A method for determining machinable ceramic turning surface roughness

Abstract

The application is a kind of method for determining the surface roughness of machinable ceramic turning, comprising the following steps: calculating the length of the initial surface; calculating the actual cutting layer parameters, the stress on the rake face and the stress on the relief face during machinable ceramic turning; calculating the normal stress and shear stress of the initial surface of the surface fracture pit of machinable ceramic turning; obtaining the relationship between the stress intensity factor of I-type crack tip and the stress intensity factor of II-type crack tip; calculating the deflection cross-section angle and deflection length of the surface fracture pit of machinable ceramic turning; calculating the upward extension cross-section length of the surface fracture pit of machinable ceramic turning; establishing the geometric interference surface roughness considering elastic recovery; establishing the broken surface roughness considering the actual shape of the cross-section of the fracture pit; superimposing the geometric interference roughness and the broken roughness on each other to establish a brittle surface roughness theoretical model; and based on the theoretical model of the brittle surface roughness, the surface roughness of machinable ceramic turning is determined.

Description

Technical Field

[0001] This invention belongs to the field of machinable ceramic processing technology, and relates to a method for determining the surface roughness of machinable ceramic turning surfaces. Background Technology

[0002] Machinable ceramics possess superior corrosion resistance, wear resistance, and high-temperature resistance, making them widely used in aerospace, military, chemical, machinery, and metallurgical fields. However, their inherent hardness and brittleness inevitably lead to cracking during machining, resulting in poor surface finish and increased machining difficulty. Turning is one of the most basic and important machining methods in the machinery manufacturing industry, and surface roughness is a crucial indicator for measuring the quality of turned surfaces. Surface roughness is a comprehensive reflection of the influence of cutting parameters and system variables on the cutting process. Many factors affect surface roughness, and the hardness and brittleness of machinable ceramics make their surface formation mechanism more complex and machining quality difficult to control. Therefore, establishing an accurate theoretical model of surface roughness is of great significance for improving the surface quality of machinable ceramics and achieving efficient and precise machining of brittle materials.

[0003] Current research mainly focuses on the theoretical study of surface roughness models under plastic removal modes, while the formation mechanism of surface roughness under brittle removal or mixed plastic-brittle removal modes has not been fully understood and explained, and related theoretical models are few. Machinable ceramics are typical brittle materials, and the removal modes of turning machinable ceramics include plastic shearing and brittle fracture, with brittle fracture being the predominant mode. Existing methods for determining the surface roughness of brittle materials approximate the cross-sectional shape of the fracture pit formed on the surface as an isosceles triangle when establishing the model, without considering the elastic recovery during the cutting process of brittle materials, the actual cutting layer parameters, and the actual shape of the fracture pit cross-section. Therefore, the predicted values ​​of the established surface roughness models are not high. Summary of the Invention

[0004] To solve the above problems, the technical solution adopted by the present invention is: a method for determining the surface roughness of machinable ceramic turning surfaces, further comprising the following steps:

[0005] Define the angle δ between the initial surface and the free surface of the breakage pit on the machinable ceramic turning surface, and calculate the length L of the initial surface. M ;

[0006] Calculate the actual cutting layer parameters, including the nominal cutting width b. D and the actual nominal cutting thickness h D ;

[0007] Based on the actual nominal cutting width b D Calculate the stress σ on the rake face during turning of machinable ceramics. a The stress σ on the back face of the tool p ;

[0008] Based on the stress σ on the rake face a The stress σ on the back face of the tool p Calculate the normal stress σ on the initial surface of the fracture pit on the machined surface of a machinable ceramic. n and shear stress τ s ;

[0009] Based on the stress σ on the rake face a The stress σ on the back face of the tool p Based on the relationship between stress intensity factor and stress, the stress intensity factor K at the tip of a type I crack is calculated under combined type I and type II loading. I and the stress intensity factor K at the tip of a type II crack Ⅱ The relationship between them;

[0010] Based on the formula for the stress field at the crack tip under combined loading, the deflection section angle θ of the fracture pit on the machined surface of machinable ceramics is calculated.

[0011] Based on the deflection section angle θ of the fracture pit, the deflection section length L of the fracture pit on the machinable ceramic turning surface is calculated according to the stress intensity factor fracture criterion under combined loading conditions.

[0012] Based on the calculation of the initial surface length L M and the actual nominal cutting thickness h D Based on the principle of energy conservation, calculate the upward extension section length L of the fracture pit on the machinable ceramic turning surface. N ;

[0013] Based on the formulas for elastic recovery height and ideal groove height, a geometric interference surface roughness R considering elastic recovery is established. ag ;

[0014] Based on the angle δ between the initial surface and the free surface of the crater, and the length L of the initial surface... M Deflection section angle θ, deflection length L, upward extension section length L N Determine the actual shape of the crushing crater cross-section and establish the surface roughness R of the crushing surface. ab ;

[0015] Geometric interference roughness R ag and fracture roughness R ab By superimposing these elements, a theoretical model R for brittle surface roughness is established. a ;

[0016] Based on the theoretical model R of brittle surface roughness a This allows for the determination of the surface roughness of machinable ceramic turning surfaces.

[0017] Further: the length L of the initial surfaceM The calculation formula is as follows:

[0018]

[0019] Where: K c For fracture toughness, α is the boundary correction factor, and σ is the fracture toughness. c This refers to the bending strength.

[0020] Furthermore: the actual cutting layer parameters include the nominal cutting width b. D and the actual nominal cutting thickness h D as follows:

[0021]

[0022]

[0023] Wherein: γ ε It is the radius of the blade tip arc, a p f is the depth of cut, and f is the feed rate.

[0024] Furthermore: the nominal width b based on the actual cutting D Calculate the stress σ on the rake face during turning of machinable ceramics. a The stress σ on the back face of the tool p as follows:

[0025]

[0026]

[0027] Wherein: F c The main cutting force, F p For the depth resistance, k1 is a constant fitted by measurements, γ β α0 is the cutting edge blunt radius, H is the hardness, E is the elastic modulus, and α0 is the tool clearance angle.

[0028] Furthermore: based on the stress σ on the rake face a The stress σ on the back face of the tool p Calculate the normal stress σ on the initial surface of the fracture pit on the machined surface of a machinable ceramic. n and shear stress τ s .

[0029] σ n =σ p cos 2 δ+σ a sin2δ (6)

[0030] τ s =σ a sinδcosδ-σp sinδcosδ (7)

[0031] Furthermore: based on the stress σ on the rake face a The stress σ on the back face of the tool p Under combined loading of type I and type II cracks, the stress intensity factor K at the tip of a type I crack is... I and the stress intensity factor K at the tip of a type II crack Ⅱ The relationship between the two factors and the deflection section angle θ based on the fracture pit, and the process of calculating the deflection section length L of the fracture pit on the machinable ceramic turning surface according to the stress intensity factor fracture criterion under composite loading conditions, is as follows:

[0032]

[0033] According to the maximum tensile stress criterion

[0034]

[0035] The angle θ of the deflection section of the fracture pit can be calculated using formulas (8) and (9):

[0036]

[0037] σ yy It is the tensile stress perpendicular to the crack propagation direction, σ c It is the tensile strength σ, when σ yy =σ c At that time, the crack deflects, that is:

[0038]

[0039] The deflection section length L of the fracture crater can be calculated as follows:

[0040]

[0041] Furthermore: the length L of the calculated initial surface M and the actual nominal cutting thickness h D Based on the principle of energy conservation, calculate the upward extension section length L of the fracture pit on the machinable ceramic turning surface. N The process is as follows:

[0042] Crater depth h c for:

[0043] h c =L M sinδ+Lsin(δ+θ) (13)

[0044] Energy W input to the tool c for:

[0045] W c =F c L M cosδ (14)

[0046] Surface energy U formed by fracture S for:

[0047] U S =4(L M +L+L U )b D r (15)

[0048] Among them, L U is the upward extension length of the chip, and r is the free surface energy per unit area;

[0049] The brittle fracture energy for chip formation is:

[0050] U C =σ c V (16)

[0051] Therefore, the brittle fracture energy that forms the chip is:

[0052]

[0053] Based on the principle of energy conservation, the upward extension length L of the chip can be calculated. U Based on the geometry of the chips, the length L of the upward extension section of the fracture crater can be calculated. N for.

[0054]

[0055] Furthermore, the process of establishing the geometric interference roughness considering elastic recovery is as follows:

[0056] Ideal groove height h on machined surface i for:

[0057]

[0058] Due to elastic recovery, the actual trench height h a for:

[0059]

[0060] Based on the definition of arithmetic mean roughness, the geometric interference roughness R considering elastic recovery can be calculated. ag ,as follows.

[0061]

[0062] Furthermore: the angle δ between the initial surface and the free surface of the fracture crater, and the length L of the initial surface... M Deflection section angle θ, deflection length L, upward extension section length L N Determine the actual shape of the crushing crater cross-section and establish the surface roughness R of the crushing surface. ab The process is as follows:

[0063] Based on the actual shape of the crater cross-section, and assuming the centerline height is h, the following can be obtained using geometric relationships:

[0064]

[0065] l4=h c cot(θ+δ) (23)

[0066] l5 = L M cosδ-L M sinδcot(δ+θ) (24)

[0067] By the principle of similar triangles, we can obtain:

[0068]

[0069] The areas of the ceramic turned surface contours A, B, and C are respectively:

[0070]

[0071]

[0072]

[0073] Based on the definition of the median, the value of k can be calculated:

[0074]

[0075] According to the definition of surface roughness

[0076]

[0077] Substituting equations (22) to (24) and (26) to (28) into equation (30), the surface roughness R of the broken surface is thus obtained. ab The theoretical model is as follows:

[0078]

[0079] Furthermore: Establish a theoretical model R for brittle surface roughness. a The process is as follows:

[0080] The brittle surface roughness R is formed by superimposing the geometric interference roughness considering elastic recovery and the fracture roughness considering the fracture pit. a :

[0081] R a =R ag +R ab (32)

[0082] Right now:

[0083]

[0084] This invention provides a method for determining the surface roughness of machinable ceramic turning surfaces. It establishes a theoretical model for brittle surface roughness by comprehensively considering multiple factors, including the actual shape of the fracture crater cross-section, actual cutting layer parameters, tool angle, material properties, interference relationship between the tool and workpiece, and elastic recovery. This method for determining surface roughness considers all factors, is closer to experimental values ​​than existing surface roughness theoretical models, and provides more accurate prediction results, offering a completely new concept for establishing surface roughness models for brittle materials. Attached Figure Description

[0085] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0086] Figure 1 This is a flowchart of the method;

[0087] Figure 2 This is a diagram of the actual cutting layer parameters;

[0088] Figure 3 Figures showing the stress field analysis at the crack tip and the initial surface stress analysis under combined loading;

[0089] Figure 4 This is a schematic diagram of the chip geometry.

[0090] Figure 5 A schematic diagram of the geometric interference surface considering elastic recovery;

[0091] Figure 6 This is a schematic diagram of the actual shape of the cross-section of the crater;

[0092] Figure 7 This is a schematic diagram of the geometric relationship of the cross-section of the fracture pit;

[0093] Figure 8 This is a graph showing the change in surface roughness with cutting speed.

[0094] Figure 9 This is a graph showing the change in surface roughness as a function of feed rate.

[0095] Figure 10 This is a graph showing the change in surface roughness with cutting depth. Detailed Implementation

[0096] It should be noted that, unless otherwise specified, the embodiments and features in the embodiments of the present invention can be combined with each other. The present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0097] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the present invention or its application or use. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0098] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0099] Unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps described in these embodiments do not limit the scope of the invention. It should also be understood that, for ease of description, the dimensions of the various parts shown in the drawings are not drawn to actual scale. Techniques, methods, and devices known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the specification. In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters in the following figures denote similar items; therefore, once an item is defined in one figure, it need not be further discussed in subsequent figures.

[0100] In the description of this invention, it should be understood that the orientation or positional relationship indicated by directional terms such as "front, back, up, down, left, right", "horizontal, vertical, horizontal" and "top, bottom" is generally based on the orientation or positional relationship shown in the accompanying drawings, and is only for the convenience of describing this invention and simplifying the description. Unless otherwise stated, these directional terms do not indicate or imply that the device or element referred to must have a specific orientation or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on the scope of protection of this invention. The directional terms "inner" and "outer" refer to the inner and outer contours relative to the outline of each component itself.

[0101] For ease of description, spatial relative terms such as "above," "over," "on the upper surface of," "above," etc., are used herein to describe the spatial positional relationship of a device or feature as shown in the figures to other devices or features. It should be understood that spatial relative terms are intended to encompass different orientations in use or operation besides the orientation of the device as described in the figures. For example, if the device in the figures is inverted, a device described as "above" or "above" other devices or structures would subsequently be positioned as "below" or "under" other devices or structures. Thus, the exemplary term "above" can include both "above" and "below." The device may also be positioned in other different ways (rotated 90 degrees or in other orientations), and the spatial relative descriptions used herein will be interpreted accordingly.

[0102] Furthermore, it should be noted that the use of terms such as "first" and "second" to define components is merely for the purpose of distinguishing the corresponding components. Unless otherwise stated, the above terms have no special meaning and therefore should not be construed as limiting the scope of protection of this invention.

[0103] Figure 1 This is a flowchart of the method;

[0104] A method for determining the surface roughness of a machinable ceramic turning surface includes the following steps:

[0105] S1: Define the angle δ between the initial surface and the free surface of the breakage pit on the machinable ceramic turning surface, and calculate the length L of the initial surface. M ;

[0106] S2: Calculate the actual cutting layer parameters, including the nominal cutting width b. D and the actual nominal cutting thickness h D ;

[0107] S3: Based on the actual nominal cutting width b D Calculate the stress σ on the rake face during turning of machinable ceramics. aThe stress σ on the back face of the tool p ;

[0108] S4: Based on the stress σ on the rake face a The stress σ on the back face of the tool p Calculate the normal stress σ on the initial surface of the fracture pit on the machined surface of a machinable ceramic. n and shear stress τ s ;

[0109] S5: Based on the stress σ on the rake face a The stress σ on the back face of the tool p Based on the relationship between stress intensity factor and stress, the stress intensity factor K at the tip of a type I crack is calculated under combined type I and type II loading. I and the stress intensity factor K at the tip of a type II crack Ⅱ The relationship between them;

[0110] S6: Calculate the deflection section angle θ of the fracture pit on the machined ceramic surface by combining the formula of the stress field at the crack tip under composite loading.

[0111] S7: Based on the deflection section angle θ of the fracture pit, calculate the deflection section length L of the fracture pit on the machinable ceramic turning surface according to the stress intensity factor fracture criterion under composite loading conditions;

[0112] S8: Based on the calculated length L of the initial surface M and the actual nominal cutting thickness h D Based on the principle of energy conservation, calculate the upward extension section length L of the fracture pit on the machinable ceramic turning surface. N ;

[0113] S9: Based on the formulas for elastic recovery height and ideal groove height, establish the geometric interference surface roughness R considering elastic recovery. ag ;

[0114] S10: Based on the angle δ between the initial surface and the free surface of the crater, and the length L of the initial surface... M Deflection section angle θ, deflection length L, upward extension section length L N Determine the actual shape of the crushing crater cross-section and establish the surface roughness R of the crushing surface. ab ;

[0115] S11: Geometric interference roughness R ag and fracture roughness R ab By superimposing these elements, a theoretical model R for brittle surface roughness is established. a ;

[0116] S12: Based on the theoretical model R of brittle surface roughness aThis allows for the determination of the surface roughness of machinable ceramic turning surfaces.

[0117] Furthermore, the angle of the initial surface of the fracture crater is defined, and the length of the initial surface is calculated as follows:

[0118] By extracting the profile of the machined ceramic turning surface, the angle δ between the initial surface and the free surface was measured to be approximately 3°-5°, and the angle between the initial surface and the free surface was defined as 3°.

[0119] The length L of the initial surface of the fracture crater M for:

[0120]

[0121] Where: K c For fracture toughness, α is the boundary correction factor, and σ is the fracture toughness. c This refers to the bending strength.

[0122] Further: Calculate the actual cutting layer parameters, including the actual nominal cutting width b. D Actual cutting nominal thickness h D ;

[0123] Actual cutting layer parameters are as follows Figure 2 As shown.

[0124] Based on geometric relationships, the actual cutting layer parameters include the nominal cutting width b. D and the actual nominal cutting thickness h D as follows:

[0125]

[0126]

[0127] Wherein: γ ε It is the radius of the blade tip arc, a p f is the depth of cut, and f is the feed rate.

[0128] Furthermore: the nominal width b based on the actual cutting D Calculate the stress σ on the rake face during turning of machinable ceramics. a The stress σ on the back face of the tool p as follows:

[0129]

[0130]

[0131] Wherein: F c The main cutting force, F p For the depth resistance, k1 is a constant fitted by measurements, γβ α0 is the cutting edge blunt radius, H is the hardness, E is the elastic modulus, and α0 is the tool clearance angle.

[0132] Furthermore, the stress σ on the rake face... a The stress σ on the back face of the tool p Calculate the normal stress σ on the initial surface of the fracture crater. n and shear stress τ s as follows:

[0133] σ n =σ p cos 2 δ+σ a sin2δ (6)

[0134] τ s =σ a sinδcosδ-σ p sinδcosδ (7)

[0135] Figure 3 Figures showing the stress field analysis at the crack tip and the initial surface stress analysis under combined loading;

[0136] Furthermore, based on the deflection section angle θ of the fracture crater, and according to the stress intensity factor fracture criterion under combined loading conditions, the deflection section angle θ and the deflection section length L of the fracture crater are calculated as follows:

[0137] Based on the stress σ on the rake face a The stress σ on the back face of the tool p Under combined loading of type I and type II cracks, the stress intensity factor K at the tip of a type I crack is... I and the stress intensity factor K at the tip of a type II crack Ⅱ The following relationship must be satisfied;

[0138]

[0139] According to the maximum tensile stress criterion

[0140]

[0141] The angle θ of the deflection section of the fracture pit can be calculated using formulas (8) and (9):

[0142]

[0143] σ yy It is the tensile stress perpendicular to the crack propagation direction, σ c For tensile strength, when σ yy =σ c At that time, the crack deflects, that is:

[0144]

[0145] The length L of the deflection section of the fracture crater can be obtained as follows:

[0146]

[0147] Furthermore, based on the calculated length L of the initial surface M and the actual nominal cutting thickness h D Based on the principle of energy conservation, calculate the length L of the upward-extending cross section of the fracture crater. N The process is as follows:

[0148] Figure 4 This is a schematic diagram of the chip geometry, where the depth of the breakage pit is h. c for:

[0149] h c =L M sinδ+Lsin(δ+θ) (13)

[0150] Energy W input to the tool c for:

[0151] W c =F c L M cosδ (14)

[0152] Surface energy U formed by fracture S for:

[0153] U S =4(L M +L+L U )b D r (15)

[0154] In the formula, L U is the upward extension length of the chip, and r is the free surface energy per unit area.

[0155] The brittle fracture energy for chip formation is:

[0156]

[0157] Therefore, the brittle fracture energy that forms the chip is:

[0158]

[0159] Based on the principle of conservation of energy, the upward extension length L of the chip can be calculated. U .

[0160] Based on the geometry of the chips, the length L of the upward extension section of the fracture crater can be calculated. N for:

[0161]

[0162] Furthermore: Based on the formulas for elastic recovery height and ideal groove height, a geometric interference surface roughness R considering elastic recovery is established. ag The process is as follows:

[0163] A schematic diagram of the geometric interference surface considering elastic recovery is shown below. Figure 5 As shown.

[0164] Ideal groove height h on machined surface i for:

[0165]

[0166] Due to elastic recovery, the actual trench height h a for:

[0167]

[0168] Based on the definition of arithmetic mean roughness, the geometric interference roughness R considering elastic recovery can be calculated. ag ,as follows:

[0169]

[0170] Furthermore, a crushing roughness R considering the cross-sectional shape of the crushing crater is established. ab The theoretical modeling process is as follows:

[0171] Figure 6 This is a schematic diagram of the actual cross-sectional shape of the fracture crater. The angle δ between the initial surface and the free surface of the fracture crater, and the length L of the initial surface are determined. M Deflection section angle θ, deflection length L, upward extension section length L N By obtaining the value of , the actual shape of the fracture pit cross-section can be obtained, thereby establishing a more accurate theoretical model of surface roughness.

[0172] Figure 7 This is a schematic diagram of the geometric relationship of the cross-section of the fracture crater. Let the height of the centerline be h. Based on the geometric relationship, we can obtain:

[0173]

[0174] l4=h c cot(θ+δ) (23)

[0175] l5 = L M cosδ-L M sinδcot(δ+θ) (24)

[0176] By the principle of similar triangles, we can obtain:

[0177]

[0178] Figure 7 The areas of contours A, B, and C are respectively:

[0179]

[0180]

[0181]

[0182] Based on the definition of the contour centerline, the value of k can be calculated:

[0183]

[0184] According to the definition of surface roughness

[0185]

[0186] Substituting equations (22) to (24) and (26) to (28) into equation (30), the surface roughness R of the broken surface is thus obtained. ab The theoretical model is as follows:

[0187]

[0188] Furthermore, the brittle surface roughness R is established. a The theoretical modeling process is as follows:

[0189] The theoretical model R of brittle surface roughness is constructed by superimposing geometric interference roughness considering elastic recovery and fracture roughness considering fracture pits. a :

[0190] R a =R ag +R ab (32)

[0191] Right now:

[0192]

[0193] The model comprehensively considers factors such as the actual shape of the fracture crater cross section, actual cutting layer parameters, tool angle, material properties, interference relationship between the tool and the workpiece, and elastic recovery.

[0194] Example:

[0195] This model can accurately predict the surface roughness of machined ceramic surfaces through calculation. Therefore, by conducting experiments and comparing the experimental measurements with the theoretical predictions, the accuracy of the model can be verified. The experimental demonstration of the model's effectiveness serves as an example.

[0196] To verify the accuracy of the theoretical model for brittle surface roughness, a verification experiment was conducted. The turning test conditions and results are shown in Table 1.

[0197] Table 1 Turning Test Conditions

[0198]

[0199] The workpiece material is fluorophlogopite machinable ceramic, and its performance parameters are shown in Table 2.

[0200] Table 2 Material Properties of Workpieces

[0201]

[0202] The cutting tool used is a Yg6 carbide tool. The tool parameters are shown in Table 3.

[0203] Table 3 Tool Angles

[0204]

[0205] Model Validation

[0206] Common geometric models for predicting surface roughness in metal turning are as follows:

[0207]

[0208] When studying the theoretical model of surface roughness in brittle materials, an isosceles triangle is used to approximate the fracture pit. The theoretical model of fracture roughness is as follows:

[0209]

[0210] Substituting the material parameters, tool parameters, and turning parameters into equations (33), (34), and (35) respectively, we obtain the predicted values ​​of the three surface roughness models.

[0211] Figures 8 to 10 The comparisons between the three models and experimental measurements are presented, and the verification results show that the newly established theoretical model R for brittle surface roughness is valid. a The trend is the same as the experimental value, compared to the geometric model R. a1 and the fragmentation model R a2 The new theoretical model for brittle surface roughness, R, is closer to experimental values ​​and provides more accurate predictions. a It can serve as a theoretical basis for predicting surface roughness in the cutting of brittle materials.

[0212] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions 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 the surface roughness of a machinable ceramic turning surface, characterized in that: Includes the following steps: Define the angle δ between the initial surface and the free surface of the breakage pit on the machinable ceramic turning surface, and calculate the length L of the initial surface. M ; Calculate the actual cutting layer parameters, including the nominal cutting width b. D and the actual nominal cutting thickness h D ; Based on the actual nominal cutting width b D Calculate the stress σ on the rake face during turning of machinable ceramics. a The stress σ on the back face of the tool p ; Based on the stress σ on the rake face a The stress σ on the back face of the tool p Calculate the normal stress σ on the initial surface of the fracture pit on the machined surface of a machinable ceramic. n and shear stress τ s ; Based on the stress σ on the rake face a The stress σ on the back face of the tool p Based on the relationship between stress intensity factor and stress, the stress intensity factor K at the tip of a type I crack is calculated under combined type I and type II loading. I and the stress intensity factor K at the tip of a type II crack Ⅱ The relationship between them; Based on the formula for the stress field at the crack tip under combined loading, the deflection section angle θ of the fracture pit on the machined surface of machinable ceramics is calculated. Based on the deflection section angle θ of the fracture pit, the deflection section length L of the fracture pit on the machinable ceramic turning surface is calculated according to the stress intensity factor fracture criterion under combined loading conditions. Based on the calculation of the initial surface length L M and the actual nominal cutting thickness h D Based on the principle of energy conservation, calculate the upward extension section length L of the fracture pit on the machinable ceramic turning surface. N ; Based on the formulas for elastic recovery height and ideal groove height, a geometric interference surface roughness R considering elastic recovery is established. ag ; Based on the angle δ between the initial surface and the free surface of the fracture crater, and the length L of the initial surface... M Deflection section angle θ, deflection section length L, upward extension section length L N Determine the actual shape of the crushing crater cross-section and establish the surface roughness R of the crushing surface. ab ; Geometric interference roughness R ag and fracture roughness R ab By superimposing these elements, a theoretical model R for brittle surface roughness is established. a ; Based on the theoretical model R of brittle surface roughness a This allows for the determination of the surface roughness of machinable ceramic turning surfaces.

2. The method for determining the surface roughness of a machinable ceramic turning surface according to claim 1, characterized in that: The length L of the initial surface M The calculation formula is as follows: (1) Where: K c For fracture toughness, α is the boundary correction factor, and σ is the fracture toughness. c This refers to the bending strength.

3. The method for determining the surface roughness of a machinable ceramic turning surface according to claim 2, characterized in that: The actual cutting layer parameters include the nominal cutting width b. D and the actual nominal cutting thickness h D ,as follows: (2) (3) Wherein: γ ε It is the radius of the blade tip arc, a p f is the depth of cut, and f is the feed rate.

4. The method for determining the surface roughness of a machinable ceramic turning surface according to claim 3, characterized in that: The basis is the actual nominal cutting width b D Calculate the stress σ on the rake face during turning of machinable ceramics. a The stress σ on the back face of the tool p as follows: (4) (5) Wherein: F c The main cutting force, F p For the depth resistance, k1 is a constant fitted by measurements, γ β α0 is the cutting edge blunt radius, H is the hardness, E is the elastic modulus, and α0 is the tool clearance angle.

5. The method for determining the surface roughness of a machinable ceramic turning surface according to claim 4, characterized in that: Based on the stress σ on the rake face a The stress σ on the back face of the tool p Calculate the normal stress σ on the initial surface of the fracture pit on the machined surface of a machinable ceramic. n and shear stress τ s ; (6) (7)。 6. The method for determining the surface roughness of a machinable ceramic turning surface according to claim 5, characterized in that: Based on the stress σ on the rake face a The stress σ on the back face of the tool p Under combined loading of type I and type II cracks, the stress intensity factor K at the tip of a type I crack is... I and the stress intensity factor K at the tip of a type II crack Ⅱ The relationship between the two factors and the deflection section angle θ based on the fracture pit, and the process of calculating the deflection section length L of the fracture pit on the machinable ceramic turning surface according to the stress intensity factor fracture criterion under composite loading conditions, is as follows: (8) According to the maximum tensile stress criterion (9) The angle θ of the deflection section of the fracture pit can be calculated using formulas (8) and (9): (10) σ yy It is the tensile stress perpendicular to the crack propagation direction, σ c It is tensile strength, when σ yy= σ c At that time, the crack deflects, that is: (11) The deflection section length L of the fracture crater can be calculated as follows: (12)。 7. The method for determining the surface roughness of a machinable ceramic turning surface according to claim 6, characterized in that: The length L based on the calculation of the initial surface M and the actual nominal cutting thickness h D Based on the principle of energy conservation, calculate the upward extension section length L of the fracture pit on the machinable ceramic turning surface. N The process is as follows: Crater depth h c for: (13) Energy W input to the tool c for: (14) Surface energy U formed by fracture S for: (15) Among them, L U is the upward extension length of the chip, and r is the free surface energy per unit area; The brittle fracture energy for chip formation is: (16) Therefore, the brittle fracture energy that forms the chip is: (17) Based on the principle of conservation of energy, the upward extension length L of the chip can be calculated. U Based on the geometry of the chips, the length L of the upward extension section of the breakage pit can be calculated. N for: (18)。 8. The method for determining the surface roughness of a machinable ceramic turning surface according to claim 7, characterized in that: The process of establishing the geometric interference roughness considering elastic recovery is as follows: Ideal groove height h on machined surface i for: (19) Due to elastic recovery, the actual trench height h a for: (20) Based on the definition of arithmetic mean roughness, the geometric interference roughness R considering elastic recovery can be calculated. ag ,as follows: (21)。 9. The method for determining the surface roughness of a machinable ceramic turning surface according to claim 8, characterized in that: The angle δ between the initial surface and the free surface of the fracture crater, and the length L of the initial surface are used as the basis. M Deflection section angle θ, deflection length L, upward extension section length L N Determine the actual shape of the crushing crater cross-section and establish the surface roughness R of the crushing surface. ab The process is as follows: Based on the actual shape of the crater cross-section, and assuming the centerline height is h, the following can be obtained using geometric relationships: (22) (23) (24) By the principle of similar triangles, we can obtain: (25) The areas of the ceramic turned surface contours A, B, and C are respectively: (26) (27) (28) Based on the definition of the median, the value of k can be calculated: (29) According to the definition of surface roughness (30) Substituting equations (22) to (24) and (26) to (28) into equation (30), the surface roughness R of the broken surface is thus obtained. ab The theoretical model is as follows: (31)。 10. The method for determining the surface roughness of a machinable ceramic turning surface according to claim 9, characterized in that: Establish a theoretical model for brittle surface roughness R a The process is as follows: The brittle surface roughness R is formed by superimposing the geometric interference roughness considering elastic recovery and the fracture roughness considering the fracture pit. a : (32) Right now: (33)。

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