Abstract
Metal cutting is a dynamic process that produces forces with a wide array of frequencies and amplitudes. Typically, dynamometers are used to measure these forces, but they are usually limited to a frequency bandwidth of 3 kHz. This maximum bandwidth is further limited by the natural frequency of the measurement setup and force transmissibility through the structure to the dynamometer. While this is acceptable for most metals, research shows that additively manufactured metals produce high magnitude vibrations at frequencies above those recorded by a dynamometer. The magnitude of the forces produced is unknown. Accelerometers are small enough to be placed near the tool-chip interface, reducing transmissivity losses, and can measure frequencies an order of magnitude higher than that of a dynamometer. The challenge is that the collected acceleration data cannot be directly translated into exogenous force data. This paper attempts to reconstruct the missing dynamic forces using a mass-spring-damper system approximation. For proof of concept, the experiment is conducted on a cantilever beam to represent a toolholder. Exogenous cyclic forces are applied using a small, lightweight electric motor rotating an eccentric mass. This eccentric mass produces a known force thanks to the centripetal mass equation. Furthermore, the forces are separately verified by mounting the motor directly to a dynamometer and measuring the outputted forces across a range of frequencies. Hammer testing is used to determine the cantilever beam system’s order and the constitutive constants for the system’s equations of motion (EOM). Next, the exogenous cyclic forces are applied to the free end of the beam. The cyclic forces are measured using the attached accelerometer. The EOM is used to convert the collected acceleration data into a predicted force. The frequency of the cyclic forces is varied across a wide frequency range, from fifty percent below the system’s natural frequency to fifty percent above the natural frequency, and the predicted and applied forces are compared. The results show a match between the predicted dynamic force and the applied force across the entire frequency range and reveals the limitations of using a dynamometer in the same frequency range. The study also discusses the potential applications of this method on an actual machine tool and the associated challenges and limitations. One potential application of this research is that of measuring the high frequency cutting forces produced by additively manufactured parts. One limitation of this method is that it does not capture static and low frequency forces.
