In order to quickly solve the low order frequency of the constrained mode of double circular arc gear and reveal the sensitivity of the main parameters of the gear to the natural frequency, the constrained mode of double circular arc gear is solved by finite element method; On this basis, the orthogonal test method is used to solve and compare different gear parameter combinations. Analysis of variance and multiple nonlinear regression calculation are carried out on the test results, and the accuracy of the regression equation is verified. The following conclusions are drawn:
(1) the first six vibration modes of the constrained mode of double circular arc gear: the first order is circumferential vibration, the second and third orders are first-order half folded vibration, the fourth order is umbrella vibration, and the fifth and sixth orders are second-order half folded vibration;
(2) according to the significance probability P in the analysis of variance results, the mean value of the significance probability of the number of teeth and modulus of the geometric parameters of the double circular arc gear is less than 0 005, it is concluded that the number of teeth and modulus have a significant influence on the natural frequency of constrained mode of double circular arc gear;
(3) the natural frequency of double circular arc gear is inversely proportional to the geometric parameters (number of teeth, modulus, helix angle and tooth width). The number of teeth and modulus have a great impact on the natural frequency, while the helix angle and tooth width have a small impact;
In this study, the finite element calculation and statistical analysis are combined to establish the calculation model of the first natural frequency of the constrained mode of double circular arc gear. The established model is simple and easy to calculate, which provides a reference for studying the coupling relationship between gear parameters and modal natural frequency. In this study, the selection of independent variables in the constrained modal orthogonal test is not comprehensive enough. Only the key parameters of the gear are tested and studied. In the later test, the independent variable factors should be further expanded and the test method should be optimized, so as to understand the influence of gear parameters on natural frequency more comprehensively.