Study On Simultaneous Identification Of Rotor Unbalance And Bearing Coefficients Of A Rotor

Identification of rotor unbalance and support dynamic coefficients plays a critical role in operation safety of large rotating machinery,which is always the research focus of rotor dynamics.However,it has not been well solved yet.Relationship between the dynamic characteristics of rotor-bearing system and the key characteristic parameters in dynamics such as bearing stiffness and damping parameters and unbalance parameters are very complex,which plays an important role in operation safety of large rotating machinery.However,it is difficult to obtain bearing dynamic parameters and unbalance parameters because of the influence of complex factors such as the installation,operation and maintenance conditions and test environment.Hence,two kinds of analytical modelling,numerical simulation and experimental study for simultaneous identification of residual unbalance and bearing coefficients of a single-disc and single-span rotor is investigated in the dissertation.The proposed algorithms can be regarded as a means for further studies aim to more practical and complicated rotors,such as rotors with multiple discs and rotors with multiple spans.The main contents are the following:1)Based on the Rayleigh model based analytical method of dynamic response of the unbalanced continuous single-disc and single-span rotor-bearing system,the unbalance response can be expressed as a nonlinear transcendental function of position,rotor unbalance,and bearing stiffness and damping coefficients.Four computational examples,whose numerical data is representative for the rotor-dynamic applications,are used in the numerical simulation to study the Rayleigh model based analytical method of dynamic response of the unbalanced rotor.They represent the symmetrical rotor with rolling bearings,the non-symmetrical rotor with rolling bearings,the symmetrical rotor with oil-journal bearings and the non-symmetrical rotor with oil-journal bearings.The Rayleigh model based-analytical method are validated via comparison with the finite element method(FEM),which is a classical method for calculating unbalance response.MATLAB programs are written to calculate the unbalance responses for numerical experiment.It demonstrated that the trends of the calculated unbalance response with the frequency are the same when the FEM and the Rayleigh model based-analytical method are applied.The unbalance response calculated by the Rayleigh model based-analytical method is close to the response calculated by the FEM when the rotor speed is far away from the critical speed.Around the low-order frequency,the difference between the calculated unbalance responses of the two methods is slightly large.Therefor,the Rayleigh model based-analytical method are validated.Accordingly,sufficient equations,in which the rotor unbalance and bearing stiffness and damping coefficients are unknown variables,can be obtained using the measured unbalance responses of some positions on the rotating shaft.However,it is difficult to solve these equations together because the expression of the unbalance response is nonlinear and too many unknown variables exist.Therefore,a inverse model is proposed to deduce an algorithm called identification method by fusion of four measured points in frequency domain.It can be used for the simultaneous identification of the rotor unbalance and the bearing coefficients.Only a measured response registered for the disc,the two bearings,and any other selected cross section of the rotor shaft under steady-state operating conditions is required when applying the proposed identification method.2)The first proposed algorithm can only be applied to rolling-bearing coefficients identification.To conquer its inadequacy,another algorithm called identification method by changing rotor speed and fusion of four measured points in frequency domain is proposed.The model of the relationship between the bearing's principal coefficient and cross coupling coefficient in the same direction is proposed.However,enough equations can not be obtained simply by adding more measured points.In this case,it is proposed that changing the rotating speed slightly to obtain another set of equations.By solving these equations,the proposed algorithm for simultaneous identification of the rotor unbalance and the bearing coefficients is developed.Only four measured unbalance responses,which are on the two bearings or around them,are required.It can be applied to both rolling-bearing rotors and oil journal bearing rotors.Moreover,compared with the first algorithm,the unbalance response of the eccentric disc is not needed to be measured,which is not easy for application.However,changing the rotating speed slightly under operating conditions once is needed.It provides an efficient means for on-line monitoring of the rotor unbalance and bearing coefficients.3)Two computational examples,whose numerical data is representative for the rotor-dynamic applications,are in the numerical simulation to exam the first proposed identification algorithm.They represent the symmetrical rotor with rolling bearings and the non-symmetrical rotor with rolling bearings.The proposed identification algorithm is examined by comparing identified values with set values,and the unbalance responses calculated by the Rayleigh model based-analytical method are used as measured responses.MATLAB programs are written based on the proposed identification algorithm to obtain the rotor unbalance and rolling-bearing coefficients.Numerical experiment demonstrated that the proposed algorithm has high identification accuracy.The identified results has high relationship with precision of the measured points and has low relationship with accuracy of the measured points.4)Four computational examples,whose numerical data is representative for the rotor-dynamic applications,are used in the numerical simulation.They represent the symmetrical rotor with rolling bearings,the non-symmetrical rotor with rolling bearings,the symmetrical rotor with oil-journal bearings and the non-symmetrical rotor with oil-journal bearings.The second identification algorithm is examined by comparing identified values with set values,and the unbalance responses calculated by the Rayleigh model based-analytical method are also used as measured responses.MATLAB programs are written based on the proposed identification algorithm.Numerical experiment demonstrated that the proposed novel algorithm can identify the bearing stiffness and damping coefficients,which means it be applied to both the oil-journal bearing rotor and the rolling bearing rotor.Moreover,it has high identification accuracy.The identified results has high relationship with precision of the measured points and has low relationship with accuracy of the measured points.5)In order to study the the identification accuracy of the two proposed algorithm by experiment,a single-disc and single-span rotor laboratorial platform is developed and experiments are conducted on it.Experiment results have indicated that the two algorithm are effective for engineering application and the identification accuracy of the first algorithm is better than the second.The precision and consistency of the eddy current vibration displacement sensor and measurement device plays a key role in improving the identification accuracy of the two proposed algorithm.