CN112711836B - Method for rapidly obtaining technological parameters of metal rubber component - Google Patents
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Abstract
A method for rapidly obtaining technological parameters of a metal rubber component relates to a method for obtaining technological parameters of a metal rubber component. The invention solves the problem that the prior art can not quickly and accurately obtain the required process parameters of the metal rubber component. The invention comprises the following steps: fitting the metal rubber compression stress-strain curve in a linear stage; step two: fitting the metal rubber compression stress-strain curve in a nonlinear stage; step three: obtaining a change curve of the elastic modulus in a linear stage along with the inner-outer diameter ratio through a stress-strain equation, and fitting the curve; step four: determining a demarcation strain value of a linear stage and a nonlinear stage to obtain an equation of the ratio of the maximum linear elastic strain to the inner diameter and the outer diameter; step five: and integrating the obtained relational expressions to obtain the relation among the mechanical parameters, the maximum linear elasticity and the inner-outer diameter ratio of the metal rubber component. The method is used for rapidly obtaining the technological parameters of the metal rubber component.
Description
Technical Field
The invention relates to a method for obtaining process parameters, in particular to a method for quickly obtaining process parameters of a metal rubber component, and particularly relates to a method for quickly obtaining the internal-external diameter ratio and the relative density of a required metal rubber component.
Background
Vibration damping, noise reduction, and sealing are becoming more and more of a concern in the operation of mechanical equipment. Meanwhile, the method puts high requirements on the operation of mechanical equipment in severe environment. The rubber is widely used as an ideal vibration damping, noise reduction and sealing material in the field of engineering machinery. However, the rubber has high hardness and modulus in a low-temperature environment, is easy to age in a severe marine environment, and has short alternative service life at high and low temperatures. The metal rubber is an elastic material with low temperature resistance and wide temperature range, has good elasticity and damping performance, and has mechanical properties similar to those of rubber, so the metal rubber is called as the metal rubber. The metal rubber is prepared from metal wires by a special preparation process to obtain a homogeneous porous material, wherein the preparation process of the metal rubber comprises the following steps: winding the metal wire into a spring spiral coil with certain diameter and screw pitch, laying the spring spiral coil into a three-dimensional blank, and finally performing punch forming.
The compressive stress-strain curve of the metal rubber member includes three stages of linear elasticity, soft characteristics and index hardening, but each characteristic point of the curve is affected by the shape and size of the member. Therefore, it is difficult to obtain the desired result because a lot of work is required to obtain the dimensional parameters of the metal rubber member having certain properties in engineering.
In summary, the prior art has a problem that the required process parameters of the metal rubber component cannot be rapidly and accurately obtained in engineering application.
Disclosure of Invention
The invention aims to solve the problem that the required process parameters of the metal rubber component cannot be quickly and accurately obtained in engineering application in the prior art. Provides a method for rapidly obtaining the process parameters of the metal rubber component.
The technical scheme of the invention is a method for rapidly obtaining technological parameters of a metal rubber component, which comprises the following steps:
the method comprises the following steps: fitting the metal rubber compression stress-strain curve in a linear stage to obtain the elastic modulus and the maximum strain value of the metal rubber in the linear stage with different inner-outer diameter ratios;
step two: fitting the metal rubber compression stress-strain curve in a nonlinear stage to obtain polynomial coefficients of the metal rubber nonlinear stage stress-strain equation with different inner-outer diameter ratios;
step three: inputting the elastic modulus values of the metal rubber in the linear stage with different inner-outer diameter ratios into Origin software to obtain a curve of the elastic modulus changing along with the inner-outer diameter ratios, and fitting the curve to obtain an equation of the elastic modulus changing along with the inner-outer diameter ratios in the linear stage;
step four: inputting each coefficient of the stress-strain equation of the metal rubber in the nonlinear stage with different inner-outer diameter ratios into Origin software to obtain a curve of each coefficient changing along with the inner-outer diameter ratio, and fitting the curve to obtain a mathematical relation between each coefficient in the nonlinear stage and the inner-outer diameter ratio;
step five: and determining the demarcation strain values of the linear stage and the nonlinear stage, and introducing the maximum strain value of the linear stage into Origin software to obtain a curve of the maximum linear elastic strain changing along with the change of the inner diameter ratio and the outer diameter ratio. Fitting the curve to obtain an equation of the maximum linear elastic strain changing along with the change of the inner diameter ratio and the outer diameter ratio;
step six: and (4) sorting the equation of the elastic modulus of the linear stage, which is obtained in the third step, changing along with the inner diameter ratio, the equation of the stress-strain curve of the nonlinear stage, which is obtained in the fourth step, and the equation of the maximum linear elastic strain and the inner diameter ratio, which is obtained in the fifth step, so as to obtain the relationship among the mechanical parameters of the metal rubber component, the maximum linear elastic strain and the inner diameter ratio.
Compared with the prior art, the invention has the following improvement effects:
in the invention, the first step to the fifth step are analyzed by adopting Origin data analysis software, the characteristic points of the compressive stress-strain curve are analyzed, the relation between the performance parameters of each stage and the geometric dimension of the member is deduced, and the constitutive equation of the metal rubber member is obtained through the sixth step. A constitutive relation model of the maximum linear elastic strain, the elastic modulus and the structural size of the metal rubber component is deduced. According to the invention, Origin software is adopted to fit the curves obtained in the first step to the fifth step, the coefficients of the polynomial are obtained through fitting, and the relation between the performance parameters and the geometric dimension of the member at each stage is deduced, so that the inner-outer diameter ratio and the relative density of the metal rubber member can be rapidly and accurately determined in engineering application. The method and the device really solve the problem that the required process parameters of the metal rubber component cannot be quickly and accurately obtained in engineering application, and can quickly determine the process parameters of the metal rubber component according to the performance requirements of the material.
Drawings
FIG. 1 is a linear phase fit of the stress-strain curve for the O-shaped metal rubber component of the present invention;
FIG. 2 is a non-linear phase fit of the stress-strain curve for the O-shaped metal rubber component of the present invention;
FIG. 3 is a graph showing the change of the linear elastic modulus of the O-type metal rubber member according to the present invention with respect to the ratio of inner to outer diameters;
FIG. 4 is a fitting curve of the elastic modulus of the O-shaped metal rubber member of the present invention as a function of the inner/outer diameter ratio;
FIG. 5 is a graph showing the maximum linear elastic strain of the O-shaped metal rubber member according to the present invention as a function of the inner/outer diameter ratio;
FIG. 6 is a maximum linear elastic strain fitting curve of the O-shaped metal rubber member of the present invention.
Detailed Description
The specific implementation mode is as follows: the embodiment is described with reference to fig. 1 to 6, and the method for rapidly obtaining the process parameters of the metal rubber component of the embodiment comprises the following steps:
the method comprises the following steps: fitting the metal rubber compression stress-strain curve in a linear stage to obtain the elastic modulus and the maximum strain value of the metal rubber in the linear stage with different inner-outer diameter ratios;
step two: fitting the metal rubber compression stress-strain curve in a nonlinear stage to obtain polynomial coefficients of the metal rubber nonlinear stage stress-strain equation with different inner-outer diameter ratios;
step three: inputting the elastic modulus values of the metal rubber in the linear stage with different inner-outer diameter ratios into Origin software to obtain a curve of the elastic modulus changing along with the inner-outer diameter ratios, and fitting the curve to obtain an equation of the elastic modulus changing along with the inner-outer diameter ratios in the linear stage;
step four: inputting each coefficient of the stress-strain equation of the metal rubber in the nonlinear stage with different inner-outer diameter ratios into Origin software to obtain a curve of each coefficient changing along with the inner-outer diameter ratio, and fitting the curve to obtain a mathematical relation between each coefficient in the nonlinear stage and the inner-outer diameter ratio;
step five: and determining the demarcation strain values of the linear stage and the nonlinear stage, and introducing the maximum strain value of the linear stage into Origin software to obtain a curve of the maximum linear elastic strain changing along with the change of the inner diameter ratio and the outer diameter ratio. Fitting the curve to obtain an equation of the maximum linear elastic strain changing along with the change of the inner diameter ratio and the outer diameter ratio;
step six: and (4) sorting the equation of the elastic modulus of the linear stage, which is obtained in the third step, changing along with the inner diameter ratio, the equation of the stress-strain curve of the nonlinear stage, which is obtained in the fourth step, and the equation of the maximum linear elastic strain and the inner diameter ratio, which is obtained in the fifth step, so as to obtain the relationship among the mechanical parameters of the metal rubber component, the maximum linear elastic strain and the inner diameter ratio.
The invention will be described in further detail below with reference to the accompanying figures 1 to 6:
taking an O-type metal rubber member with a relative density of 0.2 as an example, the elastic modulus of the O-type metal rubber member in the linear stage can be obtained by performing 1-order polynomial fitting on the stress-strain linear stage of the O-type metal rubber member by adopting Origin software, and the corresponding polynomial coefficient can be obtained by performing 6-order polynomial fitting on the nonlinear stage of the O-type metal rubber member.
FIG. 1 is a linear stage fitting of a stress-strain curve of an O-shaped metal rubber member having an outer diameter of 10mm and an inner/outer diameter ratio of 0.2,
FIG. 2 is a non-linear stage fitting of the stress-strain curve of the O-shaped metal rubber member having an outer diameter of 10mm and an inner/outer diameter ratio of 0.2.
The maximum strain at the wire elastic stage of the O-shaped metal rubber member with an outer diameter of 10mm and an inner diameter-to-outer diameter ratio of 0.2 is about 0.18, and the elastic modulus is about 0.87 MPa.
The stress-strain equation of the metal rubber member with the outer diameter of 10mm and the inner-outer diameter ratio of 0.2 is as follows
σ＝0.04255+0.86862ε(ε≤0.18) (1)
σ＝0.05667-3.436ε+79.375ε2-609.01ε3+2356.89ε4
-3706.86ε5+2406.30ε6(ε＞0.18) (2)
The stress-strain linear equation of the O-shaped metal rubber component with the inner diameter ratio and the outer diameter ratio of 0.4, 0.6 and 0.8 in the online elastic stage can be obtained by adopting the same method:
σ＝-0.00324+0.51318ε(ε≤0.26) (3)
σ＝0.0232+0.15596ε(ε≤0.35) (4)
σ＝0.00702+0.0039ε(ε≤0.44) (5)
the polynomial coefficients of the nonlinear stage are shown in table 1:
the elastic modulus of the O-type metal rubber in the linear stage is obtained by the formulas (1), (3), (4) and (5) with the inner/outer diameter ratio of 0.2, 0.4, 0.6 and 0.8.
FIG. 3 is a graph showing the change of the modulus of elasticity with the ratio of the inner diameter to the outer diameter
Using Origin software to perform polynomial fitting of degree 3 on the curve,
FIG. 4 is a fitting curve of linear elastic modulus varying with inner and outer diameter ratio
An equation that the elastic modulus of the O-shaped metal rubber component changes along with the inner-outer diameter ratio in the linear stage is obtained
E＝1.19533-1.24133x-2.09411x2+2.22397x3 (6)
Wherein the ratio of the inner diameter to the outer diameter of the metal rubber member of x- (O) -type, R2/R1
Similarly, according to the mathematical relationship between each coefficient and the inner and outer diameter ratio values in the nonlinear stage stress-strain 6 degree polynomial relationship of the O-shaped metal rubber component, as shown in the formula (7),
b＝C0+C1x (7)
wherein C is0、C1The parameter values of each item are shown in table 2.
| b0 | b1 | b2 | b3 | b4 | b5 | b6 | |
| C0 | 0.07942 | -4.493 | 103.64 | -798.29 | 2938.89 | -4632.27 | 3068.62 |
| C1 | -0.1058 | 6.288 | -138.01 | 1095.61 | -4181.94 | 6554.99 | -4313.01 |
Due to the difference of constitutive equations of the linear stage and the nonlinear stage, it is necessary to determine a boundary strain value of the linear elastic stage and the nonlinear stage, that is, the maximum strain of the o-type metal rubber member in the linear elastic stage.
FIG. 5 is a graph showing the maximum linear elastic strain of the O-shaped metal rubber member as a function of the inner/outer diameter ratio.
As can be seen from fig. 5, the maximum linear elastic strain of the o-type metal rubber member has a linear relationship with the inner-outer diameter ratio. The curve in figure 5 was linearly fitted by Origin software,
FIG. 6 is a fitting curve of the maximum linear elastic strain of the O-shaped metal rubber component, and the equation for obtaining the ratio of the maximum linear elastic strain to the inner diameter and the outer diameter is as follows:
ε＝0.1057+0.4103x (8)
epsilon-maximum linear elastic strain
X-O-type metal rubber member inner-outer diameter ratio, R2/R1
Through research and formula derivation on various performances of the O-shaped metal rubber component in the online elastic stage, the relation among mechanical parameters, maximum linear elastic strain and internal and external diameter ratios of the O-shaped metal rubber component with the relative density of 0.2 is obtained as follows:
E○＝1.19533-1.24133x-2.09411x2+2.22397x3(ε≤0.1057+0.4103x) (9)
σ○＝b0+b1ε+b2ε2+b3ε3+b4ε4+b5ε5+b6ε6(ε＞0.1057+0.4103x) (10)
in the formula: e○Linear elastic modulus, MPa, of O-type metal rubber Member
X-O-type metal rubber member inner-outer diameter ratio, R2/R1
Wherein the coefficients of the polynomial of formula (10) are calculated from the values of the parameters in Table 2 by formula (7)
Through the formulas (9) and (10), the inner-outer side length ratio and the relative density of the O-shaped metal rubber component can be determined according to the mechanical property of the required material in engineering application. Namely, the process parameters of the O-shaped metal rubber component are rapidly determined according to the performance requirements of the material.
The above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.
Claims (6)
1. A method for rapidly obtaining technological parameters of a metal rubber component is characterized by comprising the following steps: it comprises the following steps:
the method comprises the following steps: fitting the metal rubber compression stress-strain curve in a linear stage to obtain the elastic modulus and the maximum strain value of the metal rubber in the linear stage with different inner-outer diameter ratios;
step two: fitting the metal rubber compression stress-strain curve in a nonlinear stage to obtain polynomial coefficients of the metal rubber nonlinear stage stress-strain equation with different inner-outer diameter ratios;
step three: inputting the elastic modulus values of the metal rubber in the linear stage with different inner-outer diameter ratios into Origin software to obtain a curve of the elastic modulus changing along with the inner-outer diameter ratios, and fitting the curve to obtain an equation of the elastic modulus changing along with the inner-outer diameter ratios in the linear stage;
step four: inputting each coefficient of the stress-strain equation of the metal rubber in the nonlinear stage with different inner-outer diameter ratios into Origin software to obtain a curve of each coefficient changing along with the inner-outer diameter ratio, and fitting the curve to obtain a mathematical relation between each coefficient in the nonlinear stage and the inner-outer diameter ratio;
step five: determining boundary strain values of a linear stage and a non-linear stage, importing the maximum strain value of the linear stage into Origin software to obtain a curve of the maximum linear elastic strain changing along with the change of the inner diameter ratio and the outer diameter ratio, and fitting the curve to obtain an equation of the maximum linear elastic strain changing along with the change of the inner diameter ratio and the outer diameter ratio;
step six: and (4) sorting the equation of the elastic modulus of the linear stage, which is obtained in the third step, changing along with the inner diameter ratio, the equation of the stress-strain curve of the nonlinear stage, which is obtained in the fourth step, and the equation of the maximum linear elastic strain and the inner diameter ratio, which is obtained in the fifth step, so as to obtain the relationship among the mechanical parameters of the metal rubber component, the maximum linear elastic strain and the inner diameter ratio.
2. The method for rapidly acquiring the process parameters of the metal rubber component according to claim 1, characterized in that: and (3) performing 1-time item fitting on the linear stage to obtain a stress-strain equation of the linear stage.
3. The method for rapidly acquiring the process parameters of the metal rubber component according to claim 2, characterized in that: and step two pairs of nonlinear stages are subjected to 6-degree polynomial fitting to obtain a stress-strain equation of the nonlinear stage.
4. A method for rapidly obtaining the process parameters of the metal rubber component according to claim 3, characterized in that: and step three, performing 3-degree polynomial fitting on a change curve of the elastic modulus in the linear stage along with the inner-outer diameter ratio.
5. The method for rapidly acquiring the process parameters of the metal rubber component according to claim 4, characterized in that: and step three, obtaining an equation of the elastic modulus in the linear stage changing along with the change of the inner diameter ratio through a stress-strain equation with different inner diameter ratios.
6. The method for rapidly acquiring the process parameters of the metal rubber component according to claim 5, characterized in that: and the maximum linear elastic strain in the step five is in a linear relation with the inner diameter ratio and the outer diameter ratio.
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