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Vibration reduction of pulse tube cryocooler driven by single piston compressor
Cryogenics 52 (2012) 816–818
Contents lists available at SciVerse ScienceDirect
Cryogenics journal homepage: www.elsevier.com/locate/cryogenics
Technical Note
Vibration reduction of pulse tube cryocooler driven by single piston compressor Chen Houlei, Xu Nana, Liang Jingtao, Yang Luwei ⇑ Technical Institute of Physics and Chemistry, CAS, P.O. Box 2711, Beijing 100190, China
a r t i c l e
i n f o
Article history: Received 26 May 2012 Received in revised form 7 August 2012 Accepted 6 September 2012 Available online 12 October 2012 Keywords: High frequency Pulse tube (E) Single piston Vibration
a b s t r a c t The development of pulse tube coolers has progressed significantly during the past two decades. A single piston linear compressor is used to in order to reduce the size and mass of a high frequency pulse tube cryocooler. The pulse tube achieved a no-load temperature of 61 K and a cooling power of 1 W@80 K with an operating frequency of 80 Hz and an electrical input power of 50 W. By itself, the single piston compressor generates a large vibration, so a set of leaf springs with an additional mass is used to reduce the vibration. The equation relating the mass, the elasticity coefficient of leaf spring and the working frequency is obtained through an empirical fit of the experimental data. The vibration amplitude is reduced from 55 mm/s to lower than 5 mm/s by using a proper leaf spring. This paper demonstrates that a single piston compressor with vibration reduction provides a good choice for a PTC. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Pulse tube coolers (PTCs) have the advantage of long lifetime, simple configuration and high reliability. For certain special applications it is necessary to reduce the mass and size of the cooler as much as possible in which case the ultra-high frequency pulse tube coolers provides a favorable option. Progress has been made on ultra-high frequency pulse tubes, such as those reported by Northrop Grumman Space Technology [1,2], National Institute of Standards and Technology [3–6], Zhejiang University [7], and the Technical Institute of Physics and Chemistry [8]. Some research groups developed miniature-type PTCs with 1 W of cooling power at 80 K, while some target 10 W at 80 K cooling [1,7–10]. A miniature pulse tube cold finger designed to provide 1 W at 80 K has been fabricated and tested, driven by the dual opposedpiston compressor in our lab [9,10]. The coaxial cold finger has been designed for operating at 100 Hz with a outer diameter of 9 mm and a length of 35 mm. The cold finger is rather small, while the big compressor makes the overall mass of the cooler to be more than 6 kg. For reducing its mass and volume of the cooler further, use only one half of the compressor with single piston is feasible. In that case, the cold finger can be directly connected to the compressor, so that no additional support of the cold finger is necessary with such a configuration. A set of vibration reduction devices is fixed at the compressor to counteract the vibration of the single piston. The miniature pulse tube cooler becomes more convenient for applications. Previously, TRW [11,12] reported on the performance
⇑ Corresponding author. Tel.: +86 10 62627901; fax: +86 10 82543446. E-mail address: [email protected] (L. Yang). 0011-2275/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.cryogenics.2012.09.005
of a pulse tube cooler with self-induced vibration force reduction, but there are no details about the reduction structure and effect. In the present paper, the vibration reduction characteristics of an ultra-high frequency PTC with single piston compressor are reported.
2. Experimental apparatus The single piston compressor is comprised of half of the dualpiston compressor, so the mass and the size are decreased proportionately. However, due to the absence of the opposing, balancing component, the imbalanced motion of the single piston results in a large vibration in the axial direction. Because the spring will allow the system to resonate at its natural frequency, it is possible to identify that frequency and subsequently reduce the system’s vibration. Fig. 1 displays the photo of the spring component used to reduce the system vibration. A different spring and mass correspond to a different operating frequency. When driven by a dual-piston compressor the cooler can provide 1 W at 80 K with 40 W of electrical input power cooled by water. However, in this case it is driven by the single piston compressor. Figs. 2 and 3 display the photo and typical dimensions of the integrated pulse tube cooler, with the PTC cold finger directly connected to the compressor. With cooling provided only by a fan, the small dimensions at the hot end of the PTC experiences a higher reject temperature and this worsens the performance noticeably. The overall mass of the prototype is around 4 kg, and the weight can be decreased below 3.5 kg by changing the outer shell of the compressor further. So, the weight and volume of the cooler are highly decreased by using a single piston compressor and the in-line integrated structure makes it more comfortable for use.
817
H. Chen et al. / Cryogenics 52 (2012) 816–818
Fig. 3. Typical dimension of PTC system (unit: mm).
1.0
3. Performance of the cooler The maximum output power of the single piston compressor is about 50 W, half of that provided by the dual opposed piston compressor. Fig. 4 displays the cooling ability when the pulse tube is driven by the single piston. The optimum frequency decreases to 80 Hz. The no-load refrigeration temperature is 61 K, and the cooling power is 1 W at 80 K with 50 W of electrical input power.
0.8
Cooling power, W
Fig. 1. Photo of the vibration reduction component.
0.6 0.4 0.2 0.0 60
ð1Þ
The displacement associated with a half cycle is:
Z 0
T=2
V sinð2pftÞ ¼
V
pf
70
75
80
85
Fig. 4. Typical cooling power of integrated PTC.
A laser vibration survey meter (PDV-100) was used to measure the compressor’s axial vibration signal. The laser beam produced by the device radiates onto the side surface of the compressor. By combining the radiated and reflected signal and the meter is able to measure the velocity of the moving compressor surface and characterize the vibration. The velocity of the surface is sinusoidal. The velocity amplitude remains fixed for a given output voltage, even when the operating frequency is varied. The instantaneous velocity can be described as:
s¼
65
Temperature, K
4. Vibration analysis and reduction
v ¼ V sinð2pftÞ
Input power 50W 37W 30W 20W
ð2Þ
With 50 W of electrical input power and at an operating frequency of 80 Hz the velocity amplitude is measured to be 55 mm/s. Thus, the displacement is ±0.22 mm during one cycle. The displacement decreases as the operating frequency increases.
Shown in Table 1 is the details of the experimental spring parameters, where k represents the spring’s elasticity coefficient; m1 and m2 represent the mass of the spring and the additional aluminum ring respectively. Fig. 5 displays the vibration curve measured with different vibration reduction components fixed on the PTC. As frequency increases, the vibration velocity initially decreases to a minimum, then rapidly increases to a maximum, and finally decreases to the original level. The frequency where the sharp minimum/maximum velocity change is observed correlated with the spring’s elasticity coefficient, the mass of the spring and the mass of the additional aluminum ring. The minimum vibration depends on the entire mass of the vibration-reducing component and the electrical input power of the compressor. The natural frequency of the system can be calculated as:
fspring ¼
1 2p
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k=ðc1 m1 þ c2 m2 Þ
ð3Þ
At the natural frequency, the system resonates and thus counteracts the vibration of the single piston compressor. In order to carefully define the relationship between k, m1 and m2, additional experiments have been carried out with different measured
Table 1 Details of experimental spring parameters.
Fig. 2. Photo of integrated PTC with single piston compressor.
Case Case Case Case Case Case
1 2 3 4 5 6
k (N/mm)
m1 (g)
m2 (g)
0 7.6 27.3 42 34.6 42
0 65 126.7 151.2 138.8 151.2
0 0 6.7 73.7 170.2 210.7
818
H. Chen et al. / Cryogenics 52 (2012) 816–818
Velocity Amplitude , mm/s
120
frequencies. The frequency dependence is the same as shown in Fig. 5. Fitting the experimental results described in Table 2 with Eq. (3), we obtain the coefficient values of c1 = 0.75, c2 = 0.8. Fig. 6 displays the relationship between the mass and minimum velocity amplitude. The minimum amplitude decreases as the mass increases, but when the mass is high enough, the velocity amplitude decreases to about 3 mm/s, and further increase of the mass has little effect on the minimum velocity amplitude. The amplitude of 3 mm/s corresponds to the displacement of 0.012 mm, demonstrating that the vibration has been reduced effectively and the miniature cryocooler can be used in some applications.
100 80 60 40 20
5. Conclusion
0 40
50
60
70
80
90
100
Frequency , Hz Fig. 5. Typical results of the vibration reduction experiments.
Table 2 Comparison of fitting and experimental results. Number
k (N/ mm)
m1 (g)
m2 (g)
Experimental minimum vibration frequency (Hz)
Fitting minimum vibration frequency (f/Hz)
1 2 3 4 5 6 7 8 9 10
7.6 10.9 15.2 21.2 13.6 16.9 27.3 34.6 24.3 42
51.5 89.5 102.7 114.8 63.3 101.3 126.7 138.8 113.5 151.2
20.1 6.7 33.3 73.7 53.5 53.5 110.1 170.2 103.3 210.7
59.2 62.39 62.37 61.67 61.18 60.67 61.67 61.3 62.06 62.87
59.4 61.75 60.97 60.87 61.8 60.06 61.49 60.43 60.6 61.46
Acknowledgement This work is supported by National Natural Science Foundation of China (Grant No. 50890181, 51076160, 51006112). References
Minimum velocity amplitude, mm/s
60 50 40 30 20 10 0 0
50
100
150
200
250
300
350
Mass of the vibration reduction component, g Fig. 6. Relation between mass and minimum vibration.
The weight and volume of a ultra-high frequency PTC can be decreased by using single piston linear compressor, which is more suitable for portable applications. Such a miniature pulse tube cooler produced a no-load temperature of 61 K and a cooling power of 1 W at 80 K when operating at 80 Hz with 50 W of electrical input power. The minimum vibration of the system can be reduced to below 3 mm/s (5% of the original value), by using an appropriately designed leaf spring at the resonance frequency. The results of this test demonstrate that a single piston compressor could be used to drive a PTC with proper vibration reduction.
400
[1] Petach M, Waterman M, Tward E. Pulse tube microcooler for space applications. Cryocoolers 2007;14:89–93. [2] Petach M, Waterman M, Pruitt G, et al. High frequency coaxial pulse tube microcooler. Cryocoolers 2009;15:97–103. [3] Radebaugh R, O’Gallagher A. Regenerator optimization at very high frequency for microcryocoolers. Adv in Cryogenics Eng 2006;51:1919–28. [4] Srinivas V, Gan ZH, Radebaugh R, et al. 120 Hz pulse tube cryocooler for fast cool down to 50 K. Appl Phys Lett 2007;90:1–3. [5] Garaway I, Gan Zhihua, Bradley P, et al. Development of a miniature 150Hz pulse tube cryocooler. Cryocoolers 2009;15:105–14. [6] Garaway I, Veprik A, Radebaugh R. Diagnostics and optimization of a miniature high frequency pulse tube cryocooler. Adv in Cryogenics Eng: Trans of the Cryogenics Eng Conf 2010;55:167–74. [7] Wu YZ, Gan ZH, Qiu LM, et al. Study on a single-stage 120 Hz pulse tube cryocooler. Adv in Cryogenics Eng 2010;55:175–82. [8] Wang XT, Dai W, Luo EC, et al. Characterization of a 100 Hz miniature pulse tube cooler driven by a linear compressor. Adv in Cryogenics Eng 2010;55:1077–84. [9] Xu Nn, Chen Hl, Yang Lw, et al. Cryogenics 2010;5:1–5 [In Chinese]. [10] Xu Nn, Chen Hl, Liang Jt, et al. Investigation on the ultra-high frequency coaxial pulse tube. Chinese J Mech Eng 2011;6:156–9. In Chinese. [11] Chan CK, Jaco CB, Raab J et al. Miniature pulse tube cooler. In: Proc. 7th int. cryocooler conf. Kirtland AFB (USA): Phillips Laboratory Press; 1992. p. 113-6. [12] Chan CK, Clancy P, Godden J. Pulse tube cooler for flight hyper spectral imaging. Cryogenics 1999;39(12):1007–14.
Contents lists available at SciVerse ScienceDirect
Cryogenics journal homepage: www.elsevier.com/locate/cryogenics
Technical Note
Vibration reduction of pulse tube cryocooler driven by single piston compressor Chen Houlei, Xu Nana, Liang Jingtao, Yang Luwei ⇑ Technical Institute of Physics and Chemistry, CAS, P.O. Box 2711, Beijing 100190, China
a r t i c l e
i n f o
Article history: Received 26 May 2012 Received in revised form 7 August 2012 Accepted 6 September 2012 Available online 12 October 2012 Keywords: High frequency Pulse tube (E) Single piston Vibration
a b s t r a c t The development of pulse tube coolers has progressed significantly during the past two decades. A single piston linear compressor is used to in order to reduce the size and mass of a high frequency pulse tube cryocooler. The pulse tube achieved a no-load temperature of 61 K and a cooling power of 1 W@80 K with an operating frequency of 80 Hz and an electrical input power of 50 W. By itself, the single piston compressor generates a large vibration, so a set of leaf springs with an additional mass is used to reduce the vibration. The equation relating the mass, the elasticity coefficient of leaf spring and the working frequency is obtained through an empirical fit of the experimental data. The vibration amplitude is reduced from 55 mm/s to lower than 5 mm/s by using a proper leaf spring. This paper demonstrates that a single piston compressor with vibration reduction provides a good choice for a PTC. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Pulse tube coolers (PTCs) have the advantage of long lifetime, simple configuration and high reliability. For certain special applications it is necessary to reduce the mass and size of the cooler as much as possible in which case the ultra-high frequency pulse tube coolers provides a favorable option. Progress has been made on ultra-high frequency pulse tubes, such as those reported by Northrop Grumman Space Technology [1,2], National Institute of Standards and Technology [3–6], Zhejiang University [7], and the Technical Institute of Physics and Chemistry [8]. Some research groups developed miniature-type PTCs with 1 W of cooling power at 80 K, while some target 10 W at 80 K cooling [1,7–10]. A miniature pulse tube cold finger designed to provide 1 W at 80 K has been fabricated and tested, driven by the dual opposedpiston compressor in our lab [9,10]. The coaxial cold finger has been designed for operating at 100 Hz with a outer diameter of 9 mm and a length of 35 mm. The cold finger is rather small, while the big compressor makes the overall mass of the cooler to be more than 6 kg. For reducing its mass and volume of the cooler further, use only one half of the compressor with single piston is feasible. In that case, the cold finger can be directly connected to the compressor, so that no additional support of the cold finger is necessary with such a configuration. A set of vibration reduction devices is fixed at the compressor to counteract the vibration of the single piston. The miniature pulse tube cooler becomes more convenient for applications. Previously, TRW [11,12] reported on the performance
⇑ Corresponding author. Tel.: +86 10 62627901; fax: +86 10 82543446. E-mail address: [email protected] (L. Yang). 0011-2275/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.cryogenics.2012.09.005
of a pulse tube cooler with self-induced vibration force reduction, but there are no details about the reduction structure and effect. In the present paper, the vibration reduction characteristics of an ultra-high frequency PTC with single piston compressor are reported.
2. Experimental apparatus The single piston compressor is comprised of half of the dualpiston compressor, so the mass and the size are decreased proportionately. However, due to the absence of the opposing, balancing component, the imbalanced motion of the single piston results in a large vibration in the axial direction. Because the spring will allow the system to resonate at its natural frequency, it is possible to identify that frequency and subsequently reduce the system’s vibration. Fig. 1 displays the photo of the spring component used to reduce the system vibration. A different spring and mass correspond to a different operating frequency. When driven by a dual-piston compressor the cooler can provide 1 W at 80 K with 40 W of electrical input power cooled by water. However, in this case it is driven by the single piston compressor. Figs. 2 and 3 display the photo and typical dimensions of the integrated pulse tube cooler, with the PTC cold finger directly connected to the compressor. With cooling provided only by a fan, the small dimensions at the hot end of the PTC experiences a higher reject temperature and this worsens the performance noticeably. The overall mass of the prototype is around 4 kg, and the weight can be decreased below 3.5 kg by changing the outer shell of the compressor further. So, the weight and volume of the cooler are highly decreased by using a single piston compressor and the in-line integrated structure makes it more comfortable for use.
817
H. Chen et al. / Cryogenics 52 (2012) 816–818
Fig. 3. Typical dimension of PTC system (unit: mm).
1.0
3. Performance of the cooler The maximum output power of the single piston compressor is about 50 W, half of that provided by the dual opposed piston compressor. Fig. 4 displays the cooling ability when the pulse tube is driven by the single piston. The optimum frequency decreases to 80 Hz. The no-load refrigeration temperature is 61 K, and the cooling power is 1 W at 80 K with 50 W of electrical input power.
0.8
Cooling power, W
Fig. 1. Photo of the vibration reduction component.
0.6 0.4 0.2 0.0 60
ð1Þ
The displacement associated with a half cycle is:
Z 0
T=2
V sinð2pftÞ ¼
V
pf
70
75
80
85
Fig. 4. Typical cooling power of integrated PTC.
A laser vibration survey meter (PDV-100) was used to measure the compressor’s axial vibration signal. The laser beam produced by the device radiates onto the side surface of the compressor. By combining the radiated and reflected signal and the meter is able to measure the velocity of the moving compressor surface and characterize the vibration. The velocity of the surface is sinusoidal. The velocity amplitude remains fixed for a given output voltage, even when the operating frequency is varied. The instantaneous velocity can be described as:
s¼
65
Temperature, K
4. Vibration analysis and reduction
v ¼ V sinð2pftÞ
Input power 50W 37W 30W 20W
ð2Þ
With 50 W of electrical input power and at an operating frequency of 80 Hz the velocity amplitude is measured to be 55 mm/s. Thus, the displacement is ±0.22 mm during one cycle. The displacement decreases as the operating frequency increases.
Shown in Table 1 is the details of the experimental spring parameters, where k represents the spring’s elasticity coefficient; m1 and m2 represent the mass of the spring and the additional aluminum ring respectively. Fig. 5 displays the vibration curve measured with different vibration reduction components fixed on the PTC. As frequency increases, the vibration velocity initially decreases to a minimum, then rapidly increases to a maximum, and finally decreases to the original level. The frequency where the sharp minimum/maximum velocity change is observed correlated with the spring’s elasticity coefficient, the mass of the spring and the mass of the additional aluminum ring. The minimum vibration depends on the entire mass of the vibration-reducing component and the electrical input power of the compressor. The natural frequency of the system can be calculated as:
fspring ¼
1 2p
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k=ðc1 m1 þ c2 m2 Þ
ð3Þ
At the natural frequency, the system resonates and thus counteracts the vibration of the single piston compressor. In order to carefully define the relationship between k, m1 and m2, additional experiments have been carried out with different measured
Table 1 Details of experimental spring parameters.
Fig. 2. Photo of integrated PTC with single piston compressor.
Case Case Case Case Case Case
1 2 3 4 5 6
k (N/mm)
m1 (g)
m2 (g)
0 7.6 27.3 42 34.6 42
0 65 126.7 151.2 138.8 151.2
0 0 6.7 73.7 170.2 210.7
818
H. Chen et al. / Cryogenics 52 (2012) 816–818
Velocity Amplitude , mm/s
120
frequencies. The frequency dependence is the same as shown in Fig. 5. Fitting the experimental results described in Table 2 with Eq. (3), we obtain the coefficient values of c1 = 0.75, c2 = 0.8. Fig. 6 displays the relationship between the mass and minimum velocity amplitude. The minimum amplitude decreases as the mass increases, but when the mass is high enough, the velocity amplitude decreases to about 3 mm/s, and further increase of the mass has little effect on the minimum velocity amplitude. The amplitude of 3 mm/s corresponds to the displacement of 0.012 mm, demonstrating that the vibration has been reduced effectively and the miniature cryocooler can be used in some applications.
100 80 60 40 20
5. Conclusion
0 40
50
60
70
80
90
100
Frequency , Hz Fig. 5. Typical results of the vibration reduction experiments.
Table 2 Comparison of fitting and experimental results. Number
k (N/ mm)
m1 (g)
m2 (g)
Experimental minimum vibration frequency (Hz)
Fitting minimum vibration frequency (f/Hz)
1 2 3 4 5 6 7 8 9 10
7.6 10.9 15.2 21.2 13.6 16.9 27.3 34.6 24.3 42
51.5 89.5 102.7 114.8 63.3 101.3 126.7 138.8 113.5 151.2
20.1 6.7 33.3 73.7 53.5 53.5 110.1 170.2 103.3 210.7
59.2 62.39 62.37 61.67 61.18 60.67 61.67 61.3 62.06 62.87
59.4 61.75 60.97 60.87 61.8 60.06 61.49 60.43 60.6 61.46
Acknowledgement This work is supported by National Natural Science Foundation of China (Grant No. 50890181, 51076160, 51006112). References
Minimum velocity amplitude, mm/s
60 50 40 30 20 10 0 0
50
100
150
200
250
300
350
Mass of the vibration reduction component, g Fig. 6. Relation between mass and minimum vibration.
The weight and volume of a ultra-high frequency PTC can be decreased by using single piston linear compressor, which is more suitable for portable applications. Such a miniature pulse tube cooler produced a no-load temperature of 61 K and a cooling power of 1 W at 80 K when operating at 80 Hz with 50 W of electrical input power. The minimum vibration of the system can be reduced to below 3 mm/s (5% of the original value), by using an appropriately designed leaf spring at the resonance frequency. The results of this test demonstrate that a single piston compressor could be used to drive a PTC with proper vibration reduction.
400
[1] Petach M, Waterman M, Tward E. Pulse tube microcooler for space applications. Cryocoolers 2007;14:89–93. [2] Petach M, Waterman M, Pruitt G, et al. High frequency coaxial pulse tube microcooler. Cryocoolers 2009;15:97–103. [3] Radebaugh R, O’Gallagher A. Regenerator optimization at very high frequency for microcryocoolers. Adv in Cryogenics Eng 2006;51:1919–28. [4] Srinivas V, Gan ZH, Radebaugh R, et al. 120 Hz pulse tube cryocooler for fast cool down to 50 K. Appl Phys Lett 2007;90:1–3. [5] Garaway I, Gan Zhihua, Bradley P, et al. Development of a miniature 150Hz pulse tube cryocooler. Cryocoolers 2009;15:105–14. [6] Garaway I, Veprik A, Radebaugh R. Diagnostics and optimization of a miniature high frequency pulse tube cryocooler. Adv in Cryogenics Eng: Trans of the Cryogenics Eng Conf 2010;55:167–74. [7] Wu YZ, Gan ZH, Qiu LM, et al. Study on a single-stage 120 Hz pulse tube cryocooler. Adv in Cryogenics Eng 2010;55:175–82. [8] Wang XT, Dai W, Luo EC, et al. Characterization of a 100 Hz miniature pulse tube cooler driven by a linear compressor. Adv in Cryogenics Eng 2010;55:1077–84. [9] Xu Nn, Chen Hl, Yang Lw, et al. Cryogenics 2010;5:1–5 [In Chinese]. [10] Xu Nn, Chen Hl, Liang Jt, et al. Investigation on the ultra-high frequency coaxial pulse tube. Chinese J Mech Eng 2011;6:156–9. In Chinese. [11] Chan CK, Jaco CB, Raab J et al. Miniature pulse tube cooler. In: Proc. 7th int. cryocooler conf. Kirtland AFB (USA): Phillips Laboratory Press; 1992. p. 113-6. [12] Chan CK, Clancy P, Godden J. Pulse tube cooler for flight hyper spectral imaging. Cryogenics 1999;39(12):1007–14.