# Prediction of Tooth Profile Deviation for WEDM Rigid Gears Based on ISSA-LSSVM
## 1 Introduction
These methods allow for higher precision and the ability to handle intricate designs that are challenging for traditional techniques. [PERSON] et al. [13] studied the effect of WEDM process parameters on surface morphology, highlighting its significant impact on gear quality. Additionally, the importance of free-form milling has been underscored in the recent literature. This method offers a universal tool geometry and the ability to machine various gear types and sizes within one manufacturing system. Studies have shown that free-form milling enhances the quality and performance of gears by providing higher flexibility and precision [14]. Moreover, the emergence of 5-axis double-flank CNC machining for spiral bevel gears presents new opportunities in flank form design and manufacturing, overcoming kinematic restrictions of traditional methods [15]. However, there are limited studies on the impact of actual machining process parameters and changes in tooth profile deviations. In this paper, we investigate the tooth profile machining process of rigid gears, a key challenge in the manufacturing process of harmonic gears. The study utilizes wire electrical discharge machining (WEDM), a machining method that employs pulsed spark discharges from an electrode wire to machine workpieces. Unlike conventional machining technologies that rely on mechanical force and energy, WEDM can machine workpieces with complex shapes [16; 17]. Currently, the setting of WEDM process parameters mostly relies on the operator's experience, which is unable to adapt to the processing of variable working conditions and affects the processing quality of the workpiece. Prediction problems have been tackled using a range of algorithms in recent years, including neural networks, random forests, support vector machines (SVMs), and the least squares support vector machine (LSSVM) [18; 19; 20; 21]. Neural networks, despite their complex structure, have poor generalization ability. Random forest has drawbacks, including a long training time and poor interpretability. An SVM is primarily used for classification problems and is not well-suited for data prediction. For this particular study, we have chosen to use the LSSVM as the preferred predictive algorithm model. The LSSVM is an efficient machine learning technique employed when dealing with limited sample data analysis. However, it encounters challenges regarding intricate parameter selection and a lack of interpretability [22]. In order to tackle this issue, researchers have been investigating the application of various methods like particle swarm optimization (PSO), grey wolf optimization (GWO), genetic algorithm (GA), and others for the purpose of optimizing parameter selection [23; 24; 25]. This practice has led to an enhancement in prediction accuracy. The sparrow search algorithm (SSA) is a commonly used intelligent optimization algorithm. However, as with other algorithms, increasing the number of iterations can result in a reduction in population diversity, leading to a tendency for local optimization. Hence, the objective of this research is to enhance the diversity of the SSA through the utilization of a hybrid strategy. Additionally, the parameters in the LSSVM model are optimized to make it more suitable for predicting the tooth profile deviation in rigid gears with limited sample sizes. In summary, this paper presents a novel approach to predict tooth profile deviation in rigid gears by proposing an ISSA-optimized LSSVM model. By incorporating Tent chaotic mapping, adaptive adjustment strategy, dynamic adaptive weights, and grey wolf hierarchy strategy to refine the SSA algorithm, the LSSVM model is enhanced. Based on these improvements, an ISSA-LSSVM model is established to accurately predict tooth profile deviation in rigid gears using WEDM experimental data as input. The study's primary components are categorized as follows: In Section 2, the algorithmic principles and innovations of the research are outlined. Section 3 presents the experimental design and data analysis.