CN113836656B - Calculation method for reducing amount of fluorine-silicon modified PERT barrier liner pipe by adopting finite element algorithm - Google Patents

Calculation method for reducing amount of fluorine-silicon modified PERT barrier liner pipe by adopting finite element algorithm Download PDF

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CN113836656B
CN113836656B CN202111073605.XA CN202111073605A CN113836656B CN 113836656 B CN113836656 B CN 113836656B CN 202111073605 A CN202111073605 A CN 202111073605A CN 113836656 B CN113836656 B CN 113836656B
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褚展鹏
金崇阳
刘跃明
霍福磊
陈江慧
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Linhai Weixing New Building Materials Co Ltd
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Abstract

The invention discloses a method for calculating the diameter reduction of a fluorine-silicon modified PERT barrier liner pipe by adopting a finite element algorithm, wherein the fluorine-silicon modified PERT barrier liner pipe comprises a protective outer layer, a second hot melt adhesive layer, a barrier layer, a first hot melt adhesive layer and a functional inner layer, and the method comprises the following steps of: testing and determining necessary parameters corresponding to each layer and the whole, calculating to obtain the minimum critical external pressure of the whole lining pipe, modeling in finite element software, applying the minimum critical external pressure, calculating to obtain the lower limit of the reducing quantity of the whole lining pipe, calculating to obtain the buckling critical external pressure of the whole lining pipe, modeling in the finite element software, applying the buckling critical external pressure, calculating to obtain the upper limit of the whole reducing quantity, and taking values in the range interval of the upper limit and the lower limit as the reducing quantity of the fluorine-silicon modified PERT barrier lining pipe. The invention provides a theoretical calculation method for the blocking shrinkage of the fluorine-silicon modified PERT, and the method reduces experiments, reduces errors and improves efficiency in the actual operation process.

Description

Calculation method for reducing amount of fluorine-silicon modified PERT barrier liner pipe by adopting finite element algorithm
Technical Field
The invention belongs to the technical field of calculation of the reduction of a lining pipe, and particularly relates to a calculation method of the reduction of a fluorine-silicon modified PERT barrier lining pipe by adopting a finite element algorithm.
Background
The fluorine-silicon modified PERT barrier liner pipe is used as a multilayer pipe, the pipe material and the size of each layer of pipe are different, the required reducing amount is also different, and the reducing amount suitable for one layer cannot be selected at will for reducing in the actual operation process, so that a uniform reducing amount needs to be selected for the multilayer pipe.
In the actual operation process, the multilayer pipe may be subjected to diameter reduction operation by adopting an appropriate diameter reduction amount empirically, and a mature diameter reduction amount calculation method for different materials, different temperatures and different sizes is lacked.
Disclosure of Invention
In order to solve the problems, the invention aims to provide a calculation method for the reducing amount of a fluorine-silicon modified PERT barrier liner pipe by adopting a finite element algorithm.
In order to achieve the purpose, the following technical scheme is provided:
the calculation method of the reducing amount of the fluorine-silicon modified PERT blocking lining pipe adopts a finite element algorithm, the fluorine-silicon modified PERT blocking lining pipe comprises a functional inner layer, a first hot melt adhesive layer, a blocking layer, a second hot melt adhesive layer and a protective outer layer, and the functional inner layer is made of fluorine-silicon modified PERT; the material of the barrier layer is EVOH; the material of the protective outer layer is PERT, and the calculation method comprises the following steps:
1) Measuring and determining corresponding necessary parameters of the functional inner layer, the first hot-melt adhesive layer, the barrier layer, the second hot-melt adhesive layer and the protective outer layer, and testing the mechanical property of the prepared integral pipe to obtain corresponding parameters of the integral lining pipe;
2) Determining the minimum shear strength tau of the shear strength of the fluorine-silicon modified PERT barrier liner pipe and the steel pipe min ：
3) Calculating the minimum critical external pressure P of the whole lining pipe min : calculating the minimum critical external pressure P according to the friction coefficient f of the lining pipe and the steel pipe min ＝τ min /f；
4) Modeling in finite element software according to the geometric dimension parameters obtained in the step 1), substituting the geometric dimension parameters into the material parameters of each layer, and applying corresponding P to the whole pipe min The lower limit L of the reducing quantity value of the whole lining pipe is obtained by running and calculating min ；
5) Calculating the buckling critical external pressure Pc of each layer: respectively substituting the material parameters obtained in the step 1) into a calculation formula of the buckling critical external pressure, which comprises the following specific steps:
Figure GDA0003758588580000021
wherein
Figure GDA0003758588580000022
P C Is critical point of bucklingExternal pressure, P eL Is the elastic term of the buckling pressure, calculated from the Young's modulus, t wall thickness, D outer diameter and v Poisson's ratio of the E monoblock liner, P p Is the plasticity term of buckling pressure, where SMYS is the characteristic yield strength, f 0 Substituting the elastic term and the plastic term of the calculated yield pressure into the solution to obtain respective P of each layer for the out-of-roundness of the pipe C The value of (d);
6) Modeling in finite element software according to the geometric dimension parameters obtained in the step 1), substituting the geometric dimension parameters into the material parameters of each layer, and applying P to the whole pipe C The upper limit L of the reducing quantity value of the whole lining pipe is obtained by running and calculating the uniform external pressure max ；
7) L obtained according to steps 4) and 6) min And L max According to the actual engineering, take L max And L min The value in the range interval is taken as the reducing quantity of the fluorine-silicon modified PERT barrier liner pipe.
Further, the functional inner layer comprises the following components: 50-60 parts of PERT II type granules, 30-40 parts of PE granules, 10-15 parts of fluorine-containing monomer, 0.5-1 part of antioxidant 330, 0.15 part of initiator and 0.075 part of calcium carbonate.
Further, modeling in finite element software is to solve three simultaneous basic equations:
1) Equation of equilibrium
Figure GDA0003758588580000031
Figure GDA0003758588580000032
In the formula f r Representing radial friction force, f θ Indicating the circumferential friction force;
2) Physical equation (relationship between stress and strain)
Figure GDA0003758588580000033
Figure GDA0003758588580000034
Figure GDA0003758588580000035
Wherein E is Young's modulus and v is Poisson's ratio;
3) Deformation coordination equation (relationship between displacement and strain)
Figure GDA0003758588580000036
Where σ is the principal stress, τ is the shear stress, and ε and γ are strains.
Further, the stress and strain components are independent of the angle θ, σ r = P, P obtained in step 3) and step 5) min And P C Sequentially substituting all the equations to simultaneously solve to obtain corresponding radial strain epsilon r The integral calculation in the thickness direction is carried out to obtain the radial integral deformation, namely the reducing diameter L min And L max 。
Further, the integral calculation in the thickness direction is
Figure GDA0003758588580000041
Where D is the outer diameter and D is the inner diameter.
Further, the minimum shear strength τ min ≥0.15MPa。
Furthermore, the value range of D is 50mm-315mm, and the value range of t is 0.05D-0.15D.
Further, f in step 5) 0 ≥0.5％。
The invention has the beneficial effects that: a theoretical calculation method is provided for the fluorine-silicon modified PERT barrier liner pipe, unnecessary experiments are reduced, operation errors are reduced, and the working efficiency is improved.
Drawings
FIG. 1 is a schematic view of the structure of a fluorosilicone modified PERT barrier liner tube of the present invention;
FIG. 2 is a flow chart of the calculation of the present invention.
In the figure: 1. a functional inner layer; 2. a first hot melt adhesive layer; 3. a barrier layer; 4. a second hot melt adhesive layer; 5. and (4) protecting the outer layer.
Detailed Description
The invention will be further described with reference to the drawings and examples in the following description, but the scope of the invention is not limited thereto.
A fluorine-silicon modified PERT barrier liner pipe is shown in figure 1 and sequentially comprises a functional inner layer, a first hot melt adhesive layer 2, a barrier layer 3, a second hot melt adhesive layer 4 and a protective outer layer 5 from inside to outside.
FIG. 2 represents the operation of the diameter reduction calculation method: obtaining the minimum critical external pressure through the calculation of the minimum shear strength, and then carrying out finite element modeling calculation to obtain the lower limit of the diameter shrinkage value; and (3) calculating to obtain buckling critical external pressure through a buckling instability criterion, then performing finite element modeling calculation to obtain an upper limit of a reducing quantity value, and determining a final reducing quantity value through the upper limit and the lower limit.
Example 1
1) Preparing a fluorine-silicon modified PERT barrier liner pipe: the functional inner layer 1 comprises the following components: 55 parts of PERT II type granules, 30 parts of PE granules, 10 parts of fluorine-containing monomer, 3301 parts of antioxidant, 0.15 part of initiator and 0.075 part of calcium carbonate; the prepared fluorine-silicon modified PERT barrier liner pipe has the outer diameter of 110mm and the thickness of 10mm, the material performance test is carried out on the whole pipe section, and the density is 0.958g/cm 3 The overall equivalent Young's modulus E is 996MPa, the Poisson ratio v is 0.35, the tensile yield strength is 25MPa,
Figure GDA0003758588580000051
Figure GDA0003758588580000052
the tolerance allowed for this series of tubes in actual production is +0.7mm,so that f is calculated 0 =0.64%, and f is required by formula 0 Not less than 0.5%, so that f 0 Take 0.64%, SMYS =25 × 0.8=20mpa.
2) Determining the minimum shear strength tau of the shear strength of the outer layer of the fluorine-silicon modified PERT barrier lining pipe and the steel pipe min The minimum shear strength needs to be greater than 0.15MPa.
3) Calculating the minimum critical external pressure P of the whole lining pipe min : calculating the minimum critical external pressure P according to the friction coefficient f =0.25 of the lining pipe and the steel pipe min ＝τ min /f＝0.6MPa；
4) Modeling in finite element software according to the geometric dimension parameters obtained in the step 1), substituting the geometric dimension parameters into the material parameters (shown in the table 1) of each layer, and correspondingly applying P min The lower limit L of the reducing quantity value of the whole lining pipe is obtained by running and calculating min ＝1.08mm。
Table 1 corresponding parameters of fluorosilicone modified PERT barrier liner pipe prepared in example 1
Figure GDA0003758588580000053
Figure GDA0003758588580000061
5) Calculating the buckling critical external pressure Pc of the integral lining pipe: respectively substituting the material parameters obtained in the step 1) into a calculation formula of the buckling critical external pressure, which comprises the following specific steps:
Figure GDA0003758588580000062
wherein
Figure GDA0003758588580000063
P C I.e. critical external pressure of buckling, P eL Is the elastic term of the buckling pressure, which is calculated from E overall equivalent Young's modulus, t wall thickness, D outer diameter and v Poisson's ratio, P p The plasticity term for buckling pressure, where SMYS is the characteristic yield strength, f 0 Substituting the calculated elastic term and plastic term of the yield pressure into the solution to obtain the integral P of the pipe section for the out-of-roundness of each layer of pipe C Numerical value of (A), P eL ＝0.819MPa， P p =6.83MPa, and solving a cubic equation set to obtain the buckling critical external pressure P C ＝2.25MPa；
6) Modeling in finite element software according to the geometric dimension parameters obtained in the step 1), substituting the geometric dimension parameters into the material parameters of each layer, and applying P C The upper limit L of the reducing quantity value of the whole lining pipe is obtained by running and calculating the uniform external pressure max ＝6.53mm；
7) L obtained according to steps 4) and 6) min And L max And at a minimum L max And maximum L min The value in the range interval of (A) is taken as the reducing quantity of the fluorine-silicon modified PERT barrier liner pipe, the value range of the reducing quantity is [1.08mm]The diameter reduction can be taken to be 3.8mm according to the linear difference.
Example 2
1) Preparing a fluorine-silicon modified PERT barrier liner pipe: the functional inner layer 1 comprises the following components: 55 parts of PERT II type granules, 30 parts of PE granules, 10 parts of fluorine-containing monomer, 3301 parts of antioxidant, 0.15 part of initiator and 0.075 part of calcium carbonate; the prepared fluorine-silicon modified PERT barrier liner pipe has the outer diameter of 250mm and the thickness of 22.7mm, the material performance test is carried out on the whole pipe section, and the density is 0.958g/cm 3 The overall equivalent Young's modulus E is 996MPa, the Poisson ratio v is 0.35, the tensile yield strength is 25MPa,
Figure GDA0003758588580000071
the tolerance of the series of pipes in actual production is +0.7mm, so f is calculated 0 =0.64%, and f is required by formula 0 Not less than 0.5%, so that f 0 Taking 0.64% and SMYS =25 × 0.8=20MPa;
2) Determining the minimum shear strength tau of the shear strength of the outer layer of the fluorine-silicon modified PERT barrier lining pipe and the steel pipe min The minimum shear strength needs to be more than 0.15MPa;
3) Calculating the minimum critical external pressure P of the whole lining pipe min : calculating the minimum critical external pressure P according to the friction coefficient f =0.25 of the lining pipe and the steel pipe min ＝τ min /f＝0.6MPa；
4) Modeling in finite element software according to the geometric dimension parameters obtained in the step 1), substituting the geometric dimension parameters into the material parameters of each layer (shown in Table 2), and correspondingly applying P min The lower limit L of the reducing value of the whole lining pipe is obtained by running calculation min ＝1.86mm；
Table 2 corresponding parameters of the fluorosilicone modified pertt barrier liner tube prepared in example 2
Materials of the layers Young's modulus (MPa) Poisson ratio Tensile Strength (MPa)
Functional inner layer 1020 0.36 25
Barrier layer 2253 0.1 13.6
Hot melt adhesive layer 435 0.5 31.7
Protective outer layer 920 0.3 22
5) Calculating the buckling critical external pressure Pc of the integral lining pipe: respectively substituting the material parameters obtained in the step 1) into a calculation formula of buckling critical external pressure, which comprises the following specific steps:
Figure GDA0003758588580000081
wherein
Figure GDA0003758588580000082
P C I.e. critical external pressure of buckling, P eL An elastic term for the buckling pressure, calculated from E overall equivalent Young's modulus, wall thickness of t, D outer diameter and v Poisson's ratio, P p The plasticity term for buckling pressure, where SMYS is the characteristic yield strength, f 0 Substituting the calculated elastic term and plastic term of the yield pressure into the solution to obtain the integral P of the pipe section for the out-of-roundness of each layer of pipe C Numerical value of (A), P eL ＝1.965MPa；
P p =5.54MPa, solving a cubic equation set to obtain the buckling critical external pressure P C ＝3.31MPa；
6) Modeling in finite element software according to the geometric dimension parameters obtained in the step 1), substituting the geometric dimension parameters into the material parameters of each layer, and applying P C The upper limit L of the reducing quantity value of the whole lining pipe is obtained by running and calculating the uniform external pressure max ＝8.93mm。
7) L obtained according to steps 4) and 6) min And L max And at a minimum L max And maximum L min The value of the range interval is taken as the reducing quantity of the fluorine-silicon modified PERT barrier liner pipe, the value range of the reducing quantity is [1.86mm ]3mm]And measuring the diameter reduction amount to 5.395mm.
Except the above examples, the material proportions for preparing the fluorine-silicon modified PERT barrier liner pipe are 50-60 parts of PERT II type granules, 30-40 parts of PE granules, 10-15 parts of fluorine-containing monomer, 0.5-1 part of antioxidant, 0.15 part of initiator and 0.075 part of calcium carbonate in parts by weight; the overall equivalent Young's modulus and Poisson's ratio parameters of the pipes prepared from different materials are changed.

Claims (8)

1. The method for calculating the reducing quantity of the fluorine-silicon modified PERT barrier liner pipe by adopting a finite element algorithm is characterized in that the fluorine-silicon modified PERT barrier liner pipe comprises a functional inner layer (1), a first hot melt adhesive layer (2), a barrier layer (3), a second hot melt adhesive layer (4) and a protective outer layer (5), wherein the functional inner layer (1) is made of fluorine-silicon modified PERT; the material of the barrier layer (3) is EVOH; the material of the protective outer layer (5) is PERT, and the calculation method comprises the following steps:
1) measuring and determining corresponding necessary parameters of the functional inner layer (1), the first hot-melt adhesive layer (2), the barrier layer (3), the second hot-melt adhesive layer (4) and the protective outer layer (5), and testing the mechanical property of the prepared integral pipe to obtain corresponding parameters of the integral lining pipe;
2) Determining the minimum shear strength tau of the shear strength of the fluorine-silicon modified PERT barrier liner pipe and the steel pipe min ：
3) Calculating the minimum critical external pressure P of the whole lining pipe min : calculating the minimum critical external pressure P according to the friction coefficient f of the lining pipe and the steel pipe min ＝τ min /f；
4) Modeling in finite element software according to the geometric dimension parameters obtained in the step 1), substituting the geometric dimension parameters into the material parameters of each layer, and applying corresponding P to the whole pipe min The lower limit L of the reducing quantity value of the whole lining pipe is obtained by running and calculating min ；
5) Calculating the buckling critical external pressure Pc of each layer: respectively substituting the material parameters obtained in the step 1) into a calculation formula of the buckling critical external pressure, which comprises the following specific steps:
Figure FDA0003758588570000011
wherein
Figure FDA0003758588570000012
P C I.e. critical external pressure of buckling, P eL Is the elastic term of the buckling pressure, calculated from the Young's modulus, t wall thickness, D outer diameter and v Poisson's ratio of the E integral lining tube, P p Is the plasticity term of buckling pressure, where SMYS is the characteristic yield strength, f 0 Substituting the calculated elastic term and plastic term of the yield pressure into the solution to obtain P for the out-of-roundness of the pipe C The value of (d);
6) Modeling in finite element software according to the geometric dimension parameters obtained in the step 1), substituting the geometric dimension parameters into the material parameters of each layer, and applying P to the whole pipe C The upper limit L of the reducing quantity value of the whole lining pipe is obtained by running and calculating the uniform external pressure max ；
7) L obtained according to steps 4) and 6) min And L max According to the actual engineering, take L max And L min The value in the range of (2) is taken as the reducing quantity of the fluorine-silicon modified PERT barrier liner pipe.
2. The calculation method for the reducing diameter of the fluorine-silicon modified PERT barrier liner pipe adopting the finite element algorithm according to the claim 1, wherein the functional inner layer (1) comprises the following components: 50-60 parts of PERT II type granules, 30-40 parts of PE granules, 10-15 parts of fluorine-containing monomer, 0.5-1 part of antioxidant, 0.15 part of initiator and 0.075 part of calcium carbonate.
3. The method for calculating the diameter reduction of the fluorine-silicon modified PERT barrier liner pipe by using the finite element algorithm according to claim 1, wherein modeling in finite element software is solved by three simultaneous basic equations:
1) Equation of equilibrium
Figure FDA0003758588570000021
Figure FDA0003758588570000022
In the formula f r Representing radial friction force, f θ Expressing the circumferential friction force;
2) Physical equation
Figure FDA0003758588570000031
Figure FDA0003758588570000032
Figure FDA0003758588570000033
Wherein E is Young's modulus and v is Poisson's ratio;
3) Equation of coordination of deformation
Figure FDA0003758588570000034
Where σ is the principal stress, τ is the shear stress, and ε and γ are strains.
4. The method of claim 3, wherein the stress component and the strain component are independent of the angle θ, and σ is the diameter of the liner tube r = P, P obtained from step 3) and step 5) min And P C Sequentially substituting all the equations to simultaneously solve to obtain the corresponding radial strain epsilon r The integral calculation in the thickness direction is carried out to obtain the radial integral deformation, namely the shrinkage L min And L max 。
5. The method for calculating the diameter reduction of the fluorine-silicon modified PERT barrier liner pipe by using the finite element algorithm according to claim 4, wherein the integral calculation formula in the thickness direction is
Figure FDA0003758588570000035
Where D is the outer diameter and D is the inner diameter.
6. The method of claim 1, wherein the minimum shear strength τ is calculated by using a finite element algorithm to calculate the reduction of the PFA-PERT barrier liner tube min ≥0.15MPa。
7. The method for calculating the reducing diameter of the fluorine-silicon modified PERT barrier liner pipe by using the finite element algorithm according to claim 1, wherein the value range of D is 50mm-315mm, and the value range of t is 0.05D-0.15D.
8. The method for calculating the diameter reduction of the fluorine-silicon modified PERT barrier liner pipe by using the finite element algorithm according to claim 1, wherein f) in the step 5) 0 ≥0.5％。
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