Bifurcations and the penetrating rate analysis of a model for percussive drilling. (English) Zbl 1269.70032
Summary: In this paper, we investigate a low dimensional model of percussive drilling with vibro-impact to mimic the nonlinear dynamics of the bounded progression. Non-holonomity which arises in the stick-slip caused by the impact during drilling fails to be correctly identified via the classical techniques. A reduced model without non-holonomity is derived by the introduction of a new state variable, of which averaging technique is employed successfully to detect the periodic motions. Local bifurcations are presented directly by using C-L method. Numerical simulations and the penetrating rate analysis along different choices of parameters have been carried out to probe the nonlinear behaviour and the optimal penetrating rate of the drilling system.
MSC:
| 70K50 | Bifurcations and instability for nonlinear problems in mechanics |
| 70K55 | Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics |
References:
| [1] | Cavanough G.L., Kochanek M., Cunningham J.B. et al.: A self-optimizing control system for hard rock percussive drilling. IEEE ASME Trans. Mech. 13(2), 153–157 (2008) · doi:10.1109/TMECH.2008.918477 |
| [2] | Wiercigroch M., Krivtsov A.M., Wojewoda J.: Vibrational energy transfer via modulated impacts for percussive drilling. J. Theor. Appl. Mech. 46(3), 715–726 (2008) |
| [3] | Al-Hamdan A.: Effect of misalignment on the cutting force signature in drilling. J. Mater. Process. Technol. 124(1–2), 83–91 (2002) · doi:10.1016/S0924-0136(02)00051-1 |
| [4] | Krivtsov A.M., Wiercigroch M.: Molecular dynamics simulation of mechanical properties for ploy crystal materials. Mater. Phys. Mech. 3, 345–351 (2001) |
| [5] | Krivtsov A.M.: Molecular dynamics simulation of impact fracture in polycrystalline materials. Mechanica 38, 61–70 (2003) · Zbl 1023.74051 · doi:10.1023/A:1022019401291 |
| [6] | Chiang L.: Dynamic force-penetration curves in rock by matching theoretical to experimental wave propagation response. Exp. Mech. 44(2), 167–175 (2004) |
| [7] | Wiercigroch M., Pavlovskaia E.: Nonlinear dynamics of vibro-impact systems: theory and experiments. Mod. Pract. Stress Vib. Anal. Mater. Sci. Forum 440(4), 513–520 (2003) · Zbl 1045.70517 · doi:10.4028/www.scientific.net/MSF.440-441.513 |
| [8] | Bustamante, M., Boato, R.: Polymer slurry in large diameter pile drilling-case histories. In: Proceedings of the 16th international conference on soil mechanics and geotechnical engineering, Osaka, Japan, 12–16 September 2005. 1–5, 2083–2086 (2005) |
| [9] | Cai S., Wang S.G., Long X.M.: A simple estimation of the force exerted by internal solitons on cylindrical piles. Ocean Eng. 33, 974–980 (2006) · doi:10.1016/j.oceaneng.2005.05.012 |
| [10] | Zhang L., Wang L., Wang X.: Study on vibration drilling of fiber reinforced plastics with hybrid variation parameters method. Compos. A Appl Sci Manuf 34(3), 237–244 (2003) · doi:10.1016/S1359-835X(02)00207-5 |
| [11] | Jantunen E.: A summary of methods applied to tool condition monitoring in drilling. Int. J. Machine Tools Manuf. 42(9), 997–1010 (2002) · doi:10.1016/S0890-6955(02)00040-8 |
| [12] | Benamar A.: Dynamic pile response using two pile-driving techniques. Soil Dyn. Earthq. Eng. 20(1–4), 243–247 (2000) · doi:10.1016/S0267-7261(00)00057-9 |
| [13] | Wiercigroch M., Neilson R.D., Player M.A.: Material removal rate prediction for ultrasonic drilling of hard materials using an impact oscillator approach. Phys. Lett. A 259(2), 91–96 (1999) · doi:10.1016/S0375-9601(99)00416-8 |
| [14] | Xu L., Lu M., Cao Q.: Bifurcation and chaos of a harmonically excited oscillator with both stiffness and viscous damping piecewise linearities by incremental harmonic balance method. J. Sound Vib. 264(4), 873–882 (2003) · doi:10.1016/S0022-460X(02)01194-X |
| [15] | Xu L., Lu M., Cao Q.: Nonlinear vibrations of dynamical systems with a general form of piecewise-linear viscous damping by incremental harmonic balance method. Phys. Lett. A 301(1–2), 65–73 (2002) · Zbl 0997.70022 · doi:10.1016/S0375-9601(02)00960-X |
| [16] | Yang S.P., Chen Y.H.: The bifurcations and singularities of the parametrical vibration in a system with Davidenkov hysteretic nonlinearity. Mech. Res. Commun. 19(4), 267–272 (1992) · doi:10.1016/0093-6413(92)90043-A |
| [17] | Yang S.P., Shen Y.J.: Bifurcations and the singularities in the nonlinear system with the present of hysteresis. Science Press, Beijing (2003) |
| [18] | Li S.H., Yang S.P., Guo W.W.: Investigation on chaotic motion in hysteretic non-linear suspension system with multi-frequency excitations. Mech. Res. Commun. 31(2), 229–236 (2004) · Zbl 1045.70516 · doi:10.1016/j.mechrescom.2003.10.002 |
| [19] | Strenkowski J.S., Hsieh C.C., Shih A.J.: An analytical finite element technique for predicting thrust force and torque in drilling. Int. J. Machine Tools Manuf. 44(12–13), 1413–1421 (2004) · doi:10.1016/j.ijmachtools.2004.01.005 |
| [20] | Hamade R.F., Seif C.Y., Ismail F.: Extracting cutting force coefficients from drilling experiments. Int. J. Machine Tools Manuf. 46(3-4), 387–396 (2006) · doi:10.1016/j.ijmachtools.2005.05.016 |
| [21] | Zitoune R., Collombet F.: Numerical prediction of the thrust force responsible of delamination during the drilling of the long-fibre composite structures. Compos. A Appl. Sci. Manuf. 38(3), 858–866 (2007) · doi:10.1016/j.compositesa.2006.07.009 |
| [22] | Ramkumar J., Malhotra S.K., Krishnamurthy R.: Effect of workpiece vibration on drilling of GFRP laminates. J. Mater. Process. Technol. 152(3), 329–332 (2004) · doi:10.1016/S0924-0136(03)00622-8 |
| [23] | Kim D., Ramulu M.: Drilling process optimization for aphite/bismaleimide-titanium alloy stacks. Compos. Struct. 63(1), 101– 114 (2004) · doi:10.1016/S0263-8223(03)00137-5 |
| [24] | Altındaǧ R.: Estimation of penetration rate in percussive drilling by means of coarseness index and mean particle size. Rock Mech. Rock Eng. 36(4), 323–332 (2003) · doi:10.1007/s00603-003-0002-3 |
| [25] | Pavlovskaia E., Wiercigroch M.: Modelling of vibro-impact system driven by beat frequency. Int. J. Mech. Sci. 45(4), 623–641 (2003) · Zbl 1045.70517 · doi:10.1016/S0020-7403(03)00113-9 |
| [26] | Woo K.C., Rodger A.A., Neilson R.D., Wiercigroch M.: Phase shift adjustment for harmonic balance method applied to vibro-impact systems. Mechanica 41(3), 269–282 (2006) · Zbl 1158.74383 · doi:10.1007/s11012-005-5897-1 |
| [27] | Golubitsky M., Schaeffer D.G.: Singluarities and Groups in Bifurcation theory, vol. I. Springer-Verlag, New York (1984) |
| [28] | Chen Y.S., Langford W.F.: The subharmonic bifurcation solution of nonlinear Mathieu’s equation and Euler dynamic buckling problems. Acta Mech. Sin. 4, 350–362 (1988) · Zbl 0732.73036 · doi:10.1007/BF02486668 |
| [29] | Chen Y.S., Ding Q.: C-L method and its application to engineering nonlinear dynamical problems. Appl. Math. Mech. 22(2), 144–153 (2001) · Zbl 1033.70014 · doi:10.1023/A:1015576412107 |
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