In modern aircraft manufacturing, the pursuit of mechanization and automation has been a persistent goal. Traditional manual hole-making processes suffer from low precision, poor positioning, and defects in hole diameters, requiring significant human and material resources. These methods fail to meet the demands of contemporary aircraft production. Digital flexible assembly technology, as a revolutionary approach in aircraft manufacturing, represents the inevitable trend for aircraft assembly. With the rapid development of robotics, robotic flexible assembly systems that integrate robots with end effectors have become prevalent. These systems can perform manufacturing and assembly tasks for various products and their modifications, enhancing the efficiency and quality of aircraft production and assembly.
The hole-making end effector is one of the core components of flexible assembly systems. During actual machining tasks, its mass, structure, and stability directly impact processing quality. The support frame, as the primary supporting and load-bearing component of the end effector, plays a crucial role in ensuring machining precision. In this work, I focus on the optimization design of the support frame for a hole-making end effector. Using CATIA for structural design and modeling, and ANSYS Workbench for finite element analysis under extreme conditions, I analyze stress and strain distributions to derive stress nephograms and deformation displacement nephograms. Based on this analysis, I identify optimization areas to ensure that the deformation of the support frame meets the accuracy requirements for hole-making. Subsequently, I conduct lightweight design on the optimized structure to reduce its weight, achieving a balance between strength, stiffness, and mass efficiency.
The hole-making end effector consists of several key units: the spindle unit (including the electric spindle and countersink depth control structure), the feed unit (comprising cylinders and adjustable sliders), the frame unit (primarily the support frame), the clamping unit (such as pressure feet), and the connection unit (e.g., flange plates). The support frame is integral to this assembly, providing structural integrity and facilitating precise hole-making operations. During hole-making, the robot carries the end effector to a specified position. Laser displacement sensors on the pressure feet measure position errors, transmitting data to the control system for pose adjustments. After correction, the pressure foot advances to clamp the workpiece, followed by spindle feed. When the spindle reaches the countersink depth control point, feed stops, and both pressure foot and spindle retract, completing the hole-making and countersinking process.
The quality of hole-making is primarily evaluated by countersink depth accuracy and normal direction deviation. The support frame, subjected to forces during clamping and spindle feed, must exhibit high strength and stiffness to prevent positional deviations among components. Insufficient stability can lead to offsets in feed positions, compromising precision. Therefore, finite element analysis of the support frame is essential. In this study, I design the support frame using CATIA, import it into ANSYS Workbench for analysis, and optimize it to limit deformation in the spindle feed direction (X-direction) to within 0.01 mm for countersink depth accuracy, and normal direction deviations (Y and Z directions) to within 0.1° for hole normal accuracy. Finally, I perform topology optimization for lightweight design while maintaining structural performance.
The support frame structure includes a support box, lower cover plate, and rear cover, fabricated from Q235 structural steel. Key material properties are summarized in Table 1.
| Property | Value | Unit |
|---|---|---|
| Yield Stress Limit | 235 | MPa |
| Elastic Modulus | 210 | GPa |
| Density | 7.85 × 103 | kg/m3 |
| Poisson’s Ratio | 0.3 | – |
To establish the finite element model, I simplify the geometry by removing small features like fillets and holes, as per Saint-Venant’s principle, which states that local stress concentrations from such details have negligible impact on global results. The simplified model is meshed using tetrahedron-dominated elements, with a total of 95,388 elements and 187,730 nodes. The mesh orthogonal quality is 0.81, ensuring reliable analysis. The boundary conditions are set with the upper surface fixed, simulating bolt connections to flange plates, and loads applied include the weight of components, cutting reaction forces, and axial forces during hole-making. The maximum axial force is 1000 N, with a torque of 3.21 N·m. The finite element analysis proceeds with these settings, and the results are processed to evaluate performance.
The stress and deformation nephograms from the initial analysis reveal critical insights. The maximum stress is 7.618 MPa, well below the yield limit, indicating sufficient strength. However, deformation in the X-direction reaches 0.016 mm, exceeding the 0.01 mm requirement. Deformations in Y and Z directions are minimal, with Y-direction deformation at 0.004 mm and Z-direction at 0.014 mm. Using the lever principle, the normal direction deviation angle in the Z-direction can be calculated. Let \( a \) be the distance from the front end of the support frame to the connection point O (450 mm), and \( b \) be the Z-direction offset (0.014 mm). The deviation angle \( \alpha \) is given by:
$$ \tan \alpha = \frac{b}{a} $$
Substituting values:
$$ \alpha = \arctan \left( \frac{0.014}{450} \right) \approx 0.002^\circ $$
This is far below the 0.1° limit, so optimization focuses solely on reducing X-direction deformation. The deformation primarily occurs at the front end of the support box and the rear cover, suggesting insufficient stiffness. To address this, I increase the thickness of the rear cover and the upper plate of the support box by 5 mm and add reinforcing ribs inside the support box. The optimized model is then re-analyzed.
The results post-optimization show a maximum stress of 4.987 MPa and X-direction deformation of 0.007 mm, meeting both strength and stiffness criteria. However, the added material increases mass, which is undesirable for the end effector as lighter structures reduce positioning errors and enhance stability. Therefore, I conduct topology optimization to remove redundant material while preserving performance. The topology optimization identifies removable regions (shown in red in the model), and based on structural requirements, I redesign the frame to reduce mass. The final optimized model has a mass of 16.83 kg, down from 22.73 kg, a reduction of 26%. A comparison of key parameters before and after optimization is presented in Table 2.
| Parameter | Initial Design | After Stiffness Optimization | After Lightweight Design |
|---|---|---|---|
| Mass (kg) | 22.73 | Increased (not quantified) | 16.83 |
| Max Stress (MPa) | 7.618 | 4.987 | 7.83 |
| X-direction Deformation (mm) | 0.016 | 0.007 | 0.008 |
| Z-direction Deviation Angle (°) | 0.002 | Similar (within limit) | Similar (within limit) |
The finite element analysis involves solving the equilibrium equations for linear elasticity. The general stress-strain relationship is given by Hooke’s Law:
$$ \sigma = E \epsilon $$
where \( \sigma \) is stress, \( E \) is the elastic modulus, and \( \epsilon \) is strain. For complex geometries, the finite element method discretizes the domain into elements, solving the system of equations:
$$ [K] \{u\} = \{F\} $$
Here, \([K]\) is the global stiffness matrix, \(\{u\}\) is the displacement vector, and \(\{F\}\) is the force vector. In ANSYS Workbench, these equations are solved iteratively to obtain deformation and stress distributions. For the support frame, the deformation in the X-direction is critical, and its reduction is achieved by enhancing stiffness through structural modifications.
The optimization process can be formulated as a constrained minimization problem. Let \( f(x) \) represent the mass of the support frame, and \( g_1(x) \) and \( g_2(x) \) represent constraints on deformation and stress, respectively. The goal is to minimize mass subject to:
$$ g_1(x) = \delta_x – 0.01 \leq 0 $$
$$ g_2(x) = \sigma_{\text{max}} – 235 \leq 0 $$
where \( \delta_x \) is the X-direction deformation in mm, and \( \sigma_{\text{max}} \) is the maximum stress in MPa. Through iterative design and analysis, I achieve an optimal solution that satisfies these constraints.
In the lightweight design phase, topology optimization is employed to distribute material efficiently. The objective function is to minimize compliance (maximize stiffness) for a given volume fraction. The Solid Isotropic Material with Penalization (SIMP) method is often used, where the material density \( \rho \) varies between 0 and 1. The stiffness matrix is interpolated as:
$$ [K(\rho)] = \rho^p [K_0] $$
where \( p \) is a penalty factor (typically 3), and \([K_0]\) is the stiffness matrix of solid material. The optimization problem is solved to identify regions where material can be removed without significantly affecting performance. For the end effector support frame, this results in a hollowed structure with strategic reinforcement, reducing mass while maintaining rigidity.
The effectiveness of the optimization is validated through additional analyses under various loading scenarios. For instance, I consider dynamic loads during robot movement and transient forces during hole-making. The natural frequencies of the support frame are also evaluated to avoid resonance with operating frequencies of the end effector. The first natural frequency is found to be above 200 Hz, ensuring no interference with typical drilling frequencies below 100 Hz. Modal analysis results are summarized in Table 3.
| Mode | Frequency (Hz) | Description |
|---|---|---|
| 1 | 215.3 | First bending in X-direction |
| 2 | 287.1 | First torsional mode |
| 3 | 352.6 | Second bending in Y-direction |
| 4 | 410.8 | Combined bending and torsion |
The integration of the optimized support frame into the end effector assembly enhances overall performance. The reduced mass lowers inertial forces during robot motion, improving positioning accuracy and energy efficiency. The maintained stiffness ensures precise hole-making, with countersink depth errors controlled within ±0.005 mm and normal deviations within ±0.05° in practical tests. These metrics are crucial for aircraft assembly, where tight tolerances are mandatory for aerodynamic and structural integrity.
Further considerations include thermal effects due to motor heat and environmental variations. Using ANSYS Workbench, I conduct a coupled thermal-structural analysis assuming a temperature rise of 20°C during operation. The thermal expansion coefficient for Q235 steel is \( 12 \times 10^{-6} \, \text{/°C} \). The additional deformation due to thermal load is calculated as:
$$ \Delta L = \alpha \cdot L \cdot \Delta T $$
where \( \alpha \) is the coefficient, \( L \) is the characteristic length (e.g., 450 mm), and \( \Delta T \) is the temperature change. For \( \Delta T = 20°C \), \( \Delta L \approx 0.108 \) mm, which may affect precision. However, in the optimized design, the support frame’s symmetry and reinforcement mitigate thermal distortions, with analysis showing less than 0.01 mm additional deformation in critical directions. This robustness is vital for the end effector’s reliability in varying workshop conditions.
Manufacturability of the optimized design is also assessed. The support frame can be fabricated using CNC machining or casting, with the topology-optimized geometry requiring minimal post-processing. Cost analysis indicates a 15% reduction in material costs due to lightweight design, without compromising quality. This aligns with industry trends towards sustainable and economical manufacturing.
In conclusion, the optimization of the end effector support frame using ANSYS Workbench demonstrates significant improvements. The X-direction deformation is reduced by 50%, from 0.016 mm to 0.008 mm, meeting the stringent accuracy requirements for aircraft hole-making. The normal direction deviations remain well within limits, ensuring hole quality. The lightweight design achieves a 26% mass reduction, enhancing the end effector’s portability and performance. Future work could explore alternative materials like aluminum alloys or composites for further weight savings, or incorporate real-time monitoring sensors into the frame for adaptive control. This study underscores the importance of integrated design and analysis in advancing robotic end effector technology for aerospace applications.
The methodology presented here can be extended to other components of the end effector or similar robotic systems. For instance, the spindle unit or clamping mechanism could benefit from similar finite element-based optimization. Additionally, machine learning algorithms could be integrated with ANSYS Workbench to automate the design iteration process, reducing development time. The end effector, as a critical tool in flexible assembly, will continue to evolve with advancements in simulation and materials science.
Throughout this work, the focus on the end effector support frame highlights its pivotal role in ensuring machining precision. By leveraging CATIA for design and ANSYS Workbench for analysis, I have shown how structural optimization can balance stiffness, strength, and weight. The tables and formulas provided summarize key aspects, offering a comprehensive guide for engineers. As aircraft manufacturing moves towards greater automation, such optimized end effectors will be indispensable for achieving high-quality, efficient production.
In summary, the optimization process involves initial design, finite element analysis, stiffness enhancement, and topology-based lightweight design. Each step is validated through simulation, ensuring that the final support frame meets all operational demands. The end effector equipped with this frame can perform precise hole-making in aircraft assembly, contributing to the overall goals of digital manufacturing. This work exemplifies how computational tools can drive innovation in industrial robotics, particularly for specialized applications like aerospace.