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Modeling the dynamic performance of machining operations is an important research and development topic. Process model inputs typically include the tool and workpiece structural dynamics, represented by frequency response functions (FRFs); mechanistic cutting force coefficients that depend on the workpiece material, tool geometry and coolant/lubricant application, if any; and machining parameters, such as spindle speed, axial depth of cut, radial depth of cut, cutting direction (up or down) and feed per tooth for milling. Machining dynamics model predictions include the boundary between stable and unstable (chatter) combinations of spindle speed and axial depth for milling; surface location error due to forced vibrations during stable milling; and time-dependent cutting force and tool/workpiece displacements during material removal. Modeling approaches include time domain, frequency domain and semi-discretization, for example.

Despite the significant advances in modeling machining operations over the past decades, process damping remains a topic of interest, including new tool designs that increase the effect. The stability map displayed in Figure 1 offers an effective predictive capability for selecting stable spindle speed-axial depth combinations in milling. However, the increase in allowable axial depth at higher spindle speeds is diminished at lower spindle speeds. Fortunately, the process damping effect can serve to increase the stable axial depth at these low speeds. The increased stability at low spindle speeds is particularly important for hard-to-machine materials that exhibit prohibitive tool wear at high cutting speeds.

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Prior studies have described process damping as energy dissipation due to interference between the cutting tool flank face and the machined surface during relative vibrations between the tool and workpiece. It has been shown that, given fixed system dynamics, the influence of process damping increases at low spindle speeds because the number of undulations on the machined surface between teeth increases, which also increases the slope of the wavy surface. This, in turn, leads to increased interference and additional energy dissipation.

To describe the physical mechanism for process damping, consider a tool moving on a sine wave while shearing away the chip as shown in Figure 2. Four locations are identified: 1) the clearance angle, g, between the flank face of the tool and the work surface tangent is equal to the nominal relief angle for the tool; 2) g is significantly decreased and can become negative (which leads to interference between the tool’s flank face and surface); 3) g is again equal to the nominal relief angle; and 4) g is significantly larger than the nominal value.

At points 1 and 3 in Figure 2, the clearance angle is equal to the nominal value so there is no effect due to cutting on the sinusoidal path. However, at point 2 the clearance angle is small (or negative) and the thrust force in the surface normal direction, n, is increased. At point 4, on the other hand, the clearance angle is larger than the nominal and the thrust force is decreased. Because the change in force caused by the sinusoidal path is 90 degrees (that is, a quarter wave) out of phase with the displacement and has the opposite sign from velocity, it is considered to be a viscous damping force (or a force that is proportional to velocity). Given this description, the process damping force in the surface normal direction can be expressed as a function of velocity, axial depth and spindle speed (or cutting speed). This process damping force model can be included in milling simulations to predict the process damping zone as shown in Figure 1.