In the semiconductor packaging industry, the integrated circuit (IC) substrate serves as a critical intermediary, connecting the chip to external circuits through meticulous fabrication processes. The efficiency and reliability of substrate testing and transmission directly impact overall production throughput. During detection, the substrate must be rapidly and precisely transferred between various workstations, a task predominantly handled by specialized robotic systems. Among these, the end effector of the substrate transmission robot plays a pivotal role. It is responsible for securely gripping and moving the substrate, and its structural integrity, stiffness, and dynamic performance are paramount for achieving high-speed, stable, and efficient operation. Any vibration, deformation, or instability in the end effector can lead to substrate misalignment, damage, or reduced transmission speed, thereby compromising the entire testing line’s productivity. Therefore, optimizing the design of the end effector to enhance its performance while reducing its weight—a key aspect for accelerating robotic arm movements and minimizing inertial loads—is of significant engineering importance. This work focuses on the structural topology optimization of such an end effector, aiming to develop a lightweight, high-stiffness design that maintains operational reliability under maximum load conditions.
Traditionally, structural optimization methods include size optimization and shape optimization. However, these approaches often rely on an initial design configuration and offer limited degrees of freedom for substantial improvement. Topology optimization, in contrast, is a more radical and innovative technique. It operates at a conceptual design level, determining the optimal material distribution within a given design space subject to loads and constraints, without being preconceived by existing structural forms. For the end effector, this means we can seek the most efficient load-bearing paths, potentially removing redundant material to achieve significant mass reduction. The primary objective here is to minimize the volume (and thus mass) of the end effector while ensuring that its maximum stress under operational load remains below the material’s yield strength and that its natural frequencies are sufficiently high to avoid resonance with the robot’s drive system. The constraint is the preservation of functional regions, such as mounting interfaces and substrate gripping surfaces. The performance metric is the structural compliance (inverse of stiffness), which we aim to minimize for a given volume fraction.
The initial step involved creating a three-dimensional geometric model of the end effector. To streamline subsequent finite element analysis (FEA) and reduce computational cost without sacrificing accuracy, non-essential features like small fillets, threaded holes, and minor chamfers were omitted during this preliminary modeling phase. The core structure was designed to provide a robust platform for substrate suction and attachment to the robotic arm. The material selected for the end effector was 7075 aluminum alloy, chosen for its excellent strength-to-weight ratio, which is crucial for high-speed robotic applications. Its key properties are summarized in Table 1.
| Property | Value | Unit |
|---|---|---|
| Elastic Modulus (E) | 71,000 | MPa |
| Poisson’s Ratio (ν) | 0.33 | – |
| Density (ρ) | 2,810 | kg/m³ |
| Yield Strength (σ_y) | 455 | MPa |
This model was then imported into ANSYS finite element analysis software for static structural and modal analyses. The static analysis is essential to verify that the end effector can withstand the maximum operational loads without failure. The primary load on the end effector arises from the vacuum suction holding the substrate. The maximum pressure exerted by the substrate was calculated to be approximately 0.026 MPa. This pressure was applied uniformly over the gripping surface area. The interface where the end effector connects to the robotic arm was defined as a fixed support, simulating a rigid connection. An automated meshing routine was employed with a global element size of 3 mm, resulting in a model with 4,540 elements and 9,536 nodes, ensuring a balance between solution accuracy and computational efficiency.
The static analysis yielded the von Mises stress distribution and total deformation of the initial end effector design. The results indicated that the maximum stress was concentrated at the connection region to the robotic arm, with a value of 1.3117 MPa. This is significantly lower than the yield strength of 455 MPa for 7075 aluminum, implying a substantial safety factor and confirming that the initial design is more than adequate from a pure strength perspective. The maximum deformation was found to be on the order of 10⁻⁵ mm, which is negligible for the precision requirements of substrate handling. While this validated the structural safety, it also highlighted an opportunity for optimization, as the low stress levels suggested the presence of excess material that could be removed without compromising performance.
Beyond static strength, the dynamic characteristics of the end effector are critical. In high-speed cyclic operations, excitation frequencies from the robot’s servo motors can induce vibrations. If these excitation frequencies coincide with the natural frequencies of the end effector, resonance occurs, leading to amplified vibrations, potential loss of precision, and accelerated fatigue. Therefore, a modal analysis was conducted to extract the first several natural frequencies and corresponding mode shapes of the end effector. The servo motors used in the transmission robot typically operate at a rated speed of 3,000 RPM, corresponding to a rotational frequency of 50 Hz. To avoid resonance, the end effector’s fundamental natural frequency should be sufficiently higher than this excitation frequency. The results of the modal analysis for the first four modes are presented in Table 2.
| Mode Order | Natural Frequency (Hz) | Mode Shape Description | Max Deformation (mm) |
|---|---|---|---|
| 1 | 146.83 | Swinging along the Z-axis | 0.05783 |
| 2 | 188.47 | Vertical bending in the Z-direction | – |
| 3 | 717.43 | Torsional vibration about the Z-axis | – |
| 4 | 731.13 | Coupled twisting in X and Z directions | – |
The data shows that the first natural frequency of the initial end effector design is 146.83 Hz, which is nearly three times the motor’s excitation frequency of 50 Hz. This indicates a good margin against resonance, affirming the design’s dynamic stiffness. However, the relatively high mass associated with the robust initial design could limit acceleration capabilities. This provided a clear direction for optimization: reduce mass while maintaining or even improving stiffness to keep natural frequencies high.
The core of this work lies in applying topology optimization to the end effector. The mathematical formulation for the topology optimization problem, based on the Solid Isotropic Material with Penalization (SIMP) method, can be expressed as follows:
Find the material density distribution \( \rho_e \) (where \( 0 < \rho_{min} \leq \rho_e \leq 1 \)) for each element \( e \) in the design domain \( \Omega \) that:
\[
\text{Minimize: } C(\boldsymbol{\rho}) = \mathbf{U}^T \mathbf{K}(\boldsymbol{\rho}) \mathbf{U} = \sum_{e=1}^{N} (\rho_e)^p \mathbf{u}_e^T \mathbf{k}_0 \mathbf{u}_e
\]
\[
\text{Subject to: } \frac{V(\boldsymbol{\rho})}{V_0} = f, \quad \mathbf{K}(\boldsymbol{\rho}) \mathbf{U} = \mathbf{F}, \quad 0 < \rho_{min} \leq \rho_e \leq 1
\]
where:
– \( C \) is the structural compliance (the objective function to minimize, inversely related to stiffness).
– \( \boldsymbol{\rho} \) is the vector of element densities.
– \( \mathbf{U} \) and \( \mathbf{F} \) are the global displacement and force vectors, respectively.
– \( \mathbf{K} \) is the global stiffness matrix, dependent on \( \boldsymbol{\rho} \).
– \( p \) is the penalization power (typically \( p=3 \)) to drive densities towards 0 or 1.
– \( V(\boldsymbol{\rho}) \) and \( V_0 \) are the optimized and initial volumes, respectively.
– \( f \) is the prescribed volume fraction.
In practical terms within ANSYS, we defined the optimization problem for the end effector. The regions where loads are applied (substrate contact surface) and constraints exist (arm mounting interface) were designated as non-design regions, meaning their material was preserved. The entire remaining volume of the end effector was set as the design domain, allowing the algorithm to freely redistribute material within it. The objective was to minimize compliance (maximize stiffness) with a constraint on material volume, aiming for a 20% reduction from the original volume. The optimization was run for 12 iterations, which was sufficient for convergence. The resulting material density contour plot showed areas where material was essential (high density, colored red/yellow) and areas where material could be removed (low density, colored blue). This output served as a conceptual blueprint for redesigning the end effector.
Guided by the topology optimization results, a new geometry for the end effector was conceived. The algorithm suggested removing material from the central web and internal sections of the structure where stress levels were low, effectively creating a more organic, truss-like or rib-reinforced design that followed the principal stress paths. The new design maintained all functional features but with a significantly different internal topology, featuring strategic voids and thinner walls in non-critical areas. This redesigned end effector model was then reconstructed in the CAD environment.
To validate the optimized end effector, a new round of finite element analysis was performed. The same boundary conditions and loads were applied. The static analysis results for the optimized end effector are summarized and compared with the initial design in Table 3.
| Parameter | Initial Design | Optimized Design | Change (%) |
|---|---|---|---|
| Mass (kg) | 0.12333 | 0.090399 | -26.7 |
| Max Von Mises Stress (MPa) | 1.3117 | 1.704 | +29.9 |
| Max Total Deformation (mm) | 2.5718 × 10⁻⁵ | 2.9789 × 10⁻⁵ | +15.8 |
| First Natural Frequency (Hz) | 146.83 | 138.08 | -5.95 |
The results are compelling. The mass of the end effector was reduced by 26.7%, achieving the primary goal of lightweighting. This reduction directly translates to lower inertia, allowing for faster acceleration and deceleration of the robotic arm, potentially increasing the overall cycle speed of the substrate transmission process. The maximum stress in the optimized end effector increased to 1.704 MPa, which is a 29.9% rise from the initial design but remains critically well below the 455 MPa yield strength of the material. The safety factor is still exceedingly high, confirming structural integrity. The slight increase in maximum deformation (15.8%) is negligible in practical terms and does not affect the positioning accuracy required for substrate handling. Furthermore, the first natural frequency decreased slightly by 5.95% to 138.08 Hz. While there is a minor reduction, this frequency is still far above the 50 Hz excitation frequency, maintaining a strong margin against resonance. The higher-order modes also remained at elevated frequencies. This demonstrates that the topology optimization successfully removed inefficient material while preserving the global stiffness and dynamic performance of the end effector.
The success of this optimization can be further understood by examining the stress flow in the new design. The topology optimization algorithm essentially identified and reinforced the primary load-bearing paths between the load application point (substrate) and the fixed support (robotic arm). Material was removed from regions subjected to minimal stress, leading to a more efficient structure. The relationship between stress, strain, and displacement in the linear elastic regime is governed by Hooke’s Law and the equilibrium equations, which for the finite element formulation are solved iteratively during the optimization process. The final design of the end effector embodies a balance where the stiffness-to-mass ratio is significantly improved.
In conclusion, this study demonstrates the effective application of topology optimization in the structural design of an end effector for a high-speed IC substrate transmission robot. By employing finite element-based static and modal analysis followed by a systematic topology optimization routine, a new end effector geometry was developed. The optimized end effector achieves a substantial 26.7% reduction in mass, directly contributing to the goal of lightweighting for enhanced dynamic performance. Crucially, this weight reduction was accomplished without compromising operational safety, as the maximum stress remains orders of magnitude below the material yield limit, and the dynamic characteristics are preserved with natural frequencies safely distant from potential excitation sources. The methodology outlined—combining digital prototyping, FEA validation, and advanced topology optimization—provides a robust and efficient framework for designing high-performance, lightweight components in robotics and automation. For the specific application of substrate handling, this optimized end effector design promises to contribute to faster, more stable, and more energy-efficient transmission cycles, ultimately supporting higher throughput in semiconductor manufacturing. Future work could involve prototyping and experimental validation of the optimized end effector, as well as exploring multi-objective optimization including thermal effects or fatigue life for even more comprehensive design improvement.