Study On Dynamic Characteristics Of Suspension Packaging System Under Typical Pulse Excitation

The suspension system uses springs as vibration damping cushioning elements to hang the product symmetrically in the outer packaging box,so that the product can obtain effective buffer protection in different directions when the external load acts,and it is suitable for the protection of low-brittle value products.In this paper,the two-degree-of-freedom suspension system considering the critical component was taken as the research object,and the fourth-order Runge-Kutta method was used to solve the system dynamics equations.The dynamic response characteristics of critical component were discussed,and the influence of relevant parameters was analyzed.The main work and conclusions were as follows:According to the mechanical model of the suspension system,the nonlinear dynamic equations of the system under rectangular pulse excitation were established according to the mechanical principle;The Taylor series formula was used in the nonlinear term of the system dynamics equations,and obtaining approximate dynamic equations without considering high-order small quantities under small displacement conditions.The dimensionless dynamic equations under rectangular pulse excitation were obtained by introducing dimensionless parameters.The analysis shows that the shock response characteristics of the critical component significantly affected by the system frequency ratio,the suspension angle and the damping of the main body and the foundation joint.When the pulse amplitude,mass ratio and suspension angle are given,the displacement and acceleration response of the critical component is sensitive to the low frequency ratio,and there is an internal resonance phenomenon when the frequency ratio is near 1;Compared to linear systems（φ₀=90°）,with the decrease of the suspension angle,the absolute displacement amplitude of the critical component can be increased,the relative displacement amplitude and the acceleration amplitude can be decreased,the response period is extended,and the damping effect is better than the linear system;Given the system suspension angle,frequency ratio,and mass ratio,the displacement response is sensitive to the damping of the main body and the foundation joint,the displacement response can be changed significantly.The increase of the damping ratio can effectively suppress the absolute displacement amplitude.With the increase of response time,the damping ratio is more effective in suppressing the response amplitude.With the increase of damping ratio,the acceleration response of the critical component can be decreased and then increased;Given the suspension angle,frequency ratio,and mass ratio,with the increase of the dimensionless pulse amplitude and pulse time,the response of critical component can be increased.The analysis of the shock spectrum and influencing factors of the critical component shows that the shock spectrum of the critical component is greatly affected by the frequency ratio,the suspension angle,and the damping of the main body and the foundation joint.The peak of the acceleration response of the critical component is sensitive to the low frequency ratio（λ₁＜3）,when the frequency nearby λ₁=1,the peak value of the acceleration response can be changed significantly,and there is a multi-peak phenomenon,the shock response spectrum of the critical component is stable at high frequency（λ₁≥3）,so the system design should make the system frequency meet λ₁＞3 as much as possible;Compared with the linear system（φ₀=90°）,the system has better shock resistance when the suspension angle is smaller,but when the frequency ratio is low,the shock resistance is not necessarily better than the linear system by decreasing suspension angle;Under the condition of high frequency ratio,the system has the best damping ratio,and it varies with parameters such as suspension angle,pulse amplitude and frequency ratio.The analysis of the damage boundary and influencing factors of the critical component shows that the damage boundary of the critical component is sensitive to the low frequency ratio.When the frequency ratio is near 1,the damage boundary safety zone is obviously reduced,and the trend of the safety zone reduction is the same for different parameters.With the increase of the frequency ratio,under the condition of high frequency ratio,the damage boundary surface of the critical component can be changed stably and the trend is basically unchanged when the parameters such as the initial suspension angle of the system change;Compared with the linear system,with the decrease of the suspension angle,the safety area can be increased under the condition of high frequency ratio,and the trend is basically not affected by the variation of the pulse amplitude;Under the condition of high frequency ratio,with the increase of the damping ratio of the main body and the foundation joint,the safety zone of the critical component can be increased and then decreased,and the optimal damping ratio exists for different system parameters.However,it should be noted that when the parameters such as the suspension angle of the system change,the optimal damping ratio can be changed accordingly.