Dynamic Characteristics of Spur Gear Pair with Dynamic Center Distance and Backlash

Effect of dynamic backlash and rotational speed is investigated on the six-degree-of-freedom model of the gear-bearing system with the time-varying meshing stiffness. The relationship between dynamic backlash and center distance can be defined clearly. The nonlinear differential equations of the model are solved by the Newmark-β method. The results show that system amplitude increases in the wake of increasing rotational speed. After reaching a certain rotational speed, the system jumps from periodic motion to chaos motion, and the effective amplitude is changed violently. Comparing the dynamic backlash with fixed backlash, the amplitude of the dynamic backlash is augmented and the frequency components are diversified. The vibration displacement is enlarged by the dynamic backlash and the chaotic behavior of the system becomes complex with increasing rotational speed. The numerical results provide a useful reference source for engineers to select rotational speed section for steady running.

Nonlinear Dynamics Analysis of a Gear-Shaft-Bearing System with Breathing Crack and Tooth Wear Faults

Considering backlash, time-varying mesh stiffness and radial clearance of bearing, nonlinear dynamic model of gear bearing flexible shaft system is established taking into account breathing crack in shaft and tooth wear. Nonlinear dynamic equations are solved by Runge-Kutta method. Effect of backlash, crack in shaft and tooth wear faults on the nonlinear dynamic behavior of gear-shaft-bearing system is studied. The results show that gear-shaft-bearing system may change from periodic motion to non-periodic motion as backlash increases, and gear pair change from normal mesh to tooth separation, double-sided impact fault. If crack fault appears, quasi-periodic and chaos motion region increases, and gentle crack fault can result in instantaneous tooth separation and double-sided impact faults. Serious tooth wear fault will also induce tooth separation and double-sided impact faults. If both shaft crack and tooth wear faults exist, tooth wear fault will be intensified by double-sided impact fault from shaft crack, which will result in early failure of the gear system.

Chaos Research of Asymmetric System Based on Melnikov Method

Based on Helmholtz-Duffing which is a typical nonlinear asymmetric dynamical system, According to homoclinic bifurcations, prerequisites for chaos motion are obtained by use of Melnikov theory. As a result of verifying the analytic solutions, the safe basin and the phenomena of erosion of the safe basin are simulated by numerical method in the end. The research indicates that the value range of is closely related to the area influenced by the value itself: when is located in the range of from zero to one, the left part of system is mainly affected; when is larger than one, the right part of system is mainly affected. For the same symmetry parameter , there exist a critical frequency at which the threshold value of the amplitudes of both left and right part of system are equal.

Chaos Generation of Induction Motor Based on Time-Delayed State Variable Feedback

In order to realize chaos generation in running process of three-phase AC induction motor, exact linearization via time-delayed state variable feedback is used in this paper. By discussing the condition of exact linearization of induction motor using differential geometry, the induction motor system realizes chaos generation. Running mode changes from steady state to periodic or even chaos motion. Designing the chaos generation controller; getting the chaos generation when induction motor running with this controller. The simulation results show that the time-delayed state variable feedback method which using differential geometry theory design chaos generation on induction motor model is feasible and the control result is satisfied.

The Stiffness Change and Dynamic Characteristics of the RC Frame Weak Layer under Strong Earthquakes

In China Wenchuan earthquake, the main characteristic of reinforced concrete frame structure is the weak layer yielding or collapse. Through the analysis of the stiffness change of the reinforced concrete frame weak layer during the whole process form the elasticity, yielding till collapse, the dynamic characteristics of reinforced concrete frame weak layer in the yielding and collapse processes were discussed. The lateral stiffness of the frame weak layer includes two parts: the lateral stiffness and the equivalent negative stiffness of column under the load action. It is shown that when the value of former decrease to the latter, the weak layer is in a collapse critical status. The frame weaker experiences form steady periodic vibration to variable periodic vibration then aperiodic motion. Some obvious chaos characteristics exist in the aperiodic motion in the plastic stage. It deserves further study to avoid weak layer collapse caused by the chaos motion.

Optimal Control Research for the Wind Turbine PMSG Chaos Motion

In this paper, the dynamic motion of the wind turbine permanent magnet synchronous generator is studied. After the permanent magnet synchronous generator motion is analyzed, the system has a complex chaotic motion in some parameters condition. A controller is designed based on optimal control theory. The optimal controller is used to avoid PMSG chaos and ensure the system is stable. This controller is simple and easy to implement. The simulation results show the whole control system has the good performance. The wind turbine PMSG optimal controller can be used by the other researchers.

Nonlinear Dynamics Analysis of Gear System Considering Unbalance and Loosening Faults

Considering backlash, radial clearance of bearing and time-varying mesh stiffness, nonlinear dynamic model of gear bearing rotor system is established considering unbalance and loosening fault. Nonlinear dynamic equations are solved using Runge-Kutta method and Newton-Raphson method. Numerical simulations of the dynamic equations and the affection of the depth of crack and length of wear to the nonlinear dynamic behavior are studied. The results shows that tooth off, bilateral impact phenomenon are occurred, with increasing gear failure when unbalance occurs, and the gear system exhibits a diverse range of periodic, quasi-periodic and chaotic motion. When loosening fault occurs, the range of chaos motion is increased, and gear burnishing is also intensified.

Multi-Objective Optimization for Rolling Schedule of High Strength Sheet Based on ACPSO

Rolling schedule is an important parameter in high strength production of cold tandem rolling process, and the reasonable rolling schedule setting is important to cutting down energy consumption of unit, endurance of product stable and improving flatness as well as surface quality of sheet. Consequently, according to lots of theory research and spot experiment, taking relative balance of rolling force, flatness well of finished sheet and minimal rolling power as the control goal, the multi-object model for high strength sheet is built. Simultaneously, considering that PSO algorithm has shortcomings of initial randomness and premature convergence, the ACPSO algorithm is proposed which takes advantage of periodicity of the chaos motion and the inertial weight is adjust according to premature convergence extent of particle swarm and accommodate value of individual. It can improve convergence speed and accuracy. When the improved PSO algorithm is applied into rolling schedule model, it has good effect in spot experiment and productive practice.

Experiment Study of Chaos Motion of Cable-Stayed

The cable-stayed is one of the principal force members of cable-stayed bridges. It would be prone to exhibit vibration of large amplitude on the action of wind, earthquake and traffic load,so it reduces the life of stayed cable and even cause destruction. In order to reduce the cable damage, it is very necessary to study the mechanism of vibration of cable-stayed. Experiments are conducted to explore the nonlinear vibration of cable under the periodic external force. A cable model with 14.3 meters long is set up and an acceleration sensor is installed on the midpoint of cable. Time-history acceleration data are obtained by using of acceleration sensor under three cycle load. From the data a Poincare Map is provided and chaos motion is confirmed by using of Smale Horseshoe Map theory.

Study on the Global Bifurcation of Quasi-Zero-Stiffness System

According to the characteristics of the quasi zero stiffness (QZS) system, a dynamics approximation model is established. The effect of excitation force amplitude, frequency and stiffness on the dynamic characteristics of the system is studied by continuation algorithm. The global bifurcation diagram with a wide range of parameters is achieved by using Poincaré mapping method. Results show that when the exciting force amplitude increases to a certain extent, the system will come into multi-cycle and chaos motion state. When exciting force frequency is lower, the system dynamic behavior is complicated, which is helpful for the engineering optimization design.