The organization is affected by a variety of random factors during the exercise. In order to improve the motion reliability of the mechanism, it is very important to evaluate the motion reliability at the beginning of design. The error model of collaborative robot mechanism is established based on D⁃H method and finite⁃element method. The fourth⁃order moment method is used to establish the mechanism motion reliability model. The reliability model of mechanism motion interval is established based on envelope function method. The model of rigid⁃flexible coupling parameterization with clearance is established by using ADAMS. Motion reliability simulation of collaborative robot was made with ADAMS/insight. And calculate the motion reliability within 9 s. Compared with Monte Carlo simulation（MCS）. The advantages of the fourth⁃moment method and the envelope function method in the analysis of motion reliability are proved.

In order to ensure the long⁃term safe, stable and efficient operation of the rotating machinery, a risk cloud model evaluation method for the rotating machinery rotor system is proposed for the actual risk status of the rotor system. The evaluation method firstly uses FMECA to summarize the failure mode of the rotating machinery rotor system, finds the defects and weak links of its reliability, and identifies the main failure modes that cause the rotor system to fail. Then, based on the stress⁃strength interference model, the three digital characteristics of the rotor system cloud model in the single failure mode are constructed, which combines with the fuzzy and randomness of the cloud model to obtain the risk cloud model evaluation of the rotor system. Qualitative and quantitative results.It is applied to the turbine rotor system, and the rotor system is comprehensively evaluated by MATLAB simulation and visually presented in the form of cloud droplets.

In order to study the vibration characteristics of the downhole gear transmission system,based on the 3D modeling software CREO, a three⁃dimensional geometric model of the main and driven gears of the downhole gear transmission system was established. And using the ANSYS software import function to establish the three⁃dimensional finite element model of transmission gear. By reading the dynamic mechanical modal analysis of the finite element model of gear, the natural frequencies of the gears and the corresponding main modes are obtained. This study can be used as a theoretical reference to avoid the frequency of external excitation response in the design process, so as to avoid the resonance of the transmission system and effectively improving the fatigue strength of the gear transmission system.

Dynamic reliability models and failure rate models of bolted flange systems were developed, which took into account the failure dependence of components in the systems. It was proposed that the traditional static reliability models could not accurately describe the dynamic characteristics of reliability and failure rate of bolted flange systems. Moreover, the effects of failure dependence on system reliability and failure rate were analyzed via numerical examples. The results showed that the failure dependence had great influences on system reliability. Furthermore, the assumption that components in a system were independent of each other might cause large error in system reliability estimation. Traditional assumption of constant failure rate for mechanical systems might underestimate the system reliability. The increase in the number of bolts could enhance the ability of the system to resist the risk of failure.