Dynamic Analysis And Prediction On Reliability Of Multi-body System With Uncertainty

The traditional dynamic model of multi-body system is based on the certainty,namely, all kinds of physical factors are considered as certain datum in the process ofanalysis, and they are accurate or can be accurately measured. But there are plenty oferror and uncertain factors in actual engineering because uncertainty is objective andinevitable. The dynamic model based on the accurate assumption cannot effectivelydiscrible the dynamic action of multi-body system, and may lead to contradictory results.With the development of modern mechanisms increasingly towards high-speed,lightweight and high precision, the dynamic analysis and prediction on reliability ofmulti-body with uncertainty have important theoretical significance and researchworthiness. Concertrated on the uncertain phenomenon existing in engineeringproblems, multibody systems including rigid-flexible coupling, dynamic stiffeningterms, multiple stochastic inputs and outputs, clearance joint and lubricate joint arepresented and their solutions are proposed. Furthermore the reliability of them is studied,the engineering examples are simulated according to the above theories and theeffectiveness and validity of the theories are verified by the results as well as somebenefit conclusions are obtained. The main research works can be described as follows:1. Dynamic analysis of multibody systems with probabilistic parameters waspresented. Dynamic modeling of multibody systems was obtained by Lagrange’smethod. The Probabilistic Differential Algebraic equations were transformed into pureProbabilistic Differential equations by Generalized Coordinate Partitioning method. TheNewmark step by step integration method was used to calculate the results. Using themethod of random factor method, the numerical characteristics of responses of thesystem were derived, and the results were expressed in statistic. As an illustratingexample, dynamic modeling of a rotating bar and sliding block system considering theprobabilistic of load, geometric and physical parameters is presented and the accuracyand efficiency of the method are verified. The results illustrate the probabilisticparameters affect the dynamic response of the multibody system and the dynamicmodeling with probabilistic parameters can objectively reflect the dynamic behavior ofthe objective systems.2. Based on the Lagrange’s equations and the assumed mode method, therigid-flexible coupling dynamic model of a rotating flexible beam which took the coupling term of the deformation in the expression of longitudinal deformation wasstudied. Then considering the physical and geometrical parameters under randomness,the randomness analysis of dynamic responses was developed and the motion functionreliability was forecasted by stochastic response surface method. The rationality andefficiency of the modeling and the method presented were verified by an example. Theresults demonstrate third order stochastic response surface method has good precisionwith acceptable time consumption.3. The Lagrange dynamic differential equations and the assumed mode methodwere combined to establish the modeling of a two-link flexible robot manipulatorconsidering friction in the joints. Considering the effect of stochastic factors, therandom factor method was embedded into the stochastic response surface method toimprove the analysis method of two-link flexible robot manipulator with multiplestochastic inputs. The system performance functions of strength, stiffness and themotion function were developed. Then, the dynamic responses and the reliability of thesystem were analysised. The rationality and feasibility of the modeling and the methodpresented were verified by an example, and the reliability of the system was predicted.Some expressions of random parameters about the two-link fexible robot manipulatorare derived.4. The dynamic responses and the reliability of output displacement for slider-cranksystem with clearance considering of the friction forces and the randomness of systemparameters were developed. The continuous contact force approach and a modifiedCoulomb`s friction model were used to evaluate the contact force and the friction of theintra-joint respectively. The dynamic model of mechanism was set up based onLagrange method. The approximate functional relationship between the system randomparameters and the dynamic responses was given by using the BP neural network andthe support vector machine method, respectively. The numerical characteristics of thesystem dynamic responses and the reliability of the output displacement of the sliderwere solved by moment method. The effects of the system physical parameters andgeometric parameters on the system dynamic response and the reliability were inspected.In addition, the results illustrate that the randomness of the system parameters can’t beignored, and the randomness of the clearance has greatest effect on the randomness ofthe responses and the reliability of the system under the same coefficient of variationconditions.5. The reliability of the slider-crank mechanism considering realistic jointcharacteristic, namely, joint with clearance and lubrication, and the randomness of the system parameters is presented. The continuous approach and the hydrodynamic theoryare used to evaluate the contact force for the case of joints modeled as a contact pairwith dry contact and the force generated by lubrication action respectively. The systemdynamic model was set up based on Lagrange’s equation. The prediction accurary ofSupport Vector Machine Regression is difficult to reach the target accurary because theselection of parameters isn’t accurate. In order to overcome this limitation, theparameters are pretreated through Genetic Algorithm to get the optimum parametersvalues. The precision of analysis on the system is effectively improved, which providesan effectively way to solve the problem of parameters selection in Support VectorMachine Regression. Then the reliability of the reaction force developed in thelubricated revolute joint of the crank-slider mechanism is discussed by the method.Finally, take an example to verify the feasibility and effectiveness of the proposedmethod.