CN113312705A - Method for sequencing rotor blades of low-pressure fan of aircraft engine - Google Patents

Abstract

The invention discloses a method for sequencing rotor blades of a low-pressure fan of an aircraft engine. The method takes the mass moment of the rotor blade and the initial unbalance amount of the rotor as input, introduces annealing selection operation, and establishes a fan rotor blade sequencing model based on an annealing single-parent genetic algorithm. The method can obtain a result superior to that of the traditional genetic algorithm without manual fine adjustment, has high reliability and high optimization speed, is not easy to fall into local convergence, and is favorable for efficient, rapid and accurate fan rotor blade sequencing.

Description

Method for sequencing rotor blades of low-pressure fan of aircraft engine

Technical Field

The invention belongs to the technical field of aero-engines, and particularly relates to a blade sorting method of an aero-engine.

Background

In recent years, the assembly quality of the aeroengine in China has a great gap with the overseas in the aspect of control, and one of the core problems restricting the development of the engine at present is the vibration problem of a rotor structure rotating at a high speed. The unbalance of the rotor is the main reason for the vibration overrun of the engine during test run, and in order to avoid the unbalance phenomenon, the most fundamental measure is to change the arrangement sequence of the rotor blades, so that the centrifugal forces generated by the rotor blades are symmetrically distributed relative to the rotating shaft, the centrifugal forces in opposite directions are mutually offset, and the unbalance force is eliminated, thereby the rotor is balanced.

The application of genetic algorithm to compressor blade sequencing, aeronautics and dynamics, 2005, Vol20(3), p518-522 discloses a sequencing optimization method in compressor blade assembly based on genetic algorithm. The method is characterized in that n blades of the compressor are uniformly distributed on the edge of a disc, the edge of the disc is divided into m quadrants, the difference between the total mass of each quadrant blade and the total mass of the adjacent quadrant blade is not allowed to exceed a p (unit: g) value, the oscillation frequency difference between the two adjacent blades is not allowed to be smaller than a q (unit: hz) value, and the solution meeting the requirement is a feasible solution. On the basis, the smaller the variance of the quality difference between quadrants is, the larger the variance of the frequency difference between the blades is, and the optimal corresponding solution is. The method disclosed by the literature converts the blade ordering problem into a traveling salesman problem, and the conventional genetic algorithm is used for solving the blade ordering problem, so that the time consumption is long, the precision is not high, and local convergence often occurs; in addition, when the number of the blades is large, quadrant division is complicated, the requirement of the unbalance amount of the rotor is difficult to meet, and certain limitation is realized.

Disclosure of Invention

In order to overcome the defects of the prior art, the invention provides a method for sequencing rotor blades of a low-pressure fan of an aircraft engine. The method takes the mass moment of the rotor blade and the initial unbalance amount of the rotor as input, introduces annealing selection operation, and establishes a fan rotor blade sequencing model based on an annealing single-parent genetic algorithm. The method can obtain a result superior to that of the traditional genetic algorithm without manual fine adjustment, has high reliability and high optimization speed, is not easy to fall into local convergence, and is favorable for efficient, rapid and accurate fan rotor blade sequencing.

The technical scheme adopted by the invention for solving the technical problem comprises the following steps:

step 1: setting an initial population;

assuming that the number of rotor blades is N, the solution space S is expressed as a cyclically arranged combination of all blade sequences, i.e., S { (pi) }₁，π₂…π_N)|(π₁，π₂…π_N) A cyclic permutation of (1,2, … N), where each cyclic permutation represents a loop of N rotor blades, the initial solution being {1,2, … N-1, N };

based on the initial solution, randomly disorganizing the circularly arranged sequence, setting the times of exchanging the sequence, exchanging the sequence between u and v by optional sequence numbers u, v (u < v), wherein the new sequence at the moment is as follows: pi₁…π_u-1π_vπ_v-1…π_u+1π_uπ_v+1…π_N(ii) a Starting iteration by taking the N rotor blade individuals as initial points;

step 2: establishing a physical model of the mass moment of the rotor blade;

step 2-1: suppose the theoretical mass of blade i is m_iTheoretical radius of gyration of

The theoretical mass moment is therefore

The actual mass of blade i is m_i+Δm_iThe actual radius of gyration is

Actual mass moment of

Due to the fact that

So the latter item is omitted, then

Step 2-2: the sum of the mass moment vectors of the N rotor blades to the rotor rotation axis is

Ideally, the sum of the mass moment vectors of all the blades about the axis of rotation is 0, i.e. the

Will be provided with

Finally simplified into

Step 2-3: let the initial unbalance of the rotor be

Combining the sum of the moment vectors of the blade masses in the step 2-2, the final unbalance model of the rotor is

And step 3: designing a fitness function;

the residual unbalance amount of the rotor after the blades are sequenced is used as an evaluation index, and a fitness function is designed to be

And 4, step 4: setting the initial temperature T₀Maximum genetic algebra itercount;

and 5: judging whether the current algebra is smaller than the maximum genetic algebra, if so, turning to a step 6, otherwise, stopping circulation, and turning to a step 9;

step 6: performing temperature reduction operation;

setting the temperature T at the beginning of a genetic iteration₀The following cooling mode is adopted:

T(t+1)＝k×T(t)

in the formula: t is the number of recorded iterations; k is an integer and the value interval is [0.9,0.95 ];

when the maximum genetic generation number is itercount, the final temperature is T_uAnd then k is:

and 7: performing cross mutation operation on the current population, and receiving new individuals according to the annealing selection probability, namely setting the probability that one filial individual replaces a parent individual;

if the parent individual is x, the child individual is x', and T is the current temperature, the replacement probability is:

and 8: saving the individual with the minimum fitness function value of the past generation, namely the optimal individual, and storing the optimal individual in the vector bestInividual; before the next iteration, comparing the stored optimal individual with the current optimal individual, if the value of the bestIndvial is smaller than that of the current optimal individual, replacing the worst individual in the population with the bestIndvial, and continuing to step 5;

and step 9: and outputting the blade sequencing result when the fitness is minimum.

The invention has the following beneficial effects:

the invention provides a method for establishing a blade sequencing model of an engine low-pressure fan rotor based on an annealing monadic genetic algorithm, which is characterized in that the blade sequencing model is established by adopting the annealing monadic genetic algorithm, so that a result superior to that of the traditional genetic algorithm can be obtained without manual fine adjustment, the reliability is higher, the optimization speed is high, the local convergence is not easy to occur, the occurrence of faults of the aero-engine rotor is reduced, and the method has good effectiveness and feasibility.

Drawings

FIG. 1 is a flow chart of the method of the present invention.

FIG. 2 is a schematic representation of an engine rotor blade sequencing in an embodiment of the present invention.

Detailed Description

The invention is further illustrated with reference to the following figures and examples.

A sequencing method for rotor blades of a low-pressure fan of an aircraft engine comprises the following steps:

step 1: setting an initial population;

assuming that the number of rotor blades is N, the solution space S is expressed as a cyclically arranged combination of all blade sequences, i.e., S { (pi) }₁，π₂…π_N)|(π₁，π₂…π_N) A cyclic permutation of (1,2, … N), where each cyclic permutation represents a loop of N rotor blades, the initial solution being {1,2, … N-1, N };

based on the initial solution, randomly disorganizing the circularly arranged sequence, setting the times of exchanging the sequence, exchanging the sequence between u and v by optional sequence numbers u, v (u < v), wherein the new sequence at the moment is as follows: pi₁…π_u-1π_vπ_v-1…π_u+1π_uπ_v+1…π_N(ii) a And the fitness is carried into the fitness function in the step three to calculate the fitness, and if the new fitness is smaller than the former fitness, the sequence is reserved. And repeating the steps until the required population number is obtained. In order to ensure the global search performance and the optimization speed of the algorithm, the diversity of the initial population must be ensured when initializing the population. On the premise of not neglecting any one leaf serial number, the diversity of the population can be ensured by ensuring that the number of individuals is large enough. Starting iteration by taking the N rotor blade individuals as initial points;

step 2: establishing a physical model of the mass moment of the rotor blade;

step 2-1: suppose the theoretical mass of blade i is m_iTheoretical radius of gyration of

The theoretical mass moment is therefore

The actual mass of blade i is m_i+Δm_iThe actual radius of gyration is

Actual mass moment of

Due to the fact that

So the latter item is omitted, then

Step 2-2: the sum of the mass moment vectors of the N rotor blades to the rotor rotation axis is

Ideally, the sum of the mass moment vectors of all the blades about the axis of rotation is 0, i.e. the

Will be provided with

Finally simplified into

Step 2-3: let the initial unbalance of the rotor be

Combining the sum of the moment vectors of the blade masses in the step 2-2, the final unbalance model of the rotor is

And step 3: designing a fitness function;

the residual unbalance of the rotor after the blade sequencing is used as an evaluation index, and the smaller the numerical value of the residual unbalance is, the better the sequencing result is.

The fitness function is designed as

And 4, step 4: setting the initial temperature T₀Maximum genetic algebra itercount;

and 5: judging whether the current algebra is smaller than the maximum genetic algebra, if so, turning to a step 6, otherwise, stopping circulation, and turning to a step 9;

step 6: performing temperature reduction operation;

setting the temperature T at the beginning of a genetic iteration₀The following cooling mode is adopted:

T(t+1)＝k×T(t)

in the formula: t is the number of recorded iterations; k is an integer slightly smaller than 1, and the value interval is [0.9,0.95 ]; and (3) gradually reducing the temperature in iteration, when the new individual is worse than the parent individual, receiving the new individual according to the replacement probability in the step (7), wherein the probability is gradually reduced, and at the later stage of iteration, because the temperature is very low, the replacement probability is almost 0 when the parent individual is worse than the parent individual.

When the maximum genetic generation number is itercount, the final temperature is T_uAnd then k is:

and 7: performing cross mutation operation on the current population, and receiving new individuals according to the annealing selection probability, namely setting the probability that one filial individual replaces a parent individual;

if the parent individual is x, the child individual is x', and T is the current temperature, the replacement probability is:

and 8: saving the individual with the minimum fitness function value of the past generation, namely the optimal individual, and storing the optimal individual in the vector bestInividual; before the next iteration, comparing the stored optimal individual with the current optimal individual, if the value of the bestIndvial is smaller than that of the current optimal individual, replacing the worst individual in the population with the bestIndvial, and continuing to step 5;

and step 9: and outputting the blade sequencing result when the fitness is minimum.

In summary, the following steps: the invention provides a method for establishing a blade sequencing model of an engine low-pressure fan rotor based on an annealing monadic genetic algorithm, which is characterized in that the blade sequencing model is established by adopting the annealing monadic genetic algorithm, so that a result superior to that of the traditional genetic algorithm can be obtained without manual fine adjustment, the reliability is higher, the optimization speed is high, the local convergence is not easy to occur, the occurrence of faults of the aero-engine rotor is reduced, and the method has good effectiveness and feasibility.

The method for establishing the blade sequencing model of the low-pressure fan rotor of the aero-engine based on the annealing single-parent genetic algorithm is utilized, and the blade sequencing model is established according to the assembly data of the low-pressure fan rotor of a certain enterprise.

The program of the annealing single parent genetic algorithm in the arithmetic example is realized based on Python programming language.

The final blade sequence is exemplified by a certain stage of rotor blade, and a schematic diagram is shown in fig. 2.

Claims (1)

1. A sequencing method for rotor blades of a low-pressure fan of an aircraft engine is characterized by comprising the following steps:

step 1: setting an initial population;

assuming that the number of rotor blades is N, the solution space S is expressed as a cyclically arranged combination of all blade sequences, i.e., S { (pi) }₁,π₂…π_N)|(π₁,π₂…π_N) A cyclic permutation of (1,2, … N), where each cyclic permutation represents a loop of N rotor blades, the initial solution being {1,2, … N-1, N };

based on the initial solution, randomly disorganizing the circularly arranged sequence, setting the times of exchanging the sequence, and selecting the sequence numbers u, v (u)<v) exchange the order between u and v, the new order at this time being: pi₁…π_u-1π_vπ_v-1…π_u+1π_uπ_v+1…π_N(ii) a Starting iteration by taking the N rotor blade individuals as initial points;

step 2: establishing a physical model of the mass moment of the rotor blade;

step 2-1: suppose the theoretical mass of blade i is m_iTheoretical radius of gyration of

The theoretical mass moment is therefore

The actual mass of blade i is m_i+Δm_iThe actual radius of gyration is

Actual mass moment of

Due to the fact that

So the latter item is omitted, then

Step 2-2: the sum of the mass moment vectors of the N rotor blades to the rotor rotation axis is

Ideally, the sum of the mass moment vectors of all the blades about the axis of rotation is 0, i.e. the

Will be provided with

Finally simplified into

Step 2-3: let the initial unbalance of the rotor be

Combining the sum of the moment vectors of the blade masses in the step 2-2, the final unbalance model of the rotor is

And step 3: designing a fitness function;

the residual unbalance amount of the rotor after the blades are sequenced is used as an evaluation index, and a fitness function is designed to be

And 4, step 4: setting the initial temperature T₀Maximum genetic algebra itercount;

and 5: judging whether the current algebra is smaller than the maximum genetic algebra, if so, turning to a step 6, otherwise, stopping circulation, and turning to a step 9;

step 6: performing temperature reduction operation;

setting the temperature T at the beginning of a genetic iteration₀The following cooling mode is adopted:

T(t+1)＝k×T(t)

in the formula: t is the number of recorded iterations; k is an integer and the value interval is [0.9,0.95 ];

when the maximum genetic generation number is itercount, the final temperature is T_uAnd then k is:

and 7: performing cross mutation operation on the current population, and receiving new individuals according to the annealing selection probability, namely setting the probability that one filial individual replaces a parent individual;

if the parent individual is x, the child individual is x', and T is the current temperature, the replacement probability is:

and 8: saving the individual with the minimum fitness function value of the past generation, namely the optimal individual, and storing the optimal individual in the vector bestInividual; before the next iteration, comparing the stored optimal individual with the current optimal individual, if the value of the bestIndvial is smaller than that of the current optimal individual, replacing the worst individual in the population with the bestIndvial, and continuing to step 5;

and step 9: and outputting the blade sequencing result when the fitness is minimum.

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