Preload relaxation analysis and reliable life prediction of space connection and separation device based on accelerated degradation tests

Gen LIU, Qiong WU, Zhihu WANG,*, Yixin LUO, Yufeng QI

a School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, China

b Institute of Spacecraft System Engineering, China Academy of Space Technology, Beijing 100081, China

KEYWORDS Accelerated degradation tests;Life prediction;Preload relaxation;Reliability-analysis;Space connection and separation device

Abstract The safety and reliability of space connection and separation device has become a key issue due to the increasing service span of deep space exploration mission.The long-term preload relaxation(a key failure mode)of connection and separation devices is focused in this paper.A series of tests have been designed and implemented to investigate the preload relaxation regulation and a comprehensive method has been constructed to analyze and predict the reliable lifetime of the device.The two-stage preload relaxation law of the device is found and reasonably considered.Due to the different relaxation mechanism, the first-stage preload relaxation is assessed based on the working-condition test results,and the second-stage preload relaxation is characterized by accelerated test results.Finally,the service reliability and reliable life are evaluated.The experiment and assessment results demonstrate the reasonability and effectiveness of the proposed method which can achieve long-service reliability analysis for space connection and separation device within limited time.

1.Introduction

Reliable connection and separation between structural components of spacecrafts are very critical to the success of a space exploration mission.To this end, connection and separation devices have been commonly adopted to accomplish the connection and separation functions.1Recently, long-time service has become an essential property of spacecrafts, especially for those focusing on deep-space exploration missions.The longservice span brings enormous challenges for reliable connection and separation.For a connection and separation device,a specified preload level has to be maintained to achieve a successful separation function until the end of its long service span.This results in a necessary consideration of the preload relaxation issue.

Focusing on a typical problem in practical engineering, the connection and separation device in a specific type of spacecraft is required to maintain a certain level of preload after two years of service span.However, the test time available to verify the reliability is very limited.Consequently, it has become a key focus to verify the long-lifetime reliability effectively.In recent years, one should note that such problems have become more and more common in aeronautical and mechanical fields with the continuous improvement of product service life.

Preload relaxation of the connection and separation device has become a new concern for deep space exploration missions, but few literatures have been reported focusing on this issue.Current studies mainly focus on the preload relaxation of conventional bolted joints,2–7and the approaches can be categorized into physical analysis and test investigation.The former is dedicated to building a physical model to characterize the preload relaxation law based on material viscoelastic properties.8–11These approaches are usually inconvenient in engineering applications because they are only suitable for situations where the viscoelastic property of the material, rather than the structural characteristics, plays a vital role in the relaxation process.The gap adjustment and deformation coordination within the structure cannot be reasonably considered by physical analysis approaches.

Test analysis methods, from another perspective, investigate the preload relaxation law by conducting tests and derive empirical preload formula based on measurements.12–15They are suitable for situations focusing on the preload relaxation analysis of devices in practical engineering because these approaches are often more intuitive, and require fewer model parameters compared to physical analysis methods.

In this paper, the preload relaxation of a connection and separation device during long service span is studied based on a test analysis method.It is worth noticing that the connection and separation device illustrates a considerably complicated structure (see details in Section 2.1) compared with conventional bolted joints.Components like lock block and gear ring are incorporated to realize the connection and separation functions.After the preload is applied, these components participate in the coordination of the structure, making the preload relaxation law more complicated.

Meanwhile, the demand of long-time prediction with reliability is urgently required.Consequently, the main challenges can be summarized as two aspects:(A)How to design and conduct an effective preload relaxation test for the connection and separation device within a limited test time; (B) How to reasonably analyze and predict long-time preload relaxation law with the concept of reliability.

Due to its complex structure,the preload relaxation for the connection and separation device is more complicated than that of conventional bolted joints.First, the connected bolt is entirely wrapped by other components during the assembly state,making it very challenging to monitor the preload relaxation process of the device.Second,we found that the preload relaxation procedure of the device exhibits obvious two-stage characteristics through experiment exploration and analysis.Researches have shown that after the tightening torque is applied, the initial preload often drops rapidly within a short period of time.16–17The mechanism of this rapid relaxation process is quite different from that of the following slow relaxation stage.The early stage where the preload drops rapidly is regarded as the first-stage relaxation,while the slow and stable preload relaxation caused by material creep is defined as the second-stage relaxation.For long-time service products, both stages mentioned above cannot be ignored.So far,no research has comprehensively considered the two stages of preload relaxation to test and evaluate life and reliability of such products.Finally, since the available test time is quite limited, it is necessary to conduct accelerated tests which can collect more useful information by increasing the accelerated stress level under the premise of maintaining the failure mechanism.18,19To this end, it is the first objective of the current study to establish a reasonable and effective test scheme, which can comprehensively consider the two-stage preload relaxation characteristics of the device.

Based on the two-stage preload relaxation test measurements,the second objective of this paper is to construct a comprehensive test data modeling and analyzing method to reasonably evaluate the long-time preload relaxation of the device, where the two-stage regulation and the prediction demand considering reliability bring enormous challenges.For the first stage, the total amount of preload relaxation can be obtained by the test results directly.However, due to multiple random factors, the test results of different test samples may be different.Consequently, the evaluation results considering reliability should be derived by analyzing the distribution of the first-stage preload relaxation.

Furthermore, the second stage of preload relaxation lasts much longer than the first stage, which can be considered as a degradation process.An effective accelerated degradation model and corresponding reliable life assessment method must be established based on the accelerated test results.For the connection and separation device, these issues have not been investigated yet.To assess long-term preload relaxation law considering reliability, a stochastic-process-based degradation analysis method is focused.According to the literature, this method can successfully account for the influence of random factors and has been applied to analyze the degradation of bearings,20laser generators,21hard disk drives,22Li-ion batteries23and rotary lip seals in aircraft.24Wiener process,25Gamma process26and Inversed Gaussian process27are commonly applied stochastic process models.Due to its good physical and mathematical features, the Wiener process has been extensively researched.Wiener process can represent linear and nonlinear degradation regulations.28–29A Wiener process accelerated degradation model is usually built by considering the accelerated stress level variable into the degradation rate expression.30In the current study, a reasonable accelerated degradation model is firstly constructed based on the accelerated preload relaxation test results.Then the failure time distribution is constructed according to the first hitting time concept.Finally, reliable life prediction and reliability analysis method are derived accordingly.

The rest of the paper is laid out as follows.In Section 2,the structure of the connection and separation device and a series of preload relaxation tests are introduced.Section 3 focuses on analyzing and predicting the long-time preload relaxation and evaluating the reliability and lifetime under working condition.Section 4 summarizes the results and conclusions of the paper.

2.Preload relaxation tests for the connection and separation device

This section first introduces the structural composition of the connection and separation device for a better understanding of the preload relaxation mechanism.Then the test platform and test method are introduced based on the research objectives and reliability assessment demands.Finally, a series of accelerated preload relaxation tests are implemented as foundations for the reliability analysis.

2.1.Structure introduction and discussion

The complex structure of the connection and separation device is shown in Fig.1.31It mainly includes a connected bolt,combustion chambers, pistons, lock blocks and ring gears.After the device is assembled,a specific amount of preload is applied to guarantee reliable connection.More important, a certain level of this preload has to be maintained during its longtime service span, otherwise the connection and separation performance of the device will degrade.The device may be considered as failed when the residual load is lower than a preset threshold.From this viewpoint,the preload relaxation regulation of the device during service time must be investigated and assessed to ensure the connection reliability.

It can be seen from Fig.131that load(or stress)undertaken by the connected bolt can reflect the preload of the structure.However, the entire connected bolt is wrapped inside the device after assembly,making it very difficult to directly monitor the preload change.Since the preload is within the material’s elastic range, the stress change can be determined through a constitutive relationship via the strain variation.To this end, we monitor the strain of the connected bolt by pasting a set of strain gauges on its surface before assembly.

One can understand that the multiple components involved in Fig.131will inevitably bear a certain amount of load and undergo gap adjustment in the early stage after assembly.This procedure will cause the device preload to drop rapidly in a short time,which is regarded as the first-stage relaxation.After that, the device will further endure a stable and slow preload relaxation procedure mainly due to material creep, which is defined as the second-stage relaxation.Due to the significant difference between these two phases, two corresponding preload relaxation tests have been designed and implemented.

The connection and separation device is a typical longservice time product.To obtain the long-time preload relaxation law within a limited test time, it is necessary to conduct a reasonable accelerated test.According to the literature,temperature has been well recognized as a critical factor affecting preload relaxation.Therefore, it is selected as the accelerated stress in the current study.Consequently,it is a necessary task to verify the rationality of strain gauge high-temperature monitoring.Corresponding verification tests have been designed and implemented.See Section 2.3 for details.

2.2.Test platform and test procedure

A comprehensive test platform for the preload relaxation investigation of the connection and separation device is shown in Fig.2., which consists of a temperature control system, a strain measurement system and an automatic data collecting system.

According to the literature discussion, temperature is adopted as the accelerated stress.Then a temperature control system is formed via a high-temperature test chamber, which can provide a stable high-temperature environment for specimens with strain gauges.

The strain measurement system focuses on monitoring the connecting bolt preload through strain investigations and the constitutive relationship.It is composed of strain gauges,wires and a strain monitor equipment.High-temperature strain gauges are pasted on the connected bolt, and then specimens are assembled.The senor wire is connected to the strain monitor equipment,and the strain variation of the connecting bolt can be monitored.

The variation of the connected bolt strain over time has to be recorded to analyze the preload relaxation law.The automatic data collecting system includes a computer and a strain recording software.The strain data can be recorded automatically with a preset measurement interval until a specified terminate time.When the preload relaxation tests are completed,the recorded strain data can be adopted for further analysis.

Fig.1 Essential structure of connection and separation device31.

Fig.2 Test platform for preload relaxation.

2.3.Summary of the preload relaxation test

This section introduces a series of preload relaxation tests conducted to effectively analyze and predict the long-time preload relaxation of the connection and separation device.The rationality of high-temperature strain gauge monitoring is verified in the first step.Besides,we found that there is a short period of rapid preload relaxation after assembly, and it is obviously different from the stable preload relaxation procedure afterward.Thus, a first-stage preload relaxation test and a secondstage accelerated preload relaxation test are carried out to analyze the preload relaxation regulation comprehensively.

2.3.1.High-temperature monitoring rationality test

A high-temperature monitoring rationality test is conducted to verify whether the strain value obtained by the strain gauge can reasonably depict the preload relaxation of the connected bolt.To facilitate the simultaneous monitoring of strain and stress, a high temperature tensile test shown in Fig.3 is performed focusing on the core element (connected bolt) of the device.To be more specific, the connected bolt with strain gauges is loaded by the mechanical testing machine under a high-temperature condition.In this procedure, the mechanical testing machine force sensor can collect the load of the connected bolt over time, while the strain gauge can monitor the strain.By comparing the index transformed by the strain monitoring result with the force data measured by the force sensor,the rationality of strain monitoring can be examined.

Results show that the load after transformation of the strain monitoring result is consistent with the one recorded by the force sensor,demonstrating the rationality of the strain monitoring.

2.3.2.First-stage preload relaxation test

The first-stage relaxation generally occurs within a few hours after the tightening process.According to the test, this relaxation procedure is significantly influenced by the quality of tightening process and illustrates no obvious correlation with temperature.A main factor is the gap coordination of the multiple components.Through experimental exploration, we found that retightening can effectively reduce the first-stage preload relaxation amount.This is because the coordination inside the overall structure will be faster and the amount of coordination will be reduced after the first-round tightening action.Then the device tightening procedure can be improved based on this discovery.

Consequently, in the current study, the first-stage preload relaxation test is conducted under the working condition.Since preload relaxation ratio(defined as the ratio of the preload loss to the initial preload) has been commonly adopted to characterize the preload relaxation degree in the literature, it is considered as the focused index in the current study.The firststage preload relaxation ratio of 6 test specimens is summarized in Table 1.

Fig.3 High-temperature monitoring rationality test sample and test equipment.

2.3.3.Second-stage accelerated preload relaxation test

According to mission requirements, the reliable preload loss ratio of the connection and separation device after 2 years is focused.As previously discussed,the preload of the connection and separation device slowly decreases during its long-time service in the 60°C-temperature environment because of material creep.In order to investigate the law of this second-stage relaxation within a limited test time, temperature is selected as the accelerating stress to conduct an accelerated test.

When determining the acceleration stress level, the relaxation rate should be accelerated as much as possible under the premise that the relaxation mechanism remains unchanged.The test temperature levels and test time are determined based on the following issues.

(A) The working temperature of the device is 60 °C, therefore the accelerated temperature should be higher than 60 °C.

(B) A piece of composite material is incorporated in the device, and its mechanical property will change when temperature is higher than 120°C.Therefore,the highest acceleration temperature level is set as 120 °C.

(C)Based on both the principle of accelerated tests and the pre-test foundations,another temperature level is set as 100°C to guarantee an effective observation dataset.

(D) The test time is determined based on the continuous measure ability that the test equipment can support and the completeness of the test data(relaxation regulation of the second phase can be reasonably demonstrated).

The measurements are shown in Fig.4 one can see that the preload relaxation of the device illustrates both stable timeincreasing characteristic and random property.It can be reasonably considered as a degradation process.Consequently,degradation modeling based on Wiener process is focused to characterize the regulation of the second-stage preload relaxation.

3.Preload relaxation analysis and reliability assessment

According to the above tests, one can see that the preload relaxation of the connection and separation device illustrates a two-stage preload relaxation law and this has to be comprehensively considered to assess the reliability.

In this section, the reliability analysis of the first-stage preload relaxation is conducted according to statistical methods.Then, an accelerated degradation model for the second-stage preload relaxation is established based on the statistical prop-erties of the degradation procedure.Finally,the preload relaxation analysis and reliability assessment considering the overall service life of the focused device are implemented and discussed.

Table 1 Measurements of the first-stage preload relaxation ratio.

Fig.4 Measurements of the second-stage preload relaxation ratio.

3.1.The first-stage preload relaxation analysis

Curves of distribution function Fn(x )and F0(x )are further shown in Fig.5,from which one can see that the empirical distribution is in good agreement with the estimated normal distribution.

Fig.5 Curves of distribution function Fn (x ) andF0 (x ).

To further obtain the quantitative analysis results, test statistic D is defined as maximum vertical displacement between the two distribution functions in Fig.5 Testing of the null hypothesis proceeds by comparison of D against critical values Dcritcalwhich are functions of the confidence level and the number of samples.The confidence level of the hypothesis test is set as 0.95, and the number of test sample is 6.The calculated Kolmogorov–Smirnov statistic is D=0.31, while the critical value with 0.95 confidence level is D0.95-critical=0.555.Consequently, the null hypothesis can be accepted under the confidence level of 0.95.This means the first-stage preload relaxation can be regarded as normally distributed.

According to the statistical theory,x0.5=μxcan provide an average level of the preload relaxation ratio.This means that the actual preload relaxation ratio may be 50 % greater than this result, and 50 % less.From a practical viewpoint in reliability engineering, the 95-percental value is further focused.According to the distribution characteristics, the 95-percental value can be derived byx0.95=μx+u0.95?σx, in which u0.95is the standard normal quantile with the probability of 0.95.The analysis results of the first-stage preload relaxation ratio are listed in Table 2.One can see that the average first-stage preload relaxation ratio is 3.5%,and this ratio will not exceed 3.8 % under a reliability of 0.95.

3.2.The second-stage preload relaxation analysis

The second-stage preload relaxation test measurements in Fig.4 demonstrate a time-increasing trend with nonlinear property.It is also worth noticing that the observations of a specific unit are not strictly monotonous over time due to multiple random factors.This situation is very common in practical engineering, and can be properly described by a Wiener process (as a proper stochastic processes).In this regard, a stochastic-process based accelerated degradation model is constructed in this study.

Table 2 Analysis results of the first-stage preload relaxation ratio.

The time-varying statistical characteristics of the test measurements are the basis to construct a reasonable accelerated degradation model.To intuitively demonstrate the degradation law, the sample averages and sample variances at each observation time point are calculated and plotted in Fig.6.

For a clear understanding of the modeling procedure,both degradation modeling (focuses on depicting the deterioration regulation at each single temperature level) and accelerated degradation modeling (focuses on depicting the overall degradation regulation throughout multiple temperature levels) are concentrated.

For the degradation modeling, the key issue lies in the proper description of time-varying degradation characteristics at each single temperature level.From Fig.6,the mean degradation path exhibits nonlinear characteristics over time.Besides, the sample variance also shows obvious timevarying statistical characteristics.This can be properly described by the Wiener process with a transformed time scale Λ(t ).The form of Λ(t ) is determined by data fitting effect of different empirical stress relaxation model, and it can be expressed as.

where Y(t )is the degradation performance at test time t;B(?)is a standard Brownian motion; Λ(t ) is the transformed time scale; μ is the drift parameter indicating the degradation rate and σ is the diffusion coefficient describing the variability of the preload relaxation process; c1,c2are parameters to be estimated.

Considering the accelerated degradation modeling,the central focus is the reasonable characterization of the temperature-varying degradation properties.To construct the accelerated degradation model and extrapolate the lifetime or preload relaxation rate under the working temperature,temperature-related model parameters have to be reasonably considered first.From Fig.6, the degradation rate obviously become higher at a higher temperature, which indicates the degradation rate is temperature-related.On the other hand,the sample variance shows no obvious relationship with temperature.Consequently, the drift coefficient μ in Eq.(4) is regarded as the degradation rate, so it is treated as a function of the temperature.

The Arrhenius model has been well recognized to describe the relationship between temperature and the degradation rate,which can be denoted as.

Fig.6 Time-varying statistical characteristics of measurements.

The next focus is to estimate the unknown model parameters and characterize the preload relaxation law based on the measurements.In the accelerated preload relaxation test, two temperature levels S1,S2are involved.Three units are investigated at time sequence t1,t2,???,tniunder temperature levelSi(i=1,2), respectively.The k th performance observation of unit j under Siis denoted asyijk,i=1,2,j=1,2,3,k=1,2,???,ni, where nirepresents the measurement times for i th stress level.

Model parameters can be estimated based on the above loglikelihood function, and results are shown in Table 3.

To verify the accelerated degradation model’s fitting performance, the mean and 95-percental degradation curves of 100 °C and 120 °C are plotted, which are shown in Fig.7.According to the definition of a percental curve, one can conclude from an average viewpoint that 50 % of the test data should be below the mean degradation curve and 95%should be below the 95-percentile degradation curve.The results illustrate that the constructed accelerated degradation model can be considered as a reasonable one to describe the preload relaxation law.

3.3.Relaxation prediction and reliability analysis

In this section,the preload relaxation prediction and reliability assessment of the connection and separation device are focused.The preload relaxation after two years of service is first predicted,and then the reliable life and reliability function are derived and analyzed.

The two-stage preload relaxation characteristic should be considered comprehensively.For the first-stage preload relaxation,it only lasts for a few hours and exhibits no obvious relationship with temperature.Based on the first-stage preload relaxation test results, the mean and 95-percental value of first-stage preload relaxation has been derived in Section 3.1.

Table 3 Model parameters estimation results.

Fig.7 Mean and fifth percentile curves of the device.

Table 4 Prediction results of the second-stage preload relaxation ratio.

According to the practical requirements, the preload relaxation ratio cannot exceed 10 % during the service time.The prediction results indicate that the device can meet this requirement.

Fig.8 Reliability curve of the connection and separation device.

In many real applications, reliable lifetime is usually another concern.For example,the 5th failure time distribution quantile t0.05under working condition is often focused.This index represents that 95% of the population of the products will not fail before t0.05.In this study, the reliable lifetime can be assessed if the failure threshold of the second stage preload relaxation is preset.Detailed derivation process is as follow.

The connection and separation device is considered as failed when the second-stage preload relaxation ratio exceeds a preset threshold D for the first time(the first hitting time concept).The Failure time distribution can be expressed as.

According to the practical requirements and the analysis results of the first stage relaxation, the second phase preload relaxation threshold can be set as 6.2 %.Therefore, the reliability curve of the device can be plotted, which is shown in Fig.8.

From the calculated reliability curve,the device’s reliability still maintains at a high level after two years of service,indicating that the device meets the reliability requirements.

The estimated 5th failure time distribution quantile ︿t0.05under working condition can be calculated by.

4.Conclusions

This study focuses on the preload relaxation tests and reliability analysis of connection and separation devices in spacecrafts.The main conclusions are as follows.

1.The preload relaxation of the connection and separation device exhibits an obvious two-stage feature.The firststage relaxation is mainly caused by the contact surface deformation and gap adjustment of the connected parts,and the second-stage preload relaxation is mainly induced by material creep.

2.The first-stage preload relaxation only last for a few hours and we found that it is significantly influenced by the tightening process.Based on testing exploration,it is also found that retightening process can effectively reduce the firststage preload relaxation.A reasonable and effective tightening strategy is formulated based on the characteristics of the preload relaxation at this stage.

3.The second-stage preload relaxation can be regarded as a degradation process,which is analyzed via a series of accelerated preload relaxation tests and a reasonable accelerated degradation model.The reliable results of the second-stage preload relaxation ratio are predicted.Furthermore, the failure time distribution and reliability function are derived,and the reliable lifetime of the connection and separation device under working conditions are analyzed and predicted.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

This study was supported by the National Natural Science Foundation of China (No.11872085).