Machining Nomex honeycomb composites (NHCs), which are widely-used materials in the aerospace industry, is an imperative process to obtain desired profiles. However, when machining NHCs to obtain a thin-edged surface, some problems can arise due to large cutting forces. To avoid these defects, a method of ultrasonic vibration machining with variable angles of the down milling disc cutter was proposed in this study. The processing principles and motion characteristics of this method were elaborated. A theoretical model of its cutting process was established. The principle of cutting force reduction was qualitatively analyzed based on the model, and an experimental validation was conducted. The results demonstrated that, due to a smaller swing angle in each pass, the proposed method could reduce the fractal dimension of the machined surface by 6.01% compared to 1° with 10° of angle in each pass. And severe machining defects were decreased. Additionally, comparing the process of the fixed 10° angle of ultrasonic vibration machining with the process of a 1° angle in a pass, cutting force can be significantly reduced by 33.5%, demonstrating the effectiveness of the proposed method which improved surface quality by reducing cutting forces.
Fractal dimension (D) is widely utilized in various fields to quantify the complexity of signals and other features. However, the fractal nature is limited to a certain scope of concerned scales, i.e., scaling region, even for a theoretically fractal profile generated through the Weierstrass-Mandelbrot (W-M) function. In this study, the scaling characteristics curves of profiles were calculated by using the roughness scaling extraction (RSE) algorithm, and an interception method was proposed to locate the two ends of the scaling region, which were named corner and drop phenomena, respectively. The results indicated that two factors, sampling length and flattening order, in the RSE algorithm could influence the scaling region length significantly. Based on the scaling region interception method and the above findings, the RSE algorithm was optimized to improve the accuracy of the D calculation, and the influence of sampling length was discussed by comparing the lower critical condition of the W-M function. To improve the ideality of fractal curves generated through the W-M function, the strategy of reducing the fundamental frequency was proposed to enlarge the scaling region. Moreover, the strategy of opposite operation was also proposed to improve the consistency of generated curves with actual signals, which could be conducive to practical simulations.
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