Planar secondary envelopment planetary reducer has the advantages of high bearing capacity, small wear, smooth transmission, long life and so on. It has been widely used in the field of national defense and civil industry, but so far no relevant strength test and calculation method has been published to the public. For a long time, the design of the transmission is mainly carried out by referring to the standards of other countries or GB16444, but all of them are conservative and rough, which limits the development of the transmission. Therefore, how to develop an effective strength calculation method on the basis of previous studies is an urgent research topic to be solved.

The plane secondary envelopment reducer has the advantages of high bearing capacity, small wear, smooth transmission and long service life, etc. It has been widely used in the field of national defense and civil industry, but the relevant strength test and calculation method have not been published to the public so far. For a long time, the design of the transmission is mainly carried out by referring to the standards of other countries or GB16444, but all of them are conservative and rough, which limits the development of the transmission. Therefore, how to develop an effective strength calculation method on the basis of previous studies is an urgent research topic to be solved.

Based on the space meshing principle, elastic mechanics and finite element method, this paper carried out theoretical analysis, combined with the gear tooth stress state simulation test and the worm pair bearing capacity test, so as to develop the strength analysis method suitable for the plane secondary enveloping ring surface worm planetary reducer. The main work of this paper can be summarized as follows: Based on the space meshing principle, the meshing equation, the boundary function and the microscopic meshing parameter equation of the worm pair are derived; The distribution laws of induced normal curvature radius, lubrication Angle and relative entrainment velocity on the tooth surface were studied, and the influence of optimizable parameters on the contact state and microscopic meshing parameter distribution law of tooth surface was analyzed. Combined with engineering practice, the shape characteristics of worm and worm gear of plane secondary enveloping reducer are analyzed deeply, and the mathematical model of tooth surface boundary is established considering the effect of tooth clearance. Taking the secondary region of worm gear tooth surface as an example, the construction method of space surface with non-equidistant distribution of information points is discussed. The solid modeling program of plane envelop ring surface worm drive was programmed on Unigraphics-GRIP platform, and the accuracy of the solid model was verified by an example, which laid a foundation for the simulation analysis of worm pair. The finite element analysis model of worm pair contact was established to study the influence of load and tooth profile parameters on the stress distribution state of tooth surface and load distribution coefficient between teeth. The load distribution coefficients of the big teeth with different number of contained teeth under different loads were studied. The distribution of root bending stress along worm gear tooth width was analyzed, and the influence of load and tooth profile parameters on the distribution of root bending stress was studied. Through linear regression analysis, the formula of radius coefficient of induced normal curvature with worm diameter coefficient as variable was derived, the formula of instantaneous average length and small length of contact line was established, and the formula of load distribution coefficient between teeth was regress based on finite element analysis. Based on Hertz theory, the formula for calculating the average contact stress of the plane quadratic enveloping ring surface worm drive and the formula for calculating the contact stress of the large gear pair under load were deduced. Based on the cantilever beam theory, the calculation formula of bending stress suitable for the transmission is established. By considering the load distribution coefficient between the teeth, the improved formula for calculating the transmission of ordinary cylindrical worm and Niemann worm can be applied to the plane two packages, and a better result can be obtained.