## 5 Conclusions  
This study presents three characteristics of milling force fluctuations: uniformity, periodicity and symmetry. By applying the proposed theory, it is only needed to test the force fluctuations in the range of [0, \(A_{\text{{poc}}}\)/2] to obtain the actual force fluctuations in the range of [0, +\(\infty\)]. This greatly reduces the test workload of a milling force experiment on the axial depth of cut and makes the proposed theory a useful approach during the study and development of a new advanced milling process.  
The main contributions of this study can be summarized as follows:  
1. A milling force modeling method is proposed to fulfill the requirements of mathematical expression of the milling force fluctuation. By using the peak-to-peak difference of milling force, the milling force fluctuations are quantified and defined, which provides an opportunity to study the characteristics of milling force fluctuations by mathematical methods;
2. A virtual-edge projection method, which enables the milling force on every cutting edge to be projected and replaced directly to the same virtual edge, is proposed. Therefore, the milling force fluctuation can be analyzed intuitively from discontinuities and overlaps of the projected virtual edge;
3. The relationship between the force fluctuation characteristics and axial depth of cut is revealed. A one-cycle standard of the axial depth of cut (\(A_{\text{{poc}}}\)) is defined. It is also proven that the force fluctuation is always zero when the axial depth of cut is \(A_{\text{{poc}}}\). In addition, it is demonstrated that the milling force fluctuates periodically and the minimum period is \(A_{\text{{poc}}}\). Furthermore, in a period, the milling force fluctuation always first ascends and then descends as the value of \(A_{p}\) increases and the amplitude is symmetric about \(A_{\text{{poc}}}\). Then, the milling force fluctuations of all periods can be understood by experimental test of only half periods, which significantly reduced the milling test workload;
4. Two prediction methods of milling force fluctuations are proposed: fast estimation method and simulation method. The fast estimation method has a simple calculation process and does not require determining the milling force coefficient. However, it only displays a percentage result of force fluctuations and there is no specific force value, which makes this method less accurate and suitable for precise engineering applications. In contrast, the simulation method has higher prediction accuracy and the average error is less than 3 N, which meets the experimental requirements.  
In summary, this study reveals the force fluctuation characteristics in different axial depths of milling and proposes the theory of uniformity, periodicity and symmetry. The application of this theory can not only reduce the test workload, but also predict and understand the actual force fluctuations at different axial depths of milling. In future work, we will study the relationship between milling force fluctuation characteristics and other parameters, such as radial depth of cut.  
Conceptualization, B.M.; methodology, B.M.; validation, B.M. and Z.W.; writing--original draft preparation, B.M.; writing--review and editing, S.Y.L. and M.L.; project administration, X.L.; funding acquisition, X.L. and L.W. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Projects of International Cooperation and Exchanges NSFC, grant number 5171001055.  
Not applicable.  
We thank LetPub (www.letpub.com) for its linguistic assistance during the preparation of this manuscript. And thanks to the English editing service of MDPI.  
The authors declare no conflict of interest.