CN1280909A - Method of vulcanizing tyre using predetermined degree of vulcanization - Google Patents

Abstract

Method for vulcanizing a tire by predetermining a degree of vulcanization, comprising the steps of determining specified structural and dimensional parameters of the tire and of a vulcanization mould, determining the change over a time (t) of specified thermodynamic parameters of the tire, of the mould, of heat-supply fluids and of a cooling fluid, determining a parameter consisting of an equivalent vulcanization time t0, and determining an equivalent degree of vulcanization X(t0) at specified points within the tire by means of an equivalent isothermal rheometric curve at a reference temperature T0, comprising three consecutive sections having the following equations.

Description

Come tire curing method by pre-determining its state of cure (vulcanization)

The present invention relates to a kind of by pre-determining the next tire curing method of its state of cure (vulcanization).

In the tire production field,, multiple sulfuration kinetic model has been proposed in order to improve curing cycle.The temperature history of curing cycle generally is used to attempt improve sulfuration according to model.But, verified these models or too complexity or reliability are low.

The limitation that the objective of the invention is to avoid described problem and overcome known method.

On the one hand, the present invention relates to pre-determine the tire curing over time method of its sulfided state by the parameter of forming by its state of cure (vulcanization) by means of, but described tire comprises specific cured blend and specific fabric, described sulfuration is by means of by the sulfurizing mould of heat donor fluid heating and described tire is cooled off through specific cooling fluid carry out, and described method comprises the following steps:

A) determine the ad hoc structure and the dimensional parameters (geometry) of described tire and described mould,

B) determine variation, comprise the temperature T (t) and the diffusion coefficient α of described tire, mould, heat donor fluid and cooling fluid through time t particular thermal mechanics parameter,

C) determine one by equivalent vulcanization time t ₀The parameter of forming, it is at particular constant reference temperature T ₀In time, makes and might obtain an equivalent cure degree X (t ₀), described equivalent cure degree equals the state of cure (vulcanization) X (t) at particular moment t and time dependent specified temp T (t), described equivalent vulcanization time t ₀By described reference temperature T ₀, described temperature T (t) and described time t specific function obtain,

D) determine at described equivalent vulcanization time t ₀During variation at the described equivalent cure degree X (t of described inside tires specified point ₀), described equivalent cure degree X (t ₀) pass through at described reference temperature T ₀Equivalent isothermal flow varied curve obtain, described curve comprises having three continuous parts that establish an equation down:

Here, above-mentioned first equation is applicable to t ₀Be less than or equal to first specific equivalent time value (t ₀≤ t ₆₀) situation, at this first specific equivalent time, first specific equivalent cure degree (X (t is arranged ₆₀)=60%), above-mentioned the 3rd equation is applicable to t ₀More than or equal to second specific equivalent time value (t ₀〉=100%) situation is at this second specific equivalent time, to second specific equivalent cure degree value (X (t should be arranged ₁₀₀)=100% or 1), second above-mentioned equation is applicable to t ₀(t between first value of described equivalent time and second value ₆₀≤ t ₀≤ t ₁₀₀) situation,

Here, t _XXBe the 3rd specific equivalent time value, at described first (t ₆₀) and second (t ₁₀₀) centre between the equivalent time value, at the 3rd specific equivalent time, to the particular value (X (t of the 3rd equivalent cure degree should be arranged _XX)=90%),

Here, f (t ₀-t _XX) be a cube of interpolating function, for t ₀(t when being less than or equal to described the 3rd equivalent time value ₀≤ t _XX), f (t ₀-t _XX) equal 0, and work as t ₀(t in the time of between described the 3rd equivalent time value and described second equivalent time value _XX≤ t ₀≤ t ₁₀₀), it makes described function X (t ₀) pass through one by described equivalent cure degree (X (t _XX)) intermediate point formed of median, and end at second value X (t by described equivalent cure degree to have the horizontal tangent mode ₁₀₀) some place of forming,

Here, C equals 1-X _∞, X _∞Be the 4th asymptote value of described equivalent time value described equivalent cure degree when being tending towards infinity,

Here, by setting corresponding every couple of equivalent state of cure (vulcanization) value (X ₁, X ₂), according at a c) described program determines corresponding equivalent vulcanization time (t ₁, t ₂) and from each of above-mentioned three equations, obtain two equation systems that have three unknown numbers, determine every couple of above-mentioned parameter (n ₁, k ₁n _X, k _Xn _R, k _R).

Preferably, in described step b), determine described temperature (T) through the following steps:

B1) determine the FEM model of described tire and described mould by the grid (grid) that forms by particular finite element and node;

B2) by specific initial temperature and each above-mentioned node are combined definite initial boundary condition;

B3) determine in described sulfuration process over time and convection coefficient to the temperature of the described fluid of described mould heat supply;

B4) determine over time and convection coefficient in the temperature of cooling fluid described in the cooling procedure of described tire;

B5) adopt the Fourier heat transfer equation,, determine over time in the described temperature T (t) of described tire and described mould inside specified point by finite element model for solving.

For convenience, in step c), determine described equivalent vulcanization time t ₀Used described specific function is expressed as follows: $t_0\left(t\right)=\underset{0}{\overset{t}{\∫}}{e}^{a\frac{T\left(t\right)-T_0}{{\left(T\left(t\right)T_0\right)}^{\mathrm{\β}}}}\mathrm{dt}$

Here determine T (t), step b5 in front), the sample by every kind of mixture is at three specified temp (T _A, T _B, T _C) descend three isothermal rheograms of acquisition to determine α and β, each rheogram is represented as the variation of the moment of torsion S ' of the described mixture of the function of time and corresponding state of cure (vulcanization) (X _A(t); X _B(t); X _C(t)) variation is in above-mentioned three rheograms, with above-mentioned three temperature (T _A, T _B, T _C) and make described state of cure (vulcanization) from first particular value X ₁₁Change to second particular value X ₂₁Three incremental time (△ t _A, △ t _B, △ t _C), determine β by above-mentioned equation, with two said temperature (T _A, T _B) and above-mentioned three rheograms in two in two described incremental time (△ t _A, △ t _B) determine α.

Preferably, described method also comprises the following steps:

E) given above-mentioned state of cure (vulcanization) X (t ₀), determine the parameter that a moment of torsion S ' during by specified temp T forms by establishing an equation down:

S′(T，X)=S′ _min(T)+X*(S′ _max(T)-S′ _min(T))

Wherein ${\{}_{S_{\max }^{\′}\left(T\right)=S^{\′}(T,1)=S_{\max }^{\′}\left(T_0\right)+D_{\max }(T,T_0)}^{S_{\min }^{\′}\left(T\right)=S^{\′}(T,0)=S_{\min }^{\′}\left(T_0\right)+D_{\min }(T-T_0)}$

Wherein, S ' _Min(T ₀)=at described reference temperature T ₀Under minimal torque; S ' _Max(T ₀)=at described reference temperature T ₀Under peak torque; D _Min=S ' _MinDerivative with respect to described temperature T; D _Max=S ' _MaxDerivative with respect to described temperature T.

Preferably, for above-mentioned first equation, above-mentioned a pair of equivalent cure degree value (X ₁, X ₂) by X ₁=30%, X ₂=60% forms.

And then, for above-mentioned second equation, the value (X of above-mentioned a pair of equivalent cure degree ₁, X ₂) by X ₁=60%, X ₂=90% forms.

Preferably, for above-mentioned the 3rd equation, the value (X of above-mentioned a pair of equivalent cure degree ₁, X ₂) by X ₁=20%, X ₂=60% forms, and X's reduced to be set at X when t was tending towards infinity _R=100%.

The method according to this invention is basically based on the temperature history of-given boundary, finite element (FEA) model method of the variations in temperature by simulation inside tires every bit, determine Temperature Distribution in the tire and the functional relation of time, and-determine the distribution of consequential sulfided state by the sulfide model of in FEM model, realizing; Described sulfide model is made up of the program (program) of the described FEA model of a usefulness integration, uses state of cure (vulcanization) (X) model based on the rheological property of described mixture, determines the sulfided state of tire every bit when described program is pursued.

The method according to this invention needs following input data: the structure of-described tire and physical dimension; The thermodynamic characteristics of-described mixture; The physical dimension of-described mould and thermal conductivity;-cure time table; The cooling condition of-described tire.

Usually, described cure time table draws with form, and expression is to the parts of described mould, promptly sector (sector) and cheek (cheek) and any vulcanizing chamber or interior metal mould provide heat fluid temperature over time.Described fluid comprises the steam of heating sector (tyre surface), the steam of heating cheek (sidewall), the water or the inert gas of steam that vulcanizing chamber is inflated for the first time and the inflation second time of described vulcanizing chamber.

Described method provides following output data :-described temperature profile;-real and conventional state of cure (vulcanization) figure and associated Parameter Map (for example, equivalent time and moment of torsion).

In the method according to the invention, described FEA model also expands to described mould and described vulcanizing chamber.By being fixed on each temperature value that occurs on the described cure time table, therefore, described model can be provided in the correct temperature of the boundary of described tire.

Estimate sulfided state by state of cure (vulcanization) and have the advantage of using the parameter that does not rely on described mixture; When described state of cure (vulcanization) equaled 1, described sulfuration process was finished.

But, the shortcoming that depends on described mixture is arranged based on traditional criterion of the evaluation sulfided state of equivalent time.

The method according to this invention makes might adjust all parameters, especially the cure time table that influences described sulfuration process, regulates the cure time table usually and optimizes described sulfuration process.

Described method be a kind of reliably, flexibly and be familiar with the easy-to-use instrument of engineer (or process engineer) of sulfuration process.Described method provides information in the end-state of described sulfuration process and aspect changing two in time, and describes its feature in described tire construction inside in detail.This makes the engineer can find crucial problem also to propose the suggestion of dealing with problems.

To with the example and the accompanying drawing of the embodiment of non-limited way explanation the features and advantages of the present invention be described by example now, wherein:

The tire that Fig. 1 schematically illustrates a sulfurizing mould and wherein places with partial cross section, and according to FEA model divided into unit;

Fig. 2 is variation and the variation of the functional relation of time and state of cure (vulcanization) X thereof and the figure of the functional relation of time of moment of torsion S ' of the sample of a kind of rubber composition of expression;

Fig. 3 is the equivalent isothermal flow varied curve of determining with the method according to this invention;

Fig. 4 is illustrated under three different temperatures, a kind of variation of experiment flow varied curve of sample of rubber composition;

Fig. 5,6 and 7 is illustrated in a kind of experimental temperature distribution curve of three points of specific tires and the temperature distribution history of calculating;

Fig. 8,9 and 10 is illustrated in a kind of experiment and moment of torsion/time diagram calculating of some some place of specific tires;

Figure 11 and 12 states of cure (vulcanization) of representing with two kinds of definite tires of the method according to this invention;

Figure 13 and 14 is represented the state of cure (vulcanization) with the definite other two kinds of tires of the method according to this invention;

Figure 15 and 16 contains the sulfurizing mould of tire and the sectional view of tire;

The state of cure (vulcanization) that Figure 17 and 18 expressions are determined with the method according to this invention at the tire shown in Figure 15 and 16;

Fig. 1 represents to be used for the parts of the sulfurizing mould 1 of tire 2.Especially, top four/part of representing described mould.Mould 1 comprises sector 3, goes up cheek 4, vulcanizing chamber 5, sector clamping device 6 and cheek clamping device 7.Do not express down cheek, following cheek is the mirror image of cheek 4.

Usually, described mould obtains heat from a kind of fluid (normally steam), the passage that described fluid is flowed through and formed in described sector and cheek grip device, and direct contact with the outer surface of described mould (steam dome vulcanizing tank).

In inside, provide institute's calorific requirement and pressure for mould by one or more fluids (hot water of steam, pressurization, nitrogen, inert gas etc.).Between described fluid and described tire, can have also and can not have vulcanizing chamber.Also may use other interior metal mould, provide the mode of heat to provide heat to described interior metal mould with being similar to described mould and described cheek.

The example of representing the tyre vulcanization cycle below:

1. introduce saturated vapor (7 crust to described vulcanizing chamber; 170 ℃)=2 '

2. steam off is also introduced the hot water (25 crust, 200 ℃)=10 ' of pressurization

3. discharge=1 '

Amount to=13 '

4. introduce saturated vapor (15 crust to described vulcanizing chamber; 201 ℃)=5 '

5. steam off is also introduced the nitrogen (26 crust)=9 ' of pressurization

6. discharge=30 "

Amount to=14 ' 30 "

In both cases, by (for example, 175 ℃ of saturated vapors; 7.95 crust) described mold heated is arrived to fixed temperature.

Described steam can increase pressure gradually by choke valve, can have more than once exhaust (for example, be vented to one and add hydraulic circuit, then by being vented to for the second time a low tension loop, by being vented to atmospheric pressure for the third time).

A FEM model is applied to mould 1 and tire 2, simulates their behaviors in sulfuration process.

Described FEA is made up of following part: geometric description; Material is described; Primary condition at boundary; In the condition of boundary over time.

Described output provides temperature over time, and is as described below, determines the variation of sulfided state from described variations in temperature.

In order to carry out described geometric description, described FEA model is divided into three independently parts: mould 1, vulcanizing chamber 5 and tire 2.In these models, the outline of described tire is consistent with the interior profile of described mould, the interior profile of described tire consistent with the outline of described vulcanizing chamber (Fig. 1).

The finite element of determining by their layout by a cover and described three parts are described by the cover node that their space coordinates is determined each.Paired unit and node form the grid (grid) of described model.Node on the contact surface between two parts is separately-in other words, so described mould, chamber and tire do not have shared node-each part to determine its oneself specific primary condition.Fig. 1 represents from the grid of the two-dimentional unit formation of the axial symmetry that has 4 nodes.

Preferably, constructing described vulcanizing chamber grid on the original geometry size rather than on the physical dimension of inflation, before described heat is calculated, contact with the inner surface of described tire until it by calculate its inflation of simulation with independent FEA.This has guaranteed the more accurate distribution of the thickness of described chamber.In addition, in advance using near closeer grid (for example, described mould and surface of tyre that the chamber contact), on the contrary in respect of the zone of bigger thermograde, use the less grid (for example, at mould inside) of density in the zone that gradient is less with high thermal conductivity with the metal manufacturing.

In order to determine described Temperature Distribution, suppose that all heats provide from the outside, and supposition is owing to the heat of the chemical reaction generation of described sulfuration process can be ignored.So this is a heat transfer process of describing,, must determine the diffusion coefficient value of described mixture in order to characterize them.

Each part of described model is undertaken by the surface of two well-separated types with outside heat exchange, is promptly independently carrying out on the contact surface between grid and the outer surface.

Contact surface 8,9 and 10 (representing with thick line in the drawings) between described tire and described mould, between described tire and the described chamber, and, for the short part of being discussed, between described chamber and described mould.They have guaranteed the conduction between the part of two contacts, are characterised in that high thermal conductivity factor.When a part separates with one other component, can remove them.

Provide described outer surface by the face that is positioned at the unit on the described outer surface.They combine with convection coefficient, obtain heat by convection current from external fluid, represent with arrow 11,12 and 13 in Fig. 1, be positioned at described indoor and with die surface that described steam contacts on.

The material of the part of described model is described with thermal conductivity (k), specific heat (C) and density (ρ).

Material for through described sulfuration process for each point, is described in three isothermal flow varied curves of three different temperatures, and from these curves, finds out all parameters of the function of determining that X is used with the method according to this invention.

According to hot conduction phenomenon, utilize the Fourier heat transfer equation, by described finite element model for solving, determine described thermal conductivity and specific heat: $\frac{\mathrm{\&delta;T}}{\mathrm{\&delta;t}}=\mathrm{\&alpha;}(\frac{{\mathrm{\&delta;}}^{2}T}{\mathrm{\&delta;}{x}^2}+\frac{{\mathrm{\&delta;}}^{2}T}{\mathrm{\&delta;}{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="0012024900312.png"\; state="\{\{state\}\}">y</figure-callout>}}^2}+\frac{{\mathrm{\&delta;}}^{2}T}{\mathrm{\&delta;}{z}^2})-----\left(1\right)$

It is the function of diffusion coefficient α, is determined by following formula: $\mathrm{\&alpha;}=\frac{k}{\mathrm{C\&rho;}}-----\left(2\right)$

By giving the unit value (C=1, ρ=1) of constant specific heat and density, replace thermal conductivity k with diffusion coefficient α.

Directly in the laboratory, determine diffusion coefficient α,, determine the value of diffusion coefficient with the form of form because it not with temperature constant, varies with temperature.For example, be provided at two numerical value under the continuous temperature, and between them, make interpolation calculation.

Considered that various factors determines the diffusion coefficient of tyre surface.Described FEA model uses the axially unit of symmetry, and these axially only represent the groove that is positioned at the tyre surface on the circumference in the unit of symmetry.In order to consider to be positioned at the existence of horizontal groove and decorative pattern (sipe), the diffusion coefficient of the tyre surface mixture in the zone that influenced by these horizontal grooves and decorative pattern carries out described program by only revising.

When described tire was in described mould, the metal tape of sector penetrated tyre surface, obviously increased its average diffusion coefficient.But in cooling stage, described tire is in described mould outside, and the air that described groove and decorative pattern are lowered average diffusion coefficient occupies.So, depend on two diffusion coefficient value of a parameter (FIELD) by use, determined the diffusion coefficient that the condition with described boundary changes.When described tire was in described mould, described parameter was set at 0, and when described tire was in air, described parameter was set at 1.

The average diffusion coefficient of the average diffusion coefficient of mould-rubber " mixing " and air-rubber " mixing " is respectively applied for determines described two diffusion coefficients.

Determine as follows:

R _vThe area in=space (groove, decorative pattern) and the ratio of the gross area

R _pThe area of=solid section (piece, muscle) and the ratio of the gross area

α _aThe diffusion coefficient of=air

α _sThe diffusion coefficient of=mould (metal)

α _gThe diffusion coefficient of=rubber

Two average diffusion coefficients, mould-rubber (α _Sg) and air-rubber (α _Ag) provide by following formula respectively:

Wherein, described two ratio R _vAnd R _pThe gross area with the groove around getting rid of calculates, and R _v+ R _p=1.

In order to determine the diffusion coefficient of described fabric, the fact below allowing: what have metal cords contains fabric unit not only because the existence of described metal causes diffusion coefficient to increase, and owing to the particular orientation of described line (cord) has anisotropic diffusion coefficient.

For every kind of fabric, three diffusion coefficients on three main directions of described fabric are consistent:

α ₌=be parallel to the diffusion coefficient of described line

α ₊=on the thickness direction of described fabric perpendicular to the diffusion coefficient of described line

α _x=be parallel to the diffusion coefficient of described fabric face perpendicular to described line.

These have determined the quadrature component of diffusion coefficient.

Order:

V _gThe specific volume of=described rubber

V _f=1-V _gThe specific volume of=described line

α _fThe diffusion coefficient of=described line

α _gThe diffusion coefficient of=described rubber.

If the thickness of described line equals the thickness of described fabric, can think α ₌=α ₊So:

α ₌=α ₊=α _gV _g+α _fV _f????(4) ${\mathrm{\&alpha;}}_x=\frac{{\mathrm{\&alpha;}}_g{\mathrm{\&alpha;}}_f}{{\mathrm{\&alpha;}}_g{V}_f+{\mathrm{\&alpha;}}_f{V}_g}-----\left(5\right)$

If the thickness of described fabric, should be considered this difference greater than the thickness of described line and determine α _xAnd α ₊

Order:

The thickness of φ=described line

The thickness of the described fabric of H=

V _iThe inner specific volume (promptly in the thickness of described line) of=Φ/H

V _e=1-V _i=outside specific volume (specific volume of rubber outer)

S _f=V _f/ V _iThe ratio of the volume of=described line and internal volume

S _g=1-S _fThe ratio of=described rubber and internal volume; So

α=identical with (4)

For H=Φ, (6) are identical with (4), and (7) are identical with (5).

Give the diffusion coefficient on three characteristic directions that fix on described fabric, on the following column direction of described tire, determine described diffusion coefficient: circumference (3), meridian (2) and vertical (1), according to cutting angle θ, in other words, described cord is with respect to the inclination angle of circumference:

The inventor has been found that in order to optimize the thickness of vulcanizing chamber, might redesign the physical dimension and the grid of described chamber by the simulation by the varied in thickness of adjusting the acquisition of described thermal conductivity and specific heat in each case.

Use a cover symbol, wherein:

S _MBe the thickness of described model, S _RBe described actual (real) thickness,

k _MBe the thermal conductivity of described model, k _RBe described actual thermal conductivity,

C _MBe the specific heat of described model, C _RBe described true specific heat,

If R=S _M/ S _R, it is obeyed:

k _M=k _RR

C _M=C _RR

When the thickness of described chamber reduced, thermal conductivity increased, and simultaneously, considers reducing of described volume, and thermal capacitance also reduces.

Temperature when beginning in conjunction with the node of described model and described sulfuration process is determined primary condition.Described tire is set at room temperature, and is temperature when the described cycle begins when these parts are operated under usual conditions the temperature that described mould and described vulcanizing chamber are set.

The temperature of described chamber is set to the constant value at each node.With the similar sulfuration process of study condition in, the moment between a circulation and next circulation before described mould is closed is measured described value by experiment.As guidance, described value is approximately equal to half of described heating steam maximum temperature.

Yet, set the temperature of described mould in such a way, make that described temperature is variable in described mould.Though because the supply of steam is continuous, the inner surface of described mould is cooled when opening.Therefore,, set three initial temperatures at least for described vulcanizing chamber, promptly the temperature at sector place, on side panel vapor (steam) temperature, close the temperature of the described inner surface of eve measuring at described mould.Described temperature distributes in the integral body of described mould with the form of stable state circulation.According to a kind of effective method, separate described mould by removing described contact surface from the other parts of model, given boundary temperature, and adopt the stable state circulation to determine the temperature of described internal node, be in stable situation as described mould.Again activate described contact surface then and continue described simulation.

The temperature history of the fluid by the described surface of heating (or cooling) and the convection coefficient (film coefficient) of these fluids are determined the condition of described boundary.

Carry out described process with two steps: a sulfuration (curing) process, wherein, described tire is in described mould and cooling (solidifying the back) step, and in described cooling step, described sulfuration process continues in described mould outside.In each step, determine described temperature by described step being divided into the line integral that many enough little incremental times carry out, high accuracy is provided and does not too prolong described simulated time.

In described sulfuration (curing) step, perhaps direct given described temperature, the vapor (steam) temperature in described mould is constant, and perhaps the hygrogram of drawing by pointwise as the heat donor fluid of the function of time is determined described temperature.

Described convection coefficient is constant with respect to the numerical value at described mould place, and directly given.But described indoor, described fluid becomes steam (or N under some situation by water ₂), therefore, corresponding convection coefficient also changes.In this case, the figure that draws as the function of time by pointwise determines described convection coefficient to each point.

Carry out described cooling (solidifying the back) step by removing all contact surfaces to the mode of the heat supply of described tire with interruption.The temperature of ambient atmosphere, and convection coefficient are applicable to the whole outer surface of described tire.This coefficient depends on the mobility of described external fluid, so, may in zones of different, change: lower usually when non-moving air, as the bottom of groove and as described in the inner lining surface of tire.

If carry out described cooling in free atmosphere, described cooling remains on stationary temperature (a little more than room temperature); But, if carry out in hot box, described environment temperature raises in the described tire process of cooling, under this second kind of situation, with the numerical value of the described air themperature of each incremental adjustments, as the function of the insulative properties of the volume of the heat that leaves described tire, contained air and described case.

Finish at described sulfuration process, when described temperature reached insignificant numerical value, described cooling step stopped.

In the variation (output) of the point accounting temperature of unit, described variation of temperature also can be extrapolated to node.It can be represented with various numerical value, chart and distribution map.This is an important data cell, because it is used for determining state of cure (vulcanization) subsequently and helping the engineer to understand occurent phenomenon.It also can be used to verify described model, because it can be determined by experiment by thermocouple.In the method according to the invention, described sulfide model is a kind of semiempirical model of the rheological property based on the rubber composition of representing by the function relation curve of moment of torsion S ' and time t (Fig. 2).The curve of S ' is represented the elastic response of described mixture to described sulfuration process, and determines in the laboratory, for example MDR 2000 types (the Moving Die Rheometer) flow graph made from Monsanto.Described sulfuration process carries out under constant temperature and an isothermal flow varied curve is provided.

On by minimum of a value that S ' got and peaked basis, determine state of cure (vulcanization) (X).If research rheological curve (Fig. 2) will be found, the initial period (being called induction time) of the minimum steady state value S ' min of S ' maintenance therein, S ' began to be elevated to maximum S ' max afterwards.

State of cure (vulcanization) X at moment t is provided by following formula: $X\left(t\right)=\frac{S^{\&prime;}\left(t\right)-S_{\min }^{\&prime;}}{S_{\max }^{\&prime;}-S_{\min }^{\&prime;}}-----\left(9\right)$

This is a nondimensional numerical value.It uses moment of torsion S ' expression sulfided state:

For S '=S ' _Min, in other words, (moment t when the sulfuration beginning ₁), X (t)=0,

For S '=S ' _Max, in other words, (moment t when sulfuration finishes ₁₀₀), X (t)=1.

For the rheogram that increases and tend to a horizontal asymptote always, state of cure (vulcanization) (9) is suitable for.Yet more commonly, the moment of torsion S ' that is shaped as of described rheological curve reaches a maximum, reduces to being lower than described maximum height of level asymptote then.When described sulfuration process reduces part by this, be referred to as the process of reverting, in the described process of reverting, though sulfuration is finished, state of cure (vulcanization) is less than 1.

In order to adapt to this fact, the inventor has considered the state of cure (vulcanization) in the process of reverting: $X_R\left(t\right)=\frac{S_{\max }^{\&prime;}-S^{\&prime;}\left(t\right)}{S_{\max }^{\&prime;}-S_{\&infin;}^{\&prime;}}-----\left(10\right)$

And the time t that reverts _R:

t _R=t-t ₁₀₀????(11)

Here, t ₁₀₀Be that moment of torsion reaches maximum S '=S ' as previously mentioned _MaxThe time time, S ' _∞Moment of torsion when being described rheological curve convergence asymptote.

But this state of cure (vulcanization) definition has only the constant temperature process to carrying out on the small sample of laboratory to be suitable for.On the other hand, in the sulfuration process of tire, described process is always non-isothermal.

The method according to this invention provides the rule of the state of cure (vulcanization) variation that is suitable for for non-isothermal process.

It is directly related with temperature that the inventor observes the speed of sulfuration process, and proposed a function, and described process can be carried out under the different temperatures that will compare.

If carry out two isothermal vulcanization technologies on the mixture of same type, first is at reference temperature T ₀Under carry out, second is carried out in any temperature T, we can say at described reference temperature T ₀The following cure time t that carries out ₀Be equivalent to the time t that carries out under described second temperature T, its condition is in temperature T ₀Under moment t ₀State of cure (vulcanization) equal the state of cure (vulcanization) of the moment t under temperature T:

X(T ₀，t ₀)=X(T，t)

Usually use Arrhenius equation and Van ' t Hoff equation to determine described equivalent time.

The Arrhenius equation is as follows: $t_0\left(t\right)=\underset{0}{\overset{t}{\&Integral;}}{e}^{\frac{E_0}{R}{(\frac{1}{T_0}-\frac{1}{T\left(t\right)})}_{\mathrm{dt}}}$

Here, described temperature is represented with kelvin degree, E _aBe the activation energy of mixture, R is the aerodynamic force mathematic(al) constant; Activation energy is the characteristic value of every kind of mixture, is determined by experiment with two isothermal flow varied curves under the different temperatures.

Van ' t Hoff equation is as follows: $t_0\left(t\right)=\underset{0}{\overset{t}{\&Integral;}}{2}^{\frac{T\left(t\right)-{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="0012024900341.png"\; state="\{\{state\}\}">T</figure-callout>}}_0}{\mathrm{\&theta;}}}\mathrm{dt}$

Here, θ makes the described cure time required temperature difference that reduces by half.

By the experiment of carrying out with flow graph, the inventor has been verified do not have strict obey described two rules any, first rule is more accurate for some mixture, and second rule is more accurate to other mixture.Yet they have found that is shown in a following more accurate conversion rule, are used for determining described equivalent time t ₀: $t_0\left(t\right)=\underset{0}{\&Integral;}{e}^{\mathrm{\&alpha;}\frac{T\left(t\right)-T_0}{{(T\left(t\right)\&CenterDot;T_0)}^{\mathrm{\&beta;}}}}\mathrm{dt}----\left(12\right)$

Here, make α=E _a/ R, β=1 obtains the Arrhenius equation; Make α=(log2)/θ, β=0 obtains Van ' t Hoff equation.

Use this conversion rule (12) in the method according to the invention.

In order to determine the factor alpha and the index β of conversion rule (12), three isothermal rheograms of the sample acquisition of specific mixture are for example used in utilization, as shown in Figure 4.

By concrete given state of cure (vulcanization) interval (scope) (X ₁₁, X ₂₁) and on described three figure, measure and make state of cure (vulcanization) from X ₁₁Change to X ₂₁Corresponding incremental time (△ t _A, △ t _B, △ t _C) determine index β.Different with β, factor alpha is determined with the numerical value of two temperature.

Make T _A, T _B, T _CThree temperature for described rheogram make △ t _A, △ t _B, △ t _CBe three corresponding temperature intervals.

Provide:

We obtain:

Because found through experiments described equation is not irrelevant with the time, so, depend on state of cure (vulcanization) by a jump function setup parameter α.In reality is carried out, be calculated as follows:

Be used for the single β value of whole rheogram in 0.3≤X≤0.6, interval,

With in 0.0≤X≤0.3 at interval

0．3≤X≤0．6

0．6≤X≤XX

In three α values,

Here XX is that a designated value makes 0.9≤XX≤1.0.

The other parts that also are used for described rheogram for the α value of last interval calculation.

In order to calculate β (β is along with the variation of X is constant), suppose:

X ₁₁=30%, X ₂₁=60%, in other words:

△t _A=t ₆₀(T _A)-t ₃₀(T _A)

△t _B=t ₆₀(T _B)-t ₃₀(T _B)

△t _C=t ₆₀(T _C)-t ₃₀(T _C)。

In order to calculate α (α changes with the variation of X):

For 0≤X≤30%, described designated value is X ₁₁=0%, X ₂₁=30%

For 30%≤x≤60%, described designated value is X ₁₁=30%, X ₂₁=60%

For X＞60%, described designated value is X ₁₁=60%, X ₂₁=XX%, (wherein, 90%≤XX%≤100%) XX% here select (for example, XX% is set at 90%) according to engineer's judgment.

The method according to this invention is applied to the sulfuration process of variable temperature, and based on above-mentioned conversion rule (12), the diagram method (Fig. 3) of the equivalent isothermal flow varied curve under given reference temperature.Determine described state of cure (vulcanization) with described equivalent isothermal flow varied curve.

Provide each state of cure (vulcanization) X of t constantly by following relationship:

X(t)=X(t ₀)

Here, determine equivalent time t by above-mentioned conversion rule (12) ₀

The inventor has been divided into three continuous parts to described rheological curve, is made up of two major parts that a coupling part connects, and they establish an equation under having:

Here, first equation is applicable to t ₀≤ t ₆₀, here, t ₆₀Be equivalent cure degree X (t ₆₀The equivalent time of)=60% o'clock; Second equation is applicable to t ₆₀≤ t ₀≤ t ₁₀₀, here, t ₁₀₀Be equivalent cure degree X (t ₁₀₀The equivalent time of)=100% or 1 o'clock; The 3rd equation is applicable to t ₀〉=t ₁₀₀

In equation (15) system, t _XXBe at t ₆₀And t ₁₀₀Middle numerical value is at t _XXThe place, the equivalent cure degree is X (t _XX)=90% (X (t _XX) corresponding to above-mentioned numerical value XX%); F (t ₀-t _XX) be an interpolating function, t ₀≤ t _XXThe time equal 0, for t _XX≤ t ₀≤ t ₁₀₀, f (t ₀-t _XX) pass through by equivalent cure degree X (t _XX) intermediate point formed and flatly end at (the t by equivalent cure degree X ₁₀₀) form a bit.For example, f (t ₀-t _XX) be a cubic function.At last, C equals 1-X _∞, here, X _∞It is the asymptotic value of t state of cure (vulcanization) when being tending towards infinity.

First equation is made up of a known Isayev-Deng equation, and second equation and the 3rd equation are found by the inventor.Wherein, the 3rd equation is made up of the equation that is similar to the Isayev-Deng equation, but through transforming, change in proportion and having put upside down; Second equation connects equation by one and forms, and it provides the continuity with other two equations.

For the equivalent isothermal flow varied curve that under given reference temperature, draws, in equation (15) system, determine t ₀≤ t ₆₀The a pair of parameter n of (start-up portion), k, t _6.≤ t ₀≤ t ₁₀₀The a pair of parameter n of (interpolation part) _X, k _X, t ₀〉=t ₁₀₀The a pair of parameter n of (part of reverting) _R, k _R

For described part each, set corresponding a pair of equivalent cure degree (X ₁, X ₂).For example, for start-up portion, use a logarithm value 30% and 60%; For described interpolation part, use a logarithm value 60% and an XX%; For returning part, use a logarithm value X _R=20% and X _R=60%, and the decay X of t X when being tending towards infinity _RBe set at 100% (X _RCalculate with relation (10)).

For each to (X ₁, X ₂), determine corresponding equivalent vulcanization time (t ₁, t ₂).Usually can not draw at the rheological curve of equivalent temperature,, determine the described time from the figure that draws for different temperatures with above-mentioned conversion rule (12).

In order to determine every couple of above-mentioned parameter (n, k; n _X, k _Xn _R, k _R), two equation systems of two unknown numbers of each acquisition of utilization from three equations (15).For example, begin to determine the value of index n, obtain the value of coefficient k then.This be because, in case determined n, single point, for example (a t ₁, X ₁) be enough to be used in determining k.

Especially, following system: ${\{}_{x_2=\frac{k{t}_2^n}{1+k{t}_2^n}}^{x_1=\frac{k{t}_1^n}{1+k{t}_1^n}}$

Be used for index access n and coefficient k:

Equation (16) and (17) also are used to determine the n partly that reverts _RAnd k _R, consider with the state of cure (vulcanization) in the part of reverting of equation (10) expression.

In order to determine described contiguous function, in other words, second equation of system (15), the district is (Fig. 3): t in two kinds of situation _XX=t ₂Situation and t ₂＜t _XX＜t ₁₀₀Situation.

Under first kind of situation, the rising part of rheological curve passes through by t ₁, t ₂And t ₁₀₀Three points of expression; Under second kind of situation, it also passes through at t ₂And t ₁₀₀Between the 4th some t _XX

Under first kind of situation, suppose n _X=n and k _X=k.

Under second kind of situation, equation (16) button (17) is used for determining by (t ₂, X ₂) and (t _XX, X _TXX) first of second equation (15).

For negative t=t _XX, Equation f (t-t _∞) equal zero, and for example, be the cubic function part, have at t _XXAnd t ₁₀₀Between the extreme value tangent line of two branches. $f(t-t_{\mathrm{XX}})={{\{}^0}_{c_2{(t-t_{\mathrm{XX}})}^2+c_3{(t-t_{\mathrm{XX}})}^3}-----\left(18\right)$

Described cubic function correction first of second equation (15), make it for t=t ₁₀₀Sentencing the horizontal tangent value is 1, at t=t _XXThe place is the tangent line of itself.So described cubic function and its derivative are at t=t _XXThe place is zero.By being set in t ₁₀₀The condition at place is determined the coefficient c of described connection cubic function ₂And c ₃If X ' expression X is about the derivative of time, X _X(t) and X ' _X(t) represent the first and the derivative thereof of described equation respectively. ${\{}_{X^{\&prime;}\left(t_{100}\right)=0=X_X^{\&prime;}\left(t_{100}\right)+2c_2(t_{100}-t_{\mathrm{XX}})+3c_3{(t_{100}-t_{\mathrm{XX}})}^2}^{X\left(t_{100}\right)=1=X_X\left(t_{100}\right)+c_2{(t_{100}-t_{\mathrm{XX}})}^2+c_3{(t_{100}-t_{\mathrm{XX}})}^3{}_{}}$

Given z=t ₁₀₀-t _XX

A=1-X _X(t ₁₀₀)

D=-X’ _X(t ₁₀₀)

We obtain: ${\{}_{c_3\frac{\mathrm{zD}-2A}{z^3}}^{c_2=\frac{3A-\mathrm{zD}}{z^2}}-----\left(19\right)$

In Fig. 3, first section of the extended line of the first of curve X (t) and second part dots outside its domain of definition end.

For example, as previously mentioned, suppose:

For first,

t ₁=t ₃₀, make X ₁=X (t ₁)=0.3

t ₂=t ₆₀, make X ₂=X (t ₂)=0.6

And, for the part that returns,

t ₁=t ₁₂₀, make X _1rev=K _R(t ₁)=0.2

t ₂=t ₁₆₀, make X _2rev=X _R(t ₂)=0.6

For the coupling part, select t _XXValue makes it accurately duplicate empirical curve.Especially, use t _XX=t ₉₀, make X (t ₉₀)=0.9.

Can use method of the present invention to determine the moment of torsion S ' (component of elasticity) of non-isothermal flow varied curve, so, make and might verify described sulfide model, because S ' is the numerical value that can measure by experiment.

Have good being similar to, S ' depends on state of cure (vulcanization) X, depends on the temperature that is reached, and linearity reduces with the latter's rising.

For the definition of state of cure (vulcanization) X (equation (9)), for the temperature T of a broad sense, moment of torsion S ' is with following The Representation Equation:

S′(T，?X)?=?S′ _min(T)+X*(S′ _max(T)-?S′ _min?(T))????????????????(20)

Here: ${\{}_{S_{\max }^{\&prime;}\left(T\right)=S^{\&prime;}(T,1)=S_{\max }^{\&prime;}\left(T_0\right)+D_{\max }(T-T_0)}^{S_{\min }^{\&prime;}\left(T\right)=S^{\&prime;}(T,0)=S_{\min }^{\&prime;}\left(T_0\right)+D_{\min }(T-T_0)}$

Wherein, S ' _Min(T ₀)=at reference temperature T ₀Under minimal torque; S ' _Max(T ₀)=in temperature T ₀Under peak torque; D _Min=S ' _MinDerivative about temperature T; D _Max=S ' _MaxDerivative about temperature T.

Given reference temperature T ₀, determine the peak torque under reference temperature and the numerical value and the corresponding slope of minimal torque from the peak torque of two rheological curves and minimal torque value and corresponding temperature.

So in the method according to the invention, above-mentioned finite element (FEA) model has obtained temperature distribution in time in the tire in sulfuration process, and can determine the state of cure (vulcanization) that in the curing cycle of described tire, reaches with the sulfide model of wherein realizing.

In practice, determine the sulfided state of described tire at each point place by the program (program) of a separated into two parts (i.e. a variable part and a constant portion).First is made up of a collection of input data that are described in the rheological behavior of mixture used in the model of being studied; Second portion can be used for determining to follow the time dependent sulfided state of temperature and provide by state of cure (vulcanization) and can being used to analyzing the output data that the parameter of described process is formed.These two parts are as described below.

In first part of described program, determined following variable: the quantity of-listed material;-be used for determining equivalent time t ₀Reference temperature (T ₀) (default value is 151 ℃);-with reference to state of cure (vulcanization) X _REF, equivalent time is associated, obtains standardized time value (default value is 0.9).

For each mixture, the variable of given its rheological behavior of description.Especially, describe the rheological curve of two risings, and use the mixture sample to be determined by experiment the rheological curve that returns part for two temperature.Also provide the index β of equation (12) or at two points of the rheological curve of medium temperature.Described rheological curve is determined by three points: for rising part, provide with state of cure (vulcanization) be 30%, 60% and the corresponding time of XX% (wherein 60%＜XX%＜100%); For returning part, state of cure (vulcanization) (X provides and reverts _R) be 0%, 20% and 60% corresponding time.

Determine following parameters: the title of-described mixture ,-for described first-class varied curve (at a lower temperature): temperature (for example 140 ℃); Minimal torque; Peak torque; The time of X=30%; The time of X=60%; The time of X=XX%;-for described second rheological curve (under higher temperature): temperature (for example the tire of extra large size is 160 ℃, is 180 ℃ for tyres for passenger cars); Minimal torque; Peak torque; The time of X=30%; The time of X=60%; The time of X=XX%; Rheological curve for recurrence: temperature (for example the tire of extra large size is 160 ℃, is 180 ℃ for tyres for passenger cars); Minimal torque in the regression process; Peak torque in the regression process; X _R=0% time; X _R=20% time; X _R=60% time;-in order to determine index β, provide thermal profile: temperature (for example 151 ℃); The time of X=30%; The time of X=60%.Second part of described program provides following output data:

(this is the basis of determining state of cure (vulcanization) X to the equivalent time of SV1=under reference temperature; It has and the advantage that is illustrated in the time correlation that reaches the X=1 post consumption, though it has the shortcoming that depends on described mixture);

SV2=is at reference state of cure (vulcanization) X _REFUnder the standardization equivalent time (by the equivalent time that is reached with corresponding to reference state of cure (vulcanization) X _REF, for example equal 0.9, equivalent time between ratio obtain, be higher than describedly with reference to state of cure (vulcanization), begin to think that state of cure (vulcanization) is good; It has the advantage that does not rely on described mixture);

SV3=at the standardization equivalent time of X=100% (in this case, with reference to state of cure (vulcanization) X _REFEqual 1, this is different from standardization equivalent time SV2);

The conventional state of cure (vulcanization) of SV4=(this is used for, and expression has surpassed described maximum sulfuration value on described figure, for X≤1, and by equation (9) definition, for X 〉=1 (situation of reverting), by

(this is the moment of torsion S ' corresponding to the state of cure (vulcanization) of calculating on the rheogram under the described Current Temperatures and measuring to the SV5=moment of torsion; It can be used for the described result of calculation of experimental verification);

SV6=logarithm standardization equivalent time equals log (SV2);

SV7=logarithm standardization equivalent time equals log (SV3);

The actual state of cure (vulcanization) of SV8=(is determined by equation (9); Can be used for the functional arrangement of time on represent any situation of reverting immediately).

Begin the second portion of described program by the relevant data of point of collecting the unit of studying with current time from finite element FEA model, particularly, the output data of calculating in the title of temperature, mixture, incremental time, the increment in front (SV1, SV2, SV3, SV4, SV5, SV6, SV7, SV8).Described program provides the output data of upgrading.

When the second portion of described program was carried out for the first time, described first read in the data of all mixtures that store in the history file, and every kind of mixture is determined to calculate subsequently required coefficient.After this, when carrying out the second portion of described program, carry out following continued operation:

The identification of the parameter of-described mixture;

-determine equivalent time (SV1) and all other variablees that can from then on obtain;

-determine described standardization equivalent time (SV2, SV3, SV6, SV7);

-determine conventional state of cure (vulcanization) (SV4);

-determine actual state of cure (vulcanization) (SV8);

-determine the moment of torsion (SV5) of actual state of cure (vulcanization).

An auxiliary subprogram (subprogram) makes it need not calculate the characteristic parameter of mixture when carrying out said procedure.Described auxiliary routine reads in the first of described program the data by raisonne every kind of mixture, and all these data are once changed (conversion) becomes reference temperature.Then they are converted to the calculating desired parameters, make it can be used for subsequently processing.Described parameter is:

The coefficient of equation (12), in other words, the factor alpha of 0.0＜X＜0.3; 0.3 the factor alpha of＜X＜0.6; 0.6 the factor alpha of＜X; Index β; (calculating β by equation (13)) by equation (14) alpha value calculated;

The equivalent isothermal flow varied curve X=X (t at described reference temperature place is described ₀) coefficient of (15), in other words, for the coefficient k of the first of 0.0＜X≤0.6 described curve; Index n for the first of 0.0＜X≤0.6 described curve; Coefficient k for the second portion of 0.6＜X≤described curve of XX _XIndex n for the second portion of 0.6＜X≤described curve of XX _XThe coefficient c that connects cubic function ₂The coefficient c that connects cubic function ₃The coefficient k of the part of reverting of described curve _RThe index n of the part of reverting of described curve _R

Equivalent time T30 makes X (T30)=0.3;

Equivalent time T60 makes X (T60)=0.6;

Equivalent time TRF makes X (TRF)=X _REF

Equivalent time TXX makes X (TXX)=XX (0.6＜XX≤1);

Equivalent time TMX makes X (TMX)=1;

Minimal torque TQN under the described reference temperature;

Derivative DMN as the minimum of a function moment of torsion of temperature;

Peak torque TQX under the described reference temperature;

Derivative DMX as the peak torque of the function of temperature;

The ratio R XR of X in reverting (△ TQ _Revert/ △ TQ _Raise).

If there is not the β value in data block, it is determined with equation (13); Use equation (14) to determine three values of α then.

Rheological curve under the above-mentioned low temperature is determined equivalent time T30, T60 and TXX by the integration of equation (12).

Integration by equation (12) is determined equivalent time TMX.In order to accomplish this point, need be from t ₀The heating curve (in other words, since the zero-time) of beginning.Setting has only t for the curve that reverts ₁₀₀Be known, by in equation (12), inserting following numerical value, from T30, T60 and TXX, initial definite data (t that is lacked ₃₀, t ₆₀, t _XX): T ₀The temperature of=the curve that reverts and T=reference temperature.In equation (12), insert T specifically ₀=reference temperature is calculated TMX then.Continue integration, calculate the equivalent time (X of other two points of the described curve that reverts _R=20% and X _R=60%).

As mentioned above, use, determine the coefficient and the index of equation (15) by formula (16) and (17) in the X of two somes value and time, and the parameter n of the time (TMX, TXX) of use extreme point and curve to be connected _XAnd k _X, determine the coefficient c of described connection cube curve by formula (19) ₂And c ₃

Given described reference temperature, the minimal torque by two rheological curves and the numerical value of peak torque and corresponding temperature are determined minimal torque and peak torque and their derivative (slope) in described reference temperature, (TQN, DMN, TQX and DMX).

Ratio R XR is the coefficient C=(1-X of the 3rd equation (15) _∞).In order to determine this value, at first determine the S ' in the process of reverting _MinAnd S ' _Max, remove the maximum decrease of S ' in the process of reverting then with their difference.

For the reference value of X, determine equivalent time TRF by inverting of function X=X (t).

The parameter that characterizes described mixture is confirmed by the name of described mixture.

Determine the equivalent time increment from incremental time with by the temperature that described FEA model provides.In the time increase process of setting, it is constant that described temperature keeps.

Identity basis method of the present invention is reliably, and wherein, it is the variations in temperature of playback experiment mensuration accurately, and is successfully used in the various actual conditions, comprises the thickness of optimization timetable and selection vulcanizing chamber.

The inventor has carried out the confirmatory experiment of the inventive method, especially for the checking of the program of the FEA verification of model of determining temperature and definite sulfided state.

For first kind of checking, vulcanize experiment, by inserting the variations in temperature of thermocouple measurement at some important point of tire.The lip-deep temperature of the mould of measuring the variations in temperature of fluid (steam and water) simultaneously and contacting with described tire to the mould heat supply.In order to be the correct primary condition of described FEA model specification, measure a moment before inserting the raw material tire on the surface at vulcanizing chamber and the temperature of mould.

By (water temperature and steam) setting measurement condition and by require the variations in temperature at the identical experiment measurement point, the FEA model that is configured to contrast in output place on described border.

Fig. 5,6 and 7 is illustrated in the experimental temperature curve of three points of P3000 175/65 R14 tire and the comparison between the accounting temperature curve.As can be seen, the difference between the temperature curve of described experimental temperature curve and calculating is very little.

For second kind of checking, allow the following fact, unique parameter of the experimental data that is used to obtain is that as previously mentioned, moment of torsion S ' records by the MDR2000 flow graph with variable heating curve experiment.The heating curve that records by experiment on a kind of tire (or calculating with described FEA model) is used for verifying described temperature and interrelates with different mixtures.Same curve is incorporated in the described program, is used for directly or calculates and determine sulfided state by carrying out FEA on the single unit.Fig. 8,9 and 10 represents for the moment of torsion/time diagram experiment of some point of P6000 205/60 R15 tire and that calculate.When contrast experiment and calculated curve, described as can be seen very gratifying as a result the time.

Provide some embodiment that uses the method according to this invention below:

Embodiment 1

Verify that its rheological behavior is different from a kind of state of cure (vulcanization) of mixture of the characteristic of design.

Usually in tire production, use and have the mixture that is different from the rheological behavior of developing characteristic.For example, the sulfuration dynamics of using the natural rubber from Thailand to produce in band coat with rubber mixture (AMET) is considerably slower than usefulness and contains the sulfuration dynamics that produces in the mixture from Malay natural rubber.Though this is unimportant in " length " curing cycle, when described curing cycle was reduced to minimum technical feasibility degree, described slower mixture became unacceptable.

Figure 11 and 12 expressions are for two kinds of P3000 tires, and the result with the method according to this invention obtains uses 10 ' 00 " the cure time table, and a kind of AMET with two kinds of various flows varied curves, a kind of is at 151 ℃, t ₉₀=19 ' (Figure 11), another kind of at 151 ℃, t ₉₀=28 ' (Figure 12).Can observe (t under first kind of situation ₉₀=19 '), described band coat with rubber mixture 20 is in about 90% state of cure (vulcanization), and with the slow mixture of glue, at band edge 21 about 75%, even also be no more than 80% at more not crucial point 22.

Embodiment 2

Determine " the best " curing cycle by material modification.

Chemistry one physical analysis (solidifying the back) by sulfuration, discovery follows the minimizing of controlling the machine cycles of cooling off can not obtain the obvious minimizing of the over cure of described rubbery mixture (especially carcass) under the situation of tyres for passenger cars (P6000 205/60R15) subsequently.Therefore developed more stable band and carcass rubbery mixture, and calculated " the best " circulation by the method according to this invention.Verify result of calculation then by experiment.

Figure 13 is illustrated in above-mentioned P6000 tire institute in 14 ' circulation and n.p. (ordinary production) material and reaches final state of cure (vulcanization) level (30-32).

Figure 14 represents that above-mentioned P6000 tire is 12 ' 00 " circulation in the final state of cure (vulcanization) (33-38) that reached.

Embodiment 3

Employing reduces the described curing cycle of thickness optimization of described vulcanizing chamber.

The inventor has been found that under the situation that described vulcanizing chamber thickness reduces (from 6 to 4.5mm), and the simple shortening of circulation timei is not enough to optimize the state of cure (vulcanization) at described tire difference.The inventor can be at 3 of cure time table ⁴" the best " circulation is determined in the recurrence of carrying out on=81 the FEA analog result.

Use following independent variable:

1. the temperature of described mold heated steam (175 ℃, 180 ℃, 185 ℃),

2. the temperature of described cheek heating steam (170 ℃, 175 ℃, 180 ℃),

The time of the initial inflation process of carrying out with steam (180 ", 210 ", 240 "),

Total cycle time (10 ' 45 ", 11 ' 15 ", 12 ' 00 ").

Carry out determining of 81 kinds of situations, by the statistics program result, the concrete total time of generation is 10 ' 45 " curing cycle, with ordinary production 11 ' 15 " different.In the curing cycle of described optimization, the initial inflation process time is reduced to 3 ' 45 from 4 ' ", the temperature of cheek heating steam is reduced to 165 ℃ from 173 ℃.The circulation of optimizing has reappeared with the approaching state of cure (vulcanization) of ordinary production and has limited too much undue sulfuration.On the other hand, the simple shortening of described circulation can not solve described problem, still, undesirably produces undue sulfuration, and is as shown in table 1.

The result of the gained that table 1 expression is represented with the standardization equivalent time (t of equivalent time/151 ℃ ₉₀).

Table 1

The part of tire	Ordinary production circular chamber: 6mm	Optimize circular chamber: 4.5mm	The circular chamber that shortens: 4.5mm only
				Tire tread: outside	2．06	?1．89	?2．00
Tire tread: shoulder	1．98	?1．93	?2．08
				Band: under groove	1．53	?1．65	?1．75
Band: shoulder	1．50	?1．66	?1．80
				Carcass: shoulder	2．97	?3．38	?3．56
Carcass: sidewall	4．48	?4．01	?4．98
				Carcass: tyre bead	4．47	?4．52	?5．29
Carcass: rim strip	3．59	?3．13	?4．00
				Bead filler	2．76	?2．44	?3．21
Wear-resistant surface	2．28	?1．64	?2．29
				Sidewall	2．17	?1．54	?2．13

Embodiment 4

Analyze doughnut 50 with the method according to this invention, be called P6000, the 205/60R15 level, state of cure (vulcanization) or state of cure (vulcanization) (Figure 15 and 16), Figure 15 is illustrated in the tire 50 in the described sulfurizing mould; Figure 16 represents the tire 50 made.

Described P6000 205/60 R15 tire has following composition: tyre surface 51; The cord ply 52 (0 ° of band) that has rayon cord; The tyre 53 that has the steel cord; Have the steel cord in be with 54; The carcass 55 that has rayon cord; Liner 56; Bead filler 57; The edge 58 that has rayon cord; Rub resistance face 59; Sidewall 60.

Figure 17 represents to optimize by method of the present invention, the state of cure (vulcanization) (61-65) of the P6000 205/60 R15 tire that obtains with the ordinary production curing cycle, and Figure 18 represents the area (70,71) of correct sulfuration and undervulcanization area (73).

Use following cure time table.

In described vulcanizing chamber:

1. the saturated vapor that is introduced in 187 ℃ continues 3 ' 45 ".

2. the superheated water that is introduced in 203 ℃ continues 9 ' 15 ".

3. discharge 1 '.

Amount to 15 '

Mould: sector, the steam cheek that constant temperature is 180 ℃, the steam that constant temperature is 160 ℃.

Claims (7)

1. the vulcanization process of tire (2), comprise by means of the parameter of forming by its state of cure (vulcanization) by pre-determining its sulfided state over time, described tire (2) comprises specific vulcanizable mixture and specific fabric, described sulfuration is by means of carrying out described tire (2) cooling by the sulfurizing mould (1) of employing heat donor fluid heating and by specific cooling fluid, and described method comprises the following steps:

A) determine the ad hoc structure and the dimensional parameters (geometry) of described tire (2) and described mould (1),

B) determine variation, comprise the temperature T (t) and the diffusion coefficient α of described tire (2), mould (1), heat donor fluid and cooling fluid through time t particular thermal mechanics parameter,

C) determine one by equivalent vulcanization time t ₀The parameter of forming, it is at the reference temperature T of particular constant ₀Make and to obtain an equivalent cure degree X (t ₀), described equivalent cure degree X (t ₀) equal the state of cure (vulcanization) X (t) that locates to obtain at particular moment t and time dependent specified temp T (t), described equivalent vulcanization time t ₀By described reference temperature T ₀, described temperature T (t) and described time t specific function obtain,

D) determine at described equivalent vulcanization time t ₀During variation, the described equivalent cure degree X (t of the specified point in described tire (2) ₀), described equivalent cure degree X (t ₀) pass through at described reference temperature T ₀Utilize equivalent isothermal flow varied curve to obtain, described curve comprises that three have the continuous part that establishes an equation down:

Wherein, above-mentioned first equation is applicable to t ₀Be less than or equal to first specific equivalent time value (t ₀≤ t ₆₀) situation, at described equivalent time value place, to first particular value (X (t of equivalent cure degree should be arranged ₆₀)=60%), above-mentioned the 3rd equation is applicable to t ₀More than or equal to second specific equivalent time value (t ₀〉=t ₁₀₀) situation, at described equivalent time value place, to second particular value (X (t of equivalent cure degree should be arranged ₁₀₀)=100% or 1), above-mentioned second equation is to be used for t ₀(t between described first and second value of described equivalent time ₆₀≤ t ₀≤ t ₁₀₀) situation, wherein, t _XXBe the 3rd specific equivalent time value, at described first (t ₆₀) and second (t ₁₀₀) between the equivalent time value, at described the 3rd specific equivalent time value place, to the 3rd particular value (X (t of an equivalent cure degree should be arranged _XX)=90%),

Wherein, f (t ₀-t _XX) be a cube of interpolating function, for t ₀Be less than or equal to described the 3rd equivalent time value (t ₀≤ t _XX) situation, f (t ₀-t _XX) equal 0, and for t ₀(t between described the 3rd equivalent time value and described second equivalent time value _XX≤ t ₀≤ t ₁₀₀) situation, f (t ₀-t _XX) make function X (t ₀) by described median (X (t by the equivalent cure degree _XX)) intermediate point formed and end at by described second equivalent cure degree value X (t to have the horizontal tangent mode ₁₀₀) the some place that forms,

Wherein, C equals 1-X _∞, X _∞Be the 4th, asymptote value of the equivalent cure degree of described equivalent time value when being tending towards infinity, wherein, by setting corresponding a pair of equivalent cure degree value (X ₁, X ₂), by at c) the described program of point determines corresponding equivalent vulcanization time (t ₁, t ₂), and from each of above-mentioned three equations, obtain two equation systems with three unknown numbers, determine that each is to above-mentioned parameter (n, k; n _X, k _Xn _R, k _R).

2. according to the method for claim 1, it is characterized in that in described step (b), determine described diffusion coefficient (α) and temperature (T) through the following steps:

B1) by determine the FEM model of described tire (2) and described mould (1) from the grid (grid) of particular finite element and node formation;

B2) determine the initial boundary condition by specific initial temperature with the combining of each in the above-mentioned node,

B3) determine in described sulfuration process over time and convection coefficient the temperature of the described fluid of described mould (1) heat supply,

B4) determine over time and convection coefficient in the temperature of cooling fluid described in the cooling procedure of described tire (2),

B5),, determine over time in the described temperature T (t) of the inner specified point of described tire (2) and described mould (1) by finite element model for solving by means of the Fourier heat transfer equation.

3. according to the method for claim 1 or 2, it is characterized in that in step c), determining described equivalent vulcanization time t ₀Used described specific function is expressed as follows: $t_0\left(t\right)=\underset{0}{\overset{1}{\&Integral;}}{e}^{a\frac{T\left(t\right)-T_0}{{\left(T\left(t\right)T_0\right)}^{\mathrm{\&beta;}}}}\mathrm{dt}$

Wherein, at above-mentioned steps b5) in determine T (t), the sample by every kind of mixture is at three specified temp (T _A, T _B, T _C) three isothermal rheograms obtaining determine α and β, each rheogram is represented as the variation of the described mixture moment of torsion S ' of the function of time and corresponding state of cure (vulcanization) (X _A(t); X _R(t); X _C(t)) variation by means of above-mentioned equation, is used above-mentioned three temperature (T in above-mentioned three rheograms _A, T _B, T _C) and make state of cure (vulcanization) from first particular value X ₁₁Change to second particular value X ₂₁Three incremental time (△ t _A, △ t _B, △ t _C) determine β, by above-mentioned equation, use two (T in two the said temperature in above-mentioned three rheograms _A, T _B) and two (△ t of described incremental time _A, △ t _B) determine α.

4. according to the method for claim 1, it is characterized in that it also comprises the following steps:

E) given above-mentioned state of cure (vulcanization) X (t ₀), utilize array function down, determine a parameter of forming by the moment of torsion S ' under the specified temp T:

S′(T，X)=S′ _min(T)+X*(S′ _max(T)-S′ _min(T))

Wherein ${\{}_{S_{\max }^{\&prime;}\left(T\right)=S^{\&prime;}(T,1)=S_{\max }^{\&prime;}\left(T_0\right)+D_{\max }(T-T_0)}^{S_{\min }^{\&prime;}\left(T\right)=S^{\&prime;}(T,0)=S_{\min }^{\&prime;}\left(T_0\right)+D_{\min }(T-T_0)}$

Wherein, S ' _Min(T ₀)=at described reference temperature T ₀Minimal torque; S ' _Max(T ₀)=at described reference temperature T ₀Peak torque; D _Min=S ' _MinDerivative with respect to described temperature T; D _Max=S ' _MaxDerivative with respect to described temperature T.

5. according to the method for claim 1, it is characterized in that above-mentioned a pair of equivalent cure degree value (X for above-mentioned first equation ₁, X ₂) by X ₁=30% and X ₂=60% forms.

6. according to the method for claim 1, it is characterized in that above-mentioned a pair of equivalent cure degree value (X for above-mentioned second equation ₁, X ₂) by X ₁=60% and X ₂=90% forms.

7. according to the method for claim 1, it is characterized in that for above-mentioned the 3rd equation above-mentioned a pair of equivalent cure degree value (X ₁, X ₂) by X ₁=20% and X ₂=60% forms, and X's reduced to be set at X when t was tending towards infinity _R=100%.

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