CN110227985B - Design method of magnetic core structure of needle type magnetic composite fluid polishing head - Google Patents

Design method of magnetic core structure of needle type magnetic composite fluid polishing head Download PDF

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CN110227985B
CN110227985B CN201910446251.5A CN201910446251A CN110227985B CN 110227985 B CN110227985 B CN 110227985B CN 201910446251 A CN201910446251 A CN 201910446251A CN 110227985 B CN110227985 B CN 110227985B
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magnetic field
polishing
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permanent magnet
needle
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CN110227985A (en
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姜晨
王璐璐
李佳音
管华双
彭涛
林文鑫
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University of Shanghai for Science and Technology
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B24—GRINDING; POLISHING
    • B24B—MACHINES, DEVICES, OR PROCESSES FOR GRINDING OR POLISHING; DRESSING OR CONDITIONING OF ABRADING SURFACES; FEEDING OF GRINDING, POLISHING, OR LAPPING AGENTS
    • B24B1/00—Processes of grinding or polishing; Use of auxiliary equipment in connection with such processes
    • B24B1/005—Processes of grinding or polishing; Use of auxiliary equipment in connection with such processes using a magnetic polishing agent
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B24—GRINDING; POLISHING
    • B24B—MACHINES, DEVICES, OR PROCESSES FOR GRINDING OR POLISHING; DRESSING OR CONDITIONING OF ABRADING SURFACES; FEEDING OF GRINDING, POLISHING, OR LAPPING AGENTS
    • B24B13/00—Machines or devices designed for grinding or polishing optical surfaces on lenses or surfaces of similar shape on other work; Accessories therefor
    • B24B13/01—Specific tools, e.g. bowl-like; Production, dressing or fastening of these tools
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation

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  • General Engineering & Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Finish Polishing, Edge Sharpening, And Grinding By Specific Grinding Devices (AREA)

Abstract

The invention relates to needle type magnetic composite fluid polishingThe design method of head magnetic core structure includes setting the number of permanent magnets as T, selecting different ratio mu, where mu is the ratio of the radius to the center distance of the permanent magnets, calculating the magnetic field strength of each point in the magnetic field in different ratio mu magnetic field range, and calculating the corresponding standard deviation sigma by standard deviation formulaHSo as to obtain the magnetic field uniformity under different mu values, and finally obtain the optimal solution of the ratio mu according to the magnetic field uniformity; perfecting the structure of the needle type magnetic composite fluid polishing head. The design size of the magnetic core structure of the needle-type magnetic composite fluid polishing head is further optimized, so that the effect of uniformly removing the surface of the material in the polishing process is obtained.

Description

Design method of magnetic core structure of needle type magnetic composite fluid polishing head
Technical Field
The invention relates to a magnetofluid composite polishing technology, in particular to a design method of a magnetic core structure of a needle type magnetic composite fluid polishing head.
Background
With the continuous development of optical technology and material science, the plane efficient polishing technology of optical precision parts is realized. People have higher and higher requirements on the traditional mechanical polishing technology, so the magnetic fluid composite polishing technology is produced. The deep hole processing and polishing technology has the most obvious characteristic that the polishing head of the flexible medium is not easy to deform and is more suitable for materials with complex profiles and difficult processing. The magnetic fluid composite polishing technology is widely applied to the fields of automobiles, machinery, buildings, aviation, medical treatment and the like, and the current theoretical model for calculating and analyzing the deep hole processing magnetic fluid composite polishing approximately considers that the distribution of a magnetic field in the magnetic rheological fluid is uniform, and further considers that the magnetic field intensity generated by the magnetic rheological fluid is also uniform. The actual distribution of the magnetic field is not uniform, so that the calculated area meeting the uniformity of the magnetic field strength plays an important role in the magnetic composite fluid polishing technology, and the polishing liquid is positioned in the processing area as much as possible, so that the polishing quality is highest. Therefore, the method has important significance for calculating the proper geometric dimension of the magnetic core structure dimension of the deep hole polishing lower needle type magnetic composite fluid polishing head. Thereby promoting the mechanism research of the removal rate uniformity of the material under the deep hole polishing process.
Disclosure of Invention
The invention provides a design method of a magnetic core structure of a needle type magnetic composite fluid polishing head aiming at the problem of the application of a magnetofluid composite polishing technology, and the method can promote the material removal uniformity mechanism under the deep hole polishing technology and the industrial application thereof.
The technical scheme of the invention is as follows: a design method of a magnetic core structure of a needle type magnetic composite fluid polishing head specifically comprises the following steps:
1) designing a test structure: the needle type magnetic composite fluid polishing head comprises a three-jaw chuck, a movable pin, a polishing needle box, an elastic nut, a polishing needle opening and a polishing needle; the three-jaw chuck is provided with three movable feet, the movable feet are the clamping feet of the three-jaw chuck, the cylindrical surface of a cylindrical polishing needle box is fixed on the three-jaw chuck through three movable foot buckles, the polishing needle box is provided with a loose nut and a polishing needle opening at the center, the loose nut is arranged at two sides of the bottom end of the polishing needle box, the polishing needle is inserted into the polishing needle opening and then is screwed and fixed in the polishing needle box through the loose nuts at two sides, T cylindrical magnets are stacked and arranged to form a magnetic core polishing needle, and N poles and S poles of the magnets are used for adsorbing polishing liquid to meet the requirement on workpiece polishing;
2) calculating the magnetic flux phi of any point in the outer space of the single permanent magnet: introducing a related calculation formula of magnetic flux phi according to a Maxwell equation set, and selecting a magnetic charge model to obtain a phi calculation formula;
3) the magnetic field strength H of the permanent magnet at any point P (x, y, z) in the outer space on a single permanent magnet is calculated: the magnetizing direction of the selected permanent magnet is the upper surface and the lower surface, and the divergence is calculated for phi to obtain the magnetic field intensity H of a single permanent magnet;
4) t identical magnets are coaxially arranged, the magnetic induction intensity at any point on the axis is the vector sum of the magnetic induction intensity at the point when the T coils exist independently, and the vector sum is calculatedThe magnetic field intensity generated by the T permanent magnets is calculated, and the average value of the magnetic field intensity is obtained
Figure BDA0002073724610000021
5) Selecting different ratio mu, wherein mu is the ratio of the radius of the permanent magnet to the center distance, and in the step 3), the height of a single permanent magnet is substituted into a magnetic field intensity H formula by using L-mu R to obtain the magnetic field intensity of each point selected in the magnetic field range with different ratio mu in the magnetic field, and calculating the corresponding standard deviation sigma by using a standard deviation formula againHSo as to obtain the magnetic field uniformity degree under different mu values;
6) finally, obtaining the optimal solution of the ratio mu according to the uniformity degree of the magnetic field;
7) and (4) perfecting the structure of the needle type magnetic composite fluid polishing head in the step 1) according to the ratio mu obtained in the step 6).
The invention has the beneficial effects that: the design method of the magnetic core structure of the needle-type magnetic composite fluid polishing head can further optimize the design size of the magnetic core structure of the needle-type magnetic composite fluid polishing head, so that the effect of uniformly removing the surface of a material in the polishing process is obtained.
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FIG. 1 is a schematic flow chart of a method for designing a magnetic core structure of a needle-type magnetic composite fluid polishing head according to the present invention;
FIG. 2 is a schematic view of a magnetic composite fluid polishing head structure according to the present invention;
FIG. 3 is a diagram showing the layout of the core formed by the arrangement of T magnets according to the present invention;
FIG. 4 is a schematic view of the present invention with axially magnetized permanent magnets placed in a coordinate system;
FIG. 5 is a schematic view of the axially magnetized permanent magnet of the present invention;
FIG. 6 is a schematic diagram of the external magnetic field test of the permanent magnet after the arrangement of T magnets according to the present invention.
Detailed Description
As shown in fig. 1, the flow chart of the design method of the magnetic core structure of the needle-type magnetic composite fluid polishing head includes the following steps:
the method comprises the following steps: as shown in fig. 2, the structure of the needle-type magnetic composite fluid polishing head includes a three-jaw chuck 1, a movable leg 2, a polishing needle box 3, a turnbuckle 4, a polishing needle port 5, and a polishing needle. Three movable feet 2 are arranged on the three-jaw chuck 1, the movable feet 2 are clamping feet of the three-jaw chuck 1, the cylindrical surface of the cylindrical polishing needle box 3 is fixed on the three-jaw chuck 1 through the three movable feet 2 in a buckling mode, an elastic nut 4 and a polishing needle opening 5 in the center are arranged on the polishing needle box 3, the elastic nut 4 is arranged on two sides of the bottom end of the polishing needle box 3, and the polishing needles are screwed and fixed in the polishing needle box through the elastic nuts 4 on two sides after being inserted into the polishing needle opening 5. As shown in FIG. 3, T cylindrical magnets are stacked and arranged to form a magnetic core polishing needle, and N poles and S poles of the magnets are used for adsorbing polishing liquid, so that the requirement on workpiece polishing is met. The invention obtains the optimal structure through calculation, thereby achieving the optimal use effect.
Step two: calculating the magnetic flux phi of any point in the outer space of a single permanent magnet
And introducing a related calculation formula of the magnetic flux phi according to a Maxwell equation system. According to design requirements, a magnetic charge model is selected, as shown in a schematic diagram of fig. 4, in which an axially magnetized permanent magnet is placed in a coordinate system, a bottom single permanent magnet S pole face is taken as an xoy face, the center of the S pole face is taken as an origin o, an xyz coordinate system is established by taking a cylindrical permanent magnet axis as a Z axis, and if any point coordinate on a permanent magnet external space is P (x, y, Z), a calculation expression of the magnetic flux phi (x, y, Z) of the point is as follows:
Figure BDA0002073724610000031
wherein M is the magnetization intensity of a single permanent magnet along the axial direction; a is the curved surface area surrounding the outer surface of a single permanent magnet; r is the radius of a single permanent magnet; n is the normal vector of the outer surface of the single permanent magnet; tau is a tangential vector of the outer surface of the single permanent magnet;
Figure BDA0002073724610000032
is a divergence factor.
According to the magnetic charge model, the magnetic charge surface density rho of a single permanent magnetSAnd magnetismDensity of charge rhomIs defined as:
ρS＝M·n， (2)
substituting the formula (2) into the formula (1) to obtain:
Figure BDA0002073724610000041
step three: calculating the magnetic field intensity H of the permanent magnet at any point P (x, y, z) on the outer space of the single permanent magnet; obtaining phi through the formula (3), and then obtaining the magnetic field intensity H of a single permanent magnet by solving the divergence of phi:
Figure BDA0002073724610000042
as shown in fig. 5, since the permanent magnet is uniformly magnetized in the axial direction, the magnetization M ═ B in the axial direction of the single permanent magnetr/μ0Is a constant vector. B isrThe magnetic induction intensity retained in the permanent magnet is gradually reduced to zero after the single permanent magnet is magnetized to a saturation state. Magnetic permeability mu0＝4π×10-7H/m, because the magnetizing direction of the selected permanent magnet is the upper surface and the lower surface, the selected permanent magnet presents only surface magnetic charges on the upper surface and the lower surface, and no body magnetic charge exists:
ρm＝0 (5)
substituting formula (5) into (3) can yield:
Figure BDA0002073724610000043
the formula (6) may be substituted for the formula (4):
Figure BDA0002073724610000044
wherein
Figure BDA0002073724610000045
The distribution of the magnetic field intensity of the individual permanent magnets can be determined by equation (7).
Because the permanent magnet is symmetrical, a coordinate system as shown in fig. 4 is established for any point P (x, y, z) in space, where y is 0 and there are:
Figure BDA0002073724610000051
the second type of surface integration in surface integration needs to integrate the upper surface and the lower surface of the permanent magnet respectively in the direction with flow.
First, when integrating the upper surface of the permanent magnet, the arrangement can be:
(1) the upper surface is integrated along the x-field coordinates to find:
Figure BDA0002073724610000052
wherein (x)0，y0，z0)The point coordinate of the intersection point of the excircle of the upper surface and the xoz plane is a constant value; s represents the curved surface differential of the upper surface;
the surface integral is calculated and sorted to obtain a fixed integral form of x, y and z:
Figure BDA0002073724610000053
substituting the P-point coordinate P (x, y, z) to obtain a constant integral only related to theta, and obtaining a result; wherein
Figure BDA0002073724610000054
(2) The result of the integration of the upper surface along the y-field coordinate is:
Figure BDA0002073724610000055
(3) the integral of the upper surface along the z-field coordinate can be found as:
Figure BDA0002073724610000056
the result of formation into a definite integral form is:
Figure BDA0002073724610000061
for the side surfaces, the surface integral is zero.
And finally, performing surface integral on the lower surface of the permanent magnet, and finishing to obtain a result:
Figure BDA0002073724610000062
Figure BDA0002073724610000063
Figure BDA0002073724610000064
where L is the individual permanent magnet height.
It can be seen that the magnetic induction H (x, y, z) generated at any point in space by the permanent magnet is uniformly magnetized in the axial direction, and the different fields and the different coordinates are superimposed by the equations (10), (11), (13), (14), (15) and (16), thereby forming an analytical formula of the magnetic field:
Figure BDA0002073724610000065
wherein i, j, k are unit vectors on x, y, z axes, respectively.
Step four: calculating the magnetic field intensity generated by the T permanent magnets, and calculating the average value
Figure BDA0002073724610000066
T identical magnets are coaxially arranged, and the magnetic induction intensity at any point on the axis is the vector sum of the magnetic induction intensity at the point when the T coils exist independently. The circle center is a coordinate origin, a coordinate axis is established along a common axis, and when T permanent magnets are overlapped, the T permanent magnets are arranged in an arrangement mode from top to bottom N-S-N-S in the direction perpendicular to the machining direction.
Figure BDA0002073724610000067
Wherein HxRefers to the magnetic field independently generated by a single permanent magnet along the x field in a coordinate system.
Analyzing the average magnetic field intensity again, and setting the central distance from the permanent magnet at the top end of the arrangement sequence to the permanent magnet at the bottom end of the arrangement sequence as L1k( k 2, 3, …, T), T-total permanent magnets, the topmost permanent magnet being the first permanent magnet, the last in turn being the T-th permanent magnet, L12The center distance between the first permanent magnet and the second permanent magnet, L12＝Lmin；L1TCenter distance between the first permanent magnet and the T-th permanent magnet, L1T＝Lmax(ii) a Taking the maximum value L of the center-to-center distancemaxAnd a minimum value LminSubstituting the formula (18) and (19) to obtain the average value of the magnetic field intensity
Figure BDA0002073724610000071
The following were used:
Figure BDA0002073724610000072
step five: selecting different specific values mu, wherein mu is the ratio of the radius of the permanent magnet to the center distance, the height of a single permanent magnet in the step three is introduced by L-mu R, the magnetic field intensity of each point selected in the magnetic field range of different specific values mu in the magnetic field is solved, and the corresponding standard deviation sigma is calculated by using a standard deviation formula againHTo obtain magnetic fields at different mu valuesThe degree of homogeneity.
In example analysis, the solid permanent magnet is selected to have the size specification of 30mm in diameter, the axial thickness is determined by the ratio of the center distance to the radius, namely L/R, namely mu R, the material is N35 sintered rubidium iron boron (NdFeB), axial magnetization is carried out, and in order to replace the interference of magnetic fields of a plurality of permanent magnets to a great extent, five permanent magnets are selected to be superposed for data analysis, and the optimal solution is obtained under different mu values.
First, the magnetic field strength at 10 × 10 points is calculated on the xoz plane using the magnetic field strength analytical expressions (10) (11) (13) (14) (15) (16) (17). Since five permanent magnets are selected, L in the formula (19)min＝μR，LmaxA uniform magnetic field can be obtained at 5 μ R.
As shown in FIG. 6, the external magnetic field test of the permanent magnet after 5 magnets are arranged is schematically illustrated, the selected point in the first row is P10(x＝1.0R，y＝0，z＝0)，P11(x＝1.1R，y＝0，z＝0)，P12(x＝1.2R，y＝0，z＝0)，P13(x＝1.3R，y＝0，z＝0)，P14(x＝1.4R，y＝0，z＝0)，P15(x＝1.5R，y＝0，z＝0)，P16(x＝1.6R，y＝0，z＝0)，P17(x＝1.7R，y＝0，z＝0)，P18(x＝1.8R，y＝0，z＝0)，P19(x＝1.9R，y＝0，z＝0)，P20(x＝2.0R，y＝0，z＝0).
The first column has a longitudinal point P10(x＝1.0R，y＝0，z＝0)，P20(x＝1.0R，y＝0，z＝1.0R)P30(x＝1.0R，y＝0，z＝1.5R)，P40(x＝1.0R，y＝0，z＝2.0R)，P50(x＝1.0R，y＝0，z＝2.5R)，P60(x＝1.0R，y＝0，z＝3.0R)，P70(x＝1.0R，y＝0，z＝3.5R)P80(x＝1.0R，y＝0，z＝4.0R)，P90(x＝1.0R，y＝0，z＝4.5R)，P100(x＝1.0R，y＝0，z＝5R)。
The magnetic field strength of these points in the five superimposed permanent magnets can be obtained by substituting the specific values of the point coordinates corresponding to xyz at 10x10, where R is 15, L is μ R, and T is 5, into equation (18).
There is the standard deviation formula:
Figure BDA0002073724610000081
and then the value of n in the example analysis is 5 according to the deviation formula (20), so that the magnetic field uniformity degree under different mu values can be obtained.
After a plurality of times of calculation and arrangement, the following data can be obtained:
L/R(μ) standard deviation value L/R(μ) Standard deviation value
0.1 0.04632 0.7 0.01632
0.2 0.04128 0.8 0.01324
0.3 0.03912 0.9 0.01979
0.4 0.03513 1.0 0.02796
0.5 0.02830 1.1 0.03183
0.6 0.02530 1.2 0.04060
Step six: finally, according to the magnetic field uniformity degrees under different mu values, obtaining the optimal solution of the mu values;
from a careful inspection of the table, it is clear that the value of μ is minimized between 0.7 and 0.8, i.e. the ratio of the center-to-center distance L to the radius R is between 0.7 and 0.8, and the uniformity of the magnetic field becomes more uniform. The calculation of the density in the vicinity was increased, and thus, it was found that the standard deviation values of 0.72, 0.74, 0.76, and 0.78 for μ were 0.01610, 0.01546, 0.11468, and 0.01297, respectively, i.e., μ was 0.78, and the standard deviation was the smallest, i.e., the magnetic field was the most uniform. The size design of the magnetic composite fluid magnetic core is reasonable, and the standard deviation value in the range is small and stable, so that the ratio mu of the center distance to the radius of the selected polishing size permanent magnet is 76% when the size of the polishing head magnetic core structure is designed. The magnetic field intensity distribution is relatively uniform.

Claims (1)

1. A design method of a magnetic core structure of a needle type magnetic composite fluid polishing head is characterized by comprising the following steps:
1) designing a test structure: the needle type magnetic composite fluid polishing head comprises a three-jaw chuck, a movable pin, a polishing needle box, an elastic nut, a polishing needle opening and a polishing needle; the three-jaw chuck is provided with three movable feet, the movable feet are the clamping feet of the three-jaw chuck, the cylindrical surface of a cylindrical polishing needle box is fixed on the three-jaw chuck through three movable foot buckles, the polishing needle box is provided with a loose nut and a polishing needle opening at the center, the loose nut is arranged at two sides of the bottom end of the polishing needle box, the polishing needle is inserted into the polishing needle opening and then is screwed and fixed in the polishing needle box through the loose nuts at two sides, T cylindrical magnets are stacked and arranged to form the polishing needle, and the N pole and the S pole of the magnets are used for adsorbing polishing liquid to meet the requirement on workpiece polishing;
2) calculating the magnetic flux phi of any point in the outer space of the single permanent magnet: introducing a related calculation formula of magnetic flux phi according to a Maxwell equation set, and selecting a magnetic charge model to obtain a phi calculation formula;
3) the magnetic field strength H of the permanent magnet at any point P (x, y, z) in the outer space on a single permanent magnet is calculated: the magnetizing direction of the selected permanent magnet is the upper surface and the lower surface, and the divergence is calculated for phi to obtain the magnetic field intensity H of a single permanent magnet;
4) t identical magnets are coaxially arranged, the magnetic induction intensity at any point on the axis is the vector sum of the magnetic induction intensity at the point when the T coils exist independently, the magnetic field intensity generated by the T permanent magnets is calculated, and the average value of the magnetic field intensity is calculated
Figure FDA0002644453370000011
5) Selecting different ratio mu, wherein mu is the ratio of the radius R of the permanent magnet to the center distance, and the height of a single permanent magnet in the step 3) is substituted into a magnetic field intensity H formula by using L-mu R to obtain the magnetic field intensity of each point selected in the magnetic field range with different ratio mu in the magnetic field, and calculating the corresponding standard deviation sigma by using a standard deviation formula againHSo as to obtain the magnetic field uniformity degree under different mu values;
6) finally, obtaining the optimal solution of the ratio mu according to the uniformity degree of the magnetic field;
7) and (4) perfecting the structure of the needle type magnetic composite fluid polishing head in the step 1) according to the ratio mu obtained in the step 6).
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