## 4 Simulation and Experimental Validation
### Experimental Validation of Force Fluctuation Characteristics
The tested amplitude of the milling force fluctuation was 24.5 N with a slight fluctuation of 3 N, which could be caused by the influence of filtering and other noise data. The measured milling force at \(A_{p}\) = 2.6 mm was used for comparison of the simulation error. The comparison of the two force fluctuations showed that the simulation method could accurately predict the milling force fluctuations with an error of less than 3 N. This comparison also confirmed by the correctness of the uniformity characteristics of the milling force fluctuations. Figure 10: Experiment result and force fluctuation data: (**a**) FFT analysis at spindle speed 2279.8 rpm, \(A_{e}\) = 2.5 mm, \(A_{p}\) = 0–10 mm; (**b**) milling force fluctuation data at tool pass frequency and (**c**) milling force data without cutter runout influence. The results presented in Figure 11a verify the uniformity characteristics of the milling force fluctuation theory. The minimum value of the milling force fluctuation with \(A_{poc}\), which was calculated by Equation (14), was compared with the actual measured milling force fluctuation. The tested amplitude of the milling force fluctuation was 24.5 N with a slight fluctuation of \(\pm\)1.5 N, which could be caused by the influence of filtering and other noise data. The measured milling force at \(A_{p}\) = 2.6 mm was used for comparison of the simulation error. The comparison of the two force fluctuations showed that the simulation method could accurately predict the milling force fluctuations with an error of less than 3 N. This comparison also confirmed the correctness of the uniformity characteristics of milling force fluctuations. The results in Figure 11b verify the periodicity characteristics of the milling force fluctuation theory. Although there were certain differences between the measured and simulation data, due to the simplified force prediction model, the measured data at \(A_{p}\) = 1 mm are high similarity with the measured data at \(A_{p}\) = 6.2 mm, having a constant difference of approximately 23N. This result proves the correctness of the periodicity theory defined by Equation (22). The results in Figure 11c show two sets of force data at \(A_{p}\) = 1 mm and \(A_{p}\) = 4.2 mm; the first \(A_{p}\) is arbitrary and the second one is determined according to Equation (25). The collected data were realigned by the fluctuation characteristics of the milling force. As shown in Figure 11c, the force fluctuation at \(A_{p}\) = 1 mm was approximately 9.5 N and that at \(A_{p}\) = 4.2 mm was approximately 8 N. Due to the instability of milling force fluctuations, a small, inconsistent fluctuation of 1.5 N can be regarded as a calculation error. Therefore, Equation (23) is verified to be correct. Then, other features of the symmetry characteristics of Equations (24) and (26) can also be observed in Figure 11c. Based on the comparison results of the two sets of data, it can be concluded that the two forces were symmetrical on the input axis of \(A_{p}\) = 2.6 mm and the output axis of \(F\) = 12.5 N. This result confirmed the proposed symmetry characteristics of the milling force fluctuation theory. Figure 11: Enlarged view of milling force data: (**a**) enlarged view of the milling force data at \(A_{p}\) = 2.6 mm and \(A_{p}\) = 5.2 mm; (**b**) enlarged view of milling force data at \(A_{p}\) = 1 mm and \(A_{p}\) = 6.2 mm; and (**c**) enlarged view of the milling force data at \(A_{p}\) = 1 mm and \(A_{p}\) = 4.2 mm.