Uncertainty Analysis Of The Statics Of The Dual Automobile Crane System

As one of the heavy duty lifting equipment widely used in the heavy engineering,the dual automobile crane system(DACS)is a system making up of two automobile cranes,which hoist a same payload.Compared with traditional single automobile crane,the DACS is capable of bearing higher loads,which usually can meet more complex lifting requirements.Every automobile crane is mainly composed of one lifting arm,one luffing cylinder,one rotating table and one hoisting rope.Thus,it is rather complex to derive the satic model of the DACS.In addition,the uncertainty of the statics of the DACS may be resulted from the effects of external and inner factors,such as mechanical tolerances(e.g.,design/manufacturing/assembling errors),and unpredictable external excitations(e.g.,vibration of ropes,disturbance of wind wave),etc.Thus,the key step to further study the reliability and control of the DACS is how to accurately establish the static model of the DACS,and analyze the impacts of different kinds of uncertain factors on the satics of the DACS.In this thesis,based on the techniques of the random theory,the perturbation theory,the interval arithmetic,and the differential properties of compound functions and etc.,taking the DACS as a research object,establishing the static model of the DACS based on the principle of virtual work,from one kind of uncertainty(random model or interval model)to multiple kinds of uncertainties(hybrid random and interval models),a systematical research on the effects of the uncertainty on the statics of the DACS was conducted,and the numerical analysis methods of the DACS with uncertainty were designed in this thesis.The main research contents and innovations of this thesis are summarized as follows.(1)A modified hybrid uncertain analysis method(MHUAM)was designed to calculate the static response of the luffing system of an automobile crane(LSOAAC)with random and interval parameters.In the MHUAM,the static response expression of the LSOAAC with hybrid random and interval models was approximated by the first-order Taylor series expansion,the first-order Neumann series expansion and the random interval perturbation method.Subsequently,the maximum and minimum of bounds of the static response were determined by the interval analysis method,and the expectations and variances of extrema of bounds of the static response were determined by the random interval moment method and the monotonic technique.The numerical results on the LSOAAC with hybrid random interval models showed that the MHUAM can be accurately and efficiently employed to solve the problem of calculating the static response of the LSOAAC with hybrid random and interval parameters.(2)The static model of the DACS was constructed,and a method of static-model-based nonsingular interval parameters was designed.Firstly,the kinematics of the DACS was analyzed by the inverse kinematic method,and the static model of the DACS was established based on the virtual work principle and the Jacobian matrix.Thus,the effects of structure parameters on the driving ability of every automobile crane were analyzed based on the static model.Nonsingular interval parameters were designed based on the static model.The numerical results on the DACS showed that the reasonable bounds of uncertain variables of the DACS can be determined according to the design method of static-model-based nonsingular interval parameters.(3)A modified hybrid random method(MHRM)was designed to calculate the luffing angular of the DACS with narrowly stochastic uncertainty.In the MHRM,the equilibrium equations of luffing angular vectors of crane 1 and crane 2 with random parameters were solved by the random perturbation method,the differential properties of compound functions,the first-order Neumann series expansion and the designed perturbation-based random composite function method.Thus,the expectations and variances of the luffing angular of the DACS were calculated by the random interval moment method,the differential properties of compound functions and the designed random variable functional moment method.The numerical results on the stochastic DACS problems with small uncertainty showed that the relative errors between the luffing angular field yielded by the MHRM and that obtained by the Monte-Carlo method(MCM)were lower than 5% when the coefficients of variance of random variables were less than 0.01,and the computational time of the MHRM can be reduced greatly compared with that of the MCM in the side of computational efficiency.(4)A first-order compound-function-based interval perturbation method(FCFIPM)and a modified first-order compound-function-based interval perturbation method(MFCFIPM)were designed for the calculation of the luffing angular of the DACS with narrowly bounded uncertainty.In the FCFIPM,the luffing angular vector expressions of crane 1 and crane 2 of the DACS were approximated based on the first-order Taylor series expansion,the first-order Neumann series expansion and the differential properties of compound functions.Thus,the lower and upper bounds of the interval luffing angular vector of the crane 1 and crane 2 of the DACS were determined by the interval perturbation method(IPM),the monotonic technique and the differential properties of compound functions.To improve the accuracy,the MFCFIPM employed the surface rail generation method to expand the compound-function-based vectors,and a modified Sherman–Morrison–Woodbury formula was introduced to analyze the impact of the high-order terms of the Neumann series expansion on the luffing angular.The numerical results on the interval DACS problems with small uncertainty showed that the MFCFIPM can achieve a better accuracy than the FCFIPM,and a higher efficiency than the MCM for the luffing angular field problems of the DACS with narrow interval variables.(5)A hybrid perturbation compound function-based moment method(HPCFMM)was designed to calculate the luffing angular of the DACS with random and interval parameters.In the HPCFMM,the expression of luffing angular was developed according to the designed random interval perturbation compound function-based method and the first-order Neumann series expansion.Thus,the expectations and variances of the bounds of the luffing angular were calculated by the designed random interval compound function-based moment method and the monotonic technique.The numerical results on the luffing angular problems of the DACS with hybrid uncertainties showed that the HPCFMM can be accurately and efficiently employed to solve the luffing angular problems of the DACS with hybrid uncertainties compared with the MCM and the IPM.