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Cutter-Workpiece Engagement Modeling and Stability Analysis in Ball-End Milling of Sculptured Surfaces

Ghorbani, Mohammad | 2020

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 52746 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Movahhedy, Mohammad Reza; Ahmadian, Mohammad Taghi
  7. Abstract:
  8. Features with sculptured or free-form surfaces appear frequently in computer-aided design of parts common to aerospace, automotive, and die and mold industries. Because of their ability to machine complex features and to achieve good surface finish, ball-end tools are widely used in the finish milling process of sculptured parts. This research has been devoted to the modeling of cutter-workpiece engagement (CWE) boundaries, cutting forces, and stability prediction in ball-end finish milling process of sculptured parts. In the first step, a new analytical model taking into account the effect of surface curvatures was presented for three-axis and five-axis ball-end milling processes. In this model, a mathematical description containing explicit form of the principal curvatures of the surface was employed to locally describe the workpiece surface around the contact region. The CWE boundaries were extracted analytically for all slotting, first-cutting, and following-cutting modes. Comparison studies with solid modeling method show that the proposed model is capable of calculating engagement boundaries in all convex, concave, saddle, cylindrical and inclined regions of the sculptured surface. Furthermore, the performed simulations indicate that the model is nearly three times faster than Z-map method. In the next step, a new algorithm was developed for extracting the principal curvatures and directions of the workpiece surface from tool path data. A geometrical module which takes the finishing stage tool path data as input and calculates the map of entry-exit immersion angles was also constructed by combining the CWE model and the developed algorithm. This module increases the flexibility of the proposed CWE model for integration into CAD/CAM systems. In the next step, a mechanistic cutting force model was presented for helical ball-end tools with the inclusion of radial run-out effect. Experimental tests were performed to verify the model predictions, and the variation of cutting forces along curved tool paths and also the influence of surface curvatures on milling forces were studied. The obtained results show that neglecting the effect of surface curvatures can considerably affect milling forces. Moreover, it has been shown that depending on the machining tolerance used in the tool path generation step, saw-tooth-like fluctuations can appear in the time history of milling forces originating from the approximation of curved paths by single steps (straight lines). In the final step, chatter stability of the process was investigated. The dynamics of machine tool at cutter contact point was modeled as a 2-DOF vibrating system whose parameters were obtained from experimental modal tests. Then, delayed differential equations governing the dynamic behavior of cutter were established considering chip load regeneration mechanism. Full-discretization method was utilized to discretize equations over a tooth-passing period and to obtain transition matrix at each tool location and cutting condition, and the stability of process was assessed by applying Floquet theory to the transition matrix. Three dimensional stability diagrams were extracted along curved tool paths indicating the effect of CWE variations on the critical cutting depth. Furthermore, by simulating the process with and without taking into account the effect of surface curvatures on the CWE, the impact of surface curvatures on the stability lobes was investigated
  9. Keywords:
  10. Milling ; Chatter Detection ; Ball End Mill ; Chatter Stability ; Cutter-Workpiece Engagement ; Tool Path ; Sculptured Surface ; Principal Curvatures

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