Abstract
Chatter in machining caused by self-excited vibration limits the capability of high-speed spindles and results in poor surface finish and tool wear. Stability lobe diagram (SLD) is widely used to determine chatter-free machining parameters. The SLD for milling needs accurate measurement of frequency response function (FRF) at the cutting tool tip. However, asymmetry and complex geometry of end mills contribute to FRF data with low coherence. The impact testing is difficult due to the minimum area available on the cutting tool’s sharp edges for its excitation and attaching accelerometer. Hence, accurate FRF measurement is time-consuming. The problem gets more prominent when cutting tool rotates. To address this, a calibration rod that mimics the cutting tool is proposed. However, there are limited efforts in identifying optimal design of the calibration rod to capture tool’s dynamic behavior.
The present work aims to develops a design strategy for realizing a calibration rod for an end mill cutter. Towards this, a receptance coupling substructure analysis (RCSA) based approach is employed to evaluate the tool tip FRF for a given length (L) and diameter (D) of the calibration rod. The spindle with solid HSS cylinder of 10 mm diameter as substructure A and cylinder with varying L and D as substructure B were considered. The FRF of substructure A is evaluated by impact test, whereas for substructure B, is evaluated analytically. By minimizing the error between the FRFrcsa and FRFexp of the targeted end mill cutter, the optimal L and D for a calibration rod were obtained. The optimal rods are manufactured to validate the equivalency with the end mill cutter. Experimental validation showed close dynamic responses from the end mill and designed calibration rod. The proposed method’s performance is evaluated for two fluted and four fluted end mills. For the 10 mm four-fluted end mill cutter, the optimal L and D are obtained as 33.5 mm and 7mm, respectively. The evaluated natural frequencies for milling cutter and corresponding calibration rod are observed as 832Hz and 849 Hz, respectively. For 10 mm two-fluted end mill the optimized length and diameter are obtained as 28 mm and 7 mm. Corresponding natural frequencies for end mill and calibration rod are observed as 886 Hz and 888 Hz, respectively.
