Dynamic Reaction Forces Research Articles

Development of a Real-Time On-Line Vibration Testing System by Substructuring Method.

On-line testing is a useful way to investigate nonlinear dynamic behavior of structures subjected to seismic excitation. The pseudo-dynamic testing methed is usually used for the on-line testing, in which the time duration in testing to realize the deformation within one time increment is much longer than that in calculation. However, to obtain the dynamic reaction force from on-line testing, the real-time excitation is required. For this purpose, we developed a real-time on-line testing system controlled by a parallel processor with high-speed A/D and D/A converters. The real-time controller can simulate the seismic response of structural models with up to 100 degrees of freedom within the frequency range of 10 Hz. The applicability of the real-time on-line testing method was verified by a comparative shaking table test.

Experimental Study of Dynamic Fluid Forces and Moments for a Long Annular Seal

The dynamic fluid reaction forces and moments of a long annular seal were experimentally studied. A new testing apparatus was constructed in order to measure restoring forces and moments caused by the cylindrical whirling motion of a rotor. Experiments were conducted at various rotor speeds, whirling speeds, and with different pressure drops across the long seal. The rotor and outer cylinder were set in concentric alignment. The tangential force component was derived from the measured fluid force in order to determine the unstable threshold. Moments developed by the long seal were also obtained. Restoring forces and moments were expressed as stiffness, damping coefficients and added mass. These coefficients were then compared with Childs’ theory and found to be compatible.

Influence of Long Seal on the Stability of Fluid Machineries.

The influence of dynamic fluid reaction forces and moments of a long seal on the stability of fluid machinery was investigated. The stability analysis was carried out using a submerged motor pump in a boiler circulate, in order to explain the effect of the long seal. In the stability analysis, the individual contribution of the fluid forces and moments due to rotor conical and cylindrical whirl movements were evaluated according to logarithmic decrements. As a result, the individual contributions depend on the mode shapes of the vibration. The fluid forces acting on the long seal to conical and cylindrical whirl movements should not be ignored because they play an important role in the stability.

Experimental study of dynamical characteristics of a long annular seal. Influence of inlet swirl on the dynamic fluid moment and force.

The influence of inlet swirls on dynamic fluid reaction moments and forces of a long annular seal was experimentally studied. The experiment was conducted under the parameters of rotor speeds, cylindrical whirling speeds and seal inlet swirl velocities. The rotor and the outer cylinder were set in a concentric condition. The tangential and restitutional moments were derived from the measured dynamical fluid forces in order to investigate the influence of the inlet swirl. Moments and forces were expressed as stiffness, damping coefficients and added mass. As a result, it was found that the dynamic characteristics of moments and forces are affected by the inlet swirl velocity. The cross-coupling terms of moment coefficients change their sign when the inlet swirl velocity turns to the opposite direction.

Experimental Study of Dynamical Charateristics of a Long Annular Seal (In the Case of Concentric Rotor and Outer Cylinder)

This paper describes an experimental study of the dynamic fluid reaction force which is generated in the axially long annular clearance between the rotor and stator of a submerged motor pump or in the balance piston of a turbo pump where fluid flows axially. For measuring the dynamic fluid force, a test rig was made to demonstrate the spin and whirl motion of the rotor. In the test, the rotor and the stator were set in the concentric condition and the pressure fluctuation, fluid reaction force and flow rate were measured under the basic parameters of rotational speeds and pressure drop across the long seal. The tangential force component was obtained from the dynamic fluid force and the instability threshold (limit) was determined. In addition, the dynamic fluid force was expressed in terms of the stiffness coefficient, damping coefficient and added mass; each coefficient is discussed in detail in this paper.

Experimental study of dynamical characteristics of a long annular seal. Moment due to cylindrical whirl movement.

This paper describes the experimental study on dynamic fluid reaction force and moment generated in axially long annular clearance between the rotor and stator of a submerged motor pump or in the balance piston of a turbo pump. For measuring the dynamic fluid force, a test rig was made for having spin and whirl motion of the rotor. In the test, the rotor and the stator were set in concentric conditions and pressure fluctuation, fluid reaction force and flow rate were measured under the basic parameters of rotational speeds and pressure drop across the long seal. In measurement, the moment was obtained from dynamic fluid force and instability threshold (limit) of fluid force was determined. In addition, dynamic fluid force was expressed in terms of the stiffness coefficient, damping coefficient and added mass. It was recognized that moment stiffness coefficient and direct-moement damping coefficient increase with axial flow velocity.

Dynamic Simulation of Legged Machines Using a Compliant Joint Model

A computerized simulation of the dynamics of multilegged walking machines is presented. The simulation includes the effects of leg mass and compliance, joint compliance and friction, as well as the effects of leg contact with the ground. An approach is presented in which the Newton-Euler formu lation is used to develop the dynamic equations of each link. Kinematic constraints are not imposed explicitly. Instead, a compliant joint model is used to relate the dynamic reaction forces between neighboring links. The approach can handle multiloop devices with a combination of closed and open kinematic chains. Simulation results for the Ohio State Uni versity Hexapod walking machine are presented and shown to be in close agreement with previously published experi mental data.

Dynamic Simulation of Legged Machines Using a Compliant Joint Model

A computerized simulation of the dynamics of multilegged walking machines is presented. The simulation includes the effects of leg mass and compliance, joint compliance and friction, as well as the effects of leg contact with the ground. An approach is presented in which the Newton-Euler formu lation is used to develop the dynamic equations of each link. Kinematic constraints are not imposed explicitly. Instead, a compliant joint model is used to relate the dynamic reaction forces between neighboring links. The approach can handle multiloop devices with a combination of closed and open kinematic chains. Simulation results for the Ohio State Uni versity Hexapod walking machine are presented and shown to be in close agreement with previously published experi mental data.

Linear Dynamic Coupling in Geared Rotor Systems

The ability to analyze accurately the torsional-axial-lateral coupled response of geared systems is the key to the prediction of dynamic gear forces, shaft moments and torques, dynamic reaction forces, and moments at all bearing points. These predictions can, in turn, be used to estimate gear-tooth lives, shaft lives, housing vibrational response, and noise generation. Typical applications would be the design and analysis of gear drives in heavy-lift helicopters, industrial speed reducers, Naval propulsion systems, and heavy, off-road equipment. In this paper, the importance of certain linear dynamic coupling terms on the predicted response of geared rotor systems is addressed. The coupling terms investigated are associated with those components of a geared system that can be modeled as rigid disks. First, the coupled, nonlinear equations of motion for a disk attached to a rotating shaft are presented. The conventional argument for ignoring these dynamic coupling terms is presented and the error in this argument is revealed. It is shown that in a geared system containing gears with more than about 50 teeth, the magnitude of some of the dynamic-coupling terms is potentially as large as the magnitude of the linear terms that are included in most rotor analyses. In addition, it is shown that the dynamic coupling terms produce the multi-frequency responses seen in geared systems. To quantitatively determine the effects of the linear dynamic-coupling terms on the predicted response of geared rotor systems, a trial problem is formulated in which these effects are included. The results of this trial problem shows that the inclusion of the linear dynamic-coupling terms changed the predicted response up to eight orders of magnitude, depending on the response frequency. In addition, these terms are shown to produce sideband responses greater than the unbalanced response of the system.

Theory of Bloch-line and Bloch-wall motion

A theory of Bloch-line (BL) dynamics in magnetic bubble materials is proposed and applied to the problem of domain collapse with a small number of BLs. We derive from the Landau-Lifshitz-Gilbert equation the dynamic reaction force, composed of gyrotropic and viscous terms, on a single moving BL. From this follows easily the wall mobility for equally spaced BLs. However, we show that BLs tend to cluster statically at distances comparable to the BL width. If the BLs are clustered on one side of a circular-cylinder domain, then a change of the bias field causes the centers of bubble and cluster to move on spiral trajectories. The predicted displacement of the bubble center is large enough for visual confirmation, but the bound on coervicity required to confirm the spiral shape may be too stringent. The collapse mobility for the clustered case is typically much greater than that for the case of uniform spacing. The theory is supported by collapse-time data of Malozemoff for a garnet film of medium viscosity (α=0.12). In garnets of low viscous damping of (α≲0.01) we predict that coercivity Hc gives rise to nonlinearity of the velocity-drive relation, with a characteristic ``knee'' veolcity, (2/π)γHcr, for collapse of a domain of radius r.