As living standards improve, there is a growing emphasis on vehicle comfort, and in both traditional fuel vehicles and electric SUVs, powertrain vibration is a key factor affecting overall NVH performance. Thus, the rational design of the powertrain mounting system becomes critically important. With the integration of platformization and intelligent technologies in automotive R&D, many vehicle models now achieve synchronized development of the powertrain mounting system and the body system during the design phase. This allows for more in-depth and comprehensive analysis of the mounting system early in the process. In this study, I focus on a rear-wheel-drive electric SUV’s powertrain mounting system, utilizing Adams/View to construct a six-degree-of-freedom model. I optimize the system based on energy decoupling and perform simulation analysis under the forward longitudinal loading condition from the 28工况 set. By comparing data curves before and after optimization, I validate the rationality and accuracy of the design, providing a holistic reference for mounting system development.
The powertrain mounting system modeling requires precise parameters, such as the position and stiffness of rubber mount elements, as well as the mass, center of gravity, and moment of inertia of the powertrain. For this electric SUV, the key parameters are summarized in the following tables. Table 1 details the moment of inertia components, which are essential for understanding the rotational dynamics of the system.
| Parameter | Value (kg·m²) |
|---|---|
| Jxx | 0.829 |
| Jyy | 0.556 |
| Jzz | 0.964 |
| Jxy | 0.0189 |
| Jyz | 0.0441 |
| Jxz | -0.0901 |
Table 2 provides the mass and center of gravity coordinates, which are fundamental for defining the powertrain’s spatial characteristics in the model.
| Parameter | Value |
|---|---|
| Mass (kg) | 68.6 |
| X (mm) | 2768.96 |
| Y (mm) | -20.32 |
| Z (mm) | -21.66 |
The mounting points for the rubber elements are specified in Table 3, illustrating their positions in the vehicle coordinate system, which is crucial for accurate model assembly.
| Mount Element | X (mm) | Y (mm) | Z (mm) |
|---|---|---|---|
| Left Mount | 3051.29 | -158.40 | 21.96 |
| Right Mount | 3051.29 | 158.40 | 21.96 |
| Rear Mount | 2586.10 | -10.00 | 108.00 |
Table 4 lists the initial stiffness values of the mount elements in both static and dynamic states, serving as a baseline for optimization in this electric SUV study.
| Mount Element | Static Stiffness (N/mm) | Dynamic Stiffness (N/mm) |
|---|---|---|
| Left Mount (x, y, z) | 420, 55, 125 | 588, 77, 175 |
| Right Mount (x, y, z) | 420, 55, 125 | 588, 77, 175 |
| Rear Mount (x, y, z) | 265, 45, 300 | 371, 63, 420 |
Using these parameters, I simplified the powertrain as a rigid body with six degrees of freedom and built the model in Adams/View. This approach allows for efficient simulation of the system’s dynamics without excessive computational load. The mathematical model of the powertrain mounting system is derived using Lagrangian mechanics, which is widely applied in automotive engineering for multi-body dynamics. The Lagrangian differential equation is given by:
$$ \frac{d}{dt} \left( \frac{\partial C}{\partial \dot{q}} \right) – \frac{\partial C}{\partial q} + \frac{\partial P}{\partial q} + \frac{\partial I}{\partial \dot{q}} = F $$
where \( C \) represents the kinetic energy, \( P \) the potential energy, \( I \) the dissipative energy, \( F \) the generalized force, and \( q \) the generalized coordinates. The kinetic energy \( C \) comprises translational and rotational components:
$$ C = \frac{1}{2} m (\dot{x}^2 + \dot{y}^2 + \dot{z}^2) + \frac{1}{2} (J_{xx} \omega_x^2 + J_{yy} \omega_y^2 + J_{zz} \omega_z^2 + 2J_{xy} \omega_x \omega_y + 2J_{yz} \omega_y \omega_z + 2J_{xz} \omega_x \omega_z) $$
Here, \( m \) is the mass, and \( J_{xx}, J_{yy}, J_{zz}, J_{xy}, J_{yz}, J_{xz} \) are the moments of inertia. In matrix form, this becomes:
$$ C = \frac{1}{2} \dot{q}^T M \dot{q} $$
with \( M \) as the mass matrix. The potential energy \( P \) is expressed in terms of the mount stiffnesses:
$$ P = \frac{1}{2} \sum_{i=1}^{n} (k_{ui} u_i^2 + k_{vi} v_i^2 + k_{wi} w_i^2) $$
where \( u_i, v_i, w_i \) are the displacements along the principal axes of the mount, and \( k_{ui}, k_{vi}, k_{wi} \) are the corresponding stiffness components. This leads to the stiffness matrix \( K \), and the dissipative energy \( I \) involves the damping matrix \( D \). Substituting into the Lagrangian equation yields the system’s equation of motion:
$$ M \ddot{q} + D \dot{q} + K q = F $$
For free vibration analysis, ignoring damping and external forces, the equation simplifies to:
$$ M \ddot{q} + K q = 0 $$
Solving the eigenvalue problem \( M^{-1} K L = \omega^2 L \) provides the natural frequencies and mode shapes, where \( \omega \) is the angular frequency and \( L \) the mode shape vector. The energy distribution across degrees of freedom is critical; low decoupling rates can lead to poor comfort and durability in an electric SUV. The energy distribution for the i-th mode is calculated as:
$$ E_i = \frac{1}{2} \omega_i^2 L_i^T M L_i $$
and the percentage of energy in the b-th degree of freedom is:
$$ C_p = \frac{(L_i^T M)_{b}^2}{(L_i^T M L_i)(M_{bb})} \times 100\% $$
If \( C_p = 100\% \), the mode is fully decoupled. In practice, electric SUV powertrain mounting systems often exhibit coupling, so optimization aims to maximize decoupling. I employed the energy decoupling method, which focuses on concentrating vibration energy in specific degrees of freedom. The objective function for optimization is defined as:
$$ J = \sum_{i=1}^{6} u_i (1 – D_i) $$
where \( u_i \) is a weighting factor and \( D_i \) the energy distribution ratio for the i-th mode. Design variables include the stiffnesses of the mount elements in x, y, and z directions, totaling nine variables for the three mounts in this electric SUV. Constraints include limits on powertrain displacement and rotation, frequency separation from operational ranges, and stiffness variations within 30% of initial values, as shown in Tables 6 and 7.
| Direction | Limit (mm) |
|---|---|
| X | ±15 |
| Y | ±8 |
| Z | ±15 |
| Angle | Limit (°) |
|---|---|
| Yaw | ±3.5 |
| Roll | ±1.5 |
| Pitch | ±1.5 |
Using Adams/Insight, I optimized the design variables, resulting in updated stiffness values listed in Table 8. This optimization significantly improved the decoupling rates for the electric SUV powertrain mounting system.
| Mount Element | Dynamic Stiffness (N/mm) |
|---|---|
| Left Mount (x, y, z) | 448, 77, 224 |
| Right Mount (x, y, z) | 448, 77, 224 |
| Rear Mount (x, y, z) | 266, 91, 294 |
The modal analysis post-optimization, conducted with Adams/Vibration, showed enhanced decoupling rates, as summarized in Table 9. This demonstrates the effectiveness of the energy decoupling approach for this electric SUV application.
| Mode | Decoupling Rate (%) |
|---|---|
| 1 | 95.86 |
| 2 | 88.7 |
| 3 | 85.91 |
| 4 | 86.2 |
| 5 | 98.36 |
| 6 | 96.5 |
To validate the optimization, I simulated the forward longitudinal loading condition from the 28工况 set, which represents typical driving scenarios for an electric SUV. This involves applying equivalent forces and torques at the powertrain center of gravity. I measured displacements and dynamic reaction forces at the mounts and compared pre- and post-optimization data. The results indicate substantial improvements: for instance, the left mount’s x-direction displacement peak decreased from 5.23 mm to 3.69 mm, and the dynamic reaction force dropped from 3075 N to 1649.9 N. Similar reductions were observed for the right and rear mounts, confirming better vibration isolation in the optimized electric SUV powertrain mounting system.
In conclusion, I successfully optimized the powertrain mounting system for a rear-wheel-drive electric SUV using a six-degree-of-freedom model and energy decoupling method. The optimization led to higher decoupling rates and improved vibration isolation, as evidenced by the 28工况 simulation. This approach enhances ride comfort and provides a robust framework for developing mounting systems in electric SUVs, contributing to better NVH performance and overall vehicle quality. The use of advanced simulation tools like Adams ensures accuracy and efficiency in the design process, paving the way for future innovations in electric vehicle dynamics.