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Based on gear transmission conjugate-curve theory research， taking the internal meshing gear transmission with curve element as the object， general meshing equation of spatial conjugate curves along the designated contact angle position is derived and general expressions of space conjugate curves under internal contact conditions are also obtained. According to space equidistant-enveloping method， conjugate surfaces which inherit the meshing characteristics of spatial conjugate curves are generated and three contact types including convex-to-convex， convex-to-plane and convex-to-concave forms are proposed if changing the relative motion position and equidistant radius. Taking the spatial cylindrical spiral curve as an example， combined with the theoretical analysis results and given design parameters， three-dimensional solid models of internal meshing gear pair with convex-to-concave contact are established. The pressure angle on the tooth surface contact point is defined and calculation method of sliding ratio for the mated tooth surfaces is also put forward in terms of space conjugate curves. Calculation and analysis of the contact locus of conjugated internal meshing tooth surfaces are conducted. Further studies on meshing characteristics， contact mechanics and manufacturing method of tooth profiles will be carried out.

Aiming at the problem of time-varying friction in the meshing process of spur gear pair, the meshing model of spur gear pair is established, and the relative sliding velocity, rolling speed, sliding-rolling ratio, comprehensive radius of curvature and tooth contact pressure of the gear pair at the meshing point are deduced. The variation of the friction coefficient of the tooth surface under the change of single tooth load during the single-to-double tooth alternating meshing process is studied. Based on the potential energy method, the analytical formulas of meshing stiffness of spur gear pair with time-varying friction are deduced, the variation law of meshing stiffness of spur gear pair under non-friction, constant friction and time-varying friction is analyzed, and then the influence of the parameters such as gear modulus, tooth width, pressure angle, roughness and input torque on the time-varying meshing stiffness of spur gear pairs under time-varying friction is studied. The results show that the time-varying friction coefficient changes suddenly in the single-to-double tooth alternating meshing zone, and tend to zero at the pitch point; the effect of friction makes the stiffness of single teeth increase at the approach process, and decreases during the recess process; the constant friction force makes the meshing stiffness change suddenly at the pitch point; the time-varying friction force makes the meshing stiffness change suddenly at the single-to-double tooth alternating meshing zone, and the change law is consistent with the non-friction situation at the pitch point; the meshing stiffness of gear pair increases with the increase of modulus and tooth width, and decreases with the increase of pressure angle; the variation of meshing stiffness increases with the increase of tooth surface roughness; and decreases with the increase of input torque.