Continuous Dynamics And Parameter Identification Methods Of Multi-disk Multi-span Rotors And Numerical Experiments

The safe and stable operation of large rotating machinery is vital to important sectors of the national economy such as coal and electric power.Bearing-rotor system(hereinafter referred to as "rotor")is the core component of rotating machinery.Its dynamic characteristics have complex relationships with parameters such as rotor imbalance,bearing stiffness and damping,which directly affect the operational reliability of rotating machinery.As a research hotspot of rotor dynamics,rotor parameter identification has always been concerned by scholars,but it has not been solved well.Although the rotor imbalance and bearing stiffness and damping coefficient can be well identified under laboratory conditions,engineering applications are also relatively mature.However,for large rotors,the actual production requires continuous operation of such rotors,and it is not allowed to stop or move away from the site at will,which makes the implementation of laboratory identification technology difficult,and the laboratory measured values are different from the actual values under operating conditions.In view of this,this article focuses on the multi-disk multi-span rotor system to study the continuous dynamics of rotor unbalance(forward problem)and the identification of unbalance and bearing stiffness and damping coefficient(inverse problem).This article realizes the online identification of rotor imbalance and bearing stiffness and damping coefficient,provides theoretical basis for solving the common technical problems of large-scale rotor system failures and low reliability,and provides technical support for improving the service reliability and safety level of large-scale rotors,which has important theoretical significance and engineering value.Limited by experimental conditions,this article uses a combination of theoretical analysis and numerical experiments to carry out in-depth research.The main contents are as follows:(1)Based on the Rayleigh theory,a rotor unbalance continuous dynamic model expressed in the form of homogeneous boundary non-homogeneous fourth-order partial differential equations is established.Aiming at the problem that the existing general solution theory is not applicable,Fourier transform,Green’s function,Riemann-Merlin inversion and Residue theorem are used to solve the unbalanced response analytical solution.The unbalance response at any point on the rotating shaft is expressed as a function of point position,unbalance amount,bearing stiffness damping,rotor inherent parameters and time,forming a continuous dynamic analysis method for multi-disk multi-span rotor unbalance.Using the idea of comparing with the two classic methods of finite method and Ricatti transfer matrix method,a numerical simulation program based on Matlab was developed,and the curve of unbalance response with rotation frequency(speed)obtained by three calculation methods was obtained,which verified this method.Numerical experiment results show that the unbalanced response obtained by the three methods has the same trend with the rotation frequency.The curves almost overlap when far away from the critical frequency,the curve is inconsistent when at or near the critical frequency.However,this method is closer to the calculation result of the finite element method,and the calculation speed is faster than the finite element method,slower than the Ricatti transfer matrix method,and the numerical stability is not as good as the two traditional methods.(2)For the m-disk and n-span rotor,because the unbalance response is a nonlinear transcendental function with the unbalance and the bearing stiffness and damping,there are as many as 2m+8n unknowns.Moreover,they are coupled with each other,and it is difficult to directly solve several equations with known unbalanced response of measuring points.In order to solve this problem,the idea of matrix expression is adopted,and the unbalanced response of m+n measuring points is known,and the mathematical model of rotor parameter identification is established.This model realizes the decoupling of unbalance and bearing stiffness and damping,and obtains the functional relationship between the amplitude and phase of the unbalance of the eccentric turntable and the unbalanced response at the turntable.The unidirectional algorithm and bidirectional fusion algorithm are deduced,and the online recognition of each imbalance is realized.The algorithm only needs m+n+1 measuring points,and the eccentric turntable to be identified must be used as the measuring point.Using the idea of calculating the unbalanced response as input and comparing the identification value of the two methods with the set value,a numerical simulation program was developed based on Matlab software,and the variation curve of the amplitude and phase of the unbalance identification with the rotation frequency was obtained,which verified the proposed algorithm.Numerical experiment results show that: when the measurement error of the unbalanced response of all measuring points is equal,the algorithm recognition error is equal to the measurement error,that is,the accuracy is closely related to the accuracy(repeat accuracy)of the unbalanced response measurement of the measuring point.Setting an adjustment point at the eccentric turntable to be identified can improve the accuracy of unbalance identification at that place.The higher the sensor accuracy,the higher the recognition accuracy.The unidirectional algorithm has higher recognition accuracy than the bidirectional fusion algorithm.(3)Based on the established mathematical model of rotor parameter identification,the linear function relationship between the bearing coefficient to be identified and the unbalanced response at the bearing is obtained.Ignoring the bearing cross-coupling coefficient,a frequency domain fusion recognition algorithm for rolling bearings with multiple measuring points is proposed.Theoretical research found that: for a single-disk single-span rotor,when the rotation frequency is constant,the slope of the linear function is also constant.Theoretical research found that: for a single-disk single-span rotor,when the rotation frequency is constant,the slope of the linear function is also constant.In order to solve this problem,the idea of establishing a set of equations by fine-tuning the speed is cleverly proposed,and a frequency-domain fusion algorithm for multi-measurement points of the fine-tuning speed is deduced,which realizes the simultaneous identification of main coefficients and cross-coupling coefficients.The above two methods need to measure the unbalanced response in the x and y directions.The number of measurement points required is equal to the number of turntables + the number of bearings +1,and the unbalanced response at the bearing to be identified must be measured.Using the idea of calculating the unbalanced response as input and comparing the identification value of the two methods with the set value,a numerical simulation program was developed based on Matlab software,and the curve of the bearing coefficient with the rotation frequency was obtained.The results show that:when the measurement error of each measuring point is the same,the bearing coefficient recognition error is 0,that is,the recognition accuracy is closely related to the repeatability of the measurement system.Adjusting the measuring point can effectively improve the accuracy of the bearing coefficient identification.The higher the sensor accuracy,the higher the recognition accuracy.