WU Qiong (吳 瓊), YANG Jian-zhong (楊建中), FU Hui-min (傅惠民), XU Qing-hua (徐青華), MAN Jian-feng (滿劍鋒)

1 Institute of Spacecraft System Engineering, China Academy of Space Technology, Beijing 100094, China 2 College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China 3 Research Center of Small Sample Technology, Beijing University of Aeronautics and Astronautics, Beijing 100191, China

Deployment Reliability Test and Assessment for Landing Gear of Chang’E-3 Probe

WU Qiong (吳 瓊)1*, YANG Jian-zhong (楊建中)1,2, FU Hui-min (傅惠民)3, XU Qing-hua (徐青華)1, MAN Jian-feng (滿劍鋒)1

1InstituteofSpacecraftSystemEngineering,ChinaAcademyofSpaceTechnology,Beijing100094,China2CollegeofAerospaceEngineering,NanjingUniversityofAeronauticsandAstronautics,Nanjing210016,China3ResearchCenterofSmallSampleTechnology,BeijingUniversityofAeronauticsandAstronautics,Beijing100191,China

Chang’E-3 probe incorporates four landing gears to assure the soft-landing, which are stowed while launching and deployed after separated from rocket. Deployment reliability is quite crucial for this mission. The deployment reliability test (DRT) method and assessment method were developed in this paper. Then DRT was conducted and the deployment reliability estimate of Chang’E-3 probe was used to verify the proposed methods.

Chang’E-3;landinggear;deployment;reliability;test;assessment

Introduction

Chang’E-3 probe, which is the third spacecraft of China’s Lunar Exploration Program, landed on the Moon’s Sinus Iridum on December 14, 2013 (Fig.1). The main objective of this mission is to achieve China’s first soft-landing and roving exploration on an extraterrestrial object[1-2]. The probe incorporates a lander and a rover (i.e., Yutu Rover). In order to attenuate the landing shock and assure the landing safety, four landing gears are designed on sides of the lander. The landing gears sustain the entire probe during landing process and also continuously support the lander after landing. Therefore, the landing gears need to acquire a large support area to insure a safe and stable soft-landing. However, due to the restriction of the internal envelop of Long March 3B Rocket which launches the probe, the landing gears must be stowed and attached to sides of the lander while launching. When the probe has been separated from rocket in the Earth-Moon Transfer Orbit (EMTO), the landing gears deploy to the predefined position and latch which can ensure the probe acquire expectant support area[3-9], as shown in Fig.2.

Fig.1 Chang’E-3 lander on the lunar surface imaged by Yutu Rover on December 22, 2013

(a) Stowed state (i.e., undeployed)

(b) Deployed state

If the landing gears do not deploy to the predefined position, the valuable payload on the probe may be damaged resulting from the severe landing impact. Furthermore, the probe may overturn on the surface of the Moon in landing process due to the small support area. It means that the soft-landing mission is failed to some extent. Therefore, the deployment reliability of landing gears is quite crucial to the landing mission of Chang’E-3.

In the following study, the operating principle of landing gear is studied, and the failure modes and effects for the deployment are analyzed, from which the critical failure mode is identified. The reliability characteristic parameter (RCP) in deploying process is accordingly identified. Deployment reliability test (DRT) method of landing gear and deployment reliability assessment (DRA) method are then presented. In the reliability assessment method, deployment reliability estimates of landing gear and probe are both given, and the lower confidence limit of them are also obtained. Finally, DRT of Chang’E-3 probe is carried out and the deployment reliability is assessed.

1 Failure Mode and Effects Analysis

The four landing gears have the same functions and operating principle. They also have similar structural composition, as shown in Fig.3. Each landing gear mainly consists of a primary strut (PS), a multi-function secondary strut (MFSS), a single-function secondary strut (SFSS),etc. As a driving device for deployment, a compressed spring is stowed in MFSS. When the probe is sent into EMTO, driven by the stored deformation energy of the compressed springs, the landing gears deploy to the predefined position independently (Fig.3).

(a) Before deployment

(b) After deployment

In the deploying process, MFSS lengthens with linear velocityvin phase with the spring restoring. And at the same time, the combination of PS and SFSS revolves around thePRline with angular velocityω. Here thePRline connects the center of PS’s upper end with that of SFSS, as shown in Fig.3(a). When MFSS lengthens to the predefined length, it is locked and the deployment of landing gear is completed, as shown in Fig.3(b).

The deployment of landing gear is essentially a work done process in which the driving force of compressed spring overcomes the resisting force resulting from frictions of moving pairs in landing gear. Apparently, it is a representative stress-strength interference problem[10].

During the deploying, the possible main failure modes are undeploying to the predefined position, as a result of a large resisting force or a inadequate driving force. For any landing gear, it can successfully deploy as long as the spring’s driving energy is bigger than the resisting work to be overcome. Therefore, the DRT and DRA can be carried out based on this failure mode.

2 DRT Method

2.1 RCP analysis

As mentioned above, the landing gear’s deployment is essentially a work done process. According to the stress-strength interference theory, the deployment reliabilityRis equal to the probability that the driving energyEdis bigger than the resisting workWr, that is

R=P{Ed>Wr}.

(1)

However, it is difficult to obtain the measurement of the resisting workWrin engineering, because of the resisting force rising from frictions of several joints in the landing gear, as shown in Fig.3(b). And the deploying process is a three-dimensional movement. Thus the value and direction of the resisting force,i.e. the combined effect of the joints’ frictions, continuously vary when deploying. Therefore, it is nearly impossible to accurately measure the resisting force or the resisting work in engineering.

According to the law of conservation of energy and the theorem of kinetic energy, we have

(2)

=P{ω>0}

(3)

It can be seen that the driving energyEdmust be bigger than the resisting workWras long as the angular velocityωcorresponding to the predefined position is bigger than zero. More importantly, the angular velocity can be measured easily by high-speed photography technology, compared to the resisting work value. Therefore, the angular velocity at the predefined position (AVPP) of the combination of PS and SFSS can be considered as RCP of deployment.

2.2 RCP testing

In DRT, a test system is firstly designed and manufactured. The system contains installing equipment, suspending equipment and high-speed photography equipment, as shown in Fig.4.

Fig.4 DRT sysytem for landing gear

By the installing equipment, the landing gear can be placed with thePRline vertical. Then the combination of PS and SFSS revolves around a vertical axis. With the installing equipment, the AVPP can be obtained easily and accurately.

The suspending equipment can overcome the gravity the landing gear subjected in deploying test to simulate the actual weightless condition in EMTO.

The high-speed photography equipment contains of a high-speed camera and a photo processing platform. The camera can shoot the whole deploying process parallel with thePRline,i.e., vertical to the deploying movement direction of the combination of PS and SFSS. And based on the photos of the high-speed camera, AVPP can be calculated with the photo processing platform.

3 DRA Method

SupposemAVPPs, denoted asω1,ω2, …,ωm, are obtained in the DRT. And the mean value and standard deviation can be derived by

(4)

Usually, the AVPP follows normal distribution, which can be validated with Shapiro-Wilk test or Epps-Pulley test[11].

To ensure a successful deployment, the AVPP must be bigger than zero, thus the lower limit of AVPP is zero. If defineωL=0, we can conservatively rewrite the deployment reliabilityRas

R=P{ω>ωL}.

(5)

The lower confidence limitRLof deployment reliability with given confidenceγcan be defined as

P{R>RL}=γ.

(6)

According to the concept of the two-dimensional one-side tolerance factor, the estimate of the deployment reliability (corresponding to the confidence of 50%) is[10-12]

(7)

(8)

where Φ(·) is the distribution function of standard normal distribution;βis the correct factor which makes the standard deviation estimate unbiased; and Γ(·) is the Gamma function.

And the lower confidence limit of deployment reliability with confidenceγis

(9)

whereuγ=Φ-1(γ) is the 100γth percentile of standard normal distribution.

Chang’E-3 probe has four identical landing gears. The deployments of them are conducted respectively. If any landing gear fails to deploy, the probe can be considered losing the deployment function. Therefore, the four landing gears continue a series system and the estimate of deployment reliability of the Chang’E-3 probe can be obtained by

(10)

According to the reliability theory for series system consisted of identical elements, the lower confidence limit of deployment reliability for Chang’E-3 probe with confidenceγis

(11)

4 Deployment Reliability for Landing Gear of Chang’E-3

In the reliability test of Chang’E-3 landing gear, a high-speed camera, which is set to obtain 1000 pictures per second, is adopted. The 28 deployments are conducted and the AVPPs are all derived with a measurement accuracy of 0.01 rad/s, as shown in Fig.5.

Fig.5 Reliability test data of Chang’E-3 landing gear

According to Shapiro-Wilk test method, the estimate of Shapiro-Wilk statistic is calculated,i.e.,W=0.975. If we take the significance levelα=0.05, then the 100αth of Shapiro-Wilk test statistic isWα=0.924. Apparently, we haveW>Wα, and the AVPP follows normal distribution.

The mean value and standard deviation of AVPP are

(12)

From Eqs. (7) - (8), the deployment reliability of landing gear can be estimated by

(13)

Here, we take the confidence as 90%. From Eq. (9), the lower confidence limit of deployment reliability for landing gear is

RL>0.99999.

(14)

Finally, the deployment reliability estimate of Chang’E-3 probe and the lower confidence limit of it withγ=90% are derived as follows

(15)

5 Conclusions

In this paper, the operating principle for the deployment function of landing gear is firstly studied, and the failure modes and effects are also analyzed. Then the most critical failure mode is identified. The corresponding reliability characteristic parameter is defined,i.e., the angular velocity at the predefined position for the combination of PS and SFSS. The DRT method which can be carried out easily in engineering is accordingly proposed. The DRA method is further presented, which gives the deployment reliability estimates and the lower confidence limits of a landing gear and the series system of four landing gears. Finally, DRT of Chang’E-3 probe is carried out, and the lower confidence limit of deployment reliability with confidence of 90% for the probe is obtained, which is bigger than 0.99996. The assessment results indicate that landing gear has a very high reliability, as validated by the deployment of Chang’E-3 probe in the EMTO.

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Foundation item: National Science and Technology Major Project, China

1672-5220(2014)06-0782-03

Received date: 2014-08-08

* Correspondence should be addressed to WU Qiong, E-mail: wing21@126.com

CLC number: V476.3; O212 Document code: A