| Since1990s, in the Beijing International Automobiles and Technological EquipmentsExhibition, spring shock absorbers, a tilted support spring vibration reduction system, wasinstalled in Toyota, which attracted widespread attention from various engineering fields. Thetilted support spring packaging system is an improved cushion structure, which is used toconnect an inner body with an outer body by four tilted support springs and is applied toprotect precise instruments from damage. The system can protect the engine from damage bythe use of geometric nonlinearity of oblique springs, and its damping effect is superior to thelinear system, which is composed of vertical suspension springs. During the transportationprocess, product damage usually occurs in some weak links first of all, namely criticalcomponents. Therefore, it is more close to facts to take products as two degrees of freedomnonlinear geometry buffer system.According to available research situation, based on numerical analysis theoreticalmethod, Newton’s second law and product damage assessment and so on, the dynamicalcharacteristics of the tilted support spring system with critical components were studied. Themain research contents are as follows.Firstly, the dynamical model of the system was obtained. According to Newton’s secondlaw, the dynamical equations of the system were established. The natural vibration and shockdynamical equations were simplified using Tailor series expansion and nondimensionalized.Secondly, the natural vibration characteristics of the system were analyzed. The naturalvibration equations were solved using Runge-Kutta method and the displacement responseand acceleration response of critical components were obtained. On basis of the numericalresults, the effects of the angle, the frequency ratio, the mass ratio and the dimensionlessinitial displacement of the main body on the displacement response and acceleration responseof critical components were discussed. Based on the results, it demonstrates that increasingthe frequency ratio or decreasing the dimensionless initial displacement of the main body canremarkably reduce the maximum displacement response of critical components, and themaximum displacement response of critical components declines and the period extends withthe decrease of the angle or the increase of the mass ratio. It also shows that with the angledecreasing, the frequency ratio increasing, the mass ratio increasing, or the dimensionlessinitial displacement of the main body decreasing, the maximum acceleration response ofcritical components can decrease correspondingly.Finally, the shock characteristics of the system were studied under the action of arectangular pulse. The shock dynamical equations of the system were solved usingRunge-Kutta method and the acceleration response of critical components was obtained.Combining with traditional fragility theory, the shock response spectra and damage boundaryof critical components were obtained. Based on the numerical results, it displays thatdecreasing the angle of the system can reduce the maximum shock response acceleration ofcritical components and enlarge the safety zone of damage boundary, and increasing the massratio can restrain the maximum shock response acceleration of critical components at a low frequency ratio. Under the action of considering damping, with the increase of damping ratiobetween critical components and the main body or damping ratio of the tilted support springsystem, the maximum shock response acceleration of critical components can decrease andthe safety zone of damage boundary can enlarge. On the basis of results, the frequency ratioof the system is an important parameter in the design and it is necessary to increase thefrequency ratio as possible in the permissive condition. |
