Results of optimisation

The charts shown in F1gure 48(a, b) depict the calculated absolute deflection of the v1brat1on 1solated platform at fnctionless operation of the SPB-compressor.

Chart (a) reflects the case of no external vibration, and chart (b) reflects the case when environmental broadband exc1tation is applied. The related charts, which are given in F1gure 49(a, b), show the platform Jltter when a maximum fnct1on force anses between the sliding surfaces. In these charts, the absolute deflection IS shown versus natural undamped frequency of the compressor decoupler at the different damping rat1os. The deflection of the platform, excited by a sinusoidal force exported from a dual-piston compressor, is superimposed on every chart as a reference.

An analys1s of the obta1ned charts 1s given below.

F1gure 48(a) - FnctJonless operation without enwonmental broadband Vibration.

The system demonstrates noticeable dependence of the platform j1tter on the natural frequency of the compressor decoupler. Such behaviour IS obvious, because st1ffening of the decoupler evidently increases force export from the compressor to the platform. However, the Influence of the dampmg rat1o 1s negligible in the considered range. This phenomenon 1s most probably due to the operation of the vibrat1on absorber, which attenuates the absolute and relative veloc1ty of the decoupled compressor, and consequently, d1m1n1shes the component of the viscous force transferred to the platform.

F1gure 4B(b)- Fnct1ontess operation under environmental broadband vibration.

The system under consideration demonstrates the optimal natural frequency in the v1cin1ty of 90 Hz, where Jltter of the platform is lowest at the ent1re spec1f1ed range of damping ratios. Compared to the prev1ous chart, the Influence of the damp1ng ratio IS slightly greater. Most probably th1s occurs because of the act1on of the environmental broadband v1brat1on, yield1ng the Intensive

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participation of the decoupler's damping ratio in a suppression of the platform jitter.

"' Damping ratio or decoupler

0..

Nalural undamped frequency or decoupler, Hz

(a)

Nalural undamped frequency or decoupler, Hz

(b)

Figure 48. Absolute deflection of system platform under longitudinal g-load, (a) - unexcited, (b) -randomly excited.

120 130

In the range of natural frequencies lying below 90 Hz, the platform jitter increases with softer decoupler, approaching the natural frequency of the platform's vibration isolator, which is assigned to be 40Hz.

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Regarding the range lying above 90 Hz, the slope of the family of curves is eo-directional with the slope obtained for the unexcited system. That slope is also originated as a result of intensified force transfer from the compressor to the platform thanks to a stiffer decoupler. The only difference is that the slope considerably depressed by the characteristic of theplatform vibration-isolator.

3

Natural undamped frequency of decoupler, Hz

(a)

Malt random, max friction

OaJT1)11l9 ra1Jo IX decoupler

- 01 - 02

- 03 - 04

05 - Duai·Pt&ton

40 50 60 70 eo 90 100 110

Naturallndall..,ed frequency ol decoupler, Hz

(b)

Figure 49. Absolute deflection of system platform under transversal g-load, (a) - unexcited, (b) -randomly excited.

120 130

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From the analysed chart, it is obvious that the undamped natural frequency of the decoupler needs to be as low as possible, but however, is limited from below by jitter amplification at the partial natural frequency of the randomly vibrated platform.

Figure 49 (a,b) -Operation at maximal friction force

The system demonstrates the insensitivity of the platform jitter to the decoupler parameters when it is either unexcited or exposed to random vibration. lt is reasonable to assume, that the friction adds a dominant amount of damping to the system, which effectively suppresses all the resonances of the subsystems.

As mentioned above, the relative deflection of the platform was also acquired throughout the mapping. The compiled charts of relative deflections are shown in Figure 50(a, b). From the figure, it can be seen, that the considered system can be optimised in terms of either absolute or relative deflections, thanks to their very similar characteristics.

Finally, relying on the obtained charts, the optimal parameters of the compressor suspension were assigned as follows:

• Undamped natural frequency- 90 Hz

• Damping ratio- 0.2

Although the highest damping ratio is estimated to be preferable, use of a commercial-off-the-shelf (COTS) or uncomplicated custom vibration isolator is still one of the desired parameters.

One of the advantages of the optimised system is that the achieved optimal natural frequency of the decoupler is considerably higher than the driving frequency of the cryocooler (58 Hz). That feature is desirable for the SPB-compressor to endure typical quasi-static accelerations, along with minimisation

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of fatigue deformations of a gas pipe connecting the moving compressor with the static expander assembly.

Damping ratio of decoupler

- 0.1

Natural undamped frequency of decoupler, Hz

~--- ---~

Natural undamped frequency of decoupler. Hz

L---

(b)

Figure 50. Relative deflection of IR Camera's platform under applied random excitation, (a) - longitudinal g-load (b)-transversal g-load

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