Centrifugal pump rotor system design method considering long-period operation

Abstract

The invention relates to a design method of a centrifugal pump, in particular to a design method of a multi-stage centrifugal pump rotor system considering long-period operation. According to the method, fusion design is conducted on the structure of the multi-stage centrifugal pump from flowing regulation and control, flow field excitation and manufacturing process factors, so that the stability of a rotor under the operation working condition is improved. According to the technical scheme, the method comprises the following steps that 1, the hydraulic performance and the structure of the centrifugal pump are designed; 2, extracting a main flow field exciting force and a gap flow field exciting force; 3, a quantitative control target is determined for the assembly precision of the centrifugal pump; 4, analyzing the assembly coaxiality of the rotor of the multi-stage centrifugal pump; 5, according to a multidisciplinary design optimization method, a design variable needing to be optimized is selected, an optimization function is constructed, and a mathematical model for optimization of the centrifugal pump rotor system is determined; 6, solving the mathematical model by using a multi-target artificial bee colony algorithm to obtain an optimal solution set; and 7, based on the optimal solution set, constructing an optimized centrifugal pump rotor system model, and performing long-period operation analysis.

Description

Technical Field

[0001] The invention relates to a design method for a centrifugal pump, in particular to a design method for a rotor system of a multi-stage centrifugal pump taking long-cycle operation into consideration. Background Art

[0002] When designing a centrifugal pump rotor system, traditional methods mainly focus on the design and optimization of the centrifugal pump rotor components. Therefore, the dynamic characteristics and vibration response of the rotor system are not fully considered, which may cause excessive vibration or instability of the system during long-term operation.

[0003] CN110674596 A discloses a method for designing rotor components of a multi-stage centrifugal pump taking into account the operating environment and stability, which optimizes the structural design of the multi-stage centrifugal pump by taking into account the influence of the local environment and the fluid force factors, improves the stability of the rotor under the operating conditions, and can design the rotor components in accordance with the deformation law of the rotor components. However, only the structural design of the rotor components is considered, and no multidisciplinary design optimization is performed on the centrifugal pump rotor system, so it cannot ensure that the centrifugal pump has stable and reliable working performance during long-term operation. Summary of the invention

[0004] The purpose of the present invention is to overcome the shortcomings of the above-mentioned background technology and provide a design method for a rotor system for a multi-stage centrifugal pump. The method integrates the design of the structure of the multi-stage centrifugal pump from the perspectives of flow regulation, flow field excitation and manufacturing process factors to improve the stability of the rotor under operating conditions.

[0005] The present invention solves the technical problem by the following technical solutions:

[0006] A method for designing a centrifugal pump rotor system considering long-term operation comprises the following steps:

[0007] Step 1: Design the hydraulic performance and structure of the centrifugal pump according to the long-term operation requirements of the centrifugal pump;

[0008] Step 2: Comprehensively analyze the rotor dynamics to extract the main flow field excitation force and the gap flow field excitation force, with the goal of reducing the fluid excitation force;

[0009] Step 3: Determine the quantitative control target for the centrifugal pump assembly accuracy from the perspective of structural discipline, with the goal of optimizing tolerance design;

[0010] Step 4: Analyze the coaxiality of the multistage centrifugal pump rotor assembly from the perspective of manufacturing process discipline, with the goal of determining the optimal coaxiality;

[0011] Step 5: According to the multidisciplinary design optimization method, select the design variables to be optimized, construct the optimization function, and establish the mathematical model for centrifugal pump rotor system optimization;

[0012] Step 6: Use a multi-objective artificial bee colony algorithm to solve the mathematical model and obtain the optimal solution set;

[0013] Step 7: Based on the optimal solution set, construct an optimized centrifugal pump rotor system model and conduct long-term operation analysis.

[0014] Furthermore, the step 1 of designing the hydraulic performance and structure of the centrifugal pump includes:

[0015] According to the long-cycle requirements of the centrifugal pump, the formula that satisfies the long-cycle operation of the centrifugal pump rotor system is set as:

[0016] G(t>t0) <G0±5%

[0017] in:

[0018] G is the actual vibration amplitude of the centrifugal pump, G0 is the specified vibration amplitude, t is the time for the centrifugal pump to operate continuously without fault, and t0 is the time limit for the centrifugal pump to operate continuously without fault.

[0019] Furthermore, the extraction of the main flow field excitation force and the gap flow field excitation force in step 2 includes:

[0020] Step 2.1 Solution of mainstream field excitation force:

[0021] The fluid exciting force specifically includes the fluid exciting force F acting on the inducer C ( Figure 4 The x-axis component F of the fluid excitation force on the two inducers is shown in cx1 、F cx2 And the y-axis force F cy1 、F cy2 ), the excitation force F of the impeller ring clearance kh ( Figure 4 The figure shows the component F of the impeller ring gap excitation force in the x-axis direction. khx And the y-axis force F khy ), fluid exciting force F on the impeller im ( Figure 4 The figure shows the x-axis component F of the fluid excitation force on the impeller. imx And the y-axis force F imy ), the excitation force F of the gap between the impeller and the cover gb ( Figure 4 The figure shows the component F of the impeller cover gap excitation force in the x-axis direction. gbx And the y-axis force F gby ) and the excitation force F caused by the unbalanced mass of the impeller umb ( Figure 4 The figure shows the component F of the exciting force in the x-axis direction caused by the unbalanced mass of the impeller. umbxAnd the y-axis force F umby ), fluid exciting force F on the balance drum bp ;

[0022] Comprehensively analyze the mainstream field exciting force. For the extraction method of the mainstream field exciting force, the mainstream field exciting force component can be obtained by integrating the surface of the centrifugal pump rotor component under pressure.

[0023]

[0024] Its mainstream field excitation force can be expressed as:

[0025]

[0026] Among them: F main is the mainstream field excitation force, F r 、F θ The two flow field exciting forces are respectively the radial direction of the rotor and the circumferential direction of the rotor perpendicular to the rotation axis, r is the radial variable of the rotor, θ is the circumferential variable of the rotor, and u r is the speed of the rotor in the radial direction, u θ is the speed of the rotor in the circumferential direction, ρ is the fluid density, V is the fluid flow rate, A1 is the rotor starting shaft end area, A2 is the rotor ending shaft end area, Q is the fluid flow rate, and ω is the rotor angular velocity.

[0027] Step 2.21 Construct the microelement control equations of the gap flow field excitation force:

[0028] By introducing the radial and axial momentum equations into the microelement control equations of the gap flow field, the boundary conditions can be obtained and the exciting force of the gap flow field can be calculated; a fluid microelement control equation group based on the Moody friction model is created, which includes the axial momentum equation, the circumferential momentum equation, the radial momentum equation and the continuity equation:

[0029]

[0030] The formulas in the above fluid microelement control equation group are, from top to bottom, the axial momentum equation, the circumferential momentum equation, the radial momentum equation and the continuity equation.

[0031] Where: S is the local gap of the fluid, R is the rotor radius, τ is the shear force, τ r is the shear force in the radial direction of the rotor, τ z is the shear force in the rotor axial direction, τ θ is the shear force in the circumferential direction of the rotor, z is the axial variable of the rotor, u is the speed, and u z is the speed of the rotor in the axial direction, t′ is the time variable, and P is the pressure inside the centrifugal pump;

[0032] Step 2.22 Solution of the fluid infinitesimal control equations:

[0033] By using the perturbation method to solve the fluid microelement control equations, the original equations can be simplified into zero-order and first-order perturbation equations about the perturbation quantity, and further transformed into the numerical solution problem of the first-order differential equations. By solving the equations by the shooting method, the velocity, pressure pulsation, exciting force and equivalent dynamic characteristic parameters of the fluid in the gap flow channel can be obtained.

[0034] According to the force of the rotor system, the dynamic characteristic equation of the rotor system is constructed as follows:

[0035]

[0036] Where: On the left side of the equation, M is the mass matrix, C is the damping matrix, K is the stiffness matrix, and on the right side of the equation, F gap is the gap flow field exciting force, G is the rotor system weight matrix, x is an unknown quantity. By obtaining the eigenvalue of the rotor motion equation, the critical speed, response and other dynamic characteristics and behaviors of the rotor system can be obtained. B1, B2 and B3 are the position matrices of the rotor system after node division.

[0037] Furthermore, the quantitative control objectives for the centrifugal pump assembly accuracy determined in step 3 include:

[0038] Step 3.1 Determine the total tolerance allowable range A≤5% according to the coaxiality requirement;

[0039] Step 3.2 Construct the radial force extreme value function according to the centrifugal pump assembly process:

[0040]

[0041] Where:

[0042]

[0043] in: is the radial force component of the i-th part to be optimized on the X-axis, is the radial force component of the i-th part to be optimized on the Y axis, is the radial force of the i-th part to be optimized, p i is the pressure of the i-th part to be optimized, α is the time, β is the angle, γ is the radius, l i is the axial length of the i-th part to be optimized.

[0044] Combined with the above model, the correlation function between the tolerance design value and the radial force extreme value is:

[0045]

[0046] in: is the maximum radial force on a single part to be optimized, h i is the tolerance design value of a part to be optimized, the ith one among n individual parts to be optimized, a, b, c are the coefficients of the corresponding functional relationship, which are determined by the specific functional relationship;

[0047] Step 3.3 Determine the allowable tolerance range of each part to be optimized:

[0048] The tolerance design value h of the part to be tested is calculated through step 3.2 i ; Determine the allowable tolerance range A of each part to be optimized i , 0 i ≤h i and

[0049] Furthermore, the step 4 of analyzing the assembly of the multistage centrifugal pump rotor includes:

[0050] Step 4.1 In the actual operation process, the assembly error has an important influence on the stable operation of the rotor system. Based on the centrifugal pump rotor system, the assembly error is analyzed, which consists of positioning and orientation errors; the positioning error is determined by the translation matrix, and the orientation error is determined by the rotation matrix; then the cumulative eccentricity error of the multi-stage centrifugal pump rotor assembly can be expressed by a general expression:

[0051]

[0052] Where: T ri is the transformation matrix between the rotor interfaces of the two-stage centrifugal pump, T Zi is the eccentricity of the ideal center of the centrifugal pump rotor i, T clearancei is the translation transformation matrix of the centrifugal pump rotor i reference plane eccentricity, T dzi is the translation transformation matrix caused by the machining error of the centrifugal pump rotor i reference surface, T orientationi is the rotation transformation matrix from the reference surface of the centrifugal pump rotor to the center of rotation of the assembly surface, R ri is the rotation matrix of the rotor reference plane of the i-th stage centrifugal pump around the Z axis, R xi is the rotation matrix of the rotor reference plane of the i-th stage centrifugal pump around the X axis, R yi is the rotation matrix of the rotor reference plane of the i-th stage centrifugal pump around the Y axis, R r(j-1) is the rotation matrix of the j-1th stage centrifugal pump rotor around the Z axis, R x(j-1) is the rotation matrix of the j-1th stage centrifugal pump rotor reference plane around the X axis, R y(j-1) is the rotation matrix of the j-1th stage centrifugal pump rotor reference plane around the Y axis, P i is the ideal position vector of the center of the rotor assembly surface of the i-th stage centrifugal pump, dP​i is the machining error vector of the center position of the rotor assembly surface of the i-th stage centrifugal pump, dP′ i is the eccentric position vector of the rotor of the i-th stage centrifugal pump.

[0053] Step 4.2 analyzes the assembly error of the multi-stage centrifugal pump rotor and the single-stage centrifugal pump rotor. The cumulative eccentricity error expression of the n-th stage centrifugal pump rotor after assembly is:

[0054]

[0055] in:

[0056] T deformationi is the translation transformation matrix of the deformation eccentricity caused by the centrifugal pump rotor fit, R rj is the rotation matrix of the j-th centrifugal pump rotor around the Z axis, R xj is the rotation matrix of the j-th centrifugal pump rotor reference plane around the X axis, R yj is the rotation matrix of the j-th centrifugal pump rotor reference plane around the Y axis, dP″ i is the matching error value of the single-stage rotor;

[0057] Step 4.3 The axial projection of the rotor axis position of the nth stage centrifugal pump after assembly can be expressed as:

[0058]

[0059] The coaxiality expression required for the optimization of the multi-stage centrifugal pump rotor assembly is:

[0060]

[0061] in:

[0062] x i ,y i is the offset of the axis of the i-th level component relative to the reference axis in the x-direction and the y-direction.

[0063] In step 5, according to the multidisciplinary design optimization method, appropriate design variables are selected, the objective function is constructed, and a mathematical model for centrifugal pump rotor system optimization is established;

[0064] Furthermore, the process of selecting the design variables to be optimized, constructing the optimization function, and establishing the mathematical model for centrifugal pump rotor system optimization in step 5 is as follows:

[0065] Based on the multidisciplinary optimization design of the centrifugal pump rotor system, the structural discipline, rotor dynamics discipline and manufacturing process discipline analysis are comprehensively considered to select the number of impeller blades, impeller inlet angle and impeller outlet angle, and the tolerance design value h of a certain part to be optimized. iand the offset x of the axis of the i-th level component in the x-direction and y-direction relative to the reference axis i ,y i As the design variable, the vibration amplitude is selected as the optimization objective function, and the correlation function between the design variable and the objective function is constructed as follows:

[0066] G=f(X、β1、β2;h i ;x i ,y i )

[0067] in:

[0068] G is the vibration amplitude of the centrifugal pump, X is the number of impeller blades, β1 is the impeller inlet angle, and β2 is the impeller outlet angle.

[0069] By selecting the design variables, determining the constraints and selecting the objective function for the multidisciplinary optimization design of the centrifugal pump rotor system, the mathematical model of the optimization problem can be established:

[0070] min G=f(X、β1、β2;h i ;x i ,y i )

[0071] Constraints: 3≤X≤5;

[0072] 10°≤β1≤30°;

[0073] 20°≤β2≤40°;

[0074] 0 i ≤h i and

[0075]

[0076] in:

[0077] R is the maximum allowable offset relative to the reference axis.

[0078] In step 6, a multi-objective artificial bee colony algorithm is used to solve the mathematical model to obtain an optimal solution set to optimize the operation of the centrifugal pump rotor system.

[0079] Furthermore, the process of solving the mathematical model using the multi-objective artificial bee colony algorithm in step 6 is as follows:

[0080] The formulas for solving the optimization operation model using the multi-objective artificial bee colony algorithm include:

[0081]

[0082] v​i =x i +(2×rand()-1)×(x i -S k );

[0083]

[0084] in:

[0085] x ij is the j-th dimension variable value of the solution corresponding to the i-th bee, i is the bee number, j is the dimension number, For x ij The upper and lower bounds of rand() are random numbers in the interval [0,1], and v i For the new solution, x i is the original solution, S k is a hired bee randomly selected from the optimal solution set, d q (x k ) is the hired bee x k The crowding distance on q objective functions, D(x k ) is the hired bee x k The crowding distance, q is the objective function number, f q (x k ), f q (x j ) is the nearest non-dominated solution of the qth objective function, max(f q )、min(f q ) is the maximum and minimum value of all Pareto optimal solutions on the qth objective function.

[0086] The calculation formula of the fitness of the nectar source is:

[0087]

[0088] in:

[0089] Z i For x i is the number of dominated solutions, and SN is the number of initial populations.

[0090] Follow-up bees make judgments in a roulette manner, based on the transfer probability:

[0091]

[0092] in:

[0093] P i is the probability, fit i For x i The fitness value of .

[0094] Furthermore, the process of constructing the optimized centrifugal pump rotor system model in step 7 is as follows:

[0095] Based on the optimized centrifugal pump rotor system operation plan, the finite element analysis software is used to establish an accurate finite element model of the centrifugal pump rotor system. Determine the operating conditions and vibration excitations encountered by the system during long-term operation, and apply the corresponding vibration loads. Apply vibration excitation in the model and perform accelerated vibration analysis at different frequencies. By analyzing the vibration modes of the multi-stage centrifugal pump rotor system, evaluate whether the vibration stability and performance of the system during long-term operation meet the long-term operation requirements.

[0096] At the same time, the ANSYS finite element software is used to calculate the natural frequency of the corresponding vibration mode diagram of the multi-stage centrifugal pump and the nonlinear deformation of the rotor system under prestress, change the rotation speed of the rotor components, calculate and output the Campbell diagram with prestress of the multi-stage water pump, and finally determine the critical speed of the rotor through the Campbell diagram. By comparing the critical speed with the rated speed of the pump, it can be determined whether the pump rotor meets the design requirements. If it meets the requirements, the optimal operation plan of the centrifugal pump rotor system is output. If it does not meet the requirements, the centrifugal pump rotor system structure is reset, and then a multidisciplinary optimization analysis is performed.

[0097] The beneficial effects of the present invention are as follows: the present invention is a multidisciplinary collaborative optimization algorithm, which comprehensively considers structural disciplines, rotor dynamics disciplines and manufacturing process disciplines, and integrates the design of the structure of the multi-stage centrifugal pump from the perspectives of flow regulation, flow field excitation and manufacturing process factors, which can improve the stability of the rotor under operating conditions and provide new design ideas and methods for the optimization and design of the multi-stage centrifugal pump. BRIEF DESCRIPTION OF THE DRAWINGS

[0098] Figure 1 The present invention is a flowchart of a method for designing a multi-stage centrifugal pump rotor system according to an embodiment of the present invention.

[0099] Figure 2 Schematic diagram of the structure of a multi-stage centrifugal pump before optimization in an embodiment of the present invention.

[0100] Figure 3 It is a schematic diagram of the optimized structure of the multi-stage centrifugal pump described in an embodiment of the present invention.

[0101] Figure 4 yes Figure 3 Simple force diagram of the rotor system of a medium-stage centrifugal pump.

[0102] Figure 5a Schematic diagram of the Campbell method of the rotor in the embodiment of the present invention.

[0103] Figure 5b 1 is a symbolic explanation of the Campbell method schematic diagram of the rotor in the embodiment of the present invention.

[0104] Figure 6 It is the distribution diagram of the x-axis vibration displacement over time before the optimization of the multi-stage centrifugal pump in the implementation case and the distribution diagram of the x-axis vibration displacement over time after the optimization.

[0105] Figure 7 It is the distribution diagram of the vibration displacement along the y-axis over time before the optimization of the multi-stage centrifugal pump in the implementation case and the distribution diagram of the vibration displacement along the y-axis over time after the optimization.

[0106] Figure 8 This is the time distribution diagram of the vibration displacement along the z-axis before and after optimization of the multi-stage centrifugal pump in the implementation case.

[0107] Numbers in the figure: inducer 1, impeller 2. DETAILED DESCRIPTION

[0108] The present invention is further described below with reference to the embodiments shown in the accompanying drawings.

[0109] like Figure 1 The centrifugal pump rotor system design method considering long-term operation includes the following steps:

[0110] Step 1: Design the hydraulic performance and structure of the centrifugal pump according to the long-term operation requirements of the centrifugal pump;

[0111] According to the requirements of multistage centrifugal pumps, preliminary structural design of multistage centrifugal pumps is carried out (see Figure 1 )

[0112] According to the long-cycle requirements of centrifugal pumps, the time limit for continuous trouble-free operation of centrifugal pumps is 1.5 years, and the maximum vibration does not exceed 16μm. The formula for long-cycle operation of the centrifugal pump rotor system is:

[0113] G(t>1.5 years)<16μm±5%

[0114] in:

[0115] G is the actual vibration amplitude of the centrifugal pump, G0 is the specified vibration amplitude of 16μm, t is the continuous trouble-free operation time of the centrifugal pump, and t0 is the time limit for the continuous trouble-free operation of the centrifugal pump, which is 1.5 years.

[0116] The design parameters of the centrifugal pump selected in this embodiment are: flow rate Q d =10m 3 / h, n=10000rpm, head H=50m, the blades in the impeller are all long blades, the number of blades is 3, the blade inlet angle β1=20°, and the blade outlet angle β2=30°.

[0117] Step 2: Comprehensively analyze the rotor dynamics to extract the main flow field exciting force and the gap flow field exciting force;

[0118] The mainstream field exciting force is comprehensively analyzed, and the mainstream field exciting force component is extracted by integrating the surface of the centrifugal pump rotor components under pressure.

[0119]

[0120] Its mainstream field excitation force can be expressed as:

[0121]

[0122] By introducing the radial and axial momentum equations into the microelement governing equations of the gap flow field, the boundary conditions can be obtained and the exciting force of the gap flow field can be calculated. Create a fluid microelement governing equations based on the Moody friction model, which includes the axial, circumferential and radial momentum equations and the continuity equation:

[0123]

[0124] The formulas in the above fluid microelement control equation group are, from top to bottom, the axial momentum equation, the circumferential momentum equation, the radial momentum equation and the continuity equation.

[0125] By using the perturbation method to solve the fluid microelement control equations, the original equations can be simplified into zero-order and first-order perturbation equations about the perturbation quantity, and further transformed into the numerical solution problem of the first-order differential equations. By solving the equations by the shooting method, the velocity, pressure pulsation, exciting force and equivalent dynamic characteristic parameters of the fluid in the gap flow channel can be obtained.

[0126] According to the force of the rotor system, the dynamic characteristic equation of the rotor system is constructed as follows:

[0127]

[0128] Where: On the left side of the equation, M is the mass matrix, C is the damping matrix, K is the stiffness matrix, and on the right side of the equation, F gap is the gap flow field exciting force, G is the rotor system weight matrix, x is an unknown quantity. By obtaining the characteristic value of the rotor motion equation, the critical speed, response and other dynamic characteristics and behaviors of the rotor system can be obtained; B1, B2 and B3 are the position matrices of the rotor system after node division; (such as Figure 4 shown).

[0129] Step 3: Determine the quantitative control target of centrifugal pump assembly accuracy from the perspective of structural discipline;

[0130] Determine the total tolerance allowable range A≤5% according to the coaxiality requirements;

[0131] Construct the radial force extreme value function according to the centrifugal pump assembly process:

[0132]

[0133] Where:

[0134]

[0135] in: is the radial force component of the i-th part to be optimized on the X-axis, is the radial force component of the i-th part to be optimized on the Y axis, is the radial force of the i-th part to be optimized, p i is the pressure of the i-th part to be optimized, α is the time, β is the angle, γ is the radius, l i is the axial length of the i-th part to be optimized.

[0136] Combined with the above model, the correlation function between the tolerance design value and the radial force extreme value is:

[0137]

[0138] in: is the maximum radial force on a single part to be optimized, h i is the tolerance design value of a certain part to be optimized, the ith one among n individual parts to be optimized, a, b, c are the coefficients of the corresponding functional relationship, which are determined by the specific functional relationship.

[0139] Quantitatively control the allowable tolerance range A of the part to be optimized i 4%;

[0140] Step 4: Analyze the coaxiality of the multi-stage centrifugal pump rotor assembly from the perspective of manufacturing technology;

[0141] In the actual operation process, the assembly error has an important influence on the stable operation of the rotor system. Based on the analysis of the assembly error of the centrifugal pump rotor system, it is composed of positioning error and orientation error. The positioning error is determined by the translation matrix, and the orientation error is determined by the rotation matrix. Then the cumulative eccentricity error of the multi-stage centrifugal pump rotor assembly can be expressed by the general expression:

[0142]

[0143] Where: T ri is the transformation matrix between the rotor interfaces of the two-stage centrifugal pump, T Zi is the eccentricity of the ideal center of the centrifugal pump rotor i, T clearancei is the translation transformation matrix of the centrifugal pump rotor i reference plane eccentricity, T dzi is the translation transformation matrix caused by the machining error of the centrifugal pump rotor i reference surface, Torientationi is the rotation transformation matrix from the reference surface of the centrifugal pump rotor to the center of rotation of the assembly surface, R ri is the rotation matrix of the rotor reference plane of the i-th stage centrifugal pump around the Z axis, R xi is the rotation matrix of the rotor reference plane of the i-th stage centrifugal pump around the X axis, R yi is the rotation matrix of the rotor reference plane of the i-th stage centrifugal pump around the Y axis, R r(j-1) is the rotation matrix of the j-1th stage centrifugal pump rotor around the Z axis, R x(j-1) is the rotation matrix of the j-1th stage centrifugal pump rotor reference plane around the X axis, R y(j-1) is the rotation matrix of the j-1th stage centrifugal pump rotor reference plane around the Y axis, P i is the ideal position vector of the center of the rotor assembly surface of the i-th stage centrifugal pump, dP i is the machining error vector of the center position of the rotor assembly surface of the i-th stage centrifugal pump, dP′ i is the eccentric position vector of the rotor of the i-th stage centrifugal pump.

[0144] For the assembly error analysis of multi-stage centrifugal pump rotors and single-stage centrifugal pump rotors, the cumulative eccentricity error expression of the n-th stage centrifugal pump rotor after assembly is:

[0145]

[0146] in:

[0147] T deformationi is the translation transformation matrix of the deformation eccentricity caused by the centrifugal pump rotor fit, dP′ i is the eccentric position vector caused by the rotor matching of the i-th stage centrifugal pump, R rj is the rotation matrix of the j-th centrifugal pump rotor around the Z axis, R xj is the rotation matrix of the j-th centrifugal pump rotor reference plane around the X axis, R yj is the rotation matrix of the j-th centrifugal pump rotor reference plane around the Y axis, dP″ i is the matching error value of the single-stage rotor.

[0148] The axial projection of the rotor axis position of the nth stage centrifugal pump after assembly can be expressed as:

[0149]

[0150] The design determines the optimized coaxiality required for the multi-stage centrifugal pump rotor assembly:

[0151]

[0152] in:

[0153] x i ,y iis the offset of the axis of the i-th level component relative to the reference axis in the x-direction and the y-direction.

[0154] Step 5: According to the multidisciplinary design optimization method, select the design variables to be optimized, construct the optimization function, and establish the mathematical model for centrifugal pump rotor system optimization;

[0155] Based on the multidisciplinary optimization design of the centrifugal pump rotor system, the structural discipline, rotor dynamics discipline and manufacturing process discipline analysis are comprehensively considered to select the number of impeller blades, impeller inlet angle and impeller outlet angle, and the tolerance design value h of a certain part to be optimized. i and the offset x of the axis of the i-th level component in the x-direction and y-direction relative to the reference axis i ,y i As the design variable, the vibration amplitude is selected as the optimization objective function, and the correlation function between the design variable and the objective function is constructed as follows:

[0156] G=f(X、β1、β2;h i ;x i ,y i )

[0157] in:

[0158] G is the vibration amplitude of the centrifugal pump, X is the number of impeller blades, β1 is the impeller inlet angle, and β2 is the impeller outlet angle.

[0159] By selecting the design variables, determining the constraints and selecting the objective function for the multidisciplinary optimization design of the centrifugal pump rotor system, the mathematical model of the optimization problem can be established:

[0160] min G=f(X、β1、β2;h i ;x i ,y i )

[0161] Constraints: 3≤X≤5;

[0162] 10°≤β1≤30°;

[0163] 20°≤β2≤40°;

[0164] 0 i ≤h i and

[0165]

[0166]

[0167] in:

[0168] ​R is the maximum allowable offset relative to the reference axis, which is 14 μm.

[0169] Step 6: Use a multi-objective artificial bee colony algorithm to solve the mathematical model and obtain the optimal solution set;

[0170] The formulas for solving the optimization operation model using the multi-objective artificial bee colony algorithm include:

[0171]

[0172] v i =x i +(2×rand()-1)×(x i -S k );

[0173]

[0174] in:

[0175] x ij is the j-th dimension variable value of the solution corresponding to the i-th bee, i is the bee number, j is the dimension number, For x ij The upper and lower bounds of rand() are random numbers in the interval [0,1], and v i For the new solution, x i is the original solution, S k is a hired bee randomly selected from the optimal solution set, d q (x k ) is the hired bee x k The crowding distance on q objective functions, D(x k ) is the hired bee x k The crowding distance, q is the objective function number, f q (x k ), f q (x j ) is the nearest non-dominated solution of the qth objective function, max(f q )、min(f q ) is the maximum and minimum value of all Pareto optimal solutions on the qth objective function.

[0176] The calculation formula of the fitness of the nectar source is:

[0177]

[0178] in:

[0179] Z i For x i is the number of dominated solutions, and SN is the number of initial populations.

[0180] Follow-up bees make judgments in a roulette manner, based on the transfer probability:

[0181]

[0182] in:

[0183] P i is the probability, fit i For x i The fitness value of .

[0184] The optimized results are as follows: the centrifugal pump vibration amplitude G is 13 μm, the number of impeller blades X is 4, the impeller inlet angle β1 is 19°, the impeller outlet angle β2 is 32°, and the centrifugal pump rotor system tolerance design value h i The displacement x of the axis of the centrifugal pump rotor system components in the x and y directions relative to the reference axis is 3%. i ,y i 3.3μm and 3.5μm.

[0185] Step 7: Based on the optimal solution set, construct an optimized centrifugal pump rotor system model and conduct long-term operation analysis.

[0186] Based on the optimized centrifugal pump rotor system operation plan, the finite element analysis software is used to establish an accurate finite element model of the centrifugal pump rotor system, such as Figure 3 . Determine the operating conditions and vibration excitations encountered by the system during long-term operation, and apply the corresponding vibration loads. Apply vibration excitation in the model and perform accelerated vibration analysis at different frequencies. Analyze the vibration modes of the multi-stage centrifugal pump rotor system and evaluate whether the vibration stability and performance of the system during long-term operation meet the long-term operation requirements.

[0187] At the same time, the ANSYS finite element software is used to calculate the natural frequency of the corresponding vibration mode diagram of the multi-stage centrifugal pump and the nonlinear deformation of the rotor system under prestress, change the rotation speed of the rotor components, calculate the output multi-stage water pump with prestress Campbell diagram (as shown in Figure 5), and finally determine the critical speed of the rotor through the Campbell diagram. By comparing the critical speed and the rated speed of the pump, it can be concluded that the pump rotor meets the design requirements, and the optimized rotor vibration displacement along the x, y, and z directions meets the long-term operation requirements of the centrifugal pump rotor system. The vibration results of the optimal operation scheme of the optimized centrifugal pump rotor system are as follows: Figure 6-8 As shown. Then the optimal operation scheme of the centrifugal pump rotor system is output.

[0188] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for designing a centrifugal pump rotor system considering long-term operation, comprising the following steps: Step 1: Design the hydraulic performance and structure of the centrifugal pump according to the long-term operation requirements of the centrifugal pump; Step 2: Comprehensively analyze the rotor dynamics to extract the main flow field exciting force and the gap flow field exciting force; Step 3: Determine the quantitative control target of centrifugal pump assembly accuracy from the perspective of structural discipline; Step 4: Analyze the coaxiality of the multi-stage centrifugal pump rotor assembly from the perspective of manufacturing technology; Step 5: According to the multidisciplinary design optimization method, select the design variables to be optimized, construct the optimization function, and establish the mathematical model for centrifugal pump rotor system optimization; Step 6: Use a multi-objective artificial bee colony algorithm to solve the mathematical model and obtain the optimal solution set; Step 7: Based on the optimal solution set, construct an optimized centrifugal pump rotor system model and conduct long-term operation analysis.

2. The centrifugal pump rotor system design method considering long-term operation according to claim 1 is characterized in that: The step 1 of designing the hydraulic performance and structure of the centrifugal pump includes: According to the long-cycle requirements of the centrifugal pump, the formula that satisfies the long-cycle operation of the centrifugal pump rotor system is set as: G(t>t0) <G0±5% in: G is the actual vibration amplitude of the centrifugal pump, G0 is the specified vibration amplitude, t is the time for the centrifugal pump to operate continuously without fault, and t0 is the time limit for the centrifugal pump to operate continuously without fault.

3. The centrifugal pump rotor system design method considering long-term operation according to claim 2 is characterized in that: The extraction of the main flow field exciting force and the gap flow field exciting force in step 2 includes: Step 2.1 Solution of mainstream field excitation force: The main flow field exciting force component is obtained by integrating the surface of the centrifugal pump rotor component under pressure; Its mainstream field excitation force can be expressed as: Among them: F main is the mainstream field excitation force, F r 、F θ are the flow field exciting forces in the rotor radial direction and the rotor circumferential direction perpendicular to the rotation axis, r is the rotor radial variable, θ is the rotor circumferential variable, u r is the speed of the rotor in the radial direction, u θ is the speed of the rotor in the circumferential direction, ρ is the fluid density, V is the fluid flow rate, A1 is the rotor starting shaft end area, A2 is the rotor ending shaft end area, Q is the fluid flow rate, and ω is the rotor angular velocity; Step 2.2 Solution of gap flow field exciting force: Step 2.21 Construct the microelement control equations of the gap flow field excitation force: Create a set of fluid microelement control equations based on the Moody friction model: The above equations are, from top to bottom, the axial momentum equation, the circumferential momentum equation, the radial momentum equation, and the continuity equation; Where: S is the local gap of the fluid, R is the rotor radius, τ is the shear force, τ r is the shear force in the radial direction of the rotor, τ z is the shear force in the rotor axial direction, τ θ is the shear force in the circumferential direction of the rotor, z is the axial variable of the rotor, u is the speed, and u z is the speed of the rotor in the axial direction, t′ is the time variable, and P is the pressure inside the centrifugal pump; Step 2.22 Solution of the fluid infinitesimal control equations: The perturbation method is used to solve the fluid microelement control equations, and the original equations are simplified into zero-order and first-order perturbation equations about the perturbation quantity, which are further transformed into the numerical solution problem of the first-order differential equations. By solving the equations by the targeting method, the velocity, pressure pulsation, exciting force and equivalent dynamic characteristic parameters of the fluid in the gap flow channel can be obtained.

4. The centrifugal pump rotor system design method considering long-term operation according to claim 3 is characterized in that: The dynamic characteristic equation of the rotor system is constructed as follows: Where: On the left side of the equation, M is the mass matrix, C is the damping matrix, K is the stiffness matrix, and on the right side of the equation, F gap is the gap flow field exciting force, G is the rotor system weight matrix, x is an unknown quantity. By obtaining the eigenvalue of the rotor motion equation, the critical speed, response and other dynamic characteristics and behaviors of the rotor system can be obtained. B1, B2 and B3 are the position matrices of the rotor system after node division.

5. The centrifugal pump rotor system design method considering long-cycle operation according to claim 4 is characterized in that: The quantitative control objectives of the centrifugal pump assembly accuracy determined in step 3 include: Step 3.1 Determine the total tolerance allowable range A≤5% based on the coaxiality requirements: Step 3.2 Construct the radial force extreme value function according to the centrifugal pump assembly process: Where: in: is the radial force component of the i-th part to be optimized on the X-axis, is the radial force component of the i-th part to be optimized on the Y axis, is the radial force of the i-th part to be optimized, p i is the pressure of the i-th part to be optimized, α is the time, β is the angle, γ is the radius, l i is the axial length of the i-th part to be optimized; Combined with the above model, the correlation function between the tolerance design value and the radial force extreme value is: in: is the maximum radial force on a single part to be optimized, h i is the tolerance design value of a part to be optimized, the ith one among n individual parts to be optimized, a, b, c are the coefficients of the corresponding functional relationship, which are determined by the specific functional relationship; Step 3.3 Determine the allowable tolerance range A of each part to be optimized i , 0 i ≤h i and ​ 6. The centrifugal pump rotor system design method considering long-term operation according to claim 5, characterized in that: The step 4 of analyzing the assembly of the multistage centrifugal pump rotor includes: The cumulative eccentricity error expression of the nth-stage centrifugal pump rotor after assembly is: in: T deformationi is the translation transformation matrix of the deformation eccentricity caused by the centrifugal pump rotor fit, dP′ i is the eccentric position vector of the rotor of the i-th stage centrifugal pump, R rj is the rotation matrix of the j-th centrifugal pump rotor around the Z axis, R xj is the rotation matrix of the j-th centrifugal pump rotor reference plane around the X axis, R yj is the rotation matrix of the j-th centrifugal pump rotor reference plane around the Y axis, dP″ i is the matching error value of the single-stage rotor; The axial projection of the rotor axis position of the nth stage centrifugal pump after assembly can be expressed as: The coaxiality expression required for the optimization of the multi-stage centrifugal pump rotor assembly is: in: x i ,y i is the offset of the axis of the i-th level component relative to the reference axis in the x-direction and the y-direction.

7. The centrifugal pump rotor system design method considering long-cycle operation according to claim 6, characterized in that: The process of establishing the mathematical model for centrifugal pump rotor system optimization in step 5 is as follows: Through the selection of design variables, determination of constraints and selection of objective function for the multidisciplinary optimization design of the centrifugal pump rotor system, the mathematical model of the optimization problem is established: min G=f(X、β1、β2;h i ;x i 、y i ) Constraints: 3≤X≤5; 10°≤β1≤30°； 20°≤β2≤40°； 0 i ≤h i and ​ in: G is the vibration amplitude of the centrifugal pump, X is the number of impeller blades, β1 is the impeller inlet angle, β2 is the impeller outlet angle, and R is the maximum allowable offset relative to the reference axis.

8. The centrifugal pump rotor system design method considering long-term operation according to claim 7, characterized in that: In step 6, a multi-objective artificial bee colony algorithm is used to solve the mathematical model to obtain an optimal solution set to optimize the operation of the centrifugal pump rotor system.

9. The centrifugal pump rotor system design method considering long-term operation according to claim 8, characterized in that: The process of constructing the optimized centrifugal pump rotor system model in step 7 is as follows: Based on the optimized centrifugal pump rotor system operation plan, use finite element analysis software to establish an accurate finite element model of the centrifugal pump rotor system; determine the operating conditions and vibration excitations encountered by the system during long-term operation, and apply corresponding vibration loads; apply vibration excitation in the model and perform accelerated vibration analysis at different frequencies; by analyzing the vibration modes of the multi-stage centrifugal pump rotor system, evaluate whether the vibration stability and performance of the system during long-term operation meet the long-term operation requirements; At the same time, the natural frequency of the corresponding vibration mode diagram of the multi-stage centrifugal pump and the nonlinear deformation of the rotor system under prestress are calculated through ANSYS finite element software; By changing the rotation speed of the rotor components, the prestressed Campbell diagram of the multi-stage water pump is calculated and output, and finally the critical speed of the rotor is determined by the Campbell diagram; by comparing the critical speed with the rated speed of the pump, it can be concluded whether the pump rotor meets the design requirements; if it does, the optimal operation plan of the centrifugal pump rotor system is output; if it does not, the centrifugal pump rotor system structure is reset, and then a multidisciplinary optimization analysis is performed.

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