The rotating internal damping or nonconservative circulatory force in a rotor shaft system causes instability beyond a certain threshold rotor spinning speed. However, if the source loading of the drive is considered, then the rotor spin is entrained at the stability threshold and a stable whirl orbit is observed about the unstable equilibrium. As we move toward the use of more and more lightweight rotor dynamic components such as the shaft and the motor, overlooking this frequency entrainment phenomenon while sizing the actuator in the design stage may lead to undesirable performance. This applies to many emerging areas of strategic importance such as in vivo medical robots where flexible probes are used and space robotics applications involving rotating tools. We analyze this spin entrainment phenomenon in a distributed parameter model of a spinning shaft, which is driven by a nonideal dc motor. A drive whose dynamics is influenced by the dynamics of the driven system is called a nonideal source and the whole system is referred to as a nonideal system. In particular, we show the advantages of representing such nonideal drive-system interactions in a modular manner through bond graph modeling as compared to standard equation models where the energetic couplings between dynamic variables are not explicitly shown. The developed modular bond graph model can be extended to include rotor disks and bearings placed at different locations on the shaft. Moreover, the power conserving property of the junction structure of the bond graph model is exploited to derive the source loading expressions, which are then used to analytically derive the steady-state spinning frequency and whirl orbit amplitude as functions of the drive and the rotor system parameters. We show that the higher transverse modes may become unstable before the lower ones under certain parametric conditions. The shaft spinning speed is entrained at the lowest stability threshold among all transverse modes. The bond graph model is used for numerical simulation of the system to validate the steady-state results obtained from the theoretical study.
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November 2010
Modeling Applications
Bond Graph Modeling of an Internally Damped Nonideal Flexible Spinning Shaft
A. K. Samantaray,
A. K. Samantaray
Department of Mechanical Engineering, Systems, Dynamics, and Controls Laboratory,
Indian Institute of Technology
, Kharagpur 721302, Indiasamantaray@lycos.com
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S. S. Dasgupta,
S. S. Dasgupta
Department of Mechanical Engineering, Systems, Dynamics, and Controls Laboratory,
Indian Institute of Technology
, Kharagpur 721302, India
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R. Bhattacharyya
R. Bhattacharyya
Department of Mechanical Engineering, Systems, Dynamics, and Controls Laboratory,
Indian Institute of Technology
, Kharagpur 721302, India
Search for other works by this author on:
A. K. Samantaray
Department of Mechanical Engineering, Systems, Dynamics, and Controls Laboratory,
Indian Institute of Technology
, Kharagpur 721302, Indiasamantaray@lycos.com
S. S. Dasgupta
Department of Mechanical Engineering, Systems, Dynamics, and Controls Laboratory,
Indian Institute of Technology
, Kharagpur 721302, India
R. Bhattacharyya
Department of Mechanical Engineering, Systems, Dynamics, and Controls Laboratory,
Indian Institute of Technology
, Kharagpur 721302, IndiaJ. Dyn. Sys., Meas., Control. Nov 2010, 132(6): 061502 (9 pages)
Published Online: October 29, 2010
Article history
Received:
January 21, 2009
Revised:
November 13, 2009
Online:
October 29, 2010
Published:
October 29, 2010
Citation
Samantaray, A. K., Dasgupta, S. S., and Bhattacharyya, R. (October 29, 2010). "Bond Graph Modeling of an Internally Damped Nonideal Flexible Spinning Shaft." ASME. J. Dyn. Sys., Meas., Control. November 2010; 132(6): 061502. https://doi.org/10.1115/1.4002483
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