A validation study of ACS-SSI for online condition monitoring of vehicle suspension systems

2.1. Experiment Set-up

Four springs were employed to represent the suspension system in the vehicle and a steel plate was adopted to stand for the vehicle body. The steel plate was hanged up by four springs, shown as Fig. 2. Fig. 2(c) shows the dimensions of the plate. In this experiment, four acceleration sensors were installed on the four corners of the plate referring to the measure method in reference [1, 13]. The sensors were connected with a four channel data acquisition device and then connected with a laptop to collect the vibration signals. The sensors are piezoelectric accelerometers and model is CA-YD-185, shown as Fig. 3(a). This type of sensors used widely in condition monitoring based vibration measurement because it has small mass and wide useful measurement frequency band, from 0.5 Hz to 5000 Hz. The 4-channel data acquisition device used in this experiment has independent A/D (analogue/digital) converter in each channel and with sampling frequency from 0 Hz to 96 kHz, shown as Fig. 3(b).

Fig. 2Test Set-up

a) Photos of Test Set-up

b) Schematic of Test Set-up

c) Dimension of Test Set-up

Fig. 3Acceleration sensors and data acquisition

a) Acceleration sensors

b) Data acquisition

2.2. 3-DOF model

The simplified suspension system only considers three degree of freedoms when developing the mathematical model, including the bounce, pitch and roll, shown as Fig. 2(b). The dynamic equation was developed basing on the Newton second law, shown as Eqs. (3)-(5). In the dynamic equations, $k_i$ ($i=$ 1, 2, 3, 4) stand for the stiffness of the four springs. They have the same value in this system so they will be written in a same form as $k$ in the stiffness matrix ($k_1=k_2=k_3=k_4=k$). Additionally, $z$, $\theta$, $\varphi$ were employed to stand for the movement of bounce, pitch and roll, respectively and $z_i$ ($i=$ 1, 2, 3, 4) were used to stand for the vertical displacement of the four springs. The pitch and roll are small movement so $z_i$ ($i=$ 1, 2, 3, 4) have the relationship with bounce movement $z$ shown as Eq. (1) and Eq. (2). $a$ and $b$ are the distance between the springs. Eq. (1)-(2) has been submitted into Eqs. (3)-(5):

The dynamic equations can be written in matrix format to develop the state space matrix and then calculate the modal parameters of this system. Basing on the dynamic equations, the mass matrix and stiffness matrix can be written as follows:

The state matrix can be written as:

The theoretical resonance frequencies of this system can be obtained through the eigenvalue (${\lambda }_i$) calculation and the mode shapes were the correspond eigenvector (${\nu }_i$), shown as Eq. (8). The mass of the steel plate including the four sensors was measured through a balance. The measurement result is $m=$1.7138 kg. The stiffness of four springs were measured via Hooke’s law and the average result is $k=$159.5 N/m.

The natural frequency of the first three orders of this system can be obtained via submitting the measured parameters. The results of bounce, pitch and roll are 3.05 Hz, 3.94 Hz and 4.47 Hz, respectively. This is the calculation result for an ideal 3-DOF simplified suspension system without damping effect. However, the test rig developed for the 3-DOF simplified suspension experiment was not ideal as the mathematical model. The same problem that theory mathematical model was not fully represent the real vehicle suspension was exist in the suspension study. For this reason, different configurations of the springs in the simplified suspension system will be discussed in the next section and compared with the theory calculation result:

3.1. Placement of sensors

The sensor placement under on road test conditions have some constraints. One of the case which may have important influences on the identification result is the center of gravity and sensors are not in the same plane. This section will investigate two different cases of the springs connecting with the steel plate in different configurations to study the influences of sensor not in the same plane with the center gravity. The first case is the springs connected with the steel plate directly via the bolt, shown as Fig. 4(a). In this case, the sensor and the gravity center are almost in the same plane. The second case is the springs connected the steel plate through a long bolt (Fig. 4(b)) that the spring has a distance from the steel plate. In the second case, the force of the spring is not directly loading on the steel plate. The force analysis schematic is shown as Fig. 4(c). $F_k$ is the force produced by spring and $F_l$ is one of the resolution of $F_k$ which is vertical to the steel plate; $F_d$ is another resolution of $F_k$ which is parallel with the steel plate. $F_d$ is the main factor of roll movement. However, $F_k$ equal with $F_l$ and $F_d$ equal zero when the spring directly load on the steel plate. Therefore, the second connecting method should have a big effect on the modal parameter of roll modes. The experiment results of the two configurations would be given in the follows.

The modal parameters, modal shapes and natural frequencies, of the two experiments are given in Fig. 5. Comparing the theory calculation result with direct connection, the ACS-SSI identification errors of bounce, pitch and roll frequencies are 12.5 %, 5.3 % and 6.1 %, respectively. A considerable reason for this error is the theoretical calculation of the natural frequency does not consider the damping effects. In other words, the direct connection methods indicate that the ACS-SSI is an effective method to identify the system modal parameters.

Moreover, it can be seen from Fig. 5 that the connection method has little effect on the bounce and pitch frequency. The errors of the two different connection methods of bounce and pitch resonance frequencies are 0.8 % and 1.0 %, respectively. However, the error of the roll natural frequency in the two experiment cases is 45.3 %. The result has a good agreement with the expectation which means the online monitoring of vehicle suspension should consider the placement of sensors.

Fig. 4Different connection methods

a) Directly connect

b) Connect through long bolt

c) Force analysis of the long bolt connection

Fig. 5Modal parameters of different spring configuration

a) Directly connection

b) Long bolt connection

3.2. Different excitation amplitudes

The vehicle may be driven on different road conditions. In order to study the effectiveness of ACS-SSI when vehicle under different road conditions, the set-up (directly connection) was excited by random excitation with different amplitudes. The excitation was also provided via a hammer with rubber head. The amplitudes of the excitations were classified into three grades, including strong excitation, medium excitation and light excitation. Fig. 6 presents the RMS values of each test. From the RMS values we can see that the amplitudes are different of the three tests and the inputs are non-stationary because the RMS values are nonzero.

Fig. 6RMS of different amplitudes signal

a) Strong excitation

b) Medium excitation

c) Light excitation

Fig. 7 presents the identification results of the set-up with different excitation amplitudes. On one hand, it can be seen that the three expected modes were excited by strong and medium amplitude excitation. However, a repeat modal shape (4.14 Hz and 4.16 Hz) and a harmonic modal shape (7.46 Hz) were excited by strong excitation but roll mode not appeared when load light excitation on the system. These errors can be avoided by improve the ACS-SSI.

Fig. 7Modal parameters of different identification

a) Strong excitation

b) Medium excitation

c) Light excitation

On the other hand, the resonance frequencies of bounce, pitch and roll modes have a good coherence under different amplitudes of excitation, which means ACS-SSI is an effective method to meet the requirements of online monitoring. Nevertheless, the accuracy of ACS-SSI should be improved to suppress the condition that the excitations are strong or light to obtain a more accurate result.

Moreover, even though the system is simple and near linearity, the identification results still has errors compared with the theory calculation result from the 3-DOF model. However, a vehicle is a much more complicated system which contains nonlinear elements like dampers, so the 7-DOF linear full vehicle model which adopted in [1, 13] cannot fully present the vehicles’ dynamic performances and yet a more complicated model need to be developed.