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The geometrical parameters of the valve spools such as its cone angle(α andφ )，the length and diameter of the orifices (X, Y and Z) are all measured. The complete list of parameters used in the simulation studies are listed in the following Table 1. 5. Results of simulation The parametric studies on the dynamic performance of the pilot operated pressure reduction valve have been carried out by solving the system equations obtained in Section 3 numerically with the help of software Symbols 2000 [9]. This particular package readily lends itself to the Bond graph representation and it can also take into account the various nonlinearities of the model. The various system responses are obtained considering the step input Ts (supply flow rate). Fig. 5 shows the transient response of the system for different pre-compression of the pilot spring. It shows that with the increase in the pre-compression, the peak pressure as well as the steady state pressure increase. It increases the working range of the hydraulic system where such a valve is incorporated. Fig. 6 shows the response of the system for the variation of the exit flow angle a. Figs. 7 and 8 show the settling and peak time of the main spool displacement for the different ratios of damping coefficients between main and pilot spools. Here the settling time means the time until the valve response reaches the steady state value when it is subjected to step input; whereas the peak rise time indicates the time taken to reach the peak of the first overshoot with the same input. It indicates that both the settling and peak times are smaller when the ratio RSP/RP, varies from the value 0.01-1. However, it is found that when the damping coefficient of the main spool (RSP) is below 200 N s/m the valve response is unstable. The best performance of the system is attained when the value of RSP is in the range of 700-900 N s/m. The results obtained by Chin [5] are also compared in the figure; where, this range varies from 500-700 N s/m. This difference may be due to the consideration of the oil compressibility effect and other minor differences in the geometrical parameters of the valve. Fig. 9 shows the system response for the variation of the orifice diameter dX. It indicates that with the increase in the orifice diameter, the settling times as well as the maximum overshoot decrease; whereas the peak time increases.
From these simulation studies, it can be concluded that the damping coefficient of the main and pilot valve spools as well as their shape of the cone tip(α andφ )are the important design variables for the improvement of the responsiveness of the system. Similarly, reducing the diameter of the orifice X may increase the system response; however, it would be at the cost of the increasing settling time. 6. Conclusion In this article a dynamic model of a two stage pilot reduction valve is discussed. The effects of various design parameters on the overall response of the system are investigated through simulation. The verification of the simulation results with the earlier studies conducted by Chin, justifies the proposed model. The model takes into account the various non-linearity of the system. The effects of changes of the diameter of the orifice X and the cone angle(α )of the main spool on the peak rise time and settling time of the system's performance have been presented. It implies that the shape of the tip of the main spool is an important design feature affecting the dynamic characteristics of the system. It is also shown that increasing the pre-compression of the pilot spring increases the operating range of the valve. The factors, having significant effect on the stability are the damping coffidents of the main and pilot spools. It may be difficult to control the damping coefficients of the valve spools in real situation; however, the experimental procedure described by Chin may be a useful method for validating the same. The model can be further refined by incorporating the dynamic behavior of the pilot and main springs, dynamic flow forces on the valve spools. The model does lack the flexibility of the linearised model as proposed by Ray and Chin; however, its simplicity lends itself to be used for wider variation of system parameters.