Numerical Investigation of Rotor and Journal Bearing Parameters on Nonlinear Vibration of a Highly Flexible Rotor Considering Journal Angular Motion With Experimental Verification

2020 ◽  
Author(s):  
Nuntaphong Koondilogpiboon ◽  
Tsuyoshi Inoue
Keyword(s):  
Nonlinear Vibration ◽  
Limit Cycles ◽  
Shooting Method ◽  
Journal Bearing ◽  
Angular Motion ◽  
Experimental Results ◽  
Rolling Element Bearing ◽  
Motion Model ◽  
Flexible Rotor ◽  
Large Disk

Abstract In this study, the nonlinear vibration (bifurcation type) of a highly flexible rotor supported by a journal bearing (JB) and self-aligning rolling element bearing (REB) under various configurations of rotor large disk mass/position, bearing length-to-diameter (L/D) ratio, and preload was investigated using two different bearing models: the model that considers both lateral and angular motion (Model A) and the model that considers just lateral motion (Model B). The rotor was modelled by 1-D finite elements (FE), and its degrees-of-freedom (DOF) was reduced to the DOF of the JB’s node by real mode component mode synthesis (CMS). Then, the shooting method and arclength continuation were applied to the reduced rotor model to obtain nonlinear limit cycles. Also, parallel computing was applied to the shooting method to shorten the calculation time. The stability of the obtained limit cycles was then determined by Floquet multiplier analysis. The experiment on the test rig with the same rotor and bearing parameters utilized in the calculation was carried out to verify the bearing models in each configuration. The calculation and experimental results showed that the bifurcation type calculated by Model A agreed with experimental results in all configurations. In addition, if the L/D ratio was short or the large disk position was near the rotor midspan, the bifurcation type obtained from both Model A and B agreed with the experimental results. The discrepancy in bifurcation type obtained from both bearing models only occurred in the cases that the L/D ratio was long and the large disk position was near the JB. Lastly, decreasing the L/D ratio, increasing preload, and moving the large disk position closer to the JB tended to change the bifurcation type from subcritical to supercritical.

Nonlinear Vibration Analysis of a Flexible Rotor Supported by a Journal Bearing Considering Journal Angular Motion

2020 ◽  
Vol 15 (9) ◽  
Author(s):  
Nuntaphong Koondilogpiboon ◽  
Tsuyoshi Inoue
Keyword(s):  
Nonlinear Vibration ◽  
Degrees Of Freedom ◽  
Shooting Method ◽  
Journal Bearing ◽  
Angular Motion ◽  
Motion Model ◽  
Flexible Rotor ◽  
Large Disk ◽  
Supercritical Bifurcation ◽  
Multiplier Analysis

Abstract The effect of bearing length to diameter (L/D) ratio and large disk position on nonlinear vibration of a flexible rotor-bearing system was investigated. The rotor consisted of a shaft modeled by one-dimensional finite elements (FEs) and disks. It was supported by a self-aligning ball bearing (BB) and an axial-groove journal bearing (JB). Two JB's L/D ratios of 0.4 and 0.6, two large disk positions of 340 and 575 mm measured from the BB, and two bearing models that consider both journal's lateral and angular motion (model A) and consider only journal's lateral motion (model B) were investigated. The degrees-of-freedom (DOF) of the equation of motion (EOM) were reduced to those of the boundary DOF by real mode component mode synthesis (CMS) that retains only the first forward and backward modes of the internal DOF. Shooting method and Floquet multiplier analysis were applied to the reduced EOM to obtain limit cycles and their stability, which indicates Hopf bifurcation type. Numerical results indicated that supercritical bifurcation only occurred in the case of L/D = 0.4 and large disk position 575 mm for both bearing models. Otherwise, the subcritical bifurcation occurred except the case of L/D = 0.6 with the large disk position 575 mm that supercritical bifurcation occurred if model B was used. The experiment with the same parameters used in the calculation was conducted as verification. The experimental results showed the same bifurcation type as calculated by using model A.

Nonlinear Vibration Prediction of a Highly Flexible Rotor Supported by an Axial Groove Journal Bearing Considering Journal Angular Whirling Motion

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Nuntaphong Koondilogpiboon ◽  
Tsuyoshi Inoue
Keyword(s):  
Nonlinear Vibration ◽  
Journal Bearing ◽  
Rolling Element Bearing ◽  
Flexible Rotor ◽  
Large Disk ◽  
Subcritical Bifurcation ◽  
Whirling Motion ◽  
Vibration Prediction ◽  
Rotor Bearing ◽  
Bearing System

Abstract The difference in dynamic behavior of the rotor-bearing system supported by the bearing model that considers both lateral and angular whirling motions of the journal (model A), and the model that considers only lateral whirling motion (model B) is investigated. The rotor model consists of a slender shaft, a large disk, and two small disks supported by a self-aligning rolling element bearing (REB) and an axial groove journal bearing (JB) of length-to-diameter ratio (L/D) = 0.6. Three positions of the large disk: 410, 560, and 650 mm measured from the REB, are investigated. Numerical integration of the rotor-bearing system which is modally reduced to the first forward (FWD) mode is performed at above the onset speed of instability until either a steady-state journal orbit or contact between the journal and the bearing occurs to identify the bifurcation type. Numerical results using model A indicate subcritical bifurcation with the contact between the journal and the inboard (IB) side of the bearing in all three large disk positions, whereas those of model B indicate subcritical bifurcation when the large disk position is at 410 mm, and supercritical bifurcation is observed in the other two cases. Finally, the experiments at the same three large disk positions are performed. Subcritical bifurcation with the contact between the journal and the IB side of the bearing is observed in all large disk positions, which conforms with the calculation result of model A. Hence, model A is essential in nonlinear vibration analysis of a highly flexible rotor system.

Nonlinear Vibration Analysis of a Flexible Rotor Supported by a Journal Bearing Considering Journal Angular Motion

2019 ◽  
Author(s):  
Nuntaphong Koondilogpiboon ◽  
Tsuyoshi Inoue
Keyword(s):  
Nonlinear Vibration ◽  
Ball Bearing ◽  
Journal Bearing ◽  
Angular Motion ◽  
Experimental Result ◽  
Flexible Rotor ◽  
Large Disk ◽  
Rotor Bearing ◽  
Bearing Force ◽  
Bearing System

Abstract The effect of bearing length to diameter (L/D) ratio and large disk position on nonlinear vibration (limit cycle and bifurcation type) of a flexible rotor-bearing system is investigated. The rotor consists of a shaft modeled by 1-D finite elements (FE), two small disks and a large disk. It is supported by a self-aligning ball bearing and an axial-groove journal bearing with L/D ratio of 0.4 and 0.6. Two large disk positions: 340 and 575 mm measured from the ball bearing are investigated. The journal angular motion, which is essential for the highly flexible rotor but typically not considered in the previous nonlinear vibration literature; is considered in nonlinear bearing force calculation. The degrees of freedom (DOF) of the rotor-bearing system are reduced to those of the node that the nonlinear journal bearing force and moment act on by real mode component mode synthesis (CMS) that retains only the 1st forward and backward modes. Shooting method and Floquet multiplier analysis are applied to the reduced rotor-bearing system to obtain limit cycles and their stability of each bearing L/D ratio and large disk position case. Numerical results indicate that supercritical Hopf bifurcation only occurs in the case of L/D = 0.4 and large disk position 575 mm, otherwise subcritical occurs. However, if the typical bearing model that does not consider journal angular motion is used, the bifurcation type for the case of L/D = 0.6 with large disk position 575 mm will change to supercritical. Lastly, the experiments with the same L/D ratio and large disk position investigated in the calculation are performed as a validation. The experimental result of each case shows the same bifurcation type as the calculation result using the bearing model that considers the journal angular motion.

Nonlinear Vibration Prediction of a Highly Flexible Rotor Supported by an Axial Groove Journal Bearing Considering Journal Angular Whirling Motion

2019 ◽  
Author(s):  
Nuntaphong Koondilogpiboon ◽  
Tsuyoshi Inoue
Keyword(s):  
Nonlinear Vibration ◽  
Ball Bearing ◽  
Journal Bearing ◽  
Flexible Rotor ◽  
Large Disk ◽  
Subcritical Bifurcation ◽  
Whirling Motion ◽  
Vibration Prediction ◽  
Rotor Bearing ◽  
Bearing System

Abstract In this study, the difference in dynamic behavior of the rotor-bearing system supported by the bearing model that considers both lateral and angular whirling motions of the journal (model A), and the model that considers only lateral whirling motion (model B) is investigated. The rotor model consists of a slender shaft, a large disk and two small disks supported by a self-aligning ball bearing and an axial groove journal bearing of L/D = 0.6. Three positions of the large disk: 410, 560, and 650 mm measured from the ball bearing, are investigated. Numerical integration of the rotor-bearing system which is modally reduced to the 1st forward mode is performed at above the onset speed of instability until either a steady state journal orbit or contact between the journal and the bearing occurs to identify the bifurcation type. Numerical results using model A indicate subcritical bifurcation with the contact between the journal and the inboard side of the bearing in all three large disk positions, whereas those of model B indicate subcritical bifurcation when the large disk position is at 410 mm, and supercritical bifurcation is observed in the other two cases. Lastly, the experiments at the same three large disk positions are performed. Subcritical bifurcation with the contact between the journal and the inboard side of the bearing is observed in all large disk positions, which conforms with the calculation result of model A. As a result, model A is essential in nonlinear vibration analysis of a highly flexible rotor system.

Nonlinear Analysis of Rigid Rotor System Supported by 2 Lobes Journal Bearing in Comparison With Circular Journal Bearing

2018 ◽  
Author(s):  
Nuntaphong Koondilogpiboon ◽  
Tsuyoshi Inoue
Keyword(s):  
Limit Cycles ◽  
Shooting Method ◽  
Reynolds Equation ◽  
Journal Bearing ◽  
Equation Of Motion ◽  
Rigid Rotor ◽  
Floquet Multiplier ◽  
Multiplier Analysis ◽  
Speed Range ◽  
Bearing Force

The effect of 2 lobes journal bearing parameters such as L/D ratio and pad preload on the bifurcation of the rigid rotor is investigated in comparison with the circular bearing. Nonlinear bearing force in the equation of motion is obtained by solving Reynolds equation using the finite difference method. Shooting method and Floquet multiplier analysis are employed to obtain limit cycles and their stability. The results show that, for some bearing parameters, multiple limit cycles coexist at a specific shaft rotational speed range. Comparing with the circular bearing of same L/D ratio, the 2 lobes bearing without pad preload decreases the onset speed of instability and also decreases speed range from the onset speed of instability (Hopf) point to the limit point of the bifurcation (saddle-node) in the subcritical bifurcation case. Increasing the pad preload only increases the onset speed of instability significantly in the small L/D ratio case. For both circular and 2 lobes bearing, increasing the L/D ratio decreases the onset speed of instability and tends to change the type of the bifurcation from supercritical to subcritical.

scholarly journals Novel Aiming Method for Spin-Stabilized Projectiles with a Course Correction Fuze Actuated by Fixed Canards

Electronics ◽  
2019 ◽  
Vol 8 (10) ◽  
pp. 1135
Author(s):  
Cheng ◽  
Shen ◽  
Deng ◽  
Deng
Keyword(s):  
Traditional Method ◽  
Angular Motion ◽  
Hardware In The Loop ◽  
Motion Model ◽  
Simulation Based ◽  
Spinning Projectile ◽  
Gyroscopic Effects

Spin-stabilized projectiles with course correction fuzes actuated by fixed canards have the problem of great coupling in both the normal and lateral directions due to intensive gyroscopic effects, which leads to inconsistent maneuverability in different directions. Due to the limited correction ability, which results from the miniaturization of the fuze and fixed canards, a target-aiming method is proposed here to make full use of the correction ability of the canards. From analysis on how the canards work and building an angular motion model, the correction characteristics of a spinning projectile with fixed canards have been studied, and the inconsistent maneuverability in different directions of the projectile has been explained and used to help establish the proposed target aiming method. Hardware-in-the-loop simulation based on a 155 mm howitzer shows that when the correction ability of fixed canards is unchanged, the proposed method can improve the striking accuracy by more than 20% when compared to the traditional method.

Steady-State and Dynamic Properties of the Floating-Ring Journal Bearing

1968 ◽  
Vol 90 (1) ◽  
pp. 243-253 ◽  
Author(s):  
F. K. Orcutt ◽  
C. W. Ng
Keyword(s):  
Steady State ◽  
Journal Bearing ◽  
Dynamic Properties ◽  
Calculated Data ◽  
Experimental Results ◽  
Supply Pressure ◽  
Pressure Parameter

Calculated data on steady-state and dynamic properties of the plain cylindrical floating-ring bearing with pressurized lubricant supply are given. The data are for a bearing with L/D of 1, and values of the ratio of inner to outer film clearances of 0.7 and 1.3. One value of dimensionless supply pressure parameter is covered. Experimental results are presented which verify the calculated results and which supplement them, particularly with respect to stability characteristics of the bearing.

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