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精品論文study on the technology ofultrasonic-magnetorheological compound finishing1wang huijun, zhang feihu, liu jianfeng, luan dianrongharbin institute of technology, west dazhi street 92, harbin（150001）e-mail: hj_abstractultrasonic-magnetorheological compound finishing (umc finishing), as a kind of newlydeveloped optical polishing method, is presented in the paper. the machining principle and experimental set-up of umc finishing are introduced in the paper. material removal model for optical glass in umc finishing is discussed in the paper. experiment is carried out to testify the model. processing experiments are carried out to study the effects of the main processing parameters on the material removal rate and the surface quality in umc finishing. the curves of the corresponding relationships are obtained. the newly developed umc finishing technology offers a new way to fabricate ultraprecision aspheric surfaces.keywords: ultrasonic-magnetorheological; compound finishing; polishing, ultraprecisionmachining1introductionwith the rapid development of modern optical technology, more and more aspheric lenses have been applied for many new requirements of the optical systems. most existing technologies for modern optical fabrication can not be applied in the machining of concave aspheres with small radius, because the restriction of their machining conditions. the ultraprecision machining technology for concave aspheric elements with small radius is the great puzzle facing with modern optical fabrication. therefore, it is urgent for the optical fabrication industry to explore a new ultraprecision machining technology which is suitable for aspheres with small radius and freeform surfaces.ultrasonic-magnetorheological compound finishing (umc finishing) is proposed by the authors, which offers a new way to fabricate ultraprecision aspheric optical elements, especially to fabricate ultraprecision small-radial concave surfaces and freeform surfaces of the optical elements. umc finishing is enlightened from the theories of the following two methods. one is magnetorheological finishing (mrf), which has been successfully developed by the center foroptics manufacturing (com) in rochester university and qed technology inc. in u.s.a.1,2.the other is ultrasonic polishing3. umc finishing possesses the advantages of the two polishing methods. materials can be removed in small spots in the process of umc finishing. therefore, umc finishing can be applied to the polishing of small-radial concave surface.in the previous studies, some experiments have been carried out to compare the polishing efficiency of the new method with that of the conventional mrf4,5. the model of material removal rate of optical glass k9 in umc finishing has also been developed in our previous work6.the processing of optical glass by the method have been also discussed7,8.2mechanics of umc finishingthe mechanics of umc finishing is illustrated in figure 1, in which a small-radial polishing head is used.1 本課題得到國家自然科學(xué)基金(50575059) ,教育部博士點(diǎn)基金 (20050213040)的資助。- 9 -polishing head zmagnetorheological n1fluidworkpiecebultrasonic vibrationpolishing headmagnetorheological fluidworkpiecez n1ultrasonic vibrationbyn2xa) scheme of umc finishing of flat/convex surfacesyn2xb) scheme of umc finishing of concave surfacesfigure 1: scheme of mechanics of umc finishingas shown in figure 1, after the workpiece is fixed, the magnetorheological fluid is delivered to the polishing zone to form a flexible polishing tool, while the magnetic field with the flux density b is applied to the polishing head. vertical ultrasonic vibration is applied to the polishing head simultaneously, so the ultrasonic vibration energy is applied to the polishing zone directly to improve the polishing efficiency of optical elements by the co-action of the magnetic field. since a small-radial polishing head is used in umc finishing, the nanometer-scaled polishing of both the small-radial concave surface and the freeform surface can be realized. the polishing efficiency can be improved by the application of ultrasonic vibration.figure 1(a) is the scheme of umc finishing of flat/convex surfaces. the polishing head can not only vibrate vertically with the ultrasonic frequency, but also rotate simultaneously on its own spindle axis with the rotational speed n1 . there is a small controllable gap between the polishing head and the workpiece, where the magnetorheological fluid can form a flexible polishing tool by the gradient magnetic field. the workpiece rotates on its own spindle axis with the rotational speed n2 , which is in contrary direction to n1 . therefore, a shearing force is generated in the polishing zone, and the material is removed from the surface of the workpiece. ultrasonic vibration can improve the polishing efficiency. the whole surface is polished by the linear motions of the nc system.figure 1(b) is the scheme of umc finishing of concave surface. there is an extra swingmotion in the polishing head when polishing concave surface compared with figure 1(a). the axis of the polishing head can be at some angle to that of the workpiece, therefore, the polishing for the whole concave surface is realized.3experimental set-up of umc finishingfigure 2 is the scheme of the developed experimental set-up of umc finishing. the experimental set-up is composed of a ultrasonic generator, a magnetic generator, a polishing head, a recycling system for the magnetorheological fluid, and a viscosity-controlling system for the magnetorheological fluid, and etc.the experimental set-up is based on the mechanism of umc finishing mentioned above. the polishing head can vibrate with some amplitude, which is controlled by the ultrasonic generator. the recycling of the magnetorheological fluid can be realized to deliver the heat and debris out of the polishing zone. the viscosity-controlling system for the magnetorheological fluid is aimed at the realization of the viscous stability of the polishing fluid, so that the material removalcharacteristics during the polishing process are kept stable.123164515671481391211101magnetorheological fluid 2motor 3sliding table 4ultrasonic generator 5magnetic generator6polishing head 7workpiece 8rotary table 9cross slide table 10bed 11recycling device12mixing device 13pump 14-viscosity-controlling system 15recycling pipes 16nozzlefigure 2: scheme of the experimental set-up of umc finishing4material removal model of umc finishingthe figure 3 is the scheme of the polishing zone in umc finishing when the workpiece is stationary.the shape of the end of the polishing head is spherical, whose radius is r as shown in figure 3. the polishing head is ultrasonically vibrating in the vertical direction while the magnetic field is applied at the same time, whose flux density is b . the rotational speed of the polishing head is n1 , the minimum distance between the polishing head and the workpiece is h0 , and the distance between the polishing point to the center of the polishing zone is x .zpolishing headmagnetorheologicaln1fluidrultrasonic vibrationh0xbworkpiecefigure 3: scheme of the polishing zone in umc finishing when the workpiece is stationarythe material removal depth z when polishing optical glass k9 by means of umc finishing is composed of z1 , which is caused by the relative rotational speed between the polishing head andthe workpiece in the polishing zone, andz can be expressed byz 2 , which is caused by the impaction of the pressures.z1 can be expressed by6z = z1 + z 2z1 = k1(pu + pm + pd )vrt(1)(2)where k1 is the preston coefficient,pu is the pressure caused by the ultrasonic vibration, pmis thepressure caused by the magnetic field, pdis the pressure caused by hydrodynamic,vr is therelative velocity between the polishing head and the workpiece，and t is the polishing time.6z 2 can be expressed by22 0.2 h 0.422z = k 0.2 1 1+ 1 1 d 4 f0v0 a0e(pu + pm + pd ) t(3) 1vp2 1 uwhere k 2 is the ultrasonic pressure coefficient, d is the diameter of the abrasive grit, is thedensity of the abrasive grit,e1 and1 are the young s modulus and the poissons ratio of theabrasive respectively,e2 and 2 are the youngs modulus and the poissons ratio of the workpiecerespectively, f is the frequency of the ultrasonic vibration,0 is the density of the polishing head,a0 is the vibration amplitude of the polishing head,v1 is the ultrasonic wave velocity of thepolishing head,v0 is the ultrasonic wave velocity of the polishing slurry with the magnetic field, is the attenuation coefficient of ultrasonic in the polishing slurry with the magnetic field,and h is the distance between the polishing head and the workpiece.figure 4 is the material removal model for the optical glass k9 in umc finishing when the workpiece is stationary. the experimental conditions are as follows: the ultrasonic vibration frequency is 20khz, the ultrasonic vibration amplitude is 5m, the magnetic flux density is1500gs, the minimum gap between the polishing head and the workpiece is 0.3mm, the rotational speed of the polishing head is 280rpm, and the polishing time is 10min.x ( mm )material removal depth (m)figure 4: material removal model of umc finishing when the workpiece is stationarythe shape of the model is similar to the letter w as shown in figure 4. there is some material removal depth at the center of the polishing zone. the material removal depth at the end of the polishing zone is less. the maximum material removal depth is about 1.4m, therefore, the maximum material removal rate is about 0.14m/min.figure 5 is the material removal profile measured by a profile meter (form talysurf s4c) inumc finishing when the workpiece is stationary. the polishing time is 10 min.figure 5: material removal profile of umc finishing when the workpiece is stationaryfrom figure 5, it can be concluded that the shape of the material removal profile is similar to that of in figure 4. the maximum material removal rate measured is about 0.138m/min. the experimental result obtained testifies that the material removal model mentioned above is correct.5processing experiment and resultthe material removal rate and the surface quality in umc finishing can be influenced by many processing parameters. the experiments are carried out to get the effects of the main processing parameters including the magnetic flux density, the minimum gap between the polishing head and the workpiece, the rotational speed of the workpiece on the polishing result in umc finishing. the experiments are carried out in the set-up as shown in figure 2.5.1 the effects of the magnetic flux density on the polishing resultthe experimental conditions are as follows: the ultrasonic vibration frequency is 20khz, the ultrasonic vibration amplitude is 5m, the minimum gap between the polishing head and the workpiece is 0.3mm, the rotational speed of the polishing head is 280rpm, and the polishing time is 10min. experiments are carried out at different magnetic flux densities, for example, 750 gs,1000 gs, 1500 gs and 2000 gs, while the other processing parameters are kept the same value to get the relationship curves of effects of the magnetic flux density on the material removal rate and surface roughness as shown in figure 6.in the figure, triangular symbols stand for the data of the surface roughness obtained, and the corresponding red lines stand for the relationship curve for the surface roughness. the circular symbols stand for the data of the material removal rate in umc finishing, and the corresponding red lines stand for the relationship curve for the material removal rate. the rules will be the samefor the following figures.surface roughnessmaterial removal rate5material removal rate (m/min)0. 2surface roughness ra (nm)40. 1 530.1 20. 0 510750 1000 1500 02000 the magnetic flux density (gs)figure 6: effects of the magnetic flux density on the material removal rate and surface roughnessfrom figure 6, it can be concluded that, with the existing experimental conditions, the stronger the magnetic field, the higher the material removal rate, and the higher the value of the surface roughness ra in umc finishing.5.2 the effects of the minimum gap between the polishing head and the workpiece on the polishing resultsurface roughnessmaterial removal rate0.3 9surface roughness ra (nm)80. 2570.2 650. 154material removal rate (m/min)0.1 320. 050.400.5the minimum gap between the polishing head and theworkpiece (mm)figure 7: effects of the minimum gap between the polishing head and the workpiece on the material removal rate and surface roughnessthe experimental conditions are as follows: the ultrasonic vibration frequency is 20khz, the ultrasonic vibration amplitude is 5m, the magnetic flux density is 1500gs, the rotational speed of the polishing head is 280rpm, and the polishing time is 10min. experiments are carried out at different minimum gaps between the polishing head and the workpiece, for example, 0.1mm,0.2mm, 0.3mm, 0.4mm and 0.5mm, while the other processing parameters are kept the same value to get curves of the effects of the minimum gap on the material removal rate and surface roughness as shown in figure 7.from figure 7, it can be concluded that, with the existing experimental conditions, the larger the minimum gap between the polishing head and the workpiece, the lower the material removal rate, and the higher the value of the surface roughness ra in umc finishing.5.3 the effect of the rotational speed of the workpiece on the polishing resultthe experimental conditions are as follows: the ultrasonic vibration frequency is 20khz, the ultrasonic vibration amplitude is 5m, the magnetic flux density is 1500gs, the minimum gap between the polishing head and the workpiece is 0.3mm, the rotational speed of the polishing head is 280rpm, and the polishing time is 10min. experiments are carried out at different rotational speeds of the workpiece, for example, 0rpm, 65rpm, 130rpm and 260rpm, while the other processing parameters are kept the same to get the curves of effects of the rotational speed of the workpiece on the material removal rate and surface roughness as shown in figure 8.surface roughnessmaterial removal rate0.25 5surface roughness ra (nm)0.2 40.15 30.1 20.05 100651300260the rotational speed of the workpiece (rpm)figure 8: effects of the rotational speed of workpiece on the material removal rate and the surface roughnessfrom figure 8, it can be concluded that, with the existing experimental conditions, the higher the rotational speed of the workpiece, the higher the material removal rate, and the higher the value of the surface roughness ra in umc finishing.6conclusionsthe maximum material removal rate in umc finishing with stationary workpiece is about0.14m/min after simulation. the material removal profile measured by the profile meter testifies that the material removal model derived is correct. the effects of three main processing parameters on the polishing result are studied. the curves of the corresponding relationships are obtained. the study will be useful for the further application of umc finishing technology.acknowledgementsthe authors wish to thank both the national natural science fundation of china (grant no.50575059) and the fundation for the doctoral program of higher education of china (grantno.20050213040).references1d. golini, s. d. jacobs and w. i. kordonsky (1995) fabrication of glass aspheres using deterministic microgrinding and magnetorheological finishing, proc. of spie, vol.2536: pp.208-2112w. i. kordonsky and d. golini (2000) fundamentals of magnetorh