The influences of torsion stiffness of harmonic gear drive considering crack were studied by use of fracture splits mechanics, the material mechanics and the system dynamics theories. The analytic calculation formulas of flexibility and stiffness coefficient on each member considering crack were deduced, the calculation methods of torsion stiffness were given and example enumerated. This method is simple and applicable to engineering calculation.

The fractal interpolation method based on affine transformation is a kind of method of fractal interpolation function by iterative function system (IFS). Through the derivation, the fractal interpolation function model was introduced. And a GM(1,1) model was established to predict oil and gas pipeline corrosion. Prediction accuracy and case analysis show that the result accords with the ideal. It indicates that when the original data is missing, grey prediction can still be used; it has certain practical value to take corresponding measures to provide reliable basis for preventing corrosion.

The theory of rupture mechanics was applied into harmonic gear driving to study the fatigue failure mechanism of flexspline. The fatigue failure models of flexspline were set up, and the fuzzy reliability compute formulas of anti-fatigue fracture for flexspline were deduced, Then the cracks reliability and reliable life were estimated by a specific example. This new calculation method can make up for the shortage of the normal regulations design for flexspline.

The reciprocating seal is a kind of commonly used seal forms. The mechanism of reciprocating seals under thin film lubrication state was researched. The various factors were considered and the computing formulas of leak quantity and friction coefficient were deduced. An actual example and its computing result were given，and the change trends were analyzed. The research result provides necessary foundations for applications of thin film lubrication seals.

The technology of applying fuzzy liability design to the harmonic gear drive was introduced, membership functions were determined, fuzzy reliability expressions were deduced, and performance function and standard deviation of various strength calculations were given. An example explains calculation process. The result shows that as a result of considering simultaneously the randomicity and fuzziness of variables, the fuzzy reliability is better than the general reliability under the same conditions.