Modeling method of sawtooth chip bevel cutting considering fracture toughness

Abstract

The present invention relates to a mechanical modeling method for sawtooth chip bevel cutting process, and in particular to a modeling method for fracture toughness, yield stress and dissipated energy of difficult-to-machine tough metals and alloy materials during milling. The method first divides the cutting edge of the end mill into numerous micro-elements along the tool axis, and regards the cutting of each blade micro-element as an oblique cutting process; then, a cutting force model in the chip generation process is established for a single blade micro-element, and the cutting force, speed and shear strain in the oblique cutting are projected into a plane perpendicular to the cutting edge, and fracture toughness is introduced at the tool tip, and then the cutting force analysis is performed using the theory and method of orthogonal cutting, and an equation that can predict the fracture toughness and yield stress in the milling process is derived, and then the fracture toughness is used to calculate the work done by the fracture of the material at the tool tip, and the work done by the fracture of the material between the saw teeth is calculated based on the energy conservation. Finally, the energy distribution dissipated in the sawtooth chip generation process during milling and the percentage of each energy are obtained.

Description

Technical Field

[0001] The invention relates to a mechanical modeling method in a sawtooth chip bevel cutting process, and in particular to a modeling method suitable for the fracture toughness, yield stress and dissipated energy of difficult-to-machine tough metals and alloy materials in the milling process. Background Art

[0002] Classical metal cutting theory holds that in the process of material removal, from the perspective of cutting force balance, the energy loss path is mainly through the plastic deformation of the material in the first deformation zone and the friction between the chip and the front cutting edge. The energy loss caused by the initiation and expansion of cracks due to material fracture is negligible. However, in the actual processing of ductile metals and alloys, the workpiece is very likely to produce serrated chips; at this time, material fracture occurs between the tool tip and the chip serrations, accompanied by the initiation and expansion of cracks, forming a new surface, and the classical metal cutting theory is no longer applicable to this situation. Therefore, finding fracture toughness, yield stress and energy distribution modeling methods suitable for the milling process of difficult-to-process ductile metals and alloys has important theoretical and engineering application value.

[0003] The document "MEMerchant, Mechanics of the metal cutting process. I. Orthogonal cutting and a type 2 chip, Journal of Applied Physics 16 (1945) 267–275." discloses a modeling method for calculating cutting force and cutting force work in orthogonal cutting based on the balance of cutting force in the established cutting force circle. However, this method only considers the shear force work of the plastic deformation of the first deformation zone of the material and the friction work between the chip and the front cutting edge of the tool, and considers that the total work consumed by cutting is the sum of the work consumed by the friction between the chip and the tool and the work consumed by shearing the metal in the first deformation zone. The essence of this logical result is to check the correctness of the simple schematic diagram of the cutting process and its force system proposed in the article.

[0004] The document "AG Atkins, Modelling metal cutting using modern ductile fracture mechanics: quantitative explanations for some longstanding problems, International Journal of Mechanical Sciences 45 (2003) 373–396." For ductile metal cutting, fracture force is introduced into the cutting force circle, the energy consumed by material fracture at the tool tip is considered, and a modeling method for calculating cutting force and cutting force work in orthogonal cutting is disclosed. This method takes into account the shear force work of plastic deformation in the first deformation zone of the material, the friction work between the chip and the front face of the tool, and the energy consumed by the fracture of the tool tip material, and it is believed that the total work consumed by cutting is the sum of these three parts of energy loss. However, serrated chips are prone to be produced in ductile metal processing. Although this method takes into account the energy consumed by material fracture at the tool tip, it does not take into account the energy consumed by the initiation and expansion of cracks caused by material fracture between the serrations.

[0005] The document "B. Wang, ZQ Liu, QB Yang, Investigations of yield stress, fracture toughness, and energy distribution in high speed orthogonal cutting, International Journal of Machine Tools and Manufacture 73 (2013) 1–8." discloses a modeling method for calculating the cutting force and the work done by the cutting force in the process of producing sawtooth-shaped chips by right-angle slot milling. This method takes into account the shear force work of the plastic deformation of the first deformation zone of the material, the friction work between the chip and the front face of the tool, the energy consumed by the fracture of the tool tip material, and the energy consumed by the fracture of the material between the saw teeth, and considers that the total work consumed by cutting is the sum of these four parts of energy loss. However, this method uses a straight-edge slot milling cutter with a tool rake angle of 0 degrees. Therefore, although this method uses milling, the straight-edge slot milling process can be regarded as a two-dimensional orthogonal cutting process.

[0006] The typical characteristics of the above references are: in the metal cutting process, from the perspective of cutting force balance, the energy loss caused by the initiation and expansion of cracks due to material fracture is not considered; or from the perspective of energy conservation, the energy loss caused by the initiation and expansion of cracks due to material fracture is considered. However, serrated chips are easily generated during the cutting of ductile metal materials, and the initiation and expansion of cracks occur not only at the tip of the tool, but also between the teeth. Moreover, whether analyzing the cutting force and the work done by the cutting force from the perspective of cutting force balance or from the perspective of energy conservation, two-dimensional orthogonal cutting is used, which requires specific tools and workpieces to ensure plane cutting, and the metal processing method is not universal. Summary of the invention

[0007] In order to overcome the defects of the existing methods in the process of cutting force modeling of metal processing, from the perspective of cutting force balance, only the shear force work in the first deformation zone and the friction work between the chip and the tool are considered, while the energy consumed by material fracture that causes crack initiation and expansion is ignored, and the cutting force work in the cutting process cannot be properly modeled; or the energy consumed by the initiation and expansion of cracks due to material fracture is considered, but the processing method is simple two-dimensional orthogonal cutting. The present invention proposes an angle modeling method suitable for the milling process of tough and difficult-to-process materials, which simultaneously considers the energy consumption of the expansion and initiation of cracks at the tool tip and the energy consumption of the expansion and initiation of cracks between saw teeth. Refer to the attached Figure 6 (b), firstly, the cutting edge of the end mill is divided and discretized into countless micro-elements along the tool axis, and the cutting of each micro-element of the blade is regarded as an oblique cutting process; then, the cutting force model of the chip generation process is established for the single micro-element of the blade, and the cutting force, speed and shear strain in the oblique cutting are projected into the plane perpendicular to the cutting edge. At the same time, fracture toughness is introduced at the tool tip, and then the cutting force analysis is performed using the theory and method of orthogonal cutting. The equations that can predict the fracture toughness and yield stress in the milling process are derived, and then the fracture toughness is used to calculate the work done by the material fracture at the tool tip, and the work done by the material fracture between the serrations is calculated based on the energy conservation. Finally, the energy distribution dissipated in the serrated chip generation process during milling and the percentage of each energy are obtained.

[0008] Expected technical effect: The modeling method based on fracture toughness and yield stress during milling provided by the present invention can take into account the energy consumed by the fracture of the tool tip material and the energy consumed by the fracture of the material between the teeth at the same time, and model the energy dissipated and the percentage of sawtooth-shaped chips generated by tough and difficult-to-process metals and their alloys during the milling process.

[0009] The technical solution adopted by the present invention to solve the technical problem is: a method for modeling energy dissipated when sawtooth chips are generated during ductile metal milling, which is characterized by comprising the following steps:

[0010] Step 1: Use the following formula to calculate the cutting edge length w3 involved in the bevel cutting, the width w2 of the chip after cutting, and the shear plane area A of the first deformation zone: s :

[0011]

[0012] w2=w3 cosβ

[0013]

[0014] Where w1 is the width of the undeformed chip, γ is the inclination angle of the bevel cutting edge, β is the flow direction angle of the chip on the rake face, and φ n is the normal shear angle of the first deformation zone, and t1 is the undeformed chip thickness.

[0015] Step 2: Calculate the cutting force F according to the chip generation geometry model and cutting force model during bevel cutting using the following formula: R Direction angles λ, λ n , the plastic shear flow direction angle δ in the first deformation zone, and the chip flow direction angle β on the rake face.

[0016]

[0017] cotλ=cosβcotλ n

[0018]

[0019]

[0020] Where α is the tool rake angle, λ is the cutting force F R With the normal force F N The friction angle between n is the normal friction angle perpendicular to the cutting edge plane, F c is the main cutting force, F t is the lateral force, F l is the lateral force.

[0021] Step 3: Project the cutting force, cutting speed and shear strain in the bevel cutting onto the plane perpendicular to the cutting edge, and calculate the cutting force, cutting speed and shear strain projection according to the following formula:

[0022] F' c =F c cosγ

[0023] F' s =F s cosδ

[0024] F'f =F f cosβ

[0025] V' c =V c cosγ

[0026]

[0027]

[0028]

[0029] where F' c , F' s , F' f The main cutting force F c , shear force F in the first deformation zone s , the friction force F between the chip and the tool rake face f The projection component in the plane perpendicular to the cutting edge; V' c , V' s , V' chip The cutting speed V c , shear velocity V in the first deformation zone s , the chip flow velocity V on the tool rake face chip The projection component in the plane perpendicular to the cutting edge; γ' s is the shear strain in the first deformation zone γ s The projection component in the plane perpendicular to the cutting edge, θ AB is the transition angle.

[0030] Step 4: According to the cutting force balance on the shear plane of the first deformation zone, the following equation is obtained for linear fitting:

[0031]

[0032] Among them G c is the fracture toughness of the material at the tool tip during bevel cutting, σ Y is the yield stress in the shear plane of the first deformation zone during oblique cutting

[0033] Step 5. Calculate the energy distribution and percentage of tough and difficult-to-machine metals and their alloys when generating sawtooth chips during milling according to the following formula:

[0034] W fracture =G c w3V c =G c wxya c

[0035]

[0036]

[0037] W' fracture =F c V c -(W plasticity +W friction +W fracture )

[0038] where τ s Shear stress in the first deformation zone, W fracture W is the work done by the material breaking at the tip of the tool. plasticity is the work done by the plastic shear deformation of the material in the first deformation zone, W friction is the work done by the friction between the chip and the tool rake face, W' fracture The work done in breaking the material between the teeth.

[0039] The beneficial effects of the present invention are as follows: the method first establishes a continuous chip generation geometric model and a cutting force analysis model during the bevel cutting process, and establishes equations to calculate the friction angles λ, λ during the chip generation process. n , the shear flow direction angle δ in the first deformation zone, and the chip flow direction angle β on the rake face of the tool; then a geometric model of the sawtooth chip generation process is established, and equations are established to calculate the projection of cutting force, cutting speed, and shear strain in the plane perpendicular to the cutting edge, and then the fracture toughness G is introduced. c Perform material fracture analysis and establish an equation to predict the material fracture toughness G at the tool tip during bevel cutting c and the yield stress σ in the shear plane of the first deformation zone Y Finally, the above equation is used in combination with the milling test data to calculate the fracture toughness G of the material at the tool tip. c and the yield stress σ in the shear plane of the first deformation zone Y , and the energy distribution and percentage of each energy dissipated in the process of sawtooth chip generation. Compared with the given literature, the present invention takes into account the energy consumed by the fracture of the tool tip material and the energy consumed by the fracture of the material between the saw teeth, and establishes the material fracture toughness G at the tool tip when the sawtooth chip is generated during the bevel cutting process. c and the yield stress σ in the shear plane of the first deformation zone Y The prediction model can solve the problem of calculating the energy loss caused by crack initiation and expansion due to material fracture during the processing of difficult-to-process ductile metals and alloy materials, and improve the prediction accuracy of energy analysis during the processing of difficult-to-process ductile metals and alloy materials.

[0040] The present invention is described in detail below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 It is a perspective view of different projection directions during the bevel cutting process.

[0042] Figure 2 It is a schematic diagram of the bevel cutting geometry model.

[0043] Figure 3 It is a schematic diagram of the cutting force model for oblique cutting.

[0044] Figure 4 This is the relationship between the force projection and velocity projection of bevel cutting from three-dimensional representation to two-dimensional representation.

[0045] Figure 5 is from Figure 4 (c) Evolved geometric model of serrated chip formation

[0046] Figure 6 This is a schematic diagram of the geometric model of side milling.

[0047] Figure 7 The sawtooth chip morphology at different milling speeds

[0048] Figure 8 The test results and the fitted straight line under different milling speed conditions are shown in Figure 2.

[0049] Fig. 9 The energy dissipated under different milling speed conditions and its percentage DETAILED DESCRIPTION

[0050] The following examples serve to illustrate the invention.

[0051] The experiment selected the number of teeth N = 4 teeth, radius R = 8 mm, helix angle γ = 35 degrees, normal angle α n = 10 degrees, back angle γ0 = 6 degrees, AlCrN coated flat-bottom carbide end milling cutter in the three-axis vertical machining center using down-milling cutting method, radial cutting depth a e =0.1 mm, axial cutting depth a p The milling test of nickel-based high-temperature alloy Inconel 718 was carried out with the cutting parameters of feed per tooth c = 2 mm and feed per tooth c = 0.01 mm / tooth.

[0052] Step 1: Refer to the attached Figure 5 and attached Figure 7 , using the collected sawtooth chips, measure the maximum thickness t of the sawtooth chips under a microscope c_max , minimum thickness t c_min , the length of the upper side of each sawtooth Bottom side length Pitch L p and the contour angle [φ saw ] mea . (Attached Figure 7 The sawtooth chip morphology at a cutting speed of 110m / min has an unclear sawtooth profile due to the formation of fracture burrs between the saw teeth, and the sawtooth morphology parameters cannot be effectively measured. However, the sawtooth chip morphology at this speed shows that the material fracture between the saw teeth and the energy consumed cannot be ignored.

[0053] Step 2: Calculate the average thickness of sawtooth chips according to the following formula: chip , sawtooth segment inclination angle φ seg , sawtooth segment profile angle ρ seg :

[0054]

[0055]

[0056] Reuse saw ] cal =ρ seg +φ seg The resulting sawtooth profile angle [φ saw ] cal The measured sawtooth profile angle [φ saw ] mea Compare and calculate the relative error The results are shown in Table 1. According to the calculated relative error ε, the φ obtained by this calculation method is judged. seg and ρ seg It is reasonable.

[0057] Table 1 Measurement and calculation results of sawtooth chip morphology under different cutting speed conditions

[0058]

[0059] Step 3: Calculate the transition angle θ according to the following formula: AB , normal shear angle φ in the first deformation zone n , and the chip thickness ratio r c :

[0060]

[0061]

[0062]

[0063] Step 4: Calculate the undeformed chip thickness t1 of the sawtooth chip and the width w1 of the uncut workpiece material according to the following formula:

[0064] t1=r c t chip

[0065]

[0066] Where D is the cutter diameter, φ ex is the cutting end position angle when the tool penetrates the workpiece material, and φ is the cutting position angle at the undeformed chip thickness t1 (i.e., the uncut workpiece material thickness h).

[0067] Step 5: Calculate the cutting force F at the cutting position angle φ according to the following formula c 、F t 、F l :

[0068]

[0069] where F x , F y , F z They are the cutting force components in the X, Y, and Z directions at the cutting position angle φ measured by the dynamometer.

[0070] Step 6: Calculate the ordinate based on the milling test data and the horizontal axis Perform straight line fitting to obtain the slope and intercept of the fitting line, and then calculate the yield stress σ in bevel cutting Y and fracture toughness G c , the results are shown in Table 2:

[0071] Table 2 Yield stress and fracture toughness under different milling speed conditions

[0072]

[0073] Step 7: Calculate the work of plastic shear deformation of the material in the first deformation zone, the work done by friction on the front face of the tool, the work consumed by the fracture of the material at the tip of the tool, and the work consumed by the fracture of the material between the teeth according to the equation, and obtain the energy distribution and percentage of the serrated chips generated by tough and difficult-to-machine metals and their alloys during milling. Figure 8-9 It can be seen that the yield stress σ is obtained by using the mechanical modeling method of the sawtooth chip milling process of the present invention. Y and fracture toughness G c, as well as the energy distribution and percentage of serrated chips, and referring to the orthogonal cutting test results of ductile metals and alloys disclosed in the literature "B. Wang, ZQ Liu, Acoustice mission signal analysis during chip formation process in high speed machining of 7050-T7451 aluminum alloy and Inconel 718 superalloy, Journal of Manufacturing Processes 27 (2017) 114-125." and the literature "AG Atkins, Modelling metal cutting using modern ductile fracture mechanics: quantitative explanations for some longstanding problems, International Journal of Mechanical Sciences 45 (2003) 373-396.", which can better match the milling experimental results, proving the effectiveness of the modeling method for the fracture toughness, yield stress and dissipated energy distribution of difficult-to-machine ductile metals and alloy materials in the milling process.

Claims

1. A method for modeling the energy dissipated when sawtooth chips are generated during ductile metal milling, characterized in that: The following steps are involved: Step 1: Use the following formula to calculate the cutting edge length w3 involved in the bevel cutting, the width w2 of the chip after cutting, and the shear plane area A of the first deformation zone: s : w2=w3cosβ Where w1 is the width of the undeformed chip, γ is the inclination angle of the bevel cutting edge, β is the flow direction angle of the chip on the rake face, and φ n is the normal shear angle of the first deformation zone, t1 is the undeformed chip thickness; Step 2: Calculate the cutting force F according to the chip generation geometry model and cutting force model during bevel cutting using the following formula: R Direction angles λ, λ n , plastic shear flow direction angle δ in the first deformation zone, and chip flow direction angle β on the rake face; cotλ=cosβcotλ n Where α is the tool rake angle, λ is the cutting force F R With the normal force F N The friction angle between n is the normal friction angle perpendicular to the cutting edge plane, F c is the main cutting force, F t is the lateral force, F l is the lateral force; Step 3: Project the cutting force, cutting speed and shear strain in the bevel cutting onto the plane perpendicular to the cutting edge, and calculate the cutting force, cutting speed and shear strain projection according to the following formula: F' c =F c cosγ In s =F s cosδ In f =F f cosβ In' c =V c cosγ where F' c , F' s , F' f The main cutting force F c , shear force F in the first deformation zone s , the friction force F between the chip and the tool rake face f The projection component in the plane perpendicular to the cutting edge; V' c , V' s , V' chip The cutting speed V c , shear velocity V in the first deformation zone s , the chip flow velocity V on the tool rake face chip The projection component in the plane perpendicular to the cutting edge; γ' s is the shear strain in the first deformation zone γ s The projection component in the plane perpendicular to the cutting edge, θ AB is the transition angle; Step 4: According to the cutting force balance on the shear plane of the first deformation zone, the following equation is obtained for linear fitting: Among them G c is the fracture toughness of the material at the tool tip during bevel cutting, σ Y is the yield stress in the shear plane of the first deformation zone during oblique cutting Step 5: Calculate the energy distribution and percentage of tough and difficult-to-machine metals and their alloys when generating sawtooth chips during milling according to the following formula: W fracture =G c w3V' c =G c w1V c W' fracture =F c V c -(W plasticity +W friction +W fracture ) where τ s Shear stress in the first deformation zone, W fracture W is the work done by the material breaking at the tip of the tool. plasticity W is the work done by the plastic shear deformation of the material in the first deformation zone, friction is the work done by the friction between the chip and the tool rake face, W' fracture The work done in breaking the material between the teeth.

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