This study proposes a model for the erosion cutting profile to predict the cutting depth under different process parameters for abrasive waterjet (AWJ) cutting. The model follows the Gaussian distribution and is experimentally validated. Additionally, the effects of the dimensional characteristics and process parameters on the kerf geometry were analyzed. It was found that the water pressure, abrasive flow rate, and focusing tube traverse speed changed the slope of the kerf wall without changing the kerf width. However, the standoff distance (SOD) changes the kerf width, whereas the slope of the kerf wall induces minor changes. Furthermore, based on the first-order derivation of the extracted kerf profile, the relationship between jet energy, cutting depth, and kerf width was analyzed. The experimental results revealed that: 1) the relationship between the reduction in the jet energy distribution and cutting depth is non-linear; 2) the jet energy distribution is smallest at the kerf top edge and bottom section. The predictive cutting depth model and jet energy distribution will enable the subsequent optimization of process parameters in the AWJ process.
Since its inception as an emerging versatile and cool-machine processing technology, abrasive waterjet (AWJ) machining has been acclaimed for its extraordinary advantages over traditional machining technologies and holds great promise for the next generation of low-cost , high-efficiency , and pollution-free processing technologies . However, the cutting depth and energy distribution are high-precision machining parameters in AWJ. For practical applications, controllable and precise cutting depths are a topic of great interest.
The cutting depth model has been widely studied by several researchers from various perspectives. Previous research exploring erosive processes adopted a mathematical model using the erosion model and impact damage to develop the maximum cutting depth . Huang et al.  developed a modified erosion model using kinematic jet-solid penetration to predict the cutting depth based on different erosion methods along the kerf. Paul et al.  introduced the concept of a generalized kerf shape by AWJ to develop the total cutting depth, which considers the along-kerf width and increasing cutting depth. Mohankumar et al.  used modified process parameters to attain the peak cutting depth and develop a semi-empirical equation using Buckingham’s theorem. Niranjan et al.  experimentally and systematically determined the cutting depth using a profile projector to investigate the effects of process parameters. Ketan et al.  experimented with an AA2014 alloy to establish a predictive cutting depth using a fuzzy-logic technique. Recently, surface roughness and cutting depth have also been studied. Ozcelik et al.  used different cutting parameters to develop a cuttability abacus to predict the cutting depth and surface roughness. Aydin et al.  investigated the machinability of granite to relate the cutting depth to the cutting wear zone using a Taguchi orthogonal array. Nie et al.  studied the effect of different water pressures on the cutting depth to analyze the topographic characteristics and formation mechanisms of the cut faces. Yuvaraj et al.  used the variation in the erosion angle to analyze its effect on the cutting depth and machining quality. Aydin et al.  conducted an experimental investigation to evaluate the cutting process, cutting depth, surface roughness, and kerf angle of granite.
This study proposes a mathematical model of cutting depth based on the ductile material erosion process, in which the jet energy distribution follows a Gaussian function. This analytical model analyzes the change in kerf width following the cutting depth through micro-cutting and plastic deformation, which is explained using a Gaussian distribution. In addition, first-order partial derivatives of the profile prediction model of the cutting depth and kerf width were performed to analyze the distribution of jet energy and its jet decline process. The study is summarized as follows:
(1) Kerf profiles, such as binarization and image filling, are characterized by digital image processing and statistical analysis of their surface morphology. The extracted profiles were profile-fitted using a stepwise approximation. The stepwise approximation of the kerf profiles strongly corresponds to the predicted profiles.
(2) Combined with the Gaussian distribution of the jet cutting depth and width, the mathematical model calculates variations in the erosion angle and jet energy at different cutting depths during micromachining. The correlation coefficients between the experimental and predicted values of the aluminum 6061 alloy, 304 stainless steel, and Ti6Al4V are 0.9643, 0.9912, and 0.9753, respectively, which shows that the predicted value is highly correlated with the experimental value.
(3) Based on the first-order partial derivatives of the kerf profile, it is clear that the slopes of the kerf profile vary at different profile widths. At the kerf top edge and bottom, the slope of the profile is the smallest and close to zero, whereas at the kerf top edge and bottom, the slope of the profile increases and then decreases, which verifies that the energy of the jet plume is the lowest at the edge and bottom of the kerf, whereas the energy is the highest within the kerf profiles.