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In this paper, the formula of non-load transmission error (TE) and time-varying backlash is derived through the incremental meshing line method based on the eccentricity error model of 2K-V gear pair with small tooth difference. Considering the influence of uneven load contact between two gear pairs with small tooth difference, the static transmission error (STE) of a 2K-V gear pair with small tooth difference is deduced. This work helps to predict the TE caused by eccentricity error and provide inference to compensate backlash. Also, we establish the nonlinear dynamic model of 2K-V small tooth difference under eccentricity excitation, in which non-linear factors such as non-uniform load, time-varying backlash, transmission error and contact stiffness are considered, and validated the theoretical model by comparing the dynamic transmission error in simulation and in theory. Furthermore, the transmission error of the 2K-V gear reducer was tested, and the test results further verified the uneven load contact phenomenon of the gear pair with small tooth difference in the meshing process. At the same time, the experimental transmission error frequency spectrum is consistent with the theoretical results, indicating that the transmission accuracy of the 2K-V reducer is mainly caused by the eccentricity error of the gear pair with small tooth difference. Finally, we optimized the initial eccentricity phase and predicted the minimum transmission error, providing theoretical guidance for the assembly of 2K-V small tooth difference gear pairs. Keywords: 2K-V reducer, nonlinear dynamics, transmission error, uneven load contact, eccentricity error Highlights • The formula of the non-load transmission error and time-varying backlash based on the eccentricity error model of a 2K-V gear pair with small tooth difference is derived. • The static transmission error of a 2K-V gear pair with small tooth difference involving the influence of uneven load contact is deduced. • The nonlinear dynamic model of a 2K-V small tooth difference under eccentricity excitation is established. • The simulation and experiment further validate the dynamic model and theory formula.

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A new type of conical involute gear, proposed in this paper, can be applied in precise gear transmission for adjusting the backlash because of the special characteristics of its teeth. The meshing states of parallel external gear transmission based on the proposed gears are analysed and presented. The expressions of the length of contact and relative sliding velocity at any meshing position are derived. Then, the calculation formula of meshing efficiency is given by utilizing the piecewise equivalent method. Next, the variation of the length of contact line, unit load, meshing efficiency in a meshing period with different gear parameters and different operations are illustrated by employing numerical examples, and the influences of gear parameters and operations on meshing efficiency of the proposed gears are discussed based on the computing results. In the end, the applicability of the calculation is introduced.