Effect of the MRE Thickness on Valve Behavior

The behavior of the MRE valves is mainly described by the following two aspects: (a) the breakthrough pressure and (b) the flowrate under different current supplies (flowrate-current profile). Breakthrough pressure is defined as the maximum pressure the valve can withstand without leaking when the electrical current is engaged in the coil. This value is of interest as it ensures the valve can deliver enough pressure to drive the pneumatic soft actuators efficiently. The flowrate-current profile confirms the valve can be operated in an analog manner with repeatability. With increasing current, the airflow decreases monotonically due to the increase of the magnetic force and the reduction of the opening width of the valve channel. This variable pneumatic resistance can be used to control the soft pneumatic actuators similar to an industrial proportional valve.
To investigate the effect on valve behavior brought by the different MRE membrane thicknesses, samples with membrane thicknesses ranging from 1 mm to 3 mm with a step size of 0.5 mm were tested. The flowrate and threshold pressure characterization results are presented in Figure \ref{793304}(A) and (B), respectively.
Figure \ref{793304}(A) indicates that the increase in MRE thickness significantly enhances the regulation of the airflow. As the MRE thickness increases from 1 mm to 3 mm, the electric current required to fully shut down the flow decreases from over 3 A to 1.75 A. This is because the increase in MRE membrane thickness increases the exerted attractive force due to more magnetization, meaning that a weaker magnetic flux density is required to shut down the flow. However, one should also note that the flowrate of the valve without electric current ("fully open" state) is decreased by a thicker MRE membrane, even if the air channel width is kept constant. As the MRE thickness increases from 1 mm to 3 mm, the flowrate without electric current decreases by 33.1%. This is because the thicker MRE performs less deformation when air passes beneath it.

Effect of the Air Channel Width on Valve Behavior

As shown in Figure \ref{793304}(A), the increase in MRE membrane thickness not only decreases the current required to regulate the airflow, but also decreases the volume flowrate when the valve is in its fully "open" stage (with no electric current going through). This lack of flowrate is undesirable as it increases the response time of the soft robots with large internal volumes. One possible way to easily compensate for the flowrate reduction is by increasing the width of the air channel. This can be easily achieved by increasing the width of the Mylar strip used during the fabrication. Three samples with different air channel widths (1 mm, 2 mm, and 3 mm) were fabricated here and tested. The obtained characterization results are shown in Figure \ref{793304}(C) and (D).
As shown in Figure \ref{793304}(C), the increase in air channel width significantly scales up the volume flowrate. The valve with a 3 mm channel width brings an additional 406\% flowrate at "fully open" state, compared to the one with a 1 mm channel width. Meanwhile, the electric current required to fully shut down the airflow does not see a significant change as the channel width increases. (see Figure \ref{793304}(D)). 

Temperature Response

The heat generated during the operation of the valve inevitably raises its temperature, therefore potentially changing the performance and characteristics of the valve. This experiment aims to investigate the performance of the valve during long-term continuous operation, including the temperature and the flowrate through the valve. An MRE valve sample with 3 mm channel width and 2 mm MRE thickness was used here. A constant electric current was applied to the coil. The temperature of the valve was kept monitored throughout the process by a temperature sensor placed in the middle of the bottom surface of the valve. The input pressure of the valve was kept at 20 kPa. The temperature and flowrate curves under three different levels of electric current (1 A, 1.75 A, and 2.5 A) were tested and presented in Figure \ref{793304}(E) and (F). These electric current values were selected as they cover the range within which the pneumatic resistance of the valve changes most rapidly, according to Figure \ref{793304}(C). The test was stopped when the surface temperature reaches 70 oC for safety. Sufficient time (1 hr) was placed between each trial to ensure that the valve returns to the ambient temperature. 
It can be observed that it takes 62 s, 130 s, and 348 s for the MRE valve to reach 70 oC with a continuous electric current of 1 A, 1.75 A, and 2.5 A, respectively. The flowrate through the valve channel sees a 30.2 % and 23.8 % reduction over the entire heating process with 1 A and 1.75 A electric current, indicating a small change in the pneumatic resistance due to the temperature change. This thermal drift is most likely caused by the thermal deformation of the MRE membrane and the silicone. When 2.5 A current is applied, the valve is able to shut down the airflow completely without leaking throughout the entire heating process.