The transition towards electrification in heavy machinery, such as excavators, presents unique challenges, particularly concerning the durability and operational safety of high-voltage EV battery packs. Unlike passenger vehicles, electric excavators operate under extremely harsh conditions characterized by high-impact loads, continuous vibrations from multiple powerful actuators, and complex, transient working cycles. The EV battery pack, being a dense assembly of sensitive electrochemical cells, connectors, and management systems, is highly susceptible to mechanical stress. Excessive vibration can lead to issues such as connector loosening, busbar fatigue, internal cell damage, and accelerated degradation of battery performance and safety. Therefore, a profound understanding of the vibration characteristics of the EV battery pack and its dynamic interaction with the primary excitation sources of the excavator is paramount for reliable design.
This paper focuses on analyzing the vibration response of the EV battery pack in a stationary electric excavator. The primary excitations originate from three key subsystems: the traction electric motor, the hydraulic piston pump, and the working device (boom, arm, and bucket). A comprehensive multi-body dynamic model of the entire excavator is developed to capture the coupling effects of these excitations. The vibration transmission paths from these sources to the EV battery pack are investigated, and the influence of different operational modes—idling, slewing, and digging—is analyzed both theoretically and validated through experimental measurements.
1. Integrated Dynamic Model of the Electric Excavator
To analyze the vibration transmission to the EV battery pack, a lumped-parameter dynamic model of the stationary electric excavator is established. The model incorporates the major components that significantly influence the low to mid-frequency vibration characteristics relevant to the EV battery pack mounting system.
Modeling Assumptions and Simplifications:
- The superstructure (upper frame), electric motor, piston pump, and the EV battery pack casing are modeled as rigid bodies due to their high stiffness relative to their mounting systems.
- The working device is modeled as a three-link (boom, arm, bucket) mechanism with revolute joints. Its motion generates reaction forces and moments at its mounting point on the superstructure.
- The electric motor and the piston pump are connected via a rigid coupling and are considered as a single combined rigid body (Motor-Pump System) for dynamic analysis.
- All mounting elements—motor mounts, pump hose clamps, and particularly the EV battery pack isolation mounts—are modeled as linear spring-damper elements in three translational directions.
- Auxiliary components like the counterweight, operator cabin, and cooling system are accounted for as added mass on the superstructure.
The resulting schematic of the dynamic model highlights the key masses, degrees of freedom (DOFs), and connecting elements. The EV battery pack is centrally located on the superstructure, connected through an array of isolators.
Generalized Coordinates and System Matrices: The system’s motion is described by a set of generalized coordinates, Q:
$$
\mathbf{Q} = [x_1, y_1, z_1, \phi_1, \theta_1, x_2, y_2, z_2, \phi_2, \theta_2, x_3, y_3, z_3, \phi_3, \theta_3, \alpha_{boom}, \alpha_{arm}]^T
$$
where subscripts 1, 2, and 3 denote the superstructure, motor-pump system, and the EV battery pack, respectively. The coordinates \(x, y, z\) represent translational motions, and \(\phi, \theta\) represent rotations about the vehicle’s lateral and longitudinal axes. \(\alpha_{boom}\) and \(\alpha_{arm}\) are the angular displacements of the boom and arm joints.
The equations of motion for the entire system are derived using Lagrange’s formalism and can be written in matrix form:
$$
\mathbf{M}\mathbf{\ddot{Q}} + \mathbf{C}\mathbf{\dot{Q}} + \mathbf{K}\mathbf{Q} = \mathbf{F}(t)
$$
where \(\mathbf{M}\), \(\mathbf{C}\), and \(\mathbf{K}\) are the global mass, damping, and stiffness matrices, respectively. \(\mathbf{F}(t)\) is the vector of external excitation forces and moments, which is a superposition of contributions from the three main sources:
$$
\mathbf{F}(t) = \mathbf{F}_{motor}(t) + \mathbf{F}_{pump}(t) + \mathbf{F}_{work}(t)
$$
The stiffness matrix \(\mathbf{K}\) is assembled from the individual stiffness contributions of all mounting elements. For example, the contribution of a single EV battery pack mount located at position \((r_x, r_y, r_z)\) relative to the pack’s center of gravity to the pack’s stiffness sub-matrix is:
$$
\mathbf{K}_{pack, mount} = \mathbf{J}^T \begin{bmatrix}
k_x & 0 & 0 \\
0 & k_y & 0 \\
0 & 0 & k_z
\end{bmatrix} \mathbf{J}, \quad \mathbf{J} = \begin{bmatrix}
1 & 0 & 0 & 0 & r_z & -r_y \\
0 & 1 & 0 & -r_z & 0 & r_x \\
0 & 0 & 1 & r_y & -r_x & 0
\end{bmatrix}
$$
where \(k_x, k_y, k_z\) are the mount stiffnesses in three directions, and \(\mathbf{J}\) is the transformation matrix from mount local coordinates to the pack’s generalized coordinates.
The damping matrix \(\mathbf{C}\) is typically formulated based on a proportional damping model (e.g., Rayleigh damping) or from known damping ratios of the isolation systems.
| Component | Parameter | Value | Unit |
|---|---|---|---|
| EV Battery Pack | Mass | 1200 | kg |
| Moment of Inertia (Ixx) | 450 | kg·m² | |
| Moment of Inertia (Iyy) | 980 | kg·m² | |
| Battery Mount Stiffness (per mount) | Vertical (kz) | 2.5e5 | N/m |
| Lateral (kx, ky) | 1.8e5 | ||
| Motor-Pump System | Mass | 850 | kg |
| Motor Mount Stiffness (per mount) | 3.0e5 | N/m | |
| Superstructure (including added mass) | Mass | 9500 | kg |
2. Characterization of Primary Excitation Sources
The vibration environment for the EV battery pack is dominated by three distinct mechanical excitations.
2.1 Electric Motor Excitation
The permanent magnet synchronous motor (PMSM) generates electromagnetic force waves due to the interaction between the stator magnetic field and the rotor permanent magnets. The dominant source of vibration is the radial electromagnetic force density \(f_r(\theta, t)\) in the air gap. It can be expressed as a function of space and time harmonics:
$$
f_r(\theta, t) \approx \frac{1}{2\mu_0} \left[ \sum_{\nu} \hat{B}_{\nu} \cos(\nu p \theta – \omega_{\nu} t – \varphi_{\nu}) \right]^2
$$
where \(\mu_0\) is the permeability of free space, \(p\) is the number of pole pairs, \(\hat{B}_{\nu}\) and \(\omega_{\nu}\) are the amplitude and frequency of the \(\nu\)-th magnetic flux density harmonic, and \(\varphi_{\nu}\) is its phase. The square of the flux density sum leads to force harmonics at frequencies that are multiples of the fundamental electrical frequency. The principal forcing frequency for a synchronous motor is related to its rotational speed \(N\) (in rpm):
$$
f_{motor} = \frac{p \cdot N}{60}
$$
For a motor with \(p = 4\) poles operating at \(N = 1500\) rpm, the dominant electromagnetic excitation frequency is \(f_{motor} = 100\) Hz. This force acts on the stator, creating a distributed load that translates into global forces and moments on the motor housing, which are then transmitted through its mounts to the superstructure and ultimately to the EV battery pack.
2.2 Piston Pump Pressure Pulsation Excitation
The axial or swashplate piston pump is a major vibration and noise source in hydraulic systems. The periodic filling and emptying of the piston chambers generate significant flow and pressure ripples. The pressure pulsation \(\Delta P(t)\) can be modeled as a Fourier series around the mean system pressure \(P_0\):
$$
\Delta P(t) = P_0 + \sum_{n=1}^{\infty} \hat{P}_n \sin(2\pi n f_{pump} t + \psi_n)
$$
The fundamental pulsation frequency \(f_{pump}\) is determined by the number of pistons \(Z\) and the pump shaft speed:
$$
f_{pump} = \frac{Z \cdot N}{60}
$$
Considering a pump with \(Z = 9\) pistons driven at the same \(N = 1500\) rpm, \(f_{pump} = 225\) Hz. This pressure pulsation acts on the effective area \(A_{piston}\) of the pistons and the pump casing, generating an oscillating force \(F_{pump}(t) = A_{piston} \cdot \Delta P(t)\). This force is primarily axial along the pump shaft but also induces structural vibrations in the pump housing. The pulsation is transmitted through the hydraulic fluid to actuators and through the rigid pump mounting and hose connections to the structure. The stiff hydraulic lines connected to the pump can act as efficient vibration transmission paths to the superstructure, affecting the EV battery pack.
2.3 Working Device Impact Excitation
The dynamic loading from the working device is highly transient and nonlinear, occurring during actions like digging, dumping, or sudden stop/start of boom/arm movement. A simplified model for the impact force transmitted to the superstructure at the boom foot joint can be derived from momentum exchange. When the bucket strikes material or a motion is abruptly halted, an impulsive reaction force \(F_{work}(t)\) is generated. A common approximation for such an impact is a half-sine pulse:
$$
F_{work}(t) =
\begin{cases}
\hat{F}_{imp} \sin\left(\frac{\pi t}{\tau}\right), & 0 \leq t \leq \tau \\
0, & t > \tau
\end{cases}
$$
where \(\hat{F}_{imp}\) is the peak impact force and \(\tau\) is the impact duration (typically between 0.05s and 0.2s). The frequency content of this impulse is broad, but its dominant energy is concentrated below \(1/(2\tau)\) Hz. For \(\tau = 0.1\) s, significant frequency components exist up to about 5 Hz. This low-frequency, high-amplitude excitation directly shakes the superstructure, exciting its rigid body and low-frequency flexible modes, which directly impacts the EV battery pack.
| Excitation Source | Dominant Frequency Range | Nature of Excitation | Main Transmission Path to EV Battery Pack |
|---|---|---|---|
| Electric Motor | Medium-High (e.g., 50-400 Hz) | Periodic, Harmonic | Motor mounts → Superstructure → Battery mounts |
| Piston Pump | High (e.g., 200-1000 Hz) | Periodic, Harmonic/Pulsating | Pump mounts & Hydraulic lines → Superstructure → Battery mounts |
| Working Device | Low (0-20 Hz) | Transient, Impulsive | Boom foot joint → Superstructure → Battery mounts |
3. Vibration Analysis of the EV Battery Pack
3.1 Modal Analysis: Natural Frequencies and Mode Shapes
The inherent dynamic characteristics of the integrated system are found by solving the undamped eigenvalue problem derived from the homogeneous equation \(\mathbf{M}\mathbf{\ddot{Q}} + \mathbf{K}\mathbf{Q} = 0\). Assuming a harmonic solution \(\mathbf{Q} = \boldsymbol{\Phi} e^{j\omega t}\), we get:
$$
(\mathbf{K} – \omega^2 \mathbf{M}) \boldsymbol{\Phi} = 0
$$
Solving this yields the system’s natural frequencies \(\omega_n\) (rad/s) and the corresponding mode shapes \(\boldsymbol{\Phi}_n\). Of particular interest are the modes involving significant motion of the EV battery pack. These typically include:
- Bounce Mode: The EV battery pack and superstructure moving in phase vertically.
- Pitch/Roll Modes: The EV battery pack rocking on its isolators relative to the superstructure.
- Lateral Translation Mode: The EV battery pack moving side-to-side.
The effectiveness of the isolation for the EV battery pack depends on the frequency ratio between the excitation frequencies and these natural frequencies. The design goal is to keep the pack’s rigid body modes well below the dominant harmonic excitation frequencies (e.g., from the motor and pump).
3.2 Forced Response Analysis Under Different Operational Modes
The response of the EV battery pack varies significantly with the excavator’s operating mode, which dictates which excitation sources are active.
Mode 1: Stationary Idling. Only the electric motor is running to power auxiliary systems. The excitation vector simplifies to \(\mathbf{F}(t) = \mathbf{F}_{motor}(t)\). The system response is steady-state vibration dominated by harmonics of \(f_{motor}\). The amplitude is generally low as no hydraulic or digging loads are present. The EV battery pack experiences continuous, low-level vibration which is critical for assessing long-term fatigue.
Mode 2: Stationary Slewing. The motor runs, driving the pump to power the swing drive. Excitations include both \(\mathbf{F}_{motor}(t)\) and \(\mathbf{F}_{pump}(t)\). The response contains frequency components at \(f_{motor}\), \(f_{pump}\), and their harmonics. The combined input often leads to higher overall vibration levels on the superstructure compared to idling, which transmits to the EV battery pack.
Mode 3: Stationary Digging/Loading. This is the most severe condition. All three excitations are present: \(\mathbf{F}(t) = \mathbf{F}_{motor}(t) + \mathbf{F}_{pump}(t) + \mathbf{F}_{work}(t)\). The system response is a complex mixture of:
- High-frequency, steady-state vibration from the motor and pump.
- Low-frequency, high-amplitude transient shocks from the working device impacts.
This combination poses the greatest challenge for the EV battery pack mounting system, as it must simultaneously isolate high-frequency content and manage large low-frequency displacements.
The frequency-domain response at the EV battery pack center of gravity can be obtained from:
$$
\mathbf{Q}_3(\omega) = \mathbf{H}_{33}(\omega) \mathbf{F}_{eq}(\omega)
$$
where \(\mathbf{H}_{33}(\omega) = (-\omega^2 \mathbf{M}_{33} + j\omega \mathbf{C}_{33} + \mathbf{K}_{33})^{-1}\) is the frequency response function (FRF) matrix relating forces applied directly to the pack’s coordinates to its response, and \(\mathbf{F}_{eq}(\omega)\) represents the equivalent force vector projected onto the pack’s degrees of freedom from all excitation sources.
4. Case Study: Experimental Validation on a 20-ton Electric Excavator
The theoretical model and analysis were validated using experimental data from a 20-ton class electric excavator prototype.
4.1 Test Setup and Instrumentation
Vibration measurements were conducted with the excavator in a stationary condition. Tri-axial ICP accelerometers were installed at critical locations:
- On the EV battery pack casing and its mounting brackets (8 locations).
- On the superstructure near the motor/pump mounts and the boom foot joint (18 locations).
Data was acquired at a high sampling rate (e.g., 5120 Hz) to capture frequency content up to 2000 Hz. Tests were performed for the three operational modes: Idling (motor at 600 rpm), Slewing, and Digging.
4.2 Modal Validation
Experimental Modal Analysis (EMA) was performed on the isolated EV battery pack mounting system using impact hammer testing. The identified natural frequencies were compared with those predicted by the model’s subsystem containing the pack and its isolators. The results showed good correlation, validating the modeling approach for the EV battery pack dynamics.
| Mode Description | Model Prediction (Hz) | Experimental Result (Hz) | Relative Error |
|---|---|---|---|
| Vertical Bounce | 10.8 | 11.0 | 1.8% |
| Lateral Translation | 4.8 | 5.0 | 4.0% |
| Longitudinal Rocking | 10.2 | 10.1 | 1.0% |
4.3 Operational Vibration Results and Analysis
Idling Condition: The vibration spectrum at a EV battery pack bracket showed a distinct peak at approximately 20 Hz. This aligns perfectly with the calculated motor excitation frequency \(f_{motor} = (4*600)/60 = 20\) Hz. No significant energy was observed at the pump frequency, confirming it was inactive. This validates that during idling, the motor is the sole significant source of vibration for the EV battery pack.
Digging Condition: The vibration spectrum became markedly richer. Prominent peaks were observed at three key frequency bands:
- ~44 Hz: Corresponding to the fundamental frequency of the working device’s cyclic digging motion (impact repetition rate).
- ~83 Hz: Matching the motor excitation frequency (\(f_{motor}\)) at the higher operating speed during digging.
- ~278 Hz: Aligning with the piston pump excitation frequency (\(f_{pump}\)) at the same operating speed.
The amplitudes, especially at the lower frequencies associated with digging impacts, were significantly higher than during idling. This clearly demonstrates the coupling effect of multiple excitation sources. The combined forcing from the motor, pump, and working device creates a complex vibration environment for the EV battery pack, with energy concentrated at several distinct frequencies spanning from low (impact) to high (pump pulsation).
| Operational Mode | Dominant Peaks in Spectrum (Hz) | Corresponding Excitation Source | Relative Amplitude |
|---|---|---|---|
| Idling | 20, 40 (harmonic) | Electric Motor | Low |
| Digging | 44, 83, 278 | Work Device, Motor, Pump | High (especially at 44 Hz) |
5. Conclusion
This study presents a systematic approach to analyze the vibration characteristics of an EV battery pack in a stationary electric excavator. A comprehensive multi-body dynamic model was developed, successfully incorporating the major structural components and excitation mechanisms. The analysis of the three primary excitation sources—electric motor electromagnetic forces, piston pump pressure pulsations, and working device impact loads—reveals their distinct frequency signatures and transmission paths to the superstructure and the EV battery pack.
The key findings are:
- The vibration environment of the EV battery pack is highly dependent on the excavator’s operational mode. Idling generates low-level, periodic vibration primarily from the motor. In contrast, digging operation subjects the EV battery pack to a complex mix of high-frequency harmonic content (motor, pump) and low-frequency, high-energy shocks (working device), representing the most severe loading condition.
- The developed integrated dynamic model provides an effective tool for predicting system modal properties and forced responses. Good agreement between model predictions and experimental modal tests validates the modeling methodology for the EV battery pack isolation system.
- Experimental data from a 20-ton excavator confirmed the theoretical excitation frequencies. During digging, clear spectral peaks corresponding to the motor, pump, and working device cycle were identified at the EV battery pack mounting points, demonstrating the multi-source coupling effect.
This work underscores the necessity of a system-level dynamic analysis in the design phase of electric construction machinery. For optimal protection of the EV battery pack, the mounting system must be designed considering the combined spectrum of excitations. Future work will focus on optimizing the EV battery pack mount stiffness and damping parameters using this model to minimize vibration transmissibility across the critical frequency ranges identified, thereby enhancing the longevity and reliability of the EV battery pack in these demanding applications.