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Ikada, R. Hino and E. 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P!%5 L,~^{qڏӾ׊Xp6>W9HbOYcg=z`>_ endstreamendobj51 0 obj<>endobj33 0 obj<>stream BT 0 0 0 1 k /GS0 gs /TT0 1 Tf 0.025 Tc -0.025 Tw 5.95 0 0 7 547.9449 42.1865 Tm (37)Tj ET q 0 g /GS1 gs 0 Tc 0 Tw /Fm0 Do Q BT /T1_0 1 Tf 0.019 Tc 0.125 Tw 9.8 0 0 10 65.1968 757.1339 Tm [(As a simple e)14.9(xample of a ball end mill in use, )]TJ /T1_1 1 Tf 10 0 0 10 269.1573 757.1339 Tm [(Fig)14.9(.)]TJ /Span<>> BDC 1.67 0 Td ( )Tj EMC (3)Tj /T1_0 1 Tf 0 Tc 0 Tw 9.8 0 0 10 294.8032 757.1339 Tm ( )Tj 0.03 Tw -24.008 -1.21 Td [(sho)40(ws an anal)25(ysis of the contact length in the axis direction )]TJ 0.007 Tc 0.125 Tw 0 -1.21 TD [(b)24.9(y the NC pro)24.9(g)-20.1(ram based on CAM. In this e)15(xample, the)7( )]TJ 0.024 Tc T* [(contact length in the axis direction rises shar)-30.1(pl)24.9(y at the)24( )]TJ 0 Tc 0.036 Tw T* [(moment of re)25.1(v)14.9(ersing the feed direction of the ball end mill. )]TJ 0.013 Tc 0.125 Tw T* [(Excessi)25.3(v)15.3(e cutting force is applied to the tool in the par)-19.7(t)13( )]TJ 0 Tc 0.05 Tw T* [(e)15(xperiencing the shar)-30(p rise in the contact length in the axis )]TJ 0.125 Tw 0 -1.21 TD [(direction, w)19.6(hich can trigger prob)19.5(lems such as chipping of )]TJ 0.001 Tc 0 -1.21 TD [(the edge of the cutting tool. In the actual cutting process,)1( )]TJ 0 Tc 0.059 Tw 0 -1.21 TD [(it is dif)25(f)-60(icult to appropriatel)25(y modify the pro)25(g)-20(ram to adjust )]TJ 0.056 Tw T* [(for )0.5(such a sudden )0.5(change )0.5(in cutting conditions. )50.5(This lea)35(v)15(es )]TJ 0.042 Tw T* [(no )0.5(other )0.5(alter)-20(nati)25(v)15(e )0.5(b)-4.9(ut )0.5(to )0.5(minimize )0.5(the )0.6(feed )0.5(amount )0.5(of )0.5(the )]TJ 0.009 Tc 0.125 Tw 0 -1.21 TD [(entire pro)25(g)-20(ram, w)20.1(hich ine)25(vitab)19.9(l)25(y prolongs the processing)9( )]TJ 0 Tc 0 Tw 0 -1.21 TD (time.)Tj /T1_1 1 Tf 0.011 Tc 0.125 Tw 10 0 0 10 65.1969 587.7184 Tm [(Figur)29.7(e)]TJ /Span<>> BDC ( )Tj EMC (4)Tj /T1_0 1 Tf 9.8 0 0 10 102.8798 587.7184 Tm [( sho)39.7(ws an e)14.7(xample of optimization of the NC)11.1( )]TJ 0 Tc 0.073 Tw -4.424 -1.21 Td [(pro)25(g)-20(ram, w)20(herein the feed rate is adjusted w)20(hile tangential )]TJ 0.006 Tc 0.125 Tw 0 -1.21 TD [(force is chosen as an optimization v)24.9(ariab)19.9(le. )]TJ /T1_1 1 Tf 10 0 0 10 242.362 563.5162 Tm [(Figur)29.9(e)]TJ /Span<>> BDC ( )Tj EMC (4-\(a\))Tj /T1_0 1 Tf 0 Tc 0 Tw 9.8 0 0 10 294.8032 563.5162 Tm ( )Tj 0.125 Tw -24.008 -1.21 Td [(sho)39.9(ws the pre)24.9(vious state optimization. )29.9(W)39.9(ith respect to the )]TJ 0.014 Tc 0 -1.21 TD [(p)0.5(r)0.5(o)0.5(c)0.5(es)0.5(s)0.5(i)0.5(n)0.5(g)0.5( m)0.5(a)0.5(c)0.5(h)0.5(i)0.5(n)0.5(e)0.5( a)0.5(n)0.5(d)0.5( )0.5(t)0.5(oo)0.5(l)0.5( )0.5(s)0.5(t)0.5(if)25.5(f)0.5(n)0.5(e)0.5(s)0.5(s,)0.5( )0.5(a)0.5( )0.5(d)0.5(i)0.5(f)25.4(f)0.5(e)0.5(r)0.5(e)0.5(n)0.5(c)0.5(e)0.5( f)0.5(r)0.5(o)0.5(m)14( )]TJ 0.013 Tc 0 -1.21 TD [(t)0.5(he)0.5( a)0.5(ll)0.5(o)40.4(w)25.5(ab)20.5(le)0.5( u)0.5(pp)0.5(er)0.5( l)0.5(im)0.5(it)0.5( o)0.5(f )0.5(ta)0.5(ng)0.5(en)0.5(ti)0.5(a)0.5(l f)0.5(or)0.5(c)0.5(e )0.5(is)0.5( o)0.5(bs)0.5(er)-19.5(v)15.5(ed)13( )]TJ 0.002 Tc 0 -1.21 TD [(because the tool\222)140.3(s capacity is not suf)25.3(f)-59.6(icientl)25.3(y raised up in)2( )]TJ 0.004 Tc T* [(some par)-20(ts and e)14.9(xceeding the upper limit in the other)55(. In)4( )]TJ 0 Tc 0.054 Tw T* [(contrast, as a result of optimization as sho)40(wn in )]TJ /T1_1 1 Tf 10 0 0 10 252.8212 490.9096 Tm [(Fig)15(.)]TJ /Span<>> BDC 1.594 0 Td ( )Tj EMC (4-\(b\))Tj /T1_0 1 Tf 0 Tw 9.8 0 0 10 292.3531 490.9096 Tm (, )Tj 0.007 Tc 0.125 Tw -23.758 -1.21 Td [(the feed rate is adjusted to stab)20(l)25.1(y maintain the tangential)7( )]TJ 0.045 Tc T* [(force at the upper limit in order to optimize the NC)45( )]TJ 0.004 Tc T* [(pro)24.9(g)-20.1(ram. F)49.9(eed rate adjustment can be made for each line)4( )]TJ 0.007 Tc 26.611 30.253 Td [(of the NC pro)24.7(g)-20.2(ram \(fur)-20.3(ther di)24.7(vision is possib)19.7(le\), making)7( )]TJ 0.036 Tc 0 -1.21 TD [(pinpoint adjustment possib)20.2(le. Usuall)25.2(y)85.2(, there are man)25.3(y)35.9( )]TJ 0.008 Tc 0 -1.21 TD [(par)-20.4(ts with a lo)39.7(w cutting force in the NC pro)24.7(g)-20.4(ram output)8.1( )]TJ 0.011 Tc 0 -1.21 TD [(b)25.6(y)0.5( )0.5(C)0.6(A)0.6(M)0.5(.)0.6( )50.5(T)0.6(h)0.5(i)0.6(s)0.5( )0.6(o)0.5(f)0.6(t)0.6(e)0.5(n)0.6( )0.5(m)0.6(a)0.6(k)10.5(e)0.6(s)0.5( )0.6(i)0.5(t)0.6( )0.5(p)0.6(o)0.5(s)0.6(s)0.6(i)0.5(b)20.5(l)0.6(e)0.6( )0.5(t)0.6(o)0.5( )0.6(s)0.5(i)0.6(m)0.5(u)0.6(l)0.5(t)0.6(a)0.5(n)0.6(e)0.6(o)0.5(u)0.6(s)0.5(l)25.6(y)11( )]TJ 0 Tc 0.015 Tw 0 -1.21 TD [(e)15(xtend the tool life and enhance precision b)25(y smoothing out )]TJ 0.088 Tw 0 -1.21 TD [(the cutting force, as w)35(ell as reduce machining time. In the )]TJ 0.009 Tc 0.125 Tw 0 -1.21 TD [(e)15.1(xample sho)40.1(wn in )]TJ /T1_1 1 Tf 10 0 0 10 398.6932 684.5273 Tm [(Fig)15.1(.)]TJ /Span<>> BDC 1.629 0 Td ( )Tj EMC (4)Tj /T1_0 1 Tf 9.8 0 0 10 423.9155 684.5273 Tm (, a 59)Tj /T1_2 1 Tf 0 Tc 0 Tw (%)Tj /T1_0 1 Tf 0.009 Tc 0.125 Tw 3.339 0 Td [( reduction in machining)9( )]TJ 0 Tc 0 Tw -13.911 -1.21 Td [(time w)25(as achie)25(v)15(ed.)]TJ /T1_1 1 Tf 10 0 0 10 320.3149 660.3251 Tm [(3)4(.)-21.1(2)]TJ /Span<>> BDC ( )Tj EMC 2.551 0 Td [(C)9.6(a)-9.8(s)-6.4(e e)11.5(x)-5.3(a)-7.8(m)4.3(pl)-4(e o)9.7(f a)2.4(p)1.4(pl)-26.2(i)-1.4(c)-8.3(a)5.2(t)-27.6(i)-1.4(o)6.4(n)]TJ /T1_0 1 Tf 0.006 Tc 0.125 Tw 9.8 0 0 10 320.3149 648.224 Tm [(An e)15.1(xample of application of this technolo)25(gy to impeller)6( )]TJ 0 Tc 0.105 Tw 0 -1.21 TD [(processing is introduced. )50.4(T)80(angential force is chosen as the )]TJ 0.076 Tw T* [(optimization v)25(ariab)20(le in order to set the standard condition )]TJ 0.006 Tc 0.125 Tw T* [(based on the results from the anal)25.2(ysis of tangential force)6( )]TJ 0 Tc 0.015 Tw T* [(according to the pre)25(vious cutting condition. )54.8(After e)15(xcluding )]TJ 0.024 Tc 0.125 Tw 0 -1.21 TD [(momenta)0.5(r)-19.6(y peak v)25.4(a)0.5(lues, half of )0.5(the maximum v)25.4(a)0.5(lue in)24( )]TJ 0.02 Tc 0 -1.21 TD [(the remaining par)-20.1(t w)24.9(as set as the standard condition of)20( )]TJ 0.008 Tc 0 -1.21 TD [(tangential force \(condition 1\). )50.1(T)120(w)40.1(o more conditions w)35(ere)8( )]TJ 0 -1.21 TD [(added that raise the tar)17.9(get v)24.9(alue of tangential force from)8( )]TJ 0.007 Tc 0 -1.21 TD [(t)0.5(h)0.6(e)0.5( )0.6(s)0.5(t)0.6(a)0.5(n)0.6(d)0.5(a)0.6(r)0.5(d)0.6( )0.5(c)0.6(o)0.5(n)0.5(d)0.6(i)0.5(t)0.6(i)0.5(o)0.5(n)0.6(.)0.5( )0.6(O)0.5(p)0.6(t)0.5(i)0.6(m)0.5(i)0.5(z)0.6(a)0.6(t)0.5(i)0.5(o)0.6(n)0.5( )0.6(w)25.5(a)0.6(s)0.5( )0.6(p)0.5(e)0.6(r)0.5(f)0.6(o)0.5(r)-19.4(m)0.5(e)0.6(d)0.5( )0.6(w)0.5(i)0.6(t)0.5(h)7( )]TJ 0 Tc 0.065 Tw T* (a total of three conditions for test production. )Tj /T1_1 1 Tf 10 0 0 10 505.3264 527.213 Tm [(T)92(a)10(b)20(le 1)]TJ /T1_0 1 Tf 9.8 0 0 10 536.7062 527.213 Tm ( lists )Tj 0.016 Tc 0.125 Tw -22.081 -1.21 Td [(tar)18.1(get v)25(alues of optimization v)25.1(ariab)20(les for each process.)16( )]TJ 0.027 Tc T* [(F)20.1(igures of conditions 2 and 3 are sho)40.1(wn in propor)-19.9(tion)27( )]TJ 0.018 Tc T* [(to the f)-59.8(igure of condition 1. )50.2(T)80.2(ar)18.2(get v)25.2(alues w)35.3(ere set lo)40.2(w)18( )]TJ 0.017 Tc T* (in processes )Tj /C2_0 1 Tf 0 Tc 0 Tw 8.82 0 0 9 375.0334 478.8085 Tm <1B08>Tj /T1_0 1 Tf 0.017 Tc 0.125 Tw 9.8 0 0 10 385.7751 478.8085 Tm ( and )Tj /C2_0 1 Tf 0 Tc 0 Tw 8.82 0 0 9 408.1189 478.8085 Tm <1B09>Tj /T1_0 1 Tf 0.017 Tc 0.125 Tw 9.8 0 0 10 418.8607 478.8085 Tm [(, w)19.8(hich g)-20.2(reatl)24.8(y af)24.8(fect machining)17( )]TJ 0.006 Tc -10.056 -1.21 Td [(precision. F)50.1(eed rate in process )]TJ /C2_0 1 Tf 0 Tc 0 Tw 8.82 0 0 9 449.19 466.7074 Tm <1B0A>Tj /T1_0 1 Tf 0.006 Tc 0.125 Tw 9.8 0 0 10 459.8323 466.7074 Tm [( with suf)25.1(f)-60(icientl)25(y small)6( )]TJ 0.026 Tc -14.236 -1.21 Td [(axial depth of cut is set constant with reference to the)26( )]TJ ET 0 0 0 0 k /GS1 gs 59.528 260.989 496.063 171.41 re f /PlacedPDF /MC0 BDC q 102.0473052 0 0 99.2450903 150.1803436 305.6876871 cm /Im0 Do Q q 121.585 283.023 371.949 149.376 re W n BT 0 0 0 1 k /T1_3 1 Tf 0 Tc 0 Tw 7 0 0 7 121.5843 387.8223 Tm (Tool)Tj ET Q BT 0 0 0 1 k /T1_3 1 Tf 0 Tc 0 Tw 7 0 0 7 197.6673 287.8203 Tm (\(Example of tool path\))Tj 7.202 17.774 Td (Change in direction)Tj 0 7 -7 0 278.0082 330.066 Tm (Contact length in )Tj -1.235 -1.143 Td (the axis direction)Tj ( \(mm\))Tj ET q 121.585 283.023 371.949 149.376 re W n BT /T1_3 1 Tf 7 0 0 7 381.201 284.5352 Tm (Time)Tj ( \(s\))Tj ET Q BT /T1_3 1 Tf 7 0 0 7 293.442 402.4642 Tm (5)Tj 0 -2.835 TD (4)Tj 0 -2.835 TD (3)Tj 0 -2.835 TD (2)Tj 0 -2.835 TD (1)Tj 0 -2.835 TD (0)Tj 0.155 -1.054 Td (250)Tj 5.386 0 Td (251)Tj 5.386 0 Td (252)Tj 5.386 0 Td (253)Tj 5.386 0 Td (254)Tj ET q 121.585 283.023 371.949 149.376 re W n BT /T1_3 1 Tf 7 0 0 7 483.037 295.8613 Tm (255)Tj ET Q q 299.789 305.438 188.503 58.253 re W n q 188.5035769 0 0 58.2538699 299.7888031 305.4383527 cm /Im1 Do Q Q 0 0 0 1 K 0.3 w 4 M q 1 0 0 1 299.7821 305.4453 cm 0 0 m 188.503 0 l S Q q 1 0 0 1 299.7821 305.4453 cm 0 0 m 0 99.212 l S Q q 1 0 0 1 299.7821 404.6578 cm 0 0 m 2.834 0 l S Q q 1 0 0 1 299.7821 384.8155 cm 0 0 m 2.834 0 l S Q q 1 0 0 1 337.4828 305.4453 cm 0 0 m 0 2.835 l S Q q 1 0 0 1 375.183 305.4453 cm 0 0 m 0 2.835 l S Q q 1 0 0 1 412.8841 305.4453 cm 0 0 m 0 2.835 l S Q q 1 0 0 1 450.5853 305.4453 cm 0 0 m 0 2.835 l S Q q 1 0 0 1 488.2855 305.4453 cm 0 0 m 0 2.835 l S Q q 1 0 0 1 299.7821 364.9727 cm 0 0 m 2.834 0 l S Q q 1 0 0 1 299.7821 345.1304 cm 0 0 m 2.834 0 l S Q q 1 0 0 1 299.7821 325.2875 cm 0 0 m 2.834 0 l S Q 0 1 1 0 K 1 w 10 M 2 j q 1 0 0 1 188.1693 338.3203 cm 0 0 m 16.25 33 l 33 29.75 l 13.75 -8 l -0.25 -5.75 l 17 30.75 l 34 27.75 l 17.75 -5 l S Q q 121.585 283.023 371.949 149.376 re W n 0 1 1 0 k q 1 0 0 1 205.8402 331.7773 cm 0 0 m 0.709 0.756 1.243 1.21 1.883 1.781 c -0.828 3.127 l -0.833 2.812 -0.935 1.572 -1.107 0.55 c -1.292 -0.544 -1.523 -1.504 -1.731 -2.098 c -1.383 -1.573 -0.759 -0.809 0 0 c f Q 0 0 0 1 K 0.75 w [3]0 d q 1 0 0 1 202.4193 330.9453 cm 0 0 m 0 -3.797 -4.645 -6.875 -10.375 -6.875 c -16.105 -6.875 -20.75 -3.797 -20.75 0 c -20.75 3.797 -16.105 6.875 -10.375 6.875 c -4.645 6.875 0 3.797 0 0 c h S Q q 1 0 0 1 222.6693 369.9453 cm 0 0 m 0 -3.797 -4.645 -6.875 -10.375 -6.875 c -16.105 -6.875 -20.75 -3.797 -20.75 0 c -20.75 3.797 -16.105 6.875 -10.375 6.875 c -4.645 6.875 0 3.797 0 0 c h S Q q 1 0 0 1 360.6693 359.9453 cm 0 0 m 0 -3.797 -4.645 -6.875 -10.375 -6.875 c -16.105 -6.875 -20.75 -3.797 -20.75 0 c -20.75 3.797 -16.105 6.875 -10.375 6.875 c -4.645 6.875 0 3.797 0 0 c h S Q q 1 0 0 1 398.1693 359.9453 cm 0 0 m 0 -3.797 -4.645 -6.875 -10.375 -6.875 c -16.105 -6.875 -20.75 -3.797 -20.75 0 c -20.75 3.797 -16.105 6.875 -10.375 6.875 c -4.645 6.875 0 3.797 0 0 c h S Q 0.3 w []0 d q 1 0 0 1 266.1693 408.5703 cm 0 0 m 72.75 -43.25 l S Q 0 0 0 1 k q 1 0 0 1 340.2601 365.1494 cm 0 0 m -0.612 0.669 -0.974 1.165 -1.429 1.761 c -2.783 -0.516 l -2.508 -0.542 -1.433 -0.712 -0.553 -0.93 c 0.389 -1.164 1.211 -1.429 1.716 -1.649 c 1.281 -1.312 0.655 -0.716 0 0 c f Q q 1 0 0 1 266.4193 408.5703 cm 0 0 m -43 -31.5 l S Q q 1 0 0 1 222.7372 375.9034 cm 0 0 m 0.855 0.302 1.453 0.44 2.18 0.626 c 0.615 2.763 l 0.483 2.52 -0.094 1.597 -0.64 0.873 c -1.223 0.098 -1.789 -0.555 -2.189 -0.933 c -1.708 -0.666 -0.916 -0.323 0 0 c f Q 0 0 0 0 K q 1 0 0 1 251.9193 397.9482 cm 0 0 m -28.5 -20.878 l S Q 0 0 0 0 k q 1 0 0 1 222.7372 375.9034 cm 0 0 m 0.855 0.302 1.453 0.44 2.18 0.626 c 0.615 2.763 l 0.483 2.52 -0.094 1.597 -0.64 0.873 c -1.223 0.098 -1.789 -0.555 -2.189 -0.933 c -1.708 -0.666 -0.916 -0.323 0 0 c f Q 0 0 0 1 K 4 M 0 j q 1 0 0 1 138.1693 390.0703 cm 0 0 m 36.75 -5.25 l S Q 0 0 0 1 k q 1 0 0 1 176.223 385.1777 cm 0 0 m -0.822 0.382 -1.347 0.701 -1.997 1.076 c -2.371 -1.545 l -2.107 -1.463 -1.049 -1.208 -0.153 -1.071 c 0.806 -0.925 1.667 -0.854 2.218 -0.863 c 1.687 -0.718 0.88 -0.409 0 0 c f Q 0 0 0 0 K q 1 0 0 1 150.1693 388.356 cm 0 0 m 24.75 -3.536 l S Q 0 0 0 0 k q 1 0 0 1 176.223 385.1777 cm 0 0 m -0.822 0.382 -1.347 0.701 -1.997 1.076 c -2.371 -1.545 l -2.107 -1.463 -1.049 -1.208 -0.153 -1.071 c 0.806 -0.925 1.667 -0.854 2.218 -0.863 c 1.687 -0.718 0.88 -0.409 0 0 c f Q 0 0 0 1 K q 1 0 0 1 229.1693 297.0703 cm 0 0 m -16 43.5 l S Q 0 0 0 1 k q 1 0 0 1 212.2362 341.5483 cm 0 0 m 0.054 -0.905 0.022 -1.518 0 -2.268 c 2.485 -1.354 l 2.288 -1.161 1.561 -0.351 1.016 0.374 c 0.432 1.148 -0.04 1.873 -0.292 2.362 c -0.168 1.826 -0.058 0.969 0 0 c f Q 0 0 0 0 K q 1 0 0 1 225.951 305.8203 cm 0 0 m -12.782 34.75 l S Q 0 0 0 0 k q 1 0 0 1 212.2362 341.5483 cm 0 0 m 0.054 -0.905 0.021 -1.518 0 -2.268 c 2.485 -1.354 l 2.288 -1.161 1.561 -0.351 1.016 0.374 c 0.432 1.148 -0.04 1.873 -0.292 2.362 c -0.168 1.826 -0.058 0.969 0 0 c f Q Q q 121.585 283.023 371.949 149.376 re W n BT /T1_4 1 Tf 7 0 0 7 162.3797 426.4203 Tm (\(a\) )Tj /T1_5 1 Tf 1.666 -0.028 Td (Example of tool path)Tj /T1_4 1 Tf 18.986 0.037 Td (\(b\) )Tj /T1_5 1 Tf 1.722 -0.028 Td (Analysis result of contact length in the axis direction)Tj ET EMC Q BT /GS0 gs /T1_1 1 Tf 8 0 0 8 189.644 262.3748 Tm [(Fig)15(.)30( 3)]TJ /T1_6 1 Tf 2.344 0.018 Td ( )Tj /T1_0 1 Tf 0.888 -0.018 Td [(Anal)25(ysis case in)40.1(v)20(olving the axial depth of cuts in ball-end milling)]TJ ET 0 0 0 0 k /GS1 gs 59.528 76.535 496.063 167.158 re f /PlacedPDF /MC1 BDC q 95.46 98.597 424.197 145.097 re W n BT 0 0 0 1 k /T1_7 1 Tf 0 7 -7 0 101.4491 137.2401 Tm (Tangential force )Tj 6.831 -0.049 Td ( \()Tj (N)Tj (\))Tj ET Q BT 0 0 0 1 k /T1_7 1 Tf 7 0 0 7 145.6903 100.5331 Tm (Proportion to the total machining time)Tj ET q 95.46 98.597 424.197 145.097 re W n BT /T1_7 1 Tf 6.9999 0 0 7 252.8295 100.1903 Tm ( \()Tj ET Q BT /T1_8 1 Tf 7 0 0 7 258.6606 100.5331 Tm (%)Tj ET q 95.46 98.597 424.197 145.097 re W n BT /T1_7 1 Tf 6.9999 0 0 7 264.4916 100.1903 Tm (\))Tj ET Q BT /T1_7 1 Tf 6.9999 0 0 7 107.8828 211.4553 Tm (300)Tj 0 -2.193 TD (250)Tj T* (200)Tj 0 -2.193 TD (150)Tj 0.5 -4.387 Td (50)Tj -0.5 2.193 Td (100)Tj 1 -4.387 Td (0)Tj 0.655 -1.09 Td (0)Tj 4.609 0 Td (20)Tj 4.859 0 Td (40)Tj 4.859 0 Td (60)Tj 4.859 0 Td (80)Tj 4.609 0 Td (100)Tj 0 7 -7 0 325.5517 137.2401 Tm (Tangential force )Tj 6.831 -0.049 Td ( \()Tj (N)Tj (\))Tj 7 0 0 7 369.2958 100.5331 Tm (Proportion to the total machining time)Tj ET q 95.46 98.597 424.197 145.097 re W n BT /T1_7 1 Tf 6.9999 0 0 7 476.435 100.1903 Tm ( \()Tj ET Q BT /T1_8 1 Tf 7 0 0 7 482.266 100.5331 Tm (%)Tj ET q 95.46 98.597 424.197 145.097 re W n BT /T1_7 1 Tf 6.9999 0 0 7 488.0971 100.1903 Tm (\))Tj ET Q BT /T1_7 1 Tf 6.9999 0 0 7 343.5702 111.6983 Tm (0)Tj 4.581 0 Td (20)Tj 4.831 0 Td (40)Tj 4.831 0 Td (60)Tj 4.831 0 Td (80)Tj ET q 95.46 98.597 424.197 145.097 re W n BT /T1_7 1 Tf 6.9999 0 0 7 509.1528 111.6983 Tm (100)Tj ET Q 0 0 0 1 K 0.3 w 4 M 0 j q 1 0 0 1 446.7748 121.5252 cm 0 0 m 0 2.834 l S Q q 1 0 0 1 480.5922 121.5252 cm 0 0 m 0 2.834 l S Q q 1 0 0 1 514.4096 121.5252 cm 0 0 m 0 2.834 l S Q q 121.231 121.518 170.077 80.599 re W n q 170.0787074 0 0 80.5986569 121.2304497 121.5179432 cm /Im2 Do Q Q q 345.333 121.515 72.284 66.636 re W n q 72.2837764 0 0 66.6366035 345.3329468 121.5150765 cm /Im3 Do Q Q BT /T1_7 1 Tf 6.9999 0 0 7 331.9867 211.4554 Tm (300)Tj 0 -2.193 TD (250)Tj T* (200)Tj 0 -2.193 TD (150)Tj 0.5 -4.387 Td (50)Tj -0.5 2.193 Td (100)Tj 1 -4.387 Td (0)Tj ET q 1 0 0 1 345.3236 121.5252 cm 0 0 m 0 92.126 l S Q q 1 0 0 1 345.3236 213.6512 cm 0 0 m 2.835 0 l S Q q 1 0 0 1 345.3236 182.9427 cm 0 0 m 2.835 0 l S Q q 1 0 0 1 345.3236 198.2967 cm 0 0 m 2.835 0 l S Q q 1 0 0 1 345.3236 167.5882 cm 0 0 m 2.835 0 l S Q q 1 0 0 1 345.3236 152.2337 cm 0 0 m 2.835 0 l S Q q 1 0 0 1 345.3236 136.8797 cm 0 0 m 2.835 0 l S Q q 1 0 0 1 121.2211 121.5252 cm 0 0 m 0 92.126 l S Q q 1 0 0 1 121.2211 213.6512 cm 0 0 m 2.834 0 l S Q q 1 0 0 1 121.2211 182.9427 cm 0 0 m 2.834 0 l S Q q 1 0 0 1 121.2211 198.2967 cm 0 0 m 2.834 0 l S Q q 1 0 0 1 121.2211 167.5882 cm 0 0 m 2.834 0 l S Q q 1 0 0 1 121.2211 152.2337 cm 0 0 m 2.834 0 l S Q q 1 0 0 1 121.2211 136.8797 cm 0 0 m 2.834 0 l S Q q 95.46 98.597 424.197 145.097 re W n q 1 0 0 1 157.6781 189.8163 cm 0 0 m 0.46 2.438 2.109 2.418 v 3.998 2.395 57.491 2.367 58.812 2.418 c 60.149 2.47 60.767 4.841 y 61.075 4.841 l 61.726 2.407 63.03 2.418 v 64.581 2.431 118.46 2.4 119.729 2.418 c 121.173 2.438 121.841 0 y S Q Q 0 1 1 0 K 0.5 w [3]0 d q 1 0 0 1 416.2631 187.0057 cm 0 0 m -260.417 0 l S Q BT /T1_7 1 Tf 7 0 0 7 180.4023 198.0697 Tm (Increase of tangential force)Tj ET 0 0 0 0 k q 1 0 0 1 239.4818 181.203 cm 0 0 m 2.813 0 l 2.813 -7.818 l 8.533 -7.818 l 8.533 0 l 11.338 0 l 5.67 4.783 l h f* Q 0 0 0 1 K 0.3 w []0 d q 1 0 0 1 239.4818 181.203 cm 0 0 m 2.813 0 l 2.813 -7.818 l 8.533 -7.818 l 8.533 0 l 11.338 0 l 5.67 4.783 l 0 0 l h S Q q 1 0 0 1 294.4877 207.8338 cm 0 0 m -2.813 0 l -2.813 7.818 l -8.533 7.818 l -8.533 0 l -11.338 0 l -5.67 -4.783 l h f* Q q 1 0 0 1 294.4877 207.8338 cm 0 0 m -2.813 0 l -2.813 7.818 l -8.533 7.818 l -8.533 0 l -11.338 0 l -5.67 -4.783 l 0 0 l h S Q q 1 0 0 1 179.8149 181.203 cm 0 0 m 2.813 0 l 2.813 -7.818 l 8.533 -7.818 l 8.533 0 l 11.338 0 l 5.67 4.783 l h f* Q q 1 0 0 1 179.8149 181.203 cm 0 0 m 2.813 0 l 2.813 -7.818 l 8.533 -7.818 l 8.533 0 l 11.338 0 l 5.67 4.783 l 0 0 l h S Q BT 0 0 0 1 k /T1_7 1 Tf 7 0 0 7 269.5399 227.7362 Tm (Reduction of )Tj -1.346 -1.286 Td (tangential resistance)Tj 14.64 -1.381 Td (Upper limit of tangential force)Tj 9.181 -5.476 Td (Reduction in machining time)Tj ET q 1 0 0 1 382.5961 205.4002 cm 0 0 m -14.666 -15.667 l S Q q 95.46 98.597 424.197 145.097 re W n q 1 0 0 1 367.476 188.4603 cm 0 0 m 0.784 0.455 1.346 0.701 2.025 1.019 c 0.093 2.829 l 0.009 2.566 -0.389 1.552 -0.79 0.739 c -1.22 -0.13 -1.655 -0.877 -1.979 -1.322 c -1.556 -0.97 -0.84 -0.486 0 0 c f Q 0 1 1 0 K 0.5 w [3]0 d q 1 0 0 1 514.2631 121.5252 cm 0 0 m 0 92.126 l S Q 0 0 0 0 k q 1 0 0 1 421.9672 158.349 cm 0 0 m 0 2.813 l 91.818 2.813 l 91.818 8.533 l 0 8.533 l 0 11.339 l -4.782 5.67 l h f* Q 0 0 0 1 K 0.3 w []0 d q 1 0 0 1 421.9672 158.349 cm 0 0 m 0 2.813 l 91.818 2.813 l 91.818 8.533 l 0 8.533 l 0 11.339 l -4.782 5.67 l 0 0 l h S Q q 1 0 0 1 189.2514 121.5252 cm 0 0 m 0 2.834 l S Q q 1 0 0 1 223.268 121.5252 cm 0 0 m 0 2.834 l S Q q 1 0 0 1 257.2841 121.5252 cm 0 0 m 0 2.834 l S Q q 1 0 0 1 291.2997 121.5252 cm 0 0 m 0 2.834 l S Q q 1 0 0 1 379.141 121.5252 cm 0 0 m 0 2.834 l S Q q 1 0 0 1 412.9584 121.5252 cm 0 0 m 0 2.834 l S Q q 1 0 0 1 345.3236 121.5252 cm 0 0 m 169.087 0 l S Q q 1 0 0 1 155.2372 121.5252 cm 0 0 m 0 2.834 l S Q q 1 0 0 1 121.2211 121.5252 cm 0 0 m 170.079 0 l S Q Q q 95.46 98.597 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In addition, w)35.1(e ha)35(v)15.1(e created)21( )]TJ 0.012 Tc T* [(a pro)25(g)-19.9(ram to predict forced chatter vibrations caused b)25.1(y)12( )]TJ 0.036 Tc T* [(the periodic impact force associated with inter)-19.9(mittent)36( )]TJ 0.001 Tc -0.001 Tw T* (cutting)Tj 6.37 0 0 6.5 66.9888 191.882 Tm (\(1\))Tj 0.125 Tw 9.8 0 0 10 74.4382 188.382 Tm [(. In this w)24.9(a)34.8(y w)34.9(e are stri)24.8(ving for the de)24.9(v)14.8(elopment)1( )]TJ 0.011 Tc -3.546 -1.21 Td [(of)0.5( o)0.5(ur )0.5(o)40.4(w)0.5(n t)0.5(ec)0.5(hn)0.5(olo)25.5(gy )0.5(fo)0.5(r m)0.5(ak)0.5(ing)0.5( a)0.5( c)0.5(oup)0.5(le)0.5(d )0.5(ana)0.5(l)25.4(y)0.5(sis)0.5( o)0.5(f)11( )]TJ 0.003 Tc T* [(both types of chatter vibrations and successfull)24.8(y a)34.7(v)19.7(oiding)3( )]TJ 0.01 Tc T* [(them without compromising the ef)25.1(f)-59.8(icienc)15.2(y in the cutting)10( )]TJ 0 Tc 0 Tw T* (process. )Tj /T1_1 1 Tf 0.12 Tw 10 0 0 10 75.1474 139.9777 Tm [(Figur)30(e)]TJ /Span<>> BDC ( )Tj EMC (2)Tj /T1_0 1 Tf 9.8 0 0 10 111.8737 139.9777 Tm [( sho)40(ws an e)15(xample of the application to )]TJ 0 Tw -7.366 -1.21 Td (the machining process.)Tj 0.018 Tc 0.125 Tw 0.578 -1.21 Td [(Element test results and contact conditions of the tool)18( )]TJ 0.003 Tc -0.578 -1.21 Td [(and w)39.9(ork during the cutting process are used to calculate)3( )]TJ /C2_0 1 Tf 0 Tc 0 Tw 8.82 0 0 9 39.685 91.5732 Tm <1B05>Tj /T1_0 1 Tf 0.049 Tc 0.125 Tw 9.8 0 0 10 50.7045 91.5732 Tm ( )Tj /Span<>> BDC ( )Tj EMC [(stability lobes of re)15.3(generati)25.3(v)15.3(e chatter vibrations)49( )]TJ 0.013 Tc -1.124 -1.21 Td [(predicted b)25.1(y CUTPR)40.1(O)]TJ 0 Tc 0 Tw 6.37 0 0 6.5 133.7302 82.9721 Tm (\256)Tj 0.013 Tc -0.013 Tw 9.8 0 0 10 138.6537 79.4721 Tm (, )Tj /C2_0 1 Tf 0 Tc 0 Tw 8.82 0 0 9 145.032 79.4721 Tm <1B06>Tj /T1_0 1 Tf 0.013 Tc 0.125 Tw /Span<>> BDC 9.8 0 0 10 155.7361 79.4721 Tm ( )Tj EMC [(occur)-29.9(rence prediction range)13( )]TJ 0.033 Tc 14.769 38.724 Td [(o)0.5(f)0.5( f)0.5(o)0.5(r)0.5(c)0.5(e)0.5(d )0.5(c)0.5(h)0.5(a)0.5(t)0.5(t)0.5(er)0.5( )0.5(v)0.5(i)0.5(br)0.5(a)0.5(t)0.5(i)0.5(on)0.5(s)0.5( )0.5(p)0.5(r)0.5(ed)0.5(i)0.5(c)0.5(t)0.5(e)0.5(d )0.5(b)25.5(y)0.5( t)0.5(h)0.5(e)0.5( )0.5(pr)0.5(o)25.5(g)-19.5(r)0.5(a)0.5(m,)33( )]TJ 0.069 Tc -0.069 Tw T* (and )Tj /C2_0 1 Tf 0 Tc 0 Tw 8.82 0 0 9 321.0154 454.6063 Tm <1B07>Tj /T1_0 1 Tf 0.069 Tc 0.125 Tw /Span<>> BDC 9.8 0 0 10 332.2167 454.6063 Tm ( )Tj EMC [(spindle speed causing abnor)-20.3(mal tool w)34.7(ear)54.7(.)69( )]TJ 0 Tc 0.123 Tw -3.239 -1.21 Td [(Consideration )0.5(of )0.5(these )0.5(three )0.5(phenomena )0.6(helps )0.5(not )0.5(onl)25(y )0.5(to )]TJ 0.01 Tc 0.125 Tw T* [(a)35.1(v)20.1(oid re)15.1(generati)25.1(v)15.1(e chatter vibrations, b)-5(ut also to identify)10( )]TJ 0.011 Tc T* [(spindle speed and axial depth of cut that can a)35.3(v)20.2(oid both)11( )]TJ 0 Tc 0.085 Tw T* (the forced chatter vibration range and the range associated )Tj 0.064 Tc 0.125 Tw T* [(with abnor)-19.7(mal tool w)35.2(ear)55.2(. 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In addition, )]TJ 0.008 Tc 0.125 Tw T* [(it is dif)24.6(f)-60.3(icult for the con)39.7(v)14.7(entional functions of Computer)8( )]TJ 0.021 Tc T* [(Aided Manuf)-9.8(acturing \(CAM\) to stab)20.1(l)25.3(y achie)25.2(v)15.2(e selected)21( )]TJ 0.035 Tc T* [(optim)0.5(al cut)0.5(ting condi)0.5(tions du)0.5(ring 5-a)0.5(xis si)0.5(multaneo)0.5(us)35( )]TJ 0 Tc 0 Tw 0 -1.21 TD [(machining process of a comple)15.1(x shape.)]TJ ET 0 0 0 0 k /GS1 gs 39.685 478.77 235.276 286.584 re f /PlacedPDF /MC0 BDC 0.6 0.1 0.05 0 k 94.124 558.805 17.09 75.291 re f* 0 0 0 1 K 0.3 w q 1 0 0 1 94.1239 558.8055 cm 0 0 m 17.09 0 l 17.09 75.291 l 0 75.291 l h S Q 153.651 558.805 17.092 158.816 re f* q 1 0 0 1 153.6509 558.8055 cm 0 0 m 17.092 0 l 17.092 158.816 l 0 158.816 l h S Q 213.177 558.805 17.095 92.35 re f* q 1 0 0 1 213.1769 558.8055 cm 0 0 m 17.095 0 l 17.095 92.35 l 0 92.35 l h S Q 0 0.5 0.98 0 k 111.215 572.922 17.091 -14.117 re f* q 1 0 0 1 111.2149 572.9225 cm 0 0 m 17.091 0 l 17.091 -14.117 l 0 -14.117 l h S Q 170.743 578.805 17.091 -20 re f* q 1 0 0 1 170.7429 578.8055 cm 0 0 m 17.091 0 l 17.091 -20 l 0 -20 l h S Q 230.271 574.099 17.09 -15.295 re f* q 1 0 0 1 230.2709 574.0995 cm 0 0 m 17.09 0 l 17.09 -15.295 l 0 -15.295 l h S Q 2 J q 1 0 0 1 81.7459 761.7353 cm 0 0 m 0 -217.105 l S Q q 1 0 0 1 81.7449 581.1562 cm 0 0 m 2.551 0 l S Q q 1 0 0 1 81.7449 604.0995 cm 0 0 m 2.551 0 l S Q q 1 0 0 1 81.7449 626.4501 cm 0 0 m 2.551 0 l S Q q 1 0 0 1 81.7449 649.3885 cm 0 0 m 2.551 0 l S Q q 1 0 0 1 200.886 544.6288 cm 0 0 m 0 17.008 l S Q q 1 0 0 1 141.3152 544.6288 cm 0 0 m 0 17.005 l S Q q 54.167 501.831 206.312 263.524 re W n q 1 0 0 1 260.3289 544.6288 cm 0 0 m 0 17.005 l S Q Q q 1 0 0 1 81.7449 671.7431 cm 0 0 m 2.551 0 l S Q q 1 0 0 1 81.7449 694.6825 cm 0 0 m 2.551 0 l S Q q 1 0 0 1 81.7449 739.3842 cm 0 0 m 2.551 0 l S Q q 1 0 0 1 81.7449 761.7353 cm 0 0 m 2.551 0 l S Q q 1 0 0 1 81.7449 717.0331 cm 0 0 m 2.551 0 l S Q q 1 0 0 1 81.7459 558.8051 cm 0 0 m 178.584 0 l S Q BT 0 0 0 1 k /T1_2 1 Tf 7 0 0 7 95.365 550.1898 Tm (X)Tj ( direction)Tj 8.547 0 Td (Y)Tj ( direction)Tj 8.519 0 Td (Z)Tj ( direction)Tj ET q 54.167 501.831 206.312 263.524 re W n BT /T1_2 1 Tf 0 7 -7 0 59.9832 609.4374 Tm (Analytical error of cutting force \()Tj /T1_3 1 Tf (%)Tj /T1_2 1 Tf (\))Tj 7 0 0 7 68.409 759.538 Tm (180)Tj ET Q BT /T1_2 1 Tf 7 0 0 7 68.409 736.991 Tm (160)Tj 0 -6.442 TD (120)Tj 0 3.221 TD (140)Tj 0 -6.442 TD (100)Tj 0.5 -3.221 Td (80)Tj 0 -3.221 TD (60)Tj T* (40)Tj T* (20)Tj 0.5 -3.221 Td (0)Tj ET 0.6 0.1 0.05 0 k 93.083 752.999 5.669 5.669 re f* 0 J q 1 0 0 1 93.0829 752.9995 cm 0 0 m 5.669 0 l 5.669 5.669 l 0 5.669 l h S Q 0 0.5 0.98 0 k 93.083 750.007 5.669 -5.669 re f* q 1 0 0 1 93.0829 750.0074 cm 0 0 m 5.669 0 l 5.669 -5.669 l 0 -5.669 l h S Q BT 0 0 0 1 k /T1_2 1 Tf 7 0 0 7 102.1189 754.3446 Tm (: Default data)Tj 0 -1.286 TD (: IHI)Tj (\222)Tj (s original integrated data)Tj 4.529 -30.714 Td [(\(Note\) )-784.6(Cutting conditions)]TJ T* [( )-3394.5(- Spindle speed )-1683(: )-79.4(1 400 rpm)]TJ T* [( )-3394.5(- Feed rate )-3573.1(: )-79.3(0.15 mm/edge)]TJ ET q 54.167 501.831 206.312 263.524 re W n BT /T1_2 1 Tf 7 0 0 7 133.8219 503.3386 Tm [( )-3394.5(- Axial depth of cut )-17(: )170.6(0.3 mm)]TJ ET EMC Q BT /GS0 gs /T1_1 1 Tf 8 0 0 8 45.2043 490.1834 Tm [(Fig)15(.)30( 1)]TJ /T1_4 1 Tf 2.344 0.018 Td [( Comparison of material pr)19.2(operties f)19.1(or analytical err)19.1(or)19(s )]TJ /T1_1 1 Tf -3.034 -1.268 Td ( )Tj /T1_4 1 Tf 0.25 0.018 Td [( r)19.1(elated t)19.1(o cutting f)19.1(or)19(ce)]TJ ET 0 0 0 0 k /GS1 gs 300.472 494.2 235.276 271.863 re f /PlacedPDF /MC1 BDC q 300.542 517.247 235.136 248.816 re W n 0.3 0 0.1 0 k q 1 0 0 1 409.7487 539.6706 cm 0 0 m 0 78.442 l -0.615 61.583 l -0.844 61.125 l -0.99 52.875 l -1.453 52.875 l -1.24 45.75 l -1.823 45.625 l -1.698 40.5 l -2.156 40.417 l -3.531 28.042 l -3.823 27.917 l -4.948 23.875 l -5.984 22.6 -6.314 22.586 v -7.156 22.813 -7.167 22.963 -7.563 23.625 c -9.406 27 -10.188 35.125 -10.079 39.828 c -14.7 43.674 -14.25 92.469 -15.188 93.125 c -15.469 80.594 -16.906 31.156 -18.019 30.56 c -18.138 29.138 -17.833 28.155 -17.938 27.929 c -18.594 28 -19.339 22.407 -19.672 22.464 c -20.665 22.166 -21.608 25.69 -22.269 31.652 c -23.188 37.594 -22.938 56 -23.844 55.813 c -23.959 58.576 -23.75 61.031 -23.813 64.125 c -23.823 64.447 -24.148 64.115 -24.159 64.438 c -24.94 88.73 -25.25 114.75 -25.015 116.936 c -26.351 117.179 -25.864 25.379 -29.386 22.828 c -29.828 22.828 -30.319 23.737 -30.648 25.621 c -31.142 28.444 -31.406 36.521 -31.594 37.094 c -31.781 37.667 -31.792 45.012 -31.938 49.188 c -32.331 50.916 -32 68.406 -32.188 73.188 c -32.75 73.875 -32.625 78.688 y -32.591 78.362 -33.359 77.795 v -33.442 75.143 -33.208 68.284 -33.32 65.53 c -33.494 65.502 -33.744 65.937 -33.844 65.25 c -34.063 61.625 -33.985 51.451 -34.655 47.397 c -35.06 33.959 -35.639 22.986 -36.406 22.625 c -37.243 21.509 -38.096 27.929 -37.934 37.278 c -39.027 37.967 -38.217 54.886 -38.736 72.129 c -39.294 55.701 -40.079 41.569 v -41.031 42.5 -39.593 36.388 -40.889 35.336 c -41.131 28.131 -41.39 22.707 -42.015 22.707 c -43.109 25.003 -43.313 37.625 -43.313 45.656 c -43.531 46.094 -43.844 47.563 y -44.313 40.25 -44.808 41.043 v -44.774 36.873 -45.26 37.198 v -45.387 31.701 -45.351 22.496 -46.265 22.828 c -46.993 24.528 -47.479 45.657 y -47.446 40.799 -48.012 40.759 v -48.579 40.719 -48.329 45.778 y -48.458 41.853 -48.741 41.487 v -48.884 35.172 -48.875 23.446 -49.3 22.95 c -50.499 22.267 -50.441 34.405 -50.724 40.84 c -50.745 41.312 -51.291 43.026 y -51.739 38.119 -51.817 37.157 v -52.182 32.664 -51.986 22.828 -52.546 22.504 c -53.177 22.14 -52.336 29.467 -53.186 29.993 c -53.388 30.924 -52.788 45.131 -53.921 45.778 c -54.765 23.071 l -54.891 23.071 -54.906 25.219 -55.344 25.531 c -55.605 30.938 -55.37 43.438 -55.5 48.731 c -55.676 49.894 -55.911 50.633 -56.222 50.757 c -56.14 28.737 l -57.344 28.5 -56.95 22.343 y -57.193 32.543 l -58.091 34.89 l -58.617 27.119 l -59.346 38.047 -59.669 37.967 v -60.351 22.464 l -61.046 31.248 l -61.613 22.545 l -62.293 29.629 l -62.778 22.586 l -63.312 36.59 l -64.081 24.771 l -65.532 28.981 -66.664 28.9 v -67.797 28.819 -69.579 23.558 y -69.579 0 l h f Q 0 0.3 0.1 0 k 519.723 676.642 -110.146 -136.972 re f 0 1 1 0 K 0.75 w 8 M q 1 0 0 1 519.7233 676.642 cm 0 0 m -110.146 0 l -110.146 -136.972 l 0 -136.972 l h S Q 0 0.1 0.3 0 k 450.184 674.109 -20.533 -134.438 re f 0 0 0 1 K 0.3 w q 1 0 0 1 450.1843 674.109 cm 0 0 m -20.533 0 l -20.533 -134.438 l 0 -134.438 l h S Q 10 M 2 J q 1 0 0 1 326.9673 561.948 cm 0 0 m 2.834 0 l S Q q 1 0 0 1 326.9673 584.2248 cm 0 0 m 2.834 0 l S Q q 1 0 0 1 327.0552 606.5022 cm 0 0 m 2.659 0 l S Q q 1 0 0 1 327.0552 628.7795 cm 0 0 m 2.659 0 l S Q q 1 0 0 1 327.0552 651.0564 cm 0 0 m 2.659 0 l S Q q 1 0 0 1 327.0552 673.3337 cm 0 0 m 2.659 0 l S Q q 1 0 0 1 327.0552 695.6111 cm 0 0 m 2.659 0 l S Q q 1 0 0 1 327.0552 717.8884 cm 0 0 m 2.659 0 l S Q q 1 0 0 1 327.0552 740.1653 cm 0 0 m 2.659 0 l S Q q 1 0 0 1 327.0552 762.4426 cm 0 0 m 2.659 0 l S Q q 1 0 0 1 326.9673 539.6706 cm 0 0 m 0 222.771 l S Q 0.5 w 2 j 1 J q 1 0 0 1 340.1694 574.0198 cm 0 0 m 0 3.523 l S Q q 1 0 0 1 340.1694 577.5432 cm 0 0 m 0 3.963 l S Q q 1 0 0 1 340.1694 581.5066 cm 0 0 m 0 1.321 l 0 2.202 l 0.44 3.523 l 0.44 3.964 l S Q q 1 0 0 1 340.61 585.4705 cm 0 0 m 0 0 l 0 -0.44 l 0 -1.762 l S Q q 1 0 0 1 340.61 583.7087 cm 0 0 m 0 -0.881 l 0 -2.202 l 0 -4.844 l S Q q 1 0 0 1 340.61 578.8645 cm 0 0 m 0 -4.404 l S Q q 1 0 0 1 340.61 574.4607 cm 0 0 m 0 -2.201 l 0 -3.963 l S Q q 1 0 0 1 340.61 570.4978 cm 0 0 m 0 -1.322 l 0 -2.643 l S Q q 1 0 0 1 340.61 567.8552 cm 0 0 m 0 -1.321 l 0 -2.203 l S Q q 1 0 0 1 340.61 565.6526 cm 0 0 m 0 -0.88 l 0 -1.321 l S Q q 1 0 0 1 340.61 564.3318 cm 0 0 m 0 -0.88 l 0 -1.321 l S Q q 1 0 0 1 340.61 563.011 cm 0 0 m 0 -0.44 l S Q q 1 0 0 1 340.61 562.5706 cm 0 0 m 0 -0.44 l S Q q 1 0 0 1 340.61 562.1306 cm 0 0 m 0 0 l S Q q 1 0 0 1 340.61 562.1306 cm 0 0 m 0 0.44 l S Q q 1 0 0 1 340.61 562.5706 cm 0 0 m 0 0.881 l S Q q 1 0 0 1 340.61 563.4514 cm 0 0 m 0 0.88 l S Q q 1 0 0 1 340.61 564.3318 cm 0 0 m 0 1.321 l S Q q 1 0 0 1 340.61 565.6526 cm 0 0 m 0 1.762 l S Q q 1 0 0 1 340.61 567.4143 cm 0 0 m 0 0.881 l 0 1.761 l S Q q 1 0 0 1 340.61 569.1755 cm 0 0 m 0 1.322 l 0.44 2.643 l S Q q 1 0 0 1 341.0504 571.8186 cm 0 0 m 0 1.321 l 0 2.642 l S Q q 1 0 0 1 341.0504 574.4607 cm 0 0 m 0 1.761 l 0 3.523 l S Q q 1 0 0 1 341.0504 577.9836 cm 0 0 m 0 1.762 l 0 2.643 l 0 3.523 l S Q q 1 0 0 1 341.0504 581.5066 cm 0 0 m 0 0.441 l S Q q 1 0 0 1 341.0504 581.9475 cm 0 0 m 0 -0.441 l 0 -0.881 l S Q q 1 0 0 1 341.0504 581.0662 cm 0 0 m 0 -0.439 l S Q q 1 0 0 1 341.0504 580.6267 cm 0 0 m 0 -1.322 l 0 -3.523 l S Q q 1 0 0 1 341.0504 577.1038 cm 0 0 m 0 -2.203 l 0 -4.405 l S Q q 1 0 0 1 341.0504 572.699 cm 0 0 m 0 -1.762 l 0 -3.082 l S Q q 1 0 0 1 341.0504 569.6169 cm 0 0 m 0 -2.203 l S Q q 1 0 0 1 341.0504 567.4143 cm 0 0 m 0 -1.762 l S Q q 1 0 0 1 341.0504 565.6526 cm 0 0 m 0 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0 0 m 0 -0.441 l 0 -1.322 l S Q q 1 0 0 1 341.4902 579.3049 cm 0 0 m 0 -0.881 l 0 -2.201 l 0 -4.404 l S Q q 1 0 0 1 341.4902 574.9011 cm 0 0 m 0 -3.523 l S Q q 1 0 0 1 341.4902 571.3777 cm 0 0 m 0 -2.642 l S Q q 1 0 0 1 341.4902 568.7361 cm 0 0 m 0 -0.881 l 0 -1.761 l S Q q 1 0 0 1 341.4902 566.9748 cm 0 0 m 0 -0.881 l 0.439 -1.762 l S Q q 1 0 0 1 341.9297 565.2131 cm 0 0 m 0 -1.321 l S Q q 1 0 0 1 341.9297 563.8918 cm 0 0 m 0 -0.881 l S Q q 1 0 0 1 341.9297 563.011 cm 0 0 m 0 -0.44 l S Q q 1 0 0 1 341.9297 562.5706 cm 0 0 m 0 -0.44 l S Q q 1 0 0 1 341.9297 562.1306 cm 0 0 m 0 0 l S Q q 1 0 0 1 341.9297 562.1306 cm 0 0 m 0 0.44 l S Q q 1 0 0 1 341.9297 562.5706 cm 0 0 m 0 0.44 l S Q q 1 0 0 1 341.9297 563.011 cm 0 0 m 0 0.44 l S Q q 1 0 0 1 341.9297 563.4514 cm 0 0 m 0 0.44 l 0 1.321 l S Q q 1 0 0 1 341.9297 564.7727 cm 0 0 m 0 1.321 l S Q q 1 0 0 1 341.9297 566.0935 cm 0 0 m 0 1.321 l S Q q 1 0 0 1 341.9297 567.4143 cm 0 0 m 0 1.761 l S Q q 1 0 0 1 341.9297 569.1755 cm 0 0 m 0 2.202 l S Q q 1 0 0 1 341.9297 571.3777 cm 0 0 m 0 2.642 l S Q q 1 0 0 1 341.9297 574.0198 cm 0 0 m 0 2.643 l S Q q 1 0 0 1 341.9297 576.6623 cm 0 0 m 0 1.762 l 0 3.083 l S Q q 1 0 0 1 341.9297 579.7454 cm 0 0 m 0 0.881 l S Q q 1 0 0 1 341.9297 580.6267 cm 0 0 m 0 0.439 l S Q q 1 0 0 1 341.9297 581.0662 cm 0 0 m 0 0 l 0.44 0.44 l S Q q 1 0 0 1 342.3701 581.5066 cm 0 0 m 0 0.441 l 0 0.881 l S Q q 1 0 0 1 342.3701 582.3874 cm 0 0 m 0 0 l S Q q 1 0 0 1 342.3701 582.3874 cm 0 0 m 0 -0.881 l 0 -2.202 l 0 -3.523 l 0 -4.844 l S Q q 1 0 0 1 342.3701 577.5432 cm 0 0 m 0 -1.762 l 0 -3.523 l S Q q 1 0 0 1 342.3701 574.0198 cm 0 0 m 0 -3.083 l S Q q 1 0 0 1 342.3701 570.9373 cm 0 0 m 0 -1.32 l 0 -2.642 l S Q q 1 0 0 1 342.3701 568.2956 cm 0 0 m 0 -1.762 l S Q q 1 0 0 1 342.3701 566.5339 cm 0 0 m 0 -1.321 l S Q q 1 0 0 1 342.3701 565.2131 cm 0 0 m 0 -1.321 l S Q q 1 0 0 1 342.3701 563.8918 cm 0 0 m 0 -0.881 l S Q q 1 0 0 1 342.3701 563.011 cm 0 0 m 0 -0.44 l S Q q 1 0 0 1 342.3701 562.5706 cm 0 0 m 0 -0.44 l S Q q 1 0 0 1 342.3701 562.1306 cm 0 0 m 0 0 l S Q q 1 0 0 1 342.3701 562.1306 cm 0 0 m 0 0.44 l S Q q 1 0 0 1 342.3701 562.5706 cm 0 0 m 0 0 l S Q q 1 0 0 1 342.3701 562.5706 cm 0 0 m 0 0.44 l 0 0.881 l S Q q 1 0 0 1 342.3701 563.4514 cm 0 0 m 0 0.44 l S Q q 1 0 0 1 342.3701 563.8918 cm 0 0 m 0 0.44 l 0.44 1.321 l S Q q 1 0 0 1 342.8106 565.2131 cm 0 0 m 0 1.321 l S Q q 1 0 0 1 342.8106 566.5339 cm 0 0 m 0 1.321 l S Q q 1 0 0 1 342.8106 567.8552 cm 0 0 m 0 1.762 l S Q q 1 0 0 1 342.8106 569.6169 cm 0 0 m 0 2.202 l S Q q 1 0 0 1 342.8106 571.8186 cm 0 0 m 0 2.201 l S Q q 1 0 0 1 342.8106 574.0198 cm 0 0 m 0 2.643 l S Q q 1 0 0 1 342.8106 576.6623 cm 0 0 m 0 1.762 l 0 3.083 l S Q q 1 0 0 1 342.8106 579.7454 cm 0 0 m 0 1.321 l 0 2.642 l S Q q 1 0 0 1 342.8106 582.3874 cm 0 0 m 0 0.44 l 0 0.881 l S Q q 1 0 0 1 342.8106 583.2683 cm 0 0 m 0 0.881 l 0 1.321 l S Q q 1 0 0 1 342.8106 584.5896 cm 0 0 m 0 0.881 l S Q q 1 0 0 1 342.8106 585.4705 cm 0 0 m 0 0.439 l 0 0.88 l 0 1.321 l S Q q 1 0 0 1 342.8106 586.7917 cm 0 0 m 0 -0.882 l 0 -1.762 l 0 -3.083 l 0 -4.404 l S Q q 1 0 0 1 342.8106 582.3874 cm 0 0 m 0 -2.202 l 0 -4.404 l S Q q 1 0 0 1 342.8106 577.9836 cm 0 0 m 0 -3.523 l S Q q 1 0 0 1 342.8106 574.4607 cm 0 0 m 0 -3.083 l S Q q 1 0 0 1 342.8106 571.3777 cm 0 0 m 0 -2.202 l S Q q 1 0 0 1 342.8106 569.1755 cm 0 0 m 0 -0.88 l 0.44 -1.761 l S Q q 1 0 0 1 343.2505 567.4143 cm 0 0 m 0 -1.762 l S Q q 1 0 0 1 343.2505 565.6526 cm 0 0 m 0 -1.321 l S Q q 1 0 0 1 343.2505 564.3318 cm 0 0 m 0 -0.88 l S Q q 1 0 0 1 343.2505 563.4514 cm 0 0 m 0 -0.44 l S Q q 1 0 0 1 343.2505 563.011 cm 0 0 m 0 -0.44 l S Q q 1 0 0 1 343.2505 562.5706 cm 0 0 m 0 -0.44 l S Q q 1 0 0 1 343.2505 562.1306 cm 0 0 m 0 0 l S Q q 1 0 0 1 343.2505 562.1306 cm 0 0 m 0 0.44 l S Q q 1 0 0 1 343.2505 562.5706 cm 0 0 m 0 0 l S Q q 1 0 0 1 343.2505 562.5706 cm 0 0 m 0 0.44 l 0 0.881 l S Q q 1 0 0 1 343.2505 563.4514 cm 0 0 m 0 0.44 l S Q q 1 0 0 1 343.2505 563.8918 cm 0 0 m 0 0.881 l S Q q 1 0 0 1 343.2505 564.7727 cm 0 0 m 0 1.321 l S Q q 1 0 0 1 343.2505 566.0935 cm 0 0 m 0 1.321 l S Q q 1 0 0 1 343.2505 567.4143 cm 0 0 m 0 1.322 l S Q q 1 0 0 1 343.2505 568.7361 cm 0 0 m 0 1.762 l S Q q 1 0 0 1 343.2505 570.4978 cm 0 0 m 0 2.201 l S Q q 1 0 0 1 343.2505 572.699 cm 0 0 m 0 0.881 l 0.44 2.202 l S Q q 1 0 0 1 343.6904 574.9011 cm 0 0 m 0 2.642 l S Q q 1 0 0 1 343.6904 577.5432 cm 0 0 m 0 3.083 l S Q q 1 0 0 1 343.6904 580.6267 cm 0 0 m 0 1.321 l 0 3.082 l S Q q 1 0 0 1 343.6904 583.7087 cm 0 0 m 0 2.201 l 0 3.963 l S Q q 1 0 0 1 343.6904 587.6716 cm 0 0 m 0 1.322 l 0 2.203 l S Q q 1 0 0 1 343.6904 589.8743 cm 0 0 m 0 0.88 l 0 1.762 l S Q q 1 0 0 1 343.6904 591.636 cm 0 0 m 0 0.44 l S Q q 1 0 0 1 343.6904 592.0764 cm 0 0 m 0 -0.882 l 0 -2.643 l 0 -4.405 l 0 -5.726 l S Q q 1 0 0 1 343.6904 586.3508 cm 0 0 m 0 -4.844 l S Q q 1 0 0 1 343.6904 581.5066 cm 0 0 m 0 -3.963 l S Q q 1 0 0 1 343.6904 577.5432 cm 0 0 m 0 -1.762 l 0 -3.523 l S Q q 1 0 0 1 343.6904 574.0198 cm 0 0 m 0 -2.642 l S Q q 1 0 0 1 343.6904 571.3777 cm 0 0 m 0 -2.202 l S Q q 1 0 0 1 343.6904 569.1755 cm 0 0 m 0 -1.761 l S Q q 1 0 0 1 343.6904 567.4143 cm 0 0 m 0 -1.321 l S Q q 1 0 0 1 343.6904 566.0935 cm 0 0 m 0 -1.321 l S Q q 1 0 0 1 343.6904 564.7727 cm 0 0 m 0 -0.881 l S Q q 1 0 0 1 343.6904 563.8918 cm 0 0 m 0 -0.881 l S Q q 1 0 0 1 343.6904 563.011 cm 0 0 m 0 -0.44 l 0.44 -0.44 l S Q q 1 0 0 1 344.1304 562.5706 cm 0 0 m 0 0 l S Q q 1 0 0 1 344.1304 562.5706 cm 0 0 m 0 0 l 0 -0.44 l S Q q 1 0 0 1 344.1304 562.1306 cm 0 0 m 0 0 l S Q q 1 0 0 1 344.1304 562.1306 cm 0 0 m 0 0.44 l S Q q 1 0 0 1 344.1304 562.5706 cm 0 0 m 0 0 l S Q q 1 0 0 1 344.1304 562.5706 cm 0 0 m 0 0.44 l 0 0.881 l S Q q 1 0 0 1 344.1304 563.4514 cm 0 0 m 0 0.44 l S Q q 1 0 0 1 344.1304 563.8918 cm 0 0 m 0 0.881 l S Q q 1 0 0 1 344.1304 564.7727 cm 0 0 m 0 0.88 l S Q q 1 0 0 1 344.1304 565.6526 cm 0 0 m 0 1.322 l S Q q 1 0 0 1 344.1304 566.9748 cm 0 0 m 0 1.321 l S Q q 1 0 0 1 344.1304 568.2956 cm 0 0 m 0 1.762 l S Q q 1 0 0 1 344.1304 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1 0 0 1 513.562 597.8005 cm 0 0 m 0 0 l S Q q 1 0 0 1 513.562 597.8005 cm 0 0 m 0 0 l S Q q 1 0 0 1 513.562 597.8005 cm 0 0 m 0 0 l 0.44 -0.439 l S Q q 1 0 0 1 514.0026 597.3611 cm 0 0 m 0 0 l S Q q 1 0 0 1 514.0026 597.3611 cm 0 0 m 0 0 l S Q q 1 0 0 1 514.0026 597.3611 cm 0 0 m 0 0 l S Q q 1 0 0 1 514.0026 597.3611 cm 0 0 m 0 0 l 0 -0.44 l S Q q 1 0 0 1 514.0026 596.9206 cm 0 0 m 0 0 l S Q q 1 0 0 1 514.0026 596.9206 cm 0 0 m 0 0 l S Q q 1 0 0 1 514.0026 596.9206 cm 0 0 m 0 0 l S Q q 1 0 0 1 514.0026 596.9206 cm 0 0 m 0 0 l 0 -0.441 l S Q q 1 0 0 1 514.0026 596.4797 cm 0 0 m 0 0 l S Q q 1 0 0 1 514.0026 596.4797 cm 0 0 m 0 0 l S Q q 1 0 0 1 514.0026 596.4797 cm 0 0 m 0 0 l S Q q 1 0 0 1 514.0026 596.4797 cm 0 0 m 0 0 l S Q q 1 0 0 1 514.0026 596.4797 cm 0 0 m 0 0 l 0 -0.441 l S Q q 1 0 0 1 514.0026 596.0388 cm 0 0 m 0 0 l S Q q 1 0 0 1 514.0026 596.0388 cm 0 0 m 0 0 l S Q q 1 0 0 1 514.0026 596.0388 cm 0 0 m 0 0 l S Q q 1 0 0 1 514.0026 596.0388 cm 0 0 m 0 0 l 0 -0.439 l S Q q 1 0 0 1 514.0026 595.5994 cm 0 0 m 0 0 l 0.44 0 l S Q q 1 0 0 1 514.4424 595.5994 cm 0 0 m 0 0 l S Q q 1 0 0 1 514.4424 595.5994 cm 0 0 m 0 0 l S Q q 1 0 0 1 514.4424 595.5994 cm 0 0 m 0 0 l 0 -0.441 l S Q q 1 0 0 1 514.4424 595.1584 cm 0 0 m 0 0 l S Q q 1 0 0 1 514.4424 595.1584 cm 0 0 m 0 0 l S Q q 1 0 0 1 514.4424 595.1584 cm 0 0 m 0 0 l S Q q 1 0 0 1 514.4424 595.1584 cm 0 0 m 0 0 l 0 -0.44 l S Q q 1 0 0 1 514.4424 594.718 cm 0 0 m 0 0 l S Q q 1 0 0 1 514.4424 594.718 cm 0 0 m 0 0 l S Q q 1 0 0 1 514.4424 594.718 cm 0 0 m 0 0 l S Q q 1 0 0 1 514.4424 594.718 cm 0 0 m 0 0 l 0 -0.441 l S Q q 1 0 0 1 514.4424 594.2771 cm 0 0 m 0 0 l S Q q 1 0 0 1 514.4424 594.2771 cm 0 0 m 0 0 l S Q q 1 0 0 1 514.4424 594.2771 cm 0 0 m 0 0 l S Q q 1 0 0 1 514.4424 594.2771 cm 0 0 m 0 0 l 0 -0.439 l S Q q 1 0 0 1 514.4424 593.8376 cm 0 0 m 0 0 l S Q q 1 0 0 1 514.4424 593.8376 cm 0 0 m 0 0 l S Q q 1 0 0 1 514.4424 593.8376 cm 0 0 m 0 0 l 0.439 0 l S Q q 1 0 0 1 514.882 593.8376 cm 0 0 m 0 0 l S Q q 1 0 0 1 514.882 593.8376 cm 0 0 m 0 0 l 0 -0.441 l S Q q 1 0 0 1 514.882 593.3967 cm 0 0 m 0 0 l S Q q 1 0 0 1 514.882 593.3967 cm 0 0 m 0 0 l S Q q 1 0 0 1 514.882 593.3967 cm 0 0 m 0 0 l S Q q 1 0 0 1 514.882 593.3967 cm 0 0 m 0 0 l S Q q 1 0 0 1 514.882 593.3967 cm 0 0 m 0 0 l 0 -0.44 l S Q q 1 0 0 1 514.882 592.9563 cm 0 0 m 0 0 l S Q q 1 0 0 1 514.882 592.9563 cm 0 0 m 0 0 l S Q q 1 0 0 1 514.882 592.9563 cm 0 0 m 0 0 l S Q q 1 0 0 1 514.882 592.9563 cm 0 0 m 0 0 l S Q q 1 0 0 1 514.882 592.9563 cm 0 0 m 0 0 l 0 -0.44 l S Q q 1 0 0 1 514.882 592.5159 cm 0 0 m 0 0 l S Q q 1 0 0 1 514.882 592.5159 cm 0 0 m 0 0 l S Q q 1 0 0 1 514.882 592.5159 cm 0 0 m 0 0 l S Q q 1 0 0 1 514.882 592.5159 cm 0 0 m 0 0 l 0 -0.439 l S Q q 1 0 0 1 514.882 592.0764 cm 0 0 m 0 0 l S Q q 1 0 0 1 514.882 592.0764 cm 0 0 m 0 0 l S Q q 1 0 0 1 514.882 592.0764 cm 0 0 m 0 0 l 0.441 0 l S Q q 1 0 0 1 515.3229 592.0764 cm 0 0 m 0 0 l S Q q 1 0 0 1 515.3229 592.0764 cm 0 0 m 0 0 l 0 -0.44 l S Q q 1 0 0 1 515.3229 591.636 cm 0 0 m 0 0 l S Q q 1 0 0 1 515.3229 591.636 cm 0 0 m 0 0 l S Q q 1 0 0 1 515.3229 591.636 cm 0 0 m 0 0 l S Q q 1 0 0 1 515.3229 591.636 cm 0 0 m 0 0 l S Q q 1 0 0 1 515.3229 591.636 cm 0 0 m 0 0 l 0 -0.441 l S Q q 1 0 0 1 515.3229 591.1946 cm 0 0 m 0 0 l S Q q 1 0 0 1 515.3229 591.1946 cm 0 0 m 0 0 l S Q q 1 0 0 1 515.3229 591.1946 cm 0 0 m 0 0 l S Q q 1 0 0 1 515.3229 591.1946 cm 0 0 m 0 0 l S Q q 1 0 0 1 515.3229 591.1946 cm 0 0 m 0 0 l 0 -0.44 l S Q q 1 0 0 1 515.3229 590.7541 cm 0 0 m 0 0 l S Q q 1 0 0 1 515.3229 590.7541 cm 0 0 m 0 0 l S Q q 1 0 0 1 515.3229 590.7541 cm 0 0 m 0 0 l S Q q 1 0 0 1 515.3229 590.7541 cm 0 0 m 0 0 l S Q q 1 0 0 1 515.3229 590.7541 cm 0 0 m 0 0 l 0 -0.439 l S Q q 1 0 0 1 515.3229 590.3147 cm 0 0 m 0 0 l 0.44 0 l S Q q 1 0 0 1 515.7628 590.3147 cm 0 0 m 0 0 l S Q q 1 0 0 1 515.7628 590.3147 cm 0 0 m 0 0 l S Q q 1 0 0 1 515.7628 590.3147 cm 0 0 m 0 0 l S Q q 1 0 0 1 515.7628 590.3147 cm 0 0 m 0 0 l 0 -0.44 l S Q q 1 0 0 1 515.7628 589.8743 cm 0 0 m 0 0 l S Q q 1 0 0 1 515.7628 589.8743 cm 0 0 m 0 0 l S Q q 1 0 0 1 515.7628 589.8743 cm 0 0 m 0 0 l S Q q 1 0 0 1 515.7628 589.8743 cm 0 0 m 0 0 l S Q q 1 0 0 1 515.7628 589.8743 cm 0 0 m 0 0 l 0 -0.441 l S Q q 1 0 0 1 515.7628 589.4333 cm 0 0 m 0 0 l S Q q 1 0 0 1 515.7628 589.4333 cm 0 0 m 0 0 l S Q q 1 0 0 1 515.7628 589.4333 cm 0 0 m 0 0 l S Q q 1 0 0 1 515.7628 589.4333 cm 0 0 m 0 0 l S Q q 1 0 0 1 515.7628 589.4333 cm 0 0 m 0 0 l S Q q 1 0 0 1 515.7628 589.4333 cm 0 0 m 0 0 l 0 -0.44 l S Q q 1 0 0 1 515.7628 588.9934 cm 0 0 m 0 0 l S Q q 1 0 0 1 515.7628 588.9934 cm 0 0 m 0 0 l S Q q 1 0 0 1 515.7628 588.9934 cm 0 0 m 0 0 l 0.44 0 l S Q q 1 0 0 1 516.2031 588.9934 cm 0 0 m 0 0 l S Q q 1 0 0 1 516.2031 588.9934 cm 0 0 m 0 0 l 0 -0.44 l S Q q 1 0 0 1 516.2031 588.553 cm 0 0 m 0 0 l S Q q 1 0 0 1 516.2031 588.553 cm 0 0 m 0 0 l S Q q 1 0 0 1 516.2031 588.553 cm 0 0 m 0 0 l S Q q 1 0 0 1 516.2031 588.553 cm 0 0 m 0 0 l S Q q 1 0 0 1 516.2031 588.553 cm 0 0 m 0 0 l S Q q 1 0 0 1 516.2031 588.553 cm 0 0 m 0 0 l 0 -0.44 l S Q q 1 0 0 1 516.2031 588.1125 cm 0 0 m 0 0 l S Q q 1 0 0 1 516.2031 588.1125 cm 0 0 m 0 0 l S Q q 1 0 0 1 516.2031 588.1125 cm 0 0 m 0 0 l S Q q 1 0 0 1 516.2031 588.1125 cm 0 0 m 0 0 l S Q q 1 0 0 1 516.2031 588.1125 cm 0 0 m 0 0 l 0 -0.441 l S Q q 1 0 0 1 516.2031 587.6716 cm 0 0 m 0 0 l S Q q 1 0 0 1 516.2031 587.6716 cm 0 0 m 0 0 l S Q q 1 0 0 1 516.2031 587.6716 cm 0 0 m 0 0 l S Q q 1 0 0 1 516.2031 587.6716 cm 0 0 m 0 0 l S Q q 1 0 0 1 516.2031 587.6716 cm 0 0 m 0 0 l S Q q 1 0 0 1 516.2031 587.6716 cm 0 0 m 0 0 l 0.439 -0.439 l S Q q 1 0 0 1 516.6426 587.2322 cm 0 0 m 0 0 l S Q q 1 0 0 1 516.6426 587.2322 cm 0 0 m 0 0 l S Q q 1 0 0 1 516.6426 587.2322 cm 0 0 m 0 0 l S Q q 1 0 0 1 516.6426 587.2322 cm 0 0 m 0 0 l S Q q 1 0 0 1 516.6426 587.2322 cm 0 0 m 0 0 l S Q q 1 0 0 1 516.6426 587.2322 cm 0 0 m 0 0 l 0 -0.44 l S Q q 1 0 0 1 516.6426 586.7917 cm 0 0 m 0 0 l S Q q 1 0 0 1 516.6426 586.7917 cm 0 0 m 0 0 l S Q q 1 0 0 1 516.6426 586.7917 cm 0 0 m 0 0 l S Q q 1 0 0 1 516.6426 586.7917 cm 0 0 m 0 0 l S Q q 1 0 0 1 516.6426 586.7917 cm 0 0 m 0 0 l S Q q 1 0 0 1 516.6426 586.7917 cm 0 0 m 0 0 l 0 -0.441 l S Q q 1 0 0 1 516.6426 586.3508 cm 0 0 m 0 0 l S Q q 1 0 0 1 516.6426 586.3508 cm 0 0 m 0 0 l S Q q 1 0 0 1 516.6426 586.3508 cm 0 0 m 0 0 l S Q q 1 0 0 1 516.6426 586.3508 cm 0 0 m 0 0 l S Q q 1 0 0 1 516.6426 586.3508 cm 0 0 m 0 0 l S Q q 1 0 0 1 516.6426 586.3508 cm 0 0 m 0 0 l 0.44 -0.441 l S Q q 1 0 0 1 517.0825 585.9099 cm 0 0 m 0 0 l S Q q 1 0 0 1 517.0825 585.9099 cm 0 0 m 0 0 l S Q q 1 0 0 1 517.0825 585.9099 cm 0 0 m 0 0 l S Q q 1 0 0 1 517.0825 585.9099 cm 0 0 m 0 0 l S Q q 1 0 0 1 517.0825 585.9099 cm 0 0 m 0 0 l S Q q 1 0 0 1 517.0825 585.9099 cm 0 0 m 0 0 l S Q q 1 0 0 1 517.0825 585.9099 cm 0 0 m 0 0 l 0 -0.439 l S Q q 1 0 0 1 517.0825 585.4705 cm 0 0 m 0 0 l S Q q 1 0 0 1 517.0825 585.4705 cm 0 0 m 0 0 l S Q q 1 0 0 1 517.0825 585.4705 cm 0 0 m 0 0 l S Q q 1 0 0 1 517.0825 585.4705 cm 0 0 m 0 0 l S Q q 1 0 0 1 517.0825 585.4705 cm 0 0 m 0 0 l S Q q 1 0 0 1 517.0825 585.4705 cm 0 0 m 0 0 l 0 -0.44 l S Q q 1 0 0 1 517.0825 585.03 cm 0 0 m 0 0 l S Q q 1 0 0 1 517.0825 585.03 cm 0 0 m 0 0 l S Q q 1 0 0 1 517.0825 585.03 cm 0 0 m 0 0 l S Q q 1 0 0 1 517.0825 585.03 cm 0 0 m 0 0 l S Q q 1 0 0 1 517.0825 585.03 cm 0 0 m 0 0 l 0.44 0 l S Q q 1 0 0 1 517.5231 585.03 cm 0 0 m 0 0 l 0 -0.44 l S Q q 1 0 0 1 517.5231 584.5896 cm 0 0 m 0 0 l S Q q 1 0 0 1 517.5231 584.5896 cm 0 0 m 0 0 l S Q q 1 0 0 1 517.5231 584.5896 cm 0 0 m 0 0 l S Q q 1 0 0 1 517.5231 584.5896 cm 0 0 m 0 0 l S Q q 1 0 0 1 517.5231 584.5896 cm 0 0 m 0 0 l S Q q 1 0 0 1 517.5231 584.5896 cm 0 0 m 0 0 l S Q q 1 0 0 1 517.5231 584.5896 cm 0 0 m 0 0 l 0 -0.44 l S Q q 1 0 0 1 517.5231 584.1492 cm 0 0 m 0 0 l S Q q 1 0 0 1 517.5231 584.1492 cm 0 0 m 0 0 l S Q q 1 0 0 1 517.5231 584.1492 cm 0 0 m 0 0 l S Q q 1 0 0 1 517.5231 584.1492 cm 0 0 m 0 0 l S Q q 1 0 0 1 517.5231 584.1492 cm 0 0 m 0 0 l S Q q 1 0 0 1 517.5231 584.1492 cm 0 0 m 0 0 l 0 -0.44 l S Q q 1 0 0 1 517.5231 583.7087 cm 0 0 m 0 0 l S Q q 1 0 0 1 517.5231 583.7087 cm 0 0 m 0 0 l S Q q 1 0 0 1 517.5231 583.7087 cm 0 0 m 0 0 l S Q q 1 0 0 1 517.5231 583.7087 cm 0 0 m 0 0 l 0.44 0 l S Q q 1 0 0 1 517.9634 583.7087 cm 0 0 m 0 0 l S Q q 1 0 0 1 517.9634 583.7087 cm 0 0 m 0 0 l S Q q 1 0 0 1 517.9634 583.7087 cm 0 0 m 0 0 l 0 -0.44 l S Q q 1 0 0 1 517.9634 583.2683 cm 0 0 m 0 0 l S Q q 1 0 0 1 517.9634 583.2683 cm 0 0 m 0 0 l S Q q 1 0 0 1 517.9634 583.2683 cm 0 0 m 0 0 l S Q q 1 0 0 1 517.9634 583.2683 cm 0 0 m 0 0 l S Q q 1 0 0 1 517.9634 583.2683 cm 0 0 m 0 0 l S Q q 1 0 0 1 517.9634 583.2683 cm 0 0 m 0 0 l S Q q 1 0 0 1 517.9634 583.2683 cm 0 0 m 0 0 l S Q q 1 0 0 1 517.9634 583.2683 cm 0 0 m 0 0 l 0 -0.44 l S Q q 1 0 0 1 517.9634 582.8279 cm 0 0 m 0 0 l S Q q 1 0 0 1 517.9634 582.8279 cm 0 0 m 0 0 l S Q q 1 0 0 1 517.9634 582.8279 cm 0 0 m 0 0 l S Q q 1 0 0 1 517.9634 582.8279 cm 0 0 m 0 0 l S Q q 1 0 0 1 517.9634 582.8279 cm 0 0 m 0 0 l S Q q 1 0 0 1 517.9634 582.8279 cm 0 0 m 0 0 l S Q q 1 0 0 1 517.9634 582.8279 cm 0 0 m 0 0 l 0 -0.44 l S Q q 1 0 0 1 517.9634 582.3874 cm 0 0 m 0 0 l 0.439 0 l S Q q 1 0 0 1 518.4025 582.3874 cm 0 0 m 0 0 l S Q q 1 0 0 1 518.4025 582.3874 cm 0 0 m 0 0 l S Q q 1 0 0 1 518.4025 582.3874 cm 0 0 m 0 0 l S Q q 1 0 0 1 518.4025 582.3874 cm 0 0 m 0 0 l S Q q 1 0 0 1 518.4025 582.3874 cm 0 0 m 0 0 l S Q q 1 0 0 1 518.4025 582.3874 cm 0 0 m 0 0 l S Q q 1 0 0 1 518.4025 582.3874 cm 0 0 m 0 0 l 0 -0.44 l S Q q 1 0 0 1 518.4025 581.9475 cm 0 0 m 0 0 l S Q q 1 0 0 1 518.4025 581.9475 cm 0 0 m 0 0 l S Q q 1 0 0 1 518.4025 581.9475 cm 0 0 m 0 0 l S Q q 1 0 0 1 518.4025 581.9475 cm 0 0 m 0 0 l S Q q 1 0 0 1 518.4025 581.9475 cm 0 0 m 0 0 l S Q q 1 0 0 1 518.4025 581.9475 cm 0 0 m 0 0 l S Q q 1 0 0 1 518.4025 581.9475 cm 0 0 m 0 0 l 0 -0.441 l S Q q 1 0 0 1 518.4025 581.5066 cm 0 0 m 0 0 l S Q q 1 0 0 1 518.4025 581.5066 cm 0 0 m 0 0 l S Q q 1 0 0 1 518.4025 581.5066 cm 0 0 m 0 0 l S Q q 1 0 0 1 518.4025 581.5066 cm 0 0 m 0 0 l 0.441 0 l S Q q 1 0 0 1 518.8434 581.5066 cm 0 0 m 0 0 l S Q q 1 0 0 1 518.8434 581.5066 cm 0 0 m 0 0 l S Q q 1 0 0 1 518.8434 581.5066 cm 0 0 m 0 0 l S Q q 1 0 0 1 518.8434 581.5066 cm 0 0 m 0 0 l 0 -0.44 l S Q q 1 0 0 1 518.8434 581.0662 cm 0 0 m 0 0 l S Q q 1 0 0 1 518.8434 581.0662 cm 0 0 m 0 0 l S Q q 1 0 0 1 518.8434 581.0662 cm 0 0 m 0 0 l S Q q 1 0 0 1 518.8434 581.0662 cm 0 0 m 0 0 l S Q q 1 0 0 1 518.8434 581.0662 cm 0 0 m 0 0 l S Q q 1 0 0 1 518.8434 581.0662 cm 0 0 m 0 0 l S Q q 1 0 0 1 518.8434 581.0662 cm 0 0 m 0 0 l 0 -0.439 l S Q q 1 0 0 1 518.8434 580.6267 cm 0 0 m 0 0 l S Q q 1 0 0 1 518.8434 580.6267 cm 0 0 m 0 0 l S Q q 1 0 0 1 518.8434 580.6267 cm 0 0 m 0 0 l S Q q 1 0 0 1 518.8434 580.6267 cm 0 0 m 0 0 l S Q q 1 0 0 1 518.8434 580.6267 cm 0 0 m 0 0 l S Q q 1 0 0 1 518.8434 580.6267 cm 0 0 m 0 0 l S Q q 1 0 0 1 518.8434 580.6267 cm 0 0 m 0 0 l 0.44 0 l S Q q 1 0 0 1 519.2838 580.6267 cm 0 0 m 0 0 l S Q q 1 0 0 1 519.2838 580.6267 cm 0 0 m 0 0 l 0 -0.441 l S Q q 1 0 0 1 519.2838 580.1858 cm 0 0 m 0 0 l S Q q 1 0 0 1 519.2838 580.1858 cm 0 0 m 0 0 l S Q q 1 0 0 1 519.2838 580.1858 cm 0 0 m 0 0 l S Q q 1 0 0 1 519.2838 580.1858 cm 0 0 m 0 0 l S Q q 1 0 0 1 519.2838 580.1858 cm 0 0 m 0 0 l S Q q 1 0 0 1 519.2838 580.1858 cm 0 0 m 0 0 l S Q q 1 0 0 1 519.2838 580.1858 cm 0 0 m 0 0 l S Q q 1 0 0 1 519.2838 580.1858 cm 0 0 m 0 0 l S Q q 1 0 0 1 519.2838 580.1858 cm 0 0 m 0 0 l 0 -0.44 l S Q q 1 0 0 1 519.2838 579.7454 cm 0 0 m 0 0 l S Q q 1 0 0 1 519.2838 579.7454 cm 0 0 m 0 0 l S Q q 1 0 0 1 519.2838 579.7454 cm 0 0 m 0 0 l S Q q 1 0 0 1 519.2838 579.7454 cm 0 0 m 0 0 l S Q q 1 0 0 1 519.2838 579.7454 cm 0 0 m 0 0 l S Q q 1 0 0 1 519.2838 579.7454 cm 0 0 m 0 0 l S Q q 1 0 0 1 519.2838 579.7454 cm 0 0 m 0 0 l 0.44 0 l S Q q 1 0 0 1 519.7236 579.7454 cm 0 0 m 0 0 l 0 -0.44 l S Q q 1 0 0 1 519.7236 579.3049 cm 0 0 m 0 0 l S Q q 1 0 0 1 519.7236 579.3049 cm 0 0 m 0 0 l S Q q 1 0 0 1 519.7236 579.3049 cm 0 0 m 0 0 l S Q q 1 0 0 1 519.7236 579.3049 cm 0 0 m 0 0 l S Q q 1 0 0 1 519.7236 579.3049 cm 0 0 m 0 0 l S Q q 1 0 0 1 519.7236 579.3049 cm 0 0 m 0 0 l S Q q 1 0 0 1 519.7236 579.3049 cm 0 0 m 0 0 l S Q q 1 0 0 1 519.7236 579.3049 cm 0 0 m 0 0 l S Q q 1 0 0 1 519.7236 579.3049 cm 0 0 m 0 0 l 0 -0.44 l S Q q 1 0 0 1 519.7236 578.8645 cm 0 0 m 0 0 l S Q q 1 0 0 1 519.7236 578.8645 cm 0 0 m 0 0 l S Q q 1 0 0 1 519.7236 578.8645 cm 0 0 m 0 0 l S Q q 1 0 0 1 519.7236 578.8645 cm 0 0 m 0 0 l S Q q 1 0 0 1 519.7236 578.8645 cm 0 0 m 0 0 l S Q q 1 0 0 1 519.7236 578.8645 cm 0 0 m 0 0 l S Q q 1 0 0 1 519.7236 578.8645 cm 0 0 m 0 0 l S Q q 1 0 0 1 519.7236 578.8645 cm 0 0 m 0 0 l S Q q 1 0 0 1 519.7236 578.8645 cm 0 0 m 0 0 l S Q BT 0 0 0 1 k /T1_5 1 Tf 7 0 0 7 312.881 760.2454 Tm (0.10)Tj ET Q BT 0 0 0 1 k /T1_5 1 Tf 7 0 0 7 312.881 715.6904 Tm (0.08)Tj 0 -6.365 TD (0.06)Tj T* (0.04)Tj T* (0.02)Tj T* (0.00)Tj 0 22.277 TD (0.07)Tj 0 -6.365 TD (0.05)Tj T* (0.03)Tj T* (0.01)Tj 0 25.459 TD (0.09)Tj ET q 300.542 517.247 235.136 248.816 re W n BT /T1_5 1 Tf 0 7 -7 0 306.3589 579.2278 Tm (Axial depth of regenerative chatter vibration)Tj ( \(mm\))Tj ET Q BT /T1_5 1 Tf 7 0 0 7 332.8008 692.2444 Tm (Condition )Tj 0.723 -1 Td (before )Tj -1.265 -1 Td (improvement)Tj 7.364 2 Td (Condition )Tj 1.085 -1 Td (after )Tj -1.626 -1 Td (improvement)Tj -4.67 -4.905 Td (Range )Tj -1.097 -1 Td (with chatter )Tj 0.499 -1 Td (vibrations)Tj -2.098 -14.016 Td (0)Tj 6.634 0 Td (10)Tj 6.884 0 Td (20)Tj 6.884 0 Td (30)Tj 6.884 0 Td (40)Tj /C0_0 1 Tf 0.873 1.083 Td <0073>Tj /T1_5 1 Tf 0.549 0.049 Td (10)Tj ET q 300.542 517.247 235.136 248.816 re W n BT /T1_5 1 Tf 5 0 0 5 533.1787 542.3801 Tm (3)Tj 7 0 0 7 391.6548 518.7595 Tm (Spindle speed)Tj ( \(min)Tj ET Q BT /C0_0 1 Tf 5 0 0 5 447.4581 521.1765 Tm <000D>Tj /T1_5 1 Tf 0.549 0.049 Td (1)Tj ET q 300.542 517.247 235.136 248.816 re W n BT /T1_5 1 Tf 7 0 0 7 452.7031 518.7595 Tm (\))Tj ET Q BT /T1_5 1 Tf 7 0 0 7 467.5501 619.3005 Tm (Range )Tj -1.097 -1 Td (with chatter )Tj 0.499 -1 Td (vibrations)Tj 3.747 -5.672 Td (Range )Tj -0.25 -1 Td (without )Tj 0.167 -1 Td (chatter )Tj -0.515 -1 Td (vibrations)Tj ET q 300.542 517.247 235.136 248.816 re W n 1 w q 1 0 0 1 346.2422 675.3933 cm 0 0 m 0 -13.768 l S Q q 1 0 0 1 346.8569 660.2082 cm 0 0 m 0.3 0.992 0.576 1.637 0.895 2.433 c -2.131 2.433 l -1.996 2.147 -1.536 0.992 -1.236 0 c -0.916 -1.062 -0.696 -2.024 -0.618 -2.649 c -0.54 -2.024 -0.32 -1.062 0 0 c f Q q 1 0 0 1 394.4318 675.3933 cm 0 0 m 0 -13.768 l S Q q 1 0 0 1 395.0464 660.2082 cm 0 0 m 0.3 0.992 0.576 1.637 0.895 2.433 c -2.131 2.433 l -1.996 2.147 -1.536 0.992 -1.236 0 c -0.916 -1.062 -0.696 -2.024 -0.618 -2.649 c -0.54 -2.024 -0.32 -1.062 0 0 c f Q 0.3 w q 1 0 0 1 468.189 643.4919 cm 0 0 m -15.219 -7.124 l S Q q 1 0 0 1 452.0748 635.3552 cm 0 0 m 0.897 0.131 1.511 0.151 2.26 0.193 c 1.137 2.592 l 0.962 2.379 0.216 1.585 -0.458 0.98 c -1.181 0.332 -1.862 -0.199 -2.328 -0.492 c -1.805 -0.323 -0.96 -0.14 0 0 c f Q q 1 0 0 1 476.3423 555.5456 cm 0 0 m -7.83 5.375 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<1B07>Tj ET q 300.542 517.247 235.136 248.816 re W n 2 J q 1 0 0 1 519.7236 539.6706 cm 0 0 m -192.756 0 l S Q 0.3 0 0.1 0 k 352.479 752.212 -14.173 7.086 re f 8 M 0 J q 1 0 0 1 352.4793 752.212 cm 0 0 m -14.173 0 l -14.173 7.086 l 0 7.086 l h S Q Q BT /T1_5 1 Tf 7 0 0 7 333.5923 754.2956 Tm [( )-1451( )-1289(: Suitable cutting condition range)]TJ /C2_1 1 Tf 1.164 Tc -1.164 Tw 6 0 0 6 333.5923 745.613 Tm <00031B05>Tj /T1_5 1 Tf 0 Tc 0 Tw 7 0 0 7 349.0996 745.2956 Tm [( )-774(: Stability lobes of regenerative chatter vibrations)]TJ /C2_1 1 Tf 1.164 Tc -1.164 Tw 6 0 0 6 333.5923 736.613 Tm <00031B06>Tj /T1_5 1 Tf 0 Tc 0 Tw 7 0 0 7 349.0996 736.2956 Tm [( )-774(: Occurrence prediction range of forced chatter vibrations)]TJ /C2_1 1 Tf 1.164 Tc -1.164 Tw 6 0 0 6 333.5923 727.613 Tm <00031B07>Tj /T1_5 1 Tf 0 Tc 0 Tw 7 0 0 7 349.0996 727.2956 Tm [( )-774(: Spindle speed causing abnormal tool wear)]TJ ET EMC BT /GS0 gs /T1_1 1 Tf 8 0 0 8 304.0797 505.5991 Tm [(Fig)15(.)30( 2)]TJ /T1_4 1 Tf 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T)-24.8(h)-23.9(i)-4.3(s p)-6.5(a)-5.3(p)-12.7(e)-11.4(r s)-1.5(h)-1.1(o)17.7(ws t)-17.7(h)-4(e p)-10.8(o)-5.5(s)-7.4(s)2.8(i)-2(b)4.7(i)-12.9(l)-12.9(i)7.7(t)-21.5(i)6.9(e)-9.5(s f)13.4(o)-3.5(r i)-23.5(m)-5.8(p)-4.8(r)-5.3(o)18.2(v)-19.6(i)-23.5(n)-1(g )]TJ 0.011 Tc 0.125 Tw 0 -1.158 TD [(m)-14.8(a)-11.3(c)2.6(h)-23.8(i)-23.4(n)-23.7(i)-23.4(n)-0.8(g e)9.3(f)-21.5(f)-44.4(i)7.1(c)-3.2(i)7.1(e)-11.3(n)-1(c)-2.2(y u)-17.2(s)3(i)-23.4(n)-0.9(g m)-14.8(a)-11.3(c)2.6(h)-23.8(i)-23.4(n)-23.7(i)-23.4(n)-0.8(g s)2.9(i)-23.4(m)3.4(u)-20.1(l)-3.2(a)-2.8(t)-21.4(i)10(o)-3.4(n t)-17.5(h)-14.3(a)-2.7(t e)-11.3(m)-5.7(p)11.1(l)10(o)17(y)0.5(s t)-17.6(h)-3.8(e f)-44.4(i)-23.3(n)-23.8(i)7.8(t)-15.1(e e)9.6(l)7.2(e)-11.4(m)-1.4(e)-11.4(n)2.7(t m)-1.4(e)-5.1(t)-17.5(h)-1(o)-9.5(d)-21.9(, t)-17.6(h)-3.8(e p)-4.7(r)-9.1(e)-9.9(d)-22.5(i)7.2(c)-9.1(t)-21.4(i)10(o)-3.3(n o)18.4(f)11( )]TJ 0 Tc 0.071 Tw 0 -1.158 TD [(c)2.4(h)-14.4(a)-2.9(t)-30.7(t)-15.3(e)-11.4(r v)-19.6(i)-2(b)-5.8(r)-17.3(a)-2.8(t)-21.6(i)9.9(o)-3.5(n i)-23.5(n )0.5(m)-14.9(a)-11.5(c)2.4(h)-23.9(i)-23.5(n)-23.9(i)-23.5(n)-1(g )0.5(t)-17.7(h)-34.5(r)-5.3(o)1.4(u)-8.7(g)-21.6(h )0.5(v)-19.6(i)-2(b)-5.8(r)-17.3(a)-2.9(t)-21.6(i)9.9(o)-3.5(n )0.5(a)-22.6(n)-14.4(a)-12(l)6.7(ys)2.8(i)-4.3(s )0.5(a)-22.6(n)-1.1(d )0.5(t)-17.7(h)-4(e )0.5(o)-2.9(p)-1.1(t)-21.6(i)-23.5(m)-24.4(i)-20.6(z)-13.5(a)-2.9(t)-21.6(i)9.9(o)-3.5(n )0.5(o)18.2(f )0.5(N)8.4(C )0.5(p)-4.8(r)-5.3(o)5.7(g)-31.2(r)-17.3(a)-22.6(m)-15.8(s )0.5(t)-17.7(h)-34.5(r)-5.3(o)1.4(u)-8.7(g)-21.6(h )0.5(c)-3.9(u)-2.5(t)-30.7(t)-21.6(i)-23.5(n)-1(g )]TJ 0 Tw 0 -1.158 TD [(f)13.4(o)-3.5(r)-7.2(c)-9.1(e)-9.5(s a)-22.6(n)-14.4(a)-12(l)6.7(ys)2.8(i)-4.3(s)-0.9(.)]TJ /T1_0 1 Tf -0.007 Tc 0.686 Tw 12 0 0 12 59.5276 412.2018 Tm [(1)18.1(.)]TJ /Span<>> BDC 0.725 0 Td ( )Tj EMC [(I)-13.9(n)10.6(t)-21.4(ro)-6.5(d)8.6(u)5.3(c)-10.4(t)-27.4(io)7.8(n)]TJ /T1_1 1 Tf 0.008 Tc 0.125 Tw 9.8 0 0 10 59.5276 394.1008 Tm [(Rec)0.5(ent mark)10.4(et de)0.5(mands for )0.5(e)25.3(v)15.5(er higher qu)0.5(ality products)0.5(,)8( )]TJ 0 Tc 0.036 Tw 0 -1.21 TD [(shor)-20(ter lead-time, and )0.5(slashed costs ha)35(v)15(e )0.5(led to )0.5(the demand )]TJ 0.036 Tc 0.125 Tw T* [(for e)25.3(v)15.4(er higher precision and ef)25.3(f)-59.6(icienc)15.4(y in machining)35.9( )]TJ 0.008 Tc T* [(i)0.5(n)0.6(d)0.5(u)0.6(s)0.5(t)0.6(r)0.5(i)0.6(e)0.5(s)0.6(.)0.5( )90.6(Y)160.5(e)0.6(t)0.5( )0.5(e)25.6(v)15.6(e)0.5(n)0.6( )0.5(t)0.5(o)0.6(d)0.5(a)35.6(y)85.5(,)0.6( )0.5(i)0.5(m)0.6(p)0.5(r)0.6(o)45.5(v)15.6(e)0.5(m)0.6(e)0.5(n)0.6(t)0.5(s)0.6( )0.5(i)0.6(n)0.5( )0.5(m)0.6(a)0.5(c)0.6(h)0.5(i)0.6(n)0.5(i)0.6(n)0.5(g)0.6( )0.5(i)0.6(n)7.9( )]TJ 0 Tc 0.05 Tw T* [(actual w)40(ork sites continue to rel)25(y upon past e)15.1(xperience and )]TJ 0.125 Tw T* [(trial and er)-30.4(ror)54.7(. Ho)39.6(w)34.7(e)24.6(v)14.7(er)39.7(, this e)14.7(xperimental approach f)-10.3(aces )]TJ 0.099 Tw T* [(limitations in ter)-20(ms of both time and the cost of repeating )]TJ 0.015 Tc 0.125 Tw T* [(tests and trial productions. )50.3(This is par)-19.6(ticularl)25.3(y tr)-19.6(ue with)14.9( )]TJ 0.013 Tc T* [(the sor)-19.7(t of products our compan)25.3(y handles, such as lar)18.2(ge)13( )]TJ 0.014 Tc T* [(str)-20(uctures and jet engine components that use e)15.1(xpensi)25.1(v)15(e)14( )]TJ 0 Tc 0.054 Tw T* [(and dif)25(f)-60(icult-to-cut materials, including titanium allo)45(ys and )]TJ 0 Tw 0 -1.21 TD [(nick)10(el base allo)45(ys.)]TJ 0.038 Tc 0.125 Tw 0.578 -1.21 Td [(Meanw)19.9(hile, simulation is being increasingl)24.8(y applied)38( )]TJ 0.027 Tc -0.578 -1.21 Td [(t)0.5(o )0.5(m)0.5(ac)0.5(h)0.5(in)0.5(i)0.5(ng)0.5(,)0.5( a)0.5(n)0.5(d)0.5( t)0.5(h)0.5(is)0.5( i)0.5(s)0.5( e)0.5(n)0.5(c)0.5(ou)0.5(r)0.5(a)0.5(ge)0.5(d)0.5( b)25.5(y)0.5( a)0.5(d)0.5(v)25.4(a)0.5(n)0.5(c)0.5(em)0.5(e)0.5(n)0.5(ts)27( )]TJ 0.06 Tc T* [(i)0.5(n )0.5(n)0.5(u)0.5(me)0.5(r)0.5(ic)0.5(a)0.5(l)0.5( a)0.5(n)0.5(a)0.5(l)25.5(ys)0.5(i)0.5(s,)0.5( )0.5(w)20.5(hi)0.5(c)0.5(h )0.5(h)0.5(a)35.5(v)15.4(e)0.5( )0.5(m)0.5(ad)0.5(e)0.5( )0.5(it)0.5( )0.5(po)0.5(s)0.5(s)0.5(ib)20.5(l)0.5(e)60( )]TJ 0.088 Tc 0 -1.21 TD [(to predict phenomena in)40.4(v)20.3(olv)15.3(ed in the machining)88( )]TJ 0.027 Tc 0 -1.21 TD [(process. )30.1(W)100.2(e ha)35.2(v)15.1(e been stri)25.1(ving for the de)25.2(v)15.1(elopment of)27( )]TJ 0 Tc 0.084 Tw T* [(optimization technolo)25(gy for deri)25(ving machining conditions )]TJ 0.055 Tc 0.125 Tw 0 -1.21 TD [(b)25.5(y)0.5( c)0.5(o)0.5(m)0.5(bi)0.5(n)0.5(i)0.5(ng)0.5( )0.5(o)0.5(ur)0.5( )0.5(o)0.5(r)0.5(ig)0.5(i)0.5(n)0.5(al)0.5( )0.5(m)0.5(a)0.5(c)0.5(hi)0.5(n)0.5(i)0.5(ng)0.5( )0.5(s)0.5(im)0.5(u)0.5(l)0.5(a)0.5(to)0.5(r)0.5( )0.5(a)0.5(nd)55( )]TJ 0.032 Tc 0 -1.21 TD [(c)0.5(o)0.6(m)0.5(m)0.6(e)0.5(r)0.6(c)0.5(i)0.5(a)0.6(l)0.5(l)25.6(y)0.5( )0.5(a)35.6(v)25.5(a)0.6(i)0.5(l)0.5(a)0.6(b)20.5(l)0.6(e)0.5( )0.6(g)0.5(e)0.5(n)0.6(e)0.5(r)0.6(a)0.5(l)0.6(-)0.5(p)0.5(u)0.6(r)-29.5(p)0.6(o)0.5(s)0.5(e)0.6( )0.5(s)0.6(o)0.5(f)0.6(t)0.5(w)25.5(a)0.6(r)0.5(e)0.6(.)0.5( )50.5(T)0.6(h)0.5(i)0.6(s)32( )]TJ 0 Tc 0 Tw T* [(paper pro)45(vides case e)15.1(xamples of our initiati)25(v)15(es.)]TJ /T1_0 1 Tf 12 0 0 12 59.5276 133.8765 Tm [(2)-12.4(.)]TJ /Span<>> BDC ( )Tj EMC 1.654 0 Td [(M)1.1(a)10.7(c)15.6(h)-13.4(i)-10.4(n)-13.4(i)-10.4(n)4.1(g s)2.9(i)-10.4(m)18.8(u)-13.4(la)13.6(t)-20.4(i)6.9(o)14.7(n te)-4.9(c)15.6(h)-4.9(n)12.3(o)8.8(l)6.8(o)3.1(g)-22.4(y)]TJ 10 0 0 10 59.5276 115.7754 Tm [(2)-19.9(.)19.7(1)]TJ /Span<>> BDC ( )Tj EMC 2.551 0 Td [(F)-18(EM)-10.7(-)-11(b)3.3(a)-9.8(s)-6.4(e)-10.1(d c)4.8(u)3.8(t)-29.1(t)-27.6(i)-18(n)-4(g s)-5.1(i)-18(m)10.2(u)-20.9(l)-7.8(a)5.2(t)-27.6(i)-1.4(o)6.4(n)]TJ /T1_1 1 Tf 0.014 Tc 0.125 Tw 9.8 0 0 10 59.5276 103.6743 Tm [(Cutting simulation emplo)45(ying the f)-60(inite element method)14( )]TJ 0 Tc 0.02 Tw T* [(\(FEM\) can help to deri)25(v)15(e the inter)-20(nal stress of the materials )]TJ 0.027 Tc 0.125 Tw T* [(and edge tools, as w)34.9(ell as the temperature of the edge)27( )]TJ 0.01 Tc 26.611 33.883 Td [(of cutting tools that are hard to measure in e)14.9(xperiments.)10( )]TJ 0.056 Tc 0 -1.21 TD [(Thus, simulation promises g)-20.2(reater understanding of)56( )]TJ 0.004 Tc 0 -1.21 TD [(cutting phenomena and ef)24.9(fecti)25(v)14.9(e impro)44.9(v)14.9(ements of cutting)4( )]TJ 0.005 Tc 0 -1.21 TD [(technique. )55.2(Accordingl)25.3(y)85.2(, w)35.3(e ha)35.2(v)15.3(e introduced )55.3(Adv)25.2(antEdge)]TJ 0 Tc 0 Tw 6.37 0 0 6.5 550.7494 385.4997 Tm (\256)Tj 9.8 0 0 10 555.5905 381.9997 Tm ( )Tj 0.041 Tc 0.125 Tw -24.008 -1.21 Td [(in our compan)25.1(y)85(. Obtaining the ph)30(ysical proper)-20(ties of)41( )]TJ 0.021 Tc T* [(materials to be used for the simulation is dif)24.9(f)-60.1(icult. But)21( )]TJ 0.013 Tc T* [(this softw)24.9(are has def)-10.2(ault data \(i.e., pre-installed data\) in)13( )]TJ 0.018 Tc T* [(its database, w)19.7(hich allo)39.6(ws for simulation with o)44.6(v)14.7(er 100)18( )]TJ 0.029 Tc T* [(kinds of materials. Ho)39.6(w)34.6(e)24.6(v)14.5(er)39.6(, in man)24.5(y cases, suf)24.6(f)-60.4(icient)29( )]TJ 0 Tc 0.122 Tw T* [(precision cannot be ensured from the def)-9.9(ault data. Higher )]TJ 0.045 Tw T* [(precision simulations are pursued b)25(y obtaining the ph)30(ysical )]TJ 0.086 Tw T* [(proper)-20(ties )0.5(of )0.5(materials )0.5(from the )0.6(results )0.5(of )0.5(v)25(arious )0.5(material )]TJ 0 Tw T* [(tests stored in our compan)25(y)85(. )50(This adds to our kno)39.9(w-ho)40(w)90(.)]TJ /T1_0 1 Tf 0.016 Tc 0.125 Tw 10 0 0 10 325.9842 260.9886 Tm [(F)0.6(i)0.5(g)0.6(u)0.5(r)30.6(e)]TJ /Span<>> BDC 2.896 0 Td ( )Tj EMC 0.39 0 Td (1)Tj /T1_1 1 Tf 9.8 0 0 10 364.0005 260.9886 Tm [( )0.6(s)0.5(h)0.6(o)40.5(w)0.6(s)0.5( )0.6(a)0.5(n)0.6( )0.5(e)15.6(x)0.5(a)0.6(m)0.6(p)0.5(l)0.6(e)0.5( )0.6(o)0.5(f)0.6( )0.5(c)0.6(o)0.6(m)0.5(p)0.5(a)0.6(r)0.6(i)0.5(s)0.6(o)0.5(n)0.6(s)0.5( )0.6(o)0.5(f)0.6( )0.5(c)0.6(u)0.6(t)0.5(t)0.6(i)0.5(n)0.6(g)16( )]TJ 0.039 Tc -4.458 -1.21 Td [(f)0.5(or)0.5(c)0.5(e)0.5( )0.5(e)0.5(r)-29.6(r)0.5(o)0.5(r)0.5(s)0.5( b)0.5(e)0.5(t)0.5(w)35.4(e)0.5(e)0.5(n)0.5( )0.5(th)0.5(e)0.5( )0.5(re)0.5(s)0.5(u)0.5(l)0.5(ts)0.5( )0.5(fr)0.5(o)0.5(m)0.5( )0.5(e)15.4(x)0.5(p)0.5(e)0.5(ri)0.5(m)0.5(e)0.5(n)0.5(t )0.5(a)0.5(n)0.5(d)39( )]TJ 0.014 Tc 0 -1.205 TD [(anal)24.8(ysis perfor)-20.1(med with the f)-10.1(acemill \()]TJ /T1_2 1 Tf 0 Tc 0 Tw (f)Tj /T1_1 1 Tf 0.014 Tc 0.125 Tw /Span<>> BDC 16.949 0 Td ( )Tj EMC 0.139 0 Td (32)Tj /Span<>> BDC ( )Tj EMC [(mm, 2-fluted)14( )]TJ 0.047 Tc -17.088 -1.216 Td [(tool\) for SCM440H. )55.4(Anal)25.4(ysis results w)35.4(ere compared)47( )]TJ 0.039 Tc 0 -1.21 TD [(betw)35.1(een cases w)20.1(hen the def)-9.9(ault data of )55.1(Adv)25(antEdge)]TJ 0 Tc 0 Tw 6.37 0 0 6.5 550.7494 216.0842 Tm (\256)Tj 9.8 0 0 10 555.5905 212.5842 Tm ( )Tj 0.005 Tc 0.125 Tw -24.008 -1.21 Td [(w)25.4(as)0.5( used)0.5( and w)20.5(hen th)0.5(e obta)0.5(ined p)0.5(h)30.4(ysic)0.5(al pro)0.5(per)-19.6(ty )0.5(of the)5.1( )]TJ 0 Tc 0.054 Tw T* [(material w)25(as used. In this e)15(xample, w)20(hen the obtained data )]TJ 0.018 Tc 0.125 Tw T* [(w)25.5(as)0.5( u)0.5(se)0.5(d)60.4(,)0.5( w)35.5(e)0.5( w)35.5(er)0.5(e)0.5( a)0.5(b)20.4(l)0.5(e )0.5(to)0.5( k)10.5(ee)0.5(p)0.5( t)0.5(he)0.5( c)0.5(ut)0.5(ti)0.5(ng)0.5( f)0.5(or)0.5(c)0.5(e )0.5(e)0.5(r)-29.6(r)0.5(or)0.5(s)18( )]TJ 0.012 Tc T* [(betw)35.1(een the results from e)15.1(xperiments and anal)25.1(ysis to no)12( )]TJ 0 Tc 0.07 Tw T* (more than 20)Tj /T1_3 1 Tf 0 Tw (%)Tj /T1_1 1 Tf 0.07 Tw [( in the X, )89.9(Y)129.1(, and Z directions as the cutting )]TJ 0 Tw T* [(w)25(as perfor)-20(med.)]TJ /T1_0 1 Tf 10 0 0 10 320.3149 127.8765 Tm [(2)-19.9(.)-21.1(2)]TJ /Span<>> BDC ( )Tj EMC 2.551 0 Td [(S)-4(i)-18(m)10.2(u)-20.9(l)-7.8(a)5.2(t)-27.6(i)-1.4(o)6.4(n f)11.8(o)6.4(r p)6.2(r)-1.5(e)-10.2(d)-23.3(i)-1.4(c)-11.2(t)-27.6(i)-1.4(o)6.4(n o)9.7(f c)4.8(u)3.8(t)-29.1(t)-27.6(i)-18(n)-4(g f)11.8(o)6.4(r)-1.5(c)-4.9(e)-12.7(s)]TJ /T1_1 1 Tf 0.087 Tc 0.125 Tw 9.8 0 0 10 320.3149 115.7754 Tm [(FEM-based simulations can onl)25.2(y anal)25.1(yze cutting)87.1( )]TJ 0.007 Tc T* [(phenomena o)45.3(v)15.3(er e)15.3(xtremel)25.3(y shor)-19.7(t periods of time because)7( )]TJ 0 Tc T* [(of the shor)-20.1(tness of its allo)39.9(w)25(ab)19.9(le anal)24.9(ysis time. 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