This paper presents the operation status and results of ground thermal cycling test of pulse tube refrigerators (PTRs) for space application. Firstly, a thermal cycling degradation model was proposed by considering two physical mechanisms: contamination and fatigue damage. Then, a thermal cycling test scheme of two types of PTRs was designed and performed to demonstrate their long lifetime and high thermal stability. Two type A PTRs with cooling capacity of 1W@60 K and two type B PTRs with cooling capacity of 5W@80 K were continuously operated for about two years in a simulated vacuum thermal cycling environment. Effects of heat rejection temperature variation on thermal stability and dynamic performance of the PTRs were investigated. Furthermore, the thermal cycling degradation model was validated with the actual thermal cycling test data. Finally, the predicted pseudofailure lifetime was acquired via experimental data and degradation model. Moreover, the estimated reliability of PTRs was obtained through using the Weibull distribution. The proposed thermal cycling test scheme and innovative lifetime prediction and reliability estimation method provide a quick and accurate approach for the cooler manufacturer to assess the lifetime and reliability of the space PTRs.
Cryogenic technology has become more and more important as cryogenic detectors play a critical role in the fields of meteorological forecast, earth observation, and astronomical research. The longlife infrared detectors are required to operate at a cryogenic temperature in order to decrease background noise and provide high sensitivity and resolution [
The PTRs installed on high orbit satellites are commonly subjected to a longterm repeated thermal cycling environment due to passing of the illuminated and shaded areas induced by solar eclipse and sun illumination in space. Previous studies [
In this study, theoretical and experimental research on the thermal stability and lifetime of pulse tube refrigerators in a thermal cycling environment is carried out. A thermal cycling degradation model was proposed by considering outgassing property of nonmetal materials and lowcycle mechanical fatigue of ductile and brittle materials. The effects of thermal cycling on operational stability and dynamic performance of two types of PTRs are investigated rigorously with a combination of numerical analysis and experimental study. The experimental data show good fitting with the thermal cycling degradation model. Finally, a reliability estimation of PTRs was obtained through using the Weibull distribution. The proposed novel methodology enables the cooler manufacturers to more quickly and accurately assess the lifetime and reliability of the space PTRs. The rest of the paper is organized as follows. Section
In order to simulate the flightlike environment, coldtip temperature and cooling power of the PTRs were almost kept constant to cool the instruments while the input electrical power was periodically varied in response to the heat reject temperature evolution. If the cooling temperature was increased due to performance degradation, input electrical voltage would be increased to maintain coldtip temperature constant. Therefore, the power consumption evolution could indicate the performance degradation of the PTRs. In this paper, performance degradation of the PTRs is defined as an increase of the initial power consumption to maintain cooling temperature constant during longterm operation.
Generally, typical failure mechanisms, i.e., gaseous contamination, wear, fatigue, and leakage, influence stable and longterm operation of PTRs [
The factors that influence the cooling performance of PTRs are the number of thermal cycle and cycle frequency, heat reject temperature difference, and maximum heat reject temperature. The functional form of the thermal cycling degradation model can be expressed as
Due to lack of failure life data of PTRs, most manufacturers cannot provide enough lifetime information. The degradation model of PTRs should reflect the two failure mechanisms as contamination and fatigue induced by thermal cycling. Previous studies [
With respect to the influence of reject temperature fluctuation and power evolution, lowcycle (few hundred or thousand cycles to produce failure) mechanical fatigue data for either ductile or brittle materials are effectively modeled using CM model as [
Consequently, based on the above outgassing property of nonmetal materials and thermal cycle fatigue model, a theoretical thermal cycling degradation model is established to describe the correlation between power consumption increment of the PTRs and cycle number, reject temperature fluctuation, thermal cycling frequency, and maximum reject temperature based on the following assumptions:
Thermal cycling is the only related factor for performance degradation of the PTRs
The failure mechanism of the PTRs at thermal cycling condition is consistent with that at normal condition
Performance of the PTRs degrades continuously; each thermal cycle causes performance damages
The higher frequency of the thermal cycle will lead to the greater thermal shock and accelerate the performance degradation process of the PTRs. The repeated varying heat reject temperature and cyclic power consumption will cause fatigue of ductile and brittle materials of the PTRs. In this study, the low frequency of the thermal cycle means low temperature change rate (2.08 K/h) and the influence of the thermal shock on the performance of the PTR will be small. Thus, the frequency term can be neglected in the thermal cycling degradation mode. So, equation (
Then, the nonlinear degradation model (equation (
According to the mission requirements, two types of pulse tube refrigerators with required cooling capacity of 1W@60 K with maximum input electrical power of 80 W (type A) and 5W@80 K with maximum input electrical power of 120 W (type B) have been developed and provided in the test. The experimental specimens have undergone a verification testing to verify the thermal performance before carrying out the thermal cycling test. A schematic diagram of the pulse tube refrigerator is shown in Figure
Schematic diagram of the pulse tube refrigerator.
Prototypes provided for the thermal cycling test. (a) Type A pulse tube cryocooler. (b) Type B pulse tube cryocooler.
Basic specification of the PTRs.
Parameter  Value  

Type A  Type B  
Cooling capacity  1 W at 60 K  5 W at 80 K 
Total mass  7.5 kg  8.2 kg 
Operational frequency  50 Hz  50 Hz 
Maximum power consumption  80 W  120 W 
Configuration  Single stage  Single stage 
Pressure of helium gas  3.25 MPa  3.25 MPa 
Designed lifetime  8 years  8 years 
Sample size  2  2 
Reject temperature  
Nonoperation  223–323 K  223–323 K 
Operation  243–283 K  243–283 K 
In our preliminary test, the PTR has the capability to successfully work after experiencing the extreme nonoperational temperature range from 223 K to 323 K. To demonstrate the capability at operational conditions, the PTRs were needed to continuous operate at the simulated space environment. Therefore, the testing profile of the thermal cycling test was designed and defined as depicted in Figure
Schematic of testing profile for the thermal cycling test.
Details of the thermal cycling test profile.
Parameters  Values 

Heat reject temperature range (K)  243–283 
Dwell time (h)  60 
Ramp time (h)  24 
Ramp rate (K/h)  2.08 
One cycle time (h)  168 
Test status  Continuous operation 
Figure
Experimental facilities. (1) Heat plate; (2) heat pipe; (3) linear compressor; (4) base of the compressor; (5) after cooler; (6) hot end heat exchanger; (7) reservoir; (8) two vacuum chambers; (9) data acquisition modules; (10) data acquisition software; (11) input power supply.
The lifetime requirement of the PTRs is achieved at least after 8 years continuous operation in orbit. The cooling capacity of type A PTR is required to provide cooling power of 1 W with stable coldtip temperature of 60 K, and the type B PTR is required to provide cooling power of 5 W with coldtip temperature of 80 K. As the PTRs have to provide sufficient cooling for the science instruments and optical system as well as to meet the 8 years lifetime requirement, the failure criterion of pulse tube refrigerator is mainly determined by the power consumption increment and the coldtip temperature. During the thermal testing, a PTR is considered as performance degradation or failure if it could not meet the criteria which are specifically declared in Table
Failure criterion of PTRs.
Prototype  Performance parameter  Case 1  Case 2  Case 3 

Type A PTR  Input power increment (W) 



Coldtip temperature difference (K) 


 
Conclusion  Operates well  Degradation  Failure  
Type B PTR  Input power increment (W) 



Coldtip temperature difference (K) 


 
Conclusion  Operates well  Degradation  Failure 
Two years of thermal cycling tests have been completed from August 2016 to September 2018 for about 100 cycles to assure adequate thermomechanical stability and demonstrate long lifetime and high reliability of the type A and type B PTRs. Two type A prototypes and two type B prototypes have been prepared and tested for about 18000 hours. The experimental results are obtained as shown in Figures
Operation status of the PTRs in the thermal cycling test: (a, b) 1 W@60 K PTR; (c, d) 5 W@80 K PTR.
Effect of reject temperature cycle on cooling performance of the prototypes with constant heat power and cooling temperature: (a, b) 1 W@60 K PTR; (c, d) 5 W@80 K PTR.
Summary of thermal cycling test results.
Prototype  Sample  Testing  Heat reject temperature (K)  Coldtip temperature (K)  Input electrical power (W)  

Time (h)  Preset value  Result  Requirement  Result  Requirement  Result  
Type A  No. 1  16000  243∼283  241.1∼283.2  ≤63  60 ± 0.2 

47.02∼56.21 
No. 2  16000  243∼283  242.9∼282.7  60 ± 0.6  45.73∼54.62  
Type B  No. 1  16000  243∼283  241.8∼286.4  ≤83  80 ± 0.7 

64.95∼97.31 
No. 2  16000  243∼283  240.2∼283.7  80 ± 0.6  67.56∼96.73 
Figure
Figure
Dependence of PTR performance on the heat reject temperature: (a, b) 1 W@60 K PTR; (c, d) 5 W@80 K PTR.
The increasing modern spaceborne cryogenic detectors have driven the demands for higher thermal stability to obtain high quality of signal and image. Thermal stability is an important indicator to verify the high reliability and long lifetime of PTRs. At thermal cycling condition, the period of cooldown, restabilization, and heating up has adverse impact on thermal stability of PTRs. A PTR should maintain its thermal performance even if it is subjected to thermal cycling environment. In this sense, changes in coldtip temperature and power consumption were investigated and determined after thermal cycling tests.
The mission requirement of longterm and shortterm (one cycle) coldtip temperature stability of the PTRs is to keep the detectors at a specified cryogenic temperature with fluctuation less than 3 K and 1 K, respectively. Figures
Shortterm stability of cold head temperature in the 10th reject temperature cycle: (a, b) type A PTRs; (c, d) type B PTRs.
Longterm stability of cold head temperature for 16000 h operation: (a) type A; (b) type B.
Furthermore, the average power consumption at upper reject temperature is adopted to indicate the performance instability or degradation of the PTRs. These data can be obtained from the test results in Section
Average power consumption of the PTRs versus number of thermal cycle: (a) type A prototypes; (b) type B prototypes.
Figure
In order to determine the dynamic performance of the investigated PTRs, the cooling capacity parameters, such as COP (coefficient of performance) and relative Carnot efficiency under thermal cycling condition are used and calculated as equations (
Relative Carnot efficiency of PTRs depending on the thermal cycle: (a) type A; (b) type B.
The dynamic COP vs. thermal cycle: (a) type A; (b) type B.
Figures
As the performance degradation of the PTRs did not reach the preset failure criterion, the actual failure lifetime of the PTRs could not be obtained during thermal cycling tests. Therefore, the pseudofailure lifetime (Figure
The pseudofailure lifetime.
Establish a performance degradation model based on the failure mechanism of the PTRs and use experimental data
Estimate the parameters
Obtain the pseudofailure life
Using the estimated pseudofailure lifetime
The average power consumption data of the PTRs at upper heat rejection temperature were utilized as the thermal cycling degradation data after eliminating off abnormal conditions (as shown points A and B in Figure
Simulation data of the average power consumption of the PTRs at upper heat reject temperature condition: (a, b) 1 W@60 K prototypes; (c, d) 5 W@80 K prototypes.
Estimated values of the model parameters.
Parameters  Type A No. 1  Type A No. 2  Type B No. 1  Type B No. 2 


48.25  47.34  92.29  91.06 

0.2673  0.2656  0.2639  0.2716 

0.0830  0.0798  0.0778  0.0756 

76.7335  83.2887  71.2825  68.9857 
The performance degradation models are established via the estimated model parameters as shown in the following equations with the type A No. 1, No. 2 and type B No. 1, No. 2, respectively:
According to the performance degradation curves and the given failure criterion as presented in Section
Predicted lifetimes of the PTRs under thermal cycling condition.
Prototype  Cycle to failure ( 
Lifetime prediction (hour) 

Type A No. 1  690  115900 
Type A No. 2  753  126500 
Type B No. 1  733  123100 
Type B No. 2  748  125600 
The failure time data of the PTRs are commonly described by a twoparameter Weibull distribution, which was widely applied by the previous studies [
The lower confidence limit of the reliability of the PTRs based on the Weibull distribution can be expressed as
The methods for estimating the Weibull parameters are based on the null hypothesis (
There are various goodnessoffit test methods (Kolmogorov–Smirnov, Cramer–von Mises, chisquared, etc.) based on the empirical distribution function (EDF) statistics [
Therefore,
The reliability estimation of the PTRs can be calculated by equation (
Reliability curve of SPTRs.
The 8 years designed lifetime of space PTRs have the challenge to maintain stable operation in despite of rigorous space environment. In this study, theoretical and experimental research on the thermal stability, lifetime prediction, and reliability estimation of PTRs in a thermal cycling environment is carried out. The ground vacuum thermal cycling tests for two types of space PTRs have been completed for about two years, and the effects of heat rejection temperature on thermal stability and dynamic performance of PTRs were investigated. Moreover, the innovative thermal cycling degradation model and reliability estimation methodology were established and validated to quickly and accurately assess the lifetime and reliability of the space PTRs. The reliability of the PTRs was obtained as 0.935 at continuous operation for 8 years under thermal cycling. The results show that performance and thermal stability of type A (1 W@60 K) and type B (5 W@80 K) PTRs meet the program requirements as expected, and the PTRs could fulfill the lifetime requirement of 8 years on orbit. Further investigation will continue to research the detailed performance degradation factors of the PTRs.
The data used to support the findings of this study are available from the corresponding author upon request.
The authors declare that they have no conflicts of interest.
This study was conducted as a part of a project supported by the National Natural Science Foundation of China (grant no. 51375487).