CN101996272B - Method for simulating vulcanization process of rubber product - Google Patents

Abstract

The invention discloses a method for simulating the vulcanization process of a rubber product, which comprises the following steps of: measuring a rubber flow curve and thermal physical parameters through tests; establishing a hybrid dynamic model and a thermal physical function of the rubber; establishing a heat transfer-chemical reaction coupled equation of the rubber product; performing numerical calculation on the equation based on a Newton iteration method; and acquiring at least one physical parameter related to the rubber product model. The method can more accurately simulate the heat transfer process and the crosslinking process of the rubber vulcanization.

Description

The method of simulating vulcanization process of rubber product

Technical field

The present invention relates to a kind of method of Vulcanization Process of Rubber simulation, the method can be simulated heat transmission and the cross-linking reaction state with the rubber of uniform temperature sulfuration, accurately calculates temperature and the state of cure (vulcanization) situation of change of the inner every bit of rubber.

Background technology

The method of the tradition research vulcanization of rubber is to measure the temperature history at the inner key point of rubber place by thermopair, then to use rational kinetic model be the each point temperature inversion state of cure (vulcanization), determines the necessary time of sulfuration with this.But the change of formula Design and curing medium temperature will affect the sulfur vulcanization chemistries reaction, and then have influence on final cross-linking density and the mechanical property of rubber.And after finishing test, must cut open the position of finding out thermopair to rubber parts at every turn.Therefore, this trial and error method cost is high, the time is long.

In recent years, people are used for computer simulation the research of the vulcanization of rubber.Total institute is known, and Pirelli company (PCT/EP2002/004488) discloses the patent of tyre vulcanization simulation method.In " Computational Materials " book that Nova Science publishing house publishes, " NUMERICALSIMULATION OF THE CURING PROCESS OF RUBBER ARTICLES " chapter of being write by Mir Hamid Reza Ghoreishy, summarized vulcanization of rubber numerical simulation overview, pointed out that the research emphasis of vulcanization of rubber emulation is that the rubber thermal physical property parameter changes and the statement of sulfuration kinetic model.

For rubber thermal physical property parameter research, usually coefficient of heat conductivity and temperature are made as the first-order linear inversely prroportional relationship, but the thermal conductivity of rubber there are much relations with wherein types of carbon black and content, sometimes along with the temperature increase, sometimes also reduces; The density of rubber usually increases and reduces along with temperature, and the rubber thermal capacitance increases and increases along with temperature.In addition, density and thermal capacitance also depend on cross-linking density, therefore should consider the impact of state of cure (vulcanization) (extent of reaction).Can solve this problem with two kinds of methods, a kind of is that density and thermal capacitance product are regarded as constant; Another kind is that assumed density is constant, and thermal capacitance is along with temperature and state of cure (vulcanization) change.But half finished rubber and oneself sulfuration have only been considered in these researchs, and do not consider the impact of semi-finished rubber research.

The vulcanization of rubber is chemical reaction process in essence, and the sulfuration kinetic model is the mathematical model of quantitative description chemical reaction degree and time and temperature relation, is also the key factor of determining vulcanization of rubber reaction heat.Typical vulcanization of rubber phenomenology kinetic model mainly contains n rank model, Piloyan model, Kamal-Ryan model (K-R model), Kamal-Sourour model (K-S model) and the correction K-S model (seeing that Rafei writes, " Development of an advanced computer simulation technique for themodeling of rubber curing process " literary composition of Computational MaterialsScience the 47th volume in 2009) that proposes of Rafei afterwards.Wherein, first three model can't provide the explicit expression of state of cure (vulcanization), in order to overcome this defective, has proposed latter two model.But do not have so far a kind of model can accurately describe on the whole the sulfuration dynamics of rubber.

Summary of the invention

The present invention seeks to provide for the defective that prior art exists a kind of method of simulating vulcanization process of rubber product.

The present invention adopts following technical scheme for achieving the above object: the method for simulating vulcanization process of rubber product of the present invention comprises the steps: by experimental measurement rubber flow varied curve and thermal physical property parameter; Set up the hot physical property function of hybrid dynamics model and rubber; Set up the heat transfer of rubber-chemical reaction coupled wave equation; Based on Newton iteration method, equation is carried out numerical evaluation; Obtain at least one physical parameter relevant to described rubber model.

Wherein, the test condition of described measurement rubber flow varied curve is constant temperature, and temperature range is measured the rubber flow varied curve of three kinds of different temperatures at least at 135-180 ℃.

Wherein, the test sample of described measurement thermal physical property parameter comprises the thermal physical property parameter of half finished rubber, semi-finished rubber and own vulcanized rubber at least.

Wherein, described hybrid dynamics model establishment step comprises: use K-R model and K-S models fitting, numerical value is demarcated, and determines initial state of cure (vulcanization), and sets up the hybrid dynamics model.Wherein, described numerical value scaling method is as follows: ${\∂}_j={\∂}_{j-1}+{\left(\frac{d\∂}{\mathrm{dt}}\right)}_{j-1}*\mathrm{\Δt}$ Wherein,

Determined by typical kinetic model,

Be current state of cure (vulcanization),

Be a upper incremental step state of cure (vulcanization), Δ t is time increment.

Wherein, described hybrid dynamics model is as follows:

Wherein,

Wherein,

Be vulcanization reaction speed,

Be state of cure (vulcanization), E, E ₁And E ₂Be energy of activation, R is gas law constant Determined by the numerical value calibration result.Wherein, the hot physical property function of described rubber comprises that coefficient of heat conductivity and specific heat capacity are along with the variation of temperature and state of cure (vulcanization).Wherein, described coefficient of heat conductivity is shown below: $k=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left(\underset{j=1,j=i}{\overset{n}{\mathrm{\&Pi;}}}\frac{\&PartialD;-{\&PartialD;}_j}{{\&PartialD;}_i-{\&PartialD;}_j}\right)*k_i,n\&GreaterEqual;3$ $k_i=\left\{\begin{array}{c}{a}_{\mathrm{<figure-callout\; id="1"\; label="i"\; filenames="101022151029.png,101022151036.png"\; state="\{\{state\}\}">i</figure-callout>}1}+b_{i1}T,T\&GreaterEqual;T_0\\ a_{i2}+b_{i2}T,T<T_0\end{array}\right.i=\mathrm{1,2},...n$ Wherein, k is the up time coefficient of heat conductivity, k ₁For state of cure (vulcanization) is The time rubber coefficient of heat conductivity, i.e. k ₁Be the coefficient of heat conductivity of half finished rubber, k ₂Be the coefficient of heat conductivity of own vulcanized rubber, k ₂Be the coefficient of heat conductivity of semi-finished rubber, 1＜i＜n,

Be the state of cure (vulcanization) of rubber, T is temperature, T0, a _i1, b _i1, a _i2And b _i2It is the constant of being determined by test.Wherein, described thermal capacitance is shown below: $c_p=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left(\underset{j=1,j=i}{\overset{n}{\mathrm{\&Pi;}}}\frac{\&PartialD;-{\&PartialD;}_j}{{\&PartialD;}_i-{\&PartialD;}_j}\right)*c_{\mathrm{pi}},n\&GreaterEqual;3$ $c_{\mathrm{pi}}=\left\{\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="c\; i"\; filenames="101022151029.png,101022151036.png"\; state="\{\{state\}\}">c</figure-callout>}}_i+d_{i1}T,T\&GreaterEqual;T_0\\ c_{i2}+d_{i2}T,T<T_0\end{array}\right.i=\mathrm{1,2},...,n$ Wherein,

Be the up time coefficient of heat conductivity,

For state of cure (vulcanization) is The time rubber coefficient of heat conductivity, i.e. c _i3Be the specific heat capacity of half finished rubber,

Be the specific heat capacity of own vulcanized rubber, Be the specific heat capacity of semi-finished rubber, 1＜i＜n.

Be the state of cure (vulcanization) of rubber, T is temperature, T ₀, c _i1, d _i1, c _i2And d _i2It is the constant of being determined by test.The inventive method is in conjunction with half finished rubber, the coefficient of heat conductivity of semi-finished rubber and own vulcanized rubber and specific heat capacity, rubber coefficient of heat conductivity and specific heat capacity have been proposed at the function of sulfidation along with the variation of temperature and state of cure (vulcanization), and based on the achievement in research of forefathers to vulcanization of rubber kinetic model.Propose a kind of hybrid dynamics model and described the situation of vulcanization reaction.Therefore, can more accurately be simulated diabatic process and the cross-linking process of the vulcanization of rubber by the present invention.

Description of drawings

Fig. 1 is for being used for implementing the computer system skeleton view of analogy method of the present invention; Fig. 2 is the process flow diagram for the example (water pocket sulfuration) of the treatment step of the analogy method of invention; Fig. 3 is state of cure (vulcanization) and the relation curve of time and the K-S models fitting curve of rubber at three kinds of temperature; Fig. 4 is the state of cure (vulcanization) of rubber at three kinds of temperature and relation curve and the K-R models fitting curve of vulcanization reaction speed; Fig. 5 is rubber specific heat and coefficient of heat conductivity variation with temperature under three kinds of sulfided states; Fig. 6 is the calibration result of K-R model, K-S model and hybrid dynamics model; Fig. 7 is Arrhenius Function Fitting result induction period; Fig. 8 is the rotational symmetry sectional view of rubber pressure head curing system to be simulated; Fig. 9 is the skeleton view of the grid model of rubber pressure head curing system to be simulated; Figure 10 vulcanizes the dimensionless group that whether finishes induction period for reaction

Cloud atlas; Figure 11 is each time point rubber pressure head state of cure (vulcanization) cloud atlas; Figure 12 is each time point rubber pressure head temperature cloud picture; Figure 13 is temperature and the state of cure (vulcanization) course of rubber pressure head typical parts; Figure 14 is the curingprocess rate course of rubber pressure head typical parts.

Embodiment

The specific embodiment of the present invention is described as an example of certain rubber pressure head example below in conjunction with accompanying drawing.The invention provides a kind of method of simulating vulcanization process of rubber product, in order to use computer installation shown in Figure 1, computer simulation is carried out in the vulcanization of rubber.

Computer installation 1 comprises main frame 1a, as keyboard 1b and the mouse 1c of input equipment, and as the display 1d of output device.The hardware of main frame 1a is that a general configuration gets final product, and operating system is WindowsXP64 or Lunix.In order to carry out the hereinafter described treatment step of method (being program).

Fig. 2 has shown the flow process for the example (sulfuration of rubber pressure head) of the treatment step of the analogy method of invention.In embodiments of the present invention, at first a step S1 measures rubber flow varied curve and thermal physical property parameter, provides test figure for setting up the hybrid dynamics model and characterizing the hot physical property of sizing material.Fig. 3, Fig. 4 are respectively the rubber vulcanization degree of rubber under 135 ℃, 145 ℃ and 160 ℃ and the relation curve of the relation curve of time and state of cure (vulcanization) and vulcanization reaction speed; Fig. 5 is half finished rubber

Semi-finished rubber

With own vulcanized rubber

Specific heat and coefficient of heat conductivity variation with temperature.

Then, step S2 uses respectively K-R model and K-S model to carry out match (seeing Fig. 3 and Fig. 4) to test findings, and match software is Origine, and the fitting result of two models is as shown in table 1 below.In conjunction with the result data of K-R model, correction K-S model and table 1, utilize formula (1) to carry out numerical value and demarcate, use mathematical software (MATLAB) to carry out iterative computation as means, result is as shown in Figure 6.K-R models fitting precision is higher at the isothermal vulcanization initial stage, and it is higher in the isothermal vulcanization later stage to revise the K-S model, therefore, adopts the K-R model at initial vulcanization step, and the later stage adopts and revises the K-S model, namely adopts the hybrid dynamics model, as formula 2,

Hybrid dynamics modeling result as shown in Figure 6, it is best that result of calculation and test findings are coincide, and improved computational accuracy.[table 1] ${\&PartialD;}_j={\&PartialD;}_{j-1}+{\left(\frac{d\&PartialD;}{\mathrm{dt}}\right)}_{j-1}*\mathrm{\&Delta;t}---\left(t\right)$

For the rubber thermal physical property parameter, assumed density is constant.Coefficient of heat conductivity and specific heat capacity are used respectively formula (3) and formula (4) statement, wherein n=3 (if n=2, formula 3 and formula 4 are exactly coefficient of heat conductivity and specific heat capacity computing function commonly used at present). Be respectively half finished rubber, the state of cure (vulcanization) of T＞0 semi-finished rubber and own vulcanized rubber.Use formula (3) and formula (4) to carry out linear to the test findings of Fig. 5 or the linear match of segmentation. $\begin{array}{cc}\left[0017\right]& k=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left(\underset{j=1j\&NotEqual;i}{\overset{n}{\mathrm{\&Pi;}}}\frac{\&PartialD;-{\&PartialD;}_j}{{\&PartialD;}_i{-\&PartialD;}_j}\right)\end{array},*k_{i}n\&GreaterEqual;3,,$ $k_i=\left\{\begin{array}{c}{a}_{i1}+b_{i1}T,T\&GreaterEqual;T_0\\ a_{i2}+b_{i2}T,T<T_0\end{array}\right.j=\mathrm{1,2},...n---\left(3\right)$ $c_p=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\left(\underset{j=1,j=i}{\overset{n}{\mathrm{\&Pi;}}}\frac{\&PartialD;-{\&PartialD;}_j}{{\&PartialD;}_i-{\&PartialD;}_j}\right)*c_{\mathrm{pi}},n\&GreaterEqual;3,$ $c_{\mathrm{pi}}=\left\{\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="c\; i"\; filenames="101022151029.png,101022151036.png"\; state="\{\{state\}\}">c</figure-callout>}}_i+d_{i1}T,T\&GreaterEqual;T_0\\ c_{i2}+d_{i2}T,T<T_0\end{array}\right.i=\mathrm{1,2},...,n---\left(4\right)$ Water pocket sulfuration is a non-homogeneous sulfidation, and its sizing material is respectively 32.76 at the induction time of 135 ℃, 145 ℃ and 160 ℃ lower constant temperature sulfurations, 25.34s and 17.63s, uses the Arrhenius function

And dimensionless group

Describe, when

Less than 1 o'clock, sulfuration was in induction period, otherwise vulcanization reaction begins (seeing formula (5)), wherein Arrhenius Function Fitting result as shown in Figure 7, t ₀=0.00114, T ₀=4186.86. $\tilde{t}={\&Integral;}_0^t\frac{\mathrm{dt}}{t_i\left(T\right)}---\left(5\right)$ Fig. 8 is the rotational symmetry sectional view of rubber pressure head curing system 2 to be simulated, and rubber pressure head curing system to be simulated is physical presence not.Being that perhaps such anchor winch is that prototype has been arranged, can be also imaginary system.Rubber pressure head curing system 2 comprises that one is full of capsule 3, rubber pressure head 4 and the external stability indenter shape of certain pressure superheated water and the metal die 5 that the surface is provided with well heater in pressure head inside.The rubber pressure head is implemented the constant temperature sulfuration, and the temperature in the inboard and metal die of capsule 35 outsides is respectively 165 ℃ and 155 ℃, and the initial temperature of capsule 3, rubber pressure head 4 and metal die 5 is room temperature (25 ℃).

The present invention adopts Finite Element Method Simulation rubber pressure head sulfidation, for the simplification problem, does not consider the waste heat sulfidation that the pressure head depanning is later.Capsule 3, rubber pressure head 4 and metal die 5 are carried out grid divide, Fig. 9 is the skeleton view of the grid model of rubber pressure head curing system to be simulated.Again in conjunction with the material model of describing coefficient of heat conductivity and specific heat capacity, the vulcanization of rubber dimensionless group of induction period is described, the hybrid dynamics model of reaction sulfuration reaction rate, and sulfuration boundary condition, use business software ABAQUS and user's subroutine UMATHT thereof, set up the heat transfer of rubber pressure head curing system-chemical reaction coupled wave equation (step S3), as shown in equation (6).In equation (6) for the rubber heat generation rate

Test out vulcanization reaction total amount of heat Q (3354.2J/kg) and vulcanization reaction speed product by DSC and determine, and the thermal physical property parameter of capsule 3 and metal die 5 adopts and uses general expression method to get final product.Based on Newton iteration method, coupled wave equation is carried out numerical evaluation (step S4), be decided to be 3800 seconds analysis time, in order to guarantee the computational accuracy of state of cure (vulcanization), the time increment definition of numerical evaluation 1 second. $\begin{array}{cc}\left[0019\right]& \mathrm{\&rho;C}\frac{\&PartialD;T}{\&PartialD;t}=\frac{1}{r}\frac{\&PartialD;}{\&PartialD;r}\left(\mathrm{rk}\frac{\&PartialD;T}{\&PartialD;r}\right)+\frac{\&PartialD;}{\&PartialD;z}\left(k\frac{\&PartialD;T}{\&PartialD;z}\right)+Q\end{array}---\left(6\right)$ At last, obtain the physical parameter relevant to described rubber model, as parameters such as temperature, state of cure (vulcanization), vulcanization reaction speed.

Figure 10 vulcanizes for the judgement reaction dimensionless group cloud atlas that whether finishes induction period, and in the time of 27.54 seconds, pressure head begins to occur cross-linking reaction in sulfuration; In sulfuration 275.6 seconds the time, the pressure head bottom all begins cross-linking reaction; In sulfuration 482.6 seconds the time, the pressure head side all begins cross-linking reaction; In sulfuration 740.6 seconds the time, pressure head corner all begins cross-linking reaction, and this moment, whole pressure head all entered the cross-linking reaction heat cure stage.

Figure 11 is each time point rubber pressure head state of cure (vulcanization) cloud atlas, and at first the pressure head outside surface begins to occur cross-linking reaction, and in the time of 1510 seconds, the whole vulcanization reactions in pressure head bottom finish in sulfuration; When vulcanizing 2600 seconds, pressure head side vulcanization reaction end; In sulfuration 3720 seconds the time, pressure head corner vulcanization reaction finishes, and the state of cure (vulcanization) of the inner any point of whole pressure head this moment is all in 1 left and right, and vulcanization reaction is completed; Figure 12 is each time point rubber pressure head temperature cloud picture, and pressure head bottom temperature rise is the fastest, when vulcanizing 1200 seconds, temperature reaches more than 149.4 ℃, and the temperature variation of pressure head corner is the slowest, takes second place in the side, when sulfuration finished, the temperature of whole pressure head was all more than 149.4 ℃.

Figure 13 be the rubber pressure head in the bottom, the variation course of side and the unique point N2173 of corner, N2620 and N2404 temperature and state of cure (vulcanization) in sulfidation, the temperature of bottom characteristic point N2173 and state of cure (vulcanization) reach maximal value the earliest, sulfuration is completed at first, side unique point N2620 takes second place, and corner features point N2404 intensification is the slowest, and sulfuration is completed at last.

Figure 14 be the rubber pressure head in the bottom, the variation course of side and the unique point N2173 of corner, N2620 and N2404 curingprocess rate in sulfidation, the peak value of bottom characteristic point N2173 vulcanization reaction speed is maximum, time of occurrence the earliest, side unique point N2620 takes second place, the peak value of the vulcanization reaction speed of the unique point N2404 of corner is minimum, and time of occurrence at the latest.

Claims (1)

1. the method for a simulating vulcanization process of rubber product, it is characterized in that: the method comprises the steps:

A) by experimental measurement rubber flow varied curve, and measure and comprise at least half finished rubber, semi-finished rubber and the thermal physical property parameter of vulcanized rubber, provide test figure for setting up the hybrid dynamics model and characterizing the hot physical property of sizing material;

B) demarcate and determine initial state of cure (vulcanization) by K-R model and K-S models fitting, numerical value, setting up the hybrid dynamics model, and setting up expression coefficient of heat conductivity and specific heat capacity along with the hot physical property function of rubber of the variation of temperature and state of cure (vulcanization);

C) set up the heat transfer of rubber-chemical reaction coupled wave equation;

D) based on Newton iteration method, equation is carried out numerical evaluation;

E) obtain at least one physical parameter relevant to described vulcanization process of rubber product, described physical parameter comprises: temperature, state of cure (vulcanization), vulcanization reaction speed.

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