Физика вибрации: как резонанс влияет на стабильность обработки на токарном станке

Chatter in Turning: How Tool Vibration Affects Machining Stability Learn the physics behind chatter and how stability maps can help you choose the right cutting conditions. Share Phillips Corporation Featured Content View More Phillips Corporation - Education Featured Content View More In turning, the cutting tool is not rigid, so the cutting force causes tool vibration. When the tool is vibrating as it removes material, these vibrations are imprinted on the workpiece surface as a wavy profile. Figure 1 shows an exaggerated view, where the initial impact with the workpiece surface causes the tool to begin vibrating and the oscillations in the normal direction to be copied onto the workpiece. When the workpiece begins its second revolution, the vibrating tool encounters the wavy surface produced during the first revolution. Therefore, the chip thickness at any instant depends both on the tool deflection at that time and the workpiece surface from the previous revolution. Vibration of the tool therefore leads to a variable chip thickness which gives a variable cutting force since the force is proportional to the chip thickness. The cutting force governs the current tool deflection and, subsequently, the system exhibits feedback. In other words, the current behavior depends on previous behavior; the system has memory. Fig. 1: Description of regenerative chatter in turning. The tool deflections are copied onto the workpiece surface and are encountered in subsequent revolutions. This varies the chip thickness and cutting force which, in turn, affects the resulting tool deflections. The tool dynamics are described by its mass (m), stiffness (k) and damping coefficient (c). Source (all figures): Tony Schmitz From a modeling standpoint, this regeneration of waviness appears as a time-delayed term in the chip thickness equation. Figure 2 shows an unwrapped view of the turning operation, where the surface on the left was produced in the previous revolution and the surface to the right of the tool (offset by the feed per revolution) was just cut away by the oscillating tool. This column will consider only vibrations in the normal direction, y (positive direction out of the cut), which has the most direct influence on the chip thickness. Fig. 2: Depiction of turning where the surface from the previous revolution, shown to the left of the tool, is removed by the vibrating cutter to produce a new wavy surface to the right of the tool. The time dependent, instantaneous chip thickness, h(t), is determined using Equation 1. It is seen that larger positive vibration during the previous revolution, y(t-τ), where τ is the time for one rotation, gives an increased chip thickness (that is, less material was removed so the current chip is thicker). Larger positive current vibration, y(t), on the other hand, yields a thinner chip. See Figure 3, where hm is the mean chip thickness commanded by the feed per revolution. The relative phasing between the surface waviness from one pass to the next determines the level of force variation and whether the operation is stable or unstable (chatter occurs). The wavy surfaces between two revolutions may be in phase or out of phase. If the vibrations are in phase, even though vibration is present during material removal, the chip thickness variation (vertical distance between the two curves) is negligible and there is no appreciable force variation. This enables stable cutting at larger chip widths. Considering that the tool tends to vibrate at its natural frequency, it is intuitive that matching the workpiece rotating frequency (spindle speed) to the tool’s natural frequency will lead to this preferred in-phase situation. However, this is counter-intuitive based on our traditional understanding of resonance, where we avoid exciting the system at its natural frequency. Fig. 3: The figure demonstrates the instantaneous chip-thickness calculation. It depends on the mean chip thickness, the current deflection, and the vibration during the previous revolution of the workpiece (to the left of the tool). Figure 4 shows the out-of-phase relationship where there is significant variation in the chip thickness. This leads to unstable cutting at smaller chip widths than the previous case due to the force variations and subsequent tool deflections. Depending on the feedback system gain, or chip width b, and spindle speed, Ω, the turning operation will either be stable or will exhibit chatter (unstable cutting with self-excited vibration), which causes large vibrations and forces and leads to poor surface finish and, potentially, tool/workpiece damage. In stable machining, the vibrations diminish from revolution to revolution. In unstable machining, on the other hand, the vibrations grow from revolution to revolution until limited in some way. The vibrations may even become large enough that the tool jumps out of the cut, losing contact with the workpiece. The vibrations in unstable cutting may be as large or larger than the chip thickness and these large vibrations may result in damage to the workpiece, tool, and machine. The governing relationships for this behavior are provided in Equations 2 through 4. In these equations, blim is the limiting chip width to avoid chatter; Ks and β are terms in the cutting force model; FRF is the frequency response function at the tool tip; fc is the chatter frequency (should it occur); N is the integer number of waves of vibration imprinted on the workpiece surface in one revolution; and ε/2π is any additional fraction of a wave, where ε is the phase (in radians) between current and previous tool vibrations. Note that for units consistency in Equation 3, if fc is expressed in cycles/s (Hertz, Hz), then Ω must be specified in rev/s. Figure 5 shows an example stability map where the Ω versus blim family of curves (N = 0, 1, 2, …) separate the domain into two regions. Any (Ω, blim) pair that appears above the collective boundary indicates unstable behavior, while any pair below the boundary is predicted to be stable. Related Content 4+2 Machining Cuts Cycle Times From Days to Minutes By moving from legacy jig bores and tilt tables to a milling and boring machine, Highland Manufacturing cut cycle times from days to minutes on high-tolerance, large-diameter parts. Read More How to Build Out a Machine Shop for Submarine Parts Five-axis large-format machining has given Granite State Manufacturing the ability to take on complex submarine parts — and has also worked as a recruiting tool for experienced machinists. Read More Addressing Manufacturing Challenges with Automation GrayMatter Robotics’ Physical AI robotic cells for manufacturing offer immediate impact and results. Read More DN Solutions and HELLER: A United Vision for U.S. Manufacturing Renewal With new technical centers in North America and the pending acquisition of HELLER, DN Solutions is expanding service, capacity and technical support for U.S. manufacturers. In this exclusive interview, CEO WJ Kim outlines what customers can expect. Read More Read Next WEBINAR: From Machine Data to Guided Action: How Modern Shops Are Closing the Execution Gap In this webinar, MachineMetrics Product Manager Josh Fish is joined by Pindel Global Precision's Thomas Deslongchamps, for a candid look at what closing the execution gap actually looks like inside a precision machining shop. Read More