Nonlinear Torsional Stiffness Research Articles

Finite-Time Refined Antidisturbance Velocity Tracking Control for Gimbal System of Control Moment Gyros With Harmonic Drive

This paper is concerned with high-precision and fast velocity-tracking control for the harmonic drive-based gimbal system of control moment gyro (CMG). As a major challenge in the controller design, the simultaneous presence of multiple matched and mismatched disturbances should be carefully addressed. Specifically, the rotor imbalance inherent in the CMG will cause vibration of the output torque that significantly degrades the tracking performance. On the other hand, the integration of harmonic drives will lead to nonlinear torsional stiffness and introduce additional frictions into the control system. Furthermore, practical tasks such as fast attitude maneuver have posed higher requirement on the rapidity of the anti-disturbance control schemes. To overcome the aforementioned difficulties, we propose a finite-time refined anti-disturbance velocity tracking controller, which consists of a finite-time harmonic disturbance observer (FTHDO) to compensate for the imbalance vibration, an adaptive finite-time extended state observer (AFTESO) to handle the remaining disturbances with unknown rate of change, and a finite-time controller to ensure fast convergence of the tracking error. Both numerical simulation and hardware-in-the-loop (HIL) experimental results show that the proposed scheme outperforms the existing methods in terms of accuracy and rapidity.

Nonlinear Torsional Stiffness Analysis of Harmonic Drives Using Flexible Multibody Dynamics Simulation

Predicting the nonlinear torsional stiffness of harmonic drives is important not only for system control but also for the further development of the drive. However, it is difficult to predict the torsional stiffness because of the elastic deformation of the flexspline and the many contacts involved. Furthermore, nonlinear dynamic contact simulations between the elastic components of the harmonic drive are disadvantaged by high computational burden and convergence problems. To address these challenges, we establish a flexible multibody modeling process using augmented formulations of a floating reference frame to simulate the operation of the harmonic drive. The elastic deformation of the flexspline and the dynamic contacts between the main components are considered in the reproduction of the contact mechanism of the drive. Coordinate reduction techniques are used to properly replicate an elastic shaft, enabling the effective simulation of flexible multibody dynamics, including nonlinear elastic tooth contact analysis. The performance of the proposed modeling process is evaluated using catalog and experimental data on two types of standard harmonic drives (SHG-25-100-UH and SHG-40-100-UH). The hysteresis curve is predicted through flexible multibody dynamics simulation and the accuracy of parameters of torsional stiffness is approximately 91.7% on average. The proposed modeling method can be improved to predict other measures of performance and it remains a potential research topic.

Magnet based bi-stable nonlinear energy sink for torsional vibration suppression of rotor system

This paper investigates the application of a magnetic bi-stable nonlinear energy sink (MBNES) on torsional vibration suppression of the rotor system. Firstly, the structure of the proposed nonlinear energy sink is introduced, which simultaneously combines a set of positive stiffness connecting rods with the overlapping magnet negative stiffness configurations together to produce the bi-stable characteristic. Furthermore, the analytical expression of the nonlinear torsional stiffness of the MBNES is derived by applying the magnetic charge theorem, and the dynamic model of the rotor-MBNES system is established in turn. Next, the vibration attenuation performances of the MBNES under transient and steady-state excitations are evaluated, respectively, and the parameter affections are studied. Finally, experimental studies are carried out on the coupled system. The results demonstrate that adding MBNES to the main system can obtain 2.22 times dissipating speed in transient response, and the vibration suppression rates of 65.68% in simulation and 54.10% in experiment are achieved in steady-state response.

A nonlinear torsional vibration model of harmonic gear reducer and the effect of various factors on torsional vibration during start and stop

The torsional vibration problems often occur to industrial robots during start and stop due to the use of flexible wheel in harmonic gear reducer as a transmission pair. Because of the influence of nonlinear stiffness, transmission error, and other factors, the nonlinear torsional vibration of harmonic gear reducer will affect the stability and reliability of transmission system. In this article, based on the structural characteristics of the harmonic gear reducer, considering the nonlinear torsional stiffness, transmission error, meshing damping, and other factors, the nonlinear torsional dynamic model of the harmonic gear reducer was established with the theoretical analysis and the experimental results. Based on this model, the influence of various factors such as rotational speed, moment of inertia, torsional stiffness, and transmission error on the nonlinear torsional vibration of harmonic gear reducer was discussed. The results show that the vibration amplitude of harmonic gear reducer increases with the increase of speed, transmission error, and motor inertia, and decreases with the increase of load inertia and damping. The dynamic model and analysis method established in the study can provide the theoretical guidance for the optimal design and the vibration reduction of harmonic gear reducer.

Parametric Investigation of Dual‐Mass Flywheel Based on Driveline Start‐Up Torsional Vibration Control

This paper is aimed to investigate the influence of dual‐mass flywheel (DMF) kinetic parameters on driveline torsional vibration in engine start‐up process, which prescribes the design requirements under start‐up condition for DMF matching. On the basis of driveline excitation analysis during engine start‐up, the analytical model of DMF driveline torsional vibration system is built and simulated. The vehicle start‐up test is conducted and compared with the simulation results. On account of the partial nonstationary characteristic of driveline during start‐up, the start‐up process is separated into 3 phases for discussing the influence of DMF rotary inertia ratio, hysteresis torque, and nonlinear torsional stiffness on attenuation effect. The test and simulation results show that the DMF undergoes severe oscillation when driveline passes through resonance zone, and the research model is verified to be valid. The DMF design requirements under start‐up condition are obtained: the appropriate rotary inertia ratio (the 1st flywheel rotary inertia‐to‐the 2nd flywheel rotary inertia ratio) is 0.7∼1.1; the interval of DMF small torsion angle should be designed as being with small damping, while large damping is demanded in the interval of large torsion angle; DMF should be equipped with low torsional stiffness when working in start‐up process.

Dimensionless modeling and nonlinear analysis of a coupled pitch–plunge–leadlag airfoil-based piezoaeroelastic energy harvesting system

In this paper, an airfoil-based piezoaeroelastic energy harvesting system is proposed with an additional supporting device to harvest the mechanical energy from the leadlag motion. A dimensionless dynamic model is built considering the large-effective-angle-of-attack vibrations causing (1) the nonlinear coupling between the pitch–plunge–leadlag motions, (2) the inertia nonlinearity, and (3) the aerodynamic nonlinearity modeled by the ONERA dynamic stall model. Cubic hardening stiffness is introduced in the pitch degree of freedom for persistent vibrations with acceptable amplitude beyond the flutter boundary. The nonlinear aeroelastic response and the average power output are numerically studied. Limit cycle oscillations are observed and, as the flow velocity exceeds a secondary critical speed, the system experiences complex vibrations. The power output from the leadlag motion is smaller than that from the plunge motion, whereas the gap is narrowed with increasing flow velocity. Case studies are performed toward the effects of several dimensionless system parameters, including the nonlinear torsional stiffness, airfoil mass eccentricity, airfoil radius of gyration, mass of the supporting devices, and load resistances in the external circuits. The optimal parameter values for the power outputs from the plunge and leadlag motions are, respectively, obtained. Beyond the secondary critical speed, it is shown that the variations of the power outputs with those parameters become irregular with fluctuations and multiple local maximums. The bifurcation analysis shows the mutual transitions between the limit cycle oscillations, multi-periodic vibrations, and possible chaos. The influences of these complex vibrations on the power outputs are discussed.

Influence of Nonlinear Stiffness on the Dynamics of a Slender Elastic Beam under Torsional Oscillations

This study focuses on analysing the effects of nonlinear torsional stiffness on the dynam-ics of a slender elastic beam under torsional oscillations, which can be subject to helical buckling.The helical buckling of an elastic beam confined in a cylinder is relevant to many applications. Someexamples include oil drilling, medical cateters and even the conformation and functioning of DNAmolecules. A recent study showed that the formation of the helical configuration is a result of onlythe torsional load, confirming that there is a different path to helical buckling which is not related tothe sinusoidal buckling, stressing the importance of the geometrical behaviour of the beam. A lowdimensional model of an elastic beam under torsional oscillations is used to analyse its dynamical be-haviour with different stiffness characteristics, which are present before and after the helical buckling.Hardening and softening characteristics are present, as the effects of torsion and bending are coupled.With the use of numerical algorithms applied to nonlinear dynamics, such as bifurcation diagramsand basins of attraction, it is shown that the nonlinear stiffness can shift the bifurcations and inducechanges in the stability of the desirable and undesirable solutions. Therefore, the proper modellingof these stiffness nonlinearities seems to be important for a better understanding of the dynamicalbehaviour of such beams

Research on Flexible Joint Stiffness Test and Trajectory Planning of Space Manipulator

Both Natural Coordinate Formulation describing rigid bodies and Absolute Nodal Coordinate Formulation describing flexible bodies are used to model a flexible manipulator with flexible joint and flexible link. The torsional stiffness of flexible joint is tested using a specialized stiffness test equipment, and then the nonlinear torsional stiffness is determined by fitting the experimental data. A new trajectory planning function called the cosine-based function is proposed to design the joint trajectory, which is smoother than the fifth-polynomial and cycloidal motion functions. Finally, a one-link manipulator with flexible joint and flexible link is used to compare the performance of the three trajectory planning functions. Results show that residual vibration can be remarkably reduced by the proposed cosine-based function, which exhibits a significantly better performance than the fifth-polynomial and cycloidal motion functions.

Discrete Model Reference Adaptive Control for Gimbal Servosystem of Control Moment Gyro with Harmonic Drive

The double-gimbal control moment gyro (DGCMG) demands that the gimbal servosystem should have fast response and small overshoot. But due to the low and nonlinear torsional stiffness of harmonic drive, the gimbal servo-system has poor dynamic performance with large overshoot and low bandwidth. In order to improve the dynamic performance of gimbal servo-system, a model reference adaptive control (MRAC) law is introduced in this paper. The model of DGCMG gimbal servo-system with harmonic drive is established, and the adaptive control law based on POPOV super stable theory is designed. The MATLAB simulation results are provided to verify the effectiveness of the proposed control algorithm. The experimental results indicate that the MRAC could increase the bandwidth of gimbal servo-system to 3 Hz and improve the dynamic performance with small overshoot.

Effect of uncertainty on the bifurcation behavior of pitching airfoil stall flutter

In this paper the effect of system parametric uncertainty on the stall flutter bifurcation behavior of a pitching airfoil is studied. The aerodynamic moment on the two-dimensional rigid airfoil with nonlinear torsional stiffness is computed using the ONERA dynamic stall model. The pitch natural frequency, a cubic structural nonlinearity parameter, and the structural equilibrium angle are assumed to be uncertain. The effect on the amplitude of the response, the bifurcation of the probability distribution, and the flutter boundary is considered. It is demonstrated that the system parametric uncertainty results already in 5% probability of pitching stall flutter at a 12.5% earlier position than the point where a deterministic analysis would predict unstable behavior. Probabilistic collocation is found to be more efficient than the Galerkin polynomial chaos method and Monte Carlo simulation for modeling uncertainty in the post-bifurcation domain.

Bifurcation Control of Aeroelastic Limit Cycle Oscillations

An active flutter suppression using linear saturated control is investigated for a 2dof wing section with nonlinear torsional stiffness and limited deflection amplitude of its single control effector. The suppression of limit cycle oscillations in the nonlinear closed-loop system is achieved through maximization of the stability region of the linearized system. A bifurcation sequence leading to limit cycle disappearance is revealed. With increase of the maximum control input amplitude, the closed-loop limit cycle is transformed into a stable torus, which disappears at higher control amplitude through a nonlocal bifurcation similar to a boundary crisis in chaotic systems. Finally, a saddle-node bifurcation of the limit cycle gives necessary conditions for global stability in the closed-loop system.