A method for predicting the morphological characteristics of polishing pads after mortar particle trimming
By establishing a contact area and contact stress model of the plane of the micro-convex body and the trimming disk, as well as a contact mechanical model constructed by the mortar particle concentration, we predict the morphological characteristics of the pad after trimming of the mortar particles, and solving the slow prediction speed and accuracy in the existing technology The problem of low results enables fast and accurate morphological characteristics prediction.
Patent Information
- Application Number
- CN202210905736.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-07-29
- Publication Date
- 2025-02-11
- Estimated Expiration
- 2042-07-29
AI Technical Summary
In the prior art, the calculation method for the rough surface microconvex radius and height distribution of the mortar particles after trimming the mortar particles is slow, the workload is large, and the accuracy is low, so it is impossible to quickly and accurately predict the morphological characteristics of the mortar pad.
By establishing a plane contact area and contact stress model between a single microconvex body and a trimming disk, a contact mechanical model between the microconvex body and the mortar particle concentration is constructed, and the relationship equation of the microconvex body radius and the root mean square distribution of the exposure height is obtained. Predict the morphological characteristics of the pad after trimming the mortar particles.
It realizes rapid and accurate prediction of the radius and height distribution of the micro-convex body on the rough surface of the mortar particles after trimming, and eliminates offline detection processes and improves production efficiency.
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Figure CN115519476B_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the technical field of abrasive processing, and in particular to a method for predicting the morphological characteristics of a grinding and polishing pad after mortar particles are trimmed. Background Art
[0002] The surface morphology of the grinding and polishing pad will greatly affect the efficiency of grinding and polishing. Before the grinding and polishing process, the grinding and polishing pad is generally trimmed with a dressing disc and a water-based suspension of mortar particles to change its surface morphology. The two parameters of the radius and the root mean square of the height distribution of the micro-protrusions on the rough surface of the grinding and polishing pad directly determine the morphological characteristics of the grinding and polishing pad. Generally, reducing the standard deviation of the height of the micro-protrusions of the abrasive pad base or increasing its radius will lead to an increase in the material removal rate. In addition, moderately increasing the hardness of the grinding and polishing pad is conducive to reducing the ratio of the root mean square of the height distribution of the micro-protrusions to the radius and improving the material removal rate. However, there is currently no method for calculating the radius and root mean square of the height distribution of the micro-protrusions on the rough surface of the grinding and polishing pad after mortar particle trimming. Generally, the radius and root mean square of the height distribution of the micro-protrusions are determined by offline observation after trimming to predict the morphological characteristics of the grinding and polishing pad, which is slow, labor-intensive and low in accuracy. Summary of the invention
[0003] Aiming at the problem that relying on instruments to detect the radius and root mean square of height distribution of micro-convexities on the rough surface of the polishing pad after mortar particle trimming offline to predict the morphological characteristics of the polishing pad is slow, labor-intensive and has low accuracy, the present invention proposes a fast and accurate method for predicting the morphological characteristics of the polishing pad after mortar particle trimming.
[0004] In order to achieve the above purpose, a method for predicting the morphological characteristics of the polishing pad after mortar particle trimming is proposed, comprising the following steps:
[0005] (1) Determine the contact area and contact stress between a single micro-protrusion and the plane of the dressing disk according to the deformation of the micro-protrusion when the single micro-protrusion on the rough surface of the polishing pad contacts the plane of the dressing disk;
[0006] (2) according to the contact area and contact stress between the single micro-protrusion and the plane of the dressing disk, a contact mechanics model between the single micro-protrusion and the mortar abrasive grains is established based on the mortar particle concentration;
[0007] (3) According to the contact state between the micro-asperities / mortar particles and the plane of the dressing disk under different loads, the relationship equation between the radius and the root mean square of the height distribution of the micro-asperities on the rough surface of the polishing pad after the mortar particles are trimmed is obtained;
[0008] (4) Solve the relationship equation in step 3 to obtain the root mean square of the radius and the exposed height distribution of the micro-protrusions on the rough surface of the polishing pad after the mortar particles are trimmed, and use this to predict the morphological characteristics.
[0009] Furthermore, in step 1, the contact area A between the single micro-convex body and the plane of the trimming disk isa for:
[0010]
[0011] The contact stress P between the single micro-protrusion and the dressing disk plane a for:
[0012]
[0013] Where: a is the deformation of a single micro-convex body when it contacts the plane of the dressing disk, R a is the radius of the top of the micro-convex body on the rough surface of the polishing pad, σ y,a is the yield strength of the micro-convex body, H a is the hardness of the microconvex body, the initial yield deformation δ y,a for The total plastic deformation of the micro-convex body δ f-p,a =54δ y,a .
[0014] Furthermore, the step 2 specifically includes:
[0015] (2.1) Determine the load on a single micro-protrusion based on the contact state between the mortar particles and the micro-protrusions on the rough surface of the polishing pad;
[0016] Low-pressure contact: The external load is completely borne by the mortar particles, and the nominal contact area between a single micro-convex body and the mortar particles can be approximated as A a , single asperity load F a The F is carried by a single mortar particle. g The number of mortar particles in contact with N = A a / λ p 2 Decide:
[0017]
[0018] Where: p is the distance between adjacent particles;
[0019] Critical contact: The load applied by the single micro-convex body to a single mortar particle reaches the upper limit F g,max :
[0020]
[0021] Where: R p is the particle radius;
[0022] The critical contact stress P between the mortar particles and the dressing disk c,a :
[0023]
[0024] High-pressure contact: The micro-convex body will directly contact the surface of the dressing disk. g Keep constant:
[0025]
[0026] (2.2) Obtain the volume concentration of the mortar particles and the critical contact stress P between the mortar particles and the trimming disk c,a relationship;
[0027] The mortar particle volume concentration C vol for:
[0028]
[0029] Where: N p is the number of particles per unit volume. Assuming that the mortar particles are evenly distributed, then Substituting into the mortar particle volume concentration formula, we get:
[0030]
[0031] The mortar particle volume concentration C vol The critical contact stress P between the mortar particles and the dressing disk c,a The relationship is:
[0032]
[0033] (2.3) According to the obtained contact stress P between the single micro-protrusion and the trimming disk plane a and the critical contact stress P between the mortar particles and the dressing disk c,a , and obtain the critical deformation of the micro-convex body δ c,a :
[0034]
[0035] Furthermore, the step 3 comprises:
[0036] (3.1) Obtain the relationship between the average contact area <△A> and the average contact stress <△P> between the micro-protrusion and the trimming disk plane and the root mean square distribution of the micro-protrusion radius and the exposed height:
[0037] The distribution of the exposed height of the micro-protrusions obeys the exponential distribution, and its probability density function Φ(z) is:
[0038]
[0039] Where: z is the height of the micro-convex body, σ z is the root mean square of the height distribution of the micro-asperities;
[0040] The average contact area <ΔA> between the micro-protrusion and the plane of the dressing disk can be expressed as:
[0041]
[0042] Where: N a is the total number of asperities covering the plane of the trimmed disk, f A (ψ) is the actual contact area A between the polishing pad and the dressing disc plane about ψ ar Function of
[0043]
[0044] In addition, ξ=(zs) / σ z is a dimensionless variable, the plasticity factor
[0045] The average contact area <△A> between the micro-protrusion and the plane of the dressing disk can be approximately simplified as:
[0046]
[0047] The average contact stress <△P> between the micro-protrusion and the dressing disk plane:
[0048]
[0049] Where: f P (ψ) is the contact load P about ψ a function:
[0050]
[0051] (3.2) according to the contact state between the micro-protrusions and the mortar particles and the plane of the dressing disk under different loads, the relationship between the micro-protrusion radius and the root mean square distribution of the exposed height is obtained;
[0052] The ratio of the actual contact area between the micro-convex body on the rough surface of the polishing pad and the dressing disc to the nominal contact area A ar / A a It is expressed as:
[0053]
[0054] When the convex body undergoes only pure elastic deformation, the above formula can be simplified as:
[0055]
[0056] At this time P a =P c,a , by F a =P a *Aa =P c,a <△A> gives:
[0057]
[0058] The initial yield deformation δ y,a and the critical deformation of the micro-convex body δ c,a Substitute the expression into the above formula to obtain the radius R of the top of the microconvex body a The root mean square of the height distribution of the micro-asperities z The relationship is:
[0059]
[0060] When the micro-convex body undergoes complete plastic deformation, the actual contact area is determined by the contact stress P a and the hardness H of the microconvex body a Decision, A ar / A a Simplified to:
[0061]
[0062] The completely plastically deformed micro-convex body is completely in contact with the dressing disk. At this time, the distance between the dressing disk and the grinding pad is s = 0, P a =H a , we get:
[0063]
[0064] Get N a R a σ z ≈λR w ;
[0065] Lian Li and get:
[0066]
[0067] Let P a =P y,a s=2R p -δ y,a , and get R a With σ z relation:
[0068]
[0069] Furthermore, in step 4, the following equation is solved to obtain the root mean square of the radius and the exposed height distribution of the micro-convex body on the rough surface of the polishing pad after the mortar particles are trimmed:
[0070]
[0071]
[0072] The present invention also provides a device for predicting the morphological characteristics of a polishing pad after mortar particles are trimmed, which is characterized by comprising:
[0073] Contact area and contact stress determination module: Determine the contact area and contact stress between a single micro-protrusion and the plane of the dressing disk according to the deformation of the micro-protrusion when the single micro-protrusion on the rough surface of the polishing pad contacts the plane of the dressing disk;
[0074] Modeling module: according to the contact area and contact stress between the single micro-protrusion and the trimming disk plane, a contact mechanics model between the single micro-protrusion and the mortar particles is established based on the mortar particle concentration;
[0075] Micro-protrusion radius and exposed height distribution root mean square determination module: used to obtain the relationship equation between the micro-protrusion radius and the exposed height distribution root mean square of the rough surface of the polishing pad after mortar particle dressing according to the contact state between the micro-protrusion / mortar particles and the dressing disk plane under different loads;
[0076] Prediction module: used to solve the relationship equation, obtain the root mean square of the radius and the exposed height distribution of the micro-convex body on the rough surface of the polishing pad after the mortar particles are trimmed, and use this to predict the morphological characteristics.
[0077] The present invention also provides a device, including 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 predicting the morphological characteristics of the polishing pad after mortar particle trimming as described above is implemented.
[0078] The present invention also 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 method for predicting the morphological characteristics of a polishing pad after mortar particle trimming as described above.
[0079] Beneficial effects of the present invention:
[0080] The present invention can predict the radius and height distribution root mean square of the micro-convex body on the rough surface of the polishing pad after the mortar particles are trimmed, which can save the process of detecting the surface morphology of the polishing pad before processing and improve production efficiency. In addition, based on the processing requirements, the trimming process can be reversed through the prediction results of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS
[0081] Figure 1 The present invention is a flow chart of a method for predicting the morphological characteristics of a polishing pad after mortar particles are trimmed according to an embodiment of the present invention.
[0082] Figure 2Schematic diagram of the contact states between mortar particles and the micro-protrusions on the rough surface of the polishing pad in an embodiment of the present invention: (a) low-pressure contact, (b) critical contact and (c) high-pressure contact.
[0083] Figure 3 Schematic diagram of the surface morphology and profile parameters of the resin substrate of the polishing pad after trimming in the embodiments of the present invention: (a) 1# pad and (b) 2# pad.
[0084] Figure 4 The present invention is a schematic diagram of the device process for predicting the morphological characteristics of the polishing pad after mortar particles are trimmed. DETAILED DESCRIPTION
[0085] The present invention provides a method for predicting the root mean square of the radius and height distribution of micro-convex bodies on the rough surface of a polishing pad after mortar particle trimming. The basic process is as follows: Figure 1 The preferred specific real-time method includes:
[0086] S101, determining the contact area and contact stress between the single micro-protrusion and the plane of the dressing disk according to the deformation of the micro-protrusion when the single micro-protrusion on the rough surface of the polishing pad contacts the plane of the dressing disk;
[0087] The micro-convex body on the rough surface of the polishing pad can be regarded as a top radius of R a The contact area between a single microconvex body and the trimming disk plane is A a and contact stress P a They are:
[0088]
[0089]
[0090] In the formula, δ a is the deformation of a single micro-convex body when it contacts the plane of the dressing disk, σ y,a is the yield strength of the micro-convex body, H a is the hardness of the micro-convex body, and the complete plastic deformation of the micro-convex body δ f-p,a =54δ y,a , initial yield deformation δ y,a :
[0091]
[0092] S102, establishing a contact mechanics model between a single micro-protrusion and a mortar abrasive grain according to the contact area and contact stress between a single micro-protrusion and a dressing disk plane and based on the mortar particle concentration;
[0093] Specifically, the increase in the external load of the dressing disk causes the contact state between the micro-convex body and the mortar particles to change, such as Figure 2Assume that the mortar particles are evenly distributed and the particles are regarded as having a radius of R. p The number of particles per unit volume is N p , the distance between adjacent particles is λ p , then the following relationship exists:
[0094]
[0095] Low-pressure contact: the external load will be completely borne by the mortar particles ( Figure 2 (a)), that is, the micro-protrusions are not in direct contact with the trimming disk. At this time, the nominal contact area between a single micro-protrusion and the mortar particles can be approximated as A a Therefore, a single asperity is loaded with a The F is carried by a single mortar particle. g and the number of mortar particles in contact A a / λ p 2 Decide:
[0096]
[0097] For low-voltage contacts, F g With F a Directly proportional.
[0098] Critical contact: Through the analysis of the upper limit of the spherical indentation area, Figure 2 (b) shows that there is an upper limit F on the load exerted by a single micro-convex body on a single mortar particle. g,max :
[0099]
[0100] When the load F applied to a single mortar particle g When the critical contact stress P between the mortar particles and the trimming disk is reached, the combined equations (5) and (6) are obtained: c,a :
[0101]
[0102] High-pressure contact: If the critical contact stress between the mortar particles and the dressing disc exceeds P c,a , the dressing disc cannot be supported by the mortar particles alone. In order to bear the extra load, the micro-asperities will directly contact the dressing disc surface ( Figure 2 (c)). And when the stress on a single mortar particle reaches the maximum value P g,max After that, even if the external load is increased, P g Still remains constant:
[0103]
[0104] It can be seen that the volume concentration of mortar particles in the suspension is C vol :
[0105]
[0106] Therefore, combining equations (4) and (9) yields:
[0107]
[0108] Then, by combining equations (7) and (10), we can obtain the critical contact stress P between the mortar particles and the trimming plate: c,a :
[0109]
[0110] Therefore, the critical deformation of the micro-convex body δ can be obtained from equations (2) and (11): c,a :
[0111]
[0112] S103, according to the contact state between the micro-protrusions / mortar particles and the plane of the dressing disk under different loads, obtaining a relationship equation between the radius of the micro-protrusions and the root mean square of the height distribution on the rough surface of the polishing pad after the mortar particles are dressed;
[0113] Assuming that the distribution of the height of the micro-protrusions follows an exponential distribution, its probability density function Φ(z) is:
[0114]
[0115] Where z is the height of the micro-convex body, σ z is the root mean square of the asperity height distribution.
[0116] The average contact area between the micro-convex body and the dressing disk plane <△A>:
[0117]
[0118] Where N a is the total number of asperities covered by the trimming disk plane, and the actual contact area A between the asperities and the trimming disk plane about ψ ar The function f A (ψ):
[0119]
[0120] In the formula, the dimensionless variable ξ=(zs) / σ z , plasticity factor
[0121] Formula (14) can be simplified to:
[0122]
[0123] In fact, when the stress changes within several orders of magnitude, the average value of the microscopic contact area remains basically unchanged, and the ratio of the total contact force to the total contact area changes very slowly. The average contact stress <△P> between the micro-convex body and the dressing disk plane is:
[0124]
[0125] Where, the contact load P about ψ is a Function f P (ψ):
[0126]
[0127] The ratio of the actual contact area between the micro-convex body on the rough surface of the polishing pad and the dressing disc to the nominal contact area A ar / A a From equations (1), (13) and (18), we can get:
[0128]
[0129] When the convex body undergoes only pure elastic deformation, equation (19) can be simplified as:
[0130]
[0131] P a =P c,a , by F a =P a *A a =P c,a <△A> can be concluded:
[0132]
[0133] Therefore, substituting equations (3) and (12) into equation (21) yields the radius R of the convex tip: a The root mean square of the height distribution of the micro-asperities z relation:
[0134]
[0135] When the micro-convex body undergoes complete plastic deformation, the actual contact area is determined by the contact stress P a and the hardness H of the microconvex body a Determine, formula (19) is simplified to:
[0136]
[0137] The completely plastically deformed micro-convex body fits the trimming disk perfectly, refer to Figure 2(c) Set the distance between the dressing disc and the polishing pad to s = 0 and P a =H a Substituting into equation (19) and (23) and calculating them together, we can get
[0138]
[0139] Then we get N a R a σ z ≈λR w Combining equations (19) and (20) yields
[0140] Bring in P a =P y,a s=2R p -δ y,a R a With σ z relation:
[0141]
[0142] S104, solving the relationship equation in step 3, obtaining the root mean square of the radius and the exposed height distribution of the micro-protrusions on the rough surface of the polishing pad after the mortar particles are trimmed, and using this to predict the morphological characteristics.
[0143] Formulas (22) and (24) are combined to solve the root mean square of the radius and height distribution of the micro-asperities on the rough surface of the polishing pad after mortar particle trimming, and the morphological characteristics are predicted.
[0144] The root mean square measurement values of the radius and height distribution of the micro-convexities on the rough surface of the polishing pads after two different polishing pads were trimmed with different mortar particles are as follows: Figure 3 As shown in Table 1, the errors between the results and the predicted values are all less than 15%.
[0145] Table 1 Surface profile parameters of polishing pad substrate after trimming
[0146]
[0147] The embodiment of the present invention further provides a device for predicting the morphological characteristics of a polishing pad after mortar particles are trimmed, characterized in that it comprises:
[0148] Contact area and contact stress determination module: Determine the contact area and contact stress between a single micro-protrusion and the plane of the dressing disk according to the deformation of the micro-protrusion when the single micro-protrusion on the rough surface of the polishing pad contacts the plane of the dressing disk;
[0149] Modeling module: according to the contact area and contact stress between the single micro-protrusion and the trimming disk plane, a contact mechanics model between the single micro-protrusion and the mortar particles is established based on the mortar particle concentration;
[0150] Micro-protrusion radius and exposed height distribution root mean square determination module: used to obtain the relationship equation between the micro-protrusion radius and the exposed height distribution root mean square of the rough surface of the polishing pad after mortar particle dressing according to the contact state between the micro-protrusion / mortar particles and the dressing disk plane under different loads;
[0151] Prediction module: used to solve the relationship equation, obtain the root mean square of the radius and the exposed height distribution of the micro-convex body on the rough surface of the polishing pad after the mortar particles are trimmed, and use this to predict the morphological characteristics.
[0152] An embodiment of the present invention also provides a device, including 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, a method for predicting the morphological characteristics of a polishing pad after mortar particle trimming is implemented.
[0153] 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 a method for predicting the morphological characteristics of a polishing pad after mortar particle trimming.
[0154] Those skilled in the art should be aware that in one or more of the above examples, the functions described in the embodiments of this specification can be implemented by hardware, software, firmware, or any combination thereof. When implemented by software, these functions can be stored in a computer-readable medium or transmitted as one or more instructions or codes on a computer-readable medium.
[0155] Although specific embodiments of the present invention are described above, those skilled in the art should understand that these are merely examples and that various changes or modifications may be made to these embodiments without departing from the principles and essence of the present invention. Therefore, the scope of protection of the present invention is limited by the appended claims.
Claims
1. A method for predicting the morphological characteristics of a polishing pad after mortar particle trimming, applied to electronic devices, characterized in that: The steps include: (1) Determine the contact area and contact stress between a single micro-protrusion and the plane of the dressing disk according to the deformation of the micro-protrusion when the single micro-protrusion on the rough surface of the polishing pad contacts the plane of the dressing disk; The contact area A between the single micro-protrusion and the trimming disk plane a for: The contact stress P between the single micro-protrusion and the dressing disk plane a for: Where: a is the deformation of a single micro-convex body when it contacts the plane of the dressing disk, R a is the radius of the top of the micro-convex body on the rough surface of the polishing pad, σ y,a is the yield strength of the micro-convex body, H a is the hardness of the microconvex body, the initial yield deformation δ y,a for The total plastic deformation of the micro-convex body δ f-p,a =54δ y,a ; (2) establishing a contact mechanics model between a single micro-protrusion and mortar particles based on the contact area and contact stress between the single micro-protrusion and the plane of the dressing disk and the concentration of mortar particles; (2.1) Determining the load on a single micro-protrusion according to the contact state between the mortar particles and the micro-protrusions on the rough surface of the polishing pad; Low-pressure contact: The external load is completely borne by the mortar particles, and the nominal contact area between a single micro-convex body and the mortar particles can be approximated as A a , single asperity load F a The individual mortar particles carry F g The number of mortar particles in contact with N = A a / λ p 2 Decide: Where: p is the distance between adjacent particles; Critical contact: The load exerted by a single micro-convex body on a single mortar particle reaches the upper limit F g,max : Where: R p is the particle radius; Critical contact stress P between mortar particles and dressing disc c,a : High-pressure contact: The micro-convex body will directly contact the surface of the dressing disk. g Keep constant: (2.2) Obtain the volume concentration of the mortar particles and the critical contact stress P between the mortar particles and the trimming disk c,a relationship; The mortar particle volume concentration C vol for: Where: N p is the number of particles per unit volume. Assuming that the mortar particles are evenly distributed, then Substituting into the mortar particle volume concentration formula, we get: The mortar particle volume concentration C vol The critical contact stress P between the mortar particles and the dressing disk c,a The relationship is: (2.3) According to the obtained contact stress P between the single micro-protrusion and the trimming disk plane a and the critical contact stress P between the mortar particles and the dressing disk c,a , and obtain the critical deformation of the micro-convex body δ c,a : (3) According to the contact state between the micro-asperities / mortar particles and the plane of the dressing disk under different loads, the relationship equation between the radius of the micro-asperities and the root mean square distribution of the exposed height on the rough surface of the polishing pad after the mortar particles are trimmed is obtained; (3.1) Obtain the relationship between the average contact area <△A> and the average contact stress <△P> between the micro-protrusion and the trimming disk plane and the root mean square distribution of the micro-protrusion radius and the exposed height: The distribution of the exposed height of the micro-protrusions obeys the exponential distribution, and its probability density function Φ(z) is: Where: z is the height of the micro-convex body, σ z is the root mean square of the height distribution of the micro-protrusions; the average contact area <△A> between the micro-protrusions and the plane of the dressing disk can be expressed as: Where: N a is the total number of asperities covering the plane of the trimmed disk, f A (ψ) is the actual contact area A between the polishing pad and the dressing disc plane about ψ ar Function of Another x=(zs) / σ z is a dimensionless variable, the plasticity factor The average contact area <△A> between the micro-protrusion and the plane of the dressing disk can be approximately simplified as: The average contact stress <△P> between the micro-protrusion and the dressing disk plane: Where: f P (ψ) is the contact load P about ψ a function: (3.2) according to the contact state between the micro-protrusions and the mortar particles and the plane of the dressing disk under different loads, the relationship between the micro-protrusion radius and the root mean square distribution of the exposed height is obtained; The ratio of the actual contact area between the micro-convex body on the rough surface of the polishing pad and the dressing disc to the nominal contact area A ar / A a It is expressed as: When the convex body undergoes only pure elastic deformation, the above formula can be simplified as: At this time P a =P c,a , by F a =P a *A a =P c,a <△A> gives: The initial yield deformation δ y,a and the critical deformation of the micro-convex body δ c,a Substitute the expression into the above formula to obtain the radius R of the top of the microconvex body a The root mean square of the height distribution of the micro-asperities z The relationship is: When the micro-convex body undergoes complete plastic deformation, the actual contact area is determined by the contact stress P a and the hardness H of the microconvex body a Decision, A ar / A a Simplified to: The completely plastically deformed micro-convex body is completely in contact with the dressing disk. At this time, the distance between the dressing disk and the grinding pad is s = 0, P a =H a , we get: Get N a R a σ z ≈λR w ; Lian Li and get: Let P a =P y,a s=2R p -δ y,a , and get R a With σ z relation: (4) Solving the relationship equation in step (3) to obtain the root mean square of the radius and the exposed height distribution of the micro-protrusions on the rough surface of the polishing pad after the mortar particles are trimmed, and using this to predict the morphological characteristics.
2. The method for predicting the morphological characteristics of the polishing pad after mortar particle trimming according to claim 1 is characterized in that: In step 4, the following equation is solved to obtain the root mean square of the radius and the exposed height distribution of the micro-convex body on the rough surface of the polishing pad after the mortar particles are trimmed:
3. A device for predicting the morphological characteristics of a polishing pad after mortar particle trimming, characterized in that: include: Contact area and contact stress determination module: Determine the contact area and contact stress between a single micro-protrusion and the plane of the dressing disk according to the deformation of the micro-protrusion when the single micro-protrusion on the rough surface of the polishing pad contacts the plane of the dressing disk; The contact area A between the single micro-protrusion and the trimming disk plane a for: The contact stress P between the single micro-protrusion and the dressing disk plane a for: Where: a is the deformation of a single micro-convex body when it contacts the plane of the dressing disk, R a is the radius of the top of the micro-convex body on the rough surface of the polishing pad, σ y,a is the yield strength of the micro-convex body, H a is the hardness of the microconvex body, the initial yield deformation δ y,a for The total plastic deformation of the micro-convex body δ f-p,a =54δ y,a ; Modeling module: according to the contact area and contact stress between the single micro-protrusion and the plane of the dressing disk, a contact mechanical model between the single micro-protrusion and the mortar particles is established based on the mortar particle concentration; (2.1) according to the contact state between the mortar particles and the micro-protrusion on the rough surface of the polishing pad, the load on the single micro-protrusion is determined; Low-pressure contact: The external load is completely borne by the mortar particles, and the nominal contact area between a single micro-convex body and the mortar particles can be approximated as A a , single asperity load F a The individual mortar particles carry F g The number of mortar particles in contact with N = A a / λ p 2 Decide: Where: p is the distance between adjacent particles; Critical contact: The load exerted by a single micro-convex body on a single mortar particle reaches the upper limit F g,max : Where: R p is the particle radius; Critical contact stress P between mortar particles and dressing disc c,a : High-pressure contact: The micro-convex body will directly contact the surface of the dressing disk. g Keep constant: (2.2) Obtain the volume concentration of the mortar particles and the critical contact stress P between the mortar particles and the trimming disk c,a relationship; The mortar particle volume concentration C vol for: Where: N p is the number of particles per unit volume. Assuming that the mortar particles are evenly distributed, then Substituting into the mortar particle volume concentration formula, we get: The mortar particle volume concentration C vol The critical contact stress P between the mortar particles and the dressing disk c,a The relationship is: (2.3) According to the obtained contact stress P between the single micro-protrusion and the trimming disk plane a and the critical contact stress P between the mortar particles and the dressing disk c,a , and obtain the critical deformation of the micro-convex body δ c,a : Micro-protrusion radius and exposed height distribution root mean square determination module: used to obtain the relationship equation between the micro-protrusion radius and the exposed height distribution root mean square of the rough surface of the polishing pad after mortar particle dressing according to the contact state between the micro-protrusion / mortar particles and the dressing disk plane under different loads; (3.1) Obtain the relationship between the average contact area <△A> and the average contact stress <△P> between the micro-protrusion and the trimming disk plane and the root mean square distribution of the micro-protrusion radius and the exposed height: The distribution of the exposed height of the micro-protrusions obeys the exponential distribution, and its probability density function Φ(z) is: Where: z is the height of the micro-convex body, σ z is the root mean square of the height distribution of the micro-protrusions; the average contact area <△A> between the micro-protrusions and the plane of the dressing disk can be expressed as: Where: N a is the total number of asperities covering the plane of the trimmed disk, f A (ψ) is the actual contact area A between the polishing pad and the dressing disc plane about ψ ar Function of Another x=(zs) / σ z is a dimensionless variable, the plasticity factor The average contact area <△A> between the micro-protrusion and the plane of the dressing disk can be approximately simplified as: The average contact stress <△P> between the micro-protrusion and the dressing disk plane: Where: f P (ψ) is the contact load P about ψ a function: (3.2) according to the contact state between the micro-protrusions and the mortar particles and the plane of the dressing disk under different loads, the relationship between the micro-protrusion radius and the root mean square distribution of the exposed height is obtained; The ratio of the actual contact area between the micro-convex body on the rough surface of the polishing pad and the dressing disc to the nominal contact area A ar / A a It is expressed as: When the convex body undergoes only pure elastic deformation, the above formula can be simplified as: At this time P a =P c,a , by F a =P a *A a =P c,a <△A> gives: The initial yield deformation δ y,a and the critical deformation of the micro-convex body δ c,a Substitute the expression into the above formula to obtain the radius R of the top of the microconvex body a The root mean square of the height distribution of the micro-asperities z The relationship is: When the micro-convex body undergoes complete plastic deformation, the actual contact area is determined by the contact stress P a and the hardness H of the microconvex body a Decision, A ar / A a Simplified to: The completely plastically deformed micro-convex body is completely in contact with the dressing disk. At this time, the distance between the dressing disk and the grinding pad is s = 0, P a =H a , we get: Get N a R a σ z ≈λR w ; Lian Li and get: Let P a =P y,a s=2R p -δ y,a , and get R a With σ z relation: Prediction module: used to solve the relationship equation, obtain the root mean square of the radius and the exposed height distribution of the micro-convex body on the rough surface of the polishing pad after the mortar particles are trimmed, and use this to predict the morphological characteristics.
4. A device comprising a memory, a processor and a computer program stored in the memory and executable on the memory, characterized in that: When the processor executes the computer program, the method for predicting the morphological characteristics of the polishing pad after mortar particle trimming as described in any one of claims 1-2 is implemented.
5. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed in a computer, the computer is caused to execute the method for predicting the morphological characteristics of the polishing pad after mortar particle trimming as described in any one of claims 1 to 2.
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