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Research Papers

A Dynamic Modeling Approach for Spindle Bearing System Supported by Both Angular Contact Ball Bearing and Floating Displacement Bearing

[+] Author and Article Information
Songtao Xi

School of Mechanical Engineering,
Xi'an Jiaotong University,
Xi'an 710049, Shaanxi, China
e-mail: xst121@stu.xjtu.edu.cn

Hongrui Cao

School of Mechanical Engineering,
Xi'an Jiaotong University,
Xi'an 710049, Shaanxi, China
e-mail: chr@mail.xjtu.edu.cn

Xuefeng Chen

Professor
State Key Laboratory for Manufacturing
Systems Engineering,
Xi'an Jiaotong University,
Xi'an 710049, Shaanxi, China
e-mail: chenxf@mail.xjtu.edu.cn

Linkai Niu

School of Mechanical Engineering,
Xi'an Jiaotong University,
Xi'an 710049, Shaanxi, China
e-mail: niulinkai@stu.xjtu.edu.cn

1Corresponding author.

Manuscript received March 25, 2017; final manuscript received December 3, 2017; published online December 21, 2017. Assoc. Editor: Christopher Tyler.

J. Manuf. Sci. Eng 140(2), 021014 (Dec 21, 2017) (16 pages) Paper No: MANU-17-1165; doi: 10.1115/1.4038687 History: Received March 25, 2017; Revised December 03, 2017

This paper presents a new dynamic modeling approach for spindle bearing system supported by both angular contact ball bearing (ACBB) and floating displacement bearing (FDB). First, a dynamic model of FDB is developed based on the discrete element method with each bearing component having six degrees-of-freedom (DOFs). Based on the developed FDB dynamic model and Gupta ACBB dynamic model, a fully coupled dynamic model of the spindle bearing system combined both ACBBs, and FDB is developed. In the proposed spindle bearing system model, the spindle shaft is modeled using finite element (FE) method based on the Timoshenko beam theory with the consideration of centrifugal force and gyroscopic moment. The coupling restriction between the dynamic bearing models and the FE spindle shaft model are the restoring forces and moments that are transmitted to the shaft by the bearings and the dynamic vibration response shared by both the bearing inner races and the corresponding nodes of the shaft where bearings are installed. A Fortran language-based program has been developed for the spindle bearing system with the dynamic bearing models solved using the Runge–Kutta–Fehlberg integration method and FE shaft model solved by Newmark-β method. Based on the developed model, the effect of the FDB radial clearance, system preload, and spindle rotating speed on the system dynamics, and the effect of the FDB radial clearance on the system unbalanced response have been investigated.

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Figures

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Fig. 1

Pictures and application schematic diagram of the FDB [40]

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Fig. 2

The coupling dynamic model of spindle bearing system supported by both angular contact bearings and FDB

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Fig. 3

The geometrical relationship between different bearing components in FDBs

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Fig. 4

The interaction relationship between the ball and raceways

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Fig. 5

The interaction between the ball and outer race

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Fig. 6

Geometrical interaction between a ball and inner ring in azimuth-in-inner raceway frame

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Fig. 7

Geometry of contacting bodies: (a) ball-outer-raceway contact, (b) ball-outer-raceway contact geometrical relationship, and (c) ball-inner-raceway contact

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Fig. 8

The elastic deformation between the ball and the raceways

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Fig. 10

5DOFs Timoshenko beam element

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Fig. 9

The traction model of lubrication

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Fig. 11

Coupling restriction between the dynamic bearing models and the FE spindle shaft model

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Fig. 13

The FRFs of spindle system with different radial clearances and preloads: (a) for 600 N preload and (b) for 1000 N preload

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Fig. 12

Information of the simulation model

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Fig. 14

Comparison of first three order natural frequencies of the system with different FDB radial clearances and preloads: (a) for the first-order natural frequency, (b) for the second-order natural frequency, and (c) for the third-order natural frequency

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Fig. 21

Contact load between a ball and the outer race in three different bearings: (a) ball-outer race contact in bearing 1, (b) partial enlarged drawing of (a), (c) ball-outer race contact in bearing 2, (d) partial enlarged drawing of (c), (e) ball-outer race contact in bearing 3, and (f) partial enlarged drawing of (e)

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Fig. 22

The orbit of the spindle shaft with different radial clearances of FDB: (a) for 4 μm radial clearance, (b) for 2 μm radial clearance, (c) for 0 μm radial clearance, (d) for −2 μm radial clearance, and (e) for −4 μm radial clearance

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Fig. 23

The radial displacement response of the first and 12th node of the spindle under unbalanced excitation with different radial clearance of FDB: (a) The radial displacement response of the first node, (b) partial enlarged drawing of (a), (c) the radial displacement response of the 12th node, and (d) partial enlarged drawing of (c)

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Fig. 15

The 3D plot of FRF under different rotating speeds and preloads: (a) for 600 N preload and (b) for 1000 N preload

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Fig. 16

The comparison of the first three natural frequencies under different rotating speeds and with different preload

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Fig. 20

(a) The radial displacement of inner race of different bearings and (b) partial enlarged drawing of (a)

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Fig. 17

The FRFs at the first node with different preloads

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Fig. 18

The first three order natural frequencies under different preloads

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Fig. 19

(a) The axial displacement of inner race of different bearings and (b) partial enlarged drawing of (a)

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