CN115422671A - Multi-rotating-speed virtual assembly balance optimization method for rotary machine multi-stage rotor system - Google Patents

Multi-rotating-speed virtual assembly balance optimization method for rotary machine multi-stage rotor system Download PDF

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CN115422671A
CN115422671A CN202210997108.7A CN202210997108A CN115422671A CN 115422671 A CN115422671 A CN 115422671A CN 202210997108 A CN202210997108 A CN 202210997108A CN 115422671 A CN115422671 A CN 115422671A
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rotor system
rotating
stage
speed
rotor
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杨丰宇
徐雷
赵凯
常宏坤
潘海
姚剑飞
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AECC Guiyang Engine Design Research Institute
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Abstract

The invention discloses a multi-rotating-speed virtual assembly balance optimization method for a rotary machine multi-stage rotor system, which is based on a heuristic optimization algorithm. In the assembly process, virtual assembly is realized through simulation according to the balance requirement of the front-mounted rotor system multi-stage wheel disc and the multi-rotating-speed state, a balance optimization scheme is given according to calculation, initial unbalance distribution optimization of the multi-stage rotor system and maximum unbalance vibration minimization in the multi-rotating-speed state are finally realized, unbalance vibration response of the rotor system in the multi-rotating-speed state is accurately estimated, and the problem that the stability of the balance effect of parts or units is poor in the single rotating speed is solved.

Description

Multi-rotating-speed virtual assembly balance optimization method for rotary machine multistage rotor system
Technical Field
The invention relates to a multi-rotating speed virtual assembly balance optimization method for a multistage rotor system of a rotary machine, and belongs to the technical field of aero-engines.
Background
The design, manufacturing, assembly, etc. processes may all result in balancing problems for rotating mechanical rotor systems. When the rotor system is unbalanced, it becomes a main excitation source of the rotary mechanical vibration. For example, in a rotor system with a multi-stage disk structure of an aircraft engine (hereinafter referred to as "engine rotor system" or "rotor system"), unbalance amounts of the engine rotor system are accumulated from each stage of disk, and unbalance amounts on all the disks generate unbalanced forces and couples during operation. Meanwhile, the engine rotor system needs to stably work in a plurality of rotating speed states such as slow running, cruising, maximum rotating speed, boosting and the like. However, the balance state of the engine rotor system changes along with the change of the rotating speed state (vibration mode), and finally the transition to balance quality of the engine rotor system is influenced.
At present, most of engine rotor systems are balanced by parts or unit bodies at a single rotating speed, only one or two balancing planes are usually presented, the balancing requirements of a multistage rotor system at multiple rotating speeds are not considered in the balancing method, and the problem of poor stability of balancing effect exists.
Disclosure of Invention
In order to solve the technical problem, the invention provides a multi-rotating-speed virtual assembly balance optimization method for a rotary mechanical multi-stage rotor system.
The invention is realized by the following technical scheme.
The invention provides a multi-rotating speed virtual assembly balance optimization method for a rotary machine multi-stage rotor system, and relates to a multi-rotating speed virtual assembly balance optimization method for the rotary machine rotor system based on a heuristic optimization algorithm.
The method comprises the following steps:
s1: establishing a motion differential equation of a rotary mechanical rotor system, completing the design of the rotor system and obtaining a transmission matrix of the rotor system in a multi-rotating-speed state;
s2: establishing a mechanical model capable of accurately reflecting the dynamic characteristics of the rotor system by using finite element software or dynamic software;
s3: obtaining a transmission matrix of the rotary mechanical multistage rotor system in a multi-rotating-speed state;
s4: optimizing circumferential installation angles of unbalance amounts on various levels of wheel discs of the rotor system for adjustment;
s5: optimizing the maximum value minimization of the unbalanced vibration of the rotary mechanical rotor system in a multi-rotating speed state;
s6: the multi-rotating-speed virtual assembly balance optimization scheme of the rotary mechanical multi-stage rotor system is virtually assembled in a rotor system dynamic model, so that the unbalanced vibration response of the rotor system in a multi-rotating-speed state is accurately estimated.
The invention has the beneficial effects that: in the assembly process, virtual assembly is realized through simulation according to the balance requirement of the front-mounted rotor system multi-stage wheel disc and the multi-rotating-speed state, a balance optimization scheme is given according to calculation, initial unbalance distribution optimization of the multi-stage rotor system and maximum unbalance vibration minimization in the multi-rotating-speed state are finally realized, unbalance vibration response of the rotor system in the multi-rotating-speed state is accurately estimated, and the problem that the stability of the balance effect of parts or units is poor in the single rotating speed is solved.
Detailed Description
The technical solution of the present invention is further described below, but the scope of the claimed invention is not limited to the described.
The application relates to a multi-rotating-speed virtual assembly balance optimization method for a rotary machine multi-stage rotor system, in particular to a heuristic optimization algorithm-based multi-rotating-speed virtual assembly balance optimization method for the rotary machine rotor system, which comprises the following steps:
s1: and establishing a motion differential equation of a rotating mechanical rotor system.
Figure BDA0003805822310000031
In the formula (1), [ M ], [ G ], [ C ], [ K ] are respectively a mass matrix, a gyro matrix, a damping matrix and a rigidity matrix of the rotor system, { X } is the generalized displacement of the rotor system, and { F } is the unbalanced force of the rotor system.
Making the unbalanced force be
{F}＝uω 2 exp (j ω t) (2) in formula (2), u is the unbalance amount, and ω is the rotor speed. Forced vibration of the rotor system results when a certain stage of the disk of the rotor system is subjected to an unbalanced force F. The steady state response of the forced vibration of the rotor system is
{ X } = rexp (i ω t) (3) r in formula (3) is the rotor system imbalance response, and the equations (2) and (3) are substituted into the motion differential equation of the rotating machine rotor system to obtain the equation
([K]-ω 2 [M]+i([G]+[C])ω)·r＝uω 2 (4)
Order to
t＝ω 2 ([K]-ω 2 [M]+i([G]+[C])ω) -1 (5)
t is referred to as the transfer matrix of the rotating machine rotor system. Then
r = ut (6) by equation (5), t is related to the rotational speed ω and the stiffness matrix [ K ] of the rotor system]Quality matrix [ M ]]Gyro matrix G]And a damping matrix [ C ]]In connection with this, when the design of the rotor system is finalized, [ K ] is]、[M]、[G]、[C]It is determined that t is a function of the rotor speed omega, so that different rotor system speeds omega can be obtained i Corresponding transfer matrix t i . Will t i And combining according to the rotating speeds to obtain a transmission matrix T of the sub-rotating system in a multi-rotating-speed state.
S2: the method comprises the steps of setting nominal dimensions and material parameters according to a design drawing of a rotary mechanical rotor system, modeling according to actual working conditions of the rotary mechanical rotor system, establishing a rotor system dynamic model by utilizing finite element software or dynamic software, correcting the rotor system dynamic model by combining actual rotor system structural parameters and vibration response measurement data during specific operation in consideration of modeling errors and structural nonlinear factor influences, and finally obtaining a mechanical model capable of accurately reflecting rotor system dynamic characteristics.
S3: [ K ] for rotor systems by means of rotor system dynamics models]、[M]、[G]、[C]Reading, constructing a transmission matrix T containing different rotating speed states according to the formula (5), and distributing positions and unbalance on each stage of wheel disc of the rotor systemThe transmission matrix T is extracted from the arrangement position of the vibration sensor of the actual rotor system, and finally the transmission matrix T in the multi-rotating-speed state of the rotary mechanical multi-stage rotor system is obtained r Thus, formula (6) can be written as
R＝UT r (7) In the formula (7), R is the unbalanced vibration response of the multi-stage rotor system of the rotary machine in the multi-rotating speed state, and U is the unbalanced quantity U on each stage of wheel disc of the multi-stage rotor system of the rotary machine i And (4) forming.
S4: for a rotary mechanical rotor system with a multi-stage wheel disc structure, the unbalance amount of the rotary mechanical rotor system is superposed by the unbalance amount on each stage of wheel disc, and the unbalance amount of the single-stage wheel disc is strictly controlled during actual manufacturing, so that the first optimization target is to adjust the circumferential installation angle of the unbalance amount on each stage of wheel disc of a rotor in the assembling process, and thus the balance optimization target is achieved, namely the balance optimization target
Figure BDA0003805822310000051
Combined rotor system stage wheel disc unbalance sensitivity x i Optimally adjust (8), namely
Figure BDA0003805822310000052
S5: after the circumferential installation angle optimization of the unbalance amount on each level of wheel disc of the rotor system is completed, the optimization result is substituted into the formula (7), the unbalanced vibration response of the installation scheme of each level of wheel disc of the current rotor system under multiple rotating speeds can be obtained, and the second optimization target is the maximum value minimization of the unbalanced vibration of the rotary mechanical rotor system under the state of multiple rotating speeds due to different vibration modes of the rotor system under different rotating speeds, namely
min(max(R i ))＝min(max(U i T r )) (10)
S6: the multi-rotating-speed virtual assembly balance optimization of the rotary mechanical multistage rotor system is a multi-objective optimization problem, and two optimization objective functions are optimized and solved according to the layered optimization thought. In the assembly process, the circumferential installation angles of the unbalance amounts on the wheel discs of each stage of the rotor are adjusted to relate to space optimization, so that various solutions exist, and firstly, a first objective function is optimized and solved for many times through a heuristic algorithm to obtain an assembly optimization scheme solution set. And then substituting each scheme in the solution set of the assembly optimization scheme into a second objective function for calculation to obtain the unbalanced vibration response of the rotary mechanical rotor system corresponding to each assembly optimization scheme in the multi-rotating-speed state, screening the assembly optimization scheme according to the thought of minimizing the maximum unbalanced vibration value of the rotor system, and finally obtaining the multi-rotating-speed virtual assembly balance optimization scheme of the rotary mechanical multistage rotor system. And after a final assembly balance optimization scheme is selected, virtual assembly is carried out in a rotor system dynamic model, so that the unbalanced vibration response of the rotor system in a multi-rotation speed state can be accurately estimated.
In the assembly process, the balance requirements of the multistage wheel disc of the front rotor system and the balance requirements under the multi-rotating-speed state are met, virtual assembly is achieved through simulation, a balance optimization scheme is given according to calculation, initial unbalance distribution optimization of the multistage rotor system and maximum unbalance vibration minimization under the multi-rotating-speed state are finally achieved, and unbalance vibration response of the rotor system under the multi-rotating-speed state is accurately estimated.

Claims (7)

1. A multi-rotating-speed virtual assembly balance optimization method for a rotary machine multi-stage rotor system is characterized by being based on a heuristic optimization algorithm.
2. The multi-speed virtual assembly balance optimization method for the multistage rotor system of the rotating machine as claimed in claim 1, characterized by comprising the following steps:
s1: establishing a motion differential equation of a rotary mechanical rotor system, completing the design of the rotor system and obtaining a transmission matrix of the rotor system in a multi-rotating-speed state;
s2: establishing a mechanical model capable of accurately reflecting the dynamic characteristics of the rotor system by using finite element software or dynamic software;
s3: obtaining a transmission matrix of a rotary mechanical multistage rotor system in a multi-rotating-speed state;
s4: optimizing circumferential installation angles of unbalance amounts on various stages of wheel discs of the rotor system for adjustment;
s5: optimizing the maximum value minimization of the unbalance vibration of the rotary mechanical rotor system in a multi-rotating speed state;
s6: the multi-rotating-speed virtual assembly balance optimization scheme of the rotary mechanical multi-stage rotor system is virtually assembled in a rotor system dynamic model, so that the unbalanced vibration response of the rotor system in a multi-rotating-speed state is accurately estimated.
3. The method for optimizing the multi-speed virtual assembly balance of the multistage rotor system of the rotary machine according to claim 2, wherein the step S1 is as follows:
establishing a motion differential equation of a rotor system of the rotary machine;
Figure FDA0003805822300000011
in the formula (1), M, G, C and K are respectively a mass matrix, a gyro matrix, a damping matrix and a rigidity matrix of the rotor system, X is the generalized displacement of the rotor system, and F is the unbalanced force of the rotor system;
making the unbalanced force be
{F}＝uω 2 exp(jωt) (2)
In the formula (2), u is the unbalance amount, and omega is the rotor speed; when a certain stage of wheel disc of the rotor system is subjected to unbalanced force { F }, forced vibration of the system can be caused; the steady state response of the forced vibration of the rotor system is
{X}＝rexp(iωt) (3)
In the formula (3), r is the unbalance response of the rotor system, and the equations (2) and (3) are substituted into the motion differential equation of the rotor system of the rotary machine to obtain the equation
([K]-ω 2 [M]+i([G]+[C])ω)·r＝uω 2 (4)
Order to
t＝ω 2 ([K]-ω 2 [M]+i([G]+[C])ω)- 1 (5)
t is called a transfer matrix of the rotating mechanical rotor system; then
r＝ut (6)
It can be seen from the formula (5) that t is equal to the rotation speed omega of the rotor system, and the rigidity matrix [ K ]]Quality matrix [ M ]]Gyro matrix G]And a damping matrix [ C ]]In connection with this, when the design of the rotor system is finalized, [ K ] is]、[M]、[G]、[C]It is determined that t is a function of the rotor speed omega, so that different rotor system speeds omega can be obtained i Corresponding transfer matrix t i (ii) a Will t i And combining according to the rotating speeds to obtain a transfer matrix T of the sub-system in a multi-rotating-speed state.
4. The method for optimizing the multi-speed virtual assembly balance of the multistage rotor system of the rotary machine according to claim 2, wherein the step S2 is as follows:
the method comprises the steps of setting nominal dimensions and material parameters according to a design drawing of a rotary mechanical rotor system, modeling according to actual working conditions of the rotary mechanical rotor system, establishing a rotor system dynamic model by utilizing finite element software or dynamic software, correcting the rotor system dynamic model by combining actual rotor system structural parameters and vibration response measurement data during specific operation in consideration of modeling errors and structural nonlinear factor influences, and finally obtaining a mechanical model capable of accurately reflecting rotor system dynamic characteristics.
5. The method for optimizing the multi-speed virtual assembly balance of the multistage rotor system of the rotary machine according to claim 12, wherein the step S3 is:
[ K ] for rotor systems by means of rotor system dynamics models]、[M]、[G]、[C]Reading, constructing a transmission matrix T containing different rotation speed states according to the formula (5), and transmitting vibration of the actual rotor system according to the unbalance distribution position on each level of wheel disc of the rotor system and the actual vibration of the rotor systemThe sensor arrangement position extracts the transmission matrix T, and finally the transmission matrix T in the multi-rotating-speed state of the rotary mechanical multi-stage rotor system is obtained r Thus, the formula (6) can be written as
R＝UT r (7)
In the formula (7), R is the unbalanced vibration response of the multi-stage rotor system of the rotary machine in the multi-rotating-speed state, and U is the unbalanced amount U on each stage of wheel disc of the multi-stage rotor system of the rotary machine i And (4) forming.
6. The multi-speed virtual assembly balance optimization method for the multistage rotor system of the rotating machine according to claim 2, wherein the step S4 is:
for a rotary mechanical rotor system with a multi-stage wheel disc structure, the unbalance amount of the rotary mechanical rotor system is superposed by the unbalance amount on each stage of wheel disc, and the optimization target is to adjust the circumferential installation angle of the unbalance amount on each stage of wheel disc of the rotor in the assembling process so as to achieve the target of balance optimization, namely the target of balance optimization
Figure FDA0003805822300000041
Imbalance sensitivity x of each stage of wheel disc combined with rotor system i Optimally adjust (8), namely
Figure FDA0003805822300000042
7. The method for optimizing the multi-speed virtual assembly balance of the multistage rotor system of the rotary machine according to claim 2, wherein the step S5 is:
after the circumferential installation angle optimization of the unbalance amount on each stage of wheel disc of the rotor system is completed, the optimization result is substituted into the formula (7), the unbalance vibration response of the installation scheme of each stage of wheel disc of the current rotor system at a plurality of rotating speeds can be obtained, and the vibration mode of the rotor system is different under different rotating speeds, so that the second optimization target is the minimum of the unbalance vibration maximum value under the multi-rotating speed state of the rotary mechanical rotor system, namely
min(max(R i ))＝min(max(U i T r )) (10)。
CN202210997108.7A 2022-08-19 2022-08-19 Multi-rotating-speed virtual assembly balance optimization method for rotary machine multi-stage rotor system Pending CN115422671A (en)

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