MEC-3-59 NC High frequency variation speed control of spindle motor for self-excited chattering vibration suppression in NC Machine tools. Teruaki Ishibashi, Hiroshi Fujimoto (The University of Tokyo) Shinji Ishii, Kouji Yamamoto, Yuki Terada (MORI SEIKI Co. Ltd.) Abstract This paper proposes a spindle motor control for self-excited chatter vibration suppression in numerical control (NC) machine tools. In conventional NC machine tools, spindle speed is set to constant value during machining, and the spindle speed is determined according to analysis or operator s experience. The proposed method prevents self-excited chatter vibration by varying spindle speed with high frequency during machining. This method suppresses the disturbance deriving from cutting resistance by repetitive control, and archive spindle speed variation with high frequency by perfect tracking cotrol. Finally, we show the advantages of the proposed method by simulations and experiments. NC (NC machine tools, end milling, cutting-off processing, spindle speed control, self-exited chatter vibration, perfect tracking control, repetitive control. ). (NC) () (2) (3) (4)(8) (9) (0)(2) 2 Fig.. Experimental Fig. 2. Schematic diagram of plant. equipment. Table. Parameters of spindle. Driver GPA40L(WAKOGIKEN) Inertia J 6.8 0 3 kg m 2 Friction coefficient D 7.8 0 3 Nm s Torque coefficient K t 0.47 Nm/A (3) (4) (5) /6
3 Fig. 3. Block diagram of plant. Fig. 5. 5 Block diagram of self-exited chatter vibration. a [m] v s [m/s] h 0 [m] 4 h 0 = v s ( 2π ) (4) 2. 4 Fig. 4. Cutting off processing. 2 3 i [A] K t [Nm/A] T [Nm] T = K ti () F cut [Nm] J [kg m 2 ] D [Nm s] [rad/s] = Js + D (T F cut) (2) 3. 3 (3) G() F () Y () 3 Y () = G()F () (3) 32 4 (2) F n [N] y(t)[m] τ [s] y(t τ) 4 h [m] 5 h = y(t τ) y(t) (5) h [m] h 0 h F n K f [Pa] a 6 F n = ak f h (6) F n y G(j) 2 5 M [Ns 2 /m], D [Ns/m], K [N/m] h(s) = h 0 + ( e sτ )ak f G (7) c 8 + ( e j cτ )a lim K f (Φ + jh) = 0 (8) a lim Φ, H G 0 9, 0 + a lim K f [Φ( cos c τ) Hsin c τ] = 0 (9) Φsin c τ + H( cos c τ) = 0 (0) 9, 0 a lim a lim = () 2K f Φ( c ) 2/6
0 2 7 RVF[ ] Fig. 6. 0 0 0 0 2 0 3 6 Reference of spindle speed. Displacement of tool [µm] 2.5.5 0.5 0 0 2 0 0 RVA[ ] RVA, RVF (N 0 = 262 rad/s) Fig. 7. Dependence of RVA, RVF (N 0 = 262 rad/s). 4. 32 (2) 4 2 6 T [s] N 0 [rad/s] T N A [rad/s] RVA, RVF 2, 3 RVA = N A (2) N 0 RVF = 2π N 0 T (3) Table 2. 2 Parameters of chatter vibration. Feed rate v s Width of cut a 2 0 3 m/s 5 0 3 m Specific cutting force K t 300 MPa Dynamic mass M 0 Ns 2 /m Mechanical impedance B 200 Ns/m Dynamic rigidity K 5 0 5 N/m 42 0 4 0 6 0 8 0 0.2 0.4 0.6 0.8 RVF [-] (a) Dependence of RVF. Fig. 8. (c) RVF = 0.4. (b) RVF = 0.2. (d) RVF = 0.8. 8 RVF N 0 = 262 rad/s, RVA = 0. Dependence of RVFN 0 = 262 rad/s, RVA = 0.. 9 2 Fig. 9. Experimental equipment 2. 262 rad/s N 0 RVA, RVF 0.00 7 RVA 0.05 8(a) RVA = 0. RVF 8(b), 8(c), 8(d) RVF = 0.2, 0.4, 0.8 RVF = 0.2, 0.4 RVF = 0.8 RVF 43 9 3 0(a), (a) 0(b), (b) 0 RVA = 0.3, RVF = 0.0 RVA = 0.4, RVF = 3/6
[rad/s] ref (a) Spindle speed. (b) Vibration of tool. 3 Table 3. Cutting condition. End mill flutes 4 End mill ϕ 20 mm Radial depth of cut 20 mm Axial depth of cut 2 mm Work piece S25C Feed rate 643 mm/min (c) Vibration of tool (constant (d) Vibration of tool (variable speed. 2 RPTC Fig. 2. Repetitive Perfect tracking controller. 0 RVA = 0.3, RVF = 0.0 Fig. 0. Experimental result of chatter vibration (RVA = 0.3, RVF = 0.0). [rad/s] ref 3 Fig. 3. PSG) Periodic signal generator (PSG). (a) Spindle speed. (b) Vibration of tool. 4 Fig. 4. Disturbance table. (c) Vibration of tool (constant (d) Vibration of tool (variable RVA = 0.4, RVF = 0.02 Fig.. Experimental result of chatter vibration (RVA = 0.4, RVF = 0.02). 0.02 0(c), (c) (2) 800 Hz 0(d), (d) RVA, RVF 5. RVF RVF θ [rad] PTC 2 C PI p 00 rad/s 5 PTC 4/6
2 n n (5) PTC 45 x[k + ] = Ax[k] + Bu[k] (4) [k] = Cx[k] (5) 6 7 u 0 [k] = B ( z A)x d [k + ] (6) 0 [k] = z Cx d [k + ] (7) 52 0 e 89 = 0 P (s) + C PI(s)P (s) F cut(t) (8) e(t) = 0(t) (t) (9) F cut ˆF cut (t) = + C PI(s)P (s) e(t) (20) P (s) 3, 4 P (s)/(+c PI (s)p (s)) θ[i + ] 2 ˆθ[i + ] = θ[i] + [i] + ref[i] T u (2) 2 22 Q γ = 2 Q[z] = + γz + z 2 (22) γ + 2 6. 23 PSG 0000 [rad/s] ref (a) Spindle speed (constant [rad/s] ref [rad/s] (b) Compensation signal (constant F cut = 5 Fig. 5. 4 Table 4. Without compensation [rad/s] (c) Spindle speed (variable (d) Compensation signal (variable RPTC Simulation result of RPTC. Average of the error. with compensation.74.38 4 sinlθ (23) l=0 ref = 04.7 rad/s 5(a) 0.5 s 5(b) Q RVA = 0., RVF = 5(c), 5(d) 7. PSG 2000 ref = 04.7 rad/s 6(a) 6(c) 6.7 Hz 4 4 6(b), 6(d) 05.7 rad/s RVA = 0., RVF =.5 7 2 5/6
(a) Speed error (without compensation). (c) Frequency analysis (with compensation). Fig. 6. 7 6 [rad/s] (b) Speed error (with compensation). Frequency [Hz] (d) Frequency analysis (without compensation) RPTC Experimental result (Constant ref RVA = 0., RVF =.5 Fig. 7. Spindle speed (RVA = 0., RVF =.5). 4 8. NC RVA,RVF RVF S. Yoshimitu, S. Satonaka, Y. Kawano, Z. Dunwen and S. Yamashita, Two-dimensional Monitoring System for Tool Behavior in End Milling with Small Diameter Tool, Journal of JSPE, Vol. 77, No. 9, pp. 889 894(20)(in Japanese) 2 E. Shamoto, Mechanism and Suppression of Chatter VIbrations in Cutting, Electric Furnace Steel, Vol. No. 2, pp. 43 55(20)(in Japanese) 3 82, N. Suzuki, Chatter Vibration in Cutting, Part2, Journal of JSPE, Vol. 76, N0. 4, pp. 404 407(200)(in Japanese) 4 H. Chen, D. Li, S. Huang and P. Fu, Study on the cutting force prediction of supercritical material millling, ICNC, Vol. 3, pp. 48 52(200) 5 D. Kurihara, Y. Kakinuma and S. Katsura, Sensor-less cutting force monitoring using parallel disturbance observer, International Journal of Automation Technology, Vol. 3, No. 4, pp. 45 42(2009) 6 Y. Lakinuma, Y. Sudo and T. Aoyama, Detection of chatter vibration in end milling applying disturbance observer, Annals of the CIRP, Vol.60, No., pp. 09 2(20) 7 T. Shimizu, H. Fujimoto, and Y. Hori, Force sensorless control of cutting force for NC machine tools based on the response surface method, IIC 053, pp. 23 28(20)(in Japanese) 8 T. Ishibashi and H. Fujimoto, Force Sensorless Control of Cutting Resistance for NC Machine Tools by Spindle Motor Control Utilizing Variable Pulse Number T method, IIC 8 028(203)(in Japanese) 9 N. Suzuki, Chatter Vibration in Cutting, Part, Journal of JSPE, Vol. 76, N0. 3, pp. 280 284(200)(in Japanese) 0 S. Seguy, T. Insperger, L. Arnaud, G. Dessein and G. Peigné, SUPPRESSION OF PERIOD DOUBLING CHATTER IN HIGH SPEED MILLING BY SPINDLE SPEED VARIATION, Journal of Machining Science and Technology, Vol. 5, pp. 53 7(20) S. Seguy, T. Insperger, L. Arnaud, G. Dessein and G. Peigné, On the stability of high speed milling with spindle speed variation,the International Journal of Advanced Manufacturing Technology, Vol. 48, pp. 883 895(200) 2 D. Wu and K. Chen, Chatter suppression in fast tool servo-assisted turning by spindle speed variation, International Journal of Machine Tools and Manufacture, Vol. 50, pp. 038 047(200) 3 H. NishinaH. Fujimoto, RRO Compensation of Hard Disk Drives with RPTC for Discrete Track Media, IIC 08 65, pp. 25 30(2008)(in Japanese). 4 T. NakaiH. Fujimoto, Proposal of harmonic current suppression method of PM motor based on repetitive perfect tracking control with speed variation, SPC 08 30, pp. 55 60(2008)(in Japanese). 5 H. Fujimoto, Y. Hori, A. Kawamura Perfect Tracking Control Method Based on Multirate Feedforward Control, Journal of SICE, Vol. 36, No. 9, pp. 766 772(2000)(in Japanese). 6/6