FRF  at  y ¼ 01  is  higher  than  that  of  y ¼ 451  at  lowerfrequencies。 The arch plate (Fig。 3) has to move up at y ¼01 to cut the workpiece which is kept at the same level。Since the arch plate makes up a large fraction of the mass

J。 Dhupia et al。 / International Journal of Machine Tools & Manufacture 47 (2007)   326–334 331

Feed Force in time domain

8。2 8。25 8。3 8。35 8。4 8。45 8。5 8。55

8。2 8。25 8。3 8。35 8。4 8。45 8。5 8。55

(a) Time, t [sec]

x 104 FFT plot of feed direction forces

500 1000 1500 2000 2500

Frequency, /2[Hz]

500 1000 1500 2000 2500

Frequency, /2[Hz]

Fig。 7。  (a) Experimental Fx  plots for stable and unstable conditions at reconfiguration position, y ¼ 01 and (b) corresponding FFTs of the force data。

of the machine, the displacement of the arch on the machine has the most significant effect on the FRF of the machine structure。 The higher the arch plate moves, less stiff   the   structure   becomes。   Thus,   in   this   case,   the

configuration  at  y ¼ 01is  less  stiff  at  lower   frequencies

modes, than the configuration at y ¼ 451 since the arch plate   is   located   higher   for   y ¼ 01。   A   large  hammer

(bandwidth 0–600 Hz) was used to study the lower frequencies range of the structural FRF of  the machine。 The lowest dominant natural frequency of the machine found was around 60  Hz。

3。3。 Stability lobes

The analytical stability lobes generated for y ¼ 01 and 451 are shown in Fig。 6。 Various cutting experiments  were

done to verify the regions of stability and instability based on these lobes。 These points are marked on the stability lobe diagram and validate the stability lobe prediction。 The

cutting experiments results for y ¼ 01 and 451 were similar

at various cutting conditions。 The analytical stability lobes indicate that the chatter occurs for the y ¼ 451 configura-

tion at a smaller depth of cut compared to that for the

332 J。 Dhupia et al。 / International Journal of Machine Tools & Manufacture 47 (2007) 326–334

Feed Force in time domain

8。2 8。25 8。3 8。35 8。4 8。45 8。5 8。55