Fig. 9.    Bode diagram of the system with integral compensation

The static characteristics at open-loop and closed-loop mode are shown in Fig. 11. In the open-loop control mode, the hysteresis occupies about 22% of the input range, and the linear range is only 7%, within which the ascending sect

CHINESE JOURNAL OF MECHANICAL ENGINEERING ·425·

occupies only 1%. The reason comes from the structure of poppet valve, friction and the pilot stage. The linear control range can be extended to about 56% and the hysteresis can be reduced to 17% under closed control, but severe oscillations are easily caused due to the large hysteresis of the valve. As the key component of the whole WAIM system, the water hydraulic proportional pressure relief valve can not meet the requirement of the system  because of the high nonlinearity. Based on the least-square linear regression on the static characteristic of the valve, the hysteresis can be effectively reduced through inverse transformation and static feed-forward compensation. For the reason that the linear controllable range accounts for smaller fraction of the increase of input signal than the decrease, the pulse modulation is added to one-side hysteresis compensation. According to the static characteristic with the compensation, the linear range is above 80% and the hysteresis is reduced to about 5% as shown in Fig. 12.

Fig. 10. Structure sketch of the water hydraulic proportional pressure relief valve

Fig. 11. Static characteristics of the water hydraulic proportional pressure relief valve under open-loop and closed-loop control

The load pressure curve of ABS molding experiment is shown in Fig. 13. The delay time is set as td = 0.5 s, and the slope control time of water injection is set as ts  = 1.5 s.

It is shown that the load pressure error at the end of the slope control is 5.8%. Meanwhile, the maintaining pressure is set as 19 MPa and the steady-state error is only 0.7%. When the directional control valve switches, the impact pressure occurs with the maximum overshoot close to about 8 MPa, and the delay time for response of the on-off valve is about 0.27 s. The excessive time delay and pressure impact may cause problems of quality of products. On one hand, the water hammer in water hydraulics is greater than oil hydraulics, for the reason of high stiffness of water hydraulic system and fast propagation of pressure in water. This special property of water causes the high pressure impact and oscillation during process of valve switch. On the other hand, the underdamping may be introduced by small flow resistance at the inlet of the accumulator, and it also can cause pressure oscillation and overshoot with switch of directional valve. From the experimental  results, it is realized that the water injection pressure can be raised gradually in spite of the poor performance of the directional valves and pressure control valve. Moreover, the  peak value of the water injection pressure is controllable and the holding pressure can be stabilized at a maximum value. These results show that the design approach meets the requirements of WAIM production.

Fig. 12. Static characteristics of the water hydraulic proportional pressure relief valve with compensation

Fig. 13. Experiment results for injection water pressure control with ABS

6   Conclusions

(1) Intermittence, periodic, large pressure and flow   rate

·426·

ZHOU Hua, et al: Water-Assisted Injection Molding System Based on Water Hydraulic

Proportional Control Technique

change are main work characteristics of WAIM. The differential pressure control method with pressure cylinder is provided to regulate the accumulator pressure through back pressure control by water hydraulic proportional pressure relief valve. The load pressure can be increased over a wide range as energy is saved by the application of the accumulator.