Parameter Design Of Ball Type Double Dynamic Vibration Absorber

In order to reduce the mechanical or structural forced vibration response,especially the vibration response near the resonance point,the use of a dynamic vibration absorber is a good means of vibration control.Among them,because the passive dynamic vibration absorber does not require an external power source,the structure is simple,the stability and reliability are high,the forced vibration caused by the narrow-band excitation force has a significant inhibitory effect,so it is widely used in practical engineering and scientific research fields.The dual dynamic vibration absorber is composed of two dynamic vibration absorbers,which can further improve the vibration control effect and reduce the effect on the control performance when the parameters deviate from the optimal design value.The ball type dynamic vibration absorber is made up of vibration absorbing ball and absorbing concave surface.The structure is simple,no need for spring,and the recovery force is gained by gravity of absorber ball.Therefore,on the basis of the dual dynamic vibration absorber and the ball type dynamic vibration absorber,the ball type dual dynamic vibration absorber is proposed,and the optimal design of the parameters and the vibration control performance of the dynamic vibration absorber are studied by theoretical analysis and numerical simulation.The main contents of this paper are as follows:(1)The dynamic model of dynamic vibration absorber composed of spring,mass and damper is introduced.Through analytical and numerical calculation,the expression of the amplitude ratio of the main system is obtained,and the optimal design is carried out according to the fixed-point theory,and the optimal natural frequency ratio and the optimal damping ratio are obtained.(2)Based on the Lagrange equation,the dynamic model of a single ball type vibration absorber is established.Through the analysis and numerical calculation,the principle of vibration absorption and the influence of the main parameters on the effect of vibration absorption are studied.The optimal design is carried out by using P and Q fixed-point theory.The coordinates characteristics of fixed-point are analyzed,and the optimal frequency and damping are worked out(3)The mathematical model of the ball type double dynamic vibration absorber is set up.The amplitude ratio expression of the dynamic vibration absorber is obtained by Lagrange equation.The parameters of the dynamic absorber are optimized by the P,T and Q three points theory.The fsolve function of MATLAB and the formula of programming are used to calculate the optimum,and the optimum is obtained.The natural frequency ratio and the optimal damping ratio have been optimized.(4)In order to avoid a large number of complicated calculation of the high order complex equations in the parameter optimization design,the numerical calculation of the dual dynamic vibration absorber is deeply studied.In order to improve the calculation speed and efficiency,the complex calculation problem is solved by using MATLAB and the fsolve function in it.The calculation method is optimized.(5)Under the condition that the quality of a single ball type dynamic vibration absorber is the same as that of a two ball type vibration absorber,the overall amplitude ratio of the main system is lower and the effect of vibration absorption is better when the dual ball type dynamic vibration absorber is found.