Adaptive vibration reduction on dual-opposed piston free displacer Stirling cooler

Transcription

1 Adaptive vibration reduction on dual-opposed piston free displacer Stirling cooler R. Arts, A. de Bruin,. Willems, G. de Jonge, A. Benschop Thales Cryogenics B.V., Eindhoven, The Netherlands ABSTRACT In a Stirling-type pulse-tube cooler with a dual-opposed piston compressor, the residual vibration exported by the cooler is primarily a result of residual imbalances between compressor motors. Using an electronic feedback loop [] and driving compressor motors in a master-slave configuration, the exported force from the compressor can be regulated to negligible levels. This has been demonstrated in a multitude of commercial applications [] as well as in space applications. In a novel application of the same electronic feedback technology, the residual exported forces resulting from the motion of the free moving displacer of a Stirling cold finger are compensated, by using the linear dual-opposed piston compressor as an active balancer. Theoretical analysis of this is provided, measurements are presented on different cooler types, and the effect of integration aspects - hard mount versus suspended is discussed. The effect on exported vibration as well as power efficiency is discussed and compared between Stirling and pulse-tube type coolers. Currently available off-the-shelf hardware, the CE7, is presented and future developments are discussed. Keywords: Cryocooler, Stirling, Adaptive, Vibration, Split, Linear, isplacer. INTROUCTION Ever since the invention of the closed-cycle mechanical cryocooler as a replacement for liquid cryogens, exported vibrations have been a point of attention. As any practical implementation of a mechanical cryocooler contains moving parts, some vibrations are exported to the application. This can lead to undesired effects in the application of the cryocooler. The unwanted effects can range from system-level effects (such as the production of acoustic noise in the overlying superstructure) to sensor-level effects (such as instability of the sensor position, leading to line-of-sight instabilities). One important advance that has been made in reducing these unwanted effects is the development of the Stirling-type high frequency pulse-tube cooler. This type of cryocooler makes use of a pressure wave generator, as in a free-displacer Stirling cooler, but uses a pulse-tube cold head. As a pulse-tube cold finger does not contain any moving solid masses, the amount of vibrational force exported is greatly reduced. However, for tactical infrared applications, pulse-tubes have not seen widespread use. This is primarily due to the fact that pulse-tube coolers lack the cooling power and efficiency of similarly-sized Stirling displacer alternatives, resulting in longer cool-down times and higher power consumption. Therefore, Stirling type coolers have remained the primary choice for tactical infrared applications. In this paper, a method is presented to achieve similar vibration performance in a split-linear Stirling cooler as in a pulsetube cooler, while making use of existing (off-the-shelf) components. This is done by using the compressor as an active compensator for forces exported by the moving displacer. We explain the principles behind this active compensation, present measurements showing the effectiveness of this solution, and provide an outlook on potential future improvements.. THEORY We will regard the effectiveness of first harmonic suppression in a Stirling cooler in an in-line configuration. A schematic overview of the setup under investigation is shown in Figure. This figure shows a cut-out schematic view of Infrared Technology and Applications L, edited by Bjørn F. Andresen, Gabor F. Fulop, Charles M. Hanson, aul R. Norton, roc. of SIE Vol. 9070, 9070M 04 SIE CCC code: /4/$8 doi: 0.7/ roc. of SIE Vol M-

2 r an LSF flexure-bearing linear Stirling cooler. All moving masses are labeled in the figure (m i ). The two drive voltages for compressor motors are shown (V i ). Furthermore, the two sensors that are used to close the control loop (temperature Temp and acceleration a) are shown in the figure. Finally, the CE7 controller with active vibration reduction capability is shown at the bottom of the figure. III NMI = m MOM m iiihhhhhhhhhhhhhhhnni V Temperature Sensing iode Accelerometer Temp V THALES Ulf 7 c... on.. cr.o.a...o._.a._ Figure : In-line split-linear Stirling cooler with Active Vibration Reduction electronics. We will assume all motions to be first-order harmonic; higher harmonics of the drive frequency are neglected and therefore excluded from the analysis. For the purpose of this analysis, we will regard the compressor as a perfectly-symmetrical dual-opposed piston compressor, with m = m = and equal nominal stroke amplitude. The amplitude of the displacer is defined as mp and the phase difference with the compression volume is moving components is described with and x x ( t. In the nominal situation, the motion of the three t) = sin( ), () ( t t) = sin( ), () x t) = sin( t + ). () ( The displaced volume of the compressor equals V t) = A ( x ( t) x ( t)) = A sin( t). (4) The total exported force due to inertia equals c( p p p roc. of SIE Vol M-

3 F vib = m & x i i = m. (5) i= Because the motion of both pistons is exactly opposed, the exported vibration force is only determined by the motion of the displacer. The active vibration reduction algorithm corrects this motion with that of one of the compressor pistons, such that the total exported vibration force (equation 5) becomes zero. This means that the compressor pistons will no longer be exactly opposed. For the correction, a phase and amplitude correction is applied to one piston. The convention used below is that the phase of the uncorrected piston is 0. We will express the ratio between motion amplitudes of piston and piston (unbalance induced by the vibration reduction algorithm) as and the phase correction applied to piston as. In order to preserve cooling power and tip temperature, the displacer stroke remains the same as in the nominal (not vibration-corrected) case, so =. Equations of motion for m, m, and m then become x( t) = sin( t), (6) x t) = sin( t + ), (7) and ( x( t) = sin( t + dv + ), (8) with the additional phase shift of the swept volume dv = arctan + sin( ) cos( ) which appears in the motion of the displacer because the absolute phase of the total compression space volume shifts as well, ' Vc ( t) = Ap ( sin( t) + avr sin( t + avr)) = Vswept sin( t + pdv ). (0) The first condition that needs to be satisfied is that the swept volume, the amplitude of x ( t) x( t) remains constant ( V swept = Ap p ), to ensure = : (( cos( ) + ) ) + ( sin( )) = 4 (9). () Now, in order to cancel exported vibrations at the fundamental, we need to satisfy the d xi ( t) condition Fi = mi = 0. The factor is eliminated from the equation for readability, resulting in dt m sin( t + ) + m sin( t) m sin( t + + ) 0. () dv = Equation () can be decomposed in two orthogonal equations by separating into sin( t) and cos( t) with equation () this results in three equations to solve for the three unknowns,, and. An estimate of the effect on cooler specific power can also be made. terms. Together roc. of SIE Vol M-

4 As a first-order worst-case estimate, we will assume that one compressor piston performs an extra out-of-phase motion to compensate the force exerted by the displacer. We calculate the additional current needed to compensate the exported force via the motor constant and simply express it as I R, resulting in F = Z K () M with Z the dynamic impedance of one linear motor in Ω and K M the motor constant in N/A. The cryocooler specific power (watts of input power per watt of heat lift) will scale with this expression. Vibration reduction parameters are calculated for two example coolers in the result tables below: cooler m = = 500 g m m m = 50 g K M m Z (one motor) AC 0 N/A 0 Ω 5 mm mm 4 rad/s 0.5π rad 00 W cooler m = = 00 g m m m = 0 g K M m Z (one motor) AC 5 N/A Ω mm mm 77 rad/s 0.5π rad 0 W Corrected cooler F 7 N RMS mm = mm -0.0π AC.5 % Corrected cooler F N RMS.96 mm =.04 mm π AC 0.6 % These theoretical calculations show that the effect of vibration reduction on cryocooler efficiency will be negligible in most cases.. EERIMENTAL SETU For all tests, a CE7 Commercial Off-The-Shelf cooler drive electronics was used. This CE is available in a benchtop configuration for laboratory use and is suitable for use with most dual-drive linear Stirling coolers. The CE7 is designed for use with a low-cost MEMS accelerometer to provide vibration sensing data to the controller. Two different configurations were tested, as shown in Figure and Figure, below. In both cases, the feedback sensor for the vibration reduction algorithm is mounted on the cold finger heat sink. The -axis accelerometer used for measurements is not shown in these photos. uring testing, the coolers were placed on foam to allow for sufficient movement in the axial direction. roc. of SIE Vol M-4

5 Figure : LSF950. Figure : LSF9987. The LSF950 had a test ewar mounted, while the LSF9987 was tested with no vacuum ewar mounted. The CE7 converter was controlled using an RS- command interface. uring tests of the LSF950, a fixed temperature set point was used, while for the LSF9987 tests a fixed nominal AC voltage was applied. 4. MEASUREMENTS LSF950 We will first examine the measured vibrations along the compressor axis, which are depicted in Figure 4. What can be clearly identified is that the fundamental drive frequency is suppressed by a factor of 50 without any adverse effect on higher harmonics. By increasing the computational range of the CE7, an effective suppression can be achieved up to the 0 th harmonic. When examining off-axis vibrations (Figure 5) a much smaller effect is seen. A minimal effect is seen at the fundamental and the second harmonic. At higher harmonics, no significant effect is observed. It can be concluded that the radial exported forces are not a result of coupling between modes and cannot be effectively suppressed by a one-axis correction mechanism. The power increase measured when was enabled was %. This is in good agreement with equation () harmonics corrected 0 harmonics corrected I I Freq [Hz] Figure 4: Vibration spectrum measured along LSF950 principal axis. roc. of SIE Vol M-5

6 n 5 harmonics corrected 0 harmonics corrected 7, Freq IHzI Figure 5: Vibration spectrum measured along LSF950 radial direction (off-axis). 5. MEASUREMENTS LSF9987 Measurements were also done on an LSF9987 cryocooler, which operates at 60 Hz and has a much smaller maximum input power than the LSF950. The results are shown in Figure 6. It can be seen that the first harmonic is effectively suppressed by an approximate factor of 00. Beyond the 5th harmonic, no effective suppression was measured on this cooler harmonic corrected 5 harmonics corrected 0.60 ; Freq [Hz] Figure 6: Vibration spectrum measured along LSF9987 principal axis. The relative reduction at the higher harmonics is smaller than what was achieved with the LSF950 cooler. This is caused by the significantly lower absolute vibration levels, limiting the SNR of the accelerometer signal fed to the CE7 converter. The effect of the on input power was too small to be reliably measured with this cooler. roc. of SIE Vol M-6

7 6. INTEGRATION ASECTS In order to achieve an effective suppression of vibrations, a number of integration aspects are of importance. The primary consideration, which is supported by the difference in test results between the LSF950 and the (much smaller) LSF9987 cooler, is that of accelerometer resolution. For the purpose of our tests, a low-cost accelerometer was used. As the output from this sensor is directly proportional to its acceleration rather than force, a degree of freedom is necessary for the cryocooler, typically accomplished by mounting the cooler suspended. Furthermore, a cooler exporting a smaller nominal force (such as the LSF9987) may not generate sufficient signal for effective suppression of higher-order harmonics, especially if the cooler is not mounted in a way that allows for completely unrestricted movement along the cooler principal axis. Mounting a cooler in such a way is often impractical in a tactical infrared application, as this provides challenges both in terms of making a structurally robust infrared camera, to withstand shock & vibration loads typically associated with tactical use, and in terms of providing sufficient heat sinking capacity to the cryocooler, which usually relies either on firm metal-to-metal contact between cryocooler and support structure or on heat pipes. Furthermore, a suspended mount of the cryocooler will require careful design to avoid introducing a generally undesired degree of freedom of the focal plane along the optical axis of the infrared imager. The disadvantage caused by the flexible mounting requirement can be overcome by the use of iezo force transducers, as is typically done in high-sensitivity space instrument applications. While the Thales CE7 was not designed for use with these high-sensitivity iezo transducers, a test was performed [] in which Kistler force transducers were used to close the CE7 vibration reduction loop, to reduce vibrations exported from an LTC compressor, developed under ESA Technology Research rogramme (TR) contract [5] and currently being built for the ESA Meteosat Third Generation (MTG) program Unregulated Regulated.00, _ m Freq [Hz] 54 t 4 47 Figure 7: Vibration spectrum LTC compressor. As can be seen in Figure 7, more than a factor 50 reduction was achieved for the first harmonic. It is therefore concluded that the vibration reduction algorithm is suitable for several sensor types, as long as a signal is generated that is proportional to force or acceleration. In the specific case described in this paper, where the linear compressor is used to compensate forces exported by the moving displacer, it is of the utmost importance that there is a rigid connection between compressor and cold finger. Both compressor and cold finger need to be rigidly mounted on the same structure. This was verified by tests, with either roc. of SIE Vol M-7

8 compressor or cold finger loosened from the structure. In this configuration, effective vibration reduction could no longer be achieved. A sufficiently stiff connection between compressor and cold finger is required to enable the use of the compressor as an active balancer. The accelerometer should be hard-mounted to the cooler body and correctly aligned with the axis of motion for the displacer. In addition, it is important that the axis of motion for compressor pistons and displacer coincide, as any translational or angular deviation between the two will result in a torque, even with all linear forces perfectly balanced. The CE7 used in the experiments described herein is not suitable for integration into a portable system, as this is essentially a bench top controller. However, there is no fundamental problem with developing a smaller -enabled controller. H/LE,S T... O / Figure 8: CE4865 (left) and CE7 (right) controller. 7. CONCLUSIONS It is concluded that the exported vibrations resulting from displacer motion in a free displacer Stirling cooler can be effectively suppressed by active vibration reduction, resulting in exported vibration levels comparable to those of similar-sized Stirling-type pulse-tube coolers. It was furthermore shown that vibration reduction can be performed with existing off-the-shelf dual-opposed piston coolers when paired with existing drive electronics, removing any need for an additional actively driven counterbalancing mass. Finally, it can be concluded that the effectiveness of active vibration reduction on smaller coolers is currently limited by resolution and SNR of the off-the-shelf accelerometer sensor, but there are no principal problems involved in adapting the off-the-shelf hardware for use with high-resolution force transducers, allowing for potential future improvements. REFERENCES [] Verberne, J.F.C., Bruins,.C., van den Bosch,.J. and ter Brake, H.J.M., "Reduction of the Vibration Generated by Stirling Cryocoolers Used for Cooling a High-Tc SQUI Magnetometer," Cryocoolers 8, lenum ress, New York, pp (995). [] Bruins,.C., de Koning, A., and Hofman, T., "Low Vibration 80 K pulse-tube Cooler with flexure bearing compressor," Cryocoolers, lenum ress, New York, pp (00). [] Arts, R., "eployment of Tactical-grade COTS cryocoolers for Space Applications," 5th ESA Space Cryogenics Workshop, (0) [4] Thales Cryogenics, "Vibration sensitive integration of pulse-tubes," White paper, (008) [5] Trollier, T., Tanchon, Buquet, J., Ravex, A., Charles, I., Coynel, A., uband, L., Ercolani, E., Guillemet, L., Mullié, J., am, J., Benschop, T., Linder, M., "esign of a Large Heat Lift 40 K to 80 K pulse-tube Cryocooler for Space Applications," Cryocoolers 4, ICC ress, Boulder, CO, pp (007) roc. of SIE Vol M-8