Ting-Nung Shiau

Multi-Objective Optimal Design of Rotor-Bearing Systems under Dynamic Behavior Constraints Using a Hybrid Genetic Algorithm

A new hybrid optimization procedure of rotorbearing systems, which combines the genetic algorithm (GA) with traditional optimization methods, is presented in this paper. Most traditional optimization methods applied in engineering design require a better set of initial values for the design variables, and then converge rapidly to generate good results. In the first step of the procedure, a GA is applied to provide a set of initial design variables, thereby avoiding the trial process; thereafter, traditional algorithms are employed to determine the optimum results. This hybrid algorithm, which can be termed a hybrid genetic algorithm (HGA), is more effective than the traditional ones. The capacity of the HGA is demonstrated by the optimization of rotor-bearing systems under dynamic behavior constraints. The optimization involves minimizing, either individually or simultaneously, the shaft weight and the transmitted forces at the bearings. The results show that an HGA can identify more effectively better initial design variables. Moreover, it can identify superior optimized results; for example, reducing both the shaft weight and transmitted forces of the bearing for rotor-bearing systems under critical speed constraints.

Optimization Combines the Genetic Algorithms With Augmented Lagrange Multiplier Method for Rotor-Bearing Systems Under Dynamic Behavior Constraints

A new optimization strategy for the design of rotor-bearing system was investigated in this study. For most optimization methods applied to rotor-bearing system, it need to select a set of better initial values for design variables to get good results. This trial-and-error process is time consuming and even affects the results. To overcome this difficulty, Genetic Algorithms is applied to provide the set of initial values for design variables and Augmented Lagrange Multiplier Method is employed to determine the optimum results. Furthermore, the hybrid method is applied to minimize, individually or simultaneously, the weight of the shaft and the transmitted forces at the bearings. The results shows that the hybrid method can effectively search the better initial values set for design variables, and further, it can find the superior results to reduce both the shaft weight and the bearing transmitted forces under critical speed constraints.Copyright

Optimization Design of the Geared Rotor System With Critical Speed Constraints Using the Enhanced Genetic Algorithm

This paper presents an efficient enhanced genetic algorithm to minimize the shaft weight, the unbalance response and the response due to the transmission error simultaneously. The minimization plays an important role in designing the geared rotor system under critical speed constraints. In the process of optimization, the design variables consist of shaft inner radii, bearing stiffness and the gear mesh stiffness. The enhanced genetic algorithm of optimization comprises the Hybrid Genetic Algorithm (HGA) and the Interval Genetic Algorithm (IGA). The HGA deals with this optimal design problem and the IGA accomplishes the interval optimization design. The results show that the presented enhanced genetic algorithm can not only effectively reduce the shaft weight and the transmission error response, but also precisely determine the interval ranges of design variables with feasible corresponding objective error.Copyright

Dynamic Spur Geared Rotor Analysis of a Multi-Shaft Turbine With Gear Parameters

The dynamic analysis of the multi-shaft turbine rotor equipped with a spur gear pair for the various gear parameters is studied. Main components of the multi-shaft turbine rotor system include the outer shaft, the inner shaft, the impeller shaft, the oil shaft and the ball bearings. The global assumed mode method (GAMM) is applied to model the rotor motion and the system equation of motion is formulated using Lagrange’s approach. The dynamic behavior of the geared multi-shaft turbine rotor system includes the natural frequency, mode shape and unbalanced response. Numerical results show that large vibration amplitude is observed in steady state at self-excited rotating speed adjacent to the natural frequency. There is no influence of the various pressure angle, modulus, and modification coefficients on unbalance response. Contrary to above cases, the variation of the system unbalance response is dominated by the tooth types rather than the other gear parameters.Copyright

Nonlinear Dynamic Study on Effects of Rub-Impact Caused by Oil-Rupture in a Multi-Shafts Turbine With a Squeeze Film Damper

An investigation is carried out the analysis of nonlinear dynamic behavior on effects of rub-impact caused by oil-rupture in a multi-shafts turbine system with a squeeze film damper. Main components of a multi-shafts turbine system includes an outer shaft, an inner shaft, an impeller shaft, ball bearings and a squeeze film damper. In the squeeze film damper, oil forces can be derived from the short bearing approximation and cavitated film assumption. The system equations of motion are formulated by the global assumed mode method (GAMM) and Lagrange’s approach. The nonlinear behavior of a multi-shafts turbine system which includes the trajectories in time domain, frequency spectra, Poincare maps, and bifurcation diagrams are investigated.Numerical results show that large vibration amplitude is observed in steady state at rotating speed ratio adjacent to the first natural frequency when there is no squeeze film damper. The nonlinear dynamic behavior of a multi-shafts turbine system goes in its way into aperiodic motion due to oil-rupture and it is unlike the usual way (1T = >2T = >4T = >8T etc) as compared to one shaft rotor system. The typical routes of bifurcation to aperiodic motion are observed in a multi-shafts turbine rotor system and they suddenly turn into aperiodic motion from the periodic motion without any transition. Consequently, the increasing of geometric or oil parameters such as clearance or lubricant viscosity will improve the performance of SFD bearing.© 2014 ASME

The Effects of Bearing Stiffness on Nonlinear Dynamic Behaviors of Multi-Mesh Gear Train

In this study, the nonlinear dynamic analysis of the multi-mesh gear train with elastic bearing effect is investigated. The gear system includes the three rigid shafts, two gear pairs and elastic bearings. The stiffness and damper coefficient of elastic bearing are considered. The equations of motion of nonlinear time-varying system are derived using Lagrangian approach. The Runge-Kutta Method is employed to determine the system dynamic behaviors including the bifurcation and chaotic motion. The results show that the periodic motion, quasi-periodical motion and chaos can be excited with the elastic bearing effect. Especially, the results also indicate the dynamic response will go from periodic to quasi-periodical before the chaotic motion when the bearing stiffness is increased.Copyright

Application of the Interval Genetic Algorithm Technique for the Interval Optimization of a Disk Type Piezoelectric Motor

Most of the optimization algorithms in engineering deal with methods, which derive the exact optimal parameters for an optimal design. Actually, exact design parameters are not easy to be manufactured because of manufacturing errors and an expensive manufacturing cost. To overcome this difficulty, a new kind of interval optimization procedure is proposed in this paper. This procedure is denominated as the Interval Genetic Algorithm (IGA), which can determine the interval parameters with an allowable objective error. It can not only neglect the interval analysis in the optimization process but also can maximize the design scope. In this paper, the IGA is applied to the interval optimization of a disk type piezoelectric motor. The results show that the scopes of the single and multi objective interval optimizations can be determined separately. Furthermore, the interval optimization with constrained interval design parameters can also be determined by using the technique of the IGA.

Dynamic Analysis of a Geared Rotor-Bearing System With Viscoelastic Supports Under the Bow Effect

This paper investigates the dynamic behaviors of a geared rotor-bearing system mounted on viscoelastic supports under considerations of the gear eccentricity, excitation of the gear’s transmission error and the residual shaft bow. The finite element method is used to model the system and Lagrangian approach is applied to derive the system equations of motion. The coupling effect of lateral and torsional motions is considered in the system dynamic analysis. The investigated dynamic characteristics include system natural frequencies and steady-state response. The results show that the mass, the stiffness and the loss factor of the viscoelastic support will significantly affect system critical speeds and steady-state response. Larger loss factor and more rigid stiffness of the viscoelastic supports will suppress the systematic amplitude of resonance. Parameters, which include magnitude of the residual bow and phase angle, are also considered in the investigation of their effects on system critical speeds and steady-state response. Results show that they have tremendous influence on first critical speed when the geared system mounted on stiff viscoelastic supports. The transmission error of the gear mesh is assumed to be sinusoidal with tooth passing frequency and it will induce multiple low resonant frequencies in the system response. It is observed that the excited critical speed equals to the original critical speed divided by gear tooth number.Copyright

Dynamic Response of a Geared Rotor-Bearing System Under Residual Shaft Bow Effect

The paper presents the dynamic behaviors of a geared rotor-bearing system under the effects of the residual shaft bow, the gear eccentricity and excitation of gear’s transmission error. The coupling effect of lateral and torsional motions is considered in the dynamic analysis of the geared rotor-bearing system. The finite element method is used to model the system and Lagrangian approach is applied to derive the system equations of motion. The dynamic characteristics including system natural frequencies, mode shapes and steady-state response are investigated. The results show that the magnitude of the residual shaft bow, the phase angle between gear eccentricity and residual shaft bow will significantly affect system natural frequencies and steady-state response. When the spin speed closes to the second critical speed, the system steady state response will be dramatically increased by the residual shaft bow for the in-phase case. Moreover the zero response can be obtained when the system is set on special conditions.Copyright