Multiple Resonances and Nonlinear Behaviors of a Spindle Ball Bearings System with 3/2 Nonlinear Term

Nong

Proceedings of the Institution of Mechanical Engineers, Part K:

et al. 2012

This article presents results of vibrations of spindle system subjected to non-linear and non-smooth ball bearing stiffness. The averaging method, an approximate analytical technique, is applied directly to the non-linear and non-smooth differential equations of motion which ultimately leads to approximate analytical expressions for the frequency response relations of the system. The effects of ball bearing clearance and spindle structural damping on the frequency response curves are investigated. Hardening-type non-linear behaviours are observed in the ranges of base excitation frequency ! near the first, second and third natural frequencies. Crossing and breaking frequency response curves are also observed due to the nonlinear and non-smooth properties of ball bearing stiffness. These solutions are clear indications that significant non-linear and non-smooth phenomena are of fundamental importance in the study of spindle bearing system. They also provide direct insight into the relationship between the system parameters and vibration characteristics of the system.

Section: Discussionmentioning

confidence: 99%

Section: Without Spindle Dampingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Frequency response curves of a spindle bearings system with non-linear and non-smooth terms

Nong

Proceedings of the Institution of Mechanical Engineers, Part K:

et al. 2012

“…The ball bearings' internal geometry is quite complex 22,23 and their complicated non-linear and non-smooth dynamic behaviours [24][25][26][27] have attracted much attention. Variable compliance effects of ball bearings on the vibration responses of spindle systems have been researched (i.e.…”

Section: Introductionmentioning

confidence: 99%

Grazing contact researches for a spindle-ball bearing system

Nong

Proceedings of the Institution of Mechanical Engineers, Part K:

et al. 2013

This article combines the three-order harmonic balance method and eight-order Taylor expansion technique to give the qualitative analysis of responses for the spindle-ball bearing system. The effects of the bearing clearance and initial position of rotor on the frequency-response curves are investigated. As the number of contact balls alters due to the combining actions of the bearing clearance and initial position of rotor, the grazing phenomenon occurs and the frequency-response curve undergoes a major change. The system's characteristic coefficients are also found to sharply grow at the point the number of contact balls alters. They therefore can be treated as the signs to indicate the occurrence of the grazing phenomenon, which is helpful for the researchers to study the non-linear and non-smooth properties of the spindle-ball bearing system.

“…In former researches of the milling stability, the ball bearing Hertz contacts are usually simplified as linear springs [11][12][13]. Although the ball bearings appear to be a simple mechanism, their internal geometry is quite complex [14,15], and they often display very complicated non-linear dynamic behaviours [16][17][18][19]. Systematic researches email: gmeng@sjtu.edu.cn have been made in vibration responses contributed by varied structural effects of ball bearings (i.e.…”

Section: Introductionmentioning

confidence: 99%

Unstable islands and bifurcation analysis in a spindle milling system supported by ball bearings

Proceedings of the Institution of Mechanical Engineers, Part K:

2011

This article examines the chatter isolated islands and non-linear responses of a spindle milling system supported by ball bearings. Isolated islands of chatter vibration, which are induced by the non-linear non-smooth ball bearing Hertz contacts, can be found exist in milling processes. The existence of islands of chatter vibration phenomenon is also confirmed by the bifurcation analysis in this article. The stability trends are then examined for several up-milling and down-milling machining processes, respectively, with varying machine tool radial immersions. Results show that, with the influences of the non-linear non-smooth ball bearing Hertz contacts, the milling stability charts present very complex dynamic properties and appear more irregular unstable chatter islands than those induced by the tool helix angles. It is believed that this study complements the researches of chatter vibrations for milling systems.