The Dynamic Behavior of a Rolling Element Auxiliary Bearing Following Rotor Impact

Cole, Matthew O. T.; Keogh, Patrick; Burrows, C. R.

doi:10.1115/1.1430673

Cited by 42 publications

(15 citation statements)

References 15 publications

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“…The works [1][2][3][4][5][6][7][8][9]15,[17][18][19][21][22][23][24][25][26][27][28][29][30][32][33][34][35][36][38][39][40][41][42][43][44]48,[50][51][52] use summation over the bearing rolling elements in contact to compute bearing total loads. Houpert [10,11] replaced this summation by integration using Sjovall's [12] axial and radial load distribution integrals (J a , J r ).…”

Section: The Rolling Element Bearing Stiffness Matrixmentioning

confidence: 99%

Time-Varying Total Stiffness Matrix of a Rigid Machine Spindle-Angular Contact Ball Bearings Assembly: Theory and Analytical/Experimental Verifications

El-Saeidy

2011

Shock and Vibration

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A lagrangian formulation is presented for the total dynamic stiffness and damping matrices of a rigid rotor carrying noncentral rigid disk and supported on angular contact ball bearings (ACBBs). The bearing dynamic stiffness/damping marix is derived in terms of the bearing motions (displacements/rotations) and then the principal of virtual work is used to transfer it from the bearing location to the rotor mass center to obtain the total dynamic stiffness/damping matrix. The bearing analyses take into account the bearing nonlinearities, cage rotation and bearing axial preload. The coefficients of these time-dependent matrices are presented analytically. The equations of motion of a rigid rotor-ACBBs assembly are derived using Lagrange's equation. The proposed analyses on deriving the bearing stiffness matrix are verified against existing bearing analyses of SKF researchers that, in turn, were verified using both SKF softwares/experiments and we obtained typical agreements. The presented total stiffness matrix is applied to a typical grinding machine spindle studied experimentally by other researchers and excellent agreements are obtained between our analytical eigenvalues and the experimental ones. The effect of using the total full stiffness matrix versus using the total diagonal stiffness matrix on the natural frequencies and dynamic response of the rigid rotor-bearings system is studied. It is found that using the diagonal matrix affects natural frequencies values (except the axial frequency) and response amplitudes and pattern and causes important vibration tones to be missig from the response spectrum. Therefore it is recommended to use the full total stiffness matrix and not the diagonal matrix in the design/vibration analysis of these rotating machines. For a machine spindle-ACBBs assembly under mass unbalnce and a horizontal force at the spindle cutting nose when the bearing time-varying stiffness matrix (bearing cage rotation is considered) is used, the peak-to-valley variation in time domain of the stiffness matrix elements becomes significant compared to its counterpart when the bearing standard stiffness matrix (bearing cage rotation is neglected) is used. The vibration spectrum of the time-varying matrix case is marked by tones at bearing outer ring ball passing frequency, rotating unbalnce frequency and combination compared to spectrum of the standard stiffness matrix case which is marked by only the rotating unbalnce frequency. Therfore, it is highly recomended to model bearing stiffness matrix to be a time-dependent.

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Section: The Rolling Element Bearing Stiffness Matrixmentioning

confidence: 99%

Time-Varying Total Stiffness Matrix of a Rigid Machine Spindle-Angular Contact Ball Bearings Assembly: Theory and Analytical/Experimental Verifications

El-Saeidy

2011

Shock and Vibration

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“…where the e terms indicate the thermal expansions as defined in Eqs. (5)- (7). The relative deflections d at the contacts are then…”

Section: Housingmentioning

confidence: 99%

“…Fumagalli et al [5] and Fumagalli [6] studied the effect of air gap, friction coefficient, and CB damping on the impact dynamics and also conducted rotor drop tests. Cole et al [7] studied the effects of bearing width, and inner race speed on the rotordynamic response. Sun et al [8,9] proposed a nonlinear ball bearing model with thermal growth, providing a more accurate component model for the CB.…”

Section: Introductionmentioning

confidence: 99%

Catcher Bearing Life Prediction Using a Rainflow Counting Approach

Lee

Palazzolo

2012

Journal of Tribology

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Catcher bearings (CB) are an essential component for rotating machine with active magnetic bearings (AMBs) suspensions. The CB's role is to protect the magnetic bearing and other close clearance component in the event of an AMB failure. The contact load, the Hertzian stress, and the sub/surface shear stress between rotor, races, and balls are calculated, using a nonlinear ball bearing model with thermal growth, during the rotor drop event. Fatigue life of the CB in terms of the number of drop occurrences prior to failure is calculated by applying the Rainflow Counting Algorithm to the sub/surface shear stress-time history. Numerical simulations including high fidelity bearing models and a Timoshenko beam finite element rotor model show that CB life is dramatically reduced when high-speed backward whirl occurs. The life of the CB is seen to be extended by reducing the CB clearances, by applying static side-loads to the rotor during the drop occurrence, by reducing the drop speed, by reducing the support stiffness and increasing the support damping and by reducing the rotor (journal)-bearing contact friction.

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“…Foiles and Allaire [6] also numerically analyzed the effects of parameters for non-linear models on two types of rotors: generator or turbine rotor and centrifugal compressor rotor. Cole et al [7] developed a deep groove AB model considering the elastic deformation of the inner race, mainly studied the impact force and effects of bearing width as well as ball load distributions. Kaur [8] tested the performances of powder lubricated bearings used as AB.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Responses of Rotor Drops onto Auxiliary Bearing with the Support of Metal Rubber Ring

Zhu¹,

Zhang²

2015

TOMEJ

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In an active magnetic bearing (AMB) system, the Auxiliary bearings (ABs) are indispensable to protect the rotor and stator in case of AMB failure. Most of the former researches try to modify relevant design parameters of ABs to buffer the following impacts and heating after rotor drop. Based on the analysis of the disadvantages of traditional ABs, a new type of AB with the support of metal rubber ring is proposed to enhance the AB work performance in AMB system. Detailed simulation models containing rigid rotor model, contact model between rotor and inner race as well as AB system model after rotor drop are established. Then, using those established models the dynamic responses are simulated to obtain proper metal rubber ring support characteristics. Finally, relevant rotor drop experiments are carried out on the established AMB test bench. The experiment results verify the advantages of the new type ABs and the correctness of simulation analysis.

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The Dynamic Behavior of a Rolling Element Auxiliary Bearing Following Rotor Impact

Cited by 42 publications

References 15 publications

Time-Varying Total Stiffness Matrix of a Rigid Machine Spindle-Angular Contact Ball Bearings Assembly: Theory and Analytical/Experimental Verifications

Time-Varying Total Stiffness Matrix of a Rigid Machine Spindle-Angular Contact Ball Bearings Assembly: Theory and Analytical/Experimental Verifications

Catcher Bearing Life Prediction Using a Rainflow Counting Approach

Dynamic Responses of Rotor Drops onto Auxiliary Bearing with the Support of Metal Rubber Ring

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