Method for determining surface roughness in turning of brittle materials considering tool-workpiece coupled contact

Abstract

The present invention provides a method for determining the surface roughness of brittle material turning considering tool-piece coupled contact, comprising the following steps: calculating the collision contact force F between the rake face and the brittle material; r ; Calculate the adhesive contact force F between the blunt cutting edge and the brittle material a and the fracture crushing force P of the brittle material during tool-piece extrusion contact; Calculate the normal load F in the Hertzian contact between the flank face and the brittle material f and plowing force f f ; Calculate the contact radius b and height h between a single hard protrusion peak and the back cutting edge r Calculate the initial angle δ, crack propagation length c, and deflection angle α of the surface pit formed by the fracture and crushing of the brittle material; and establish a theoretical model for surface roughness during turning of brittle materials based on the data obtained in these steps. This invention, which belongs to the technical field of brittle material machining, for the first time considers both the tool and the workpiece as simultaneously affected by the tool-workpiece coupled contact relationship, innovatively incorporating tool wear and tool material properties into the parameters of the theoretical surface roughness model.

Description

Technical Field

[0001] The present invention relates to the technical field of brittle material processing, and in particular to a method for determining surface roughness of brittle material turning by considering tool-workpiece coupled contact. Background Art

[0002] Surface roughness is a key indicator for evaluating machined surface quality. With technological advancements, performance requirements for mechanical products and their components are becoming increasingly stringent. Many of the materials used in manufacturing these products and their components are high-performance, difficult-to-machine materials, such as ceramics and silicon crystals. Unlike metals, brittle materials have high hardness, low fracture toughness, and are sensitive to defects and cracks, resulting in poor machined surface quality.

[0003] Current research on theoretical models of surface roughness for brittle materials generally treats the tool as a rigid body, ignoring tool wear and material properties. This theoretical modeling of surface roughness for brittle materials focuses on the changes in the workpiece during cutting, while changes in the tool during cutting are often overlooked. Surface roughness theoretical models for brittle materials are primarily developed by analyzing the elastic-plastic deformation and brittle fracture caused by workpiece forces under different cutting parameters. However, extensive experiments have shown that the tool has a significant influence on the surface roughness of brittle materials. The tool factor is difficult to incorporate into theoretical surface roughness models because the influence of the coupled contact relationship between the tool and workpiece on surface roughness remains unclear. Currently, only the tool-workpiece geometric kinematic relationship is considered in brittle material cutting models, while the influence of the elastic-plastic deformation generated by the tool-workpiece contact process on surface roughness has not been considered. The tool and workpiece interact during contact, resulting in material fracture and removal, and the tool wear during the coupled contact process. Summary of the Invention

[0004] Based on the technical problems mentioned in the above background technology, a method for determining the surface roughness of brittle material turning considering the tool-workpiece coupled contact is provided. The model of the present invention regards the workpiece and the material as the influencing objects of the surface roughness of the brittle material for the first time, and innovatively incorporates the tool wear and tool material properties into the parameters of the surface roughness theoretical model. The material properties of the tool (hardness H, elastic modulus E1, Poisson's ratio v1, surface energy r1), the material properties of the workpiece (fracture strength σ c , fracture toughness K Ⅰc , Poisson's ratio v2, surface energy r2), tool geometry parameters (tool tip radius r ε , cutting edge blunt radius r β ), cutting parameters (feed rate f, cutting depth a p ), cutting force (main cutting force F c , cutting resistance F p , adhesion Fa , collision force F r , fracture force p at blunt circle, normal load F on flank face f , friction force on the flank surface f F ) and other factors. By studying the mechanism of tool-part coupled contact, the formation process of the machined surface of brittle materials was clarified. It was concluded that pits on the machined surface are the result of the tool cutting the workpiece, while hard peaks are caused by the workpiece counter-cutting the tool. A quantitative description of the hard peaks and pits, combined with the periodic grooves generated by tool-part geometric contact, established a new method for determining the surface roughness of brittle materials.

[0005] The technical means adopted in the present invention are as follows:

[0006] A method for determining surface roughness of brittle material turning considering tool-workpiece coupled contact includes the following steps:

[0007] Step 1: Calculate the collision contact force F between the rake face and the brittle material r ;

[0008] Step 2: Calculate the adhesive contact force F between the cutting edge and the brittle material a and the fracture crushing force P of the brittle material during the blade-piece extrusion contact;

[0009] Step 3: Calculate the normal load F in the Hertzian contact between the flank face and the brittle material f and plowing force f f ;

[0010] Step 4: Calculate the contact radius b and height h between a single hard protrusion peak and the flank surface r ;

[0011] Step 5: Calculate the initial angle δ, crack extension length c, and deflection angle α of the surface pit formed by the fracture and crushing of the brittle material;

[0012] Step 6: Based on the data obtained in the above steps, a theoretical model of surface roughness of brittle material turning is established.

[0013] Furthermore, in step 1, it is assumed that within time t, the collision contact force F between the rake face and the brittle material is r Work done W r for:

[0014] W r =F r v c t (35);

[0015] Among them, v c represents the cutting speed, t represents the cutting time; the brittle fracture energy U that forms the chip collapse c for:

[0016] U c =σ c V cra (36);

[0017] Among them, σ c Fracture strength of brittle materials, V cra is the volume of the layer to be cut that contacts the rake face,

[0018] V cra =a p fv c t (37);

[0019] Among them, a p represents the cutting depth, f represents the feed rate, and is given by:

[0020] W r =U c (38);

[0021] Then, the collision contact force F r for:

[0022] F r =σ c a p f (39).

[0023] Furthermore, in step 2, after the cutting edge bluntness and the brittle material are in adhesive coupling contact, the contact is separated and the adhesive portion is separated from the tool material as the brittle material breaks and shatters to form broken chips, resulting in adhesive wear of the cutting edge bluntness;

[0024] Assuming the adhesion contact radius is a, according to the adhesion contact mechanics theory, the single adhesion contact force F within a contact range is a1 for:

[0025]

[0026] Among them, γ 12 represents the adhesion energy per unit area, γ 12 =γ1+γ2, γ1 represents the free surface energy of the tool, γ2 represents the free surface energy of the brittle material; r β Indicates the radius of the blunt circle of the cutting edge;

[0027] The contact radius a is obtained by formula (7):

[0028]

[0029] Among them, E * represents the composite elastic modulus, E1 represents the elastic modulus of the tool, and v1 represents the Poisson’s ratio of the tool;

[0030] The contact arc length l between the tool tip arc and the brittle material is:

[0031]

[0032] Therefore, the contact area A between the blunt cutting edge and the brittle material is a for:

[0033]

[0034] The adhesive contact force F of the blunt cutting edge and brittle material a for:

[0035]

[0036] Right now:

[0037]

[0038] In addition, when the blunt cutting edge contacts the material, the contact stress reaches the fracture strength σ c When the material breaks and shatters, the material breaks and shatters; the breaking and shattering force P of the material during extrusion contact is:

[0039]

[0040] Furthermore, in step 3, the force of the flank is concentrated at the intersection of the cutting edge blunt circle and the flank. By analyzing the contact mechanics of the tool rake face, the cutting edge blunt circle and the brittle material, the normal load F at the intersection is f and plowing force f f :

[0041]

[0042]

[0043] Among them, F c Indicates the main cutting force of the tool, F p Indicates the tool's cutting depth resistance, F r represents the collision contact force, P represents the fracture force, F a Represents the adhesive contact force.

[0044] Furthermore, in step 4, the blunt edge of the cutting edge exerts violent pressure on the material near the back tool surface, causing the material to break and shatter, generating an uneven new surface; the fresh surface slides over the back tool surface, and the raised portion and the back tool surface are in Hertzian contact, and a part of the raised peaks on the surface may be broken for the second time under the pressure of the tool, and the raised peaks disappear; the other part of the harder raised peaks can penetrate and back-cut the back tool surface, causing wear of the back tool surface.

[0045] Furthermore, in step 4, the hard protrusion peak is assumed to be a rigid cone, that is, the contact surface of the brittle material on the back face is conical; under the normal load F f Under the action of the cone, the sliding friction is pressed into the back blade surface, generating the plowing force f f ; The hard convex peak reverses the cutting edge, causing abrasive wear on the flank surface; Assume that the contact radius of a single hard convex peak and the flank surface is b, and the height is h r ; According to the geometric relationship, the friction coefficient μ1 of a single hard protrusion is:

[0046]

[0047] The friction coefficient μ between the flank surface and the brittle material is:

[0048]

[0049] Since the friction coefficient of the same surface under the same contact environment is the same, according to equations (15) and (16):

[0050]

[0051] Calculate the contact radius b:

[0052]

[0053] Where H represents the hardness of the tool. Since the hard peaks in actual cutting may not be considered, the friction constant k of the hard peaks is introduced, and k is defined as 0.5.

[0054] Substituting equation (18) into equation (17), the height h of a single hard protrusion peak is r for:

[0055]

[0056] Furthermore, in step 5, according to the brittle fracture mechanics theory, the normal load F is simulated by using a blunt indenter fracture model. f Fracture removal of materials,

[0057] The crack extension length c is:

[0058]

[0059] Among them, K IC represents the fracture toughness of the material, and χ represents a constant, which can be expressed as follows:

[0060]

[0061] Where v2 represents the Poisson's ratio of the brittle material;

[0062] According to the concept of stress intensity factor at the crack tip under the combined loading mode, the initial angle δ is obtained as:

[0063]

[0064] The deflection angle α is:

[0065]

[0066] Furthermore, in step 6, the machined surface of the brittle material includes: hard protrusions, pits and periodic grooves;

[0067] According to the geometric relationship, we can obtain:

[0068]

[0069]

[0070] A3=h r b (60);

[0071] A4=2bh+0.5h 2 cot δ (61);

[0072] According to the definition of the contour midline, we can know that:

[0073] A1=A2+A3+A4 (62);

[0074] Substituting equations (24) to (27) into equation (28), the value of h can be obtained:

[0075]

[0076] According to the definition of surface roughness, the surface roughness R of hard convex peaks and pits is ac for:

[0077]

[0078] Substituting equations (24) to (27) and (29) into equation (30), we have:

[0079]

[0080] Substitute equations (18) to (22) into equation (31), then R ac The expression is:

[0081]

[0082] In addition, the surface roughness R of the periodic grooves af for:

[0083]

[0084] Therefore, the theoretical model of surface roughness of brittle materials R a for:

[0085]

[0086] Among them, h represents the height of the contour centerline, h r represents the height of the hard protrusion peak, 2b represents the width of the bottom edge of the hard protrusion peak, δ represents the angle between the crushing pit and the free surface, c represents the crack extension length, and α represents the pit deflection angle; R ac It represents the establishment of a theoretical model of the surface roughness of brittle materials consisting of hard protrusions and broken pits; the center line divides the contour line into four regions, corresponding to areas A1, A2, A3 and A4.

[0087] Compared with the prior art, the present invention has the following advantages:

[0088] Based on the tool-part coupled contact relationship, this invention simultaneously affects both the tool and the workpiece for the first time, innovatively incorporating tool wear and tool material properties into the parameters of the surface roughness theoretical model. A quantitative description of the crushed pits and hard protrusions on the machined surface is performed based on contact mechanics, fracture mechanics, and tribology. Combined with the periodic grooves generated by tool-part geometric contact, a new theoretical model for the surface roughness of brittle materials that takes tool wear into account is established. This model provides a completely new approach to the prediction of theoretical models for the surface roughness of brittle materials during turning. It has a significant impact on improving the surface quality, performance, and reliability of products made from brittle materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] 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 some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0090] Figure 1 Schematic diagram of the collision coupling contact between the front cutting edge and the brittle material of the present invention; wherein, (a) is the layer to be cut; (b) is a three-dimensional diagram of the collision coupling between the front cutting edge and the brittle material; (c) is a local enlarged diagram of the tool-workpiece collision contact.

[0091] Figure 2 Schematic diagram of the adhesive coupling contact between the blunt edge of the cutting edge and the brittle material of the present invention; wherein, (a) is the contact arc length between the tip arc and the brittle material; (b) is the adhesive contact between the blunt edge of the cutting edge and the brittle material; (c) is the adhesive wear of the blunt edge of the cutting edge.

[0092] Figure 3 Schematic diagram of force analysis of the tool of the present invention on the workpiece.

[0093] Figure 4 Schematic diagram of the back face of the hard raised peak anti-cutting tool of the present invention; wherein, (a) is the fresh surface of the material sliding toward the back face; (b) is the hard raised peak; and (c) is the back face of the hard raised peak anti-cutting tool.

[0094] Figure 5 Schematic diagram of blunt indentation fracture of the present invention; wherein, (a) is the location where the surface pit is formed; (b) is the blunt indentation fracture.

[0095] Figure 6 Schematic diagram of the geometric relationship between the cross-section of the hard protrusion peaks and pits of the present invention.

[0096] Figure 7 This is a schematic diagram of the experimental verification of the two cutting tools of the present invention for turning zirconia.

[0097] Figure 8 This is a schematic diagram of the experimental verification of the PCD tool of the present invention for turning two materials.

[0098] Figure 9 This is a schematic diagram of experimental verification using different tool tip arc radii for the present invention.

[0099] Figure 10 This is a schematic diagram of experimental verification using different cutting edge blunt circle radii for the present invention.

[0100] Figure 11 It is a schematic diagram of the overall process of the present invention. DETAILED DESCRIPTION

[0101] In order to enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the embodiments described 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 should fall within the scope of protection of the present invention.

[0102] It should be noted that the terms "first", "second", etc. in the description and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that the numbers used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0103] like Figure 1-6 As shown, the present invention provides a method for determining the surface roughness of brittle material turning considering tool-workpiece coupled contact, comprising the following steps:

[0104] Step 1: Calculate the collision contact force F between the rake face and the brittle material r ;

[0105] In time t, the collision contact force F between the front cutting edge and the brittle material is r The work done is:

[0106] W r =F r v c t (69);

[0107] Among them, v c represents the cutting speed, and t represents the cutting time. The brittle fracture energy required to form broken chips is:

[0108] U c =σ c V cra (70);

[0109] Among them, σ c Indicates the fracture strength of brittle materials, V cra Represents the volume of the layer to be cut that contacts the rake face,

[0110] V cra =a p fv c t (71);

[0111] Among them, a p represents the cutting depth, f represents the feed rate, and is given by:

[0112] W r =U c (72);

[0113] So Fr =σ c a p f (73);

[0114] Step 2: Calculate the adhesive contact force F between the cutting edge and the brittle material a The material's breaking and crushing force P when in contact with the tool-piece;

[0115] Schematic diagram of adhesive coupling contact between blunt cutting edge and brittle material Figure 2 shown. Figure 2 In a, l is the contact arc length between the tool tip arc and the brittle material. Figure 2 b is the adhesive contact between the cutting edge bluntness and the brittle material. As the contact separates, the adhesive part breaks off as the brittle material breaks and breaks into broken chips and separates from the tool material, resulting in adhesive wear of the cutting edge bluntness, such as Figure 2 As shown in c.

[0116] Assuming the adhesion contact radius is a, according to the adhesion contact mechanics theory, it can be known that within a contact range, a single adhesion contact force F a1 for:

[0117]

[0118] Among them, γ 12 represents the adhesion energy per unit area, γ 12 =γ1+γ2, γ1 represents the free surface energy of the tool, γ2 represents the free surface energy of the brittle material. β Indicates the cutting edge blunt radius.

[0119] The contact radius a can be obtained by formula (7):

[0120]

[0121] Where, E * is the complex elastic modulus, E1 is the elastic modulus of the tool, and v1 is the Poisson's ratio of the tool.

[0122] The contact arc length l between the tool tip arc and the brittle material is:

[0123]

[0124] Therefore, the contact area A between the blunt cutting edge and the brittle material is a for:

[0125]

[0126] The adhesive contact force F of the blunt cutting edge and brittle material can be derived a for:

[0127]

[0128] Right now:

[0129]

[0130] In addition, when the blunt cutting edge contacts the material, the contact stress reaches the fracture strength σ c When the material breaks and shatters, the material breaks and shatters. The breaking force P of the material during extrusion contact is:

[0131]

[0132] Step 3: Calculate the normal load F in the Hertzian contact between the flank face and the brittle material f and plowing force f f

[0133] Figure 3 This is the force analysis of the tool on the workpiece. The force of the flank is concentrated at the intersection of the cutting edge blunt circle and the flank. Through the contact mechanics analysis of the tool rake face, cutting edge blunt circle and brittle material, the normal load F at the intersection can be obtained. f and plowing force f f :

[0134]

[0135]

[0136] Where, F c is the main cutting force of the tool, F p It is the tool's resistance to cutting depth.

[0137] Step 4: Calculate the contact radius b and height h between a single hard protrusion peak and the flank surface r ;

[0138] Figure 4 The figure is a schematic diagram of the back face of the hard raised peak. The sharp squeeze of the material by the blunt edge near the back face causes the material to break and shatter, generating a new uneven surface. The new surface slides over the back face, such as Figure 4 As shown in a. The raised part and the back tool face are in Hertzian contact. A part of the raised peak on the surface may be crushed by the tool under the pressure of the tool, and the raised peak disappears; the other part of the harder raised peak can penetrate and back-cut the back tool face, causing back tool face wear. The hard raised peak is assumed to be a rigid cone, that is, the contact surface of the brittle material on the back tool face is conical, as shown in Figure 4 As shown in b. Under normal load F f Under the action of the cone, the sliding friction is pressed into the back blade surface, generating the plowing force f f . Figure 4In c, the hard convex peak reverses the cutting edge, causing abrasive wear on the flank. Assume that the contact radius of a single hard convex peak and the flank is b and the height is h. r According to the geometric relationship, the friction coefficient μ1 of a single hard protrusion is:

[0139]

[0140] The friction coefficient μ between the flank surface and the brittle material is:

[0141]

[0142] Since the friction coefficient of the same surface under the same contact environment is the same, according to equations (15) and (16):

[0143]

[0144] The contact radius b can be calculated using the following formula:

[0145]

[0146] Where H is the tool hardness. Because actual hard peak wear during cutting is not considered, and factors such as the actual hardness and number of hard peaks are not considered, the hard peak friction constant k is introduced, defined as k = 0.5.

[0147] Substituting equation (18) into equation (17), the height h of a single hard protrusion peak is r for:

[0148]

[0149] Step 5: Calculate the initial angle δ, crack extension length c, and deflection angle α of the surface pit formed by material fracture and crushing;

[0150] The surface pit is formed near the intersection of the blunt edge and the flank surface. According to the brittle fracture mechanics theory, the normal load F f The fracture removal of materials can be simulated using the blunt indentation fracture model

[0151] The crack extension length c is:

[0152]

[0153] Where K IC represents the fracture toughness of the material, and χ represents a constant, which can be expressed as follows:

[0154]

[0155] Where v2 represents the Poisson's ratio of the brittle material.

[0156] According to the concept of stress intensity factor at the crack tip under the combined loading mode, the initial angle δ can be calculated as:

[0157]

[0158] The deflection angle α is:

[0159]

[0160] Step 6: Establish a theoretical model for surface roughness of brittle material turning;

[0161] Through the analysis of the tool-tool coupling contact in turning brittle materials, it can be seen that the pits on the machined surface are the result of the tool cutting the workpiece, while the hard protrusions are the result of the workpiece counter-cutting the tool. The machined surface of brittle materials is composed of hard protrusions, pits and periodic grooves. The geometric relationship diagram of hard protrusions and pits is shown in the figure below. Figure 6 As shown, the height of the profile midline is h, and the height of the hard protrusion peak is h r , the bottom width is 2b, the angle between the crushing pit and the free surface is δ, the crack extension length is c, and the pit deflection angle is α. The theoretical model R of the surface roughness of brittle materials composed of hard protrusions and crushing pits is established. ac The center line divides the contour into four regions, corresponding to areas A1, A2, A3, and A4.

[0162] According to the geometric relationship, we can get:

[0163]

[0164]

[0165] A3=h r b (94);

[0166] A4=2bh+0.5h 2 cotδ (95);

[0167] According to the definition of the contour midline, we can know that:

[0168] A1=A2+A3+A4 (96);

[0169] Substituting equations (24) to (27) into equation (28), the value of h can be obtained:

[0170]

[0171] According to the definition of surface roughness, the surface roughness R of hard convex peaks and pits is ac for:

[0172]

[0173] Substituting equations (24) to (27) and (29) into equation (30), we have:

[0174]

[0175] Substitute equations (18) to (22) into equation (31), then R ac The expression is:

[0176]

[0177] In addition, the surface roughness R of the periodic grooves af for:

[0178]

[0179] Therefore, the theoretical model of surface roughness of brittle materials R a for:

[0180]

[0181] Example 1

[0182] The model described in this paper, based on tool-part coupled contact, considers both the workpiece and the material as factors influencing the surface roughness of brittle materials for the first time. This innovatively incorporates tool wear and tool material properties into the parameters of the theoretical surface roughness model. This allows for accurate prediction of surface roughness values ​​for brittle materials. Experimental comparisons of measured values ​​with theoretical predictions validate the model's accuracy. The experimental validation of the model is presented in the Examples.

[0183] Turning verification experiments were conducted using different tools, workpieces, and tool parameters. Thirteen groups of tests were conducted on a CAK5085 CNC lathe. Groups 1 and 2 tested zirconia turning using YG6 and PCD tools. Groups 2 and 3 used PCD to turn zirconia and fluorphlogopite. Groups 4 to 13 tested zirconia turning using PCD tools with different tool nose radius and cutting edge blunt radius. The turning test conditions are detailed in Table 1. Table 2 shows the main performance characteristics of the two tools. Table 3 shows the main performance characteristics of the two processed materials.

[0184] Table 1 Turning test conditions

[0185]

[0186] Table 2 Tool attributes

[0187]

[0188] Table 3 Material properties

[0189]

[0190] Figure 7 Results from experiments in groups 1 and 2: Experimental verification of zirconia turning using PCD and YG6 carbide tools. The green bars represent the measured surface roughness values, while the blue bars represent the predicted surface roughness values ​​calculated based on a theoretical model for surface roughness of brittle materials. The measured surface roughness of zirconia turning using the PCD tool was 2.394 μm, while the predicted value was 2.68 μm. The measured surface roughness of zirconia turning using the YG6 tool was 4.264 μm, while the predicted value was 4.36 μm. The measured and predicted values ​​are close, indicating a good agreement.

[0191] Figure 8 Results from Groups 2 and 3: Surface roughness of two brittle materials, measured using the same tool under identical cutting conditions. The predicted surface roughness values ​​for both materials, calculated theoretically, are close to the experimentally measured values, demonstrating the model's ability to predict surface roughness.

[0192] Figure 9 Results from experiments 4-8: Surface roughness of zirconia turned with PCD tools at different tool nose radii. Substituting different tool nose radii into the surface roughness theoretical model yielded predictions that were close to the experimental measurements, and the trends were consistent with the experimental values.

[0193] Figure 10 Results from experiments 9-13: Surface roughness of zirconia turned with PCD tools at different cutting edge radii. Comparing the predicted and experimental values ​​revealed consistent trends, with good agreement between the theoretical and experimental values.

[0194] The serial numbers of the above embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments. In the above embodiments of the present invention, the description of each embodiment has its own focus. For parts not described in detail in a particular embodiment, please refer to the relevant description of other embodiments. In the several embodiments provided in this application, it should be understood that the disclosed technical content can be implemented by other means.

[0195] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for determining surface roughness of brittle material turning considering tool-workpiece coupled contact, characterized in that: The following steps are involved: Step 1: Calculate the contact force between the rake face and the brittle material F r ; Step 2: Calculate the adhesive contact force between the cutting edge and the brittle material F a and the fracture crushing force of the brittle material during the knife-piece extrusion contact P ; Step 3: Calculate the normal load in Hertzian contact between the flank face and the brittle material F f and plowing power f f ; Step 4: Calculate the contact radius between a single hard protrusion peak and the flank surface b and height h r In step 4, the hard protrusion peak is assumed to be a rigid cone, that is, the contact surface of the brittle material on the back face is conical; under normal load F f Under the action of the cone, the sliding friction is pressed into the back blade, generating plowing force f f ; The hard convex peak reverses the cutting edge of the tool, causing abrasive wear on the tool face; Assume that the contact radius between a single hard convex peak and the tool face is b , the height is h r ; According to the geometric relationship, the friction coefficient of a single hard protrusion peak μ 1 is: (15)； The friction coefficient between the back face and the brittle material μ for: (16)； Since the friction coefficient of the same surface under the same contact environment is the same, according to equations (15) and (16): (17)； Calculate contact radius b : (18)； in, H Indicates the hardness of the tool; Since there are unconsidered factors in the actual cutting process, the friction constant of the hard peak is introduced. k ,definition k= 0.5; Substituting Equation (18) into Equation (17), the height of a single hard protrusion peak is h r for: (19)； Step 5: Calculate the initial angle of the surface pit formed by the fracture of the brittle material δ , crack extension length c , deflection angle α In step 5, according to the brittle fracture mechanics theory, the normal load is simulated by using a blunt indenter fracture model F f Fracture removal of materials; Crack extension length c for: (20)； in, K IC It represents the fracture toughness of the material. χ represents a constant, expressed as follows: (21)； in, v 2 represents the Poisson's ratio of brittle materials; According to the concept of stress intensity factor at the crack tip under the combined loading mode, the initial angle δ for: (22)； Deflection angle α for: (23)； Step 6: Based on the data obtained in the above step, a theoretical model of surface roughness of brittle material turning is established; in step 6, the machined surface of the brittle material includes: hard protrusions, pits and periodic grooves; According to the geometric relationship, we can obtain: (24)； (25)； (26)； (27)； According to the definition of the contour midline, we can know that: (28)； Substituting equations (24) to (27) into equation (28), we can obtain h value: (29)； According to the definition of surface roughness, the surface roughness of hard peaks and pits R ac for: (30)； Substituting equations (24) to (27) and (29) into equation (30), we have: (31)； Substituting equations (18) to (22) into equation (31), we get R ac The expression is: (32) In addition, the surface roughness of the periodic grooves R af for: (33)； Therefore, the theoretical model of surface roughness of brittle materials R a for: (34)； in, h Indicates the height of the contour centerline, h r Indicates the height of the hard protrusion peak, 2b Indicates the bottom width, δ represents the angle between the crushing pit and the free surface, c represents the crack extension length, α represents the pit deflection angle; R ac Indicates the establishment of a theoretical model of brittle material surface roughness consisting of hard protrusions and broken pits; the center line divides the contour line into four regions, and the corresponding areas are A 1. A 2. A 3 and A 4.

2. The method for determining surface roughness of brittle material turning considering tool-workpiece coupled contact according to claim 1, characterized in that: In step 1, set the time t Internal, collision contact force between rake face and brittle material F r Work done for: (1)； in, v c Indicates cutting speed, t Indicates the cutting time; the brittle fracture energy of the broken chips is for: (2)； in, σ c Represents the fracture strength of brittle materials, V cra is the volume of the layer to be cut that contacts the rake face, (3)； in, a p Indicates the cutting depth, f Indicates the feed rate, given by: (4)； Then, the collision contact force F r for: (5)。 3. The method for determining surface roughness of brittle material turning considering tool-workpiece coupled contact according to claim 1, characterized in that: In step 2, after the cutting edge bluntness and the brittle material are in adhesive coupling contact, the contact is separated and the adhesive portion is separated from the tool material as the brittle material breaks and breaks to form broken chips, resulting in adhesive wear of the cutting edge bluntness; Assume that the adhesive contact radius is a According to the theory of adhesive contact mechanics, a single adhesive contact force within a contact range is F a1 for: (6)； in, γ 12 represents the adhesion energy per unit area, γ 12 =γ 1 +γ 2, γ 1 represents the free surface energy of the tool, γ 2 represents the free surface energy of the brittle material; r β Indicates the radius of the blunt circle of the cutting edge; The contact radius a , obtained by formula (7): (7)； in, E * represents the composite elastic modulus, , E 1 represents the elastic modulus of the tool, v 1 represents the Poisson’s ratio of the tool; Contact arc length between tool tip radius and brittle material l for: (8)； Therefore, the contact area between the blunt cutting edge and the brittle material is A a for: (9)； Pushing out the cutting edge rounding and adhesive contact force of brittle materials F a for: (10)； Right now: (11)； In addition, when the blunt cutting edge contacts the material, the contact stress reaches the breaking strength of the material. σ c When the material breaks and breaks, the material breaks and breaks; when the material breaks and breaks, the material breaks and breaks when the material is squeezed P for: (12)。 4. The method for determining surface roughness of brittle material turning considering tool-workpiece coupled contact according to claim 1, characterized in that: In step 3, the force of the flank is concentrated at the intersection of the cutting edge blunt circle and the flank. Through the contact mechanics analysis of the tool rake face, the cutting edge blunt circle and the brittle material, the normal load at the intersection is F f and plowing power f f : (13)； (14)； in, F c Indicates the main cutting force of the tool, F p Indicates the tool's resistance to cutting depth. represents the collision contact force, P Indicates the breaking force, F a Represents the adhesive contact force.

5. The method for determining surface roughness of brittle material turning considering tool-workpiece coupled contact according to claim 1, characterized in that: In step 4, the blunt edge of the cutting edge exerts intense pressure on the material near the back face, causing the material to break and shatter, generating an uneven new surface; the fresh surface slides over the back face, and the raised portion and the back face are in Hertzian contact, and a portion of the raised peaks on the surface may be broken a second time under the pressure of the tool, and the raised peaks disappear; the other portion of the harder raised peaks can penetrate and back-cut the back face, causing wear on the back face.

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