Time-Dependent Reliability Analysis For Planar Path Mechanisms

Time-dependent(interval) reliability method for mechanisms predicts the probability of satisfying the motion requirement in a predefined period of time. Since the kinematic timedependent reliability embodies the overall motion situation of mechanisms, the nature of kinematic time-dependent reliability is a system reliability of mechanisms. For motion accuracy reliability, the current reliability analysis method is mostly for point reliability analysis at present, point reliability can provides the probability of actual motion output satisfying the required motion output or realizing the required function only at a specific time instant, that is, point reliability can only provides local reliability information of mechanisms' motion range. Time-dependent reliability can provides us the whole reliability information over the entire motion range to manage risk and predict life easily. Obviously, it is more reasonable and realistic to evaluate reliability of mechanisms over the entire motion range rather than on the one specific time instant. Therefore, the research of time-dependent(interval) reliability with the uncertain situations has very important theoretical significance and practical values.Path generating mechanism is different from function generating mechanism, which has multi-component of motion output, and the motion error on each component can be regarded as stochastic process. The method which derived from Rice formula for interval reliability analysis for function generator mechanism can be introduced to analyze time-dependent reliability of per single motion output component, however, if the system reliability of path mechanism is required to obtain, it is need to deal with joint crossing problem of multidimensional stochastic process. In the current researches, it is still difficult to deal with multidimensional stochastic process problems.In this work, two types of path mechanisms, discrete points path mechanism and continuous track path mechanism are used as research objects. Time-dependent reliability analysis model for path mechanism is established based on the Set operation by dealing the problem evaluates into a series system, joint probability method and envelope method are applied to solve system reliability of mechanism, respectively. The main contents of this research are as follows:1. The randomness of each structure parameter is introduced into consideration, the motion error probabilistic model is established based on mechanical kinematic analysis, then the kinematic error analysis of mechanism is performed.2. Point reliability analysis model and time-dependent(interval) reliability analysis model are established on both single component and multiple components of path mechanisms, solving strategy for point reliability analysis is discussed by the means of First Order and Second Moment(FOSM) method.3. Analytical formula of joint probability method for time-dependent reliability analysis of discrete points path mechanism on single component is derived, system reliability analysis model and solving strategy of discrete points path mechanism are discussed with composite influence caused by multiple components. Time-dependent(interval) reliability analysis on per single component and multi-components are performed through numerical examples by using the joint probability method, the result is compared with Monte Carlo Simulation(MCS) to demonstrate the proposed method.4. Envelope method model of time-dependent(interval) reliability analysis for continuous track path mechanism is established. Envelope approximate function of motion error function of mechanism on a single component is derived, then envelope algorithm is used to evaluate time-dependent reliability of single stochastic process for path mechanism. Composite system reliability analysis model is established by means of Set operation, the envelope approach method is then applied to multidimensional stochastic process system reliability analysis of continuous track path mechanism. The practicability is demonstrated by numerical examples of using envelope method to solve this kind of multidimensional stochastic process problems.