A design method for equal residual tension of high-precision fiber wet-wound cylindrical parts

Abstract

The present invention discloses a method for designing a high-precision fiber wet-wound cylindrical product with equal residual tension, comprising: S1, solving the temperature field distribution T (r i ); S2. Based on the known temperature field distribution, conduct experimental characterization or combine the isothermal curing model to solve the curing degree field distribution γ(r i ); S3, based on the current winding layer r i With all the implicit functions of the recursive iterative format between the winding layers outside it, the initial winding layer r1 and the outermost winding layer r n Relationship function between hoop tension; S4, solve the hoop tension F of the outermost winding layer based on the initial guess value and convergence requirements W (r n ); S5. Based on the implicit function established in S3, the hoop tension of each winding layer is solved layer by layer starting from the outermost winding layer.

Description

Technical Field

[0001] The invention relates to the field of composite material forming technology, and in particular to a method for designing equal residual tension of a high-precision fiber wet-wound cylindrical part. Background Art

[0002] Wet winding, in which resin-impregnated fibers are wound around a rotating mandrel along a preset trajectory, is the most commonly used process for fiber-reinforced composite rotating structures. Applying appropriate winding tension helps straighten the fibers, eliminate defect bubbles, and fully utilize the fiber's load-bearing properties. Although tension control systems have significantly improved in terms of control accuracy, as shown in patent documents CN215359985U and CN106217838B, traditional constant-tension winding schemes result in residual tension due to the relaxation effect of the outer winding layer on the inner winding layer. This, coupled with the temperature effect and curing shrinkage effect, produces additional residual strain and rebound deformation. The design of residual tension based on thermo-chemical compensation effects lacks theoretical guidance, which seriously restricts the control of component dimensional accuracy. Patent document CN111199125A discloses a simulation method based on the hyperelastic constitutive model of resin and the life-death unit. This method can calculate the residual tension layer by layer, but the optimization design of equal residual tension still requires a tedious trial-and-error process; Patent document CN1528586A discloses a gradient tension application method to help overcome the defect of uneven tightness of the fiber layer. However, this tension system does not take into account the influence of thermal expansion effect and the synergistic effect of resin curing shrinkage. The design accuracy is low and it is not suitable for the preparation of high-performance wound parts. Summary of the Invention

[0003] In response to the above-mentioned technical problems and the shortcomings in the field, the present invention provides a method for designing equal residual tension for high-precision fiber wet-wound cylindrical parts. It is an analytical method for applying wet-wound tension that decreases layer by layer for thin-walled or thick-walled cylindrical structures, and realizes equal residual tension design while considering the effects of thermal expansion and chemical shrinkage, thereby improving the performance of wound parts.

[0004] A design method for equal residual tension of high-precision fiber wet-wound cylindrical parts. The specific process is as follows: Figure 1 Shown, including:

[0005] S1. Solve the temperature field distribution T(r) of the winding layer based on the boundary value problem of the heat conduction differential equation i );

[0006] S2. Based on the known temperature field distribution, conduct experimental characterization or combine the isothermal curing model to solve the curing degree field distribution γ(r i );

[0007] S3, based on the current winding layer r iWith all the implicit functions of the recursive iterative format between the winding layers outside it, the initial winding layer r1 and the outermost winding layer r n Relationship function between hoop tension:

[0008] F W (r i )=g(F W (r i+1 ),F W (r i+2 ),…,F W (r n ))

[0009] F W (r1) = g(F W (r n ))

[0010] Where i = 1, 2, ..., n, represents the number of winding layers;

[0011] S4. Solve the hoop tension F of the outermost winding layer based on the initial guess value and convergence requirements W (r n ):

[0012]

[0013] in, is the target residual hoop winding tension, is the fiber winding angle of the initial winding layer;

[0014] S5. Based on the implicit function established in S3, the hoop tension F of each winding layer is solved layer by layer starting from the outermost winding layer. W (r n-1 ),F W (r n-2 ),…,F W (r1):

[0015] F W (r i )=g(F W (r i+1 ),F W (r i+2 ),…,F W (r n )).

[0016] Specifically, the winding tension design mathematical model of the present invention is as follows Figure 2As shown in the figure, the plane strain state, linear elasticity, and small deformation assumptions are met. The wound layers are in close contact with no friction and sliding. The cooperative deformation of the core mold is considered. The core mold and thermosetting resin are isotropic materials. The wet winding process meets the conditions of winding first and then curing. Heat transfer occurs in the thickness direction. Only the unidirectional coupling of temperature and curing degree is considered. Curing occurs after the heat transfer reaches a steady state.

[0017] The specific process of S1 is:

[0018] S1.1. The differential equation for steady-state heat conduction without internal heat source based on Fourier's law is:

[0019]

[0020] S1.2. The general solution and distribution equation of the heat conduction differential equation are:

[0021] T(r)=C1ln r+C2

[0022]

[0023] Among them, the core mold boundary temperature is T0, the outer winding layer boundary temperature is T n , r i is the radius of the current winding layer position, r n is the radius of the outermost winding layer, and b is the outer diameter of the core mold.

[0024] The specific process of S2 conducting experimental characterization based on the known temperature field distribution to solve the curing degree field distribution is as follows:

[0025] Characterization of curing degree γ(r i )distributed:

[0026]

[0027] Where t is the curing time, ΔH is the exothermic peak of the DSC signal, and ΔH total It is the total exothermic peak of complete curing.

[0028] The specific process of S2 solving the curing degree field distribution based on the known temperature field distribution and the isothermal curing model is as follows:

[0029] Numerical solution of curing degree γ(r i )distributed:

[0030]

[0031]

[0032] Where A is the pre-exponential factor, E is the apparent activation energy, R is the gas constant, m is the fitted reaction order, and k0 is the reaction rate constant fitted based on the Arrhenius formula.

[0033] The specific process of S3 is:

[0034] S3.1, without considering the change of circumferential temperature, based on the superposition principle, the winding residual tension F θ (r i ) includes the current winding layer tension component, the outer winding layer tension component and the solidification deformation component:

[0035]

[0036] Among them, F W (r i ) is the hoop tension of the current winding layer, ΔF ex,θ (r i ) is the hoop tension change caused by all the winding layers outside the current winding layer, F cu,θ (r i ) is the circumferential chemical shrinkage force during the curing process;

[0037] S3.2. Based on geometric relationships And equal residual tension conditions, winding residual tension F θ (r i ) in the radial contraction stress component σ′ r (r i )satisfy:

[0038]

[0039] σ′ r (r i ) is the total radial residual stress of the current winding layer, Δθ is the infinitesimal element of the circumferential rotation angle, σ′ θ (r i ) is the total residual stress in the hoop of the current winding layer, σ′ ex,r (r i ,r n ) is the radial stress change caused by the outer winding layer, σ′ th,r (r i ) is the thermal deformation radial stress, σ′ cu,r (r i ) is the radial stress, h is the layer thickness;

[0040] S3.3, substitute F in S3.1 into S3.2 to establish the current winding layer r i and all outer winding layers recursive implicit function F W (r i )=g(F W (ri+1 ),F W (r i+2 ),…,F W (r n )).

[0041]

[0042] in, is the radial stiffness of the core mold, a is the inner diameter of the core mold, v1 is the Poisson's ratio of the core mold, E1 is the modulus of the core mold, and the correlation coefficient of the winding layer is v 2θ is the Poisson's ratio of the winding layer, v 2r is the Poisson's ratio of the winding layer, E 2r is the modulus in the fiber thickness direction, E 2θ is the fiber axial modulus, and the integral term is a simplified expression of accumulation.

[0043]

[0044] Where β′ represents the volume shrinkage of the fully cured resin, γ(r i ) is the curing degree of the current layer, E c,θ =V f E 2r +γ(r i )(1-V f )E0 is the axial modulus of the composite material, V f is the fiber volume fraction of the composite material, and E0 is the fully cured resin modulus.

[0045] The radial stress change σ′ caused by the outer winding layer ex,r (r i ,r n )satisfy:

[0046]

[0047] Based on the heat conduction equation, the thermal deformation radial stress σ′ th,r (r i )for:

[0048]

[0049] in, is the modulus of the composite material in the thickness direction, α is the thermal expansion coefficient of the composite material in the thickness direction, V f is the fiber volume fraction.

[0050] Based on the assumption of uniform solidification shrinkage strain, the radial stress σ′ cu,r (r i )for:

[0051]

[0052] Compared with the prior art, the present invention has the advantage that the present invention realizes the equal residual tension design of the fiber wet-wound cylindrical product taking into account the thermal-chemical coupling effect, thereby avoiding fiber wrinkles or warping deformation defects caused by residual stress. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 This is a schematic diagram of the process of solving the equal residual tension of the present invention;

[0054] Figure 2 Schematic diagram of the mathematical model for winding tension design of the present invention. DETAILED DESCRIPTION

[0055] The present invention will be further described below with reference to the accompanying drawings and specific examples. It should be understood that these examples are only used to illustrate the present invention and are not intended to limit the scope of the present invention.

[0056] A design method for equal residual tension of high-precision fiber wet-wound cylindrical parts. The specific process is as follows: Figure 1 As shown in the figure, the mathematical model of winding tension design is as follows Figure 2 As shown in the figure, the plane strain state, linear elasticity, and small deformation assumptions are met. There is no frictional slip between the winding layers. The core mold and resin are isotropic materials. The wet winding process meets the conditions of winding first and then curing. Only the unidirectional coupling of temperature on curing degree is considered, and curing occurs after the heat transfer reaches a steady state.

[0057] The equal residual tension design method for high-precision fiber wet-wound cylindrical parts includes:

[0058] S1. Solve the temperature field distribution T(r) of the winding layer based on the boundary value problem of the heat conduction differential equation i ), the specific process is:

[0059] S1.1. The differential equation for steady-state heat conduction without internal heat source based on Fourier's law is:

[0060]

[0061] S1.2. The general solution and distribution equation of the heat conduction differential equation are:

[0062] T(r)=C1ln r+C2

[0063]

[0064] Among them, the core mold boundary temperature is T0, the outer winding layer boundary temperature is T n , r i is the radius of the current winding layer position, r n is the radius of the outermost winding layer, and b is the outer diameter of the core mold.

[0065] S2. Based on the known temperature field distribution, conduct experimental characterization or combine the isothermal curing model to solve the curing degree field distribution γ(r i ).

[0066] The specific process of conducting experimental characterization based on the known temperature field distribution to solve the curing degree field distribution is as follows:

[0067] Characterization of curing degree γ(r i )distributed:

[0068]

[0069] Where t is the curing time, ΔH is the exothermic peak of the DSC signal, and ΔH total It is the total exothermic peak of complete curing.

[0070] The specific process of solving the curing degree field distribution based on the known temperature field distribution and the isothermal curing model is as follows:

[0071] Numerical solution of curing degree γ(r i )distributed:

[0072]

[0073]

[0074] Where A is the pre-exponential factor, E is the apparent activation energy, R is the gas constant, m is the fitted reaction order, and k0 is the reaction rate constant fitted based on the Arrhenius formula.

[0075] S3, based on the current winding layer r i With all the implicit functions of the recursive iterative format between the winding layers outside it, the initial winding layer r1 and the outermost winding layer r n Relationship function between hoop tension:

[0076] F W (r i )=g(F W (r i+1 ),F W (r i+2 ),…,F W (r n ))

[0077] F W (r1) = g(F W (r n ))

[0078] Wherein, i=1,2,…,n represents the number of winding layers.

[0079] The specific process of S3 is:

[0080] S3.1, without considering the change of circumferential temperature, based on the superposition principle, the winding residual tension F θ (r i ) includes the current winding layer tension component, the outer winding layer tension component and the solidification deformation component:

[0081]

[0082] Among them, F W (r i ) is the hoop tension of the current winding layer, ΔF ex,θ (r i ) is the hoop tension change caused by all the winding layers outside the current winding layer, F cu,θ (r i ) is the circumferential chemical shrinkage force during the curing process.

[0083]

[0084] in, is the radial stiffness of the core mold, a is the inner diameter of the core mold, v1 is the Poisson's ratio of the core mold, E1 is the modulus of the core mold, and the correlation coefficient of the winding layer is v 2θ is the Poisson's ratio of the winding layer, v 2r is the Poisson's ratio of the winding layer, E 2r is the modulus in the fiber thickness direction, E 2θ is the fiber axial modulus.

[0085]

[0086] Where β′ represents the volume shrinkage of the fully cured resin, γ(r i ) is the curing degree of the current layer, E c,θ =V f E 2r +γ(r i )(1-V f )E0 is the axial modulus of the composite material, V f is the fiber volume fraction of the composite material, and E0 is the fully cured resin modulus.

[0087] S3.2. Based on geometric relationships And equal residual tension conditions, winding residual tension F θ (r i ) in the radial contraction stress component σ′ r (r i )satisfy:

[0088]

[0089] σ′ r (r i ) is the total radial residual stress of the current winding layer, Δθ is the infinitesimal element of the circumferential rotation angle, σ′ θ (r i ) is the total residual stress in the hoop of the current winding layer, σ′ ex,r (r i ,r n ) is the radial stress change caused by the outer winding layer, σ′ th,r (r i ) is the thermal deformation radial stress, σ′ cu,r (r i ) is the radial stress and h is the layer thickness.

[0090] The radial stress change σ′ caused by the outer winding layer ex,r (r i ,r n )satisfy:

[0091]

[0092] Based on the heat conduction equation, the thermal deformation radial stress σ′ th,r (r i )for:

[0093]

[0094] in, is the modulus of the composite material in the thickness direction, α is the thermal expansion coefficient of the composite material in the thickness direction, V f is the fiber volume fraction.

[0095] Based on the assumption of uniform solidification shrinkage strain, the radial stress σ′ cu,r (r i )for:

[0096]

[0097] S3.3, substitute F in S3.1 into S3.2 to establish the current winding layer r i and all outer winding layers recursive implicit function F W (r i )=g(F W (r i+1 ),F W (r i+2 ),…,F W (r n )).

[0098] S4. Solve the hoop tension F of the outermost winding layer based on the initial guess value and convergence requirements W (rn ):

[0099]

[0100] in, is the target residual hoop winding tension, is the fiber winding angle of the initial winding layer;

[0101] S5. Based on the implicit function established in S3, the hoop tension F of each winding layer is solved layer by layer starting from the outermost winding layer. W (r n-1 ),F W (r n-2 ),…,F W (r1):

[0102] F W (r i )=g(F W (r i+1 ),F W (r i+2 ),…,F W (r n )).

[0103] In addition, it should be understood that after reading the above description of the present invention, those skilled in the art may make various changes or modifications to the present invention, and these equivalent forms also fall within the scope defined by the claims attached to this application.

Claims

1. A method for designing equal residual tension for high-precision fiber wet-wound cylindrical parts, characterized in that: include: S1. Solve the temperature field distribution T(r) of the winding layer based on the boundary value problem of the heat conduction differential equation i ); S2. Based on the known temperature field distribution, conduct experimental characterization or combine the isothermal curing model to solve the curing degree field distribution γ(r i ); S3, based on the current winding layer r i With all the implicit functions of the recursive iterative format between the winding layers outside it, the initial winding layer r1 and the outermost winding layer r n Relationship function between hoop tension: F W (r i )=g(F W (r i+1 ),F W (r i+2 ),…,F W (r n )) F W (r1)=g(F W (r n )) Where i = 1, 2, ..., n, represents the number of winding layers; S4. Solve the hoop tension F of the outermost winding layer based on the initial guess value and convergence requirements W (r n ): in, is the target residual hoop winding tension, is the fiber winding angle of the initial winding layer; S5. Based on the implicit function established in S3, the hoop tension F of each winding layer is solved layer by layer starting from the outermost winding layer. W (r n-1 ),F W (r n-2 ),…,F W (r1): F W (r i )=g(F W (r i+1 ),F W (r i+2 ),…,F W (r n ))。 2. The method for designing equal residual tension for high-precision fiber wet-wound cylindrical parts according to claim 1 is characterized in that: The specific process of S1 is: S1.

1. The differential equation for steady-state heat conduction without internal heat source based on Fourier's law is: S1.

2. The general solution and distribution equation of the heat conduction differential equation are: T(r)=C1lnr+C2 Among them, the core mold boundary temperature is T0, the outer winding layer boundary temperature is T n , r i is the radius of the current winding layer position, r n is the radius of the outermost winding layer, and b is the outer diameter of the core mold.

3. The method for designing equal residual tension for high-precision fiber wet-wound cylindrical parts according to claim 1 is characterized in that: The specific process of S2 conducting experimental characterization based on the known temperature field distribution to solve the curing degree field distribution is as follows: Characterization of curing degree γ(r i )distributed: Where t is the curing time, ΔH is the exothermic peak of the DSC signal, and ΔH total It is the total exothermic peak of complete curing.

4. The method for designing equal residual tension for high-precision fiber wet-wound cylindrical parts according to claim 1 is characterized in that: The specific process of S2 solving the curing degree field distribution based on the known temperature field distribution and the isothermal curing model is as follows: Numerical solution of curing degree γ(r i )distributed: Where A is the pre-exponential factor, E is the apparent activation energy, R is the gas constant, m is the fitted reaction order, and k0 is the reaction rate constant fitted based on the Arrhenius formula.

5. The method for designing equal residual tension for high-precision fiber wet-wound cylindrical parts according to claim 1 is characterized in that: The specific process of S3 is: S3.1, without considering the change of circumferential temperature, based on the superposition principle, the winding residual tension F θ (r i ) includes the current winding layer tension component, the outer winding layer tension component and the solidification deformation component: Among them, F W (r i ) is the hoop tension of the current winding layer, ΔF ex,θ (r i ) is the hoop tension change caused by all the winding layers outside the current winding layer, F cu,θ (r i ) is the circumferential chemical shrinkage force during the curing process; S3.

2. Based on geometric relationships And equal residual tension conditions, winding residual tension F θ (r i ) in the radial contraction stress component σ′ r (r i )satisfy: σ′ r (r i ) is the total radial residual stress of the current winding layer, Δθ is the infinitesimal element of the circumferential rotation angle, σ′ θ (r i ) is the total residual stress in the hoop of the current winding layer, σ′ ex,r (r i ,r n ) is the radial stress change caused by the outer winding layer, σ′ th,r (r i ) is the thermal deformation radial stress, σ′ cu,r (r i ) is the radial stress, h is the layer thickness; S3.3, substitute F in S3.1 into S3.2 to establish the current winding layer r i and all outer winding layers recursive implicit function F W (r i )=g(F W (r i+1 ),F W (r i+2 ),…,F W (r n )).

6. The method for designing equal residual tension for a high-precision fiber wet-wound cylindrical product according to claim 5, characterized in that: in, is the radial stiffness of the core mold, a is the inner diameter of the core mold, v1 is the Poisson's ratio of the core mold, E1 is the modulus of the core mold, and the correlation coefficient of the winding layer is v 2θ is the Poisson's ratio of the winding layer, v 2r is the Poisson's ratio of the winding layer, E 2r is the modulus in the fiber thickness direction, E 2θ is the fiber axial modulus, and the integral term is a simplified expression of accumulation.

7. The method for designing equal residual tension for a high-precision fiber wet-wound cylindrical product according to claim 6, characterized in that: Where β′ represents the volume shrinkage of the fully cured resin, γ(r i ) is the curing degree of the current layer, E c,θ =V f E 2r +γ(r i )(1-V f )E0 is the axial modulus of the composite material, V f is the fiber volume fraction of the composite material, and E0 is the fully cured resin modulus.

8. The method for designing equal residual tension for high-precision fiber wet-wound cylindrical parts according to claim 7, characterized in that: The radial stress change σ′ caused by the outer winding layer ex,r (r i ,r n )satisfy:

9. The method for designing equal residual tension for a high-precision fiber wet-wound cylindrical product according to claim 8, characterized in that: Based on the heat conduction equation, the thermal deformation radial stress σ′ th,r (r i )for: in, is the modulus of the composite material in the thickness direction, α is the thermal expansion coefficient of the composite material in the thickness direction, V f is the fiber volume fraction.

10. The method for designing equal residual tension for a high-precision fiber wet-wound cylindrical product according to claim 9, characterized in that: Based on the assumption of uniform solidification shrinkage strain, the radial stress σ′ cu,r (r i )for:

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