PSI - Issue 36

O. Fomin et al. / Procedia Structural Integrity 36 (2022) 239–246 Oleksij Fomin, Alyona Lovska, Volodymyr Bohomia et al. / Structural Integrity Procedia 00 (2021) 000 – 000

243

Differential equations of motion of a tank wagon have the form: ( ) ( ) ( ) 1 1 1,1 1 1,2 2 1,3 3 1 2 , TP z M q C q C q C q F sign sign F    +  +  +  = −  + −

(1)

( ) ( 1

) (

)

(2)

2 2 2 , fr M q C q C q B q F sign k        +  +  +  =  + + + + 2,1 1 2,2 2 2,2 2 1 2 1

( ) ( 2 k 

) (     

) 4 ,

(3)

3 3 fr M q C q C q B q F sign  +  +  +  =  3,1 1 3,3 3 3,3 3

+ + + +

3

4

3

4 4 , z M q F M g  = −  4

(4)

(

)

1 z k F k y y = − −

4

It is assumed that the elastic and frictional link between the pot and the supports works during the forced oscillations of a wagon. It is taken into account that a wagon moves over a junction roughness, which is described by the periodic function (Dyomin and Chernyak (2003)):

2 h

(

)

(5)

( ) t

1 cos , t 



= −

The input parameters of the model are the technical characteristics of the load-bearing structure of a tank wagon, the spring suspension, the perturbing action (rail roughness). The solution of differential equations of motion (1 – 4) was carried out in the MathCad software package (Lovska (2015), Kiryanov (2006), Dyakonov (2000)). Initial displacements and velocities were assumed to be zero (Nalapko et al. (2021), Kalantaievska et al. (2018), Krol and Sokolov (2020), Sokolov et al. (2021)). The results of the calculation are shown in Fig. 3.

Fig. 3. Acceleration of the tank wagon pot

Therefore, the accelerations acting on the pot of a tank wagon were about 2.6 m/s 2 ( ≈ 0.26g) and do not exceed the allowable values (DSTU 7598:2014 and GOST 33211-2014), (Fig. 4). In this case, the allowable accelerations of the load-bearing structure are taken equal to 0.75g ("allowable" running). To determine the fields of distribution of accelerations relative to the load-bearing structure of a tank wagon, computer modelling of its dynamic loading was performed. The calculation was performed by the finite element method in the SolidWorks Simulation software package (Fomin et al. (2017), Lovskaya (2015), Kelrykh and Fomin (2014)). While compiling the finite-element model, isoparametric tetrahedra were used. The optimal number of elements was determined by the graph-analytical method (Vatulia et al. (2018), Vatulia et. al. (2019), Píštek et. al. (2020),