Dynamics of a Gear System with Faults in Meshing Stiffness

Gear box dynamics is characterised by a periodically changing stiffness. In real gear systems, a backlash also exists that can lead to a loss in contact between the teeth. Due to this loss of contact the gear has piecewise linear stiffness characteristics, and the gears can vibrate regularly and chaotically. In this paper we examine the effect of tooth shape imperfections and defects. Using standard methods for nonlinear systems we examine the dynamics of gear systems with various faults in meshing stiffness.Comment: 10 pages, 8 figure

The effect of preload and surface roughness quality on linear joint model parameters

The physical parameters of the contact interfaces, such as preload and surface roughness quality, significantly affect the stiffness of joints. Knowledge of the relationship between these interface parameters and the equivalent stiffness allows joints to be considered in the design stages of complex structures. Hence, this paper considers the effect of contact interface parameters on the identified equivalent stiffness parameters of joint models. First, a new generic joint model is proposed to model the contact interfaces. Then, the ability of three different joint models, including the new model proposed in this paper, to capture the linear effects of contact interfaces under different preloads and surface roughness qualities is investigated. Finally, it is concluded that the preload and surface roughness quality control the normal and shearing stiffness of the joint models respectively. Experimental investigations also reveal that a complex mechanism governs the energy dissipation in the contact interface

Normal form analysis of bouncing cycles in isotropic rotor stator contact problems

This work considers analysis of sustained bouncing responses of rotating shafts with nonlinear lateral vibrations due to rotor stator contact. The insight that this is an internal resonance phenomena makes this an ideal system to be studied with the method of normal forms, which assumes that a system may be modelled primarily in terms of just its resonant response components. However, the presence of large non smooth nonlinearities due to impact and rub mean that the method must be extended. This is achieved here by incorporating an alternating frequency/time (AFT) step to capture nonlinear forces. Furthermore, the presence of gyroscopic terms leads to the need to handle complex modal variables, and a rotating coordinate frame must be used to obtain periodic responses. The process results in an elegant formulation that can provide reduced order models of a wide variety of rotor systems, with potentially many nonlinear degrees of freedom. The method is demonstrated by comparing against time simulation of two example rotors, demonstrating high precision on a simple model and approximate precision on a larger model

Dual-Quaternion-Based Fault-Tolerant Control for Spacecraft Tracking With Finite-Time Convergence

Results are presented for a study of dual-quaternion-based fault-tolerant control for spacecraft tracking. First, a six-degrees-of-freedom dynamic model under a dual-quaternion-based description is employed to describe the relative coupled motion of a target-pursuer spacecraft tracking system. Then, a novel fault-tolerant control method is proposed to enable the pursuer to track the attitude and the position of the target even though its actuators have multiple faults. Furthermore, based on a novel time-varying sliding manifold, finite-time stability of the closed-loop system is theoretically guaranteed, and the convergence time of the system can be given explicitly. Multiple-task capability of the proposed control law is further demonstrated in the presence of disturbances and parametric uncertainties. Finally, numerical simulations are presented to demonstrate the effectiveness and advantages of the proposed control method

An Optimization-Based Framework for Nonlinear Model Selection and Identification

This paper proposes an optimization-based framework to determine the type of nonlinear model present and identify its parameters. The objective in this optimization problem is to identify the parameters of a nonlinear model by minimizing the differences between the experimental and analytical responses at the measured coordinates of the nonlinear structure. The application of the method is demonstrated on a clamped beam subjected to a nonlinear electromagnetic force. In the proposed method, the assumption is that the form of nonlinear force is not known. For this reason, one may assume that any nonlinear force can be described using a Taylor series expansion. In this paper, four different possible nonlinear forms are assumed to model the electromagnetic force. The parameters of these four nonlinear models are identified from experimental data obtained from a series of stepped-sine vibration tests with constant acceleration base excitation. It is found that a nonlinear model consisting of linear damping and linear, quadratic, cubic, and fifth order stiffness provides excellent agreement between the predicted responses and the corresponding measured responses. It is also shown that adding a quadratic nonlinear damping does not lead to a significant improvement in the results

A Relationship Between Defective Systems and Unit-Rank Modification of Classical Damping

A common assumption within the mathematical modeling of vibrating elastomechanical system is that the damping matrix can be diagonalized by the modal matrix of the undamped model. These damping models are sometimes called "classical" or "proportional." Moreover it is well known that in case of a repeated eigenvalue of multiplicity m, there may not exist a full sub-basis of m linearly independent eigenvectors. These systems are generally termed "defective." This technical brief addresses a relation between a unit-rank modification of a classical damping matrix and defective systems. It is demonstrated that if a rankone modification of the damping matrix leads to a repeated eigenvalue, which is not an eigenvalue of the unmodified system, then the modified system is defective. Therefore defective systems are much more common in mechanical systems with general viscous damping than previously thought, and this conclusion should provide strong motivation for more detailed study of defective systems