Calculation method for optimal parameters of variable diameter composite toolholder containing carbon nanomaterials

Abstract

The present invention discloses a method for calculating the optimal parameters of a variable-diameter composite tool bar containing carbon nanomaterials, which is applied to the field of vibration stability analysis of composite tool bars. The method includes: establishing a vibration differential equation for a variable-diameter composite tool bar containing carbon nanomaterials using the Hamilton principle based on Euler-Bernoulli beam theory; transforming the vibration differential equation based on the orthogonality of the principal vibration function, determining the natural frequency, and establishing a vibration differential equation that takes material damping into account; constructing a dynamic equation with a constrained damping structure based on the transformed vibration differential equation, the natural frequency, and the vibration differential equation that takes material damping into account, and determining the structural damping ratio in the dynamic equation; and determining the optimal thickness corresponding to each material layer based on the natural frequency, structural damping ratio, and equivalent mass in the vibration differential equation. The present invention achieves a more accurate analysis of the processing stability of a variable-diameter composite tool bar and calculates the optimal thickness of each material layer.

Description

Technical Field

[0001] The present invention relates to the field of vibration stability analysis of composite material tool bars, and in particular to a method for calculating optimal parameters of a variable-diameter composite tool bar containing carbon nanomaterials. Background Art

[0002] The tool bar is one of the main load-bearing components in the cutting process and is mostly used for forming the surface of the workpiece. During the cutting process, the cutting force is mostly uneven, and the rigidity of the tool bar is limited, which makes it easy for the tool bar to vibrate during the processing, making it difficult to ensure the processing quality and accuracy of the workpiece.

[0003] Due to their unique physical properties (high specific stiffness, thermal and electrical properties), adding a small amount of carbon nanomaterials to composite toolholders can significantly improve their processing stability. Traditional methods for analyzing the processing stability of variable-diameter composite toolholders containing carbon nanomaterials rarely consider the combined effects of the constraining layer, damping layer, and composite layer on processing stability. Furthermore, there is a lack of a theoretical method for calculating the optimal thickness of each material layer for variable-diameter composite toolholders containing carbon nanomaterials.

[0004] To this end, how to provide a method for calculating the optimal parameters of a variable-diameter composite tool rod containing carbon nanomaterials that can simultaneously consider the influence of the combined effects of the constraint layer, damping layer and composite material layer on the processing stability, perform processing stability analysis on a variable-diameter composite tool rod containing carbon nanomaterials with a large aspect ratio, and calculate the optimal thickness of each material layer is an issue that technical personnel in this field urgently need to solve. Summary of the Invention

[0005] In view of this, the present invention proposes a method for calculating the optimal parameters of a variable diameter composite tool bar containing carbon nanomaterials. This method is based on the Euler-Bernoulli beam theory, and through the mixed law model and Halpin-Tsai model, the Hamilton principle is used to establish the vibration differential equation of the variable diameter composite tool rod containing carbon nanomaterials; according to the orthogonality of the main vibration function, the vibration differential equation is transformed, the natural frequency is determined respectively, and the vibration differential equation considering material damping is established; according to the transformed vibration differential equation, the natural frequency and the vibration differential equation considering material damping, the dynamic equation of the composite tool rod with a constrained damping structure is constructed, and the influence of the combined action of the constrained layer, the damping tool rod and the composite tool rod on the processing stability is simultaneously considered. The processing stability of the variable diameter composite tool rod containing carbon nanomaterials with a large aspect ratio is analyzed, and the structural damping ratio in the dynamic equation of the composite tool rod with a constrained damping structure is determined; the optimal thickness corresponding to each material layer is determined according to the natural frequency, the structural damping ratio and the equivalent mass in the vibration differential equation, and the optimal thickness of each material layer is calculated; and the dynamic equation of the composite tool rod with a constrained damping structure is solved by the semi-discrete method to verify whether the obtained optimal thickness of each material layer is accurate, and the results show the feasibility of the present invention.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions:

[0007] The calculation method of the optimal parameters of the variable diameter composite tool bar containing carbon nanomaterials includes:

[0008] Step (1): Based on the Euler-Bernoulli beam theory, the Hamilton principle is used to establish the vibration differential equation of the variable diameter composite tool rod containing carbon nanomaterials.

[0009] Step (2): According to the orthogonality of the main oscillator function, transform the vibration differential equation.

[0010] Step (3): Determine the natural frequency according to the transformed vibration differential equation and establish a vibration differential equation that takes material damping into account.

[0011] Step (4): constructing a dynamic equation of the composite tool bar with a constrained damping structure based on the transformed vibration differential equation, the natural frequency and the vibration differential equation considering material damping, and determining the structural damping ratio in the dynamic equation.

[0012] Step (5): Determine the optimal thickness of each material layer according to the natural frequency, structural damping ratio and equivalent mass in the vibration differential equation.

[0013] Optionally, in step (1), the vibration differential equation is as follows:

[0014]

[0015] Among them, u y is the displacement of the cross section on the tool bar from the origin x at time t, in mm; m(x) is the equivalent mass of the variable diameter composite tool bar containing carbon nanomaterials; I m (x) is the equivalent moment of inertia of the variable diameter composite tool bar containing carbon nanomaterials; D 11 (x) is the bending stiffness; L is the overhang length of the tool bar; δ is the unit pulse function;

[0016] Among them, m(x) and I m The calculation formula for (x) is as follows:

[0017]

[0018]

[0019] D 11 (x) According to the principle of mixed law:

[0020] D 11 (x)=D1(x)+D2(x)+D3(x) (4)

[0021]

[0022]

[0023] Among them, r i (x), i=1, 2, 3 are the radii of the base layer, damping layer and constrained layer respectively; p i (x), i=1, 2, 3 are the densities of the base layer, damping layer and constrained layer respectively; E1, E2, E3 are the elastic moduli of the base layer, damping layer and constrained layer respectively, is the eccentric stiffness coefficient of the matrix composite material, which is obtained by the Halpin-Tsai principle:

[0024] E 11 =E m v m +E fL v f +E cnm v cnm (7)

[0025]

[0026]

[0027]

[0028]

[0029]

[0030] Among them, E m , E fT , E cnm are the elastic moduli of epoxy resin, carbon fiber and carbon nanomaterial in the matrix layer respectively; V m , V f , V cnm are the volume fractions of epoxy resin, carbon fiber and carbon nanomaterial in the matrix layer respectively; v 12 , v 21 is Poisson's ratio; G 12 is the shear modulus; θ is the carbon fiber ply angle.

[0031] Optionally, in step (2), the transformed vibration differential equation is as follows:

[0032] According to the orthogonality of the master oscillator function, equation (1) is transformed into:

[0033]

[0034]

[0035]

[0036]

[0037] Where, M is the modal mass; K is the modal stiffness; represents the mode function.

[0038] Optionally, in step (3), the calculation formula of the natural frequency ω is as follows:

[0039]

[0040] Optionally, in step (3), the vibration differential equation considering material damping is as follows:

[0041] Considering the influence of material damping, the damping of the material does not affect the natural frequency and vibration mode of the material itself. By introducing the tool bar damping coefficient C, Equation (13) becomes:

[0042]

[0043] The calculation formula of the tool bar damping coefficient C is as follows:

[0044]

[0045] Where m is the mass of the tool bar; k is the static stiffness of the composite tool bar with constrained damping layer; η is the loss factor;

[0046] The calculation formula of k is as follows:

[0047]

[0048] The calculation formula of η is as follows:

[0049]

[0050] Among them, ζ2 represents the loss factor of the damping layer material, G1 is the shear parameter, and G2 is the stiffness parameter;

[0051] The calculation formula of G1 is as follows:

[0052]

[0053] The calculation formula for G2 is as follows:

[0054]

[0055] Optionally, in step (4), the dynamic equation of the composite tool bar with a constrained damping structure is constructed as follows:

[0056] Considering that the magnitude of the cutting force is related to the dynamic cutting depth, and the change of the dynamic cutting depth depends only on the regeneration effect, Equation (14) can be written as:

[0057]

[0058] Among them, K c is the cutting force coefficient per unit cutting depth in the radial direction, and b is the cutting depth;

[0059] Then, the dynamic equation of the composite toolholder with constrained damping structure is:

[0060]

[0061] Among them, the structural damping ratio ζ is as follows

[0062]

[0063] Optionally, in step (5), the optimal thickness of each material layer is as follows:

[0064] Dynamic stiffness K d The calculation formula is as follows:

[0065]

[0066] The overall radius, overall taper and large end r3 of the tool bar are known. The size variation range of the base layer r1 and the damping layer r2 is determined, and the thickness optimization problem of each layer is transformed into solving the max{K d}Optimal value problem on the boundary (27);

[0067]

[0068] Optionally, after obtaining the optimal thickness in step (5), the method further includes applying a semi-discrete method to solve equation (25) to obtain the relationship between the cutting depth b and the rotation speed n, and verifying the accuracy of the optimal thickness, as follows:

[0069]

[0070] in,

[0071]

[0072] The semi-discrete method is used to transform Equation (29) into:

[0073]

[0074] in,

[0075] p i =exp(A i Δt) (32)

[0076]

[0077]

[0078]

[0079] The radius of the tool shank changes linearly along the axial direction: r(x)=[1-(1-σ)x / L]r C ;

[0080] Where L is the length of the tool bar, σ=r C / r F Indicates the taper of the composite tool shank, r C and r F They represent the large end radius and small end radius of the composite tool arbor respectively.

[0081] Through the above technical solutions, it can be seen that compared with the existing technology, the present invention proposes a method for calculating the optimal parameters of a variable diameter composite tool rod containing carbon nanomaterials. This method is based on the Euler-Bernoulli beam theory, and through the mixed law model and Halpin-Tsai model, the Hamilton principle is used to establish the vibration differential equation of the variable diameter composite tool rod containing carbon nanomaterials; according to the orthogonality of the main vibration function, the vibration differential equation is transformed, and the natural frequency is determined respectively, and the vibration differential equation considering the material damping is established; according to the transformed vibration differential equation, the natural frequency and the vibration differential equation considering the material damping, the dynamic equation of the composite tool rod with a constrained damping structure is constructed, which realizes the simultaneous consideration of the constraint layer, The influence of the combined action of the damping tool rod and the composite tool rod on the processing stability, the processing stability of the variable diameter composite tool rod with a large aspect ratio containing carbon nanomaterials is analyzed, and the structural damping ratio in the dynamic equation of the composite tool rod with a constrained damping structure is determined; the optimal thickness corresponding to each material layer is determined according to the natural frequency, structural damping ratio and equivalent mass in the vibration differential equation, and the optimal thickness of each material layer is calculated; and the dynamic equation of the composite tool rod with a constrained damping structure is solved by the semi-discrete method to verify whether the optimal thickness of each material layer obtained is accurate. The results show the feasibility of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0083] Figure 1 It is a schematic diagram of the process of the present invention.

[0084] Figure 2 This is a schematic structural diagram of the variable diameter composite tool bar made of carbon nanomaterials according to the present invention.

[0085] Figure 3 It is a schematic cross-sectional view in the radial direction of the structure of the variable diameter composite material tool rod containing carbon nanomaterials of the present invention.

[0086] Figure 4 Schematic diagram of the flutter stability lobe curve corresponding to different material layer thicknesses of the present invention. DETAILED DESCRIPTION

[0087] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0088] Embodiment 1 of the present invention discloses a method for calculating optimal parameters of a variable diameter composite tool bar containing carbon nanomaterials, comprising:

[0089] Step (1): Based on the Euler-Bernoulli beam theory, the Hamilton principle is used to establish the vibration differential equation of the variable diameter composite tool bar containing carbon nanomaterials, as follows:

[0090]

[0091] Among them, u y is the displacement of the cross section on the tool bar from the origin x at time t, in mm; m(x) is the equivalent mass of the variable diameter composite tool bar containing carbon nanomaterials; I m (x) is the equivalent moment of inertia of the variable diameter composite tool bar containing carbon nanomaterials; D 11 (x) is the bending stiffness; L is the overhang length of the tool bar; δ is the unit pulse function;

[0092] Among them, m(x) and I m The calculation formula for (x) is as follows:

[0093]

[0094]

[0095] D 11 (x) According to the principle of mixed law:

[0096] D 11 (x)=D1(x)+D2(x)+D3(x) (4)

[0097]

[0098]

[0099] Among them, r i (x), i=1, 2, 3 are the radii of the base layer, damping layer and constrained layer respectively; ρ i (x), i=1, 2, 3 are the densities of the base layer, damping layer and constrained layer respectively; E1, E2, E3 are the elastic moduli of the damping layer and constrained layer respectively, is the eccentric stiffness coefficient of the matrix composite material, which is obtained by the Halpin-Tsai principle:

[0100] E 11 =E m v m +E fL v f +E cnm v cnm (7)

[0101]

[0102]

[0103]

[0104]

[0105]

[0106] Among them, E m , E fT , E cnm are the elastic moduli of epoxy resin, carbon fiber and carbon nanomaterial in the matrix layer respectively; V m , V f , V cnm are the volume fractions of epoxy resin, carbon fiber and carbon nanomaterial in the matrix layer respectively; v 12 , v 21 is Poisson's ratio; G 12 is the shear modulus; θ is the carbon fiber ply angle.

[0107] Step (2): According to the orthogonality of the master vibration function, transform the vibration differential equation as follows:

[0108] According to the orthogonality of the master oscillator function, equation (1) is transformed into:

[0109]

[0110]

[0111]

[0112]

[0113] Where, M is the modal mass; K is the modal stiffness; represents the mode function.

[0114] Step (3): Determine the natural frequency of the variable diameter composite tool bar containing carbon nanomaterials according to the transformed vibration differential equation and establish the vibration differential equation of the variable diameter composite tool bar containing carbon nanomaterials considering material damping, as follows:

[0115] The calculation formula of the natural frequency ω of the variable diameter composite tool bar containing carbon nanomaterials is as follows:

[0116]

[0117] The vibration differential equation of the variable diameter composite tool arbor containing carbon nanomaterials considering material damping is as follows:

[0118] Considering the influence of material damping, the damping of the material does not affect the natural frequency and vibration mode of the material itself. By introducing the tool bar damping coefficient C, Equation (13) becomes:

[0119]

[0120] The calculation formula of the tool bar damping coefficient C is as follows:

[0121]

[0122] Wherein, m is the mass of the tool bar; k is the static stiffness of the composite tool bar with constrained damping layer; η is the structural loss factor of the variable diameter composite tool bar containing carbon nanomaterials;

[0123] The calculation formula of k is as follows:

[0124]

[0125] The calculation formula of η is as follows:

[0126]

[0127] Among them, ζ2 represents the loss factor of the damping layer material, G1 is the shear parameter, and G2 is the stiffness parameter;

[0128] The calculation formula of G1 is as follows:

[0129]

[0130] The calculation formula for G2 is as follows:

[0131]

[0132] Step (4): Based on the transformed vibration differential equation, the natural frequency of the variable diameter composite tool bar containing carbon nanomaterials, and the vibration differential equation of the variable diameter composite tool bar containing carbon nanomaterials considering material damping, a dynamic equation of the variable diameter composite tool bar containing carbon nanomaterials with a constrained damping structure is constructed, and the structural damping ratio in the dynamic equation is determined as follows:

[0133] Considering that the magnitude of the cutting force is related to the dynamic cutting depth, and the change of the dynamic cutting depth depends only on the regeneration effect, Equation (14) can be written as:

[0134]

[0135] Among them, K c is the cutting force coefficient per unit cutting depth in the radial direction, b is the cutting depth;

[0136] Then, the dynamic equation of the variable diameter composite tool bar made of carbon nanomaterials with a constrained damping structure is:

[0137]

[0138] Among them, the structural damping ratio ζ of the variable diameter composite tool bar containing carbon nanomaterials is as follows

[0139]

[0140] Step (5): Determine the optimal thickness of each material layer of the variable diameter composite tool bar containing carbon nanomaterials according to the natural frequency of the variable diameter composite tool bar containing carbon nanomaterials, the structural damping ratio of the variable diameter composite tool bar containing carbon nanomaterials, and the equivalent mass in the vibration differential equation, as follows:

[0141] Dynamic stiffness K d The calculation formula is as follows:

[0142]

[0143] The overall radius, overall taper and large end r3 of the tool bar are known. The size variation range of the base layer r1 and the damping layer r2 is determined, and the thickness optimization problem of each layer is transformed into solving the max{K d}Optimal value problem on the boundary (27);

[0144]

[0145] After obtaining the optimal thickness in step (5), the semi-discrete method is also used to solve equation (25) to obtain the relationship between the cutting depth b and the rotation speed n, and verify the accuracy of the optimal thickness, as follows:

[0146]

[0147] in,

[0148]

[0149] The semi-discrete method is used to transform Equation (29) into:

[0150]

[0151] in,

[0152] p i =exp(A i Δt) (32)

[0153]

[0154]

[0155]

[0156] The radius of the tool shank changes linearly along the axial direction: r(x)=[1-(1-σ)x / L]r C ;

[0157] Where L is the length of the tool bar, σ=r C / r F Indicates the taper of the composite tool shank, r C and r F They represent the large end radius and small end radius of the composite tool arbor respectively.

[0158] The base layer material is carbon fiber / epoxy resin / carbon nanomaterial, the damping layer material is polytetrafluoroethylene (Teflon); the constraint layer material is YG20C; the composite tool bar length is L=500mm; the small end diameter r3 is r F = r3 = 114mm; the taper of the composite tool bar is σ = 1.5, then the large end diameter r C =171mm; the three layers of the entire variable-section composite tool bar are of equal thickness.

[0159] Solving for the optimal thickness of each layer, we can get r1 = 10.323mm, r2 = 82mm. That is, H1 = 71.677mm, H2 = 29.875mm, H3 = 2.125mm, which can be converted into a ratio: H1:H2:H3 = 1:13.488:33.730, as shown in the following example: Figure 4 As shown in the figure, the position of the stability lobe curve on the coordinate plane shows a trend of first rising and then falling, indicating that there is a certain thickness value between the layers of material to achieve the best vibration stability of the tool bar and verify the feasibility of the optimization method.

[0160] The embodiment of the present invention discloses a method for calculating the optimal parameters of a variable diameter composite tool rod containing carbon nanomaterials. This method is based on the Euler-Bernoulli beam theory, and through the mixed law model and the Halpin-Tsai model, the Hamilton principle is used to establish the vibration differential equation of the variable diameter composite tool rod containing carbon nanomaterials; according to the orthogonality of the main vibration function, the vibration differential equation is transformed, the natural frequency is determined respectively, and the vibration differential equation considering the material damping is established; according to the transformed vibration differential equation, the natural frequency and the vibration differential equation considering the material damping, the dynamic equation of the composite tool rod with a constrained damping structure is constructed, realizing the simultaneous consideration of the constraint layer, The influence of the combined action of the damping tool rod and the composite tool rod on the processing stability, the processing stability of the variable diameter composite tool rod with a large aspect ratio containing carbon nanomaterials is analyzed, and the structural damping ratio in the dynamic equation of the composite tool rod with a constrained damping structure is determined; the optimal thickness corresponding to each material layer is determined according to the natural frequency, structural damping ratio and equivalent mass in the vibration differential equation, and the optimal thickness of each material layer is calculated; and the dynamic equation of the composite tool rod with a constrained damping structure is solved by the semi-discrete method to verify whether the optimal thickness of each material layer obtained is accurate. The results show the feasibility of the present invention.

[0161] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Reference can be made to the common and similar parts between the various embodiments. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method description.

[0162] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for calculating the optimal parameters of a variable diameter composite tool bar containing carbon nanomaterials, characterized in that: include: Step (1): Based on the Euler-Bernoulli beam theory, the Hamilton principle is used to establish the vibration differential equation of the variable diameter composite tool bar containing carbon nanomaterials; Step (2): transforming the vibration differential equation according to the orthogonality of the master vibration function; Step (3): determining the natural frequencies according to the transformed vibration differential equation and establishing the vibration differential equation taking material damping into consideration; Step (4): constructing a dynamic equation of the composite tool bar with a constrained damping structure based on the transformed vibration differential equation, the natural frequency, and the vibration differential equation considering material damping, and determining the structural damping ratio in the dynamic equation; Step (5): determining the optimal thickness of each material layer according to the natural frequency, the structural damping ratio, and the equivalent mass in the vibration differential equation; In step (1), the vibration differential equation is as follows: Among them, u y is the displacement of the section on the shank from the origin x at time t, in mm; m(x) is the equivalent mass; I m (x) is the equivalent moment of inertia; D 11 (x) is the bending stiffness, L is the overhang length of the tool bar; δ is the unit pulse function; Among them, m(x) and I m The calculation formula for (x) is as follows: D 11 (x) According to the principle of mixed law: D 11 (x)=D1(x)+D2(x)+D3(x) (4) Among them, r i (x), i=1, 2, 3 are the radii of the base layer, damping layer and constrained layer respectively; ρ i , i=1, 2, 3 are the densities of the base layer, damping layer and constrained layer respectively; E1, E2, E3 are the elastic moduli of the base layer, damping layer and constrained layer respectively, is the eccentric stiffness coefficient of the matrix composite material, which is obtained by the Halpin-Tsai principle: E 11 =E m v m +E fL v f +E cnm v cnm (7) Among them, E m , E fT , E cnm are the elastic moduli of epoxy resin, carbon fiber and carbon nanomaterial in the matrix layer respectively; v m , v f , v cnm are the volume fractions of epoxy resin, carbon fiber and carbon nanomaterial in the matrix layer respectively; v 12 , v 21 is Poisson's ratio; G 12 is the shear modulus; θ is the carbon fiber ply angle.

2. The method for calculating the optimal parameters of a variable diameter composite tool bar made of carbon nanomaterials according to claim 1, characterized in that: In step (2), the transformed vibration differential equation is as follows: According to the orthogonality of the master oscillator function, equation (1) is transformed into: Where, M is the modal mass; K is the modal stiffness; represents the mode function.

3. The method for calculating the optimal parameters of a variable diameter composite tool bar made of carbon nanomaterials according to claim 2, characterized in that: In step (3), the calculation formula of the natural frequency ω is as follows:

4. The method for calculating the optimal parameters of a variable diameter composite tool bar made of carbon nanomaterials according to claim 3, characterized in that: In step (3), the vibration differential equation considering material damping is as follows: Considering the influence of material damping, the damping of the material does not affect the natural frequency and vibration mode of the material itself. By introducing the tool bar damping coefficient C, Equation (13) becomes: The calculation formula of the tool bar damping coefficient C is as follows: Where m is the mass of the tool bar; k is the static stiffness of the composite tool bar with constrained damping layer; η is the loss factor; The calculation formula of k is as follows: The calculation formula of η is as follows: Among them, ζ2 represents the loss factor of the damping layer material, G1 is the shear parameter, and G2 is the stiffness parameter; The calculation formula of G1 is as follows: The calculation formula for G2 is as follows:

5. The method for calculating the optimal parameters of a variable diameter composite tool bar made of carbon nanomaterials according to claim 4, characterized in that: In step (4), the dynamic equation of the composite tool bar with the constrained damping structure is constructed as follows: Considering that the magnitude of the cutting force is related to the dynamic cutting depth, and the change of the dynamic cutting depth depends only on the regeneration effect, Equation (14) can be written as: Among them, K c is the cutting force coefficient per unit cutting depth in the radial direction, and b is the cutting depth; Then, the dynamic equation of the composite tool bar with constrained damping structure is:

6. The method for calculating the optimal parameters of a variable diameter composite tool bar made of carbon nanomaterials according to claim 5, characterized in that: In step (5), the optimal thickness of each material layer is as follows: Dynamic stiffness K d The calculation formula is as follows: The overall radius, overall taper and large end r3 of the tool bar are known. The size variation range of the base layer r1 and the damping layer r2 is determined, and the thickness optimization problem of each layer is transformed into solving the max{K d }Optimal value problem on the boundary (27); 7. The method for calculating the optimal parameters of a variable diameter composite tool bar made of carbon nanomaterials according to claim 5, characterized in that: After obtaining the optimal thickness in step (5), the method further includes applying the semi-discrete method to solve equation (25) to obtain the relationship between the cutting depth b and the rotation speed n, and verifying the accuracy of the optimal thickness, as follows: in, The semi-discrete method is used to transform Equation (29) into: in, p i =exp(A i Δt) (32) The radius of the tool shank changes linearly along the axial direction: r(x)=[1-(1-σ)x / L]r C ; Where L is the overhang length of the tool bar, σ=r C / r F Indicates the taper of the composite tool shank, r C and r F They represent the large end radius and small end radius of the composite tool arbor respectively.

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