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

2021 ◽  
Vol 143 (6) ◽  
Author(s):  
Janina Datz ◽  
Mahmoud Karimi ◽  
Steffen Marburg
Keyword(s):  
High Speed ◽  
Probability Distributions ◽  
Probabilistic Method ◽  
Turbine Rotor ◽  
Vibration Response ◽  
Galerkin Projection ◽  
System Response ◽  
Influence Coefficient ◽  
Uncertain Parameters ◽  
Influence Coefficient Method

Abstract 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.

Vibration Signature Analysis of a Rotor Bearing System Using Response Surface Method

2009 ◽  
Author(s):  
P. K. Kankar ◽  
Satish C. Sharma ◽  
S. P. Harsha
Keyword(s):  
Response Surface ◽  
Response Surface Method ◽  
High Speed ◽  
Vibration Response ◽  
Radial Clearance ◽  
System Response ◽  
Surface Waviness ◽  
Surface Method ◽  
Rotor Bearing ◽  
Bearing System

The vibration response of a rotor bearing system is extremely important in industries and is challenged by their highly non-linear and complex properties. This paper focuses on performance prediction using response surface method (RSM), which is essential to the design of high performance rotor bearing system. Response surface method is utilized to analysis the effects of design and operating parameters on the vibration response of a rotor-bearing system. A test rig of high speed rotor supported on rolling bearings is used. Vibration response of the healthy ball bearing and ball bearings with various faults are obtained and analyzed. Distributed defects are considered as surface waviness of the bearing components. Effects of internal radial clearance and surface waviness of the bearing components and their interaction are analyzed using design of experiment (DOE) and RSM.

scholarly journals Active Control for Multinode Unbalanced Vibration of Flexible Spindle Rotor System with Active Magnetic Bearing

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Xiaoli Qiao ◽  
Guojun Hu
Keyword(s):  
High Speed ◽  
Control Method ◽  
Magnetic Bearing ◽  
Rotor System ◽  
Active Magnetic Bearing ◽  
Influence Coefficient ◽  
Control Effect ◽  
High Speed Cutting ◽  
Influence Coefficient Method ◽  
Cutting Processes

The unbalanced vibration of the spindle rotor system in high-speed cutting processes not only seriously affects the surface quality of the machined products, but also greatly reduces the service life of the electric spindle. However, since the unbalanced vibration is often distributed on different node positions, the multinode unbalanced vibration greatly exacerbates the difficulty of vibration control. Based on the traditional influence coefficient method for controlling the vibration of a flexible rotor, the optimal influence coefficient control method with weights for multinode unbalanced vibration of flexible electric spindle rotors is proposed. The unbalanced vibration of all nodes on the whole spindle rotor is used as the control objective function to achieve optimal control. The simulation results show that the method has an obvious control effect on multinode unbalanced vibration.

Further Experiments on Balancing of a High-Speed Flexible Rotor

1974 ◽  
Vol 96 (2) ◽  
pp. 431-440 ◽  
Author(s):  
J. Tonnesen
Keyword(s):  
Computer Program ◽  
Least Squares ◽  
High Speed ◽  
Influence Coefficient ◽  
Flexible Rotor ◽  
Minimum Level ◽  
Absolute Level ◽  
Quality Class ◽  
Influence Coefficient Method ◽  
Coefficient Method

The accuracy of the influence coefficient method is experimentally investigated. The influence of the number of measurement transducers, their location, and type is demonstrated on a flexible rotor where simultaneous balancing is performed in up to five planes and passing through three critical speeds. The correction weights are calculated by means of a computer program, based on a least-squares minimizing procedure. The method itself is shown to be accurate and uses only a minimum of balancing runs to reduce the vibrations to a true minimum level. The overall accuracy in determining the unbalance weights is found to be 4.5 percent. The method’s effectiveness is demonstrated on a rotor with four balancing planes and with unbalance distributed at random in six and seven planes. The absolute level of residual vibrations is found to be in the ISO 0.4 quality class [5].

A Generalized Minmax Influence Coefficient Method for Flexible Rotor Balancing

2005 ◽  
Author(s):  
Costin Untaroiu ◽  
Paul Allaire
Keyword(s):  
High Speed ◽  
Optimization Problem ◽  
Current Method ◽  
Linear Matrix ◽  
Influence Coefficient ◽  
Flexible Rotor ◽  
Influence Coefficient Method ◽  
Rotor Balancing ◽  
Practical Constraints ◽  
Coefficient Method

Rotor balancing is a requirement for the smooth operation of high-speed rotating machinery. In field balancing, minimization of the residual vibrations at important locations/speeds under practical constraints is usually a challenging task. In this paper, the generalized minmax coefficient influence method is formulated as an optimization problem with flexible objective functions and constraints. The optimization problem is cast in a Linear Matrix Inequality (LMI) form and a balancing code is developed to solve it. Two balancing examples are run to verify the efficiency and flexibility of the proposed method. Over the existing methods, current method is more flexible for the various requirements encountered in field balancing and can be solved accurate with current mathematical software.

Dynamics of Spindle-Bearing Systems at High Speeds Including Cutting Load Effects

1998 ◽  
Vol 120 (2) ◽  
pp. 387-394 ◽  
Author(s):  
Bert R. Jorgensen ◽  
Yung C. Shin
Keyword(s):  
Natural Frequency ◽  
High Speed ◽  
Dynamic Models ◽  
Complex Geometry ◽  
Beam Theory ◽  
Coupled System ◽  
Influence Coefficient ◽  
High Speeds ◽  
Spindle Bearing ◽  
Influence Coefficient Method

Increased use of high speed machining creates the need to predict spindle-bearing performance at high speeds. Previous spindle-bearing models simplify either spindle or bearing dynamics to the extent of prohibiting a detailed analysis of a spindle with high speed motion. At high speeds, centrifugal loading in the bearing causes stiffness softening, creating a change in natural frequency. Therefore, spindle modeling requires a comprehensive representation of the dynamics of shafts with complex geometry rotating at high speeds and supported by non-linear bearings. This paper presents a coupled system of spindle and bearing dynamic models with numerical solution. Spindle dynamics are modeled using the influence coefficient method of discrete lumped masses, based on Timoshenko beam theory. Both linear and rotational bearing stiffness are included in the spindle model through solution of the angular-contact bearing model. The parameters of cutting loads, tool mass, and rotational speed are analyzed, and all are shown to affect the natural frequency. The computer model is both rapid and robust, and shows excellent agreement with experimental analysis.

scholarly journals Probabilistic and Nonprobabilistic Sensitivity Analyses of Uncertain Parameters

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Sheng-En Fang ◽  
Qiu-Hu Zhang ◽  
Bao Zhang ◽  
Xiao-Hua Zhang
Keyword(s):  
Probability Distributions ◽  
Probabilistic Method ◽  
Sensitivity Analyses ◽  
Uncertain Parameters ◽  
Stochastic Response ◽  
First Order ◽  
Simple Implementation ◽  
Probability Information ◽  
Main Effects ◽  
Mathematical Derivation

Parameter sensitivity analyses have been widely applied to industrial problems for evaluating parameter significance, effects on responses, uncertainty influence, and so forth. In the interest of simple implementation and computational efficiency, this study has developed two sensitivity analysis methods corresponding to the situations with or without sufficient probability information. The probabilistic method is established with the aid of the stochastic response surface and the mathematical derivation proves that the coefficients of first-order items embody the parameter main effects on the response. Simultaneously, a nonprobabilistic interval analysis based method is brought forward for the circumstance when the parameter probability distributions are unknown. The two methods have been verified against a numerical beam example with their accuracy compared to that of a traditional variance-based method. The analysis results have demonstrated the reliability and accuracy of the developed methods. And their suitability for different situations has also been discussed.

Missile Probability Analysis of Welding Nuclear Turbine Rotor

2014 ◽  
Author(s):  
Rong Chen ◽  
Wen Xiang Hua ◽  
Yan Lei Yang ◽  
Xiao Zhong He
Keyword(s):  
High Speed ◽  
Nuclear Power ◽  
Probabilistic Method ◽  
Nuclear Regulatory Commission ◽  
Turbine Rotor ◽  
Element Analysis ◽  
Generator System ◽  
Analysis Process ◽  
Start Up ◽  
Regulatory Commission

In this paper, a 1000MW nuclear turbine LP welded rotor was analyzed to assure the missile safety of the turbine, which is required by the Nuclear Regulatory Commission (NRC). Finite element analysis method was used to estimate the stress level of the rotor. Stress corrosion cracking (SCC) was considered as the main reason of the rotor failure. The probabilistic method was used to assess the missile safety of the turbine rotor. The high speed turbine rotor is one of the key components of the turbine-generator system which was related closely to the safety and economy of the Power Plant’s operation. In this paper the rotor design & analysis process for the Shanghai Turbine Plant’s nuclear 1000MW power station is described. The operation of the turbine rotors of the nuclear power plant suffered from the severe stresses because of high temperature and high speed during start-up, shutdown and load changes. The moisture steam environment due to the low nuclear steam temperature also increase the probability of the fatigue failure of the turbine rotor. The integrity of the turbine rotor was threatened by the material deterioration caused by fatigue and moisture corrosion of the rotor at some critical locations. The fatigue mechanisms of the turbine rotor are described. Key factors that influence missile probability are discussed. Rotor damage due to SCC is discussed and analyzed to evaluate the probability of the nuclear turbine rotor.

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

2021 ◽  
Vol 13 (4) ◽  
pp. 168781402110073
Author(s):  
Wangqun Deng ◽  
Mengyu Tong ◽  
Qingyang Zheng ◽  
Xingmin Ren ◽  
Yongfeng Yang
Keyword(s):  
Turbine Rotor ◽  
Influence Coefficient ◽  
Type I ◽  
Dynamic Balancing ◽  
Single Plane ◽  
Transient Dynamic ◽  
Butterworth Filter ◽  
Power Turbine ◽  
Influence Coefficient Method ◽  
Coefficient Method

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.

Research on Calibration Method of Tire Dynamic Balance Detection System

2012 ◽  
Vol 542-543 ◽  
pp. 828-832 ◽  
Author(s):  
Jing Fang Yang ◽  
Xian Ying Feng ◽  
Hong Jun Fu ◽  
Lian Fang Zhao
Keyword(s):  
High Speed ◽  
Detection System ◽  
Dynamic Balance ◽  
Calibration Method ◽  
Engineering Practice ◽  
Influence Coefficient ◽  
Quality Factors ◽  
High Speed Rotation ◽  
Speed Rotation ◽  
Upper Rim

Tire dynamic balance detection plays an important part in tire quality detection area. This paper uses the two-sided balance method to obtain the unbalance of the tire. According to the engineering practice, builds kinetic model and then introduces the calculating principle and operating procedures. In order to accurately determine the influence coefficient, a calibration method without tire is put forward. Further more, this new method is able to eliminate the unbalance caused by non-quality factors to some extent. But this method is presented based on the relative position invariance of the upper rim and lower rim, even both of them are under high-speed rotation situation. Finally, the experimental data acquired from both of the two methods are compared. The calibration method without tire is proved to be more feasible, efficient and accurate.

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