CN111037464B - Optimization design method for size of needle type magnetic composite fluid electromagnetic polishing head - Google Patents

Optimization design method for size of needle type magnetic composite fluid electromagnetic polishing head Download PDF

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CN111037464B
CN111037464B CN201911317219.3A CN201911317219A CN111037464B CN 111037464 B CN111037464 B CN 111037464B CN 201911317219 A CN201911317219 A CN 201911317219A CN 111037464 B CN111037464 B CN 111037464B
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magnetic field
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point
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composite fluid
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CN111037464A (en
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姜晨
万欣
王璐璐
洪小兰
康赛
洪琛
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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
    • B24B41/00—Component parts such as frames, beds, carriages, headstocks
    • B24B41/04—Headstocks; Working-spindles; Features relating thereto
    • 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
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B24—GRINDING; POLISHING
    • B24D—TOOLS FOR GRINDING, BUFFING OR SHARPENING
    • B24D18/00—Manufacture of grinding tools or other grinding devices, e.g. wheels, not otherwise provided for

Abstract

The invention relates to an optimal design method for the size of a needle type magnetic composite fluid electromagnetic polishing head, which is characterized in that firstly, based on the structural design of the needle type magnetic composite fluid electromagnetic polishing head, under the condition of determining the polishing depth of a workpiece, the diameter of an electromagnet core of a current-carrying solenoid is set as D, the length of the electromagnet core is set as L, electromagnets with different length-diameter ratios a as L/D are selected, the magnetic field strengths B of different points selected in the magnetic field ranges under different iron cores are obtained, and then a standard deviation sigma formula is utilized to calculate the corresponding standard deviation sigmaBThe magnetic field intensity uniformity under different iron core length-diameter ratios a is obtained, the optimal solution of the iron core length-diameter ratios is obtained according to the uniform intensity of the magnetic field, the number of turns of the coil is adjusted, the magnetic composite fluid is controlled to reach the ultimate shear yield strength, and the structure of the needle type magnetic composite fluid electromagnetic polishing head is perfected. The design of the size of the electromagnet core of the needle type magnetic composite fluid electromagnetic polishing head is further optimized, so that the effect of uniformly removing the surface of the material in the polishing process is obtained.

Description

Optimization design method for size of needle type magnetic composite fluid electromagnetic polishing head
Technical Field
The invention relates to a magnetofluid composite polishing technology, in particular to an optimization design method for the size of a needle type magnetic composite fluid electromagnetic polishing head.
Background
Among the high-efficiency polishing technologies of optical precision parts, the deep hole processing and polishing technology has the most remarkable characteristic that a polishing head of a flexible medium is not easy to deform and is more suitable for materials with complex profiles and difficult processing.
Magnetic composite fluid polishing is a novel nano-scale ultra-precision machining technology, the viscosity of fluid can be continuously and steplessly changed under the action of a controllable magnetic field, and controllable and deterministic machining can be realized.
At present, the theoretical model for calculating and analyzing the composite polishing of the magnetic fluid for processing the deep hole is similar to the theory that the distribution of a magnetic field in the magnetic rheological fluid is uniform, and the magnetic field intensity generated by the magnetic rheological fluid is also considered to be 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 structure dimension of the needle type magnetic composite fluid electromagnetic polishing head under the deep hole polishing process, and the mechanism research on the removal rate uniformity of the material under the deep hole polishing process is promoted.
Disclosure of Invention
Aiming at the defects in the prior art, the technical problem to be optimized is how to make the distribution of a magnetic field in the magnetorheological fluid uniform and achieve the ultimate shear yield strength, and therefore, the invention provides an optimization design method for the size of the needle type magnetic composite fluid electromagnetic polishing head.
In order to achieve the purpose, the technical scheme of the invention is as follows: a method for optimally designing the size of a needle type magnetic composite fluid electromagnetic polishing head is characterized by comprising the following steps of:
the method comprises the following steps: designing a test structure: the needle type magnetic composite fluid electromagnetic polishing head comprises a polishing head body; the device comprises a case, a motor and a transmission device are arranged on the case; the electromagnet is connected with the motor through a transmission mechanism to rotate, and an electrified spiral coil is wound on the electromagnet; installing a shell outside the electrified spiral coil; under the power-on state, the magnetic composite fluid forms the requirement of a polishing head on the surface of the shell for polishing the workpiece under the action of a magnetic field generated by the power-on spiral coil;
step two: setting the length-diameter ratio of the electromagnet core as a, calculating the magnetic field intensity B generated by any point P on the central axis of the single-layer current-carrying spiral tubez: the current-carrying spiral pipe can be regarded as being composed of a series of current-carrying rings, the axis of the spiral pipe is set as the z axis, the magnetic induction intensity of each circle of current-carrying rings at any point P of the central axis is calculated, and the magnetic field intensity of all current-carrying rings of the whole spiral pipe at the point P is calculated according to integral;
step three: calculating the magnetic field intensity B of any point P on the z-axis of the multilayer current-carrying spiral tubez: for a multilayer solenoid, the magnetic field strength on the axis can be regarded as the superposition of the magnetic field strength of a plurality of single-layer solenoids on the axis;
step four: calculating the magnetic field intensity of any point P (r, z) outside the axis of the multilayer spiral tube: the magnetic field intensity of any point outside the axis of the spiral pipe can be expanded according to the axial magnetic field formula and the Siertz formula;
step five: selecting electromagnet cores a with different length-diameter ratios as L/D, calculating the magnetic field intensity of each point selected in the magnetic field range under different iron cores, and calculating the corresponding standard deviation sigma by using a standard deviation formulaHSo as to obtain the magnetic field uniformity under different iron core length-diameter ratios a;
step six: according to the uniformity degree of the magnetic field, the optimal solution of the length-diameter ratio a of the iron core is obtained on the basis;
step seven: the shearing stress strength of the magnetic composite fluid at each point is adjusted by changing the number of turns of the coil, so that the magnetic composite fluid reaches the ultimate yield shearing stress required by polishing, and finally the optimal solution of the thickness of the coil is obtained;
step eight: and perfecting the size design of the needle type magnetic composite fluid electromagnetic polishing head according to the optimal solution obtained in the sixth step and the seventh step.
Further, in step 2), the current-carrying spiral pipe can be regarded as being composed of a series of current-carrying rings, the axis of the spiral pipe is taken as the z axis, the origin is at the midpoint of the pipe length, the pipe length is L, the number of the ring turns contained in the unit pipe length is n, and the coordinate of any point P on the central axis is taken as zpTaking the unit tube length dzThe number of turns contained is:
dn＝ndz (1)
the magnetic induction intensity generated by each circle of current-carrying ring at the central axis point P is as follows:
Figure BDA0002326160260000021
in the formula: mu is the relative magnetic conductivity of the electromagnet core; i is the input current of the current-carrying spiral tube; z is the distance to the origin;
so dnThe coil current-carrying spiral pipe generates a magnetic field:
dBz＝Bzdn (3)
the magnetic induction formula (2) generated by the current-carrying ring is substituted into the formula (3), and the coordinate of the point on the coil is z, so that:
Figure BDA0002326160260000031
the magnetic field of all current-carrying rings of the whole spiral tube to the point P is integrated by the formula (4) to obtain:
Figure BDA0002326160260000032
the magnetic field intensity B generated by each point on the central axis on the vertical plane of the single-layer current-carrying spiral tube can be obtained by calculationz:
Figure BDA0002326160260000033
Further, in the step 3), for the multilayer current-carrying spiral pipe, the axial magnetic field intensity of the multilayer current-carrying spiral pipe is superposed according to the axial magnetic field intensity of the plurality of single-layer current-carrying spiral pipes. The outer diameter of the current-carrying spiral pipe is set as D0And the inner diameter is D, the thickness of the coil is (D)0D/2), n turns per unit length of each layer of solenoid and n layers per unit thickness1And calculating the axial magnetic field intensity of any point in the axial direction of the multilayer solenoid by superposing the magnetic field intensities of the plurality of single-layer solenoids:
Figure BDA0002326160260000034
and (3) obtaining the length-diameter ratio of the electromagnet core as L/D, substituting the L as aD into the formula (8):
Figure BDA0002326160260000035
Figure BDA0002326160260000041
further, in the step 4), according to a magnetic field formula in the axial direction of the multilayer spiral tube, the magnetic field formula is expanded according to a Shertz formula, and the expansion formula is as follows:
Figure BDA0002326160260000042
Figure BDA0002326160260000043
the magnetic induction at a point outside the space is then its vector sum:
Figure BDA0002326160260000044
further, in the step 5), electromagnet cores with different length-diameter ratios a are selected, a plurality of uniformly distributed points are selected in the magnetic field range under different iron core length-diameter ratios a, the magnetic field intensity of each point in the magnetic field is calculated by using the formula (11), and then the standard deviation formula is used
Figure BDA0002326160260000045
Calculating the corresponding standard deviation sigmaBSo as to obtain the magnetic field uniformity under different iron core length-diameter ratios a, wherein:
Figure BDA0002326160260000046
the average value of the magnetic field intensity of each point is obtained.
The invention has the beneficial effects that: the optimal design method of the dimension structure of the needle-type magnetic composite fluid electromagnetic polishing head can further optimize the design dimension of the magnetic core structure of the needle-type magnetic composite fluid electromagnetic polishing head, so that the effect of uniformly removing the surface of a material in the polishing process is obtained.
Drawings
FIG. 1 is a flow chart of the method for optimally designing the dimensional structure of a needle-type magnetic composite fluid electromagnetic polishing head according to the present invention;
FIG. 2 is a schematic diagram of a test structure designed by the present invention;
FIG. 3 is a schematic view of an electromagnetic polishing head of the present invention.
Detailed Description
The invention is further described with reference to the following figures and examples.
As shown in fig. 1, a flow chart of a method for optimally designing a dimension structure of a needle-type magnetic composite fluid electromagnetic polishing head includes the following steps:
the method comprises the following steps: a test structure of a needle type magnetic composite fluid electromagnetic polishing head is set up, as shown in fig. 2, the needle type magnetic composite fluid electromagnetic polishing head comprises: the device comprises a case 1, wherein a motor 2 and a transmission device are arranged on the case 1; the electromagnet 3 is connected with the motor 2 through a transmission mechanism to rotate, and an electrified spiral coil 4 is wound on the electromagnet 3; a housing 5 is mounted outside the energized spiral coil 4; under the power-on state, the magnetic composite fluid forms the requirement of a polishing head on the surface of the shell 5 for polishing a workpiece under the action of a magnetic field generated by the power-on spiral coil 4;
step two: as shown in fig. 3, let the diameter of the electromagnet core be D and the length of the electromagnet core be L, that is, the length-diameter ratio of the electromagnet core be a ═ L/D, and calculate the magnetic field strength B generated at any point P on the central axis of the single-layer current-carrying spiral tubez：
The current-carrying spiral pipe can be regarded as being composed of a series of current-carrying circular rings, the axis of the spiral pipe is taken as the z axis, the origin point is at the middle point of the pipe length, the pipe length is L, and the number of the circular rings contained in the unit pipe length is n.
Taking the coordinate of any point P on the central axis as zpTaking the unit tube length dzThe number of turns contained is:
dn＝ndz (1)
the magnetic induction intensity generated by each circle of current-carrying ring at the central axis point P is as follows:
Figure BDA0002326160260000051
in the formula: mu is the relative magnetic conductivity of the electromagnet core; i is the input current of the current-carrying spiral tube; z is the distance to the origin;
so dnThe coil current-carrying spiral pipe generates a magnetic field:
dBz＝Bzdn (3)
the magnetic induction formula (2) generated by the current-carrying ring is substituted into the formula (3), and the coordinate of the point on the coil is z, so that:
Figure BDA0002326160260000052
the magnetic field of all current-carrying rings of the whole spiral tube to the point P is integrated by the formula (4) to obtain:
Figure BDA0002326160260000061
the magnetic field intensity B generated by each point on the central axis on the vertical plane of the single-layer current-carrying spiral tube can be obtained by calculationz:
Figure BDA0002326160260000062
Step three: calculating the magnetic field intensity of any point P on the z-axis of the multilayer current-carrying spiral pipe:
for a multilayer current-carrying spiral tube, the axial magnetic field strength of the multilayer current-carrying spiral tube is superposed according to the axial magnetic field strength of a plurality of single-layer current-carrying spiral tubes. The outer diameter of the current-carrying spiral pipe is set as D0And the inner diameter is D, the thickness of the coil is (D)0D/2), n turns per unit length of each layer of solenoid and n thickness per unitThe number of layers in degrees is n1And calculating the axial magnetic field intensity of any point in the axial direction of the multilayer solenoid by superposing the magnetic field intensities of the plurality of single-layer solenoids:
Figure BDA0002326160260000063
and (3) obtaining the length-diameter ratio of the electromagnet core as L/D, substituting the L as aD into the formula (8):
Figure BDA0002326160260000064
step four: calculating the magnetic field intensity of any point P (r, z) outside the axis of the multilayer spiral tube:
regarding the magnetic field intensity of any point outside the axial line of the multilayer spiral pipe, setting the coordinate of any point P outside the axial line as (r, z), wherein r is the radial distance from the point P to the original point, and z is the axial distance from the point P to the original point, according to the magnetic field formula in the axial direction of the multilayer spiral pipe, the expansion formula is as follows:
Figure BDA0002326160260000071
Figure BDA0002326160260000072
the magnetic induction at a point outside the space is then its vector sum:
Figure BDA0002326160260000073
step five: selecting electromagnet cores with different length-diameter ratios a, and solving the magnetic field uniformity degree under different iron core length-diameter ratios a:
selecting electromagnet cores with different length-diameter ratios a, selecting a plurality of uniformly distributed points in the magnetic field range under different length-diameter ratios a of the electromagnet cores, calculating the magnetic field intensity of each point in the magnetic field by using the formula (11), and calculating the standard deviation formula
Figure BDA0002326160260000074
In the formula:
Figure BDA0002326160260000075
the average value of the magnetic field intensity of each point is obtained;
calculating the corresponding standard deviation sigmaBSo as to obtain the magnetic field uniformity under different iron core length-diameter ratios a;
step six: from the degree of homogeneity of the magnetic field, the value at σ is obtainedBThe optimal solution of the iron core length-diameter ratio a under the minimum condition;
minσB (13)
step seven: the shearing stress strength of the magnetic composite fluid at each point is adjusted by changing the number of turns of the coil, so that the magnetic composite fluid reaches the ultimate yield shearing stress required by polishing, and finally the optimal solution of the thickness of the coil is obtained;
τ＝τmax (14)
step eight: and perfecting the design of the size of the needle type magnetic composite fluid electromagnetic polishing head according to the optimal solution obtained in the sixth step and the seventh step.

Claims (3)

1. An optimal design method for the size of a needle type magnetic composite fluid electromagnetic polishing head is characterized by comprising the following steps:
1) designing a test structure: the needle type magnetic composite fluid electromagnetic polishing head comprises a polishing head body; the device comprises a case, a motor and a transmission device are arranged on the case; the electromagnet is connected with the motor through a transmission mechanism to rotate, and an electrified spiral coil is wound on the electromagnet; installing a shell outside the electrified spiral coil; under the power-on state, the magnetic composite fluid forms the requirement of a polishing head on the surface of the shell for polishing the workpiece under the action of a magnetic field generated by the power-on spiral coil;
2) setting the length-diameter ratio of the electromagnet core and calculating any one of the single-layer current-carrying spiral tube in the central axis directionMagnetic field strength B generated by point Pz: the current-carrying spiral pipe can be regarded as being composed of a series of current-carrying rings, the axis of the spiral pipe is set as the z axis, the magnetic induction intensity of each circle of current-carrying rings at any point P of the central axis is calculated, and the magnetic field intensity of all current-carrying rings of the whole spiral pipe at the point P is calculated according to integral;
3) calculating the magnetic field intensity of any point P on the z-axis of the multilayer current-carrying spiral pipe: for a multilayer solenoid, the magnetic field strength on the axis can be regarded as the superposition of the magnetic field strength of a plurality of single-layer solenoids on the axis;
4) calculating the magnetic field intensity of any point P (r, z) outside the axis of the multilayer spiral tube: the magnetic field intensity of any point outside the axis of the spiral pipe can be expanded according to the axial magnetic field formula and the Siertz formula;
5) selecting electromagnet cores with different length-diameter ratios a, calculating the magnetic field intensity of each point selected in the magnetic field range under different iron cores, and calculating the corresponding standard deviation sigma by using a standard deviation formulaHSo as to obtain the magnetic field uniformity under iron cores with different length-diameter ratios;
6) according to the uniformity degree of the magnetic field, the optimal solution of the length-diameter ratio a of the iron core is obtained on the basis;
7) the shearing stress strength of the magnetic composite fluid at each point is adjusted by changing the number of turns of the coil, so that the magnetic composite fluid reaches the ultimate yield shearing stress required by polishing, and finally the optimal solution of the thickness of the coil is obtained;
8) and perfecting the size design of the needle type magnetic composite fluid electromagnetic polishing head according to the optimal solution obtained in the step 6) and the step 7).
2. The method for optimally designing the size of the needle-type magnetic composite fluid electromagnetic polishing head according to claim 1, wherein the method comprises the following steps of: in step 2), the current-carrying spiral tube can be regarded as being composed of a series of current-carrying rings, the axis of the spiral tube is set as the z axis, the origin is at the midpoint of the tube length, the tube length is L, the number of the ring turns contained in the unit tube length is n, and the coordinate of any point P on the central axis is taken as zpTaking the unit tube length dzThe number of turns contained is:
dn＝ndz (1)
the magnetic induction intensity generated by each circle of current-carrying ring at the central axis point P is as follows:
Figure FDA0002940036180000021
in the formula: mu is the relative magnetic conductivity of the electromagnet core; i is the input current of the current-carrying spiral tube; z is the distance to the origin;
so dnThe coil current-carrying spiral pipe generates a magnetic field:
dBz＝Bzdn (3)
the magnetic induction formula (2) generated by the current-carrying ring is substituted into the formula (3), and the coordinate of the point on the coil is z, so that:
Figure FDA0002940036180000022
the magnetic field of all current-carrying rings of the whole spiral tube to the point P is integrated by the formula (4) to obtain:
Figure FDA0002940036180000023
the magnetic field intensity B generated by each point on the central axis on the vertical plane of the single-layer current-carrying spiral tube can be obtained by calculationz：
Figure FDA0002940036180000031
3. The method for optimally designing the size of the needle-type magnetic composite fluid electromagnetic polishing head according to claim 1, wherein the method comprises the following steps of: in the step 3), for the multilayer current-carrying spiral pipes, the axial magnetic field intensity of the multilayer current-carrying spiral pipes is superposed on the axial magnetic field intensity of the plurality of single-layer current-carrying spiral pipes; is provided withThe outer diameter of the current-carrying spiral tube is D0And the inner diameter is D, the thickness of the coil is (D)0D/2), n turns per unit length of each layer of solenoid and n layers per unit thickness1And calculating the axial magnetic field intensity of any point in the axial direction of the multilayer solenoid by superposing the magnetic field intensities of the plurality of single-layer solenoids.
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Citations (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN202221946U (en) * 2011-08-24 2012-05-16 合肥凯泉电机电泵有限公司 Mandrel tool for processing stator core of mine motor
CN106863020A (en) * 2017-01-20 2017-06-20 上海理工大学 Spiral magnetorheological finishing device
CN108942646A (en) * 2018-07-12 2018-12-07 上海理工大学 Planetary gear type magnetic coupling fluid polishing device
CN109551310A (en) * 2018-12-10 2019-04-02 上海理工大学 A kind of electromagnet type magnetic coupling fluid polishing device
CN110227985A (en) * 2019-05-27 2019-09-13 上海理工大学 The design method of pin type magnetic coupling fluid polishing head core structure
CN110281083A (en) * 2019-06-14 2019-09-27 上海理工大学 A kind of small thin tube inner wall magnetic coupling fluid polishing device
CN110340736A (en) * 2019-06-19 2019-10-18 华中科技大学 A kind of magnetorheological finishing device and method based on flow field focusing

Patent Citations (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN202221946U (en) * 2011-08-24 2012-05-16 合肥凯泉电机电泵有限公司 Mandrel tool for processing stator core of mine motor
CN106863020A (en) * 2017-01-20 2017-06-20 上海理工大学 Spiral magnetorheological finishing device
CN106863020B (en) * 2017-01-20 2019-05-24 上海理工大学 Spiral magnetorheological finishing device
CN108942646A (en) * 2018-07-12 2018-12-07 上海理工大学 Planetary gear type magnetic coupling fluid polishing device
CN109551310A (en) * 2018-12-10 2019-04-02 上海理工大学 A kind of electromagnet type magnetic coupling fluid polishing device
CN110227985A (en) * 2019-05-27 2019-09-13 上海理工大学 The design method of pin type magnetic coupling fluid polishing head core structure
CN110281083A (en) * 2019-06-14 2019-09-27 上海理工大学 A kind of small thin tube inner wall magnetic coupling fluid polishing device
CN110340736A (en) * 2019-06-19 2019-10-18 华中科技大学 A kind of magnetorheological finishing device and method based on flow field focusing

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