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.

Improved model to solve influence coefficients of work roll deflection

According to the concept of virtual bending force,a rational explanation for SHOHET's model was presented. Considering the deformation characters of the work rolls in four-high mill,the deformation model of the work roll was regarded as a cantilever beam and new influence coefficients were deduced.The effect of the bending force was taken into account independently. Therefore,the contribution to work roll deflection caused by rolling load,rolling pressure between rolls and bending force can be got from the new formulas.To validate the accuracy of the formulas,the results obtained from the new formulas were compared with those from SHOHET's formulas.It is found that they highly coincide,which illustrates that the formulas are reliable.

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 presencd 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.

Establishment of Constraint Relation of Robot Dynamics Equation Based on Kinematic Influence Coefficients Method

Due to the diversity of work requirements and environment,the number of degrees of freedom(DOFs)and the complexity of structure of industrial robots are constantly increasing.It is difficult to establish the accurate dynamical model of industrial robots,which greatly hinders the realization of a stable,fast and accurate trajectory tracking control.Therefore,the general expression of the constraint relation in the explicit dynamic equation of the multi-DOF industrial robot is derived on the basis of solving the Jacobian matrix and Hessian matrix by using the kinematic influence coefficients method.Moreover,an explicit dynamic equation with general constraint relation expression is established based on the Udwadia-Kalaba theory.The problem of increasing the time of establishing constraint relationship when the multi-DOF industrial robots complete complex task constraints is solved.With the SCARA robot as the research object,the simulation results show that the proposed method can provide a new idea for industrial robot system modeling with complex constraints.

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.

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.

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.

Numerical analysis of elastic coated solids in line contact

A line contact model of elastic coated solids is presented based on the influence coefficients(ICs) of surface displacement and stresses of coating-substrate system and the traditional contact model. The ICs of displacement and stresses are obtained from their corresponding frequency response functions(FRF) by using a conversion method based on fast Fourier transformation(FFT). The contact pressure and the stress field in the subsurface are obtained by employing conjugate gradient method(CGM) and discrete convolution fast Fourier transformation(DC-FFT). Comparison of the contact pressure and subsurface stresses obtained by the numerical method with the exact analytical solutions for Hertz contact is conducted, and the results show that the numerical solution has a very high accuracy and verify the validity of the contact model. The effect of the stiffness and thickness of coatings is further numerically studied. The result shows that the effects on contact pressure and contact width are opposite for hard and soft coatings and are intensified with the increase of coating thickness; the locations of crack initiation and propagation are different for soft and hard coatings; the risk of cracks and delaminations of coatings can be brought down by improving the lubrication condition or optimizing the non-dimensional parameter h/bh. This research offers a tool to numerically analyze the problem of elastic coated solids in line contact and make the blindness and randomness of trial-type coating design less.

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.

An extended input-output table for environmental and resources accounting

Environmentally Extended Input-Output(EEIO)tables have become a powerful element in supporting information-based environmental and economic policies.National-and provincial-level 10 tables are currently published by the National Bureau of Statistics of the People's Republic of China according to well-defined conventions.However,county-level 10tables are not provided as a rule by official statistics organizations.This paper conducts an overview of compiling EEIO tables for environmental and resources accounting at the county level and then answers several questions:First,what kind of data should be prepared for the compilation of county-level EEIO tables?Second,how can we set up comprehensive EEIO tables at the county level?Third,regarding the survey methods and the indirect modeling,which one should be chosen to build EEIO tables at the county level?Finally,what policy questions could such a table answer?EEIO tables at the county level can be used to predict the economic impacts of environmental policies and to perform trend and scenario analysis.

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.

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.

Flow Stress Model of Stainless Steel 0Cr13Ni5Mo at Elevated Temperature

For a more accurate forming calculation and numerical simulation of hydraulic turbine blade, ex- perimental studies on the flow stress of stainless steel 0Crl3Ni5Mo were carried out upon Gleeble-1500 thermal simulator under different deformation conditions. The results then were analyzed and the effects of all influencing factors were summarized consequently. New mathematic models were conceived. Utilizing the software Matlab, regression coefficients were calculated by the least square method. The model has an eminent capability of curve-fitting performance with impact structure whose correlation coefficient is up to 0.908 0 and the cosine coefficient is 0.995 8. All mathematic models and process parameters can be used in engineering calculations or computer simulations.

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.

A preliminary experimental validation of superposition strategy in thermal management of integrated circuit with multiple hot-spots

Thermal management is a key issue in the integrated circuit(IC)design.In this paper,the superposition strategy was experimentally validated using a modeling IC device,which was fabricated by laboratory-level microfabrication technique.Metal thin film resistors on the top of dielectric layer were used to analogize the multiple hot-spots in the modeling IC device.The measured temperature rise with multiple hot-spots agrees well with the predictions given by the superposition calculations.With the help of the superposition strategy,thermal management of IC device can be significantly simplified by decomposing the system into sub-systems and optimizing each part individually.The influence coefficients in the superposition strategy extracted from the experimental measurement offer the IC designers a useful engineering tool to facility the thermal optimization and evaluate the thermal performance of IC devices.

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.