CN102590076A - Measurement device of polymer viscoelastic model and measurement method of model element parameters - Google Patents

Abstract

The invention relates to a measurement device of a polymer viscoelastic model and a measurement method of model element parameters, which relate to a measurement device of a viscoelastic model and a measurement method of model element parameters. The measurement device of the polymer viscoelastic model and the measurement method of the model element parameter are established to solve the problems of a classic viscoelastic model that: the classic viscoelastic model is only an abstract model on paper and can not be a practical mechanical model. In the device of scheme 1: springs are connected with dashpots in series. In the device of scheme 2: springs are connected with dashpots in parallel. In the device of scheme 3: one of the two springs is connected with one of the two dashpots in series to form a Maxwell model, the other spring is connected with the other dashpot in parallel to form a Kelvin model and then the Kelvin model is connected with the Maxwell model in series. The method comprises the following steps: obtaining stress relaxation curves by the measurement device of the Maxwell model; obtaining creep curves by the measurement device of the Kelvin model; applying a constant stress sigma 0 on the measurement devices of four element mechanical models to obtain creep curves. The method can be used for establishing the practical polymer viscoelastic mechanical model.

Description

The measuring method of the measurement mechanism of polymer viscoelastic model and model element parameter

Technical field

The present invention relates to the measuring method of a kind of viscoelastic model measurement mechanism and model element parameter.

Background technology

Classical polymer viscoelastic mechanical model is a kind of abstract concept, and theoretical research person can only use some model elements on paper, promptly form various Viscous Elastic Mechanics models with abstract spring and abstract glutinous kettle and study its Viscous Elastic Mechanics behavior.For example: abstract spring and the abstract glutinous kettle composition Maxwell model that is together in series; Be together in parallel abstract spring and abstract glutinous kettle and form degree Kelvin model etc.; But the viscosity of the elastic modulus of abstract spring and abstract glutinous kettle does not have concrete numerical value, only its physical significance of expression in some differential equations.

Summary of the invention

The purpose that the present invention is is to exist only in the abstract model on the paper for solving at present to classical polymer viscoelastic mechanical model; The problem of a mechanical model tool elephant, can practical application be can't become, a kind of measurement mechanism of polymer viscoelastic model and the measuring method of model element parameter therefore proposed.

The present invention solves the problems of the technologies described above the technical scheme of taking to be:

The measurement mechanism of polymer viscoelastic model of the present invention has three schemes, respectively as follows:

Scheme one: the measurement mechanism of polymer viscoelastic model of the present invention; The measurement mechanism of said polymer viscoelastic model is the measurement mechanism of Maxwell model, and the measurement mechanism of said Maxwell model comprises base, dynamometer, spring, glutinous kettle, two fixed charge method end plates, four pull bars and three portable plates; Two fixed charge method end plates are respectively first fixed charge method end plate and second fixed charge method end plate, and three portable plates are respectively first portable plate, second portable plate and the 3rd portable plate;

Two fixed charge method end plates vertically and side by side are fixed on the base; Level and rectangular array are fixed with four pull bars between two fixed charge method end plates, form tower structure by four pull bars and two fixed charge method end plates, and three portable plates and two fixed charge method end plates laterally arrange and between two fixed charge method end plates; The adjacent setting of first portable plate with first fixed charge method end plate; The adjacent setting with second fixed charge method end plate of the 3rd portable plate, second portable plate are arranged between first portable plate and the 3rd portable plate, are provided with four through holes with four pull bar opposite positions on each portable plate; Four through holes of each portable plate are sleeved on four pull bars; Three portable plates and four pull bars are slidingly connected, and are fixed with spring between first portable plate and second portable plate, are fixed with glutinous kettle between second portable plate and the 3rd portable plate; Dynamometer is arranged between first portable plate and second portable plate, and the dynamometer and first portable plate and second portable plate are affixed.

Scheme two: the measurement mechanism of polymer viscoelastic model; The measurement mechanism of said polymer viscoelastic model is the measurement mechanism of degree Kelvin model, and the measurement mechanism of said degree Kelvin model comprises base, stay cord, pallet, counterweight, fixed pulley, strainmeter, spring, glutinous kettle, connecting rod, two fixed charge method end plates, four pull bars and three portable plates; Two fixed charge method end plates are respectively first fixed charge method end plate and second fixed charge method end plate, and three portable plates are respectively first portable plate, second portable plate and the 3rd portable plate;

Two fixed charge method end plates vertically and side by side are fixed on the base, and level and rectangular array are fixed with four pull bars between two fixed charge method end plates, form tower structure by four pull bars and two fixed charge method end plates; Three portable plates and two fixed charge method end plates laterally arrange and between two fixed charge method end plates, the adjacent setting with first fixed charge method end plate of first portable plate, the adjacent setting with second fixed charge method end plate of the 3rd portable plate; Second portable plate is arranged between first portable plate and the 3rd portable plate; Be provided with four through holes with four pull bar opposite positions on each portable plate, four through holes of each portable plate are sleeved on four pull bars, and three portable plates and four pull bars are slidingly connected; Pallet is arranged on the outside of first fixed charge method end plate; Fixed pulley is fixed on the lateral surface of first fixed charge method end plate, and counterweight is contained on the pallet, and first fixed charge method end plate is provided with stay cord and passes the hole; One end and the pallet of stay cord are affixed; The stay cord that the other end of stay cord is walked around fixed pulley and passed said first fixed charge method end plate passes the hole and first portable plate is affixed, and parallelly connected spring and the glutinous kettle of being provided with between second portable plate and the 3rd portable plate is fixed with a connecting rod between first portable plate and second portable plate; Strainmeter is arranged between first portable plate and second portable plate, and strainmeter and first portable plate are affixed.

Scheme three: the measurement mechanism of polymer viscoelastic model; The measurement mechanism of said polymer viscoelastic model is the measurement mechanism of quaternary part model, and the measurement mechanism of said quaternary part model comprises base, stay cord, pallet, counterweight, fixed pulley, dynamometer, strainmeter, two glutinous kettles, two springs, two fixed charge method end plates, four pull bars and three portable plates; Two fixed charge method end plates are respectively first fixed charge method end plate and second fixed charge method end plate, and three portable plates are respectively first portable plate, second portable plate and the 3rd portable plate;

Two fixed charge method end plates vertically and side by side are fixed on the base, and level and rectangular array are fixed with four pull bars between two fixed charge method end plates, form tower structure by four pull bars and two fixed charge method end plates; Three portable plates and two fixed charge method end plates laterally arrange and between two fixed charge method end plates, the adjacent setting with first fixed charge method end plate of first portable plate, the adjacent setting with second fixed charge method end plate of the 3rd portable plate; Second portable plate is arranged between first portable plate and the 3rd portable plate; Be provided with four through holes with four pull bar opposite positions on each portable plate, four through holes of each portable plate are sleeved on four pull bars, and three portable plates and four pull bars are slidingly connected; Pallet is arranged on the outside of first fixed charge method end plate; Fixed pulley is fixed on the lateral surface of first fixed charge method end plate, and counterweight is contained on the pallet, and first fixed charge method end plate is provided with stay cord and passes the hole; One end and the pallet of stay cord are affixed; The stay cord that the other end of stay cord is walked around fixed pulley and passed said first fixed charge method end plate passes the hole and dynamometer is affixed, and the dynamometer and first portable plate are affixed, and strainmeter is arranged between first portable plate and second portable plate; And the strainmeter and first portable plate are affixed; A spring in two springs is connected between first portable plate and second portable plate, and the spring of residue in glutinous kettle in two glutinous kettles and two springs is parallel between second portable plate and the 3rd portable plate, and the glutinous kettle of residue in two glutinous kettles is fixed between the 3rd portable plate and second fixed charge method end plate.

The measuring method of utilizing the measurement mechanism implementation model component parameters of polymer viscoelastic model of the present invention, said measuring method is accomplished by following steps:

Step 1: let first portable plate and the 3rd portable plate in the measurement mechanism of Maxwell model produce constant displacement simultaneously, make Maxwell model produce constant deformation ε ₀, and the dynamometer of the measurement mechanism through Maxwell model measures the size that Maxwell model is carved stress at a time, draws stress and time relation curve, i.e. stress relaxation curve;

On the pallet of the measurement mechanism of degree Kelvin model, add counterweight, be equivalent to apply a constant stress σ ₀, the strainmeter of the measurement mechanism through the degree Kelvin model is measured the size that the degree Kelvin model is carved strain at a time, draws strain and time relation curve, i.e. creep curve.

According to the stress relaxation formula:

$\mathrm{\σ}={\mathrm{\σ}}_0{e}^{-\frac{E}{\mathrm{\η}}\·t}---\left(1\right)$

In the formula: the elastic modulus of E-spring;

The viscosity of η-glutinous kettle;

T-action time;

According to the creep formula:

$\mathrm{\ϵ}={\mathrm{\ϵ}}_0(1-e^{-\frac{E}{\mathrm{\η}}\·t})---\left(2\right)$

Derive the elastic modulus formula of spring:

$E=\frac{{\mathrm{\σ}}_0-\mathrm{\σ}\left(t\right)}{\mathrm{\ϵ}\left(t\right)}---\left(3\right)$

In the formula: the stress of σ (t)-sometime;

The strain of ε (t)-sometime;

The viscosity calculations formula of glutinous kettle:

$\mathrm{\η}=\frac{E\left(t\right)}{\ln \frac{{\mathrm{\σ}}_0}{\mathrm{\σ}}}---\left(4\right)$

If the elastic modulus E of the spring in the measurement mechanism of Maxwell model ₁, Maxwell model measurement mechanism in the viscosities il of glutinous kettle ₁

If the elastic modulus E of the spring in the measurement mechanism of degree Kelvin model ₂, the degree Kelvin model measurement mechanism in the viscosities il of glutinous kettle ₂

Try to achieve the elastic modulus E of the spring in the measurement mechanism of Maxwell model according to above-mentioned formula (3) ₁And the elastic modulus E of the spring in the measurement mechanism of degree Kelvin model ₂Try to achieve the viscosities il of the glutinous kettle in the measurement mechanism of Maxwell model according to above-mentioned formula (4) ₁And the viscosities il of the glutinous kettle in the measurement mechanism of degree Kelvin model ₂

Step 2: the pallet of the measurement mechanism of past quaternary part model adds counterweight, is equivalent to apply a constant stress σ ₀, the strainmeter of the measurement mechanism through said quaternary part model is measured the size of quaternary part model strain, draws strain and time relation curve, i.e. creep curve; Again with the elastic modulus E of the spring in the measurement mechanism of above-mentioned Maxwell model of trying to achieve through calculating ₁, the degree Kelvin model measurement mechanism in the elastic modulus E of spring ₂, Maxwell model measurement mechanism in the viscosities il of glutinous kettle ₁And the viscosities il of the glutinous kettle in the measurement mechanism of degree Kelvin model ₂In the creep equation of substitution quaternary part mechanical model,

$\mathrm{\&epsiv;}\left(t\right)=\frac{{\mathrm{\&sigma;}}_0}{E_1}+\frac{{\mathrm{\&sigma;}}_0}{E_2}(1-e^{-\frac{{\mathrm{<figure-callout\; id="2"\; label="E"\; filenames="HDA0000141004390000021.png,HDA0000141004390000031.png"\; state="\{\{state\}\}">E</figure-callout>}}_2}{{\mathrm{\&eta;}}_2}})+\frac{{\mathrm{\&sigma;}}_0}{{\mathrm{\&eta;}}_1}t---\left(5\right)$

Substitution different time t obtains the creep curve of a calculating, and with the superimposed contrast of creep curve that creep curve that calculates and mensuration obtain, the result who obtains is that above-mentioned two kinds of creep curves are identical basically.

The invention has the beneficial effects as follows: the present invention a kind of classics, exist only in the polymer viscoelastic mechanical model measurement mechanism that polymer viscoelastic mechanical model on the paper transforms into a reality; Proved all that through theoretical derivation and experimental data this mechanical model device can reflect the viscoelastic certain law of polymkeric substance more exactly; And proved that the polymer viscoelastic mechanical model no longer is an abstract mechanical model; A but mechanical model tool elephant, can practical application; The elastic modulus E value of actual spring can be come out with the viscosities il value of actual glutinous kettle in measurements and calculations; Actual mechanics curve also can be measured out, so the present invention has filled up the blank that the polymer viscoelastic theory and practice combines.

Description of drawings

Fig. 1 a is the front view of the measurement mechanism of polymer viscoelastic model of the present invention, and what represent among the figure is the front view of the measurement mechanism of Maxwell model; Fig. 1 b is the front view of the measurement mechanism of polymer viscoelastic model of the present invention, and what represent among the figure is the front view of the measurement mechanism of degree Kelvin model; Fig. 1 c is the front view of the measurement mechanism of polymer viscoelastic model of the present invention, and what represent among the figure is the front view of the measurement mechanism of element model; Fig. 1 d is the front view of the measurement mechanism of polymer viscoelastic model of the present invention, and what represent among the figure is the front view of the measurement mechanism of quaternary part model; Fig. 2 is the stress relaxation curve figure that the measurement mechanism test of the Maxwell model of composition after spring I and the glutinous kettle I series connection obtains; Fig. 3 is the creep curve figure that spring I and the glutinous kettle I parallel connection measurement mechanism test of the degree Kelvin model of composition later on obtain; Fig. 4 is the stress relaxation curve figure that the measurement mechanism test of the Maxwell model of composition after spring II and the glutinous kettle II series connection obtains; Fig. 5 is the creep curve figure that spring II and the glutinous kettle II parallel connection measurement mechanism test of the degree Kelvin model of composition later on obtain; Fig. 6 is the creep curve figure that the measurement mechanism test of the quaternary part model of spring I, glutinous kettle I, spring II and glutinous kettle II composition obtains; Fig. 7 is the E that calculates ₁, E ₂, η ₁, η ₂The creep equation of substitution quaternary part mechanical model, the creep curve figure of the calculating that substitution different time t obtains; Fig. 8 is experiment creep curve and the superimposed correlation curve figure of calculating creep curve, and curve close with Fig. 7 shape among the figure is for calculating creep curve, and another curve is the experiment creep curve.

Embodiment

Embodiment one: combine Fig. 1 a explanation; The measurement mechanism of the polymer viscoelastic model of this embodiment is the measurement mechanism of Maxwell model, the measurement mechanism base 1 of said Maxwell model, dynamometer 2, spring 3, glutinous kettle 4, two fixed charge method end plates 5, four pull bars 6 and three portable plates 7; Two fixed charge method end plates 5 are respectively the first fixed charge method end plate 5-1 and the second fixed charge method end plate 5-2, and three portable plates 7 are respectively the first portable plate 7-1, the second portable plate 7-2 and the 3rd portable plate 7-3;

Two fixed charge method end plates 5 vertically and side by side are fixed on the base 1; Level and rectangular array are fixed with four pull bars 6 between two fixed charge method end plates 5; Form tower structure by four pull bars 6 and two fixed charge method end plates 5; Three portable plates 7 and two fixed charge method end plates 5 laterally arrange and between two fixed charge method end plates 5, the first portable plate 7-1 and the adjacent setting of the first fixed charge method end plate 5-1, the 3rd portable plate 7-3 and the adjacent setting of the second fixed charge method end plate 5-2; The second portable plate 7-2 is arranged between the first portable plate 7-1 and the 3rd portable plate 7-3; Be provided with four through holes with four pull bar 6 opposite positions on each portable plate 7, four through holes of each portable plate 7 are sleeved on four pull bars 6, three portable plates 7 and four pull bars 6 be slidingly connected (three portable plates 7 can be done parallel sliding on four pull bars 6); Be fixed with spring 3 between the first portable plate 7-1 and the second portable plate 7-2; Be fixed with glutinous kettle 4 between the second portable plate 7-2 and the 3rd portable plate 7-3, dynamometer 2 is arranged between the first portable plate 7-1 and the second portable plate 7-2, and the dynamometer 2 and the first portable plate 7-1 and the second portable plate 7-2 are affixed.

Glutinous kettle 4 in the Maxwell model is connected with spring 3, move the 3rd portable plate 7-3 and make it keep a constant deformation, then the Maxwell model stress relaxation phenomenon that can produce (be stress in time increase and reduce).

Embodiment two: combine Fig. 1 b explanation; The measurement mechanism of the polymer viscoelastic model of this embodiment is the measurement mechanism of degree Kelvin model, and the measurement mechanism of said degree Kelvin model comprises base 1, stay cord 8, pallet 9, counterweight 10, fixed pulley 11, strainmeter 12, spring 3, glutinous kettle 4, connecting rod 13, two fixed charge method end plates 5, four pull bars 6 and three portable plates 7; Two fixed charge method end plates 5 are respectively the first fixed charge method end plate 5-1 and the second fixed charge method end plate 5-2, and three portable plates 7 are respectively the first portable plate 7-1, the second portable plate 7-2 and the 3rd portable plate 7-3;

Two fixed charge method end plates 5 vertically and side by side are fixed on the base 1; Level and rectangular array are fixed with four pull bars 6 between two fixed charge method end plates 5, form tower structure by four pull bars 6 and two fixed charge method end plates 5, and three portable plates 7 and two fixed charge method end plates 5 laterally arrange and between two fixed charge method end plates 5; The first portable plate 7-1 and the adjacent setting of the first fixed charge method end plate 5-1; The 3rd portable plate 7-3 and the adjacent setting of the second fixed charge method end plate 5-2, the second portable plate 7-2 is arranged between the first portable plate 7-1 and the 3rd portable plate 7-3, is provided with four through holes with four pull bar 6 opposite positions on each portable plate 7; Four through holes of each portable plate 7 are sleeved on four pull bars 6; Three portable plates 7 and four pull bars 6 are slidingly connected (three portable plates 7 can be done parallel sliding on four pull bars 6), and pallet 9 is arranged on the outside of the first fixed charge method end plate 5-1, and fixed pulley 11 is fixed on the lateral surface of the first fixed charge method end plate 5-1; Counterweight 10 is contained on the pallet 9; The first fixed charge method end plate 5-1 is provided with stay cord and passes hole 5-1-1, and an end and the pallet 9 of stay cord 8 are affixed, and the stay cord that the other end of stay cord 8 is walked around fixed pulley 11 and passed the said first fixed charge method end plate 5-1 passes hole 5-1-1 and the first portable plate 7-1 is affixed; Parallelly connected spring 3 and the glutinous kettle 4 of being provided with between the second portable plate 7-2 and the 3rd portable plate 7-3; Be fixed with a connecting rod 13 between the first portable plate 7-1 and the second portable plate 7-2, strainmeter 12 is arranged between the first portable plate 7-1 and the second portable plate 7-2, and strainmeter 12 and the first portable plate 7-1 are affixed.

Select certain counterweight 10 to be contained in to make on the pallet 9 the degree Kelvin model to produce a constant stress, then the degree Kelvin model can produce a creep (be deformation in time increase and increase).

Embodiment three: combine Fig. 1 c explanation; The measurement mechanism of the polymer viscoelastic model of this embodiment is the measurement mechanism of element model, and the measurement mechanism of said element model comprises base 1, stay cord 8, pallet 9, counterweight 10, fixed pulley 11, dynamometer 2, strainmeter 12, glutinous kettle 4, two springs 3, two fixed charge method end plates 5, four pull bars 6 and three portable plates 7; Two fixed charge method end plates 5 are respectively the first fixed charge method end plate 5-1 and the second fixed charge method end plate 5-2, and three portable plates 7 are respectively the first portable plate 7-1, the second portable plate 7-2 and the 3rd portable plate 7-3;

Two fixed charge method end plates 5 vertically and side by side are fixed on the base 1; Level and rectangular array are fixed with four pull bars 6 between two fixed charge method end plates 5; Form tower structure by four pull bars 6 and two fixed charge method end plates 5, three portable plates 7 and two fixed charge method end plates 5 laterally arrange and between two fixed charge method end plates 5, the first portable plate 7-1 and the adjacent setting of the first fixed charge method end plate 5-1; The 3rd portable plate 7-3 and the adjacent setting of the second fixed charge method end plate 5-2; The second portable plate 7-2 is arranged between the first portable plate 7-1 and the 3rd portable plate 7-3, is provided with four through holes with four pull bar 6 opposite positions on each portable plate 7, and four through holes of each portable plate 7 are sleeved on four pull bars 6; Three portable plates 7 and four pull bars 6 be slidingly connected (three portable plates 7 can be done parallel sliding on four pull bars 6); Pallet 9 is arranged on the outside of the first fixed charge method end plate 5-1, and fixed pulley 11 is fixed on the lateral surface of the first fixed charge method end plate 5-1, and counterweight 10 is contained on the pallet 9; The first fixed charge method end plate 5-1 is provided with stay cord and passes hole 5-1-1; One end and the pallet 9 of stay cord 8 are affixed, and the stay cord that the other end of stay cord 8 is walked around fixed pulley 11 and passed the said first fixed charge method end plate 5-1 passes hole 5-1-1 and dynamometer 2 is affixed, and the dynamometer 2 and the first portable plate 7-1 are affixed; Strainmeter 12 is arranged between the first portable plate 7-1 and the second portable plate 7-2; And the strainmeter 12 and the first portable plate 7-1 are affixed, and one in two springs 3 is connected between the first portable plate 7-1 and the second portable plate 7-2, and one of residue and glutinous kettle 4 in two springs 3 are connected in parallel between the second portable plate 7-2 and the 3rd portable plate 7-3.Add that on pallet 9 counterweight 10 produces a horizontal force through fixed pulley 11, the size of horizontal force shows that through dynamometer 2 deformation that element model (mechanical model) produces shows through strainmeter 12.

Embodiment four: combine Fig. 1 d explanation; The measurement mechanism of the polymer viscoelastic model of this embodiment is the measurement mechanism of quaternary part model, and the measurement mechanism of said quaternary part model comprises base 1, stay cord 8, pallet 9, counterweight 10, fixed pulley 11, dynamometer 2, strainmeter 12, two glutinous kettles 4, two springs 3, two fixed charge method end plates 4, four pull bars 6 and three portable plates 7; Two fixed charge method end plates 5 are respectively the first fixed charge method end plate 5-1 and the second fixed charge method end plate 5-2, and three portable plates 7 are respectively the first portable plate 7-1, the second portable plate 7-2 and the 3rd portable plate 7-3;

Two fixed charge method end plates 5 vertically and side by side are fixed on the base 1; Level and rectangular array are fixed with four pull bars 6 between two fixed charge method end plates 5; Form tower structure by four pull bars 6 and two fixed charge method end plates 5; Three portable plates 7 and two fixed charge method end plates 5 laterally arrange and between two fixed charge method end plates 5, the first portable plate 7-1 and the adjacent setting of the first fixed charge method end plate 5-1, the 3rd portable plate 7-3 and the adjacent setting of the second fixed charge method end plate 5-2; The second portable plate 7-2 is arranged between the first portable plate 7-1 and the 3rd portable plate 7-3; Be provided with four through holes with four pull bar 6 opposite positions on each portable plate 7, four through holes of each portable plate 7 are sleeved on four pull bars 6, three portable plates 7 and four pull bars 6 be slidingly connected (three portable plates 7 can be done parallel sliding on four pull bars 6); Pallet 9 is arranged on the outside of the first fixed charge method end plate 5-1; Fixed pulley 11 is fixed on the lateral surface of the first fixed charge method end plate 5-1, and counterweight 10 is contained on the pallet 9, and the first fixed charge method end plate 5-1 is provided with stay cord and passes hole 5-1-1; One end and the pallet 9 of stay cord 8 are affixed; The stay cord that the other end of stay cord 8 is walked around fixed pulley 11 and passed the said first fixed charge method end plate 5-1 passes hole 5-1-1 and dynamometer 2 is affixed, and the dynamometer 2 and the first portable plate 7-1 are affixed, and strainmeter 12 is arranged between the first portable plate 7-1 and the second portable plate 7-2; And the strainmeter 12 and the first portable plate 7-1 are affixed; A spring 3 in two springs 3 is connected between the first portable plate 7-1 and the second portable plate 7-2, and the spring 3 of residue in glutinous kettle 4 in two glutinous kettles 4 and two springs 3 is parallel between the second portable plate 7-2 and the 3rd portable plate 7-3, and the glutinous kettle 4 of residue in two glutinous kettles 4 is fixed between the 3rd portable plate 7-3 and the second fixed charge method end plate 5-2.

Adding on the pallet 9 that counterweight 10 produces a horizontal force action and to quaternary part model, makes it produce a constant stress through fixed pulley 11, the size of horizontal force can show that the deformation that quaternary part model produces shows through strainmeter 12 through dynamometer 2.

Embodiment five: the measuring method of the measurement mechanism implementation model component parameters that utilizes embodiment one, two and four polymer viscoelastic models of this embodiment, said measuring method is accomplished by following steps:

Step 1: let the first portable plate 7-1 and the 3rd portable plate 7-3 in the measurement mechanism of Maxwell model produce constant displacement simultaneously, make Maxwell model produce constant deformation ε ₀, and the dynamometer 2 of the measurement mechanism through Maxwell model measures the size that Maxwell model is carved stress at a time, draws stress and time relation curve, i.e. stress relaxation curve;

On the pallet 9 of the measurement mechanism of degree Kelvin model, add counterweight 10, be equivalent to apply a constant stress σ ₀, the strainmeter 12 of the measurement mechanism through the degree Kelvin model is measured the size that the degree Kelvin model is carved strain at a time, draws strain and time relation curve, i.e. creep curve.

According to the stress relaxation formula:

$\mathrm{\&sigma;}={\mathrm{\&sigma;}}_0{e}^{-\frac{E}{\mathrm{\&eta;}}\&CenterDot;t}---\left(1\right)$

In the formula: the elastic modulus of E-spring;

The viscosity of η-glutinous kettle;

T-action time;

According to the creep formula:

$\mathrm{\&epsiv;}={\mathrm{\&epsiv;}}_0(1-e^{-\frac{E}{\mathrm{\&eta;}}\&CenterDot;t})---\left(2\right)$

Derive the elastic modulus formula of spring:

$E=\frac{{\mathrm{\&sigma;}}_0-\mathrm{\&sigma;}\left(t\right)}{\mathrm{\&epsiv;}\left(t\right)}---\left(3\right)$

In the formula: the stress of σ (t)-sometime;

The strain of ε (t)-sometime;

The viscosity calculations formula of glutinous kettle:

$\mathrm{\&eta;}=\frac{E\left(t\right)}{\ln \frac{{\mathrm{\&sigma;}}_0}{\mathrm{\&sigma;}}}---\left(4\right)$

If the elastic modulus E of the spring 3 in the measurement mechanism of Maxwell model ₁, Maxwell model measurement mechanism in the viscosities il of glutinous kettle 4 ₁

If the elastic modulus E of the spring 3 in the measurement mechanism of degree Kelvin model ₂, the degree Kelvin model measurement mechanism in the viscosities il of glutinous kettle 4 ₂

Try to achieve the elastic modulus E of the spring 3 in the measurement mechanism of Maxwell model according to above-mentioned formula (3) ₁And the elastic modulus E of the spring 3 in the measurement mechanism of degree Kelvin model ₂Try to achieve 4 viscosities il of the glutinous kettle in the measurement mechanism of Maxwell model according to above-mentioned formula (4) ₁And the viscosities il of the glutinous kettle 4 in the measurement mechanism of degree Kelvin model ₂

Step 2: the pallet 9 of the measurement mechanism of past quaternary part model adds counterweights 10, is equivalent to apply a constant stress σ ₀, the strainmeter 12 of the measurement mechanism through said quaternary part model is measured the size of quaternary part model strain, draws strain and time relation curve, i.e. creep curve; Again with the elastic modulus E of the spring 3 in the measurement mechanism of above-mentioned Maxwell model of trying to achieve through calculating ₁, the degree Kelvin model measurement mechanism in the elastic modulus E of spring 3 ₂, Maxwell model measurement mechanism in 4 viscosities il of glutinous kettle ₁And the viscosities il of the glutinous kettle 4 in the measurement mechanism of degree Kelvin model ₂(the E that promptly calculates ₁, E ₂, η ₁, η ₂) in the creep equation of substitution quaternary part mechanical model,

$\mathrm{\&epsiv;}\left(t\right)=\frac{{\mathrm{\&sigma;}}_0}{E_1}+\frac{{\mathrm{\&sigma;}}_0}{E_2}(1-e^{-\frac{{\mathrm{<figure-callout\; id="2"\; label="E"\; filenames="HDA0000141004390000021.png,HDA0000141004390000031.png"\; state="\{\{state\}\}">E</figure-callout>}}_2}{{\mathrm{\&eta;}}_2}})+\frac{{\mathrm{\&sigma;}}_0}{{\mathrm{\&eta;}}_1}t---\left(5\right)$

Substitution different time t obtains the creep curve of a calculating; With the creep curve that calculates with measure the superimposed contrast of creep curve obtain; The result who obtains is that above-mentioned two kinds of creep curves are identical basically; Explain that actual spring and glutinous kettle can replace abstract spring and glutinous kettle, show that therefore mechanical model actual, the tool elephant can replace classical, abstract mechanical model.

Embodiment 1: present embodiment is a measuring method of utilizing the measurement mechanism implementation model component parameters of polymer viscoelastic model of the present invention, and the concrete grammar step is following:

One, E ₁And η ₁Mensuration:

Choose a steel wire pulling force spring, setting spring I is as flexible member in the present embodiment, and steel wire diameter is 1.54mm, and middle footpath is that 17.16mm, active length are 260mm; Choose a glutinous kettle, set glutinous kettle I in the present embodiment as adhesive elements, glutinous kettle I internal diameter is that 19mm, active length are 166mm, and actuating medium is a Newton type fluid glycerine.At first two kinds of elements (spring I and glutinous kettle I) series connection (is utilized the measurement mechanism of Maxwell model, sees Fig. 1 a), form the Maxwell model of a reality, apply a constant strain stress again ₀, obtain a stress relaxation curve through test, see Fig. 2;

Secondly, more above-mentioned two kinds of element parallel connections (utilize the measurement mechanism of degree Kelvin model, see Fig. 1 b) are obtained the Kelvin model of a reality, apply a constant stress σ ₀, through test, obtain a creep curve, see Fig. 3; Calculating and pass through arithmetic mean by formula (3) and formula (4) obtains: E ₁=1068.99MPa, η ₁=3013.66MPas; E ₁Be the elastic modulus of spring I, η ₁Viscosity for glutinous kettle I;

Step 2: E ₂And η ₂Mensuration:

Choose a steel wire pulling force spring, setting spring II is as flexible member in the present embodiment, and the steel wire diameter of spring II is that 1.75mm, middle footpath are that 18.78mm, active length are 90mm; Choose a glutinous kettle, set glutinous kettle II in the present embodiment as adhesive elements, the internal diameter of glutinous kettle II is that 30mm, active length are 136mm, and actuating medium is a glycerine.Same quadrat method, (utilize the measurement mechanism of Maxwell model, see that Fig. 1 a) forms the Maxwell model, the stress relaxation curve that obtains is seen Fig. 4 with above-mentioned two kinds of element connected in series; The Kelvin model is formed in above-mentioned two kinds of element parallel connections (utilize the measurement mechanism of degree Kelvin model, see Fig. 1 b), and the creep curve that obtains is seen Fig. 5; Obtain E through calculating and arithmetic mean ₂=1299.80MPa, η ₂=77347.37MPas; E ₁Be the elastic modulus of spring II, η ₁Viscosity for glutinous kettle II;

Step 3: the mechanics curve determination of quaternary part mechanical model:

Two elements (spring II and glutinous kettle II) in two elements in the step 1 (spring I and glutinous kettle I) and the step 2 are formed the quaternary part model of a reality in the measurement mechanism of constructing quaternary part model, see Fig. 1 d, measure its creep curve, see Fig. 6; Again with the E that calculates ₁, E ₂, η ₁, η ₂The creep equation of substitution quaternary part mechanical model, substitution different time t obtains the creep curve of a calculating, sees Fig. 7.

Step 4: will test creep curve and see Fig. 8 with the superimposed contrast of calculating creep curve; Visible by figure; Two kinds of curves are identical basically; Explain that actual spring and glutinous kettle can replace abstract spring and glutinous kettle, show that therefore the mechanical model that actual, tool resembles (abstract antonym) can replace classical, abstract mechanical model.

In sum; The proving installation of a kind of polymer viscoelastic model of the present invention no longer is a kind of abstract concept; But the device of a reality can be accomplished different model combination of elements with it, forms actual Maxwell model, degree Kelvin model, element model and quaternary part model.Can investigate then and the parameter of measuring its relevant element and mechanics curve.

Through Maxwell model and degree Kelvin model determination to reality, the elastic modulus that can calculate two elastic model elements is E ₁, E ₂Viscosities il with two viscosity model elements ₁, η ₂It is updated in the creep equation of quaternary part mechanical model, can obtains a creep curve.The quaternary part mechanical model of forming a reality again through this device; Determine a creep curve; This determines a creep curve and compares with the creep curve of calculating; Two kinds of curves are identical basically, prove that therefore the mechanical model tool elephant, reality can replace classical, abstract mechanical model.

Claims (4)

1. the measurement mechanism of a polymer viscoelastic model; It is characterized in that: the measurement mechanism of said polymer viscoelastic model is the measurement mechanism of Maxwell model, and the measurement mechanism of said Maxwell model comprises base (1), dynamometer (2), spring (3), glutinous kettle (4), two fixed charge method end plates (5), four pull bars (6) and three portable plates (7); Two fixed charge method end plates (5) are respectively first fixed charge method end plate (5-1) and second fixed charge method end plate (5-2), and three portable plates (7) are respectively first portable plate (7-1), second portable plate (7-2) and the 3rd portable plate (7-3);

Two fixed charge method end plates (5) vertically and side by side are fixed on the base (1); Level and rectangular array are fixed with four pull bars (6) between two fixed charge method end plates (5); Form tower structure by four pull bars (6) and two fixed charge method end plates (5); Three portable plates (7) and two fixed charge method end plates (5) laterally arrange and are positioned between two fixed charge method end plates (5), first portable plate (7-1) and the adjacent setting of first fixed charge method end plate (5-1), the 3rd portable plate (7-3) and the adjacent setting of second fixed charge method end plate (5-2); Second portable plate (7-2) is arranged between first portable plate (7-1) and the 3rd portable plate (7-3); Each portable plate (7) is gone up with four pull bars (6) opposite position and is provided with four through holes, and four through holes of each portable plate (7) are sleeved on four pull bars (6), and three portable plates (7) are slidingly connected with four pull bars (6); Be fixed with spring (3) between first portable plate (7-1) and second portable plate (7-2); Be fixed with glutinous kettle (4) between second portable plate (7-2) and the 3rd portable plate (7-3), dynamometer (2) is arranged between first portable plate (7-1) and second portable plate (7-2), and dynamometer (2) is affixed with first portable plate (7-1) and second portable plate (7-2).

2. the measurement mechanism of a polymer viscoelastic model; It is characterized in that: the measurement mechanism of said polymer viscoelastic model is the measurement mechanism of degree Kelvin model, and the measurement mechanism of said degree Kelvin model comprises base (1), stay cord (8), pallet (9), counterweight (10), fixed pulley (11), strainmeter (12), spring (3), glutinous kettle (4), connecting rod (13), two fixed charge method end plates (5), four pull bars (6) and three portable plates (7); Two fixed charge method end plates (5) are respectively first fixed charge method end plate (5-1) and second fixed charge method end plate (5-2), and three portable plates (7) are respectively first portable plate (7-1), second portable plate (7-2) and the 3rd portable plate (7-3);

Two fixed charge method end plates (5) vertically and side by side are fixed on the base (1); Level and rectangular array are fixed with four pull bars (6) between two fixed charge method end plates (5); Form tower structure by four pull bars (6) and two fixed charge method end plates (5); Three portable plates (7) and two fixed charge method end plates (5) laterally arrange and are positioned between two fixed charge method end plates (5), first portable plate (7-1) and the adjacent setting of first fixed charge method end plate (5-1), the 3rd portable plate (7-3) and the adjacent setting of second fixed charge method end plate (5-2); Second portable plate (7-2) is arranged between first portable plate (7-1) and the 3rd portable plate (7-3); Each portable plate (7) is gone up with four pull bars (6) opposite position and is provided with four through holes, and four through holes of each portable plate (7) are sleeved on four pull bars (6), and three portable plates (7) are slidingly connected with four pull bars (6); Pallet (9) is arranged on the outside of first fixed charge method end plate (5-1); Fixed pulley (11) is fixed on the lateral surface of first fixed charge method end plate (5-1), and counterweight (10) is contained on the pallet (9), and first fixed charge method end plate (5-1) is provided with stay cord and passes hole (5-1-1); One end of stay cord (8) and pallet (9) are affixed; It is affixed with first portable plate (7-1) that the stay cord that the other end of stay cord (8) is walked around fixed pulley (11) and passed said first fixed charge method end plate (5-1) passes hole (5-1-1), and parallelly connected spring (3) and the glutinous kettle (4) of being provided with between second portable plate (7-2) and the 3rd portable plate (7-3) is fixed with a connecting rod (13) between first portable plate (7-1) and second portable plate (7-2); Strainmeter (12) is arranged between first portable plate (7-1) and second portable plate (7-2), and strainmeter (12) is affixed with first portable plate (7-1).

3. the measurement mechanism of a polymer viscoelastic model; It is characterized in that: the measurement mechanism of said polymer viscoelastic model is the measurement mechanism of quaternary part model, and the measurement mechanism of said quaternary part model comprises base (1), stay cord (8), pallet (9), counterweight (10), fixed pulley (11), dynamometer (2), strainmeter (12), two glutinous kettles (4), two springs (3), two fixed charge method end plates (4), four pull bars (6) and three portable plates (7); Two fixed charge method end plates (5) are respectively first fixed charge method end plate (5-1) and second fixed charge method end plate (5-2), and three portable plates (7) are respectively first portable plate (7-1), second portable plate (7-2) and the 3rd portable plate (7-3);

Two fixed charge method end plates (5) vertically and side by side are fixed on the base (1); Level and rectangular array are fixed with four pull bars (6) between two fixed charge method end plates (5); Form tower structure by four pull bars (6) and two fixed charge method end plates (5); Three portable plates (7) and two fixed charge method end plates (5) laterally arrange and are positioned between two fixed charge method end plates (5); First portable plate (7-1) and the adjacent setting of first fixed charge method end plate (5-1); The 3rd portable plate (7-3) and the adjacent setting of second fixed charge method end plate (5-2), second portable plate (7-2) is arranged between first portable plate (7-1) and the 3rd portable plate (7-3), and each portable plate (7) is gone up with four pull bars (6) opposite position and is provided with four through holes; Four through holes of each portable plate (7) are sleeved on four pull bars (6); Three portable plates (7) are slidingly connected with four pull bars (6), and pallet (9) is arranged on the outside of first fixed charge method end plate (5-1), and fixed pulley (11) is fixed on the lateral surface of first fixed charge method end plate (5-1); Counterweight (10) is contained on the pallet (9); First fixed charge method end plate (5-1) is provided with stay cord and passes hole (5-1-1), and an end of stay cord (8) and pallet (9) are affixed, and it is affixed with dynamometer (2) that the stay cord that the other end of stay cord (8) is walked around fixed pulley (11) and passed said first fixed charge method end plate (5-1) passes hole (5-1-1); Dynamometer (2) is affixed with first portable plate (7-1); Strainmeter (12) is arranged between first portable plate (7-1) and second portable plate (7-2), and strainmeter (12) is affixed with first portable plate (7-1), and the spring (3) in two springs (3) is connected between first portable plate (7-1) and second portable plate (7-2); Glutinous kettle (4) in two glutinous kettles (4) and the spring of residue (3) in two springs (3) are parallel between second portable plate (7-2) and the 3rd portable plate (7-3), and a glutinous kettle of the residue in two glutinous kettles (4) (4) is fixed between the 3rd portable plate (7-3) and second fixed charge method end plate (5-2).

4. measuring method of utilizing the measurement mechanism implementation model component parameters of claim 1,2 and 3 said polymer viscoelastic models, it is characterized in that: said measuring method is accomplished by following steps:

Step 1: let first portable plate (7-1) and the 3rd portable plate (7-3) in the measurement mechanism of Maxwell model produce constant displacement simultaneously, make Maxwell model produce constant deformation ε ₀, and the dynamometer (2) of the measurement mechanism through Maxwell model measures the size that Maxwell model is carved stress at a time, draws stress and time relation curve, i.e. stress relaxation curve;

The pallet (9) of the measurement mechanism of past degree Kelvin model is gone up and is added counterweight (10), is equivalent to apply a constant stress σ ₀, the strainmeter (12) of the measurement mechanism through the degree Kelvin model is measured the size that the degree Kelvin model is carved strain at a time, draws strain and time relation curve, i.e. creep curve.

According to the stress relaxation formula:

$\mathrm{\&sigma;}={\mathrm{\&sigma;}}_0{e}^{-\frac{E}{\mathrm{\&eta;}}\&CenterDot;t}---\left(1\right)$

In the formula: the elastic modulus of E-spring;

The viscosity of η-glutinous kettle;

T-action time;

According to the creep formula:

$\mathrm{\&epsiv;}={\mathrm{\&epsiv;}}_0(1-e^{-\frac{E}{\mathrm{\&eta;}}\&CenterDot;t})---\left(2\right)$

Derive the elastic modulus formula of spring:

$E=\frac{{\mathrm{\&sigma;}}_0-\mathrm{\&sigma;}\left(t\right)}{\mathrm{\&epsiv;}\left(t\right)}---\left(3\right)$

In the formula: the stress of σ (t)-sometime;

The strain of ε (t)-sometime;

The viscosity calculations formula of glutinous kettle:

$\mathrm{\&eta;}=\frac{E\left(t\right)}{\ln \frac{{\mathrm{\&sigma;}}_0}{\mathrm{\&sigma;}}}---\left(4\right)$

If the elastic modulus E of the spring in the measurement mechanism of Maxwell model (3) ₁, Maxwell model measurement mechanism in the viscosities il of glutinous kettle (4) ₁

If the elastic modulus E of the spring in the measurement mechanism of degree Kelvin model (3) ₂, the degree Kelvin model measurement mechanism in the viscosities il of glutinous kettle (4) ₂

Try to achieve the elastic modulus E of the spring (3) in the measurement mechanism of Maxwell model according to above-mentioned formula (3) ₁And the elastic modulus E of the spring (3) in the measurement mechanism of degree Kelvin model ₂Try to achieve (4) viscosities il of the glutinous kettle in the measurement mechanism of Maxwell model according to above-mentioned formula (4) ₁And the viscosities il of the glutinous kettle (4) in the measurement mechanism of degree Kelvin model ₂

Step 2: the pallet (9) of the measurement mechanism of past quaternary part model adds counterweight (10), is equivalent to apply a constant stress σ ₀, the strainmeter (12) of the measurement mechanism through said quaternary part model is measured the size of quaternary part model strain, draws strain and time relation curve, i.e. creep curve; Again with the elastic modulus E of the spring (3) in the measurement mechanism of above-mentioned Maxwell model of trying to achieve through calculating ₁, the degree Kelvin model measurement mechanism in the elastic modulus E of spring (3) ₂, Maxwell model measurement mechanism in (4) viscosities il of glutinous kettle ₁And the viscosities il of the glutinous kettle (4) in the measurement mechanism of degree Kelvin model ₂In the creep equation of substitution quaternary part mechanical model,

$\mathrm{\&epsiv;}\left(t\right)=\frac{{\mathrm{\&sigma;}}_0}{E_1}+\frac{{\mathrm{\&sigma;}}_0}{E_2}(1-e^{-\frac{E_2}{{\mathrm{\&eta;}}_2}\&CenterDot;t})+\frac{{\mathrm{\&sigma;}}_0}{{\mathrm{\&eta;}}_1}t---\left(5\right)$

Substitution different time t obtains the creep curve of a calculating, and with the superimposed contrast of creep curve that creep curve that calculates and mensuration obtain, the result who obtains is that above-mentioned two kinds of creep curves are identical basically.

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