Abstract
Using the cutter bar made with composite rather than metal in high rotating speed milling or boring operations is a new attempt for suppressing chatter of the cutting system. This is because composite material has much higher specific stiffness and damping as well as dynamic stiffness compared to metal. But, for a rotating composite cutter bar, larger internal damping (or rotational damping) occurs, and such damping may cause the rotor instability in the perspective of rotor dynamics. On the other hand, the effect of internal damping of a rotating composite cutter bar on the chatter stability in high speed cutting process is also an important issue worthy of concern. In this paper, a new dynamic model of the cutting system with a rotating composite cutter bar is presented. The cutter bar is modelled as a rotating, cantilever, tapered, composite Euler–Bernoulli shaft, subjected to a regenerative cutting force. Modal damping loss factors are described based on the viscoelastic constitutive relation of composite combined with an energy approach. The governing equations of the system are obtained by employing Hamilton principle. Galerkin method is used to discretize the partial differential equations of motion. The frequency-domain solution of stability proposed by Altintas and Budak [14] is extended and used to predict the chatter stability of the cutting system. The results reveal the inherent relationship between internal damping instability and cutting chatter. The effects of the geometry parameters of the cutter bar, ply angle, stacking sequences, and internal and external damping are examined.
Highlights
Mathematical Model(1) Calculate the directional matrix in accordance with the milling cutter’s material and geometrical parameters (2) Start a loop incrementing the spindle speed Ω (3) Calculate the natural frequency corresponding to the rotating speed (4) Scan the chatter frequency ωc by using the natural frequency as the reference, and calculate the transfer function (5) Calculate real and imaginary parts according to equation (40), and solve the critical axial cutting depth blim and the corresponding rotating speed Ω (6) If the difference between the rotating speed obtained in step 5 and input rotating speed in step 2 satisfies the required precision, plot the stability lobes by using Ω the x-axis and blim as the y-axis, respectively; otherwise, repeat the iterative procedures until the results converge (7) Select the new j and calculate the adjacent lobes
Lee and Suh [6] developed a fixed type graphite/epoxy composite boring bar whose l/d was 5.6 and allowable depth of cut was 5 times higher than that of the conventional steel boring bar
Since composite has relatively high-damping characteristics, for a shaft made with composite materials, instability caused by internal damping cannot be ignored
Summary
(1) Calculate the directional matrix in accordance with the milling cutter’s material and geometrical parameters (2) Start a loop incrementing the spindle speed Ω (3) Calculate the natural frequency corresponding to the rotating speed (4) Scan the chatter frequency ωc by using the natural frequency as the reference, and calculate the transfer function (5) Calculate real and imaginary parts according to equation (40), and solve the critical axial cutting depth blim and the corresponding rotating speed Ω (6) If the difference between the rotating speed obtained in step 5 and input rotating speed in step 2 satisfies the required precision, plot the stability lobes by using Ω the x-axis and blim as the y-axis, respectively; otherwise, repeat the iterative procedures until the results converge (7) Select the new j and calculate the adjacent lobes
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