CN104573199A - Topological optimization method for constraining and damping blades of aeroengine - Google Patents

Abstract

The invention relates to a topological optimization method for constraining and damping blades of an aeroengine. The method comprises the following steps: taking lightweight aluminum foil as a constraining material, sequentially sticking a viscoelastic material and the constraining material onto the surface of each blade of the aeroengine, carrying out constraining and damping processing on the blades, and establishing finite element models of the constrained and damped blades; carrying out modal analysis on the constrained and damped blades according to the finite element models of the constrained and damped blades, and filtering sensitivity of constrained and damped cell units by adopting an independent grid filtering technology; solving an optimization model by adopting an asymptotic optimization algorithm, programming an optimization program, searching for the optimal layout of a constraining and damping material on each blade, and cutting and regularizing optimized layout, so as to adapt to engineering application. The method has the advantages that the aim of achieving the maximal aeroengine blade damping vibration reduction effect with the minimal damping material additionally-added amount is realized, so that the vibration stress of the blades of the aeroengine is remarkably lowered, and the fatigue damage resistance of the blades is improved.

Description

A kind of Topology Optimization Method of damping-constraining blade of aviation engine

Technical field

The present invention relates to constrained damping structure Optimization Design, particularly a kind of Topology Optimization Method of damping-constraining blade of aviation engine.

Background technology

The structural intergrity of blade of aviation engine is the key of aeromotor security of operation, and along with the increase of aeromotor thrust-weight ratio, the vibration stress of blade increases, and Fatigue Damage Problem is outstanding day by day.At present, many forms such as employing damping shroud or dry-friction damping etc., increase blade damping, reduce blade vibration stress.Constrained damping structure, as a kind of version of effective increase damping, has the simple and efficient feature of process.

The general all standing of traditional constraints damping, in the surface of pending structure, although effectively can increase structural damping, considerably increases additional mass, is unfavorable for the lightweight of aeromotor.

Summary of the invention

The object of the invention is is the optimization of material collocation method proposing the process of a kind of blade of aviation engine damping-constraining, for the target order optimized and constraint damping material use amount, sets up the Topological optimization model of aeromotor damping-constraining blade.Adopt gradual optimization algorithm, the damping-constraining material layout on blade is optimized.By optimizing, with minimum damping-constraining material additional mass, significantly reducing the vibration stress of blade of aviation engine, reaching best damping vibration attenuation effect.

The invention provides a kind of Topology Optimization Method of damping-constraining blade of aviation engine, it is characterized in that: the Topology Optimization Method of described damping-constraining blade of aviation engine, adopt lightweight aluminium foil as constraint material, viscoelastic material and constraint material is pasted successively on the surface at blade of aviation engine, damping-constraining process is carried out to blade, sets up the finite element model of damping-constraining blade;

Determine target order and the constraint damping material use amount of optimization, set up the Topological optimization model of damping-constraining blade:

$\left\{\begin{array}{c}\mathrm{find}:x_i,i=\mathrm{1,2}...n\\ \min :{\mathrm{\η}}_r,r=\mathrm{1,2,3}.\\ s.t:\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}_i{M}_i-M^{*}\≤0\\ 0\≤x_i\≤1,i=1,...n\end{array}\right.$

Wherein, x _ifor design variable, η _rfor the modal loss factor on r rank, M _ifor the quality of damping-constraining born of the same parents unit, M ^*for the use amount of damping-constraining material;

According to the finite element model of damping-constraining blade, model analysis is carried out to damping-constraining blade, adopt Sensitivity Analysis Method, calculate the modal loss factor sensitivity of each damping-constraining born of the same parents unit, adopt the sensitivity of independent grid filtering technique to damping-constraining born of the same parents unit to carry out filtering;

Adopt gradual optimization algorithm, solving-optimizing model, establishment optimizer, searches the optimal location of damping-constraining material on blade, and carries out cutting and regular to optimizing distribution, with applicable engineer applied.

The finite element model of the damping-constraining blade of described foundation, adopts the hybridised units of four nodes.

Described design variable x _ifor damping-constraining born of the same parents unit existence whether, its value is that { 0,1} works as x _iwhen=0, represent that damping-constraining born of the same parents unit i is deleted; Work as x _iwhen=1, represent damping-constraining born of the same parents unit i place, be coated with damping-constraining material, the initial value of design variable is 1.

The modal loss factor Calculation of Sensitivity formula of described damping-constraining born of the same parents unit is:

According to modal strain energy method, the r rank modal loss factor of constrained damping structure is calculated as follows:

${\mathrm{\η}}_r={\mathrm{\η}}_v\frac{U_{\mathrm{vr}}}{U_r}$

Wherein, η _vfor the dissipation factor of damping material; U _vrand U _rbe respectively damping material strain energy and the constrained damping structure total strain energy of r rank mode;

Make η _rto design variable x _iask local derviation, r rank modal loss factor is to design variable x _isensitivity expression formula be:

$\frac{\∂\left({\mathrm{\η}}_r\right)}{\∂x_i}={\mathrm{\η}}_v\frac{U_{\mathrm{vri}}^e{U}_r-(U_{\mathrm{cri}}^e+U_{\mathrm{vri}}^e)U_{\mathrm{vr}}}{U_r^2}$

In formula, with be respectively the modal strain energy of the modal strain energy of the damping unit i of r rank mode and restraint layer unit corresponding to damping unit i.

The present invention adopts topological optimization technology, for the target order optimized and damping-constraining materials'use amount, damping-constraining material layout on blade of aviation engine is optimized, makes that the additional mass of blade is minimum, modal loss factor is maximum, vibration stress is minimum, damping vibration attenuation best results.

Advantage of the present invention:

The Topology Optimization Method of damping-constraining blade of aviation engine of the present invention, adopt topological optimization technology, for the target order optimized and constraint damping material use amount, target is turned to so that modal loss factor is maximum, set up blade of aviation engine damping-constraining material layout Optimized model, adopt gradual optimization algorithm, establishment Optimization Calculation Program, obtain the optimal location of damping-constraining material on blade, achieve with minimum damping material additional mass, reach the target of maximum blade of aviation engine damping vibration attenuation effect, the vibration stress of blade of aviation engine is significantly declined, improve the ability of blade antifatigue damage.

Accompanying drawing explanation

Below in conjunction with drawings and the embodiments, the present invention is further detailed explanation:

Fig. 1 is the damping-constraining blade after optimizing;

Fig. 2 is three-dimensional spectrum, excitation air pressure 0.20MPa, blade;

Fig. 3 is three-dimensional spectrum, the damping-constraining blade after excitation air pressure 0.20MPa, optimization.

Embodiment

Embodiment 1

Present embodiments provide a kind of Topology Optimization Method of damping-constraining blade of aviation engine, it is characterized in that: the Topology Optimization Method of described damping-constraining blade of aviation engine, adopt lightweight aluminium foil as constraint material, viscoelastic material and constraint material is pasted successively on the surface at blade of aviation engine, damping-constraining process is carried out to blade, sets up the finite element model of damping-constraining blade;

Determine target order and the constraint damping material use amount of optimization, set up the Topological optimization model of damping-constraining blade:

$\left\{\begin{array}{c}\mathrm{find}:x_i,i=\mathrm{1,2}...n\\ \min :{\mathrm{\η}}_r,r=\mathrm{1,2,3}.\\ s.t:\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}_i{M}_i-M^{*}\≤0\\ 0\≤x_i\≤1,i=1,...n\end{array}\right.$

Wherein, x _ifor design variable, η _rfor the modal loss factor on r rank, M _ifor the quality of damping-constraining born of the same parents unit, M ^*for the use amount of damping-constraining material;

According to the finite element model of damping-constraining blade, model analysis is carried out to damping-constraining blade, adopt Sensitivity Analysis Method, calculate the modal loss factor sensitivity of each damping-constraining born of the same parents unit, adopt the sensitivity of independent grid filtering technique to damping-constraining born of the same parents unit to carry out filtering;

Adopt gradual optimization algorithm, solving-optimizing model, establishment optimizer, searches the optimal location of damping-constraining material on blade, and carries out cutting and regular to optimizing distribution, with applicable engineer applied.

The finite element model of the damping-constraining blade of described foundation, adopts the hybridised units of four nodes.

Described design variable x _ifor damping-constraining born of the same parents unit existence whether, its value is that { 0,1} works as x _iwhen=0, represent that damping-constraining born of the same parents unit i is deleted; Work as x _iwhen=1, represent damping-constraining born of the same parents unit i place, be coated with damping-constraining material, the initial value of design variable is 1.

The modal loss factor Calculation of Sensitivity formula of described damping-constraining born of the same parents unit is:

According to modal strain energy method, the r rank modal loss factor of constrained damping structure is calculated as follows:

${\mathrm{\η}}_r={\mathrm{\η}}_v\frac{U_{\mathrm{vr}}}{U_r}$

Wherein, η _vfor the dissipation factor of damping material; U _vrand U _rbe respectively damping material strain energy and the constrained damping structure total strain energy of r rank mode;

Make η _rto design variable x _iask local derviation, r rank modal loss factor is to design variable x _isensitivity expression formula be:

$\frac{\∂\left({\mathrm{\η}}_r\right)}{\∂x_i}={\mathrm{\η}}_v\frac{U_{\mathrm{vri}}^e{U}_r-(U_{\mathrm{cri}}^e+U_{\mathrm{vri}}^e)U_{\mathrm{vr}}}{U_r^2}$

In formula, with be respectively the modal strain energy of the modal strain energy of the damping unit i of r rank mode and restraint layer unit corresponding to damping unit i.

The present invention adopts topological optimization technology, for the target order optimized and damping-constraining materials'use amount, damping-constraining material layout on blade of aviation engine is optimized, makes that the additional mass of blade is minimum, modal loss factor is maximum, vibration stress is minimum, damping vibration attenuation best results.

Claims (4)

1. the Topology Optimization Method of a damping-constraining blade of aviation engine, it is characterized in that: the Topology Optimization Method of described damping-constraining blade of aviation engine, adopt lightweight aluminium foil as constraint material, viscoelastic material and constraint material is pasted successively on the surface at blade of aviation engine, damping-constraining process is carried out to blade, sets up the finite element model of damping-constraining blade;

Determine target order and the constraint damping material use amount of optimization, set up the Topological optimization model of damping-constraining blade:

$\left\{\begin{array}{c}\mathrm{find}:x_i,i=\mathrm{1,2}...n\\ \min :{\mathrm{\η}}_r,r=\mathrm{1,2,3}.\\ s.t:\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}_i{M}_i-M^{*}\≤0\\ 0\≤x_i\≤1,i=1,...n\end{array}\right.$

Wherein, x _ifor design variable, η _rfor the modal loss factor on r rank, M _ifor the quality of damping-constraining born of the same parents unit, M ^*for the use amount of damping-constraining material;

According to the finite element model of damping-constraining blade, model analysis is carried out to damping-constraining blade, adopt Sensitivity Analysis Method, calculate the modal loss factor sensitivity of each damping-constraining born of the same parents unit, adopt the sensitivity of independent grid filtering technique to damping-constraining born of the same parents unit to carry out filtering;

Adopt gradual optimization algorithm, solving-optimizing model, establishment optimizer, searches the optimal location of damping-constraining material on blade, and carries out cutting and regular to optimizing distribution, with applicable engineer applied.

2. according to the Topology Optimization Method of damping-constraining blade of aviation engine according to claim 1, it is characterized in that: the finite element model of the damping-constraining blade of described foundation, adopts the hybridised units of four nodes.

3. according to the Topology Optimization Method of damping-constraining blade of aviation engine according to claim 1, it is characterized in that: described design variable x _ifor damping-constraining born of the same parents unit existence whether, its value is that { 0,1} works as x _iwhen=0, represent that damping-constraining born of the same parents unit i is deleted; Work as x _iwhen=1, represent damping-constraining born of the same parents unit i place, be coated with damping-constraining material, the initial value of design variable is 1.

4. according to the Topology Optimization Method of damping-constraining blade of aviation engine according to claim 1, it is characterized in that: the modal loss factor Calculation of Sensitivity formula of described damping-constraining born of the same parents unit is:

According to modal strain energy method, the r rank modal loss factor of constrained damping structure is calculated as follows:

${\mathrm{\η}}_r={\mathrm{\η}}_v\frac{U_{\mathrm{vr}}}{U_r}$

Wherein, η _vfor the dissipation factor of damping material; U _vrand U _rbe respectively damping material strain energy and the constrained damping structure total strain energy of r rank mode;

Make η _rto design variable x _iask local derviation, r rank modal loss factor is to design variable x _isensitivity expression formula be:

$\frac{\∂\left({\mathrm{\η}}_r\right)}{{\∂x}_i}={\mathrm{\η}}_v\frac{U_{\mathrm{vri}}^e{U}_r-(U_{\mathrm{cri}}^e+U_{\mathrm{vri}}^e)U_{\mathrm{vr}}}{U_r^2}$

In formula, with be respectively the modal strain energy of the modal strain energy of the damping unit i of r rank mode and restraint layer unit corresponding to damping unit i.