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

Abstract

A measuring device for a polymer viscoelastic model and a measuring method for model element parameters relate to a measuring device for a viscoelastic model and a measuring method for model element parameters. The classic viscoelastic mechanical model is an abstract model that only exists on paper and cannot become a practical mechanical model. Device 1: the spring is connected in series with the sticky pot; device 2: the spring is connected in parallel with the sticky pot; device 3: one of the two springs is connected in series with one of the two sticky pots to form a Maxwell model, and the other spring is connected in parallel with the other sticky pot The Kelvin model, and then the Maxwell model in series with the Kelvin model. Method: The stress relaxation curve is measured by the measuring device of the Maxwell model; the creep curve is measured by the measuring device of the Kelvin model, and the creep curve is measured by applying a constant stress σ ₀ to the measuring device of the four-element mechanical model. The invention can be used to construct the actual polymer viscoelasticity model.

Description

Measuring device for polymer viscoelasticity model and method for measuring model element parameters

technical field

The invention relates to a viscoelastic model measuring device and a method for measuring model element parameters.

Background technique

The classic polymer viscoelasticity model is only an abstract concept, and theoretical researchers can only use some model elements on paper, that is, use abstract springs and abstract sticky pots to form various viscoelasticity models to study its viscoelasticity. Behavior. For example: connect the abstract spring and the abstract sticky pot in series to form the Maxwell model, connect the abstract spring and the abstract sticky pot in parallel to form the Kelvin model, etc. However, there are no specific values for the elastic modulus of the abstract spring and the viscosity of the abstract sticky pot. Its physical meaning is expressed in some differential equations.

Contents of the invention

The purpose of the present invention is to solve the problem that the classical polymer viscoelastic mechanical model only exists as an abstract model on paper and cannot become a concrete mechanical model that can be used in practice. Therefore, a polymer viscoelastic model is proposed. A measuring device for an elastic model and a method for measuring parameters of model elements.

The technical scheme that the present invention takes for solving the problems of the technologies described above is:

The measuring device of polymer viscoelasticity model of the present invention has three schemes, respectively as follows:

Option one: the measuring device of the polymer viscoelastic model of the present invention, the measuring device of the polymer viscoelastic model is the measuring device of the Maxwell model, and the measuring device of the Maxwell model includes a base, a dynamometer, a spring, a sticky pot , two fixed end plates, four pull rods and three movable plates; the two fixed end plates are respectively the first fixed end plate and the second fixed end plate, and the three movable plates are respectively the first movable plate and the second movable plate and a third movable panel;

The two fixed end plates are fixed vertically and side by side on the base. Four tie rods are fixed horizontally and in a rectangular array between the two fixed end plates. The frame structure is composed of four tie rods and two fixed end plates. Three movable The plate is set parallel to the two fixed end plates and is located between the two fixed end plates, the first movable plate is adjacent to the first fixed end plate, the third movable plate is adjacent to the second fixed end plate, and the second movable plate The plate is arranged between the first movable plate and the third movable plate, and each movable plate is provided with four through holes corresponding to the four pull rods, and the four through holes of each movable plate are set on the four pull rods, Three movable plates are slidingly connected with four pull rods, a spring is fixedly connected between the first movable plate and the second movable plate, and a sticky pot is fixedly connected between the second movable plate and the third movable plate, and the dynamometer is set at the Between the first movable plate and the second movable plate, the dynamometer is fixedly connected with the first movable plate and the second movable plate.

Option two: the measuring device of the polymer viscoelastic model, the measuring device of the polymer viscoelastic model is the measuring device of the Kelvin model, and the measuring device of the Kelvin model includes a base, a drawstring, a tray, and a weight , fixed pulley, strain gauge, spring, sticky pot, connecting rod, two fixed end plates, four pull rods and three movable plates; the two fixed end plates are respectively the first fixed end plate and the second fixed end plate, and the three The first movable board is respectively the first movable board, the second movable board and the third movable board;

The two fixed end plates are fixed vertically and side by side on the base. Four tie rods are fixed horizontally and in a rectangular array between the two fixed end plates. The frame structure is composed of four tie rods and two fixed end plates. Three movable The plate is set parallel to the two fixed end plates and is located between the two fixed end plates, the first movable plate is adjacent to the first fixed end plate, the third movable plate is adjacent to the second fixed end plate, and the second movable plate The plate is arranged between the first movable plate and the third movable plate, and each movable plate is provided with four through holes corresponding to the four pull rods, and the four through holes of each movable plate are set on the four pull rods, The three movable plates are slidingly connected with the four pull rods, the tray is arranged on the outside of the first fixed end plate, the fixed pulley is fixed on the outer surface of the first fixed end plate, the weight is mounted on the tray, and the first fixed end plate is set There is a stay cord passing through the hole, one end of the stay cord is fixedly connected to the tray, the other end of the stay cord goes around the fixed pulley and passes through the stay cord of the first fixed end plate through the hole and is fixedly connected to the first movable plate. A spring and a sticky pot are arranged in parallel between the second movable plate and the third movable plate, a connecting rod is fixedly connected between the first movable plate and the second movable plate, and the strain gauge is arranged between the first movable plate and the second movable plate between, and the strain gauge is fixedly connected to the first movable plate.

Scheme three: the measuring device of the polymer viscoelastic model, the measuring device of the polymer viscoelastic model is the measuring device of the four-element model, and the measuring device of the four-element model includes a base, a pull cord, a tray, a weight, a fixed Pulley, dynamometer, strain gauge, two sticky pots, two springs, two fixed end plates, four pull rods and three movable plates; the two fixed end plates are the first fixed end plate and the second fixed end respectively board, the three movable boards are respectively the first movable board, the second movable board and the third movable board;

The two fixed end plates are fixed vertically and side by side on the base. Four tie rods are fixed horizontally and in a rectangular array between the two fixed end plates. The frame structure is composed of four tie rods and two fixed end plates. Three movable The plate is set parallel to the two fixed end plates and is located between the two fixed end plates, the first movable plate is adjacent to the first fixed end plate, the third movable plate is adjacent to the second fixed end plate, and the second movable plate The plate is arranged between the first movable plate and the third movable plate, and each movable plate is provided with four through holes corresponding to the four pull rods, and the four through holes of each movable plate are set on the four pull rods, The three movable plates are slidingly connected with the four pull rods, the tray is arranged on the outside of the first fixed end plate, the fixed pulley is fixed on the outer surface of the first fixed end plate, the weight is mounted on the tray, and the first fixed end plate is set There is a stay rope passing through the hole, one end of the stay rope is fixedly connected to the pallet, the other end of the stay rope goes around the fixed pulley and passes through the stay rope on the first fixed end plate and is fixedly connected to the dynamometer through the hole, and the force measurement The gauge is fixedly connected to the first movable plate, the strain gauge is arranged between the first movable plate and the second movable plate, and the strain gauge is fixedly connected to the first movable plate, and one of the two springs is fixedly connected to the first movable plate Between the second movable plate, one of the two sticky pots and the remaining one of the two springs are connected in parallel between the second movable plate and the third movable plate, and the remaining one of the two sticky pots It is fixedly connected between the third movable plate and the second fixed end plate.

The measuring device utilizing polymer viscoelasticity model of the present invention realizes the measuring method of model element parameter, and described measuring method is finished by the following steps:

Step 1: Let the first movable plate and the third movable plate in the measuring device of the Maxwell model produce constant displacement at the same time, so that the Maxwell model produces a constant deformation ε ₀ , and measure the Maxwell model at The magnitude of the stress at a certain moment, draw the relationship curve between stress and time, that is, the stress relaxation curve;

Adding weights to the tray of the measuring device of the Kelvin model is equivalent to applying a constant stress σ ₀ , and the strain gauge of the measuring device of the Kelvin model is used to measure the strain of the Kelvin model at a certain moment, and draw The relationship between strain and time, that is, the creep curve.

According to the stress relaxation formula:

$\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; E.</span>}}{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

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

η-viscosity of sticky pot;

t-action time;

According to the creep formula:

$\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; E.</span>}}{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

The formula for the modulus of elasticity of the spring is derived:

$\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

In the formula: σ(t)-stress at a certain time;

ε(t) - strain at a certain time;

The formula for calculating the viscosity of the sticky pot:

$\mathrm{<span\; class="notranslate">\; \&eta;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; ln</span>}\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

Suppose the elastic modulus E ₁ of the spring in the measuring device of the Maxwell model, the viscosity η ₁ of the sticky pot in the measuring device of the Maxwell model;

Assuming the elastic modulus E ₂ of the spring in the measuring device of the Kelvin model, the viscosity η ₂ of the sticky pot in the measuring device of the Kelvin model;

Obtain the modulus of elasticity E ₁ of the spring in the measuring device of Maxwell model and the elastic modulus E ₂ of the spring in the measuring device of Kelvin model according to above-mentioned formula (3); Obtain Maxwell's model according to above-mentioned formula (4) The viscosity η ₁ of the sticky pot in the measuring device and the viscosity η ₂ of the sticky pot in the measuring device of the Kelvin model;

Step 2: Add weights to the tray of the measuring device of the four-element model, which is equivalent to applying a constant stress σ ₀ , measure the strain of the four-element model through the strain gauge of the measuring device of the four-element model, and draw the strain and The relationship curve of time, that is, the creep curve; then the elastic modulus E ₁ of the spring in the measuring device of the Maxwell model obtained by the above calculation, the elastic modulus E ₂ of the spring in the measuring device of the Kelvin model, The viscosity η of the sticky pot in the measuring device of the Maxwell model and the viscosity η of the sticky pot in the measuring device of _the Kelvin model ₂ are substituted in the creep equation of the four-element mechanics model,

$\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

A calculated creep curve is obtained by substituting different times t, and the calculated creep curve is superimposed and compared with the measured creep curve, and the result obtained is that the above two creep curves are basically consistent.

The beneficial effects of the present invention are: the present invention converts a classic polymer viscoelasticity model that only exists on paper into an actual polymer viscoelasticity model measuring device, through theoretical derivation and experimental data It proves that the mechanical model device can accurately reflect some laws of polymer viscoelasticity, and proves that the polymer viscoelastic mechanical model is no longer an abstract mechanical model, but a concrete mechanical model that can be used in practice , the elastic modulus E value of the actual spring and the viscosity η value of the actual sticky pot can be measured and calculated, and the actual mechanical curve can also be measured, so the present invention fills up a gap in the combination of polymer viscoelasticity theory and practice .

Description of drawings

Fig. 1 a is the front view of the measuring device of the polymer viscoelastic model of the present invention, and what represent among the figure is the front view of the measuring device of Maxwell model; Fig. 1 b is the front view of the measuring device of the polymer viscoelastic model of the present invention, Represented among the figure is the front view of the measuring device of the Kelvin model; Fig. 1c is the front view of the measuring device of the polymer viscoelasticity model of the present invention, and what represent among the figure is the front view of the measuring device of the three-element model; Fig. 1d is the front view of the measuring device of the polymer viscoelasticity model of the present invention, and what represent among the figure is the front view of the measuring device of the four-element model; Fig. 2 is the measuring device of the Maxwell model that spring I and sticky pot I are connected in series The stress relaxation curve obtained from the test; Figure 3 is the creep curve obtained from the test of the measuring device of the Kelvin model composed of the spring I and the sticky pot I in parallel; Figure 4 is the Maxwell model composed of the spring II and the sticky pot II in series The stress relaxation curve obtained from the measurement device test of the model; Fig. 5 is the creep curve obtained from the measurement device test of the Kelvin model formed after spring II and sticky pot II are connected in parallel; Fig. 6 is the spring I, sticky pot I, The creep curve obtained from the test of the measuring device of the four-element model composed of spring II and sticky pot II; Figure 7 is the calculated creep equation of E ₁ , E ₂ , η ₁ , η ₂ substituted into the four-element mechanical model, The calculated creep curve obtained by substituting different time t; Figure 8 is a comparison curve of the superposition of the experimental creep curve and the calculated creep curve. The curve is the experimental creep curve.

Detailed ways

Specific embodiment one: in conjunction with Fig. 1a explanation, the measuring device of the polymer viscoelasticity model of the present embodiment is the measuring device of Maxwell model, the measuring device base 1 of described Maxwell model, dynamometer 2, spring 3, glue pot 4 , two fixed end plates 5, four pull rods 6 and three movable plates 7; the two fixed end plates 5 are respectively the first fixed end plate 5-1 and the second fixed end plate 5-2, and the three movable plates 7 Respectively the first movable board 7-1, the second movable board 7-2 and the third movable board 7-3;

Two fixed end plates 5 are fixed vertically and side by side on the base 1, four tie rods 6 are fixed horizontally and in a rectangular array between the two fixed end plates 5, and the frame is composed of four tie rods 6 and two fixed end plates 5 type structure, three movable plates 7 are arranged in parallel with two fixed end plates 5 and are located between the two fixed end plates 5, the first movable plate 7-1 is arranged adjacent to the first fixed end plate 5-1, and the third The movable plate 7-3 is arranged adjacent to the second fixed end plate 5-2, and the second movable plate 7-2 is arranged between the first movable plate 7-1 and the third movable plate 7-3, and each movable plate 7 Four through holes are arranged on the corresponding position with four pull rods 6, and four through holes of each movable plate 7 are set on four pull rods 6, and three movable plates 7 are slidingly connected with four pull rods 6 (three movable Plate 7 can do parallel sliding on four pull rods 6), is fixedly connected with spring 3 between the first movable plate 7-1 and the second movable plate 7-2, the second movable plate 7-2 and the third movable plate 7 -3 is fixedly connected with a sticky pot 4, and the dynamometer 2 is arranged between the first movable plate 7-1 and the second movable plate 7-2, and the dynamometer 2 is connected to the first movable plate 7-1 and the second movable plate 7-1. Movable plate 7-2 is fixedly connected.

The sticky pot 4 in the Maxwell model is connected in series with the spring 3, and the third movable plate 7-3 is moved to keep a constant deformation, then the stress relaxation phenomenon (that is, the stress increases with time) will be produced by the Maxwell model.

Specific embodiment two: in conjunction with Fig. 1 b explanation, the measuring device of the polymer viscoelasticity model of the present embodiment is the measuring device of Kelvin model, and the measuring device of described Kelvin model comprises base 1, stay cord 8, tray 9 , weight 10, fixed pulley 11, strain gauge 12, spring 3, sticky pot 4, connecting rod 13, two fixed end plates 5, four pull rods 6 and three movable plates 7; the two fixed end plates 5 are respectively The first fixed end plate 5-1 and the second fixed end plate 5-2, and the three movable plates 7 are respectively the first movable plate 7-1, the second movable plate 7-2 and the third movable plate 7-3;

Two fixed end plates 5 are fixed vertically and side by side on the base 1, four tie rods 6 are fixed horizontally and in a rectangular array between the two fixed end plates 5, and the frame is composed of four tie rods 6 and two fixed end plates 5 type structure, three movable plates 7 are arranged in parallel with two fixed end plates 5 and are located between the two fixed end plates 5, the first movable plate 7-1 is arranged adjacent to the first fixed end plate 5-1, and the third The movable plate 7-3 is arranged adjacent to the second fixed end plate 5-2, and the second movable plate 7-2 is arranged between the first movable plate 7-1 and the third movable plate 7-3, and each movable plate 7 Four through holes are arranged on the corresponding position with four pull rods 6, and the four through holes of each movable plate 7 are set on the four pull rods 6, and the three movable plates 7 are slidably connected with the four pull rods 6 (three movable Plate 7 can do parallel sliding on four pull rods 6), tray 9 is arranged on the outside of first fixed end plate 5-1, fixed pulley 11 is fixed on the outer surface of first fixed end plate 5-1, weight 10 Installed on the tray 9, the first fixed end plate 5-1 is provided with a drawstring through hole 5-1-1, one end of the drawstring 8 is fixedly connected to the tray 9, and the other end of the drawstring 8 bypasses the fixed pulley 11 And the stay cord passing through the first fixed end plate 5-1 is affixed to the first movable plate 7-1 through the hole 5-1-1, and the second movable plate 7-2 is connected to the third movable plate 7-3. A spring 3 and a sticky pot 4 are arranged in parallel between them, a connecting rod 13 is fixedly connected between the first movable plate 7-1 and the second movable plate 7-2, and the strain gauge 12 is arranged on the first movable plate 7-1 and the second movable plate 7-2. Between the second movable plates 7-2, the strain gauge 12 is fixedly connected to the first movable plate 7-1.

Select a certain weight 10 to be installed on the tray 9 to make the Kelvin model produce a constant stress, then the Kelvin model will produce a creep phenomenon (that is, the deformation increases with time).

Specific embodiment three: in conjunction with Fig. 1 c explanation, the measuring device of the polymer viscoelasticity model of the present embodiment is the measuring device of three-element model, and the measuring device of described three-element model comprises base 1, pull cord 8, pallet 9, weight Code 10, fixed pulley 11, dynamometer 2, strain gauge 12, sticky pot 4, two springs 3, two fixed end plates 5, four pull rods 6 and three movable plates 7; two fixed end plates 5 are respectively It is the first fixed end plate 5-1 and the second fixed end plate 5-2, and the three movable plates 7 are respectively the first movable plate 7-1, the second movable plate 7-2 and the third movable plate 7-3;

Two fixed end plates 5 are fixed vertically and side by side on the base 1, four tie rods 6 are fixed horizontally and in a rectangular array between the two fixed end plates 5, and the frame is composed of four tie rods 6 and two fixed end plates 5 type structure, three movable plates 7 are arranged in parallel with two fixed end plates 5 and are located between the two fixed end plates 5, the first movable plate 7-1 is arranged adjacent to the first fixed end plate 5-1, and the third The movable plate 7-3 is arranged adjacent to the second fixed end plate 5-2, and the second movable plate 7-2 is arranged between the first movable plate 7-1 and the third movable plate 7-3, and each movable plate 7 Four through holes are arranged on the corresponding position with four pull rods 6, and the four through holes of each movable plate 7 are set on the four pull rods 6, and the three movable plates 7 are slidably connected with the four pull rods 6 (three movable Plate 7 can do parallel sliding on four pull rods 6), tray 9 is arranged on the outside of first fixed end plate 5-1, fixed pulley 11 is fixed on the outer surface of first fixed end plate 5-1, weight 10 Installed on the tray 9, the first fixed end plate 5-1 is provided with a drawstring passing hole 5-1-1, one end of the drawstring 8 is fixedly connected to the tray 9, and the other end of the drawstring 8 bypasses the fixed pulley 11 And the stay cord passing through the first fixed end plate 5-1 is fixedly connected with the dynamometer 2 through the hole 5-1-1, the dynamometer 2 is fixedly connected with the first movable plate 7-1, and the strain gauge 12 It is arranged between the first movable plate 7-1 and the second movable plate 7-2, and the strain gauge 12 is fixedly connected to the first movable plate 7-1, and one of the two springs 3 is fixedly connected to the first movable plate 7 Between -1 and the second movable plate 7-2, the remaining one in the two springs 3 is connected in parallel with the glue pot 4 between the second movable plate 7-2 and the third movable plate 7-3. Adding a weight 10 on the pallet 9 generates a horizontal force through the fixed pulley 11, the size of the horizontal force is displayed by the load cell 2, and the deformation generated by the three-element model (mechanical model) is displayed by the strain gauge 12.

Specific embodiment four: in conjunction with Fig. 1d explanation, the measuring device of the polymer viscoelasticity model of the present embodiment is the measuring device of four-element model, and the measuring device of described four-element model comprises base 1, pull cord 8, pallet 9, weight Code 10, fixed pulley 11, dynamometer 2, strain gauge 12, two sticky pots 4, two springs 3, two fixed end plates 4, four pull rods 6 and three movable plates 7; two fixed end plates 5 are respectively the first fixed end plate 5-1 and the second fixed end plate 5-2, and the three movable plates 7 are respectively the first movable plate 7-1, the second movable plate 7-2 and the third movable plate 7- 3;

Two fixed end plates 5 are fixed vertically and side by side on the base 1, four tie rods 6 are fixed horizontally and in a rectangular array between the two fixed end plates 5, and the frame is composed of four tie rods 6 and two fixed end plates 5 type structure, three movable plates 7 are arranged in parallel with two fixed end plates 5 and are located between the two fixed end plates 5, the first movable plate 7-1 is arranged adjacent to the first fixed end plate 5-1, and the third The movable plate 7-3 is arranged adjacent to the second fixed end plate 5-2, and the second movable plate 7-2 is arranged between the first movable plate 7-1 and the third movable plate 7-3, and each movable plate 7 Four through holes are arranged on the corresponding position with four pull rods 6, and four through holes of each movable plate 7 are set on four pull rods 6, and three movable plates 7 are slidingly connected with four pull rods 6 (three movable Plate 7 can do parallel sliding on four pull rods 6), tray 9 is arranged on the outside of first fixed end plate 5-1, fixed pulley 11 is fixed on the outer surface of first fixed end plate 5-1, weight 10 Installed on the tray 9, the first fixed end plate 5-1 is provided with a drawstring passing hole 5-1-1, one end of the drawstring 8 is fixedly connected to the tray 9, and the other end of the drawstring 8 bypasses the fixed pulley 11 And the stay cord passing through the first fixed end plate 5-1 is fixedly connected with the dynamometer 2 through the hole 5-1-1, the dynamometer 2 is fixedly connected with the first movable plate 7-1, and the strain gauge 12 It is arranged between the first movable plate 7-1 and the second movable plate 7-2, and the strain gauge 12 is fixedly connected to the first movable plate 7-1, and one of the two springs 3 is fixedly connected to the first movable plate Between the plate 7-1 and the second movable plate 7-2, one sticky pot 4 in the two sticky pots 4 and the remaining spring 3 in the two springs 3 are connected in parallel to the second movable plate 7-2 and the third movable plate. Between the plates 7-3, the remaining one of the two sticky pots 4 is fixedly connected between the third movable plate 7-3 and the second fixed end plate 5-2.

A weight 10 is added to the tray 9 to generate a horizontal force through the fixed pulley 11 to act on the four-element model to generate a constant stress. The magnitude of the horizontal force can be displayed by the dynamometer 2, and the deformation generated by the four-element model is passed through The strain gauge 12 is displayed.

Specific embodiment five: the measuring device of the utilization specific embodiment one, two and four polymer viscoelasticity models of this embodiment realizes the measuring method of model element parameter, and described measuring method is finished by the following steps:

Step 1: Let the first movable plate 7-1 and the third movable plate 7-3 in the measuring device of the Maxwell model produce constant displacement at the same time, so that the Maxwell model produces a constant deformation ε ₀ , and measure the force through the measuring device of the Maxwell model Meter 2 measures the magnitude of the stress of the Maxwell model at a certain moment, and draws the relationship curve between stress and time, that is, the stress relaxation curve;

Adding a weight 10 to the tray 9 of the measuring device of the Kelvin model is equivalent to applying a constant stress σ ₀ , and the strain gauge 12 of the measuring device of the Kelvin model is used to measure the strain of the Kelvin model at a certain moment Size, plot the relationship between strain and time, that is, the creep curve.

According to the stress relaxation formula:

$\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; E.</span>}}{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

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

η-viscosity of sticky pot;

t-action time;

According to the creep formula:

$\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; E.</span>}}{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

The formula for the modulus of elasticity of the spring is derived:

$\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&sigma;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

In the formula: σ(t)-stress at a certain time;

ε(t) - strain at a certain time;

The formula for calculating the viscosity of the sticky pot:

$\mathrm{<span\; class="notranslate">\; \&eta;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; ln</span>}\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

Assuming the elastic modulus E ₁ of the spring 3 in the measuring device of the Maxwell model, the viscosity η ₁ of the sticky pot 4 in the measuring device of the Maxwell model;

The elastic modulus E ₂ of the spring 3 in the measuring device of the Kelvin model, the viscosity η 2 of the sticky pot ₄ in the measuring device of the Kelvin model;

Obtain the modulus of elasticity E ₁ of the spring 3 in the measuring device of Maxwell model and the elastic modulus E ₂ of the spring 3 in the measuring device of the Kelvin model according to above-mentioned formula (3); Obtain according to above-mentioned formula (4) 4 viscosity η ₁ of sticky pot in the measuring device of Maxwell model and the viscosity η ₂ of sticking pot 4 in the measuring device of Kelvin model;

Step 2: adding a weight 10 to the tray 9 of the measuring device of the four-element model, which is equivalent to applying a constant stress σ ₀ , and measuring the strain of the four-element model through the strain gauge 12 of the measuring device of the four-element model, Draw the relationship curve of strain and time, i.e. the creep curve; then the elastic modulus E ₁ of the spring 3 in the measuring device of the Maxwell model obtained by calculation and the elasticity of the spring 3 in the measuring device of the Kelvin model Modulus E ₂ , the viscosity η 1 of the sticky pot ₄ in the measuring device of the Maxwell model and the viscosity η 2 of the sticky pot ₄ in the measuring device of the Kelvin model (that is, the calculated E ₁ , E ₂ , η ₁ , η ₂ ) into the creep equation of the four-element mechanical model,

$\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{<span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{{\mathrm{<span\; class="notranslate">\; \&eta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

Substituting different time t to get a calculated creep curve, and comparing the calculated creep curve with the measured creep curve, the result is that the above two creep curves are basically consistent, indicating that the actual spring and viscous The pot can replace the abstract spring and sticky pot, thus showing that the actual, concrete mechanical model can replace the classical, abstract mechanical model.

Embodiment 1: The present embodiment is to utilize the measuring device of polymer viscoelasticity model of the present invention to realize the measuring method of model element parameter, and concrete method step is as follows:

One, the mensuration of E ₁ and η ₁ :

Choose a steel wire tension spring, set spring I as elastic element in the present embodiment, steel wire diameter is 1.54mm, middle diameter is 17.16mm, working length is 260mm; Choose a sticky pot, set sticky pot I as in the present embodiment Viscous components, the inner diameter of the sticky pot I is 19mm, the working length is 166mm, and the working medium is Newtonian fluid glycerin. First, two elements (spring I and sticky pot I) are connected in series (using the measuring device of the Maxwell model, see Figure 1a) to form an actual Maxwell model, and then a constant strain ε ₀ is applied, and a stress relaxation curve is obtained after testing , see Figure 2;

Secondly, connect the above two components in parallel (use the Kelvin model measuring device, see Figure 1b) to obtain an actual Kelvin model, apply a constant stress σ ₀ , and obtain a creep curve after testing, as shown in Figure 3 ; Calculated by formula (3) and formula (4) and obtained through arithmetic average: E ₁ =1068.99MPa, η ₁ =3013.66MPa·s; E ₁ is the elastic modulus of spring I, and η ₁ is the viscosity of sticky pot I ;

Step 2: the mensuration of E ₂ and η ₂ :

Choose a steel wire tension spring, set spring II as the elastic element in this embodiment, the steel wire diameter of spring II is 1.75mm, the middle diameter is 18.78mm, and the working length is 90mm; choose a sticky pot, set sticky pot in this embodiment The pot II is used as a viscous element. The inner diameter of the sticky pot II is 30mm, the working length is 136mm, and the working medium is glycerin. In the same way, the above two components are connected in series (using the measuring device of the Maxwell model, see Figure 1a) to form a Maxwell model, and the stress relaxation curve obtained is shown in Figure 4; the above two components are connected in parallel (using the measuring device of the Kelvin model, See Figure 1b) to form the Kelvin model, and the obtained creep curve is shown in Figure 5; after calculation and arithmetic mean, E ₂ =1299.80MPa, η ₂ =77347.37MPa·s; E ₁ is the elastic modulus of spring II, and η ₁ is Viscosity of Sticky Pot II;

Step 3: Determination of the mechanical curve of the four-element mechanical model:

The two components in step 1 (spring I and sticky pot I) and the two components in step 2 (spring II and sticky pot II) form an actual four-component model in the measuring device for constructing the four-component model, see Figure 1d, measure its creep curve, see Figure 6; then substitute the calculated E ₁ , E ₂ , η ₁ , η ₂ into the creep equation of the four-element mechanical model, and substitute different times t to obtain a calculated creep Curve, see Figure 7.

Step 4: Superimpose and compare the experimental creep curve and the calculated creep curve, as shown in Figure 8. It can be seen from the figure that the two curves are basically consistent, indicating that the actual spring and sticky pot can replace the abstract spring and sticky pot, so it shows that the actual , Concrete (the antonym of abstract) mechanical model can replace the classic, abstract mechanical model.

In summary, the test device of a polymer viscoelastic model of the present invention is no longer an abstract concept, but a practical device, with which the combination of different model elements can be completed to form an actual Maxwell model, Kelvin model, three-element model, and four-element model. The parameters and mechanical curves of its associated components can then be investigated and measured.

By measuring the actual Maxwell model and Kelvin model, the elastic moduli of the two elastic model elements can be calculated as E ₁ , E ₂ and the viscosities η ₁ and η ₂ of the two viscous model elements. Substituting it into the creep equation of the four-element mechanical model, a creep curve can be obtained. Then use this device to form an actual four-element mechanical model, and measure a creep curve. Compared with the calculated creep curve, the two curves are basically consistent, so it proves the concrete and actual mechanics. Models can replace classical, abstract mechanical models.

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.

Images