Heat dissipation fan multi-direction spring pre-tightening force balancing and wide frequency vibration energy optimization method and fan

Abstract

The present application relates to the technical field of vibration simulation, and discloses a multi-direction spring pre-tightening force balancing and wide-frequency vibration energy optimization method for a cooling fan and the fan. The method comprises the following steps: performing simulation calculation on the cooling fan to obtain first power spectral density data in the axial direction, second power spectral density data in the radial direction, third power spectral density data in the tangential direction, and a set of aerodynamic excitation main frequencies; calculating each order natural frequency and first distribution coefficients in the axial direction, second distribution coefficients in the radial direction, and third distribution coefficients in the tangential direction; and based on a set of resonance risk modes, the first distribution coefficients, the second distribution coefficients, and the third distribution coefficients, solving first spring pre-tightening forces in the axial direction, second spring pre-tightening forces in the radial direction, and third spring pre-tightening forces in the tangential direction. The present application solves the technical problem that the prior art relies on steady-state time-averaged aerodynamic force and cannot represent the wide-frequency excitation characteristics, and outputs optimal values of three-direction spring pre-tightening forces under the premise of ensuring calculation efficiency, thereby realizing the collaborative balancing and suppression of three-direction vibration energy.

Description

Technical Field

[0001] This invention relates to the field of vibration simulation technology, and in particular to a method for balancing the preload of multi-directional springs and optimizing broadband vibration energy in a cooling fan, as well as the fan itself. Background Technology

[0002] Cooling fans are the core components of the thermal management system of electronic equipment. When operating at high speed, the unsteady aerodynamic excitation force generated by the rotation of the blades acts on the bearing-spring support system simultaneously in three directions: axial, radial, and tangential. This causes broadband structural vibration, resulting in increased bearing wear, excessive noise, and shortened equipment life.

[0003] In existing technologies, vibration suppression schemes for cooling fans only use a single preload spring in the axial direction, relying on engineering experience to determine the spring preload parameters. There is a lack of simulation methods to quantitatively correlate the frequency domain characteristics of the three-dimensional aerodynamic excitation force with the structural dynamic response. This results in a severe mismatch between the spring stiffness and the actual aerodynamic load spectrum, with the radial and tangential vibration modes remaining unconstrained for a long time. A large amount of broadband vibration energy is radiated as structural noise through the fan frame, leading to long design iteration cycles and difficulty in reliably reproducing the vibration suppression effect in physical products. Summary of the Invention

[0004] The main objective of this invention is to provide a method for balancing the preload of multi-directional springs and optimizing broadband vibration energy in a cooling fan, as well as a fan itself. This invention solves the technical problem that existing technologies rely on steady-state aerodynamic forces and cannot characterize broadband excitation characteristics. Under the premise of ensuring computational efficiency, it outputs the optimal value of the three-directional spring preload, thereby achieving coordinated balance and suppression of three-directional vibration energy.

[0005] To achieve the above objectives, the present invention provides a method for balancing the preload of multi-directional springs and optimizing broadband vibration energy in a cooling fan, comprising the following steps: Simulation calculations were performed on the cooling fan to obtain the first power spectral density data in the axial direction, the second power spectral density data in the radial direction, the third power spectral density data in the tangential direction, and the set of aerodynamic excitation frequencies. Based on the first power spectral density data, the second power spectral density data, and the third power spectral density data, calculate the natural frequencies of each order and the first axial allocation coefficient, the second radial allocation coefficient, and the third tangential allocation coefficient. Based on the aerodynamic excitation main frequency set and the natural frequencies of each order, a set of resonant risk modes is determined, and based on the set of resonant risk modes, the first allocation coefficient, the second allocation coefficient, and the third allocation coefficient, the first spring preload in the axial direction, the second spring preload in the radial direction, and the third spring preload in the tangential direction are solved.

[0006] Optionally, in a first implementation of the first aspect of the present invention, the step of performing simulation calculations on the cooling fan to obtain axial first power spectral density data, radial second power spectral density data, tangential third power spectral density data, and aerodynamic excitation frequency set includes: The cooling fan was simulated using the COMSOL turbulence CFD module. The surface pressure and viscous shear force of the blades were integrated and projected along the axial, radial and tangential directions to obtain the first aerodynamic excitation force data in the axial direction, the second aerodynamic excitation force data in the radial direction and the third aerodynamic excitation force data in the tangential direction. Fast Fourier transform is performed on the first aerodynamic excitation force data, the second aerodynamic excitation force data, and the third aerodynamic excitation force data respectively to obtain the first power spectral density data in the axial direction, the second power spectral density data in the radial direction, the third power spectral density data in the tangential direction, and the corresponding aerodynamic excitation frequency set.

[0007] Optionally, in a second implementation of the first aspect of the present invention, the step of performing fast Fourier transform on the first aerodynamic excitation force data, the second aerodynamic excitation force data, and the third aerodynamic excitation force data to obtain axial first power spectral density data, radial second power spectral density data, tangential third power spectral density data, and the corresponding aerodynamic excitation frequency set includes: Fast Fourier transform is performed on the first aerodynamic excitation force data, the second aerodynamic excitation force data, and the third aerodynamic excitation force data respectively to obtain the axial single-sided amplitude spectrum, the radial single-sided amplitude spectrum, and the tangential single-sided amplitude spectrum; The root mean square (RMS) value of the first full-band frequency is calculated based on the axial unilateral amplitude spectrum; the root mean square (RMS) value of the second full-band frequency is calculated based on the radial unilateral amplitude spectrum; and the root mean square (RMS) value of the third full-band frequency is calculated based on the tangential unilateral amplitude spectrum. The first axial power spectral density data and the first aerodynamic excitation frequency data are extracted based on the first full-band root mean square value; the second radial power spectral density data and the second aerodynamic excitation frequency data are extracted based on the second full-band root mean square value; and the third tangential power spectral density data and the third aerodynamic excitation frequency data are extracted based on the third full-band root mean square value. The first aerodynamic excitation frequency data, the second aerodynamic excitation frequency data, and the third aerodynamic excitation frequency data are merged and deduplicated to obtain the aerodynamic excitation frequency set.

[0008] Optionally, in a third implementation of the first aspect of the present invention, the calculation of each natural frequency and the first axial allocation coefficient, the second radial allocation coefficient, and the third tangential allocation coefficient based on the first power spectral density data, the second power spectral density data, and the third power spectral density data includes: Establish a finite element model of the coupled structure of the cooling fan in the COMSOL solid mechanics module; The first power spectral density data, the second power spectral density data, and the third power spectral density data are used as load boundary conditions and input into the finite element model to solve for each natural frequency and each mode shape. The ratio of the elastic potential energy of each mode on the axial spring array, radial spring array, and tangential spring array to the total strain energy of each mode is calculated to obtain the first distribution coefficient, the second distribution coefficient, and the third distribution coefficient.

[0009] Optionally, in a fourth implementation of the first aspect of the present invention, the step of inputting the first power spectral density data, the second power spectral density data, and the third power spectral density data as load boundary conditions into the finite element model to solve for each natural frequency and each mode shape includes: The first power spectral density data, the second power spectral density data, and the third power spectral density data are imported into the finite element model in COMSOL interpolation function format as load boundary conditions for the corresponding nodes on the blade surface. The ARPACK solver was used to solve the finite element model to obtain the natural frequencies and mode shapes of each order.

[0010] Optionally, in a fifth implementation of the first aspect of the present invention, the step of determining the set of resonant risk modes based on the set of aerodynamic excitation main frequencies and the natural frequencies of each order, and solving for the axial first spring preload, the radial second spring preload, and the tangential third spring preload based on the set of resonant risk modes, the first allocation coefficient, the second allocation coefficient, and the third allocation coefficient, includes: Calculate the set of resonant risk modes based on the set of aerodynamic excitation dominant frequencies and the natural frequencies of each order; Based on the resonant risk mode set, the first allocation coefficient, the second allocation coefficient, and the third allocation coefficient, a first Kriging surrogate model is constructed using axial spring preload, a second Kriging surrogate model is constructed using radial spring preload, and a third Kriging surrogate model is constructed using tangential spring preload. Multi-objective optimization calculations are performed based on the first Kriging surrogate model, the second Kriging surrogate model, and the third Kriging surrogate model to obtain the first spring preload in the axial direction, the second spring preload in the radial direction, and the third spring preload in the tangential direction.

[0011] Optionally, in a sixth implementation of the first aspect of the present invention, the step of performing multi-objective optimization calculations based on the first Kriging surrogate model, the second Kriging surrogate model, and the third Kriging surrogate model to obtain the axial first spring preload, the radial second spring preload, and the tangential third spring preload includes: Multi-objective optimization calculations are performed based on the first Kriging surrogate model to obtain a first candidate solution set; multi-objective optimization calculations are performed based on the second Kriging surrogate model to obtain a second candidate solution set; multi-objective optimization calculations are performed based on the third Kriging surrogate model to obtain a third candidate solution set. The first optimal solution is selected from the first candidate solution set as the first spring preload in the axial direction; the second optimal solution is selected from the second candidate solution set as the second spring preload in the radial direction; and the third optimal solution is selected from the third candidate solution set as the third spring preload in the tangential direction.

[0012] Optionally, in a seventh implementation of the first aspect of the present invention, after solving for the axial first spring preload, the radial second spring preload, and the tangential third spring preload, the method further includes: The static deformation of the cooling fan coupling structure is solved based on the first spring preload, the second spring preload, and the third spring preload. A wideband frequency domain sweep simulation is performed using the first power spectral density data, the second power spectral density data, and the third power spectral density data to obtain the first frequency response data in the axial direction, the second frequency response data in the radial direction, and the third frequency response data in the tangential direction. Based on the first frequency response data, the second frequency response data, and the third frequency response data, spring preload verification is performed. The verified first spring preload, second spring preload, and third spring preload are divided by the spring linear stiffness to obtain the axial first spring assembly compression, the radial second spring assembly compression, and the tangential third spring assembly compression.

[0013] Optionally, in an eighth implementation of the first aspect of the present invention, the step of performing static deformation calculation on the cooling fan coupling structure based on the first spring preload, the second spring preload, and the third spring preload, and performing wideband frequency domain sweep simulation using the first power spectral density data, the second power spectral density data, and the third power spectral density data to obtain axial first frequency response data, radial second frequency response data, and tangential third frequency response data includes: The first spring preload, the second spring preload, and the third spring preload are applied to the finite element model to solve for static deformation, thereby obtaining the static deformation field and the stress stiffening matrix. Based on the static deformation field and the stress stiffening matrix, the first power spectral density data, the second power spectral density data, and the third power spectral density data are input into the finite element model to perform frequency domain sweep simulation, thereby obtaining the first frequency response data in the axial direction, the second frequency response data in the radial direction, and the third frequency response data in the tangential direction.

[0014] The present invention also provides a fan for implementing the steps of the method described in any of the above embodiments.

[0015] In summary, this invention solves the technical problem of existing technologies that rely on steady-state time-averaged aerodynamic forces and cannot characterize broadband excitation characteristics by integrating and projecting the aerodynamic loads on the blade surface along the axial, radial, and tangential directions and extracting the corresponding power spectral density data, and simultaneously acquiring the frequency domain distribution characteristics of the three-dimensional aerodynamic excitation forces in the same simulation environment. Furthermore, this invention calculates the axial, radial, and third distribution coefficients of each vibration mode in the finite element model of a cooling fan coupled with a three-dimensional decoupled spring array, achieving accurate tracing of the energy direction of each resonance mode vibration in a broadband band. Through the collaborative solution of the Kriging surrogate model and a multi-objective optimization algorithm, with the three-dimensional vibration acceleration equilibrium objective function, the broadband vibration total energy objective function, and the resonance risk mode forced response amplitude objective function as optimization objectives, the optimal value of the three-dimensional spring preload is output while ensuring computational efficiency, achieving collaborative equilibrium suppression of three-dimensional vibration energy. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the steps of the method for balancing the preload of the multi-directional spring of the cooling fan and optimizing the broadband vibration energy in one embodiment of the present invention; Figure 2 This is a schematic diagram illustrating the steps of the cooling fan simulation calculation in an embodiment of the present invention; Figure 3 This is a schematic diagram illustrating the steps of calculating power spectral density data and aerodynamic excitation frequency set in an embodiment of the present invention; Figure 4 This is a schematic diagram illustrating the steps for calculating the anisotropic allocation coefficients in an embodiment of the present invention; Figure 5 This is a schematic diagram illustrating the steps for calculating the spring preload in each direction in an embodiment of the present invention; Figure 6 This is a schematic diagram illustrating the steps for calculating the spring assembly compression in an embodiment of the present invention.

[0017] The realization of the objective, functional features and advantages of the present invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0019] Reference Figure 1 This embodiment provides a method for balancing the preload of multi-directional springs and optimizing broadband vibration energy in a cooling fan, including the following steps: S100, simulates the cooling fan to obtain the first power spectral density data in the axial direction, the second power spectral density data in the radial direction, the third power spectral density data in the tangential direction, and the set of aerodynamic excitation main frequencies; S200, based on the first power spectral density data, the second power spectral density data, and the third power spectral density data, calculates the natural frequencies of each order and the first axial allocation coefficient, the second radial allocation coefficient, and the third tangential allocation coefficient. S300 determines the set of resonant risk modes based on the set of aerodynamic excitation main frequencies and the natural frequencies of each order, and solves for the first spring preload in the axial direction, the second spring preload in the radial direction, and the third spring preload in the tangential direction based on the set of resonant risk modes, the first allocation coefficient, the second allocation coefficient, and the third allocation coefficient.

[0020] In this embodiment of the invention, by integrating and projecting the aerodynamic load on the blade surface along the axial, radial, and tangential directions and extracting the corresponding power spectral density data, the frequency domain distribution characteristics of the three-dimensional aerodynamic excitation force are obtained synchronously in the same simulation environment. This solves the technical problem of existing technologies relying on steady-state time-averaged aerodynamic forces and being unable to characterize broadband excitation characteristics. By calculating the axial, radial, and third distribution coefficients of each vibration mode in the finite element model of the cooling fan coupling structure containing a three-dimensional decoupled spring array, the precise source of vibration energy direction of each resonance mode in the broadband is achieved. Through the collaborative solution of the Kriging surrogate model and the multi-objective optimization algorithm, with the three-dimensional vibration acceleration equilibrium objective function, the broadband vibration total energy objective function, and the resonance risk mode forced response amplitude objective function as optimization objectives, the optimal value of the three-dimensional spring preload is output under the premise of ensuring computational efficiency, thus achieving the collaborative equilibrium suppression of three-dimensional vibration energy.

[0021] In one specific embodiment, such as Figure 2 S100 includes: S101 uses the COMSOL turbulence CFD module to simulate and calculate the cooling fan. The surface pressure and viscous shear force of the blades are integrated and projected along the axial, radial and tangential directions to obtain the first aerodynamic excitation force data in the axial direction, the second aerodynamic excitation force data in the radial direction and the third aerodynamic excitation force data in the tangential direction. S102, perform fast Fourier transform on the first aerodynamic excitation force data, the second aerodynamic excitation force data, and the third aerodynamic excitation force data respectively to obtain the first power spectral density data in the axial direction, the second power spectral density data in the radial direction, the third power spectral density data in the tangential direction, and the corresponding aerodynamic excitation main frequency set.

[0022] In this simulation, an unsteady flow field model of the cooling fan was established in COMSOL Multiphysics. The fan blades, hub, and surrounding air domain were divided into a rotating domain and a stationary domain. The rotating domain, centered on the blades and hub, had an outer diameter that could be 1.15 times the blade tip radius, preserving space for tip vortex development without significantly increasing computational load. The stationary domain surrounded the rotating domain, with the inlet boundary approximately 3 times the blade chord length from the upstream end face of the rotating domain and the outlet boundary approximately 5 times the blade chord length from the downstream end face, thus reducing the impact of inlet disturbance and outlet recirculation on the pressure distribution on the blade surface. Subsequently, the turbulence CFD module was called, employing a realizable k-ε turbulence model to describe the fan's rotating flow field. Enhanced wall treatment was enabled to maintain high computational accuracy in the near-wall region of the blades in both the low Reynolds number and logarithmic law regions, avoiding distortion in pressure and shear force calculations due to the limited applicability of standard wall functions. In the mesh setup, a boundary layer mesh was used for the blade surface and near-wall region, with the first layer mesh height meeting certain conditions. The boundary layer can be set to 15 layers with a growth ratio of 1.2. A free tetrahedral mesh is used within the rotating domain, with the maximum element size being 1 / 20th of the blade's minimum chord length. A structured hexahedral mesh is used in the stationary domain, with the maximum element size being three times that of the rotating domain. This ensures that blade surface pressure, viscous shear force, and unsteady wake fluctuations can all be effectively captured. A sliding mesh interface is set between the rotating and stationary domains, and the physical time step and effective sampling duration are determined based on the target frequency upper limit and frequency resolution. If the target frequency upper limit is set to 20000Hz, the sampling frequency meets the following requirements: ,in Thus we obtain The corresponding time step satisfies If the frequency resolution is set to 1Hz, then the effective sampling duration satisfies the following conditions. The simulation runtime covers the transition period required for flow field stabilization and an effective sampling period of no less than 1 second, discarding the initial transition period and performing triaxial aerodynamic integration and frequency domain analysis only on stable unsteady results. At the end of each effective time step, the pressure and viscous shear force on all grid nodes of the blade surface are read and projected into the axial, radial, and tangential directions according to the fan coordinate system. The axial direction corresponds to the direction perpendicular to the blade rotation plane, the radial direction corresponds to the blade spanwise direction, and the tangential direction corresponds to the tangential direction of the blade rotation direction. Then, the surface forces projected onto each node are numerically integrated to obtain the first aerodynamic excitation force data in the axial direction, the second aerodynamic excitation force data in the radial direction, and the third aerodynamic excitation force data in the tangential direction, which are three sets of unsteady aerodynamic force sequences that vary with time. , , All three are in units of N.

[0023] After obtaining the three-dimensional aerodynamic time-domain sequences, mean removal, equal-time interval verification, and outlier removal are performed on each data set to prevent steady-state bias and numerical spikes from affecting the frequency domain results. Then, Hanning windows are applied to reduce spectral leakage. Fast Fourier transforms are performed on the first, second, and third aerodynamic excitation force data to obtain the axial, radial, and tangential frequency domain spectra. The three-dimensional frequency domain results are uniformly organized into a single-sided spectrum form and covered a wide frequency range from 20Hz to 20000Hz with a frequency resolution of 1Hz, thereby generating the first axial power spectral density data, the second radial power spectral density data, and the third tangential power spectral density data. At the same time, based on the significant peaks in the power spectral density data of each direction, the corresponding aerodynamic excitation master frequency data are initially formed. Then, the three-dimensional master frequency data are merged and deduplicated to obtain the aerodynamic excitation master frequency set.

[0024] In one specific embodiment, such as Figure 3 S102 includes: S1021, perform fast Fourier transform on the first aerodynamic excitation force data, the second aerodynamic excitation force data, and the third aerodynamic excitation force data respectively to obtain the axial single-sided amplitude spectrum, the radial single-sided amplitude spectrum, and the tangential single-sided amplitude spectrum. S1022, Calculate the root mean square value of the first full-band based on the axial single-sided amplitude spectrum; calculate the root mean square value of the second full-band based on the radial single-sided amplitude spectrum; calculate the root mean square value of the third full-band based on the tangential single-sided amplitude spectrum; S1023, extract the first power spectral density data and the first aerodynamic excitation main frequency data in the axial direction based on the root mean square value of the first full-band; extract the second power spectral density data and the second aerodynamic excitation main frequency data in the radial direction based on the root mean square value of the second full-band; extract the third power spectral density data and the third aerodynamic excitation main frequency data in the tangential direction based on the root mean square value of the third full-band. S1024, merge and deduplicate the first aerodynamic excitation frequency data, the second aerodynamic excitation frequency data, and the third aerodynamic excitation frequency data to obtain the aerodynamic excitation frequency set.

[0025] Specifically, the first, second, and third aerodynamic excitation force data are organized into three time-domain sequences with equal time intervals. All three sets of data use the same sampling period, effective sampling length, and start and end times to avoid incomparability between the three-dimensional spectra due to different sampling conditions. Since the preceding unsteady CFD simulation discarded the first three rotational cycles as transition periods, only the axial, radial, and tangential aerodynamic force sequences within the stable period are used as the frequency domain analysis objects. Mean removal processing is performed before performing the Fast Fourier Transform to focus the spectral analysis on unsteady pulsating aerodynamic forces rather than steady-state average aerodynamic forces. Hanning window functions were applied to the three sets of aerodynamic time-domain sequences to reduce spectral leakage caused by truncation. When a 1Hz frequency resolution was required, the length of the time-domain sequence was extended by zero-padding. Then, fast Fourier transforms were performed to convert the time-domain signals into frequency-domain results. The positive frequency part was retained according to the single-sided spectrum rule and the amplitude was corrected, thus obtaining the axial single-sided amplitude spectrum, radial single-sided amplitude spectrum, and tangential single-sided amplitude spectrum.

[0026] After the single-sided amplitude spectrum is formed, the overall energy level of the three-dimensional spectrum values ​​is statistically analyzed within the effective frequency range of 20Hz to 20000Hz. The axial single-sided amplitude spectrum is used to calculate the root mean square value of the first full-band, the radial single-sided amplitude spectrum is used to calculate the root mean square value of the second full-band, and the tangential single-sided amplitude spectrum is used to calculate the root mean square value of the third full-band. This root mean square value is not used as the final load input, but as an energy threshold reference for identifying significant frequency peaks.

[0027] Based on the single-sided amplitude spectrum in each direction or the power spectral density results derived from it, the first power spectral density data in the axial direction, the second power spectral density data in the radial direction, and the third power spectral density data in the tangential direction are generated respectively. , , Its unit is N 2 / Hz, and the frequency range covers 20Hz to 20000Hz, with a frequency resolution set to 1Hz. Simultaneously, the local background spectrum value of the power spectral density curve in each direction is used as the peak selection criterion, and the mean or median of the background spectrum within a preset neighborhood near the target frequency point is recorded as... When the power spectral density satisfy Furthermore, when this frequency point satisfies the local peak condition, it is extracted as the aerodynamic excitation main frequency data in the corresponding direction, where... , is the peak significance coefficient.

[0028] The three-dimensional dominant frequency data are merged according to frequency values, and adjacent peaks with repetitive frequencies or frequency intervals smaller than the preset resolution are deduplicated. For example, at a resolution of 1 Hz, peaks falling into the same frequency grid or adjacent grids but with the same source can be grouped into a single dominant frequency point to obtain a unified set of aerodynamic excitation dominant frequencies. At the same time, the three-dimensional power spectral density data and the set of aerodynamic excitation dominant frequencies are exported in COMSOL interpolation function format so that they can continue to participate in natural frequency comparison, resonance risk mode identification, and three-dimensional spring preload optimization calculation as load boundary conditions in the structural mechanics module.

[0029] In one specific embodiment, such as Figure 4 S200 includes: S201, Establish a finite element model of the coupled structure of the cooling fan in the COMSOL solid mechanics module; S202, input the first power spectral density data, the second power spectral density data, and the third power spectral density data as load boundary conditions into the finite element model, and solve for each natural frequency and each mode shape. S203, calculate the ratio of the elastic potential energy of each mode on the axial spring array, radial spring array, and tangential spring array to the total strain energy of each mode, and obtain the first distribution coefficient, the second distribution coefficient, and the third distribution coefficient.

[0030] In this study, a complete coupled structural model was established in the COMSOL solid mechanics module, comprising fan blades, blade hub, main shaft, inner and outer rings of rolling bearings, spring support, and fan mounting frame. The solid components, such as blades, hub, and main shaft, were assigned measured elastic modulus, Poisson's ratio, and density. The support relationship between the inner and outer rings of the rolling bearings was equated to a linear spring. Three sets of spring arrays—axial, radial, and tangential—were arranged between the support and the mounting frame, ensuring that the axial springs provided only axial constraints, the radial springs only radial constraints, and the tangential springs only tangential constraints, thus avoiding confusion of the three-dimensional stiffnesses in the model. The blades and hub were modeled using free tetrahedral elements, with the maximum element size set to 1 / 4 of the thickness at the thinnest point of the blade. The main shaft and spring support were modeled using swept hexahedral elements, and the frame plates were modeled using shell elements with five integration points in the thickness direction, effectively capturing the low-order bending modes of the 2-5mm thick frame plates.

[0031] In the finite element model, the characteristic frequencies are first solved based on the mass matrix, stiffness matrix, and boundary constraints to obtain the natural frequencies and corresponding mode shapes in the range of 20Hz to 20000Hz. If the stress stiffening effect caused by the spring preload is considered, the preload is first applied to complete the static linearization, and then the natural frequencies and mode shapes under the preload state are solved based on the linearized stiffness matrix. After the characteristic frequencies are solved, the first, second, and third power spectral density data are used as load spectrum inputs for frequency domain response analysis or random vibration analysis, and mapped to the triaxial load boundaries of the blade surface or corresponding stress nodes.

[0032] For each mode shape, the displacement components of the nodes containing the axial, radial, and tangential spring arrays are extracted, and the proportion of the elastic potential energy of that mode shape on the triaxial springs to the total strain energy of that mode shape is calculated, yielding the first, second, and third distribution coefficients. These coefficients are calculated according to the triaxial spring modal strain energy distribution relationship as follows: , , ,in , , They represent the first The energy distribution ratio of the mode shape on the axial, radial, and tangential spring array. , , For the linear stiffness of the triaxial spring, , , For the first The first mode shape Each corresponds to a displacement component at a spring node. For the first Total strain energy of a certain mode. If the first distribution coefficient of a certain mode is large, it indicates that the vibration energy of that mode is mainly absorbed by the axial spring support; if the second or third distribution coefficient is large, it indicates that the radial or tangential support is more sensitive to that mode.

[0033] In one specific embodiment, S202 includes: The first power spectral density data, the second power spectral density data, and the third power spectral density data are imported into the finite element model using the COMSOL interpolation function format and used as the load boundary conditions for the corresponding nodes on the blade surface. The ARPACK solver was used to solve the finite element model, and the natural frequencies and mode shapes of each order were obtained.

[0034] Specifically, the first, second, and third power spectral density data were organized into a COMSOL-readable table file. Each table contains a frequency column and a corresponding power spectral density column, maintaining consistency in the frequency range, frequency step size, and units for all three data streams. For example, each data stream covers 20Hz to 20000Hz, with a frequency step size of 1Hz, and the power spectral density unit is maintained as N. 2 / Hz. Three interpolation functions are established in the COMSOL solid mechanics model. The axial power spectral density data is imported into the first interpolation function, the radial power spectral density data into the second interpolation function, and the tangential power spectral density data into the third interpolation function. The independent variable of each interpolation function is uniformly set to frequency, enabling it to automatically call the corresponding load spectrum values ​​according to the frequency point in characteristic frequency analysis and subsequent frequency domain response analysis. To ensure a strict correspondence between the load direction and the structural coordinates, the axial, radial, and tangential coordinate definitions in the finite element model are first confirmed to be consistent with the CFD output coordinates. Then, load boundary conditions are applied to the blade surface or the corresponding node set mapped from the blade surface. The first interpolation function is used as the axial load spectrum input, the second interpolation function as the radial load spectrum input, and the third interpolation function as the tangential load spectrum input. The load application area is limited by a node selection set or boundary selection set to avoid incorrectly applying aerodynamic loads to the hub, support base, or frame area. After the load is imported, check whether there is any extrapolation anomaly at the end of the frequency range of the interpolation function, and correctly map the power spectral density data to the blade surface nodal load by unit conversion or area allocation method, so that the load boundary conditions can not only retain the frequency domain distribution of the triaxial aerodynamic excitation, but also establish a correspondence with the finite element mesh nodes.

[0035] After completing the load configuration, in the COMSOL characteristic frequency study node, set the solution frequency range to 20Hz to 20000Hz, and enable the ARPACK solver to solve the eigenvalues ​​of the finite element model, that is, to solve the characteristic equation composed of the structural mass matrix and stiffness matrix: ,in Here is the system stiffness matrix. The system quality matrix, For the first First natural frequency, For the first Mode shape vectors. Since the fan coupling structure includes blades, hub, main shaft, equivalent bearing supports, triaxial spring array, and mounting frame, the model has high degrees of freedom. The ARPACK implicit restart Arnoldi method can extract the required modes within a specified frequency band, avoiding unnecessary complete eigenvalue decomposition of the entire matrix. After solving, the output results are modally checked to remove rigid body drift modes, pseudo-modes caused by local mesh distortion, and irrelevant modes exceeding the target frequency band. The natural frequencies and corresponding mode shape displacement fields are saved.

[0036] In one specific embodiment, such as Figure 5 The S300 includes: S301, calculate the set of resonant risk modes based on the set of aerodynamic excitation main frequencies and the natural frequencies of each order; S302, based on the resonant risk mode set, the first allocation coefficient, the second allocation coefficient, and the third allocation coefficient, constructs a first Kriging surrogate model with axial spring preload, a second Kriging surrogate model with radial spring preload, and a third Kriging surrogate model with tangential spring preload; S303, based on the first Kriging surrogate model, the second Kriging surrogate model and the third Kriging surrogate model, performs multi-objective optimization calculations to obtain the first spring preload in the axial direction, the second spring preload in the radial direction and the third spring preload in the tangential direction.

[0037] In this process, the natural frequencies, mode shapes, and first, second, and third allocation coefficients of each order are used as baseline data for structural dynamics. The set of aerodynamic excitation dominant frequencies is compared one by one with each natural frequency to determine which structural modes are easily excited by aerodynamic excitation frequencies. The axial, radial, and tangential aerodynamic excitation dominant frequencies are compiled into a unified dominant frequency list, and each dominant frequency is compared with the first... Calculate the relative deviation of the first natural frequency: ,in Indicates the first The first natural frequency and the second natural frequency The relative deviation between the main frequencies of aerodynamic excitation Indicates the first First natural frequency, This represents any aerodynamic excitation frequency in the axial, radial, or tangential direction. If the calculated result is less than 0.05, it is considered that there is a resonance risk between this mode and the aerodynamic excitation frequency, and the corresponding mode is added to the set of resonant risk modes. The 5% judgment threshold can cover the resonant bandwidth of typical low-damped structures, while avoiding misjudging non-resonant frequencies that are far away as risk modes.

[0038] The resonant risk mode set is correlated with the triaxial energy distribution ratio of each vibration mode. The first, second, and third distribution coefficients are used as the basis for judging the contribution of springs in different directions to the risk modes. If the first distribution coefficient of a certain risk mode is high, it indicates that the mode is mainly related to the energy of the axial spring array. If the second or third distribution coefficient is high, it indicates that the radial or tangential spring array is more critical in constraining the risk mode. This avoids simply relying on experience to uniformly increase the spring preload, but instead determines the optimization direction of the triaxial preload based on the source of the modal energy. Using the axial spring preload, radial spring preload, and tangential spring preload as design variables, the first, second, and third Kriging surrogate models are constructed respectively. Before the model is established, Latin hypercube sampling can be used to generate 100 initial sample points in the triaxial preload design space, and a COMSOL frequency domain simulation is performed on each sample point to record the corresponding triaxial vibration acceleration response, broadband total vibration energy, and forced response amplitude at the resonant risk mode. The range of preload values ​​needs to be limited by spring assembly and bearing safety constraints. For example, the minimum compression of the spring can be 5% of the free length to ensure that the spring is always in a compressed state, and the maximum compression should not exceed 30% of the free length to avoid failure of the linear stiffness assumption. The equivalent static load generated by the triaxial preload at the bearing housing should not exceed 60% of the rated static load of the bearing, and the static resultant displacement of the entire fan under the combined action of the triaxial preload should not exceed 10% of the blade tip clearance. This ensures that the optimized preload is not only effective in simulation, but can also be converted into actual assembly parameters. Since the computational cost of performing full-frequency domain sweeping in the 20Hz to 20000Hz range for a 500,000 to 1,000,000 node model is relatively large, a reduced-order frequency domain response data is first constructed based on the modal superposition method, risk band encryption, and non-risk band sparse sampling. Then, Latin hypercube sampling is used to generate initial samples and train a joint Kriging surrogate model. The accuracy of the surrogate model is jointly verified by leave-one-out cross-validation and retained sample verification. When the relative root mean square error is greater than 5% or the risk peak frequency band error is greater than the preset peak error threshold, sample points are added near the Pareto front and the resonance risk frequency band. Finally, the complete finite element model is used to verify the final candidate solution.

[0039] Multi-objective optimization calculations were performed based on three Kriging surrogate models. With the common objectives of balancing triaxial vibration acceleration, reducing broadband total vibration energy, and suppressing peak values ​​of resonant risk modal responses, candidate solution sets were searched while satisfying constraints on spring compression, bearing static load, and blade tip clearance. From these candidate solutions, the axial first spring preload, radial second spring preload, and tangential third spring preload were selected. This ensured that the triaxial spring array was no longer merely a passive support structure, but rather that it was collaboratively matched based on the aerodynamic excitation frequency, the proximity of natural frequencies, and modal energy distribution results, thereby achieving balanced suppression of broadband vibration energy.

[0040] In one specific embodiment, S303 includes: Multi-objective optimization calculations are performed based on the first Kriging surrogate model to obtain the first candidate solution set; multi-objective optimization calculations are performed based on the second Kriging surrogate model to obtain the second candidate solution set; multi-objective optimization calculations are performed based on the third Kriging surrogate model to obtain the third candidate solution set. The first optimal solution is selected from the first candidate solution set as the first spring preload in the axial direction; the second optimal solution is selected from the second candidate solution set as the second spring preload in the radial direction; and the third optimal solution is selected from the third candidate solution set as the third spring preload in the tangential direction.

[0041] After training and verifying the accuracy of the first, second, and third Kriging surrogate models, the optimization of the triaxial spring preload was transformed from time-consuming direct COMSOL frequency sweep calculation to fast optimization calculation based on the surrogate models. The first Kriging surrogate model describes the impact of axial spring preload variation on axially correlated vibration response, resonant risk modal response, and triaxial equilibrium index; the second Kriging surrogate model describes the impact of radial spring preload variation on radially correlated response; and the third Kriging surrogate model describes the impact of tangential spring preload variation on tangentially correlated response. The verified parameters... The surrogate model was used as the fitness evaluator, and the NSGA-II genetic algorithm was used to search within the preload design range in three directions. The population size was set to 200, the maximum number of generations was set to 500, the crossover probability was set to 0.9, the polynomial mutation probability was set to 1 / 3, and the distribution index was set to 20. At the same time, hard constraints were set, such as the static compression of the spring not exceeding 30% of the free length, the equivalent static load generated by the three-way spring preload at the bearing not exceeding 60% of the rated static load of the bearing, and the static displacement of the entire fan not exceeding 10% of the blade tip clearance. This enabled the algorithm to automatically remove invalid individuals that could not be assembled or that might cause bearing overload or blade tip clearance imbalance during the search process. As the iteration progresses, the non-dominated solutions output by the first Kriging surrogate model form the first candidate solution set, the non-dominated solutions output by the second Kriging surrogate model form the second candidate solution set, and the non-dominated solutions output by the third Kriging surrogate model form the third candidate solution set. Each candidate solution set retains a preload value that does not exhibit a significant disadvantage among vibrational equilibrium, broadband total energy reduction, and resonance peak suppression, thus avoiding the pursuit of minimizing vibration in only one direction at the expense of increased vibrational energy in the other two directions. When the algorithm converges, a stopping criterion can be used, where the hypervolume change rate of the Pareto front is less than 0.1% for 50 consecutive generations. The optimal solution is then selected from each candidate solution set according to a unified screening rule, prioritizing the retention of solutions that satisfy the following criteria. The solution should ensure that the root mean square deviation of the triaxial vibration acceleration does not exceed 10% of the triaxial mean, and then the solution should be selected from the candidate solutions that satisfy this equilibrium condition. The minimum solution prioritizes suppressing the peak value of the forced vibration response at each modal frequency in the resonant risk mode set, while also combining... Determine whether the total vibration energy of the broadband is at a low level.

[0042] The first optimal solution selected from the first candidate solution set is determined as the first spring preload in the axial direction; the second optimal solution selected from the second candidate solution set is determined as the second spring preload in the radial direction; and the third optimal solution selected from the third candidate solution set is determined as the third spring preload in the tangential direction. To prevent incorrect selection due to local errors in the surrogate model, the preloads selected in the three directions can be combined. Perform a full frequency domain simulation again using COMSOL. When the relative deviation between the simulation results and the predicted values ​​of the surrogate model is less than 5%, it is confirmed as the final preload combination. If the deviation does not meet the requirements, the simulation result is added to the sample set to retrain the Kriging surrogate model and optimize again until the output axial, radial and tangential preloads meet the multi-objective optimization requirements and can be verified by complete simulation.

[0043] In one specific embodiment, such as Figure 6After solving for the axial first spring preload, the radial second spring preload, and the tangential third spring preload, the following steps are also included: S400, based on the first spring preload, the second spring preload, and the third spring preload, the static deformation of the cooling fan coupling structure is solved, and wideband frequency domain sweep simulation is performed using the first power spectral density data, the second power spectral density data, and the third power spectral density data to obtain the first frequency response data in the axial direction, the second frequency response data in the radial direction, and the third frequency response data in the tangential direction. S500 performs spring preload verification based on the first frequency response data, the second frequency response data, and the third frequency response data. The verified first spring preload, second spring preload, and third spring preload are divided by the spring linear stiffness to obtain the axial first spring assembly compression, the radial second spring assembly compression, and the tangential third spring assembly compression.

[0044] In this process, the preload forces of the first, second, and third springs are incorporated into the established finite element model of the cooling fan coupling structure and applied to the connection points between the support seats and the frame corresponding to the axial, radial, and tangential spring arrays, respectively, ensuring that the loading direction of the preload forces aligns with the aforementioned three-dimensional spring stiffness directions. In COMSOL, a static solution is performed first, rather than directly performing a frequency domain sweep. This is because the spring preload forces induce initial static displacements and initial stress states in the fan support seats, bearing seats, frame, and blade system. Ignoring this preload state would only reflect the linear vibration characteristics of the unpreloaded structure in the frequency domain response, failing to reflect the geometric stiffening effect introduced by the preload. Therefore, the first, second, and third spring preload forces are applied as static preloads to the finite element model to obtain the static deformation field and stress stiffening matrix of the cooling fan coupling structure. The geometric configuration after static deformation is then used as the linearized reference configuration for the frequency domain study, ensuring consistency between the frequency domain simulation and the physical boundaries during the training of the Kriging proxy model. The first, second, and third power spectral density data are used as the boundary inputs of the triaxial aerodynamic excitation model. A wideband sweep frequency simulation is performed in the COMSOL frequency domain research node. For example, the sweep frequency range is set to 20Hz to 20000Hz, the frequency step size is set to 1Hz, and the frequency response functions or vibration acceleration response data in the axial, radial, and tangential directions are solved respectively. Thus, the first frequency response data in the axial direction, the second frequency response data in the radial direction, and the third frequency response data in the tangential direction are obtained.

[0045] The spring preload was verified based on the triaxial frequency response data. The optimized triaxial vibration energy was compared with the baseline model, which can be referenced by the preload corresponding to the initial spring stiffness and rated working displacement. The broadband total vibration energy suppression rate was then calculated. ,in The total vibrational energy suppression rate is a broadband signal. , , To optimize the total energy of triaxial vibration acceleration after the application of preload, , , The total energy of triaxial vibration acceleration under the baseline model is suppressed by a rate of no less than 30%. During the verification process, the following are checked simultaneously: whether the triaxial vibration acceleration meets the equilibrium requirements; whether the response peak at the resonance risk mode is suppressed; whether the static compression of the spring does not exceed 30% of the free length; whether the equivalent static load generated by the triaxial preload at the bearing housing does not exceed 60% of the rated static load of the bearing; and whether the static combined displacement of the entire fan does not exceed 10% of the blade tip clearance. After all the above verifications are passed, the verified first spring preload, second spring preload, and third spring preload are divided by the corresponding spring linear stiffness to calculate the axial first spring assembly compression, radial second spring assembly compression, and tangential third spring assembly compression.

[0046] In one specific embodiment, S400 includes: The preload of the first spring, the preload of the second spring, and the preload of the third spring are applied to the finite element model to solve the static deformation, and the static deformation field and stress stiffening matrix are obtained. Based on the static deformation field and stress stiffening matrix, the first power spectral density data, the second power spectral density data, and the third power spectral density data are input into the finite element model to perform frequency domain sweep simulation, thereby obtaining the first frequency response data in the axial direction, the second frequency response data in the radial direction, and the third frequency response data in the tangential direction.

[0047] In this process, static research nodes are established in the finite element model where the mesh, materials, constraints, and triaxial spring array definitions have been completed. The first, second, and third spring preloads are applied to the support-frame connection areas corresponding to the axial, radial, and tangential spring arrays, respectively, ensuring that each set of preloads acts only in its corresponding direction, avoiding the axial preload from being mistakenly introduced into the radial or tangential constraints. Static solving is then employed, using the triaxial spring preloads as preloads to solve for the static displacement, stress distribution, and contact constraint states of the fan blades, hub, main shaft, equivalent bearing supports, spring supports, and mounting frame under preloaded assembly conditions. The geometric stiffening effect caused by the preload is preserved during the solution process, forming a static deformation field and stress stiffening matrix.

[0048] After completing the static solution, the statically deformed geometric configuration is set as the linearized reference configuration for the frequency domain study, and the stress stiffening matrix is ​​substituted into the frequency domain solution, so that the frequency domain response calculation is based on the structural state of "pre-tightened, deformed, and stiffened". The first, second, and third power spectral density data are imported into the COMSOL frequency domain study node and used as the axial, radial, and tangential aerodynamic load power spectrum inputs for the blade surface or corresponding nodes, respectively. The frequency sweep range is set to 20Hz to 20000Hz, and the frequency step is set to 1Hz, thus covering the blade passage frequency, harmonic frequency, and broadband background excitation that may occur during fan operation. During the frequency domain sweep, the finite element model solves the structural response at each frequency point according to the triaxial aerodynamic excitation load and outputs the axial, radial, and tangential vibration acceleration frequency response functions, obtaining the vibration acceleration power spectral density response at each frequency point, for example... , , The frequency response function, acceleration response spectrum, peak frequency, and corresponding response amplitude in the axial direction are compiled into the first frequency response data. The similar results in the radial direction are compiled into the second frequency response data, and the similar results in the tangential direction are compiled into the third frequency response data. The correspondence between each response data and frequency point, load direction, and observation node is retained, so that it can continue to be used to determine whether the triaxial preload reduces broadband vibration energy, whether it reduces the response peak at the resonance risk mode, and whether it meets the spring assembly compression conversion requirements.

[0049] This embodiment provides a fan for implementing the steps of any of the methods described above, which will not be repeated here.

[0050] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, apparatus, article, or method that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, apparatus, article, or method. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, apparatus, article, or method that includes that element.

[0051] The above description is merely a preferred embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural or procedural transformations made based on the content of the present invention's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A method for balancing the preload of a multi-directional spring and optimizing broadband vibration energy in a cooling fan, characterized in that, include: Simulation calculations were performed on the cooling fan to obtain the first power spectral density data in the axial direction, the second power spectral density data in the radial direction, the third power spectral density data in the tangential direction, and the set of aerodynamic excitation frequencies. Based on the first power spectral density data, the second power spectral density data, and the third power spectral density data, calculate the natural frequencies of each order and the first axial allocation coefficient, the second radial allocation coefficient, and the third tangential allocation coefficient. Based on the aerodynamic excitation main frequency set and the natural frequencies of each order, a set of resonant risk modes is determined, and based on the set of resonant risk modes, the first allocation coefficient, the second allocation coefficient, and the third allocation coefficient, the first spring preload in the axial direction, the second spring preload in the radial direction, and the third spring preload in the tangential direction are solved.

2. The method for balancing the preload of multi-directional springs and optimizing broadband vibration energy in a cooling fan according to claim 1, characterized in that, The simulation calculation of the cooling fan yields the first power spectral density data in the axial direction, the second power spectral density data in the radial direction, the third power spectral density data in the tangential direction, and the set of aerodynamic excitation frequencies, including: The cooling fan was simulated using the COMSOL turbulence CFD module. The surface pressure and viscous shear force of the blades were integrated and projected along the axial, radial and tangential directions to obtain the first aerodynamic excitation force data in the axial direction, the second aerodynamic excitation force data in the radial direction and the third aerodynamic excitation force data in the tangential direction. Fast Fourier transform is performed on the first aerodynamic excitation force data, the second aerodynamic excitation force data, and the third aerodynamic excitation force data respectively to obtain the first power spectral density data in the axial direction, the second power spectral density data in the radial direction, the third power spectral density data in the tangential direction, and the corresponding aerodynamic excitation frequency set.

3. The method for balancing the preload of multi-directional springs and optimizing broadband vibration energy in a cooling fan according to claim 2, characterized in that, The step of performing Fast Fourier Transform on the first aerodynamic excitation force data, the second aerodynamic excitation force data, and the third aerodynamic excitation force data respectively to obtain axial first power spectral density data, radial second power spectral density data, tangential third power spectral density data, and the corresponding aerodynamic excitation main frequency set includes: Fast Fourier transform is performed on the first aerodynamic excitation force data, the second aerodynamic excitation force data, and the third aerodynamic excitation force data respectively to obtain the axial single-sided amplitude spectrum, the radial single-sided amplitude spectrum, and the tangential single-sided amplitude spectrum; The root mean square (RMS) value of the first full-band frequency is calculated based on the axial unilateral amplitude spectrum; the root mean square (RMS) value of the second full-band frequency is calculated based on the radial unilateral amplitude spectrum; and the root mean square (RMS) value of the third full-band frequency is calculated based on the tangential unilateral amplitude spectrum. The first axial power spectral density data and the first aerodynamic excitation frequency data are extracted based on the first full-band root mean square value; the second radial power spectral density data and the second aerodynamic excitation frequency data are extracted based on the second full-band root mean square value; and the third tangential power spectral density data and the third aerodynamic excitation frequency data are extracted based on the third full-band root mean square value. The first aerodynamic excitation frequency data, the second aerodynamic excitation frequency data, and the third aerodynamic excitation frequency data are merged and deduplicated to obtain the aerodynamic excitation frequency set.

4. The method for balancing the preload of multi-directional springs and optimizing broadband vibration energy in a cooling fan according to claim 3, characterized in that, The calculation of each natural frequency and the first axial allocation coefficient, the second radial allocation coefficient, and the third tangential allocation coefficient based on the first power spectral density data, the second power spectral density data, and the third power spectral density data includes: Establish a finite element model of the coupled structure of the cooling fan in the COMSOL solid mechanics module; The first power spectral density data, the second power spectral density data, and the third power spectral density data are used as load boundary conditions and input into the finite element model to solve for each natural frequency and each mode shape. The ratio of the elastic potential energy of each mode on the axial spring array, radial spring array, and tangential spring array to the total strain energy of each mode is calculated to obtain the first distribution coefficient, the second distribution coefficient, and the third distribution coefficient.

5. The method for balancing the preload of multi-directional springs and optimizing broadband vibration energy in a cooling fan according to claim 4, characterized in that, The step of inputting the first power spectral density data, the second power spectral density data, and the third power spectral density data as load boundary conditions into the finite element model to solve for each natural frequency and each mode shape includes: The first power spectral density data, the second power spectral density data, and the third power spectral density data are imported into the finite element model in COMSOL interpolation function format as load boundary conditions for the corresponding nodes on the blade surface. The ARPACK solver was used to solve the finite element model to obtain the natural frequencies and mode shapes of each order.

6. The method for balancing the preload of multi-directional springs and optimizing broadband vibration energy in a cooling fan according to claim 5, characterized in that, The step of determining the set of resonant risk modes based on the set of aerodynamic excitation main frequencies and the natural frequencies of each order, and solving for the axial first spring preload, radial second spring preload, and tangential third spring preload based on the set of resonant risk modes, the first allocation coefficient, the second allocation coefficient, and the third allocation coefficient, includes: Calculate the set of resonant risk modes based on the set of aerodynamic excitation dominant frequencies and the natural frequencies of each order; Based on the resonant risk mode set, the first allocation coefficient, the second allocation coefficient, and the third allocation coefficient, a first Kriging surrogate model is constructed using axial spring preload, a second Kriging surrogate model is constructed using radial spring preload, and a third Kriging surrogate model is constructed using tangential spring preload. Multi-objective optimization calculations are performed based on the first Kriging surrogate model, the second Kriging surrogate model, and the third Kriging surrogate model to obtain the first spring preload in the axial direction, the second spring preload in the radial direction, and the third spring preload in the tangential direction.

7. The method for balancing the preload of multi-directional springs and optimizing broadband vibration energy in a cooling fan according to claim 6, characterized in that, The multi-objective optimization calculation based on the first Kriging surrogate model, the second Kriging surrogate model, and the third Kriging surrogate model to obtain the axial first spring preload, the radial second spring preload, and the tangential third spring preload includes: Multi-objective optimization calculations are performed based on the first Kriging surrogate model to obtain a first candidate solution set; multi-objective optimization calculations are performed based on the second Kriging surrogate model to obtain a second candidate solution set; multi-objective optimization calculations are performed based on the third Kriging surrogate model to obtain a third candidate solution set. The first optimal solution is selected from the first candidate solution set as the first spring preload in the axial direction; the second optimal solution is selected from the second candidate solution set as the second spring preload in the radial direction; and the third optimal solution is selected from the third candidate solution set as the third spring preload in the tangential direction.

8. The method for balancing the preload of multi-directional springs and optimizing broadband vibration energy in a cooling fan according to claim 7, characterized in that, After solving for the axial first spring preload, the radial second spring preload, and the tangential third spring preload, the following steps are also included: The static deformation of the cooling fan coupling structure is solved based on the first spring preload, the second spring preload, and the third spring preload. A wideband frequency domain sweep simulation is performed using the first power spectral density data, the second power spectral density data, and the third power spectral density data to obtain the first frequency response data in the axial direction, the second frequency response data in the radial direction, and the third frequency response data in the tangential direction. Based on the first frequency response data, the second frequency response data, and the third frequency response data, spring preload verification is performed. The verified first spring preload, second spring preload, and third spring preload are divided by the spring linear stiffness to obtain the axial first spring assembly compression, the radial second spring assembly compression, and the tangential third spring assembly compression.

9. The method for balancing the preload of multi-directional springs and optimizing broadband vibration energy in a cooling fan according to claim 8, characterized in that, The static deformation calculation of the cooling fan coupling structure based on the first spring preload, the second spring preload, and the third spring preload, followed by wideband frequency domain sweep simulation using the first power spectral density data, the second power spectral density data, and the third power spectral density data, yields axial first frequency response data, radial second frequency response data, and tangential third frequency response data, including: The first spring preload, the second spring preload, and the third spring preload are applied to the finite element model to solve for static deformation, thereby obtaining the static deformation field and the stress stiffening matrix. Based on the static deformation field and the stress stiffening matrix, the first power spectral density data, the second power spectral density data, and the third power spectral density data are input into the finite element model to perform frequency domain sweep simulation, thereby obtaining the first frequency response data in the axial direction, the second frequency response data in the radial direction, and the third frequency response data in the tangential direction.

10. A fan, characterized in that, The steps are for implementing the method for balancing the preload of the multi-directional spring of a cooling fan and optimizing broadband vibration energy as described in any one of claims 1 to 9.

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