Radial deformations of working cylinder of hydraulic Legs depending on their extension

Current methods of calculation of parameters of hydraulic legs of powered supports are in most cases analytical and do not consider all complex of factors. Finite element model was developed to study this problem and used to analyze the influence of hydraulic legs extension on radial deformations of cylinder of different producers of powered supports at variation of hydraulic fluid pressure. It was revealed that radial deformations of cylinders along the axis of hydraulic legs increase in magnitude in direct proportion to the hydraulic fluid pressure and extension. Research results can be recommended to define optimal geometric parameters of hydraulic legs in respect to the minimal radial deformations of hydraulic cylinder increasing its impermeability and improving the work of cup seals. It is recommended to use the obtained results at power support designing.


Introduction
Hydraulic leg is a hydraulic power cylinder. Its impermeability is determined by the size of the gap between the piston and the cylinder bridged by the seal. Numerical value of the gap includes two components: 1) tolerance for production of piston and cylinder (constant component), which determines minimal Z min and maximal Z max gaps during assemblage; 2) radial deformations of interior surface of cylinder (dR) under the hydraulic liquid pressure (variable component), which depend on the value of this pressure (P), production technique [1][2][3][4], support construction [5], hydraulic leg construction [6][7][8] and their hydraulic extension (l p ).

Methods
To calculate radial deformations finite element method was used as it is one of modern computational approaches allowing to carry out calculations with high accuracy and speed for constructions with complicated configuration using computer aids.

Work Description.
Finite element model was developed for research of the influence of hydraulic leg parameters on their strained state.  figure 1 has an expanding section from the side of the head end and a convergent section from the side of the rod end. To pit-point locations of radial deformations along the length of the cylinder during comparative calculations the following key points were used: point 1 -has maximal radial deformations near the piston (at this point radial deformations are equal to dR 1 ); point 2 -is situated in the ares of stable radial deformations in the cylinder main body (dR 2 ); point 3 -has negative radial deformations (compression of the cylinder) in the limits of the piston location (dR 3     Numerical values of radial deformations of hydraulic leg M138 at the point situated in the limits of piston area (dR 3 ) are two times less than these of the rest (table 2), as this leg has minimal length of piston (75mm) and maximal value of constringent deformations is beyond its limits. Thus, for example, for this leg deformations in the piston area dR 3 = -0,0000214 mm at P=50 MPa and l p =(2/3)l p max whereas minimum value of these deformations is -0,00410 mm. The length of piston of the rest of legs is 90 mm (table 2) and minimum values of radial deformations dR 3 are situated in piston area.   Variation of radial deformations (dR 3 and dR 4 ) at extension alteration from l p =(2/3)l p max to l p =l p max (change of relative extension l p /l p max from 2/3 to 1) is shown in Figure 5. The leg M138 is exposed to maximal variations of constringent radial deformations dR 3 due to small piston length. The change of dR 3 by 40-50 % corresponds to legs OKP70, 1M130 and Glinik. Variations of hydraulic leg Joy make up 25 % and these of legs M142 and M145 -near 4 %.  Radial deformations in seal area (dR 4 ) at l p =l p max increase: for hydraulic leg M138 -at initial thrust pressure (32 MPa) by 13 %, approximately, and at high pressure (50 and 70 MPa) -by 27 %, approximately; for hydraulic leg M142-by 17,5 % over all pressure range; for the rest of hydraulic legs over working range of pressure -from 2,5 to 8 %.
For hydraulic leg M145 radial deformations (dR 4 ) at l p =l p max decrease by 10-15 % at different hydraulic liquid pressure.
Conclusions. Realized researches allow to conclude that with increase of hydraulic leg extension the gap between the piston and the cylinder increases in the area of the first seal from the side of the head end (+dR 4 ) and decreases from the side of the rod end in the limits of the piston (dR 3 ).