Micro-drill cutting force modeling method associated with cutting edge location and shear stress

Abstract

The present application relates to a kind of micro drill cutting force modeling methods associated with cutting edge position and shearing stress, belong to mechanical processing technical field.The method first obtains material relevant attribute and tool parameter, then through Johnson-Cook constitutive model, the equation of shearing stress and tool rake angle, shearing angle, friction angle, cutting speed is established, then the numerical value of shearing stress is obtained by solving, finally according to shearing stress, the cutting force generated by main cutting edge and horizontal blade is obtained, and finally total cutting force is obtained.The cutting force modeling method considering the influence of workpiece material shearing stress of cutting edge position provided by the present application considers the change of workpiece material attribute and cutting force coefficient in different cutting positions, realizes the accurate prediction of micro drill cutting force.

Description

Technical Field

[0001] This invention belongs to the field of machining technology, and relates to a micro-drill cutting force modeling method, particularly a micro-drill cutting force modeling method that considers the influence of the cutting edge position on the shear stress of the workpiece material. Background Technology

[0002] In micro-drilling, the cutting edges of the drill bit are arranged radially along the tool. Different positions on the cutting edges result in varying cutting velocities and different rake angles, leading to inconsistent shear stress in the workpiece material and consequently affecting the prediction of drilling forces. Therefore, the influence of the cutting position on the cutting force coefficient must be considered during drilling force modeling.

[0003] Reference 1, "Anand RS, Patra K., Steiner M., Biermann D.. Mechanistic modeling of micro-drilling cutting forces[J]. The International Journal of Advanced Manufacturing Technology, 2017, 88: 241–254," discloses a cutting force model suitable for micro-drilling. This model first calibrates the average shear force coefficient and friction coefficient of the cutting edge using micro-drilling experimental data, and then uses the calibration coefficients to establish a drilling force prediction model. However, this method is empirical and cannot reveal the drilling force generation mechanism; furthermore, the model does not consider the variation of shear stress at different positions of the cutting edge.

[0004] Reference 2, "Sambhav K., Tandon P., Kapoor SG, Dhande SG. Mathematical modeling of cutting forces in microdrilling[J]. Journal of Manufacturing Science and Engineering-transactions of The ASME, 2013, 135:014501," discloses a cutting force model for the main cutting edge of micro-drilling tools. This method discretizes the main cutting edge into a series of orthogonal cutting micro-elements along the tool radial direction and solves for the cutting force of different micro-elements based on the slip line, thereby establishing a calculation model for the axial force of the main cutting edge. Finally, it is corrected based on experimental results. However, this method ignores the influence of the cutting edge position on the shear stress.

[0005] The typical characteristic of the above literature is that, when modeling the cutting force of micro-drills, none of them considered the changes in shear stress and cutting force coefficient caused by different cutting positions. Summary of the Invention

[0006] Technical problems to be solved

[0007] To overcome the shortcomings of existing micro-drill cutting force modeling methods, this invention provides a micro-drill cutting force modeling method that considers the influence of the cutting edge position on the shear stress of the workpiece material. This method first obtains relevant material properties and tool parameters. Then, using the Johnson-Cook constitutive model, it establishes equations relating shear stress to the tool rake angle, shear angle, friction angle, and cutting speed. Next, it solves for the numerical value of the shear stress. Finally, based on the shear stress, it calculates the cutting forces generated by the main cutting edge and the chisel edge, respectively, ultimately obtaining the total cutting force.

[0008] Expected technical effects: The cutting force modeling method provided by this invention, which considers the influence of workpiece material shear stress at the cutting edge position, takes into account the changes in workpiece material properties and cutting force coefficients at different cutting positions, and achieves accurate prediction of cutting force in the micro-drilling process.

[0009] Technical solution

[0010] A method for modeling micro-drill cutting forces in relation to the cutting edge position and shear stress, characterized by the following steps:

[0011] Step 1: Measure the tool parameters. Divide the main cutting edge into N orthogonal cutting micro-units of length p along the radial direction of the tool. The effective rake angle α of the j-th micro-unit is... j Calculated using the following formula:

[0012]

[0013] h = 0.5f sin k t

[0014] h lim,j =r e (1+sinα)

[0015]

[0016] In the formula, α is the nominal front angle of the micro-element, and r j It is the distance from the micro-unit to the center of the tool, w is the radius of the chisel edge, and h is the distance from the micro-unit to the center of the tool. R It is the helix angle, k t It is the half-peak angle, h is the cutting thickness, f is the feed rate, h lim,j It is the critical undeformed cutting thickness;

[0017] Step 2: Material shear stress τ j Calculated using the following formula:

[0018]

[0019]

[0020]

[0021]

[0022] In the formula, A, B, C, m, and n are all parameters of the Johnson-Cook material constitutive model, and β j Let V be the friction angle. j γ is the micro-unit cutting speed, σ is the spindle speed, γ is the percentage of shear energy converted into temperature, and T is the temperature. m It is the melting point of the material, C. p ρ is the specific heat of the material, T is the density of the material, and ρ is the specific heat of the material. r It is room temperature, λ s,j It is the heat distribution coefficient on the shear plane, φ j It is the shear angle, K w It is thermal conductivity;

[0023] Step 3: Tangential shear force coefficient K at the j-th micro-unit tc,j Radial shear force coefficient K rc,j Tangential plow shear force coefficient K te,j Radial plowing shear force coefficient K re,j Calculated using the following formula:

[0024]

[0025]

[0026]

[0027]

[0028] In the formula, the parameter θ0 is taken as 14°;

[0029] Step 4: The cutting force of the j-th micro-unit is calculated using the following formula:

[0030]

[0031] b j =pcosi j / sink t

[0032] dF t,j =K tc,j b j h+K te,j b j

[0033] dF r,j =K rc,j b j h+Kre,j b j

[0034] In the formula i j It is the tilt angle, b j It is the cutting width, dF t,j It is the tangential cutting force of the micro-unit, dF r,j It is the radial cutting force of the micro-unit;

[0035] Step 5: Convert the cutting force of the j-th micro-unit to the z-direction of the machine tool coordinate system:

[0036]

[0037] In the formula dF z,j It is the cutting force in the z-direction of the micro-unit;

[0038] Step 6: The total drilling force F1 of the main cutting edge is calculated using the following formula:

[0039] F1=2∑dF z,j

[0040] Step 7: Divide the chisel edge into a second cutting edge and a compression zone. Divide the second cutting edge into M orthogonal cutting micro-units. The effective rake angle α of the s-th micro-unit is... s Calculated using the following formula:

[0041]

[0042] In the formula It is the oblique angle of the horizontal blade;

[0043] Step 8: Calculate the cutting force dF of the s-th micro-element using the method from Step 4. t,s The total axial force F2 of the second cutting edge is calculated using the following formula:

[0044] F2=2∑dF t,s

[0045] Step 9: Solve the following equations simultaneously:

[0046]

[0047] In the formula, ψ is the wedge angle, δ is the slip line rotation angle, and the axial force F3 in the compression zone is calculated by the following formula:

[0048]

[0049] Step 10: The final total axial cutting force F is calculated using the following formula:

[0050] F = F1 + F2 + F3.

[0051] A computer system is characterized by comprising: one or more processors, and a computer-readable storage medium for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the method described above.

[0052] A computer-readable storage medium is characterized by storing computer-executable instructions, which, when executed, are used to implement the above-described method.

[0053] Beneficial effects

[0054] This invention provides a micro-drilling cutting force modeling method that correlates cutting edge position with shear stress. The method first discretizes the cutting edge into a finite number of micro-elements, then obtains the cutting parameters corresponding to each micro-element. Next, using the Johnson-Cook constitutive model, an equation for shear stress is established with respect to the tool rake angle, shear angle, friction angle, and cutting speed, and the numerical value of the shear stress is obtained. Finally, the cutting forces of the main cutting edge and the chisel edge are calculated based on the shear stress, ultimately yielding the micro-drilling force. Compared to Reference 1, this invention obtains the shear stress at different positions of the cutting edge through analytical calculation, revealing the generation mechanism of the micro-drilling force. Compared to Reference 2, this invention considers the variation of shear stress at different positions of the cutting edge, improving the prediction accuracy of the micro-drilling force. Attached Figure Description

[0055] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts.

[0056] Figure 1 This is a schematic diagram of the main cutting edge model of the micro-drill of the present invention.

[0057] Figure 2 This is a schematic diagram of the micro-drill cross-blade model of the present invention.

[0058] Figure 3 This is a schematic diagram of the slip line model of the extrusion zone of the present invention.

[0059] Figure 4 This is a comparison of the predicted and measured cutting force images of a carbide twist micro drill bit with a tool radius of 0.45 mm, a helix angle of 30°, a chisel edge angle of 128°, a chisel edge tilt angle of 128°, a chisel edge radius of 0.1 mm, and a tool tip blunt roundness of 0.003 mm, performing micro-drilling on aluminum alloy 7050-T7451 under the conditions of a spindle speed of 5000 rpm and a feed rate f of 0.01 mm. Detailed Implementation

[0060] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0061] Example 1:

[0062] Step 1: The experiment selected a radius of 0.45 mm and a helix angle h. R 30°, cross-edge angle It is 128°, and the half-peak angle is k. t The angle is 64°, the cross-edge radius w is 0.1mm, and the tip blunt radius r is... e Micro-drilling of aluminum alloy 7050-T7451 was performed using a 0.003mm carbide twist micro drill bit. The cutting parameters were: spindle speed θ = 5000 rpm, feed rate f = 0.01mm. (Refer to...) Figure 1 The main cutting edge of the tool is divided radially into 350 orthogonal cutting micro-elements with a length of 0.001 mm. The effective rake angle α of the tool on the j-th micro-element is... j Calculated using the following formula:

[0063]

[0064] h = 0.5f sin k t

[0065] h lim,j =r e (1+sinα)

[0066]

[0067] In the formula, α is the nominal front angle of the micro-element, and r j h is the distance h between the micro-unit and the center of the tool. lim,j It is the thickness of the cut without deformation.

[0068] Step 2: Referring to the parameters disclosed in the literature "Wan M., Wen DY, Ma YC, Zhang WH. On materials separation and cutting force prediction in micro milling through involving the effect of dead metal zone[J]. International Journal of Machine Tools and Manufacture, 2019, 146: 103452.", for 7050-T7451 aluminum alloy, A is taken as 500MPa, B as 240MPa, C as 0.003, m as 2.50, n as 0.22, C p It is 963 J / (kg·℃), and ρ is 2800 kg / m³. 3 T m It is 500℃, T r It is 20℃, and γ is 0.9.

[0069] Material shear stress τ j Calculated using the following formula:

[0070]

[0071] β j =25.877-1.283h-0.007V j +0.181α j

[0072]

[0073]

[0074]

[0075] In the formula β j It is the friction angle, φ j It is the shear angle, V j It is the micro-unit cutting speed.

[0076] Step 3: Tangential shear force coefficient K at the j-th micro-unit tc,j Radial shear force coefficient K rc,j Tangential plow shear force coefficient K te,j Radial plowing shear force coefficient K re,j Calculated using the following formula:

[0077]

[0078]

[0079]

[0080]

[0081] In the formula, the parameter θ0 is approximately taken as 14°.

[0082] Step 4: The cutting force of the j-th micro-unit is calculated using the following formula:

[0083]

[0084] b j =p cosi j / sin k t

[0085] dF t,j =K tc,j b j h+K te,j b j

[0086] dF r,j =K rc,j b j h+K re,j b j

[0087] In the formula i j It is the tilt angle, b j It is the cutting width, dF t,j It is the tangential cutting force of the micro-unit, dF r,j It is the radial cutting force of the micro-unit.

[0088] Step 5: Convert the cutting force of the j-th micro-element into the z-direction of the Cartesian coordinate system:

[0089]

[0090] In the formula dF z,j It is the cutting force in the z-direction of the micro-unit.

[0091] Step 6: The drilling force F1 generated by the main cutting edge is calculated using the following formula:

[0092]

[0093] Step 7, Refer to Figure 2 The chisel edge is divided into a second cutting edge and a compression zone. The second cutting edge is further divided into 90 orthogonal cutting micro-units. The effective rake angle α of the s-th micro-unit is... i Calculated using the following formula:

[0094]

[0095] Step 8: Calculate the cutting force of the s-th micro-unit using Step 4. The total axial force F2 of the second cutting edge is calculated using the following formula:

[0096]

[0097] Step 9: Solve the following equations simultaneously:

[0098]

[0099] In the formula, ψ is the included angle of the wedge, which is 51.56°, and δ is the rotation angle of the slip line, which is 3.85°. (Refer to...) Figure 3 The total axial force F3 in the compression zone is calculated using the following formula:

[0100]

[0101] Step 10: The final total axial cutting force F is calculated using the following formula:

[0102] F = F1 + F2 + F3

[0103] The final axial force F is 21.04 N.

[0104] pass Figure 4 As can be seen, the axial drilling force predicted by this method is 21.04 N, while the measured average axial drilling force is 20.96 N. The predicted results and the measured results are in good agreement, proving the effectiveness of this method.

[0105] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the scope of the technology disclosed in the present invention, and such modifications or substitutions should all be covered within the scope of protection of the present invention.

Claims

1. A method for modeling micro-drill cutting forces by relating the cutting edge position to shear stress, characterized in that... The steps are as follows: Step 1: Measure the tool parameters and divide the main cutting edge into equal parts along the radial direction of the tool. A length of The orthogonal cutting micro-element, the first Effective rake angle of micro-unit tool Calculated using the following formula: In the formula It is the nominal front angle of the micro-unit. It is the distance from the micro-unit to the center of the tool. It is the radius of the transverse blade. It is the helix angle. It is half-peak angle. It refers to the cutting thickness. It's the feed rate. It is the critical undeformed cutting thickness. The tool is blunt and rounded; Step 2: Material Shear Stress Calculated using the following formula: In the formula , , , , All parameters are from the Johnson-Cook material constitutive model. Let be the friction angle. It is the micro-unit cutting speed. It is the spindle speed. It represents the percentage of shear energy converted into temperature. It is the melting point of the material. It is a material with a higher heat melt ratio. It is the material density. It is room temperature. It is the heat distribution coefficient on the shear plane. It is the shear angle. It is thermal conductivity; Step 3: Tangential shear force coefficient at each micro-unit Radial shear force coefficient Tangential plow shear force coefficient Radial plowing shear force coefficient Calculated using the following formula: Parameters in the formula Set to 14°; Step 4: The cutting force of each micro-unit is calculated using the following formula: In the formula It is the tilt angle. It is the cutting width. It is the tangential cutting force of the micro-unit. It is the radial cutting force of the micro-unit; Step 5: Place the first The cutting force of each micro-unit is converted into the machine tool coordinate system. direction: In the formula Microunit Directional cutting force; Step 6: Total drilling force at the main cutting edge Calculated using the following formula: Step 7: Divide the transverse cutting edge into a second cutting edge and a pressing zone. Divide the second cutting edge into... The orthogonal cutting micro-element, the first Effective rake angle of the tool per micro-unit Calculated using the following formula: In the formula It is the oblique angle of the horizontal blade; Step 8: Calculate the result from step 4. Cutting force of a micro unit Total axial force of the second cutting edge Calculated using the following formula: Step 9: Solve the following equations simultaneously: In the formula It is the included angle of the wedge. It is the rotation angle of the slip line and the axial force in the compression zone. Calculated using the following formula: Step 10: The final total axial cutting force Calculated using the following formula: 。 2. A computer system, characterized in that... include: One or more processors, a computer-readable storage medium for storing one or more programs, wherein, when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the method of claim 1.

3. A computer-readable storage medium, characterized in that... The device stores computer-executable instructions, which, when executed, are used to implement the method of claim 1.

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