Nonlinear dynamic stability analysis of the coupled axial-torsional motion of the rotary drilling considering the effect of axial rigid-body dynamics

Study on dynamic stability of structure is a hot subject in the fields of engineering mechanics, but its basic theory and analytical method still need to be further improved. This paper improved the current method for dynamic stability analysis called “dynamic eigenvalue method”, and the method for nonlinear dynamic stability analysis based on ANSYS platform is proposed. A long column under harmonic loads is taken as the research objective, dynamic eigenvalues affected by the load frequency, load amplitude and damping ratio are studied. Results show that, the increasing of load frequency or dynamic load amplitude will lead to the increase of maximum dynamic eigenvalue and decrease of minimum dynamic eigenvalue, which is not beneficial to dynamic stability of structure. The increasing of damping ratio will lead to the decrease of maximum dynamic eigenvalue and increase of minimum dynamic eigenvalue, this make the dynamic eigenvalue more stable. Therefore, the high damping is beneficial to dynamic stability of structure.

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On the Stability of Robot Compliant Motion Control: Theory and Experiments

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.2896159 ◽

1990 ◽

Vol 112 (3) ◽

pp. 417-426 ◽

Cited By ~ 64

Author(s):

H. Kazerooni ◽

B. J. Waibel ◽

S. Kim

Keyword(s):

Stability Analysis ◽

Rigid Body ◽

Dynamic Behavior ◽

Stability Condition ◽

Robot Manipulator ◽

Rigid Body Dynamics ◽

Robot Dynamics ◽

Direct Drive ◽

Body Dynamics ◽

The Stability

The work presented here is a nonlinear approach for the stability analysis of robot manipulators in compliant maneuvers. Stability of the environment and the manipulator taken as a whole has been investigated, and a bound for stable manipulation has been derived. The stability analysis has been investigated using unstructured models for the dynamic behavior of the robot manipulator and the environment. This unified approach of modeling robot dynamics is expressed in terms of sensitivity functions as opposed to the rigid body dynamics derived by Lagrangian approach. It allows us to incorporate the dynamic behavior of all the elements of a robot manipulator (i.e., actuators, sensors and the structural compliance of the links) in addition to the rigid body dynamics. We show that for stability of the robot, there must be some initial compliancy either in the robot or in the environment. According to this stability condition, smaller sensitivity either in the robot or in the environment leads to a narrower stability range. In the limit, when both robot and environment have zero sensitivity, stability cannot be guaranteed. The general stability condition has been extended to the particular case where the environment is very rigid in comparison with the robot stiffness. This condition has been verified via simulation and experiment on the Minnesota direct drive robot.

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Nonlinear dynamic stability of laminated beams subjected to pulsing thermal loads

AIAA Journal ◽

10.2514/3.14204 ◽

1999 ◽

Vol 37 ◽

pp. 521-524

Author(s):

R. Suresh ◽

Gajbir Singh ◽

G. V. Rao

Keyword(s):

Dynamic Stability ◽

Nonlinear Dynamic ◽

Thermal Loads ◽

Laminated Beams ◽

Nonlinear Dynamic Stability

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Slipping–rolling transitions of a body with two contact points

Nonlinear Dynamics ◽

10.1007/s11071-021-06538-5 ◽

2021 ◽

Author(s):

Mate Antali ◽

Gabor Stepan

Keyword(s):

Rigid Body ◽

Contact Point ◽

Static Friction ◽

Rigid Body Dynamics ◽

Contact Forces ◽

Friction Forces ◽

Contact Points ◽

Body Dynamics ◽

Coulomb Model ◽

Rigid Surfaces

AbstractIn this paper, the general kinematics and dynamics of a rigid body is analysed, which is in contact with two rigid surfaces in the presence of dry friction. Due to the rolling or slipping state at each contact point, four kinematic scenarios occur. In the two-point rolling case, the contact forces are undetermined; consequently, the condition of the static friction forces cannot be checked from the Coulomb model to decide whether two-point rolling is possible. However, this issue can be resolved within the scope of rigid body dynamics by analysing the nonsmooth vector field of the system at the possible transitions between slipping and rolling. Based on the concept of limit directions of codimension-2 discontinuities, a method is presented to determine the conditions when the two-point rolling is realizable without slipping.

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