Modeling of Cutting Based on Fracture Mechanics and FEM
There is a huge potential for automation of cutting fruits and vegetables in the kitchen and food industry as this can not only save time and labor on meal preparation and food packaging but also improve workspace safety. Foods may undergo large deformations, and the knife can experience different forces, which together make it difficult to carry out cutting as intended. With an accurate model, the contact force between the knife and the cutting board can be extracted from the sensor data for control to realize a smooth knife movement.
To model fracture and deformation during a cutting action, the use of an object's 3D mesh model can be computationally prohibitive for achieving a desired accuracy since numerous tiny elements must be used near the knife's moving edge. To address this issue, we represent the object as evenly spaced slices normal to the cutting plane such that the 3D modeling task is reduced to multiple 2D modeling tasks followed by an interpolation. We present a procedure that computes the area of fracture and shape deformation created by cutting via solution of an energy-based equation. Fracture propagates whenever the energy release rate exceeds the material's fracture toughness.
To understand the reduction in the cutting force with a slice motion, we have performed a stress-based analysis to derive a closed form which shows that the fracture toughness (measured as the ratio to its value during a downward knife motion) depends on the slice-push ratio as well as Poisson's ratio in a highly nonlinear manner. This contrasts with prior models assuming a reduction rate proportional to the slice-push ratio only. Modeling is completed over the effects of the knife's edge geometry and cutting path (with translation and rotation).
Experiments with an Adept arm and a WAM arm have been conducted numerous food items have demonstrated good matches between the modeled force, torque, and work experienced by the knife, and the measurements by a six-axis force/torque sensor. They have yielded precision depth cuts that would not be possible without deformable modeling.
Our cutting scheme has also been incorporated into a cutting control strategy from the authors' research lab to perform the knife skill of rock chop on soft objects. For more information, we refer to the following submission:
For more information, we refer to the following submission:
- Prajjwal Jamdagni and Yan-Bin Jia. Robotic Cutting of fruits and vegetables: modeling the effects of deformation, fracture toughness, knife edge geometry, and motion. IEEE Transactions on Robotics, 2024. DOI: 10.1109/TRO.2024.3462943.
- Prajjwal Jamdagni and Yan-Bin Jia. Robotic slicing of food and vegetables: Modeling the effects of fracture toughness and knife geometry. In Proceedings of the IEEE International Conference on Robotics and Automation, pp. 6607-6613, Xi'an, China, May 30-Jun 5, 2021.
- Prajjwal Jamdagni and Yan-Bin Jia. Robotic Cutting of Solids Based on Fracture Mechanics and FEM. In Proceedings of the IEEE International Conference on Intelligent Robots and Systems, pp. 8246-8251, Macau, China, Nov 3-8, 2019.
This material is in part based upon work supported by the National Science Foundation under Grant IIS-1651792.
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the
author(s) and do not necessarily reflect the views of the National Science Foundation.
Last updated on Sep 30, 2024.