Nonlinear response and nonsmooth bifurcations of an unbalanced machine-tool spindle-bearing system

Gao, Shanghan; Long, Xinhua; Meng, Guang

doi:10.1007/s11071-008-9336-4

Cited by 39 publications

(17 citation statements)

References 22 publications

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“…With the increase of the frequency ratio, there are three possible routes to chaos in the spindle-bearing system: (1) through a period doubling bifurcation, (2) through a tori doubling process, and (3) through a grazing bifurcation [19]. These results enrich our understanding on the dynamics of the spindle-bearing system and are of great significance to the design and fault diagnosis for the spindle-bearing system.…”

Section: Route To Chaos Through Period-doubling Processmentioning

confidence: 82%

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Nonlinear response and stability of a spindle system supported by ball bearings

2009

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In this effort, the nonlinear responses and stability of a spindle system supported by ball bearings are presented. The dynamics of this system is described by a set of second order differential equations with a nonlinear piecewise smooth force. The Floquet theory is applied to investigate the stability of the periodic solution. Due to the loss of contact between the raceways and balls in the ball bearing, the bending of the frequency response curves switch to the left at the weak resonance region, which is similar to the frequency response curves of a system with a soft spring. With the decrease of the bearing clearance, the bending of the frequency response curves switch to the right, which is similar to the frequency response curves of a system with a hard spring. Increase of the frequency ratio, the bending of frequency response curves transforms from left to right. The route to chaos through a period doubling process is also observed in this spindle-bearing system.Keywords Spindle-bearing system · Piecewise stiffness · Floquet theory · Stability · Period-doubling bifurcation InstructionAs one of the sources of vibrations in the spindle system, ball bearing attracts a lot of interests. To compensate the thermal and centrifugal expansion, initial clearance between the raceways and balls is designed for the ball bearing. A lot of efforts have been devoted to the study of the nonlinear responses and the routes to chaos of rotor-bearing system with clearance. In the early work of rotor dynamics, Yamamoto [1] considered the nonlinear effect of bearing clearance and investigated the vibratory behaviors of a vertical Jeffcott rotor supported by ball bearings. The results show that the maximum amplitude at the critical speed decreases with the increase of radial clearance. Following the effort of Yamamoto, Tiwari et al. [2] investigated the effects of the bearing clearance and varying compliance on the dynamic characteristics of a horizontal Jeffcott rotor with the unbalance force. Harsha et al. [3] analyzed the effects of surface waviness and bearing clearance on the nonlinear vibration response of rotor-ball bearing system. Bercea et al. [4] proposed a general methodology for modeling the relationship between the contact pressure distribution and the elastic deflection in several types of double-row rolling bearings with the effects of bearing clearance and the initial preload. Sopanen and Mikkola [5,6] proposed a dynamic model of a deep-groove ball bearing with six DOF. By investigating this model, the effects of the bearing clearance on the natural frequencies and the vibration responses of the rotor bearing system were studied. All the works presented in Refs. [1-6] mainly focus on the nonlinear response of the system with positive clearance. However, due to the thermal expansion of the races and balls of the bearing

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Section: Route To Chaos Through Period-doubling Processmentioning

confidence: 82%

“…(19) into (16), expanding F in a Taylor series about the nominal periodic solution X * , and retaining the linear terms of the perturbation X, the resulting system of linear time-varying coefficient differential equations is given,…”

Section: Floquet Multipliersmentioning

confidence: 99%

Nonlinear response and stability of a spindle system supported by ball bearings

2009

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“…Sopanen and Mikkola proposed a dynamic model of a ball bearing-rotor system with six degrees of freedom to study the effects of the bearing clearance on the natural frequencies and the vibration responses of the system [15,16]. Based on it, Gao found that appropriate negative internal clearance helps to reduce the vibration responses of the spindle and improve the stability of the system [17,18]. Bearing preload could keep the bearing in a negative internal clearance state by eliminating the clearance, but too large preload will produce much frictional heat, leading to the rise of temperature and the decline of bearing life [19].…”

Section: Introductionmentioning

confidence: 99%

Dynamics Analysis of Unbalanced Motorized Spindles Supported on Ball Bearings

Liu

Lai

Chen

2016

Shock and Vibration

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This paper presents an improved dynamic model for unbalanced high speed motorized spindles. The proposed model includes a Hertz contact force model which takes into the internal clearance and an unbalanced electromagnetic force model based on the energy of the air magnetic field. The nonlinear characteristic of the model is analysed by Lyapunov stability theory and numerical analysis to study the dynamic properties of the spindle system. Finally, a dynamic operating test is carried out on a DX100A-24000/20-type motorized spindle. The good agreement between the numerical solutions and the experimental data indicates that the proposed model is capable of accurately predicting the dynamic properties of motorized spindles. The influence of the unbalanced magnetic force on the system is studied, and the sensitivities of the system parameters to the critical speed of the system are obtained. These conclusions are useful for the dynamic design of high speed motorized spindles.

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“…Gao et al. 25 studied the grazing contacts between bearing races and balls on the dynamic responses of a rotor-ball bearing system. Numerical results showed that when the ball-race contact speed is low, grazing bifurcation occurs.…”

Section: Introductionmentioning

confidence: 99%

Parametric representation of stationary points in rotor-ball bearing system

Gao

Nong

Zhu

et al. 2014

Proceedings of the Institution of Mechanical Engineers, Part K:

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The frequencies of the stationary points in rotor-ball bearing system are difficult to determine due to the nonlinear and non-smooth ball supporting effects. This paper presents a linearized discriminant to calculate the frequency of the stationary points of the system. The influences of system parameters on the stationary points with the Timoshenko beam and the Bernoulli–Euler beam models are also discussed. The comparison between the linear and nonlinear results indicates that the underlying assumptions are reasonable for the range of parameters considered. With the help of linearized discriminant, the frequency values of the stationary points can be found conveniently. Taking the frequency values of stationary points into the linearized discriminant, the corresponding system parameters can also be obtained by setting the linear determinant to be zero.

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Nonlinear response and nonsmooth bifurcations of an unbalanced machine-tool spindle-bearing system

Cited by 39 publications

References 22 publications

Nonlinear response and stability of a spindle system supported by ball bearings

Nonlinear response and stability of a spindle system supported by ball bearings

Dynamics Analysis of Unbalanced Motorized Spindles Supported on Ball Bearings

Parametric representation of stationary points in rotor-ball bearing system

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