1. From: Numerical Study of Forward and Backward Whirling of Drill-String
Date of download: 10/11/2017
Copyright © ASME. All rights reserved.
From: Numerical Study of Forward and Backward Whirling of Drill-String
J. Comput. Nonlinear Dynam. 2017;12(6): doi: /
Figure Legend:
(a) A schematic of the 2DOF rotor system to describe a planar motion of the BHA using a disk of mass m rotating around its centroid (point O2) with velocity Ω, inside the borehole of clearance γ and (b) a velocity diagram

2. From: Numerical Study of Forward and Backward Whirling of Drill-String
Date of download: 10/11/2017
Copyright © ASME. All rights reserved.
From: Numerical Study of Forward and Backward Whirling of Drill-String
J. Comput. Nonlinear Dynam. 2017;12(6): doi: /
Figure Legend:
Conditions determining transitions between the operational modes of the system: N—noncontact, C—contact, and CS—contact-stick

3. From: Numerical Study of Forward and Backward Whirling of Drill-String
Date of download: 10/11/2017
Copyright © ASME. All rights reserved.
From: Numerical Study of Forward and Backward Whirling of Drill-String
J. Comput. Nonlinear Dynam. 2017;12(6): doi: /
Figure Legend:
A parameter space diagram showing the most probable whirling responses, for given mass M and angular speed Ω. The examples of the main whirling types are NPF (orange color, Ω = 3.0 rad/s, top left panel), CPF (red color, Ω = 4.5 rad/s, top right panel), CCF (black color, Ω = 5.5 rad/s, bottom left panel), and CPB (blue color, Ω = 10.5 rad/s, bottom right panel) (see color figure online).

4. From: Numerical Study of Forward and Backward Whirling of Drill-String
Date of download: 10/11/2017
Copyright © ASME. All rights reserved.
From: Numerical Study of Forward and Backward Whirling of Drill-String
J. Comput. Nonlinear Dynam. 2017;12(6): doi: /
Figure Legend:
Probabilities of observing different whirling responses as a function of Ω for different WOBs: (a) M = 209.98 kg, (b) M = 221.20 kg, (c) M = 232.41 kg, (d) M = 243.12 kg, (e) M = 253.82 kg, (f) M = 265.04 kg, and (g) M = 276.25 kg. The panels on the left present an overall trend where forward/backward responses are considered together as noncontact periodic (pink), contact periodic (green), and chaotic (black) whirls, whereas the panels on the right depict probabilities for each specific case (see color figure online).

5. From: Numerical Study of Forward and Backward Whirling of Drill-String
Date of download: 10/11/2017
Copyright © ASME. All rights reserved.
From: Numerical Study of Forward and Backward Whirling of Drill-String
J. Comput. Nonlinear Dynam. 2017;12(6): doi: /
Figure Legend:
Basins of attraction showing possible co-existing whirling solutions depending on the initial conditions (r0, θ0) and the angular velocity Ω: (a) Ω = 3.0 rad/s, (b) Ω = 4.5 rad/s, (c) Ω = 5.5 rad/s, and (d) Ω = 10.5 rad/s (see color figure online)