A method for evaluating the stiffness performance of multilayer composite cylindrical structures

Abstract

The present invention belongs to the technical field of rotating machinery or pressure vessels, and specifically relates to a method for evaluating the stiffness performance of a multilayer composite material cylinder structure, comprising the following steps: S101: establishing a balance equation of a composite material cylinder; S102: regarding the composite material cylinder as a whole, adjusting the balance equation, and adjusting the stress-strain equation after regarding the composite material cylinder as a whole; S103: comparing the balance equation and the stress-strain equation in S101-S102, respectively introducing the equivalent stiffness matrix of the spiral layer and the hoop layer, and sorting out the balance equation group: S104: solving the balance equation group, that is, obtaining the stiffness of the cylinder structure. By establishing a calculation analytical formula for the equivalent modulus of a multilayer fiber composite material cylinder structure, a non-experimental method for evaluating the stiffness performance of a composite material cylinder structure is determined, so as to achieve the purpose of accurately and quickly calculating the structural stiffness of different layer cylinder structures, and provide a basis for the reasonable design and evaluation of composite material cylinder structures.

Description

Technical Field

[0001] The invention belongs to the technical field of rotating machinery or pressure vessels, and in particular relates to a method for evaluating the rigidity performance of a multilayer composite material cylinder structure. Background Art

[0002] Composite materials have been rapidly developed and applied due to their high specific strength, specific stiffness, strong designability, and good fatigue resistance. In the fields of rotating machinery or pressure vessels, in order to meet the overall stiffness and strength performance requirements of the structure, the composite cylinder is usually wound by a combination of spiral winding and hoop winding. Unlike metal materials, composite materials are anisotropic materials. At the same time, the composite cylinder contains both spiral layers and hoop layers, making the overall structure highly anisotropic. Does the stiffness of the cylinder formed by winding meet the requirements? It is often necessary to use tests such as blasting tests to measure the isotropic modulus of the cylinder structure. However, this method is time-consuming and labor-intensive. Each time, it is necessary to specially make specimens and use special blasting devices for testing. It is also necessary to process the test results. In addition, there is a large uncertainty in the performance of composite materials, resulting in large dispersion of test results. Therefore, in response to this problem, it is considered to establish a fast and economical method for evaluating the stiffness performance of cylindrical structures to calculate and evaluate the equivalent modulus of composite cylindrical structures. Summary of the invention

[0003] The purpose of the present invention is to provide a method for evaluating the stiffness performance of a multi-layer composite cylindrical structure. By establishing an analytical formula for calculating the equivalent modulus of a multi-layer fiber composite cylindrical structure, a non-experimental method for evaluating the stiffness performance of a composite cylindrical structure is determined, so as to achieve the purpose of accurately and quickly calculating the structural stiffness of cylindrical structures with different layups, and provide a basis for the reasonable design and evaluation of composite cylindrical structures.

[0004] The technical solution adopted by the present invention to solve this problem is:

[0005] A method for evaluating the stiffness performance of a multilayer composite material cylinder structure comprises the following steps:

[0006] S101: Establish the equilibrium equation of the composite cylinder;

[0007] S102: Considering the composite cylinder as a whole, adjusting the equilibrium equation, and adjusting the stress-strain equation after considering the composite cylinder as a whole;

[0008] S103: Comparing the equilibrium equations and stress-strain equations in S101-S102, the equivalent stiffness matrices of the helical layer and the hoop layer are introduced respectively, and the equilibrium equations are obtained:

[0009] S104: Solve the equilibrium equations to obtain the stiffness of the cylinder structure.

[0010] The fiber composite material cylinder consists of a spiral layer and a hoop layer.

[0011] The equilibrium equation of the composite material cylinder in step S101 is as follows:

[0012]

[0013] Where: A ij , B ij , (i,j=1,2,3) are the stiffness matrices of the helical layer and the hoop layer composite materials respectively, which are related to the material parameters and layer thickness, and ε is the strain.

[0014] The equilibrium equation of the composite material cylinder in step S102 is as follows:

[0015]

[0016] Where: σ is stress and h is the wall thickness of the cylinder.

[0017] The stress-strain equation in step S102 is as follows:

[0018]

[0019] Where: C is the stiffness matrix of the cylinder, which is composed of the equivalent modulus of the cylinder structure, as follows,

[0020]

[0021] C 66 =G xy .

[0022] The equilibrium equations in step S103 are as follows:

[0023]

[0024] Helical winding layer k = 1, hoop winding layer k = 2, h k is the ratio of the thickness of the k layer to the total thickness.

[0025] The rigidity of the cylinder structure in step S104 is as follows:

[0026]

[0027] Where:

[0028] x is the axial direction of the cylinder, y is the circumferential direction, E x is the axial modulus, E y is the hoop modulus, G xyis the shear modulus.

[0029] The advantages and positive effects of the present invention are:

[0030] 1. The present invention realizes the calculation of the stiffness performance of a fiber composite cylindrical structure containing different plies. The method is clear and the result can be obtained by inputting basic material parameters.

[0031] 2. The present invention can quickly and conveniently estimate the stiffness of cylinders with different layup systems, and can be used to judge whether the cylinder winding stiffness meets the design requirements, thereby omitting the test link and saving costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] The technical solution of the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments, but it should be understood that these drawings are designed only for explanation purposes and are not intended to limit the scope of the present invention. In addition, unless otherwise specified, these drawings are intended only to conceptually illustrate the structural configurations described herein and are not necessarily drawn to scale.

[0033] Figure 1 It is a schematic diagram of the structure of a spiral winding plus annular winding drum;

[0034] Figure 2 It is a flow chart of the present invention. DETAILED DESCRIPTION

[0035] First of all, it should be noted that the specific structure, features and advantages of the present invention will be specifically described below by way of example, but all descriptions are only for illustration and should not be understood as limiting the present invention in any way. In addition, any single technical feature described or implied in the embodiments mentioned herein, or any single technical feature displayed or implied in the drawings, can still be combined or deleted between these technical features (or their equivalents) to obtain more other embodiments of the present invention that may not be directly mentioned in this document. In addition, in order to simplify the drawings, the same or similar technical features may be marked only in one place in the same drawing.

[0036] In the present invention, unless otherwise clearly specified and limited, the terms "installation", "setting", "connection", "fixation", "screwing" and the like should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral one; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium, it can be the internal connection of two elements or the interaction relationship between two elements, unless otherwise clearly defined, for ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to the specific circumstances. The present invention is described in detail below with reference to the accompanying drawings.

[0037] Example:

[0038] Fiber composite cylinder, consisting of helical and hoop layers.

[0039] The method for evaluating the stiffness performance of a multilayer composite cylinder structure comprises the following steps:

[0040] Step 1: Establish the equilibrium equation of the composite cylinder as follows:

[0041]

[0042] Where: A ij , B ij , (i,j=1,2,3) are the stiffness matrices of the helical layer and the hoop layer composite materials respectively, which are related to the material parameters and layer thickness, and ε is the strain.

[0043] Step 2: When the cylinder is regarded as a whole, the equilibrium equation is:

[0044]

[0045] Where: σ is stress and h is the wall thickness of the cylinder.

[0046] The stress-strain equation after being considered as a whole is:

[0047]

[0048] Where: C is the stiffness matrix of the cylinder, which is composed of the equivalent modulus of the cylinder structure, as follows,

[0049]

[0050] C 66 =G xy .

[0051] Step 3: Compare equations (1) to (3), introduce the equivalent stiffness matrices of the helical layer and the hoop layer respectively, and obtain the following equilibrium equations:

[0052]

[0053] Helical winding layer k = 1, hoop winding layer k = 2, h k is the ratio of the thickness of the k layer to the total thickness.

[0054] Step 4: Solve equation (4) to obtain the cylindrical structure stiffness:

[0055]

[0056] Where:

[0057]

[0058]

[0059] x is the axial direction of the cylinder, y is the circumferential direction, E x is the axial modulus, E y is the hoop modulus, G xy is the shear modulus.

[0060] It should be noted that the equivalent modulus of the cylindrical structure is a direct reflection of the stiffness performance of the cylindrical structure.

[0061] Embodiment 1:

[0062] 1. The thickness h of the composite material cylinder is 2.8mm; the thickness of the spiral layer is 1.5mm, the winding angle is 30 degrees (angle with the axial direction of the cylinder), the longitudinal modulus is 170GPa, the hoop modulus is 6GPa, the shear modulus is 5GPa, and the Poisson's ratio is 0.3; the thickness of the hoop layer is 1.3mm, the winding angle is 90 degrees, the longitudinal modulus is 160GPa, the hoop modulus is 8GPa, the shear modulus is 6GPa, and the Poisson's ratio is 0.3.

[0063] 2. The calculation results are shown in the following table:

[0064] Table 1 Structural equivalent modulus of cylinder in Example 1

[0065] Axial modulus / GPa Hoop modulus / GPa Shear modulus / GPa 57.1 74.7 20.6

[0066] Embodiment 2:

[0067] 1. The thickness h of the composite material cylinder is 3mm; the thickness of the spiral layer is 1.3mm, the winding angle is 25 degrees (angle with the axial direction of the cylinder), the longitudinal modulus is 190GPa, the hoop modulus is 6GPa, the shear modulus is 5GPa, and the Poisson's ratio is 0.3; the thickness of the hoop layer is 1.7mm, the winding angle is 90 degrees, the longitudinal modulus is 155GPa, the hoop modulus is 8GPa, the shear modulus is 6GPa, and the Poisson's ratio is 0.3.

[0068] 2. The calculation results are shown in the following table:

[0069] Table 2 Structural equivalent modulus of cylinder in Example 2

[0070] Axial modulus / GPa Hoop modulus / GPa Shear modulus / GPa 54.2 92.1 19.6

[0071] Embodiment 3:

[0072] 1. The thickness h of the composite material cylinder is 2 mm; the thickness of the spiral layer is 1.4 mm, the winding angle is 20 degrees (angle with the axial direction of the cylinder), the longitudinal modulus is 130 GPa, the hoop modulus is 6 GPa, the shear modulus is 5 GPa, and the Poisson's ratio is 0.3; the thickness of the hoop layer is 0.6 mm, the winding angle is 90 degrees, the longitudinal modulus is 140 GPa, the hoop modulus is 8 GPa, the shear modulus is 6 GPa, and the Poisson's ratio is 0.3.

[0073] 2. The calculation results are shown in the following table:

[0074] Table 3 Structural equivalent modulus of cylinder in Example 3

[0075] Axial modulus / GPa Hoop modulus / GPa Shear modulus / GPa 53.8 49 20.1

[0076] In summary, the present invention provides a fast and economical method for evaluating the stiffness performance of a cylindrical structure, and calculates and evaluates the equivalent modulus of a composite cylindrical structure.

[0077] The above embodiments describe the present invention in detail, but the contents are only preferred embodiments of the present invention and cannot be considered to limit the scope of the present invention. All equivalent changes and improvements made within the scope of the present invention should still fall within the scope of the present invention.

Claims

1. A method for evaluating the stiffness performance of a multilayer composite cylindrical structure. Features: The following steps are involved: S101: Establish the equilibrium equation of the composite material cylinder. The equilibrium equation of the composite material cylinder is as follows: Where: A ij , B ij , (i, j = 1, 2, 3) are the stiffness matrices of the helical layer and the hoop layer composite materials, which are related to the material parameters and layer thickness, and ε is the strain; S102: Consider the composite cylinder as a whole, adjust the equilibrium equation, and adjust the stress-strain equation after considering the composite cylinder as a whole. The equilibrium equation of the composite cylinder is as follows: Where: σ is stress, h is the cylinder wall thickness; The stress-strain equation is as follows: Where: C is the stiffness matrix of the cylinder, which is composed of the equivalent modulus of the cylinder structure, as follows, C 66 =G xy ; S103: Comparing the equilibrium equations and stress-strain equations in S101-S102, the equivalent stiffness matrices of the helical layer and the hoop layer are introduced respectively, and the equilibrium equations are obtained. The equilibrium equations are as follows: Helical winding layer k = 1, hoop winding layer k = 2, h k is the ratio of the thickness of the k layer to the total thickness: S104: Solve the equilibrium equations to obtain the cylindrical structure stiffness, which is as follows: Where: x is the axial direction of the cylinder, y is the circumferential direction, E x is the axial modulus, E y is the hoop modulus, G xy is the shear modulus.

2. A method for evaluating the stiffness performance of a multilayer composite cylindrical structure according to claim 1, Features: The composite material cylinder consists of a spiral layer and a hoop layer.

Images