The experimental results obtained by punching with the aforementioned three different diameter 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 ultrasonic time of 0.4 s and cylinder pressure of 0.1 MPa respectively, and the average values of the obtained sample size error *fd* and roundness error *fr* and their ranges were shown in Fig. 9.

For 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 *fd* and roundness error *fr* and their ranges were shown in Fig. 10.

For effect of cylinder pressure on sample error, the cylinder pressure was taken as 0.2 MPa, 0.3 MPa, 0.4 MPa and 0.5 MPa at ultrasonic power of 50% and ultrasonic time of 0.4 s respectively, and the average values of the obtained sample size error *fd* and roundness error *fr* and their ranges were shown in Fig. 11.

The lower limit of the error bars of the roundness error was found negative for the 700 mm samples at the ultrasonic powers of 55% and 65% in Fig. 9b and at the ultrasonic time of 0.55 s and 0.60 s in Fig. 10b, which indicated that the roundness error of some samples was smaller than that of the die (Equation (2)). This was mainly due to that the die with 700 mm 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 from Fig. 9 to Fig. 11, the maximum values of size error *fd* and roundness error *fr* were 8.48 mm and 8.45 mm, 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 *fd* and roundness error *fr* (i.e., the length of the error bars in Fig. 9-Fig. 11) were 4.09 mm and 4.19 mm, respectively, and the maximum values of the ratio of the range of size error and roundness error to the actual diameter of the die were 0.70% and 0.72%, respectively, indicating that the micro-hole punched by the Micro-USF method had a high form precision.

In Fig. 9-Fig. 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 55–70% (Fig. 9a). But on the other hand, the amount of this change was relative small to the corresponding error range (the length of the error bars in the 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 leaded to an essential change in the variation curve. For example, for the 500 mm samples in Fig. 9a, as the ultrasonic power changed from 55–60%, 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 mm 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 Fig. 9-Fig. 11 by the corresponding actual diameters of the die micro-holes, the values lie in the interval from 0–0.72%. 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.