Frequency, /2(Hz)

500 1000 1500 2000 2500

Spindle Speed, N [RPM]

Fig。 6。 Analytical stability lobes showing the regions of stability and instability verified by cutting experiments。

0 100 200 300 400 500 600 700 800 900

Frequency, /2(Hz)

3。 Results  and discussion

3。1。 Cutting model

Fig。 4 shows the results for force measurements while cutting AISI 1018 steel at depth of cut, ap ¼ 3:3 mm, spindle    speed,    N ¼ 1700 RPM    and    feed    per tooth, f t ¼ 0:127 mm=tooth。 The cutting coefficients determined by the least-squares method, using the force signal after the initial transients due to the tool entering the workpiece decayed were

Ktc ¼ 2309:94 N=mm2; Krc ¼ 1337:79 N=mm2,论文网

Kte ¼ 24:79 N=mm; Kre ¼ 17:69 N=mm:

The correlation factors for the estimated and experimental data have large values of 0。98 for feed (X) direction and

Fig。   5。  Experimental   arch-type   RMT’s   tool   FRF   for   01   and  451

reconfiguration position with valenite V490 cutter。 (a) Excitation in X, measured response in X direction。 (b) Excitation in Y, measured response in  Y direction。

edge constants, and  ft  represents  the  feed  per tooth。 While the tangential cutting coefficient, Ktc,  appears directly in Eq。 (3), the matrix  A0  is  dependent  on  Krc。 The edge constants are needed for the cutting coefficient estimation。

All the cutting experiments were carried out using a Valenite V490 square shoulder end mill with rectangular inserts (outer diameter: 50。8 mm, insert width: 15。875 mm) and AISI 1018 steel。 While two inserts were used for cutting model estimation, stability lobe  diagram  and chatter estimation was carried out for four inserts。 Since the goal of the paper is to provide a comparison between the different reconfiguration positions of the arch-type RMT, the tool and the workpiece were kept the same in different  reconfiguration positions。

0。96 for cross feed (Y) direction, indicating a good   fit。

3。2。 Frequency response functions

Modal tests were performed on the arch-type RMT at various reconfiguration positions。 Fig。 5 shows the FRFs

GXX  and GYY  for the y ¼ 01 and y ¼ 451  reconfiguration

positions。 It may be noted that the FRFs have very similar pattern at the higher frequencies (4250 Hz), but at lower frequencies the patterns are quite different。 This is because the lower frequencies arise from the structure of the machine tool, i。e。, lower frequency are primarily due to structural modes other than the spindle, tool and  tool holder。 Since the structure of an RMT changes from one reconfiguration position to another, the lower frequencies (o250 Hz) are affected significantly。 The magnitude of   the