A method for determining the amount of effective cutting abrasive in the lapping and polishing of brittle workpieces with fixed abrasives

Abstract

The present invention provides a method for determining the effective amount of cutting abrasive in polishing a brittle workpiece with a fixed abrasive, and belongs to the field of abrasive processing technology. The method comprises: first, determining the amount of concession in the abrasive pad base according to the depth of the abrasive scratching the workpiece; then, determining the number of effective abrasives involved in the processing according to the geometric position relationship between the fixed abrasive pad and the workpiece; finally, establishing a global contact model between the fixed abrasive and the workpiece according to the number of effective abrasives involved in the processing, and determining the number of effective abrasives involved in the cutting. The present invention clarifies the contact state between the fixed abrasive pad and the workpiece under different loads, emphasizes the actual role of the abrasive involved in the processing, and is more comprehensive and accurate than the calculation method of the effective abrasive number that only focuses on the probability of abrasive exposure. The material removal rate of the fixed abrasive pad polishing a brittle workpiece can be predicted by the accurate number of effective cutting abrasives, and then the fixed abrasive pad can be reversely designed according to the processing requirements.

Description

Technical Field

[0001] The invention relates to the technical field of abrasive processing, in particular to a method for determining the effective cutting abrasive amount in grinding and polishing a brittle workpiece with a fixed abrasive. Background Art

[0002] The advantages of bonded abrasive polishing are that the abrasive is evenly distributed, the motion trajectory is basically determined, the abrasive is subjected to relatively uniform force, and uniform material removal can be achieved; the abrasive is not completely exposed, resulting in less scratches; the abrasive utilization rate is high and it is environmentally friendly. Bonded abrasive pads have become a common tool for finishing materials such as metals, glass, and ceramics, and are expected to replace traditional free abrasives. Among them, the number of effective abrasives that can be used by bonded abrasive tools to cut the workpiece and cause material removal directly determines the processing efficiency and surface quality. However, due to the different shapes and sizes of bonded abrasives and the different exposed heights, it is difficult to calculate the number of effective abrasives involved in cutting. At present, only the number of abrasives that are actually in contact with the workpiece in the contact area of the bonded abrasive pad and do not fall off is usually calculated as the effective abrasive number. However, these calculation methods do not take into account the actual contact between the bonded abrasive and the workpiece. There is a problem that some abrasives are only in pure elastic contact with the workpiece and cannot remove material, and the calculated values are too large. Summary of the Invention

[0003] In response to the problem that the existing method for calculating the effective cutting abrasive amount in the polishing of brittle workpieces with fixed abrasives is imperfect and ignores the contact state between the abrasive pad and the workpiece, resulting in large errors in the calculation results, the present invention proposes a comprehensive and accurate method for calculating the effective cutting abrasive amount in the polishing of brittle workpieces with fixed abrasives.

[0004] To achieve the above objectives, the present invention provides a method for determining the amount of effective cutting abrasive in polishing a brittle workpiece with a fixed abrasive, which is applied to electronic devices and includes the following steps:

[0005] (1) Determine the amount of relief in the abrasive pad base based on the depth of the abrasive grain scratching the workpiece;

[0006] (2) Determine the effective number of abrasives involved in the machining based on the geometric position relationship between the fixed abrasive pad and the workpiece;

[0007] (3) Based on the number of effective abrasives involved in the processing, a global contact model between the fixed abrasive and the workpiece is established to determine the number of effective abrasives involved in the cutting.

[0008] Furthermore, in step 1, the depth δ of the workpiece is scratched by the abrasive particles. w Determine the amount of relief d in the abrasive pad base p The formula is:

[0009]

[0010] in: is the equivalent elastic modulus of the matrix, E a is the Young's elastic modulus of the matrix, v a is the Poisson's ratio of the matrix; is the equivalent elastic modulus of the workpiece, E w is the Young's elastic modulus of the workpiece, v w is the Poisson's ratio of the workpiece; R is the radius of the abrasive grain; σ y,w is the yield strength of the workpiece; δ w is the depth of the abrasive scratching the workpiece, δ y,w is the initial yield deformation of the workpiece. When the abrasive scratches the workpiece to a depth of δ y,w When , the workpiece surface undergoes irreversible deformation;

[0011]

[0012] is the yield strain coefficient of the workpiece;

[0013] When the depth of the abrasive scratching the workpiece is δ y,w When the yield amount d in the abrasive pad base is y,p Specifically:

[0014]

[0015] Furthermore, the step 2 is specifically as follows:

[0016] (2.1) The distance between the geometric surface of the workpiece and the geometric reference of the abrasive pad base is s, and the height of the abrasive grain exposed on the abrasive pad surface is h p , according to the depth δ of the abrasive scratching workpiece w and the setback d in the abrasive pad base p Determine that the relationship between the two satisfies: w =h p -sd p ;

[0017] (2.2) Ignoring abrasive shedding, the exposed height of abrasive grains h p It obeys uniform distribution on 0~D, so its exposure height probability density function f(h p ):

[0018]

[0019] (2.3) The workpiece radius is R w The ratio of the raised area of the abrasive pad to its total area is λ, and the nominal contact area between the abrasive pad and the wafer is A. w-p :

[0020]

[0021] (2.4) According to quantitative metallography, the volume fraction of abrasive in the abrasive pad V V and area fraction A A equal:

[0022]

[0023] Where: M p 、M a are the masses of abrasive and matrix, respectively, ρ p , ρ a are the densities of abrasive and matrix, respectively;

[0024] (2.5) The height h of the exposed abrasive particles during the polishing process p When ≥kR, the abrasive particles fall off from the substrate surface, s≤h p ﹤kR is the height of the exposed abrasive particles involved in scratching. From steps 2.1 to 2.4, the effective number of abrasive particles involved in scratching, N, can be obtained. pr :

[0025]

[0026] Furthermore, the step 3 includes:

[0027] (3.1) Actual exposed height of abrasive particles h p The probability density function of the wear particle exposure height g(h p ):

[0028]

[0029] (3.2) The effective abrasive material involved in the processing must not cut deeper than the initial yield deformation of the brittle material δ y,w =kR-sd y,p When the workpiece surface only undergoes elastic deformation, the maximum pure elastic total contact load F between the abrasive and the workpiece is petotalmax :

[0030]

[0031] (3.3) The effective abrasive material involved in the machining cuts the workpiece to a depth exceeding the initial yield deformation δ of the brittle material. y,w =kR-sd y,p When the workpiece surface is subjected to elastic-plastic / elastic-plastic-brittle deformation, the effective cutting abrasive quantity N pp :

[0032]

[0033] The present invention also provides a device for determining the effective amount of cutting abrasive in polishing a brittle workpiece with a fixed abrasive, comprising:

[0034] A setback determination module is used to determine the setback in the abrasive pad base according to the depth of the abrasive grains scratching the workpiece;

[0035] Effective abrasive number determination module: used to determine the effective number of abrasives involved in processing based on the geometric position relationship between the fixed abrasive pad and the workpiece;

[0036] The module for determining the number of effective cutting abrasives is used to establish a global contact model between the fixed abrasive and the workpiece according to the number of effective abrasives involved in the processing, and to determine the number of effective abrasives involved in the cutting.

[0037] The present invention also provides a device comprising a memory, a processor and a computer program stored in the memory and executable on the memory, wherein when the processor executes the computer program, the method for determining the effective amount of cutting abrasive in polishing brittle workpieces with fixed abrasives is implemented.

[0038] A computer-readable storage medium stores a computer program, which, when executed in a computer, causes the computer to execute the above-mentioned method for determining the effective amount of cutting abrasive in polishing a brittle workpiece with a fixed abrasive.

[0039] Beneficial effects of the present invention:

[0040] This method clarifies the contact state between the fixed abrasive pad and the workpiece under different loads, emphasizing the actual role of the abrasive in the machining process. Compared to methods that only focus on the probability of abrasive exposure, this method provides a more comprehensive and accurate calculation of the effective abrasive quantity. This accurate calculation of the effective cutting abrasive quantity can be used to predict the material removal rate of a fixed abrasive pad when polishing brittle workpieces, enabling reverse engineering of the fixed abrasive pad based on machining requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 The present invention is a flowchart of a method for determining the effective amount of cutting abrasive in polishing a brittle workpiece with a fixed abrasive.

[0042] Figure 2 Schematic diagram of the contact between the fixed abrasive pad and the brittle workpiece according to an embodiment of the present invention.

[0043] Figure 3 Schematic diagram of the contact states between a single abrasive particle and a brittle workpiece according to an embodiment of the present invention: (a) pure elastic contact, (b) elastic-plastic contact, and (c) elastic-plastic-brittle contact.

[0044] Figure 4 The present invention is a flow chart of an apparatus for determining the effective amount of cutting abrasive in polishing a brittle workpiece with a fixed abrasive. DETAILED DESCRIPTION

[0045] In order to make the technical solution of the present invention clearer, the present invention will be further described below with reference to the accompanying drawings and embodiments. Figure 1 As shown, an embodiment of the present invention provides a method for determining the effective amount of cutting abrasive in polishing a brittle workpiece with a fixed abrasive, comprising:

[0046] S101, determining the amount of concession in the abrasive pad base according to the depth of the abrasive grains scratching the workpiece;

[0047] like Figure 2 、 Figure 3 As shown:

[0048] (1) When the machining load is low, the abrasive particles with a radius of R scratch the brittle workpiece. When the two are in pure elastic contact, the contact radius a w , average contact stress P w The depth of the abrasive scratching the workpiece δ w relation:

[0049]

[0050]

[0051] Where, is the equivalent elastic modulus of the workpiece, E w is the Young's elastic modulus of the workpiece, v w is the Poisson's ratio of the workpiece.

[0052] (2) When the machining load is medium, the abrasive cuts into the workpiece surface, and the brittle material immediately below the contact center undergoes initial yielding. The abrasive and the workpiece come into elastic-plastic contact, and the initial yield deformation of the workpiece δ y,w With the average contact stress P w :

[0053]

[0054]

[0055] Where, σ y,w is the yield strength of the workpiece, C w is the yield strain coefficient of the workpiece, which is related to the v w Related:

[0056]

[0057] (3) When the machining load is high, the contact stress exceeds P y,w , average contact stress P w :

[0058]

[0059] Critical cutting depth δ of workpiece brittle-ductile transition c,w :

[0060]

[0061] Where α is the brittle-ductile transition coefficient, which is generally taken as 0.15, H w is the microhardness of the workpiece, K IC is the fracture toughness of the workpiece.

[0062] The depth of the abrasive scratching the workpiece reaches δ c,w When the workpiece surface is brittle, the average contact stress P exerted by the abrasive on the workpiece w =H w =3σ y,w , introduce coefficient K to P w Correction:

[0063]

[0064] Where δ w =δ c,w

[0065] Correction coefficient K:

[0066]

[0067] δ y,w It is a continuous point on the average contact stress curve between the abrasive and the workpiece under medium and high loads. Set δ w =δ y,w , Equations (4) and (8) can be established in parallel Then we get the corrected δ y,w :

[0068]

[0069] (4) Pure elasticity between abrasive particles and workpiece (0≤δ w <δ y,w ) and elastic-plastic / elastic-plastic-brittle (δ w ≥δ y,w ) Average contact stress P w :

[0070]

[0071] Dynamic contact area A of abrasive particles on the workpiece surface w :

[0072]

[0073] Cutting depth δ of abrasive scratching wafer surface w and the amount of abrasive retreat in the matrix d p Relationship:

[0074]

[0075] Where, is the matrix equivalent elastic modulus, E a is the Young's modulus of elasticity of the matrix, v a is the matrix Poisson's ratio.

[0076] When the depth of the abrasive scratching the workpiece is δ y,w When the yield amount d in the abrasive pad base is y,p Specifically:

[0077]

[0078] S102, determining the effective number of abrasives involved in processing based on the geometric position relationship between the fixed abrasive pad and the workpiece;

[0079] The distance between the geometric surface of the workpiece and the geometric reference of the abrasive pad base is s, and the height of the abrasive grains exposed on the abrasive pad surface is h. p , the relationship between the two satisfies:

[0080] δ w =h p -sd p (14)

[0081] Without considering the shedding of abrasive, the exposed height of abrasive grains h p It obeys uniform distribution on 0~D, so its exposure height probability density function f(h p ):

[0082]

[0083] The exposed height of the abrasive is h p When the normal projection area A on the substrate surface p :

[0084] A p =p(2Rh p -h p 2 ) (16)

[0085] Then calculate the expected normal projection area E(A p ):

[0086]

[0087] The workpiece radius is R w Since the abrasive pad has a convex structure, the convex area of the abrasive pad accounts for a proportion of its total area λ, and the nominal contact area between the abrasive pad and the wafer is A. w-p :

[0088]

[0089] According to quantitative metallography, the volume fraction of abrasive in the abrasive pad is V V and area fraction A A Equal, the volume fraction of abrasive V V :

[0090]

[0091] Where M p 、M a are the masses of abrasive and matrix, respectively, ρ p , ρ a are the densities of abrasive and matrix, respectively.

[0092] The exposed height h of the abrasive during the polishing process p When s is less than kR, the holding force of the substrate on the abrasive grains exceeds the limit, the abrasive grains fall off from the substrate surface, and the abrasive grains involved in the scratching must contact the workpiece, so s≤h p ≤kR is the height of the exposed abrasive particles involved in scratching. Combining equations (17), (18) and (19) yields the effective number of abrasive particles involved in scratching, N pr :

[0093]

[0094] S103. According to the number of effective abrasives involved in the processing, a global contact model between the fixed abrasive and the workpiece is established to determine the number of effective abrasives involved in the cutting.

[0095] Actual exposed height of abrasive particles h p The probability density function of the wear particle exposure height g(h p ):

[0096]

[0097] Pure elastic contact load F between a single abrasive grain and a wafer pe :

[0098]

[0099] The pure elastic average contact load E(F) between the effective abrasive and the wafer involved in the processing pe ) and the total contact load F petotal :

[0100]

[0101]

[0102] The effective abrasive cutting depth of the workpiece involved in the processing does not exceed the initial yield deformation δ of the brittle material y,w =kR-sd y,pWhen the workpiece surface only undergoes elastic deformation, the maximum pure elastic total contact load F between the abrasive and the workpiece is petotalmax :

[0103]

[0104] When the workpiece surface undergoes elastic-plastic / elastic-plastic-brittle deformation, the number of abrasives N that only causes pure elastic deformation of the workpiece surface pe :

[0105]

[0106] The pure elastic average contact load E(F) between this type of abrasive and the workpiece pe ) and the total contact load F petotal :

[0107]

[0108]

[0109] Causes elastic-plastic / elastic-plastic-brittle deformation of the workpiece surface, that is, the effective cutting abrasive quantity N pp :

[0110]

[0111] The material removal rate of abrasive pads used for polishing brittle workpieces can be predicted by accurately measuring the effective amount of cutting abrasive, and the abrasive pads can then be reverse-designed according to the machining requirements.

[0112] According to another embodiment, there is also provided a device for determining the effective amount of cutting abrasive in polishing a brittle workpiece with a fixed abrasive. Figure 4 As shown, including:

[0113] The yield determination module 410 is used to determine the yield in the abrasive pad base according to the depth of the abrasive grains scratching the workpiece;

[0114] The effective abrasive number determination module 420 is used to determine the effective number of abrasives involved in the processing based on the geometric position relationship between the fixed abrasive pad and the workpiece;

[0115] The effective cutting abrasive number determination module 430 is used to establish a global contact model between the fixed abrasive and the workpiece according to the effective number of abrasives involved in the processing, and determine the number of effective abrasives involved in the cutting.

[0116] The material removal rate of abrasive pads used for polishing brittle workpieces can be predicted by accurately measuring the effective amount of cutting abrasive, and the abrasive pads can be reversely designed according to the machining requirements.

[0117] An embodiment of the present invention also provides a device comprising a memory, a processor, and a computer program stored in the memory and executable on the memory, wherein when the processor executes the computer program, the method for determining the effective amount of cutting abrasive in polishing brittle workpieces with fixed abrasives is implemented.

[0118] An embodiment of the present invention further provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed in a computer, the computer is caused to execute the above-mentioned method for determining the effective amount of cutting abrasive in polishing a brittle workpiece with a fixed abrasive.

[0119] Those skilled in the art will appreciate that, in one or more of the above examples, the functions described in the embodiments of this specification may be implemented using hardware, software, firmware, or any combination thereof. When implemented using software, these functions may be stored in a computer-readable medium or transmitted as one or more instructions or codes on a computer-readable medium.

[0120] The above describes the specific embodiments of the present invention in conjunction with the accompanying drawings. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art may make various variations or modifications within the scope of the claims, which do not affect the essence of the present invention.

Claims

1. A method for determining the effective amount of cutting abrasive in polishing a brittle workpiece with a fixed abrasive, applied to electronic devices, characterized in that: The steps include: (1) Determine the amount of relief in the abrasive pad base based on the depth of the abrasive grain scratching the workpiece; Determine the amount of relief d in the abrasive pad base p The formula is: Where: K is the correction coefficient, is the equivalent elastic modulus of the matrix, E a is the Young's elastic modulus of the matrix, v a is the Poisson's ratio of the matrix; is the equivalent elastic modulus of the workpiece, E w is the Young's elastic modulus of the workpiece, v w is the Poisson's ratio of the workpiece; R is the radius of the abrasive grain; σ y,w is the yield strength of the workpiece; δ w is the depth of the abrasive scratching the workpiece, δ y,w is the initial yield deformation of the workpiece. When the abrasive scratches the workpiece to a depth of δ y,w When , the workpiece surface undergoes irreversible deformation; is the yield strain coefficient of the workpiece; (2) Determine the effective number of abrasives involved in the machining based on the geometric position relationship between the fixed abrasive pad and the workpiece; (3) Based on the number of effective abrasives involved in the processing, a global contact model between the fixed abrasive and the workpiece is established to determine the number of effective abrasives involved in the cutting.

2. A method for determining the effective amount of cutting abrasive in polishing a brittle workpiece with a fixed abrasive according to claim 1, characterized in that: The step (2) is specifically as follows: (2.1) The distance between the geometric surface of the workpiece and the geometric reference of the abrasive pad base is s, and the height of the abrasive grain exposed on the abrasive pad surface is h p , according to the depth δ of the abrasive scratching workpiece w and the amount of relief d in the abrasive pad base p Determine that the relationship between the two satisfies: w =h p -sd p ; (2.2) Ignoring abrasive shedding, the exposed height of abrasive grains h p It obeys uniform distribution on 0~D, so its exposure height probability density function f(h p ): (2.3) The workpiece radius is R w The ratio of the raised area of the abrasive pad to its total area is λ, and the nominal contact area between the abrasive pad and the wafer is A. w-p : (2.4) According to quantitative metallography, the volume fraction of abrasive in the abrasive pad V V and area fraction A A equal: Where: M p 、M a are the masses of abrasive and matrix, respectively, ρ p , ρ a are the densities of abrasive and matrix, respectively; (2.5) The height h of the exposed abrasive particles during the polishing process p When >kR, the abrasive particles fall off from the substrate surface, s≤h p ≤kR is the height of the exposed abrasive grains involved in scratching. The effective number of abrasive grains involved in scratching, N, is obtained from steps (2.1) to (2.4). pr :

3. A method for determining the effective amount of cutting abrasive in polishing a brittle workpiece with a fixed abrasive according to claim 2, characterized in that: The step (3) comprises: (3.1) Actual exposed height of abrasive particles h p The probability density function of the wear particle exposure height g(h p ): (3.2) The effective abrasive material involved in the processing must not cut deeper than the initial yield deformation of the brittle material δ y,w When the workpiece surface only undergoes elastic deformation, the maximum pure elastic total contact load F between the abrasive and the workpiece is petotalmax : (3.3) The effective abrasive material involved in the machining cuts the workpiece to a depth exceeding the initial yield deformation δ of the brittle material. y,w When the workpiece surface is subjected to elastic-plastic / elastic-plastic-brittle deformation, the effective cutting abrasive quantity N pp :

4. A device for determining the effective amount of cutting abrasive in polishing a brittle workpiece with a fixed abrasive, characterized in that: include: A setback determination module is used to determine the setback in the abrasive pad base according to the depth of the abrasive grains scratching the workpiece; Determine the amount of relief d in the abrasive pad base p The formula is: Where: K is the correction coefficient, is the equivalent elastic modulus of the matrix, E a is the Young's elastic modulus of the matrix, v a is the Poisson's ratio of the matrix; is the equivalent elastic modulus of the workpiece, E w is the Young's elastic modulus of the workpiece, v w is the Poisson's ratio of the workpiece; R is the radius of the abrasive grain; σ y,w is the yield strength of the workpiece; δ w is the depth of the abrasive scratching the workpiece, δ y,w is the initial yield deformation of the workpiece. When the abrasive scratches the workpiece to a depth of δ y,w When , the workpiece surface undergoes irreversible deformation; is the yield strain coefficient of the workpiece; Effective abrasive number determination module: used to determine the effective number of abrasives involved in processing based on the geometric position relationship between the fixed abrasive pad and the workpiece; The module for determining the number of effective cutting abrasives is used to establish a global contact model between the fixed abrasive and the workpiece according to the number of effective abrasives involved in the processing, and to determine the number of effective abrasives involved in the cutting.

5. A device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the method for determining the effective cutting abrasive amount in polishing a brittle workpiece with fixed abrasives according to any one of claims 1 to 3 is implemented.

6. A computer-readable storage medium having a computer program stored thereon, which, when executed in a computer, causes the computer to execute the method for determining the effective amount of cutting abrasive in polishing a brittle workpiece with a fixed abrasive according to any one of claims 1 to 3.

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