Sensors & Transducers 2013 by IFSA http://www.sensorsportal.com Strength Study of Spiral of Stirling Cryocooler WANG Wen-Rui, NIE Shuai, ZHANG Jia-Ming School of Mechanical Engineering, University of Science and Technology Beijing, 100083, China Received: 13 November 2013 /Accepted: 27 November 2013 /Published: 30 November 2013 Abstract: Stirling cryocooler becomes the research focus in many countries, because of high efficiency and compact structure. But the structure design, material selection and mechanical performance of spiral flexure spring, which is the key component of stirling cryocooler, is always an important problem. By means of in-depth study of spiral flexure spring of stirling cryocooler, the force model is established by finite element method. It is necessary to study its strength characteristics and analyze the influence factors. The simulation results are compared with the experimental results, which show that the method of the research, which the paper adopts, is feasible and effective. It also provides theoretical and engineering basis for design and analysis of spiral flexure spring of stirling cryocooler. Copyright 2013 IFSA. Keywords: Stirling cryocooler, Spiral flexure spring, Strength, Finite element, Experimental study. 1. Introduction At present, stirling cryocooler adopts the technology projects, which include linear motor, clearance seal and spiral flexure spring. In addition, stirling cryocooler uses unique the way of closed cycle, which makes the research of stirling cryocooler become the current hot topic in the study of low temperature refrigeration system [1]. Spiral flexure spring ensures that stirling cryocooler steadily and properly works. When stirling cryocooler is working, spiral flexure spring is connected to reciprocating pistons, which ensures that there is clearance between piston and cylinder and provides necessary restoring force for reciprocating movement of the piston [2]. The performance of spiral flexure spring is directly related to running stability and output efficiency of stirling cryocooler. The research of inherent stiffness and strength of spiral flexure spring has an important theoretical and engineering value for the performance and life of Stirling cryocooler [3]. In this paper, the mechanical model of strength of spiral flexure spring is established by finite element method. In addition, simulation data is contrasted with experimental results in the mechanical environment of spiral flexure spring, which verifies that spiral flexure spring meets the job requirements. Finally, the above conclusions provide theoretical and engineering basis for design and analysis of spiral flexure spring of stirling cryocooler. 2. Theoretical Research Model of Spiral Through the line design of spiral flexure spring, theoretical model of spiral flexure spring is set up in this paper. The line of spiral flexure spring is constructed with the method of circle involute. Then the parameters of circle involute equation are changed to construct different line of spiral flexure spring. In addition, spiral flexure spring with exact lines is produced by modern machining technology, 404 Article number P_RP_0023
because the expression of circle involute is simple [4]. At present, there are not many systemic descriptions to the generation process of spiral line. Not only geometric equations of spiral groove are provided, but also fore and aft closure and spatial distribution is considered in this paper [5]. The special properties of circle involute are used to get geometric equations of spiral groove with the same base circle radius and different gradually open Angle. The following formulas are the equations of spiral flexure spring. check of spiral flexure spring [8]. So, finite element model is established to check the strength of spiral flexure spring in this paper. Maximum displacement of spiral flexure spring is 10 mm in order to satisfy the requirements of the work. After axial displacement is loaded which is from 10 mm to 20 mm in the edge of spiral flexure spring, the maximum stress is contrasted with the allowable stress of material. If the maximum stress is lower than the allowable stress, the strength of spiral flexure spring meets requirements. On the contrary, it will be failure. x y x y ( cosα α sinα ( sinα α cosα = R + 1 1 1 1 = R 1 1 1 1 ( cosα α sinα ( sinα α cosα = R + 2 2 2 2 = R 2 2 2 2 (1 (2 Because the spiral groove width is small, convenience and reliability of the processing is considered, as closing two spiral lines. Meanwhile, the smooth transition will be used to avoid stress concentration [6]. Spiral flexure spring is designed as is shown in Fig. 1 by arranging spiral line in a certain way. Fig. 2. Mechanics diagram of spiral flexure spring. Fig. 1. Spiral flexure spring. 3. Finite Element Analysis of Spiral In the finite element analysis, the solid model of spiral flexure spring will be swept and meshed [9]. The solid model and meshing of spiral flexure spring are shown in Fig. 3 and Fig. 4. Spring material is spring steel, which elasticity modulus is 210 GPa and which Poisson s ratio is 0.3. Outer diameter and inner diameter of spiral flexure spring are 125 mm and 15 mm. Movement and rotation degrees of freedom is restricted in outer edge of spiral flexure spring [10]. Axial concentration is loaded in the edge of spiral flexure spring. Boundary constraints of spiral flexure spring and Loading way of spiral flexure spring are shown in Fig. 5 and Fig. 6. 3.1. Finite Element Model of Spiral Flexure Spring When stirling cryocooler is working, spiral flexure spring is connected to reciprocating pistons, which ensures that there is clearance between piston and cylinder and provides necessary restoring force for reciprocating movement of the piston [7]. Spiral flexure spring is fixed around and free in the middle. Its force situation can be simplified as what is shown in Fig. 2. Finite element analysis of spiral flexure spring mainly refers to the analysis of strength performance. At present, there is no theoretical method to strength Fig. 3. Solid model of spiral flexure spring. 405
450 400 Maximum stress (MPa 350 300 250 200 Fig. 4. Meshing of spiral flexure spring. 10 12 14 16 18 20 Displacement (mm Fig.7. The diagram of displacement and maximum stress. 4. Strength Experimental Study of Spiral 4.1. Selection and Pasting of Resistance Strain Gage Fig. 5. Boundary constraints of spiral flexure spring. Resistance strain gage is used in the experiment, which has a resistance of 120 Ω and sensitivity coefficient of 2.08. Poisson s ratio of the material is 0.28 and the modulus of elasticity is 210 GPa. First of all, The pasting location must be identified. It is very important to find a correct pasting position for strain test, in order to get a good response to the output signal from the fixed strain gauge, by analyzing the line structure of spiral flexure spring. The position of tension and compression is to be identified when the spiral flexure spring has an alternating vibration [8]. According to the analysis of finite element method, deformation at the roots of vortex arms is very big, which has enough space for the strain gauges. So the strain gauges are pasted at radial and axial direction at the roots of vortex arms of spiral flexure spring, which are numbered 1-7, as is shown in Fig. 8. Fig. 6. Loading way of spiral flexure spring. 3.2. Finite Element Study of Spiral Flexure Spring From Fig. 7, it can be obtained that maximum stress of spiral flexure spring is from 215.3 MPa to 430.6 MPa when axial displacement which is from 10 mm to 20 mm is loaded in the edge of spiral flexure spring. The material of spiral flexure spring is 65 Mn which yield strength is 1000 MPa. The maximum working stress is lower than yield strength of the material so that spiral flexure spring meets the strength requirements. Fig. 8. The actual patch position. 406
4.2. Form of Bridge and Data Collection Method of half bridge measurement is chosen in the experiment, which is suitable for simple tension, compression or bending strain measurement, and has less demanding for the test environment. Fig. 9 is the circuit of bridge. The number of strain gauges is 2, which are one for work and another for compensation. Before measuring, the bridge circuit should be welded correctly and then connected to test system through DH3810 resistance strain adapter. Fig. 9. A half bridge measurement circuit. 4.3. Analysis of Experiment Data At the experiment, the data is recorded and analyzed by changing the excitation current and the sampling frequency of the test system. Next, it has a detailed study of strain situations at various positions of spiral flexure spring during the piston movement. Firstly, when the sampling frequency is kept at 200 Hz, the load at spiral flexure spring will be changed by adjusting excitation current of the motor. Then, when the sampling frequency is raised to 10 khz and kept unchanged, the load at spiral flexure spring will be changed by adjusting excitation current of the motor. Maximum strain value(με 1800 1600 1400 1200 1000 800 600 400 200 0-200 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Excitation current (A Fig. 10. The diagram of exciting current and strain value. 200Hz 10KHz It can be drawn through the recording and analysis of above experimental data: When the sampling frequency is kept at 200 Hz, the strain at spiral flexure spring will increase as the increase of motor excitation current. Therefore, strain at spiral flexure spring also increases with increase of load. When the sampling frequency is raised to 10 KHz, the relationship is the same as that when the sampling frequency is kept at 200 Hz. Through the field experiment, the deformation of axial load in the case of surrounding fixed and center free of spiral flexure spring is obtained. For further confirmation of the reality of the experiment data, the comparison between experiment data and theoretical results through finite element method is as follows. The 4-line eccentric spiral flexure spring in finite element modeling is adopted as the experiment. The sinusoidal excitation load is the same as the experiment, and the direction is axial. From the time and auto-power spectrum strain oscillograph, the natural frequency of spring is 59.96 Hz, and the load function is ( F = Asin 2π 59.96t (3 A is amplitude parameter. Different excitation current is corresponding to different amplitude; Natural frequency f is 59.96 Hz; T is time variable. It can be seen from above experimental analysis and simulation results. At different sinusoidal excitation, the maximum strain values of spiral flexure spring match with the experimental values at corresponding excitation by finite element analysis. 5. Conclusions In this paper, theoretical calculation and experimental research is studied for the stiffness and strength of spiral flexure spring, which is the core component of stirling cryocooler. The performance of spiral flexure spring is analyzed and studied comprehensively by theoretical calculation of stiffness, finite element analysis and strain test. The main research work and the conclusion are: 1 The strain situation at the maximum working displacement of spiral flexure spring through simulation model is obtained. The maximum working strain is considerably below the yield strength of material by comparing them, so the strength of designed spiral flexure spring meets the requirement. 2 In this experiment, the strain values of 7 spots on spiral flexure spring are measured and analyzed by varying excitation current of the motor and the sampling frequency of test system. The strain values of the spots on spiral flexure spring rise as the excitation current of the motor increases. By comparing with the strain value of simulation model, the experimental values are corresponding with theoretical values. Then the sinusoidal excitation is constantly increased in simulation model, and the 407
maximum strain on spiral flexure spring becomes continually larger, but is still lower than the allowable stresses of material of spiral flexure spring, so its strength meets the requirements as long as it satisfies the working performance requirements. Acknowledgement Research in this paper was supported by major national special scientific instruments funds developed (2011YQ14014507. References [1]. Ding G. Z., Study on linear compressor for stirling refrigerator, Cryogenics, 2007, 35, 6, pp. 458-461. [2]. Kaushik S. C., Kumar S., Finite Time Thermo dynamic Evaluation of Irreversible Ericsson and Stirling Heat Engines, Energy Conversion and Management, 2001, 42, pp. 295-312. [3]. Gao W. L., Finite element analysis and experimental study of spiral flexure spring, Cryogenics, 37, 9, 2009, pp. 6-9. [4]. Yuan Z. Y., Chen X., Qi Y. X., Liu Y., Li J., Influence of structure parameters on flexure spring performance based Fermat curve, Cryogenics, 4, 2011, pp. 27-31. [5]. Chen X., Liu Y., Yuan Z. Y., Zhang H., Wu Y. N., Theory and experimental study on flexure spring based Fermat curve, Journal of Mechanical Engineering, 47, 18, 2011, pp. 130-136. [6]. Song G. Q., Allen A., Flexure Design and Testing for STC Stirling Convertors, in Proceedings of the 1 st International Energy Conversion Engineering Conference, 6040, 2003, pp. 1-7. [7]. Yuan Z. Y., Chen X., Liu Y., Qi Y. X., Finite element analysis of three molded lines of flexure springs, Cryogenics, 39, 7, 2011, pp. 21-24. [8]. Liu Y., Chen X., Qi Y. X., Wu W. D., Zhang H., Development of flexure spring for cryocooler, Cryogenics, 38, 4, 2010, pp. 8-13. [9]. Li J. G., Yan T., Cai J. H., Finite element analysis of flexure spring in pulse tube cooler, Cryogenics, 1, 2012, pp. 40-43. [10]. Chen N., Key components and overall performance study of the moving-magnet linear compressor for striling refrigerator with large cooling capacity, Shanghai Jiao Tong University, Shanghai, 2007. 2013 Copyright, International Frequency Sensor Association (IFSA. All rights reserved. (http://www.sensorsportal.com 408