JP4741212B2 - Magnetorheological polishing apparatus and method - Google Patents

Abstract

A method of polishing an object is disclosed. In one embodiment, as shown in the figure, the method comprises the steps of creating a polishing zone (10) within a magnetorheological fluid (2); determining the characteristics of the contact between the object and the polishing zone necessary to polish the object (4); controlling the consistency of the fluid (2) in the polishing zone (10); bringing the object (4) into contact with the polishing zone (10) of the fluid (2); and moving at least one of said object (4) and said fluid (2) with respect to the other. Also disclosed is a polishing device (1). In one embodiment, the device comprises a magnetorheological fluid (2), a means (6) for inducing a magnetic field, and a means for displacing the object (4) to be polished or the means (6) for inducing a magnetic field relative to one another.

Description

  The present invention relates to a method for polishing a surface using a magnetorheological fluid.

  For example, glass optical lenses, semiconductors, tubes, and ceramic artifacts have been polished with techniques using a one-piece polishing tool made of resin, rubber, polyurethane, or other solid material. The working surface of the abrasive tool must match the surface of the workpiece. This complicates the polishing composite surface and is difficult to adapt to large scale manufacturing. Furthermore, heat transfer from such solid abrasive tools is generally undesirable, and further results in overheated and deformed workpieces and abrasive tools, and thus the surface of the workpiece and / or the shape of the tool. Will be damaged.

  Co-pending application No. 966,919 filed on October 27, 1992 and co-pending application No. 930,116 filed on Aug. 14, 1992 are the compositions of magnetorheological fluid, magnetic Disclosed are a method of polishing an object using a viscous fluid and a polishing apparatus that can be used in accordance with the disclosed polishing method. Although the method and apparatus disclosed in that application disclose sufficient improvements over the prior art, further improvements that improve the apparatus, method, and results achieved are possible.

  The present invention relates to an improved apparatus and method for polishing objects with a magnetorheological polishing fluid (MP fluid). More particularly, the present invention relates to an automatically controllable and highly accurate method of polishing objects with a magnetorheological fluid and an improved polishing apparatus. The method of the present invention creates a polishing region in a magnetorheological fluid, contacts the object to be polished with the polishing region of the fluid, determines the removal rate of material from the surface of the object to be polished, and provides optimum polishing efficiency. For this purpose, it comprises calculating operating parameters, for example magnetic field strength, rest time and spindle speed, and further moving at least one of the object and the fluid relative to the other according to the operating parameters.

  The polishing apparatus comprises an object to be polished, a magnetorheological fluid contained in or not contained in a container, a means for generating a magnetic field, and at least one component relative to one or more other components. Means for moving. The object to be polished is contacted with a magnetorheological fluid, the magnetorheological fluid, means for generating a magnetic field, and / or the object to be polished is moved and all surfaces of the object are exposed to the magnetorheological fluid.

  In the method and apparatus of the present invention, the magnetorheological fluid is actuated by a magnetic field in the region where the fluid contacts the object to be polished. Due to the magnetic field, the MP fluid gains the characteristics of a plasticized solid whose yield point depends on the strength and viscosity of the magnetic field. The yield point of the fluid is sufficiently high that the fluid forms a suitable abrasive surface and further allows movement of the abrasive particles. The preferred viscosity and elasticity of the magnetorheological fluid provides resistance to the abrasive particles when actuated by a magnetic field, so that the particles have sufficient force to polish the workpiece.

  FIG. 1 is a schematic diagram of a polishing apparatus operated with respect to the method of the present invention. In FIG. 1, a cylindrical container 1 has a magnetorheological polishing fluid (MP fluid) 2. In a preferred embodiment, the MP fluid 2 has an abrasive. The container 1 is preferably composed of a non-magnetic material that is inert to the MP fluid 2. In FIG. 1, the container 1 has a cylindrical shape with a half cross section and has a flat lower portion. However, as will be explained in more detail, the specific shape of the container 1 can be altered to suit the work being polished.

  For example, a tool 13, which is a blade, is disposed in the container 1 and continuously agitates the MP fluid during polishing. The workpiece 4 to be polished is coupled to a rotatable workpiece spindle 5. The production spindle 5 is preferably made of a non-magnetic material. The work spindle 5 is fixed to the spindle feed base 8 and is movable in the vertical direction. The spindle feed 8 can be driven by a conventional servo motor that operates according to electrical signals from a control system 12 that can be programmed.

  The rotation of the container 1 is controlled by a container spindle 3 which is preferably arranged in a central position below the container 1. The container spindle 3 can be driven by a conventional motor or other power source.

  The electromagnet 6 is disposed in the vicinity of the container 1 and can influence the MP fluid 2 in an area in which the product 4 is accommodated. The electromagnet 6 must be capable of producing a magnetic field sufficient to perform polishing, and preferably produces a magnetic field of at least about 100 kA / m. The electromagnet 6 is actuated by a winding 7 from a power supply unit 11 coupled to the control system 12. The electromagnet 6 is installed on an electromagnet feed base 9 and more preferably movable in the horizontal direction along the radial direction of the container 1. The electromagnet feed base 9 can be driven by a conventional servo motor that operates in accordance with electrical signals from a control system 12 that can be programmed.

  The winding 7 is actuated by the power supply unit 11 during polishing, causing a magnetic field and affecting the MP fluid 2. Preferably, the MP fluid is affected by an irregular magnetic field in the area proximate to the workpiece 4. In this preferred embodiment, the lines of equal field strength are perpendicular or perpendicular to the field gradient and the magnetic field force is directed perpendicular to the surface of the product 4 and towards the bottom of the container. Is a slope. Application of a magnetic field from the electromagnet 6 changes the viscosity and plasticity of the MP fluid in the limited polishing region 10 proximate to the surface to be polished. The size of the polishing region 10 is defined by the gap between the pole pieces of the electromagnet 6 and the shape of the tip of the electromagnet 6. Preferably, the abrasive particles of the MP fluid are substantially affected by the MP fluid only in the polishing region 10 and the pressure of the MP fluid against the surface of the workpiece 4 is highest in the polishing region 10.

  The composition of the MP fluid 2 used in the methods and apparatus described herein is preferably co-pending application 966, filed Oct. 27, 1992, incorporated herein by reference. No. 919, copending application No. 966,929 filed October 27, 1992, copending application No. 930,116 filed August 14, 1992, and April 1992 This is described in co-pending application No. 868,466 filed on the 14th. In a preferred embodiment, co-pending application No. 966,919 or 930,116 comprising a plurality of magnetic particles, a stabilizer, and a carrier fluid selected from a collection consisting of water and glycerin. MP fluids constructed according to No. are used. In a more preferred embodiment, the magnetic particles (preferably carbonyl iron particles) are covered with a protective layer of polymeric material that inhibits oxidation. Preferably, the protective layer withstands mechanical stresses and is thin enough to be implemented. In a preferred embodiment, the coating material is Teflon ™. The particles can be coated by conventional methods of microencapsulation.

The polishing apparatus shown in FIG. 1 can operate as follows. The work piece 4 is coupled to the work piece spindle 5 and is arranged by the spindle feed 8 with a clearance h with respect to the lower part of the container 1, and preferably a part of the work piece 4 to be polished is immersed in the MP fluid 2. Is done. The clearance h can be any suitable clearance that allows the workpiece to be polished. Clearance h, as described in Figure 8, affect the removal rate V of the workpiece 4 material, it affects the size of the contact area R _Z further polishing region 10 contacts the workpiece 4. Preferably, the clearance h is selected, the surface area of the contact region R _Z is smaller than one third of the surface area of the workpiece 4. The clearance h can also be changed during the polishing process.

  In a preferred embodiment, both the workpiece 4 and the container 1 are rotated, preferably rotated in opposite directions. The container spindle 3 is rotated, and the container 1 rotates. The container spindle 3 rotates about the central axis and preferably provides sufficient centrifugal force to eject the MP fluid 2 from the container 1 or create splashes, although it is sufficient to effect polishing. The container 1 is rotated at a speed not so high as to occur. In a preferred embodiment, the container is rotated at a constant speed. The movement of the container 1 continuously provides a new part of the MP fluid 2 up to the area where the work piece 4 is arranged, and further the continuous movement of the MP fluid 2 in contact with the surface of the work piece to be polished in the polishing area 10. Bring. In a preferred embodiment, an additional carrier fluid, preferably water or glycerin, is added during polishing to replenish the vaporized carrier fluid and thus maintain fluid properties.

  The production spindle 5 is also rotated around the central axis, giving the production 4 a rotational movement. In a preferred embodiment, the production spindle 5 operates at speeds up to 2000 rpm, with about 500 rpm being particularly preferred. The movement of the work piece spindle 5 continuously brings a new part of the surface of the work piece 4 into contact with the polishing area 10, so that the removal of the material along the periphery of the surface to be polished is approximately regular. Become.

  Since the abrasive particles of the MP fluid 2 are in contact with the polishing region, the annular region having the width of the polishing region is gradually polished to the surface of the product 4. Polishing is accomplished in one or more cycles, with each cycle removing an incremental amount of material from the workpiece. Polishing of the entire surface of the product 4 is achieved by moving the electromagnet 6 in the radial direction by using the electromagnet feed base 9, and the electromagnet feed base 9 forms a polishing region 10 with respect to the surface of the product. Moved.

The radial movement of the electromagnet 6 can be a continuous or discontinuous step. If movement of the electromagnet 6 is continuous, a suitable speed U _Z electromagnets 6 for each point of movement of the track is calculated. Speed U _Z electromagnets can be calculated according to the following equation.

(I) U _Z = 2R _Z / t
Or (II) U _Z ≦ 2R _Z V / k ₃
Here, R _Z is the radius (mm) of the contact area of the polishing area in contact with the product 4, t is the time (second) in which the contact area R _Z is polished in one cycle, and V is the material removal rate (μm). / min), and k ₃ is the thickness of the material layer of the workpiece to be removed during one cycle of polishing ([mu] m).

R _Z is a function of clearance h, as described above. The material removal speed V can be determined empirically from the clearance h and the speed at which the container 1 is rotated. The material removal rate V can be determined by measuring the amount of material removed from a point in time. The thickness k ₃ of the workpiece material layer that is removed during one polishing cycle is a function of the accuracy required for the finished workpiece, and k ₃ is selected to minimize local error accumulation. Can be done. For example, if the optical glass is polished, the value of k ₃ are determined by the suitability for the required wave shape. Time contact area R _Z is polished in one cycle is calculated according to the following equation.

t ≦ k ₃ / V
If k ₃ and the velocity U _Z of the magnet is determined, it is possible that the time required for the number of cycles and polishing required is determined. In order to calculate the total number N of cycles for polishing the workpiece 4, the thickness K of the material layer removed during polishing is calculated according to the following formula:

K = k ₁ + k ₂
Here, k ₁ is the initial surface roughness (μm), and k ₂ is the thickness (μm) of the damaged layer under the surface. Thus, the required number of cycles N can be determined using the following equation:

N = K / k ₃
The time t _c required for each cycle can be calculated using the following equation:

t _c = R _W / U _Z
Here, R _W is the radius of the workpiece. FIG. 5 shows the relationship between the product radius R _W , the contact area R _Z , the clearance h, and the speed U _Z of the magnet of a flat product, for example as shown in FIG.

  The total time T required for polishing can be calculated using the following equation.

T = NR _W / U _Z
Here, N number of cycles required, R _W is the workpiece radius, the U _Z is the speed of the electromagnet 6.

If the electromagnet 6 is moved in individual steps, the rest time of each step must be determined. In a preferred embodiment, the removal of all material is kept constant at each step. In order to remove a certain amount of material during gradual polishing, it must be taken into account that the contact region _RZ is overlapped and removed in successive steps. The overlap coefficient I is determined by the following equation.

I = r / 2R _Z
Here, r is the displacement (mm) of the product in one step, and R _Z is the radius of the contact area. The displacement r in one step can be determined empirically using results from preliminary tests, for example as detailed in the following example.

The rest time t _d of each step in a cycle can be determined according to the following equation:

t _d = k ₃ I / V
Here, k ₃ is the thickness of the workpiece material layer to be removed during one cycle of polishing, I is an overlap factor, V is, the workpiece at a rate of some clearance h and the container 1 This is the material removal rate V.

, The number of steps n _s in a cycle for stepwise polishing may be determined using the following equation.

n _s = R _W / r
Here, R _W is the radius of the workpiece, r is a workpiece displacement per step. The total number N of cycles required to polish the workpiece can be calculated using the following formula used for continuous polishing.

N = K / k ₃
Here, K is the thickness of the material layer to be removed during polishing, k ₃ is the thickness of the material layer of the workpiece to be removed during one cycle of polishing. The total time T required for stepwise polishing is calculated using the following formula:

T = t _{dn s} N
Here, t _d is the stationary time of each step, n _s is the number of steps in one cycle, and N is the total number of cycles.

  In a preferred embodiment of the invention, the computer program of the control unit 12 can be prepared on the basis of these calculations for continuous or stepwise polishing. Thus, the entire process of polishing the workpiece 4 can be processed under automatic control. As shown in FIG. 1, the control unit 12 preferably includes an input device 26, a processing unit 27, and a signal transmission device 28.

In another embodiment of the present invention, the precision of generation of the shape, or match finished workpiece to the required shape and tolerances, the removal of the material as a function V of R _Z in the contact area R _Z [R _Z] Improvements can be made by performing tests to determine the spatial distribution of velocities. The spatial distribution of the removal rate can be determined by a continuous approximation method, which is described in detail in the following example and FIG. Thus, the spatial distribution of the removal rate can be used to more accurately determine the parameters of the polishing program, for example the rest time t _d using the above-described equation. In this case, the rest time can be determined using the following equation:

t _d = k ₃ I / V [R _Z ]
Referring to FIG. 2, another embodiment of the present invention is shown. This embodiment achieves very effective polishing of convex work pieces, for example spherical and non-spherical optical lenses. In FIG. 2, the container 201 is a circular recess, and the radius of the curved portion of the inner wall proximate to the polishing region 210 is greater than the largest radius of the curved portion of the workpiece 204. During polishing, it is desirable to minimize the movement of the fluid 202 with respect to the container 201. In order to minimize this movement or slip of the MP fluid 202, the inner wall of the container 201 can be covered with a layer of nap or porous material 215, and the MP fluid 202 and the wall of the container 201 Provides a reliable mechanical adhesive between.

  The product spindle 205 is coupled to a spindle feed 208 coupled to a rotatable table 216. The rotatable table 216 is coupled to a table feed base 217. The spindle feed 208, the rotatable table 216, and the table feed 217 can be driven by a conventional servo motor that operates according to electrical signals from a control system 212 that can be programmed. With the rotatable table 216, the production spindle 205 can swing continuously around the horizontal axis 214, or can be arranged at an angle α with respect to the initial vertical axis 218 of the spindle 205. Preferably, the shaft 214 is located in the middle of the curvature of the surface to be polished in the initial vertical position of the production spindle. The spindle feed 208 allows the center of the curved portion of the surface to be polished to be moved vertically by δ with respect to the axis 214. The table feed 217 moves on a rotatable table 216 having a spindle feed 208 and a work spindle 205 to provide the necessary clearance between the surface of the work 204 to be polished and the lower part of the container 201. Earn and maintain. In this embodiment, the electromagnet 206 is stationary and disposed below the container 201 so that when the production spindle shaft 218 is perpendicular to the surface of the polishing area 210, the magnetic gap is Symmetric about the axis. The apparatus described in FIG. 2 is similar to the apparatus shown in FIG. 1 in all other respects.

  The polishing apparatus operates as follows. When the product 204 attached to the product spindle 205 is disposed to polish the product 204, the center of the radius of the curved portion of the product 204 is the rotational position (rotation) of the rotatable table 216. Is aligned with axis 214). The removal rate of the product to be polished is then determined empirically using a test product similar to the product to be polished. Subsequent polishing of the workpiece 204 is then performed automatically by moving its surface with respect to the polishing area 210 using a rotatable table 216 that swings the workpiece spindle 205. Move and change the angle α according to the calculated processing regime.

  The maximum angle α at which the spindle 205 is swung is determined using the following equation:

cos α _max = (R _sf −L) / R _sf
Here, R _sf is the radius of the entire sphere. As shown in FIG. 6, R _sf represents what the radius of the product is based on the radius of the curved portion of the actual product 204 when the product is a spherical surface. L represents the thickness of the workpiece 204 as shown in FIG. 6, and L is calculated using the following equation:

L = R _sf −R _sf ² −R _W ²
Furthermore, the angular dimension β of the contact area shown in FIG. 6 can be determined using the following equation:

cos β = (R _sf −h ₀ ) / R _sf
Here, R _sf is the radius of the entire sphere, and h ₀ is the clearance between the lower part of the container 201 and the end of the contact area R _Z of the curved product as shown in FIG. . The height h ₀ of the contact area can be determined using the following equation:

h ₀ = R _sf −R _sf ² −R _Z ²
Here, R _sf is the radius of the entire sphere, and R _Z is the width of the contact area.

The swing of the production spindle 205 can be continuous or stepwise. When the workpiece spindle 205 is swung in succession, the angular velocity omega _Z of this movement is determined by the following equation.

ω _Z ≧ βV / k ₃
Where β is the angular dimension of the contact area, V is the material removal rate, and k ₃ is the thickness of the material layer of the workpiece that is removed during one polishing cycle. Thus, the duration t _c of a cycle can be calculated using the following equation:

t _c = α _max / ω _Z
Here, α _max is the maximum angle α at which the spindle 205 is swung, and ω _Z is the angular velocity of the rocking motion.

  In order to calculate the total number of cycles N for polishing the workpiece 204, the thickness of the material layer removed during polishing is calculated according to the following equation:

K = k ₁ + k ₂
Here, k ₁ is the initial surface roughness (μm) and k ₂ is the thickness (μm) of the damaged subsurface layer. Thus, the required number of cycles N is determined using the following equation:

N = K / k ₃
Here, k ₃ is the thickness of the material layer of the workpiece to be removed during one cycle of polishing.

  Therefore, the total time T required to polish the product can be calculated using the following formula:

T = t _c N
Here, t _c is the duration of one cycle and N is the number of cycles required.

  If the production spindle 205 is swung in individual steps, the rest time of each step must be calculated. When calculating the stationary time of each step, it is necessary to consider the overlap coefficient I. The overlap coefficient I is determined by the following equation.

I = α _s / β
Where β is the angular dimension of the contact area and α _s is the angular displacement per step. The angular displacement α _s per step can be calculated by the following equation.

α _s = α _max / _ns
Here, α _max is the maximum angle α at which the spindle 205 is swung, and n _s is the number of steps per cycle. The number of steps per cycle can be calculated using the following formula:

n _s = α _max / β
Here, α _max is the maximum angle α at which the spindle 205 is swung, and β is the angular dimension of the contact area. The current angle during polishing can be calculated using the following formula:

α = α _s N _s
Here, α _s is the angular displacement per step, and N _s is the current number of steps.

  In order to calculate the total number of cycles to polish the workpiece 204, the thickness of the material layer removed during polishing is calculated according to the following equation:

K = k ₁ + k ₂
Here, k ₁ is the initial surface roughness (μm) and k ₂ is the thickness (μm) of the damaged layer under the surface. Thus, the required number of cycles N can be determined using the following equation:

N = K / k ₃
Here, k ₃ is the thickness of the material layer of the workpiece to be removed during one cycle of polishing.

  The quiesce time of each step can be calculated using the following formula:

t _d = k ₃ I / V
Here, k ₃ is the thickness of the material layer of the workpiece to be removed during one cycle of polishing, I is an overlap factor, V is a rate of removal of material. Therefore, the total time T required to polish the product can be calculated using the following formula:

T = t _{dn s} N
Here, t _d is the stationary time of each step, n _s is the number of steps per cycle, and N is the required number of cycles.

  If it is required that the shape of the surface cannot be changed, or that a specific material removal target at each location on the surface can be achieved by changing the rest time, polishing is performed from each location on the surface. This is done under conditions that evenly remove material.

  When the aspheric product 204 is polished, the procedure is generally the same as that described for the spherical product. The aspherical workpiece 204 can be polished to the required shape by changing the rest time depending on the radius of curvature of the part of the workpiece to be polished. In another embodiment of polishing an aspheric workpiece, the workpiece spindle 205 is also movable vertically during polishing. In order to polish an aspherical object, the calculations described above can be achieved for each part of the work piece having a different radius of curvature. When the product is swung to an angle α, the radius of the curved portion of the part of the aspheric product to be polished changes. In order to match the instantaneous radius of the curved portion of the part of the workpiece 204 to be polished to the rotational position 214, the spindle of the workpiece spindle 205 is rotated when the aspherical object is polished. Is accompanied by a vertical motion.

  Furthermore, if necessary, the strength of the magnetic field can also be changed at each processing stage during polishing. The material removal rate V is a function of the magnetic field strength G, as shown in FIG. It is therefore possible to change the amount of the operating parameter, for example the resting time or the clearance. Thus, the strength of the magnetic field can be used as another means of controlling the polishing process.

Referring to FIG. 3, another embodiment of the present invention is shown. In FIG. 3, the inner wall of the container 301 has an additional circular recess that extends through the gap of the electromagnet 306. This configuration of the inner wall of the container 301 results in a smaller and more concentrated polishing region 310 and further achieves increased adhesion between the MP fluid 302 and the container 301. Smaller, the more concentrated abrasive region, a smaller contact area R _Z is provided. In all other respects, the embodiment shown in FIG. 3 is similar to the embodiment shown in FIG.

Example 1
Glass lens polishing was accomplished using the apparatus shown in FIG. The product 204 has the following initial parameters.

a) Glass type ... BK7
b) Shape ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ Spherical surface c) Diameter, mm ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ 20
d) Radius of the curved part, mm ... 40
e) Center thickness, mm ... 15
f) Initial suitability for shape, wave ... 0.5
g) Initial surface roughness, nm, rms ... 100
A container 201 in which the radius of the curved portion of the inner wall adjacent to the electromagnet pole piece 206 is 200 mm was used. The radius from the central axis 219 was 145 mm, and the width of the container recess was 60 mm. Container 201 was filled with 300 ml of MP fluid 202 having the following composition.

Ingredient Weight percentage Polirit (cerium oxide) 10
Carbonyl iron powder 60
Aerosil (fumed silica) 2.5
Glycerin 5.5
Distilled Water Residue To determine the material removal rate, a test product 204 identical to the product to be polished was polished with arbitrarily selected standard parameters. The test product is attached to the product spindle 205 and placed by the spindle feed 208 and the distance between the surface of the product to be polished and the rotational position of the rotatable table 216 (shaft 214) is , 40 mm (radius of the curved portion of the surface of the manufactured product 204). Using a rotatable table 216, the axis of rotation of the workpiece 205 was adjusted to a vertical position with an angle α = 0 °. The clearance h between the surface of the workpiece 204 to be polished and the lower part of the container 201 was adjusted to 2 mm using a table feed base 217.

  Subsequently, both the production spindle 205 and the container 201 were rotated. The rotation speed of the production spindle was 500 rpm, and the rotation speed of the container was 150 rpm. An electromagnet 206 with a magnetic gap equal to 20 mm was operated at a level where the strength of the magnetic field near the surface of the workpiece was about 350 kA / m. All parameters were kept constant and the workpiece was polished for about 10 minutes, sufficient to produce a clear area.

  Next, the product was removed from the product spindle 205. Measurements were then made using an appropriate optical microscope to determine the amount of material removed from the original surface, H (μm), as a function of distance R (mm) from the center of the product. In the example described here, a Chapman Instrument MP2000 optical profiler was used to measure the amount of material removed. Depending on the available metrology, about 20 measurements are made over a distance of 20 mm. In this example, 16 measurements were taken over 19.7 mm. The results of these measurements for this example are depicted in FIG. These results define the polishing area of the installed machine and are used as input values for the calculation of the polishing program required to complete the product. The input values obtained in this example for the calculation of the polishing program are as follows:

1. Product parameters:
a) Radius of the entire spherical surface, R _sf , mm ... 39.6
b) Radius of the work, R _W , mm ... 24.3
2. Polishing area parameters:
a) Radius of the contact area, R _Z , mm... 17.9
b) (d / dr) (dH / dr) = 0, R _d , mm
Position radius ... 10
c) Maximum value of H, H _max , μm 21.5
d) Minimum value of H, H _min , μm 0.5
3. Spatial distribution of removed material in the polishing area:
R, mm H, μm
0.0 15.2
3.3 19.5
5.1 21.5
6.4 20.9
7.5 19.2
8.9 16.8
10.8 11.9
12.4 9.8
13.8 6.7
15 5.1
16.2 3.8
17.2 3.0
18.2 1.9
18.6 1.3
19.3 1.3
19.7 0.5
These input values are used to determine the polishing required to complete the product. In the preferred embodiment of the present invention, a computer program is used to calculate the necessary parameters and control the operation of the polishing. The determination of the polishing requirements includes the determination of the number of steps to change the angle α, the value of the angle α of each step, and the rest time of each step, and as a result, as described above, due to overlapping polishing regions. The removal of material on the surface of the work is kept constant.

  The parameters of the example workpiece, the parameters of the polishing area, and the spatial distribution of the removed material in the polishing area are used to control the system during the polishing method. In this example, the results were entered into a computer program for this purpose. The calculation results were as follows.

Polishing regime
Table 1
Angle α Time coefficient Control radius, mm
0.00 1.000 0.00
1.79 1.000 1.25
3.58 1.000 2.49
5.37 1.000 3.74
7.16 1.000 4.98
8.95 1.000 6.22
10.74 1.208 7.45
12.53 1.208 8.68
14.32 1.208 9.89
16.11 1.416 11.10
17.90 1.624 12.29
19.70 1.832 13.48
21.49 2.040 14.65
23.28 2.040 15.81
25.07 2.040 16.95
26.86 1.624 18.07
28.65 1.832 19.18
30.44 38.119 20.26
As used herein, the control radius represents the relative position of the polishing area relative to the central vertical axis of the workpiece. The control radius is determined by the angle α, and during polishing, the control radius is determined by the angle α rather than the controlled control radius.

  The rest time for each angle is then converted to minutes by increasing the time factor in Table 1 by a constant. The constant used to convert the time factor to rest time depends on the characteristics of the product. In this example, this invariant was empirically determined to be 5 minutes.

  Using the results from Table 1, the controller 212 that can be created into a program was programmed. The work piece 204 to be polished was attached to the work piece spindle 205 and the described procedure for the test work piece was repeated under the automatic control of the controller 212, which can be programmed. The following results were obtained.

Polishing result Final conformity to shape, wave ... 1
Final roughness, μm ・ ・ ・ 0.0011
In addition to the embodiments described above, there are multiple alternative embodiments of the device of the present invention. Some of these alternative embodiments are shown in FIGS. As shown by these figures, only the magnetorheological fluid, the means for causing the magnetic field, and the means for moving the object to be polished or the means for causing the magnetic field relative to each other are necessary for the construction of the apparatus according to the invention. For example, FIGS. 9-11 illustrate embodiments of the present invention in which the magnetorheological fluid is not contained in a container.

  In FIG. 9, the MP fluid 902 is disposed on the pole piece of the electromagnet 906. The electromagnet 906 is arranged so that the magnetic field produced by the electromagnet 906 acts only on the specific surface portion of the object 904 to be polished, creating a polishing area. In operation, the object 904 is rotated. Subsequently, either the electromagnet 906 and the object 904 or both the electromagnet 906 and the object 904 are moved, and as a result, the entire surface of the object is polished stepwise. The electromagnet 906, the object to be polished 904, or both can move in a vertical and / or horizontal plane with respect to each other. During polishing, the strength of the magnetic field is also adjusted as necessary to polish the object 904. The rotation of the object 904 according to a predetermined program of polishing, the movement of the electromagnet 906 and / or the object 904, and the adjustment of the strength of the magnetic field control the removal of material from the surface of the object 904 to be polished.

  FIG. 10 illustrates an apparatus for polishing a curved surface. In FIG. 10, the MP fluid 1002 is disposed on the pole piece of the electromagnet 1006. The electromagnet 1006 is configured to generate a magnetic field that affects only some surface portions of the object 1004 to be polished. The object 1004 to be polished having a spherical or aspherical surface is rotated. The electromagnet 1006 is moved by an angle α along a trajectory corresponding to the radius of the curved portion of the object 1004, as shown by the arrow in FIG. 10, so that the electromagnet is applied to the surface of the object according to a predetermined polishing program. Is moved in parallel, thus controlling the removal of material along the partial surface.

  In FIG. 11, the MP fluid 1102 is further disposed on the pole piece of the electromagnet 1106. The electromagnet is configured to generate a magnetic field that acts only on some surface portions of the object 1104 to be polished. In operation, the polished object 1104 having a spherical or aspheric surface is rotated. Subsequently, the object 1104 to be polished is swung, and as a result, the angle α shown in FIG. 11 changes from 0 to a value depending on the size and shape of the product. By swinging the workpiece 1104 with respect to the electromagnet 1106 and thus changing the angle α with respect to a predetermined polishing program, the removal of material along the surface of the object to be polished is controlled.

  In FIG. 12, the MP fluid 1202 is disposed in the container 1201. An electromagnet 1206 is disposed and configured under the container 1201 to cause a magnetic field that affects only a portion of the MP fluid 1202 in the container 1201 or the polishing region 1210. The MP fluid in the polishing region 1210 requires plastic properties to effectively remove material in the presence of a magnetic field. The object to be polished 1204 is rotated and the electromagnet 1206 is moved along the surface to be polished. The workpiece can then be polished according to a predetermined program that controls the removal of material along the surface of the object to be polished.

  In FIG. 13, the MP fluid 1302 is disposed in the container 1301. The electromagnet 1306 is configured to cause a magnetic field that affects only a portion of the MP fluid 1302 or the polishing region 1310. Accordingly, the MP fluid 1302 only affects the portion of the object 1304 to be polished disposed in the polishing region 1310. The object to be polished 1304 and the container 1301 with matching axes are rotated in the same or opposite direction at a constant or different speed. By rapidly moving the electromagnet 1306 along the surface of the container according to the assigned program, the polishing region 1310 is moved and the removal of material along the surface of the object to be polished is controlled.

  In FIG. 14, the MP fluid 1402 is disposed in the container 1401. A casing 1419 that houses a system of permanent magnets 1406 is placed under the container 1401. The electromagnetic field produced by each magnet 1406 only affects a portion of the object being polished or the polishing area 1410. In operation, the object to be polished 1404 and the container 1401 are rotated simultaneously. The rotational axes of the object 1404 to be polished and the container 1401 are eccentric with respect to each other. The casing 1419 or the object to be polished 1404 or both are moved simultaneously in accordance with a predetermined program of polishing to control the removal of material along the surface of the object to be polished.

  In FIG. 15, the MP fluid 1502 is disposed in the container 1501. The electromagnet 1506 is placed under the container so that the magnetic field of the electromagnet affects only a portion of the MP fluid 1502 in the container 1501 or the polishing region 1510. The object 1504 to be polished having a spherical or curved shape and the container 1501 are rotated in the same or opposite directions. During polishing, the object 1504 is oscillated and the angle α shown in FIG. 15 changes from 0 to a value that depends on the size and shape of the object 1504. The rotation of the object 1504 and the container 1501 and the angle α are controlled according to a predetermined polishing program. As a result, the removal of material along the surface of the object being polished is controlled.

  In FIG. 16, the MP fluid 1602 is placed in a longitudinal container 1601. The shape of the recesses inside the container 1601 is selected parallel to the surface of the object 1604, and the inner wall of the container is equidistant from the generatrix of the object 1604 when α = 0. The electromagnet 1606 is disposed below the container 1601 and causes a magnetic field in a portion of the MP fluid 1602 or the polishing region 1610. In operation, the electromagnet 1606 is moved along the bottom of the container 1601 and the object 1604 and container 1601 are rotated. Furthermore, the object is swung to an angle α during the polishing program. The removal of material from the surface of the object 1604 to be polished is controlled by rotation of the object 1604 and container 1601, movement of the electromagnet 1606, and swinging of the object 1604 according to a predetermined polishing program.

  In FIG. 17, the MP fluid 1702 is placed in a circular container 1701 with an annular recess. The electromagnet 1706 is disposed under the container 1701. An electromagnet 1706 is selected and the magnetic field of the electromagnet affects a portion of the MP fluid 1702 or the polishing region 1710. The object to be polished 1704 and the container 1701 are rotated at the same speed or different speeds in the same or opposite directions. The rapid movement of the electromagnet 1706 along the bottom of the annular recess of the container 1701 in accordance with the polishing program controls the removal of material along the surface of the object 1704 being polished.

  In FIG. 18, the MP fluid 1802 is disposed in a circular container 1801 with an annular recess. The lower part of the container is covered with nap material 1815, which prevents slippage of MP fluid 1802 relative to the lower part 1801 of the container and further increases the rate of material removal from the surface of the object. The electromagnet 1806 is disposed under the concave portion 1801 of the container. The pole pieces of the electromagnet 1806 are selected and the magnetic field of the electromagnet affects only a portion of the MP fluid or the polishing region 1810, and therefore the electromagnet 1806 affects only the portion of the surface of the object 1804 being polished.

  The object to be polished 1804, the longitudinal container 1801, or both are rotated in the same or opposite direction at constant or different speeds. Further, the electromagnet 1806 is moved relative to the surface of the object 1804 to be polished according to a polishing program.

  In FIG. 19, the MP fluid 1902 is disposed in an annular recess of a circular container 1901. The radius of the curved portion of the concave portion of the container is selected corresponding to the radius of the curved portion of the necessary object 1904 after polishing, and the inner wall of the concave portion 1901 is equidistant to the surface of the object 1904 to be polished. The object to be polished 1904 and the container 1901 disposed on the spindle 1905 are rotated in the same or opposite direction at a constant speed or different speeds. The electromagnet 1906 is moved along the bottom of the container recess 1901 in accordance with a predetermined program to control the removal of material along the surface of the object to be polished.

  In FIG. 20, the MP fluid 2002 is further placed in a circular 2001 container with an annular recess. The electromagnet 2006 is disposed under the container 2001. The pole pieces of the electromagnet 2006 are selected such that the electromagnet's magnetic field affects only a portion of the MP fluid 2002 or the polishing region 2010, and therefore the electromagnet's magnetic field affects only the surface portion of the object 2004 being polished. .

  The object to be polished 2004 and the container 2001 are rotated in the same or opposite direction at a constant speed or at different speeds. Further, the object 2004 to be polished is rocked with respect to the container. The object is rocked from a vertical position to an angle α during polishing according to a predetermined program to control the removal of material along the surface to be polished.

  In FIG. 21, the MP fluid 2102 is placed in a circular container 2101 with an annular recess having a recess 2120. The pole pieces of the electromagnet 2106 are selected such that the magnetic field of the electromagnet affects only a portion of the MP fluid 2101 or the polishing region 2110. In FIG. 21, that portion of the MP fluid 2102 that is affected by the magnetic field is located within or on the indentation 2120.

  The object 2104 to be polished is rotated. Furthermore, the object 2104 to be polished is rocked to an angle α with respect to an axis perpendicular to the plane of rotation of the container according to the assigned program, and the removal of material along the surface of the object to be polished is controlled.

  In FIG. 22, the MP fluid 2202 is placed in a cylindrical container 2201. The objects 2204a, 2204b, etc. to be polished are fixed to the spindles 2205a, 2205b, etc., and the spindles 2205a, 2205b, etc. are fixed to a disk 2221 that can rotate in a horizontal plane. An electromagnet 2206 is attached under the container and produces a magnetic field along the entire surface of the container 2201.

  The disk 2221, the container 2201, and the objects to be polished 2204a, 2204b are rotated at the same speed or different speeds in the same or opposite directions. By adjusting the strength of the magnetic field and the rotation of the disk, container, and object, the rate of material removal from the surface of the object being polished is controlled.

  In FIG. 23, the MP fluid 2302 is placed in the container 2301. The electromagnet 2306 is attached below the lower portion of the container. The pole pieces of the electromagnet are selected and the electromagnet produces a magnetic field that affects only a portion of the MP fluid 2302 in the container 2301 or the polishing region 2310. The objects to be polished 2304a, 2304b, etc. are fixed to the spindles 2305a, 2305b, etc., and the spindles 2305a, 2305b, etc. can rotate with respect to the disk 2321 and are mounted on the disk 2321. Further, the disk 2321 is rotatable with respect to the container 2301.

  The disk 2321, the objects to be polished 2304a, 2304b, etc., and the container 2301 are rotated in the same or opposite direction at the same speed or different speeds. Furthermore, the electromagnet 2306 is quickly moved along the surface of the container. This rotation and movement of the electromagnet 2306 along the surface of the container is adjusted to control the removal of material from the surface of the object being polished.

  In FIG. 24, the MP fluid 2402 is disposed in the container 2401. The electromagnets 2406a, 2406b, etc. are arranged near the bottom of the container. The pole pieces, such as electromagnets 2406a, 2406b, are selected to create a field where each electromagnet affects only a portion of the container fluid 2402, or the polishing regions 2410a, 2410b, etc. The objects to be polished 2404a, 2404b, etc. are disposed on the spindles 2405a, 2405b, etc., and the spindles 2405a, 2405b, etc. are rotatable with respect to the disc 2421 to be attached. The disc 2421, the objects to be polished 2404a, 2404b, etc., and the container 2401 are rotated in the same or opposite directions at the same speed or different speeds. Furthermore, the electromagnets 2406a, 2406b, and the like are moved in the radial direction along the lower surface of the container 2401. This rotation and movement of electromagnets 2406a, 2406b, etc. along the surface of the container are adjusted to control the removal of material from the surface of the object to be polished.

  In FIG. 25, the MP fluid 2502 is placed in a circular container 2501 with an annular recess. The objects 2504a and 2504b to be polished are arranged on the spindles 2505a and 2505b. Electromagnets 2506a, 2506b, etc. are placed under the container 2501, and the magnetic field induced in the electromagnet affects the total volume of the MP fluid and the entire surface of the object to be polished. The container 2501 and the objects to be polished 2504a, 2504b, etc. are rotated at the same speed or different speeds in the same or opposite directions. Furthermore, the strength of the magnetic field caused by the electromagnet is also controlled. As a result, the removal of material from the surface of the object to be polished is controlled.

  In FIG. 26, the MP fluid 2602 is placed in a circular container 2601 with an annular recess. The objects to be polished 2604a, 2604b, 2604c, 2604d, etc. are arranged on the spindles 2605a, 2605b, 2605c, 2605d, etc., and the spindles 2605a, 2605b, 2605c, 2605d, etc. are attached to a disk 2621 which can rotate in a horizontal plane. .

  Electromagnets 2606a, 2606b, etc. are attached below the surface of the container. The pole pieces of the electromagnet are selected and the electromagnet creates a magnetic field across the full width of the container.

  By rotating the container 2601, the disk 2621, and the object to be polished 2604a, 2604b, 2604c, 2604d at the same speed or different speeds in the same or opposite directions, the removal rate of the material with a certain magnetic field strength is controlled.

  In FIG. 27, the MP fluid 2702 is disposed in a circular container 2701 having an annular container. The electromagnet 2706 causes a magnetic field along the entire surface of the container 3501. The objects to be polished 2704a, 2704b, 2704c, 2704d and the like are arranged on the spindles 2705a, 2705b, 2705c, 2705d and the like. The spindles 2705a, 2705b, 2705c, 2705d, and the like are disposed on disks 2721a, 2721b, and the like that can rotate in a horizontal plane. The disks 2721a, 2721b, etc. are arranged on the spindles 2724a, 2724b, etc. This figure illustrates one concept that allows multiple objects to be polished simultaneously.

  In FIG. 28, the MP fluid 2802 is disposed within the container 2801. Two units 2822a and 2822b with permanent magnets 2823 are attached to the inside of the container 2801.

  A flat object 2804 to be polished is disposed between the units 2822a and 2822b. Units 2822a and 2822b are rotated about a horizontal axis. These units are rotated at a constant speed, and the magnetic field and polishing region 2810 are created when pole pieces of different signs are positioned opposite each other. The object 2804 to be polished is moved so that the polishing area is fabricated on both surfaces of the object. The material removal rate is controlled by the rotational speed of the units 2822a, 2822b and the speed at which the object 2804 is moved vertically.

  In FIG. 29, MP fluid 2902 is placed in a container 2901. A unit 2922 having a magnet 2923 is disposed inside the container and is rotatable along an axis perpendicular to the moving direction of the object 2904 to be polished. The magnets are arranged in units, and the permanent magnets arranged in parallel have pole pieces with different signs with respect to each other, and a polishing region 2910 is produced between the magnets.

  Polishing is accomplished by rotating unit 2922 and applying a scanning motion to object 2904 to be polished in a vertical plane. The material removal rate is controlled by changing the rotational speed of the unit 2922 and the speed at which the object to be polished is moved.

  FIG. 30 illustrates an apparatus for polishing a spherical object. Objects 3004a, 3004b, etc. are placed in a groove 3025 formed between the top container 3001b and the lower container 3001a. The groove 3025 is filled with an MP fluid 3002 that is affected by the magnetic field caused by the electromagnet 3006. In operation, the top container 3001a and the lower container 3001b are rotated in opposite directions. When the MP fluid 3002 rotates together with the containers 3001a and 3001b, the spherical object is polished.

It is a side view of the section of the polish device of the present invention. It is a side view of the cross section of other embodiment of this invention. It is a side view of the cross section of other embodiment of this invention. FIG. 6 is a graph showing the amount of material removed as a function of distance from the center of a product for a typical product. FIG. 6 is a schematic diagram illustrating parameters used in the method of the present invention for controlling the polishing of a flat workpiece. FIG. 4 is a schematic diagram illustrating parameters used in the method of the present invention for controlling the polishing of a curved workpiece. It is a graph which shows the relationship between the removal speed of the material in the case of grinding | polishing, and the intensity | strength of a magnetic field. It is a graph which shows the relationship between the removal speed of the material in the case of grinding | polishing, and the clearance between the lower part of the container where the product is manufactured and a product is polished. It is a side view of the cross section of other embodiment of this invention. It is a side view of the cross section of other embodiment of this invention. It is a side view of the cross section of other embodiment of this invention. It is a side view of the cross section of other embodiment of this invention. It is a side view of the cross section of other embodiment of this invention. It is a side view of the cross section of other embodiment of this invention. It is a side view of the cross section of other embodiment of this invention. It is a side view of the cross section of other embodiment of this invention. It is a side view of the cross section of other embodiment of this invention. It is a side view of the cross section of other embodiment of this invention. It is a side view of the cross section of other embodiment of this invention. It is a side view of the cross section of other embodiment of this invention. It is a side view of the cross section of other embodiment of this invention. It is a side view of the cross section of other embodiment of this invention. It is a side view of the cross section of other embodiment of this invention. It is a side view of the cross section of other embodiment of this invention. It is a side view of the cross section of other embodiment of this invention. It is a side view of the cross section of other embodiment of this invention. It is a side view of the cross section of other embodiment of this invention. It is a side view of the cross section of other embodiment of this invention. It is a side view of the cross section of other embodiment of this invention. It is a side view of the cross section of other embodiment of this invention.

Claims (54)

Positioning the work piece with clearance from the surface adapted to hold a magnetic viscous fluid including magnetic particles, a layer of protective material to inhibit oxidation of the magnetic particles, a stabilizer and a carrier fluid;
Introducing the flow of the magnetorheological fluid through the clearance;
A magnetic field is generally applied to the clearance to create a polishing or machining area in the magnetorheological fluid, the area engaging a portion of the surface of the workpiece to remove material in the portion. Forming a tool, said area engaging the surface of the work piece in an area smaller than the area of the surface of the work piece to be finished,
The product or the region is moved relative to each other so that different portions of the surface of the product are exposed to the region for a predetermined rest time, thereby predetermining those portions of the surface of the product. To be selectively finished to the degree,
Including steps,
A method of finishing a work using a magnetorheological fluid.   The method of claim 1, wherein the magnetorheological fluid includes non-magnetic abrasive particles to facilitate material removal at the surface of the workpiece.   The method according to claim 1, further comprising circulating the magnetorheological fluid by reintroducing the magnetorheological fluid circulated through the clearance through the clearance.   The method according to claim 3, further comprising agitating the magnetorheological fluid circulated through the clearance.   The method of claim 4, wherein the magnetorheological fluid includes a carrier fluid and further includes the step of adding the carrier fluid to the magnetorheological fluid to restore the evaporated carrier fluid.   The step of introducing the flow of the magnetorheological fluid through the clearance deposits the magnetorheological fluid on the surface adapted to hold the magnetorheological fluid and moves the surface with respect to the product to move the magnetorheological The method of claim 1 including the step of causing a fluid to flow through the clearance.   The step of holding the magnetorheological fluid includes a lower surface of a bowl-shaped body having a donut shape, and the step of moving the surface adapted to hold the magnetorheological fluid comprises: The method of claim 6 including the step of rotating the rod.   The method of claim 1, wherein applying a magnetic field comprises maximizing the magnetic field of the clearance.   The method of claim 1, further comprising rotating the workpiece with respect to the region.   The product is mounted on a pivoting product holder, and the step of moving the product or the region with respect to each other pivots the product holder so that the surface of the product is in the region. 2. The method of claim 1, including the step of allowing the sweep to cross.   The method of claim 1, wherein moving the product or the region with respect to each other comprises moving the product along a plane.   The method of claim 11, wherein moving the product along a plane includes moving the product along a plane generally perpendicular to the direction of flow of the magnetorheological fluid through the clearance.   The method of claim 1, wherein moving the product or the region with respect to each other comprises moving the region by moving a magnetic field with respect to the surface adapted to hold a magnetorheological fluid. A surface for holding a volume of magnetorheological fluid including magnetic particles, a layer of protective material for inhibiting oxidation of the magnetic particles, a stabilizer, and a carrier fluid;
A workpiece holder for holding and positioning the workpiece with clearance from the surface, thereby causing the surface to generate a flow of the magnetorheological fluid through the clearance;
In the magnetorheological fluid flowing through the clearance by applying a magnetic field to the clearance to engage a portion of the surface of the work piece and form a temporary tool to remove material at the portion. A magnet for producing a machined or polished area, wherein the area is engaged with the surface of the workpiece in a smaller area than the area of the surface of the finished workpiece;
The product or the region is moved relative to each other so that different portions of the surface of the product are exposed to the region for a predetermined rest time, thereby predetermining those portions of the surface of the product. Means to be selectively finished to a degree;
With
A device that uses a magnetorheological fluid to finish a product.   15. The surface for holding a magnetorheological fluid includes a lower surface of a rotatable donut-shaped bowl, the bowl configured to circulate the magnetorheological fluid. The device described in 1.   The apparatus of claim 15 further comprising means for adding the carrier fluid to the magnetorheological fluid to compensate for evaporation of the carrier fluid from the magnetorheological fluid.   The apparatus of claim 15, further comprising a mixer for stirring the magnetorheological fluid.   15. The apparatus of claim 14, further comprising means for rotating the product with respect to the region.   15. The apparatus of claim 14, wherein the product is mounted on a pivoting product holder so that the surface of the product is swept across the region.   15. The apparatus of claim 14, further comprising means for moving the workpiece along a plane generally perpendicular to the direction of flow of the magnetorheological fluid through the clearance. The method of claim 1 , wherein the protective material comprises a polymer. The method of claim 1 , wherein the protective material comprises polytetrafluoroethylene. The method of claim 1 , wherein the carrier fluid comprises water. The method of claim 1 , wherein the carrier fluid comprises glycerin. The method of claim 1 , wherein the magnetic particles comprise carbonyl iron particles. The method of claim 1 , wherein the magnetorheological fluid further comprises abrasive particles. The method of claim 26 wherein the abrasive particles comprise a CeO _2. A polishing region is produced in a magnetorheological fluid including magnetic particles, a layer of a protective material for suppressing oxidation of the magnetic particles, a stabilizer, and a supporting fluid,
Controlling the consistency of the fluid in the polishing region;
Bringing an object into contact with the polishing region of the fluid;
Moving the object and the polishing region relative to each other;
Determine the removal rate of the material of the object,
Determining the direction and speed of movement of the polishing region relative to the object;
Determine the number of polishing cycles required,
Including steps,
The step of determining the required number of polishing cycles includes:
Determine the initial surface roughness,
Determine the thickness of the damaged layer under the surface,
Determine the initial surface shape,
Determining the thickness of the layer of material that is removed during one polishing cycle;
Including steps,
Determining the removal rate of said material,
Determine the spatial distribution of material removal,
Determining the size of the contact portion of the object that contacts the polishing region at any given time;
A method for polishing an object, comprising a step. 29. The method of claim 28 , wherein the movement of the polishing region with respect to the article is continuous. Determining the direction and speed of movement of the polishing region relative to the article,
Determining the size of the contact portion of the object that contacts the polishing region at any given time;
Determine the thickness of the layer of material removed during one polishing cycle;
Determining the speed of the polishing region;
30. The method of claim 29 , comprising steps. 29. The method of claim 28 , wherein the movement of the polishing region with respect to the article is a discontinuous step. Determining the direction and speed of movement of the polishing region relative to the article,
Determining the size of the contact portion of the object that contacts the polishing region at any given time;
Determining the amount of movement of the polishing area in one step;
Determine the overlap factor,
Determining the thickness of the layer of material removed during one polishing cycle;
Determine the rest time of each step of polishing,
Determine the number of steps required,
32. The method of claim 31 , comprising a step. 29. The method of claim 28 , further comprising moving the object from a vertical axis of the object to an angle [alpha]. 34. The method of claim 33 , wherein the object is moved at a continuous speed from the vertical axis to an angle [alpha]. Moving the object from the vertical axis to the angle α at a continuous speed,
Determine the angular dimension of the contact area,
Determining the thickness of the layer of material removed during one polishing cycle;
Determining the angular velocity of movement of the object up to the angle α,
35. The method of claim 34 , comprising a step. 34. The method of claim 33 , wherein the object is moved in discrete steps from the vertical axis to an angle [alpha]. The step of moving the object from the vertical axis to the angle α in a discontinuous step further includes:
Determine the angular dimension of the contact area,
Determining the thickness of the layer of material removed during one polishing cycle;
Determine the value of angular displacement in one step,
Determine the overlap factor,
Determine the rest time of each step,
40. The method of claim 36 , comprising steps. 29. The method of claim 28 , further comprising controlling the properties of the magnetorheological fluid by replenishing the carrier fluid during polishing. 30. The method of claim 28 , wherein the container is moved relative to the object. 40. The method of claim 39 , wherein the container is rotated at a specified speed. 29. The method of claim 28 , wherein the polishing area is one third of the surface area of the article. The process of creating a polishing area in a magnetorheological fluid is as follows:
Causing a magnetic field in proximity to the magnetorheological fluid;
Controlling the direction and intensity of the magnetic field;
30. The method of claim 28 , comprising steps. The process of creating a polishing area in a magnetorheological fluid is as follows:
Subjecting the magnetorheological fluid to an inhomogeneous magnetic field in a region proximate to the object, the inhomogeneous magnetic field having a magnetic field line perpendicular to the gradient of the magnetic field;
30. The method of claim 28 . 44. The method of claim 43 , wherein the magnetic field gradient is directed toward a lower portion of the reference plane of the container. 43. The method of claim 42 , wherein the magnetic field is produced by means for causing a magnetic field disposed outside the container. 43. The method of claim 42 , further comprising controlling polishing of the object by controlling the strength of the magnetic field and the position of the polishing region with respect to the surface of the object. 47. The method of claim 46 , wherein the polishing is controlled by a programmable control unit. 30. The method of claim 28 , wherein the magnetorheological fluid includes an abrasive. 29. The method of claim 28 , wherein determining the required number of polishing cycles comprises determining the number of cycles according to the following equation:
(The surface roughness + the thickness of the damaged layer under the surface) / (the thickness of the layer of material to be removed) 32. The method of claim 30 , wherein determining the polishing region speed comprises determining the polishing region speed according to the following equation:
(2 × radius of contact portion × material removal rate) / (layer thickness of material to be removed) Determining the overlap factor includes determining a speed of the overlap factor according to the following equation:
(Movement amount per step) / (2 x radius of contact part)
Determining the rest time of each step of the polishing includes determining the rest time of each step of the polishing according to the following equation:
(Removed material layer x overlap factor) / (Material removal rate)
Determining the required number of steps includes determining the required number of steps according to the following equation:
(Radius of the object to be polished) / (Movement amount per step)
The method of claim 32 . Determining an angular velocity of movement of the object up to the angle α includes determining the angular velocity according to the following equation:
(Angular dimension of contact area × material removal speed) / (layer thickness of material to be removed)
36. The method of claim 35 . Determining the quiesce time of each step includes determining the quiesce time according to the following equation:
(Layer thickness of material to be removed × duplication factor) / (material removal rate)
38. The method of claim 37 . 30. The method of claim 28 , wherein the magnetorheological fluid includes an abrasive.

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