Abstract
Grinding vibrations caused by regenerative cutting force and workpiece imbalance are discussed in this study. To regenerate workpiece surface, a grinding wheel is rotated, and pushed towards a rotating workpiece, rubbing and cutting its surface, with regenerative and frictional interactive forces generated. Besides, any mass imbalances of the rotating workpiece or the wheel is another source of vibration. To investigate both effects of the regeneration and the mass eccentricity on the grinding dynamics, a mathematical model with time delays and sinusoid excitation has been developed and analysed. By calculating eigenvalues with continuation scheme, linearly grinding stability is obtained and presented in a lobes diagram, where chatter-free and chatter regions are identified. For chatter without workpiece imbalance, a classical periodic chatter induced by the regenerative effect is found. With imbalance, forced periodic vibration, chatter quenching, quasi-periodic chatter and periodic chatter are obtained in different regions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Altintas Y, Weck M (2004) Chatter stability of metal cutting and grinding. CIRP Ann - Manuf Technol 53(2):619–642. doi:10.1016/S0007-8506(07)60032-8
Arnold RN (1946) The mechanism of tool vibration in the cutting of steel. In: Proceedings of the Institution of Mechanical Engineers, vol 154, London, pp 261–284
Badger J, Murphy S, O’Donnell G (2011) The effect of wheel eccentricity and run-out on grinding forces, waviness, wheel wear and chatter. Int J Mach Tools Manuf 51(10–11):766–774. doi:10.1016/j.ijmachtools.2011.06.006.2011/11//
Chatterjee S (2011) Self-excited oscillation under nonlinear feedback with time-delay. J Sound Vibr 330 (9):1860–1876. doi:10.1016/j.jsv.2010.11.005
Chung K.W, Liu Z (2011) Nonlinear analysis of chatter vibration in a cylindrical transverse grinding process with two time delays using a nonlinear time transformation method. Nonlinear Dyn 66:441–456. doi:10.1007/s11071-010-9924-y
Dassanayake AV, Suh CS (2007) Machining dynamics involving whirling part i: model development and validation. J Vibr Control 13(5):475 –506. doi:10.1177/1077546307074230
Dassanayake AV, Suh CS (2007) Machining dynamics involving whirling part ii: machining motions described by nonlinear and linearized models. J Vibr Control 13(5):507 –526. doi:10.1177./1077546307074238
Diken H (2001) Non-linear vibration analysis and subharmonic whirl frequencies of the jeffcott rotor model. J Sound Vibr 243(1):117–125. doi:10.1006/jsvi.2000.3394
Durgumahanti USP, Singh V, Rao PV (2010) A new model for grinding force prediction and analysis. Int J Mach Tools Manuf 50(3):231–240. doi:10.1016/j.ijmachtools.2009.12.004
Hahn RS (1954) Worcester, Mass: on the theory of regenerative chatter in precision-grinding operations. Trans ASME 76(1): 593–597
Huang J, Luo ACJ (2015) Analytical solutions of period-1 motions in a buckled, nonlinear jeffcott rotor system. Int J Dyn Control:1–8. doi:10.1007/s40435-015-0149-2
Huang J, Luo ACJ (2015) Periodic motions and bifurcation trees in a buckled, nonlinear jeffcott rotor system. Int J Bifurcation Chaos 25(01):1550,002. doi:10.1142/S0218127415500029
Huang P, Lee WB, Chan CY (2015) Investigation of the effects of spindle unbalance induced error motion on machining accuracy in ultra-precision diamond turning. Int J Mach Tools Manuf 94:48–56. doi:10.1016/j.ijmachtools.2015.04.007
Inasaki I, Karpuschewski B, Lee H.S Grinding chatter0—origin and suppression. CIRP Ann - Manuf Technol 2(50):515–534. doi:10.1016/S0007-8506(07)62992-8
Inazaki I, Yonetsu S (1969) Forced vibrations during surface grinding. Bull JSME 12(50):385–391
Jeffcott H.H (1919) The lateral vibration of loaded shafts in the neighbourhood of a whirling speed.—the effect of want of balance. Philos Mag Series 6 37(219):304–314. doi:10.1080/14786440308635889
Karpenko E.V, Pavlovskaia E.E, Wiercigroch M (2003) Bifurcation analysis of a preloaded jeffcott rotor. Chaos, Solitons Fractals 15(2):407–416. doi:10.1016/S0960-0779(02)00107-8 10.1016/S0960-0779(02)00107-8
Karpenko E.V, Wiercigroch M, Pavlovskaia E.E, Cartmell M.P (2002) Piecewise approximate analytical solutions for a jeffcott rotor with a snubber ring. Int J Mech Sci 44(3):475–488. doi:10.1016/S0020-7403(01)00108-4
Kim P, Jung J, Lee S, Seok J (2013) Stability and bifurcation analyses of chatter vibrations in a nonlinear cylindrical traverse grinding process. J Sound Vibr 332(15):3879 – 3896. doi:10.1016/j.jsv.2013.02.009
Kuznetsov YA (2000) Elements of applied bifurcation theory
Li H, Shin YC (2007) A study on chatter boundaries of cylindrical plunge grinding with process condition-dependent dynamics. Int J Mach Tools Manuf 47:1563–1572
Lichun L, Jizai F, Peklenik J (1980) A study of grinding force mathematical model. CIRP Ann - Manuf Technol 29(1):245–249. doi:10.1016/S0007-8506(07)61330-4
Liu X, Vlajic N, Long X, Meng G, Balachandran B (2013) Nonlinear motions of a flexible rotor with a drill bit: stick-slip and delay effects. Nonlinear Dyn 72(1-2):61–77. doi:10.1007/s11071-012-0690-x
Liu ZH, Payre G (2007) Stability analysis of doubly regenerative cylindrical grinding process. J Sound Vibr 301(2):950–962. doi:10.1016/j.jsv.2006.10.041
Long XH, Balachandran B (2007) Stability analysis for milling process. Nonlinear Dyn 49(3):349–359. doi:10.1007/s11071-006-9127-8
Malkin S, Guo C (2007) Grinding technology. Industrial Press Inc., USA
Molnár TG, Insperger T, Hogan SJ, Stépán G (2016) Estimation of the bistable zone for machining operations for the case of a distributed cutting force model. ASME J Comput Nonlinear Dyn 11:051,008. doi:10.1115/1.4032443
Nayfeh AH (2008) Order reduction of retarded nonlinear systems—the method of multiple cales versus center-manifold reduction. Nonlinear Dyn 51:483–500. doi:10.1007/s11071-007-9237-y 10.1007/s11071-007-9237-y
Nayfeh AH, Balachandran B (2004) Applied nonlinear dynamics: analytical, computational, and experimental methods. WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Páez Chávez J, Wiercigroch M (2013) Bifurcation analysis of periodic orbits of a non-smooth jeffcott rotor model. Commun Nonlinear Sci Numer Simul 18(9):2571–2580. doi:10.1016/j.cnsns.2012.12.007
Páez Chávez J, Vaziri Hamaneh V, Wiercigroch M (2015) Modelling and experimental verification of an asymmetric jeffcott rotor with radial clearance. J Sound Vibr 334:86–97. doi:10.1016/j.jsv.2014.05.049
Rafieian F, Girardin F, Liu Z, Thomas M, Hazel B (2014) Angular analysis of the cyclic impacting oscillations in a robotic grinding process. Mech Syst Signal Process 44(1–2):160–176. doi:10.1016/j.ymssp.2013.05.005
Rao J.S (2001) A note on jeffcott warped rotor. Mech Mach Theory 36(5):563–575. doi:10.1016/S0094-114X(01)00008-8
Rowe WB (2009) Principles of modern grinding techonology. William Andrew, Burlington, MA
Snoeys R (1969) Dominating parameters in grinding wheel and workpiece regenerative chatter. In: Proceeding of The 10th International Conference on Machine Tool Design and Research. University of Birmingham, pp 325–348
Tauhiduzzaman M, Yip A, Veldhuis SC (2015) Form error in diamond turning. Precis Eng 42:22–36. doi:10.1016/j.precisioneng.2015.03.006 10.1016/j.precisioneng.2015.03.006
Thompson RA (1974) On the doubly regenerative stability of a grinder. ASME J Eng Ind 96(1):275–280. doi:10.1115/1.3438310
Thompson R.A (1977) On the doubly regenerative stability of a grinder: the combined effect of wheel and workpiece speed. ASME J Eng Ind 99(1):237–241. doi:10.1115/1.3439144
Thompson RA (1986) On the doubly regenerative stability of a grinder: the mathematica analysis of chatter growth. ASME J Eng Ind 108(2):83–92. doi:10.1115/1.3187055
Thompson R.A (1986) On the doubly regenerative stability of a grinder: the theory of chatter growth. ASME J Eng Ind 108(2):75–82. doi:10.1115/1.3187054
Thompson R.A (1992) On the doubly regenerative stability of a grinder: the effect of contact stiffness and wave filtering. ASME J Eng Ind 114(1):53–60. doi:10.1115/1.2899758
Vlajic N, Liu X, Karki H, Balachandran B (2014) Torsional oscillations of a rotor with continuous stator contact. Int J Mech Sci 83:65–75. doi:10.1016/j.ijmecsci.2014.03.025
Wiercigroch M, Budak E (2001) Sources of nonlinearities, chatter generation and suppression in metal cutting. Philos Trans Royal Soc London. Ser A: Math, Phys Eng Sci 359(1781):663–693. doi:10.1098/rsta.2000.0750
Yan Y, Xu J (2013) Suppression of regenerative chatter in a plunge-grinding process by spindle speed. ASME J Manuf Sci Eng 135(4):041,019–041,019. doi:10.1115/1.4023724
Yan Y, Xu J, Wang W (2012) Nonlinear chatter with large amplitude in a cylindrical plunge grinding process. Nonlinear Dyn 69(4):1781–1793. doi:10.1007/s11071-012-0385-3
Yan Y, Xu J, Wiercigroch M (2014) Chatter in a transverse grinding process. J Sound Vibr 333 (3):937–953. doi:10.1016/j.jsv.2013.09.039
Yan Y, Xu J, Wiercigroch M (2015) Non-linear analysis and quench control of chatter in plunge grinding. Int J Non-Linear Mech 70:134–144. doi:10.1016/j.ijnonlinmec.2014.06.012
Yuan L, Keskinen E, Jarvenpaa VM (2005) Stability analysis of roll grinding system with double time delay effects. In: Ulbrich H, Gunthner W (eds) Proceedings of IUTAM Symposium on Vibration Control of Nonlinear Mechanisms and Structures, vol 130. Springer, Netherlands, pp 375–387
Zhai L, Luo Y, Wang Z, Kitauchi S, Miyagawa K (2016) Nonlinear vibration induced by the water-film whirl and whip in a sliding bearing rotor system. Chin J Mech Eng 29(2):260–270. doi:10.3901/CJME.2015.0713.092
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yan, Y., Xu, J. & Wiercigroch, M. Regenerative chatter in a plunge grinding process with workpiece imbalance. Int J Adv Manuf Technol 89, 2845–2862 (2017). https://doi.org/10.1007/s00170-016-9830-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00170-016-9830-7