CN107738142B - A method for predicting the microstructure of dental zirconia ceramics by ultrasonic vibration grinding - Google Patents

Abstract

The present invention proposes a kind of prediction technique of ultrasonic vibration grinding dental zirconium oxide ceramic micro-structure, firstly, establishing the Movement Locus Equation of single abrasive particle the characteristics of according to being ground under the conditions of ultrasonic vibration；And the crackle system generated on dental zirconium oxide ceramics according to single abrasive particle, the length of the width and depth and surface crater that obtain transversal crack is calculated, according to result above, establishes and cheats model (M1 model) without dimple single under interference effect；It is based on interference mechanism, seeks the distance between center line of adjacent pit according to the random distribution feature of abrasive grain in the random distribution model of cutter end face secondly, establishing abrasive grain, to establish single dimple hole model (M2 model) under interference effect；Finally, carrying out supersonic vibration assistant grinding dental zirconium oxide ceramic test, the microstructure of different machining parameters lower surface is observed, and M2 model is verified, the results show that predicted value and test value matching are preferable.

Description

A method for predicting the microstructure of dental zirconia ceramics by ultrasonic vibration grinding

technical field

The invention belongs to the technical field of ultrasonic vibration-assisted grinding, in particular to a method for predicting the microstructure of dental zirconia ceramics by ultrasonic vibration grinding.

Background technique

In the traditional mechanical engineering field, improving the friction and wear performance between parts is mainly to improve the surface microtexture and improve the performance of the lubricant. However, in the field of prosthodontics, the possibility of changing the saliva in the human mouth is very small. Therefore, the improvement and optimization of the surface microtexture of denture materials will become the main measures to improve the friction and wear performance. In recent years, ceramic materials have become one of the main denture materials to replace the hard tissue of natural teeth due to their excellent simulated aesthetic effects, chemical stability, biocompatibility and wear resistance. Among them, dental zirconia ceramics are currently the most popular. choose. The manufacturing process of traditional full zirconium crowns is obtained by high-speed milling or grinding of pre-sintered ceramic blocks and then secondary sintering, as shown in Figure 2. The shrinkage rate is difficult to precisely control due to the influence of the crown wall thickness and the molding pressure, powder particle size, pressure maintenance time and moisture content during the secondary sintering process. However, the manufacturing precision of dental crowns not only seriously affects the patient's wearing comfort, but also is the main factor leading to its fracture failure. In order to solve the above problems, the most ideal and convenient way is to introduce the ultrasonic vibration-assisted grinding technology into the field of oral restoration to realize the direct processing of dental zirconia ceramics.

The existing ultrasonic vibration-assisted grinding technology has been introduced into the field of prosthodontics. Because the ultrasonic vibration-assisted grinding technology can not only change the manufacturing process of traditional ceramic crowns (to realize the one-time molding of dental zirconia ceramics), but also can form a large-area isotropic surface texture, which is different from the traditional ordinary diamond grinding. There is a sharp contrast in the furrow-like texture. However, the research on the surface microstructure of ultrasonic vibration-assisted grinding of dental zirconia ceramics is still unclear, and the formation process of the surface microstructure of dental zirconia ceramics by ultrasonic vibration-assisted grinding is still unclear.

SUMMARY OF THE INVENTION

The purpose of the present invention is to predict the surface microstructure of dental zirconia ceramics assisted by ultrasonic vibration, and a method for predicting the microstructure of dental zirconia ceramics by ultrasonic vibration is proposed, which can predict the ultrasonic vibration assisted dental zirconia ceramic materials. Surface microstructure during grinding.

The technical solution that realizes the object of the present invention is:

A method for predicting the microstructure of dental zirconia ceramics by ultrasonic vibration grinding, comprising the following steps:

Step (1): Establish the motion trajectory equation of a single abrasive particle: In the process of ultrasonic vibration grinding dental zirconia ceramics, there are three forms of motion: the rotational motion of the spindle, the ultrasonic vibration of the spindle and the feed motion of the tool , according to the three motion forms, establish the motion trajectory equation of a single abrasive particle;

Step (2): Establish a crack system for a single abrasive particle: According to the brittle material brittleness removal mechanism, obtain the expressions of the width _CL and depth C _h of the crack generated by a single abrasive particle, according to the total axial force and the total number of abrasive particles The ratio of to obtain the axial force of a single abrasive particle, and according to the properties of dental zirconia ceramics, obtain the expressions of width C _L and depth C _h based on machining and vibration parameters;

Step (3): establish a single micro-pit model without interference: ultrasonic vibration grinding of dental zirconia is a process of intermittent cutting, obtain the effective cutting time t _AB , and obtain the effective cutting length L _d based on the effective cutting time, based on The motion trajectory equation of a single abrasive particle and the crack system of a single abrasive particle are used to establish a single micro-pit model without interference based on the width C _L , the depth C _h and the effective cutting length L _d ;

Step (4): establish a random distribution model of the abrasive particles on the end face of the tool: assuming that the abrasive particles on the end face of the tool are uniformly distributed, obtain the probability density function f(r);

Step (5): Distance between adjacent pit centerlines: Assuming that the distance between adjacent pit centerlines is Δd, according to the joint probability density function f(d ₁ , d ₂ ) and the probability density function f(r), obtain The probability density function of Δd to obtain the expected value of Δd;

Step (6): establish a single micro-pit model under the interference action: according to the expected value of Δd, obtain the width, depth and length values of the single micro-pit model under the average interference action;

Step (7): Predict the microstructure under different parameters according to the single micro-pit model under the interference action.

The calculation process of the present invention is more in line with the actual processing conditions, and considers the interference effect of the pits and the actual working conditions. Can be used to predict the surface microstructure of ultrasonic vibration-assisted grinding of dental zirconia ceramics.

The present invention will be described in further detail below with reference to the accompanying drawings.

Description of drawings

FIG. 1 is a flow chart of the microstructure prediction method of the present invention.

Figure 2 is a schematic diagram of the motion relationship of ultrasonic vibration grinding

Figure 3 is a schematic diagram of a single micro-pit model without interference

FIG. 4 is a schematic diagram of continuous pit interference.

Figure 5 is a schematic diagram of a single micro-pit model under interference action

Figure 6 shows the comparison between the experimental value and the predicted value of the surface microstructure width

Figure 7 shows the comparison between the experimental value and the predicted value of the surface microstructure depth

Figure 8 shows the comparison between the experimental value and the predicted value of the surface microstructure length

Detailed ways

In order to better understand the technical content of the present invention, specific examples are given and described in conjunction with the accompanying drawings as follows.

1 is a flowchart of the prediction method of the present invention; the ultrasonic vibration grinding dental zirconia ceramic microstructure prediction method of the present invention specifically includes the following steps:

Step 1. Establish the motion trajectory equation of a single abrasive particle: In the process of ultrasonic vibration-assisted grinding of dental zirconia ceramics, there are three forms of motion: the rotational motion of the spindle, the ultrasonic vibration of the spindle and the feed motion of the tool, According to the three motion forms, as shown in Figure 2, the motion trajectory equation of a single abrasive particle is established;

1.1. According to the feed movement of the tool, establish the motion equation in the feed direction:

x=V _s t+r cos(ωt) (1)

1.2. According to the rotational motion of the main shaft, establish the equation of motion:

y=r sin(ωt) (2)

1.3. According to the ultrasonic vibration of the main shaft, the axial motion equation is established:

z=A sin(2πft) (3)

Among them, V _s is the feed speed, mm/s; t is the cutting time of a single abrasive particle, s; r is the position of the abrasive particle in the radial direction, mm; ω is the angular velocity of the abrasive particle, rad/s; A is Ultrasonic amplitude, μm; f is vibration frequency, Hz,

Step 2. Establish a crack system for a single abrasive particle: According to the brittle material brittleness removal mechanism, obtain the expressions of the width _CL and depth C _h of the crack generated by a single abrasive particle, and according to the ratio of the total axial force to the total number of abrasive particles Obtain the axial force of a single abrasive particle, and according to the properties of dental zirconia ceramics, obtain the expressions of width C _L and depth C _h based on machining and vibration parameters;

2.1. According to the brittleness removal mechanism of brittle materials, the expressions of crack width _CL and depth C _h can be obtained:

Among them, C ₂ is a dimensionless constant, C ₂ =0.226; β is the angle value of two opposite sides of a single abrasive particle; E is the Young's modulus of dental zirconia ceramics, MPa; H _v is the hardness value of the material, MPa ; K _IC is the structural strength, MPa; υ is the Poisson's ratio of the material; F is the axial force of a single abrasive particle, N,

2.2. The overall axial force of the tool, that is, the axial force of all abrasive particles on the end face of the tool is:

Among them, k ₀ is a dimensionless constant, k ₀ =2 ^-33/16 ×360 ^7/8 ×ξ ^1/16 ×π ^-7/8 =14.60; k ₁ is related to cutting parameters, k ₁ =0.0614n ^0.5738 · V _s ^-0.8564 · a _p ^-0.5313 ; R ₁ is the inner radius of the tool, mm; D ₂ is the outer diameter of the tool, mm; C ₀ is a dimensionless constant, C ₀ =[3×0.88×10 ^-3 /(100× 2 ^0.5 ρ)] ^2/3 , ρ is the density of dental zirconia ceramics, g/cm ³ ; Ca is the concentration of tool abrasive particles, which is related to the specific model of the tool, and generally takes 100; R ₂ is the outer radius of the tool , mm; e is the size of abrasive particles, which is related to the specific model of the tool, mm; n is the spindle speed of the tool, r/min; A is the ultrasonic amplitude, μm; a _p is the cutting depth of the tool, mm;

2.3. The effective number of abrasive grains on the end face of the tool is:

2.4. Axial force on a single abrasive particle:

2.5. Bring the F value into equations (4) and (5) to obtain the expressions of the width C _L and the depth C _h based on the machining and vibration parameters:

C _L = m·n ^-0.2599 · V _s ^0.07853 · a _p ^-0.2906 · (A+ _ap ) ^0.5469 · A ^-0.07813 (9)

C _h = m ₁ ·n ^-0.1865 ·V _s ^-0.06207 · a _p ^-0.2324 · (A+a _p ) ^0.4375 · A ^-0.0625 (11)

Step 3. Establish a single micro-pit model (M1 model) without interference: ultrasonic vibration-assisted grinding of dental zirconia is a process of intermittent cutting, obtain the effective cutting time t _AB , and obtain the effective cutting length L based on the effective cutting time _d . Based on the motion trajectory equation of a single abrasive particle and the crack system of a single abrasive particle, a single micro-pit model (M1 model) without interference based on the width C _L , the depth C _h and the effective cutting length L _d is established, as shown in the figure 3 shown;

3.1. The ultrasonic vibration-assisted grinding of dental zirconia is a process of intermittent cutting, and the effective cutting time t _AB is obtained:

3.2. Obtain the maximum depth of cut δ:

Among them, ξ is the geometric factor, which is 1.85,

3.3. Obtain the effective cutting length:

3.4. Combining equations (13), (14) and (15), the expression of effective cutting length can be obtained:

3.5. According to the established formulas (9), (11) and (16), establish a single micro-pit model (M1 model) without interference based on the width _CL , the depth C _h and the effective cutting length L _d .

Step 4. Establish a random distribution model of abrasive particles on the end face of the tool: assuming that the abrasive particles on the end face of the tool are distributed uniformly, obtain the probability density function f(r);

4.1.: Assume that the random distribution model of abrasive particles on the end face of the tool is uniform distribution, and obtain its probability density function f(r);

Among them, r is the position of the abrasive grain in the radial direction.

Step 5. The distance between the centerlines of adjacent pits, as shown in Figure 4: Assuming that the distance between the centerlines of adjacent pits is Δd, according to the joint probability density function f(d ₁ , d ₂ ) and the probability density function f( r), obtain the probability density function of Δd, thereby obtaining the expected value of Δd;

5.1. The distance between the centerlines of two continuous pits is Δd, which is expressed as:

Δd=|r _x+1 -r _x | (18)

where x represents the xth pit,

5.2. Set d ₁ =r _x+1 -r _x , d ₂ =r _x , then r _x and r _x+1 can be expressed as

r _x =d ₂ (19)

r _x+1 =d ₁ +d ₂ (20)

5.3. In order to obtain the expected value of Δd, obtain the expression of the joint probability density function f(d ₁ , d ₂ ):

f(d ₁ ,d ₂ )=f(r ₁ (d ₁ ,d ₂ ),r ₂ (d ₁ ,d ₂ ))|J| (21)

where J is the Jacobian,

5.4. Find the probability density equation f(d ₁ ) of d ₁ :

When d ₁ > 0,

When d ₁ <0,

5.5. Based on the definition of d, it can be known that Δd=|d ₁ |, therefore, the probability density equation of Δd can be expressed as

P(|d ₁ |≤Δd)=P(d ₁ ≤-Δd)+P(d ₁ ≤-Δd) (24)

5.6. According to the above calculation, the expected value of Δd can be obtained:

5.7. From d=2C _L , the expected value of Δd can be obtained:

Step 6. Establish a single micro-pit model (M2 model) under the interference action, as shown in Figure 5: According to the expected value of Δd, obtain the width, depth and length values of the single micro-pit model (M2 model) under the average interference action;

6.1. According to formula (26), the expected value of Δd is less than 2C _L , so the pits interfere, and according to formula (26), the distance between the center lines of the interference pits is _2CL /3, according to the interference mechanism , obtain the width, depth and length values of a single micro-pit model (M2 model) under the action of average interference, where the width value is 8C _L /3, the depth value is C _h , and the length value is L _d .

Step 7: Predict the surface microstructure under different parameters according to the single micro-pit model (M2 model) under the interference action. Step 7.1. From the above analysis, the predicted value of the surface microstructure is:

The width value W of the surface microstructure is:

The depth value D of the surface microstructure is:

D=C _h =m ₁ ·n ^-0.1865 ·V _s ^-0.06207 ·a _p ^-0.2324 ·(A+a _p ) ^0.4375 ·A ^-0.0625 (28)

The length value L of the surface microstructure is:

Step 7.2. Carry out an experiment to compare the predicted value of the surface microstructure with the experimental value.

Example 1:

The ultrasonic vibration-assisted grinding test was carried out on the German DMG ultrasonic equipment. The ultrasonic frequency was 25 kHz, and the ultrasonic amplitude increased from 2 μm to 5 μm with increasing power ratio. The outer diameter of the diamond tool is 8mm, the wall thickness is 0.6mm, and the size of the diamond abrasive grain is D126. The workpiece is a fully sintered dental zirconia ceramic, which was provided by Aidite (Qinhuangdao) Technology Co., Ltd., and its mechanical properties are shown in Table 1.

Table 1 Mechanical properties of fully sintered zirconia ceramics

Obviously, these parameters are determined by the characteristics of dental zirconia ceramics and the structure of the tool, and the parameters of the above examples are not intended to limit the present invention.

In this example, the influence factor (spindle speed) that has been significantly changed has been tested and verified. The test parameters are shown in Table 2. The experimental and predicted values of the surface microstructure are shown in Figures 6, 7, and 8:

Table 2 Processing test parameter values

As mentioned above, the prediction formulas for the width, depth and length of the surface microstructure can be used to predict the surface microstructure of dental zirconia ceramics by ultrasonic vibration-assisted grinding at different spindle speeds. Substitute the relevant parameters into equations (27), (28) and (29) to obtain the predicted values of the width, depth and length of the surface microstructure; the comparison between the experimental and predicted values is shown in Figure 6, Figure 7 and Figure 8 , it can be seen that the predicted value and the experimental value of ultrasonic vibration-assisted grinding have good consistency. Therefore, the present invention can predict the surface microstructure of ultrasonic vibration-assisted grinding of dental zirconia ceramics.

Claims (8)

1. a prediction method of ultrasonic vibration grinding dental zirconia ceramic microstructure, is characterized in that, comprises the following steps: Step (1): Establish the motion trajectory equation of a single abrasive particle: In the process of ultrasonic vibration grinding dental zirconia ceramics, there are three forms of motion: the rotational motion of the spindle, the ultrasonic vibration of the spindle and the feed motion of the tool , according to the three motion forms, establish the motion trajectory equation of a single abrasive particle; Step (2): Establish a crack system for a single abrasive particle: According to the brittle material brittleness removal mechanism, obtain the expressions of the width _CL and depth C _h of the crack generated by a single abrasive particle, according to the total axial force and the total number of abrasive particles The ratio of to obtain the axial force of a single abrasive particle, and according to the properties of dental zirconia ceramics, obtain the expressions of width C _L and depth C _h based on machining and vibration parameters; Step (3): establish a single micro-pit model without interference: ultrasonic vibration grinding of dental zirconia is a process of intermittent cutting, obtain the effective cutting time t _AB , and obtain the effective cutting length L _d based on the effective cutting time, based on The motion trajectory equation of a single abrasive particle and the crack system of a single abrasive particle are used to establish a single micro-pit model without interference based on the width C _L , the depth C _h and the effective cutting length L _d ; Step (4): establish a random distribution model of the abrasive particles on the end face of the tool: assuming that the abrasive particles on the end face of the tool are uniformly distributed, obtain the probability density function f(r); Step (5): Distance between adjacent pit centerlines: Assuming that the distance between adjacent pit centerlines is Δd, according to the joint probability density function f(d ₁ , d ₂ ) and the probability density function f(r), obtain The probability density function of Δd to obtain the expected value of Δd; Step (6): establish a single micro-pit model under the interference action: according to the expected value of Δd, obtain the width, depth and length values of the single micro-pit model under the average interference action; Step (7): Predict the microstructure under different parameters according to the single micro-pit model under the interference action. 2. a kind of prediction method of ultrasonic vibration grinding dental zirconia ceramic microstructure as claimed in claim 1, is characterized in that, in aforementioned step (1), the motion trajectory equation step of establishing single abrasive particle is as follows: Step 1.1, according to the feed movement of the tool, establish the motion equation in the feed direction: x=V _s t+r cos(ωt) (1) Step 1.2, according to the rotational motion of the main shaft, establish the motion equation: y=r sin(ωt) (2) Step 1.3, according to the ultrasonic vibration of the main shaft, establish the axial motion equation: z=Asin(2πft) (3) Among them, V _s is the feed speed, mm/s; t is the cutting time of a single abrasive particle, s; r is the position of the abrasive particle in the radial direction, mm; ω is the angular velocity of the abrasive particle, rad/s; A is Ultrasonic amplitude, μm; f is vibration frequency, Hz. 3. a kind of ultrasonic vibration grinding dental zirconia ceramic microstructure prediction method as claimed in claim 2, is characterized in that, in aforementioned step (2), establish the crack system of single abrasive particle, and the steps are as follows: Step 2.1, according to the brittleness removal mechanism of brittle materials, the expressions of crack width _CL and depth C _h can be obtained: Among them, C ₂ is a dimensionless constant, C ₂ =0.226; β is the angle value of two opposite sides of a single abrasive particle; E is the Young's modulus of dental zirconia ceramics, MPa; H _v is the hardness value of the material, MPa ; K _IC is the structural strength, MPa; υ is the Poisson's ratio of the material; F is the axial force of a single abrasive particle, N; Step 2.2. The overall axial force of the tool, that is, the axial force of all abrasive particles on the end face of the tool is: Among them, k ₀ is a dimensionless constant, k ₀ =2 ^-33/16 ×360 ^7/8 ×ξ ^1/16 ×π ^-7/8 =14.60; k ₁ is related to cutting parameters, k ₁ =0.0614n ^0.5738 · V _s ^-0.8564 · a _p ^-0.5313 ; R ₁ is the inner radius of the tool, mm; D ₂ is the outer diameter of the tool, mm; C ₀ is a dimensionless constant, C ₀ =[3×0.88×10 ^-3 /(100× 2 ^0.5 ρ)] ^2/3 , ρ is the density of dental zirconia ceramics, g/cm ³ ; Ca is the concentration of tool abrasive particles, which is related to the specific model of the tool; R ₂ is the outer radius of the tool, mm; e is The size of the abrasive particles is related to the specific model of the tool, mm; n is the spindle speed of the tool, r/min; A is the ultrasonic amplitude, μm; a _p is the cutting depth of the tool, mm; In step 2.3, the effective number of abrasive grains on the end face of the tool is: Step 2.4, Axial force on a single abrasive particle: Step 2.5, bring the F value into equations (4) and (5), and obtain the expressions of the width C _L and the depth C _h based on the machining and vibration parameters: C _L = m·n ^-0.2599 · V _s ^0.07853 · a _p ^-0.2906 · (A+ _ap ) ^0.5469 · A ^-0.07813 (9) C _h = m ₁ ·n ^-0.1865 ·V _s ^-0.06207 · a _p ^-0.2324 · (A+a _p ) ^0.4375 · A ^-0.0625 (11) 4. a kind of ultrasonic vibration grinding dental zirconia ceramic microstructure prediction method as claimed in claim 3, is characterized in that, in the aforementioned step (3), establishes the single micro-pit model under non-interference action, and concrete steps are: : Step 3.1, the ultrasonic vibration grinding process of dental zirconia is a process of intermittent cutting, and the effective cutting time t _AB is obtained: Step 3.2, get the maximum depth of cut δ: Among them, ξ is the geometric factor, which is 1.85, Step 3.3, get the effective cutting length: Step 3.4, combining equations (13), (14) and (15), the expression of effective cutting length can be obtained: Step 3.5, according to the established formulas (9), (11) and (16), establish a single micro-pit model without interference based on the width _CL , the depth C _h and the effective cutting length L _d . 5. the prediction method of a kind of ultrasonic vibration grinding dental zirconia ceramic microstructure as claimed in claim 4, is characterized in that, in aforementioned step (4), establishes the random distribution model of tool end face abrasive grain, and concrete steps are: Step 4.1: Assume that the random distribution model of abrasive particles on the end face of the tool is uniform distribution, and obtain its probability density function f(r); Among them, r is the position of the abrasive grain in the radial direction. 6. a kind of ultrasonic vibration grinding dental zirconia ceramic microstructure prediction method as claimed in claim 5, is characterized in that, in aforementioned step (5), establishes adjacent pit centerline spacing, and concrete steps are: In step 5.1, the distance between the centerlines of two consecutive pits is Δd, which is expressed as: Δd=|r _x+1 -r _x | (18) where x represents the xth pit, Step 5.2, set d ₁ =r _x+1 -r _x , d ₂ =r _x , then r _x and r _x+1 can be expressed as r _x =d ₂ (19) r _x+1 =d ₁ +d ₂ (20) Step 5.3, in order to obtain the expected value of Δd, obtain the expression of the joint probability density function f(d ₁ , d ₂ ): f(d ₁ ,d ₂ )=f(r ₁ (d ₁ ,d ₂ ),r ₂ (d ₁ ,d ₂ ))|J| (21) where J is the Jacobian, Step 5.4, find the probability density equation f(d ₁ ) of d ₁ : When d ₁ > 0, When d ₁ <0, Step 5.5, based on the definition of d, it can be known that Δd=|d ₁ |, therefore, the probability density equation of Δd can be expressed as P(|d ₁ |≤Δd)=P(d ₁ ≤-Δd)+P(d ₁ ≤-Δd) (24) Step 5.6, according to the above calculation, the expected value of Δd can be obtained: Step 5.7, from d=2C _L , the expected value of Δd can be obtained: 7. the prediction method of a kind of ultrasonic vibration grinding dental zirconia ceramic microstructure as claimed in claim 6, is characterized in that, in aforementioned step (6), set up single micro-pit model under interference action, concrete steps are: Step 6.1, according to formula (26), the expected value of Δd is less than 2C _L , so the pits interfere, and according to formula (26), the distance between the center lines of the interference pits is _2CL /3, according to the interference According to the mechanism, the width, depth and length values of a single micro-pit under the action of average interference are obtained, wherein the width value is 8C _L /3, the depth value is C _h , and the length value is L _d . 8. The method for predicting the microstructure of dental zirconia ceramics by ultrasonic vibration grinding as claimed in claim 7, wherein in the aforementioned step (7), a test is carried out, and the predicted value and the test value of the microstructure are compared , Step 7.1, from the above analysis, the predicted value of the microstructure is: The width value W of the microstructure is: The depth value D of the microstructure is: D=C _h =m ₁ ·n ^-0.1865 ·V _s - ^0.06207 ·a _p - ^0.2324 ·(A+a _p ) ^0.4375 ·A ^-0.0625 (28) The length value L of the microstructure is: In step 7.2, experiments are carried out to compare the predicted and experimental values of the microstructure.