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The dropping damage evaluation for packaging system is essential for safe transportation and storage. A dynamic model of nonlinear cubic-quintic Duffing oscillator for the suspension spring packaging system was proposed. Then, a first-order approximate solution was obtained by applying He’s variable iteration method. Based on the results, a damage evaluation equation was derived, which reveals the main controlling physical parameters for damage potential of drop to packaged products concretely. Finally, the dropping damage boundary curves and surfaces for the system were discussed. It was found that decreasing the suspension angle can improve the safe region of the system.

Newton [

The suspension spring system with eight springs as cushioning components performs geometric nonlinearity and is suitable for protecting high precision instrument with low fragility. Wu and Yang [

In this paper, by applying the VIM, we solve the nondimensional dynamic equation of the suspension spring system under the excitation of dropping shock to obtain a first-order approximate solution and obtain the nondimensional maximum acceleration expression. Then, a damage evaluation equation presenting the relationship between physical parameters and the damage boundary is suggested. Finally, the dropping damage boundary curves and surfaces of the system are discussed according to the damage evaluation equation.

The dynamic model of the suspension spring packaging system is shown in Figure

Dynamic model of the suspension spring system.

Wang and Chen [

Here are the coefficients:

By introducing new nondimensional parameters, (

A nonlinear equation can be written as

The VIM is proposed by He et al. [

Applying the VIM, construct the following correction functional of the system:

According to the principle of stationary, (

For the nondimensional dynamic equation (

Let the coefficient of

Substitute

For the following amounts,

The impact energy under dropping shock is related not only to the maximum acceleration, but also to the whole waveform. Hence, it is necessary to prove that the overall precision of the waveform can meet the requirement. The nondimensional acceleration response curves can be obtained just as shown in Figure

Comparison of the nondimensional acceleration

Wang [

The dropping shock acceleration of the system can be written as follows:

Set

Equation (

Respectively, we choose the suspension angle

Dropping damage boundary curves of the system when the suspension angle

By selecting the suspension angle as the third evaluation quantity, set product fragility

Dropping damage boundary surfaces of the system when the product fragility (a)

According to Figures

A dynamic model with nonlinear cubic-quintic Duffing oscillators is proposed for thesuspension spring packaging system, and the first-order approximate solution of the equation is obtained by He’s variable iteration method. Based on the results, the damage evaluation equation for the packaging system is derived, revealing the main controlling parameters of the damage potential of dropping shock to packaged products. Finally, the damage boundary curves and surfaces for the system are discussed. It is found that decreasing the suspension angle can help to protect the packaged product.

The authors declare that there is no conflict of interests regarding the publication of this paper.