CN102837435B - Flow front prediction method of non-isothermal resin transfer molding based on mid-plane model - Google Patents

Abstract

The invention provides a flow front prediction method of non-isothermal resin transfer molding based on a mid-plane model, comprising the following steps: (1) constructing a node three-dimensional control volume by a die cavity mid-plane grid; (2) setting molding technological parameters; (3) setting material parameters; (4) calculating resin flowing pressure and speed; (5) calculating resin solidifying reaction; (6) calculating the temperatures of resin and fiber reinforcements; (7) updating flow front and material physical properties so as to ensure time step; (8) ensuring whether the die cavity is filled, and entering the step (9) if the die cavity has already been filled, or entering the step (5); and (9) predicting the distribution of dry spots. Based on the mid-plane grid, the three-dimensional control volume is constructed and the finite element method of the control volume is used, the changes of viscidity, speed, temperature, curing degree and the like in the thickness direction and the influence to the calculation of pressure field are considered in the calculation, and the flow front of resin transfer molding and the distribution of various physical quantity fields can be predicted more accurately.

Description

The flow front Forecasting Methodology of the non-isothermal resin transfer moulding based on middle surface model

Technical field

The invention belongs to numerical simulation method, be particularly related to a kind of flow front Forecasting Methodology of the non-isothermal resin transfer moulding based on middle surface model, the non-isothermal resin transfer molding for in-plane size much larger than the composite product of thickness direction size.

Background technology

Resin transfer moulding (Resin Transfer Molding, RTM) be a kind ofly will in resin injection close die, to infiltrate the technique of reinforcing material curing molding, also be one of important method of producing in high quality fibers reinforced composite goods, compare with hot press molding technique with prepreg technique, the equipment investment of RTM technological forming is few, production environmental protection, stick with paste technique ratio with traditional hand, RTM quality of item is stable, discharge unwanted volatile matter few, and RTM Mechanical Properties of Products tool designability, stowing pressure is low, cost is low, be applicable to production and the mechanization production of large complicated part, be widely used in Aero-Space, boats and ships, automobile, the fields such as power electronics.

The operations such as resin transfer moulding mainly comprises laying, blanking, dipping, moulding, solidify.Wherein resin-dipping process is a vital ring, and dip process directly reacts on stowing operation flow front.Injection pressure, injection speed, inject time, temperature, curing reaction, gate location, gate size, the factors such as cast gate quantity and shape of product and thickness have material impact to resin flows forward position, inhomogeneous or the flow front of flow front development converges the quality problems that all can cause composite product, as: the excessive distortion that causes washing away fibre reinforcement and cause fibre reinforcement of injection pressure, the too fast dipping that causes that flows is bad, flow front meet can form dry spot, long meeting inject time make resin, in flow process, a large amount of curing reactions just occur and production efficiency low, etc..If the solution of these problems relies on traditional empirical method, trial and error, constantly repeatedly after die trial, evaluate again product design and technological parameter, can make the cost of resin transfer molding (RTM) process high, the construction cycle is long, and the rejection rate of product is high, it is unstable to produce, therefore, can waste a large amount of manpower and materials.And the flow front of method prediction resin transfer moulding based on numerical simulation provides a kind of means of economic, practical and science for RTM product design and technological design.

There is scholar to adopt the flow front of the method research resin transfer moulding of numerical simulation, as the RTM resin simulation softward of BJ University of Aeronautics & Astronautics's exploitation, in filling process, do not consider the impact in temperature and curing reaction flow forward position.In addition, also have and consider temperature and the impact of degree of cure flow forward position in resin fill die cavity process, see and " execute and fly, Dong Xianghuai. the numerical simulation of non-isothermal RTM technique. compound substance journal, 26 (4): 146-150, 2009 " and " Chen Ren-liang, Li Ming-cheng.Study of flow and temperature in resin transfer molding process by numerical model.Transactions of Nanjing University of Aeronautics & Astronautics.20 (2): 165-171, 2003 ", but what it adopted on middle surface grids in-plane is Green's (Green) formula or divergence theorem, on thickness direction, adopt finite difference method, and only consider the variation of temperature on thickness direction, do not consider that other physical quantity is (as speed, viscosity, degree of cure, flow rate etc.) variation on thickness direction.In Pressure solution process, said method does not consider that temperature and the degree of cure on thickness direction changes the viscosity variation causing, and then cause the variation of the flowing velocity of diverse location on thickness direction, in temperature solution procedure, said method adopts 1 poor rank upstreame scheme of precision in the processing of convective term, on thickness direction, flowing velocity does not change, the dipping part that is not coupled is conducted with the heat of not flooding the heat transfer of part and ignore on middle surface grids in-plane, in curing reaction solves, said method is not considered the variation of the resin flows speed of diverse location on thickness direction, different curing reaction speed and degree of cure.

Along with global market competition is growing more intense, require as far as possible science, design RTM product and technological parameter is set exactly, improve product quality and production efficiency, therefore, need a kind of method of prediction flow front of overall scientific.

Summary of the invention

The object of the invention is to provide a kind of flow front Forecasting Methodology of the non-isothermal resin transfer moulding based on middle surface model, on thickness direction, adopt finite difference method with the method for numerical simulation that solves non-isothermal RTM technique of the prior art, and only consider the variation of temperature on thickness direction, do not consider that other physical quantity is (as speed, viscosity, degree of cure etc.) variation on thickness direction, do not consider impregnation of fibers reinforcement and the Coupled Heat Transfer between impregnation of fibers reinforcement and only adopt the not high technical matters of precision of the numerical evaluation that 1 rank upstreame scheme etc. causes on middle surface grids in-plane not.

The object of the invention is achieved through the following technical solutions:

A flow front Forecasting Methodology for non-isothermal resin transfer moulding based on middle surface model, comprises the following steps:

(1) by the three-dimensional volume of controlling of surface grids structure node in die cavity;

(2) molding technique parameter is set;

(3) material parameter is set;

(4) calculate resin flows pressure and speed;

(5) calculate resin solidification reaction;

(6) temperature of calculating resin and fibre reinforcement;

(7) upgrade flow front and material property, determine time step;

(8) determine whether die cavity is full of, full if mold cavity has been filled, enter step (9), otherwise enter step (5);

(9) prediction dry spot distributes.

Preferably, further being comprised by the three-dimensional volume step of controlling of surface grids structure node in die cavity of described step (1): import surface grids in die cavity, according to the reticulate layer that thickness direction divided, connect the corresponding node of adjacent two layers unit on thickness direction, obtain multilayer prism elements, the body-centered of connecting edge pole unit, the center of area, limit mid point can structure node three-dimensional be controlled volume.

Preferably, in the calculating resin flows pressure and speed step of described step (4), ignoring products thickness side upwards pressure and changes and the speed component of through-thickness, resin plane flowing velocity on thickness direction changes, and the calculation procedure of pressure and speed further comprises:

(1) according to the viscosity of diverse location in Viscosity Model calculating products thickness direction, resin viscosity is the function of temperature and degree of cure:

$\mathrm{\η}(T,\mathrm{\α})=\mathrm{B\; exp}\left(\frac{T_b}{T}\right)\·{\left(\frac{{\mathrm{\α}}_{\mathrm{gel}}}{{\mathrm{\α}}_{\mathrm{gel}}-\mathrm{\α}}\right)}^{C_1+C_2\mathrm{\α}}$

In formula, η is dynamic viscosity, and T is temperature, and α is degree of cure, B, T _b, C ₁, C ₂, α _gelfor material parameter;

(2) adopt Darcy formula and mass-conservation equation as the governing equation that solves pressure and speed:

$\begin{array}{c}{u}_i=-\frac{{\mathrm{\λ}}_{\mathrm{ij}}}{\mathrm{\η}}{p}_{,j}\\ u_{i,i}=0\end{array}$

In above-mentioned two formulas, above formula is Darcy formula, and following formula is mass-conservation equation, and subscript ", " represents local derviation, u _ifor the superficial velocity of resin fluid, i, j=1,2 for the local Cartesian coordinates on middle surface grids in-plane is coordinate components, λ _ij, η is respectively permeability tensor component and the dynamic viscosity of resin, p is resin flows pressure;

Consider the variation of viscosity on thickness direction, the pressure equation based on middle surface model is:

${\∫}_{\mathrm{\Γ}}({\∫}_0^h-\frac{{\mathrm{\λ}}_{\mathrm{ij}}}{\mathrm{\η}\left(z\right)}{p}_{,\mathrm{ij}}\mathrm{dz})n_i\mathrm{dS}=0$

In formula, h is products thickness, and η (z) represents that viscosities il is the function of thickness direction coordinate z, and Γ is node control volume surface, n _i(i=1,2) be node control volume surface along in method vector outside the unit of surface grids in-plane;

(3) utilize and control volume finite element model for solving pressure equation;

(4) by node pressure, according to the resin flows speed of diverse location in Darcy formula calculated thickness direction.

Preferably, in the calculating resin solidification reactions steps of described step (5), utilize and control volume finite element model for solving curing reaction equation, be divided into multilayer on thickness, every layer of resin flows speed is different, and convective term adopts quality weighting upstreame scheme; Because temperature and the resin flows speed of diverse location on thickness direction are inconsistent, so the degree of cure of diverse location is also inconsistent on thickness direction;

$\begin{array}{c}\mathrm{\φ}{\mathrm{\α}}_{,t}+u_i{\mathrm{\α}}_{,i}=\mathrm{\φ}\stackrel{\·}{G}(T,\mathrm{\α})\\ \stackrel{\·}{G}(T,\mathrm{\α})=[A_1\exp (-\frac{E_1}{\mathrm{RT}})+A_2\exp (-\frac{E_2}{\mathrm{RT}}){\mathrm{\α}}^m]{({\mathrm{\α}}_f-\mathrm{\α})}^n\\ {\mathrm{\α}}_f=a_{0}T+b_0\end{array}$

In formula, for curing reaction speed, be the function of temperature and degree of cure, subscript ", " represents local derviation, and φ is fibre reinforced materials porosity, and t is the time, and T is absolute temperature, u _ithe speed component of surface grids in-plane in expression, i=1,2 for the local Cartesian coordinates on middle surface grids in-plane is coordinate components, α _frepresent the final degree of conversion of isothermal under assigned temperature, A ₁, A ₂, E ₁, E ₂, m, n, a ₀, b ₀for material constant, R=8.314J/ (molK) is universal gas constant.

Preferably, in the calculating resin of described step (6) and the temperature step of fibre reinforcement, utilize and control volume finite element model for solving energy conservation equation, it is temperature equation, on thickness, be divided into multilayer, every layer of resin flows speed is different, and convective term adopts quality weighting upstreame scheme, in calculating, consider not impregnation of fibers reinforcement and the Coupled Heat Transfer of impregnation of fibers precast body, the heat conduction on heat conduction and thickness direction in simultaneously considering on surface grids in-plane;

$\begin{array}{c}[\mathrm{\φ}{\mathrm{\ρ}}_r{C}_{\mathrm{pr}}+(1-\mathrm{\φ}){\mathrm{\ρ}}_f{C}_{\mathrm{pf}}]T_{,t}+{\mathrm{\ρ}}_r{C}_{\mathrm{pr}}\left(u_j{T}_{,j}\right)=k{T}_{,\mathrm{ii}}+\mathrm{\φ\ΔH}\stackrel{\·}{G}\\ (1-\mathrm{\φ}){\mathrm{\ρ}}_f{C}_{\mathrm{pf}}{T}_{,t}={\mathrm{kT}}_{,\mathrm{ii}}\end{array}$

In above-mentioned two formulas, above formula is the energy conservation equation of impregnation of fibers reinforcement, and following formula is the energy conservation equation of impregnation of fibers reinforcement not, this step solves above-mentioned two formula couplings, and subscript ", " represents local derviation, T is the temperature of fibre reinforcement and resin, and t is the time, u _jthe speed component of surface grids in-plane in expression, i, j=1,2 for the local Cartesian coordinates on middle surface grids in-plane is coordinate components, and i=3 is the coordinate components on thickness direction, the porosity that φ is fibre reinforcement, ρ _r, C _prbe respectively resin density, specific heat at constant pressure, ρ _f, C _pfbe respectively fiber reinforcement volume density, specific heat at constant pressure, for the thermal source item of mold filling process, wherein Δ H, be respectively curing reaction heat, curing reaction speed, k is equivalent heat transmissibility factor;

$k=\frac{k_r{k}_f}{k_r{w}_f+k_f{w}_r},w_r=\frac{\mathrm{\φ}/{\mathrm{\ρ}}_f}{\mathrm{\φ}/{\mathrm{\ρ}}_f+(1-\mathrm{\φ})/{\mathrm{\ρ}}_r},w_f=1-w_r$

In formula, w _r, w _fbe respectively the mass ratio of resin and fibre reinforcement, k _r, k _fbe respectively the heat-conduction coefficient of resin and fiber.

Preferably, the described molding technique parameter in described step (2) comprises mold temperature, resin temperature and fiber reinforcement temperature, and described molding technique parameter also comprises the one in injection pressure, inject time or injection speed.

Preferably, the described material parameter in described step (3) comprises density, specific heat capacity, heat-conduction coefficient, porosity and the permeability of resin and fibre reinforcement, and described material parameter also comprises the material constant of Viscosity Model and curing reaction model.

Preferably, the material constant of described curing reaction model comprises A ₁, A ₂, E ₁, E ₂, m, n, a ₀, b ₀, the material constant of Viscosity Model comprises B, T _b, C ₁, C ₂, α _gel; Wherein, A ₁and A ₂for pre-exponential factor (1/s), E ₁and E ₂for reaction activity (J/mol), m (without unit), n (without unit), a ₀(1/K), b ₀for matching material constant, B is pre-exponential factor (Pas), T _bfor reference temperature (K), C ₁and C ₂for matching is without unit materials parameter, α _geldegree of cure during for material gel.

Preferably, described step (7) further comprises: according to the velocity field calculating, adopt flow network analytic approach, select the shortest required filling time of the control volume of each node on whole thickness direction in current flow front as time step, upgrade the filling rate of other node control volume and the material property of diverse location in flow front, described material property comprises viscosity, specific heat, density and heat-conduction coefficient.

Preferably, described step (9) further comprises: according to the loading time of each node on grid, the morning and evening of contrast filling, prediction dry spot distributes, the position that dry spot may occur.

Compared with prior art, the present invention has following advantage:

1, compared with traditional middle surface model, in the present invention, construct three-dimensional control volume and used control volume finite-element method, in calculating, consider viscosity on thickness direction, speed, temperature, the variation of degree of cure etc. and the impact that pressure field is calculated thereof, in energy conservation equation, adopt thermal balance model, consider the heat conduction on Coupled Heat Transfer and the middle surface grids in-plane of impregnation of fibers reinforcement not and impregnation of fibers precast body, the convective term processing of temperature and degree of cure has adopted quality weighting upstreame scheme, stability and the computational accuracy of numerical evaluation are improved, the formulations of resin transfer molding processes of more approaching reality, can predict more accurately the distribution of resin transfer moulding flow front and various Physical Quantity Field,

2, the present invention is taking the fundamental equation of porous medium fluid mechanics as basis, introduce reasonably hypothesis and simplification, by middle surface grids Construction of A Model Nodes Three-dimensional control volume, adopt the volume Finite Element Method Simulation resin fill die cavity process of controlling, calculate pressure, speed, degree of cure and temperature in resin flows process, the flow front of prediction resin fill, can be and rational gate location, gate size, cast gate quantity and flash mouth position are set scientific basis is provided, avoid the generation of dryspot, thereby improve product quality and production efficiency.

Brief description of the drawings

Fig. 1 is the middle surface grids model of certain goods and the schematic diagram of cast gate;

Fig. 2 is FB(flow block) of the present invention;

Fig. 3 is the three-dimensional volume schematic diagram of controlling of structure node of the present invention;

Fig. 4 is quality weighting upstreame scheme schematic diagram of the present invention;

Fig. 5 is the degree of cure distribution schematic diagram of mold filling products thickness central core while finishing;

Fig. 6 is the Temperature Distribution schematic diagram of mold filling products thickness central core while finishing;

Fig. 7 is flow front result of calculation schematic diagram of the present invention;

Fig. 8 is dry spot position prediction schematic diagram of the present invention.

Embodiment

Below in conjunction with accompanying drawing, describe the present invention in detail.

Referring to Fig. 1, is the schematic diagram of surface grids and gate location in the geometric model of certain goods, and this products thickness is 5mm.As shown in Figure 2, concrete steps are as follows for the step of prediction flow front.

(1) by the three-dimensional volume of controlling of surface grids structure node in die cavity.Refer to Fig. 3, subscript i, i+1 (l >=i>0 in figure, l is the unit number of plies of middle surface model thickness direction, l=13 in this example) represent i on thickness direction, i+1 node layer, connect i, i+1 layer unit corresponding node is configured to tri-prism element, connect the sub-control volume of tri-prism element body-centered, the center of area, limit mid point structure node, the sub-control volume of node in all tri-prism elements merged into Nodes Three-dimensional control volume again.

(2) molding technique parameter is set.Molding technique parameter comprises injection pressure or inject time or injection speed (3 optional 1), mold temperature, resin temperature, fiber reinforcement temperature etc.; It is 30 DEG C that resin injection temperature is set, and fiber reinforcement temperature is 60 DEG C, and die cavity wall temperature is 60 DEG C.

In the time that the technological parameter arranging is injection pressure, the boundary condition calculating injection pressure as pressure equation;

In the time that the technological parameter arranging is injection rate, by continuous adjustment injection pressure, make the flow injecting equal or meet injection rate requirement close to the injection rate arranging;

In the time that the technological parameter arranging is inject time, is translated into injection rate according to the volume of goods, then solves pressure equation according to the mode of injection rate; In this example, injection pressure being set is 100KPa.

(3) material parameter is set.In this example, adopt parameter, Viscosity Model and the curing reaction model of certain material, while selecting other material, only need the relevant material parameter of amendment can realize the flow front prediction of the non-isothermal resin transfer moulding of other material, fibre reinforcement porosity is 60%, and material parameter and resin viscosity parameter, resin solidification reaction rate parameter are as shown in table 1-table 3.

Table 1, material parameter

Table 2, resin viscosity parameter

Table 3, resin solidification reaction rate parameter

In the resin viscosity of material parameter and curing reaction speed, T is temperature, and α is degree of cure;

(4) calculate resin flows pressure and speed.The viscosity of calculating diverse location in products thickness direction according to Viscosity Model, resin viscosity is the function of temperature and degree of cure, adopts the resin viscosity model in step (3).

Adopt Darcy formula and mass-conservation equation as the governing equation that solves pressure and speed:

$\begin{array}{c}{u}_i=-\frac{{\mathrm{\λ}}_{\mathrm{ij}}}{\mathrm{\η}}{p}_{,j}\\ u_{i,i}=0\end{array}$

In above-mentioned two formulas, above formula is Darcy formula, and following formula is mass-conservation equation, and subscript ", " represents local derviation, u _ifor the superficial velocity of resin fluid, i, j=1,2 for the local Cartesian coordinates on middle surface grids in-plane is coordinate components, λ _ij, η is respectively permeability tensor component and the viscosity of resin, p is resin flows pressure;

Consider the variation of viscosity on thickness direction, the pressure equation based on middle surface model is:

${\∫}_{\mathrm{\Γ}}({\∫}_0^h-\frac{{\mathrm{\λ}}_{\mathrm{ij}}}{\mathrm{\η}\left(z\right)}{p}_{,\mathrm{ij}}\mathrm{dz})n_i\mathrm{dS}=0$

In formula, h is products thickness, and η (z) represents that viscosities il is the function of thickness direction coordinate z, and Γ is node control volume surface, n _i(i=1,2) be node control volume surface along in method vector outside the unit of surface grids in-plane; In this example, establishing infiltration principal direction and fibre reinforcement consistent with resin flows speed principal direction is isotropic material, and permeability tensor component is:

${\mathrm{\λ}}_{\mathrm{ij}}=\left\{\begin{array}{cc}1.0\×{10}^{-8}& i=j\\ 0& i\≠j\end{array}\right.,$

Set up the pressure equation on the control volume of each node, apply boundary condition, all node pressure equation solutions of simultaneous can calculate node pressure.

Utilize and control volume finite element model for solving pressure equation, through-thickness pressure partial derivative is 0, and tri-prism element internal pressure partial derivative adopts the partial derivative of the shape function of Plain Triangular Element:

p _,i＝N _β,ip _β

In formula, N _β(β=1,2,3) are the shape function of β node of Plain Triangular Element, p _βfor the pressure of β node of triangular element;

By node pressure, according to the resin flows speed of diverse location in Darcy formula calculated thickness direction.

(5) calculate resin solidification reaction.Adopt and control volume finite-element method, time difference adopts backward difference, and convective term adopts the upstreame scheme of quality weighting, each node control volume is set up to the semi-implicit prediction-correction equation of node degree of cure:

$\begin{array}{c}{\∫}_v\mathrm{\φ}\frac{{\mathrm{\α}}^{t+\mathrm{\θ\Δt}}-{\mathrm{\α}}^t}{\mathrm{\θ\Δt}}\mathrm{dV}+{\∫}_{\mathrm{\Γ}}{m}_{\mathrm{\γ}}{\mathrm{\α}}_{\mathrm{\γ}}^{t+\mathrm{\θ\Δt}}{n}_i\mathrm{dS}={\∫}_v\mathrm{\φ}\stackrel{\·}{G}(T,{\mathrm{\α}}^t)\mathrm{dV}\\ {\∫}_v\mathrm{\φ}\frac{{\mathrm{\α}}^{t+\mathrm{\Δt}}-{\mathrm{\α}}^t}{\mathrm{\Δt}}\mathrm{dV}+{\∫}_{\mathrm{\Γ}}{m}_{\mathrm{\γ}}{\mathrm{\α}}_{\mathrm{\γ}}^{t+\mathrm{\Δt}}{n}_i\mathrm{dS}={\∫}_v\mathrm{\φ}\stackrel{\·}{G}(T,{\mathrm{\α}}^{t+\mathrm{\θ\Δt}})\mathrm{dV}\end{array}$

In formula, above formula is predictive equation, and following formula is correction equation, the volume that V is node control volume, α ^{t+ Δ t}for the t+ Δ degree of cure in t moment, α ^tfor the degree of cure in t moment, Δ t is time step, 0< θ≤1, and employing prediction-alignment technique can improve the computational accuracy of degree of cure, m _γ(γ=r, s, t), for controlling the flow on volume surface gamma, due to the speed component of ignoring on thickness direction, therefore convective term exists only in the in-plane of middle surface grids, as shown in Figure 4, for controlling the lip-deep degree of cure of volume:

${\stackrel{\&CenterDot;}{m}}_r={\&Integral;}_o^a{u}_i\&CenterDot;n_i\frac{h}{l}\mathrm{ds}$

${\stackrel{\&CenterDot;}{m}}_s={\&Integral;}_o^b{u}_i\&CenterDot;n_i\frac{h}{l}\mathrm{ds}$

${\stackrel{\&CenterDot;}{m}}_s={\&Integral;}_o^c{u}_i\&CenterDot;n_i\frac{h}{l}\mathrm{ds}$

${\mathrm{\&alpha;}}_r=\left\{\begin{array}{ccc}{f}_P{\mathrm{\&alpha;}}_t+(1-f_P){\mathrm{\&alpha;}}_1& f_P=\min [\max (-{\stackrel{\&CenterDot;}{m}}_t/{\stackrel{\&CenterDot;}{m}}_r,0),1]& {\stackrel{\&CenterDot;}{m}}_r>0\\ f_P{\mathrm{\&alpha;}}_s+(1-f_P){\mathrm{\&alpha;}}_2& f_P=\min [\max (-{\stackrel{\&CenterDot;}{m}}_s/{\stackrel{\&CenterDot;}{m}}_r,0),1]& {\stackrel{\&CenterDot;}{m}}_r<0\end{array}\right.$

${\mathrm{\&alpha;}}_s=\left\{\begin{array}{ccc}{f}_P{\mathrm{\&alpha;}}_t+(1-f_P){\mathrm{\&alpha;}}_3& f_P=\min [\max ({\stackrel{\&CenterDot;}{m}}_t/{\stackrel{\&CenterDot;}{m}}_s,0),1]& {\stackrel{\&CenterDot;}{m}}_s>0\\ f_P{\mathrm{\&alpha;}}_r+(1-f_P){\mathrm{\&alpha;}}_2& f_P=\min [\max (-{\stackrel{\&CenterDot;}{m}}_r/{\stackrel{\&CenterDot;}{m}}_s,0),1]& {\stackrel{\&CenterDot;}{m}}_s<0\end{array}\right.$

${\mathrm{\&alpha;}}_t=\left\{\begin{array}{ccc}{f}_P{\mathrm{\&alpha;}}_r+(1-f_P){\mathrm{\&alpha;}}_1& f_P=\min [\max (-{\stackrel{\&CenterDot;}{m}}_r/{\stackrel{\&CenterDot;}{m}}_t,0),1]& {\stackrel{\&CenterDot;}{m}}_s>0\\ f_P{\mathrm{\&alpha;}}_s+(1-f_P){\mathrm{\&alpha;}}_3& f_P=\min [\max ({\stackrel{\&CenterDot;}{m}}_s/{\stackrel{\&CenterDot;}{m}}_t,0),1]& {\stackrel{\&CenterDot;}{m}}_s<0\end{array}\right.$

In formula, α _γ(γ=r, s, t) represents the degree of cure of an Atria node.The degree of cure of mid-depth layer when end-of-fill distributes as shown in Figure 5.

(6) temperature of calculating resin and fibre reinforcement.Adopt and control volume finite-element method, time difference adopts backward difference, and convective term adopts the upstreame scheme (similar degree of cure) of quality weighting, and half implicit equation of each node control volume being set up to node temperature is:

$\begin{array}{c}{\&Integral;}_V[\mathrm{\&phi;}{\mathrm{\&rho;}}_r{C}_{\mathrm{pr}}+(1-\mathrm{\&phi;}){\mathrm{\&rho;}}_f{C}_{\mathrm{pf}}]\frac{T^{t+\mathrm{\&Delta;t}}-T^t}{\mathrm{\&Delta;t}}\mathrm{dV}+{\&Integral;}_{\mathrm{\&Gamma;}}{\mathrm{\&rho;}}_r{C}_{\mathrm{pr}}{m}_{\mathrm{\&gamma;}}{T}_{\mathrm{\&gamma;}}^{t+\mathrm{\&Delta;t}}{n}_i\mathrm{dS}\\ -{\&Integral;}_{\mathrm{\&Gamma;}}k{T}_{,i}^{t+\mathrm{\&Delta;t}}{n}_i\mathrm{dS}={\&Integral;}_V\mathrm{\&phi;\&Delta;H}\stackrel{\&CenterDot;}{G}\mathrm{dV}\\ {\&Integral;}_V\left[(1-\mathrm{\&phi;}){\mathrm{\&rho;}}_f{C}_{\mathrm{pf}}\right]\frac{T^{t+\mathrm{\&Delta;t}}-T^t}{\mathrm{\&Delta;t}}\mathrm{dV}-{\&Integral;}_{\mathrm{\&Gamma;}}{\mathrm{kT}}_{,i}^{t+\mathrm{\&Delta;t}}{n}_i\mathrm{dS}=0\end{array}$

In formula, T _{, i}=N _{β, i}t _β, on middle surface grids in-plane, N _βfor the shape function of middle surface grids unit, on thickness direction, N _βbe 2 dotted line unit shape functions.Above-mentioned two equations of simultaneous can solve the temperature in whole die cavity.The Temperature Distribution of mid-depth layer when end-of-fill as shown in Figure 6.

(7) upgrade flow front and material property, determine time step step.According to the velocity field calculating, adopt flow network analytic approach, select the shortest required filling time of each node control volume in current flow front as time step, upgrade the filling rate of other node control volume and the material property of diverse location (viscosity, density, specific heat, heat-conduction coefficient etc.) in flow front.

(8) determine whether die cavity is full of step.If mold cavity has been filled full, enter (9), otherwise enter step (5).The flow front that cavity filling obtains when full distributes as shown in Figure 7, and in figure, on goods, the color at every place represents the moment that this place is full of.

(9) prediction dry spot distribution step.According to the loading time of each node on grid, the morning and evening of contrast filling,, may there is dry spot in the Nodes of all node loading times around loading time is later than, as red some position in Fig. 8.

Compared with traditional middle surface model, in the present invention, construct three-dimensional control volume and used control volume finite-element method, in calculating, consider viscosity on thickness direction, speed, temperature, the variation of degree of cure etc. and the impact that pressure field is calculated thereof, in energy conservation equation, adopt thermal balance model, consider the heat conduction on Coupled Heat Transfer and the middle surface grids in-plane of impregnation of fibers reinforcement not and impregnation of fibers precast body, the convective term processing of temperature and degree of cure has adopted quality weighting upstreame scheme, stability and the computational accuracy of numerical evaluation are improved, the formulations of resin transfer molding processes of more approaching reality, can predict more accurately the distribution of resin transfer moulding flow front and various Physical Quantity Field.The present invention is taking the fundamental equation of porous medium fluid mechanics as basis, introduce reasonably hypothesis and simplification, by middle surface grids Construction of A Model Nodes Three-dimensional control volume, adopt the volume Finite Element Method Simulation resin fill die cavity process of controlling, calculate pressure, speed, degree of cure and temperature in resin flows process, the flow front of prediction resin fill, can be and rational gate location, gate size, cast gate quantity and flash mouth position are set scientific basis is provided, avoid the generation of dryspot, thereby improve product quality and production efficiency.

Disclosed is above only several specific embodiments of the application, but the application is not limited thereto, and the changes that any person skilled in the art can think of, all should drop in the application's protection domain.

Claims (5)

1. a flow front Forecasting Methodology for the non-isothermal resin transfer moulding based on middle surface model, is characterized in that, comprises the following steps:

(1) by the three-dimensional volume of controlling of surface grids structure node in die cavity; This step further comprises: import surface grids in die cavity, according to the reticulate layer that thickness direction divided, the corresponding node that connects adjacent two layers unit on thickness direction, obtains multilayer prism elements, and the body-centered of connecting edge pole unit, the center of area, limit mid point can structure node three-dimensional be controlled volume;

(2) molding technique parameter is set;

(3) material parameter is set;

(4) calculate resin flows pressure and speed; In this step, to ignore products thickness side and upward pressure and change and the speed component of through-thickness, the resin plane flowing velocity on thickness direction changes, and the calculation procedure of pressure and speed further comprises:

A. the viscosity of calculating diverse location in products thickness direction according to Viscosity Model, resin viscosity is the function of temperature and degree of cure:

$\mathrm{\&eta;}(T,\mathrm{\&alpha;})=\mathrm{B\; exp}\left(\frac{T_b}{T}\right)\&CenterDot;{\left(\frac{{\mathrm{\&alpha;}}_{\mathrm{gel}}}{{\mathrm{\&alpha;}}_{\mathrm{gel}}-\mathrm{\&alpha;}}\right)}^{C_1+C_2\mathrm{\&alpha;}}$

In formula, η is dynamic viscosity (Pas), and T is temperature (K), and α is degree of cure, and B is pre-exponential factor (Pas), T _bfor reference temperature (K), C ₁and C ₂for matching is without unit materials parameter, α _geldegree of cure during for material gel;

B. adopt Darcy formula and mass-conservation equation as the governing equation that solves pressure and speed:

$\begin{array}{c}{u}_i=-\frac{{\mathrm{\&lambda;}}_{\mathrm{ij}}}{\mathrm{\&eta;}}{p}_{,j}\\ u_{i,i}=0\end{array}$

In above-mentioned two formulas, above formula is Darcy formula, and following formula is mass-conservation equation, and subscript ", " represents local derviation, u _ifor the superficial velocity of resin fluid, i, j=1,2 for the local Cartesian coordinates on middle surface grids in-plane is coordinate components, λ i _j, η is respectively permeability tensor component and the dynamic viscosity of resin, p is resin flows pressure;

Consider the variation of viscosity on thickness direction, the pressure equation based on middle surface model is:

${\&Integral;}_{\mathrm{\&Gamma;}}({\&Integral;}_0^h-\frac{{\mathrm{\&lambda;}}_{\mathrm{ij}}}{\mathrm{\&eta;}\left(z\right)}{p}_{,\mathrm{ij}}\mathrm{dz})n_i\mathrm{dS}=0$

In formula, h is products thickness, and η (z) represents that viscosities il is the function of thickness direction coordinate z, and Γ is node control volume surface, n _i(i=1,2) be node control volume surface along in method vector outside the unit of surface grids in-plane;

C. utilize and control volume finite element model for solving pressure equation;

D. by node pressure, according to the resin flows speed of diverse location in Darcy formula calculated thickness direction;

(5) calculate resin solidification reaction; In this step, utilize and control volume finite element model for solving curing reaction equation, on thickness, be divided into multilayer, every layer of resin flows speed is different, and convective term adopts quality weighting upstreame scheme; Because temperature and the resin flows speed of diverse location on thickness direction are inconsistent, so the degree of cure of diverse location is also inconsistent on thickness direction;

$\begin{array}{c}\mathrm{\&phi;}{\mathrm{\&alpha;}}_{,t}+u_i{\mathrm{\&alpha;}}_{,i}=\mathrm{\&phi;}\stackrel{\&CenterDot;}{G}(T,\mathrm{\&alpha;})\\ \stackrel{\&CenterDot;}{G}(T,\mathrm{\&alpha;})=[A_1\exp (-\frac{E_1}{\mathrm{RT}})+A_2\exp (-\frac{E_2}{\mathrm{RT}}){\mathrm{\&alpha;}}^m]{({\mathrm{\&alpha;}}_f-\mathrm{\&alpha;})}^n\\ {\mathrm{\&alpha;}}_f=a_{0}T+b_0\end{array}$

In formula, for curing reaction speed, be the function of temperature and degree of cure, subscript ", " represents local derviation, and φ is fibre reinforced materials porosity, and t is the time, and T is absolute temperature, u _ithe speed component of surface grids in-plane in expression, i=1,2 for the local Cartesian coordinates on middle surface grids in-plane is coordinate components, α _frepresent the final degree of conversion of isothermal under assigned temperature, A ₁and A ₂for pre-exponential factor (1/s), E ₁and E ₂for reaction activity (J/mol), m, (without unit) n (without unit), a ₀(1/K), b ₀for matching material constant, R=8.314J/ (molK) is universal gas constant;

(6) temperature of calculating resin and fibre reinforcement; In this step, utilize and control volume finite element model for solving energy conservation equation, it is temperature equation, on thickness, be divided into multilayer, every layer of resin flows speed is different, convective term adopts quality weighting upstreame scheme, considers not impregnation of fibers reinforcement and the Coupled Heat Transfer of impregnation of fibers precast body in calculating, the heat conduction on heat conduction and thickness direction in simultaneously considering on surface grids in-plane;

$\begin{array}{c}[\mathrm{\&phi;}{\mathrm{\&rho;}}_r{C}_{\mathrm{pr}}+(1-\mathrm{\&phi;}){\mathrm{\&rho;}}_f{C}_{\mathrm{pf}}]T_{,t}+{\mathrm{\&rho;}}_r{C}_{\mathrm{pr}}\left(u_j{T}_{,j}\right)=k{T}_{,\mathrm{ii}}+\mathrm{\&phi;\&Delta;H}\stackrel{\&CenterDot;}{G}\\ (1-\mathrm{\&phi;}){\mathrm{\&rho;}}_f{C}_{\mathrm{pf}}{T}_{,t}={\mathrm{kT}}_{,\mathrm{ii}}\end{array}$

In above-mentioned two formulas, above formula is the energy conservation equation of impregnation of fibers reinforcement, and following formula is the energy conservation equation of impregnation of fibers reinforcement not, this step solves above-mentioned two formula couplings, and subscript ", " represents local derviation, T is the temperature of fibre reinforcement and resin, and t is the time, u _jthe speed component of surface grids in-plane in expression, i, j=1,2 for the local Cartesian coordinates on middle surface grids in-plane is coordinate components, and i=3 is the coordinate components on thickness direction, the porosity that φ is fibre reinforcement, ρ _r, C _prbe respectively resin density, specific heat at constant pressure, ρ _f, C _pfbe respectively fiber reinforcement volume density, specific heat at constant pressure, for the thermal source item of mold filling process, wherein Δ H, be respectively curing reaction heat, curing reaction speed, k is equivalent heat transmissibility factor;

$k=\frac{k_r{k}_f}{k_r{w}_f+k_f{w}_r},w_r=\frac{\mathrm{\&phi;}/{\mathrm{\&rho;}}_f}{\mathrm{\&phi;}/{\mathrm{\&rho;}}_f+(1-\mathrm{\&phi;})/{\mathrm{\&rho;}}_r},w_f=1-w_r$

In formula, w _r, w _fbe respectively the mass ratio of resin and fibre reinforcement, k _r, k _fbe respectively the heat-conduction coefficient of resin and fiber;

(7) upgrade flow front and material property, determine time step; This step further comprises: according to the velocity field calculating, adopt flow network analytic approach, select the shortest required filling time of the control volume of each node on whole thickness direction in current flow front as time step, upgrade the filling rate of other node control volume and the material property of diverse location in flow front, described material property comprises viscosity, specific heat, density and heat-conduction coefficient;

(8) determine whether die cavity is full of, full if mold cavity has been filled, enter step (9), otherwise enter step (5);

(9) prediction dry spot distributes.

2. the flow front Forecasting Methodology of the non-isothermal resin transfer moulding based on middle surface model as claimed in claim 1, it is characterized in that, described molding technique parameter in described step (2) comprises mold temperature, resin temperature and fiber reinforcement temperature, and described molding technique parameter also comprises the one in injection pressure, inject time or injection speed.

3. the flow front Forecasting Methodology of the non-isothermal resin transfer moulding based on middle surface model as claimed in claim 1, it is characterized in that, described material parameter in described step (3) comprises density, specific heat capacity, heat-conduction coefficient, porosity and the permeability of resin and fibre reinforcement, and described material parameter also comprises the material constant of Viscosity Model and curing reaction model.

4. the flow front Forecasting Methodology of the non-isothermal resin transfer moulding based on middle surface model as claimed in claim 1, is characterized in that, the material constant of described curing reaction model comprises A ₁, A ₂, E ₁, E ₂, m, n, a ₀, b ₀, the material constant of Viscosity Model comprises B, T _b, C ₁, C ₂, α _gel; Wherein, A ₁and A ₂for pre-exponential factor (1/s), E ₁and E ₂for reaction activity (J/mol), m (without unit), n (without unit), a ₀(1/K), b ₀for matching material constant, B is pre-exponential factor (Pas), T _bfor reference temperature (K), C ₁and C ₂for matching is without unit materials parameter, α _geldegree of cure during for material gel.

5. the flow front Forecasting Methodology of the non-isothermal resin transfer moulding based on middle surface model as claimed in claim 1, it is characterized in that, described step (9) further comprises: according to the loading time of each node on grid, the morning and evening of contrast filling, prediction dry spot distributes, the position that dry spot may occur.