Structural Parameters Of System Research Articles

Structure and dynamic viscosity of CaO–SiO2 and CaO–SiO2–B2O3 model slag systems

Correlation dependencies between the dynamic viscosity of slag and its structural parameters were studied to determine an optimal basicity of silicon smelting slag under the addition of boron oxide to eliminate slagging of the bottom of ore-smelting furnaces. Experimental studies were conducted on CaO–SiO2 and CaO– SiO2–B2O3 model slags obtained at 1600°С. Raman spectroscopic analysis was carried out using a Horiba JobinYvon HR800UV analyzer (France). Theoretical calculations of slag viscosity were performed using Urbain and Mills models. During the experiments, the key structural parameters of slag systems varied within the following limits: the experimental Raman spectrum deconvolution function from 1.41 to 2.45 and optical basicity from 0.58 to 0.68. The obtained experimental and theoretical data were related by mathematical dependencies. It was found that the dynamic viscosity of slag can be promptly determined by Raman spectroscopy on the basis of mathematical models. The dependence obtained shows that slag viscosity decreases upon an increase in the number of bridging oxygen atoms in the silicate anion structure. Notably, this decrease in slag viscosity is observed up to the value of the experimental Raman spectrum deconvolution function of ~1.55-1.60 or slag optical basicity of 0.60–0.62. When B2O3 is added, the viscosity undergoes a further decrease. In practice, for CaO–SiO2 slag systems, the use of boroncontaining flux as a liquefying agent is reasonable at CaO/SiO2 = 0.61–0.63 while maintaining the content of B2O3 in the slag at a level of 1%. The two models (classical and modified) proposed by Urbain were established to be more suitable for theoretical calculation of viscosity in CaO–SiO2 and CaO–SiO2–B2O3 systems. Mills’ model is not suitable for these purposes, since the correlation coefficients in the corresponding mathematical model are not sufficiently large. Further research in this direction is required in order to establish appropriate dependencies of slag viscosity on its structural parameters at different temperatures.

Error Analysis and Optimization of Structural Parameters of Spatial Coordinate Testing System Based on Position-Sensitive Detector.

For the research on real-time accurate testing technology for the explosion point spatial coordinate of munitions, its currently commonly used methods such as acoustic-electric detection or high-speed imaging are limited by the field conditions, response rate, cost, and other factors. In this paper, a method of spatial coordinate testing for the explosion point based on a 2D PSD (position-sensitive detector) intersection is proposed, which has the advantages of a faster response, better real-time performance, and a lower cost. Firstly, a mathematical model of the spatial coordinate testing system was constructed, and an error propagation model for structural parameters was developed. The influence of the position of the optical axes' intersection as well as the azimuth angle and pitch angle on the test accuracy of the system was simulated and analyzed, thus obtaining the distribution and variation trend of the overall error propagation coefficient of the system. Finally, experiments were designed to obtain the test error of the system for validation. The results show that the system test accuracy is high when the azimuth angle is 20°-50°, the overall error propagation coefficient does not exceed 48.80, and the average test error is 56.17 mm. When the pitch angle is -2.5°-2.5°, the system has a higher test accuracy, with the overall error propagation coefficient not exceeding 44.82, and the average test error is 41.87 mm. The test accuracy of the system is higher when the position of the optical axes' intersection is chosen to make sure that explosion points fall in the region of the negative half-axis of the Zw-axis of the world coordinate system, with an overall error propagation coefficient of less than 44.78 and an average test error of 73.38 mm. It is shown that a reasonable selection of system structure parameters can significantly improve the system test accuracy and optimize the system deployment mode under the long-distance field conditions so as to improve the deployment efficiency.

Improving kitchen thermal comfort in summer based on optimization of airflow distribution

To quantitatively analyze the comfort of kitchen environment, this paper presents a thermal comfort analysis method for kitchen with air-conditioned range hood. It corrects the deficiency in the original comfort formula involving humidity, thereby reasonably quantifying the impact of the cooling airflow from air-conditioning, including humidity, on kitchen thermal comfort. By adjusting the structural parameters of the air conditioning system, the airflow distribution in the kitchen space during summer has been optimized, thereby further enhancing its thermal comfort. This method employs Fluent analyses and its User-Defined Functions (UDF) to analyze the indoor flow field, temperature, humidity, and the distribution of PMV-PPD within the kitchen equipped with air-conditioned range hood. Additionally, experimental data are applied to validate the accuracy and effectiveness of the simulation model. The results indicate that under high temperature climate conditions in summer, air-conditioned range hood significantly enhances the thermal comfort of kitchen environment during cooking. Moreover, optimal thermal comfort for both the kitchen space and local respiratory area of the human body is achieved when the air supply angle is set at 45°, the air conditioning outlet flow rate is 5.5 m3/min and the air supply temperature is set at 21 °C. Compared to the initial operating conditions, Human thermal sensitivity weighted PMV decreased by 98.17 %, and the weighted PPD decreased by 82.07 %. This study provides valuable insights for the design and operation of air-conditioned range hoods, contributing to improved thermal comfort and energy efficiency in residential kitchens.

Transient thermal analysis model of nitrogen-cooled cryogenic system for superconducting electromagnetic suspension magnet

This paper proposes a transient thermal analysis model for a nitrogen-cooled cryogenic system used in superconducting electromagnetic suspension magnets. First, the structural parameters of the nitrogen cryogenic system and the internal high-temperature superconducting magnet are detailed. Subsequently, temperature change simulations during the system's cooling process using a cryocooler, as well as during the cooling and nitrogen-insulation process, were conducted using COMSOL software. Finally, simulations of the temperature variations during the system's offline operation were performed. This study provides valuable references for the design and optimization of nitrogen-cooled cryogenic systems.

Chatter and Surface Waviness Analysis in Oerlikon Face Hobbing of Spiral Bevel Gears

A vectorized analytical model for the cutting dynamics in the spiral bevel gear face hobbing process has been developed, which is based on machine tool kinematics and vibration vectorization. The structural modal parameters of the cutter head spindle system are obtained through experimental modal analysis with hammer impact testing. The analytical model is utilized to simulate the generation of simulated vibration acceleration signals during spiral bevel gear hobbing. A wavelet threshold denoising method is applied to process the simulated vibration signals of the spiral bevel gear face hobbing with added white noise. Signal processing methods, including short-time Fourier transform are employed for time-domain analysis, frequency-domain analysis, and time–frequency-domain analysis of measured signals and simulated signals, thereby extracting the corresponding statistical features. In addition to the results of the experimental modal analysis, the causes of chatter in spiral bevel gear hobbing are discussed in detail, revealing that the main factor is cutter head vibration in the Y direction of the Hunan ZDCY CNC EQUIPMENT YKA2260 machine tool used in this research. The error in the time-domain characteristic parameters between simulated signals and measured vibration acceleration signals is within 15%, with a difference of 3.5% in spectral peak values. The predicted tooth surface morphology from simulation matches the actual morphology on the workpiece, comprehensively validating the reliability of the cutting dynamics model for the spiral bevel gear face hobbing process. Another conclusion drawn from numerical simulation experiments is that the amount of tooth surface waviness of the spiral bevel gears is the ratio of tool chatter frequency to cutting fundamental frequency.

Influence of Structural Parameters of Gearbox Seal System of Electrical Multiple Units on Seal Performance

The gearbox seal system is a critical component of the electrical multiple units drive system, with a direct impact on the safety and reliability of train operations. This study intends to analyze how structural parameters of the gearbox seal system influence the seal performance from the viewpoint of “oil–air separation and scavenge oil” by using a discrete phase model and volume of fluid. The results show that the oil–air separation performance is mainly affected by the oil droplets’ inertia force and the airflow traction force, and the scavenge oil performance is decided by the oil–air separation performance of each seal chamber. The relationships between seal chamber size, axial seal clearance width, height difference, scavenge oil hole diameter, and seal performance are analyzed, and the study also found that optimizing the stator chamber depth–width ratio of the seal system studied in this paper at 2.5, reducing the rotor chamber depth–width ratio and axial seal clearance width, and increasing the relative height difference can improve the seal performance. And increasing the scavenge oil hole diameter also enhances the seal system’s performance. The simulation results can be used as design references for gearbox seal systems.

МОДЕЛЬ КОНСТРУКТИВНЫХ ПАРАМЕТРОВ СИСТЕМЫ ОТОПЛЕНИЯ ИНДИВИДУАЛЬНОГО ЖИЛОГО ЗДАНИЯ

The paper presents a model of the relationship between the structural parameters of the water heat-ing system of an individual building and its space-planning solution

Administering AEC Professionals’ Project Delivery Cross-Culture Productivity: Malaysia vs United Kingdom

Borderless world is transforming construction professionals on how to communicate and work across the globe. Many missed communication and different work culture could result in many variation orders and time wastage in construction. This paper looks to discuss the mixed research methodology results on how to administer architect, engineer and contractor (AEC) professionals’ cross-work culture productivity during building deployment. 34 participants were selected for semi-structured interviews and participatory observations were conducted in two multidisciplinary teams of architect, engineer, and contractor from the United Kingdom (UK) and the Malaysia firms for six months. Then, SimVision® simulations were use as the Cognitive Organizational Theory (COT) protocols based on structural system and project dexterity parameters. Statistics corroborations were then conducted to obtain generalization and reliability. The case study results showed that the UK and the Malaysian team have similarities in operating nature of building deployment and differences in practice and value preferences when delivering a project, whilst model MMsRwB is the ideal for replicating UK’s project productivity efficiency. The findings could guide international construction professionals or teams from developed and developing countries to joint venture in their country successfully especially for Malaysian context. The paper would firstly discuss the literature, secondly describe the mixed method methodology and then present the expected result. The paper recommends future research on formalizing communication system for AEC professionals through integrating Malaysian AEC transdisciplinary global practice in a design studio education program.

Real-Time Integration of Identification and Semiactive Optimization Control for Mass Damper-Building Combined Systems under Known/Unknown Seismic Excitations

The integration of structural identification and vibration optimal control has been studied. Since the semiactive optimization vibrational control of civil structures needs to be implemented by massive control devices such as mass dampers, it is necessary to investigate the real-time integration of identification and semiactive optimization vibration control for mass damper-building combined systems. However, there is a lack of such studies in the literature. In this paper, a methodology is presented for real-time integration of identification and semiactive optimization vibration control of the mass damper-building combined system under known/unknown seismic excitations. For the combined system under known seismic excitations, the identification is implemented by the extended Kalman filter (EKF) using only partial structural acceleration responses. The identified structural state and parameters of mass damper-building systems are integrated in real time for the optimal control of systems by the linear-quadratic regulator (LQR) control algorithm and the Hrovat semiactive optimization control strategy via semiactive optimization mass dampers (SAMD). Then, it is extended to the scenario of unknown seismic excitations. The partially measured structural acceleration responses are absolute ones in this case, so the generalized extended Kalman filter with unknown input (GEKF-UI) developed by the authors is used to identify the structural input-state parameters of the mass dampers-building combined systems. The identification results are also integrated in real time for the semiactive optimization control of the combined system via SAMD. Two numerical simulation examples are used to test the proposed integration methods. It is shown that the proposed integration methods can reach almost the same optimal control effects as the conventional semiactive optimization control with known parameters of the mass damper-building combined systems under known/unknown seismic excitations.

Structural optical design of multi-group, high zoom ratio optical systems

In this paper, we propose a method for the structural optical design of multi-group, high zoom ratio optical systems based on matrix optics and Particle Swarm Optimization (PSO) algorithm. This method effectively addresses the problems of initial structural calculation difficulties, large volume, and unsmooth zoom curves with large inflection points in high zoom ratio optical systems. To design the zoom optical system, the matrix equations of the multi-group zoom system are derived using geometric optics; and a mathematical model is built to solve the initial structural parameters of the zoom system based on the matrix. Then, a new fitness function is introduced as an indicator to iteratively optimize the initial structural parameters of the system in multi-dimensional space, considering factors such as maximum zoom ratio, total optical length, and full field of view angle. Finally, this method is validated in two complex optical system designs including a 20x four-group and a 35x five-group zoom optical system, showing strong retrieval capabilities. Independent of traditional trial-and-error investigations for solutions, our method facilitates the automatic intelligent design of complex optical systems.

Multi‐Objective Optimization Design of Vacuum Interrupter Structure Based on Improved Artificial Jellyfish Search Algorithm

An improved multi‐objective optimization method based on artificial jellyfish search algorithm is proposed to solve the multivariable and multi‐objective optimization problem of vacuum interrupter with mutual coupling of structural parameters and mutual restriction of performance indexes. The finite element model of 40.5 kV/31.5kA vacuum interrupter is established. The structural parameters of seven important parts such as contact diameter and contact sheet thickness in vacuum interrupter are taken as optimization variables. The optimization objective is to maximize the longitudinal magnetic field strength and minimize the conductor resistance at the peak breaking short‐circuit current of vacuum interrupter. The artificial jellyfish search algorithm is improved on the population position initialization strategy and the population mutation cross‐update strategy. The Pareto front solution of the structural parameters of the vacuum interrupter is obtained by the joint simulation of finite element analysis and numerical calculation software. Finally, the multi‐parameter and multi‐objective optimization design of vacuum interrupter structure is realized. The comprehensive performance index is introduced into the optimal parameter group of jellyfish on the Pareto front. Under the constraint of weight variables, the optimal structural parameters of contact system are obtained. The axial magnetic induction intensity of the optimized vacuum interrupter contact is increased by 13.2%, and the conductor resistance is reduced by 25.4%. The comprehensive performance of vacuum interrupter is improved by 17.8%, and the stability and reliability of the power system are further improved. © 2023 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC.

A nonlinear unbiased minimum-variance filter for structural identification with unknown external excitations

Excitations identification and structural identification are two pivotal factors in the field of structural health monitoring. The extended Kalman filter (EKF) is widely used for identifying structural dynamic systems. However, it has been demonstrated that an inevitable linearization error exists, which can make it difficult to deal with situations when external excitations are unknown. To address this issue, this paper proposes a novel derivative-free version of the nonlinear unbiased minimum variance filter for structural identification with unknown external excitations (NUMVF-UEE) based on the unscented Kalman filter (UKF). This method derives optimal estimations of structural parameters and unknown external excitations by minimizing the traces of the covariance matrices with respect to the augment vectors. To demonstrate the effectiveness of the proposed method, several numerical examples are introduced. The results show that NUMVF-UEE can simultaneously provide accurate estimations of both structural system parameters and unknown external excitations in real-time.

MATHEMATICAL MODELLING OF WATER REGULATION PROCESSES ON DUAL-ACTION DRAINAGE SYSTEMS

The solution of the problem of increasing water regulation areas in the Polissia zone of Ukraine requires investigation and development of new, more effective methods for determining structural parameters of drainage systems when developing projects for their reconstruction in accordance with the requirements aimed at ensuring water regulation during systems’ operation. The paper considers the problem of improving the efficiency of water regulation on dual-action drainage systems by using mathematical modelling tools to determine the structural parameters of the systems and the parameters of their operational management. The proposed means are based on the use of Richards equation stated in terms of water head. As a tool for scenario modelling, an initial-boundary value problem of modelling moisture transfer on dual-action systems is formulated and a finite-difference scheme for obtaining its numerical solution is given. We consider the problem of determining the depth of drains installation and the distance between them at which the system provides not only the drainage of soil’s surface layer, but also the maintenance of its moisture supply level in a given range with a minimum need for irrigation during the growing season. The algorithm for solving such a problem is presented. It is based on the construction of a set of admissible values of system’s parameters using, in particular, the bisection method, followed by the minimization of an objective function on this set. Under the conditions when the implementation of underground water supply technology is economically impractical, the possibility of supplementing the drainage system with an irrigation system is considered. In this case, the cost of building a drainage system and an additional irrigation system is a criterion for the optimality of system’s parameters. Additionally, we consider the problem of operational management of water regulation, i.e., the determination, given the initial distribution of moisture, of the optimal control influences necessary to ensure an acceptable level of moisture availability during a given period of time. This minimization problem is proposed to be solved by a genetic algorithm. The results of modelling the operation of a dual-action system and the optimization of its parameters under the conditions of drained peat soils of the Panfyly Research Station (Ukraine, Kyiv region) are presented.

THE NECESSITY, SCIENTIFIC AND PRACTICAL PRINCIPLES OF IMPROVING METHODS OF DRAINAGE SYSTEMS DESIGN AND CALCULATION

The paper presents a new approach to improving the methods of design and calculation of drainage systems and their technical elements in the drainage mode and in the subsoil moistening mode. This was done on the basis of substantiating the connection of all technical elements of the system and taking into account the influence of their work efficiency on the effectiveness of regulating the water regime of drained lands. The existence and structure of the hierarchical and hydraulic relationship between the parameters of soil flow movement, the parameters of the closed collector-drainage network, and the parameters of canals and structures of drainage systems were determined based on the application of the system methodology. A physical model, a structural model, a mathematical model, and a hydraulic model of the drainage system were developed. By using these models, the principles of determining the parameters of the hydraulic characteristics of drainage or water supply (discharge, pressure, velocity etc.) for all elements (drained massif of reclaimed field, collector and drainage network, open canals of the network, main canal, water intake) in the entire range of variation with possible consideration of changes in slopes were obtained. The considered approach will make it possible to evaluate the efficiency of water flow movement simultaneously on every technical element and on the drainage system as their interconnection. In the future, this will make it possible to improve the methods of designing and calculating the technological and structural parameters of drainage systems, and thereby ensure the overall technical, technological, economic, and ecological efficiency of their functioning in accordance with modern conditions and requirements. This is a further improvement of the methods of design and calculation of drainage systems and their technical elements, taking into account the structural, hierarchical, and hydraulic relationship between them in accordance with modern conditions and requirements. This will make it possible to increase the validity and general technical, technological, ecological and economic efficiency of the creation and functioning of drainage systems during the implementation of adaptive measures regarding the changes in climatic conditions and the level of agricultural production in the area of drainage reclamation, for example, in Ukrainian Polissia. It will also provide an opportunity to ensure the necessary level of food security in the region and the country as a whole in the war and post-war periods.

Structural and radiation shielding parameters of heavy metal-based environment-friendly glass systems for nuclear radiation security applications

This work used theoretical and experimental approaches to examine the effects of the partial substitution of cadmium (II) oxide for boron trioxide on structural, optical, and physical characteristics. Using the melt quenching technique, we created a cadmium (Cd)-borate glass group with the following nominal composition: (60-X)B2O3 + 20Na2O + 5NiO + 15CaCO3 + xCdO system, where x = 0, 2.5, 5, 7.5 and 10 wt%. The amorphous structure of the Cd-borate glasses was determined using an experimental X-ray diffraction technique. Additionally, density and UV studies were used to investigate optical and material properties. To determine the effect of this substitution on the improvement of nuclear radiation shielding, the linear attenuation coefficients at 80, 356, 662, 1173, and 1333 keV were measured using a narrow beam geometry and an experimental gamma-ray transmission technique. When the CdO level was raised from 0 to 10% (by weight), both the molar volume and transmission decreased in value while hardness of the glass increased. In addition, adding 5% CdO to this glass in its current composition led to a greater absorption of neutrons. The absorption of gamma rays required the addition of 10% CdO. Thus, the best radiation filter was a Cd-borate glass that contained 10% CdO.

Transient subordinate clauses in Balkan Turkic in its shift to Standard Average European subordination. Dialectal and historical evidence

Abstract The Turkic varieties of the Balkans use two main diametrically opposed subordination strategies: (i) the Turkic model, where typical subordinate clauses are prepositive, nonfinite, contain clause-final subordinators, etc. and (ii) the Indo-European model, where typical subordinate clauses are postpositive, finite, contain clause-initial subordinators, etc. The paper observes that Balkan Turkic additionally uses several kinds of subordinate clause that allow for problematic mixtures of these two models (‘X-clauses’). Spread over a spectrum between the Turkic and Indo-European extremes, X-clauses can, for instance, be prepositive but contain clause-initial subordinators. The paper, then, hypothesizes that X-clauses emerge due to uncertainties in the structural parameters of the Balkan Turkic subordination system. Such uncertainties are typical of complex systems undergoing change and arise in the present case due to the shift in Balkan Turkic away from Turkic towards Indo-European subordination.

Optimal allocation of generalized heat storage in distribution network of renewable energy

In order to solve the problem of optimal allocation of general heat resources in high permeability renewable energy distribution network, an optimal allocation scheme of general heat resources in renewable energy distribution network is proposed. The optimal allocation scheme in renewable energy distribution network is proposed. In this paper, the internal and external two-layer structure is designed. The outer layer uses genetic algorithm to search the structural parameters of general energy system, and the inner layer uses dynamic programming method to get the optimal performance of general energy system. The internal and external alternate adjustment methods are used to optimize the general-purpose power distri?bution capability of the continuous-wave power supply network with different permeability and controllability, and the proposed method is verified in IEEE 33 node distribution network. The experimental results show that the general strength storage capacity is 26.6% and 45.7% higher than that of the process with a continuous strength renewable permeability of 30% and 40%, respectively. The utility rates were increased by 18.4% and 27.8%, respectively. Under the condition of high permeability renewable energy, the proposed method can increase the efficiency of resource management of distribution network by regulating load, decrease the distribution capacity of energy stability, and reduce the operation cost of the system.

Wooden roof structures of the Moberg house

The preservation of cultural heritage sites is an important task. Historical monuments are a reflection and documentary evidence of the past, information about which must be preserved and passed on to future generations. One of the most vulnerable and fragile structures in a building is the roof. This work provides historical information and presents the results of a survey of the structures of the building of engineer Moberg in the urban-type settlement of Kalevala in the Republic of Karelia of the Russian Federation. The structural system of the roof and the joint work of its elements have been studied. The expediency of preserving the structural system, shape and geometric parameters of the roof, as well as replacing the existing structures before the reconstruction with new elements from modern sawn timber has been substantiated. The cultural heritage site “House of Engineer Moberg” is an architectural monument of regional significance of the early 20th century and the main historical building of the urban-type settlement of Kalevala, built under the influence of the ideas of Finnish national romanticism. According to archival sources, the house was built in 1906 and renovated in 1925-1926 with the participation of engineer Eduard Moberg and builder Tuomas Waller. Nowadays, the building houses the ethnocultural center kalevalatalo.

WAYS OF IMPROVING THE VERTICAL LAYER APPARATUS FOR PROCESSING LIQUID PIG MANURE

Technologies for processing (manure processing) manure depend on the system and method of keeping animals. This is due to the physical properties of the obtained manure, primarily its moisture content. By using litter, solid (litter) manure is obtained, which has a moisture content of 60...80%. If litter is not used when keeping pigs, then manure without litter is obtained, which is divided into two groups by moisture content: solid (60-80%) and liquid (82-98%). Vortex layer devices are equipped with different types of working bodies and layout of the working area. When carrying out liquid-phase processes, using ferromagnetic elements as a working body, trap screens or labyrinths designed to keep ferromagnetic particles in the working area can be installed on the ends of the non-magnetic insert (or only at the outlet). Grinding and mixing can occur not only with the help of ferromagnetic particles, but also with the help of knives, tubes or a rotor. In these cases, the sieves act as filters (separators). Ferromagnetic elements are added to the working area using an electromagnetic dispenser. Analyzing the results of previous scientific studies, it can be stated that increasing the efficiency of the vortex layer devices is proposed due to the improvement of the design or the substantiation of the structural and technological parameters of individual systems, without taking into account their interconnection. It should be noted that most of the obtained results from the substantiation of structural and technological parameters are experimental and do not have a theoretical justification. In order to solve the problems, the structural and technological scheme of the vortex layer apparatus for liquid manure processing, which allows to obtain liquid organic fertilizers of high quality with increased productivity and level of automation, is substantiated.

Study on Optimization of Pump Shaft Transmission System of Plastic Centrifugal Pump

At present, the design of the pump shaft transmission system mostly refers to the design method of the metal pump transmission system. The dynamic and static characteristics of the plastic centrifugal pump are not related to the structural parameters of the pump shaft. Aiming at the influence of the structural parameters of the pump shaft transmission system on the dynamic and static performance of the plastic centrifugal pump, the three-dimensional model of the impeller and volute chamber was drawn by Creo5.0. The CFD calculation of the load of the plastic centrifugal pump was carried out. The flow field of the plastic centrifugal pump under ideal working conditions was simulated by ANSYS FLUENT. Combined with the application principle of singular function in mechanics, the mathematical model of a deflection of the pump shaft transmission system was constructed. Considering the minimum deflection and the maximum critical speed of the first order as the objective function, an optimization model of the structural parameters of the pump transmission system was established. The NSGA-II multiobjective optimization method was used to solve the optimal structural parameters of the optimization model, and the optimization design of the pump shaft span, cantilever, front, and rear bearing clearance was completed. The optimal span cantilever ratio of the rotor model of the single span cantilever structure was 1:0.75. Compared with the traditional design model, the optimized pump shaft deflection is reduced by 52.35%, and the first-order critical speed is increased by 42.77%. Simultaneously, using polynomial fitting as a mathematical tool, the experimental data were analyzed, and the mathematical expression of the rotation speed deflection relationship of the pump shaft at the first critical rotation speed and the corresponding function curve was obtained.