CN103837343B - Based on the ships and light boats axle system life-span prediction method of vibrating fatigue coupling analysis - Google Patents

Abstract

The invention discloses a kind of ships and light boats axle system life-span prediction method based on vibrating fatigue coupling analysis, comprise and select Measuring Time point t _iand measure ships and light boats axle system and be in this Measuring Time point t _itime natural frequency ω _i(n time is measured, i=1,2,3 ..., n, i are positive integer), then calculate ships and light boats axle system and be in this Measuring Time point t _itime expection N fatigue lifetime _i, finally calculate ships and light boats axle system and be in this Measuring Time point t _itime residual life M _i.Instant invention overcomes now methodical shortcoming, from ships and light boats axle system model, based under vibration and tired coupling environment, ships and light boats axle system is calculated in the life-span, solve in prior art the problem not relating to and ships and light boats axle system is carried out to life-span calculating and prediction, the method easy to understand, easy realization, is more suitable for calculating and the prediction of ships and light boats axle system residual life.

Description

Based on the ships and light boats axle system life-span prediction method of vibrating fatigue coupling analysis

Technical field

The present invention relates to a kind of Life Calculating Methods, particularly relate to a kind of ships and light boats axle system life-span prediction method based on vibrating fatigue coupling analysis, belong to ships and light boats field of power equipment technology.

Background technology

Under sail, the vibration of axle system is one of key factor affecting the safe operation of ships and light boats propulsion system to ships and light boats, if can not get effective control, by a series of serious consequence of appearance, as the fracture etc. of axle system.Correct evaluation is made in vibration in order to shaft, avoids the generation of malicious event, not only should carry out detailed vibration calculating in the design phase, also needs to carry out vibration-testing in the operation phase, to investigate this propulsion system vibration characteristics whether reach required standard.Existing Many researchers has carried out deep discussion and analysis to the theory calculate of vibration and test both at home and abroad.

But for the life prediction of ships and light boats axle system, existing method then seldom relates to.Wherein main cause is: one is current check standard, and normally being derived by the fatigue strength of this axle as permissible stress draws, as long as meet standard, usually just thinks that this axle cording has infinite life, obviously, this inadequate science, not pointed yet; Two is that shaft is carried out life prediction itself and had certain complicacy because the environment residing for axle system.Under the effect of dynamic loading, ships and light boats axle system can vibrate, and vibration can produce alterante stress, if under being in alterante stress environment for a long time, structure fatigue damage can occur; In addition, the existence of fatigue damage reduces the rigidity of structure, reduces the natural frequency of structure, have impact on the vibration characteristics of structure.So axle system is in vibration with under the tired environment that is coupled.How to predict the life-span of ships and light boats axle system, answer the problem of " how long can also use ", depend on effective vibrating fatigue model of coupling to a great extent.

The existing pertinent literature about vibrating fatigue coupling analysis, from application, all there is specific suitable environment, such as tack-weld, plate etc., dynamic perfromance Changing Pattern in document all sets off a discussion based on these models, thus is not suitable for vibrating shaft system life prediction here; From damage type, be confined to crackle, the main theory of life prediction in document is according to the defect theory being fracturing mechanics Crack Extension, and with regard to ships and light boats axle system, as long as there is crackle, just must take measures in time, so fatigue lifetime refers to crack initiation life, main theory is according to being classical fatigue cumulative damage theory.

Summary of the invention

Object of the present invention, is to carry out on the basis of vibrating fatigue coupling analysis to ships and light boats axle system, provides a kind of ships and light boats axle system Life Calculating Methods.

To achieve these goals, the technical solution adopted in the present invention is as follows:

Based on a ships and light boats axle system life-span prediction method for vibrating fatigue coupling analysis, comprise and select Measuring Time point t _iand measure ships and light boats axle system and be in this Measuring Time point t _itime natural frequency ω _i, n time is measured, i=1,2,3 ..., n, i are positive integer, then calculate ships and light boats axle system and be in this Measuring Time point t _itime expection N fatigue lifetime _i, finally calculate ships and light boats axle system and be in this Measuring Time point t _itime residual life M _i, described ships and light boats axle system residual life M _icomputing method be:

Situation 1: ω ₀during < ω, M _i=N ₀-N _α;

Situation 2: ω ₀> > ω, and ω _nduring > ω, $\begin{array}{cc}{M}_i=N_i(1-\underset{p=1}{\overset{i}{\&Sigma;}}{t}_p/N_p)& i=1,2,3,...,n\end{array};$

Situation 3: ω ₀> ω ₁> ... > ω _j-1> ω > ω _j> ... > ω _ntime, make D ^*=max (1/N _j-1, 1/N _j),

$M_i\left\{\begin{array}{cc}{N}_i\left(1-\underset{p=1}{\overset{i}{\&Sigma;}}{t}_p/N_p\right)& i=1,2,3,\mathrm{...},j-1\\ N_i\left(1-\underset{p=1}{\overset{i-1}{\&Sigma;}}{t}_p/N_p-D^{*}\&CenterDot;t_i\right)& i=j\\ M_j-N_{\mathrm{\&beta;}}& i=j+1,\mathrm{...},n\end{array}\right.;$

Wherein: ω is the sinusoidal interference moment frequency of ships and light boats axle system, N ₀for natural frequency ω when ships and light boats axle system does not use ₀corresponding expection fatigue lifetime, N _αthe stress-number of cycles that when being i-th prediction, ships and light boats axle system has used, N _pbe the p time Measuring Time point t _pthe ships and light boats axle system expection fatigue lifetime of calculating, N _j-1for natural frequency ω when ships and light boats axle system is in jth-1 Measuring Time point _j-1corresponding expection fatigue lifetime, N _jfor natural frequency ω when ships and light boats axle system is in jth time Measuring Time point _jcorresponding expection fatigue lifetime, M _jfor the ships and light boats axle system residual life calculated when jth time is measured, N _βfor the stress-number of cycles that ships and light boats axle system when measuring to i-th time after jth time measurement has used.

Preferably, described selection Measuring Time point t _imethod be, residual life M when selecting ships and light boats axles system not use ₀1/2 place as first time Measuring Time point (obvious M ₀=N ₀), i.e. t ₁=M ₀/ 2, thereafter, 1/2 place of the residual life of prediction after each Measuring Time point is selected in and measures for last time, i.e. t ₂=M ₁/ 2 ..., t _n=M _n-1/ 2, wherein M ₁, M ₂..., M _n-1for Measuring Time point t ₁, t ₂..., t _n-1corresponding residual life.

Preferably, described expection N fatigue lifetime _icomputing formula be N _i=C (W _p/ T ₀) ^mμ _i ^-m, wherein: μ _ifor ships and light boats natural frequency of shafting ω _icorresponding vibration amplification factor, m, C are two material constants of the ships and light boats axle system curve of fatigue, W _pfor the torsion section factor of ships and light boats axle system, T ₀for the amplitude of ships and light boats axle system periodic disturbing torque.

Preferably, described ships and light boats natural frequency of shafting ω _icorresponding vibration amplification factor μ _icomputing formula be ${\mathrm{\&mu;}}_i=1/\sqrt{{\&lsqb;1-{(\mathrm{\&omega;}/{\mathrm{\&omega;}}_i)}^2\&rsqb;}^2+{(2\mathrm{\&xi;}\mathrm{\&omega;}/{\mathrm{\&omega;}}_i)}^2},$ Wherein: ξ is the damping ratio of ships and light boats axle system.

After adopting such scheme, ships and light boats axle system life-span prediction method based on vibrating fatigue coupling analysis of the present invention, its beneficial effect is: instant invention overcomes now methodical shortcoming, from ships and light boats axle system model, based under vibration and tired coupling environment, ships and light boats axle system is calculated in the life-span, solve in prior art the problem not relating to and ships and light boats axle system is carried out to life-span calculating and prediction, the method easy to understand, easy realization, is more suitable for calculating and the prediction of ships and light boats axle system residual life.

Accompanying drawing explanation

Fig. 1 is ships and light boats axle system simple substance amount torsional vibration system schematic diagram in the embodiment of the present invention.

Fig. 2 is ships and light boats axle system of the present invention graph of relation.

Fig. 3 is " residual life-natural frequency " i.e. M in the embodiment of the present invention _i-ω _igraph of relation.

Embodiment

Below in conjunction with accompanying drawing, technical scheme of the present invention is described in further detail.

Based on the ships and light boats axle system life-span prediction method of vibrating fatigue coupling analysis, comprise the following steps:

1, the natural frequency of ships and light boats axle system is measured at specific Measuring Time point

Cause is in the early stage of fatigue lifetime, and natural frequency reduces smaller, and to the later stage of fatigue lifetime, natural frequency reduces very fast, and more and more faster, is namely nonlinear, so there is ω ₀> ω ₁> ... > ω _n.For this reason, following natural frequency measurement, method is provided: each Measuring Time point is selected in 1/2 place of the residual life calculated when measuring for last time.

Suppose that measuring corresponding residual life through n time is followed successively by: M ₁, M ₂..., M _n, natural frequency when ships and light boats axle system does not use is ω ₀, and the residual life M of correspondence ₀=N ₀(N ₀expection fatigue lifetime for when ships and light boats axle system does not use).1st time Measuring Time point exists: t ₁=M ₀/ 2 places; Thereafter, the time interval that each natural frequency Measuring Time point experiences relative to last Measuring Time point is expressed as successively: t ₂, t ₃..., t _n.So:

t ₁＝M ₀/2,t ₂＝M ₁/2,…,t _n＝M _n-1/2。(1)

If the large, medium and small phase lead time of repairing of certain Measuring Time point and ships and light boats axle system is little, this Measuring Time point can be arranged in and large, medium and smallly repaiies the phase; If certain Measuring Time point once does not also arrive, but because task needs, current Measuring Time point also can be artificially given.

2, the expection fatigue lifetime of ships and light boats axle system is calculated

The vibration of ships and light boats axle system is rather complicated, from the form of vibration, can be divided into extensional vibration, whirling vibration and twisting vibration; From analytical model, single-degree-of-freedom, multiple degrees of freedom and continuous system model can be divided into.The present invention discusses for shafting torsional oscillation single-mode system, and (i.e. single quality system, only consider the quality of screw propeller, other quality are not considered, suppose that main frame rigidity is very large, quality is infinitely great simultaneously.For other system, method is similar).As shown in Figure 1, be the simple substance amount torsional vibration system schematic diagram in the embodiment of the present invention, wherein K ₀for torsional rigidity when ships and light boats axle system does not use, W _pfor the torsion section factor of ships and light boats axle system, ξ is the damping ratio of ships and light boats axle system, and ω is the sinusoidal interference moment frequency of ships and light boats axle system, and I is the moment of inertia of screw propeller, acts on the periodic disturbing torque T=T that ships and light boats axle is fastened ₀e ^{j ω t}, T ₀for the amplitude of ships and light boats axle system periodic disturbing torque, the vibration amplification factor can trying to achieve ships and light boats axle system is:

$\mathrm{\&mu;}=\frac{1}{\sqrt{{\&lsqb;1-{\left(\frac{\mathrm{\&omega;}}{{\mathrm{\&omega;}}_0}\right)}^2\&rsqb;}^2+{\left(2\mathrm{\&xi;}\frac{\mathrm{\&omega;}}{{\mathrm{\&omega;}}_0}\right)}^2}},---\left(2\right)$

Wherein, ω ₀for natural frequency when ships and light boats axle system does not use,

Maximum stress in ships and light boats axle system one-period can try to achieve into: suppose that ships and light boats axle system Fatigue Property Curve meets: wherein, N is expection fatigue lifetime, and m, C are two material constants of the ships and light boats axle system curve of fatigue, relevant with axle based material character etc., τ _maxfor the maximum stress that ships and light boats axle system bears, then expection is fatigue lifetime:

$N=C/{\mathrm{\&tau;}}_{max}^m=C{(W_p/T_0)}^m{\mathrm{\&mu;}}^{-m}.---\left(3\right)$

Utilize Miner linear progressive damage theory to calculate accumulative fatigue damage, after the circulation of experience primary stress, to the single damage that ships and light boats axle system causes be:

D＝1/N。(4)

Suppose that ships and light boats axle system measures through i time the natural frequency obtained and is followed successively by ω ₁, ω ₂..., ω _n, because natural frequency reduces gradually, have ω ₁> ω ₂> ... > ω _n, corresponding expection is followed successively by N fatigue lifetime ₁, N ₂..., N _n, corresponding single damage is followed successively by D ₁, D ₂..., D _n.By (3) Shi Ke get, natural frequency ω when ships and light boats axle system does not use ₀corresponding expection fatigue lifetime is N ₀, by (4) Shi Ke get, corresponding single damage is D ₀.

The natural frequency ω obtained is measured to i-th time _i, with ω _inatural frequency ω when replacing ships and light boats axle system not use ₀, tried to achieve by (2), (3), (4) formula, ω _iunder amplification factor μ _i, expection fatigue lifetime N _iand single damage D _i.Draw relation curve as shown in Figure 2.

3, the residual life of ships and light boats axle system is calculated

Based on the principle of security, point residual life of three kinds of situations to ships and light boats axle system calculates.

Situation 1: work as ω ₀during < ω, ω > ω ₀> ω ₁> ω ₂> ... > ω _n, therefore D ₀> D ₁> D ₂> ... > D _n.

Get D ₀for the fatigue damage that each Cyclic Stress is brought, expection N fatigue lifetime of ships and light boats axle system ₀obtained by (3) formula.Now, do not need to arrange natural frequency measurement, re-use N _αresidual life after secondary is measurable is:

M _i＝N ₀-N _α，i＝1,2,3,…,n，(5)

N _αthe stress-number of cycles that when being i-th prediction, ships and light boats axle system has used.

Situation 2: work as ω ₀during > > ω, can imagine and work as ω _n> ω, so: D ₀< D ₁< D ₂< ... < D _n.The residual life of prediction is:

$M_i=N_i(1-\frac{t_1}{N_1}-\frac{t_2}{N_2}-...-\frac{t_i}{N_i})=N_i(1-\underset{p=1}{\overset{i}{\&Sigma;}}\frac{t_p}{N_p}),i=1,2,3,...,n,---\left(6\right)$

Wherein: t ₁, t ₂..., t _nvalue calculates according to formula (1).Note, as wherein certain Measuring Time point is artificially given once or several times, then replace with set-point.

Situation 3: work as ω ₀during > ω, ω may be had _i< ω.From the angle avoiding resonating, this kind of situation should be avoided as far as possible.The mode improving ω can be taked, make ω ₀< ω, now becomes situation 1; Also can reduce ω, make ω _n> ω, now becomes situation 2.Certainly, also can improve ships and light boats shafting structure and then change ω ₀, make it become situation 1 or 2.But in some occasion, if above-mentioned measure all cannot be carried out, quickly through resonance region, can be handled as follows: suppose now have ω ₀> ω ₁> ... > ω _j-1> w > w _j> ... > ω _n, and D ^*=max (1/N _j-1, 1/N _j), the residual life of prediction is:

$M_i\left\{\begin{array}{cc}{N}_i\left(1-\underset{p=1}{\overset{i}{\&Sigma;}}\frac{t_p}{N_p}\right)& i=1,2,3,\mathrm{...},j-1\\ N_i\left(1-\underset{p=1}{\overset{i-1}{\&Sigma;}}\frac{t_p}{N_p}-D^{*}\&CenterDot;t_i\right)& i=j\end{array}\right.,---\left(7\right)$

Wherein: t ₁, t ₂..., t _jvalue still according to formula (1) calculate, as wherein certain Measuring Time point is artificially given once or several times, then replace with set-point.After secondary from jth, do not need to arrange natural frequency measurement, re-use N _βresidual life after secondary:

M _i＝M _j-N _β，i＝j+1,…,n(8)

N _βfor the stress-number of cycles that ships and light boats axle system when predicting to i-th time after jth time measurement has used.

After the residual life of the natural frequency and correspondence that draw each Measuring Time point, " residual life-natural frequency " i.e. M can be drawn _i-ω _irelation curve, draws the residual life under arbitrary natural frequency, as shown in Figure 3, is the M of embodiment below _i-ω _igraph of relation.

Embodiment

1, embodiment explanation

Certain ships and light boats two stroke diesel engine screw propeller can be simulated with simple substance amount torsional vibration system, as shown in Figure 1.Torsional oscillation stiffness K when this axle does not use ₀=94.336MNm/rad, reverses section factor W _p=0.0260m ³, damping ratio ξ=0.1 of this axle, the moment of inertia I=31420Kgm of screw propeller ³, act on periodic disturbing torque T=167.428sin12.4tKNm (the i.e. periodic disturbing torque amplitude T on this axle ₀=167.428KNm).

This axle Fatigue Property Curve meets: i.e. C=10 ¹¹, m=0.75.Diesel engine is two-stroke, and a Cyclic Stress turns around, so this diesel engine speed is 1 hour number of stress cycles is n _r60=118.460=7104 secondary, for clarity, hereinafter the unit in life-span is all converted into hour.

2, result of calculation

Natural frequency when this axle does not use is must expection N fatigue lifetime of this axle by formula (3) ₀=18839 hours.

The sinusoidal interference moment frequencies omega of this axle=12.4rad/s, ω ₀> 4 ω, meet the situation 2 in " the 3rd step calculates residual life ", technician has arranged natural frequency measurement, according to preceding method, and has carried out life-span calculating.

Residual life M when not using ₀=N ₀, then have: M ₀=18839 hours.

By formula (1): the 1st time Measuring Time point exists: t ₁=M ₀/ 2=9419 hour.

Measure to obtain ω 1st time ₁=52.7rad/s, with ω ₁replace natural frequency ω when not using ₀, substituting into formula (3) must expect fatigue lifetime: N ₁=18779 hours.

By formula (6): residual life $M_1=N_1(1-\frac{t_1}{N_1})=N_1-t_1=9360$ Hour.

By formula (1): the 2nd time Measuring Time point exists: t ₂=M ₁/ 2=4680 hour.

Measure to obtain ω 2nd time ₂=50.3rad/s, with ω ₂replace natural frequency ω when not using ₀, substituting into formula (3) must expect fatigue lifetime: N ₂=18700 hours.

By formula (6): residual life hour.

By formula (1): the 3rd time Measuring Time point exists: t ₃=M ₂/ 2=2320 hour.

……

The like, arrange 4 natural frequency measurement,s.After the 4th is measured, ships and light boats have worked again 200 hours, although be less than due Measuring Time point, because task needs, have organized a natural frequency measurement, on request.5 times measurement result is as shown in the table.Now wonder how long this axle can also work, the navigation in 300 hours can finishing the work required.

Table natural frequency is measured and residual Life Calculation result

Number of times	0	1	2	3	4	5
							Interval (unit: hour)	0	9419	4680	2320	1132	200
Natural frequency (unit: rad/s)	54.8	52.7	50.3	45	42.8	41.5

Residual life (unit: hour)

18839

9360

4640

2265

1118

913

Residual life-natural frequency and M _i-ω _icurve as shown in Figure 3.For clarity, test interval and residual life are also listed in table.After visible the 5th is measured, residual life is 913 hours, is greater than 300 hours, the 300 hours navigational duties namely can finishing the work required.

Above embodiment is only and technological thought of the present invention is described, can not limit protection scope of the present invention with this, and every technological thought proposed according to the present invention, any change that technical scheme basis is done, all falls within scope.

Claims (4)

1., based on a ships and light boats axle system life-span prediction method for vibrating fatigue coupling analysis, comprise and select Measuring Time point t _iand measure ships and light boats axle system and be in this Measuring Time point t _itime natural frequency ω _i, n time is measured, i=1,2,3 ..., n, i are positive integer, then calculate ships and light boats axle system and be in this Measuring Time point t _itime expection N fatigue lifetime _i, finally calculate ships and light boats axle system and be in this Measuring Time point t _itime residual life M _i, it is characterized in that: described ships and light boats axle system residual life M _icomputing method be:

Situation 1: ω ₀during < ω, M _i=N ₀-N _α;

Situation 2: ω ₀> > ω, and ω _nduring > ω, $\begin{array}{cc}{M}_i=N_i(1-\underset{p=1}{\overset{i}{\&Sigma;}}{t}_p/N_p)& i=1,2,3,...,n\end{array};$

Situation 3: ω ₀> ω ₁> ... > ω _j-1> ω > ω _j> ... > ω _ntime, make D ^*=max (1/N _j-1, 1/N _j),

$M_i=\left\{\begin{array}{cc}{N}_i\left(1-\underset{p=1}{\overset{i}{\&Sigma;}}{t}_p/N_p\right)& i=1,2,3,...,j-1\\ N_i\left(1-\underset{p=1}{\overset{i-1}{\&Sigma;}}{t}_p/N_p-D^{*}\&CenterDot;t_i\right)& i=j\\ M_j-N_{\mathrm{\&beta;}}& i=j+1,...,n\end{array}\right.;$

Wherein: ω is the sinusoidal interference moment frequency of ships and light boats axle system, N ₀for natural frequency ω when ships and light boats axle system does not use ₀corresponding expection fatigue lifetime, N _αthe stress-number of cycles that when being i-th prediction, ships and light boats axle system has used, N _pbe the p time Measuring Time point t _pthe ships and light boats axle system expection fatigue lifetime of calculating, N _j-1for natural frequency ω when ships and light boats axle system is in jth-1 Measuring Time point _j-1corresponding expection fatigue lifetime, N _jfor natural frequency ω when ships and light boats axle system is in jth time Measuring Time point _jcorresponding expection fatigue lifetime, M _jfor the ships and light boats axle system residual life calculated when jth time is measured, N _βfor the stress-number of cycles that ships and light boats axle system when measuring to i-th time after jth time measurement has used.

2. as claimed in claim 1 based on the ships and light boats axle system life-span prediction method of vibrating fatigue coupling analysis, it is characterized in that: described selection Measuring Time point t _imethod be, residual life M when selecting ships and light boats axles system not use ₀1/2 place as first time Measuring Time point, i.e. t ₁=M ₀/ 2, thereafter, 1/2 place of the residual life of prediction after each Measuring Time point is selected in and measures for last time, i.e. t ₂=M ₁/ 2 ..., t _n=M _n-1/ 2, wherein M ₁, M ₂..., M _n-1for Measuring Time point t ₁, t ₂..., t _n-1corresponding residual life.

3., as claimed in claim 1 based on the ships and light boats axle system life-span prediction method of vibrating fatigue coupling analysis, it is characterized in that: described expection N fatigue lifetime _icomputing formula be N _i=C (W _p/ T ₀) ^mμ _i ^-m, wherein: μ _ifor ships and light boats natural frequency of shafting ω _icorresponding vibration amplification factor, m, C are two material constants of the ships and light boats axle system curve of fatigue, W _pfor the torsion section factor of ships and light boats axle system, T ₀for the amplitude of ships and light boats axle system periodic disturbing torque.

4., as claimed in claim 3 based on the ships and light boats axle system life-span prediction method of vibrating fatigue coupling analysis, it is characterized in that: described ships and light boats natural frequency of shafting ω _icorresponding vibration amplification factor μ _icomputing formula be

${\mathrm{\&mu;}}_i=1/\sqrt{{\&lsqb;1-{(\mathrm{\&omega;}/{\mathrm{\&omega;}}_i)}^2\&rsqb;}^2+{(2\mathrm{\&xi;}\mathrm{\&omega;}/{\mathrm{\&omega;}}_i)}^2},$ Wherein: ξ is the damping ratio of ships and light boats axle system.