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1. Trochoidal milling: investigation of dynamic stability and time domain simulation in an alternative path planning strategy

   https://doi.org/10.1007/s00170-018-03280-y  

   Akhavan Niaki, F ; Pleta, A ; Mears, L ; Potthoff, N ; Bergmann, Jim A ; Wiederkehr, P ( July 2019 , International journal, advanced manufacturing technology)

   Trochoidal milling is an alternative path planning strategy with the potential of increasing material removal rate per unit of tool wear and therefore productivity cost while reducing cutting energy and improving tool performance. These characteristics in addition to low radial immersion of the tool make trochoidal milling a desirable tool path in machining difficult-to-cut alloys such as nickel-based superalloys. The objective of this work is to study the dynamic stability of trochoidal milling and investigate the interaction of tool path parameters with stability behavior when machining IN718 superalloy. While there exist a few published works on dynamics of circular milling (an approximated tool path for trochoidal milling), this work addresses the dynamics of the actual trochoidal tool path. First, the chip geometry quantification strategy is explained, then the chatter characteristic equation in trochoidal milling is formulated, and chatter stability lobes are generated. It is shown that unlike a conventional end-milling operation where the geometry of chips remains constant during the cut (resulting in a single chatter diagram representing the stability region), trochoidal milling chatter diagrams evolve in time with the change in geometry (plus cutter entering and exiting angles) of each chip. The limit of the critical depth of cut is compared with conventional end milling and shown that the depth of cut can be increased up to ten times while preserving stability. Finally, the displacement response of the cutting tool is simulated in the time domain for stable and unstable cutting regions; numerical simulation and theoretical results are compared. 

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2. Uncertainty Quantification and Optimal Robust Design for Machining Operations

   https://doi.org/10.1115/1.4055039  

   Wan, Jinming ; Che, Yiming ; Wang, Zimo ; Cheng, Changqing ( February 2023 , Journal of Computing and Information Science in Engineering)

   Abstract In this study, we carry out robust optimal design for the machining operations, one key process in wafer polishing in chip manufacturing, aiming to avoid the peculiar regenerative chatter and maximize the material removal rate (MRR) considering the inherent material and process uncertainty. More specifically, we characterize the cutting tool dynamics using a delay differential equation (DDE) and enlist the temporal finite element method (TFEM) to derive its approximate solution and stability index given process settings or design variables. To further quantify the inherent uncertainty, replications of TFEM under different realizations of random uncontrollable variables are performed, which however incurs extra computational burden. To eschew the deployment of such a crude Monte Carlo (MC) approach at each design setting, we integrate the stochastic TFEM with a stochastic surrogate model, stochastic kriging, in an active learning framework to sequentially approximate the stability boundary. The numerical result suggests that the nominal stability boundary attained from this method is on par with that from the crude MC, but only demands a fraction of the computational overhead. To further ensure the robustness of process stability, we adopt another surrogate, the Gaussian process, to predict the variance of the stability index at unexplored design points and identify the robust stability boundary per the conditional value at risk (CVaR) criterion. Therefrom, an optimal design in the robust stable region that maximizes the MRR can be identified. 

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3. Stability Performance of a Stochastic Toolpath in Machining

   Grimm, Tyler ; Kharat, Nilesh ; Potthoff, Nils ; Mears, Laine ; Wiederkehr, Petra ( November 2021 , Proceedings of ASME International Mechanical Engineering Conference and Exposition)

   null (Ed.)

   The overall quality of a machined part relies heavily on the tool path that is used. Several methods of toolpath generation are currently employed. A more recently developed toolpath method is known as trochoidal milling, which is also known by several other terms, such as adaptive milling. This type of path benefits the machining process by attempting to reduce chip thickness on entry and exit to the workpiece. In doing so, utilization of this type of path can reduce tool wear and enables higher feed rates, thus improving machining efficiency.\par Another advantage of the trochoidal approach is that it often creates paths which are relatively more smooth compared to traditionally designed paths. In order to follow the contours of the final geometry, the path can yield a significant number of direction changes which result in constantly changing forces directions on the tool. Chatter, or self-excited vibration that occurs in the tool or workpiece, can therefore be mitigated or avoided since resonance does not have time to increase the vibration’s amplitude. The trochoidal milling tool path strategy typically operates on the XY plane. The operator will assign a step-down value, which defines the Z-depth at each pass. This strategy can create issues during freeform milling: because of this step-down effect, the trochoidal path may only be able to perform clearing and not finishing. This is due to the excess material left on the workpiece when a large step-down value is used. A significant and randomized variation range of the trochoidal path is tested in this research. Using this new proposed method, stochastic behavior of the toolpath is implemented. The toolpath consists entirely of circular arcs which drive the tool in a pseudo-random fashion. As the tool nears completion of the pass, the generator will give heavier probabilistic weight to points which have not yet been machined, thereby improving the efficiency of the process. It is hypothesized that this toolpath can generate the same chip-inhibiting properties of the trochoidal path while granting the ability to perform finishing cuts. The stability of such a path is determined in this work. A key parameter of this path is the allowable radius range of the circular arcs. For example, short, tight arcs or long, relatively straight arcs can be used. The influence of these arcs is analyzed against several different metrics, such as generation time, path efficiency, and chatter. The stability lobes for several radii parameters were determined. It was found that the most efficient path utilized a median parameter value, signifying a negative parabolic relationship between path efficiency and tool path radius. It was also discovered that smaller arcs result in decreased chatter. Future studies will explore the behaviors of this path when milling 3D surfaces. 

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4. Effect of Directional Relations on Milling Chatter Stability and Development of a Stability Index

   https://doi.org/https://doi.org/10.1016/j.promfg.2018.07.045  

   Maulimov, Mukhtar ; Sencer, Burak ( July 2018 , Procedia manufacturing)

   This paper analyzes effect of directional relationships on chatter vibrations experienced in peripheral milling process. Based on the directional relationships, a geometry-based chatter stability index (CSI) is proposed to improve chatter stability of the process. It is well-known that chatter stability depends on cutting conditions and tool geometry; whereas it is less known that it also depends strongly on the directional relations between the machining process and the flexible directions of the machine. In this research, these directional factors affecting chatter stability are extracted from process kinematics and dynamically compliant directions of the structure. Three cases are considered and analyzed; namely, 1) if the machine tool/workpiece structure is flexible only in single direction, 2) if it is flexible in two orthogonal directions and finally 3) when those flexible directions are not orthogonal. Tool feed direction is considered to be the optimization parameter to maximize process stability. Overall, this research aims to present new knowledge on the effect of directional relationships for chatter stability and how they can be utilized in a practical manner based on a chatter stability index (CSI) that can be computed from geometry, process kinematics and limited knowledge of machine dynamics. 

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5. Effect of Directional Relations on Milling Chatter Stability and Development of a Stability Index

   Maulimov, Mukhtar ; Sencer, Burak ( January 2018 , Procedia manufacturing)

   This paper analyzes effect of directional relationships on chatter vibrations experienced in peripheral milling process. Based on the directional relationships, a geometry-based chatter stability index (CSI) is proposed to improve chatter stability of the process. It is well-known that chatter stability depends on cutting conditions and tool geometry; whereas it is less known that it also depends strongly on the directional relations between the machining process and the flexible directions of the machine. In this research, these directional factors affecting chatter stability are extracted from process kinematics and dynamically compliant directions of the structure. Three cases are considered and analyzed; namely, 1) if the machine tool/workpiece structure is flexible only in single direction, 2) if it is flexible in two orthogonal directions and finally 3) when those flexible directions are not orthogonal. Tool feed direction is considered to be the optimization parameter to maximize process stability. Overall, this research aims to present new knowledge on the effect of directional relationships for chatter stability and how they can be utilized in a practical manner based on a chatter stability index (CSI) that can be computed from geometry, process kinematics and limited knowledge of machine dynamics. 

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