Hub Inertia Research Articles

Nonlinear electro-elastic dynamics of a hub–cantilever bimorph rotor structure

Dynamics of a rotating mini hub–bimorph structure excited by periodic torque supplied to the hub is studied in this paper. The mathematical model of the system is formulated by means of the extended Hamilton’s principle. In the analysis the nonlinear constitutive behaviour of the piezoceramic material is adopted based on experimental results published in literature. Moreover, nonlinear inertia effects related to the system rotation are taken into account. The derived system of three integro-partial differential equations represents the electro-mechanical behaviour of the beam (transverse displacement and transducer output voltage) and the hub rotation coordinate. The state equations are discretized and solved numerically around the first resonance zone for the system excited by a periodic torque supplied to the hub. The obtained response curves reveal strong softening behaviour with additional unstable solutions identified out of the resonance zones. Within the framework of the performed numerical simulations the impact of torque excitation amplitude, torque mean value, hub inertia and electrical load resistance on system behaviour is discussed. Finally, the responses of the system with parallel vs series connected transducers are compared.

Tangent barrier Lyapunov function‐based constrained control of flexible manipulator system with actuator failure

AbstractThis article puts forward an adaptive neural network fault‐tolerant control scheme under the state constraints for the flexible manipulator system with uncertain terms. The dynamic model of the system is described by partial differential equations. The tangent barrier Lyapunov functions are chosen in the design process for the sake of ensuring that all states in the system satisfy the constrained conditions. The uncertainties resulted from load mass, hub inertia, and bending stiffness in the system are approximated by using the universal approximation property of neural networks. The adaptive method is used to counteract the influence of joint motor actuator failure. At the same time, combining with the backstepping design framework to design effective controllers to assure that all signals in the closed‐loop system are bounded. Lyapunov stability analysis method is used to prove the stability of the system. Finally, the simulation results prove the availability of the raised control method.

Nonlinear vibrations of a rotating thin-walled composite piezo-beam with circumferentially uniform stiffness (CUS)

A rotating system comprising a hub and a thin-walled laminate cantilever beam with embedded nonlinear piezoelectric layers is analysed in the paper. The reinforcing fibres set-up in composite material conforms to circumferentially uniform stiffness lamination scheme. This configuration exhibits the mutual bending couplings in two orthogonal planes. Nonlinear analytical model of a piezoelectric material embedded onto the beam walls is postulated by considering the higher-order constitutive relations with respect to electric field variable. Moreover, to properly model electromechanical structural behaviour, the full two-way coupling piezoelectric effect is considered. To this aim, the assumption of a spanwise electric field variation is postulated in the mathematical model of the structure. Based on previous authors’ research, the system of mutually coupled nonlinear equations of motion is formulated. In the numerical analysis the forced response of the system under zero and nonzero mean value harmonic torque excitation is considered. In particular, the influence of hub inertia, excitation amplitude and mean rotating speed on system dynamics is investigated. The results are presented in the form of appropriate frequency response plots and bifurcation diagrams.

토크 변동조건에서의 유성기어세트 동적 거동 해석 모델링에 대한 연구

In this paper, to reduce planetary gear noise under the neutral control condition, a dynamic analysis model for multi-stage planetary gear trains of the HMC 6th speed automatic transmissions under a torque fluctuations condition is proposed. The natural frequencies of its system are computed by solving the corresponding eigenvalue problem. Moreover, some forced torque fluctuation response to the planetary gear system is applied to check its influence during neutral control. By undertaking some parameter studies for analysis modeling, an underdrive brake torque fluctuation and underdrive hub inertia are observed to be the most effective factors of the HMC 6th speed automatic transmission’s planetary gear noise under the neutral control condition. To reduce neutral control planetary gear noise, the underdrive torque fluctuation should be reduced whereas underdrive hub inertia should be increased. However, every transmission has some torque fluctuations caused by the valve body control response and friction component characteristic and those also have some manufacturing quality distributions. Therefore, control component inertia is an important item in the neutral control condition. To adapt the neutral control to a next-generation transmission, its control component inertia should be above a certain value.

On Frequency Sensitivity and Mode Orthogonality of Flexible Robotic Manipulators

This paper presents sensitivity analysis of vibration frequencies of flexible manipulators with respect to variations of systems parameters such as rotational inertia of hub, and mass, moment, and side of tip load. Both Euler-Bernoulli and Timoshenko dynamical models of flexible manipulators are discussed. By using variational method, sensitivity indices are obtained with explicit expressions for measuring the sensitivity of frequencies. Based on variational formulations, a novel method for deriving the orthogonal relations among vibration modal shape functions of flexible manipulators is introduced. With this method, the orthogonal relations can be derived easily without invoking the tedious process of differentiation and integration by part, as commonly used in their derivation.

TWO-LINK FLEXIBLE MANIPULATOR AS AN ALTERNATIVE IN IMPROVING ENERGY EFFICIENCY OF MANIPULATOR ROBOT

The dynamic model and characterization of a two-link fl exible manipulator as an alternative for manipulator robot to achieve the effi ciency on consuming electrical energy comparing with rigid manipulator. A planar two-link fl exible manipulator was combined with structural damping, hub inertia and payload that moving horizontally. A dynamic model system was developed using the combination of Euler-Lagrange and assumed mode methods. Armed with the developed model, then some simulations were done to examine the dynamic model and the response of the system on the hub and the end point of both link that were presented and analyzed in function of time and frequency. The results show that the bang-bang input of 0.15 volt can move the link-1 on 550 and link-2 on 122 respectively. It means that the dynamic model uses more effi cient energy compared with rigid manipulator robot which required bigger input for moving

Bending–twisting vibrations of a rotating hub–thin-walled composite beam system

The dynamics of a system consisting of a rotating rigid hub and a flexible composite thin-walled beam is discussed. The nonclassical effects like material anisotropy, rotary inertia and transverse shear are considered in the mathematical model of the structure. Moreover, the hub mass moment of inertia is taken into account. The differential equations of motion featuring beam bending–twist elastic coupling are derived using the Hamilton principle, and the Galerkin method is applied in order to reduce the partial differential governing equations to the ordinary differential equations. Parametric studies are conducted to evaluate beam stiffness coefficients depending on the fiber lamination angle. Next, numerical results are obtained to investigate the impact of hub to beam relative inertia on the natural frequencies of the structure. Cases of forced vibrations of the system are examined where the driving torque is considered as the sum of a constant (mean value) and a periodic component. Simulations show the importance of the hub inertia on the complete system dynamics. A shift of the resonance zones and a vibration absorption are observed.

Dynamic Modelling and Characterisation of a Two-Link Flexible Robot Manipulator

This paper presents an investigation into the dynamic modelling and characterisation of a two-link flexible robot manipulator. A planar two-link flexible manipulator incorporating structural damping, hub inertia and payload that moves in the horizontal plane is considered. A dynamic model of the system is developed using a combined Euler-Lagrange and assumed mode method. Simulation is performed to assess the dynamic model and system responses at the hub and end-point of both links are presented and analysed in time and frequency domains. Moreover, effects of payload on the dynamic characteristics of the flexible manipulator are studied and discussed.

반력모멘트 추정기를 이용한 단일 링크 유연 조작기의 진동제어

In this paper, a novel vibration control scheme for a single-link flexible manipulator system without using a vibration feedback sensor is proposed. In order to achieve the vibration information of the flexible link, a reaction moment estimator based on the dynamic characteristics of the flexible manipulator is proposed. While the manipulator is maneuvering the reaction moment is reciprocally acting on the flexible link and the hub inertia due to the vibration of the link. A sliding mode controller based on the equivalent rigid body dynamics corresponding to the proposed flexible manipulator is then augmented with the reaction moment estimator to realize a decentralized control system. The reaction moment estimator is implemented via the first order low pass filter. The performance of the proposed control scheme is verified by computer simulation and experiment.

Dynamic Modelling of a Flexible Manipulator System Incorporating Payload: Theory and Experiments

This paper presents theoretical and experimental investigations into the dynamic characterisation of a flexible manipulator system. A constrained planar single-link flexible manipulator is considered. A dynamic model of the system, incorporating structural damping, hub inertia and payload, is developed using finite element methods. Effects of damping and payload on the response of the flexible manipulator are discussed. Performance of the algorithm in describing the dynamic behaviour of the system is assessed in comparison to an experimental test-rig. Experimental results are presented for validation of the developed finite element model in the time and frequency domains.

Dynamic modeling and mode analysis of flexible-link, flexible-joint robots

This paper presents a systematic approach to dynamic modeling and mode analysis of a single-link flexible robot, which has a flexible joint and a hub at the base end and a payload at the free end. Accurate modes of the system are obtained analytically. The following important conclusions are drawn: (1) even a small joint flexibility can significantly affect the system frequencies; (2) the fundamental frequency is insensitive to the hub inertia or payload inertia; (3) for a given flexible system, the fundamental frequency is mainly affected by the payload mass, while the second frequency is mainly affected by the payload inertia.

Communication

In this article, issues in the design of passive controllers for a class of multilink manipulators with the last link flexible are discussed. It is well known that for the single flexible-link manipulator, the mapping from the input torques to the joint ve locities is passive, whereas the mapping from the input torques to the derivative of net-tip movements (the usual output chosen) is not. However, if an appropriate output variable is selected, the transfer function can be made passive, provided that the hub inertia seen by a flexible link is sufficiently small. Then, by the Passivity theorem, using any strictly passive controller with finite gain will result in an L2-stable system. However, for a multilink industrial robot, the effective hub inertia seen by the flexible link is usually large. In addition, the dynamic equations are highly nonlinear. Approaches are examined for extending these passivity results to multilink manipulators. Experimental results are presented for a five-bar-linkage manipulator with the last link being flexible.

MULTIOBJECTIVE OPTIMIZATION DESIGN METHODOLOGY FOR INCORPORATING MANUFACTURING UNCERTAINTIES IN ADVANCED COMPOSITE STRUCTURES

Abstract A methodology is proposed herein which incorporates manufacturing uncertainties into a multiobjective optimal design algorithm for structures fabricated with fibrous composite laminated materials. Every single objective function for this class of stochastic multiobjective optimization problems and the corresponding probabilistic constraints are transformed into equivalent deterministic quantities using chance constrained programming, and then fuzzy set theory is employed as the assistant of decision making to solve a multiobjective optimization problem to get the best compromise solution. A finite element model of a single-link flexible laminated fibrous composite robot arm including the effects of damping and hub inertia demonstrates the significance of employing the proposed methodology for obtaining the high performance characteristics of composite structures with random parameters. The random parameters employed in this example for the fabrication of the composite robot arm are ply thickness, fiber orientation, and fiber volume fraction.

Real-Time Finite Difference Simulation of a Single-Link Flexible Manipulator System Incorporating Hub Inertia and Payload

This paper presents an investigation into the real-time simulation of a flexible manipulator system. A single-link flexible manipulator incorporating hub inertia and payload mass which can bend freely in the horizontal plane and is stiff in vertical bending and torsion is considered. A fourth-order partial differential equation (PDE) model of the system obtained through the utilization of the Lagrange equation and the modal expansion method is considered. A finite-dimensional simulation of the flexible manipulator system is developed using a finite difference discretization of the dynamic equation of motion of the manipulator. The algorithm proposed allows the inclusion of distributed actuator and sensor terms in the PDE and modification of boundary conditions. The real-time processing requirements of the algorithm are investigated by implementing the algorithm on several digital processing domains. Finally, simulation results verifying the performance of the algorithm in characterizing the behaviour of the manipulator under various loading conditions are presented and discussed.

Accuracy of finite dimensional dynamic models of flexible manipulators for controller design

The dynamics of mechanical systems with distributed flexibility are described by infinite dimensional mathematical models, yet a real controller must be finite dimensional due to the limited bandwidth capabilities of the sensor-actuator system and real-time control computer hardware. Therefore, simplified finite dimensional dynamic models must be obtained for the purpose of controller design. This article addresses the issue of selecting the shape and number of mode functions in developing finite order models using a flexible robot arm as an example. The results of this work have consistently shown that the clamped-free mode shape predicts the closed-loop system dynamics under a feedback controller much more accurately than pinned-free mode shapes. However, as the hub inertia increases relative to the flexible beam inertia the difference between the clamped-free and pinned-free mode shape model predictions becomes smaller.

Effect of Payload on the Dynamics of a Flexible Manipulator—Modeling for Control

The “exact” and pole/zero transfer functions are developed for a flexible beam-like single link arm with actuator on one end and payload on the other. This model represents a broader class of actuator hub and payload mass properties than is found in prior literature. The dependence of dynamics on the hub and payload inertia characteristics are studied and graphs are provided to facilitate estimation of poles and zeroes for any similar plant. It is shown that a 10:1 reduction in fundamental frequency and substantial change in the zeroes results from variations in payload through a practical range. Payload rotary inertia is shown to cause a qualitative change in the arm tip zeroes resulting in loss of observability/controllability in some cases. Results provide insight into the two-link problem and it is shown that complex values zeroes may result if the second arm is allowed to “fold back.” Implications to plant modeling and control design are discussed including sensor placement and model order reduction issues. Analytical results are compared to those measured on an experimental arm and show very good agreement in modal frequency and shape.

Modeling impact on a one-link flexible robotic arm

A finite-element model for a single-link flexible robotic arm including the effects of beam damping, hub inertia and both Coulomb and viscous hub friction is derived. The initial conditions required to represent impact loading are determined, and the motion of the arm under impact loading is simulated. Simulation results are compared to experimental data. From the experimental results it is concluded that this model provides an accurate representation of the physical process. It also provides a vehicle for investigating the effects of parameters of the process model, in particular, frictional effects and load profiles. Impact loading has been effectively represented in terms of initial conditions and can be applied to a range of finite-element models.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>