Method for calculating flow resistance and rotating torque of integrated water valve

By combining the tangent continuity method and turbulence model with the standardized operating process of the hyperelastic constitutive model, the error and period problems in the calculation of the flow resistance and torque of the integrated water valve were solved, achieving high-precision simulation and rapid design optimization.

CN120688326APending Publication Date: 2025-09-23SHANDONG MEICHEN ADVANCED POLYMER MATERIALS TECH CO LTD
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Patent Information

Application Number
CN202510852247.4
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-06-24
Publication Date
2025-09-23

AI Technical Summary

Technical Problem

Existing technologies have problems with large errors, long development cycles, and high costs in calculating the flow resistance and torque of integrated water valves. In particular, under high-speed conditions, the flow resistance prediction error is large, the torque peak omission rate is high, and the gas-liquid two-phase flow state causes a nonlinear jump in flow resistance. Existing methods lack an effective correction mechanism, the simulation is time-consuming, and cannot reflect the actual friction characteristics.

Method used

The tangent continuity method is used to establish the fluid domain geometric model. Combined with the Realizable k-epsilon turbulence model and the Mooney-Rivlin hyperelastic constitutive model, meshing and solver settings are performed through standardized operating procedures to achieve high-precision calculations of flow resistance and rotational torque.

Benefits of technology

It shortens the development cycle of integrated water valves, reduces simulation difficulty and cost, improves calculation accuracy, guides the selection of drive motors, reduces the waste of trial samples, and optimizes the design of the thermal management system.

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Abstract

A method for calculating flow resistance and rotation torque of an integrated water valve comprises the steps of 1, establishing a geometric model of a fluid domain of the integrated water valve, 2, carrying out grid division on the fluid domain, 3, importing a grid model into a solver, 4, defining physical property parameters of fluid changing along with temperature, 5, defining boundary conditions of the model, 6, calculating the rotation torque of the integrated water valve, and 7, calculating the rotation torque of the integrated water valve. Step 6, setting a pressure-velocity coupling method, a flux type and a gradient format; the torque calculation method comprises the steps of 1, establishing a three-dimensional geometric model of the integrated water valve of the electric vehicle, 2, carrying out grid division on a rubber ring and a metal part, 3, importing a grid model into an explicit dynamics solver, 4, defining nonlinear parameters of a material, 5, defining contact attributes of the model, and 6, calculating the torque of the integrated water valve of the electric vehicle. 6, defining boundary conditions of the model; and 7, creating work and submitting calculation. The simulation difficulty and period of the integrated water valve of the electric vehicle are reduced, so that sufficient time is provided for improving the structure of the integrated water valve of the electric vehicle.
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Description

Technical Field

[0001] The invention relates to the technical field of new energy vehicles, and specifically is a method for calculating the flow resistance and rotational torque of an integrated water valve. Background Art

[0002] The integrated water valve is the core executive unit for regulating the multi-circuit flow distribution of coolant in the thermal management system of new energy vehicles. It accurately controls the on-off ratio of the battery, motor and passenger compartment circuits through the displacement of the valve core, directly affecting the thermal efficiency and energy consumption level of the system; the flow resistance calculation requires quantifying the steady-state and transient pressure losses when the coolant flows through the complex flow channels inside the valve body (such as multi-branch intersections and cross-sectional mutation areas), and the torque calculation requires a comprehensive evaluation of the dynamic superposition effects of fluid dynamic pressure, sealing surface friction and valve core motion inertia. The ideal flow resistance-torque calculation model should accurately predict the characteristic curves under different valve core openings during the design stage, providing a theoretical basis for reducing water pump energy consumption and optimizing drive motor parameters.

[0003] Currently, the development of integrated water valves primarily relies on an inverse model that combines empirical formulas with actual prototype measurements. For example, flow resistance is estimated based on the Darcy-Weisbach formula, and torque is calculated using the static Coulomb friction model. The parameters are then repeatedly corrected through trial production. However, this method suffers from the following drawbacks in practical applications: First, the empirical formula assumes steady-state single-phase flow and ignores transient turbulent pulsations and inertial shocks caused by the rapid opening and closing of the valve core. This results in flow resistance prediction errors exceeding 35% and peak torque underestimation exceeding 50% under high-speed conditions. Second, the seal friction coefficient exhibits time-varying characteristics affected by temperature, surface roughness, and lubrication conditions, while traditional models simplify it to a fixed value, resulting in a 15%-25% deviation between the theoretical torque curve and the measured data. Third, when coolant mixes with gas or partially vaporizes, the gas-liquid two-phase flow pattern causes a nonlinear jump in flow resistance. Existing methods lack an effective correction mechanism. These issues force R&D personnel to produce 5-8 rounds of prototypes for multiple test verifications, extending the development cycle by 2-3 months and increasing mold rework costs by 40%-60%.

[0004] Although computational fluid dynamics (CFD) and multi-body dynamics simulation technologies have been partially applied to flow resistance-torque calculations, their engineering practicality is still limited by two major bottlenecks. On the one hand, high-precision transient simulation requires the establishment of a dynamic coupling model of valve core motion and flow field response. A single calculation takes up to 48-72 hours, which makes it difficult to meet the needs of rapid iteration. On the other hand, existing commercial software has insufficient modeling capabilities for microscopic sealing contact mechanisms (such as micron-scale asperity peak interactions and boundary lubrication film rupture behavior), and still relies on simplified elastic contact assumptions, which cannot reflect the transient nonlinear characteristics of actual friction pairs. In addition, for the flow-induced vibration effects of gas-liquid two-phase flow conditions, there is no mature computational framework that can simultaneously capture the bidirectional coupling of cavitation bubble collapse and valve core vibration. These limitations make it difficult for existing computational methods to replace physical prototype testing, seriously restricting the forward design process of integrated water valves. Summary of the Invention

[0005] In order to solve the above problems, the purpose of the invention is to provide a method for calculating the flow resistance and rotational torque of an integrated water valve.

[0006] To achieve the above objectives, the technical solution of the invention is: a method for calculating the flow resistance and torque of an integrated water valve, the flow resistance calculation method comprising the following steps: Step 1: Establish a geometric model of the integrated water valve fluid domain, hide irrelevant parts, retain only the inner cavity to be extracted, extract the fluid domain, use the extraction operation, and adopt the tangent continuity method to ensure that the extracted surface is smooth and continuous to avoid discontinuous surfaces in subsequent meshing. Stretch and extend the fluid domain outlet segment. After completion, import the fluid domain and the extended segment separately into the pre-processing software; Step 2: Mesh the fluid domain, set the inlet and outlet of the fluid domain, and add at least three layers of boundary layer meshes; Step 3: Import the mesh model into the solver, convert the units, set the reference pressure to the actual working pressure, select the pressure-based solver, use the steady-state format, select Realizable k-epsilon as the turbulence model, and select SWF as the scalable wall function; Step 4: Define the physical properties of the fluid that change with temperature, find the fluid type in the fluid database, and define the density and dynamic viscosity of the fluid respectively; Step 5. Define the boundary conditions of the model. Select the mass flow inlet as the inlet of the flow channel, set the mass flow rate according to the actual working conditions, select the pressure outlet as the outlet, and set the gauge pressure, direction specification method, and turbulence specification method. Step 6. Set the pressure-velocity coupling method, flux type, gradient format, and pressure discretization format. Select the second-order inverse wind format for the spatial discretization format. After initialization, set the number of simulation iterations and start the simulation to obtain the flow resistance calculation results of the electric vehicle integrated water valve. The torque calculation method includes the following steps: Step 1: Create a 3D geometric model of the electric vehicle integrated water valve, select the parts where the rubber ring contacts the metal rigid body, hide the other parts, and then import the rubber ring and metal rigid body parts into the finite element pre-processing software. Step 2: Mesh the rubber ring and metal parts. Use hexahedron mesh for the rubber ring and tetrahedron mesh for the metal parts. Step 3: Import the mesh model into the explicit dynamics solver, select the quasi-static solution format, select the Mooney-Rivlin hyperelastic constitutive model, analyze the dynamic slip process, and use the mass magnification factor to optimize the computational efficiency; Step 4: Define the nonlinear parameters of the material. In the rubber material parameters, set the material constants of the Mooney-Rivlin model. 、 , set the density, Young's modulus, and Poisson's ratio parameters for metal materials; Step 5. Define the contact properties of the model, set up standard face-to-face contact between the rubber inner and outer rings and the metal rigid body, and define normal and tangential friction at the contact interface; Step 6: Define the boundary conditions of the model, apply rigid body constraints to the metal parts, and apply a torsion angle to the valve core; Step 7. Create a job, submit the calculation, extract the slip torque-angle curve, and analyze the simulation results.

[0007] Furthermore, in step 1 of the flow resistance calculation method, an extraction operation is used to extract the fluid domain, and the type adopts tangent continuity. When extracting the fluid domain, only a single-layer fluid domain is extracted. When the outlet section of the fluid domain is stretched and extended, the extended length is 4 to 10 times the hydraulic diameter.

[0008] Furthermore, the Realizable k-epsilon turbulence model selected in step 3 of the flow resistance calculation method is: ; ; The definitions and units of each physical quantity in the two formulas are: .

[0009] Furthermore, the constant The calculation formula is: ; Where, S is the average strain rate tensor, k is the turbulent kinetic energy, and the unit is: , is the dissipation rate, unit: .

[0010] Furthermore, the turbulent viscosity coefficient The calculation formula is: ; ; ; ; ; ; ; ; ; Where, The angular velocity is The average rotation rate tensor observed in the rotating reference frame of , in units of: , is a constant with a value of 4.04. is the strain rate tensor, unit: .

[0011] Furthermore, when setting the inlet mass flow rate in step five of the flow resistance calculation method, the set flow rate should be the quotient of the actual flow rate of the medium and the number of flow channels occupied by the medium. In step two of the torque calculation method, the hexahedral grid unit is a linear reduced integration unit.

[0012] Furthermore, in step 3 of the torque calculation method, the selection of the mass magnification factor must satisfy the requirement that the ratio of kinetic energy to internal energy is less than 5%, the value range is 100-1000, and the proportion of system pseudo-strain energy is less than 10%.

[0013] Furthermore, in step 4 of the torque calculation method, the calculation formula of the Mooney-Rivlin hyperelastic constitutive model is: ; ; Where: is the main elongation ratio, 、 is the model material constant.

[0014] Furthermore, in step five of the torque calculation method, in the contact setting, the metal rigid body contact surface is the master surface, the rubber ring contact surface is the slave surface, and the tangential friction defines a penalty function friction algorithm.

[0015] Furthermore, in step six of the torque calculation method, the metal rigid body constraint is set to a completely fixed constraint, and the valve core rotation angle is set to be less than 0.26 rad.

[0016] Compared with the prior art, the present invention can achieve at least the following beneficial effects: (1) The present invention forms a standardized operation process from geometric modeling, meshing to solver setting (such as Simpson algorithm and second-order inverse wind scheme), lowers the simulation threshold, and reduces dependence on human experience.

[0017] (2) The present invention directly guides the selection of drive motors (such as peak torque matching) through the slip torque-angle curve, shortening the vehicle thermal management system verification cycle by more than 30%.

[0018] (3) The present invention reduces the difficulty and cycle of simulating the integrated water valve of electric vehicles. At the same time, the simulation results can guide the development and design of the integrated water valve of electric vehicles, avoiding the waste caused by repeated trial production of samples, so that there is sufficient time to improve the structure of the integrated water valve of electric vehicles. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] The invention will now be further described with reference to the accompanying drawings.

[0020] Figure 1 This is a flow chart of a method for calculating flow resistance and rotational torque of an integrated water valve of an electric vehicle provided by an embodiment of the present invention; Figure 2 Schematic diagram of the fluid domain and its extension in an embodiment of the present invention; Figure 3 is a schematic diagram of a fluid domain grid model in an embodiment of the present invention; Figure 4 is a pressure cloud diagram of the fluid domain in an embodiment of the present invention; Figure 5 is a velocity trace diagram of the fluid domain in an embodiment of the present invention; Figure 6 Schematic diagram of pressure change in the fluid domain along the flow direction in an embodiment of the present invention; Figure 7 Schematic diagram of the velocity change of the fluid domain along the flow direction in an embodiment of the present invention; Figure 8 Schematic diagram of the cross-sectional model of the rubber ring and metal parts in an embodiment of the present invention; Figure 9 Schematic diagram of the slip torque-angle curve of the integrated water valve in an embodiment of the present invention. DETAILED DESCRIPTION

[0021] like Figure 1-9 As shown, a method for calculating the flow resistance and rotational torque of an integrated water valve is provided. The flow resistance calculation method includes the following steps: Step 1: In the 3D modeling software, create a 3D digital model of the electric vehicle integrated water valve, retain the inner cavity to be extracted, hide irrelevant parts, use the extraction operation to extract the fluid domain, and stretch and extend the outlet section of the fluid domain to prevent backflow in the subsequent simulation calculation process that affects the calculation accuracy. After completion, hide the parts, retain the fluid domain and the extension section separately, and import them into the pre-processing software; When the outlet section of the fluid domain is stretched, the length of the extension section should be 4 to 10 times the hydraulic diameter, which can fully develop the flow in the subsequent simulation, avoid backflow, and improve the simulation accuracy. In this embodiment, the extension length is four times the hydraulic diameter 90.4mm. Of course, it can also be set to other values ​​according to the situation. In this embodiment, the fluid domain and the extension section are shown in FIG. Figure 2 , wherein reference numeral 1 represents an inlet section, reference numeral 2 represents an outlet extension section, and reference numeral 3 represents a fluid domain.

[0022] Step 2: Use polyhedron meshing in the pre-processing software to mesh the fluid domain and add at least three layers of boundary layer meshes; In this embodiment, in this step, in order to ensure the accuracy of CFD simulation, when meshing the model, the mesh size is controlled within 0.75mm, and three layers of boundary layer mesh are added. After meshing, the mesh model is as follows: Figure 3 shown.

[0023] Step 3: After meshing is completed, import the mesh model into the solver, perform unit conversion, set the reference pressure to the working pressure under actual working conditions, select the pressure-based solver, use the steady-state format, select Realizable k-epsilon as the turbulence model, and select SWF as the scalable wall function. The specific Realizable k-epsilon turbulence model selected is: ; ; The definitions and units of each physical quantity in the two formulas are: ; constant The calculation formula is:

[0024] Where, S is the average strain rate tensor, k is the turbulent kinetic energy, and the unit is: , is the dissipation rate, unit: ; Turbulent viscosity coefficient The calculation formula is: ; ; ; ; ; ; ; ; ; Where, The angular velocity is The average rotation rate tensor observed in the rotating reference frame of , in units of: , is a constant with a value of 4.04. is the strain rate tensor, unit: .

[0025] Step 4: Define the temperature-dependent physical properties of the fluid. Find the fluid type in the fluid database and apply it. Define the density and dynamic viscosity of the fluid, and select the defined fluid in the fluid domain conditions. In this embodiment, the working fluid used is ethylene glycol aqueous solution with a volume concentration of 50%, and the medium operating temperature is 70°C. Under this condition, the physical properties of the medium are shown in Table 1. Table 1 Physical properties of 50% ethylene glycol aqueous solution: ; The calculation formula of the Mooney-Rivlin hyperelastic constitutive model is: ; ; Where: is the main elongation ratio, 、 is the model material constant.

[0026] Step 5. Define the boundary conditions of the model. Select the mass flow inlet as the inlet of the flow channel, set the mass flow rate according to the actual working conditions, select the pressure outlet as the outlet, set the gauge pressure to 0 Pa, set the direction specification method to perpendicular to the boundary, and set the turbulence specification method to turbulence intensity and hydraulic diameter. Specifically in this embodiment, the working fluid flow rate of the electric vehicle integrated water valve is 20L / min, which is converted into a mass flow rate of approximately 0.3483kg / s. The outlet is selected as a pressure outlet, and the gauge pressure is set to 0Pa.

[0027] Step 6. Set the pressure-velocity coupling algorithm to the Simpson algorithm, select Rhie Chow based on momentum type for flux type, select Green-Gauss based on node format for gradient format, select second-order format for pressure discretization format, and select second-order inverse wind format for other spatial discretization formats; select hybrid initialization for initialization, set the number of simulation iterations, and start the simulation to obtain the flow resistance calculation results of the electric vehicle integrated water valve; In this embodiment, one of the flow channels is analyzed and the flow resistance is calculated to be 7.178 kPa. The pressure cloud and velocity trace diagrams obtained by simulation are as follows: Figure 4 Figure 5 As shown; in the center of the fluid domain, data analysis of pressure and flow rate is taken along the flow direction to observe the changes in pressure and flow rate inside the integrated water valve and verify the reliability of the simulation. The results are as follows Figure 6 Figure 7 shown.

[0028] The steps for implementing the torque calculation method are as follows: Step 1: Create a 3D geometric model of the electric vehicle integrated water valve in the modeling software. Select the parts where the rubber ring contacts the metal rigid body and hide the other parts. After completion, import the rubber ring and the metal rigid body parts into the finite element pre-processing software. In this embodiment, the cross-sectional models of the rubber ring and the metal component are as follows: Figure 8 As shown, reference numeral 4 represents a valve body, reference numeral 5 represents a rubber ring, and reference numeral 6 represents a valve core.

[0029] Step 2: To ensure the accuracy of the simulation calculation, mesh the rubber ring and metal parts in the pre-processing software. The rubber ring uses a hexahedral mesh and the metal parts use a tetrahedral mesh. The mesh size is controlled within 0.5 mm.

[0030] Step 3: Import the mesh model into the explicit dynamics solver, select the quasi-static solution format, and select the Mooney-Rivlin hyperelastic constitutive model. If the dynamic slip process is to be analyzed, a mass magnification factor is required to optimize the computational efficiency. In this embodiment, dynamic slip is analyzed, and the mass magnification factor is set to 1000.

[0031] Step 4: Define the nonlinear parameters of the material. In the rubber material parameters, set the material constants of the Mooney-Rivlin model. 、 , set the density, Young's modulus, and Poisson's ratio parameters for metal materials; In this embodiment, the rubber ring material is natural rubber, wherein the material constant Set to 0.374, Set to 0.093, and the metal rigid body is selected as 45 steel; under this condition, the physical properties of the metal rigid body material are shown in Table 2. Table 2 Physical properties of metal rigid materials: ; The calculation formula of the Mooney-Rivlin hyperelastic constitutive model is: ; ; Where: is the main elongation ratio, 、 is the model material constant.

[0032] Step 5: Define the contact properties of the model. Set standard face-to-face contact between the rubber inner and outer rings and the metal rigid body, and define normal and tangential friction on the contact interface. In this embodiment, the metal rigid body contact surface is the master surface, the rubber ring contact surface is the slave surface, and the tangential friction coefficient is set to 0.2.

[0033] Step 6: Define the boundary conditions of the model, apply rigid body constraints to the metal parts, and apply a torsion angle to the valve core. In this embodiment, the torsion angle of the valve core is set to 0.26 rad.

[0034] Step 7: Create a job, submit the calculation, extract the slip torque-angle curve, and analyze the simulation calculation results. In this embodiment, the simulation calculation results show that the rotation torque of the integrated water valve is 943.7N·m, and the slip torque-angle curve is as follows: Figure 9 shown.

[0035] The above description is only an illustrative embodiment of the invention and is not intended to limit the scope of the invention. Any equivalent changes and modifications made by any person skilled in the art without departing from the concept and principle of the invention shall fall within the scope of protection of the invention.

Claims

1. A method for calculating flow resistance and torque of an integrated water valve, characterized in that: The flow resistance calculation method includes the following steps: Step 1: Establish a geometric model of the integrated water valve fluid domain, hide irrelevant parts, retain only the inner cavity to be extracted, extract the fluid domain, use the extraction operation, and adopt the tangent continuity method to ensure that the extracted surface is smooth and continuous to avoid discontinuous surfaces in subsequent meshing. Stretch and extend the fluid domain outlet segment. After completion, import the fluid domain and the extended segment separately into the pre-processing software; Step 2: Mesh the fluid domain, set the inlet and outlet of the fluid domain, and add at least three layers of boundary layer meshes; Step 3: Import the mesh model into the solver, convert the units, set the reference pressure to the actual working pressure, select the pressure-based solver, use the steady-state format, select Realizable k-epsilon as the turbulence model, and select SWF as the scalable wall function; Step 4: Define the physical properties of the fluid that change with temperature, find the fluid type in the fluid database, and define the density and dynamic viscosity of the fluid respectively; Step 5. Define the boundary conditions of the model. Select the mass flow inlet as the inlet of the flow channel, set the mass flow rate according to the actual working conditions, select the pressure outlet as the outlet, and set the gauge pressure, direction specification method, and turbulence specification method. Step 6. Set the pressure-velocity coupling method, flux type, gradient format, and pressure discretization format. Select the second-order inverse wind format for the spatial discretization format. After initialization, set the number of simulation iterations and start the simulation to obtain the flow resistance calculation results of the electric vehicle integrated water valve. The torque calculation method includes the following steps: Step 1: Create a 3D geometric model of the electric vehicle integrated water valve, select the parts where the rubber ring contacts the metal rigid body, hide the other parts, and then import the rubber ring and metal rigid body parts into the finite element pre-processing software. Step 2: Mesh the rubber ring and metal parts. Use hexahedron mesh for the rubber ring and tetrahedron mesh for the metal parts. Step 3: Import the mesh model into the explicit dynamics solver, select the quasi-static solution format, select the Mooney-Rivlin hyperelastic constitutive model, analyze the dynamic slip process, and use the mass magnification factor to optimize the computational efficiency; Step 4: Define the nonlinear parameters of the material. In the rubber material parameters, set the material constants of the Mooney-Rivlin model. 、 , set the density, Young's modulus, and Poisson's ratio parameters for metal materials; Step 5. Define the contact properties of the model, set up standard face-to-face contact between the rubber inner and outer rings and the metal rigid body, and define normal and tangential friction at the contact interface; Step 6: Define the boundary conditions of the model, apply rigid body constraints to the metal parts, and apply a torsion angle to the valve core; Step 7. Create a job, submit the calculation, extract the slip torque-angle curve, and analyze the simulation results.

2. The method for calculating flow resistance and rotational torque of an integrated water valve according to claim 1, wherein: In step 1 of the flow resistance calculation method, an extraction operation is used to extract the fluid domain, and the type is tangent continuity. When extracting the fluid domain, only a single-layer fluid domain is extracted. When the outlet section of the fluid domain is stretched and extended, the extended length is 4 to 10 times the hydraulic diameter.

3. The method for calculating flow resistance and rotational torque of an integrated water valve according to claim 1, wherein: The Realizable k-epsilon turbulence model selected in step 3 of the flow resistance calculation method is: ; 。 4. A method for calculating flow resistance and rotational torque of an integrated water valve according to claim 3, characterized in that: constant The calculation formula is: ; Where, S is the average strain rate tensor, k is the turbulent kinetic energy, and the unit is: , is the dissipation rate, unit: .

5. The method for calculating flow resistance and rotational torque of an integrated water valve according to claim 3, characterized in that: Turbulent viscosity coefficient The calculation formula is: ; ; ; ; ; ; ; ; ; Where, The angular velocity is The average rotation rate tensor observed in the rotating reference frame of , in units of: , is a constant with a value of 4.

04. is the strain rate tensor, unit: .

6. The method for calculating flow resistance and rotational torque of an integrated water valve according to claim 1, wherein: When setting the inlet mass flow rate in step five of the flow resistance calculation method, the set flow rate should be the quotient of the actual flow rate of the medium and the number of flow channels occupied by the medium. In step two of the torque calculation method, the hexahedral grid unit is a linear reduced integration unit.

7. The method for calculating flow resistance and rotational torque of an integrated water valve according to claim 1, wherein: In step 3 of the torque calculation method, the mass amplification factor must be selected so that the ratio of kinetic energy to internal energy is less than 5%, the value range is 100-1000, and the proportion of pseudo-strain energy of the system is less than 10%.

8. The method for calculating flow resistance and rotational torque of an integrated water valve according to claim 1, wherein: In step 4 of the torque calculation method, the calculation formula of the Mooney-Rivlin hyperelastic constitutive model is: ; ; Where: is the main elongation ratio, 、 is the model material constant.

9. The method for calculating flow resistance and rotational torque of an integrated water valve according to claim 1, wherein: In step 5 of the torque calculation method, in the contact setting, the metal rigid body contact surface is the master surface, the rubber ring contact surface is the slave surface, and the tangential friction defines a penalty function friction algorithm.

10. The method for calculating flow resistance and rotational torque of an integrated water valve according to claim 1, wherein: In step six of the torque calculation method, the metal rigid body constraint is set to be a completely fixed constraint, and the valve core rotation angle is set to be less than 0.26 rad.