# Research on the Tooth Surface Integrity of Non-Circular Gear WEDM Based on HPSO Optimization SVR
## 1 Introduction  
As a non-traditional machining process, WEDM has unique advantages in manufacturing non-circular gears, because it has no cutting stress [1; 2; 3], can machine conductive materials of any hardness [4; 5; 6; 7], and can cut shaped parts that are difficult to cut using ordinary machining methods [4; 8]. The entire profile of a non-circular gear can be machined in a single setup, and the shape accuracy, dimensional accuracy, and surface quality required for actual production of the part can be achieved. [PERSON] et al. [9] thought WEDM might prove to be the only technology available to manufacture proper non-circular gears. Moreover, research has shown that the isotropic surface structure formed by WEDM leads to beneficial tribological conditions in rolling contact, which allows WEDM machined gears to reach a 228% higher number of load cycles for a load level in the finite life region than common profile ground gears [10]. Moreover, a large number of studies have shown that the structural damage of many parts starts and expands from the surface and dozens of microns below the surface [11]. The traditional single surface roughness cannot describe the physical and mechanical metallurgical properties of parts under the surface, so it is necessary to use surface integrity to describe the surface of parts. Therefore, it is of great significance to study the relationship between process parameters and the surface integrity evaluation indicators, and to predict and optimize surface integrity during WEDM machining of non-circular gears. Creating explicit mathematical models for surface integrity prediction based on fundamental knowledge of the physics of the machining process is associated with severe difficulties, because this process is a combination of many physical phenomena [12]. Machine learning algorithms have been used in many fields to predict the outcomes of laborious and expensive experiments whose outcomes are difficult to determine analytically. These fields include, but are not limited to, physics, health, materials science, electrical, civil, andmechanical engineering [13; 14; 15; 16; 17; 18]. In the area of the intelligent prediction of surface integrity, [PERSON] et al. [19] studied the prediction and analysis of titanium alloy milling parameters based on a support vector machine, compared it with a BP neural network model, and concluded that the support vector machine model was more suitable for small sample data than the BP neural network model. [PERSON] et al. [20] proposed an online estimation method for workpiece height in reciprocating wire EDM based on support vector regression and verified the method's effectiveness through experiments. [PERSON] et al. [21] developed artificial neural networks and adaptive neuro-fuzzy inference system models that could predict the through-thickness residual stress profiles in stainless steel pipe girth welds. Comparing the two models, the results showed that the neuro-fuzzy systems optimized using a hybrid technique performed slightly better than the neural network trained using the Levenberg-Marquardt algorithm. [PERSON] et al. [22] established a regression equation to predict the surface roughness, surface crack density, and overcutting of EDM copper. [PERSON] et al. [18] used peak current, wire tension, wire feed rate, and pulse on and off time as process parameters to predict the slicing speed and surface roughness of monocrystalline silicon in WEDM based on support vector regression, compared different kernel functions used for modelling, and reached the conclusion that the radial basis function had the best effects. Currently, there are no references for predicting the various indicators of surface integrity of non-circular gears using WEDM. Most of the literature only studied specific materials, and only one or two surface integrity evaluation indicators were selected for research, which is less comprehensive than the three surface integrity evaluation indicators selected in this study.