RESONANCE ANALYSIS OF VALVED LINEAR COMPRESSOR FOR REFRIGERATION APPLICATION Amit Jomde 1, A. Anderson 1, Virendra Bhojwani 2, Paresh Shinde 2, Suhas Deshmukh 2 and Sunita Phadkule 2 1 Department of Mechanical Engineering, Sathyabama University, Chennai, Tamil Nadu, India 2 Savitribai Phule Pune University, Pune, Maharashtra, India E-Mail: ammit.jomde@gmail.com ABSTRACT Resonance is a condition under which system vibrates at natural frequency. Resonance produces maximum vibration amplitude. In industry resonance is consider to be harmful for long life of the equipment as amplitude of vibration is very high which results in failure of the component. At the same time there are some equipment s and applications which work on resonance principal linear compressor is one such application. Under resonance condition it produces maximum amplitude of stroke with minimum input electric power (Exciting force). A linear compressor consists of an oscillating motor and a piston rigidly coupled to it. Oscillations of the linear motor are directly transferred to the piston. The piston is supported by resonant springs to form a free piston system. The use of linear motor reduces the mechanical linkages like crank, connecting rod necessary for converting rotary to linear motion. Hence this machine is compact, operates with very less friction and noise. It is one of the most efficient available compression technologies. The present work discusses model of a linear compressor in CREO. FEM was used to analyze natural frequency of the linear compressor. Various parameters were studied to achieve resonance at 50 Hz condition to meet the Indian power supply conditions. Keywords: linear compressor, resonance, modal analysis. Nomenclature A C COP Fn Km Kg LPH Area, m 2 Damping coefficient Coefficient of performance Natural frequency, Hz Mechanical stiffens. Nm -1 Gas stiffness, Nm -1 Liquid flow rate M P P suction P Pr X Moving mass, kg Pressure, Pa Suction pressure, Pa Mean pressure, Pa Difference pressure between discharge and suction, Pa Pressure ratio Displacement, m 1. INTRODUCTION A linear compressor is a positive displacement compressor driven by a linear motor. Piston is supported by resonating spring to form a free piston system. A resonant spring is used to obtain a piston stroke with small thrust of the linear motor. The use of the linear motor reduces the mechanical linkages like crank and connecting rod necessary for converting rotary to linear motion. Hence this machine is compact, operates with very less friction and noise. As there is no conversion of rotary to linear motion, all the forces act along axis of the piston. Chen N. et al. (2007) [1] studied the static and dynamic characteristics of moving magnet linear compressor. Static characteristic was investigated by experimentation and dynamic characteristics studied using mathematical model. Hyun Kim et al. [3] (2009) studied the dynamic characteristics of linear compressor. They also investigated effect of resonance on performance of compressor by comparing the simulation results with the experiment results. Ming Xia et al. (2010) [4] analyzed the moving magnet linear compressor of Stirling cryocooler. The simulation and experimentation results showed the effect of magnet spring on resonance frequency of moving magnet linear compressor. Tae-Won Chun et al (2008) [5] studied the PWM inverter for improving the efficiency of linear compressor. Zhengyu Lin et al. (2007) [6] introduced a new technique to achieve resonance condition by controlling electrical frequency to linear motor for increasing the efficiency of linear compressor. The linear compressor has shown high potential in cryogenics, refrigeration, air-conditioning and electronic cooling applications recently [7-12]. The present work discusses the effect of operating frequency (at resonance and off resonance conditions) of linear compressor on various parameters of vapour compression refrigeration system. FEM is used to analyze natural frequency of the linear compressor. 2. RESONANT FREQUENCY OF LINEAR COMPRESSOR Resonance is a tendency at which system oscillates with greater amplitude when operating frequency matches with natural frequency of system. Linear compressor is a resonant machine. Linear compressor operates more efficiently at resonance frequency. Figure-1 shows the structure of linear compressor composed of flexure spring, piston and moving coil linear motor. Figure-2 shows flexure spring 13810
consist of spiral cut. These spiral cuts allow each of the flexure to move itself axially on application of load in the axial direction. In practice a single flexure spring can deliver the total desired stiffness but may restrict required displacement. To achieve desired stiffness and displacement stack of flexure spring is used in parallel arrangement. Beryllium copper material is used for flexure spring as it has maximum stiffness as compare to other materials like stainless steel and copper alloys. In addition, it has high corrosive resistance, low magnet permeability and high fatigue strength. Figure-3. FBD of linear compressor. 3. MODAL ANALYSIS The resonant frequency of free piston linear compressor is a function of moving mass and stiffness which can be represented as equation (2), = ) (2) Total stiffness K = K m + K g. The gas spring stiffness can be calculated as equation (3) (Chen et al., 2007) Figure-1. Schematic diagram of linear compressor. K g = (3) Modal analysis is used to estimate natural frequency of linear compressor. Figure-4 shows the creo model of linear compressor consist of piston, coil former and flexure spring with the same material properties as that of prototype linear compressor. Figure-2. Flexure spring. The forces acting on piston of linear compressor such as spring force, damping force and electric forces are resulted from applied current. The motion equation of linear compressor can be described as follows [2]: Figure-4. CREO model of linear compressor. m e x + C e x + K e x = F The material used for piston is stainless steel, for coil former is aluminium and for the flexure spring is beryllium copper. Analysis is done for different stacks of flexure springs. Initially stiffness of 0.3mm, 0.5mm, 0.7mm and 1mm thick flexure springs were calculated. As per the analysis 0.7mm thick flexure spring has safe stress and maximum stiffness which fulfil the requirement of the 13811
experimental set-up. 0.7 mm flexure spring is used for further analysis i.e. to find natural frequency. Stiffness of single flexure spring with 0.7mm thickness is 1676 Nm -1. The linear compressor parameters are finalized as per the vapour compression system requirement and are presented in table 1 for the further experimentation. Table-1. Parameters of the linear compressor. Main parameter value Area of piston (m 2 ) 0.000397 Moving mass (Kg) 0.615 Stiffness of each spring (Nm -1 ) 1676 Displacement (m) 0.01 Suction pressure (bar) Discharge pressure (bar) 4. EXPERIMENTATION The stiffness of 0.7mm thick flexure has been validated experimentally. The experimental set up for stiffness measurement is as shown in Figure-5a. The average value of the stiffness found experimentally is 1678 N/m. Figure-5b shows the experimental setup of vapour compression refrigeration system using prototype linear compressor. This setup consists of pressure gauges at inlet and outlet of the linear compressor, flow meter and expansion valve. Linear variable differential transformer (LVDT) and an oscilloscope are used to measure the stroke of piston and natural frequency of system. The refrigerant gas used in this experiment is R134a. Linear compressor is driven by variable frequency variable voltage (VFVV) power supply. The power supply can show the voltage, current and frequency of the compressor. 2 8 Figure-5(a). Stiffness test setup. Figure-5(b). VCRS setup. According to equation (3) gas stiffness can be calculated as follows: K g = =.. = 11928 Nm -1 Table-2. Validation of FEM results for natural frequency with experimentation at operating frequency 50 Hz. Property Various specification conditions No.1 No. 2 No. 3 No. 4 No. 5 No.6 No.7 No. 8 Number of flexure spring 5 10 15 20 25 30 33 35 Total Spring Stiffness (Nm -1 ) 8380 16760 25140 33520 41900 50280 55308 58660 Natural frequency (Hz) from FEM 32.9 38.04 42.07 45.39 48.92 50.6 51.9 52.7 Freezer temperature ( )* 27 22 12 2-6 -13-10 -8 Pressure ratio 1 1.1 1.7 2.15 3.45 4 3.625 3.5 Refrigerant flow rate (LPH) 0 0.6 1.6 2.1 2.8 3.8 3.3 3 COP 0 0.3 0.95 1.63 2.23 2.84 2.56 2.39 *180 litre commercial refrigerator was used for testing performance of developed linear compressor According to equation (2), the resonant frequency can be calculated considering 30 flexure bearings as the follows, which is almost equal to the testing result, F n = π K = M F n =.8 Hz π +. 13812
Figure-6 shows the effect of natural frequency on performance of the linear compressor. From Figures 6 and 7 it is very much clear that the pressure ratio, refrigerant flow rate, COP and temperature drop in the freezer are increasing until natural frequency reaches to the operating frequency of the linear compressor and suddenly dropping down beyond the resonance condition. The lowest freezer temperature is achieved at the resonance condition as shown in Figure-7. efficiently at resonance condition i.e. highest pressure ratio, refrigerant flow rate, COP and temperature drop inside the freezer is achieved. ACKNOWLEDGEMENTS This work was supported by Department of Science and Technology, Govt. of India, New Delhi [SB/FTP/ETA-472/2012 (SERB)], and Sathyabama University, Chennai. REFERENCES [1] Chen N.; Tang Y.J.; Wu Y.N.; Chen X.; Xu L. 2007. Study on static and dynamic characteristics of moving magnet linear compressor, Cryogenics. 47: 457-467. [2] Eytan P, Werner S., Friedlaender F.J., Raymand C. 1978. Mathematical model of an electrodynamic oscillating refrigeration compressor. Purdue University, West Lafayette. pp. 246-259. Figure-6. Natural frequency Vs Pr, LPH, COP. [3] Hyun K.; Chul-gi R.; Jong-kwon K.; Jong-min S.; Yujin H.; Jae-keun L. 2009. An experimental and numerical study on dynamic characteristic of linear compressor in refrigeration system. International Journal of Refrigeration. 32: 1536-1543. [4] Ming X.; Xiaoping C. 2010. Analysis of resonant frequency of moving magnet linear compressor of stirling cryocooler. International Journal of Refrigeration. 33: 739-744. [5] Tae-Won C.; Jung-Ryol A.; Hong-Hee L.; Heung- Gun K.; Eui-Cheol N. 2008. A Novel Strategy of Efficiency Control for a Linear Compressor System Driven by a PWM Inverter. IEEE transaction on industrial electronics. Vol. 55. Figure-7. Natural frequency Vs Drop in freezer temperature. 5. CONCLUSIONS In this study, the performance characteristics of valved linear compressor at and off resonance conditions are investigated. Through Finite Element Method natural frequencies of linear compressor are obtained. Experimentation at different natural frequencies of linear compressor has been performed (natural frequency was varied by varying the mechanical stiffness) and their effects on pressure ratio, refrigerant flow rate, COP of system and temperature drop in freezer have been plotted. The results indicate that linear compressor operates more [6] Zhengyn L.; Jiabin W.; David H. 2007. A Resonant Frequency Tracking Technique for Linear Vapour Compressor. IEEE International Electric Machines and Drives Conference. pp. 370-375. [7] Hyuk Lee, Sang-sub Jeong, Chel-woong Lee, Hyeong-kook Lee. 2004. Linear Compressor for Air- Conditioner. L. G. Electronics. International Compressor Engineering Conference, Purdue University, C047, 1-7. [8] G.W. Rectenwald, J. Ramsey, S. Patankar. 1986. Predictions of Heat Transfer in Compressor Cylinders. International Compressor Engineering Conference, Purdue University. pp. 159-175. 13813
[9] Craig R. Bradshaw, Eckhard A. Groll, Suresh V. Gorimella. 2013. Linear compressors for electronics cooling: Energy Recovery and its benefits. International Journal of Refrigeration. 36: 2007-2013. [10] Craig R. Bradshaw, Eckhard A. Groll, Suresh V. Gorimella. 2013. Sensitivity analysis of a comprehensive model for a miniature-scale linear compressor for electronics cooling. International Journal of Refrigeration. 36: 1998-2006. [11] H.K. Lee, G.Y. Song, J. S. Park, E. P. Hong, W.H. Jung, (2000). Development of the Linear Compressor for a Household Refrigerator. International Compressor Engineering Conference, Purdue University. 1364: 31-38. [12] Jong Kwon Kim, Ji Hwan Jeong. 2013. Performance characteristics of a capacity-modulated linear compressor for home refrigerators. International Journal of Refrigeration. 36: 776-785. 13814