Mathematical modeling and analysis of electromagnetic direct drive air compressor

Mathematical modeling and analysis of electromagnetic direct drive air compressor | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Mathematical modeling and analysis of electromagnetic direct drive air compressor Chunlin Guo, Jiayu Lu, Wenqing Ge, Xiaochen Zhang, Bo Li This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3820183/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract To accurately simulate the motion characteristics of a reed valve and the changes in flow field in an exhaust chamber, a fluid-structure coupling model of an electromagnetic direct drive air compressor during the exhaust process was established and simulated. The alteration of the flow field within the exhaust chamber is under examination. The transient numerical simulation of the flow field in the exhaust procedure is conducted to reduce the computational model's time complexity and provide an immediate analysis of the exhaust processThis paper explores the effects of altering valve lift and relative pressure loss given different valve parameters and exhaust pressure levels. The findings reveal that when the valve plate thickness is 0.2mm and the valve section width is 3.5mm, the airflow hindrance is significantly minimized. With the valve plate unloaded, the gas flow restriction's impact on gas flow is negligible. This paper presents a theoretical basis for designing exhaust valves for electromagnetic direct-drive air compressors. Compressor air valve Computational Fluid Dynamics (CFD) Fluid-structurecoupling Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 1.Introduction The electromagnetic direct drive air compressor boasts a more compact structure and higher transmission efficiency by omitting the crank connecting rod structure, without sacrificing the advantageous sealing of traditional reciprocating compressors. The air valve, often referred to as the "heart" of the compressor, is an essential component of the piston compressor as its performance has a direct impact on energy efficiency. Tongue spring valves, commonly used in small and medium-sized piston compressors due to their simple structure and small clearance volume, are employed in solenoid direct drive air compressors as exhaust valves. [1] In the previous century, researchers primarily investigated valve discs by solving differential equations for valve disc and gas state in the cylinder [2–3]. With the advancement of computer technology, computational fluid dynamics (CFD) software is now frequently used to simulate gas flow and the stress and deformation state of the valve plate. LINK et al. discovered that the movement of air valves affects the flow loss and vibration noise of reciprocating compressors [4]. KOPPPULA explored the impact of pressure variations on the motion state of the valve disc [5]. Deng Wenjuan demonstrated that the flow area of the valve correlates with the valve disc's size parameter [6]. Han Baokun analyzed the temporal variation characteristics of valve tongue displacement and inlet flow [7]. Bao Huaiqian determined the fluid flow state changes within the cylinder [8]. Ji Jiang conducted a study on the transient change characteristics of valve disc lift [9]. In this paper, the exhaust duct of the electromagnetic direct drive air compressor is no longer directly connected to the filtration tank. Due to the reduced gas discharge from a single cylinder, as compared to the original piston compressor system, the operating environment of the intake valve group has undergone minimal changes. However, significant changes have occurred in the working environment of the exhaust valve group. Therefore, based on the principle of minimum modification, the exhaust valve group has been redesigned. A fluid-structure coupling model of the exhaust chamber has been established, which numerically simulates and analyzes the exhaust process of the electromagnetic direct drive air compressor. The relationship between valve lift, pressure loss, and different valve parameters and exhaust pressures has been elucidated, providing a theoretical basis for the selection of the compressor exhaust valve during the design phase. 2.fluid-structure coupling model in exhaust process 2.1An overview of computational fluid dynamics Computational fluid dynamics can be defined as the numerical simulation of the motion of fluids under the control of fluid motion equations. Therefore, in order to solve fluid motion problems, it is essential to establish the equations that govern fluid motion. As fluid mechanics is a branch of mechanics, the motion of fluids is also subject to the laws of physics. The fundamental conservation laws of fluid mechanics include the equations for mass conservation, energy conservation, and momentum conservation. $$\frac{{\partial \rho }}{{\partial t}}+\frac{{\partial \left( {\rho u} \right)}}{{\partial x}}+\frac{{\partial \left( {\rho v} \right)}}{{\partial y}}+\frac{{\partial \left( {\rho w} \right)}}{{\partial z}}{\text{=}}0$$ 1 equation of continuity: $$\frac{{\partial \rho }}{{\partial t}}{\text{+}}\nabla \cdot ( \rho V) {\text{=}}0$$ 2 Where, ρ represents density; u , v and w represent time as the component of velocity vector in x , y and z directions respectively; t is time. Energy conservation equation: $$\frac{{\partial \left( {\rho T} \right)}}{{\partial {\text{t}}}}+\frac{{\partial \left( {\rho uT} \right)}}{{\partial x}}+\frac{{\partial \left( {\rho vT} \right)}}{{\partial y}}+\frac{{\partial \left( {\rho wT} \right)}}{{\partial z}}=\frac{\partial }{{\partial x}}\left( {\frac{k}{{\mathop c\nolimits_{p} }}\frac{{\partial T}}{{\partial x}}} \right)+\frac{\partial }{{\partial y}}\left( {\frac{k}{{\mathop c\nolimits_{p} }}\frac{{\partial T}}{{\partial y}}} \right)+\frac{\partial }{{\partial z}}\left( {\frac{k}{{\mathop c\nolimits_{p} }}\frac{{\partial T}}{{\partial z}}} \right)+{S_t}$$ 2 Where C p is the specific heat capacity, T is the thermodynamic temperature, and k is the heat transfer coefficient, S t which is called the viscous dissipation term Momentum conservation equation: $$\left\{ \begin{gathered} \frac{{\partial \left( {\rho u} \right)}}{{\partial x}}{\text{+}}div\left( {\rho u{\text{u}}} \right)= - \frac{{\partial p}}{{\partial x}}+\frac{{\partial {\tau _{xx}}}}{{\partial x}}+\frac{{\partial {\tau _{yx}}}}{{\partial y}}+\frac{{\partial {\tau _{zx}}}}{{\partial z}}+F \hfill \\ \frac{{\partial \left( {\rho v} \right)}}{{\partial y}}+div\left( {\rho v{\text{u}}} \right)= - \frac{{\partial p}}{{\partial y}}+\frac{{\partial {\tau _{xy}}}}{{\partial x}}+\frac{{\partial {\tau _{yy}}}}{{\partial y}}+\frac{{\partial {\tau _{zy}}}}{{\partial z}}+{F_y} \hfill \\ \frac{{\partial \left( {\rho w} \right)}}{{\partial z}}+div\left( {\rho w{\text{u}}} \right)= - \frac{{\partial p}}{{\partial z}}+\frac{{\partial {\tau _{xz}}}}{{\partial x}}+\frac{{\partial {\tau _{yz}}}}{{\partial y}}+\frac{{\partial {\tau _{zz}}}}{{\partial z}}+{F_z} \hfill \\ \end{gathered} \right.$$ 3 Where, p is the pressure on the fluid element, and τ xx , τ xy and τ yz are the components of the viscous stress τ generated by the molecular viscous action. F x , F y , F z are the force on the micro body, and u is the velocity vector. 2.2 Establishment of fluid-structure coupling model in exhaust process The three-dimensional software CATIA is utilized to create the three-dimensional model of the fluid region for the cylinder of an air compressor directly. Once the model is built in the three-dimensional software, it is imported into ANSYS' Fluent unit and then into Geometry. Given that the fluid domain of the gas movement inside the cylinder is continually changing with the rotation of the crankshaft, dynamic grid technology is implemented during the calculation process. It must be acknowledged that dynamic grid technology necessitates precise grid requirements; otherwise, errors may occur, or the calculation outcomes may not be ideal. Therefore, the quality of the variable volume area of the grid is superior to that of the constant volume area. In recognition of the advantages of using tetrahedral mesh and hexahedral mesh, hexahedral mesh was chosen for in-cylinder fluid simulation in order to produce a structured mesh with regular spacing and a consistent arrangement. By reconstructing the hexahedral mesh, we can simulate the changing process of the fluid domain effectively, improve convergence speed, and shorten calculation time. As for the complex models of the exhaust reed valve and exhaust chamber, they are segmented using tetrahedral mesh due to their intricacy. Given the fact that the gas changes greatly as it flows through the valve gap, it necessitates a separate region and a smaller grid size. Unstructured grid technology is applied to the complex structure of the valve disc, while structured grid technology is utilized at the gas inlet and outlet where the gas's status changes less, reducing the amount of calculations required. To minimize the data transmission error at the interface, a common node is employed for the grid between different regions. The boundary of the fluid should be defined after the grid division is completed. The accuracy of defining the boundary is crucial to improve the simulation results' accuracy. Once the cylinder flow field model has been gridded, it is imported into the Set up module. Transient cylinder motion is selected, and the gas is set to be an ideal gas. The fluid movement inside the cylinder falls under unsteady compressible flow. The pressure implicit PISO algorithm is chosen, with the fluid material set to air and gas density set to ideal gas. The standard K-Epsilon turbulence model is applied to the fluid model, while the wall is set as adiabatic without slip. The inlet and outlet boundary of the compressor are defined. The outlet is designated as the pressure outlet, which is 1500KPa. Figure displays the boundary condition settings To accurately simulate the instantaneous changes in the airflow within the air compressor and obtain a motion condition consistent with real-world conditions, it is necessary to incorporate the flow field into a dynamic grid. This allows for adjustments to be made to both the fluid and grid models in response to changes in the flow field. Fluent offers three types of dynamic grid computing: spring-based smoothing, dynamic layering, and local remeshing. The upward motion of the piston is achieved through the use of the layup model, while the motion of the valve disc is realized through local redrawing and the elastic approximate smooth model. The move surface type was defined as rigid body motion and its movement was characterized by its profile. The FSI wall surface's moving mesh was coupled to the system and the mesh thickness for the two moving grids was set at 0.6mm and 0.3mm, respectively. Once grid division is complete, the resulting configuration is shown in Fig. 1 below: 3.Exhaust process simulation under different parameters 3.1 Pressure field and velocity field analysis Three moments of t = 0.001, t = 0.006 and t = 0.009 are selected, and the simulated pressure and velocity distribution cloud map is shown in Fig. 3 below. During the exhaust process, a significant pressure exceeding the gas pressure in the exhaust chamber is generated due to the force exerted on the valve disc. By using pressure cloud imagery and flow diagrams, the cause of this elevated pressure can be traced to the impact of gas escaping from the cylinder onto the lower section of the reed valve, which compresses the gas and leads to elevated pressure. The impact pressure of the gas helps maintain the pressure differential between the top and bottom of the reed valve, a crucial aspect of keeping it in an open state. The movement of the valve disc in the exhaust chamber has a profound effect on pressure distribution, resembling the lift curve of the reed valve during fluctuations in flow rate. When gas passes through the spring valve, uneven pressure distribution and significant changes in gas pressure gradients occur within a confined area. As the gas exits the exhaust chamber, the pressure gradient shifts downward, indicating a decrease in pressure. Consistent with Bernoulli's principle, low pressure prevails within the gas as it emerges from the exhaust chamber. The pressure at the valve port is significantly lower than the cylinder pressure. As evident from the velocity flow diagram, when the reed valve opening is minimal, the valve outlet exhibits maximum velocity, and there is also a high velocity region at the outlet of the exhaust chamber. Since the valve port area is significantly smaller than the piston's cross-sectional area, it is explicitly clear that the velocity in the valve port is much higher than that in the cylinder throughout the entire exhaust process. The gas generates a vortex above the valve disc, and the closer the flow path in the vortex to the valve disc, the higher the gas flow velocity. It can be inferred that the energy of the vortex primarily derives from the viscous forces of the exiting gas. 3.2 Simulation of exhaust process under different valve thickness The structural characteristics of the reed valve have a significant impact on the maximum stress and spring stiffness experienced by the valve during its opening phase. Among these parameters, the spring stiffness plays a fundamental role in determining the overall performance of the valve. Any unreasonable deviation from the optimal spring stiffness can lead to various complications, such as delayed opening/closing, valve vibration, and reduced fatigue life. According to the valve deformation theory, the valve thickness is a crucial parameter that affects its performance. Conventionally, reed valves are available in two thicknesses: 0.2mm and 0.3mm. In this comparative study, we have selected the superior thickness of the valve and simulated the valve's performance for both thicknesses. The results of the comparison are depicted in Fig. 4.6, which illustrates the relative pressure loss and valve disc lift for each thickness. Table 1 Maximum lift and maximum relative pressure loss of valve Valve plate thickness(mm) Valve lift(mm) Relative pressure loss(MPa) 0.2 0.59 0.04 0.3 1.43 0.17 Based on simulation results, the pressure drop at a thickness of 0.2mm is 17,000 Pa, and at a thickness of 0.3mm, the pressure drop increases to 26,700 Pa, representing 33% and 20% of the exhaust pressure, respectively. The maximum valve lift for these thicknesses are 1.9mm and 0.86mm, respectively, and there were no incidents of valve double opening. As the thickness of the exhaust valve increases, the maximum pressure in the cylinder flow field also increases due to the increase in spring force. However, excessive valve spring force may cause failure of the valve to open normally. Therefore, additional gas thrust is needed to overcome the valve spring force in order to complete the compressor exhaust process. As a result, the peak pressure in the cylinder flow field increases with valve thickness. Comparison shows that the relative pressure drop under the two thicknesses reaches its maximum prior to the valve lift. For example, the time difference between the two is 0.0004s for a valve thickness of 0.2mm and less than 0.0008s for a valve thickness of 0.3mm. In summary, a valve disc with a thickness of 0.3mm has a stronger gas-blocking effect. 3.3 Simulation results under different valve width Three different width sections of reed valves were selected: 3.7mm, 3.6mm, and 3.5mm. This enables a comparative analysis of the differences between these thicknesses, ultimately leading to the selection of the optimal valve disc thickness. The simulation results for the valve disc were then assessed, taking into consideration the relative pressure loss and valve lift, as illustrated in Fig. 4 below. Based on the simulation results, the pressure drop across the three valve plates' section widths is 18500Pa, 18000Pa, and 17000Pa, respectively. The maximum lift of the discs is almost identical, measuring at 1.90mm, 1.88mm, and 1.97mm. Considering the fundamental concept of valve plate deformation, as the exhaust valve plate's section width increases, its spring stiffness also increases, resulting in greater pressure loss. These curves exhibit similarity because the valve disc's section width remains relatively constant. The valve lift curve indicates that wider section widths lead to more pronounced tremors, with the curve displaying two extreme values at 3.7mm. This valve disc tremor condition causes frequent expansions, reducing valve lifespan, and increases pressure loss. After comprehensive simulation results review, a 3.5mm valve slice section width is selected. 3.4 Simulation results under different valve width Electromagnetic direct-drive air compressors must function within a specified range of exhaust pressures. Variations in exhaust pressure cause differences in pressure loss and valve lift during the exhaust process. To accurately simulate diverse exhaust pressures, this study utilized the gas compression model to calculate the cylinder volume for a specific exhaust pressure. By adjusting the initial calculation conditions and the fluid region's geometric model, we successfully simulated varied exhaust pressures. Specifically, we examined load and no-load conditions for exhaust pressures of 0.1 MPa and 0.5 MPa, respectively. See Table 2 for the initial conditions. Table 2 Initial conditions under load and no load Initial pressure(MPa) Total time(s) Initial piston position(mm) no-load 0.0 0.01 16 load 0.4 0.0036 4.6 Set the model according to the above initial conditions, simulate the model under load and no-load conditions, and getValve lift and relative pressure loss curves are shown in Fig. 5: The maximum pressure loss and maximum valve disc lift in the exhaust process are shown in Table 3 : Table 3 Maximum lift and maximum relative pressure loss of valve disc Exhaust pressure(MPa) Valve lift(mm) Relative pressure loss(MPa) 0.1 1.8 0.017 0.5 5.6 0.054 The simulation results demonstrate that the valve disc exerts a more robust obstructive effect on the gas during loading, resulting in greater pressure loss. Specifically, the maximum pressure loss is 54KPa, while the pressure loss under no load is 17KPa. These values represent 10.8% and 17% of the exhaust pressure, respectively. Under no load conditions, the relative pressure loss varies proportionally with the displacement of valve disc. Conversely, during loading, the valve plate's displacement curve lags behind the relative pressure loss curve. With no load present, the relative pressure loss curve and valve lift curve change gradually and essentially align with the mass flow curve of the air inlet. However, during loading, both the relative pressure loss and valve lift exhibit irregular fluctuations throughout the exhaust process, with the former experiencing more intense fluctuations in particular. Further analysis indicates that in no-load conditions, the gas inlet's mass flow rate is minimal and changes gradually, giving the valve disc ample time to deform. This is demonstrated by the fact that the valve disc's displacement essentially changes synchronously with the relative pressure drop. Under load conditions, during the initial exhaust process, the gas inlet's mass flow rate is high, and the valve plate lacks sufficient time to deform, leading to notable obstruction of the gas flow and a significant relative pressure loss. As the valve lift increases and the mass flow rate at the inlet decreases, the relative pressure loss decreases quickly. Due to its elasticity, during the latter half of the exhaust process, as the gas inlet's mass flow rate decreases, the valve lift and relative pressure loss increase, resulting in the valve disc opening twice. The valve disc's lift during the second opening is lesser than during the first and does not close in time during the final exhaust process. When there is no load, the valve disc has little impact on obstructing gas flow and can open and close promptly. However, under a load, due to the limited exhaust process time, the valve disc's deformation is not immediate, resulting in substantial pressure loss when the valve disc opens twice. Additionally, the valve disc cannot close promptly, leading to a minor backflow phenomenon. The valve disc blocks gas to some degree, mainly when there is significant exhaust pressure. 4.Carrying experimental platform 4.1 Experimental setup In this paper, the testing platform employed a real-time digital control system, specifically RTU-BOX. The hardware controller is designed with multi-core heterogeneous technology, with the processor comprised of DSP, ARM, and multiple FPGA cores. The primary processor utilized in this experiment is the floating-point digital signal processor, TMS320C28346, a product of the renowned IT company, Delfino platform, capable of a main frequency of 300MHz. The figure illustrates the experimental device used in the study. The testing platform used a robust real-time digital control system designed to deliver high performance. The hardware controller employed multi-core heterogeneous technology to ensure the system processes data more efficiently. The processor configuration consisted of multiple cores, including DSP, ARM, and FPGA, with the primary processor being the prestigious TMS320C28346 from the Delfino platform. The chosen processor boasts a main frequency of 300MHz, ensuring optimal speed in data processing. The experiment utilized the device shown in the figure, which effectively achieved the study's objectives. 4.2Analysis of experimental results Upon completion of the aforementioned settings, the software should be run in order to obtain a simulation outcome of the valve disc. The experimental findings indicate that the relative pressure loss curve and lift curve of the valve plate exhibit a smooth transition when no load is applied, thereby having little impact on the obstruction of gas flow while effectively opening and closing in a timely manner. Although the experimental results show that the relative pressure loss and valve lift are greater than those of the simulation results, the latter contains a degree of error. The possible reasons for this margin of error may include: (1) Discrepancies resulting from machining processes or friction factors between components of the linear compressor, (2) Data deviation which may have ensued due to vibrations of the linear compressor causing displacement of the laser sensor during experimentation, and (3) Discrepancy caused by disjuncture between the pistons and cylinder. Once the aforementioned steps have been taken, the software can be initiated to obtain a simulation outcome for the valve disc. 5.Conclusion The present study aimed to investigate the behavior of valve disc displacement and relative pressure loss under different parameters using an established fluid-structure coupling model. The following conclusions were drawn from the analysis: Firstly, the transient numerical simulation of the flow field in the exhaust process of the electromagnetic direct drive air compressor was carried out using the fluid-solid coupling method. The simulation results revealed that a vortex is generated above the valve disc during the process, and the gas impact is a significant factor responsible for keeping the valve disc open. Furthermore, the variation of valve disc region and fluid region under two different working conditions was also simulated. Secondly, the study analyzed the relative pressure loss and valve lift curve in relation to valve disc thickness and section width. The results showed that a valve thickness of 0.2mm and a section width of 3.5mm result in less airflow obstruction. Under no-load condition, the valve disc had minimal obstruction to gas flow and could open and close in time. However, under load condition, the valve disc is not deformed in time, resulting in large pressure loss at the beginning. In some instances, the valve disc opened twice, and closure was delayed, resulting in slight reflux phenomenon. In conclusion, the established fluid-structure coupling model helped to analyze valve disc behavior under various parameters, providing valuable insights into the functioning of the electromagnetic direct drive air compressor. The findings of this study can inform future research on improving the overall efficiency and performance of these devices. Declarations : Declarations Ethical Approval: There is no potential conflict of interest in this research The study did not involve animals The study was given informed consent Funding: This project is supported by National Natural Science Foundation of China (Grant No. 52305265、52375105), Shandong Provincial Natural Science Foundation, China (Fund No. ZR2022YQ51)and Shandong Provincial Major Scientific and Technological Innovation Project (2021CXGC010703）. Availability of data and materials: All available on fluent can be request on e-mail: [email protected] . Author Contribution ChunLin guo wrote the main text, Jiayu Lu provided the experimental ideas, WenQing ge and Xiaochen Zhang provided the technical guidance, and Bo Li provided the financial support References Y. Wang et al., Experimental investiga-tion on valve impact velocity and inclining motion of a re-ciprocating compressor, Applied Thermal Engineering. 61 (2) (2013) 149–156. B. Min et al., Geometric correlation of discharge coefficients for discharge valve system in rolling piston rotary compressor, Journal of Mechanical Scienceand Technology. 32 (8) (2018) 3943–3954. Y. P. Deng et al., Numerical Analysis on Efficiency of a Miniature High Pressure Compressor, Chinese Hydraulics& Pneumatics. (11) (2019) 63–68. KOPPPULA J S, RAJAGOPAL T K R, GUNDABAT-TINIE, Correlating the experiment and fluid structure interaction results of a suction valve model from a hermetic reciprocating compressor, SAE Technical Paper. (2017) No.2017-28-1948. F. Wang, L. L. li., Research on parameter matching and optimization of pure electric vehicle power system, Agricultural equipment and vehicle engineering. 58 (12) (2020) 93–97. W. J. Deng et al., CFD-based Performance Analysis of a Discharge Valve Plate in the Rolling Rotor Compressor,Journal of Northeastern University(Natural Science). 41 (12) (2020) 1754–1759. B. K. Han et al., Research on flow field characteristics of suction valve of reciprocating compressor based on fluid-structure coupling method, FLUID MACHINERY. 49 (05) (2021) 47–53. Huaiqian Bao et al., Analysis and Research on Flow Field Characteristics in Cylinder of Reciprocating Refrigeration Compressor, FLUID MACHINERY, 48 (07) (2020) 22–26. JIJiang. DING et al., Numerical analysis of motion characteristics of suction reed valve in DC linear compressor, FLUID MACHINERY, 49 (07) (2021) 38–44. X. Y. Zhang et al., Theoretical analysis of dynamic characteristics in linear compressors, International Journal of Refrigeration 109 (2020) 114–127. Bijanzad. A et al., Development of a new moving magnet linear compressor. Part A: Design and modeling, International Journal of Refrigeration 113 (2020) 70–79. Y. W. Liu et al., Modification of shear stress transport turbulence model using helicity for predicting corner separation flow in a linear compressor cascade, Journal of Turbomachinery 142.2 (2020) 021004. Y. L. Liu et al., Experimental investigation of the discharge valve dynamics in an oil-free linear compressor for Joule-Thomson throttling refrigerator, Applied Thermal Engineering 209 (2022) 118288. Q. Huang et al., Experimental investigation on piston offset and performance of helium valved linear compressor with an external gas bypass, International Journal of Refrigeration145 (2023) 417–424. C. Z. Li, et al. Characteristic analysis and energy efficiency of an oil-free dual-piston linear compressor for household refrigeration with various conditions, Energy 270 (2023).126931. Faisal, Mohammed, Mohammed Afzal, and Tabish Khan. Introduction to Linear Compressor and Electronics Cooling—A Review, Emerging Trends in Mechanical and Industrial Engineering: Select Proceedings of ICETMIE 2022 (2023) 331–343. Z. J. Huang et al., Theoretical and Experimental Investigation on Comparing the Efficiency of a Single-Piston Valved Linear Compressor and a Symmetrical Dual-Piston Valved Linear Compressor, Energies 15.22 (2022) 8760. Hwang, Il Sun, and Young Lim Lee. Study on the performance of linear compressor with suction system shapes using a transient CFD model, Journal of Mechanical Science and Technology 36.4 (2022) 1809–1816. Ahmad, Aftab et al., Performance Analysis of Tubular Moving Magnet Linear Oscillating Actuator for Linear Compressors, Energies 15.9 (2022: 3224. S. P. Hu et al., moving magnet linear oscillation motor electromagnetic system theory and experiment, mechanical design and research of 39.02 (2023) 202–206. Additional Declarations No competing interests reported. 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08:01:32","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3820183/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3820183/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":49212743,"identity":"4ac4f2ac-6ca5-4789-9eec-caba4c3207b1","added_by":"auto","created_at":"2024-01-05 09:21:14","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":247916,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003eSchematic diagram of cylinder grid\u003c/em\u003e\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-3820183/v1/b25ed64b8e7b2c30a83ecff6.png"},{"id":49212744,"identity":"deb17021-5b69-4e22-8426-8ed0a2a6226c","added_by":"auto","created_at":"2024-01-05 09:21:14","extension":"png","order_by":2,"title":"Figure 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09:13:14","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":109162,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003eValve lift and pressure loss under two thicknesses\u003c/em\u003e\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-3820183/v1/c2519ed633a3d796593501fe.png"},{"id":49212148,"identity":"e6e72028-6e1d-485a-af59-b6a1eb61a5a2","added_by":"auto","created_at":"2024-01-05 09:13:14","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":130770,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003eValve lift and pressure loss under two thicknesses\u003c/em\u003e\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-3820183/v1/30127c129ebcb14fc7f9aaab.png"},{"id":49212152,"identity":"814534bd-2d21-4b45-bb1f-2015ef6b1cc6","added_by":"auto","created_at":"2024-01-05 09:13:14","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":808176,"visible":true,"origin":"","legend":"\u003cp\u003eExperimental platform\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-3820183/v1/5f1f4fce959ab4b6a43b3d0e.png"},{"id":49212150,"identity":"b9d2117e-ac7f-4704-ad69-0657c0ccd960","added_by":"auto","created_at":"2024-01-05 09:13:14","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":48768,"visible":true,"origin":"","legend":"\u003cp\u003eExperimental result\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-3820183/v1/c42cb8549399be36e86658f0.png"},{"id":50308677,"identity":"faf7abcf-f50b-400f-abb8-486e2358ef91","added_by":"auto","created_at":"2024-01-29 13:59:06","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2224994,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3820183/v1/ab05103c-8a9e-4a67-a6b3-7855e5042a13.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Mathematical modeling and analysis of electromagnetic direct drive air compressor","fulltext":[{"header":"1.Introduction","content":"\u003cp\u003eThe electromagnetic direct drive air compressor boasts a more compact structure and higher transmission efficiency by omitting the crank connecting rod structure, without sacrificing the advantageous sealing of traditional reciprocating compressors. The air valve, often referred to as the \"heart\" of the compressor, is an essential component of the piston compressor as its performance has a direct impact on energy efficiency. Tongue spring valves, commonly used in small and medium-sized piston compressors due to their simple structure and small clearance volume, are employed in solenoid direct drive air compressors as exhaust valves. [1]\u003c/p\u003e \u003cp\u003eIn the previous century, researchers primarily investigated valve discs by solving differential equations for valve disc and gas state in the cylinder [2\u0026ndash;3]. With the advancement of computer technology, computational fluid dynamics (CFD) software is now frequently used to simulate gas flow and the stress and deformation state of the valve plate. LINK et al. discovered that the movement of air valves affects the flow loss and vibration noise of reciprocating compressors [4]. KOPPPULA explored the impact of pressure variations on the motion state of the valve disc [5]. Deng Wenjuan demonstrated that the flow area of the valve correlates with the valve disc's size parameter [6]. Han Baokun analyzed the temporal variation characteristics of valve tongue displacement and inlet flow [7]. Bao Huaiqian determined the fluid flow state changes within the cylinder [8]. Ji Jiang conducted a study on the transient change characteristics of valve disc lift [9].\u003c/p\u003e \u003cp\u003eIn this paper, the exhaust duct of the electromagnetic direct drive air compressor is no longer directly connected to the filtration tank. Due to the reduced gas discharge from a single cylinder, as compared to the original piston compressor system, the operating environment of the intake valve group has undergone minimal changes. However, significant changes have occurred in the working environment of the exhaust valve group. Therefore, based on the principle of minimum modification, the exhaust valve group has been redesigned. A fluid-structure coupling model of the exhaust chamber has been established, which numerically simulates and analyzes the exhaust process of the electromagnetic direct drive air compressor. The relationship between valve lift, pressure loss, and different valve parameters and exhaust pressures has been elucidated, providing a theoretical basis for the selection of the compressor exhaust valve during the design phase.\u003c/p\u003e"},{"header":"2.fluid-structure coupling model in exhaust process","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1An overview of computational fluid dynamics\u003c/h2\u003e \u003cp\u003eComputational fluid dynamics can be defined as the numerical simulation of the motion of fluids under the control of fluid motion equations. Therefore, in order to solve fluid motion problems, it is essential to establish the equations that govern fluid motion. As fluid mechanics is a branch of mechanics, the motion of fluids is also subject to the laws of physics. The fundamental conservation laws of fluid mechanics include the equations for mass conservation, energy conservation, and momentum conservation.\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\frac{{\\partial \\rho }}{{\\partial t}}+\\frac{{\\partial \\left( {\\rho u} \\right)}}{{\\partial x}}+\\frac{{\\partial \\left( {\\rho v} \\right)}}{{\\partial y}}+\\frac{{\\partial \\left( {\\rho w} \\right)}}{{\\partial z}}{\\text{=}}0$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eequation of continuity:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\frac{{\\partial \\rho }}{{\\partial t}}{\\text{+}}\\nabla \\cdot ( \\rho V) {\\text{=}}0$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere, \u003cem\u003eρ\u003c/em\u003e represents density; \u003cem\u003eu\u003c/em\u003e, \u003cem\u003ev\u003c/em\u003e and \u003cem\u003ew\u003c/em\u003e represent time as the component of velocity vector in \u003cem\u003ex\u003c/em\u003e, \u003cem\u003ey\u003c/em\u003e and \u003cem\u003ez\u003c/em\u003e directions respectively; \u003cem\u003et\u003c/em\u003e is time.\u003c/p\u003e \u003cp\u003eEnergy conservation equation:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\frac{{\\partial \\left( {\\rho T} \\right)}}{{\\partial {\\text{t}}}}+\\frac{{\\partial \\left( {\\rho uT} \\right)}}{{\\partial x}}+\\frac{{\\partial \\left( {\\rho vT} \\right)}}{{\\partial y}}+\\frac{{\\partial \\left( {\\rho wT} \\right)}}{{\\partial z}}=\\frac{\\partial }{{\\partial x}}\\left( {\\frac{k}{{\\mathop c\\nolimits_{p} }}\\frac{{\\partial T}}{{\\partial x}}} \\right)+\\frac{\\partial }{{\\partial y}}\\left( {\\frac{k}{{\\mathop c\\nolimits_{p} }}\\frac{{\\partial T}}{{\\partial y}}} \\right)+\\frac{\\partial }{{\\partial z}}\\left( {\\frac{k}{{\\mathop c\\nolimits_{p} }}\\frac{{\\partial T}}{{\\partial z}}} \\right)+{S_t}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cem\u003eC\u003c/em\u003e\u003csub\u003e\u003cem\u003ep\u003c/em\u003e\u003c/sub\u003e is the specific heat capacity,\u003cem\u003eT\u003c/em\u003e is the thermodynamic temperature, and \u003cem\u003ek\u003c/em\u003e is the heat transfer coefficient, \u003cem\u003eS\u003c/em\u003e\u003csub\u003e\u003cem\u003et\u003c/em\u003e\u003c/sub\u003e which is called the viscous dissipation term\u003c/p\u003e \u003cp\u003eMomentum conservation equation:\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\left\\{ \\begin{gathered} \\frac{{\\partial \\left( {\\rho u} \\right)}}{{\\partial x}}{\\text{+}}div\\left( {\\rho u{\\text{u}}} \\right)= - \\frac{{\\partial p}}{{\\partial x}}+\\frac{{\\partial {\\tau _{xx}}}}{{\\partial x}}+\\frac{{\\partial {\\tau _{yx}}}}{{\\partial y}}+\\frac{{\\partial {\\tau _{zx}}}}{{\\partial z}}+F \\hfill \\\\ \\frac{{\\partial \\left( {\\rho v} \\right)}}{{\\partial y}}+div\\left( {\\rho v{\\text{u}}} \\right)= - \\frac{{\\partial p}}{{\\partial y}}+\\frac{{\\partial {\\tau _{xy}}}}{{\\partial x}}+\\frac{{\\partial {\\tau _{yy}}}}{{\\partial y}}+\\frac{{\\partial {\\tau _{zy}}}}{{\\partial z}}+{F_y} \\hfill \\\\ \\frac{{\\partial \\left( {\\rho w} \\right)}}{{\\partial z}}+div\\left( {\\rho w{\\text{u}}} \\right)= - \\frac{{\\partial p}}{{\\partial z}}+\\frac{{\\partial {\\tau _{xz}}}}{{\\partial x}}+\\frac{{\\partial {\\tau _{yz}}}}{{\\partial y}}+\\frac{{\\partial {\\tau _{zz}}}}{{\\partial z}}+{F_z} \\hfill \\\\ \\end{gathered} \\right.$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere, \u003cem\u003ep\u003c/em\u003e is the pressure on the fluid element, and \u003cem\u003eτ\u003c/em\u003e\u003csub\u003e\u003cem\u003exx\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eτ\u003c/em\u003e\u003csub\u003e\u003cem\u003exy\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eτ\u003c/em\u003e\u003csub\u003e\u003cem\u003eyz\u003c/em\u003e\u003c/sub\u003e are the components of the viscous stress \u003cem\u003eτ\u003c/em\u003e generated by the molecular viscous action. \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003ey\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e are the force on the micro body, and \u003cb\u003eu\u003c/b\u003e is the velocity vector.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Establishment of fluid-structure coupling model in exhaust process\u003c/h2\u003e \u003cp\u003eThe three-dimensional software CATIA is utilized to create the three-dimensional model of the fluid region for the cylinder of an air compressor directly. Once the model is built in the three-dimensional software, it is imported into ANSYS' Fluent unit and then into Geometry.\u003c/p\u003e \u003cp\u003eGiven that the fluid domain of the gas movement inside the cylinder is continually changing with the rotation of the crankshaft, dynamic grid technology is implemented during the calculation process. It must be acknowledged that dynamic grid technology necessitates precise grid requirements; otherwise, errors may occur, or the calculation outcomes may not be ideal. Therefore, the quality of the variable volume area of the grid is superior to that of the constant volume area. In recognition of the advantages of using tetrahedral mesh and hexahedral mesh, hexahedral mesh was chosen for in-cylinder fluid simulation in order to produce a structured mesh with regular spacing and a consistent arrangement. By reconstructing the hexahedral mesh, we can simulate the changing process of the fluid domain effectively, improve convergence speed, and shorten calculation time. As for the complex models of the exhaust reed valve and exhaust chamber, they are segmented using tetrahedral mesh due to their intricacy.\u003c/p\u003e \u003cp\u003eGiven the fact that the gas changes greatly as it flows through the valve gap, it necessitates a separate region and a smaller grid size. Unstructured grid technology is applied to the complex structure of the valve disc, while structured grid technology is utilized at the gas inlet and outlet where the gas's status changes less, reducing the amount of calculations required. To minimize the data transmission error at the interface, a common node is employed for the grid between different regions.\u003c/p\u003e \u003cp\u003eThe boundary of the fluid should be defined after the grid division is completed. The accuracy of defining the boundary is crucial to improve the simulation results' accuracy. Once the cylinder flow field model has been gridded, it is imported into the Set up module. Transient cylinder motion is selected, and the gas is set to be an ideal gas. The fluid movement inside the cylinder falls under unsteady compressible flow. The pressure implicit PISO algorithm is chosen, with the fluid material set to air and gas density set to ideal gas. The standard K-Epsilon turbulence model is applied to the fluid model, while the wall is set as adiabatic without slip. The inlet and outlet boundary of the compressor are defined. The outlet is designated as the pressure outlet, which is 1500KPa. Figure displays the boundary condition settings\u003c/p\u003e \u003cp\u003eTo accurately simulate the instantaneous changes in the airflow within the air compressor and obtain a motion condition consistent with real-world conditions, it is necessary to incorporate the flow field into a dynamic grid. This allows for adjustments to be made to both the fluid and grid models in response to changes in the flow field. Fluent offers three types of dynamic grid computing: spring-based smoothing, dynamic layering, and local remeshing. The upward motion of the piston is achieved through the use of the layup model, while the motion of the valve disc is realized through local redrawing and the elastic approximate smooth model. The move surface type was defined as rigid body motion and its movement was characterized by its profile. The FSI wall surface's moving mesh was coupled to the system and the mesh thickness for the two moving grids was set at 0.6mm and 0.3mm, respectively. Once grid division is complete, the resulting configuration is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e below:\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"3.Exhaust process simulation under different parameters","content":"\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Pressure field and velocity field analysis\u003c/h2\u003e \u003cp\u003eThree moments of t\u0026thinsp;=\u0026thinsp;0.001, t\u0026thinsp;=\u0026thinsp;0.006 and t\u0026thinsp;=\u0026thinsp;0.009 are selected, and the simulated pressure and velocity distribution cloud map is shown in Fig.\u0026nbsp;3 below.\u003c/p\u003e \u003cp\u003eDuring the exhaust process, a significant pressure exceeding the gas pressure in the exhaust chamber is generated due to the force exerted on the valve disc. By using pressure cloud imagery and flow diagrams, the cause of this elevated pressure can be traced to the impact of gas escaping from the cylinder onto the lower section of the reed valve, which compresses the gas and leads to elevated pressure. The impact pressure of the gas helps maintain the pressure differential between the top and bottom of the reed valve, a crucial aspect of keeping it in an open state. The movement of the valve disc in the exhaust chamber has a profound effect on pressure distribution, resembling the lift curve of the reed valve during fluctuations in flow rate. When gas passes through the spring valve, uneven pressure distribution and significant changes in gas pressure gradients occur within a confined area. As the gas exits the exhaust chamber, the pressure gradient shifts downward, indicating a decrease in pressure. Consistent with Bernoulli's principle, low pressure prevails within the gas as it emerges from the exhaust chamber. The pressure at the valve port is significantly lower than the cylinder pressure.\u003c/p\u003e \u003cp\u003eAs evident from the velocity flow diagram, when the reed valve opening is minimal, the valve outlet exhibits maximum velocity, and there is also a high velocity region at the outlet of the exhaust chamber. Since the valve port area is significantly smaller than the piston's cross-sectional area, it is explicitly clear that the velocity in the valve port is much higher than that in the cylinder throughout the entire exhaust process. The gas generates a vortex above the valve disc, and the closer the flow path in the vortex to the valve disc, the higher the gas flow velocity. It can be inferred that the energy of the vortex primarily derives from the viscous forces of the exiting gas.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Simulation of exhaust process under different valve thickness\u003c/h2\u003e \u003cp\u003eThe structural characteristics of the reed valve have a significant impact on the maximum stress and spring stiffness experienced by the valve during its opening phase. Among these parameters, the spring stiffness plays a fundamental role in determining the overall performance of the valve. Any unreasonable deviation from the optimal spring stiffness can lead to various complications, such as delayed opening/closing, valve vibration, and reduced fatigue life. According to the valve deformation theory, the valve thickness is a crucial parameter that affects its performance. Conventionally, reed valves are available in two thicknesses: 0.2mm and 0.3mm. In this comparative study, we have selected the superior thickness of the valve and simulated the valve's performance for both thicknesses. The results of the comparison are depicted in Fig.\u0026nbsp;4.6, which illustrates the relative pressure loss and valve disc lift for each thickness.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e Maximum lift and maximum relative pressure loss of valve\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eValve plate thickness(mm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eValve lift(mm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRelative pressure loss(MPa)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e0.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.59\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.04\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.43\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.17\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eBased on simulation results, the pressure drop at a thickness of 0.2mm is 17,000 Pa, and at a thickness of 0.3mm, the pressure drop increases to 26,700 Pa, representing 33% and 20% of the exhaust pressure, respectively. The maximum valve lift for these thicknesses are 1.9mm and 0.86mm, respectively, and there were no incidents of valve double opening. As the thickness of the exhaust valve increases, the maximum pressure in the cylinder flow field also increases due to the increase in spring force. However, excessive valve spring force may cause failure of the valve to open normally. Therefore, additional gas thrust is needed to overcome the valve spring force in order to complete the compressor exhaust process. As a result, the peak pressure in the cylinder flow field increases with valve thickness. Comparison shows that the relative pressure drop under the two thicknesses reaches its maximum prior to the valve lift. For example, the time difference between the two is 0.0004s for a valve thickness of 0.2mm and less than 0.0008s for a valve thickness of 0.3mm. In summary, a valve disc with a thickness of 0.3mm has a stronger gas-blocking effect.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Simulation results under different valve width\u003c/h2\u003e \u003cp\u003eThree different width sections of reed valves were selected: 3.7mm, 3.6mm, and 3.5mm. This enables a comparative analysis of the differences between these thicknesses, ultimately leading to the selection of the optimal valve disc thickness. The simulation results for the valve disc were then assessed, taking into consideration the relative pressure loss and valve lift, as illustrated in Fig.\u0026nbsp;4 below.\u003c/p\u003e \u003cp\u003eBased on the simulation results, the pressure drop across the three valve plates' section widths is 18500Pa, 18000Pa, and 17000Pa, respectively. The maximum lift of the discs is almost identical, measuring at 1.90mm, 1.88mm, and 1.97mm. Considering the fundamental concept of valve plate deformation, as the exhaust valve plate's section width increases, its spring stiffness also increases, resulting in greater pressure loss. These curves exhibit similarity because the valve disc's section width remains relatively constant. The valve lift curve indicates that wider section widths lead to more pronounced tremors, with the curve displaying two extreme values at 3.7mm. This valve disc tremor condition causes frequent expansions, reducing valve lifespan, and increases pressure loss. After comprehensive simulation results review, a 3.5mm valve slice section width is selected.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e3.4 Simulation results under different valve width\u003c/h2\u003e \u003cp\u003eElectromagnetic direct-drive air compressors must function within a specified range of exhaust pressures. Variations in exhaust pressure cause differences in pressure loss and valve lift during the exhaust process. To accurately simulate diverse exhaust pressures, this study utilized the gas compression model to calculate the cylinder volume for a specific exhaust pressure. By adjusting the initial calculation conditions and the fluid region's geometric model, we successfully simulated varied exhaust pressures. Specifically, we examined load and no-load conditions for exhaust pressures of 0.1 MPa and 0.5 MPa, respectively. See Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e for the initial conditions.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e Initial conditions under load and no load\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eInitial pressure(MPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTotal time(s)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eInitial piston position(mm)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eno-load\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e16\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eload\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0036\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e4.6\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eSet the model according to the above initial conditions, simulate the model under load and no-load conditions, and getValve lift and relative pressure loss curves are shown in Fig.\u0026nbsp;5:\u003c/p\u003e \u003cp\u003eThe maximum pressure loss and maximum valve disc lift in the exhaust process are shown in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e:\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e Maximum lift and maximum relative pressure loss of valve disc\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eExhaust pressure(MPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eValve lift(mm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eRelative pressure loss(MPa)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e0.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.017\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e5.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.054\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe simulation results demonstrate that the valve disc exerts a more robust obstructive effect on the gas during loading, resulting in greater pressure loss. Specifically, the maximum pressure loss is 54KPa, while the pressure loss under no load is 17KPa. These values represent 10.8% and 17% of the exhaust pressure, respectively.\u003c/p\u003e \u003cp\u003eUnder no load conditions, the relative pressure loss varies proportionally with the displacement of valve disc. Conversely, during loading, the valve plate's displacement curve lags behind the relative pressure loss curve. With no load present, the relative pressure loss curve and valve lift curve change gradually and essentially align with the mass flow curve of the air inlet. However, during loading, both the relative pressure loss and valve lift exhibit irregular fluctuations throughout the exhaust process, with the former experiencing more intense fluctuations in particular.\u003c/p\u003e \u003cp\u003eFurther analysis indicates that in no-load conditions, the gas inlet's mass flow rate is minimal and changes gradually, giving the valve disc ample time to deform. This is demonstrated by the fact that the valve disc's displacement essentially changes synchronously with the relative pressure drop. Under load conditions, during the initial exhaust process, the gas inlet's mass flow rate is high, and the valve plate lacks sufficient time to deform, leading to notable obstruction of the gas flow and a significant relative pressure loss. As the valve lift increases and the mass flow rate at the inlet decreases, the relative pressure loss decreases quickly. Due to its elasticity, during the latter half of the exhaust process, as the gas inlet's mass flow rate decreases, the valve lift and relative pressure loss increase, resulting in the valve disc opening twice. The valve disc's lift during the second opening is lesser than during the first and does not close in time during the final exhaust process. When there is no load, the valve disc has little impact on obstructing gas flow and can open and close promptly. However, under a load, due to the limited exhaust process time, the valve disc's deformation is not immediate, resulting in substantial pressure loss when the valve disc opens twice. Additionally, the valve disc cannot close promptly, leading to a minor backflow phenomenon. The valve disc blocks gas to some degree, mainly when there is significant exhaust pressure.\u003c/p\u003e \u003c/div\u003e"},{"header":"4.Carrying experimental platform","content":"\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e4.1 Experimental setup\u003c/h2\u003e \u003cp\u003eIn this paper, the testing platform employed a real-time digital control system, specifically RTU-BOX. The hardware controller is designed with multi-core heterogeneous technology, with the processor comprised of DSP, ARM, and multiple FPGA cores. The primary processor utilized in this experiment is the floating-point digital signal processor, TMS320C28346, a product of the renowned IT company, Delfino platform, capable of a main frequency of 300MHz. The figure illustrates the experimental device used in the study.\u003c/p\u003e \u003cp\u003eThe testing platform used a robust real-time digital control system designed to deliver high performance. The hardware controller employed multi-core heterogeneous technology to ensure the system processes data more efficiently. The processor configuration consisted of multiple cores, including DSP, ARM, and FPGA, with the primary processor being the prestigious TMS320C28346 from the Delfino platform. The chosen processor boasts a main frequency of 300MHz, ensuring optimal speed in data processing. The experiment utilized the device shown in the figure, which effectively achieved the study's objectives.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e4.2Analysis of experimental results\u003c/h2\u003e \u003cp\u003eUpon completion of the aforementioned settings, the software should be run in order to obtain a simulation outcome of the valve disc. The experimental findings indicate that the relative pressure loss curve and lift curve of the valve plate exhibit a smooth transition when no load is applied, thereby having little impact on the obstruction of gas flow while effectively opening and closing in a timely manner. Although the experimental results show that the relative pressure loss and valve lift are greater than those of the simulation results, the latter contains a degree of error. The possible reasons for this margin of error may include:\u003c/p\u003e \u003cp\u003e(1) Discrepancies resulting from machining processes or friction factors between components of the linear compressor,\u003c/p\u003e \u003cp\u003e(2) Data deviation which may have ensued due to vibrations of the linear compressor causing displacement of the laser sensor during experimentation, and\u003c/p\u003e \u003cp\u003e(3) Discrepancy caused by disjuncture between the pistons and cylinder. Once the aforementioned steps have been taken, the software can be initiated to obtain a simulation outcome for the valve disc.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"5.Conclusion","content":"\u003cp\u003eThe present study aimed to investigate the behavior of valve disc displacement and relative pressure loss under different parameters using an established fluid-structure coupling model. The following conclusions were drawn from the analysis:\u003c/p\u003e \u003cp\u003eFirstly, the transient numerical simulation of the flow field in the exhaust process of the electromagnetic direct drive air compressor was carried out using the fluid-solid coupling method. The simulation results revealed that a vortex is generated above the valve disc during the process, and the gas impact is a significant factor responsible for keeping the valve disc open. Furthermore, the variation of valve disc region and fluid region under two different working conditions was also simulated.\u003c/p\u003e \u003cp\u003eSecondly, the study analyzed the relative pressure loss and valve lift curve in relation to valve disc thickness and section width. The results showed that a valve thickness of 0.2mm and a section width of 3.5mm result in less airflow obstruction. Under no-load condition, the valve disc had minimal obstruction to gas flow and could open and close in time. However, under load condition, the valve disc is not deformed in time, resulting in large pressure loss at the beginning. In some instances, the valve disc opened twice, and closure was delayed, resulting in slight reflux phenomenon.\u003c/p\u003e \u003cp\u003eIn conclusion, the established fluid-structure coupling model helped to analyze valve disc behavior under various parameters, providing valuable insights into the functioning of the electromagnetic direct drive air compressor. The findings of this study can inform future research on improving the overall efficiency and performance of these devices.\u003c/p\u003e \u003cp\u003e \u003cb\u003eDeclarations\u003c/b\u003e:\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eEthical Approval:\u003c/strong\u003e\u003c/p\u003e\n\u003cul\u003e\n \u003cli\u003eThere is no potential conflict of interest in this research\u003c/li\u003e\n \u003cli\u003eThe study did not involve animals\u003c/li\u003e\n \u003cli\u003eThe study was given informed consent\u003c/li\u003e\n\u003c/ul\u003e\n\u003cp\u003e\u003cstrong\u003eFunding:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis project is supported by National Natural Science Foundation of China (Grant No. 52305265、52375105), Shandong Provincial Natural Science Foundation, China (Fund No. ZR2022YQ51)and Shandong Provincial Major Scientific and Technological Innovation Project (2021CXGC010703）.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAvailability of data and materials:\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll available on fluent can be request on e-mail: [email protected].\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor Contribution\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eChunLin guo wrote the main text, Jiayu Lu provided the experimental ideas, WenQing ge and Xiaochen Zhang provided the technical guidance, and Bo Li provided the financial support\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eY. Wang et al., Experimental investiga-tion on valve impact velocity and inclining motion of a re-ciprocating compressor, Applied Thermal Engineering. 61 (2) (2013) 149\u0026ndash;156.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eB. Min et al., Geometric correlation of discharge coefficients for discharge valve system in rolling piston rotary compressor, Journal of Mechanical Scienceand Technology. 32 (8) (2018) 3943\u0026ndash;3954.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eY. P. Deng et al., Numerical Analysis on Efficiency of a Miniature High Pressure Compressor, Chinese Hydraulics\u0026amp; Pneumatics. (11) (2019) 63\u0026ndash;68.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKOPPPULA J S, RAJAGOPAL T K R, GUNDABAT-TINIE, Correlating the experiment and fluid structure interaction results of a suction valve model from a hermetic reciprocating compressor, \u003cem\u003eSAE Technical Paper.\u003c/em\u003e (2017) No.2017-28-1948.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eF. Wang, L. L. li., Research on parameter matching and optimization of pure electric vehicle power system, Agricultural equipment and vehicle engineering. 58 (12) (2020) 93\u0026ndash;97.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eW. J. Deng et al., CFD-based Performance Analysis of a Discharge Valve Plate in the Rolling Rotor Compressor,Journal of Northeastern University(Natural Science). 41 (12) (2020) 1754\u0026ndash;1759.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eB. K. Han et al., Research on flow field characteristics of suction valve of reciprocating compressor based on fluid-structure coupling method, FLUID MACHINERY. 49 (05) (2021) 47\u0026ndash;53.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHuaiqian Bao et al., Analysis and Research on Flow Field Characteristics in Cylinder of Reciprocating Refrigeration Compressor, FLUID MACHINERY, 48 (07) (2020) 22\u0026ndash;26.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eJIJiang. DING et al., Numerical analysis of motion characteristics of suction reed valve in DC linear compressor, FLUID MACHINERY, 49 (07) (2021) 38\u0026ndash;44.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eX. Y. Zhang et al., Theoretical analysis of dynamic characteristics in linear compressors, International Journal of Refrigeration 109 (2020) 114\u0026ndash;127.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBijanzad. A et al., Development of a new moving magnet linear compressor. Part A: Design and modeling, International Journal of Refrigeration 113 (2020) 70\u0026ndash;79.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eY. W. Liu et al., Modification of shear stress transport turbulence model using helicity for predicting corner separation flow in a linear compressor cascade, Journal of Turbomachinery 142.2 (2020) 021004.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eY. L. Liu et al., Experimental investigation of the discharge valve dynamics in an oil-free linear compressor for Joule-Thomson throttling refrigerator, Applied Thermal Engineering 209 (2022) 118288.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eQ. Huang et al., Experimental investigation on piston offset and performance of helium valved linear compressor with an external gas bypass, International Journal of Refrigeration145 (2023) 417\u0026ndash;424.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eC. Z. Li, et al. Characteristic analysis and energy efficiency of an oil-free dual-piston linear compressor for household refrigeration with various conditions, Energy 270 (2023).126931.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFaisal, Mohammed, Mohammed Afzal, and Tabish Khan. Introduction to Linear Compressor and Electronics Cooling\u0026mdash;A Review, \u003cem\u003eEmerging Trends in Mechanical and Industrial Engineering: Select Proceedings of ICETMIE 2022\u003c/em\u003e (2023) 331\u0026ndash;343.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZ. J. Huang et al., Theoretical and Experimental Investigation on Comparing the Efficiency of a Single-Piston Valved Linear Compressor and a Symmetrical Dual-Piston Valved Linear Compressor, \u003cem\u003eEnergies\u003c/em\u003e 15.22 (2022) 8760.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHwang, Il Sun, and Young Lim Lee. Study on the performance of linear compressor with suction system shapes using a transient CFD model, Journal of Mechanical Science and Technology 36.4 (2022) 1809\u0026ndash;1816.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAhmad, Aftab et al., Performance Analysis of Tubular Moving Magnet Linear Oscillating Actuator for Linear Compressors, \u003cem\u003eEnergies\u003c/em\u003e15.9 (2022: 3224.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eS. P. Hu et al., moving magnet linear oscillation motor electromagnetic system theory and experiment, \u003cem\u003emechanical design and research of\u003c/em\u003e 39.02 (2023) 202\u0026ndash;206.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Compressor air valve, Computational Fluid Dynamics (CFD), Fluid-structurecoupling","lastPublishedDoi":"10.21203/rs.3.rs-3820183/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3820183/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eTo accurately simulate the motion characteristics of a reed valve and the changes in flow field in an exhaust chamber, a fluid-structure coupling model of an electromagnetic direct drive air compressor during the exhaust process was established and simulated. The alteration of the flow field within the exhaust chamber is under examination. The transient numerical simulation of the flow field in the exhaust procedure is conducted to reduce the computational model's time complexity and provide an immediate analysis of the exhaust processThis paper explores the effects of altering valve lift and relative pressure loss given different valve parameters and exhaust pressure levels. The findings reveal that when the valve plate thickness is 0.2mm and the valve section width is 3.5mm, the airflow hindrance is significantly minimized. With the valve plate unloaded, the gas flow restriction's impact on gas flow is negligible. This paper presents a theoretical basis for designing exhaust valves for electromagnetic direct-drive air compressors.\u003c/p\u003e","manuscriptTitle":"Mathematical modeling and analysis of electromagnetic direct drive air compressor","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-01-05 09:13:10","doi":"10.21203/rs.3.rs-3820183/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"65a8d11c-bbb8-4f40-81a3-5425c7120d61","owner":[],"postedDate":"January 5th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-01-29T13:50:57+00:00","versionOfRecord":[],"versionCreatedAt":"2024-01-05 09:13:10","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-3820183","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3820183","identity":"rs-3820183","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}