.00 45.00～90.00

[0218] Table 3 shows the value ranges of the disc parameters

[0219] Table 4 shows the value ranges of the support parameters

[0220]

[0221]

[0222] The rigid support modal constraint is determined as follows:

[0223]

[0224] In formula (29), ω

[0225]

[0226] In formula (30), ω Lcri is any order low-pressure excitation critical speed within the working range of the intermediate-bearing double-rotor system used in this embodiment, and are the low-pressure excitation first order and the low-pressure excitation second order of the rigid support critical speed of the intermediate-bearing double-rotor system used in this embodiment, respectively. In formula (30), the value 0.9 represents the lower bound of the constraint, and the value 1.1 represents the upper bound of the constraint.

[0227] The low-pressure excitation critical speed is obtained by bringing the input conditions in step 1 and the independent variables in step 2 into the finite element through the finite element calculation method in the prior art. The rigid support critical speed is obtained by bringing the input conditions in step 1, the independent variables in step 2 except the support stiffness, and all support stiffnesses of the intermediate-bearing double-rotor system being 1×10 8 N / m into the finite element.

[0228] In formula (31), ω hcrg is any order high-pressure excitation critical speed within the working range of the intermediate-bearing double-rotor system used in this embodiment, and The first and second high pressure excitation critical speeds of the rigid support critical speed of the double rotor system with intermediate bearing used in the embodiment are obtained by using the finite element calculation method of the prior art, and the high pressure excitation critical speed is obtained by bringing the input conditions of the optimization design in step 1 and the independent variables of the optimization design in step 2 into the finite element.

[0229] III, the inertia parameter constraint of the bladed disk is determined as:

[0230] min (f (ξ L ), f (ξ h )) > 0 (32)

[0231] In formula (32), for the counter-rotating double rotor used in the embodiment:

[0232]

[0233] In formula (33), the ξ L is the ratio of the polar moment of inertia to the diametral moment of inertia of any disk on the low pressure rotor of the double rotor system with intermediate bearing used in step 2, and the ξ h is the ratio of the polar moment of inertia to the diametral moment of inertia of any disk on the high pressure rotor of the double rotor system with intermediate bearing used in step 2. In formula (33), the value 0.95 represents the lower bound of the constraint, and the value 1.05 represents the upper bound of the constraint.

[0234] Step 4, the optimization objective of the optimization design is determined.

[0235] The optimization objective of the optimization design is:

[0236]

[0237] In formula (34), m is the number of low pressure excitation modes in the working range of the double rotor system with intermediate bearing, which is obtained by bringing the input conditions in step 1 and the independent variables in step 2 into the finite element using the finite element calculation method in the prior art, n is the number of high pressure excitation modes in the working range of the double rotor system with intermediate bearing, which is obtained by bringing the input conditions in step 1 and the independent variables in step 2 into the finite element, ζ Li is the optimization weight of the i-th low pressure excitation mode, and ζ hg is the optimization weight of the g-th high pressure excitation mode, f Lito is the modal tolerability evaluation function of the i-th low pressure excitation mode of the double rotor system with intermediate bearing, and f hgto is the modal tolerability evaluation function of the g-th high pressure excitation mode of the double rotor system with intermediate bearing.

[0238] The values of the initial optimization weights of all modes are determined; in the embodiment, the initial optimization weights of all modes are all taken as 1.

[0239] the modal admissibility evaluation function f of the low-pressure-excited i-th order mode of the double-rotor system with intermediate bearing in formula (34) Lito The expression is as follows:

[0240]

[0241] In formula (35), is the total strain energy ratio of the elastic support of the low-pressure-excited i-th order mode, the total strain energy ratio of the elastic support being the sum of the strain energy ratios of the first elastic support 12, the third elastic support 10, and the fifth elastic support 8, is the intermediate bearing strain energy ratio evaluation function of the low-pressure-excited i-th order mode, is the unbalance influence factor of the low-pressure-excited i-th order mode.

[0242] The total strain energy ratio of the elastic support of the low-pressure-excited i-th order mode in formula (35) The expression is as follows:

[0243]

[0244] In formula (36), is the total strain energy of the elastic support of the low-pressure-excited i-th order mode, is the total strain energy of the rigid support of the low-pressure-excited i-th order mode, is the intermediate bearing strain energy of the low-pressure-excited i-th order mode, and are the strain energies of the high-pressure rotor shaft 3 and the low-pressure rotor shaft 2 under the low-pressure-excited i-th order mode, respectively.

[0245] The intermediate bearing is the intermediate bearing 9. The elastic support is the first elastic support 12, the third elastic support 10, and the fifth elastic support 8. The rigid support is the second rigid support 11.

[0246] The total strain energy of the elastic support of the low-pressure-excited i-th order mode in formula (36) The expression is as follows:

[0247]

[0248] In formula (37), W is the number of elastic supports of the finite element model of the double-rotor system with intermediate bearing in step 1, which is 3 in this embodiment. is the stiffness of the a-th elastic support, a = 1, is the stiffness of the first elastic support 12; a = 2, is the stiffness of the third elastic support 10; a = 3, is the stiffness of the fifth elastic support 8. r Li,eb,aThis represents the normalized displacement at the a-th elastic support in the i-th mode shape under low-pressure excitation; when a = 1, r Li,eb,1 This represents the normalized displacement at the first elastic support 12 in the i-th mode of vibration under low-pressure excitation; when a = 2, r Li,eb,2 This represents the normalized displacement at the third elastic support 10 in the i-th mode of vibration under low-pressure excitation; when a = 3, r Li,eb,3 This represents the normalized displacement at the fifth elastic support 8 in the i-th mode of vibration under low-pressure excitation; the normalized displacement is obtained by substituting the input conditions described in step 1 and the independent variables described in step 2 into the finite element method using existing finite element calculation methods.

[0249] The total strain energy of the i-th mode rigid support under low-pressure excitation described in equation (36) The expression is as follows:

[0250]

[0251] In equation (38), Z represents the number of rigid supports in the finite element model of the dual-rotor system with intermediate bearings described in step 1, which is 1 in this embodiment. r is the stiffness of the second rigid support 11. Li,rb,b This represents the normalized displacement at the second rigid support 11 in the i-th mode of low-pressure excitation.

[0252] The strain energy of the intermediate support 9 in the low-pressure excitation i-th mode described in equation (36) The expression for is as follows:

[0253]

[0254] In equation (39), S in For the stiffness of intermediate support 9, r Li,in The normalized displacements at the nine intermediate supports are calculated.

[0255] The strain energy of the high-pressure rotor shaft 3 under the i-th mode of low-pressure excitation as described in equation (36) The expression is as follows:

[0256]

[0257] In equation (40) Φ Li The i-th mode shape vector of the low-voltage excitation is obtained by substituting the input conditions described in step 1 and the independent variables described in step 2 into the finite element method. HP The stiffness matrix of the high-pressure rotor shaft 3 is obtained by substituting the input conditions described in step 1 and the independent variables described in step 2 into the finite element method.

[0258] The strain energy of the low-pressure rotor shaft 2 under the i-th mode of low-pressure excitation as described in equation (36) The expression is as follows:

[0259]

[0260] S in formula (41) LP The stiffness matrix of the low-pressure rotor shaft is obtained by bringing the input conditions described in step 1 and the independent variables described in step 2 into finite elements through a finite element calculation method.

[0261] The strain energy evaluation function f of the intermediate bearing 9 of the low-pressure excited i-th order mode described in formula (35) The expression is as follows:

[0262]

[0263] In formula (42), σ in The strain energy ratio limit value of the intermediate bearing 9 is determined to be 1% in this embodiment. The strain energy ratio of the intermediate bearing 9 of the low-pressure excited i-th order mode is as follows:

[0264]

[0265] The unbalance influence factor of the low-pressure excited i-th order mode described in formula (35) The expression is as follows:

[0266]

[0267] In formula (44), M is the number of low-pressure rotor finite element nodes of the finite element model of the double-rotor system with an intermediate bearing described in step 1, which is 9 in this embodiment, and r L (i, k) represents the normalized displacement of the low-pressure rotor at the k-th finite element node in the low-pressure excited i-th order mode shape.a i,k represents the unbalance weight coefficient at the k-th finite element node in the low-pressure excited i-th order mode shape, and the value range is [0, 1]; when there is a frequently occurring unbalance on the finite element node, the unbalance weight coefficient of the finite element node is 1; when the finite element node can achieve high-precision dynamic balancing, the unbalance weight coefficient of the finite element node is 0; in this embodiment, the values of the first finite element node 13 and the ninth finite element node 21 are 0, and the values of the remaining low-pressure rotor finite element nodes are 1.

[0268] The modal tolerability evaluation function f of the high-pressure excited g-th order mode of the double-rotor system with an intermediate bearing described in formula (34) hgto The expression is as follows:

[0269]

[0270] In formula (45), M a ratio of total strain energy of the elastic support for the g-th order mode excited by high pressure, a ratio of strain energy of the intermediate support for the g-th order mode excited by high pressure, an unbalance influence factor for the g-th order mode excited by high pressure.

[0271] a ratio of total strain energy of the elastic support for the g-th order mode excited by high pressure The expression is:

[0272]

[0273] In formula (46), a total strain energy of the elastic support for the g-th order mode excited by high pressure, a total strain energy of the rigid support for the g-th order mode excited by high pressure, a strain energy of the intermediate support for the g-th order mode excited by high pressure, and respectively, a strain energy of the high-pressure rotor shaft 3 and the low-pressure rotor shaft 2 under the g-th order mode excited by high pressure.

[0274] The intermediate support is the intermediate support 9. The elastic support is the first elastic support 12, the third elastic support 10, and the fifth elastic support 8. The rigid support is the second rigid support 11.

[0275] a total strain energy of the elastic support for the g-th order mode excited by high pressure The expression is as follows:

[0276]

[0277] In formula (20), r h,beg,a represents a normalized displacement at the a-th elastic support in the g-th order mode excited by high pressure, when a = 1, r hg,eb,1 represents a normalized displacement at the first elastic support 12 in the i-th order mode excited by high pressure, when a = 2, r hg,eb,2 represents a normalized displacement at the third elastic support 10 in the i-th order mode excited by high pressure, when a = 3, r hg,eb,3 represents a normalized displacement at the fifth elastic support 8 in the i-th order mode excited by high pressure;

[0278] a total strain energy of the rigid support for the g-th order mode excited by high pressure The expression is as follows:

[0279]

[0280] In formula (48), r hg,rb,b represents a normalized displacement at the second rigid support 11 in the g-th order mode excited by high pressure.

[0281] Strain energy of the intermediate support 9 in the high pressure excited g-th order modal The expression is as follows:

[0282]

[0283] r in formula (49) hg,in is the normalized displacement at the intermediate support 9.

[0284] Strain energy of the high pressure rotor shaft 3 in the high pressure excited g-th order modal of formula (46) The expression is as follows:

[0285]

[0286] Φ in formula (50) hg is the vibration mode vector of the high pressure excited g-th order modal, which is obtained by bringing the input conditions in step 1 and the independent variables in step 2 into finite elements through a finite element calculation method.

[0287] Strain energy of the low pressure rotor shaft 2 in the high pressure excited g-th order modal of formula (46) The expression is as follows:

[0288]

[0289] Strain energy evaluation function of the intermediate support 9 in the high pressure excited g-th order modal of formula (51) The expression is as follows:

[0290]

[0291] in formula (52) is the strain energy ratio of the intermediate support 9 in the high pressure excited g-th order modal, and the expression is as follows:

[0292]

[0293] Unbalance influence factor of the high pressure excited g-th order modal of formula (53) The expression is as follows:

[0294]

[0295] in formula (54), N is the number of high pressure rotor finite element nodes of the finite element model of the double-rotor system with an intermediate bearing in step 1, which is 5 in the present embodiment. h (g, k) represents the normalized displacement of the high pressure rotor at the j-th finite element node in the high pressure excited g-th order modal vibration mode. b g,kUnbalance weight coefficient of the jth finite element node in the gth order mode of the high pressure excited mode, the value range is [0, 1]; when the unbalance weight coefficient of the finite element node is 1, the unbalance of the finite element node is always present; when the unbalance weight coefficient of the finite element node is 0, the high precision dynamic balance of the finite element node can be achieved; in the embodiment, the value of all the high pressure rotor finite element nodes is 1.

[0296] Step 5, determining the genetic algorithm parameters

[0297] The genetic algorithm parameters include the genetic algebra, the population quantity, the population individual quantity, the migration rate, the generation gap, the crossover probability and the mutation probability.

[0298] In the embodiment, the genetic algorithm parameters are shown in Table 5:

[0299] Table 5 Genetic algorithm parameters

[0300] Parameter Value Generation number 80 Population number 5 Population individual 50 Migratory rate 0.2 Generation gap 0.9 Crossing probability 0.7 Mutation probability 0.1

[0301] Step 6, performing the optimization design.

[0302] According to the input conditions in step 1, the independent variables in step 2, the constraint conditions in step 3, the optimization target in step 4 and the genetic algorithm parameters in step 5, the optimization design is performed, and the specific process is as follows:

[0303] Step I, randomly generating a large number of initial populations of the independent variables in step 2 in the value range in step 3;

[0304] Step II, using the finite element calculation method in the prior art, bringing the initial populations and the input conditions in step 1 into the finite element, judging whether the rigid support modal constraint and the blade disc inertia parameter constraint in step 3 are satisfied, if the constraints are satisfied, the optimization is continued, if the constraints are not satisfied, step I is repeated until the constraints are satisfied;

[0305] Step III, using the finite element calculation method in the prior art, bringing the initial populations and the input conditions in step 1 into the finite element, calculating the optimization target of the optimization design in step 4;

[0306] Step IV, constantly updating the independent variables by the genetic algorithm.

[0307] The independent variables in step 2 are continuously updated by the genetic algorithm, and the updated independent variables and the input conditions in step 1 are respectively brought into the finite element to determine whether the rigid support modal constraint and the blade disc inertia parameter constraint in step 3 are satisfied. If the constraints are satisfied, the updated independent variables and the input conditions in step 1 are brought into the finite element by using the finite element calculation method in the prior art, the optimization objective of the optimization design in step 4 is calculated, and the independent variables in step 2 that maximize the optimization objective are found based on the genetic algorithm. If the constraints are not satisfied, the independent variables in step 2 are continuously updated by the genetic algorithm. The optimization is ended and the optimization result of the independent variables in step 2 is output when the following conditions are satisfied: the number of generations of the genetic algorithm exceeds the genetic number in step 5, or the optimization objective function in step 4 is greater than 0.99.

[0308] Step 7, the optimization result is verified.

[0309] The method for verifying the optimization result is as follows: the optimization result in the fourth step and the input conditions in step 1 are brought into the finite element by using the finite element calculation method in the prior art, the modal tolerance evaluation functions of the low-pressure excitation modes and the modal tolerance evaluation functions of the high-pressure excitation modes of the double-rotor system with an intermediate bearing are obtained, and the optimization result in the fifth step is the optimal result of the modal optimization design of the double-rotor system with an intermediate bearing if all the modal tolerance evaluation functions of the modes are greater than or equal to 0.8. If there is a mode whose modal tolerance evaluation function is less than 0.8, the optimization weight in step 3 is adjusted, the genetic number in step 5 is adjusted, and the first step is repeated to re-optimize until all the modal tolerance evaluation functions of the modes are greater than or equal to 0.8.

[0310] The adjustment method of the optimization weight is as follows: the weight of the mode whose modal tolerance evaluation function is less than 0.8 is increased by 150% on the basis of the weight in the previous time, and the weights of the remaining modes remain unchanged.

[0311] The adjustment method of the genetic number is as follows: the genetic number in step 5 is increased by 120%.

[0312] The optimization result of the independent variables of the double-rotor system with an intermediate bearing adopted in the embodiment is shown in Tables 6, 7 and 8.

[0313] Table 6: Optimization result of shaft element parameters

[0314] Shaft element Length / mm Inner radius / mm Outer radius / mm First finite element node to Second finite element node 45.97 6.72 15.63 Second finite element node ~ Third finite element node 59.39 7.57 15.96 Third finite element node ~ Fourth finite element node 40.64 6.58 14.76 Fourth finite element node ~ Fifth finite element node 106.68 7.25 13.88 Fifth finite element node ~ Sixth finite element node 78.71 5.90 16.44 Sixth finite element node ~ Seventh finite element node 82.28 6.37 13.88 Seventh finite element node ~ Eighth finite element node 56.94 7.12 15.79 Eighth finite element node ~ Ninth finite element node 48.39 6.90 15.13 Tenth finite element node ~ Eleventh finite element node 40.89 20.57 24.71 Eleventh finite element node ~ Twelfth finite element node 65.83 20.88 26.88 Twelfth finite element node ~ Thirteenth finite element node 74.99 18.72 22.93 Thirteenth finite element node ~ Fourteenth finite element node 58.56 19.90 27.18

[0315] Table 7: Optimization result of disc parameters

[0316] Disc Mass / kg Polar moment of inertia / 10-4kg·m2 Moment of inertia to diameter / 10-4kg·m2 Low pressure fan disc 4.62 255.96 127.98 Low pressure turbine disc 4.04 195.46 97.73 High pressure compressor disc 3.66 161.56 80.72 High pressure turbine disc 2.31 98.67 49.33

[0317] Table 8: Optimization result of bearing parameters

[0318] Support Stiffness / (N·m-1) Damping / (N·s·m-1) First elastic support 4.66×106 2000 Second rigid support 7.23×107 3000 Third elastic support 5.00×105 1000 Fourth intermediate support 5.21×107 300 Fifth elastic support 9.06×106 2000

[0319] The modal compatibility evaluation functions for each mode of the dual-rotor system with intermediate bearings used in this implementation example are shown in Table 9 after the compatibility modal optimization design.

[0320] Table 9 Modal tolerance evaluation functions

[0321]

[0322]

[0323] Thus, the accommodative modal optimization design of the dual-rotor system with intermediate bearings was completed.

[0324] This implementation example follows Figure 1 The flowchart shown is for Figure 2 The dual-rotor system with intermediate bearing shown was designed with tolerant modal optimization. During the design process, the critical speed and its margin range were not considered. The optimization was carried out for all modes of high-pressure excitation and low-pressure excitation of the dual-rotor system with intermediate bearing across the entire speed range. The optimization results show that the tolerance evaluation function value of all modes of the dual-rotor system is greater than 0.8, which enables the dual-rotor system to operate at any speed and ensures the high maneuverability of the aero-engine.

[0325] This implementation example considers rigid support modal constraints to ensure the damper will not fail, and bladed disk inertia parameter constraints to avoid critical following phenomena. The optimization objective considers the proportion of total strain energy in the elastic support, ensuring the damper's effectiveness; it considers the intermediate support strain energy proportion evaluation function to ensure the safety of the intermediate bearing; and it considers the modal imbalance influence factor, improving the dual-rotor system's tolerance to imbalance. Both the constraints and the composition of the optimization objective function make the accommodative modal optimization design method more complete.

[0326] This embodiment details the input conditions, independent variables, constraints, optimization objectives, genetic algorithm parameters, and optimization design process for the accommodative modal optimization design of a dual-rotor system with intermediate bearings, and systematically establishes a accommodative modal optimization design method for a dual-rotor system with intermediate bearings.

[0327] The method of this invention is applied to the structural dynamics design stage of a dual-rotor system with intermediate bearings. It is a process that runs through the dynamics design of dual-rotor systems for aero-engines and has important engineering application value for the structural dynamics design of dual-rotor aero-engines.

Claims

1. A method for compatible modal optimization design of a dual-rotor system with an intermediate bearing, wherein the dual-rotor system with an intermediate bearing comprises a low-pressure rotor system, a high-pressure rotor system, and a fourth intermediate support; the low-pressure rotor system includes a low-pressure fan disk, a low-pressure turbine disk, a low-pressure rotor shaft, a first elastic support, a second rigid support, and a fifth elastic support; the high-pressure rotor system includes a high-pressure compressor disk, a high-pressure turbine disk, a high-pressure rotor shaft, and a third elastic support; wherein, A low-pressure fan disk and a low-pressure turbine disk are respectively fitted at both ends of the low-pressure rotor shaft; between the low-pressure fan disk and the low-pressure turbine disk, there are a first elastic support and a second rigid support in sequence; the fifth elastic support is located on the outside of the low-pressure turbine disk and at the end of the low-pressure rotor shaft. The high-pressure rotor shaft is mounted on the low-pressure rotor shaft; the outer circumferential surface of the high-pressure rotor shaft near the low-pressure fan disk is supported by a third elastic support, and the inner circumferential surface of the high-pressure rotor shaft near the low-pressure turbine disk is supported by a fourth intermediate support; a high-pressure compressor disk and a high-pressure turbine disk are mounted on the outer circumference of the high-pressure rotor shaft, with the high-pressure compressor disk close to the low-pressure fan disk and the high-pressure turbine disk close to one end of the low-pressure turbine disk; Its features are, The specific process is as follows: Step 1, Determine the input conditions for the optimization design: The input conditions for the optimization design include the finite element node positions, material parameters, and speed control law of the one-dimensional finite element model of the dual rotor system with intermediate bearings. The element type of the one-dimensional finite element model is linear, and each finite element node is distributed along the axial direction of the low-pressure rotor shaft and the high-pressure rotor shaft in the dual rotor system with intermediate bearings. The finite element nodes include the tenth, eleventh, twelfth, thirteenth and fourteenth finite element nodes distributed on the high-pressure rotor shaft, and the first, second, third, fourth, fifth, sixth, seventh, eighth and ninth finite element nodes distributed on the low-pressure rotor shaft. The material parameters are the density, elastic modulus, and Poisson's ratio of the material in the dual-rotor system with intermediate bearings. The speed control law for the dual-rotor system with intermediate bearings is the speed Ω of the high-pressure rotor. h The rotational speed Ω of the low-pressure rotor L The control laws that are satisfied between them; The speed control law of the dual-rotor system with intermediate bearings satisfies the following relationship: Oh h =-1.5Ω L (28) In equation (28), Ω L The speed of the low-pressure rotor ranges from 0 to 20000, and the unit is r / min, Ω. h The value is the rotational speed of the high-pressure rotor, ranging from -30000 to 0, and the unit is r / min. The negative sign indicates that the high-pressure rotor rotates in the opposite direction to the low-pressure rotor, that is, the high-pressure rotor and the low-pressure rotor rotate in opposite directions. At this point, all the input conditions for the optimized design are obtained, including the finite element node positions, material parameters, and speed control law of the one-dimensional finite element model of the dual rotor system with intermediate bearings. Step 2, determine the independent variables for the optimization design: The independent variables of the optimization design include: the length, outer radius, and inner radius of each shaft element on the high-pressure rotor shaft of the dual-rotor system with intermediate bearings; the length, outer radius, and inner radius of each shaft element on the low-pressure rotor shaft; the mass, moment of inertia about diameter, and polar moment of inertia of each disk; each disk includes a low-pressure fan disk, a high-pressure compressor disk, a high-pressure turbine disk, and a low-pressure turbine disk; the stiffness and damping of each support; each support includes a fifth elastic support, a fourth intermediate support, a third elastic support, a second rigid support, and a first elastic support; wherein: the shaft element is the shaft segment between two adjacent finite element nodes in the one-dimensional finite element model of the dual-rotor system with intermediate bearings; Step 3, determine the constraints of the optimization design: The constraints of the optimization design include: the range of values ​​of the independent variables determined in step 2, the rigid support mode constraints, and the bladed disk inertia parameter constraints; the rigid support mode constraints are constraints to prevent the rotor mode with absolutely rigid support from appearing in the dual rotor system with intermediate bearings under the speed control law; the bladed disk inertia parameter constraints are constraints to prevent the dual rotor system with intermediate bearings from avoiding the dynamic critical following phenomenon. The specific process for determining the constraints of the optimization design is as follows: I. Determine the range of values ​​for the independent variable: The independent variables of the shaft elements are: the distance between adjacent finite element nodes on each low-pressure rotor shaft, the inner radius of the low-pressure rotor shaft, and the outer radius of the low-pressure rotor shaft; the distance between adjacent finite element nodes on each high-pressure rotor shaft, the inner radius of the high-pressure rotor shaft, and the outer radius of the high-pressure rotor shaft; the parameters of each disk; the parameters of each support; the disk parameters are the mass, polar moment of inertia, and moment of inertia about the diameter of each disk; each disk is a low-pressure fan disk, a low-pressure turbine disk, a high-pressure compressor disk, and a high-pressure turbine disk; The parameters of each support include the stiffness and damping of each support; each support is a first elastic support, a second rigid support, a third elastic support, a fourth intermediate support, and a fifth elastic support. The rigidly supported modal constraints determined by II are: In equation (29): In equations (29) and (30), ω Lcri This refers to any low-pressure excitation critical speed within the operating range of the dual-rotor system with intermediate bearings. and These are the first and second stages of low-pressure excitation for the rigid support critical speed of the dual rotor system with intermediate bearings, respectively; in equations (30) and (31), the value 0.9 represents the lower bound of the constraint, and the value 1.1 represents the upper bound of the constraint; The critical speed for low-pressure excitation is obtained by substituting the input conditions in step 1 and the independent variables in step 2 into the finite element method; the critical speed for rigid support is obtained by substituting the input conditions in step 1, the independent variables in step 2 excluding the support stiffness, and setting all support stiffnesses of the dual rotor system with intermediate bearings to 1×10. 8 N / m is obtained by substituting into the finite element method; in equations (29) and (31), ω hcrg The critical speed for high-pressure excitation within the operating range of the dual-rotor system with intermediate bearings is defined as any one of the following: and These are the first and second order high-pressure excitations for the rigid support critical speed of a dual-rotor system with intermediate bearings, respectively. The critical speed of this high-pressure excitation is obtained by substituting the input conditions of the optimization design described in step 1 and the independent variables of the optimization design described in step 2 into the finite element method. III. The constraints on the bladed disk inertia parameters are determined as follows: min(f(ξ L ),f(ξ h ))>0 (32) In equation (32), for counter-rotating dual rotors: In equation (33), the ξ L ξ is the ratio of the polar moment of inertia to the moment of inertia about the diameter of any disk on the low-pressure rotor of the dual-rotor system with intermediate bearings described in step 2. h The value is the ratio of the polar moment of inertia of any disk on the high-pressure rotor of the dual rotor system with intermediate bearing described in step 2 to the moment of inertia about the diameter; in formula (33), the value 0.95 represents the lower limit of the constraint, and the value 1.05 represents the upper limit of the constraint. Step 4: Determine the optimization objective of the optimization design: The optimization objective of the optimization design is: In equation (34), m represents the number of low-pressure excitation modes within the operating range of the dual-rotor system with intermediate bearings, obtained by substituting the input conditions described in step 1 and the independent variables described in step 2 into the finite element method; n represents the number of high-pressure excitation modes within the operating range of the dual-rotor system with intermediate bearings; obtained by substituting the input conditions described in step 1 and the independent variables described in step 2 into the finite element method; ζ Li ζ is the optimal weight for the i-th mode under low-voltage excitation. hg For the optimized weights of the g-th mode under high-voltage excitation, f Lito f is the modal tolerance evaluation function for the i-th order mode of a dual-rotor system with intermediate bearings under low-voltage excitation. hgto The modal tolerance evaluation function for the g-th mode of high-voltage excitation in a dual-rotor system with intermediate bearings is defined; the initial optimization weights for all modes are determined; and the initial optimization weights for all modes are set to 1. Step 5, determine the genetic algorithm parameters: The genetic algorithm parameters include the number of generations, population size, number of individuals in the population, migration rate, generation gap, crossover probability, and mutation probability. Step 6, optimize the design: The optimization design is carried out based on the input conditions described in step 1, the independent variables described in step 2, the constraints described in step 3, the optimization objective described in step 4, and the genetic algorithm parameters described in step 5. The specific process is as follows: Step 1: Randomly generate a large number of initial populations within the range of values ​​for the independent variables described in Step 2 as described in Step 3; Step 2: Using the finite element method in the prior art, substitute the initial populations and the input conditions described in Step 1 into the finite element method to determine whether the rigid support mode constraints and bladed disk inertia parameter constraints described in Step 3 are satisfied. If the constraints are satisfied, continue optimization; if the constraints are not satisfied, repeat Step 1 until the constraints are satisfied. Step III: Using the finite element method in the existing technology, the initial population and the input conditions in step 1 are substituted into the finite element method to calculate the optimization objective of the optimization design in step 4. Step IV: Continuously update the independent variables using a genetic algorithm; The independent variables described in step 2 are continuously updated using a genetic algorithm. The updated independent variables and the input conditions described in step 1 are then substituted into the finite element method to determine whether the rigid support mode constraints and bladed disk inertia parameter constraints described in step 3 are satisfied. If the constraints are satisfied, the existing finite element method is used to calculate the optimization objective of the optimization design described in step 4 by substituting the updated independent variables and the input conditions described in step 1 into the finite element method. Based on the genetic algorithm, the independent variables described in step 2 that maximize the optimization objective are found. If the constraints are not satisfied, the independent variables described in step 2 are updated again using the genetic algorithm. The optimization ends and the optimization result of the independent variables described in step 2 is output when the following conditions are met: the number of generations of the genetic algorithm exceeds the number of generations described in step 5, or the optimization objective function described in step 4 is greater than 0.

99. Step 7, verify the optimization results: The method for verifying the optimization results is as follows: using the finite element method in the existing technology, the optimization results in step IV and the input conditions in step 1 are substituted into the finite element method to obtain the modal compatibility evaluation functions for each mode of the low-pressure excitation and each mode of the high-pressure excitation of the dual rotor system with intermediate bearings in step 4; if the obtained modal compatibility evaluation functions for each mode are all ≥0.8, then the optimization results in step V are the optimal results of the modal compatibility optimization design of the dual rotor system with intermediate bearings; if there are modes with modal compatibility evaluation functions <0.8, then the optimization weights in step 3 and the genetic generations in step 5 are adjusted, and step I is repeated to start the optimization again until the obtained modal compatibility evaluation functions for each mode are all ≥0.

8. The method for adjusting the optimization weights is as follows: for modes with a modal tolerance evaluation function < 0.8, their weights are increased by 150% based on the previous weights, while the weights of the other modes remain unchanged; The method for adjusting the genetic generation is as follows: increase the genetic generation in step 5 by 120%; After the dual rotor system with intermediate bearings underwent accommodative modal optimization design, the distance between adjacent finite element nodes on the low-pressure rotor shaft, the optimized values ​​of the disk parameters, the parameter ranges of each support, and the modal accommodative evaluation functions for each mode were determined. Thus, the accommodative modal optimization design of the dual rotor system with intermediate bearings was completed.

2. The accommodative modal optimization design method for a dual-rotor system with intermediate bearings as described in claim 1, characterized in that, The specific locations of each finite element node mentioned in step 1 are as follows: A tenth, eleventh, twelfth, thirteenth, and fourteenth finite element node are distributed on the high-pressure rotor shaft. The tenth finite element node is located on the end face of the high-pressure rotor shaft near the low-pressure fan disk, and corresponds to the axis of the third elastic support. The fourteenth finite element node is located on the end face of the high-pressure rotor shaft near the low-pressure turbine disk, and corresponds to the axis of the fourth intermediate support. The eleventh finite element node is positioned relative to the axial symmetry plane of the high-pressure compressor disk. The thirteenth finite element node is positioned relative to the axial symmetry plane of the high-pressure turbine disk. The twelfth finite element node is located at the midpoint between the eleventh and thirteenth finite element nodes. A first finite element node, a second finite element node, a third finite element node, a fourth finite element node, a seventh finite element node, an eighth finite element node, and a ninth finite element node are distributed on the low-pressure rotor shaft. The first finite element node is located at the end face of the low-pressure rotor shaft where the low-pressure fan disk is located, and corresponds to the outer end face of the low-pressure fan disk. The ninth finite element node is located at the end face of the low-pressure rotor shaft where the low-pressure turbine disk is located, and corresponds to the axis of the fifth elastic support. The eighth finite element node corresponds to the axial symmetry plane of the low-pressure turbine disk. The seventh finite element node is located on one side of the inner end face of the low-pressure turbine disk and corresponds to the axis of the fourth intermediate support. The second... The finite element node, the third finite element node, and the fourth finite element node are respectively located between the inner end face of the low-pressure fan disk and the end face of the adjacent high-pressure rotor shaft. The second finite element node corresponds to the axis of the second rigid support, the third finite element node corresponds to the axis of the second rigid support, and the fourth finite element node corresponds to the axis of the third elastic support. When the distance between the fourth finite element node and the seventh finite element node is 1 / 4 of the total length of the low-pressure rotor shaft, a fifth finite element node and a sixth finite element node are provided between the fourth finite element node and the seventh finite element node, and the distance between the fifth finite element node and the sixth finite element node is 1 / 8 to 1 / 10 of the total length of the low-pressure rotor shaft.

3. The accommodative modal optimization design method for a dual-rotor system with intermediate bearings as described in claim 1, characterized in that, The range of values ​​for the independent variable of the axis element determined in step 3 is as follows: The determined range of values ​​for the independent variables of each axis element is as follows: The length of the distance between each adjacent finite element node: The distance between the first and second finite element nodes is 40.00–60.00 mm; the distance between the second and third finite element nodes is 40.00–60.00 mm; the distance between the third and fourth finite element nodes is 40.00–60.00 mm; the distance between the fourth and fifth finite element nodes is 70.00–110.00 mm; the distance between the fifth and sixth finite element nodes is 60.00–90.00 mm; and the distance between the sixth and seventh finite element nodes is 60.00–90.00 mm. mm; the distance between the seventh and eighth finite element nodes is 40.00–60.00; the distance between the eighth and ninth finite element nodes is 40.00–60.00; the distance between the tenth and eleventh finite element nodes is 40.00–60.00; the distance between the eleventh and twelfth finite element nodes is 60.00–90.00; the distance between the twelfth and thirteenth finite element nodes is 60.00–90.00; the distance between the thirteenth and fourteenth finite element nodes is 60.00–90.

00. The inner radius of the low-pressure rotor shaft element ranges from 5.00 to 8.00 mm, and the outer radius ranges from 13.00 to 17.00 mm; the inner radius of the high-pressure rotor shaft element is determined to range from 515.00 to 24.00 mm, and the outer radius ranges from 22.00 to 28.00 mm.

4. The accommodative modal optimization design method for a dual-rotor system with intermediate bearings as described in claim 1, characterized in that, The ranges of disk parameter values ​​determined in step 3 are as follows: The low-pressure fan disc has a mass of 4.00–6.00 kg and a polar moment of inertia of 240.00–280.00 / 10. -4 kg·m 2 The moment of inertia about the diameter is 120.00~140.00 / 10 -4 kg·m 2 ; The low-pressure turbine disk has a mass of 4.00–6.00 kg and a polar moment of inertia of 240.00–280.00 / 10. -4 kg·m 2 The moment of inertia about the diameter is 120.00~140.00 / 10 -4 kg·m 2 ; The mass of the high-pressure compressor disc is 2.00–4.00 kg, and its polar moment of inertia is 90.00–180.00 / 10. -4 kg·m 2 The moment of inertia about the diameter is 45.00~90.000 / 10 -4 kg·m 2 ; The mass of the high-pressure turbine disk is 2.00–4.00 kg, and the polar moment of inertia is 90.00–180.00 / 10. -4 kg·m 2 The moment of inertia about the diameter is 45.00~90.000 / 10 -4 kg·m 2 .

5. The accommodative modal optimization design method for a dual-rotor system with intermediate bearings as described in claim 1, characterized in that, The parameter ranges for each support determined in step 3 are as follows: The stiffness of the first elastic support is 5 × 10⁻⁶. 5 ~1×10 7 / N·m -1 Damping is 2000 N·s·m -1 ; The stiffness of the second rigid support is 1×10. 7 ~5×10 9 / N·m -1 The damping is 300 N·s·m -1 ; The stiffness of the third elastic support is 5×10. 5 ~1×10 7 / N·m -1 Damping is 1000 N·s·m -1 ; The stiffness of the fourth intermediate support is 1×10. 7 ~5×10 9 / N·m -1 The damping is 300 N·s·m -1 ; The stiffness of the fifth elastic support is 5 × 10⁻⁶. 5 ~1×10 7 / N·m -1 Damping is 2000 N·s·m -1 .

6. The accommodative modal optimization design method for a dual-rotor system with intermediate bearings as described in claim 1, characterized in that, In step 4, the modal tolerance evaluation function f of the i-th order mode of the low-voltage excitation of the dual rotor system with intermediate bearing in equation (34) is... Lito The expression is as follows: In equation (35), The percentage of total strain energy of the elastic support in the i-th mode under low-pressure excitation is the sum of the strain energy percentages of the first, third, and fifth elastic supports. This is the evaluation function for the proportion of intermediate support strain energy in the i-th order mode under low-pressure excitation. The unbalance influence factor for the i-th mode under low-voltage excitation; The proportion of total elastic support strain energy in the i-th order mode of low-pressure excitation as described in equation (35) The expression is: In equation (36), The total strain energy of the elastic support in the i-th mode under low-pressure excitation is... The total strain energy of the rigid support under low-pressure excitation in the i-th mode is... The strain energy of the intermediate support for the i-th mode under low-pressure excitation. and These are the strain energies of the high-pressure rotor shaft and the low-pressure rotor shaft under the i-th mode of low-pressure excitation, respectively. The intermediate support is the fourth intermediate support; the elastic support is the first elastic support, the third elastic support, and the fifth elastic support; the rigid support is the second rigid support. The total strain energy of the i-th modal elastic support under low-pressure excitation described in equation (36) The expression is as follows: In equation (37): W is the number of elastic supports in the finite element model of the dual rotor system with intermediate bearing described in step 1, which is 3; Let a be the stiffness of the a-th elastic support, when a = 1. The stiffness of the first elastic support; when a = 2, The stiffness of the third elastic support; when a = 3, The stiffness of the fifth elastic support; r Li,eb,a This represents the normalized displacement at the a-th elastic support in the i-th mode shape under low-pressure excitation; when a = 1, r Li,eb,1 This represents the normalized displacement at the first elastic support in the i-th mode of vibration under low-pressure excitation; when a = 2, r Li,eb,2 This represents the normalized displacement at the third elastic support in the i-th mode of vibration under low-pressure excitation; when a = 3, r Li,eb,3 This represents the normalized displacement at the fifth elastic support in the i-th mode shape under low-pressure excitation; the normalized displacement is obtained by substituting the input conditions described in step 1 and the independent variables described in step 2 into the finite element method. The total strain energy of the i-th mode rigid support under low-pressure excitation described in equation (36) The expression is as follows: In equation (38), Z represents the number of rigid supports in the finite element model of the dual rotor system with intermediate bearing described in step 1, which is 1; The stiffness of the second rigid support; r Li,rb,b This represents the normalized displacement at the second rigid support in the i-th order mode of low-voltage excitation. The low-pressure excitation intermediate support strain energy of the i-th mode of the intermediate support described in equation (36) The expression is as follows: In equation (39), S in For the stiffness of the intermediate support, r Li,in Normalized displacement at the intermediate support; The strain energy of the high-pressure rotor shaft under the i-th mode of low-pressure excitation as described in equation (36) The expression is as follows: In equation (40) Φ Li The i-th mode shape vector under low-voltage excitation is obtained by substituting the input conditions described in step 1 and the independent variables described in step 2 into the finite element method; S HP The stiffness matrix of the high-pressure rotor shaft is obtained by substituting the input conditions described in step 1 and the independent variables described in step 2 into the finite element method. The strain energy of the low-pressure rotor shaft under the i-th mode of low-pressure excitation as described in equation (36) The expression is as follows: In equation (41), S is... LP The stiffness matrix of the low-pressure rotor shaft is obtained by substituting the input conditions described in step 1 and the independent variables described in step 2 into the finite element method. Equation (35) is the evaluation function for the intermediate support strain energy of the i-th order mode under low-pressure excitation. The expression is as follows: In equation (42), σ in The limit for the proportion of strain energy in intermediate supports is 1%. The proportion of intermediate support strain energy in the i-th mode under low-pressure excitation is expressed as follows: The imbalance influence factor of the i-th order mode of low-voltage excitation described in equation (35) The expression is as follows: In equation (44), M is the number of low-pressure rotor finite element nodes in the finite element model of the dual rotor system with intermediate bearing described in step 1, which is 9; r L (i,k) represents the normalized displacement of the low-pressure rotor at the k-th finite element node in the i-th mode shape of low-pressure excitation; a i,k This represents the unbalance weighting coefficient at the k-th finite element node in the i-th order mode of low-pressure excitation, with a value range of [0,1]. When there is a constant unbalance on a finite element node, the unbalance weight coefficient of that finite element node is taken as 1. When a finite element node can achieve high-precision dynamic balancing, the unbalance weight coefficient of that finite element node is set to 0; the value is 0 for the first finite element node and the ninth finite element node, and 1 for the remaining low-pressure rotor finite element nodes. The modal tolerance evaluation function f of the high-voltage excitation g-th mode of the dual-rotor system with intermediate bearing described in equation (34) hgto The expression is as follows: In equation (45), This represents the proportion of the total strain energy of the elastic support during the g-th mode under high pressure excitation. Let be the evaluation function for the proportion of strain energy in the intermediate support during the g-th mode of high-pressure excitation. The unbalance influence factor of the g-th mode under high pressure excitation; The proportion of total strain energy of the elastic support in the g-th mode of high-pressure excitation as described in equation (45) The expression is: In equation (46), The total strain energy of the elastic support in the g-th mode under high pressure excitation. The total strain energy of the rigid support under high-pressure excitation in the g-th mode is given by [the relevant data]. The strain energy of the intermediate support in the high-pressure excitation of the g-th mode is given. and These are the strain energies of the high-pressure rotor shaft and the low-pressure rotor shaft under the g-th mode of high-pressure excitation, respectively. The intermediate support is the fourth intermediate support; the elastic support is the first elastic support, the third elastic support, and the fifth elastic support; the rigid support is the second rigid support. The total strain energy of the elastic support in the g-th mode under high pressure excitation described in equation (46) The expression is as follows: In equation (20), r hg,eb,a This represents the normalized displacement at the a-th elastic support in the g-th mode shape under high-pressure excitation. When a = 1, r hg,eb,1 This represents the normalized displacement at the first elastic support in the i-th mode shape under high-pressure excitation; when a = 2, r hg,eb,2 This represents the normalized displacement at the third elastic support in the i-th mode shape under high-pressure excitation; when a = 3, r hg,eb,3 This represents the normalized displacement at the fifth elastic support in the i-th order mode of high-pressure excitation. The total strain energy of the rigid support in the g-th mode under high pressure excitation described in equation (46) The expression is as follows: In equation (48), r hg,rb,b This represents the normalized displacement at the second rigid support in the g-th mode shape of high-pressure excitation; The strain energy of the intermediate support in the g-th mode of high-pressure excitation described in equation (46) The expression is as follows: In equation (49), r hg,in This represents the normalized displacement at the fourth intermediate support. The strain energy of the high-pressure rotor shaft under the g-th mode of high-pressure excitation as described in equation (46) The expression is as follows: In equation (50) Φ hg The g-th mode shape vector of high-pressure excitation is obtained by substituting the input conditions described in step 1 and the independent variables described in step 2 into the finite element method. The strain energy of the low-pressure rotor shaft under the g-th mode of high-pressure excitation as described in equation (46) The expression is as follows: The intermediate support strain energy evaluation function for the g-th mode of high-pressure excitation described in equation (51) The expression is as follows: In formula (52) The proportion of intermediate support strain energy in the g-th mode under high pressure excitation is expressed as follows: The unbalance influence factor of the g-th mode of high-pressure excitation described in equation (53) The expression is as follows: In equation (54), N is the number of high-pressure rotor finite element nodes in the finite element model of the dual rotor system with intermediate bearing described in step 1, which is 5; r h (g,k) represents the normalized displacement of the high-pressure rotor at the j-th finite element node in the g-th mode shape of high-pressure excitation; b g,k This represents the unbalance weighting coefficient at the j-th finite element node in the g-th mode shape under high pressure excitation, with a value range of [0,1]. When there is a constant unbalance on a finite element node, the unbalance weight coefficient of that finite element node is taken as 1. When a finite element node can achieve high-precision dynamic balancing, the unbalance weight coefficient of that finite element node is set to 0; all high-pressure rotor finite element nodes are set to 1.

7. The accommodative modal optimization design method for a dual-rotor system with intermediate bearings as described in claim 1, characterized in that, The genetic algorithm parameters determined in step 5 are: 80 generations, 5 population size, 50 individuals, migration rate of 0.2, generation gap of 0.9, crossover probability of 0.7, and mutation probability of 0.

1.

8. The accommodative modal optimization design method for a dual-rotor system with intermediate bearings as described in claim 1, characterized in that, In step 7, the lengths of each axis element are determined as follows: The optimized parameters for the determined axis element are as follows: i. The distance between adjacent finite element nodes in each axis element, the inner and outer radii of the high-pressure rotor shaft, and the inner and outer radii of the low-pressure rotor shaft are respectively: The distance between the first finite element node and the second finite element node is 45.97 mm; the inner radius is 6.72 mm. The outer radius is 15.63 mm; The distance between the second and third finite element nodes is 59.39 mm; the inner radius is 7.57 mm. The outer radius is 5.96 mm; The distance between the third and fourth finite element nodes is 40.64 mm; the inner radius is 6.58 mm. The outer radius is 14.76 mm; The distance between the fourth and fifth finite element nodes is 106.68 mm; the inner radius is 7.25 mm. The outer radius is 113.88 mm; The distance between the fifth and sixth finite element nodes is 78.71 mm; the inner radius is 5.90 mm; and the outer radius is 16.44 mm. The distance between the sixth and seventh finite element nodes is 82.28 mm; the inner radius is 6.37 mm; and the outer radius is 13.88 mm. The distance between the seventh and eighth finite element nodes is 56.94 mm; the inner radius is 7.12 mm; and the outer radius is 15.79 mm. The distance between the eighth and ninth finite element nodes is 48.39 mm; the inner radius is 6.90 mm; and the outer radius is 15.13 mm. The distance between the tenth and eleventh finite element nodes is 40.89 mm; the inner radius is 20.57 mm; and the outer radius is 24.71 mm. The distance between the eleventh and twelfth finite element nodes is 65.83 mm; the inner radius is 20.88 mm; and the outer radius is 26.88 mm. The distance between the twelfth and thirteenth finite element nodes is 74.99 mm; the inner radius is 18.72 mm; and the outer radius is 22.93 mm. The distance between the thirteenth and fourteenth finite element nodes is 58.56 mm; the inner radius is 19.90 mm; and the outer radius is 27.18 mm. ii. The determined optimized values ​​for the disk parameters are: The low-pressure fan disc has a mass of 4.62 kg and a polar moment of inertia of 255.96 / 10. -4 kg·m 2 The moment of inertia about the diameter is 127.98 / 10. -4 kg·m 2 ; The low-pressure turbine disk has a mass of 4.04 kg and a polar moment of inertia of 195.460 / 10. -4 kg·m 2 The moment of inertia about the diameter is 97.73 / 10. -4 kg·m 2 ; The mass of the high-pressure compressor disc is 3.66 kg, and its polar moment of inertia is 161.56 / 10. -4 kg·m 2 The moment of inertia about the diameter is 80.72 / 10. -4 kg·m 2 ; The high-pressure turbine disk has a mass of 2.31 kg and a polar moment of inertia of 98.67 / 10. -4 kg·m 2 The moment of inertia about the diameter is 49.33 / 10. -4 kg·m 2 ; The parameter ranges for each support, as determined in iii, are as follows: The stiffness of the first elastic support is 4.66 × 10⁻⁶. 6 / N·m -1 Damping is 2000 N·s·m -1 ; The stiffness of the second rigid support is 7.23 × 10⁻⁶. 7 / N·m -1 The damping is 300 N·s·m -1 ; The stiffness of the third elastic support is 5.00 × 10⁻⁶. 5 / N·m -1 Damping is 1000 N·s·m -1 ; The stiffness of the fourth intermediate support is 5.21 × 10⁻⁶. 7 / N·m -1 The damping is 300 N·s·m -1 ; The stiffness of the fifth elastic support is 9.06 × 10⁻⁶. 6 / N·m -1 Damping is 2000 N·s·m -1 .

9. The accommodative modal optimization design method for a dual-rotor system with intermediate bearings as described in claim 1, characterized in that, In step 7, the modal tolerance evaluation function for each mode is: The tolerance evaluation function for the first mode under low-voltage excitation is 0.98; The tolerance evaluation function for the second-order mode under low-voltage excitation is 0.85; The tolerance evaluation function for the third mode under low-voltage excitation is 0.92; The tolerance evaluation function for the first-order mode under high-pressure excitation is 0.99; The tolerance evaluation function for the second-order mode under high-pressure excitation is 0.87; The tolerance evaluation function for the third-order mode under high-pressure excitation is 0.91.

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