Review of All Possible Conversion Equations of Influence Coefficients with Different Formats on Two-Plane Balancing

This article lists all possible conversion equations of influence coefficients(ICs)with different formats when some of these are known to handle two-plane balancing tasks with no or less trial weight runs.There are two approaches for two-plane balancing.One can treat it as a multi-plane balance problem involving a 2×2 matrix of complex ICs where two direct ICs along with two cross-effect ICs are generated so that correction weights at one or two balance planes can be determined.One can also apply a static pare(in-phase)and/or couple pair(180 degrees out-of-phase)weights for balancing.The latter approach has been used quite often in the field,especially on steam turbine and generator rotors.Dependent on vibration mode shapes and combinations as well as balance plane accessibility,sometimes applying static or couple pair weights can be a wise choice;other times weights at one or two end planes are needed.There are totally 4 possible sets of IC data due to weights at plane 1,plane 2,static pair,and couple pair.IC data would typically be obtained by applying trial weights followed by trial weight runs.It is found,however,that all these IC data can be converted easily without trial weight runs once any two of 4 sets are known.The above findings and conversion equations have been obtained analytically and verified by experimental results.Real cases are given to demonstratetheirapplications.

Hierarchical Bayesian Calibration and On-line Updating Method for Influence Coefficient of Automatic Dynamic Balancing Machine

Measurement error of unbalance＇s vibration response plays a crucial role in calibration and on-line updating of influence coefficient（IC）. Focusing on the two problems that the moment estimator of data used in calibration process cannot fulfill the accuracy requirement under small sample and the disturbance of measurement error cannot be effectively suppressed in updating process, an IC calibration and on-line updating method based on hierarchical Bayesian method for automatic dynamic balancing machine was proposed. During calibration process, for the repeatedly-measured data obtained from experiments with different trial weights, according to the fact that measurement error of each sensor had the same statistical characteristics, the joint posterior distribution model for the true values of the vibration response under all trial weights and measurement error was established. During the updating process, information obtained from calibration was regarded as prior information, which was utilized to update the posterior distribution of IC combined with the real-time reference information to implement online updating. Moreover, Gibbs sampling method of Markov Chain Monte Carlo（MCMC） was adopted to obtain the maximum posterior estimation of parameters to be estimated. On the independent developed dynamic balancing testbed, prediction was carried out for multiple groups of data through the proposed method and the traditional method respectively, the result indicated that estimator of influence coefficient obtained through the proposed method had higher accuracy; the proposed updating method more effectively guaranteed the measurement accuracy during the whole producing process, and meantime more reasonably compromised between the sensitivity of IC change and suppression of randomness of vibration response.

The Application of Ridge Regression in Dynamic Balancing of Flexible Rotors Based on Influence Coefficient Method

Based on the model structure of the influence coefficient method analyzed in depth by matrix theory,it is explained the reason why the unreasonable and instable correction masses with bigger MSE are obtained by LS influence coefficient method when there are correlation planes in the dynamic balancing.It also presened the new ridge regression method for solving correction masses according to the Tikhonov regularization theory,and described the reason why the ridge regression can eliminate the disadvantage of the LS method. Applying this new method to dynamic balancing of gas turbine, it is found that this method is superior to the LS method when influence coefficient matrix is ill-conditioned,the minimal correction masses and residual vibration are obtained in the dynamic balancing of rotors.

Use of Conversion Equations of Influence Coefficients on Two-Plane Balancing

Typical rotors such as those on steam turbine or generator are often supported by two bearings with two balance planes at both ends.Vibrations are monitored by a pair of proximity probes at each bearing.There are two approaches to reduce 1X vibration due to unbalance at both ends via balancing with influence coefficient method.The first approach is to treat it as a multiple-plane balancing problem involving 2x2 matrix of complex influence coefficients.The second approach is to treat it as two single-plane balance problems using static(in-phase)and couple(180 degree out-of-phase)components,respectively.Conversion equations of influence coefficients between these two approaches have been found previously by the author.The corresponding spreadsheets that convert influence coefficients between these two formats are presented in the current paper.The paper shows effectiveness of these conversion equations in dealing with real balancing problems in the field.A detailed balance case is presented to demonstrate how the conversion equations are used to reduce vibration effectively.

Influence of Polar Pressure Transmission Medium on the Pressure Coefficient of Excitonic Interband Transitions in Monolayer WSe_2

The influence of the pressure transmission medium（PTM）on the excitonic interband transitions in monolayer tungsten diselenide（WSe2）is investigated using photoluminescence（PL）spectra under hydrostatic pressure up to 5GPa.Three kinds of PTMs,condensed argon（Ar）,1：1 n-pentane and isopentane mixture（PM）,and4：1 methanol and ethanol mixture（MEM,a PTM with polarity）,are used.It is found that when either Ar or PM is used as the PTM,the PL peak of exciton related to the direct K-K interband transition shows a pressure-induced blue-shift at a rate of 32±4 or 32±1 meV/GPa,while it turns to be 50±9meV/GPa when MEM is used as the PTM.The indirect A-K interband transition presents almost no shift with increasing pressure up to approximatel.y 5 GPa when Ar and PM are used as the PTM,while it shows a red-shift at the rate of-17±7meV/GPa by using MEM as the PTM.These results reveal that the optical interband transitions of monolayer WSe2 are very sensitive to the polarity of the PTM.The anomalous pressure coefficient obtained using the polar PTM of MEM is ascribed to the existence of hydrogen-like bonds between hydroxyl in MEM and Se atoms under hydrostatic pressure.

Model Building of Backup Roller Diameter Effect Rate in 4-High Mill

Software for calculating the strip profile in 4-high hot rolling mill was developed using influence coefficient method. Regularity of backup roller diameter effect rate was studied systematically using the software. The results show that backup roller diameter effect rates decrease versus the increase of strip width, increase significantly versus the increase of backup roller diameter and obscurely increase versus the increase of reduction. The difference between backup roller diameter effect rate and it is reference value increases versus strip width increasing. When backup rollers diameter is set to be 1.64 m and strip width is 1.85 m, the error of strip profile calculated using the model of backup roller diameter effect rate reference value will be 3.55μm. Based on the results, reference values of roller diameter effect rate and six power polynomial fitting coefficients of modification coefficients were determined considering coherent parameters. The high precision model of backup roller diameter effect rate was established. When the model is used to predict strip profile, the accuracy is less than 5.0 μm.

Model and algorithm of flow interception problem with multi-type of flows

To study simultaneous location of different kinds of facilities, a new model of flow interception problem with multi-type of flows is proposed, with the consideration of multi-purpose flows and the influence of facilities on each other. To be more practical, the objective is to maximize the benefits from flow-by customers instead of maximizing flows in the past. Since this problem is NP-hard and there is no optimal solution for large network, greedy and improved greedy heuristic algorithms are proposed. A computational example is presented to show that the optimal location decisions are proved to be strongly dependent on the influence coefficients and average profits by one customer and different types of facilities are almost co-located. Finally the results of sensitivity analysis are reported.

Seismic Analysis of the Connections of Buried Segmented Pipes

Seismic analysis of buried pipes has been one study focus during the last decades,but the systematic seismic research of pipe connections,especially its relationship with the connected straight pipe,is nearly blank.On the basis,the influence of pipe connections on the joint deformations(JDs)of buried segmented pipes is analyzed in detail by considering different parameters,namely,connection shapes,ground conditions,pipe diameters,branch angles,seismic incident angles,and input ground motions.Moreover,an influence coefficient,which measures the influence of pipe connections on pipe JDs,is calculated.Results show that pipe connections can reduce the JDs of segmented pipes by 40%-50%.Furthermore,the JD is more sensitive to the connection shape,ground condition and pipe diameter than the incident angle and characteristics of seismic waves.An influence coefficient of 0.65 is recommended conservatively for the design of the buried segmented pipes.

Collaborative force and shape control for large composite fuselage panels assembly

This study proposed a force and shape collaborative control method that combined method of influence coefficients(MIC)and the elitist nondominated sorting genetic algorithm(NSGA-II)to reduce the shape deviation caused by manufacturing errors,gravity deformation,and fixturing errors and improve the shape accuracy of the assembled large composite fuselage panel.This study used a multi-point flexible assembly system driven by hexapod parallel robots.The proposed method simultaneously considers the shape deviation and assembly load of the panel.First,a multi-point flexible assembly system driven by hexapod parallel robots was introduced,with the relevant variables defined in the control process.In addition,the corresponding mathematical model was constructed.Subsequently,MIC was used to establish the prediction models between the displacements of actuators and displacements of panel shape control points,deformation loads applied by the actuators.Following the modeling,the shape deviation of the panel and the assembly load were used as the optimization objectives,and the displacements of actuators were optimized using NSGA-II.Finally,a typical composite fuselage panel case study was considered to demonstrate the effectiveness of the proposed method.

Balancing method without trial weights for rotor systems based on similitude scale model

A balancing method without trial weights based on the dynamic similitude scale model was proposed as a solution to the balancing problem of a large-scale rotor system. This method could be used to directly obtain the required coefficients for the balancing problem of the prototype system through a similarity model test without a prototype test. Thus, the weight test process of the prototype system was effectively eliminated in the proposed balancing method. First, with the rotor system as the research object, the analytical expression of the influence coefficient was derived on the basis of rotor dynamics theory. Then, through calculation and dimen- sional analysis methods, the similitude relationships of the rotor system and the influence coefficient were deduced on the basis of dynamic similitude theory. The correctness of the proposed similitude relationships was verified through numerical simulation and experiment. The balancing method without trial weights was proposed based on the similitude relationship of the influence coefficient. The effect of the balancing method without trial weights was compared with that of the traditional influence coefficient method through numerical simulation, and the results verified the correctness and effectiveness of the proposed balancing method. The results of this study provide theoretical supplements for the balancing method and the similitude design of the rotor system.

A reduced order model for coupled mode cascade flutter analysis

A Reduced Order Model(ROM)based analysis method for turbomachinery cascade coupled mode flutter is presented in this paper.The unsteady aerodynamic model is established by a system identification technique combined with a set of Aerodynamic Influence Coefficients(AIC).Subsequently,the aerodynamic model is encoded into the state space and then coupled with the structural dynamic equations,resulting in a ROM of the cascade aeroelasticity.The cascade flutter can be determined by solving the eigenvalues of the ROM.Bending-torsional coupled mode flutter analysis for the Standard Configuration Eleven(SC11)cascade is used to validate the proposed method.

Drum of CTP Device Dynamic Balance Based on Theory of Wavelet Transform

Conclusion is that the soft threshold de-noising effect is better than hard threshold de-noising though the signal to noise ratio and Root Mean Square error. After analyzing, de-noising and reconstructing signal through wavelet packet from Matlab software, the average value of peak extracted from signal reconstruction is gotten to provide data for dynamic balance. Making use of the influence coefficient method to adjust drum of CTP dynamic balance, the program of Matlab is used to find phase position and weight of the mass block quickly, which can provide evidence for software for dynamic balance developed.

An invariant descriptor for conjugate forced convection-conduction cooling of 3D protruding heaters in channel flow

In this research, the temperatures of three- dimensional （3D） protruding heaters mounted on a conductive substrate in a horizontal rectangular channel with laminar airflow are related to the independent power dissipation in each heater by using a matrix G＋ with invariant coefficients, which are dimensionless. These coefficients are defined in this study as the conjugate influence coefficients （g＋） caused by the forced convec- tion-conduction nature of the heaters＇ cooling process. The temperature increase of each heater in the channel is quantified to clearly identify the contributions attributed to the self-heating and power dissipation in the other heaters （both upstream and downstream）. The conjugate coefficients are invariant with the heat generation rate in the array of heaters when assuming a defined geometry, invariable fluid and flow rate, and constant substrate and heater conductivities. The results are numerically obtained by considering three 3D protruding heaters on a twodimensional （2D） array by ANSYS/FluentTM 15.0 software. The conservation equations are solved by a coupled procedure within a single calculation domain comprising of solid and fluid regions and by considering a steady state laminar airflow with constant properties. Some examples are shown, indicating the effects of substrate thermal conductivity and Reynolds number on conjugate influence coefficients.

Efficient Determination of Turbomachinery Blade Aero-Damping Curves for Flutter Assessment via Trigonometric Interpolation

Proposed in the paper is a trigonometric interpolation method for efficient determination of turbomachinery blade aero-damping curves which are required in a flutter assessment.The trigonometric interpolation method was proposed to be incorporated with the widely used travelling wave method to replace the influence coefficient method.Through analyzing aero-damping/worksum at a few carefully chosen nodal diameters,trigonometric interpolation was applied through existing data points to get aero-damping/worksum at the rest nodal diameters.The proposed approach is much more efficient than the travelling wave method for determining the aero-damping curve of a blade.In principle,the method can be as efficient as the influence coefficient method.Unlike the influence coefficient method,the trigonometric interpolation method does not involve linear superposition,and it can include nonlinear effect and is expected to be more accurate.Two test cases were provided to validate the proposed method and demonstrate its effectiveness.The method is not only effective,but also very easy to be incorporated into existing widely used aero-damping/worksum analysis system using the travelling wave method.

Effect of Initial Crown on Shape of Hot Rolled Strip

Based on the influence coefficient method, the effect of entry strip crown on the shape of hot rolled strip was analyzed using the software of roll elastic deformation simulation. According to the practical condition of a domestic hot rolled strip plant, the unit strip crown change from the first stand to the last stand was calculated when the entry crown of hot strip varies. The calculated result shows that the entry strip crown does not significantly affect the target strip crown at the exit of the last finishing stand in respect to a fixed strip shape control reference （such as bending force）. The calculation was analyzed, and the research is helpful in modeling strip shape setup and shape control.

Analysis of the influencing factors of PAEs volatilization from typical plastic products

The primary emphasis of this research was to investigate the foundations of phthalate（PAEs） pollutant source researches and then firstly confirmed the concept of the coefficient of volatile strength, namely phthalate total content in per unit mass and unit surface area of pollutant sources. Through surveying and evaluating the coefficient of volatile strength of PAEs from typical plastic products, this research carried out reasonable classification of PAEs pollutant sources into three categories and then investigated the relationship amongst the coefficient of volatile strength as well as other environmental factors and the concentration level of total PAEs in indoor air measured in environment chambers.Research obtained phthalate concentration results under different temperature, humidity,the coefficient of volatile strength and the closed time through the chamber experiment. In addition, this study further explored the correlation and ratio of influencing factors that affect the concentration level of total PAEs in environment chambers, including environmental factors, the coefficient of volatile strengths of PAEs and contents of total PAEs in plastic products. The research created an improved database system of phthalate the coefficient of volatile strengths of each type of plastic goods, and tentatively revealed that the volatile patterns of PAEs from different typical plastic goods, finally confirmed that the coefficient of volatile strengths of PAEs is a major factor that affects the indoor air total PAEs concentration, which laid a solid foundation for further establishing the volatile equation of PAEs from plastic products.

Experimental Study of the Shear Capacity of Glass Fiber Reinforced Polymer Reinforced Concrete Beam with Circular Cross Section

In order to research the shear behavior of glass fiber reinforced polymer (GFRP) reinforced concrete beam with circular cross section, based on the test results of 36 concrete beams subjected to four-point loading up to failure, the shear capacity and mechanical properties of deformation were analyzed comparatively between GFRP reinforced concrete (GFRP-RC) beams and steel reinforced concrete (steel-RC) beams. Furthermore, influencing factors of shear capacity of GFRP-RC beam with circular cross section were also investigated. The test results indicate that the failure modes of GFRP-RC and steel-RC beams are the same, but the crack patterns are slightly different. And, the shear capacity of GFRP-RC beam firstly increases with the reduction of shear span ratio, and then decreases. In addition, it was found that the influencing coefficient of GFRP on concrete increases with shear span ratio reducing.