Life Evaluation Of Electro-hydraulic Servo Valve Based On Wear Mechanism

Wang Xiaohonga , Li Qiuxi b , Feng Yalic

School of Reliability and System Engineering, Beihang University, Beijing, 100191, P.R.China

awxhong@buaa.edu.cn, *bsubmarinelee@163.com, c531009852@qq.com

Keywords: Electro-hydraulic servo valve, SSADT, Life evaluation, Reliability analysis

Abstract. Electro-hydraulic servo valve is the key component in electro-hydraulic servo control

system, it has high reliable assemblies over a long period of time. This paper utilizes the accelerated

degradation testing to evaluate their reliability and life. Firstly, the wear failure mechanism of

electro-hydraulic servo valve is analyzed to determine. Then, by modeling the degradation process

as a drift Brown Motion, this paper generated the reliability model of the electro-hydraulic servo

valve. Finally, the maximum likelihood is used to estimate the degradation data of leakage from the

test. The methodology in this paper is demonstrated and validated by reasonability of estimation of

electro-hydraulic servo valve.

Introduction

Electro-hydraulic servo valve is the key component in electro-hydraulic servo control system,

and it is widely used in aviation, aerospace, shipbuilding and other fields because of the advantages

of fast dynamic response, high control precision, and long service life.

At present, two technical problems always exist during the development of hydraulic

technology and the development of the electro-hydraulic servo control system, that is, pollution and

leakage, especially the oil pollution. Oil pollution will cause wear of servo valve and affect its

control in precision. Severe wear could threaten safe operation of entire equipment system. This

paper aims at quantitatively studying the influence of contamination wear on life of the servo valve

with accelerated degradation test method.

Failure mechanism analysis

Wear will lead to decrease the overlap, pressure gain, and increase the leakage of

electro-hydraulic servo valve. So the pressure gain, the leakage and the overlap can be selected as

index of performance degradation for test. In the detection of these three indicators in

pre-experiment, due to the bigger error in measurement of the overlapping, only pressure gain and

leakage are taken as estimated indicators in this test.

Test method research

After a great number of researches, it shows that the oil contamination level is seven or eight

when the Electro-hydraulic servo valve works normally. Through the preliminary experiments of

electro-hydraulic servo valve, it can be found that blocking appears obviously on electro-hydraulic

servo valve when the oil pollution degree is 12. It suggests that the grade 12 has reached the limit

where the electro-hydraulic servo valve still can work. Thereby, this test decides to make

accelerated degradation test at four levels, respectively level 8,9,10 and 11. Additional, this test also

follows the equal ADT data stress model.

Analysis the test data

In Consideration of the exploratory nature of this experiment, two degradation performance

indicators are selected, namely, pressure gain and leakage. But because the leakage degradation is

more obviously. So following will only respectively analyze the degradation data of leakage.

Applied Mechanics and Materials Vols. 494-495 (2014) pp 739-742Online available since 2014/Feb/06 at www.scientific.net© (2014) Trans Tech Publications, Switzerlanddoi:10.4028/www.scientific.net/AMM.494-495.739

All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP,www.ttp.net. (ID: 130.207.50.37, Georgia Tech Library, Atlanta, USA-15/11/14,01:36:53)

1) Test data

In the test, leakage will increase gradually with the increase of degree of wear on the

electro-hydraulic servo valve. Below is the change curve of leakage of tested electro-hydraulic

servo valve under four stress levels in the test.

However, limited by the experimental condition and lack of test data, it is some kind of

difficult to process the test data and estimate the life of electro-hydraulic servo valve. So this paper

respectively interpolates the test data of leakage by neural network. Result of Interpolations shows

below:

Fig.4 Leakage degradation curve Fig.5 Interpolation of leakage data

2) Accelerated Degradation Model

Through fitting on the test data after interpolation, it is found that pressure gain linearly

decreases with time. This paper assumes that the relationship between change of leakage and test

itself abides by the Brown movement.

0( ) ( ) ( , )Y t B t g t s t yσ= + + (1)

Y (t) is the performance of the product, t is time scales, y0 is the value of performance at initial

moment t0, B (t) is the standard Brownian movement, B (t) ~ N (0, t), accelerated drift coefficient g

(t, s) is irrelevant to time t, and is only the deterministic function related to the stress. Therefore this

is an accelerated model, namely g (t, s) = d (s), σ is the diffusion coefficient.

Because the brown movement is a normal process, and if performance degradation marginal

value C is given, the invalid life distribution will obey the Inverse Gaussian Distribution, So the

corresponding reliability function is:

0 0 0

2

( ) 2 ( ) ( ) ( )( ) exp

C y d s t d s C y C y d s tR t

t tσσ σ

− − ⋅ − − + =Φ − Φ −

(2)

Φ stands for probability density function in standard normal distribution, the function above

is the reliability evaluation model based on drift Brown movement.

3) Parameter Estimation of Accelerated Degradation Model

Performance degradation data received from the accelerated degradation test can be used to

estimate the unknown parameters, thus reliability function of product can be got. Thereby, the

evaluation on the reliability of product can be realized through the reliability curve.

It is assumed that there are total n electro-hydraulic servo valve are tested under SSADT at k

levels. Time interval for the measurements of electro-hydraulic servo valve is constant, take as t∆ .

Measurement times take as Ml under each stress level, and total measurement times are M,

then1

K

k

k

M M=

=∑ . The period of time is lM t⋅∆ under every stress level, and total duration is M t⋅∆ .

Monitoring time each time is tikj（i=1,…,n；k=1,…,K；j=1,…,M）, and the performance value

detected is yikj.

740 Current Development of Mechanical Engineering and Energy

The model format is( )= exp( / )k kd S A B S−

, and its log-likelihood Function of SSADT is,

2

( 1)2

21 1 1

( ) exp( / ) )1ln ln(2 ) ln( )

2

kMn Kikj ik j k

i k j

y y A B S tL t

tπ σ

σ

−

= = =

− − − ⋅ ∆ ∝ − ∆ + + ∆

∑∑∑ (3)

Taking the derivative of all the parameters in the formula, let it equals zero, then Each of the

parameters of maximum likelihood estimation can be calculated:

22

( 1)

1 1 1

1 1 1

1ˆ ( ) exp( / )

k

k

Mn K

ikj ik j kMn Ki k j

k

i k j

y y t A B S

t M

σ−

= = =

= = =

= − − ∆ ⋅ − ∆ ⋅

∑∑∑∑∑∑

(4)

Using the maximum likelihood estimation method to estimate A and B:

( 1)

1 1 1

1 1 1

( ) exp( / )

exp(2 / )

k

k

Mn K

ikj ik j k

i k j

Mn K

i k j

y y B S

A

t B S

−

= = =

= = =

−

=

∆ ⋅

∑∑∑

∑∑∑

( 1)

1 1 1

1 1 1

1( )exp( / )

11

exp(2 / )

k

k

Mn K

ikj ik j k

i k j k

Mn K

i k j k

y y B SS

A t B TS

−

= = =

= = =

− ⋅

=

⋅ ∆ ⋅ ⋅

∑∑∑

∑∑∑ (5)

In the formula, A and B are the algebraic expression of the fitting acceleration model. It has no

dimension. The parameter σ is the diffusion coefficient of the electro-hydraulic servo valve.

Taking the parameters in the table 1 into the equation (3), it obtains the estimations of model

parameters of leakage:

Table 1 Estimations of the modle parameters

A B σ 0y

0.8491 917.2224 0.4586 4.2334

The reliability function is :

4.2334 0.0321 2*0.0321 ( 4.2334) 4.2334 0.0321( ) exp

0.21030.4586 0.4586

C t C C tR t

t t

− − ⋅ − − + = Φ − Φ −

(6)

When the failure threshold C of the pressure gain is equal to 25, the reliability curve shows

below:

Fig. 8 Reliability curve at normal working condition

From the Fig.8, when the failure threshold C of the leakage is equal to 0.7, the medium life is

2100h.

Conclusion

1) This article takes the contamination level of the working oil as the stress of this test, pressure

gain and leakage as the indicators of the performance degradation, to carry out the accelerated

degradation testing of step stress. It designs and constructs the pollution wear test system of

Electro-hydraulic Servo Valve according to this designed test method.

Applied Mechanics and Materials Vols. 494-495 741

2) It takes Drift Brown Movement to fit degradation indicator of Electro-hydraulic Servo Valve

and degradation data of leakage. According to the leakage degradation data, its evaluated

median life of the electro-hydraulic servo valve is 2100h.These predicted value is closed, and

matches with Engineering Experience Value, which explain the test validity.

2) there are still some factors that are out of consideration in the test process, which will impact

the wear of electro-hydraulic servo valve, such as the oil temperature, the frequency

etc.Therefore, it needs to consider these factors comprehensively and combine multi-source

information in the process of subsequent data analysis, so that the lifetime and reliability of

product can be evaluated more exactly.

References

[1]. Zhang Li-ping, The Principle of hydraulic valve [M] .Bei Jing: Chemical Industry

Press:368,375,388.2009.

[2]. Hou Chen-guang ,Yuan Chao-hui ,He Chang-an . Based on the fuzzy fault tree reliability

analysis of the electro-hydraulic steering gear , Machine Tool and Hydraulics. 2007.

[3]. TANG L C, XIE M.Planning of step-stress accelerated degradation test[C]//Proceedings of

Annual Reliability and Maintainability Symposium, Los Angeles, USA, January 26-29,2004：

287-292.

[4]. Haitao L,Elsayed A .E. Optimization of system reliability robustness using accelerated

degradation testing [C].RAMS.2005.48-54;

[5]. Li Xiao-yang ,Jiang Tong-min. . Constant-stress accelerated degradation testing of satellite

assemblies [J]. Acta Aeronautic et Astronautic Sinica , 2007. 28(Sup) 100-103

[6]. Zheng De-qiang, Li Hai-bo, Zhang Zheng-ping. et.al Study on Accelerated Degradation Testing

for Predicting the Life of Induction Motors .2011.10

742 Current Development of Mechanical Engineering and Energy

Current Development of Mechanical Engineering and Energy 10.4028/www.scientific.net/AMM.494-495 Life Evaluation of Electro-Hydraulic Servo Valve Based on Wear Mechanism 10.4028/www.scientific.net/AMM.494-495.739