Prediction of the Excitation Force Based on the Dynamic Analysis for Flexible Model of a Powertrain

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1 Prediction of the Excitation Force Based on the Dynamic Analysis for Flexible Model of a Powertrain Y.S. Kim, S.J. Kim, M.G. Song and S.K. ee Inha University, Mechanical Engineering, 53 Yonghyun Dong, Inchon, eublic of Korea sangkwon@inha.ac.kr 3801

2 The owertrain is one of the imortant sources for the interior noise. In order to redict the interior noise due to a owertrain, the exerimental method has been used based on the TPA (transfer ath analysis). Although this exerimental method is a useful tool for the identification of the noise source and the transfer ath due to the owertrain, it is difficult to modify the structure of a owertrain by using the exerimental method for the reduction of vibration and noise. In order to solve this roblem, the aer resents the novel aroach for the rediction of interior noise caused by the vibration of the owertrain based on the hybrid TPA technology. Therefore, the vibration of the owertrain in a vehicle is numerically analyzed by using FEM (finite element method). The vibration of the other art in a vehicle is investigated by using the exerimental method based on VATF (vibro-acoustic transfer function) analysis. These two methods are combined for the rediction of interior noise caused by owertrain. This aer resent the rediction of the excitation force of the owertrain to the vehicle body based on numerical simulation. 1 Introduction In resonse to consumers demand for a comfortable vehicle, reducing noise and vibration of the vehicle is becoming more imortant task in automotive engineering. Therefore, CAE (comuter aided engineering) technology based on numerical simulation that make it ossible to reduce total time schedule for a vehicle develoment and to redict the NVH (noise, vibration and harshness) erformance has been widely alied to the NVH develoment of the vehicle [1-3]. The aim of this research is to develo a simulation method which can redict the interior noise caused by owertrain vibration. The owertrain vibration generates interior noise in two aths: air-borne and structure-borne. The former is an acoustic transfer ath of the owertrain noise radiation. The latter is a transfer ath of the owertrain vibration. The interior noise by structure-borne is a comlex roblem because this noise related to the car body and owertrain, mount brackets, etc. Therefore, it is difficult to accurately redict the interior noise by structure-borne ath based only on the numerical method [-6]. The traditional TPA (transfer ath analysis) has been used for the rediction of interior noise by the structure-borne ath based on exerimental method [5]. However, it is hard to modify the owertrain comonent for the reduction of interior noise using only exerimental method. ecently, in order to overcome this deadlock, the hybrid CAE method has been emloyed to the sub-frame design of the front susension of a assenger car [7]. In this aer, hybrid TPA is develoed which involves CAE technology and exerimental TPA in order to redict interior noise of the vehicle due to owertrain vibration. Using owertrain vibration analysis based on CAE technology, the excitation forces at owertrain mounting oints can be simulated. These excitation forces are the inut force of a car body. The car body is excited to vibrate and to radiate the interior noise by these forces. In order to reduce the interior noise, the forces can be changed by structural modification of the owertrain based on CAE technology. The traditional TPA redicts the interior noise by multilying the inut forces obtained from exeriment together the VATF (vibro-acoustic transfer function) of a test body vehicle. The VATF gives information about couling characteristics between the vibration of a car body and the cavity acoustics inside of a test vehicle. In this research, the hybrid TPA redicts interior noise by using simulated excitation forces instead of exerimental inut forces. This aer resents a systematic aroach about the of the excitation force at owertrain mounting oints. The CAE technology for the simulation is based on the FE (finite element) model and multibody dynamic analysis of the owertrain. Fig.1 shows a flow chart of the systematic aroach for rediction of excitation forces at owertrain mounting oints. Fig.1 Flow chart for rediction of excitation forces at owertrain mounting oints The baseline test for owertrain Two ways of tests are erformed to get the vibration characteristics of a test owertrain. One is the EMA (exerimental modal analysis) for the owertrain in order to identify the modal arameters which are used for the validation of the FE model. The other is the driving test when the test owertrain is loaded with a vehicle. These vibration test results are used to confirm the numerical simulation for owertrain vibration based on CAE technology. The test owertrain consists of an in-line cylinder diesel engine and 5-ste automatic transmission which engine dislacement is. liters. This owertrain is loaded on SUV (sort utility vehicle) and the engine seed is driven from 1000 rm to 000 rm during the driving test..1 Exerimental modal analysis EMA of the test owertrain is erformed with a rig system as shown in Fig.. The owertrain is excited by an electronic shaker with stiff stinger and its vibration is measured at 80 oints by accelerometers attached on the owertrain. The test is erformed at free-free condition. Also, the test is erformed with rig system for the sake of EMA for assembled owertrain which includes engine block, crankshaft, bed late, oil an, transmission, etc. In this case, the comonents are excited by an instrumented imact hammer and its accelerations are measured by accelerometers. The transfer function for all oints and 380

3 modal arameters like natural frequency, mode shae and daming are calculated through the tests. the simulation to redict excitation forces at four mounting oints. 3. Finite element model of owertrain The mesh roduction is erformed for finite element analysis using the geometry model of owertrain. The owertrain is comosed of iston, connecting rod, crankshaft, cylinder block, cylinder head, bed late, oil an, transmission case, transmission gear and mount brackets. Most of comonents are connected by BE (rigid body element ). The transmission gear is modelled as rigid body which has mass and inertia moment. And all bearing arts are connected with sring and daming model. Fig. shows the geometry model and the FE model of owertrain used for this research. Fig. Setu for exerimental modal analysis of owertrain comonents and its assembly. Vibration measurement of owertrain The measured excitation forces at owertrain mounting oints are required for validation of the redicted excitation forces by numerical simulation. However, it is difficult to measure the excitation forces at mounting oints directly. Instead, 3-axis accelerations are measured at four mounting oints (engine mount, front roll mount, rear roll mount and transmission mount) in this aer. Fig.3 shows accelerometers attached to each mount bracket of the owertrain to measure the acceleration. Fig.3 Setu of accelerometers at each mount bracket 3 Finite element method of owertrain 3.1 Geometry modeling of owertrain The FE model of owertrain is required for the analysis of vibration characteristics of the test owertrain based on numerical method. And the FE model should be validated by the measured results through EMA. The FE model also used to create a model for dynamic analysis which erforms Fig. Geometry and FE model of the test owertrain Finally, this FE model is confirmed with the results of EMA. The number of elements and element tye for of the FE models are listed in Table 1. Comonent No. of nodes No. of elements Element Tye Engine block Tetra, BE Bed late Tetra, BE Crankshaft Tetra, BE Oil an Hexa, BE Transmission Tetra, BE Assembled owertrain Tetra, Hexa, BE Table 1 Element secification of owertrain FE model Through the finite element analysis, modal arameter such as mode shae, natural frequency and modal vector are calculated. These results are comared with those of EMA to confirm the accuracy of FE model. MAC (modal assurance criterion) analysis is generally used for this validation [8]. MAC analysis is a method of evaluating the orthogonal roerty for natural vectors of the vibration system. If two natural vectors are the same direction vector, the MAC value becomes one. If two natural vectors have orthogonal roerty, the MAC value is zero. The mathematical exression is given by MAC i T { Φ } { Φ } TEST i FEM j, j = (1) T * T * [{ ΦTEST } { ΦTEST } }{ Φ FEM } { Φ FEM } j ] i j i where Φ is the natural vector for the natural mode shae at each natural frequency of the vibration system. The modal analysis results obtained by using FEM (finite element 3803

4 method) and EMA of the owertrain are listed in Table. According to these results the FE model of owertrain is sufficient for vibration system because the MAC values for each mode are over 0.7 and errors are under 10 %. Comonent Mode Shae EMA (Hz) FEA (Hz) MAC value Error (%) Engine block Bed late Crankshaft Oil an Transmission Assembled owertrain Table Comarison of natural frequency for owertrain comonents and its assembly Fig.5, Fig.6 shows the results for the modal analysis of all comonents and assembled owertrain obtained by using FEM and EMA. Fig.5 esults of modal analysis for owertrain comonents Fig.6 esults of modal analysis obtained by using EMA and FEM at 1 st, nd, 3 rd mode shae Due to these results, the FE model of owertrain is well justified for the numerical simulation of its noise and vibration analysis. Simulation of excitation force.1 Theory of engine vibration There are two major forces which excites the owertrain. One is the combustion force, which is caused by combustion ressure and it occurred by firing of air and fuel mixture gas. This combustion force ushes the iston down and is transferred to the crankshaft. And this force is also transferred to cylinder block via main bearing. The other is the inertia force, which deends on the unbalance of the recirocating mass such as iston or connecting rod. The combustion force is related to the cylinder ressure. By assuming that the work done by iston is equal to that by crankshaft, Eq.() is derived by dv = T dθ () and ds ds dt s T = A = A = A (3) dθ dt dθ Ω where S is the dislacement of iston movement S = (cosθ + cosφ) () The velocity of the iston is obtained by the derivative of the dislacement and is given by S = (sinθ + a sin θ + a sin θ + ) (5) Ω where a = a, a = a, and 380

5 a = (6) a = + + (7) 6 56 By inserting Eq.(6) and Eq.(7) into Eq.(5), Eq.(8) is obtained as follows: (sinθ + a sin θ + a sin θ + ) = sinθ From Eq.(3) and Eq.(5) the maximum torque takes lace at θ = 90 and (sinθ + a sin θ + a sin θ + ) = 1. The maximum toque is exressed by T = ( ) A where is cylinder ressure, A is the area of the to art of the iston, and is the rotation radius of the crankshaft. The combustion force is calculated by multilying the iston area by cylinder ressure. This force is transferred to the mount bracket of the owertrain through crank train system and cylinder block. The inertia force results from the unbalance of the moving arts of the engine. The major unbalanced inertia force of a single cylinder is given by Fa = M S = M Ω (cosθ + cos θ ) (10) By utting Z = M Ω, the inertia force is given by F a = Z(cosθ + cosθ ) (11) The first term in the Eq.(11) is the first order inertia force for the revolution of the crankshaft, and the second term is the second order inertia force. By considering the hase of each cylinder, the total unbalanced force for the in-line cylinder engine, is given by F a = Z + Z ( cosθ + cosθ + cosθ + cosθ ) ( 1 cosθ + cosθ + cosθ + cosθ ) (8) (9) (1) By inserting hase differences of each cylinder into Eq.(1), the inertia force is exressed by hase of the first cylinder. F a = Z cos θ (13) 1 In order to attenuate the unbalanced force, a balance shaft is alied. In general, two tyes of balance shafts adoted in the engine: MMC tye [9] and anchester tye [10]. The former reduces the unbalanced bounce force and moment; the latter controls only the bounce force [11]. The anchester tye is adoted in the test owertrain. Therefore, the moments due to unbalanced forces, which are rolling moment, itch moment and yawing moment, still exist in the test owertrain.. Prediction of excitation force In order to estimate the excitation force, the forced vibration analysis of FE model is required. The FE model of the owertrain created in the revious section is imorted to multi-body dynamic analysis software, MSC.ADAMS [1]. The comonents of FE model are connected with boundary conditions as shown in Fig.7. The vibrations and forces at four mounting oints are analyzed through dynamic simulation using MSC.ADAMS. Fig.7 Boundary conditions for the assembly of owertrain comonents The combustion forces are alied to the to area of the istons and the inertia forces are calculated in MSC.ADAMS automatically during the simulation. Fig.8 shows the excitation forces at 000rm by the numerical simulation. According to the results, the excitation force at each mount is eriodic and the dynamic force at the engine mount is higher than other mounts. Fig.8 Excitation forces simulated by CAE technology at four mounting oints 5 Validation of the dynamic model In order to rove validity of excitation force by dynamic analysis, an indirect method is alied because it is difficult to measure the excitation forces at the mounting oints directly. Therefore, it is required to comare the measured accelerations through a test with dislacements redicted by simulation. Fig.9 shows the dislacement and acceleration at the front roll mount bracket during simulation. 3805

6 results, it is carefully inferred that the simulated force based on the CAE technology can be also used for the rediction of the interior noise caused by structure-borne ath of the owertrain vibration based on the hybrid TPA with accuracy. Acknowledgments This work was suorted by Automobile Comonent Base Technology Project No in Korea. Fig.9 Dislacement and acceleration obtained by the numerical simulation at the front roll mount And Fig.10 shows the comarison between the simulated dislacement and the measured dislacement at 000rm in the frequency domain. The dotted line is the simulated dislacement and solid line is the measured dislacement. According to these results, the simulated dislacements are very close to the measured dislacements. Some differences are due to engine friction force and modeling error of bearings. It is difficult to estimate the dislacement exactly because the owertrain structure is comlex and there are lots of comonents as well as connections in owertrain. These errors are natural and many trials are required to match the simulated results to the measured results exactly. Fig.10 Comarison between the measured dislacement and the simulated dislacement at owertrain mounting oints: (a) E/G mount (b) F/ mount (c) / mount (d) T/M mount 6 Conclusion In this aer, the dislacements, accelerations and forces at owertrain mounting oints are simulated by CAE technology based on the FE model. The simulated excitation force will be used as the inut force of the vehicle body for rediction of interior noise caused by structure-borne ath by hybrid TPA. The FE model of owertrain comonents are validated exerimentally. The dynamic analysis is erformed to redict the vibration at the owertrain mounting oints using this FE model. The redicted dislacement is comared with measured dislacement at four mount oints of owertrain. The results are very close with a minor error. According to these eferences [1] S. Winterer and J. Bretl, Efficient design studies using eigensolution reanalysis, Society of Automotive Engineering, SAE (1993) [] H. S. Sung and D. J. Nefske, Assessment of a vehicle concet finite-element model for redicting structural vibration, Society of Automotive Engineering, SAE (001) [3] N. alor and H. H. Priebsch, The rediction of lowand mid-frequency internal road vehicle noise: a literature survey, Proceedings of the Institute of Mechanical Engineers Part D, Journal of Automobile Engineering, 1(3), 5-69 (007) [] Y. Seki, T. Suzuki, M. Tsukahara and Y. Takahashi, How to redict owertrain vibration at the engine mounting oints under running conditions, Society of Automotive Engineering, SAE (001) [5] H. V. Auweraer, et al., Transfer ath analysis in critical ath of vehicle refinement: the role of fast, hybrid and oerational ath analysis, Society of Automotive Engineering, SAE (007) [6] S. K. ee, Identification of a vibration transmission ath is a vehicle by measuring vibrational ower flow, Proceedings of the Institute of Mechanical Engineers Part D, Journal of Automobile Engineering, 18(), (00) [7] T. Sakai and A. Sakamoto, Imrovement of engine noise for the 003 Accord using hybrid CAE technology, Society of Automotive Engineering, SAE (003) [8] O. Walter and H. J. Kaiser, Finite Element Analysis of Dynamic Behavior of an Engine Block and Comarison with Exerimental Modal Test esults, Proceedings MSC World Users conference (1990) [9] St. Huegen, et al., A new.3 DOHC engine with balance shaft housing stes of refinement and otimization, Society of Automotive Engineering, SAE (1997) [10] H. Nakamura, A low vibration engine with unique counter-balance shafts, Society of Automotive Engineering, SAE (1976) [11] C. F. Taylor, The internal-combustion Engine in theory and ractice, nd edition, MIT ress (1985) [1] MSC.ADAMS, Basic Full Simulation Package Training Guide, MSC. Software (005) 3806