Research paperAttenuation of Gifford-McMahon cryocooler induced vibration using mechanical vibration isolators
Introduction
Cryocoolers are usually used to cool certain devices, which require ultra-low temperatures environment to implement their performance. When the cryocooler is working, the piston within the cryocooler reciprocating moves and causes the cryocooler to vibrate. This vibration of cryocooler is transmitted to the device that is being cooled and induced the device to vibrate. As a result, the performance of the device degrades [1], [2], [3]. It can be seen that this vibration problem is related to three aspects, which are the reciprocating motion and vibration of the piston, the vibration of the cryocooler, and the vibration transmission from the cryocooler to the device. In the field of cryogenics and refrigeration, methods concerning these three aspects are proposed to solve the vibration problem.
As to the piston motion and vibration, methods are proposed to balance or suppress the piston motion or to attenuate the vibration that is transmitted from the piston to the other components that are connected with the piston. Attaching the piston with a sort of mass block using springs, the piston motion could be counterbalanced [4]. Furthermore, controlling the motion of the mass block using a proportion-integration-differentiation (PID) controlling system, the piston motion would be counterbalanced to a more extent [5]. Inspired by this, exerting certain counterforce on the piston using a sort of closed-loop controlling system that consists of sensors and piezoelectric actuators, the piston motion would be efficiently suppressed [6]. Since the piston connects with other components within the cryocooler, the vibration of the piston is transmitted to these components and causes these components to vibrate. Connecting the piston with the components using flexible structures, the vibration would be attenuated when it is transmitted along the flexible structures from the piston to the components. Taking into consideration the refrigerating performance, the flexible structures are usually made by copper or other materials with suitable thermal properties [7], [8]. As to the vibration of the cryocooler, methods focusing on supporting schemes and operating modes of the cryocooler are proposed to reduce the vibration. The cryocooler is usually supported by kinds of springs or spring-damping systems, through which the energy of the vibration is consumed and the vibration of the cryocooler is reduced [9], [10], [11], [12]. Besides, the operating mode of the cryocooler also influences the vibration of the cryocooler. Driving the displacer by a motor instead of pneumatic force, the vibration would be reduced [13]. Theoretically, the vibration will be eliminated when the cryocooler is shut down. In this case, the degradation of the refrigerating performance could be compensated by enhancing the cooling capacity of the cryocooler [14], [15]. As to the vibration transmission from the cryocooler to the device, methods focusing on suitable connection schemes are proposed to reduce the vibration that is transmitted along the structures that connect the cryocooler with the device. Mechanical connections are to the disadvantage of vibration reduction, and it should be avoided wherever possible [16]. Contrarily, it is favorable to connect the cryocooler with the device using flexible structures, which could be made by springs [17], air springs [18], bellows [19], [20], flexible tubes [21], and memory alloy [22]. Besides, spring-mass systems are capable of reducing the vibration when they connect the cryocooler with the device [23], [24]. Furthermore, applying a sort of vibration resonator as the connection, the energy of the vibration is absorbed by the resonator and the vibration is attenuated [25], [26], [27].
In this paper, aiming to attenuate the vibration that is induced by a Gifford-McMahon (G-M) cryocooler, the cryocooler is supported on a supporting system that mainly consists of several mechanical vibration isolators (MVIs), and the vibration response of the supporting system that is induced by the vibration of the cryocooler is studied. First, the structural configuration of the supporting system is proposed, to meet the demands on both the cooling and vibration performance of the cryocooler. Second, the vibration response of the supporting system that is induced by the vibration of the cryocooler is calculated using the finite element method, and it is explained based on the modal characteristics of the supporting system that is also calculated using the finite element method. Then, the influences of structural parameters of the MVIs on both the modal characteristics and the vibration response of the supporting system are investigated, and the influence rules of the stiffness and the installation sites of the MVIs are obtained. Furthermore, the minimum vibration response of the supporting system is solved, through optimizing the installation sites of the MVIs. The results demonstrate that the MVIs essentially influence the vibration response of the supporting system that is induced by the vibration of the cryocooler, and appropriate structural parameters of the MVIs are beneficial to attenuate the vibration response.
Section snippets
The supporting system of the G-M cryocooler
The supporting system mainly consists of a G-M cryocooler, a thermal conductive cylinder (TCC), a thermal shield cylinder (TSC), a supporting seat (SS), and four mechanical vibration isolators (MVIs), as shown in Fig. 1. For the convenience of description, the four MVIs are named MVI-1, MVI-2, MVI-3, and MVI-4, respectively. The cryocooler is a quasi-cylindrical shaped construction, with its dimensions are 180 mm, 265 mm, and 520 mm in the X, Y, and Z directions, respectively, and its mass is
Theoretical analysis
The vibration of the G-M cryocooler induces the vibration response of the supporting system, and this vibration response could be described as follows.where M, C, and K are the mass matrix, the damping matrix, and the stiffness matrix of the supporting system, respectively, , and X(t) are the acceleration vector, the velocity vector, and the displacement vector of the supporting system, respectively, F(t) is the loading vector that acts on the supporting
Finite element modeling of the supporting system
The vibration response of the supporting system is studied using the finite element method, and the finite element model mainly consists of the G-M cryocooler, the TCC, the TSC, the SS, and the MVIs, as shown in Fig. 3. The cryocooler, the TCC, the TSC, and the SS are solidly modeled and meshed with SOLID elements. For reducing the calculating scale and increasing the calculating efficiency, the specific structures within the cryocooler, including the piston, are ignored, and the cryocooler is
Modal characteristics
To study the vibration response of the supporting system that is induced by the vibration of the cryocooler, the modal characteristics of the supporting system is first analyzed, and then they are used to explain the vibration response. The first six orders modal shapes U(r) (r = 1, 2, …, 6) and natural frequencies ωr (r = 1, 2, …, 6) are calculated using the finite element model, and all these modal shapes and natural frequencies are related to the MVIs, as shown in Fig. 4.
For the first modal
Effects of the structural parameters of the MVIs on the vibration response of the supporting system
According to the classical vibration theory, both the stiffness and the location of the MVIs influence the reciprocating motion of the MVIs, which further affect the modal characteristics and the vibration response of the supporting system. Therefore, the effects of the stiffness and the installation location of the MVIs are investigated.
Minimizing the vibration response by optimizing the installation sites of the MVIs
As expressed above, both the stiffness and the installation sites of the MVIs influence the vibration response of the supporting system, and appropriate stiffness and installation sites are in favor of attenuating the vibration response. Considering the technical limitation, it is challenging to develop the stiffness of the MVIs. Contrarily, it is easy to change the installation sites of the MVIs. Therefore, the installation sites are optimized to minimize the vibration response of the
Conclusions
In this paper, MVIs are employed to attenuate the vibration response of the supporting system of a G-M cryocooler. The results show that the reciprocating motion of the MVIs induces the first six orders modal characteristics of the supporting system, which mainly constitute the vibration response of the supporting system under the excitation of the vibration of the cryocooler. The stiffness and the installation sites of the MVIs influence the reciprocating motion of the MVIs, through which they
Funding
This work is supported by the National High-tech Research and Development Program of China (863 Program) [grant number 2007AA804217].
CRediT authorship contribution statement
Ruifeng Su: Conceptualization, Formal analysis, Investigation. Linzhongyang E: Methodology, Validation. Xueqian Chen: Methodology, Software. Qiang Du: Data curation.
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.
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