The problem of fastening cargo on railway rolling stock

. Fastening of cargo on the car. Calculation of load shift, elongation and forces in elastic elements of fasteners. Describe the parameters of the load and the physical and geometric parameters of the load fastening; give the results of the calculation of the longitudinal forces perceived by the elements of the load fastening. The article uses the basic law of dynamics in relative motion for the non-ideal connection known from theoretical mechanics. The results of the calculation of the longitudinal forces perceived by the load fastening elements, which allowed determining the load shifts along the car, elongation and forces in the flexible fastening elements are presented. Example calculation contributes to the practical application of a new method of calculating the elements of fastening on the car in the development of schemes of placement and fastening of goods of arbitrary geometry. The results of calculations revealed that the accepted value of the coefficient of longitudinal dynamics of the car corresponds to the shunting collision of the car on the hump yard in the marshalling yards.


Introduction
This paper, as well as works [1 -22], is devoted to problems of fastening of freights on the open rolling stock. It should be noted that in [17] does not define shifts of cargo along the car, elongation and efforts in flexible fastening elements, which confirm the incorrectness of the solution of the problem of cargo fastening. It is for this reason that in [17] the calculated values of the forces in the fastenings of the goods, both in the longitudinal and transverse directions, regardless of the shape of the cargo and the useful floor space of the car, have the same value, which is not true. In [12,16,18] new methods of calculation of elastic elements of fastening of the load at influence both longitudinal, and transverse forces are stated. Specific examples of calculations against longitudinal shear using new methods are given in [18].
However, up to date, there are few examples of the application of engineering calculation of the load shift along the car, elongation and effort in the flexible fastening elements by determining the number of fasteners, which would provide guaranteed strength of flexible fastening elements according to the new method [12,16,18], which confirms the actual technical problem of securing goods on a railway platform.

Object:
-describe the parameters of the cargo and physical and geometric parameters of cargo securing; -give results of calculation of the longitudinal forces perceived by elements of cargo fastening; -describe the sequence of calculation of forces in the elastic fastening elements according to the recommended formulas.

Method of research
The research methods are based on the use of the basic law of dynamics in relative motion for non-ideal coupling, known from theoretical mechanics [12].

The main results of the study
For example, we show the results of calculations of forces in the flexible elements of fastening the winding gear LP-152 on the railway platform ( Fig. 1, Fig.2, Fig.3).   In Fig. 1 the numbers indicate flexible fastening elements; R1 -R6, R1а -R6а -elastic fastening elements in one direction; R1р -R5р, R1ар -R5ар -the other direction.
Loading is designed on a 4-axis universal railway platform with a wooden or woodmetal floor with a strip width of not more than 1100 mm. Cargo is installed on the floor of the platform without shifting the center of gravity from the transverse axis of the platform.
The longitudinal and transverse forces on the cargo during transport are perceived as: in the longitudinal direction by six pairs of extensions R1 -R6 (2 pairs of extensions from a wire with a diameter of 6 mm in 8 threads in each direction) and blocks of the position No. 10, 11, 12; in the transverse direction of five stretch marks R1 -R5 и R1р -R5р in each of the directions and blocks of the position No. 13 and 14 are nailed to the floor platform 6 nails К6х 200 (mm) each frame.

Determination of physical and geometrical parameters of cargo securing
1. Parameters of flexible fastening elements (set values and accepted from the drawing of the load).
1.1. Physical and geometric parameters of elastic fastening elements, as in [12,18]: E = 1·10 7the modulus of elasticity of the elastic fastening elements taking into account the twisting of the wire (kN/m 2 ); d = 6is the wire diameter of the elastic fixing element, mm; nis the number of strands of wire elastic fixing element (for stretch marks and bindings n = 8) (PC); R0 = 20is adopted the average value of the effort of preliminary wire twists of fastenings (kN).
Let us make a reservation that at neglect of physical and geometrical parameters of elastic elements of fastening it is not possible to make any calculations of shift of the load along the car [12,18]. Table 1 summarizes these geometric parameters of the securing devices. kd.х = aeх/g = 1,6factor longitudinal dynamics of the carriage (1,2  2) (portable longitudinal acceleration of the car with a load in the units of g); Ieх = kd.х G = 1,6·450 = 720longitudinal portable force of inertia (kN). 2. Friction force [18].   (1) Substituting in the last formula the initial data and taking into account the symmetrical placement of the load relative to the longitudinal axis of the car [ FR0reat.х1 = R0х1 = 129.7holding power in fastening elements from the efforts of preliminary twisting of the wire in one direction (kN).
1.2. Calculation of the projection of elastic forces from the force of preliminary twists of the wire fastening of the other direction:  Substituting in the last formula the initial data and taking into account the symmetrical placement of the load relative to the longitudinal axis of the car [ Substituting in the last formula the initial data and taking into account the symmetrical placement of the load relative to the longitudinal axis of the car, we will have: R0z2х = R0z1х = R0z1 = 122.37projections of elastic forces from preliminary wire twist of fastenings on the vertical axis the other direction (kN).
3. Determination of the sliding friction force from the force of preliminary twists of the fastening wire R0 on the vertical axis [12,18].
Calculation of sliding friction force:  [8], proved that the projection of the load securing elements on the vertical axis affect the magnitude of the friction force along the longitudinal axis of the car. This increases the value of the holding forces.
[Rnail] = 1,08permissible value of force on one fastener (nail) (kN) [1,2,16]; nnail.х = 16the accepted quantity of thrust blocks according to the scheme of placement and fastening of freight on the car, pieces (see Fig. 1 The positive sign of the longitudinal force ∆FR0х means that the shear force is greater than the holding force. In this case, obviously there will be a shift of the cargo along the car, which is accompanied by loss of fasteners (nail) resistant bars and twisting these bars are relatively distant from the end surfaces of the load faces. 7. Calculation of equivalent rigidity of fastening elements along the car cequiv.x at the coefficient of sliding friction (after the cargo shift occurs). 7.1. Calculation due to the asymmetry of the fastening elements relative to the transverse axis of one direction (see (3.90 a) [12] or (20) [ x equiv c (9) or, after calculations, where [lelast.i]allowable elongation of each flexible element: Here 7.854 = πE10 -6 /4 is a factor of adjustment for elastic modulus of the securing elements as affected by wire twisting (normally E = 1·10 7 for annealed wire) [12, p. 200] (kN/m 2 ); [Ri0]  the permissible value of the force in the I elastic fastening element, determined by table 30 in the [16] depending on the number of ni threads (8 PCs.) and the diameter di (6 mm) of the fastening wire, taking into account the tension of the preliminary twists of the wire R0i = 20 кН [19], т. Е.
For the given initial data, the allowable values of the elongation of each fastening element were equal to (m): [    Table 3 presents the calculated forces of securing elements. The analysis of calculation results shows, for the given initial data of a problem (i.e. at coefficient of longitudinal dynamics of the car of ktol.х = 1.6) efforts in the first, third and fourth flexible elements of fastening of one direction and in the third, fourth and fifth elements of fastening of other direction exceed admissible value (24.8 + 20 = 44.8 (kN)). Note that the assumed value of the coefficient of longitudinal dynamics of the car (ktol.х = 1.6) corresponds to shunting collision of the car on hump yard marshalling stations. In this case, additional means of fastening are required to ensure the safety of transportation, safety of the transported cargo and parts of the rolling stock. It is possible to control the process of calculation, i.e. to predict in advance the possible case of traffic safety violations. At the same time, if the shape of the load and the useful area of the car allows, it is possible to increase the number of fasteners (nail), otherwisethe number of elastic fastening elements, and sometimes perform both. For example, if instead of the accepted number of nails nbar.х = 6 (PCs). change the length of the two parallel spacing blocks 5, nailed to the floor of the car close to the transverse-mounted thrust blocks 6 (see Fig. 1), adopt nnail.х = 16 (PCs.), leaving the number of thrust bars nbar.х = 16 (PCs.), then the shift of the cargo along the car х will decrease by almost 1.3 times (more precisely, instead of 44 and 49 (mm) for both directions, respectively, will be equal to 33 and 36 (mm). Similarly, reduced elongation on the first, third and fourth fastening elements (for example, the first element is lelast.1 = 36 (mm) will be 26 (mm), the third element lelast.3 = 22 (mm) will be 16 (mm), and the fourth element lelast.4 = 34 (mm) (25 mm). Accordingly, the stress in the first member of one direction would be equal Relast1 = 40.8 instead of 55.3 (kN), i.e. almost 1.35 times (55.3/40.8 = 1.35) less in the fifth element the other direction will be equal to Relast5р = 44.2 is 59.8 (kN), i.e. almost 1.25 times (59.8/42.2 = 1.35) is less than it was in nnail.х = 6 (PCs.). From here it becomes obvious that if the forces in the fastening elements from the effects of longitudinal forces will be less than the permissible, it will be provided with guaranteed strength in the fastening elements with a margin.
We will make a special reservation that similar calculations on the strength of flexible elements of cargo fastening can be carried out also under the influence of transverse forces of one or the other direction.

Conclusions
1. The sequence of calculation of efforts in elastic elements of fastening of the load (on the example of the winch LP-152) is given on a new method of calculation of fastening is resulted [12,18].
2. The results of calculating the longitudinal forces perceived by the load securing elements are presented, which allowed to determine the shifts of the cargo along the car, elongation and forces in the flexible fastening elements.
3. The results of calculations are similar to [18] revealed that the assumed value of the coefficient of longitudinal dynamics of the car (kd.х = 1.6) corresponds to shunting collision of the car on hump yard of sorting stations. In this case, additional means of fastening, for example, fasteners (nails) are required to ensure the safety of transportation, safety of the transported cargo and parts of the rolling stock. At the same time, if the shape of the cargo and the useful area of the car allows, it is possible to increase the number of fasteners, otherwise -the number of elastic fastening elements, and sometimes perform both.
4. On particular case of the calculation is proved the possibility of calculating the shift of the load along the car and the forces in the fastening elements. The example of calculation expands the possibility of applying in practice a new method of calculation of fastening elements on the car in the development of schemes of placement and fastening of cargoes of arbitrary geometry [12,16,18].