Flexible Hub-beam System Research Articles

Dynamic analysis of the flexible hub-beam system based on rigid-flexible coupling mechanism

The flexible hub-beam system is a typical structure of the rigid-flexible coupling dynamic system. In this paper, the dynamic property of the flexible hub-beam system is investigated. First, based on the dynamic analysis of the flexible beam in the flexible hub-beam system, the dynamic model of a flexible hub-beam-tip mass system is established and researched. Second, the dynamic response of the flexible beam under different external loads, including end concentrated load, end sinusoidal load, and uniform load, is analyzed and calculated. Finally, the influence of magnitude, direction, and type of load on the dynamic response of the flexible beam is also discussed. This research can provide a novel strategy for controlling the maximum stress of the structural components to be lower than the yield stress of the material, and flexible components remain in the linear elastic range even under the condition of high-speed rotation.

Active control and experiment study of a flexible hub-beam system

The first-order approximation coupling (FOAC) model was proposed recently for dynamics and control of flexible hub-beam systems. This model may deal with system dynamics for both low and high rotation speed, while the classical zeroth-order approximation coupling (ZOAC) model is only available for low rotation speed. This paper assumes the FOAC model to present experimental study of active positioning control of a flexible hub-beam system. Linearization and nonlinear control strategies are both considered. An experiment system based on a DSP TMS320F2812 board is introduced. The difference between linearization and nonlinear control strategies are studied both numerically and experimentally. Simulation and experimental results indicate that, linearized controller can make the system reach an expected position with suppressed vibration of flexible beam, but the time taken to position is longer than expected, whereas nonlinear controller works well with precise positioning, suppression of vibration and time control.

A new dynamic model for a flexible hub-beam system

In this paper, a new dynamic model for the flexible hub-beam system is proposed by using the principle of continuum medium mechanics and the finite element discretization method. In the proposed model, the coupling deformation of any element of the beam is only related with the nodal coordinates of this element. So this model is suitable to the rotating beam in an arbitrary shape. Numerical examples of slender beams in straight and irregular shapes are carried out to demonstrate the validation of the proposed model. Simulation results indicate that the proposed model can be used valid for dynamic description of flexible rotating beam in irregular shape, and for both low and high rotation speeds.

Frequency Characteristics of a Flexible Hub-beam System with Arbitrary Settling Position of Attached Mass

In this article, the frequency characteristics of a flexible hub-beam system with an attached mass in an arbitrary position are investigated using a first-order approximation coupling (FOAC) model. Three kinds of damping are considered in the model: Damping located at the hub bearing, structural damping caused by the beam material, and damping caused by the air. Cases with both known and unknown large motion of the system are considered. First, the FOAC model is presented with an unknown large motion, using the Hamilton principle and finite element discretization method. Then the dynamic equation for a non-inertial system is presented by neglecting the large motion of the system, and the frequency characteristics of the system are studied using numerical simulations. Simulation results indicate that, for the case with a known large motion, the response frequency of the beam is degressive as the settling position of the mass moves from the fixed end to the free end of the beam. The response frequency of the beam decreases with increasing inertia of the hub. Damping affects only the dynamical equilibrium position of the flexible beam and has little effect on the response frequency of the beam. For the case with an unknown large motion, the response frequency of the beam does not show an obvious degressive trend as the settling position of the mass moves from the fixed end to the mid-point of the beam, but it becomes degressive when the mass moves from the mid-point to the free end of the beam. Damping affects not only the final position of the system, but also the vibration amplitude of the flexible beam. However, the response frequency of the beam is barely affected by the damping.

Optimal tracking control of a flexible hub–beam system with time delay

In this paper, a new technique of time-delay compensation is proposed for active control of a flexible hub–beam system. The first-order approximation coupling (FOAC) model proposed recently for dynamics of hub–beam systems is used to verify the applicability of this technique. The FOAC model is first linearized to obtain a linearized equation. The linearized equation with time delay is then transformed into a standard form with no time delay by a particular integral transformation. The time-delay controller is designed based on this standard equation using the classical optimal tracking control theory. Since the controller is a function of modal coordinates, a modal filter is presented to estimate the modal coordinates from physical sensor measurements. The effectiveness of the proposed technique for time delay is demonstrated by numerical simulations. Simulation results indicate that a very small time delay may result in instability of the control system if it is not compensated in control design. The proposed time-delay controller is effective in controlling the system even when the maximum time delay for stability without time-delay compensation is greatly exceeded. Moreover, for the system without time delay, the proposed time-delay controller may possibly obtain much better control effectiveness than the controller without time delay.

Active control of a flexible hub-beam system using optimal tracking control method

In this paper, active control of a flexible hub-beam system is investigated using optimal tracking control method and a first-order approximation coupling (FOAC) model. Using the Hamilton theory and assumed mode method (AMM) for discretization, the FOAC model considering second-order coupling quantity of axial displacement caused by transverse displacement of beam is first investigated. Subsequently a simplified FOAC model (or the SFOAC model) which neglects the effect of axial deformation of beam is presented in this paper. Active position control for the system is then studied by optimal tracking control theory. Since the controller obtained is a function of mode coordinate, an extraction method of modal coordinate from actual physical measurements is developed. Numerical simulations are carried out to demonstrate effectiveness of the proposed method. Simulation results indicate that the SFOAC model is valid for dynamic description of flexible hub-beam system and thus is available for control design. Modal filter proposed is effective in extracting modal coordinate from physical measurements. Desired position of system may be achieved by the proposed controller. Residual vibration of beam may be suppressed by this controller as well.

Modeling study of a flexible hub–beam system with large motion and with considering the effect of shear deformation

For a flexible hub–beam system with large motion, the first-order approximation coupling (FOAC) model is developed currently, which is verified numerically and experimentally to be valid for dynamic description of the system. In the FOAC model, the assumption of Euler–Bernoulli beam is adopted with neglecting the effect of shear deformation of flexible beam. So this model is only available for the case of slender beam. When the beam is short in length direction, shear deformation is a factor that may have biggish effect on system dynamics. In this paper, dynamic modeling of flexible hub–beam system with considering the effect of shear deformation is investigated. Firstly, based on the assumption of Timoshenko beam and using Hamilton's principle, a coupling dynamic model with considering shear deformation is established, in which geometric stiffness term and axial foreshortening effect caused by the transverse deformation of beam are considered in the modeling. Subsequently, the dynamic model is discretized using finite element method (FEM). Finally numerical simulations are carried out to demonstrate the effectiveness of proposed dynamic model. Simulation results indicate that, dynamics characteristics of the hub–beam system using the Timshenko beam hypothesis and the Euler–Bernoulli beam hypothesis are almost identical when the beam is a slender one. For this case, shear deformation has little effect on system dynamics. But when the beam is short in length direction, shear deformation may have biggish effect on system dynamics. This effect becomes larger as the width to length ratio increases.

Dynamic analysis of a flexible hub-beam system with tip mass

For a dynamic system of a rigid hub and a flexible cantilever beam, the traditional hybrid coordinate model assumes the small deformation in structural dynamics where axial and transverse displacements at any point in the beam are uncoupled. This traditional hybrid coordinate model is referred as the zeroth-order approximation coupling model in this paper, which may result in divergence to the dynamic problem of some rigid–flexible coupling systems with high rotational speed. In this paper, characteristics of a flexible hub-beam system with a tip mass is studied. Based on the Hamilton theory and the finite element discretization method, and in consideration of the second-order coupling quantity of the axial displacement caused by the transverse displacement of the beam, the rigid–flexible coupling dynamic model (referred as the first-order approximation coupling (FOAC) model in this paper) and the corresponding model in non-inertial system for the flexible hub-beam system with a tip mass are presented firstly, then the dynamic characteristics of the system are studied through numerical simulations under twos cases: the large motion of the system is known and is unknown. Simulation and comparison studies using both the traditional zeroth-order model and the proposed first-order model show that even small tip mass may affect dynamic characteristics of the system significantly, which may result in the largening of vibrating amplitude and the descending of vibrating frequency of the beam, and may affect end position of the hub-beam system as well. The effect of the tip mass becomes large along with the increasing of rotating speed of large motion of the system. When the large motion of the system is at low speed, the traditional ZOAC model may lead to a large error, whereas the proposed FOAC model is valid. When the large motion is at high speed, the ZOAC model may result in divergence to the dynamic problem of the flexible hub-beam system, while the proposed second model can still accurately describe the dynamic hub-beam system.

Dynamics modelling of a flexible hub–beam system with a tip mass

This paper presents a finite-element model for a flexible hub–beam system with a tip mass. Both viscous damping and air drag force are introduced into this model. The complete coupling between the system rigid and flexible degrees of freedom is allowed since the start of the formulation and developing the system kinematic variables. Based on deformation theory and geometric constraints, a second order approximation for the displacement field is proposed and the dynamic stiffening is accounted for. Hamilton's principle is utilized in deriving the equations of motion. The corresponding dynamics models of the tip mass and damping forces are developed in a consistent manner through formulating their energy expressions and applying Hamilton's principle. The finite element method is employed for spatial discretization due to its versatility, high accuracy and convergence. Numerical simulations show that the second order term in deformation field can have significant effect on dynamics behavior of flexible multibody systems. It is also shown that the traditional linear model cannot account for dynamic stiffening and may lead to erroneous result in some high-speed systems because the deformation field commonly used in structural dynamics is straight employed in this model. In contrast, the developed model (CCM) based on the second order deformation field can predict valid results. The effects of tip mass and damping on dynamics behavior of the hub–beam system are also discussed.