Marine diesel engine cylinder cover casting residual stress optimization control method considering complex geometric structure characteristics

Abstract

The invention discloses a marine diesel engine cylinder cover casting residual stress optimization control method considering complex geometric structure features, and relates to the technical field of machine manufacturing, and the method comprises the following steps: S1, complex geometric feature extraction and three-dimensional modeling; s2, grid division and process parameter setting; s3, establishing a mechanism model of casting residual stress; s4, residual stress influence factor analysis and parameter optimization; S5, finite element simulation analysis; s6, evaluating stress distribution and adjusting process parameters; and S7, determining optimal process parameters. By accurately simulating the influence of the complex geometric structure of the cylinder cover on the cooling rate, especially the cooling behavior of the thin-wall and thick-wall junction and corner parts, the residual stress distribution prediction precision is remarkably improved, and the stress concentration area is accurately identified, so that the residual stress of the key area is reduced; and the manufacturing quality and the service performance of the cylinder cover are comprehensively improved.

Description

Technical Field

[0001] The invention relates to the technical field of mechanical manufacturing, and in particular to a method for optimizing and controlling residual stress in casting of a marine diesel engine cylinder head taking into account complex geometric structure features. Background Art

[0002] The cylinder head of a marine diesel engine is a key load-bearing and sealing component in a diesel engine. Its manufacturing quality directly affects the performance and life of the entire engine. During the casting process, the cooling rate plays a decisive role in the formation of residual stress. Uneven cooling rates will lead to significant temperature gradients and thermal strain accumulation, which in turn will produce residual stress. If these stresses are not effectively controlled, they may lead to problems such as crack initiation, shortened fatigue life, and processing deformation.

[0003] For castings with simple shapes, the distribution of cooling rate is relatively uniform and can be predicted more accurately by classical heat transfer models or numerical simulations. However, due to its complex geometric structure, the cooling rate distribution of the cylinder head of a marine diesel engine is extremely uneven, which significantly increases the difficulty of prediction. The interior of the cylinder head usually has geometric features such as porous features, large variations in wall thickness, sharp corners and complex curved surfaces. These characteristics lead to complex cooling paths and large differences in cooling rates between regions, which intensifies the uncertainty of stress distribution.

[0004] The current methods for residual stress prediction and control have obvious limitations in castings with complex geometric structures. On the one hand, the existing cooling rate simulation accuracy is insufficient, especially in areas such as the junction of thin and thick walls in the inner cavity and sharp corners, resulting in large residual stress prediction errors. On the other hand, traditional process optimization methods fail to fully consider the correlation between geometric features and cooling rate distribution, making it difficult to effectively identify and optimize stress concentration areas. Summary of the invention

[0005] In view of the deficiencies in the prior art, the present invention provides a method for optimizing the control of residual stress in casting of a marine diesel engine cylinder head taking into account the complex geometric structure characteristics. The present invention significantly improves the accuracy of residual stress distribution prediction by accurately simulating the influence of the complex geometric structure of the cylinder head on the cooling rate, especially the cooling behavior at the junction of thin walls and thick walls and at corners, accurately identifies stress concentration areas, thereby reducing residual stress in key areas and comprehensively improving the manufacturing quality and service performance of the cylinder head.

[0006] The present invention achieves the above technical objectives through the following technical means.

[0007] A method for optimizing residual stress control of a cylinder head of a marine diesel engine considering complex geometric structure characteristics comprises the following steps:

[0008] S1: Complex geometric feature extraction and 3D modeling: Extract the complex geometric structure features of the inner cavity of the marine diesel engine cylinder head, and establish a 3D solid model including castings, gating system and riser as the basis for numerical simulation analysis;

[0009] S2: Meshing and process parameter setting: Set up the sand box and mesh the 3D solid model; at the same time, set boundary conditions and loads in combination with process parameters;

[0010] S3: Establish the mechanism model of casting residual stress: The heat transfer model simulates the temperature field distribution, analyzes the influence of complex geometric structure on cooling rate, introduces the thermoelastic-plastic theory based on the temperature field, and analyzes the residual stress distribution generated during the casting process;

[0011] S4: Analysis of factors affecting residual stress and parameter optimization: Based on the mechanism model of casting residual stress, the factors affecting the casting residual stress are introduced, the key factors affecting the residual stress distribution are identified, and the process parameters are designed;

[0012] S5: Finite element simulation analysis: Based on steps S1 and S2, a finite element model is constructed, and the process parameters designed in step S4 are substituted into the finite element numerical simulation to calculate the temperature field and residual stress distribution of the casting, and analyze the size and distribution law of the stress field;

[0013] S6: Stress distribution evaluation and process parameter adjustment: According to the finite element numerical simulation results in step S5, the size and distribution of the stress field are analyzed, and then the influence rules are summarized according to the mechanism model in step S3;

[0014] S7: Determine the optimal process parameters: According to the influence rules obtained in step S6, adjust and optimize the process parameters, and finally determine the optimal process parameters.

[0015] In the above scheme, in step S2, the process parameters include temperature field and heat flux density.

[0016] In the above scheme, the key factors affecting the residual stress distribution in step S4 are cooling rate, geometric characteristics and material parameters.

[0017] In the above scheme, the specific steps of S3 to establish the mechanism model of casting residual stress are:

[0018] S301: Types of heat transfer in casting process:

[0019] The numerical simulation of the temperature field during the solidification process of a casting is a typical transient thermal analysis. According to the law of conservation of energy, the transient thermal balance equation can be expressed as:

[0020]

[0021] Where [K] is the conduction matrix, which includes thermal conductivity, convection coefficient, emissivity and shape factor; [C] is the specific heat matrix, which takes into account the increase in internal energy of the system; {T} is the node temperature vector; is the derivative of temperature with respect to time; {Q} is the node heat flux vector, including heat generation; in addition, if the material's thermophysical parameters change with time, the boundary conditions change with temperature, or contain nonlinear units, the thermal analysis including these situations belongs to nonlinear thermal analysis, and the thermal balance matrix equation of nonlinear transient thermal analysis is:

[0022]

[0023] Considering the change of temperature field with time during the solidification process of casting, which belongs to the latent heat of phase change of nonlinear problem, the temperature field of the whole system belongs to nonlinear transient thermal analysis;

[0024] S302: Heat transfer method in casting process:

[0025] According to heat transfer theory, there are three ways of heat transfer between the entire casting, sand box and the external environment during sand casting: heat conduction, heat convection and heat radiation;

[0026] (1) Heat conduction: When high-temperature liquid metal is poured into a low-temperature sand box, there will be a heat conduction process, which follows Fourier's law, that is,

[0027]

[0028] Where q′ is the heat flux (W / m 2 ); k is the thermal conductivity (W / mK); the “-” here means that the heat flows in the direction of decreasing temperature; in the sand casting process, the contact heat transfer between the solid phase and the liquid phase of the casting, between the solid phase of the casting and the casting mold, and between the casting mold and the external air belongs to the heat conduction process;

[0029] (2) Convection: Convection only occurs in fluids. Since the molecules in the fluid are simultaneously undergoing irregular thermal motion, convection is inevitably accompanied by heat conduction. Convection can be divided into natural convection and forced convection. The heat transfer process when a fluid passes through the surface of an object is called convection heat transfer, which is different from convection in the general sense. Convection is described by Newton's cooling equation:

[0030] q′=h(T S -T B ) (4)

[0031] Where h is the convective heat transfer coefficient (W / m 2 .K); T S is the temperature of the solid surface; T Bis the temperature of the surrounding fluid; in the sand casting process, the heat transfer between the casting and the air, and between the mold and the air belongs to convection heat transfer;

[0032] (3) Thermal radiation: The higher the temperature of an object, the more heat it radiates per unit time. In engineering, radiation between two or more objects is usually considered. Each object in the system radiates and absorbs heat at the same time. The net heat transfer between them is calculated using the Stefan-Boltzmann equation:

[0033]

[0034] Where q is the heat flow rate; ε is the emissivity, and 0<ε<1; σ is the Stefan-Boltzmann constant, which is approximately 5.67×10 -8 W / m 2 .K; A1 is the area of ​​radiating surface 1; F 12 is the shape coefficient from radiation surface 1 to radiation surface 2; T1 is the absolute temperature of radiation surface 1; T2 is the absolute temperature of radiation surface 2;

[0035] S303: Numerical simulation method of filling process:

[0036] Mass Conservation Equation

[0037]

[0038] Among them, u x ,u y ,u z are the components of the fluid velocity in the x, y, and z directions, and ρ is the fluid density; the law of conservation of kinetic energy

[0039]

[0040] Where G is the gravitational acceleration and τ is the surface tension; D is the partial differential operator, and its complete mathematical expression is: Introducing the Laplace operator According to the simple formula: when the liquid is incompressible, there is Where μ is the dynamic viscosity coefficient, the formula can be rewritten as:

[0041]

[0042] Energy Conservation Equation

[0043]

[0044] Where T is the temperature of the fluid, C ρ is the constant pressure specific heat capacity of the fluid, and λ is the thermal conductivity of the fluid; when the density, constant pressure specific heat capacity and thermal conductivity are constants, the above formula can be simplified to:

[0045]

[0046] where a is the thermal diffusivity of the fluid, and a = λ / ρC ρ ;

[0047] Volume function equation

[0048]

[0049] where F is the volume fraction function, and its mathematical expression is:

[0050]

[0051] where V f is the volume of the fluid in a grid, V is the spatial volume of the grid, and the position of the free surface is judged by the magnitude of the volume fraction function F; when F = 0, the grid is in a blank state; when 0 < F < 1, the grid is in a semi-filled state, which is the position of the free surface; when F = 1, the grid is in a filled state;

[0052] There is a general format for the mentioned mass conservation equation, momentum conservation equation, energy conservation equation, and volume conservation function equation:

[0053]

[0054] where, from left to right, they are the unsteady term, convection term, diffusion term, and source term; where φ is the dependent variable, Γ is the diffusion coefficient, and S is the source term;

[0055] S304: Numerical simulation method for solidification process:

[0056] In the elastic part, the material stress and strain conform to the generalized Hooke's law, and their relationship is as follows:

[0057] {σ} = [D] e {ε e} (14)

[0058] where [D] e represents the elastic modulus matrix;

[0059] The strain and displacement of the material have the following relationship:

[0060] {ε e} = [B]{δ} (15)

[0061] Substituting the above formula into (14) gives the relationship between stress and displacement:

[0062] {σ} = [D] e [B]{δ} (16)

[0063] Where [B] represents the material strain-displacement matrix, and {δ} represents the material node displacement matrix. For the plastic part, the incremental theory is used to rewrite equation (14) to obtain the relationship between the elastic model stress and strain increment:

[0064] {dσ}=[D] e {dε e} (17)

[0065] Among them, d represents the increment, e represents the elastic part, p and T represent the relevant parameters of plasticity and temperature respectively; since the thermal elastic-plastic model needs to consider the influence of thermal deformation, the relationship between the thermal strain increment and the elastic modulus, linear expansion coefficient and temperature is given:

[0066]

[0067] Where T0 represents the initial temperature, T represents the instantaneous temperature, a represents the thermal expansion coefficient, {dε T} represents the strain increment caused by temperature; in the elastic part, the total deformation includes elastic strain and thermal strain, and the expression is:

[0068] {dε}={dε e}+{dε T} (19)

[0069] In the thermoelastic model, the total strain increment also needs to add the plastic increment part:

[0070] {dε}={dε e}+{dε p}+{dε T} (20)

[0071] Substituting the above equation into equation (17), we can obtain the relationship between stress and total strain:

[0072] {dσ}=[D] e ({dε}-{dε p}-{dε T}) (twenty one)

[0073] For the convenience of analysis, (21) is rewritten to obtain the constitutive equation of the thermoelastic-plastic model:

[0074] {dσ}=[D] ep ({dε}-{dε T}) (twenty two)

[0075] Among them, [D] ep is the elastic-plastic matrix in the thermo-elastic-plastic model;

[0076] Finite element method for thermo-elastoplastic model:

[0077] To solve the constitutive equation of the thermoelastic model, it is necessary to establish an equilibrium equation, the premise of which is to apply the constitutive equation to the discretized mesh model; the corresponding equilibrium equation is established according to the principle of virtual work, and its convergence condition is that the strain energy generated by the displacement reaches the minimum value; the specific form of the equilibrium equation is as follows:

[0078]

[0079] In order to minimize the strain energy generated by displacement, the first-order derivative of strain energy with respect to displacement must be 0. By taking the first-order derivative of both sides of equation (25) with respect to displacement, we can obtain:

[0080]

[0081] Changing the integral sign of the above equation to sum the values ​​at the Gaussian points within the unit, we get:

[0082]

[0083] Among them, n G is the number of Gaussian points in the unit, n is the number of units, H r , H s , H t are the integral coefficients of Gaussian points respectively; ξ r , η s , t are the coordinates of the Gaussian points respectively; define [K] ep is the overall elastic-plastic stiffness matrix, Δ{R} is the equivalent load vector caused by the thermal strain increment; [K] ep From the element stiffness matrix [k] ep The three expressions are:

[0084]

[0085] Formula (25) can be rewritten as:

[0086] [K] ep Δ{δ}=Δ{R} (27)

[0087] According to formula (27), the displacement increment at the Gaussian point is calculated, and then the stress and stress increment at the Gaussian point are obtained, and finally the stress at the node is obtained.

[0088] Beneficial effects of the present invention:

[0089] 1. The present invention aims to solve the problem in the prior art that the cooling rate cannot be accurately predicted due to complex geometric features, which in turn affects the residual stress distribution analysis and process optimization. The present invention can accurately simulate the influence of complex geometric structures on the cooling rate, accurately predict the cooling behavior and stress distribution in key areas, and optimize the process design based on this, thereby comprehensively improving the manufacturing quality and service performance of the cylinder head of a marine diesel engine.

[0090] 2. The present invention significantly improves the accuracy of residual stress distribution prediction by accurately simulating the influence of the complex geometric structure of the cylinder head on the cooling rate, especially the cooling behavior at the junction of thin-wall and thick-wall and corners, accurately identifies stress concentration areas, thereby reducing residual stress in key areas and comprehensively improving the manufacturing quality and service performance of the cylinder head.

[0091] 3. The present invention significantly improves the prediction accuracy of residual stress distribution by accurately simulating the influence of complex geometric structure characteristics on cooling rate, especially in areas where the cooling rate changes dramatically, such as the junction of thin walls and thick walls and corners, and can effectively identify and quantify stress concentration phenomena, thereby providing a scientific basis for the optimization of casting process parameters. By reducing the stress level in key areas, the present invention effectively reduces the risk of casting cracks and processing deformation, and improves the dimensional accuracy, service reliability and service life of the cylinder head of a marine diesel engine. In addition, the method has strong applicability and can be extended to the field of residual stress control of other complex geometric castings. At the same time, it significantly reduces the cost of process optimization experiments and the development cycle, and has important engineering application value and economic benefits. BRIEF DESCRIPTION OF THE DRAWINGS

[0092] Figure 1 is a flow chart of the method of the present invention;

[0093] Figure 2 This is the flow chart of the mechanism model of casting residual stress;

[0094] Figure 3 Heat transfer model of liquid metal solidifying in a mold;

[0095] Figure 4 Cold iron distribution map;

[0096] Figure 5 Schematic diagram of the cold iron contact surface;

[0097] Figure 6 Simulation flow chart;

[0098] Figure 7 Model grid diagram;

[0099] Figure 8 3D model diagram;

[0100] Fig. 9 Model point location;

[0101] Fig.10 Comparison of residual stress of cold iron with and without cold iron during sand falling;

[0102] Fig.11 Comparison chart of residual stress of cold iron with and without cold iron when sand dropping is completed;

[0103] Fig.12 Casting stress before sand falling;

[0104] Fig.13 Casting stress during sand falling;

[0105] Fig.14 Residual stress during sand falling;

[0106] Fig.15 Residual stress at the completion of sand fall;

[0107] Fig.16 Residual stress at the root of riser during sand falling;

[0108] Fig.17 Residual stress at the root of the riser when the sand is removed;

[0109] Fig.18 Average residual stress at the root of riser during sand falling;

[0110] Fig.19 Average residual stress at the root of the riser when sand falling is completed. DETAILED DESCRIPTION

[0111] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and should not be construed as limiting the present invention.

[0112] A method for controlling residual stress in casting of a marine diesel engine cylinder head based on finite element analysis comprises the following steps:

[0113] S1: Complex geometric feature extraction and 3D modeling: Extract the complex geometric structure features of the inner cavity of the marine diesel engine cylinder head, and establish a 3D solid model including castings, gating system and riser as the basis for numerical simulation analysis;

[0114] S2: Meshing and process parameter setting: Set up the sand box and mesh the 3D solid model; at the same time, set boundary conditions and loads in combination with process parameters;

[0115] S3: Establish the mechanism model of casting residual stress: simulate the temperature field distribution with heat transfer model, analyze the influence of complex geometric structure on cooling rate, introduce the thermoelastic-plastic theory based on temperature field, analyze the residual stress distribution generated in casting process, and combine with the attached Figure 2 As shown,

[0116] S301: Types of heat transfer in casting process:

[0117] Thermal analysis follows the first law of thermodynamics, the law of conservation of energy, which is expressed as follows for a closed system:

[0118] QW=ΔU+ΔKE+ΔPE (1)

[0119] Where Q is heat, W is work, ΔU is system internal energy, ΔKE is system kinetic energy and ΔPE is system potential energy. For most engineering problems, the system kinetic energy and system potential energy can be considered to be zero, and work is usually not considered. In this way, equation (1) can be simplified to Q = ΔU. For steady-state thermal analysis, the heat flow rate is 0, that is, the heat flowing into the system plus the heat generated by the system itself is equal to the heat flowing out of the system. The formula is: Q = ΔU = 0. For transient thermal analysis, q = dU / dt, that is, the heat transfer rate q flowing in or out is equal to the rate of change of the system internal energy. Steady-state heat transfer is used to analyze the influence of stable thermal loads on systems or components. Usually, before performing transient thermal analysis, a steady-state thermal analysis is performed first to determine the initial temperature distribution. In steady-state analysis, the temperature of any node does not change with time, and its energy balance equation is:

[0120] [K]{T}={Q} (2)

[0121] Where [K] is the conduction matrix, including thermal conductivity, convection coefficient, emissivity and shape factor; {T} is the node temperature vector; {Q} is the node heat flux vector, including heat generation;

[0122] The transient heat transfer process is usually a coefficient heating or cooling process. In this process, the temperature, heat flux, thermal boundary conditions and internal energy of the system change significantly with time. Therefore, the numerical simulation of the temperature field during the solidification process of the casting is a typical transient thermal analysis. According to the law of conservation of energy, the transient heat balance equation can be expressed as:

[0123]

[0124] Where [K] is the conduction matrix, which includes thermal conductivity, convection coefficient, emissivity and shape factor; [C] is the specific heat matrix, which takes into account the increase in internal energy of the system; {T) is the node temperature vector; is the derivative of temperature with respect to time; {Q) is the node heat flux vector, including heat generation. In addition, if the thermophysical parameters of the material change with time, the boundary conditions change with temperature, or contain nonlinear units, the thermal analysis including these situations belongs to nonlinear thermal analysis; the thermal balance matrix equation of nonlinear transient thermal analysis is:

[0125]

[0126] Considering the change of temperature field with time during the solidification process of casting, which is the latent heat of phase change, the temperature field of the whole system belongs to the nonlinear transient thermal analysis problem;

[0127] S302: Heat transfer method in casting process:

[0128] According to heat transfer theory, there are three ways of heat transfer between the entire casting, sand box and the external environment during sand casting: heat conduction, heat convection and heat radiation;

[0129] (1) Heat conduction: There is no relative displacement between the various parts, and the heat transfer generated only by the thermal motion of molecules, atoms and free electrons is heat conduction. When high-temperature liquid metal is poured into a low-temperature sand box, there will be an obvious heat conduction process.

[0130] Heat conduction follows Fourier's law, that is,

[0131]

[0132] Where q′ is the heat flux (W / m 2 ); k is the thermal conductivity (W / mK); the “-” here means that the heat flows in the direction of decreasing temperature; in the sand casting process, the contact heat transfer between the solid phase and the liquid phase of the casting, between the solid phase of the casting and the casting mold, and between the casting mold and the external air belongs to the heat conduction process;

[0133] (2) Thermal convection: Convection refers to the process of heat transfer caused by the relative displacement and mixing of the hot and cold parts of the fluid due to the macroscopic movement of the fluid. Convection only occurs in the fluid, and because the molecules in the fluid are simultaneously undergoing irregular thermal motion, convection is inevitably accompanied by heat conduction. Thermal convection can be divided into natural convection and forced convection. The main focus in engineering is on the heat transfer process when the fluid passes through the surface of an object, that is, convective heat transfer, to distinguish it from convection in the general sense. Convection heat transfer is often described by Newton's cooling equation:

[0134] q′=h(T S -T B ) (6)

[0135] Where h is the convective heat transfer coefficient (W / m 2 .K); TS is the temperature of the solid surface; T B is the temperature of the surrounding fluid; in the sand casting process, the heat transfer between the casting and the air, and between the mold and the air belongs to convection heat transfer;

[0136] (3) Thermal radiation: refers to a way in which heat is transmitted from a high-temperature object in the form of electromagnetic waves, independent of the material medium. This phenomenon is caused by electromagnetic radiation generated by the thermal motion of atoms or molecules inside the object; the higher the temperature of the object, the more heat is radiated per unit time. In engineering, radiation between two or more objects is usually considered. Each object in the system radiates and absorbs heat at the same time. The net heat transfer between them can be calculated using the Stefan-Boltzmann equation:

[0137]

[0138] Where q is the heat flow rate; ε is the emissivity, and 0<ε<1; σ is the Stefan-Boltzmann constant, which is approximately 5.67×10 -8 W / m 2 .N; A1 is the area of ​​radiating surface 1; F 12 is the shape coefficient from radiation surface 1 to radiation surface 2; T1 is the absolute temperature of radiation surface 1; T2 is the absolute temperature of radiation surface 2;

[0139] During the solidification process of the metal, the volume contraction of the solidified metal and the thermal expansion of the mold form a metal / mold interface layer between the metal and the mold. The interface contact state changes dynamically during the solidification process, from ideal contact to non-ideal contact. The heat transfer between the metal and the mold is not a simple heat conduction, but also involves microscopic heat convection and heat radiation.

[0140] During the casting process, there is heat radiation between the casting and the surrounding environment; when the casting begins to cool, the surface hardens and the temperature is low, so the radiation is small; the liquid phase is higher, so the radiation is large, and it is in contact with the air, accompanied by heat convection; because the liquid phase temperature is greater than the solid phase temperature and greater than the mold temperature, the direction of heat conduction is liquid to solid phase, solid to mold, and mold to air; the materials between the mold and the casting are different, so there is interface heat exchange between the contact surfaces; after the temperature of the mold rises, it will also generate heat radiation and generate heat convection when in contact with the air. With the solidification process, the solid phase thickness increases, the molecular thermal motion slows down, the overall heat transfer efficiency decreases, the cooling rate difference between each part becomes larger, and the thermal stress increases. Figure 3 As shown, R is thermal radiation; C is thermal convection; K is heat conduction; N is Newtonian interface heat transfer; X is solid phase thickness; V is molecular thermal motion rate;

[0141] S303: Numerical simulation method of filling process:

[0142] Mass conservation equation (continuity equation)

[0143]

[0144] where u x , u y , u z are the components of the fluid velocity in the x, y, and z directions respectively, and ρ is the fluid density.

[0145] Law of conservation of kinetic energy

[0146]

[0147] where G is the acceleration due to gravity; τ is the surface tension; D is the partial differential operator, and its complete mathematical expression is Introduce the Laplace operator In a simple formula: when the liquid is incompressible, there is where μ is the dynamic viscosity coefficient, and the formula can be rewritten as:

[0148]

[0149] Energy conservation equation

[0150]

[0151] where T is the temperature of the fluid, C ρ is the specific heat capacity at constant pressure of the fluid, and λ is the thermal conductivity of the fluid; in the case where the density, specific heat capacity at constant pressure, and thermal conductivity are constants, the above formula can be simplified to:

[0152]

[0153] where a is the thermal diffusivity of the fluid, a = λ / ρC ρ ;

[0154] Volume function equation

[0155]

[0156] where F is the volume fraction function, and its mathematical expression is:

[0157]

[0158] where V f is the volume of the fluid in a grid, V is the spatial volume of the grid, and the position of the free surface is judged by the magnitude of the volume fraction function F; when F = 0, the grid is in an empty state; when 0 < F < 1, the grid is in a semi-filled state, which is the position of the free surface; when F = 1, the grid is in a filled state;

[0159] There is a general format for the mass conservation equation, momentum conservation equation, energy conservation equation, and volume conservation function equation mentioned above:

[0160]

[0161] Among them, from left to right are the instability term, convection term, diffusion term and source term; among them, φ is the dependent variable, Γ is the diffusion coefficient, and S is the source term;

[0162] S304: Numerical simulation method of solidification process:

[0163] At present, the mechanical models for casting stress calculation mainly include thermoelastic model, thermoviscoelastic model, thermoelastoplastic model and thermoelastic-viscoplastic model. Among them, the thermoelastoplastic model is widely used. This model does not directly take into account the viscosity effect. It is considered that the material is elastic before yielding and plastic after yielding. The elastic modulus and yield stress are functions of temperature, and when the material approaches the melting point, the elastic modulus and yield stress both become zero. In the numerical simulation of stress in the casting process of castings, the nonlinear problem of the material in the thermoelastoplastic model is generally treated as a bilinear model, that is, the stress-strain curve is simplified to bilinear, and both the elastic stage and the plastic stage are linear. For elastoplastic materials, the incremental theory established based on the incremental relationship between stress and strain can truly describe the plastic behavior of the material;

[0164] The constitutive equations of strain and stress in the thermoelastic-plastic model are:

[0165] The constitutive equation of the material reflects the functional relationship between stress and strain. The thermoelastic-plastic model takes into account the influence of thermal strain on the material on the basis of the elastic-plastic model. The model believes that before yielding, the material is elastic and conforms to Hooke's law; after yielding, it is plastic, and the calculation is currently mainly based on flow theory; at the same time, the elastic modulus and yield stress are functions of temperature, and the influence of temperature on the model is taken into account;

[0166] In the elastic part, the material stress and strain conform to the generalized Hooke's law, which is related as follows:

[0167] {σ}=[D] e {ε e} (16)

[0168] Among them, [D] e represents the elastic modulus matrix;

[0169] The strain and displacement of a material have the following relationship:

[0170] {ε e}=[B]{δ} (17)

[0171] Substituting the above equation into (16), we can obtain the relationship between stress and displacement:

[0172] {σ}=[D] e [B]{δ} (18)

[0173] Where [B] represents the material strain-displacement matrix, and {δ} represents the material node displacement matrix. For the plastic part, the incremental theory is used to rewrite equation (16) to obtain the relationship between the elastic model stress and strain increment:

[0174] {dσ}=[D] e {dε e} (19)

[0175] Among them, d represents the increment, e represents the elastic part, and p and T will be used in the following text to represent the relevant parameters of plasticity and temperature respectively; since the thermal elastic-plastic model needs to consider the influence of thermal deformation, the relationship between the thermal strain increment and the elastic modulus, linear expansion coefficient and temperature is given below:

[0176]

[0177] Where T0 represents the initial temperature, T represents the instantaneous temperature, a represents the thermal expansion coefficient, {dε T} represents the strain increment caused by temperature; in the elastic part, the total deformation includes elastic strain and thermal strain, and its expression is:

[0178] {dε}={dε e}+{dε T} (twenty one)

[0179] In the thermoelastic model, the total strain increment also needs to add the plastic increment part:

[0180] {dε}={dε e}+{dε p}+{dε T} (twenty two)

[0181] Substituting the above equation into equation (19) we get the relationship between stress and total strain:

[0182] {dσ}=[D] e ({dε}-{d ε p}-{dε T}) (twenty three)

[0183] For the convenience of analysis, (23) is rewritten to obtain the constitutive equation of the thermoelastic-plastic model:

[0184] {dσ}=[D] ep ({dε}-{dε T}) (twenty four)

[0185] Among them, [D]ep is the elastic-plastic matrix in the thermo-elastic-plastic model;

[0186] Finite element method for thermo-elastoplastic model:

[0187] To solve the constitutive equation of the thermoelastic model, it is necessary to establish an equilibrium equation, the premise of which is to apply the constitutive equation to the discretized mesh model; the corresponding equilibrium equation is established according to the principle of virtual work, and its convergence condition is that the strain energy generated by the displacement reaches the minimum value; the specific form of the equilibrium equation is as follows:

[0188]

[0189] In order to minimize the strain energy generated by displacement, the first-order derivative of strain energy with respect to displacement must be 0. By taking the first-order derivative of both sides of equation (25) with respect to displacement, we can obtain:

[0190]

[0191] Changing the integral sign of the above equation to sum the values ​​at the Gaussian points within the unit, we get:

[0192]

[0193] Among them, n G is the number of Gaussian points in the unit, n is the number of units, H r , H s , H t are the integral coefficients of Gaussian points respectively; ξ r , η s , t are the coordinates of the Gaussian points respectively; define [K] ep is the overall elastic-plastic stiffness matrix, Δ{R} is the equivalent load vector caused by the thermal strain increment; [K] ep From the element stiffness matrix [k] ep The three expressions are:

[0194]

[0195] Formula (27) can be rewritten as:

[0196] [K] ep Δ{δ}=Δ{R} (29)

[0197] According to formula (29), the displacement increment at the Gaussian point is calculated, and then the stress and stress increment at the Gaussian point are obtained, and finally the stress at the node is obtained;

[0198] S4: Determine the factors affecting the casting residual stress based on the mechanism model and design the process parameters accordingly;

[0199] In the previous step, the mechanism of heat conduction and stress coupling during solidification was discussed from a theoretical perspective, and the cooling rate of the casting was identified as a key parameter affecting the stress field distribution. This part uses ProCAST software for simulation, and simulates the real casting environment through parameter setting to verify the rationality of the mechanism analysis results and optimize the relevant process parameters.

[0200] Through the analysis of the casting mechanism, the key role of chiller in regulating the cooling rate and stress field distribution of castings is found. In order to optimize the stress field of castings, this paper focuses on the chiller process parameters and conducts simulation optimization analysis on different chiller arrangements and sizes based on ProCAST software to determine the best process solution that can effectively reduce residual stress.

[0201] The process selection is sand casting, the material is RuT450, the pouring temperature is set to 1370℃, and the sand falling temperature is 550℃. The casting process uses chilled iron to control the cooling rate, and the chilled iron material is HT200. The distribution of chilled iron is as follows Figure 4 The contact area between the chill and the casting is shown in Figure 5 As shown, Figure 5 In (a), two 100*150(mm) chills are distributed on the side of the casting, eight 60*120(mm) chills are distributed on the bottom of the casting, five 60*200(mm) chills are distributed on the side of the casting, four 80*80(mm) chills are distributed on the bottom of the casting, and eight are distributed on the side of the casting. Figure 5 In (b), the contact area between the chiller and the casting is reduced by half, and the chiller distribution is the same as (a). According to the two groups with different contact areas, four groups with different chiller thicknesses are set up for process simulation. The specific simulation groups are shown in Table 1.

[0202] Table 1 Process scheme

[0203]

[0204] S5: Bring the process parameters into the finite element model for simulation analysis;

[0205] The diesel engine cylinder head has a complex shape and uneven wall thickness. To ensure the calculation accuracy of the model and to ensure that the calculation time is not too long, the meshes of the castings, risers and pouring system parts of the model are refined, and the number of model meshes of the sand box can be appropriately reduced. The assembled casting system model is exported from the 3D software UG to the IGES format acceptable to ProCAST. Then import the above assembly model into the Visual-Mesh module of ProCAST. Perform operations such as geometric inspection and repair, overlapping surface inspection and assembly, and body intersection inspection and repair in sequence. The subsequent simulation steps are as follows: Figure 6 shown.

[0206] The mesh size of the casting, riser and pouring system is set to 25mm, and the mesh size of the sand box and sand core is set to 50mm. After dividing the mesh, the mesh quality check and mesh repair are carried out in turn. The mesh repair function provided by the software can be used to automatically repair the mesh. After the surface mesh check is error-free, the volume mesh is automatically generated. Finally, the volume mesh is checked to see if there are bad units and Min-Jacobian units with values ​​less than 0.7. Only after the volume unit is checked correctly can the next step of setting be entered. The final optimized mesh model is as follows Figure 7 As shown, the total number of nodes is 86984, the number of surface meshes is 51832, and the number of volume meshes is 482654.

[0207] In this paper, the cylinder head is simulated and analyzed using vermicular cast iron RuT450. Vermicular cast iron not only has the advantages of castability, shock absorption, and thermal conductivity of gray cast iron, but also has the characteristics of high strength and high toughness of ductile iron. Vermicular cast iron has no fixed chemical composition. ProCAST's built-in material library system can automatically generate new materials according to the chemical composition of the material and add them to the material library. Since the material is vermicular iron, when generating new materials, the calculation model selects Lever. The chemical composition of RuT450 is shown in Table 2. Before performing casting simulation, the casting system, riser, sand box and casting need to be set up with materials. The material properties of the cylinder head, riser and casting system are set to RuT450, and the sand box material is resin sand.

[0208] Table 2 Chemical composition of RuT450 (wt%)

[0209]

[0210] The diesel engine cylinder head, as well as the gating system and riser, are the research objects. Figure 8 As shown, the cylinder head mainly consists of 2 intake holes, 2 exhaust holes and 1 starting valve on the combustion surface.

[0211] S6: Obtain the casting residual stress under process conditions, perform point analysis, and then summarize the influence rules based on the mechanism model;

[0212] Due to the complex internal structure of the cylinder head, the wall thickness and cooling rate are different, resulting in complex stress distribution. However, the stress concentration phenomenon is obvious at the root of the riser, so three points are selected on the cross section of the root of the riser to study the casting residual stress law inside the cylinder head. The distribution of measurement points is shown in the figure below. Fig. 9 As shown. On the left wall, right wall and bottom of the cut surface, points are taken every 1 mm from the surface. The maximum value point is taken at the root of the riser as the reference for the internal stress of the root of the riser.

[0213] Compare the simulation results without chiller with the simulation results of chiller process No. 5, as shown in Fig.10 , Fig.11As shown in the figure. Without the chiller, the overall stress of the cylinder head is significantly greater than the simulation result using the chiller process. Without the chiller process, the stress concentration during the cylinder head cooling process mainly occurs on the left wall of the cylinder head, and the stress gradually decreases with increasing depth. The stress on the right wall and the bottom gradually increases with increasing depth.

[0214] Fig.12 and Fig.13 It shows that before and during sand dropping, the casting stress at the bottom of the B surface is significantly higher than that at other locations, and a significant stress concentration phenomenon occurs. The stress concentration phenomenon also occurs at the bottom of the C surface. Fig.14 and Fig.15 In the figure, the residual stress at the bottom of surface B shows a downward trend as the depth increases. However, as the depth increases, the residual stress at the bottom of surface A and surface C exceeds that at the bottom of surface B after a depth of 2.5 mm. In the four different casting stages, except for the bottom of surface B, the residual stress at other locations increases with depth. On the surface of the cylinder head, the stress concentration location is the bottom of surface B. During the casting solidification process of the cylinder head, the stress is concentrated at the bottom of surface B because the cooling rate at the bottom of surface B is slower. The cooling rate inside the cylinder head is slower than that on the surface, so the internal residual stress increases with increasing depth.

[0215] Since stress concentration often occurs at the root of the riser during the casting process, the magnitude of the residual stress at the root of the riser is a key reference for evaluating the quality of the process. The smaller the residual stress at the root of the riser, the better the process. Therefore, by comparing the maximum values ​​of the root stress of the riser on three surfaces of different processes, the process with the smaller maximum value has better casting effect. Fig.16 and Fig.17 It can be seen that the casting residual stress at the root of the riser of process 5 is smaller, and the casting effect is better.

[0216] from Fig.18 and Fig.19 It can be seen that when the contact area between the chill and the cylinder head is scheme (a), the average stress at the root of the cylinder head riser shows a downward trend as the chill thickness increases. When the contact area between the chill and the cylinder head is scheme (b), the average stress at the root of the cylinder head riser shows an upward trend as the chill thickness increases. When the chill thickness is 40mm, the average stress at the root of the riser corresponding to scheme (b) exceeds the average stress at the root of the riser corresponding to scheme (a). As the chill thickness increases, the chill chilling effect increases, the cylinder head cooling rate increases, and the residual stress decreases. When the chill chilling effect is too strong, the cylinder head surface cools too quickly, the internal cooling heat transfer rate is hindered, and the residual stress increases instead.

[0217] S7: According to the influencing rules, adjust and optimize the process parameters to control the casting residual stress.

[0218] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "examples", "specific examples", or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner.

[0219] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention without departing from the principles and intent of the present invention.

Claims

1. A method for optimizing residual stress control of a cylinder head of a marine diesel engine considering complex geometric structure characteristics, characterized in that: The steps include: S1: Complex geometric feature extraction and 3D modeling: Extract the complex geometric structure features of the inner cavity of the marine diesel engine cylinder head, and establish a 3D solid model including castings, gating system and riser as the basis for numerical simulation analysis; S2: Meshing and process parameter setting: Set up the sand box and mesh the 3D solid model; at the same time, set boundary conditions and loads in combination with process parameters; S3: Establish the mechanism model of casting residual stress: The heat transfer model simulates the temperature field distribution, analyzes the influence of complex geometric structure on cooling rate, introduces the thermoelastic-plastic theory based on the temperature field, and analyzes the residual stress distribution generated during the casting process; S4: Analysis of factors affecting residual stress and parameter optimization: Based on the mechanism model of casting residual stress, the factors affecting the casting residual stress are introduced, the key factors affecting the residual stress distribution are identified, and the process parameters are designed; S5: Finite element simulation analysis: Based on steps S1 and S2, a finite element model is constructed, and the process parameters designed in step S4 are substituted into the finite element numerical simulation to calculate the temperature field and residual stress distribution of the casting, and analyze the size and distribution law of the stress field; S6: Stress distribution evaluation and process parameter adjustment: According to the finite element numerical simulation results in step S5, the size and distribution of the stress field are analyzed, and then the influence rules are summarized according to the mechanism model in step S3; S7: Determine the optimal process parameters: According to the influence rules obtained in step S6, adjust and optimize the process parameters, and finally determine the optimal process parameters.

2. The method for optimizing residual stress control of a cylinder head of a marine diesel engine considering complex geometric structure characteristics according to claim 1, characterized in that: In step S2, the process parameters include temperature and heat flux.

3. The method for optimizing residual stress control of a cylinder head of a marine diesel engine considering complex geometric structure characteristics according to claim 1, characterized in that: The key factors affecting the residual stress distribution in step S4 are cooling rate, geometric characteristics and material parameters.

4. The method for optimizing residual stress control of a cylinder head of a marine diesel engine considering complex geometric structure characteristics according to claim 1, characterized in that: The specific steps of S3 to establish the mechanism model of casting residual stress are: S301: Types of heat transfer in casting process: The numerical simulation of the temperature field during the solidification process of a casting is a typical transient thermal analysis. According to the law of conservation of energy, the transient thermal balance equation can be expressed as: Where [K] is the conduction matrix, which includes thermal conductivity, convection coefficient, emissivity and shape factor; [C] is the specific heat matrix, which takes into account the increase in internal energy of the system; {T} is the node temperature vector; is the derivative of temperature with respect to time; {Q} is the node heat flux vector, including heat generation; in addition, if the material's thermophysical parameters change with time, the boundary conditions change with temperature, or contain nonlinear units, the thermal analysis including these situations belongs to nonlinear thermal analysis, and the thermal balance matrix equation of nonlinear transient thermal analysis is: Considering the change of temperature field with time during the solidification process of casting, which belongs to the latent heat of phase change of nonlinear problem, the temperature field of the whole system belongs to nonlinear transient thermal analysis; S302: Heat transfer method in casting process: According to heat transfer theory, there are three ways of heat transfer between the entire casting, sand box and the external environment during sand casting: heat conduction, heat convection and heat radiation; (1) Heat conduction: When high-temperature liquid metal is poured into a low-temperature sand box, there will be a heat conduction process, which follows Fourier's law, that is, Where q′ is the heat flux (W / m 2 ) ; k is the thermal conductivity (W / mK); the "—" indicates that the heat flows in the direction of decreasing temperature; in the sand casting process, the contact heat transfer between the solid phase and the liquid phase of the casting, between the solid phase of the casting and the casting mold, and between the casting mold and the external air belongs to the heat conduction process; (2) Convection: Convection only occurs in fluids. Since the molecules in the fluid are simultaneously undergoing irregular thermal motion, convection is inevitably accompanied by heat conduction. Convection can be divided into natural convection and forced convection. The heat transfer process when a fluid passes through the surface of an object is called convection heat transfer, which is different from convection in the general sense. Convection is described by Newton's cooling equation: q′=h(T S -T B ) (4) Where h is the convective heat transfer coefficient (W / m 2 .K); T S is the temperature of the solid surface; T B is the temperature of the surrounding fluid; in the sand casting process, the heat transfer between the casting and the air, and between the mold and the air belongs to convection heat transfer; (3) Thermal radiation: The higher the temperature of an object, the more heat it radiates per unit time. In engineering, radiation between two or more objects is usually considered. Each object in the system radiates and absorbs heat at the same time. The net heat transfer between them is calculated using the Stefan-Boltzmann equation: Where q is the heat flow rate; ε is the emissivity, and 0<ε<1; σ is the Stefan-Boltzmann constant, which is approximately 5.67×10 -8 W / m 2 .K; A1 is the area of ​​radiating surface 1; F 12 is the shape coefficient from radiation surface 1 to radiation surface 2; T1 is the absolute temperature of radiation surface 1; T2 is the absolute temperature of radiation surface 2; S303: Numerical simulation method of filling process: Mass Conservation Equation Among them, u x ,u y ,u z are the components of the fluid velocity in the x, y, and z directions, respectively, and ρ is the fluid density; The law of conservation of kinetic energy Where G is the acceleration of gravity; τ is the surface tension; D is the partial differential operator, and its complete mathematical expression is: Introducing the Laplace operator According to the simple formula: when the liquid is incompressible, there is Where μ is the dynamic viscosity coefficient, the formula can be rewritten as: Energy Conservation Equation Where T is the temperature of the fluid, C ρ is the constant pressure specific heat capacity of the fluid, and λ is the thermal conductivity of the fluid; when the density, constant pressure specific heat capacity and thermal conductivity are constants, the above formula can be simplified to: Where a is the thermal diffusion coefficient of the fluid, a = λ / ρC ρ ; Volume function equation Among them, F is the volume fraction function, and its mathematical expression is: Among them, V f is the volume of the fluid in a grid, V is the spatial volume of the grid, and the position of the free surface is determined by the size of the volume fraction function F; when F = 0, the grid is in a blank state; when 0 < F < 1, the grid is in a half-filled state, that is, the position of the free surface; when F = 1, the grid is in a full state; There is a general format for the mentioned mass conservation equations, momentum conservation equations, energy conservation equations, and volume conservation function equations: Among them, from left to right are the instability term, convection term, diffusion term and source term; among them, φ is the dependent variable, Γ is the diffusion coefficient, and S is the source term; S304: Numerical simulation method of solidification process: In the elastic part, the material stress and strain conform to the generalized Hooke's law, which is related as follows: {σ}=[D] e {e} e } (14) Among them, [D] e represents the elastic modulus matrix; The strain and displacement of a material have the following relationship: {e} e }=[B]{δ} (15) Substituting the above equation into (14), we can obtain the relationship between stress and displacement: {σ}=[D] e [B]{d} (16) Where [B] represents the material strain-displacement matrix, and {δ} represents the material node displacement matrix. For the plastic part, the incremental theory is used to rewrite equation (14) to obtain the relationship between the elastic model stress and strain increment: {dσ}[D] e {dε e } (17) Among them, d represents the increment, e represents the elastic part, p and T represent the relevant parameters of plasticity and temperature respectively; since the thermal elastic-plastic model needs to consider the influence of thermal deformation, the relationship between the thermal strain increment and the elastic modulus, linear expansion coefficient and temperature is given: Where T0 represents the initial temperature, T represents the instantaneous temperature, a represents the thermal expansion coefficient, {dε T } represents the strain increment caused by temperature; in the elastic part, the total deformation includes elastic strain and thermal strain, and the expression is: {dε}={dε e }+{dε T } (19) In the thermoelastic model, the total strain increment also needs to add the plastic increment part: {dε}={dε e }+{dε p }+{dε T } (20) Substituting the above equation into equation (17), we can obtain the relationship between stress and total strain: {dσ}[D] e ({d}-{d p }-{dε T }) (21) For the convenience of analysis, (21) is rewritten to obtain the constitutive equation of the thermoelastic-plastic model: {dσ}[D] ep ({d)-{d T }) (22) Among them, [D] ep is the elastic-plastic matrix in the thermo-elastic-plastic model; Finite element method for thermo-elastoplastic model: To solve the constitutive equation of the thermoelastic model, it is necessary to establish an equilibrium equation, the premise of which is to apply the constitutive equation to the discretized mesh model; the corresponding equilibrium equation is established according to the principle of virtual work, and its convergence condition is that the strain energy generated by the displacement reaches the minimum value; the specific form of the equilibrium equation is as follows: In order to minimize the strain energy generated by displacement, the first-order derivative of strain energy with respect to displacement must be 0. By taking the first-order derivative of both sides of equation (25) with respect to displacement, we can obtain: Changing the integral sign of the above equation to sum the values ​​at the Gaussian points within the unit, we get: Among them, n G is the number of Gaussian points in the unit, n is the number of units, H r , H s , H t are the integral coefficients of Gaussian points respectively; ξ r , η s , t are the coordinates of the Gaussian points respectively; define [K] ep is the overall elastic-plastic stiffness matrix, Δ{R} is the equivalent load vector caused by the thermal strain increment; [K] ep From the element stiffness matrix [k] ep The three expressions are: Formula (25) can be rewritten as: [K] ep Δ{δ}=Δ{R} (27) According to formula (27), the displacement increment at the Gaussian point is calculated, and then the stress and stress increment at the Gaussian point are obtained, and finally the stress at the node is obtained.

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