Probabilistic Analysis And Synthesis Of Planar Function Mechanisms With Joint Clearance

In mechanical system, the mechanism joint is the part to connect two bars for keeping the relative motion. In order to guarantee the relative motion, the elements of a joint will use loose fit and joint clearance is needed. The proper clearance is the foundation to ensure the mechanism goes slick. However, the uncertainty of the joint clearance has severely affected the performance and reliability of the mechanism. More and more attentions have been paid on the mechanism with joint clearance, which refers to the kinematics and dynamics. However, the literatures show that there are rare studies on the reliability analysis of mechanism motion and further studies are needed.The reliability analysis methods on the mechanism motion are studied by considering the uncertainty of dimensional tolerance and joint clearance from the following aspects:(1)In order to testify the influence of the joint clearance to the reliability of mechanism motion, the probabilistic error model is constructed by considering the dimensional tolerance, uncertainty of joint clearance and error of mechanism. The difficulty of mechanism motion precision analysis with uncertainty of joint clearance using probabilistic method is probabilistic modeling of joint clearance variable and how to deal with the correlation of joint clearance variables. Addressing this difficulty, the instantaneous reliability analysis is conducted with the hybrid dimension reduction method and the reliability analysis of the crank and rocker mechanism is performed with considering the stochastic errors based on the first order second moment.(2)The time-dependent reliability could provide all the reliability information during the time interval to easily realize the risk management and probabilistic life prediction. In this paper, an effective time-dependent reliability analysis method for function generation mechanism, named by envelope function method, is proposed. The approximation of the motion output is made with the Hybrid Dimension Reduction Method and the dependence of failure probability on time is estimated through the envelope function method. The provided examples testify that the proposed envelope function method is effective.(3) The reliability synthesis is further explored by considering the uncertainty of joint clearance based on the reliability analysis, where the failure probability is minimized as objective function and motion failure probability is accounted for as probabilistic constraints. The example shows that the proposed reliability synthesis method could decrease the motion failure probability and accordingly increase the operational safety.(4)Reliability-based design optimization and robust design are the two typical design optimization methods under uncertainty. Reliability-based design optimization and robust design increase the product quality from the different aspects. In engineering practices, the reliability and robust should be satisfied at the same time. Therefore, it is necessary to integrate the two methods to improve the design quality and level of products. The reliability-robust design method is proposed and an example demonstrates the advantages of the proposed method. Furthermore, a new reliability-robust design method based on the cost-quality model is presented to obtain the optimal results with the minimal life-cycle cost under the satisfaction of reliability and robustness, which will improve the whole quality.