Simulating Effects of Suspension Damper Degradation on Common Sensor Signals for Diagnosis Models in the Context of Condition-Based Maintenance

Abstract

Degraded suspension dampers strongly influence vehicle safety and ride comfort, but often occur after several years of operation. Related workshop checks are usually not degradation-adaptive, so they can be significantly delayed to the need for maintenance. To make the maintenance adaptive to degradations, onboard diagnosis methods can be used, which rely on the degradation status extracted from sensor signals.To support the development of sensitive yet robust diagnosis models, a model that can simulate and explain the effects of damper degradation in common sensor signals is proposed. This paper focuses on low-frequency effects in signals of the wheel speed sensors, which are ultra low cost and always available in modern vehicles. As a result, the model shows a good qualitative match to real-world test drives, specifically in the frequency domain. Therefore, various real-world measurements were conducted, in particular, test bench measurements of degraded dampers and vehicle on-road tests.

1 Introduction

New trends in automotive mobility, such as shared vehicles and highly automated driving, require advanced methods to self-responsibly diagnose maintenance needs. In contrast to regular, pre-scheduled, or reactive maintenance, advanced maintenance strategies have a decisive advantage: the maintenance activity can be adapted to the actual degradation state. These maintenance strategies include so-called condition-based maintenance, based on diagnostic models that continuously monitor the degradation status of one or more components. The paper focuses on the suspension damper, which often degrades over time; according to a report, more than every hundredth vehicle fails a regular check after seven years due to faults related to suspension springs and dampers, [1]. Wheel speed sensors are ultra low cost, available in every modern vehicle and are close to suspension dampers, which makes them attractive as limited sensor set. The analysis of wheel speed signals in the presence of degraded dampers shows that effects from degradation occur in the frequency domain, see Fig. 1.

Fig. 1.

Measured effects of damper degradation on wheel speed signals

Therefore, the focus of this paper is to explain, how these effects are transmitted from the damper to the signals and how they depend on chassis parameters and environmental conditions. Existing studies focus directly on the development of diagnosis models, e.g., [2,3,4], rather than on explanations of these effects. Building up a deeper understanding of the these effects could potentially help to develop sensitive yet robust diagnosis models. In contrast, approaching the diagnosis model development purely data-driven demands excessive data collection due to the high variance of chassis parameters, including different suspension damper and spring variants and different tyres, in different vehicle models.

2 System Model

Dynamics simulation that can handle degradation effects and parameter variations can help to better understand these effects. To select a suitable model, an approximately constant vehicle speed is assumed, thus pitch and roll motions are neglected. Consequently, a quarter-car model with single-point excitation serves as a base model for this study, see, e.g., [5]. The frequency range of interest is limited to the vertical natural frequency of the un-sprung mass $m_2$, typically between 12–15 Hz [6]. To simulate the wheel speed signals, the quarter-car model is extended by a rotational degree of freedom of the wheel. The angular velocity of the wheel is denoted $\omega$. Consequently, we add to the equations of motion of the quarter-car model, Euler’s law for the wheel, equation (2), where $I_{2}$ denotes the wheel polar moment of inertia, $r_l$ is the loaded radius and $F_x$ the longitudinal tyre force. In addition, a moment $M_y$ is introduced, which represents rolling resistance effects and the influence of tyre eccentricity. Typically, the natural frequency related to the un-sprung mass in the longitudinal direction lies in the frequency range of interest. Thus, the model is further extended by the equation of motion (1) in the longitudinal direction, with longitudinal suspension stiffness $c_{Sx}$ and damping coefficient $k_{Sx}$. For all model-based analyses, the model is parametrised with values from [7]. A schema of the model is depicted in Fig. 2.

The road is modeled as stochastic excitation, [5], whereby the waviness is kept constant with a value of 2, and the degree of unevenness is varied in typical values. A single-contact-point transient tyre model, [7], is applied; decoupling of belt and rim mass is not considered since the frequency range of interest is well below the in-plane first natural frequency. Due to the assumed constant vehicle speed $v_1$, the slip states are small, and tyre forces are assumed to be linear with respect to the transient longitudinal slip $\kappa '$ in (3), where $C_{F_\kappa }$ denotes the longitudinal slip stiffness, $\kappa '$ the longitudinal transient slip, u the longitudinal tyre deflection in the contact patch and $\sigma _{\kappa }$, the relaxation length. The first-order differential Eq. (4) is employed, where the input is the longitudinal slip velocity $V_{sx}=V_2-r_{\textrm{eff}} \cdot \varOmega$. For the simulation of the effects of the degradation of the suspension damper, the damping coefficient $k_{Sz}$ is reduced by 30%.

Fig. 2.

Schema of the system model

Fig. 3.

FFT of simulated wheel speed signal

For a more detailed analysis and later comparison of simulation and measurement results, measurements with an Audi A6 are performed. The relevant model parameters are measured on a Kinematic and Compliance Test Rig. Further measurements include measuring the suspension spring and the damper in new condition and with 50% oil loss, and the suspension stiffness in the longitudinal direction.

3 Results

The simulation results are analysed in the frequency domain. Figure 3 shows the relevant characteristic frequencies. These frequencies include the natural frequencies related to the sprung mass, to the un-sprung mass in vertical and longitudinal directions, and to the rotation frequency of the wheel. In the following, the influence of $M_y$ is neglected in the simulation results and related effects in the measurement signals are filtered out.

From (2), it is evident that the wheel speed $\omega$ is influenced by the term $r_L F_x$, which depends on the parameters $r_{\textrm{eff}}, \sigma _{\kappa }, C_{F\kappa }$, all functions of wheel load $F_z$, [7]. Variations of $\sigma _{\kappa }$ and $C_{F\kappa }$ with $F_z$ do not exhibit significant effects on the simulated wheel speed. Therefore, the subsequent analysis focuses on the parameters $r_L$ and $r_{\textrm{eff}}$. For both, a linear dependency on $F_z$ is assumed based on values from [7]. If dependencies are set to zero, degradation effects cannot be observed. It becomes clear that $r_{\textrm{eff}}$ and $r_{L}$ couple the vertical motion and effects of a degraded damper (influencing the wheel load) with the rotational wheel motion and wheel speed $\omega$.

Fig. 4.

Sensitivity analysis of wheel speed signals to tyre parameter variations

Figure 4 illustrates that a variation of the loaded radius with wheel load, $f^{\textrm{eff}*}(F_z)$, affects the simulated wheel speed across the investigated frequency range; an increasing slope in the linear relationship amplifies the vibrations. The dependency of the effective rolling radius on the wheel load, $f^{\textrm{l}*}(F_z)$, affects the simulated wheel speed vibrations below 20 Hz. In addition to changes in magnitude, also the vertical natural frequency of $m_2$ is shifted. An increasing slope shifts the natural frequency towards greater values.

Besides the tyre parameters, road roughness and vehicle speed show considerable effects on the wheel speed in simulation, which are not addressed here in more detail.

Figure 5 depicts the simulated wheel speeds for a well-functioning and a degraded suspension damper. In comparison to Fig. 1, it is remarkable, that degradation-induced effects within the frequency range related to the natural frequency of the sprung mass, at approximately 1.4 Hz, are observable in the simulated signals but remain absent in the measurements. Furthermore, the measurements reveal effects spanning the frequency spectrum from 3 to 11 Hz, which are not evidently mapped by the simulation results. The measurements show an influence concentrated around the vertical natural frequency of the un-sprung mass, approximately within the range of 11 to 16 Hz. This phenomenon is captured by the simulation. Beyond 16 Hz, both the simulated and measured signals show negligible effects.

Fig. 5.

Spectra of simulated wheel speeds for a well-functioning and a degraded suspension damper

The influence of road roughness can be observed in other measurements, which is mapped well by the simulation. However, the simulation results show a strong dependency on vehicle speed, which cannot be confirmed by the measurements. If the vertical tyre stiffness $c_T$ and the effective rolling radius $r_{\textrm{eff}}$ become functions of vehicle velocity and inflation pressure, as addressed in [8], the simulation to reality gap is decreased.

4 Discussion and Conclusion

The above findings outline the potential of physics-based models to simulate the effect of suspension damper degradation on wheel speed signals. The model can be parameterised with few parameters, and it can be used to explain measured degradation effects and further to systematically develop a diagnosis model for condition-based maintenance. A respective physics-informed machine learning diagnosis will be published in a further research paper soon, which uses physics-based knowledge derived from the system model above.

First, the simulation of degradation effects can be used to engineer features with a high degradation-information to noise ratio. The simulation results indicate that frequency-based features in the range of 12 to 15 Hz are particularly suitable.

Second, the sensitivity analysis reveals that the model parameters influencing wheel speed signals, aside from damper degradation, can be confined to a limited set. This knowledge is significant as it gives an argued indication of critical parameter combinations for the development and testing of a diagnosis model, where the challenge is to remain robust against varying vehicle and environmental parameters while also being efficient, e.g., collecting no data of not influencing parameters.

The results demonstrate that vehicle speed, road roughness and the influence of tyre radii depending on wheel load should be considered for a diagnosis model. The sensitivity analysis shows, that these parameters influence the wheel speed signals within the frequency range associated with a damper degradation effect, which indicates that diagnosis purely based on wheel speed signals is difficult.

Future research may focus on methods that can fuse information from estimated environment and vehicle parameters and features that include information about the degradation state, enhancing both diagnostic sensitivity and robustness in real-world scenarios. Moreover, discrepancies between simulated and measured signals revealed areas for further refinement.