A design method of centrifugal pump rotor system considering long-period operation

Abstract

The application relates to a design method of a centrifugal pump, in particular to a multi-stage centrifugal pump rotor system design method considering long-period operation. The method respectively fuses the structure of the multi-stage centrifugal pump from flow regulation, flow field excitation and manufacturing process factors to improve the stability of the rotor under the operating condition. The technical scheme comprises the following steps: 1, designing the hydraulic performance and structure of the centrifugal pump; 2, extracting the main flow field excitation force and the gap flow field excitation force; 3, determining the quantitative control target of the assembly precision of the centrifugal pump; 4, analyzing the coaxiality of the multi-stage centrifugal pump rotor assembly; 5, according to the multi-disciplinary design optimization method, selecting the required design variables, constructing the optimization function and establishing the mathematical model of the centrifugal pump rotor system optimization; 6, using the multi-objective artificial bee colony algorithm to solve the mathematical model to obtain the optimal solution set; 7, based on the optimal solution set, constructing the optimized centrifugal pump rotor system model and performing long-period operation analysis.

Description

TECHNICAL FIELD

[0001] The present application 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. BACKGROUND

[0002] In the design of a centrifugal pump rotor system, the traditional method mainly focuses on the design and optimization of the centrifugal pump rotor components, so the dynamic characteristics and vibration response of the rotor system are not fully considered, which may lead to excessive vibration or instability of the system in long-period operation.

[0003] CN110674596A discloses a multi-stage centrifugal pump rotor component design method considering operation environment and stability, which considers the influence of local environment and fluid force factors to optimize the structural design of the multi-stage centrifugal pump, improves the stability of the rotor under operating conditions, and can design the rotor component according to the deformation law of the rotor component. However, only the structural design of the rotor component is considered, and the multi-disciplinary design optimization of the centrifugal pump rotor system is not considered, so the stable and reliable working performance of the centrifugal pump in long-period operation cannot be ensured. SUMMARY

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

[0005] The technical problem of the present application is solved by the following technical scheme:

[0006] A design method of a centrifugal pump rotor system considering long-period operation, comprising the following steps:

[0007] Step 1, according to the long-period operation requirements of the centrifugal pump, the hydraulic performance and structure of the centrifugal pump are designed;

[0008] Step 2, comprehensive analysis is performed from the rotor dynamics discipline to extract the main flow field excitation force and the gap flow field excitation force, the target being to reduce the fluid excitation force;

[0009] Step 3, quantitative control target of centrifugal pump assembly accuracy is determined from the structure discipline, the target being to optimize the tolerance design;

[0010] Step 4, the coaxiality of the multi-stage centrifugal pump rotor is analyzed from the manufacturing process discipline, the target being to determine the optimal coaxiality;

[0011] Step 5, according to the multi-disciplinary design optimization method, the required design variables are selected, the optimization function is constructed, and the mathematical model of the centrifugal pump rotor system optimization is established;

[0012] Step 6: Solve the mathematical model using the multi-objective artificial bee colony algorithm to 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, step 1, which designs the hydraulic performance and structure of the centrifugal pump, includes:

[0015] Based on the long-cycle requirements of centrifugal pumps, the formula for satisfying the long-cycle operation of the centrifugal pump rotor system is set as follows:

[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 continuous fault-free operation time of the centrifugal pump, and t0 is the time limit for continuous fault-free operation of the centrifugal pump.

[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 Solving for the excitation force of the main current field:

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

[0022] The main flow field exciting force is analyzed comprehensively, and the extraction method of the main flow field exciting force can obtain the main flow field exciting force component through the area integration of the pressure acting on the surface of the rotor component of the centrifugal pump;

[0023]

[0024] The main flow field exciting force can be expressed as:

[0025]

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

[0027] Step 2.21 constructs the micro-element control equation set of the gap flow field exciting force:

[0028] By introducing the radial and axial momentum equations into the micro-element control equation set 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 micro-element control equation set 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 micro-element control equation set are the axial momentum equation, the circumferential momentum equation, the radial momentum equation and the continuity equation from top to bottom.

[0031] Wherein: S is the local gap of the fluid, R is the radius of the rotor, 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 axial direction of the rotor, τ θ is the shear force in the circumferential direction of the rotor, z is the axial variable of the rotor, u is the velocity, u z is the velocity in the axial direction of the rotor, t' is the time variable, and P is the pressure in the centrifugal pump;

[0032] Step 2.22 solving the fluid micro-element control equation set:

[0033] Solving the fluid micro-element control equation set using the perturbation method can simplify the original equation to zero-order and first-order perturbation equations about the perturbation quantity, and further convert it into a numerical solution problem of a first-order differential equation set. By solving the equation set by the shooting method, the velocity, pressure fluctuation, exciting force and equivalent dynamic characteristic parameters of the fluid in the gap flow passage can be obtained.

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

[0035]

[0036] Where: on the left side of the equation, M is the mass matrix, C is the damping matrix, and K is the stiffness matrix; on the right side of the equation, F gap is the exciting force of the gap flow field, G is the weight matrix of the rotor system, x is the unknown quantity, by solving 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] Further, the quantitative control target of step 3 for determining the assembly precision of the centrifugal pump includes:

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

[0039] Step 3.2 constructs a radial force extreme function according to the assembly process of the centrifugal pump:

[0040]

[0041] In the formula:

[0042]

[0043] Where: is the radial force component of the i-th optimization site in the X-axis, is the radial force component of the i-th optimization site in the Y-axis, is the radial force of the i-th optimization site, p i is the pressure of the i-th optimization site, α is the time, β is the angle, γ is the radius, l i is the axial length of the i-th optimization site.

[0044] Combining the above model, the correlation function of the tolerance design value and the radial force extreme value is:

[0045]

[0046] wherein: is the maximum radial force value that a certain individual optimization site receives, h i is the tolerance design value of a certain optimization site, the i-th of n individual optimization sites, a, b, c are coefficients of the corresponding functional relationship, determined by the specific functional relationship;

[0047] Step 3.3 determines the allowable tolerance range of each optimization site:

[0048] The tolerance design value h i of the measured site is calculated through step 3.2; i The allowable tolerance range A i of each optimization site is determined, 0<A i and h ri .

[0049] Further, the step 4 assembly analysis of the multi-stage centrifugal pump rotor includes:

[0050] Step 4.1 In actual operation, assembly errors have an important influence on the stable operation of the rotor system, and the assembly errors are analyzed based on the centrifugal pump rotor system, 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; the cumulative eccentricity error of the multi-stage centrifugal pump rotor assembly can be expressed by a general expression:

[0051]

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

[0053] Step 4.2, assembly error analysis of the multi-stage centrifugal pump rotor and the single-stage centrifugal pump rotor, then the cumulative eccentric error expression of the n-th stage centrifugal pump rotor after assembly is:

[0054]

[0055] Wherein:

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

[0057] Step 4.3, the axial projection of the axial position of the n-th stage centrifugal pump rotor after assembly can be expressed as:

[0058]

[0059] Then the expression of the concentricity required to be optimized for the assembly of the multi-stage centrifugal pump rotor is:

[0060]

[0061] Wherein:

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

[0063] Said step 5, according to the multi-disciplinary design optimization method, selecting appropriate design variables, constructing the objective function, and establishing the mathematical model of the optimization of the centrifugal pump rotor system;

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

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

[0066] G = f (X, β1, β2; h i ; x i , y i )

[0067] Wherein:

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

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

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

[0071] Constraint condition: 3≤X≤5;

[0072] 10°≤β1≤30°;

[0073] 20°≤β2≤40°;

[0074] 0<A i ≤h i and

[0075]

[0076] Wherein:

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

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

[0079] Further, the process of using a multi-objective artificial bee colony algorithm to solve the mathematical model of the step 6 is:

[0080] The formula for solving the optimization operation model by the multi-objective artificial bee colony algorithm includes:

[0081]

[0082] vi = x i + (2 * rand() - 1) * (x i - S k ) ;

[0083]

[0084] wherein:

[0085] x ij is the jth dimension value of the solution corresponding to the ith bee, i is the bee number, j is the dimension number, is the upper and lower bound of x ij , rand() is a random number in the interval [0, 1], v i is a new solution, x i is the original solution, S k is a randomly selected employed bee in the optimal solution set, d q (x k ) is the crowding distance of the employed bee x k on the qth objective function, D(x k ) is the crowding distance of the employed bee x k , 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 fitness calculation formula of the nectar source is:

[0087]

[0088] wherein:

[0089] Z i is the number of solutions dominated by x i , SN is the initial population size.

[0090] The following bees are judged in the roulette wheel manner, and the judgment basis is the transition probability:

[0091]

[0092] wherein:

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

[0094] Further, the step 7 is the process of building an optimized centrifugal pump rotor system model, which is:

[0095] Based on the optimized centrifugal pump rotor system operation scheme, a precise finite element model of the centrifugal pump rotor system is established using finite element analysis software. The working conditions and vibration excitations encountered by the system during long-period operation are determined, and the corresponding vibration load is applied. The vibration excitations are applied in the model, and the accelerated vibration analysis is carried out at different frequencies. By analyzing the vibration mode of the multi-stage centrifugal pump rotor system, the vibration stability and performance of the system during long-period operation are evaluated to determine whether the long-period operation requirements are met.

[0096] At the same time, through the ANSYS finite element software, 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, the rotational speed of the rotor component is changed, the prestressed Campbell diagram of the multi-stage water pump is calculated, and finally the critical speed of the rotor is determined 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 scheme of the centrifugal pump rotor system is output, and if it does not meet the requirements, the structure of the centrifugal pump rotor system is reconfigured, and the multi-disciplinary optimization analysis is performed again.

[0097] The beneficial effects of the present application are: the present application is a multi-disciplinary collaborative optimization algorithm, which comprehensively considers the structure discipline, rotor dynamics discipline and manufacturing technology discipline, and integrates the factors of flow control, flow field excitation and manufacturing technology into the design of the multi-stage centrifugal pump, thereby improving the stability of the rotor under operating conditions, and providing a new design idea and method for the optimization and design of the multi-stage centrifugal pump. BRIEF DESCRIPTION OF DRAWINGS

[0098] Figure 1 The flowchart of the multi-stage centrifugal pump rotor system design method according to the embodiment of the present application is shown.

[0099] Figure 2 The structure diagram of the multi-stage centrifugal pump before optimization in the embodiment of the present application is shown.

[0100] Figure 3 The structure diagram of the multi-stage centrifugal pump after optimization according to the embodiment of the present application is shown.

[0101] Figure 4 is Figure 3 is a force diagram of the multi-stage centrifugal pump rotor system.

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

[0103] Figure 5b is a symbol explanation of the Campbell method diagram of the rotor in the embodiment of the present application.

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

[0105] Figure 7 The y-axis vibration displacement time distribution graph of the multi-stage centrifugal pump before optimization and the y-axis vibration displacement time distribution graph of the multi-stage centrifugal pump after optimization in the implementation case.

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

[0107] Inducer 1, impeller 2. DETAILED DESCRIPTION

[0108] The application is further illustrated below in combination with the embodiments shown in the drawings.

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

[0110] Step 1: According to the long-period operation requirements of the centrifugal pump, the hydraulic performance and structure of the centrifugal pump are designed;

[0111] According to the requirements of the multi-stage centrifugal pump, the preliminary structure design of the multi-stage centrifugal pump is performed (see Figure 1 );

[0112] According to the long-period requirements of the centrifugal pump, the time limit for continuous failure-free operation of the centrifugal pump is taken as 1.5 years, and the maximum vibration does not exceed 16 μm at all times, then the formula for meeting the long-period operation of the centrifugal pump rotor system is:

[0113] G(t>1.5 year)<16 μm±5%

[0114] Wherein:

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

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

[0117] Step 2: Comprehensive analysis is performed from the rotor dynamics discipline to extract the main flow field excitation force and the gap flow field excitation force;

[0118] The main flow field exciting force is analyzed comprehensively, and the main flow field exciting force component is extracted by area integration of the pressure acting on the surface of the rotor component of the centrifugal pump.

[0119]

[0120] The main flow field exciting force can be expressed as:

[0121]

[0122] The boundary conditions are obtained and the exciting force of the gap flow field is calculated by introducing the radial and axial momentum equations into the micro-element control equation set of the gap flow field. A micro-element control equation set of the flow field based on the Moody friction model is created, which includes the axial, circumferential and radial momentum equations and the continuity equation:

[0123]

[0124] The formulas in the above micro-element control equation set of the flow field are the axial momentum equation, the circumferential momentum equation, the radial momentum equation and the continuity equation from top to bottom.

[0125] The original equation is simplified into zero-order and first-order perturbation equations about the perturbation quantity by using the perturbation method to solve the micro-element control equation set of the flow field, which is further converted into a numerical solution problem of a first-order differential equation set. The velocity, pressure fluctuation, exciting force and equivalent dynamic characteristic parameters of the fluid in the gap flow passage are obtained by solving the equation set by the shooting method.

[0126] According to the force acting on 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, and K is the stiffness matrix; on the right side of the equation, F gap is the exciting force of the gap flow field, G is the weight matrix of the rotor system, x is the unknown quantity, and the critical speed, response and other dynamic characteristics and behaviors of the rotor system can be obtained by solving the eigenvalues of the rotor motion equation; B1, B2 and B3 are the position matrices of the rotor system after node division. Figure 4

[0129] Step 3, determine the quantitative control target of the assembly accuracy of the centrifugal pump from the structure discipline;

[0130] According to the coaxiality requirement, the total tolerance allowable range A≤5% is determined;

[0131] ​According to the centrifugal pump assembly process, a radial force extreme function is constructed:

[0132]

[0133] In the formula:

[0134]

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

[0136] In combination with the above model, the correlation function of the tolerance design value and the radial force extreme value is:

[0137]

[0138] In the formula: is the maximum radial force received by a single to-be-optimized part, h i is the tolerance design value of a to-be-optimized part, i-th in n to-be-optimized single parts, a, b, c are coefficients of the corresponding function relationship, which are determined by the specific function relationship.

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

[0140] Step 4, analyze the assembly coaxiality of the multistage centrifugal pump rotor from the manufacturing process discipline;

[0141] In actual operation, 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, the assembly error 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. The cumulative eccentric error of the assembly of the multistage centrifugal pump rotor can be expressed by a general expression:

[0142]

[0143] In the formula: ri is the transformation matrix between the interfaces of the two-stage centrifugal pump rotor, T Zi is the eccentricity of the ideal center of the centrifugal pump rotor i, T clearancei is the translation transformation matrix of the reference surface eccentricity of the centrifugal pump rotor i, T dzi is the translation transformation matrix caused by the machining error of the reference surface of the centrifugal pump rotor i, Torientationi is the rotation transformation matrix of the reference surface of the i-th stage centrifugal pump rotor to the rotation center of the assembly surface, R ri is the rotation matrix of the reference surface of the i-th stage centrifugal pump rotor around the Z axis, R xi is the rotation matrix of the reference surface of the i-th stage centrifugal pump rotor around the X axis, R yi is the rotation matrix of the reference surface of the i-th stage centrifugal pump rotor around the Y axis, R r(j-1) is the rotation matrix of the j-1-th stage centrifugal pump rotor around the Z axis, R x(j-1) is the rotation matrix of the reference surface of the j-1-th stage centrifugal pump rotor around the X axis, R y(j-1) is the rotation matrix of the reference surface of the j-1-th stage centrifugal pump rotor around the Y axis, P i is the ideal position vector of the center of the assembly surface of the i-th stage centrifugal pump rotor, dP i is the machining error vector of the center position of the assembly surface of the i-th stage centrifugal pump rotor, dP' i is the eccentric position vector of the i-th stage centrifugal pump rotor.

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

[0145]

[0146] Wherein:

[0147] T deformationi is the translation transformation matrix of the deformation eccentricity caused by the cooperation of the centrifugal pump rotor, dP' i is the eccentric position vector of the i-th stage centrifugal pump rotor caused by the cooperation, R rj is the rotation matrix of the j-th stage centrifugal pump rotor around the Z axis, R xj is the rotation matrix of the reference surface of the j-th stage centrifugal pump rotor around the X axis, R yj is the rotation matrix of the reference surface of the j-th stage centrifugal pump rotor around the Y axis, dP" i is the cooperation error value of the single-stage rotor.

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

[0149]

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

[0151]

[0152] Wherein:

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

[0154] Step 5, according to the multidisciplinary design optimization method, selecting the design variables required to be optimized, constructing the optimization function, and establishing the mathematical model of the optimization of the centrifugal pump rotor system;

[0155] Based on the multidisciplinary optimization design of the centrifugal pump rotor system, comprehensively considering the analysis of the structural discipline, the rotor dynamics discipline and the manufacturing process discipline, selecting the number of impeller blades, the impeller inlet angle, the impeller outlet angle, and the tolerance design value h of a to-be-optimized part i And the offset of the axis of the i-th component in the x direction and the y direction relative to the reference axis x i , y i As a design variable, selecting the vibration amplitude as the optimization target function, and constructing the correlation function between the design variable and the target function as:

[0156] G = f (X, β1, β2; h i ; x i , y i )

[0157] Wherein:

[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] Through the selection of the design variables of the multidisciplinary optimization design of the centrifugal pump rotor system, the determination of the constraint conditions and the selection of the target function, the mathematical model of the optimization problem can be established:

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

[0161] Constraint condition: 3 ≤ X ≤ 5;

[0162] 10° ≤ β1 ≤ 30°;

[0163] 20° ≤ β2 ≤ 40°;

[0164] 0 < A i ≤ h i and

[0165]

[0166]

[0167] Wherein:

[0168] R is 14 μm relative to the maximum allowed offset of the reference axis.

[0169] Step 6, the mathematical model is solved by using the multi-objective artificial bee colony algorithm to obtain an optimal solution set.

[0170] The formula for solving the optimization operation model by the multi-objective artificial bee colony algorithm includes:

[0171]

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

[0173]

[0174] Wherein:

[0175] x ij is the j-dimensional variable value corresponding to the solution of the i-th bee, i is the bee number, j is the dimension number, is the upper and lower bounds of x ij , rand () is a random number in the interval [0, 1], v i is a new solution, x i is the original solution, S k is a randomly selected employed bee in the optimal solution set, d q (x k ) is the crowding distance of the employed bee x k on the q objective functions, D(x k ) is the crowding distance of the employed bee x k , 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 fitness calculation formula of the honey source is:

[0177]

[0178] Wherein:

[0179] Z i is the number of solutions dominated by x i , SN is the initial population size.

[0180] Follow the bees in the way of judging, judging on the basis of transition probability:

[0181]

[0182] Wherein:

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

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

[0185] Step 7, based on the optimal solution set, an optimized centrifugal pump rotor system model is constructed, and long-period operation analysis is performed.

[0186] Based on the optimized centrifugal pump rotor system operation scheme, a precise finite element model of the centrifugal pump rotor system is established using finite element analysis software, such as Figure 3 . The working conditions and vibration excitations encountered by the system in long-period operation are determined, and the corresponding vibration loads are applied. Vibration excitations are applied in the model, and acceleration vibration analysis is performed at different frequencies. The vibration modes of the multi-stage centrifugal pump rotor system are analyzed, and whether the vibration stability and performance of the system in long-period operation meet the long-period operation requirements are evaluated.

[0187] At the same time, through the ANSYS finite element software, 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, the rotational speed of the rotor component is changed, the prestressed Campbell diagram of the multi-stage water pump is calculated (as shown in FIG. 5), and finally the critical speed of the rotor is determined through the Campbell diagram. Through the comparison of 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 in the x, y and z directions meets the long-period operation requirements of the centrifugal pump rotor system, and the vibration results of the optimized centrifugal pump rotor system optimal operation scheme are shown in Figures 6-8 . Then the optimal operation scheme of the centrifugal pump rotor system is output.

[0188] The above only describes the preferred embodiments of the present application and is not intended to limit the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. A design method for a centrifugal pump rotor system considering long-cycle operation, comprising the following steps: Step 1: Design the hydraulic performance and structure of the centrifugal pump according to the requirements of long-term operation; Step 2: Conduct a comprehensive analysis from the rotor dynamics department to extract the excitation force of the main flow field and the excitation force of the gap flow field; Step 3: Determine and quantify the assembly accuracy target of the centrifugal pump from the perspective of structural engineering. Step 4: Analyze the coaxiality of the multistage centrifugal pump rotor assembly from the perspective of manufacturing process. Step 5: Based on the multidisciplinary design optimization method, select the design variables to be optimized, construct the optimization function, and establish the mathematical model for the centrifugal pump rotor system optimization; Step 6: Solve the mathematical model using the multi-objective artificial bee colony algorithm to 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; Step 1, which designs the hydraulic performance and structure of the centrifugal pump, includes: Based on the long-cycle requirements of centrifugal pumps, the formula for satisfying the long-cycle operation of the centrifugal pump rotor system is set as follows: in: This represents the actual vibration amplitude of the centrifugal pump. The vibration amplitude is the specified value, and t is the time during which the centrifugal pump can operate continuously without failure. This is the time limit for continuous, trouble-free operation of a centrifugal pump. The extraction of the main flow field excitation force and the gap flow field excitation force in step 2 includes: Step 2.1 Solving for the excitation force of the main current field: The surface integral of the pressure acting on the surface of the centrifugal pump rotor component is used to obtain the main field excitation force component. Its mainstream field excitation force can be expressed as: in: As the main field excitation force, These are the flow field excitation forces in the radial and circumferential directions of the rotor, respectively, perpendicular to the rotation axis. For rotor radial variable, For the rotor circumferential variable, The radial velocity of the rotor. The velocity is the rotor's circumferential velocity, and ρ is the fluid density. For fluid velocity, The initial shaft end area of ​​the rotor. The area of ​​the rotor shaft end is... For fluid flow rate, This refers to the rotor angular velocity; Step 2.2 Solving for the excitation force in the gap flow field: Step 2.21 Construct the governing equations of the excitation force micro-element in the gap flow field: Create a set of fluid microequations based on the Moody friction model: The above set of equations, from top to bottom, consists of 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. Let τ be the rotor radius and τ be the shear force. This refers to the shear force in the radial direction of the rotor. This refers to the shear force in the axial direction of the rotor. Let z be the shear force in the circumferential direction of the rotor, z be the rotor axial variable, and u be the velocity. The axial velocity of the rotor. Time is the variable; P is the pressure inside the centrifugal pump. Step 2.22 Solving the fluid infinitesimal element control equations: The perturbation method is used to solve the fluid infinitesimal element control equations, simplifying the original equations into zero-order and first-order perturbation equations about the perturbation quantity, and further transforming them into a numerical solution problem of a first-order differential equation system. By solving this equation system using the target method, the velocity, pressure pulsation, excitation force, and equivalent dynamic characteristic parameters of the fluid in the gap flow channel can be obtained.

2. The centrifugal pump rotor system design method considering long-cycle operation according to claim 1, characterized in that: The dynamic characteristic equations of the rotor system are constructed as follows: ； Where: on the left side of the equation, M is the mass matrix, C is the damping matrix, and K is the stiffness matrix; on the right side of the equation... For the excitation force of the gap flow field, H The rotor system weight matrix, , , For unknown quantities, by obtaining the eigenvalues ​​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 partitioning.

Images