CN104697920A - Method for predicting service life of rubber shock absorber - Google Patents

Abstract

The invention discloses a method for predicting a service life of a rubber shock absorber; the method comprises the steps: combining aging factors, influencing the use of the rubber shock absorber, and fatigue factors; firstly, establishing an aging service life prediction mathematic model of the rubber shock absorber in use of a hot air accelerated aging test; secondly, establishing a model relationship between static rigidity of a new absorber and fatigue times by means of the aging service life prediction model and the existing performance parameter of an old absorber; further, establishing a relation model between the static rigidity and the time and obtaining a service life prediction model of the rubber shock absorber, thereby realizing prediction of the service life of the rubber shock absorber. The aging factors and the fatigue factors are combined well to predict the service life of the rubber shock absorber, and the prediction precision is high.

Description

The Forecasting Methodology in a kind of rubber shock absorber serviceable life

Technical field

The present invention relates to rubber shock absorber forecasting technique in life span field, be specifically related to the forecast model in a kind of rubber shock absorber serviceable life for vibration damping, noise reduction.

Background technology

It is adjustable that rubber shock absorber has goods elastic parameter, and can decay, absorb low frequency, dither and noise, shock stiffness is greater than dynamic stiffness and Static stiffness, and the advantage such as volume is little, lightweight, non-maintaining, therefore extensively adopt in every field.But rubber shock absorber due to the impact of the fatigure failure and rubber material ages that there is ess-strain, has the problem in a serviceable life in actual use.Once there is fatigure failure and aging in elastomeric material, the rigidity of rubber shock absorber and damping parameter will off-design values gradually, and namely its vibration isolation erosion-resisting characteristics is also subject to direct impact.Therefore the serviceable life of reasonable prediction rubber shock absorber, a urgent problem in rubber shock absorber engineering design and application has been become.

Consult domestic and international related data to learn, at present also not to carrying out predicting accurately the serviceable life of rubber shock absorber, this is because rubber shock absorber affects while being in use subject to tired and aging action simultaneously.Current people studied for the serviceable life of rubber shock absorber, still mostly adopted aging life-span and separated the method studied fatigue lifetime.Research for the aging life-span of elastomeric material begins to take shape, also achieves plentiful and substantial achievement in research, present stage, and in domestic and international rubber material ages research, conventional method is accelerated aging test method.Obtained the permanent set of elastomeric material under each test temperature and digestion time by accelerated aging test, through a series of relevant mathematical method, founding mathematical models predicts the aging life-span of rubber.Rubber shock absorber fatigue mainly refers to the mechanical fatigue that elastomeric material produces under cycle alternate load effect, thus the phenomenon that the physical and mechanical property that the crackle produced slowly increases and causes declines gradually.The large deformation periodic loading that rubber shock absorber is in use mainly compressed, is in complicated stress state.Accordingly, the present invention, by the aging action and fatigue factor that affect rubber shock absorber use being combined, invents a kind of method predicting rubber shock absorber serviceable life.

Summary of the invention

The object of the invention is to study the rubber shock absorber being subject to aging and tired double action, a kind of method in prediction rubber shock absorber serviceable life with high accuracy is provided.

To achieve these goals, the technical solution of employing is in the present invention:

The Forecasting Methodology in rubber shock absorber serviceable life, specifically comprises the following steps:

(A) establishment step of rubber shock absorber aging life-span forecast model, utilizes aging test, sets up the aging life-span forecast model of rubber shock absorber;

Wherein said aging test adopts hot-air accelerated aging test method, and this aging life-span forecast model is the relational model of ageing properties conservation rate and time, temperature.

(B) establishment step of life forecast model, this step comprises:

(B1) old of the rubber shock absorber of known existing use n, according to the aging life-span forecast model set up in step (A), reverse can go out the ageing properties conservation rate using n at normal temperatures;

By this ageing properties conservation rate P, substitute in aging life-span predictor formula under certain aging temperature T, obtain number of days d aging at this temperature;

Under aging temperature T, by the aging d days of new part of vibration damper, this new performance had has identical ageing properties parameter, as identical ageing properties conservation rate with using the vibration damper of n.

(B2) under certain condition, torture test is done to the new part of the rubber shock absorber having carried out aging test in described step (B1), accomplish that this part has identical ageing properties parameter with using old of the rubber shock absorber of n always, record this times of fatigue, this times of fatigue is identical with times of fatigue in actual application;

Rubber shock absorber application is very extensive, for single rubber shock absorber, it is in a certain specific environment for use, its behaviour in service is all substantially identical, therefore the times of fatigue that rubber shock absorber is annual is also identical, with this times of fatigue for benchmark, the times of fatigue that rubber shock absorber is annual can be calculated.

(B3) use n can also be calculated according to aging life-span forecast model ₁, n ₂, n ₃year, number of days d aging respectively under aging temperature T ₁, d ₂, d ₃my god;

Get the new part of multiple rubber shock absorber and carry out aging test respectively, by each new corresponding number of days of aging difference, make it have respectively and use n ₁, n ₂, n ₃year the identical ageing properties parameter of old of rubber shock absorber.

(B4) carry out torture test for the new part of rubber shock absorber through aging test in above-mentioned steps (B3), loading environment is identical with loading environment in described (B2), loads n respectively ₁, n ₂, n ₃the times of fatigue in year, uses n with reality after finishing torture test ₁, n ₂, n ₃the performance parameter in year is identical.

(B5) measure the performance parameter through the new part of rubber shock absorber of torture test in above-mentioned steps (B4), the relational model of performance parameter and time can be simulated.

Wherein, characterize ageing properties parameter with ageing properties conservation rate, the ageing properties parameter in described step (B1), (B3) is ageing properties conservation rate.

Characterize the performance parameter of rubber shock absorber with Static stiffness, the performance parameter in described step (B2), (B5) is Static stiffness.The Static stiffness of rubber shock absorber is the ability characterizing vibration damper in use resistance to deformation, rubber shock absorber in use, along with aging with the impact of fatigue, Static stiffness can become large gradually, and the function such as its vibration damping, noise reduction, shock resistance can directly be affected.Therefore, the present invention using Static stiffness as characterizing the rubber shock absorber important parameter that can use.

Advantage of the present invention and good effect are:

(1) during the serviceable life in the past studying rubber shock absorber, generally can ignore the impact of fatigue factor, or can study separating aging life-span and fatigue lifetime.Which kind of research mode all truly can not reflect the serviceable life of rubber shock absorber, cannot reach and predict accurately.Aging action and fatigue factor well combine and predict rubber shock absorber serviceable life by the present invention.

(2) in the past when studying the life-span of rubber shock absorber, usually rubber test piece is cut into dumbbell shape standard sample, by studying the change of the physical function parameter such as elongation at rupture, pulling strengrth of sample, the life-span of prediction vibration damper.This just have studied the life-span of rubber size, well can not reflect the life-span of vibration damper.Therefore the present invention can reflect the change of this performance parameter of Static stiffness of vibration damper service condition by research, carrys out the serviceable life of pre-vibration damper.

Accompanying drawing explanation

The graph of a relation of Fig. 1 ageing properties conservation rate and digestion time;

Fig. 2 lgK with graph of a relation;

The fit correlation curve map of Fig. 3 Static stiffness and time.

Embodiment

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

Embodiment

The Forecasting Methodology in rubber shock absorber serviceable life, specifically comprises the following steps:

(A) foundation of rubber shock absorber aging life-span forecast model.

Utilize hot-air accelerated aging test, set up the aging life-span forecast model of rubber shock absorber.

According to the requirement of aging test, 60 DEG C, 70 DEG C, 80 DEG C, 90 DEG C, 100 DEG C these five temperature are selected to carry out hot-air accelerated aging test.

(A1) before aging test, the new part of rubber shock absorber at least gets 3, under normal room temperature (23 ± 2 DEG C), measure Static stiffness numerical value and record.

(A2) ageing oven is modulated to required temperature, after steady operation, the vibration damper of numbering in advance is put into ageing oven successively, shut chamber door and start test.After the ageing oven of constant temperature put into by rubber shock absorber, namely start to calculate digestion time, after reaching official hour node, take out the vibration damper needing to detect.

(A3) rubber shock absorber taken out needs to park 12-24h at normal room temperature, then carries out the measurement of Static stiffness, and records result.

According to above step, take-off time node is the rubber shock absorber of 1d, 2d, 3d, 4d, 5d, 7d, 9d, 12d, 16d, 20d, 25d, 32d successively, and measures Static stiffness.

(A4) rubber shock absorber has been measured at 5 aging temperatures by air oven aging test, the Static stiffness numerical value under different time node.The ageing properties conservation rate P of vibration damper is calculated according to following formula (1).

$P=1-\frac{K-K_1}{K_1}---\left(2\right)$

In formula: the Static stiffness of K-aging rear rubber shock absorber; K ₁the Static stiffness of the new part of-aging front rubber shock absorber.

Rubber shock absorber Static stiffness ageing properties conservation rate data are as shown in table 1 below.The graph of a relation of ageing properties conservation rate and digestion time, as shown in Figure 1.

Table 1

The available following experimental formula of relation between ageing properties conservation rate and digestion time τ describes:

$P=B{e}^{-K{\mathrm{\τ}}^{\mathrm{\α}}}---\left(2\right)$

In formula: B-test constant; K-rate constant; τ-digestion time, d; α-empirical constant.

Between rate constant K and aging temperature T, relation obeys Arrhenius formula:

K＝Ae ^-E/RT(3)

In formula: E-apparent activation energy, Jmol ^-1; R-gas law constant, JK ^-1mol ^-1;

T-aging temperature, K; A-frequency factor, d ^-1.

(A5) adopt the method for Approach by inchmeal to solve to α, the criterion of approaching makes α be accurate to 2 significant digits, makes I minimum.

$I=\underset{i=1}{\overset{q}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{(y_{\mathrm{ij}}-{\hat{y}}_{\mathrm{ij}})}^2---\left(4\right)$

In formula: y _ijunder i-th aging temperature, the trial value of the ageing properties conservation rate of a jth test point;

under i-th aging temperature, the predicted value of the ageing properties conservation rate of a jth test point.

After a given α value, formula (2) is taken the logarithm change, obtains following form of straight lines.

Y＝a+b·X (5)

In formula: Y=lg P, a=lg B, x=τ ^α.

The coefficient in (5) formula can be calculated by Linear regression:

$b_i=\frac{\mathrm{\ΣXY}-\frac{\mathrm{\ΣX\ΣY}}{n}}{{\mathrm{\ΣX}}^2-\frac{{\left(\mathrm{\ΣX}\right)}^2}{n}}---\left(6\right)$

$a_i=\frac{\mathrm{\ΣY}}{n}-b_i\·\frac{\mathrm{\ΣX}}{n}---\left(7\right)$

Obtain the rate constant K under each aging temperature thus _i=-2.303b _iand test constant pass through obtain the estimated value of parameter B

In like manner, logarithm change is done to formula (3) and obtains following formula:

In W=C+DZ (8) formula: W=lg K, C=lg A, z=T ^-1.

The coefficient in formula (8) can be calculated by Linear regression:

$D\frac{\mathrm{\ΣWZ}-\frac{\mathrm{\ΣW\ΣZ}}{q}}{{\mathrm{\ΣZ}}^2-\frac{{\left(\mathrm{\ΣZ}\right)}^2}{q}}---\left(9\right)$

$C=\frac{\mathrm{\ΣW}}{q}-D\·\frac{\mathrm{\ΣZ}}{q}---\left(10\right)$

The estimated value of the velocity constant K under q test temperature can be obtained thus so

$I=\underset{i=1}{\overset{q}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{(y_{\mathrm{ij}}-{\hat{y}}_{\mathrm{ij}})}^2=\underset{i=1}{\overset{q}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{(y_{\mathrm{ij}}-{\hat{B}e}^{-{\hat{K}}_i{\mathrm{\τ}}_{\mathrm{ij}}^{\mathrm{\α}}})}^2---\left(11\right)$

(A6) related check of W=C+DZ equation

The related check of W=C+DZ equation, use correlation coefficient r to test, following formula is pressed in the calculating of correlation coefficient r:

$r=\frac{\mathrm{\ΣWZ}-\frac{\mathrm{\ΣW}\·\mathrm{\ΣZ}}{q}}{\sqrt{[\mathrm{\Σ}{W}^2-\frac{{\left(\mathrm{\ΣW}\right)}^2}{q}][\mathrm{\Σ}{Z}^2-\frac{{\left(\mathrm{\ΣZ}\right)}^2}{q}}]}---\left(12\right)$

Search the tabular value of degree of freedom df=q-2 when significance level is 0.01 in correlation coefficient charts, if calculated value is greater than tabular value, then W and Z is significantly relevant, and equation is set up.Otherwise equation is false, search reason, again test or have a penalty heat.

The standard deviation of W is calculated as follows:

$S_w=S\sqrt{1+\frac{1}{q}+\frac{{(Z_0-\stackrel{\‾}{Z})}^2}{[\mathrm{\Σ}{Z}^2-\frac{{\left(\mathrm{\ΣZ}\right)}^2}{q}]}}---\left(13\right)$

In formula: z ₀the T at certain temperature ^-1; five aging temperature T ^-1mean value.

Then the upper limit of the fiducial interval of W is:

W＝C+DZ+tS _w(14)

Find the numerical tabular of one-sided boundary t when t can be 0.05 from degree of freedom df=q-2 and significance level in formula.

(A7) according to above calculating, under drawing normal temperature the rate constant of (298K) the upper limit as shown in the formula:

$\hat{K}={10}^{(C+D\·\frac{1}{T_o}+t{S}_w)}---\left(15\right)$

Then the aging life-span predictive equation of rubber shock absorber is at normal temperatures:

$P=\hat{B}\exp (-\hat{K}{\mathrm{\τ}}^{\mathrm{\α}})---\left(16\right)$

When the ageing properties limit value of rubber shock absorber is P ₀, the aging life-span forecast model of rubber shock absorber under normal temperature can be obtained, namely

$\mathrm{\τ}=\exp \left[\frac{1}{\mathrm{\α}}(\ln \ln \frac{\hat{B}}{P_0}-\ln \hat{K})\right]---\left(17\right)$

By MATLAB by calculating process sequencing, when α=0.52, I is minimum.Obtain the test constant B at each temperature and rate constant K, as shown in table 2 below.

Table 2

The estimated value of B can be calculated by table 2:

$\hat{B}=\frac{\mathrm{\Σ}{B}_i}{5}=\frac{1}{5}(1.0476+1.0106+0.9795+0.9862+0.9978)=1.0043$

K value in table 2 is got common logarithm, makes lgK couple graph of a relation, as shown in Figure 2.

One-variable linear regression method is adopted to calculate the standard deviation S of coefficient C, D, correlation coefficient r and W _w, result of calculation is in table 3.

Table 3

Table look-up degree of freedom is 3, related coefficient tabular value when significance level is 0.01 is 0.959, | the calculated value of r| is greater than tabular value, so the equation set up regression effect remarkable.

Table look-up degree of freedom is 3, one-sided boundary level of significance be 0.05 t value be 2.353, so the forecast interval upper limit of lgK is:

$\mathrm{lgK}=4.8890-2031.7\·\frac{1}{T}+2.353\×0.0110=4.91488-2031.7\·\frac{1}{T}---\left(18\right)$

The rate constant under normal temperature (298K) can be calculated by above formula:

$\hat{K}={10}^{4.91488-2031.7\×\frac{1}{298}}=0.0125---\left(19\right)$

When the ageing properties limit value of rubber shock absorber is P ₀=0.3, can obtain the aging life-span forecast model of rubber shock absorber under normal temperature 25 DEG C (298K) is:

(B) process of establishing of life forecast model.

(B1) (Static stiffness is also in normal range old of the known existing use rubber shock absorber of 6 years after testing, vibration damper can also normally use), according to the aging life-span predictor formula set up, can reverse go out at the normal temperature 25 DEG C use ageing properties conservation rate P of 6 years.

$P=\hat{B}\exp (-\hat{K}{\mathrm{\τ}}^{\mathrm{\α}})=1.0043e^{-0.0125\×2190^{0.52}}=0.51$

By P=0.51, when aging temperature 100 DEG C, substitute in aging life-span forecast model.Obtain number of days aging at this temperature

At aging temperature 100 DEG C, by aging for the new part of rubber shock absorber 5.67 days, this new performance had has identical ageing properties parameter with using the rubber shock absorber of 6 years.

(B2) be 5Hz by the rubber shock absorber of aging 5.67 days at loading frequency, Plumb load displacement range: 0.5-2.5mm, torture test is done under the technical requirement that amplitude is ± 1mm, accomplish that this part has identical Static stiffness with using the rubber shock absorber of 6 years always, record times of fatigue is 1,500,000 times, and this times of fatigue is identical with times of fatigue in actual application.

With the times of fatigue of 1,500,000 times for benchmark, can calculate the annual times of fatigue of vibration damper is 250,000 times.(rubber shock absorber is applied in every field, and its annual ruuning situation is all substantially identical, and the times of fatigue that therefore rubber shock absorber is annual is also identical)

(B3) use 7,8,9,10,11,12 can also be calculated according to aging formula ... the ageing properties conservation rate in year is respectively 0.480,0.457,0.430,0.409,0.394,0.378 ...Number of days 6.7,7.6,8.7,9.6,10.5,11.5 aging respectively at aging temperature 100 DEG C ... my god.And by aging for new for rubber shock absorber part corresponding number of days.

(B4) rubber shock absorber having carried out aging test in (B3) is carried out torture test, loading environment is with identical above, times of fatigue loads 1,750,000 times, 2,000,000 times, 2,250,000 times, 2,500,000 times, 2,750,000 times, 3,000,000 times respectively ..., after finishing torture test, use 7,8,9,10,11,12 with reality ... the Static stiffness in year is identical.

(B5) after the rubber shock absorber in (B4) being measured Static stiffness respectively, simulate the graph of a relation of Static stiffness and time, as shown in Figure 3, the relational model simulating Static stiffness and time is :-2.0714x ²+ 55.071x+504.43.

Certainly, above-mentioned explanation is not limitation of the present invention, and the present invention is also not limited in above-mentioned citing, and the change that those skilled in the art make in essential scope of the present invention, remodeling, interpolation or replacement also should belong to protection scope of the present invention.

Claims (5)

1. the Forecasting Methodology in rubber shock absorber serviceable life, it is characterized in that, it comprises the following steps:

(A) establishment step of rubber shock absorber aging life-span forecast model, utilizes aging test, sets up the aging life-span forecast model of rubber shock absorber;

(B) establishment step of life forecast model, this step comprises:

(B1) old of the rubber shock absorber of known existing use n, according to the aging life-span forecast model set up, carries out aging test to the new part of a rubber shock absorber and makes it have the ageing properties parameter identical with old;

(B2) under certain condition, torture test is done to the new part of the rubber shock absorber having carried out aging test in described step (B1), accomplish that this part has identical performance parameter with using old of the rubber shock absorber of n always, record this times of fatigue, under the condition that annual times of fatigue is constant, calculate the times of fatigue that rubber shock absorber is annual;

(B3) get the new part of multiple rubber shock absorber again and carry out aging test respectively, make it have respectively and use n ₁, n ₂, n ₃year the identical ageing properties parameter of old of rubber shock absorber;

(B4) carry out torture test for the new part of rubber shock absorber through aging test in above-mentioned steps (B3), loading environment is identical with loading environment in described (B2), and times of fatigue loads n respectively ₁, n ₂, n ₃the times of fatigue in year;

(B5) measure the performance parameter through the new part of rubber shock absorber of torture test in above-mentioned steps (B4), simulate the relational model of performance parameter and time.

2. the Forecasting Methodology in rubber shock absorber according to claim 1 serviceable life, it is characterized in that, aging test described in described step (A) adopts hot-air accelerated aging test method.

3. the Forecasting Methodology in rubber shock absorber according to claim 1 and 2 serviceable life, it is characterized in that, the ageing properties parameter in described step (B1), (B3) is ageing properties conservation rate.

4. the Forecasting Methodology in rubber shock absorber according to claim 3 serviceable life, is characterized in that, the aging life-span forecast model in described step (A) is the relational model of ageing properties conservation rate and time, temperature.

5. the Forecasting Methodology in rubber shock absorber according to claim 1 serviceable life, it is characterized in that, the performance parameter in described step (B2), (B5) is Static stiffness.