In modern engineering, the demand for efficient and agile aerial systems has led to significant advancements in quadrotor drone technology. As a versatile platform for military and civilian applications, the performance of a quadrotor is heavily influenced by its structural mass. Reducing the weight of the airframe components not only enhances maneuverability and flight endurance but also improves payload capacity. This study focuses on the lightweight design of a quadrotor drone’s airframe using finite element analysis (FEA), topology optimization, and geometric reconstruction. By employing Altair Inspire software, we aim to achieve a substantial mass reduction while maintaining structural integrity and mechanical performance. The integration of orthogonal experiments allows for a comprehensive evaluation of factors affecting the optimization process, leading to an optimal design solution.
The quadrotor drone, characterized by its four-rotor configuration, operates based on the principles of aerodynamics and control systems. The airframe serves as the primary structure supporting the motors, electronic components, and payload. In this study, the initial airframe model is subjected to FEA to assess its strength under typical loading conditions. The boundary conditions include inertial relief constraints, point masses simulating payloads, and force applications representing rotor thrusts and external loads. For instance, forces $F_1$, $F_2$, $F_3$, and $F_4$ act along the Z-axis with magnitudes of 20 N each, while a force $F_5$ of 60 N opposes them, mimicking a suspended load. Two load cases are defined: Case 1 involves the rotor forces, and Case 2 the payload force. The material used is ABS plastic, with properties defined for linear elastic analysis. The initial analysis reveals a maximum von Mises stress of 2.995 MPa, a displacement of 0.2491 mm, and a safety factor of 15.0, indicating substantial over-design and potential for weight reduction.
Topology optimization is employed to determine the optimal material distribution within the design space, which is the main body of the quadrotor airframe, excluding non-design regions like mounting holes. The objective is to minimize mass while satisfying constraints on stress and displacement. The optimization problem can be formulated as:
$$ \text{Minimize: } m(\rho) = \sum_{e=1}^{N} \rho_e v_e $$
$$ \text{Subject to: } \sigma_{\text{max}} \leq \sigma_{\text{allowable}}, \quad u_{\text{max}} \leq u_{\text{allowable}}, \quad 0 < \rho_{\text{min}} \leq \rho_e \leq 1 $$
where $m(\rho)$ is the mass, $\rho_e$ is the density of element $e$, $v_e$ is the volume, $\sigma_{\text{max}}$ is the maximum stress, and $u_{\text{max}}$ is the maximum displacement. The Solid Isotropic Material with Penalization (SIMP) method is used, with a penalty factor of 3. Ten different shape control schemes are evaluated, incorporating draft directions (unidirectional, bidirectional, radial, extrusion) and symmetry controls (none, planar symmetry, periodic symmetry). The design space has an initial mass of 48.391 g. After optimization, the results are analyzed based on mass reduction, stress, and displacement. Schemes with asymmetric or impractical geometries are discarded, leading to the selection of three superior schemes: Scheme 6 (bidirectional draft with periodic symmetry), Scheme 7 (radial draft with planar symmetry), and Scheme 10 (extrusion draft).
| Scheme | Draft Type | Symmetry Control | Optimized Mass (g) | Max Displacement (mm) | Min Safety Factor |
|---|---|---|---|---|---|
| 1 | Unidirectional | None | 14.02 | 0.6804 | 5.5 |
| 2 | Unidirectional | Planar | 18.53 | 0.5393 | 3.3 |
| 3 | Unidirectional | Periodic | 25.91 | 0.4005 | 7.0 |
| 4 | Bidirectional | None | 18.39 | 0.5793 | 6.9 |
| 5 | Bidirectional | Planar | 17.88 | 0.5541 | 5.8 |
| 6 | Bidirectional | Periodic | 21.11 | 0.4976 | 6.8 |
| 7 | Radial | None | 19.30 | 0.5809 | 5.0 |
| 8 | Radial | Planar | 21.97 | 0.5268 | 4.4 |
| 9 | Radial | Periodic | 21.20 | 0.5323 | 6.2 |
| 10 | Extrusion | None | 16.74 | 0.5725 | 6.2 |
To further refine the optimization, an orthogonal experiment is conducted using an L9(3^4) array, considering four factors: shape (A), retained design space percentage (B), minimum thickness constraint (C), and mesh density (D). Each factor has three levels, as shown in Table 2. The response variables are minimum safety factor, maximum displacement, and optimized mass. A comprehensive scoring method is applied, with weights of 35% for safety factor, 35% for displacement, and 30% for mass. The score is calculated as:
$$ S = \left( \frac{\text{SF} – 2.5}{2.5} \times 0.35 + \frac{0.8 – u}{0.8} \times 0.35 + \frac{48.391 – m}{48.391} \times 0.30 \right) \times 100 $$
where SF is the safety factor, $u$ is displacement, and $m$ is mass. The orthogonal experiment results are analyzed to determine the optimal combination of factors. The range analysis indicates that factor B (retained design space percentage) has the greatest influence, followed by A (shape), D (mesh density), and C (minimum thickness). The optimal levels are A₂ (Scheme 7), B₃ (25%), C₃ (4 mm), and D₁ (4 elements). Validation shows that this combination yields a safety factor of 5.8, displacement of 0.531 mm, and mass of 18.85 g. Further adjustment reduces the mesh density to 2 elements, resulting in a final mass of 16.74 g, a safety factor of 6.2, and displacement of 0.5725 mm, all within acceptable limits.
| Factor | Level I | Level II | Level III |
|---|---|---|---|
| A: Shape | Scheme 6 | Scheme 7 | Scheme 10 |
| B: Retained Percentage (%) | 15 | 20 | 25 |
| C: Min Thickness (mm) | 3.0 | 3.5 | 4.0 |
| D: Mesh Density (elements) | 4 | 3.5 | 3 |
| Experiment | A | B (%) | C (mm) | D (elements) | Safety Factor | Displacement (mm) | Mass (g) | Score |
|---|---|---|---|---|---|---|---|---|
| 1 | I | 15 | 3.0 | 3 | 5.5 | 0.6804 | 14.02 | 118.26 |
| 2 | I | 20 | 3.5 | 3.5 | 3.3 | 0.5393 | 18.53 | 84.31 |
| 3 | I | 25 | 4.0 | 4 | 7.0 | 0.4005 | 25.91 | 126.93 |
| 4 | II | 15 | 3.5 | 4 | 6.9 | 0.5793 | 18.39 | 133.25 |
| 5 | II | 20 | 4.0 | 3 | 5.8 | 0.5541 | 17.88 | 120.01 |
| 6 | II | 25 | 3.0 | 3.5 | 6.8 | 0.4976 | 21.11 | 129.81 |
| 7 | III | 15 | 4.0 | 3.5 | 5.0 | 0.5809 | 19.30 | 104.70 |
| 8 | III | 20 | 3.0 | 4 | 4.4 | 0.5268 | 21.97 | 93.15 |
| 9 | III | 25 | 3.5 | 3 | 6.2 | 0.5323 | 21.20 | 119.70 |
Geometric reconstruction is performed to convert the optimized topology into a manufacturable model. Two approaches are compared: automatic fitting and manual reconstruction. Automatic fitting uses PolyNURBS with high smoothness settings, generating a model with a mass of 13.88 g, a safety factor of 4.1, and a displacement of 0.7550 mm. However, this method may produce irregular transitions at design boundaries. Manual reconstruction involves meticulous adjustments using PolyNURBS operations like bridging and splitting, resulting in a smoother and more rational structure. The manually reconstructed model has a mass of 12.64 g, a safety factor of 5.4, and a displacement of 0.7085 mm. The von Mises stress is 8.305 MPa, compared to 10.980 MPa for the automatic fit. The manual approach achieves a 73.9% mass reduction from the initial 48.391 g, while keeping displacement below 0.8 mm and safety factor above 2.5, ensuring structural adequacy for the quadrotor drone.
In conclusion, this study demonstrates a systematic approach to lightweight design for quadrotor drone airframe components. Through finite element analysis, topology optimization, and orthogonal experiments, we identified an optimal design that reduces mass by 73.9% while maintaining mechanical performance. The manual geometric reconstruction further enhances the model’s practicality for manufacturing. This methodology provides a robust framework for advancing quadrotor drone technology, enabling improved agility and efficiency in various applications. Future work could explore multi-physics optimization and additive manufacturing techniques to realize these complex geometries.