The transition towards electrification in the heavy machinery sector, particularly for equipment like excavators, represents a significant step in meeting global carbon neutrality goals and reducing operational emissions. The core of this transition lies in the high-capacity battery pack that replaces the internal combustion engine. However, the operational environment for machinery such as electric excavators is exceptionally demanding. Unlike passenger vehicles, these machines are subjected to intense and highly variable loads from terrain interaction, hydraulic system pulsations, and mechanical shocks from digging and slewing. This complex excitation environment poses a severe challenge to the structural integrity and electrochemical performance of the EV battery pack. The vibration transmitted to the battery pack is often non-stationary—its statistical properties, like mean and variance, change over time—making its analysis and mitigation far more complex than under simpler, steady-state vibrations. This article investigates the nature of these excitations, their transmission paths, and the resulting non-stationary vibration characteristics of the EV battery pack, providing a foundational analysis for ensuring its safety and reliability.
The operational excitations impinging on an electric excavator, and consequently its EV battery pack, are multifaceted. They can be broadly categorized into three primary types, each with the potential to exhibit non-standom characteristics.
First, road-induced excitation is a predominant source during travel modes. While classical vehicle dynamics often models road profiles as a stationary Gaussian random process for constant velocity, the reality for off-road excavators is different. The speed may vary, and the terrain roughness itself can change abruptly. Therefore, a more accurate representation is a non-stationary random process, often modeled by modulating a stationary process with a time-varying function. A common model is:
$$ F_G(t) = g(t) \cdot x(t) $$
where \( x(t) \) is a stationary random signal, for instance, represented by a sum of harmonics: \( x(t) = \sum_{n=1}^{N} A_n \sin(n\omega t + \phi_n) \). The modulation function \( g(t) \) is a slowly varying function, such as \( g(t) = (a + bt)e^{-ct} \), where parameters \( a, b, c \) define the temporal evolution of the excitation intensity. This formulation captures the time-varying intensity and frequency content characteristic of non-stationary terrain input to the EV battery pack.
Second, hydraulic system excitation originates from the pressure pulsations within the axial piston pumps that drive the excavator’s hydraulics. The fundamental frequency of this excitation is tied directly to the motor speed and the number of piston chambers:
$$ f_j = j \cdot \frac{z \cdot r}{60}, \quad j=1,2,3,… $$
Here, \( r \) is the motor rotational speed in RPM, and \( z \) is the number of pistons. The pressure pulsation \( p(t) \) can be expressed as a Fourier series: \( p(t) = B_0 + \sum_{j=1}^{\infty} B_j \sin(f_j t + \psi_j) \). In practice, variations in motor load, efficiency, and system impedance can cause the amplitudes \( B_j \) and even the fundamental frequency \( f_1 \) to fluctuate over time, introducing a non-stationary character to this high-frequency excitation transmitted to the EV battery pack structure.
Third, shock excitation occurs during the sudden start-stop cycles of the working arm (digging) or the rotary platform. A simplified model for such an impact force is:
$$ F_s(t) = m_s \frac{\Delta v}{T_s} (1 + \tau_s) \left(1 – \cos\left(\frac{2\pi}{T_s}t\right)\right) $$
where \( m_s \) is the effective mass of the impacting component, \( \Delta v \) is the change in velocity, \( T_s \) is the impact duration, and \( \tau_s \) is a restitution coefficient. In real, complex digging cycles, the parameters \( \Delta v \) and \( T_s \) are highly variable, making the shock sequence a non-stationary random process. The transmission of these shocks through the chassis to the EV battery pack can induce high-stress transients.
The transmission of these excitations to the EV battery pack follows distinct paths. Road excitations travel through the tracks and rollers to the main frame (upper structure), and then through isolation mounts to the battery pack enclosure. Hydraulic pump pulsations transmit structurally through the pump mounting and hydraulically through fluid lines and connected actuators, eventually causing frame vibrations felt by the battery pack. Shock loads from digging or slewing are directly imparted to the main frame, which then vibrates and transfers energy to the mounted EV battery pack. Understanding these paths is crucial for targeted vibration control strategies.
To analyze the dynamic response of the EV battery pack, a computational model is essential. Using the finite element method, the pack structure (enclosure, modules, busbars) can be discretized. The equations of motion are derived as:
$$ \mathbf{M}\ddot{\mathbf{U}} + \mathbf{C}\dot{\mathbf{U}} + \mathbf{K}\mathbf{U} = \mathbf{F}(t) $$
where \( \mathbf{M} \), \( \mathbf{C} \), and \( \mathbf{K} \) are the global mass, damping, and stiffness matrices of the EV battery pack system. \( \mathbf{U} \) is the vector of nodal displacements, and \( \mathbf{F}(t) \) is the time-varying force vector combining all the excitation inputs at their points of application. The natural frequencies \( \omega_n \) and mode shapes \( \mathbf{A}^{(l)} \) are found by solving the eigenvalue problem: \( (\mathbf{K} – \omega_n^2 \mathbf{M})\mathbf{A} = \mathbf{0} \).
The dynamic response of the EV battery pack to the general force \( \mathbf{F}(t) \) can be evaluated using convolution integrals (Duhamel’s principle). For a single-degree-of-freedom analogy of a specific mode, the response can be expressed as:
$$ U(\omega, t) = \frac{1}{m \omega_D} \int_{0}^{t} F(\tau) e^{-\xi \omega_n (t-\tau)} \sin\left( \omega_D (t-\tau) \right) d\tau $$
where \( \omega_D = \omega_n \sqrt{1-\xi^2} \) is the damped natural frequency and \( \xi \) is the damping ratio. When \( F(t) \) is non-stationary, the resulting response \( U(t) \) is also non-stationary. The time-varying frequency content and energy distribution are best revealed by the evolutionary power spectral density (EPSD) or a time-frequency representation. The instantaneous power spectral density can be conceptually viewed as \( S_{UU}(\omega, t) = U(\omega, t) \cdot U^*(\omega, t) \), showing how energy at frequency \( \omega \) changes with time \( t \).
A critical step in analysis is distinguishing stationary from non-stationary behavior in measured or simulated signals from the EV battery pack. Statistical tests like the Augmented Dickey-Fuller (ADF) test are used. The test regression is:
$$ \Delta U_t = \epsilon + \beta t + \gamma U_{t-1} + \sum_{o=1}^{R} \varphi_o \Delta U_{t-o} + \varepsilon_t $$
The null hypothesis (\( H_0: \gamma = 0 \)) indicates a unit root and thus non-stationarity. If the test statistic’s p-value is above a significance level (e.g., 0.05), the null hypothesis cannot be rejected, confirming the non-stationary nature of the EV battery pack vibration signal.
The following table summarizes the key characteristics of the excitations impacting the EV battery pack:
| Excitation Type | Primary Source | Typical Frequency Range | Nature & Model | Transmission Path to Battery Pack |
|---|---|---|---|---|
| Road/Terrain | Track-Terrain Interaction | 0.5 – 20 Hz | Non-stationary Random, \( F_G(t)=g(t)x(t) \) | Track → Rollers → Main Frame → Isolation Mounts |
| Hydraulic Pulsation | Axial Piston Pump | Fundamental at \( \frac{zr}{60} \) Hz & harmonics | Periodic with non-stationary modulation, \( p(t)=B_0+\sum B_j sin(f_j t+\psi_j) \) | Pump Mount → Frame / Fluid Lines → Actuators → Frame |
| Operational Shock | Digging, Slewing Start/Stop | Impulsive (Broadband) | Non-stationary Shock Sequence, \( F_s(t) = m_s \frac{\Delta v}{T_s}(1+\tau_s)(1-cos(\frac{2\pi}{T_s}t)) \) | Work Arm/Rotary Bearing → Directly to Main Frame |
For a concrete analysis, consider the case of an electric excavator operating in a low-speed travel mode over uneven ground. The measured vibration signal at a point on the main frame near the EV battery pack mount is complex, containing mixed low-frequency (road) and high-frequency (pump) components, often buried in noise. To isolate the road excitation component for force reconstruction, advanced signal processing is required. A practical approach involves a hybrid method: first, using wavelet transform to decompose the signal and perform initial denoising; second, applying Variational Mode Decomposition (VMD) optimized by the Grey Wolf Optimization (GWO) algorithm to accurately separate the intrinsic mode functions (IMFs). The GWO algorithm optimizes VMD’s critical parameters (penalty factor \(\alpha\) and mode number \(K\)), enhancing the separation fidelity. The low-frequency IMFs corresponding to road excitation can then be reconstructed.
Applying this GWO-VMD method to a 20-second measured signal segment reveals its effectiveness. The reconstructed signal predominantly contains energy below 20 Hz, aligning with the expected road excitation band. An ADF test on this reconstructed signal yields a p-value >> 0.05, statistically confirming its non-stationary character. This reconstructed, non-stationary road profile can be converted to a displacement input and fitted piecewise using a modulated harmonic model for use in simulation.
This fitted road excitation \( F_{G,fit}(t) \) is then applied as base input to a finite element model of the EV battery pack. The pack enclosure, modeled with shell elements and constrained at mounting points, has its first few fundamental modes calculated. A typical modal analysis for a steel enclosure might yield results as summarized below:
| Mode Order | Natural Frequency (Hz) | Dominant Mode Shape Description |
|---|---|---|
| 1 | 54 | Global bending of the base plate center |
| 2 | 61 | Anti-symmetric bending (left-right) of the base plate |
Notably, the first natural frequency of this EV battery pack structure (54 Hz) is well above the primary road excitation frequency range (0-20 Hz), avoiding resonance in this particular scenario. However, it may interact with higher harmonics of other excitations.
The dynamic simulation is performed by solving \( \mathbf{M}\ddot{\mathbf{U}} + \mathbf{C}\dot{\mathbf{U}} + \mathbf{K}\mathbf{U} = \mathbf{F}_{G,fit}(t) \). The simulated vibration response at a selected node on the EV battery pack base is extracted. For validation, the measured vibration response at a corresponding physical location on the test excavator is used. ADF tests on both time-history signals confirm their non-stationarity, with high p-values indicating the null hypothesis of a unit root cannot be rejected.
The most compelling evidence of non-stationary behavior in the EV battery pack response is found in the time-frequency domain. Calculating the spectrogram or a wavelet transform of the response reveals a power spectral density that is not constant over time. The energy concentration in the 0-20 Hz band fluctuates significantly in intensity throughout the operation period. Peaks appear, diminish, and shift, visually demonstrating that the statistical properties of the vibration are time-dependent. This non-stationary response is more damaging than a stationary one; it can lead to time-localized high stress cycles that accelerate fatigue crack initiation in the EV battery pack enclosure and within the module interconnects. Furthermore, for the lithium-ion cells inside, such varying mechanical stress can modulate the electrochemical interfaces, potentially leading to accelerated capacity fade and impedance rise, ultimately compromising the performance and lifespan of the entire EV battery pack.
In conclusion, the vibration environment for an EV battery pack in heavy-duty applications like electric excavators is fundamentally non-stationary. Key excitations—from terrain, hydraulic systems, and operational shocks—possess inherent time-varying characteristics that translate into complex, non-stationary dynamic responses for the battery system. Analytical and signal processing techniques, such as the GWO-optimized VMD method, are essential for accurately characterizing these input excitations. Dynamic modeling and simulation, coupled with time-frequency analysis, are crucial for predicting the resulting non-stationary vibration behavior of the EV battery pack. Recognizing and quantitatively analyzing this non-stationarity is the first critical step towards developing more robust design criteria, effective isolation strategies, and accurate durability assessments, thereby ensuring the structural integrity and long-term functional reliability of the EV battery pack under real-world operating conditions.