Although very limited, several studies have considered robotic machining processes. Fields et al. [4] have presented the design of a flexible robotic drilling system for aircraft sheet metal parts. Requiring active end point recalibration, the system has been shown to be very flexible, allowing drilling in three dimensions while maintaining good positioning accuracy and repeatability. Pan et al. [5] have investigated chatter in robotic machining processes both analytically experimentally, giving guidelines to avoid “mode coupling” as the dominant source of vibrations. Olgac and Sipahi [6] have recently studied variable-pitch cutters in milling process and provided guidelines to combine tool design features (pitch angle) and operational selections (the spindle speed and the axial depth of cut) to optimize productivity without sacrificing machining quality. Anderson et al. [7] have proposed a new design procedure to enhance the chatter stability of an end mill cutter. In this research, the principle objective is to incorporate an adaptor to enhance chatter stability of a cantilevered cutter. Altintas and Weck [8] provide a comprehensive review of chatter vibrations in cutting and grinding processes and its control in industry. Simple semi-active control technique is reported in this paper to delay the onset of chatter when turning with a two-link robotic arm. For control, it is proposed to manipulate the joint stiffness of a two-link robotic arm using a simple on-off type strategy. The control is implemented at pre-determined instances. The two primary advantages of the proposed control are robustness and requiring no additional hardware (by applying the control by using already existing joint actuators). In the following, the modeling and control methods are discussed briefly. Then representative numerical predictions are discussed to demonstrate the level of suppression. 2. A SIMPLIFIED NONLINEAR FEEDBACK CUTTING MODEL The cutting forces in turning a rigid disk are illustrated in Figure 1. Waste is removed, while the workpiece rotates in the counter-clockwise direction. The resulting cutting force F makes an angle β from the Y direction which is normal to the cut surface. Although this angle is expected to be (a rather weak) function of the cutting tool geometry, it is assumed to be constant. Here, the useful component of the force, to shear the chip from the workpiece, is the tangential component in X direction. After each pass, the tool feeds in the radial direction by hav, and leaves behind an undulated surface due to the oscillations of the structure holding the tool. Hence, hav is the intended constant chip thickness, and Yn and Yn-1 represent the surface left behind the cutter as a result of the current pass ‘n’, and the preceding pass ‘n-1’, respectively. The magnitude of the resulting cutting force F(t) is proportional to the instantaneous chip thickness h(t) F = C • b • h(t) (1) where C is specific resistance of the workpiece [18]. C is a function of the tool geometry and the material of the workpiece. It is normally provided empirically and has a unit of force per unit cross sectional area of the chip. Cross sectional area, b•h(t), is a time variant where b is the width of cut in a normal direction to the view shown in Figure 1. Y β Yn Yn-1 hav F Workpiece Cutter X Figure 1. Cutting model used in the simulations. 162
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