# Simulation verification test of noncircular gear stepless speed regulation

## 1. Construction of experimental platform

In order to verify the correctness of the design of non-circular gear, the differential equation of pitch curve of non-circular gear is approximately solved by setting enough discretization accuracy in combination with equation (3). By calculating the arc length corresponding to pitch curve at each discretization step, the (x, y) coordinate value of pitch curve of non-circular gear is obtained, Based on the secondary development of VB (Visual Basic language programming) and SolidWorks, and through Boolean operation, the non-circular gear is finally obtained. The non-circular gear pair is installed, and the corresponding test bench is built, as shown in Figure 1.

The torque of the input motor is transmitted to the input shaft through the quincunx coupling, and an input speed sensor is installed between the drive motor and the input shaft to measure the input speed. The input shaft drives the driving non-circular gear to rotate, and the time-varying speed is generated by the time-varying bit property of the non-circular gear. The output speed sensor is connected with the magnetic powder loader to ensure the necessary load for correct transmission. The parameters such as the speed and torque of the driving motor are adjusted through the operation console.

## 2. Analysis of experimental results

Because non-circular gear is the theory and design basis of CVT, this experiment mainly verifies the correctness of analysis and design of non-circular gear pair. Given the input speed of non-circular gear pair 262 rad / s and the load torque at the output end 200 N · mm, after the non-circular gear pair rotates smoothly, the input / output speed measurement structure is extracted and combined with the relationship between speed and speed ratio I21= ω 1/ ω 2 = N1 / N2, the input / output speed is processed twice, and the experimental results of speed ratio are obtained, which are compared with the theoretical results of MATLAB, as shown in Figure 2.

According to the experimental results shown in Fig. 2, the experimental transmission ratio of the non-circular gear pair ranges from 0.8 to 1.2, which is basically equal to the theoretical transmission ratio; The maximum error of output speed is 6.8%. Considering the design and machining discrete accuracy, installation error and measurement sensitivity of non-circular gear, the maximum error is within the acceptable range, which verifies the correctness of theoretical analysis.

Based on the time-varying bit property of non-circular gear, combined with the industrial practice, a non-circular gear stepless speed regulation mechanism with full gear mesh is designed, which expands the application range of non-circular gear and improves the bearing capacity of stepless transmission mechanism. Combined with the inclusion of higher-order function to lower-order function, the method of reconstruction reverse design of non-circular gear for given speed bit function is established by using the method of multi segment construction, and the influence rules of non-circular gear parameters such as branch number, speed ratio function of working section and angle range on pitch curve are obtained. The feasibility of non-circular gear design with different parameters is analyzed theoretically, The matching range of each parameter of non-circular gear is determined. Solid works and VB are used to establish the solid model of non-circular gear stepless speed regulation mechanism, which is imported into Adams for motion simulation, and the time-varying ratio characteristics of different non-circular gear branches under different phase angles are obtained; The processing and experiment of non-circular gear are completed, and compared with the theoretical structure of MATLAB, the maximum time-varying error of non-circular gear pair is obtained, which verifies the correctness of structural design and analysis, and provides a theoretical basis for the practical application of non-circular gear. 