# Modification and Optimization of Cycloidal Gear Tooth Profile Based on Machining Error Compensation
## 1 Introduction
[23] divided the synthesis of machining tolerances into three steps, finally obtaining the best machining process diagram. [PERSON] et al. [24] measured the full tooth profile error of the cycloidal gear and converted it into the change in the modification amount through Fourier transformation, while not analyzing it from the perspective of the machining error principle. [PERSON] et al. [25] utilized a coordinate measuring machine to measure the tooth profile of the cycloidal gear and analyzed the machining error. However, the error analysis was not in-depth, and they did not compensate for the error. [PERSON] et al. [26] considered the machining error of the cycloidal tooth profile to convert the tooth profile shape change caused by the machining error into the amount of angle modification for compensation. However, the processing error value is selected based on experience, which has high technical requirements and requires many production practices to obtain more accurate parameter values, thus exhibiting a long cycle and poor adaptability. [PERSON] et al. [27] established a new modification model for machining error compensation, which obtains the corresponding machining error from the actual measurement results using the regression algorithm, and then compensates for it. Compared with the empirical modification method, this modification method significantly reduces the error between the actual and ideal tooth profiles. However, this method requires an accurate measurement of the actual tooth profile, which is a complicated process. Many sampling measurements are inappropriate for this method, and the measurements must be repeated after replacing the processing equipment, which is a complicated operation. Considering the high requirements for selecting empirical parameters and the complicated operation, this paper establishes a cycloidal tooth profile modification model usingMonte Carlo simulation analysis, based on the work in previous studies. By analyzing the machining errors and verifying their item characteristics, the model employs a computer to simulate many processing errors based on the Monte Carlo simulation analysis method. Moreover, the mathematical statistics for the sampling results determine the tooth profile variation within a specific confidence range, providing a particular theory and method for analyzing the cycloidal gear machining error. Furthermore, to improve the comprehensive performance, the influence of cycloidal gear tooth profile change on the bearing capacity is comprehensively considered. However, the optimal modification parameters obtained by error compensation and the optimal modification parameters obtained by the maximum carrying capacity show a contradictory relationship. Therefore, the optimization algorithm of NSGA-II is utilized to optimize these parameters, and the modified parameters with better comprehensive performance are obtained. Figure 2 shows the structure of the paper. Section 2 theoretically analyzes the machining error of the cycloidal gear, including machining error analysis (Section 2.1), machining error compensation (Section 2.2), and sensitivity analysis of the machining error (Section 2.3). Section 3 mainly introduces the Monte Carlo simulation method, specifically including the Monte Carlo simulation steps (Section 3.1), the acquisition of the sampling formula for each machining error item (Section 3.2), and the case analysis (Section 3.3). Section 4 mainly introduces the optimization of the cycloidal gear modification parameters, mainly including the establishment of optimization models (Section 4.1), the establishment of objective function (Section 4.2), the selection of design variables (Section 4.3), constraints (Section 4.4), and final optimization results (Section 4.5).