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