Method for calculating cutting transient temperature field of fiber reinforced thermoplastic resin matrix composite

Abstract

The application belongs to the field of cutting processing, and discloses a kind of calculation method of cutting transient temperature field of fiber reinforced thermoplastic resin matrix composite material.Considering the anisotropic plastic deformation characteristics of this kind of material when cutting, and respectively solving the plastic deformation heat generation in different directions when cutting, and superimposing to obtain the total plastic deformation heat generation.On this basis, considering the friction heat generation between rake face and chip, and the friction heat generation between relief face and machined surface, the total heat generation in cutting is obtained;Based on Jaeger heat source model, the anisotropic heat transfer process when cutting thermoplastic composite material is simulated, first, the temperature field under the action of single point heat source is calculated, then all point heat sources are integrated, the overall temperature field distribution is obtained, which fundamentally solves the problem of inaccurate calculation of cutting temperature field of thermoplastic composite material.The method disclosed by the application is simple in form and practical in function, and can greatly improve the calculation accuracy of cutting temperature field of thermoplastic composite material, thereby helping to promote the development of high-quality cutting processing of thermoplastic composite material.

Description

Technical Field

[0001] This invention belongs to the field of cutting and machining, and relates to a method for calculating the instantaneous temperature field during cutting of fiber-reinforced thermoplastic resin-based composite materials. Background Technology

[0002] Fiber-reinforced thermoplastic resin matrix composites (FRTPs) are an emerging high-performance material. They are lightweight, high-strength, and possess excellent mechanical properties, making them highly promising for applications in aerospace, transportation, and military fields. FRTPs are suitable for near-net-shape forming and can be used to manufacture large components, which often require milling, drilling, and other cutting processes before assembly. At the microscopic level, FRTPs consist of high-strength carbon fibers and a cohesive, heat-sensitive resin. Due to the significant difference in properties between the two phases, they are prone to damage during processing, making them a typical difficult-to-machine material. Furthermore, the high plasticity of FRTPs leads to deformation during processing, increasing heat generation and cutting temperature. Thermoplastic resins are heat-sensitive; when the cutting temperature exceeds their glass transition temperature, a phase transition occurs, transforming them from a glassy state to a highly elastic state. This weakens the resin's constraint on the fibers, making them difficult to cut effectively and resulting in burrs, tears, and other damage. Additionally, the molten resin tends to adhere to the tool surface, increasing friction during cutting and further raising the cutting temperature. Therefore, to fundamentally improve the machining quality of FRTP, it is first necessary to understand the variation law of its cutting temperature field. How to achieve accurate calculation of the cutting temperature field of FRTP is a key challenge.

[0003] Accurately determining the heat generated during the cutting process is a crucial prerequisite for precisely calculating the temperature field of FRTP cutting. Regarding the heat generation process, due to the high plasticity of FRTP, significant plastic deformation easily occurs during machining, and the heat generated by this plastic deformation cannot be ignored. The chips produced during FRTP cutting are mostly continuous long chips, and the continuous friction between these chips and the tool rake face generates frictional heat that cannot be neglected. Furthermore, the machined surface rubs against the tool flank face after springback, and this frictional heat also needs to be calculated. Therefore, calculating the cutting heat generation of FRTP requires comprehensively considering the combined effects of these three heat sources. However, currently well-established methods for calculating cutting heat generation in fiber-reinforced thermosetting composites and metals are not applicable to FRTP. Regarding fiber-reinforced thermosetting composites, Linghao Kong et al., in their 2021 paper titled "Comparative analysis of the machining temperatures of an end mill and a novel tool in the orbital drilling of CFRP composites" published in Volume 115 of The International Journal of Advanced Manufacturing Technology, pointed out that when calculating the heat generation of fiber-reinforced thermosetting composites, it is only necessary to solve for the single heat source of friction between the flank face and the machined surface. For metallic materials, Zhou Ruihu et al., in their 2022 invention patent "Method for Predicting Workpiece Temperature for Hard Turning" (patent number CN202211458114.1), proposed that metals are isotropic materials, and plastic deformation occurs in all directions during cutting. FRTP is a typical anisotropic material, exhibiting linear elasticity along the fiber direction without plastic deformation, while exhibiting elastoplasticity perpendicular to the fiber direction and undergoing plastic deformation. If the method for calculating heat generation during plastic deformation in metals is directly applied, the heat generation along the fiber direction will also be calculated, significantly overestimating the heat generated during cutting and thus affecting the calculation accuracy. Therefore, to effectively improve the calculation accuracy of the cutting temperature field in FRTP and promote the rapid development of high-quality cutting of FRTP, it is urgently necessary to invent a method for calculating the instantaneous cutting temperature field that comprehensively considers the heat generation during anisotropic plastic deformation of composite materials. Summary of the Invention

[0004] This invention addresses the problem that existing methods cannot accurately calculate the cutting temperature field of FRTP (Flat-Formed Tripod) cutting. First, it proposes a method to calculate the total plastic deformation heat generation by separately solving for the heat generated by plastic deformation in each direction and then superimposing the results. Next, it combines the heat generated by friction between the rake face and the chip, and the heat generated by friction between the flank face and the machined surface, to obtain the total cutting heat generation. Then, based on the Jaeger heat source model, it simulates the anisotropic instantaneous heat transfer process during FRTP cutting. Finally, by combining the heat generation and heat transfer processes, it obtains an accurate method for calculating the instantaneous cutting temperature field of FRTP.

[0005] The technical solution of this invention is a precise calculation method for the instantaneous cutting temperature field of FRTP (Flat-Range Trimmed Pulse). Its key feature is that it fully considers the characteristics of anisotropic plastic deformation in FRTP and solves for the heat generated by plastic deformation in different directions. Based on this, it superimposes the heat generated by friction between the rake face and the chip, and the heat generated by friction between the flank face and the machined surface, to obtain the total cutting heat generation. Based on the Jaeger heat source model, it solves for the anisotropic heat transfer process during FRTP cutting. First, it calculates the temperature field under the action of a single-point heat source, then integrates all point heat sources to obtain the overall temperature field distribution, ultimately forming a precise calculation method for the instantaneous cutting temperature field of FRTP.

[0006] The specific steps are as follows:

[0007] Step 1: Calculate the heat generated by anisotropic plastic deformation

[0008] When a material undergoes plastic deformation, plastic deformation energy is generated, and most of this energy is converted into heat, causing the temperature to rise. The formula for calculating the plastic deformation energy over a period of time is shown in equation (1).

[0009]

[0010] In the formula, S is the deviatoric stress tensor of the element at the beginning of the current time interval, S′ is the deviatoric stress tensor of the element at the end of the current time interval, and dep is the plastic strain increment during the current time interval; in the element, there are six stress components, namely three normal stresses σ. 11 σ 22 σ 33 and three shear stresses σ 12 σ 13 σ 23 Different stress components have different directions. In the algorithm involved in this invention, S, S′, and dep each have six components, which correspond to the directions of the six stress components. S includes six components, namely S... 11 S 22 S 33 S 12 S 13 S 23 S′ consists of six components, namely S′11 S′ 22 S′ 33 S′ 12 S′ 13 S′ 23 ;dep consists of six components, namely dep 11 ,dep 22 ,dep 33 ,dep 12 ,dep 13 ,dep 23 ;deps represents the equivalent plastic strain; the calculation process for heat generation during plastic deformation is as follows:

[0011] Calculate the deviatoric stress tensor at the beginning of the current time period, as shown in equation (2).

[0012]

[0013] Calculate the deviatoric stress tensor at the end of the current time period, as shown in equation (3).

[0014]

[0015] Calculate the equivalent Mises stress at the end of the current time period, as shown in equation (4).

[0016] (4)

[0017] Calculate the plastic strain increment for the current time period, as shown in equation (5).

[0018]

[0019] Calculate the inelastic dissipation energy, i.e., the plastic deformation energy, for the current time period, as shown in equation (6).

[0020]

[0021] Let β3 be the proportion of plastic deformation energy converted into heat, then the heat generated by plastic deformation in the current time period is given by equation (7).

[0022]

[0023] Step 2: Calculate frictional heat generation

[0024] The calculation of the total heat generated by friction is shown in equation (8).

[0025] Q f =Q γ +Q α (8)

[0026] In the formula, Q γ The heat is generated by the friction between the cutting edge of the tool and the chip, Qα This refers to the heat generated by friction between the tool's flank and the machined surface. Since these two types of friction have different causes, they should be considered separately when calculating heat generation.

[0027] The frictional heat generated between the rake face and the chip is mainly due to the high plasticity of FRTP, which easily forms long chips during cutting. The chips flow out along the rake face and continuously scrape against it during the flow, thus accumulating heat. This heat source is referred to as the "chip heat source" in this paper. The chip heat source is a moving heat source for the chip, but a fixed and continuous heat source for the rake face. Therefore, it is more convenient and simple to choose the rake face as the calculation object. Let the heat generated per unit area per unit time on the rake face be as shown in equation (9).

[0028] q γ =p N1 μ1v ch β1 (9)

[0029] In the formula, p N1 The average contact pressure between the chip and the rake face of the tool is given by μ1, where μ1 is the coefficient of friction between the chip and the rake face, and v is the average contact pressure between the chip and the rake face. ch β1 represents the chip flow velocity, and β1 represents the proportion of frictional work on the rake face converted into heat.

[0030] The contact area between the chip and the rake face of the tool is calculated using equation (10).

[0031] A γ =l f a w (10)

[0032] In the formula, l f a is the contact length between the tool rake face and the workpiece. w Let be the cutting width. Then, the heat generated per unit time by friction between the tool rake face and the chip is as shown in equation (11).

[0033] Q γ =q γ ×A γ =p N1 μ1v ch β1l f a w (11)

[0034] The frictional heat generated between the tool flank and the machined surface is mainly due to the springback of the workpiece after cutting. After springback, the machined surface comes into contact with the tool flank, and as the tool continues to move, friction continues, leading to heat accumulation. This paper refers to the frictional heat source between the tool flank and the machined surface as the "tool heat source," which can be considered as a moving surface heat source, with an area of ​​A. α Then we have equation (12).

[0035] A α =l c a w (12)

[0036] In the formula, l c The contact length between the flank face and the machined surface, such as... Figure 4 As shown, equation (13) can be obtained from geometric relations:

[0037]

[0038] In the formula, Δh is the springback height of the machined surface, and α is the tool clearance angle.

[0039] The heat source for the cutting tool is a moving heat source for the machined surface, but a fixed, continuous heat source for the flank face. Therefore, choosing the flank face as the calculation object is more convenient and simpler. Let q be the heat generated per unit area per unit time on the flank face. α Equation (14)

[0040] q α =p N2 μ2v cn β2 (14)

[0041] In the formula, p N2 It is the average contact pressure between the tool's flank face and the machined surface, μ2 is the coefficient of friction between the tool's flank face and the machined surface, and v cn β1 represents the relative velocity between the flank face and the machined surface, and β2 represents the proportion of frictional work on the flank face converted into heat.

[0042] The heat generated by friction between the tool's flank and the machined surface per unit time is given by equation (15).

[0043]

[0044] The total heat generated by friction per unit time is given by equation (16).

[0045]

[0046] Step 3: Calculate the heat transfer process and determine the cutting temperature field

[0047] During FRTP cutting, the material at different distances from the tool tip undergoes different deformation behaviors due to varying cutting forces, resulting in different heat generation, which is difficult to calculate directly. This paper addresses the problem of varying heat generation at different locations during cutting and the inability to calculate it simply by proposing a "single-point solution - overall superposition" heat transfer calculation method. This involves first calculating the temperature field of each heat source acting alone, and then superimposing the temperature fields of all heat sources to obtain the temperature field throughout the entire cutting process. The Jaeger heat source model is often used to solve this problem, and its heat transfer formula is (17).

[0048]

[0049] The initial temperature condition is (18):

[0050] T=T0 (t=0,-∞<x<+∞,-∞<y<+∞,-∞<z<+∞) (18)

[0051] The heat flow boundary condition is (19):

[0052]

[0053] In the formula, k1, k2, and k3 are the thermal conductivity of FRTP along the x, y, and z axes, respectively; g(x,y,z,t) is the heat source term in the model, representing the three-dimensional coordinates of the heat source and its change with time; ρ and c represent the density and specific heat capacity of FRTP, respectively; T0 is the initial temperature of the model; and q... instant V represents the magnitude of the heat flux at a point in time; c The speed at which the heat source moves;

[0054] At the initial time t = 0, assuming the point heat source appears at (x′, y′, z′) and disappears instantaneously, the heat transfer process of this heat source in the model can be calculated by the solution method of the transient point heat source anisotropic temperature field in the Jaeger model, as shown in equation (20):

[0055]

[0056] The temperature field of the entire workpiece can be expressed as equation (21).

[0057]

[0058] In the formula, a, b, and c are the three-dimensional dimensions of the workpiece, respectively.

[0059] The beneficial effects of this invention are that the proposed method for accurately calculating the instantaneous cutting temperature field of FRTP can accurately calculate the anisotropic plastic deformation heat generation during the cutting process of FRTP, and combine it with the frictional heat generation and heat transfer process to obtain the instantaneous cutting temperature field. Compared with existing methods, the method of this invention considers the anisotropy of plastic deformation heat generation for the first time, solving the plastic deformation heat generation under different methods separately and superimposing them to obtain the total plastic deformation heat generation. This fundamentally solves the problem that the plastic deformation heat generation algorithm for homogeneous materials such as metals cannot be directly applied to the calculation of plastic deformation heat generation in FRTP. The method of this invention is simple in form and practical in function, and can significantly improve the calculation accuracy of the FRTP cutting temperature field, thereby contributing to the development of high-quality FRTP machining. Attached Figure Description

[0060] Figure 1 This is a flowchart of the cutting temperature field calculation.

[0061] Figure 2 This is a schematic diagram of an FRTP stress element;

[0062] Figure 3 This is a schematic diagram of the heat source for FRTP cutting;

[0063] Figure 4 This is a schematic diagram of the back face springback;

[0064] Figure 5 The figures show a comparison of the accuracy of temperature field calculations when cutting FRTP with different fiber orientations. Figure (a) shows the calculation results for the 0° fiber orientation, Figure (b) shows the calculation results for the 45° fiber orientation, Figure (c) shows the calculation results for the 90° fiber orientation, and Figure (d) shows the calculation results for the 135° fiber orientation. Detailed Implementation

[0065] The implementation of the method for accurately calculating the instantaneous temperature field of FRTP cutting involved in this invention will be described below with reference to the accompanying drawings and specific examples.

[0066] Taking the widely used FRTP material CF / PEEK as an example, based on the derivations made in steps one to three above, material performance parameters, tool parameters, and cutting parameters are input into the model for calculation. Simultaneously, the cutting temperature field calculation method for thermosetting composite materials (taking CF / EP as an example) is used to calculate the cutting temperature field of FRTP. Finally, experiments are conducted under the same working conditions, and the temperature change during the FRTP cutting process is measured as an indicator to compare the calculation accuracy. Material performance parameters are shown in Table 1, and tool parameters and cutting parameters are shown in Table 2. The comparison results of calculation accuracy are as follows: Figure 5 As shown.

[0067] Table 1 Material Performance Parameters

[0068]

[0069] Table 2 Tool parameters and cutting parameters

[0070]

[0071]

[0072] Depend on Figure 5 It is evident that the instantaneous temperature field calculation method for FRTP cutting proposed in this invention can significantly reduce the calculation error of FRTP cutting temperature. Compared with existing methods, the calculation accuracy can be improved by more than 33%.

Claims

1. A method for calculating the instantaneous temperature field during cutting of fiber-reinforced thermoplastic resin-based composite materials, characterized in that, The steps are as follows: Step 1: Calculate the heat generated by anisotropic plastic deformation When a material undergoes plastic deformation, plastic deformation energy is generated, and most of this energy is converted into heat, causing the temperature to rise. The formula for calculating the plastic deformation energy over a period of time is as follows: As shown: In the formula, S is the deviatoric stress tensor of the element at the beginning of the current time interval, S′ is the deviatoric stress tensor of the element at the end of the current time interval, and dep is the plastic strain increment during the current time interval; in the element, there are six stress components, namely three normal stresses σ. 11 σ 22 σ 33 and three shear stresses σ 12 σ 23 σ 31 Different stress components have different directions; S, S′, and dep each have six components, which correspond to the directions of the six stress components; S includes six components, namely S 11 S 22 S 33 S 12 S 23 S 31 S′ consists of six components, namely S′ 11 S′ 22 S′ 33 S′ 12 S′ 23 S′ 31 ;dep consists of six components, namely dep 11 ,dep 22 ,dep 33 ,dep 12 ,dep 23 ,dep 31 ;deps represents the equivalent plastic strain; the calculation process for heat generation during plastic deformation is as follows: Calculate the deviatoric stress tensor at the start of the current time period, as shown in the equation. As shown: Calculate the deviatoric stress tensor at the end of the current time period, as shown in the equation. As shown: Calculate the equivalent Mies stress at the end of the current time period, as shown in the equation. As shown: The plastic strain increment for the current time period is calculated according to the flow law, as shown in the formula. As shown: Calculate the inelastic dissipation energy, i.e., the plastic deformation energy, for the current time period, as shown in the formula. As shown: Let β3 be the proportion of plastic deformation energy converted into heat, then the heat generated by plastic deformation in the current time period is as follows: As shown: Step 2: Calculate frictional heat generation The calculation of total heat generated by friction is as follows: As shown: In the formula, Q γ The heat is generated by the friction between the cutting edge of the tool and the chip, Q α It is the heat generated by friction between the back face of the cutting tool and the machined surface; Let the heat generated per unit area per unit time on the rake face be as shown in the equation. As shown: In the formula, p N1 The average contact pressure between the chip and the rake face of the tool is given by μ1, where μ1 is the coefficient of friction between the chip and the rake face, and v is the average contact pressure between the chip and the rake face. ch β1 is the chip flow velocity, and β1 is the proportion of frictional work on the rake face converted into heat. The contact area between the chip and the rake face of the tool is shown in equation (10): In the formula, l f a is the contact length between the tool rake face and the workpiece. w Let be the cutting width; then, the heat generated per unit time by friction between the tool rake face and the chip is as follows: As shown: The frictional heat source between the tool's flank and the machined surface is called the "tooling heat source." This heat source is considered as a moving surface heat source, and its area is denoted as A. α Then by formula As shown: In the formula, l c Let be the contact length between the flank face and the machined surface. Then, from geometric relationships, we obtain the formula... : In the formula, Δh is the springback height of the machined surface, and α is the tool clearance angle; Let q be the heat generated per unit area per unit time on the flank face. α Then by formula As shown: In the formula, p N2 It is the average contact pressure between the tool's flank face and the machined surface, μ2 is the coefficient of friction between the tool's flank face and the machined surface, and v cn β1 represents the relative velocity between the flank face and the machined surface, and β2 represents the proportion of frictional work on the flank face converted into heat. The heat generated by friction between the tool's flank and the machined surface per unit time is given by the formula. As shown: The total heat generated by friction per unit time is given by equation [equation missing]. As shown: Step 3: Calculate the heat transfer process and determine the cutting temperature field First, the temperature field under the individual action of each point heat source is calculated. Then, the temperature fields of all point heat sources are superimposed to obtain the temperature field throughout the entire cutting process. The Jaeger heat source model is used for solution, and its heat transfer formula is as follows: : The initial temperature condition is as shown in the formula. As shown: The heat flux boundary condition is shown in equation (19): In the formula, k1, k2, and k3 represent the thermal conductivity of the thermoplastic composite along the x, y, and z axes, respectively; g(x,y,z,t) is the heat source term in the model, representing the three-dimensional coordinates of the heat source and its change with time; ρ and c represent the density and specific heat capacity of the thermoplastic composite, respectively; T0 is the initial temperature of the model; and q... instant This represents the instantaneous heat flow from a heat source at a specific point. The speed at which the heat source moves; At the initial time t=0, assuming the point heat source appears and disappears instantaneously at (x′,y′,z′), the heat transfer process of this heat source in the model is calculated using the solution method of the transient point heat source anisotropic temperature field in the Jaeger heat source model, as shown in the equation. As shown: The temperature field of the entire workpiece is represented by the following formula: As shown: In the formula, a, b, and w are the three-dimensional dimensions of the workpiece, respectively.

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