Effect factors and evaluation method of part accuracy formed by ultrasonic micro-punching with a flexible punch

In this paper, an automatic and quick evaluating method for the micro-hole size and form accuracy with a computer-aided technique was proposed. A special ultrasonic microforming method, that is, micro-ultrasonic thin-sheet-metal forming using molten plastic as flexible punch (short as Micro-USF), was used to punch out micro-holes with diameters of 500, 600, and 700 μm on a copper sheet with a thickness of 30 μm. Using the evaluation method proposed in this paper, the forming accuracy of micro-holes was discussed. The experimental results showed that the ratios of the maximum size error and the maximum roundness error of micro-holes to the corresponding punching die diameter were 1.40 and 1.47%, respectively. The ratios of the maximum size error range and the maximum roundness error range of micro-holes to the corresponding punching die diameter were 0.70 and 0.72%, respectively. This indicated that the accuracy and precision in the Micro-USF method were high for punching micro-holes. Moreover, it was found that there is no significant direct correlation between micro-holes sample errors and these forming parameters when the forming parameters such as ultrasonic power, ultrasonic time, and cylinder pressure were varied, which indicated that the sample errors were random to some extent.


Introduction
With the development of micro-electro-mechanical systems (MEMS), the demand for micro-holes parts in the manufacturing industry is increasing. The processing quality (such as size and form accuracy) of micro-holes largely determines the quality of the MEMS product [1,2]. At present, the methods of manufacturing micro-hole mainly include micro-drilling, electrochemical drilling, micro-electrodischarge forming, and micro-punching [3]. Among them, micro-punching is becoming more and more important and popular due to its advantages such as simple process, high quality, and high processing efficiency [4,5].
In order to improve the punching quality, it is important to find a proper way to characterize and evaluate the micro-hole shape. Optical microscopy techniques, atomic force microscopy (AFM), scanning electron microscope (SEM), focused ion beam imaging microscope (FIBM) are currently common methods to determine the size and form of micro-holes [6]. Although AFM, SEM, and FIBM are able to achieve high accuracy of morphological characterization by atomiclevel contact with the part's surface, the measurement time increases dramatically as the measurement size increases [7][8][9]. In contrast, for sub-millimeter micro-holes, the microscope technique is a faster and more accurate method to obtain the micro-hole contour and evaluate its size and form accuracy, which is widely used in the micro-scale characterizing process [10,11].
However, based on a specific morphological characterization method, there is no unified standard on how to properly evaluate the accuracy of micro-hole forming. Considering the deviations in size and form are easy to happen for micro-holes obtained by most punching methods, the evaluation of the form accuracy is crucial for whether the micro-hole meets the requirements of the application. Yu and Xu et al. [12,13] directly calculated the difference between the micro-hole diameter and the die hole diameter as the size deviation of the micro-holes. Joo et al. [14] used the difference between the maximum and minimum radius of the micro-hole contour as its roundness error. Chem et al. [15] measured the micro-hole diameter in four directions (0°, 45°, 90°, and 135°) and used the maximum difference among the data (Dmax − Dmin) to represent the roundness error. Rhim et al. [16] evaluated the accuracy of the punched hole by calculating the difference between the punched hole diameter and die hole diameter. Endo et al. [17] measured the outer contour of the hole firstly for a small hole with a diameter of about 1 mm using a universal projector. Then the outer contour of the hole was divided into 36 equal parts at 10° intervals, and subsequently, the polar coordinate form was established with the center of the contour circle as the coordinate origin. Finally, the least-squares circle radius of the micro-hole was determined according to the 36 equal parts circle radius, and the accuracy of small hole forming could be evaluated consequently.
In order to evaluate the accuracy of micro-hole formed by punching quickly and accurately, this paper proposed a rapid determination and evaluation method of micro-hole diameter size and roundness error by combining micro-imaging technology and computer-aided image processing technology. This method was then used to analyze the size and form accuracy of micro-holes punched by Micro-USF [18], and the effects of ultrasonic power, ultrasonic time, and cylinder pressure on the forming quality of micro-punching holes were also investigated.

Micro-hole size measurement and roundness error evaluation
This paper first extracted the contour of the micro-hole and then used the extracted contour to measure and evaluate the size of the micro-hole and roundness error, respectively.

Micro-hole image processing and contour extraction
The basic process of micro-hole contour extraction was shown as follows: 1. Color photo decolorization and pixel region analysis Figure 1a shows a micro-hole photo from a microscope which was first decolorized and converted to a grayscale image for the micro-hole contour extraction step (Fig. 1b). A certain part of the micro-hole contour ( Fig. 1b) was enlarged (Fig. 1c). As seen in Fig. 1c, the micro-hole contour and its nearby region were composed of pixels. From Fig. 1c, a virtual boundary could be distinguished between the upper right corner and the lower-left corner, which divided the whole photo into two triangular regions (lower left and upper right). The lower left darker region was the inner part of the hole. The brighter region on the upper right was the surface part of the hole. The transition region between these two parts was the micro-hole contour region. Figure 1d is an enlargement of the local region in Fig. 1c, where the small red rectangle meant a pixel, and the grayscale value of each pixel was added later. The grayscale values of a pixel ranged from 0 to 255, 0 for pure black and 255 for pure white, and the different grayscale values represented their different shades of gray.

Grayscale value normalization
When taking photos of micro-holes with a microscope, the overall brightness of the photos taken at different times was often different because the light brightness might vary. In order to extract the micro-holes contours from various photos accurately with a uniform method, it was necessary to first normalize the grayscale values in the grayscale image. The method of processing is shown in Fig. 2. Region A was the inner part of the micro-hole, B represented the region where the contour of the micro-hole is located, and C meant the surface region of the micro-hole (Fig. 2).
The average grayscale values in the hole region A and the hole surface region C were firstly calculated. For example, in Fig. 2a, the average grayscale values of all pixels in region A and region C were measured to be 41 and 170, respectively. Considering the region inside the hole should be black, the region on the surface of the hole should actually be white. Therefore, all grayscale values below the average value of 41 in region A were set to 0,  Fig. 2c. Figure 3 consists of color photos and images processed in Sects. 1 and 2 above. The first column, "original photos," was the original photos with three different light brightness (Fig. 3). The second column showed the images after the above Sect. 1 for color decolorization, and the third column, "after normalization," was for the images obtained after the normalization process in Sect. 2 above. After such processing, the effect of different image brightness was eliminated, and the foundation was laid for the extraction of micro-hole contour by thresholding later.

Threshold determination and image binarization
The threshold value was calculated using the Otsu method, which used the interclass variance expression to obtain 256 interclass variance values between region A (foreground black) and region C (background white) of the hole surface by traversing all grayscale values in the interval from 0 to 255. The larger the interclass variance value between foreground black and background white, the greater the difference between foreground and background, which indicated that the grayscale value with the largest interclass variance was the desired threshold value. After obtaining the threshold value, all grayscale values below the threshold were set to 0, and grayscale values above the threshold were set to 255, which transformed the previously processed image into a binary image. Processing images with the Otsu method was simple and efficient, which could be considered an adaptive method for determining the threshold.

Micro-hole contour extraction
After the above binarization process, the black and white border edge in the binary image could be identified as the micro-hole contour. The above image processing was programmed using MATLAB software. The original photos of the micro-hole were input for processing, and the micro-hole contours extracted from the photos with different light brightness are shown in Fig. 4. The image was replaced with the original color photos, which was to determine whether the micro-hole contours were accurately extracted (Fig. 4).  As seen in Fig. 4, the extracted micro-hole contours were basically consistent with the usual observations, while the extracted micro-hole contours were the same even if the brightness values of the original photos taken were different. Thus, it could be seen that the microhole contour could be determined more easily and more accurately using the prepared procedure.

Determination of micro-hole diameter and roundness error evaluation
As shown in Fig. 5, the least-squares circle was used as the ideal element to evaluate the actual circle of the micro-hole contour when the contour of the micro-hole was extracted. The diameter of the least-squares circle was used to represent the actual diameter Da of the micro-hole. Meanwhile, the maximum external circle and the minimum internal tangent circle of the contour concentric with the least-squares circle were determined, and the radius difference r between the two circles was calculated to represent the roundness error of the micro-hole. By incorporating all of the above image processing and error evaluation into a program prepared by MATLAB software, the micro-hole size and roundness error could be measured and evaluated easily and quickly. It should be mentioned that the whole process took only about 20 s to evaluate a micro-hole. Figure 6 shows the principle of the Micro-USF used in the micro-punching process. Before starting the punching experiment, fix the baseplate, place the die on the baseplate, place the thin sheet metal in the middle of the die and the pressure plate, then fix the pressure plate on the baseplate with screws, and finally put the plastic powder into the stock bin.

Forming principle of micro-USF
In the punching experiment, the ultrasonic vibration starts to be applied when the ultrasonic punch is lowered into contact with the plastic powder in the stock bin and compressed. Under the effect of ultrasonic vibration, the plastic powder in the stock bin will rub and collide with each other, which could cause the plastic powder to be melted into a viscous fluid medium to form a flexible punch. The main pressure and ultrasonic vibration of the ultrasonic punch were transferred to sheet metal through flexible punch, which caused the shear fracture along the edge of the die hole to form a micro-punched sample.
In this microforming method, the ultrasound vibration could melt the plastic powder to form a flexible punch and was also transmitted to the thin sheet metal through the molten plastic. Therefore, this method belonged to an ultrasound-assisted microforming method, and its advantages [19,20] could be effectively utilized. Fig. 4 The extracted micro-hole contours for the same sample with different brightness values at the same location. a, c, e Photos taken at 20%, 40%, and 60% light brightness, respectively. b, d, f Enlarged views of the micro-hole contour and its nearby region corresponding to photos (a, c, e), respectively

Experimental platform
The Micro-USF experimental platform was consisted of an ultrasonic plastic welding machine and a set of special micro-punching experimental setups. The main pressure of the ultrasonic punch was provided by the air cylinder built into the ultrasonic plastic welding machine, and the ultrasonic welding machine also generated ultrasonic vibration on the ultrasonic punch. The 2020 ultrasonic plastic welding machine produced by Shenzhen RIFA Ultrasonic Equipment Co., Ltd. was used in the experiment, and its main parameters were shown in Table 1. The special micro-punching experimental setup is shown in Fig. 6, which was mainly composed of a baseplate, a pressure plate, a stock bin, and some screws.

Die
The material of the die is Cr12MoV (Chinese National Standard GB/T 1299-1985) die steel plate with 1 mm thickness, and round through-holes were machined by mechanical method. The actual dies are shown in Fig. 7.
In this paper, three dies with different micro-hole diameters were used, and their design diameters were 500, 600, and 700 μm, respectively. Their actual diameters and roundness errors were measured by the methods described in Sect. 2, and the results are shown in Table 2.

Experimental materials
The experimental material was T2 purple copper (Chinese National Standard GB/T 5231-2012), and its chemical composition and material properties are shown in Table 3 and Table 4, respectively. The thickness of the T2 thin copper sheet with the rolled state used in the experiments was 30 μm.
The material for the flexible punch was EVA (ethylene vinyl acetate) plastic powder with an average particle size of 350 μm, and its melting temperature was 90 °C.

Experiment process
The samples obtained from the experiments could be divided into 3 categories, as shown in Fig. 8. In the first category, in which the experimental parameters were small, the punching could not be completed, as in the samples shown in Fig. 8a, b. In the second category, in which the experimental parameters were large, the samples fractured, as in the sample shown in Fig. 8c. The samples in the two categories of Figs. 8a, b, and c were not fully formed. In the third, category in which the punched sample was a completely round hole and no fracture happened, and sample was considered to be fully formed, as shown in Fig. 8d.
For the Micro-USF method, ultrasonic power, ultrasonic time, and cylinder pressure were three important parameters of affected micro-punching. In the experiment, the other parameters were kept constant and the above three parameters were changed to study their effects on the form accuracy of micro-hole samples punched by Micro-USF. In each set of parameters, 8 samples were punched out, and   Fig. 7 Photo of the three dies with different diameters if 5 or more were fully formed, 5 were selected for measurement, and data were recorded. If only 4 or less samples were fully formed, the samples were considered not fully formed at that parameter and were discarded from the discussion. In this paper, the parameters for obtaining fully formed samples were: ultrasonic power 50-70%, ultrasonic time 0.4-0.6 s, and cylinder pressure 0.1-0.5 MPa.

Micro-hole accuracy evaluation
Considering that there was an error between the actual diameter size and design size of the die, and the roundness error of the die might be transferred to the sample, the effect of die error should be deducted in the sample error evaluation. Therefore, the difference fd between the sample size and the actual diameter size of the die was used to evaluate the size accuracy of the punched sample, and the difference fr between the sample roundness error and the die roundness error was used to evaluate the form accuracy of the punched sample. That was Here, f d is the size error of the sample relative to the die, d d is the measured diameter of the die, and d s is the measured diameter of the sample.
Here, f r is the roundness error of the sample relative to the die, r d is the die roundness error, and r s is the sample roundness error.

Results and discussion
The experimental results obtained by punching with the aforementioned three different diameters of dies were as follows: For the effect of ultrasonic power on sample error, the ultrasonic power was taken as 55%, 60%, 65%, and 70% at the ultrasonic time of 0.4 s and cylinder pressure of 0.1 MPa, respectively, and the average values of the obtained sample size error f d and roundness error f r and their ranges are shown in Fig. 9.
For the effect of ultrasonic time on sample error, the ultrasonic time was taken as 0.45 s, 0.50 s, 0.55 s, and 0.60 s at the ultrasonic power of 50%, and the cylinder pressure of 0.1 MPa, respectively, and the average values of the obtained sample size error f d and roundness error f r and their ranges are shown in Fig. 10.
The lower limit of the error bars of the roundness error was found negative for the 700 m samples at the ultrasonic powers of 55 and 65% in Fig. 9b and at the ultrasonic time of 0.55 and 0.60 s in Fig. 10b, which indicated that the roundness error of some samples was smaller than that of the die (Eq. (2)). This was mainly due to that the die with a 700 m diameter had a larger roundness error (see Table 2). That is, some larger form accuracy deviations between the actual edge to the ideal circumference of the die hole were not fully reflected on the punching sample, which caused the roundness error of the sample was less than that of the die.
From the experimental results shown in Figs. 9, 10, and 11, the maximum values of size error f d and roundness error f r were 8.48 and 8.45 m, respectively, and the maximum values of the ratio of size error and roundness error to the actual diameter of its corresponding die were 1.40 and 1.47%, respectively, indicating that the Micro-USF method had a high degree of form accuracy. On the other hand, the maximum values of the range of size error f d and roundness error f r (i.e., the length of the error bars in Figs. 9, 10, and 11) were 4.09 and 4.19 m, respectively, and the maximum values of the ratio of the range In Figs. 9, 10, and 11, the bar height in the bar graph represented the average deviation of the sample size or roundness error from the actual size and roundness error of the die hole under a certain experimental condition. Although the sample error also changed as the experimental condition varied, as shown in the change of ultrasonic power from 55 to 70% (Fig. 9a). But on the other hand, the amount of this change was relatively small to the corresponding error range (the length of the error bars in Fig. 9), and there was a certain overlap between the error value intervals reflected by the error bars for each experimental condition (e.g., 55%, 60%, 65%, and 70% of ultrasonic power in Fig. 9a). Within the error range reflected by the error bar, it was possible to obtain samples with errors in this range. Therefore, the average error values (height of the bars in the bar graph) of the five selected samples changed with the choice of samples, which led to an essential change in the variation curve. For example, for the 500 m samples in Fig. 9a, as the ultrasonic power changed from 55 to 60%, it was possible that the curve might change from decreasing to increasing if the selected sample was different. This was because the lower end of the 500 m sample error bar at 55% ultrasonic power was lower than the average value of the sample error at 60% ultrasonic power. This indicated that changing the forming parameters did not directly affect the change in the sample error. That is to say that there was a randomness in the sample error that was not significantly and directly related to the forming parameters.
Dividing the range of all errors (error bar lengths) in Figs. 9, 10, and 11 by the corresponding actual diameters of the die micro-holes, the values lie in the interval from 0 to 0.72%. Within such a small interval, a certain slight effect could lead to a change in the results, so the effect of random factors dominated the errors obviously. This probably was the reason why the sample errors show randomness.

Conclusion
The main conclusions of this paper were as follows: 1. A method for rapid evaluation of micro-hole size and roundness errors was proposed. Based on the microscope imaging method, the actual contour of the microhole was obtained, and the micro-hole size and roundness error were evaluated by the least square method. 2. Using the Micro-USF technique to punch micro-holes with different diameters in thin T2 copper sheets with a thickness of 30 m, the experimental results showed that the technique has a high level of form accuracy and form precision. However, the sample error and the forming parameters such as ultrasonic power, ultrasonic time, and cylinder pressure did not show a direct correlation, which indicated that the sample error is random to some extent.