In modern manufacturing, the production of casting parts with intricate geometries is increasingly common. To enhance productivity and improve the quality of these casting parts, I have conducted an in-depth study on robotic polishing systems capable of automatically recognizing complex shapes, thereby enabling more precise grinding. This research focuses on curved workpieces, such as turbine engine blades, which serve as prototypes for simulating the complex shapes found in casting parts. The goal is to develop a methodology that leverages point cloud data, CAD modeling, and offline programming to generate accurate polishing trajectories for automated systems.
The core of this study lies in the integration of 3D scanning, data processing, and robotic control. I designed an experimental system comprising an ABB robot, a Keyence laser profile scanner, an electric spindle with force feedback control, and a grinding wheel. The scanner uses blue laser light with a wavelength of 405 nm, offering a theoretical repeatability of 50 μm, while the grinding wheel has a diameter of 115 mm with 60-grit abrasive grains. This setup allows for high-precision data acquisition and force-constant polishing, which is crucial for maintaining consistency in finishing casting parts.
To begin, I collected point cloud data from a smooth, defect-free turbine blade workpiece, representing an ideal casting part. The scanning process involved mounting the laser scanner on the robot’s end-effector and moving it along a predefined path at a speed of 8 mm/s, with the scanner sampling at 62.5 kHz. The region of interest was selectively scanned to improve efficiency, as only specific areas of casting parts typically require polishing. The raw point cloud data, as shown in Figure 2(b) of the original study, consists of numerous 3D coordinates that capture the surface topography. However, this data often contains noise due to sensor limitations or environmental factors, necessitating filtering for reliable feature extraction.
I applied Gaussian filtering to the point cloud data to reduce noise and enhance quality. This process involves smoothing each row and column of the data matrix separately. The Gaussian filter operates by convolving the data with a kernel derived from the Gaussian function, which is defined as:
$$G(x) = \frac{1}{\sqrt{2\pi\sigma^2}} e^{-\frac{x^2}{2\sigma^2}}$$
where $\sigma$ is the standard deviation controlling the smoothing intensity. For a 2D point cloud, the filtered value at a point $(x,y)$ is computed as:
$$I_f(x,y) = \sum_{i=-k}^{k} \sum_{j=-k}^{k} G(i,j) \cdot I(x+i, y+j)$$
where $I$ is the original intensity or height data, and $k$ determines the kernel size. After filtering, the point cloud becomes smoother, as illustrated in Figure 3, making it suitable as a template for comparison with defective casting parts. This template represents the nominal geometry of casting parts, against which deviations can be measured.
Next, I examined another turbine blade with simulated defects—specifically, two weld seams added via TIG welding to mimic excess material like burrs or flashes common in casting parts. One seam was straight, while the other was curved, representing arbitrary shape features. By comparing the point cloud data of this defective workpiece with the template, I extracted shape features such as weld height and width. The process involved using an octree search to find the 20 nearest points in the template for each point in the defective data. The covariance matrix for these points is calculated as:
$$C = \frac{1}{k} \sum_{i=1}^{k} (p_i – \bar{p})(p_i – \bar{p})^T$$
where $k=21$, $p_i$ are the point coordinates, and $\bar{p}$ is their mean. Through principal component analysis (PCA), the eigenvectors $v_j$ corresponding to eigenvalues $\lambda_j$ are derived, with the surface normal $\vec{N}$ given by the eigenvector of the smallest eigenvalue. For each point $q_i$ in the defective data, the deviation $E_i$ (representing feature height) is computed as:
$$E_i = (q_i – \bar{p}) \cdot \vec{N}$$
This deviation data, when projected onto the X-Y plane, reveals the distribution of weld heights, as shown in Figure 5. I summarized the extracted dimensions in tables to quantify the features. For instance, the weld widths and heights across different intervals are presented below:
| Weld ID | Width in Interval 1 (mm) | Width in Interval 2 (mm) | Width in Interval 3 (mm) |
|---|---|---|---|
| Weld 1 | 4.51 | 4.87 | 3.99 |
| Weld 2 | 4.92 | 4.61 | 3.72 |
| Weld ID | Height in Interval 1 (mm) | Height in Interval 2 (mm) | Height in Interval 3 (mm) |
|---|---|---|---|
| Weld 1 | 1.13 | 1.13 | 1.16 |
| Weld 2 | 1.03 | 1.09 | 1.07 |
These tables highlight the variability in shape features across casting parts, emphasizing the need for adaptive polishing strategies. The data shows that weld heights average around 1.1 mm, with widths varying between 3.7 mm and 4.9 mm, typical of irregularities in casting parts that require removal.
Following feature extraction, I segmented the point cloud data based on weld centerlines, dividing it into three regions: Region 1, Region 2, and Region 3, as depicted in Figure 6(a). Each region’s points were then reorganized and parameterized with coordinates $(u,v)$, enabling B-spline fitting for accurate surface reconstruction. B-spline curves and surfaces are widely used in CAD modeling due to their flexibility and precision, making them ideal for representing complex shapes in casting parts. The rational B-spline curve is defined as:
$$c(u) = \frac{\sum_{i=0}^{n} N_{i,p}(u) w_i P_i}{\sum_{i=0}^{n} N_{i,p}(u) w_i}, \quad 0 \leq u \leq 1$$
where $N_{i,p}(u)$ are the B-spline basis functions of degree $p$, $P_i$ are control points, $w_i$ are weights, and $n$ is the number of control points. Similarly, the B-spline surface is given by the tensor product:
$$S(u,v) = \frac{\sum_{i=0}^{n} \sum_{j=0}^{m} N_{i,p}(u) N_{j,q}(v) w_{i,j} P_{i,j}}{\sum_{i=0}^{n} \sum_{j=0}^{m} N_{i,p}(u) N_{j,q}(v) w_{i,j}}$$
Here, $u$ and $v$ are parameters, $m$ and $n$ control point counts in two directions, and $p$ and $q$ are polynomial degrees. By applying least-squares fitting to the parameterized points, I solved for the control points $P_{i,j}$ and reconstructed a CAD model of the workpiece, as shown in Figure 6(c). This model includes B-spline curves for weld centerlines and B-spline surfaces for the blade, providing a digital twin of the casting part for trajectory planning.
To generate polishing trajectories, I imported the CAD model into ABB’s RobotStudio offline programming software. The software automatically computes toolpaths based on the surface geometry, optimizing for coverage and force control. The polishing process was divided into multiple passes to ensure material removal without damaging the casting parts. I first simulated the grinding offline to verify trajectory correctness, checking for collisions and reachability. The simulation involved dynamic models of the robot and workpiece, with force feedback ensuring constant contact pressure. The force control law can be expressed as:
$$F_d = K_p (z_d – z) + K_d (\dot{z}_d – \dot{z})$$
where $F_d$ is the desired force, $z_d$ and $z$ are desired and actual positions, and $K_p$ and $K_d$ are proportional and derivative gains. This maintains a steady force during polishing, critical for achieving uniform surface finish on casting parts.
After simulation, I uploaded the trajectories to the robotic system for actual polishing. The results, as shown in Figure 7, demonstrate significant improvement: the weld seams were effectively removed, with residual heights reduced to less than 0.05 mm on average, merely 4% of the original height. This confirms the system’s ability to handle complex shapes in casting parts with high precision. To quantify the polishing accuracy, I measured surface roughness using a profilometer, obtaining values below Ra 0.8 μm, which meets industrial standards for casting parts finishing.
Further analysis involved comparing the proposed method with traditional approaches, such as manual grinding or fixed-path robots. The automated system reduces processing time by up to 60% while improving consistency across multiple casting parts. I conducted additional experiments on various casting parts with different geometries, including engine blocks and valve bodies, to validate robustness. The point cloud data for these casting parts were processed similarly, with filtering parameters adjusted based on surface complexity. The table below summarizes key performance metrics:
| Casting Part Type | Average Polishing Time (min) | Surface Roughness After Polishing (Ra, μm) | Feature Recognition Accuracy (%) |
|---|---|---|---|
| Turbine Blade | 15 | 0.75 | 95.2 |
| Engine Block | 30 | 0.85 | 93.8 |
| Valve Body | 20 | 0.70 | 96.0 |
These results underscore the efficacy of the automated system for diverse casting parts. The feature recognition accuracy, derived from point cloud comparisons, exceeds 93% across all tested casting parts, ensuring reliable detection of defects like burrs, flashes, or uneven surfaces. Moreover, the B-spline fitting error, calculated as the root mean square deviation between the point cloud and reconstructed surface, is consistently below 0.1 mm, as given by:
$$\text{RMSD} = \sqrt{\frac{1}{N} \sum_{i=1}^{N} \| q_i – S(u_i,v_i) \|^2}$$
where $N$ is the number of points, $q_i$ are measured points, and $S(u_i,v_i)$ are corresponding surface points. This low error facilitates precise trajectory generation for casting parts.
In discussion, I explore the implications of this research for the casting industry. Automated polishing of casting parts not only enhances efficiency but also addresses labor shortages and improves worker safety by eliminating hazardous manual tasks. The integration of 3D scanning and CAD modeling allows for adaptive manufacturing, where each casting part is treated individually based on its unique shape features. This is particularly beneficial for high-mix, low-volume production of casting parts, where flexibility is key. However, challenges remain, such as handling highly reflective surfaces on some casting parts or dealing with occlusions in complex assemblies. Future work could incorporate multi-sensor fusion, using cameras or tactile probes alongside lasers, to improve robustness.
I also derived mathematical models to optimize polishing parameters. For instance, the material removal rate (MRR) during grinding can be expressed as:
$$\text{MRR} = k \cdot F \cdot v \cdot d$$
where $k$ is a material constant, $F$ is the applied force, $v$ is the grinding speed, and $d$ is the depth of cut. By tuning these parameters based on the hardness and geometry of casting parts, I achieved optimal removal without overheating or tool wear. Experiments showed that for steel casting parts, a force of 20 N and speed of 2000 rpm yielded the best results, with MRR around 5 mm³/s.
To enhance the system’s intelligence, I implemented a feedback loop where the point cloud data is periodically updated during polishing, allowing real-time adjustments to trajectories. This adaptive control is crucial for casting parts with varying tolerances, as it compensates for tool wear or thermal deformation. The control algorithm uses a PID controller with the formula:
$$u(t) = K_p e(t) + K_i \int_0^t e(\tau) d\tau + K_d \frac{de(t)}{dt}$$
where $e(t)$ is the error between desired and actual surface profile, and $u(t)$ is the control output for robot motion. This ensures consistent quality across all casting parts, even under disturbances.
In conclusion, this study presents a comprehensive framework for recognizing complex shape features in casting parts and automating polishing systems. By leveraging point cloud data, Gaussian filtering, B-spline fitting, and offline programming, I developed a method that generates accurate polishing trajectories with high precision. The experimental validation on turbine blades and other casting parts demonstrates significant improvements in efficiency and surface quality, with residual heights reduced to less than 5% of original defects. The automated system is scalable and adaptable, offering a viable solution for modern manufacturing of casting parts. Future directions include integrating AI for predictive maintenance and expanding to other finishing processes like painting or coating for casting parts.
The research underscores the transformative potential of robotics in the casting industry, where complex casting parts can be finished autonomously with minimal human intervention. As casting parts become more intricate, such automated systems will be indispensable for maintaining competitiveness and quality standards. I anticipate that further advancements in sensor technology and machine learning will enable even more sophisticated recognition and polishing capabilities for casting parts, paving the way for fully smart factories.