Calculation method of sliding ratios for conjugate-curve gear pair and its application

The calculation method of sliding ratios for conjugate-curve gear pair, generated based on the theory of conjugate curves,is proposed. The theoretical model of conjugate-curve gear drive is briefly introduced. The general calculation formulas of sliding ratios are developed according to the conjugate curves. The applications to the circular arc gears based on conjugate curves and the novel involute-helix gears are studied. A comparison on the sliding coefficient with the conventional corresponding gear drive is also carried out. The influences of gear parameters such as spiral parameter, gear ratio and modulus on the sliding ratios of gear drive are discussed. Brief description of manufacturing method for conjugate-curve gear pair is given. The research results show that the sliding ratios of gear pair become smaller with the increase of spiral parameter and gear ratio, respectively. And it will be greater with the increase of modulus for the tooth profiles. The meshing characteristics of conjugate-curve gears are further reflected and the optimization design of tooth profiles with high performance may be obtained.

Vector Field Based Sliding Mode Control of Curved Path Following for Miniature Unmanned Aerial Vehicles in Winds

In this paper, a curved path following control algorithm for miniature unmanned aerial vehicles（UAVs） in winds with constant speed and altitude is developed. Different to the widely considered line or orbit following, the curved path to be followed is defined in terms of the arc-length parameter, which can be straight lines, orbits, B-splines or any other curves provided that they are smooth. The proposed path following control algorithm, named by VF-SMC, is combining the vector field（VF） strategy with the sliding mode control（SMC） method. It is proven that the designed algorithm guarantees the tracking errors to be a bounded ball in the presence of winds, with the aid of the Lyapunov method and the BIBO stability. The algorithm is validated both in Matlab-based simulations and high-fidelity semi-physical simulations. In Matlab-based simulations, the proposed algorithm is verified for straight lines, orbits and B-splines to show its wide usage in different curves.The high-fidelity semi-physical simulation system is composed of actual autopilot controller, ground station and X-Plane flight simulator in-loop. In semi-physical simulations, the proposed algorithm is verified for B-spline path following under various gain parameters and wind conditions thoroughly.All experiments show the accuracy in curved path following and the excellent robustness to wind disturbances of the proposed algorithm.