# Numerical Analysis of Fluid Stream Division to Supply Multiple Hydraulic Receivers
## 6 Summary and Conclusions  
The article concerns the numerical analysis of a hydraulic system in which it is necessary to divide the stream of working fluid into multiple receivers connected in parallel on the example of a rail grinder. This issue is crucial from a practical point of view because  
Figure 16: Operating cycle in a high load range, \(T_{Lm,max}=75\) N m, with load variation of particular motors by 10%; (**a**) flow rates and pressures; (**b**) rotational speed of hydraulic motors and load torques.  
Figure 17: Operating cycle in a high load range, \(T_{Lm,max}=75\) N m, with load variation of particular motors by 30%; (**a**) flow rates and pressures; (**b**) rotational speed of hydraulic motors and load torques.  
it reduces the device's total cost by simplifying the hydraulic supply system and not requiring advanced electronic control systems. The analyzed system included a hydraulic supply unit containing a variable displacement pump and a relief valve which supplied four operating lines connected in parallel. Each line consisted of a flow control valve, a switch valve, a hydraulic motor and a relief valve. The motors were loaded with an external torque of a constant or variable value. The system was designed to work with the nominal pressure in the supply line \(p_{0}=16\) MPa and the flow rate through each of the receivers \(Q_{0i}=25\)\(\,\mathrm{dm}^{3}\,\mathrm{min}^{-1}\). In the first stage, a geometric model of the flow control valve was built, and \(CFD\) tests were carried out to obtain pressure and velocity distributions and calculate the discharge coefficient. Then, a mathematical model of the whole hydraulic system was formulated. Based on the CFD results and the mathematical model, a simulation model was built in the Matlab/Simulink environment. Numerical analyses were carried out, which showed that the proposed solution ensures the maintenance of appropriate operating parameters, regardless of the value and course of the load torque. Detailed conclusions:
* The proposed solution can be used in practice in systems with the requirement to keep the controlled parameter above the threshold value. This work concerned, in particular, the maintenance of the minimum flow rate, and thus required rotational speed of hydraulic motors regardless of the load;
* The applied hydraulic components do not require an electric power supply, which is especially important under the track grinder working conditions: continuous movement, high temperatures in the grinding area and the influence of weather conditions;
* The flow rate settings can be adjusted to a small extent by modifying the initial tension of the valve spring \(x_{spr}\). The settings can be changed in a broader range by using a valve spring with a different stiffness \(k_{spr}\). Finally, valves of larger or smaller nominal sizes can also be used;
* It is essential to pre-define a load torque range and adapt the relief valve settings to minimize energy loss during the implementation of operating cycles. The highest energy efficiency achieved when working under a load close to the maximum was approximately 80%. However, with a low load of about 10% of the allowable value, the energy efficiency drops to 30%.  
Conceptualization, E.L.; methodology, G.F.; software, E.L. and G.F.; validation, E.L.; formal analysis, E.L.; investigation, E.L. and G.F.; resources, E.L.; writing--original draft preparation, G.F.; writing--review and editing, G.F. and E.L.; visualization, G.F.; supervision, E.L.; project administration, G.F.; funding acquisition, E.L. and G.F. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The authors declare no conflict of interest.