Nonlinear Dynamics

, Volume 74, Issue 4, pp 943–955 | Cite as

Numerical investigation on dynamic characteristics of drilling shaft in deep hole drilling influenced by minimal quantity lubrication

  • Lingfei Kong
  • Yan Li
  • Yanjun Lv
  • Qinfeng Wang
Original Paper


The dynamic characteristics of drilling shaft in deep hole drilling influenced by minimal quantity lubrication (MQL) is investigated. According to the features of the compressible fluid Reynolds equation in oil/air feature, a time-dependent mathematical model is established to describe the pressure distribution of cutting fluid with nonlinearity in MQL deep hole drilling. By introducing the differential transformation approach, the time-dependent pressure equation arising from cutting fluid is solved by the use of direct integral method. The influences of the rotational speed, the transverse displacement ratio, and radial clearance on the hydrodynamic pressure distribution of cutting fluid are obtained. The advantage of this method is to overcome much of the computational cost and has its rapid convergence rate. Furthermore, the nonlinear responses of drilling shaft influenced by MQL are analyzed, and the instability rotational speeds of drilling tool are discussed while the design parameters of drilling shaft system changing.


Minimal quantity lubrication Hydrodynamic pressure Dynamic responses Instability rotational speed Deep hole drilling 



This work is supported by National Natural Science Foundation of China (Grant No. 51105305), the Major Research Program of Shaanxi Province of China (13115 Project, Grant No. 2009ZDKG-25), Natural Science Foundation of Shaanxi Province of China (Grant No. 2011JQ7012) and Natural Science Foundation of Department of Education of Shaanxi Province of China (Grant No. 2010JK695 and No. 12JK680).


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Xi’an University of TechnologyXi’anChina

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