Review of Rotor Balancing Methods

This review is dedicated to balancing methods that are used to solve the rotor-balancing problem. To ensure a stable operation over an operating speed range, it is necessary to balance a rotor. The traditional methods, including the influence coefficient method (ICM) and the modal balancing method (MBM) are introduced, and the research progress, operation steps, advantages and disadvantages of these methods are elaborated. The classification of new balancing methods is reviewed. Readers are expected to obtain an overview of the research progress of existing balancing methods and the directions for future studies.

Investigation on transient dynamic balancing of the power turbine rotor and its application

In the dynamic balancing procedure of the rotor system, the unbalance is determined as a principal parameter which should be identified firstly. In actual engineering, the interference of external noise on the rotor is usually the main factor influencing the identification. In this paper, we focus on the unbalance identification of the power turbine rotor while the vibration response is influenced by signal interference during the balancing process in actual engineering. Fast Fourier Transform (FFT) and wavelet transform are used to analyze the collected original signal. Butterworth filter and Chebyshev type I filter are employed to test signal processing. The transient dynamic balancing method and the single plane influence coefficient method are used to balance the three balancing bosses of the rotor, and the balance efficiency is compared. The results show that, the signal fluctuation of boss 3 in high-frequency band is less than boss 1 and boss 2. Butterworth filter is more effective than Chebyshev type I filter in filtering the transient response data. The transient dynamic balancing method requires one test run without any trial-weights. More importantly, compared with the influence coefficient method, the transient dynamic balancing method has a better balancing effect.

Investigation of the tribological performance of reciprocating seals in a wide temperature range

Reciprocating seals are widely used in general industrial machines and are designed to endure rigorous working conditions. Among the harshest challenges, the wide temperature range they withstand has a significant influence on their sealing performance. However, most studies of reciprocating seals have focused only on their sealing characteristics at normal temperatures. To investigate the impacts of temperature on the seal's tribological performance, this paper examines the VL seal, a kind of combined seals, and discusses its performance in a wide temperature range. Material properties of the VL seal at temperatures from −55 °C to 135 °C are measured based on the seal product. The thermo-viscosity effect and the influence of thermal expansion and contraction are both considered in the reciprocating seal modelling. A coupling method that combines the finite-element analysis model with a mixed-lubrication procedure is implemented. For deformation calculation, a comparison between the influence coefficient method and the semi-infinite space method is conducted, and finds only minuscule disparities for the VL-seal analysis. To avoid the divergent problem due to high viscosity at low temperatures, this paper proposes the successive approaching method. Details of the sealing zone in the outstroke and instroke are systematically discussed in relation to a wide range of temperatures. The corresponding experiments are conducted and compared with the simulation. The results indicate that the temperature has a tremendous influence on the tribological performance. The leakage and the friction at the high temperature are much higher than those at the normal temperature.

Influence-Coefficient Method for Identifying Maximum-Load Configurations and Variable-Load Issues in Manipulators

The dimensioning of general-purpose machines such as manipulators involves the solution of a number of preliminary issues. The determination of reference external loads and the identification of machine configurations that give the maximum internal load for each component are two of these issues. These two problems are commonly addressed through trial-and-error procedures based on dynamic modelling, which are implemented with the support of simulation software, since static analyses are commonly considered inadequate to solve them. Despite this, here, a technique based on influence coefficients and static analyses is presented which solves them. Such technique is also able to foresee and justify dynamic issues (i.e., possible vibrations, etc.) that could heavily affect the machine behavior. The effectiveness of the proposed technique is proved by implementing it on a 3T1R parallel manipulator. The presented design method is general and applicable to any type of non-overconstrained manipulator or mechanism.

Effect of Uncertainty in the Balancing Weights on the Vibration Response of a High-Speed Rotor

This work investigates how uncertainties in the balancing weights are propagating into the vibration response of a high-speed rotor. Balancing data are obtained from a 166-MW gas turbine rotor in a vacuum balancing tunnel. The influence coefficient method is then implemented to characterize the rotor system by a deterministic multi-speed and multi-plane matrix. To model the uncertainties, a non-sampling probabilistic method based on the generalized polynomial chaos expansion (gPCE) is employed. The uncertain parameters including the mass and angular positions of the balancing weights are then expressed by gPCE with deterministic coefficients. Assuming predefined probability distributions of the uncertain parameters, the stochastic Galerkin projection is applied to calculate the coefficients for the input parameters. Furthermore, the vibration amplitudes of the rotor response are represented by appropriate gPCE with unknown deterministic coefficients. These unknown coefficients are determined using the stochastic collocation method by evaluating the gPCE for the system response at a set of collocation points. The effects of individual and combined uncertain parameters from a single and multiple balancing planes on the rotor vibration response are examined. Results are compared with the Monte Carlo simulations, showing excellent agreement.

Efficient Steady and Unsteady Flow Modeling for Arbitrarily Mis-Staggered Bladerow Under Influence of Inlet Distortion

Accurate and efficient predictions of the steady and unsteady flow responses due to the blade-to-blade variation as well as due to the non-axisymmetric inlet distortion have been continually pursued. Computation of two problems concurrently has been rarely done in the past partly because of the need to perform whole annulus bladerow simulations, despite the advances in the current state-of-the-art methods with the phaseshift single passage simulations. The current work attempts to deal with this challenge by developing a new computational approach based on the principle of the multiscale method in the framework of a commercial solver (CFX). The methodology formulation relies on summation of the constituent source terms, each of which corresponds to a particular flow perturbation. The source term element corresponding to the blade-to-blade variation effect is linearly superimposed as in the classical Influence Coefficient Method. Only the relative positions between the reference blade and its neighbor matter in this method, thus enables an arbitrarily mis-staggered bladerow to be computed efficiently. In addition, the source term arisen due to the inlet distortion is calculated based on spatial Fourier transform. A key enabler is that the source term can be pre-computed using a small set of identical blade passages. The source term is then propagated to different spatial and temporal locations depending on the combination of the mis-staggering pattern and the inlet distortion. The multiscale treatment makes it possible to predict a high-resolution flow field effects on the base coarse mesh as if the fine mesh is solved, while achieving a computational gain. The source term summation method proposed in the current work has been validated using a uniformly staggered bladerow, and an arbitrarily mis-staggered bladerow in a clean inflow condition as well as that subject to an inlet distortion.

Experimental Study on Flutter Stability of Transonic Cooled Turbine Blade Stage With 3-Dimensional Mode Shape Excitation

It is well known that mode shape plays very important role in stability of turbine blade since the aerodynamic work per cycle and aerodynamic damping depend on mode shape. With the advancements of theoretical formulation with influence coefficient method, experimental studies with rigid body blade motion have significantly improved understanding of turbine flutter mechanisms and design parameters. However rigid body motion cannot accurately match the complex mode shapes of modern turbine blade, so there are limitations of accuracy on experimental evaluation of flutter stability with rigid body blade motion. This study utilized 3-dimensional mode shapes for evaluating aerodynamic work per cycle and stability of turbine blade through experimental method. A transonic annulus turbine cascade rig was built at Notre Dame Turbomachinery Laboratory. Three center blades with modern cooled 3-dimensional aero design were instrumented with 144 EA of ultraminiature fast-response pressure transducers on the blade surface at 50%, 75%, and 95% of blade spans. Center blade and adjacent blades were designed to have the same blade mode shape as a reference turbine blade and the center blade was actuated with an electromagnetic shaker at natural frequencies of 1st bending and 1st torsional modes to simulate the same level of reduced frequencies under engine operating condition. Mode shape scanning of test blade through laser doppler vibrometer confirmed the design intent of blade bending and torsional mode shapes and their frequencies. All the dynamic pressure measurements on the three center blades were synchronized with blade position measurement and influence coefficient method was applied to calculate aerodynamic work per cycle and damping parameter. It was found that pressure side generally stabilizes the blade and that there was strong stable zone from leading edge to about 20% in arcwise coordinate torward suction side. After this zone, a destabilizing zone follows and this can be strong enough to destabilize the blade in some range of nodal diameter.