An Analysis Technique for Vibration Reduction of Motor Pump

An Analysis Technique for Vibration Reduction of Motor Pump Young Kuen Cho, Seong Guk Kim, Dae Won Lee, Paul Han and Han Sung Kim Abstract The purpose of this study was to examine the efficiency of the DoE and response surfaces with stiffness and damping coefficients in a 3D model of a motor pump and spring. In the present paper, experimental test for the moments of inertia of the 3D model and numerical test for the material properties were investigated by micro-indentation. The response surfaces could be generated by using 3D multi-body analysis and the DoE method. It showed that differences in contours of the response surfaces were clearly found for the particular area. Displacement of the center of the motor pump was the lowest at K 2000 N/M, C 12.5 N-sec/M. However, the frequency was the highest at K 2000 N/M, C 15 N-sec/M. This study suggested test techniques for vibration reduction for a motor pump in medical device. The combined method suggested in this study will greatly contribute to design of medical devices concerning vibration intervention. Keywords Motor pump, Spring, Vibration reduction, Medical devices, Moment of Inertia V I. INTRODUCTION IBRATION is one of the side effects characterized in a motor pump with springs. A number of problems of the vibration encountered in multi-body systems have been interested to engineers as well as designers. Suppression of unwanted vibrations is an important goal in many applications such as machines, buildings and bridges. The interest has increased recently due to the need for using motor pumps to drive large medical devices. In fact, the issue for vibration reduction is not only reducing amplitude, but also changing frequency. Moreover, a resonance is occurred when the frequency of vibration fits natural frequencies. This resonance ends when the frequency avoid from the natural frequency of the one of the system. The motor pump was constrained with springs in the medical device. It could relate to mechanical Young Kuen Cho is with the Department of Biomedical Engineering, Yonsei University, Wonju, Republic of Korea (e-mail: cyk012@gmail.com). Seong Guk Kim is with the Department of Biomedical Engineering, Yonsei University, Wonju, Republic of Korea (e-mail: giosk0418@gmail.com). Dae Won Lee is with the Department of Biomedical Engineering, Yonsei University, Wonju, Republic of Korea (e-mail: kagenui@naver.com). Paul Han is with the Department of Biomedical Engineering, Yonsei University, Wonju, Republic of Korea (e-mail:hanpaul04@gmail.com). Han Sung Kim is with Department of Biomedical Engineering, Yonsei University,Wonju, 220-710, Republic of Korea (corresponding author to provide phone: +82-33-760-2913; fax: +82-33-760-2913; e-mail: hanskim@ yonsei.ac.kr). responses such as vibration. Thus, the effects of vibration could be influenced directly to the characteristic of the components. The vibration generally occurred in 300 to 3600 rpm. In the start-up, generally, the frequency of the oscillating rpm matches one or many of the natural frequencies of the motor pumps. This drives high amplitude of vibration that can induce failure of the components and definitely reduces the life of the medical devices. The understanding of the phenomena is important to engineers for the purpose of vibration reduction. There are a lot of theories considering the unbalance/misalignment, vibration absorbers, and so on [3, 7, 11, 12]. Unbalance/misalignment is one of the main sources of vibration [1]. The unbalance/misalignment is a condition in which the centre of mass of a motor component is not matching with the centre of rotation. The vibration caused by the unbalance/misalignment may damage primary components of the medical device. In fact, motors cannot be completely balanced during manufacture because of non-homogeneous material properties, human errors during production [10]. Most vibration absorbers have been studied with various types of systems. Passive absorbers are the most broadly used classical vibration absorbers [4, 13]. A survey on vibration suppression theory for analysis and optimal tuning of these devices, and discuss various design configurations was given by Sun et al.[8]. They had also reviewed the developments in passive, adaptive, and active absorbers. Moreover, a numerical model of a passive absorber was investigated [6]. Detailed numerical studies on a beam-type absorber were investigated by Kawasoe et al [5]. They confirmed the effectiveness of a beam-type absorber by investigating it. In recent years, the adaptive absorbers have been proposed to suppress vibration with time-dependent frequency [9]. Vibration control with adaptive absorbers was accomplished by changing vibration absorbers dynamic properties, such as the stiffness or damping. Adaptive vibration absorbers have been proposed several types with methodology of variable stiffness. A lot of adaptive vibration absorbers with variable stiffness have been shown that these absorbers could effectively achieve vibration reduction of the important structure. A natural question is whether the performance of vibration reduction system can be enhanced by modifying the dynamic properties. Some research showed that an adaptive absorber could suppress vibration effectively. Therefore the adaptive absorber was needed to change the dynamic properties of the absorber in a wide frequency bend In the face of this evidence, a dependable and possible 33

method in practice for reducing this vibration is highly required. The main purpose of this study was to demonstrate the efficiency of the DoE and response surfaces with stiffness and damping coefficients in a 3-dimensional (3D) model of a medical device. Many kinds of optimization method are catching attention to use in recent medical industry. However, empirical study is expensive. To avoid the costs of research and development, we used design of experiments (DoE). This method is decisive to design, and effective design of medical devices from vibration reduction point of view may increase the life of medical devices. In this paper, the effects of stiffness and damping coefficient were analyzed as one of the useful factors in order to apply the model of vibration II. MATERIALS AND METHODS A. 3D Modeling of Motor Pump and Spring We consider a motor pump (Spatech Co., Korea) for vibration analysis (Fig. 1). The 3D model of motor pump and the spring was simplified and simulated by using multi-body dynamic analysis software, MSC.ADAMS (MSC.Software Co., USA; Fig. 2). Then a theoretical model is developed which accounts for stiffness and damping coefficient of the spring (Fig. 1). The appearance of motor pump had been scanned by a 3D laser digitizing scanner (DS-2016, Laser Design, USA; Fig. 1) Motor pump with spring Measurement Mechanical properties of spring (Stiffness and damping coefficient) Measurement Physical properties of motor pump (Mess, Moment of inertia) Fig. 2 Flow chart Design of experiment (DOE) Compute MSC.ADAMS Analysis Response Surface by Minitab B. Experiments and Calculation of Moments of Inertia (MoI) for the Motor Pump To measure the MoI (І), we measured first of torque (τ) and angular acceleration (α) (Fig. 3). (1) (2) Where, τ is the torque induced by a small weight, a is the acceleration, r is the radius of a driving plate. Then, the weight-force (WF) was same as tension (T) of the string which was fastened between the driving plate under the motor pump and weight. (3) (4) (5) Where, m is the mass, g is the gravity acceleration. Therefore, the weight-force could be substituted with Equation (6). (6) Z-axis X-axis Y-axis Fig. 3 An experiment of MoI for the motor pump Fig. 1 typical motor pump with spring, 3D model C. Experiments and Calculation for the Stiffness and Damping Coefficient of spring The experimental test for the spring was performed by axial-torsion fatigue testing system (8874 series, Instron, UK). Stiffness and damping coefficient of the spring was measured by experimental test with mathematical calculation (Fig. 4). To 34

rerun an experiment, each coefficient was measured and applied to 3-dimensional modeling. The material properties of the spring were obtained from tensile and compression tests to calculate the stiffness and damping coefficients. ω nd = K m C 2m 2 (7) Test Number Table. I Design of experiment by using Central Composite Design Stiffness coefficient (N/M) Damping coefficient (N-sec/M) K = F x (8) 1 1190.35 4.68 C = 2 mk (9) 2 1190.35 14.04 3 3571.05 4.68 4 3571.05 14.04 5 697.29 9.36 6 2380.70 2.74 7 2380.70 15.97 8 4064.11 9.36 Fig. 4 An experiment to measure stiffness coefficient and damping coefficients of vertical coefficients horizontal coefficients. D. Response Surface A total of 13 tests were designed and carried out in the central composite design (CCD) method (Table 1). The CCD, first described by Box and Wilson [2], is an experimental approach for seeking the optimal conditions for a multivariable system. Each experimental condition was applied to MSC.ADAMS. Then, a center-point displacement of motor pump, a reaction force of spring, and vibration frequency was analyzed by changing stiffness and damping coefficient. III. RESULTS A. Experiments and Calculation Results of Moments of Inertia (MoI) for the Motor Pump The experiment was repeated 5 times for each measurement to minimize experimenter error and to allow data to be averaged for each measurement. Three axes shown in Figure 3 consists of X-axis (a major axis of symmetry on the transverse plane), Y-axis (a minor axis of symmetry on the transverse plane), and Z-axis (a vertical axis of symmetry on the sagittal plane). The size of motor pump was 24 cm, 13 cm, and 18 cm on X, Y, and Z-axis, respectively. The weight of motor pump was 6.7 kg. The values of MoI were 0.0032 kg m2, 0.0046 kg m2, and 0.0090 kg m2 on X, Y, and Z-axis, respectively. The each character such as size, weight, and values of MoI were applied to the 3-dimensional multi-body analysis as the properties of motor pump. 9 2380.70 9.36 10 2380.70 9.36 11 2380.70 9.36 12 2380.70 9.36 13 2380.70 9.36 B. Experiments and Calculation Results for the Stiffness and Damping Coefficient of spring The experiment was repeated 10 times to minimize experimenter error and to allow data to be averaged. The values of stiffness and damping coefficient of spring were 2380.7 N/m, 9.36 N-sec/m, respectively. C. Response Surface Surfaces showed that stiffness and damping coefficients affected the motor pump on the center of mass, the reaction force, and response frequency. The result indicated that changes in stiffness coefficient affected displacement of the center of the motor pump more than damping coefficient (Fig. 6). The change of stiffness coefficient affected the center of mass in inversely proportion to its value. The decrease of stiffness coefficient caused increase of the center of mass, and the increase of stiffness coefficient caused decrease of the center of mass. However, the change of damping coefficient had been showed incidental influence to the center of mass. The change of stiffness coefficient affected the reaction 35

force in proportion to its value. Response surfaces showed that reaction forces of spring were a minimum value in specific area due to stiffness and damping coefficients (K 2000 N/M, C 12.5 N-sec/M). The decrease of damping coefficient caused increase of the reaction force. It seemed that the damping coefficient was proportional to the response frequency. The change of vibration frequency was a maximum value (K 2000 N/M, C 15 N-sec/M). The response frequency seemed to be notably change with the damping coefficient either enhancement or reduction. Fig. 6 Displacement of the center of the motor pump Reaction force of spring, (c) Vibration frequency due to stiffness and damping coefficients. IV. DISCUSSION AND CONCLUSIONS The effect of stiffness and damping coefficients on spring was examined with experimental test and numerical analysis as one of the useful factors in order to apply the system model of vibration. We analyzed a multi-body model of a motor pump and springs for preventing side effects, such as vibration, through an analysis of stiffness and damping coefficients. This study was a pilot study for analyzing vibration reduction of medical devices. A number of the vibration has been interested to engineers as well as designers. The interest had increased due to the need for using motors in medical devices to obtain large momentum. In generally, the frequency of motors in medical devices varies from 0 to 120 Hz. In the start-up, as usually, the frequency of motors in medical devices matches one or more of the natural frequencies of the medical devices themselves. It causes an amplitude of the vibration and can lead to a failure of components and lessen the life of the medical devices. Several methods in experimentally and numerically are known to reduce these vibrations. These methods are important to design, and to increasing the life of medical devices. Actually, frequency of vibration matches one of the component s natural frequencies lead to a high vibration amplitude. This condition discontinue when the excitation frequency pass-through from the natural frequency of the medical device. The DoE and RSM take simultaneously into account many variables and their interactions. The methods are also the most useful approach to obtain the optimized parameters when testing a minimum number of experiments. Therefore, it can be used in vibration reduction of a Motor Pump in Medical Device. The main purpose of this work is to demonstrate the efficiency of the DoE and response surfaces on medical devices. The response surfaces indicted that the stiffness and damping coefficients may be one of important parameters to affect medical devices on the response frequency, the reaction force, and the center of mass. The change of stiffness coefficient affected the center of mass in inversely proportion to its value. The reaction force can be decrease when the damping coefficient increased to the specific level. The response frequency seemed to be decreasing with the damping coefficient change either enhancement or reduction. The vibration frequency of center of mass in Fig. 6 might be decreased when stiffness coefficient is avoided the present value. However, the changes of these parameters were difficult to directly represent the reduction of vibration. Hard and stiff spring may deliver a vibration of motor pump corresponding to part of medical devices. There are also some other factors which may influence the vibration reduction effects. This is a method used to consider the frequency of the medical device by avoiding the resonant frequency. Resonance is generated when each frequency (motor pump, support axis of motor pump, pump fixed device and connection pipe using inhalation and exhaust) are equal. So, we will consider the resonance frequency. Suppression of unwanted vibrations is an important goal in many applications such as machines, buildings and bridges. Many medical devices are driven by motor pumps. Vibration of motor pump in medical devices causes noise problems. Noise problems of machines have recognized as environmental problem. Noise problems are one of the complaints because it causes displeasure, low work efficiency 36

and etc. Many medical devices have been developing for treatment and care of patients. Medical devices are more sensitive to noise and vibration because those intimately related with person. Therefore, noise and vibration of medical devices should be dealt with important issue. So, we will study blocking the path method which vibration is blocked and noise characteristics improvement method. Noise characteristics improvement method has a motor flow analysis. These methods may also reduce the level of vibration, notably in vibrating medical devices. If these factors could be applied to the medical devices that frequently occurs during treatment with the medical devices, the occurrence of vibration could be reduced. REFERENCES [1] Al-Hussain, K. and I. Redmond, Dynamic response of two rotors connected by rigid mechanical coupling with parallel misalignment., Journal of sound and vibration, Vol. 249, No. 3, 2002, pp. 483-498 [2] Box, G. E. P. and K. B. Wilson, "On the Experimental Attainment of Optimum Conditions.", Journal of the Royal Statistical Society. Series B (Methodological) Vol. 13, No. 1, 1951, pp.1-45., [3] DEWELL, D. L. and L. D. MITCHELL, "Detection of a misaligned disk coupling using spectrum analysis.", Journal of vibration, acoustics, stress, and reliability in design Vol. 106, No. 1. 1984, pp, 9-16. [4] Jordanov, I. N. and B. I. Cheshankov, "Optimal design of linear and non-linear dynamic vibration absorbers.", Journal of Sound and Vibration, Vol. 12, 1988, pp. 157-170. [5] Kawazoe, K., I. Kono, et al, "Beam-type dynamic vibration absorber comprised of free-free beam.", Journal of Engineering Mechanics, Vol. 124, 1998, pp. 476-479. [6] Ormandroyd, J. and J. P. D. Hartog, "The theory of dynamic vibration absorber.", Transaction of American Society of Mechanical Engineering, Vol. 50, 1928, pp. A9-A22. [7] Sekhar, A. and B. Prabhu, "Effects of coupling misalignment vibrations of rotating machinery.", Journal of sound and vibration, Vol. 185, No. 4, 1995, pp. 655-671 [8] Sun, J. Q., M. R. Jolly, et al, "Passive, adaptive and active tuned vibration absorbers-a survey.", Journal of Mechanical Design, Vol. 117, 1995, pp. 234-242 [9] Wickramasinghe, V., Y. Chen, et al., "Experimental evaluation of the smart spring impedance control approach for adaptive vibration suppression.", Journal of Intelligent Material Systems and Structures, Vol. 19, No. 2, 2008, pp. 171-179 [10] Wowk, V., "Machinery Vibration.", New York: McGraw-Hill, 1991 [11] Xu, M. and R. Marangoni, "Vibration analysis of a motor flexible coupling rotor system subject to misalignment and unbalance.1. theoretical-model and analysis., Journal of sound and vibration, Vol. 176, No. 5, 1994, pp. 663-679 [12] Xu, M. and R. Marangoni, "Vibration analysis of a motor flexible coupling rotor system subject to misalignment and unbalance 2. Experimental validation." Journal of sound and vibration, Vol. 176,No. 5, 1994, pp.681-691 [13] Xu, Y. L., K. C. S. Kwok, et al, "Control of wind-induced vibration by tuned mass dampers.", 1990 37