In order to study the effects of different geometric parameters on forming results, not only the stress contours are displayed on the deformed plate, but also the shapes of micro-channels are shown.
As it is shown in Fig. 9, stress contours and forming results are shown. When the length of the second-step structure is different, the stresses on the plate are described by contours. When the length is 5 mm, the deformation between channels is insufficient. If the length is increasing from 5 mm to 7 mm, the stress shown on the plate is increasing based on these comprehensive reasons. The forming results of the plate also become better based on this changing. This can be explained as the flow of rubber will be less restricted when the second-step structure is long enough. The channel can be formed more accurately with larger stresses.
However, as shown in Fig. 9, it is obvious that the ridge of two-step channel is not well formed. Actually, more stresses are needed, when the height of two-step channel is varied. Also, the shape of the second-step structure should be well adjusted to further improve the formability. As shown in Fig. 10, different edge chamfers of the second-step structure are researched to improve this situation.
As it can be seen in Fig.11, with the increasing of edge chamfer (D1, D2), the forming results of the plate firstly become worse and then a better result can be shown. When , the plate is suffered to a smaller stress, and the first-step channel is barely formed. When D1>0.25 mm, the stress shown on the plate is increased, the first and second step channels are obviously formed, and the forming results are better. When edge chamfer D1, D2 are 0.5 mm and 0.3 mm, the shape of the top second-step structure is changed to straight line from rectangle. Since the edges of the second-step structure are accurately formed, the forming result can be better at this time.
As it is seen in Fig. 12, The channels height ratios of the first and second step are 0.3:0.3, 0.35:0.25 and 0.4:0.2, respectively. With the increase of the height ratio of the first and second step channel, the forming results are worse and worse. This may be explained by the flow of rubber is more restricted. As the height of the second-step structure is decreasing, the volume of the second-step structure will also be decreased. When the ratio is 0.3:0.3, the plate is suffered the maximum stress and the forming result is the best.
The length, edge chamfer and height ratio all have influence on the forming result, but the width of channel seems to play a most important role on the final result. This kind of influence has nothing to do with the forming ability of the plate, but it is the location of the interaction that most affects the result. As the width of the channel is increased, the distance between channels is decreased in this experiment. As shown in the Fig. 13, when the channel width is increased from 1 mm to 1.2 mm, the forming results of the plate become worse and worse. This can be explained by the stresses applied on the ridge of the channel. When the distance between channels is too small, the plate cannot be formed accurately and smoothly with less stress. As observed in the figure, the plates are well formed when the distance is 1.4 mm and 1.3 mm, respectively. Therefore, the distance between channels should be equal or greater than 1.3 mm.
The best forming results for the two-step micro channel were found according to the above experiments. The parameters with the best forming results were selected for the following study. Multiple two-step structures are designed in one micro channel. As shown in Fig. 14, finite element simulation results were obtained when the distance between the second-step structures was 0 mm, 1 mm and 2 mm, respectively. It can be observed that the stresses applied on the channel are the same with each other. Also the depths of micro-channel are the same as the design ones. Therefore, the distances between the second-step structures have a little influence on the forming results in No.12, 13 and 14.
As shown in Fig. 15, the two-step channels with the largest number are inserted in the straight line areas. The length of the second-step structure is 7 mm, 8 mm and 9 mm in No.15 No.16 and No.17, respectively. According to the Eq. (2.2), when parameter a is a constant value, parameters b and c are determined. It can be observed that the number of second-step structures is decreased as its length is increasing. When length of second step structure is 7 mm, there will be 134 ones. When the length is 8 mm and 9 mm, the quantities of this structure will be 112 and 100, respectively. As shown in the figure, the three plates are well formed. And it can be found that, the straight line areas are all formed well. There are no obvious evidences to find a relationship between number of second step structures and formability.
In conclusion, the formable structure is obtained based on the following conditions met by each parameter.
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The length of the second-step structure should be long enough (longer than 7 mm).
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Side chamfers should be as large as possible. The second-step structure can be minimized.
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The height ratio of the first and second step structures is 1:1.
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The width of micro-channel should not be too small (greater than 1 mm is appropriate). And the distance between micro-channels should not be too small (greater than 1.3 mm is appropriate).
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Second-step structures can be spaced as close as possible. Through this, the number of second-step structures can be increased.