CN103837343A - Ship and boat shafting service life predicating method on the basis of vibration fatigue coupling analysis - Google Patents

Abstract

The invention discloses a ship and boat shafting service life predicating method on the basis of vibration fatigue coupling analysis. The method comprises the steps of selecting a measuring time point ti, measuring the inherent frequency omega i (for n times of measurements, i=1, 2, 3, ..., and n and i are positive integers) of a ship and boat shafting located in the measuring time point ti, then, calculating the expected fatigue service life Ni when the ship and boat shafting is located in the measuring time ti, and finally calculating the remaining service life Mi when the ship and boat shafting is located in the measuring time ti. The method overcomes the defects of an existing method, starts from a ship and boat shafting model, calculates the service life of the ship and boat shafting on the basis of vibration and fatigue coupling environments, solves the problem that calculation and predication of the ship and boat shafting service life are not involved in the prior art, is easy to understand and easy to realize, and is more suitable for calculation and prediction of the remaining service life of the ship and boat shafting.

Description

Ships and light boats axle based on vibrating fatigue coupling analysis is life-span prediction method

Technical field

The present invention relates to a kind of life-span prediction method, particularly relating to a kind of ships and light boats axle based on vibrating fatigue coupling analysis is life-span prediction method, belongs to ships and light boats field of power equipment technology.

Background technology

Under sail, the vibration of axle system is affect one of key factor of ships and light boats propulsion system safe operation to ships and light boats, if can not get effective control, will occur a series of serious consequences, the fracture that as axle is etc.For the vibration of axle system is made to correct evaluation, avoid the generation of malicious event, not only should carry out detailed vibration in the design phase and calculate, also need to carry out vibration-testing in the operation phase, whether reach required standard to investigate this propulsion system vibration characteristics.Existing Many researchers is calculated and is tested and carried out deep discussion and analysis the theory of vibration both at home and abroad.

But for the life prediction of ships and light boats axle system, existing method seldom relates to.Wherein main cause is: the one, and current check standard, is normally derived and is drawn by the fatigue strength of this axle as permissible stress, as long as meet standard, conventionally just thinks that this axle cording has infinite life, obviously, and this inadequate science, not pointed yet; The 2nd, because axle is residing environment, axle system is carried out to life prediction itself and there is certain complicacy.Under the effect of dynamic loading, ships and light boats axle system can vibrate, and vibration can produce alterante stress, if for a long time under alterante stress environment, fatigue damage can occur structure; In addition, the existence of fatigue damage has reduced the rigidity of structure, has reduced the natural frequency of structure, has affected the vibration characteristics of structure.So axle system is coupled under environment with tired in vibration.How to predict the life-span of ships and light boats axle system, answer the problem of " how long can also use ", depend on to a great extent effective vibrating fatigue model of coupling.

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, thereby the vibrating shaft being not suitable for is here life prediction; From damage type, be confined to crackle, in document, the main theory of life prediction foundation is the defect theory of 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 refer to crack initiation life fatigue lifetime, main theory foundation is classical fatigue cumulative damage theory.

Summary of the invention

Technical matters to be solved by this invention is: to ships and light boats axle, system carries out on the basis of vibrating fatigue coupling analysis, and it is life-span prediction method that a kind of ships and light boats axle is provided.

In order to solve the problems of the technologies described above, the technical solution adopted in the present invention is as follows:

Ships and light boats axle based on vibrating fatigue coupling analysis is a life-span prediction method, comprises State selective measurements time point t _iand to measure ships and light boats axle be in this Measuring Time point t _itime natural frequency ω _i(to n measurement, i=1,2,3 ..., n, i is positive integer), then to calculate ships and light boats axle be in this Measuring Time point t _itime expection N fatigue lifetime _i, finally calculating ships and light boats axle is in this Measuring Time point t _itime residual life M _i, described ships and light boats axle is residual life M _icomputing method be:

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

Situation 2: ω ₀> > ω, and ω _nwhen > ω, $M_i=N_i(1-\underset{p=1}{\overset{i}{\mathrm{\&Sigma;}}}{t}_p/N_p),i=\mathrm{1,2,3},...,n;$

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

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

Wherein: ω is the sinusoidal interference moment frequency of ships and light boats axle system, N ₀natural frequency ω while use for ships and light boats axle system ₀corresponding expection fatigue lifetime, N _αwhile being the i time prediction, ships and light boats axle is the stress-number of cycles having used, N _pbe the p time Measuring Time point t _pcalculate ships and light boats axle system expection fatigue lifetime, N _j-1for the natural frequency ω when the j-1 time Measuring Time point of ships and light boats axle system _j-1corresponding expection fatigue lifetime, N _jfor the natural frequency ω when the j time Measuring Time point of ships and light boats axle system _jcorresponding expection fatigue lifetime, M _jbe the j time measure time calculate ships and light boats axle be residual life, N _βbe after measuring for the j time to the i time when measurement ships and light boats axle be the stress-number of cycles having used.

Preferably, described State selective measurements time point t _imethod be, the residual life M while selecting ships and light boats axles system not use ₀1/2 place as (the obviously M of Measuring Time point for the first time 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 that ships and light boats axle is two material constants of the curve of fatigue, W _pfor the torsion section factor of ships and light boats axle system, T ₀for ships and light boats axle is the amplitude of periodic disturbing torque.

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

Adopt after technique scheme, ships and light boats axle based on vibrating fatigue coupling analysis of the present invention is life-span prediction method, its beneficial effect is: the present invention has overcome existing methodical shortcoming, be model from ships and light boats axle, based on being to calculate in the life-span to ships and light boats axle under vibration and tired coupling environment, solve that in prior art, not relate to ships and light boats axle be the problem of carrying out life-span calculating and prediction, the method easy to understand, easily realize, be more suitable for calculating and prediction that ships and light boats axle is residual life.

Accompanying drawing explanation

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

Fig. 2 is that ships and light boats axle of the present invention is

graph of relation.

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

Embodiment

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

Ships and light boats axle based on vibrating fatigue coupling analysis is life-span prediction method, comprises the following steps:

1, the natural frequency that at specific Measuring Time point measurement ships and light boats axle is

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 nonlinear, so there is ω ₀> ω ₁> ... > ω _n.For this reason, provide following natural frequency measurement, method: each Measuring Time point is selected in 1/2 place of the residual life calculating while measurement 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 is not used is ω ₀, and corresponding residual life M ₀=N ₀(N ₀expection fatigue lifetime while use for ships and light boats axle system).The 1st time Measuring Time point exists: t ₁=M ₀/ 2 places; Thereafter, each natural frequency Measuring Time point was expressed as successively with respect to the time interval of last Measuring Time point experience: 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 certain Measuring Time point is little with the large, medium and small phase lead time of repairing of ships and light boats axle system, this Measuring Time point can be arranged in to large, medium and small repairing 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, calculate the expection fatigue lifetime of ships and light boats axle system

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, can be divided into single-degree-of-freedom, multiple degrees of freedom and continuous system model.The present invention discusses as an example of shafting torsional oscillation single-mode system example, and (be single quality system, only consider the quality of screw propeller, other quality are not considered, suppose that main frame rigidity is very large, quality infinity 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 ₀torsional rigidity while use for ships and light boats axle system, 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 the moment of inertia that I is screw propeller, acts on the periodic disturbing torque T=T that ships and light boats axle is fastened ₀e ^{j ω t}, T ₀for ships and light boats axle is the amplitude of periodic disturbing torque, the vibration amplification factor that can try to achieve ships and light boats axle system is:

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

Wherein, ω ₀natural frequency while use for ships and light boats axle system,

Ships and light boats axle be the maximum stress in one-period can try to achieve into:

suppose that ships and light boats axle is that Fatigue Property Curve meets: wherein, N is expection fatigue lifetime, and m, C are that ships and light boats axle is two material constants of the curve of fatigue, relevant with axle based material character etc., τ _maxfor ships and light boats axle is the maximum stress bearing, expect that be fatigue lifetime:

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

Utilizing the linear progressive damage theory of Miner to calculate the fatigue damage of accumulative total, after the circulation of experience primary stress, is that the single damage causing is to ships and light boats axle:

D＝1/N。(4)

Suppose that ships and light boats axle system is followed successively by ω through the natural frequency measuring for i time 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 is not used ₀corresponding expection fatigue lifetime is N ₀, by (4) Shi Ke get, corresponding single damage is D ₀.

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

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

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

Situation 1: work as ω ₀when < ω, ω > ω ₀> ω ₁> ω ₂> ... > ω _ntherefore, 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 inferior is measurable is:

M _i=N ₀-N _α, i=1,2,3 ..., n, (5) N _αwhile being the i time prediction, ships and light boats axle is the stress-number of cycles having used.

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

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

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

Situation 3: work as ω ₀when > ω, may there is ω _i< ω.From avoiding the angle of resonance, this kind of situation should be avoided as far as possible.The mode that can take to improve ω, makes 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, can pass through fast resonance region, be handled as follows: suppose now to 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:

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

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, replace with set-point.After the j time, do not need to arrange natural frequency measurement,, re-use N _βresidual life after inferior:

M _i=M _j-N _β, i=j+1 ..., n (8) N _βbe that while prediction to the i time after measuring for the j time, ships and light boats axles is the stress-number of cycles having used.

Showing that after the natural frequency of each Measuring Time point and the residual life of correspondence, can draw " residual life-natural frequency " is M _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, the periodic disturbing torque T=167.428sin12.4tKNm(acting on this axle is periodic disturbing torque amplitude T ₀=167.428KNm).

This axle Fatigue Property Curve meets:

be 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 inferior, 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

expection N fatigue lifetime that must this axle by formula (3) ₀=18839 hours.

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

Residual life M while use ₀=N ₀, 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 the 1st time ₁=52.7rad/s, with ω ₁replace the natural frequency ω while use ₀, substitution formula (3) must be expected fatigue lifetime: N ₁=18779 hours.

By formula (6): residual life $M_{}$ ${}_1=N_1(1-\frac{t_1}{N_1})=N_1-{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="140319113405.png"\; state="\{\{state\}\}">t</figure-callout>}}_1=9360$ Hour.

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

Measure to obtain ω the 2nd time ₂=50.3rad/s, with ω ₂replace the natural frequency ω while use ₀, substitution formula (3) must be expected fatigue lifetime: N ₂=18700 hours.

By formula (6): residual life $M_2=N_2(1-\frac{N_2}{N_1})=t_1-t_2=4640$ Hour.

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

……

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

Above embodiment only, for explanation technological thought of the present invention, can not limit protection scope of the present invention with this, every technological thought proposing according to the present invention, and any change of doing on technical scheme basis, within all falling into protection domain of the present invention.

Claims (4)

1. the ships and light boats axle based on vibrating fatigue coupling analysis is a life-span prediction method, comprises State selective measurements time point t _iand to measure ships and light boats axle be in this Measuring Time point t _itime natural frequency ω _i(to n measurement, i=1,2,3 ..., n, i is positive integer), then to calculate ships and light boats axle be in this Measuring Time point t _itime expection N fatigue lifetime _i, finally calculating ships and light boats axle is in this Measuring Time point t _itime residual life M _i, it is characterized in that: described ships and light boats axle is residual life M _icomputing method be:

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

Situation 2: ω ₀> > ω, and ω _nwhen > ω, $M_i=N_i(1-\underset{p=1}{\overset{i}{\mathrm{\&Sigma;}}}{t}_p/N_p),i=\mathrm{1,2,3},...,n;$

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

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

Wherein: ω is the sinusoidal interference moment frequency of ships and light boats axle system, N ₀natural frequency ω while use for ships and light boats axle system ₀corresponding expection fatigue lifetime, N _αwhile being the i time prediction, ships and light boats axle is the stress-number of cycles having used, N _pbe the p time Measuring Time point t _pcalculate ships and light boats axle system expection fatigue lifetime, N _j-1for the natural frequency ω when the j-1 time Measuring Time point of ships and light boats axle system _j-1corresponding expection fatigue lifetime, N _jfor the natural frequency ω when the j time Measuring Time point of ships and light boats axle system _jcorresponding expection fatigue lifetime, M _jbe the j time measure time calculate ships and light boats axle be residual life, N _βbe after measuring for the j time to the i time when measurement ships and light boats axle be the stress-number of cycles having used.

2. the ships and light boats axle based on vibrating fatigue coupling analysis is life-span prediction method as claimed in claim 1, it is characterized in that: described State selective measurements time point t _imethod be, the residual life M while selecting ships and light boats axles system not use ₀1/2 place as Measuring Time point for the first time, 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. the ships and light boats axle based on vibrating fatigue coupling analysis is life-span prediction method as claimed in claim 1, 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 that ships and light boats axle is two material constants of the curve of fatigue, W _pfor the torsion section factor of ships and light boats axle system, T ₀for ships and light boats axle is the amplitude of periodic disturbing torque.

4. the ships and light boats axle based on vibrating fatigue coupling analysis is life-span prediction method as claimed in claim 3, it is characterized in that: described ships and light boats natural frequency of shafting ω _icorresponding vibration amplification factor μ _icomputing formula be ${\mathrm{\&mu;}}_i=1\sqrt{{[1-{(\mathrm{\&omega;}/{\mathrm{\&omega;}}_i)}^2]}^2+{(2\mathrm{\&xi;\&omega;}/{\mathrm{\&omega;}}_i)}^2},$ Wherein: ξ is the damping ratio of ships and light boats axle system.

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