⚡ electrical engineering

A non-planar slicing and hybrid path generation method for robotic wire arc additive remanufacturing of large sprockets

This paper proposes a software–hardware integrated system featuring a non-planar slicing and hybrid path generation method that utilizes curved-layer conformal slicing and coordinate transformation to achieve high-quality, defect-free remanufacturing of large sprockets by overcoming geometric mismatches and motion interference inherent in conventional planar slicing.

Original authors: Jiahua Chen, Renpei Liu, Weihang Liu, Shuaikang Wang, Yuhang Zhu, Yanhong Wei

Published 2026-06-25

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CC BY 4.0

Original authors: Jiahua Chen, Renpei Liu, Weihang Liu, Shuaikang Wang, Yuhang Zhu, Yanhong Wei

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a giant, heavy-duty gear (a sprocket) used in a coal mine conveyor belt. Over time, the "teeth" of this gear get chewed up, worn down, or chipped away. Usually, the only fix is to throw the whole thing away and buy a new one, which is expensive and causes downtime.

This paper describes a clever new way to "heal" these damaged gears using a robotic arm that acts like a super-precise welding torch. Instead of just melting metal on top of the gear, the robot builds it back up layer by layer, a process called Wire Arc Additive Remanufacturing (WAAR).

Here is the simple breakdown of the problem and the solution proposed in the paper:

The Problem: The "Staircase" and the "Gravity Slide"

Imagine trying to build a sandcastle on a steep, curved hill using flat, square bricks.

The Staircase Effect: If you use flat layers (like standard 3D printing), the curved surface of the gear tooth looks like a jagged staircase. It doesn't fit the original shape perfectly.
The Gravity Slide: Because the gear teeth are deep, curved valleys (called "gullets"), if you try to lay down molten metal on a flat layer, the hot metal wants to slide down the slope due to gravity. It pools at the bottom, creating a messy, uneven blob instead of a smooth repair.
The Robot's Dilemma: The robot arm has to twist and turn to reach these deep, narrow spaces. If it tries to follow a flat path on a curved surface, the torch might hit the gear itself, or the robot might get stuck in a position where it can't move smoothly.

The Solution: "Curved Layers" and "Splitting the Job"

The researchers built a custom system (hardware and software) to solve this. Think of it as upgrading the robot's brain and tools.

1. The "Onion Peeling" Strategy (Non-Planar Slicing)
Instead of slicing the gear model into flat, horizontal layers (like slicing a loaf of bread), they sliced it like peeling an onion.

The Analogy: Imagine the damaged gear is a bumpy hill. Instead of cutting horizontal slices through the hill, they created "skins" that hug the exact shape of the hill.
The Result: The robot now lays down metal in layers that curve with the gear. This means the molten metal sits flat on the surface it's being deposited on, so it doesn't slide down. It fits the "skin" of the gear perfectly.

2. The "Splitting the Puzzle" Strategy (Region-wise Slicing)
The space between two gear teeth is very narrow and curved. Trying to fix the whole valley at once is too hard for the robot; it would have to twist its arm into impossible angles.

The Analogy: Imagine trying to paint the inside of a deep, curved bowl. It's hard to reach the middle without hitting the sides. The researchers decided to split the bowl in half right down the middle (at the point of sharpest curve).
The Result: They treated the left side of the valley and the right side as two separate, smaller jobs. This made it much easier for the robot to find a comfortable angle to weld without bumping into the gear.

3. The "Flat Map" Trick (Hybrid Path Generation)
How do you tell a robot to draw a zigzag pattern on a curved, 3D surface? It's mathematically very hard.

The Analogy: Imagine you want to draw a pattern on a crumpled piece of paper. Instead of trying to draw directly on the crumpled mess, you first flatten the paper out, draw your perfect zigzag lines on the flat sheet, and then carefully wrap the paper back onto the object.
The Result: The computer takes the curved layer, mathematically "flattens" it into a 2D plane, draws the perfect zigzag filling pattern, and then "wraps" those lines back onto the 3D curve. This ensures the robot moves smoothly and fills the area evenly without getting confused by the curves.

The Results: A Smooth, Strong Repair

The team tested this on a real, damaged mining sprocket.

Old Way (Flat Layers): The metal slid around, formed uneven bumps, and looked like a messy staircase.
New Way (Curved Layers): The repair was smooth. The metal stayed exactly where it was put, filling the deep valleys perfectly. There were no gaps, no sliding metal, and the final shape matched the original gear almost exactly.

In short: By making the robot "think" in curved layers instead of flat ones, and by breaking the complex job into smaller, manageable pieces, they successfully repaired a massive, damaged industrial gear with high precision and no wasted material.

Technical Summary: Non-Planar Slicing and Hybrid Path Generation for Robotic WAAR of Large Sprockets

Problem Statement
Large mining coal machinery sprockets are critical components prone to wear, spalling, and local failure in the transition areas between teeth and gullet surfaces. These damaged regions are characterized by complex concave curved surfaces, significant curvature variations, and restricted spatial accessibility. Conventional Wire Arc Additive Remanufacturing (WAAR) using planar slicing strategies faces significant challenges in this context:

Geometric Mismatch: Planar layers do not conform to the substrate's curved surface, leading to poor interface quality.
Robot Interference: The narrow space between sprocket teeth limits torch posture, often causing spatial interference or forcing the robot into singular configurations.
Process Instability: Gravity-induced molten metal flow causes bead collapse and uneven formation on steep or concave surfaces.
Staircase Effect: Planar slicing on curved surfaces results in significant geometric deviations and surface roughness.

Existing methods, such as cylindrical coordinate slicing or isothermal surface slicing, are either limited to specific rotational geometries or incur prohibitive computational costs for large, complex models.

Methodology
The authors propose a software–hardware integrated WAAR system and a novel path planning framework consisting of three core components:

Integrated Hardware-Software System:
- Hardware: A 6-axis welding robot combined with a 2-axis positioner (tilting and rotating) to form an 8-axis coordinated system. This setup optimizes torch posture, keeping the torch axis perpendicular to the curved surface to mitigate gravity-induced metal flow. A handheld 3D laser scanner is used for reverse engineering the damaged workpiece.
- Software: A workflow utilizing Rhino and Grasshopper for parametric modeling, non-planar slicing, and path generation, integrated with custom robot motion planning software.
Region-Wise Non-Planar Slicing:
- Offset Surface Construction: Instead of horizontal planes, the method constructs a family of offset surfaces based on the substrate's curved geometry. The offset distance is calculated using layer thickness parameters ( $\Delta h$ ) and a reference surface normal vector.
- Region Segmentation: Recognizing that the entire concave gullet is too complex for a single global path, the damaged model is segmented at the maximum curvature transition boundary. This divides the repair area into two sub-regions, reducing the variation range of surface normals and simplifying robot kinematic constraints for each sub-region.
- Mesh Intersection: The offset surfaces are intersected with the damaged model's STL mesh to extract internal layer boundaries, ensuring the sliced layers conform to the specific geometry of the damaged region.
Transformation-Projection-Based Hybrid Path Generation:
- Coordinate Transformation: To avoid the instability of direct 3D path construction, the non-planar slicing layer is rotated via a rigid transformation matrix (Rodrigues rotation) so that its average normal aligns with the global Z-axis.
- 2D Infill Generation: In this transformed 2D plane, a standard zigzag infill path is generated using polygon offsetting (Clipper algorithm) and scanline clipping. Parameters include boundary distance, track spacing, and infill angle.
- Inverse Projection: The 2D path points are mapped back to the 3D curved surface using ray-triangle intersection to ensure points lie precisely on the mesh. Finally, an inverse coordinate transformation restores the path to the original workpiece coordinate system.

Key Contributions

Non-Planar Slicing Framework: The development of a Grasshopper-based parametric workflow that generates conformal, non-planar layers by offsetting a reference surface, replacing traditional planar slicing for complex curved substrates.
Region-Wise Segmentation Strategy: A novel approach to decompose complex concave damaged zones (sprocket gullets) at curvature boundaries, enabling feasible robot motion planning in restricted spaces.
Hybrid Path Generation Algorithm: A method that reduces 3D curved-surface path planning to a stable 2D problem through coordinate transformation, 2D infill generation, and inverse projection, ensuring spatial consistency and parameter controllability.
Integrated System Validation: The establishment of a complete WAAR system (8-axis robot + positioner + custom software) specifically tailored for the remanufacturing of large sprockets.

Experimental Results
Repair experiments were conducted on a damaged large sprocket using J507 flux-cored wire.

Formability: Compared to planar slicing, the proposed method produced a uniform outer-contour weld bead with smooth transitions, eliminating metal flow and boundary collapse. Internal filling showed no macroscopic lack of fusion or defects.
Geometric Accuracy: Point-wise coordinate measurements of the repaired surface revealed:
- X-direction deviations: -0.27 mm to -0.21 mm.
- Y-direction deviations: 0.59 mm to 0.61 mm.
- Z-direction (height) deviations: 0.09 mm to 1.54 mm (average 0.82 mm).
Process Stability: The multi-layer repair demonstrated consistent bead stability and complete filling of the damaged region without visible defects.

Significance and Claims
The paper claims that the proposed method effectively overcomes the geometric constraints of complex curved surfaces in WAAR. By integrating non-planar slicing with a hybrid path generation strategy, the system achieves:

Improved Accessibility: The 8-axis configuration and region-wise segmentation allow the robot to access restricted tooth spaces without interference.
Enhanced Quality: The conformal layers prevent molten metal flow and ensure good formability, addressing the limitations of planar slicing on irregular surfaces.
Controllability and Repeatability: The transformation-projection method provides a stable, parameterizable workflow that satisfies the requirements for industrial robotic path planning.
Engineering Applicability: The successful repair of a typical damaged sprocket validates the feasibility of this approach for high-value, large-scale component remanufacturing in harsh operating environments.

The Problem: The "Staircase" and the "Gravity Slide"

The Solution: "Curved Layers" and "Splitting the Job"

The Results: A Smooth, Strong Repair

Technical Summary: Non-Planar Slicing and Hybrid Path Generation for Robotic WAAR of Large Sprockets

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