CN102915388A - Object-oriented nonlinear and non-causal modeling and simulation method for rotor dynamics system - Google Patents

Abstract

The invention relates to the technical field of simulated modeling of a rotor dynamics system and in particular to an object-oriented nonlinear and non-causal modeling and simulation method for the rotor dynamics system. The modeling and simulation method is based on an object-oriented non-causal multi-field modeling language Modelica; the modeling language Modelica is used for writing the simulated modeling program of the rotor dynamics system; the simulated modeling of the rotor dynamics system is formed by components and faults; the components comprises a turntable component, shaft section components and a bearing component; the turntable component, the shaft section components and the bearing component comprise two connector elements respectively; the faults comprise crack fault, rubbing fault and foundation loosening fault; and by the modeling and simulation method, the rotor dynamics systems with various structures can be modeled, system characteristics and working condition of the rotor dynamics systems can be truly reflected, the faults such as crack, rubbing and foundation loosening can be introduced to perform system analysis, and a convenient analysis measure is provided for engineering technical persons and scientific researchers.

Description

The non-linear non-causal modeling and simulating method of a kind of OO rotordynamic system

[technical field]

The present invention relates to rotordynamic system Simulation and Modeling Technology field, specifically the non-linear non-causal modeling and simulating method of a kind of OO rotordynamic system.

[background technology]

Rotor dynamics be one for the research field of the rotating machinery that is widely used in industry, national defence and each field of the people's livelihood, research direction comprises dynamic response, vibration, fault diagnosis etc., and its purpose and task are rotating machinery is optimized design, raises the efficiency and reduces fault etc.The general analysis method of rotor dynamics comprises transfer matrix method and finite element method, wherein, the finite element method analysis rotor-support-foundation system sees Ruhl's " Afinite element model for distributed parameter turborotor systems " literary composition the earliest, transfer matrix method is analyzed " A general method for calculating critical speeds of flexible rotors " literary composition that rotor-support-foundation system sees Prohl the earliest, in " high rotor dynamics: theory, technology and application " book of Mr. Wen Bangchun, detailed introduction and explanation are arranged.The research of finite element method can be used such as business softwares such as Ansys, Abaqus and carry out; But use transfer matrix method need to utilize the language such as C or Matlab to carry out manual programming to the lumped parameter model analysis of rotor, for different rotor-support-foundation systems, the program form difference of writing causes and can't reuse, and efficient is lower.

Modelica is a kind of OO modeling language that is applicable to complicated physical system, has the characteristics of multi-field property, non-causality and object orientedness.The thought of Modelica language is proposed in its PhD dissertation by Hilding Elmqvist the earliest, uses DASSL or Radau5 scheduling algorithm to carry out whole model solution for the physical system that can use DAE to describe.Its programmed method is based on the broad sense Kirchhoff's law, uses the equation of no signal flow path direction that system is described, and makes things convenient for user program and improves the reusability of code, had comparatively widely at engineering field and used.

[summary of the invention]

Purpose of the present invention is exactly will solve above-mentioned deficiency and provide a kind of OO rotordynamic system non-linear non-causal modeling and simulating method, because Modelica has object orientedness, non-causality and multi-field property, thereby not only be simple and easy to use, and realized the rotordynamic system of various structures is carried out modeling analysis, efficient is very high.

Design for achieving the above object the non-linear non-causal modeling and simulating method of a kind of OO rotordynamic system, this modeling and simulating method is based on OO non-causal Multi-disciplinary Modeling language Modelica, use this modeling language Modelica to write the rotordynamic system realistic model, described rotordynamic system realistic model is built by assembly and fault, described assembly comprises rotary disc assembly, shaft part assembly and bearing assembly, described rotary disc assembly, shaft part assembly and bearing assembly comprise respectively two junction element, and described fault comprises crack fault, bump rub fault and base flexible fault.

Described junction element comprises gesture variable and flow variables, and described gesture variable is the rotor radial displacement of junction element place, and described flow variables is that junction element place rotor radial is stressed.

Described rotary disc assembly, bearing assembly are the lumped mass rigid body, and described shaft part assembly is elastic body.

Described assembly also comprises the environment assembly, and described environment assembly has been controlled rotating speed and the acceleration of gravity of rotordynamic system.

Described crack fault comprises function, stiffness variation amount and the crackle power of breathing.

Beneficial effect of the present invention: need to carry out manual programming for traditional rotor dynamics lumped parameter analytical approach, for different rotor-support-foundation systems, the program form difference of writing causes and can't reuse, the shortcoming that efficient is lower, the present invention is by using OO non-causal Multi-disciplinary Modeling language Modelica to carry out secondary development, the result shows, the non-linear non-causal modeling and simulating method of the OO rotordynamic system that obtains can carry out modeling to the rotordynamic system of various structures, system performance and the working condition that can reflect faithfully rotordynamic system, and can be with crackle, bump and rub and the fault such as base flexible is introduced and carried out systematic analysis, for engineering technical personnel and scientific research personnel provide a kind of easily analysis means.

[description of drawings]

Fig. 1 is rotor dynamical system realistic model synoptic diagram of the present invention;

Fig. 2 is junction element model synoptic diagram among the present invention;

Fig. 3 is the lumped parameter model synoptic diagram of turntable assembly of the present invention, shaft part assembly, bearing assembly and environment assembly;

Fig. 4 is crack fault model synoptic diagram among the present invention;

Fig. 5 bumps the fault model synoptic diagram that rubs among the present invention;

Fig. 6 is base flexible fault model synoptic diagram among the present invention;

Fig. 7 is the simulation result synoptic diagram of Fig. 1;

Among the figure: 1, rotary disc assembly 2, shaft part assembly 3, bearing assembly 4, environment assembly 5, junction element 6, crack fault 7, bump the fault 8 of rubbing, base flexible fault.

[embodiment]

Further specify below below in conjunction with accompanying drawing the present invention being done:

Such as accompanying drawing 1 to shown in the accompanying drawing 6, modeling and simulating method of the present invention is based on OO non-causal Multi-disciplinary Modeling language Modelica, use this modeling language Modelica to write the rotordynamic system realistic model, this rotordynamic system realistic model is built by assembly and fault, assembly comprises rotary disc assembly 1, shaft part assembly 2 and bearing assembly 3, rotary disc assembly, shaft part assembly and bearing assembly comprise respectively two junction element 5, and fault comprises crack fault 6, bumps rub fault 7 and base flexible fault 8.Junction element comprises gesture variable and flow variables, and the gesture variable is the rotor radial displacement of junction element place, and flow variables is that junction element place rotor radial is stressed.Rotary disc assembly, bearing assembly are the lumped mass rigid body, and the shaft part assembly is elastic body.Assembly also comprises environment assembly 4, and the environment assembly has been controlled rotating speed and the acceleration of gravity of rotordynamic system.Crack fault comprises function, stiffness variation amount and the crackle power of breathing.This rotordynamic system realistic model is conveniently revised with respect to traditional rotor dynamics lumped parameter method modeling ocular and clear, and is easy to use.

The present invention is directed to the lumped parameter model of rotordynamic system, based on OO non-causal Multi-disciplinary Modeling language Modelica, write the rotor dynamics Modeling and simulation platform.This platform can carry out modeling and simulating to the general dynamical model of rotor that includes rotary disc assembly, shaft part assembly and bearing assembly, and can introduce crack fault, bumps rub fault and base flexible fault etc. and analyze.Show that through the modeling analysis experiment the more original program means of this modeling and simulating method is simple and easy to usefulness, for engineering technical personnel provide a kind of relatively easily rotor dynamics analysis means.

As shown in Figure 2, be junction element, based on the broad sense Kirchhoff's law, namely equate that at node place gesture variable the flow variables sum is 0, in dynamical model of rotor, choosing the gesture variable is the rotor radial displacement of node place, and flow variables is that node place rotor radial is stressed.

As shown in Figure 3, lumped parameter model synoptic diagram for rotary disc assembly, shaft part assembly, bearing assembly and environment assembly, wherein, rotary disc assembly, shaft part assembly and bearing assembly meet equation (1) to (3), and the environment assembly has determined rotating speed and the acceleration of gravity of rotordynamic system.Namely for the lumped parameter model of rotordynamic system, rotor-support-foundation system can be decomposed into rotary disc assembly, shaft part assembly and three major parts of bearing assembly, and each several part all comprises two junction element, represents with L, R respectively.Wherein, be the lumped mass rigid body depending on rotary disc assembly, bearing assembly, the shaft part assembly is elastic body, and bearing assembly place oil-film force is reduced to rigidity-damper model, and then the equation of rotary disc assembly, shaft part assembly and bearing assembly is shown in equation (1), (2) and (3).

$m\stackrel{\&CenterDot;\&CenterDot;}{x}=F_x^L+F_x^R+\mathrm{me}{\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="DEST\_PATH\_HDA00002463153500011.png,DEST\_PATH\_HDA00002463153500032.png"\; state="\{\{state\}\}">r</figure-callout>}}^2\cos {\mathrm{\&omega;}}_{r}t$

$m\stackrel{\&CenterDot;\&CenterDot;}{y}=F_y^L+F_y^R+\mathrm{me}{\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="DEST\_PATH\_HDA00002463153500011.png,DEST\_PATH\_HDA00002463153500032.png"\; state="\{\{state\}\}">r</figure-callout>}}^2\sin {\mathrm{\&omega;}}_{r}t-\mathrm{mg}---\left(1\right)$

$x^r=x^L+\frac{{\mathrm{<figure-callout\; id="3"\; label="l"\; filenames="DEST\_PATH\_HDA00002463153500011.png,HDA00002161462400021.png"\; state="\{\{state\}\}">l</figure-callout>}}^3}{6\mathrm{EI}}{F}_x^R$

$y^R=y^L+\frac{{\mathrm{<figure-callout\; id="3"\; label="l"\; filenames="DEST\_PATH\_HDA00002463153500011.png,HDA00002161462400021.png"\; state="\{\{state\}\}">l</figure-callout>}}^3}{6\mathrm{EI}}{F}_y^R---\left(2\right)$

$F_x^L+F_x^R=0$

$F_y^L+F_y^R=0$

$m\stackrel{\&CenterDot;\&CenterDot;}{x}+c\stackrel{\&CenterDot;}{x}+\mathrm{kx}=F_x^L+F_x^R---\left(3\right)$

$m\stackrel{\&CenterDot;\&CenterDot;}{y}+c\stackrel{\&CenterDot;}{y}+\mathrm{ky}=F_y^L+F_y^R-\mathrm{mg}$

Wherein e is rotor unbalance value, ω _rBe rotor speed, EI is the rotating shaft bendind rigidity, and k and c are respectively rigidity and the damping of bearing.In addition, the environment assembly that increases then is gravity acceleration g and the rotational speed omega in order to control whole rotordynamic system _r

, be respectively crack fault, bump rub fault and base flexible fault to shown in the accompanying drawing 6 such as accompanying drawing 4, crack fault satisfies equation (4) to (6), bumps the fault of rubbing and satisfies equation (7), and the base flexible fault satisfies equation (8).

Wherein, the breathing function of crack fault, stiffness variation amount and crackle power equation are:

$\mathrm{\&lambda;}\left(\mathrm{\&theta;}\right)=\left\{\begin{array}{cc}1& -\frac{\mathrm{\&pi;}}{2}+\mathrm{\&alpha;}\&le;\mathrm{\&theta;}<\frac{\mathrm{\&pi;}}{2}-\mathrm{\&alpha;}\\ \frac{1}{2}(1+\cos \frac{\mathrm{\&theta;}-\frac{\mathrm{\&pi;}}{2}+\mathrm{\&alpha;}}{2\mathrm{\&alpha;}})& \frac{\mathrm{\&pi;}}{2}-\mathrm{\&alpha;}\&le;\mathrm{\&theta;}<\frac{\mathrm{\&pi;}}{2}+\mathrm{\&alpha;}\\ 0& \frac{\mathrm{\&pi;}}{2}+\mathrm{\&alpha;}\&le;\mathrm{\&theta;}<\frac{3\mathrm{\&pi;}}{2}-\mathrm{\&alpha;}\\ \frac{1}{2}(1+\cos \frac{\mathrm{\&theta;}-\frac{3\mathrm{\&pi;}}{2}-\mathrm{\&alpha;}}{2\mathrm{\&alpha;}})& \frac{3\mathrm{\&pi;}}{2}-\mathrm{\&alpha;}\&le;\mathrm{\&theta;}\&le;\frac{3\mathrm{\&pi;}}{2}+\mathrm{\&alpha;}\end{array}\right.---\left(4\right)$

$\mathrm{\&Delta;k}=\frac{48\mathrm{<figure-callout\; id="3"\; label="E\; l"\; filenames="DEST\_PATH\_HDA00002463153500011.png,HDA00002161462400021.png"\; state="\{\{state\}\}">E</figure-callout>}}{l^{}}\&CenterDot;\frac{{\mathrm{<figure-callout\; id="4"\; label="d"\; filenames="HDA00002161462400021.png"\; state="\{\{state\}\}">d</figure-callout>}}^4}{64}$

$\&CenterDot;\left[\begin{array}{c}\frac{\mathrm{\&pi;}}{2}-{\sin }^{-1}(1-2\frac{h}{d})\\ -2(1-2\frac{h}{d})(1-8\frac{h}{d}+8\frac{h^2}{d^2})\sqrt{\frac{h}{d}(1-\frac{h}{d})}\end{array}\right]---\left(5\right)$

(6)

Wherein

When crack depth is h, Δ k is corresponding section rigidity reduction.

Bumping the Fault Equations that rubs is:

$\left[\begin{array}{c}{F}_x\\ F_y\end{array}\right]=-\frac{(e-\mathrm{\&delta;})k_c}{e}\left[\begin{array}{cc}1& -f\\ f& 1\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]---\left(7\right)$

Wherein

Be the radial displacement of rotor, δ is for bumping the gap of rubbing, k _cFor bumping the part rigidity of rubbing, f bumps the friction factor that rubs between part and the rotor.

The base flexible Fault Equations is:

$F_x=\left\{\begin{array}{cc}k(x+b-c)& x\&le;-b-c\\ 0& -(b-c)<x\&le;b+c\\ k(x-b-c)& x>b+c\end{array}\right.$ (8)

$F_x=\left\{\begin{array}{cc}k(y-d)& x\&le;d\\ 0& d<y\&le;2b+d\\ k(y-2b+d)& y>2b+d\end{array}\right.$

Wherein b is loosening gap length, and c is the gap amount of bias, and d is quiet distortion

As shown in Figure 7, export axle center geometric locus synoptic diagram for the simulation result of accompanying drawing 1 rotor dynamical system realistic model.

The present invention is not subjected to the restriction of above-mentioned embodiment, and other any do not deviate from change, the modification done under Spirit Essence of the present invention and the principle, substitutes, combination, simplify, and all should be the substitute mode of equivalence, is included within protection scope of the present invention.

Claims (5)

1. non-linear non-causal modeling and simulating method of OO rotordynamic system, it is characterized in that, this modeling and simulating method is based on OO non-causal Multi-disciplinary Modeling language Modelica, use this modeling language Modelica to write the rotordynamic system realistic model, described rotordynamic system realistic model is built by assembly and fault, described assembly comprises rotary disc assembly, shaft part assembly and bearing assembly, described rotary disc assembly, shaft part assembly and bearing assembly comprise respectively two junction element, and described fault comprises crack fault, bump rub fault and base flexible fault.

2. modeling and simulating method as claimed in claim 1, it is characterized in that: described junction element comprises gesture variable and flow variables, and described gesture variable is the rotor radial displacement of junction element place, and described flow variables is that junction element place rotor radial is stressed.

3. modeling and simulating method as claimed in claim 1 or 2, it is characterized in that: described rotary disc assembly, bearing assembly are the lumped mass rigid body, described shaft part assembly is elastic body.

4. modeling and simulating method as claimed in claim 3, it is characterized in that: described assembly also comprises the environment assembly, described environment assembly has been controlled rotating speed and the acceleration of gravity of rotordynamic system.

5. modeling and simulating method as claimed in claim 4 is characterized in that: described crack fault comprises function, stiffness variation amount and the crackle power of breathing.

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