| Centrifugal pump is the key equipment in the process chemical industry,aerospace,power generation and fluid transportation industries.Its safety,reliability and sustainability are related to the defense buildup,national economy and social life in all aspects.With the continuous progress of science and technology and the increasing demand for defense buildup and industrial construction,centrifugal pumps gradually develop towards the direction of high speed,high power and heavy load,which puts forward higher requirements for the stable operation,mechanical efficiency and vibration and noise reduction of centrifugal pumps.Because of the accelerating effect of gear,the centrifugal pump can obtain several times the working speed of the ordinary centrifugal pump.As the main source of vibration and noise in the power transmission system,the gear system will vibrate violently during operation.Therefore,the introduction of gear pair will be a great challenge to the stability and reliability of high-speed centrifugal pump.In this paper,the rotor system of the gear speed-up centrifugal pump is simplified into a gear-rotor-seal-bearing(GRSB)system by the lumped-mass method,and the coupled lateral-torsional dynamic mode of the system is derived which were based on the principle of displacement equilibrium and Lagrange equation,then the nonlinear vibration characteristics of the GRSB system are analyzed.The main research contents of this paper are as follows:(1)The 18-degree-of-freedom dynamic differential equation of GRSB system is described which has considered the eccentric mass,dynamic meshing force,nonlinear bearing force,nonlinear seal force and dynamic torque excitation.The Fourth-order Runge-Kutta method is used to solve the equation,and the setting of boundary conditions is discussed.(2)Considering the time-varying response,the machining error and wear out of the gear teeth and the motion coupling of the gear pair system.The steady state,fluctuation and coupling function of the backlash are described.Then,the vibration response of GRSB system under different backlash function models and backlash slopeα_bare studied.The results show that the stability of the system under the fluctuation backlash model is the worst.And the motion coupling of the gear in the radial direction can suppress the nonlinear characteristics of the fluctuation backlash to a certain extent.In addition,the smaller the backlash slope is,the more obvious the nonlinear characteristics of the system are.When the backlash slope is 0,the gear has the phenomenon of unilateral impact.(3)The dynamic characteristic of the GRSB system under the different forms of the meshing stiffness are analyzed,and compared the different developing order under time-varying stiffness of dynamic meshing force F_mand the vibration response,the results show that:the response of the system under constant stiffness and time-varying stiffness exists has significant difference,and compared the different order stiffness functions,the dynamic meshing force has obvious differences,but the vibration response of the system is almost remain unchanged.In addition,the vibration responses of the system under different seal clearance c,seal length L,seal radius R_sand pressure drop D_pare solved,the obtained the vibration characteristics of the rotor.(4)The effects of different transmission ratios on the stability and vibration response of the GRSB system with variable center moment and fixed center moment are solved.The motion states of GRSB system with different transmission ratios are analyzed by using chaotic bifurcation theory,time-frequency domain analysis and Poincare mapping. |
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