Dynamical Test and Modeling for Hydraulic Shock Absorber on Heavy Vehicle under Harmonic and Random Loadings

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1 Research Journal of Applied Sciences, Engineering and Technology 4(13): , 1 ISSN: Maxwell Scientific Organization, 1 Submitted: January, 1 Accepted: March, 1 Published: July 1, 1 Dynamical Test and Modeling for Hydraulic Shock Absorber on Heavy Vehicle under Harmonic and Random Loadings Shaohua Li, Yongjie Lu and Liyang Li Mechanical Engineering School, Shijiazhuang Tiedao University, Shijiazhuang 543, hina Abstract: The aim of this study is to found the suitable loading condition during damper dynamic test and develop a testing and analysis methodology for obtaining the dynamic properties of shock absorbers for use in vehicle dynamic simulation. Using harmonic and random loadings, the dynamical characteristics of a hydraulic shock absorber on heavy vehicle are measured and analyzed. Based on the test data, a piecewise nonlinear model for the shock absorber is proposed and the model parameters are identified under different loadings. By comparing the simulation results and field test data of the vehicle responses, the effect of loading type during the test of shock absorber on model accuracy is researched. Thus it is possible to choose a suitable loading mode to impel the piston of the shock absorber and build a reasonable absorber model used in vehicle dynamic simulation. Key words: Modeling, random loading, shock absorber, test, vehicle dynamics INTRODUTION Due to high-speed and heavy duty of road transportation, people put forward higher requirements on the handling and ride comfort performances of a vehicle. The hydraulic shock absorber for vehicle is one of major factors influencing the handling and ride comfort and shows apparent nonlinearity, asymmetry and hysteresis. Modeling dynamic properties of shock absorbers is very important to allow investigation of vehicle dynamics and control the vehicle vibration. In the last forty years, many dynamic models for shock absorber have been proposed, which can be divided into three types: The parametric model: This model is expressed by the fluid-structure interacted ordinary differential equations (ODE) or partial differential equations (PDE). The real working conditions of shock absorber include the flow of oil within the shock absorber, the deformation of elastic element in throttle and so on. Due to considering the above conditions, the parametric model is very accurate and thus has attracted many scholars attention (Adrian, ; Samantaray, 9; Titurus et al., 1; zop and Slawik, 11). However, the parametric model has too many parameters and the equations are very difficult to solve. Thus this type of model is often used in damper design and seldom used in vehicle dynamic simulation. The equivalent parametric model: This model simplifies the damper into a combination of spring, damping, clearance, friction and other mechanical property components. The representative equivalent parametric models include Bouc-Wen model, (Besinger et al., 1995) model, Bingham model and so on (Besinger et al., 1995; Dyke et al., 1996; Yang et al., 5; Zubieta et al., 9). Due to simple form and fewer parameters, these models have been widely used in vehicle dynamic research. However, parameters of the equivalent parametric model are sensitive to loading amplitude and frequency and thus the model is mainly applicable to a single frequency excitation. The fitted model: The model regards the restoring force as a function of the relative displacement and velocity, without taking shock absorber structure and working conditions into account. The restoring force and displacement of shock absorber are tested under different loads and the function is fitted by test data (afferty et al., 1995; Kowalski et al., ; Worden et al., 9). The fitted model is quite suitable to modeling the ascertained shock absorber, but needs a large amount of experimental work. Since the road surface roughness is random distributed, the automobile shock absorber practically always works under random excitations. However the current industry standard method of characterizing the dynamic properties of shock absorbers only involves orresponding Author: Shaohua Li, Mechanical Engineering School, Shijiazhuang Tiedao University, Shijiazhuang 543, hina, Tel.:

2 Res. J. Appl. Sci. Eng. Technol., 4(13): , 1 testing at harmonic excitations with discrete frequencies and amplitudes. The study on modeling the shock absorber under non-harmonic or random loadings is seldom found (afferty et al., 1995; Kowalski et al., ). In this study, the dynamic properties of a shock absorber on the front suspension of a heavy-duty truck are tested and analyzed under both sinusoidal and random loadings. A fitted piecewise non-linear model for this shock absorber is proposed and the parameters of this model are indentified using test data under different loadings. By comparing vehicle simulation results with the field test data, the effect of excitation condition in damper dynamic test on model accuracy is investigated. Thus it is possible to found the suitable loading conditions during dynamic test and modelling for a damper. TEST FAILITY AND PROEDURES The test object is a shock absorber on front suspension of the heavy-duty truck DFL15A9 manufactured by Dongfeng Motor orporation Ltd., hina. The shock absorber is fixed onthe dynamic material testing machine HT-911, as shown in Fig. 1. The restoring force and relative displacement of the shock absorber are measured by a load cell and a displacement transducer fixed at the end of the damper. The loading conditions on the test platform include sinusoidal and random displacement excitations. The frequency and amplitude of the sinusoidal excitation are Fig. 1: The test machine set at.5, 1., 1.5,.,.5 Hz and 5, 1, 15, mm respectively. An eight degree-of-freedom (8DOF) vehicle model with B-class random road surface roughness according to GB/T731-5/ISO868:1995 (SA, 5) is built and shown in Fig. the equations of motion for the vehicle system are: where, [ M]{ Z } [ ]{ Z } [ K]{ Z} [ K ]{ Q} [ ]{ Q } t t (1) {Q} = [q 1 q q 3 q 4 ] T ; {Z} = [Z c Z b Z t1 Z t Z t3 Z t4 ] T [M] = diag [m c m b I p I r m t1 m t m t3 m t4 ] kc kc lxkc lykc 4 ksi kc ks l ks l ks l ks l kclx ks df ks dr ks df ks dr kcly ks ks ks k s4 i1 ks11 l ks l ks31 l ks4 l kc1lx ks11 l df ksldr ks31 l df ks4 l dr kclxly ks11 l ks l ks31 l ks4 l K Symmetry ks1d f ksdr ks3d f ks4dr kcly ks1d f ksdr ks3d f ks4dr ks1 kt1 ks kt ks3 kt3 ks4 kt4 cc cc lxcc lycc 4 csi cc cs l cs l cs l cs l cclx cs df cs dr cs df cs dr cclxly cs cs cs c s4 i1 cs11 l cs l cs31 l cs4 l cclx cs11 ldf csldr cs31 l df cs4 l dr cclxly cs11 l cs l cs31 l cs4 l Symmetry cs1d f csd f cs3d f cs4d f ccd f cs1df csdr csdf cs4dr cs c 1 t1 cs ct cs3 ct3 cs4 ct4 kt1 k kt3 kt4 t Kt ; t T 194 ct1 c t ct3 ct4 T

3 Res. J. Appl. Sci. Eng. Technol., 4(13): , 1 z c z y m c k c c c d r φ z b θ l x ly d f x d r l m b l 1 d f k s1 c s1 z t1 m t1 k s4 k t c t k s3 c s3 c s4 zt4 k t1 c t1 z t3 q q 1 m t4 m t3 k t4 c t4 k t3 c t3 q 4 q 3 Fig. : 8DOF whole-body vehicle model t/s 4 6 f/hz Fig. 3: The random loading condition 8 1 where Z c is the cab s vertical displacement. Z b, are vehicle body s vertical, pitching and rolling displacements. Z t1 Z t Z t3 Z t4 are wheel vertical displacements. m c m b are mass of cab and vehicle body. I p, I r are the moment of inertia of vehicle body in pitching and rolling directions respectively. m t1, m t m t3 m t4 are wheel masses. q 1 q q 3 q 4 are road surface roughness. d f, d r are half of front and rear wheeltrack. l 1, l 1, l x are the longitudinal distance from the front wheel, rear wheel and cab mass center to the vehicle mass center. l y are the lateral distance from the cab mass center to the vehicle mass center. K si, K ti si, ti (I = 1~4) are stiffness and damping coefficients of suspension and tire. The parameters of the vehicle system are chosen as follows: m c = kg, m b = 11485kg, I p = 1114 kg.m I r =.6 5 kg.m, m t1 = m t3 = 41 kg, m t = m t4 = 135 kg, K c = 746 N/m, K S1 = K S3 = 518 N/m, K S = K S4 = N/m, K t1 = K t3 = 11 3 N/m K t = K t4 = N/m, c = 74 N., S1 = S3 = 4 N., S = S4 = N., t1 = t3 = 35 N., t = t4 = 63 N., d f =.993 m, l x =.8 m, l y =.1 m, d r =.93 m, l 1 = 3.64 m, l =.71 m The relative displacement between vehicle body and wheel is used as the random excitation of the test platform and computed by Eq. (1). The time-domain curves and amplitude spectrum of the random loading are shown in Fig. 3. Natural frequencies of the vehicle are also computed by vibration theory, which are.8897, , 1.977,.5316, , 9.6, and Hz, which corresponds to the chair vertical motion, the vertical, pitching, and roll motion of vehicle body and the vertical motion of four wheels respectively. It can be seen from Fig. 3 that the frequency components of the platform random loading mainly concentrate on the first four natural frequencies of the vehicle. According to sampling theory, the sampling frequency of this test is set 56 Hz. DYNAMI HARATERISTIS ANALYSIS A traditional approach to characterization of the nonlinearities present in the shock absorber is accomplished by obtaining a force-velocity characteristic diagram. Thus the force-displacement-velocity and 195

4 Res. J. Appl. Sci. Eng. Technol., 4(13): , Hz 1Hz 1.5Hz Hz.5Hz force-velocity trajectories with sinusoidal loading at five frequencies and four amplitudes are obtained as shown in Fig. 4 and 5. In Fig. 4 and 5, the absorber shows nonlinearity, asymmetry and hysterisity. It can be seen from Fig. 4 that: Hz 1Hz 1.5Hz Hz.5Hz v/m/s (a) The force-displacement-velocity trajectories v/m/s (b) The force-velocity trajectories Fig. 4: Dynamic characteristics for sinusoidal test at different frequencies (A = 1 mm) mm 1mm 15mm mm 5mm 1mm 15mm mm. -. v/ m /s (a) The force-displacement-velocity trajectories v/m/s (b) The force-velocity trajectories Fig. 5: Dynamic characteristics for sinusoidal test at different amplitudes (f = 1Hz).. The dynamic characteristic trajectories of shock absorber for different excitation frequencies differ considerably from each other. At equilibrium position the difference between the trajectories is the greatest; while at limit position the difference between the trajectories is the smallest. With the increase of excitation frequency, both the damping force and the area surrounded by trajectories increase. The rise of area means that the energy consumed by the shock absorber increases. In addition, the hysteretic behavior in force-velocity trajectories become more distinct as the excitation frequency increased. At low excitation frequencies (f =.5, 1 Hz), the friction damping characteristics of the shock absorber are evident. When the excitation frequency is higher (f = 1.5,,.5 Hz), the friction damping characteristics disappeared and the saturated phenomenon occurs. It can be seen from Fig. 5 that, the characteristic trajectories of shock absorber in different amplitudes are basically parallel to each other and increase in amplitude leads to the growth of the damping force and the energy consumption. In addition, the saturated phenomenon occurs in higher amplitude. When the velocity is greater than.1 m/s, the damping force increased slowly. Hence, the shock absorber characteristics depend on both frequency and amplitude of the excitation. The effect of excitation frequency on shock absorber characteristics is bigger than that of excitation amplitude. The absorber characteristic trajectories under random excitation and sinusoidal excitation (A = 5 mm and f = 1 Hz) are shown in Fig. 6. The nonlinearity, asymmetry and hysteresis are still present under random excitation. However, the damping force distributes more widely and the energy consumption is bigger under random excitation. A piecewise non-linear model: It is easy found from the absorber characteristic trajectories that the damping force predominantly depends on the position and velocity of the piston. At the same displacement, two damping forces may exist since the relative velocity between the piston and cylinder can be positive or negative. onsequently, the absorber shows hysteretic properties. As shown in Fig. 7, the absorber characteristic curve may be divided into four parts including AB, B, D and DA, which correspond to four cases respectively. 196

5 Res. J. Appl. Sci. Eng. Technol., 4(13): , 1 Table 1: The identified parameters Parameters Loadings Groups Sinusoidal loading (1) v>, s< (A = 1mm, f = 1.5Hz) () v>, s> E (3) v<, s> E (4) v<, s< 1.8E Random loading (1) v>, s< () v>, s> (3) v<, s> (4) v<, s< B 1 D -1 A v/ m/s 4 B (a) The force-displacement-velocity trajectories A D Fig. 7: Absorber characteristic curve segments Based on the above analysis and Wallaschek model (Wallaschek, 199), a new exponential piecewise nonlinear model for the damper is proposed F v v Sgn() v Sgn() v () (b) The force-velocity trajectories Fig. 6: omparison of absorber characteristics under random and sinusoidal loading (A = 5 mm, f = 1Hz) v>, s< v>, s> v<, s> v<, s< A-B--D-A stands for a period of piston moving from equilibrium position, through negative limit position, equilibrium position and positive limit position, back to equilibrium position. Accordingly, the test data can be divided into four groups. According to every group of data, the parameters are identified, respectively. where the first term is the viscous damping force, the second term denotes the hysteresis, and the third term is friction damping force. The four parameters in this model are identified using the nonlinear least square method and listed in Table 1. Figure 8 and 9 are the fitting results of test data under sinusoidal loading (A = 1 mm and f = 1.5 Hz) and random loading. It may be found that the fitting curve computed by Eq. () is very close to the test result. Vehicle dynamic simulation and field test: When the vehicle runs on road, the shock absorber is acted on by random loads with many frequencies composed of the vehicle natural frequencies and frequencies of road surface roughness. It is an urgent question waiting to be solved that which loading condition should be used in absorber dynamic properties test and modeling with the aim of vehicle dynamics simulation. 197

6 Res. J. Appl. Sci. Eng. Technol., 4(13): , test compute 4 3 test compute v/ m/s Fig. 8: Fitting results under sinusoidal loading (A = 1 mm, f = 1.5Hz) test 5 compute v/m/s v/ m/ s 1 5 test 1 5 compute -5 5 x x 1-3 Fig. 9: Fitting results under random loading (a) The vehicle in the field test (b) Acceleration transducer on cab seat (c) Acceleration transducer on vehicle body Fig. 1: The field test The vertical accelerations at cab seat and vehicle body of DFL15A9 truck are measured in the field test, as shown in Fig. 1. Using absorber models expressed by Eq. () with parameters identified by test data under different loading conditions, dynamic responses of the 8DOF vehicle are simulated by numerical integral. The simulating accelerations and test results are compared in Fig. 11. The loading conditions includes: Random loading f =.5, 1, 1.5,,.5 Hz with A = 1 mm f = 5, 1, 15, mm with f =1 Hz It is found from Fig. 11 that: The test data of seat acceleration is the closest to the simulation result by the absorber model under 198

7 Res. J. Appl. Sci. Eng. Technol., 4(13): , 1 a (m/s-) a (m/s-) a (m/s-) Test Random.5 Hz 1. Hz (a) RMS of the seat acceleration a (m/s-) 1.5 Hz. Hz.5 Hz V/Km/h Test Random.5 Hz 1. Hz 1.5 Hz. Hz.5 Hz V/Km/h (b) RMS of the body acceleration Test Random 5 mm 1 mm 15 mm mm (c) RMS of the seat acceleration V/Km/h Test Random 5 mm 1 mm 15 mm mm V/Km/h (d) RMS of the body acceleration Fig. 11: omparison of simulation results and test results sinusoidal loading with 1 Hz. The absorber model under random loading condition goes after that. The absorber model under sinusoidal loading condition with.5 Hz leads to the maximum error between simulation result and test data. The reason for this conclusion is that the natural frequency of seat is.8897 Hz which is near to 1 Hz and in random load signal the natural frequency of seat share the largest energy. Thus, the sinusoidal loading with the frequency near to the natural frequency of seat and the random loading are the most suitable to simulate the seat responses. The effect of absorber model parameters on vehicle body acceleration simulation is much smaller than that on seat acceleration simulation. The discrepancy between simulations results and the test data may be caused by the error in measurement and the factors not included in the 8DOF model such as engine vibrations, chassis modes and so on. Nevertheless, it is suggested that the sinusoidal loading with the frequency near to the lowest natural frequency of vehicle and the random loading are the most suitable loading condition in damper dynamic properties test and modeling. In addition, the modeling method of shock absorber proposed by this work may be used to dynamic simulation of vehicles. ONLUSION By testing the shock absorber under sinusoidal and random loading, a non-parametric model for shock absorber is proposed and identified using test data. By comparing simulation results and field test data, this work tries to found the most suitable loading condition in absorber dynamic properties test and modeling. It is concluded that The tested shock absorber shows nonlinearity, asymmetry and hysteresis. Since the damping force depends on the position and velocity of piston, the test data should be divided into four groups. Using each group of measured data, the parameters of absorber model are identified respectively. Different group of parameters should be used to compute vehicle responses according to the position and velocity of piston. In absorber modeling, the loading frequency plays a more important role than the loading amplitude. The sinusoidal loading with the frequency near to the lowest natural frequency of vehicle and the random loading may be the suitable loading condition in damper dynamic properties test and modeling. AKNOWLEDGMENT The National Natural Science Foundation of hina under Grant No.1936, and Key Project of hinese Ministry of Education under Grant No.13 support this study. 199

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