Dynamical Test and Modeling for Hydraulic Shock ... - CiteSeerX

Research Journal of Applied Sciences, Engineering and Technology 4(13): 1903-1910, 2012 ISSN: 2040-7467 © Maxwell Scientific Organization, 2012 Submitted: January 02, 2012 Accepted: March 02, 2012 Published: July 01, 2012

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 050043, China 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 C

INTRODUCTION 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:

C C

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, 2002; Samantaray, 2009; Titurus et al., 2010; Czop and Slawik, 2011). 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., 2005; Zubieta et al., 2009). 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 (Cafferty et al., 1995; Kowalski et al., 2002; Worden et al., 2009). 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

Corresponding Author: Shaohua Li, Mechanical Engineering School, Shijiazhuang Tiedao University, Shijiazhuang 050043, China, Tel.: 0086-311-87935554

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Res. J. Appl. Sci. Eng. Technol., 4(13): 1903-1910, 2012 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 (Cafferty et al., 1995; Kowalski et al., 2002). 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 FACILITY AND PROCEDURES The test object is a shock absorber on front suspension of the heavy-duty truck DFL1250A9 manufactured by Dongfeng Motor Corporation Ltd., China. 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  kc       K         

 cc       C        

Fig. 1: The test machine

set at 0.5, 1.0, 1.5, 2.0, 2.5 Hz and 5, 10, 15, 20 mm respectively. An eight degree-of-freedom (8DOF) vehicle model with B-class random road surface roughness according to GB/T7031-2005/ISO8608:1995 (SAC, 2005) is built and shown in Fig. 2 the equations of motion for the vehicle system are: [ M ]{Z}  [C]{Z }  [ K ]{Z}  [ Kt ]{Q}  [Ct ]{Q } (1)

where, {Q} = [q1 q2 q3 q4]T ; {Z} = [Zc Zb 2 Zt1 Zt2 Zt3 Zt4]T [M] = diag [mc mb Ip Ir mt1 mt2 mt3 mt4]

 kc

l x kc

 l y kc

0

0

0

 ksi  kc

k s1l1  k s2l2  k s3l1  k s4l2  kclx

k s1d f  k s2dr  k s3d f  k s4 dr  kcl y

 k s1

 k s2

 k s3

k s1l12  k s2l22  k s3l12  k s4l22  kc1lx2

 k s1l1d f  k s2l2 dr  k s3l1d f  k s4l2dr  kclx l y

 k s1l1

k s2l2

k s3l1

Symmetry

k s1d 2f  ks2dr2  ks3d 2f  k s4 dr2  kcly2

 ks1d f k s1  kt 1

 ks2 dr 0 k s 2  kt 2

ks3d f 0 0 k s3  k t 3

i 1

 cc

lx cc

 l y cc

0

0

0

 csi  cc

 cs1l1  cs2l2  cs3l1  cs3l1  cclx

cs1d f  cs2dr  cs3d f  cs4dr  cclx l y

 cs1

 cs2

 cs3

cs1l12  cs2l22  cs3l12  cs4l22  cclx2

 cs1l1d f  cs2l2dr  cs3l1d f  cs4l2dr  cclx l y

 cs1l1

 cs2l2

cs3l1

Symmetry

cs1d 2f  cs2d 2f  cs3d 2f  cs4d 2f  ccd 2f

 cs1d f

 cs2dr

cs2d f

cs1  ct 1

0 cs2  ct 2

0 0

4

i 1

cs3  ct 3 T

0 0  Kt   0  0

0 0 0 0

0 0 0 0

0 k t1 0 0 0 0 0 0

0 kt2 0 0

0 0 kt3 0

0  0  0   kt4 

;

0 0 Ct   0  0

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0 0 0 0

0 0 0 0

0 ct 1 0 0 0 ct 2 0 0 0 0 0 0

0 0 ct 3 0

0 0  0  ct 4 

T

   ks4    k s4l2   k s 4 dr   0  0   0  k s4  kt 4  0

4

    cs4    cs4l2   cs4dr  0   0   0  cs4  ct 4  0

Res. J. Appl. Sci. Eng. Technol., 4(13): 1903-1910, 2012

zc mc

y

z

kc zb

dr

θ

lx

φ mb

dr

cc df

ly

x

df

l2

l1

cs1

ks1

zt1 m t1

kt2 c s4

ks4

c t2

zt4

cs3

ks3

q2

ct1

k t1 z t3 q1

m t3

m t4 kt4

c t3

kt3

c t4

q3

q4

Fig. 2: 8DOF whole-body vehicle model

mass center. Ksi, Kti Csi, Cti (I = 1~4) are stiffness and damping coefficients of suspension and tire. The parameters of the vehicle system are chosen as follows: mc = 557.5 kg, mb = 11485kg, Ip = 111004 kg.m2 Ir = 0.6 05 kg.m2, mt1 = mt3 = 412 kg, mt2 = mt4 = 1352 kg, Kc = 72460 N/m, KS1 = KS3 = 251280 N/m, KS2 = KS4 = 1195 03 N/m, Kt1 = Kt3 = 1100 03 N/m Kt2 = Kt4 = 3000×103 N/m, Cc = 7240 N.s/m, CS1 = CS3 = 400 N.s/m, CS2 = CS4 = 200 N.s/m, Ct1 = Ct3 = 3500 N.s/m, Ct2 = Ct4 = 6300 N.s/m, df = 0.993 m, lx = 2.8 m, ly = 0.1 m, dr = 0.93 m, l1 = 3.64 m, l2 = 2.71 m

10

5

0

-5

5

0

10 t/s

15

20

2

1

0 0

2

4

6

8

10

f/Hz

Fig. 3: The random loading condition

where Zc is the cab’s vertical displacement. Zb 2,  are vehicle body’s vertical, pitching and rolling displacements. Zt1 Zt2 Zt3 Zt4 are wheel vertical displacements. mc mb are mass of cab and vehicle body. Ip, Ir are the moment of inertia of vehicle body in pitching and rolling directions respectively. mt1, mt2 mt3 mt4 are wheel masses. q1 q2 q3 q4 are road surface roughness. df , dr are half of front and rear wheeltrack. l1, l1, lx are the longitudinal distance from the front wheel, rear wheel and cab mass center to the vehicle mass center. ly are the lateral distance from the cab mass center to the vehicle

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 0.8897, 1.3373, 1.9770, 2.5316, 8.8794, 9.0262, 9.1423 and 9.1170 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 256 Hz. DYNAMIC CHARACTERISTICS 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

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Res. J. Appl. Sci. Eng. Technol., 4(13): 1903-1910, 2012 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:

6000 0.5Hz 1Hz

F/N

4000

1.5Hz 2Hz 2.5Hz

2000 0 -2000 -0.02

C -0.01

0

0.01

0.2

0

-0.2

v/m/s

s/m

(a) The force-displacement-velocity trajectories

C

5000 0.5Hz 1Hz

4000

1.5Hz 2Hz 2.5Hz

F/N

3000 2000

C

1000 0 -0.2

-0.1

0 v/m/s

0.1

(b) The force-velocity trajectories Fig. 4: Dynamic characteristics for sinusoidal test at different frequencies (A = 10 mm) 6000 5mm 10mm 15mm 20mm

F/N

4000 2000 0 -2000 -0.04

-0.02

0

0.2

0 0.02

-0.2

s/m

v/m/s

(a) The force-displacement-velocity trajectories 4000

5mm 10mm 15mm 20mm

F/N

3000

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 = 0.5, 1 Hz), the friction damping characteristics of the shock absorber are evident. When the excitation frequency is higher (f = 1.5, 2, 2.5 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 0.1 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.

2000 1000 0 -1000 -0.1

-0.05

0 v/m/s

0.05

0.1

(b) The force-velocity trajectories Fig. 5: Dynamic characteristics for sinusoidal test at different amplitudes (f = 1Hz)

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. Consequently, the absorber shows hysteretic properties. As shown in Fig. 7, the absorber characteristic curve may be divided into four parts including AB, BC, CD and DA, which correspond to four cases respectively.

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Res. J. Appl. Sci. Eng. Technol., 4(13): 1903-1910, 2012 Table 1: The identified parameters

Loadings Sinusoidal loading (A = 10mm, f = 1.5Hz)

Random loading

Groups (1) v>0, s0, s>0 (3) v0 (4) v0 (3) v0 (4) v0 v0 v