A robust prediction method for centrifugal pump rotor dynamics with uncertain bearing parameters

Abstract

The present invention relates to a robust prediction method for centrifugal pump rotor dynamics with uncertain bearing parameters, and belongs to the field of multi-stage centrifugal pumps. Aiming at the problem of uncertain dynamic characteristics of a multi-stage centrifugal pump rotor system caused by manufacturing errors of sliding bearing structural parameters, the present invention proposes a robust prediction method for the critical speed of the rotor system based on rotor system dynamics simulation and improved particle swarm optimization algorithm. The method establishes a rotor system dynamics model through dynamic characteristic coefficients associated with the structural parameters of the sliding bearing, realizes automatic calculation of the critical speed of the multi-stage centrifugal pump rotor system when the bearing structural parameters change by joint simulation of MATLAB and ANSYS, establishes an optimization model with structural parameters such as the shaft diameter length, clearance ratio, aspect ratio and oil film viscosity coefficient of the sliding bearing as variables, and the critical speed of the rotor system as the target, and calculates the critical speed extreme value of the rotor system dynamics model by combining finite element simulation and improved particle swarm optimization algorithm. In addition, a large number of bearing structural parameters are sampled by using the Monte Carlo algorithm to verify the accuracy and effectiveness of the solution results of the improved particle swarm optimization algorithm. The present invention can accurately and efficiently predict the robust critical speed of the rotor system, which is helpful for the reliable design and operation of the rotor system, and provides a theoretical basis for the design of the rotor system of a multi-stage centrifugal pump.

Description

Technical Field

[0001] The invention belongs to the field of multi-stage centrifugal pumps and relates to a robust prediction method for centrifugal pump rotor dynamics with uncertain bearing parameters. Background Art

[0002] As a key equipment for fluid transportation, multistage centrifugal pumps work on the principle of converting mechanical energy into pressure potential energy and kinetic energy of the liquid medium being transported. They are widely used in various industries such as metallurgy, chemical industry, petroleum, nuclear power, electric power, urban construction, and national defense. With the rapid development of industry, the speed of multistage centrifugal pumps has been continuously improved, and its speed has rapidly increased from zero to thousands of revolutions per minute, making the safety and stability of the rotor system under operating conditions an issue that cannot be ignored. Early pumps had low speed, small head, and low power. The main cause of vibration was the eccentricity of the impeller, that is, the center of the impeller and the center of the shaft section were not on the same horizontal line. For this vibration, the static balance method can be used to eliminate the vibration problem of the pump group. With the development of the manufacturing industry, my country's pump industry is developing towards high speed, high head, and high power, which brings about interference from various uncertain factors, resulting in the vibration problem of the pump group becoming a major issue of concern to many scholars. Therefore, ensuring the stable and efficient operation of multistage centrifugal pumps has a positive impact on the development of my country's manufacturing industry. At present, the calculation and analysis of the dynamic characteristics of the bearing-rotor system of multistage centrifugal pumps is one of the main research contents of scholars at home and abroad.

[0003] Rotor dynamics is the study of the dynamic characteristics of rotating machinery rotors and their components and structures. The rotor will cause the rotor system to vibrate during operation. The amplitude of the vibration increases with the increase of the speed. When the amplitude reaches the maximum value at a certain speed, resonance will occur. As the speed continues to increase, the vibration amplitude of the system will decrease and tend to stabilize. The speed at which the vibration amplitude of the rotor system reaches the maximum value is the critical speed of the rotor. At present, the methods for critical speed analysis of multi-stage centrifugal pump rotor systems mainly include modal analysis, transfer matrix method and finite element method. Some scholars have also conducted in-depth analysis of the rotor system using the above three methods. Li Hongliang applied the fixed interface modal synthesis method to the dynamic analysis of the dual-rotor system based on the structural characteristics of the dual-rotor system, and calculated the three-dimensional waterfall diagram of the steady-state response of the eccentric disk and the critical speed of the rotor system; Li Chao et al. adopted the method of lumped parameter and distributed mass hybrid modeling to establish a mechanical model of the rotor-support system, and applied the improved Riccati transfer matrix method to comprehensively consider the influence of factors such as gyroscopic torque, support stiffness, and shear deformation to calculate the critical speed of the rotor system; D. Gayen et al. established the finite element analysis formula of the transmission shaft using beam units while considering the translational inertia, rotational inertia, lateral shear deformation and gyroscopic torque, and studied the parameters affecting the dynamic characteristics of the rotor-bearing system.

[0004] In the design and analysis of traditional multi-stage centrifugal pumps, the calculation models used are all parameter-determined models. However, under actual working conditions, there are always some external factors that cause the calculated dynamic characteristics of the rotor system to often fail to accurately describe the working state of the system. In fact, affected by many factors such as material properties, processing errors, external loads and measurement errors, the structural parameters of the rotor system will inevitably change within a certain range, and the main factors affecting the vibration of the rotor system of a multi-stage centrifugal pump include rotor geometry parameters, bearing span and bearing type. As one of the important factors affecting the dynamic characteristics of the rotor system, the structure and dynamic characteristic coefficient of the bearing directly affect the vibration form and stability of the rotor system. Sliding bearings are widely used in the pump field with their performance advantages such as high dynamic stiffness, high rotation accuracy, long life and high damping vibration reduction. Some scholars have also explored the uncertainty of rotor systems. Mao Wengui et al. proposed an interval identification method for rotor system imbalance considering the uncertainty of oil film characteristics coefficients of sliding bearings. Fang Bo et al. proposed an analysis method based on interval mathematics and interval perturbation theory for the dynamic characteristics of rotor systems with uncertain parameters, which provides a new way to solve the uncertainty of dynamic characteristics of engine rotor systems caused by manufacturing errors. Zhu Lisha et al. studied the influence of the randomness of working parameters on the vibration reliability of rotor systems and sorted them, and obtained the sensitivity of system reliability to the mean and variance of basic random variables. Therefore, analyzing the uncertainty of dynamic characteristics of centrifugal pump rotor systems caused by manufacturing errors of sliding bearing structural parameters is of great significance for setting the working speed under actual working conditions, and provides theoretical guidance for achieving stable operation of multi-stage centrifugal pumps and optimizing sliding bearing structures. Summary of the invention

[0005] In view of this, the purpose of the present invention is to provide a robust prediction method for centrifugal pump rotor dynamics with uncertain bearing parameters. Aiming at the problem of uncertain dynamic characteristics of multi-stage centrifugal pump rotor system caused by manufacturing errors of sliding bearing structural parameters, the present invention proposes a robust prediction method for the critical speed of the rotor system based on rotor system dynamics simulation and improved particle swarm optimization (PSO) algorithm. The method establishes a rotor system dynamics model through the dynamic characteristic coefficients associated with the sliding bearing structural parameters, and uses MATLAB and ANSYS joint simulation to realize the automatic calculation of the critical speed of the multi-stage centrifugal pump rotor system when the bearing structural parameters change. The optimization model is established with the structural parameters such as the shaft diameter length, clearance ratio, aspect ratio and oil film viscosity coefficient of the sliding bearing as variables and the critical speed of the rotor system as the target, and the critical speed extreme value of the rotor system dynamics model is calculated by combining finite element simulation and improved PSO. In addition, the Monte Carlo algorithm is used to sample a large number of bearing structural parameters to verify the accuracy and effectiveness of the improved PSO solution results. A super-high pressure multi-stage centrifugal pump is used as an example study. The proposed method can accurately and efficiently predict the robust critical speed of the rotor system, which is helpful for the reliable design and operation of the rotor system, and provides a theoretical basis for the design of the rotor system of a multi-stage centrifugal pump.

[0006] In order to achieve the above object, the present invention provides the following technical solutions:

[0007] A robust prediction method for centrifugal pump rotor dynamics with uncertain bearing parameters includes the following steps:

[0008] S1: Construct known sample information of sliding bearing structural parameters;

[0009] S2: The direct relationship between the bearing structure parameters and the critical speed of the system is realized through the secondary development language and data exchange interface of MATLAB and ANSYS, and the critical speed optimization model of the multi-stage centrifugal pump rotor system is constructed;

[0010] S3: Determine the extreme value of the critical speed of the sliding bearing-rotor system using the improved particle swarm optimization algorithm;

[0011] S4: Monte Carlo algorithm is used to sample a large number of samples in the sample space to calculate the extreme value of the critical speed of the sliding bearing-rotor system;

[0012] S5: Compare the improved particle swarm optimization algorithm with the Monte Carlo calculation results to verify the effectiveness of the improved particle swarm optimization algorithm.

[0013] S6: According to the predicted maximum critical speed variation range of the sliding bearing-rotor system of the multi-stage centrifugal pump, the operating speed of the pump group under actual working conditions is set to deviate from the maximum range of the critical speed to achieve stable and safe operation of the multi-stage centrifugal pump.

[0014] Further, the described step S1 is specifically as follows: the manufacturing error in the dimension parameter processing of the sliding bearing causes the shaft diameter length L of the sliding bearing to be b The structural parameters such as clearance ratio φ, aspect ratio λ and oil film viscosity coefficient η are disturbed near their nominal values, which in turn causes the dynamic characteristics of the multi-stage centrifugal pump rotor system to be uncertain. Therefore, the present invention takes the structural parameters of the sliding bearing V = (L b , φ, λ, η) as sampling samples.

[0015] Further, the described step S2 is specifically as follows:

[0016] S201: Using the main control program written in MATLAB software, call ANSYS to perform finite element simulation calculations and output the critical speed of the multi-stage centrifugal pump rotor system. In this way, a direct relationship between the bearing structure parameters and the critical speed of the system is established, and the critical speed of the rotor system is automatically calculated.

[0017] S202: The present invention uses the shaft diameter length L b , clearance ratio φ, aspect ratio λ and oil film viscosity coefficient η are the research variables; let vector V = (L b , φ, λ, η) are optimization variables, then V min and V max Indicates the lower and upper limits of a variable.

[0018] S203: Taking the extreme value of the critical speed n of the multi-stage centrifugal pump rotor system as the optimization target; the established critical speed optimization model of the multi-stage centrifugal pump rotor system is expressed as shown in the following formula (1):

[0019]

[0020] Among them, f minspeed (V) is the minimum critical speed of the multi-stage centrifugal pump rotor system; f maxspeed (V) is the maximum critical speed of the multi-stage centrifugal pump rotor system; f(V) is the constructed fitness function, and the specific construction process is as follows:

[0021] The finite difference method is programmed using MATLAB to solve the generalized fluid mechanics Reynolds equation for the sliding bearing, as shown in the following equation (2):

[0022]

[0023] After solving for the oil film pressure P, substitute it into equation (3) and integrate to obtain the 8 equivalent stiffness coefficients and damping coefficients of the sliding bearing.

[0024]

[0025] After solving the stiffness and damping coefficient of the sliding bearing, the finite element model of the multi-stage centrifugal pump rotor system was established using the ANSYS virtual simulation platform, and the modal analysis method was used to solve the critical speed n of the rotor system.

[0026] Finally, the secondary development language and data exchange interface of MATLAB and ANSYS are used to realize the automatic calculation of the critical speed of the multi-stage centrifugal pump rotor system when the bearing structure parameters change, and the fitness function for optimizing the critical speed of the multi-stage centrifugal pump rotor system is constructed.

[0027] Further, the described step S3 is specifically as follows: according to the established critical speed optimization model of the multi-stage centrifugal pump rotor system, an improved particle swarm algorithm is introduced, and the maximum and minimum critical speeds of the multi-stage centrifugal pump rotor system are solved in combination with the improved particle swarm algorithm process.

[0028] Further, the described step S4 is specifically as follows: when inputting variable L b , φ, λ, η, and generate random samples. The critical speed of the centrifugal pump rotor system is calculated by optimizing the model. A large number of random samples are used to calculate the critical speed of the rotor system and verify the effectiveness of the improved particle swarm algorithm. The basic steps are as follows:

[0029] S401: Generate m random samples X from input variables i (i=1,2,···,m).

[0030] S402: Substitute m random samples into the optimization model to calculate the critical speed g(X) of the sliding bearing-rotor system of the multistage centrifugal pump i ).

[0031] S403: Calculate the critical speed g(X i ) maximum and minimum values.

[0032] Furthermore, the described steps S5-S6 are specifically as follows: the first three critical speeds calculated by the improved particle swarm algorithm are compared with the results calculated by the Monte Carlo algorithm after a large number of sampling samples to prove the effectiveness of the improved particle swarm prediction results. The first three critical speeds calculated are compared with the rated speed of the multi-stage centrifugal pump under actual working conditions to ensure that the critical speed of the pump group deviates far from the rated critical speed to achieve safe and stable operation.

[0033] The beneficial effects of the present invention are as follows: the present invention aims at the problem of uncertainty in the dynamic characteristics of the rotor system of a multi-stage centrifugal pump caused by the manufacturing errors of the structural parameters of the sliding bearings, and proposes a robust prediction method for the critical speed of the rotor system based on the dynamic simulation of the rotor system and the improved particle swarm optimization (PSO) algorithm. The invention establishes a rotor system dynamic model through the dynamic characteristic coefficients associated with the structural parameters of the sliding bearings, and uses MATLAB and ANSYS joint simulation to realize the automatic calculation of the critical speed of the rotor system of the multi-stage centrifugal pump when the bearing structural parameters change. An optimization model is established with the structural parameters such as the shaft diameter length, clearance ratio, aspect ratio and oil film viscosity coefficient of the sliding bearing as variables and the critical speed of the rotor system as the target, and the critical speed extreme value of the rotor system dynamic model is calculated by combining finite element simulation with the improved PSO. In addition, the Monte Carlo algorithm is used to perform a large number of sampling on the bearing structural parameters to verify the accuracy and effectiveness of the improved PSO solution results. The specific advantages are as follows:

[0034] The traditional multi-stage centrifugal pump bearing-rotor system dynamics model is established based on the bearing dynamic characteristic coefficient calculated from the nominal value of the sliding bearing structural parameters. However, during the processing of the sliding bearing, there will always be certain manufacturing errors that cause the bearing structural parameters to be disturbed near their nominal values, making the theoretical prediction of the rotor system dynamic characteristics different from the actual operating performance. The present invention takes into account the processing errors, measurement errors and material errors in the sliding bearing structural parameters, which cause the uncertainty of the operating speed range of the multi-stage centrifugal pump rotor system.

[0035] The present invention combines the optimization model of a multi-stage centrifugal pump rotor system with an improved particle swarm algorithm, which can effectively determine the critical speed extreme value problem of the rotor system. The Monte Carlo method is further used to verify the effectiveness of the improved particle swarm algorithm, which involves the analysis of the influence of the joint stiffness and damping of the sliding bearing on the critical speed of the multi-stage centrifugal pump rotor system, providing technical support for the selection of outsourced components by centrifugal pump manufacturers.

[0036] By adopting the robust prediction method for centrifugal pump rotor dynamics with uncertain bearing parameters proposed in the present invention, the correlation between the shaft diameter length, clearance ratio, aspect ratio and oil film viscosity coefficient of the sliding bearing structural parameters and the stability of the multi-stage centrifugal pump rotor system can be further explored, providing a theoretical basis and data support for more comprehensive and accurate selection of component structural parameters.

[0037] Figure Description

[0038] In order to make the purpose, technical solution and beneficial effects of the present invention clearer, the present invention provides the following figure for explanation:

[0039] Figure 1 Schematic diagram of the robust prediction process of rotor system dynamic characteristics

[0040] Figure 2Multistage centrifugal pump solid 3D image

[0041] Figure 3 Schematic diagram of sliding bearing structure

[0042] Figure 4 MATLAB and ANSYS joint simulation data association

[0043] Figure 5 Critical speed convergence curve DETAILED DESCRIPTION

[0044] The following is a detailed description of the optimization implementation case of the present invention in conjunction with the figures.

[0045] The robust prediction method for centrifugal pump rotor dynamics with uncertain bearing parameters is as follows: Figure 1 As shown, the present invention takes an ultra-high pressure multi-stage centrifugal pump as an example for analysis. Figure 2 As shown in the figure, a critical speed optimization model for a multi-stage centrifugal pump rotor system is established, and a robust prediction is performed by comprehensively improving the particle swarm optimization algorithm and the Monte Carlo algorithm.

[0046] Sliding bearing structure Figure 3 As shown in Table 1, combined with the actual working conditions, the variation range of variables such as bearing length, clearance ratio, aspect ratio and oil film viscosity coefficient of the sliding bearing is set to a floating range of ±5%, as shown in Table 1.

[0047] Table 1 Range of values ​​for sliding bearings

[0048]

[0049] The structural parameters of the sliding bearing in Table 1 are used as the optimization variable input to complete the solution of the sliding bearing dynamic characteristic coefficient and establish the finite model of the multi-stage centrifugal pump. The critical speed of the rotor system is obtained through modal analysis. The fitness function of the optimization model is constructed through joint simulation of MATLAB and ANSYS, and the data of the two are related as follows: Figure 4 As shown. The critical speed of the multi-stage centrifugal pump rotor system is selected as the optimization target as the output, and the construction of the critical speed optimization model of the multi-stage centrifugal pump rotor system is completed.

[0050] The improved particle swarm optimization algorithm is used to optimize the critical speed of the multi-stage centrifugal pump rotor system. First, the basic parameters are set: the population size is set to 80; the maximum number of iterations k is set to 100; the initial values ​​of the two learning factors c1 and c2 are 2; and the initial inertia weight ω is set to 0.7. Figure 5 It is the iterative process of the maximum value of the first-order critical speed. It can be seen from the figure that after 58 iterations, the value of the first-order critical speed function has converged. By iteratively optimizing the first three critical speeds of the multi-stage centrifugal pump rotor system, the variation range of the critical speed in Table 2 is obtained.

[0051] Table 2 The range of the first three critical speeds

[0052]

[0053] The optimal values ​​of the first three critical speeds of the rotor system are obtained by improving the particle swarm optimization algorithm. The Monte Carlo algorithm is used to verify the effectiveness of the optimal value of each critical speed of the multi-stage centrifugal pump bearing-rotor system. The algorithm has the characteristics of strong versatility, and its calculation accuracy will also increase with the increase of the number of simulations.

[0054] The Monte Carlo algorithm is applied to the critical speed solution process of the multi-stage centrifugal pump rotor system. The bearing length, clearance ratio, aspect ratio and oil film viscosity coefficient are used as input variables to generate random samples. The sampling sample is 10 5 Then, the critical speed of the rotor system of the multi-stage centrifugal pump is calculated through the rotor system critical speed optimization model established by MATLAB and ANSYS, and the variation range of the first three critical speeds is obtained as shown in Table 3.

[0055] Table 3 Maximum values ​​of the first three critical speeds

[0056]

[0057] The comparison results of the first three critical speeds of the improved particle swarm algorithm and the Monte Carlo algorithm are shown in Table 4. It can be seen that the maximum error between the two is controlled within 1%, so the calculation accuracy of the improved particle swarm algorithm is within an acceptable range while reducing a large number of sampling samples and saving calculation time. In practice, the rated operating speed of the rotor of a multi-stage centrifugal pump is 1980r / min, which is far away from the first-order critical speed range [2462.1r / min, 2505.7r / min] calculated based on the improved PSO algorithm in this paper, so it can avoid the vibration of the rotor system to achieve the purpose of stable and safe operation.

[0058] Table 4 Comparison of the first three critical speeds

[0059]

[0060] Finally, it should be noted that the above preferred embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail through the above examples, those skilled in the art should understand that various changes can be made in form and details without departing from the scope defined by the claims of the present invention.

Claims

1. A robust prediction method for dynamic characteristics of a multi-stage centrifugal pump rotor system with uncertain sliding bearing parameters, characterized by: The method comprises the following steps: S1: Construct a sample with known structural parameters of the sliding bearing, considering the manufacturing errors in the processing process that will lead to the shaft diameter length L of the sliding bearing b , clearance ratio φ, aspect ratio λ and oil film viscosity coefficient η and other structural parameters are disturbed near their nominal values, which in turn causes the dynamic characteristics of the multi-stage centrifugal pump rotor system to have uncertainty. Therefore, this application uses the structural parameters of the sliding bearing V = (L b , φ, λ, η) as sampling samples; S2: The direct relationship between the bearing structure parameters and the critical speed of the system is realized through the secondary development language and data exchange interface of MATLAB and ANSYS. That is, the main control program written by MATLAB software is used to call ANSYS for finite element simulation calculation to obtain and output the critical speed of the multi-stage centrifugal pump rotor system. Based on this, a critical speed optimization model of the multi-stage centrifugal pump rotor system is established. The basic steps are as follows: Shaft length L b , clearance ratio φ, aspect ratio λ and oil film viscosity coefficient η are the research variables, and the vector V=(L b , φ, λ, η) are optimization variables, then V min and V max Represents the upper and lower limits of the variable, takes the extreme value of the critical speed n of the multi-stage centrifugal pump rotor system as the optimization target, and establishes the critical speed optimization model of the multi-stage centrifugal pump rotor system shown in formula (1): Among them, f minspeed (V) is the minimum critical speed of the multi-stage centrifugal pump rotor system, f maxspeed (V) is the maximum critical speed of the multi-stage centrifugal pump rotor system, and f(V) is the fitness function of the construction, which can be obtained by the following steps: The finite difference method is programmed using MATLAB to solve the generalized fluid mechanics Reynolds equation for the sliding bearing, as shown in the following equation (2): After solving for the oil film pressure p, substitute it into equation (3) and integrate to obtain the equivalent 8 stiffness coefficients and damping coefficients of the sliding bearing: After solving the stiffness and damping coefficient of the sliding bearing, the finite element model of the multi-stage centrifugal pump rotor system is established using the ANSYS virtual simulation platform, and the critical speed n of the rotor system is solved using the modal analysis method. Finally, the secondary development language and data exchange interface of MATLAB and ANSYS are used to realize the automatic calculation of the critical speed n of the multi-stage centrifugal pump rotor system when the bearing structure parameters change, and then the fitness function for optimizing the critical speed of the multi-stage centrifugal pump rotor system is constructed. S3: Determine the extreme value of the critical speed of the sliding bearing-rotor system using the improved particle swarm optimization algorithm; S4: Monte Carlo algorithm is used to sample a large number of samples in the sample space to calculate the extreme value of the critical speed of the sliding bearing-rotor system; S5: Compare the improved particle swarm optimization algorithm with the Monte Carlo calculation results to verify the effectiveness of the improved particle swarm optimization algorithm; S6: According to the predicted maximum critical speed variation range of the sliding bearing-rotor system of the multi-stage centrifugal pump, the operating speed of the pump group under actual working conditions is set to deviate from the maximum range of the critical speed to achieve stable and safe operation of the multi-stage centrifugal pump.

2. A robust prediction method for dynamic characteristics of a multi-stage centrifugal pump rotor system with uncertain sliding bearing parameters as claimed in claim 1, characterized in that: The described step S3 is specifically as follows: according to the established critical speed optimization model of the multi-stage centrifugal pump rotor system, an improved particle swarm algorithm is introduced, and the maximum and minimum critical speeds of the multi-stage centrifugal pump rotor system are solved in combination with the improved particle swarm algorithm process.

3. A robust prediction method for dynamic characteristics of a multi-stage centrifugal pump rotor system with uncertain sliding bearing parameters as claimed in claim 2, characterized in that: The described step S4 is specifically as follows: b , φ, λ, η, generate random samples, calculate the critical speed of the centrifugal pump rotor system through the optimization model, and use a large number of random samples to calculate the critical speed of the rotor system to verify the effectiveness of the improved particle swarm algorithm. The basic steps are as follows: S401: Generate m random samples X from input variables i (i=1,2,···,m); S402: Substitute m random samples into the optimization model to calculate the critical speed g(X) of the sliding bearing-rotor system of the multistage centrifugal pump i ); S403: Calculate the critical speed g(X i ) maximum and minimum values.

4. A robust prediction method for dynamic characteristics of a multi-stage centrifugal pump rotor system with uncertain sliding bearing parameters as claimed in claim 3, characterized in that: The described steps S5-S6 are specifically as follows: comparing the first three critical speeds calculated by the improved particle swarm algorithm with the results calculated by the Monte Carlo algorithm after a large number of sampling samples to prove the effectiveness of the improved particle swarm prediction results, and comparing the calculated first three critical speeds with the rated speed of the multi-stage centrifugal pump under actual working conditions to ensure that the critical speed of the pump group deviates far from the rated critical speed to achieve safe and stable operation.

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