Vibration source identification method of equipment and its application

INTER-NOISE 06 Vibration source identification method of equipment and its application Xuhong MIAO ;KaifuYE ;XuerenWANG 3 ; Fuzhen PANG 4 Naval Academy of Armament, Harbin Engineering University, China Naval Academy of Armament, China 3 Naval Academy of Armament, China 4 Naval Academy of Armament, Harbin Engineering University, China ABSTRACT This paper develops a vibration source identification method of equipment and examines the underwater noise radiation characteristic of an underwater vehicle. Based on Korihoff theory, assuming that equipment equivalent exciting force and mass are independent with ment and isolators, equipment-isolator- models of considering unbalanced exciting force and moment exerting separately and commonly are established. Vibration source Identification method is thus proposed and experimentally validated. To meet the demands of engineering, this method is used to obtain exciting loads of an underwater vehicle. Keywords: Identification method; underwater noise radiation; unbalanced exciting force Classification of Subjects Number(s):. I-INCE. INTRODUCTION It is difficult to determine equipment exciting force, because the mechanical equipment is complex so much. Furthermore, equipment exciting force that will vary with the form and installation method is dependent upon the characteristic of excited structure. In the condition of different installation position and installation method, the exciting force from equipment to is needed by engineering, which is used to predict and control vibration and acoustic. Generally, before the equipment leave the factory, equipment manufacturers examine the exciting force from equipment to bench by equipment bench experiment. However, equipment bench experiment can t simulate the actual installation environment of equipment, which results in the exciting force from equipment to bench is not equal to that from equipment to. So, it is necessary to obtain the characteristic of equipment as vibration source (including equivalent exciting force and mass) by proposed method in this paper. After Breeuwer and Tukker () proposed the parameter free vibration velocity ofequipment, the immutability of the characteristic of equipment as vibration source (including equivalent exciting force and mass) was gradually recognized. The free vibration velocity of equipment was the vibration velocity of machine feet with the machine working, in the condition that the machine was hung up and didn t connect with the. The free vibration velocity theory assumed that the characteristic of equipment as vibration source would keep invariant with the changing of installation environment. Soon, the assumption was confirmed by experiment. And then, the calculation methods of equipment exciting force were gradually developed and completed, all of which were d on the theory of the free vibration velocity. Based on the theory of the free vibration velocity, Mondot () described source characteristic of equipment by introducing source descriptor concept intheyear of 987. Fulford (3, 4) and Gibbs (5, 6) extended structure-borne sound source descriptor concept to multi-point and multi-directional sources, which made the source characteristic of equipment profound understood by researchers. About measuring the free vibration velocity of equipment, Juha Plunt (7) pointed out that the condition of equipment being freely hung up could be approximated as the condition of equipment being installed on the soft spring. Liang (8) derived the estimate formula of vibration acoustic energy d on admittance and energy flow, miaoxhlz@sina.com 8554903@qq.com 3 wangxueren@aliyun.com 4 pangfuzhen@hrbeu.edu.cn 4446

INTER-NOISE 06 who built the transferring relationship of vibration acoustic energy under different amounting conditions by using vibration source descriptor concept. With the analyzing of physical experiment, Yan (9) proved the testing condition of the free vibration velocity of equipment. The testing condition was that the impedance mismatch of machine feet and isolator was more than ten times. Yuan (0) described source characteristic of equipment by free vibration velocity. After analyzing the system of equipment-isolator-, Yuan established the relationship of the exciting force impacted on and the free vibration velocity of equipment. So, the exciting force can be obtained by measuring the free vibration velocity of equipment. However, for the large equipment (such as host, diesel generator company unit, etc.), the testing condition of free vibration velocity of equipment was difficult to meeting. Furthermore, due to the impedance mismatch of the machine feet and isolator, the measured result of free vibration velocity of equipment would have error. Obviously, thetheory of free vibration velocity reflects the immutable characteristic of equipment as vibration source. However, if the testing condition of free vibration velocity couldn t be met, the exciting force from equipment to hull wouldn t be obtained. The theory of this paper is different with the theory of free vibration velocity. To taking the immutable characteristic of equipment as vibration source into account, this paper obtains the characteristic of equipment as vibration source by two vibration tests, which don t have to meet the hard testing condition of free vibration velocity. After obtaining the characteristic of equipment as vibration source, vibration acceleration of machine feet can be calculated. And then, which can be input as acoustic prediction of ship.. VIBRATION SOURCE IDENTIFICATION METHOD OF EQUIPMENT By two vibration tests and appropriate conversion, the characteristic of equipment as vibration source can be obtained d on Korihoff theory. In the condition of unbalanced exciting force and moment exerting separately and commonly, vibration source identification method is established respectively. Subsequently, its application scope is expounded.. Unbalanced Exciting Force Exerting Separately According to mechanic-electric analogous theory, equipment-isolator- models can be analyzed by admittance analogy circuit, which are shown in Fig.. The equipment that is shown in Figure.(a) is elastically installed in rigid through isolator. It as vibration source includes two unknown parameters which are equivalent exciting force F and mass m e. Based on Korihoff theory, theequation of vibration for equipment is F jmev cv () j Where is circle frequency of equipment exciting force. v is vibration velocity of machine feet. k and c are respectively stiffness and damping coefficient of isolator. Based on the immutable characteristic of equipment as vibration source, if the stiffness and damping coefficient of isolator are changed more than two times, the equivalent exciting force F and mass me are obtained by testing vibration velocity of machine feet. To put it simply, assuming that twice vibration velocity test are done on the same equipment with different isolator, stiffness and damping coefficient of isolator are respectively k, c and k, c in the twice test. And, vibration velocity of machine feet are respectively v, v.eq.() can be written as follow: F jmev cv j! () F jmev cv j Eq.() can be abbreviated as F D / D (3) where 0 m D / D (4) e 0 D 0 # jv # jv (5) 4447

INTER-NOISE 06 D cv # jv j cv # jv j F cv j D (7) F cv j Obviously,theequivalent exciting force F and mass me can be calculated by Eqs.(3)-(4). Of course, in order to eliminate accident errors in a single test, the vibration velocity of equipment should be tested repeatedly. Then, the equivalent exciting force and mass can be calculated by linear regression with the least squares. (6) equipment (a) Electromechanical analogy of equipment and ment system when equipment is installed in rigid equipment (b) Electromechanical analogy of equipment and ment system when equipment is installed in elastic Figure Electromechanical analogy of equipment and ment system The equipment that is shown in Figure.(b) is elastically installed in elastic through isolator. Based on Korihoff theory,theequation of vibration at point is given by ki ( v# v) F jmev ci( v# v) (8) j The equation of vibration at point is given by i( ) b( ) ci( v# v) k v # v jmbv cb( v# v) k v # v (9) j j Being Similar to situation of equipment elastic installed in rigid, stiffness ki and damping coefficient ci of isolator are known. The vibration velocity v, v of machine feet and are measured by test. the equivalent exciting force F and mass me are obtained by testing vibration velocity twice. To put it simply, assuming that twice vibration velocity test are done on the same equipment with different isolator, stiffness and damping coefficient of isolator are respectively k i, ci and k i, ci in the twice test. And, vibration velocity of machine feet are respectively v, v in the twice test. The vibration 4448

INTER-NOISE 06 velocity of are respectively v, v in the twice test. Eq.(8) can be written as follow: ki ( v# v) F jmev ci ( v # v) j! ki( v # v) F jmev ci ( v # v) j (0) Eq.(0) can be abbreviated as F D / D () 0 m D / D () e 0 where D 0 # jv # jv (3) ki ( v# v) ci ( v# v) # jv j D (4) ki( v # v) ci ( v # v) # jv j ki ( v# v) F ci ( v# v) j D (5) ki( v # v) F ci ( v # v) j Obviously, theequivalent exciting force F and mass me can be calculated by Eqs.()-(). Of course, in order to eliminate accident errors in a single test, the vibration velocity of equipment should be tested repeatedly. Then, the equivalent exciting force and mass can be calculated by linear regression with the least squares.. Unbalanced Exciting Force and Moment Exerting Commonly In the condition of unbalanced exciting force and moment exerting commonly, the parameter of equipment-isolator- models can be obtained by mechanic-electric analogous theory, which include unbalanced exciting force F, unbalanced exciting moment M, equivalent mass me and inertia moment J. If the equipment shown in Figure.(a) is installed in rigid, the models can be equivalent into the models in Figure.(b). Iftheequipment shown in Figure.(c) is installed in elastic, the models can be equivalent into the models in Figure.(d). In Figure., F L, F R, m e, m e, x L, xr are respectively equivalent exciting force, equivalent mass and vibration displacement of left and right part for equipment. According to mechanical knowledge, the above quantities satisfy the follow equations. Fb M FL # (6) a b a b m m F R Fa M a b a b mb J a b a ab e e (7) (8) ma J (9) a b b ab xl x# a (0) 4449

INTER-NOISE 06 xr x b () For the equivalent models shown in Figure.(b) and Figure.(d), the equivalent exciting force F L, FR and mass m e, me can be obtained by the vibration source identification method in the condition of unbalanced exciting force exerting separately, which has been introduced in the chapter of. in details. Then, unbalanced exciting force F, unbalanced exciting moment M,equivalent mass me and inertia moment J can be calculated by the Eqs.(6)-(). As above, in order to eliminate accident errors in a single test, the vibration velocity of equipment should be tested repeatedly. Then, the equivalent exciting force, mass and inertia moment can be calculated by linear regression with the least squares. equipment (a) The coupled model of equipment and (b) The simplified model of equipment and equipment (c) The coupled model of equipment and (d) The simplified model of equipment and Figure Coupled and simplified model of equipment and with exciting force and moment exerting commonly Based on the above analysis, whether the equipment is installed in elastic or rigid, the characteristic of equipment as vibration source always can be obtained by the vibration source identification method of equipment, which simplifies the estimating process about exciting force of equipment. And then, the calculated method about exciting force of ship can be built by the vibration source identification method of equipment..3 Rang of Application It is the foundation to the vibration source identification method that the characteristic of equipment as vibration source is immutable, which is that the equivalent exciting force and mass of equipment will keep invariant with the changing of installation environment. As is known to all, the theory that the characteristic of equipment as vibration source is immutable has been confirmed by experiment and researchers. Subsequently, thetheory (,, 3) of free vibration velocity and source descriptor are proposed and developed d on the theory that the characteristic of equipment as vibration source is immutable. So, the method proposed in this paper is right. Being different with the free vibration velocity, the vibration source identification method will not be restricted by the testing condition. Furthermore, the characteristic of equipment as vibration source can be obtained by equipment bench test before the equipment leave factory. Its test is great available. In a word, the vibration source identification method that is proposed in this paper has huger applicability more than previous methods. 4450

INTER-NOISE 06 In conclusion, no matter whether the equipment is elastically or rigidly installed, it is guaranteed that characteristic of equipment as vibration source is immutable, as long as the impedance of is low. Furthermore, the method proposed in this paper will be available and has high accuracy, aslong as the characteristic of equipment as vibration source is immutable. And the method never be restricted by the testing condition of free vibration velocity. Through the vibration source identification method, the flowchart of solving the characteristic of equipment as vibration source is seen in Figure.3. Figure 3 The process diagram of vibration source identification method 3. VALIDATION OF THE METHOD It is difficult that the equivalent exciting force and mass are directly measured by test. However, the vibration responses of model are easily measured. Thus, this paper verifies the validity of the method by measuring the feet vibration velocity of machine. 3. Test Model JZK-0 vibration exciter is used to simulate exciting force of equipment, which is seen in Figure.4(a). The maximum output of the vibration exciter is over 00N. Its effective working frequency domain is from 5Hz to 5000Hz. The vibration exciter is connected to the test model by bolt. The dimension of the test model is 500mm % 4mm % 4mm, which is shown in Figure.4(b). Threetypes of vibration isolators BE-5, BE-5 and BE-40 are seen in Figure.5(a), whose parameters list in the Table.. The weight of vibration exciter and test model is about 75kg. The test model is installed on the rigid impedance station by vibration isolators. The rigid impedance station whose weight is ton is rigid fastened to the ground, which is shown in Figure.5(b). Table Nominal parameters and performance indicators of each isolator Isolator type BE-5 BE-5 BE-40 Stiffness (N/m) 509 60090 4770 Natural frequency of rated load (Hz) 0± 0± 0± Damping ratio of rated load C/Cc 0.08±0.0 0.08±0.0 0.08±0.0 Ultimate load (MPa) 3.9 3.9 3.9 445

INTER-NOISE 06 (a). JZK-0 vibration exciter (b).test model Figure 4 Vibrator exciter and test model (a). vibration isolator (b). rigid impedance station Figure 5 Vibration isolator and rigid impedance station 3. Test Process Initially, the test model is installed on the rigid impedance station by vibration isolators BE-5 whose known stiffness and damping are k and c. The feet vibration acceleration of model are measured by the test. To take the relation formula v a of velocity and acceleration into account, the feet vibration velocity v of model can be calculated. Next, replacing the vibration isolators BE-5 by isolators BE-40 whose known stiffness and damping are k and c, the feet vibration velocity v of model can be obtained by the above way. Then, substitution of vibration velocity v and v into Eq.(), theequivalent exciting force F and mass me can be obtained. After that, replacing the vibration isolators BE-40 by isolators BE-5 whose known stiffness and damping are k3 and c 3, the feet vibration acceleration a3 Figure 6 The process diagram of test 445

INTER-NOISE 06 of model are measured by the test. Finally, according to the formula v a, substitution of the equivalent exciting force F and mass me into Eq.(), the feet vibration acceleration a& 3 of model are calculated. Adding 0kg to the origin model and repeating above test process, the measured and calculated results of feet vibration acceleration are respectively a3 and a& 3. The diagram of test process is seen in Figure.6. 3.3 Comparison of Results In the test of the origin model, the contrast curves of the test value a3 and calculated value a& 3 of the feet vibration acceleration are shown in Figure.7-Figure.8. Obviously, the test value a3 match almost perfectly with the calculated value a& 3.Inordertofurtherverify the method proposed by this paper, adding 0kg to the origin, the test are repeated. The contrast curves of the test value a3 and calculated value a& 3 of the feet vibration acceleration are shown in Figure.9-Figure.0. The test value a3 agree well with the calculated value a& 3. Under one-dimensional and two-dimensional analysis method of the vibration source identification method, the errors between the test and the calculated value are less than 3dB. Figure 7 The contrast curve by one-dimensional analysis method of the original test model (a). The transverse unbalance moment exerting (b). The longitudinal unbalance moment exerting separately separately Figure 8 The contrast curve by two-dimensional analysis method of the original test model Figure 9 Contrast curve by one-dimensional analysis method of original test model with adding 0kg 4453

INTER-NOISE 06 (a). The transverse unbalance moment exerting separately (b). The longitudinal unbalance moment exerting separately Figure 0 The contrast curve by two-dimensional analysis method of the original test model with adding 0kg 3.4 Error Analysis By comparison, obviously, the test values of the feet vibration acceleration agree well with the calculated values at most frequency domain. However, the errors exist in few frequency points. The errors result from the following reason. () The control panel of power amplifier is fuzzy, which results in the reading errors in some test. And then, the input voltage is not exactly equal to the voltage beforereplacing the vibration isolators. () The matrix of vibration source identification method may be singular, which magnifies the error. (3) Although, the tests are done in the rigid impedance station. Actually, theimpedance station has more or less elastic. Above of all have effects on the test values and result in errors. 4. CONCLUSIONS This paper does some work on proposing the vibration source identification method of equipment. It builds the coupled vibration models of equipment-isolator-. Based on Korihoff theory, assuming that equipment equivalent exciting force and mass are independent with ment and isolators, the equivalent exciting force and mass can be calculated by linear regression with the least squares. From the detailed study, the following observations can be made:. The test results indicate that the characteristic of equipment as vibration source is immutable, and the assumption is right. The characteristic of equipment as vibration source can be obtained by the vibration source identification method of equipment.. In the one-dimensional and two-dimensional conditions, the vibration source identification method has high accuracy. The vibration acceleration results of machine feet are calculated by the identification method match almost perfectly with the results from test. The errors are less than 3 db. 3. In the three-dimensional condition, the results from the identification method agree well with the results from test in most frequency points. However, in a few frequency points, the results from the identification method and test have obvious distinction, which results from test error, the in-homogeneity of isolator s parameters and the strangeness of the vibration equation. The errors are less than 6 db. ACKNOWLEDGEMENTS The paper is supported by National Natural Science Foundation China (No.50905), Heilongjiang Province Natural Science Foundation (QC0C03), Harbin Science and Technology Development Innovation Foundation of youth (0RFQXG0), Fundamental Research Funds for the Central Universities(HEUCF407), High Technology Ship Funds of Minersity of Industry and Information Techonology of P.R.China,Opening Funds of State Key Laboratory of Cean Engineering of Shanghai Jiaotong University(No.307), funded by China Postdoctoral Science Foundation (NO.04M5566). REFERENCES. Breeuwer R, Tukker J C. Resilient mounting systems in building. Applied Acoustics, 976, 9: 77~0.. Mondot J M, Petersson B. Characterization of structure-borne sound sources: The source descriptor and 4454

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