INCREASE OF PRECISION AND EFFICIENCY OF LASER CUTTING BY MEANS OF OPTICAL SYSTEM OPTIMIZATION

Transcription

1 6th Intenational AAAM Baltic Confeence INUSTRIAL ENGINEERING 4-6 Apil 008, Tallinn, Estonia INCREASE OF PRECISION AN EFFICIENCY OF LASER CUTTING BY MEANS OF OPTICAL SYSTEM OPTIMIZATION Guescu, C. M.; Ionescu, C..; Nicoaa, I. & Beaban, F. Abstact: Lase optical systems ae nonimaging applications. The pape pesents the design of an oiginal optical system meant to wok with a lase cutting machine. The typical assemblies of such systems ae the expande and the focusing objective. All lenses ae designed as best shape lenses in ode to minimize the esidual spheical abeation. The entie calculus is woked out by means of oiginal softwae, witten as a VB application. Two solutions of objectives ae assumed to be suitable a spheical one and a hypebolic one. Both solutions ae thooughly analyzed and specific paametes such as spot size and shape, depth of focus and diffaction limited chaacte is discussed. Key wods: lase cutting pecision, expande, focusing objective, optimal design, beam waist.. OPTICAL SYSTEMS FOR LASER CUTTING MACHINES A lase beam cannot be used in machining applications diectly at the paametes povided by the souce. The geometic and enegetic paametes as well must be adjusted so that metal o plastic pieces to esult at pescibed pecision in a single machining opeation. Beside this aim, the themal potection of the optical system must be insued, so that its optical, mechanical and chemical popeties peseve in time. The adjustment of lase beam paametes is achieved by inseting an adequate optical system into the scheme of the equipment. The optical system needs to accomplish the following functions: tanspotation of enegy fom the souce to the cutting point focusing of the lase beam onto the points belonging to a tajectoy which daws the contou of the piece insuing long lasting tanspaency, geometic, chemical and dimensional stability of lenses in the system possibility to contol defocusing in ode to coelate the lase spot size with the mechanical and themal popeties of the mateial, the speed and pecision of the machining. The basic scheme of an optical system usually associated to lase cutting equipments is as shown in figue. ' F' =F f' L L L -f Expande f' ob F' Focusing objective Fig.. Basic scheme of an optical system associated to lase cutting equipments The system consists of two assemblies: the expande, which modifies the apetue of the beam emitted by the souce. Along the tanspotation path, the diamete of the beam is inceased while the enegetic paametes get lowe values. Fom optical point of view, the expande is a evesed Galileo telescope, made of a divegent and a convegent lens. Thei positioning is telescopic

2 the focusing objective, which pojects the lase beam onto the cutting points. The objective is a positive single lens o assembly. Usually, the expandes insue an expansion within the ange of [.5 0]X. The objectives ae designed fo effective focal lengths within the ange of [40 00] mm. To the taditional Galileo telescopes, lase expandes ae diffeent on the following featues: the telescopic system is evesed. Its main chaacteistic is not the magnification but the expansion, which is the evese of magnification. The expansion is positive, bigge than the unit and expesses the atio between the beam apetue at the entance and exit of the system the slope of the entance beam is pactically null (the lase beam divegence is about a few milliadians) the optical assemblies of the expande ae singlet. This majo simplifying is possible because of the monochomatic adiation and the null slope of the beam. The chomatism does not occu and the geometic abeations ae missing except the spheical one. The esidual spheical abeation bings the most impotant poblem. It influences diectly the size of the spot. Hence, the design of the lenses must apply algoithms based on spheical abeation minimization. The objective, lage-sized in apetue, is also exposed mainly to spheical abeation. The optical systems included in lase cutting manufactuing belong to the nonimaging systems. The quality paametes point to abscissa, shape and size of the spot. The depth of focus is also impotant fo the contou pecision. Regading these fou elements, the following notices ae bought to attention: the spot shape is easiest to contol. Ideally, the spot must be ound fo a unifom enegy distibution. The shape contol is achieved by mechanical means. They must allow optical alignment along the z-axis and the centing of the nozzle on the plane (x,y). At pesent, the mechanical devices ensue micometic pecision the size spot can be optically contolled. The design of the system must be optimized because its chaacteistics can no longe be modified once its geomety is established. Hence, fo the spot size, the input date fo the optical system design is vey impotant. Pactically, the spot size assumes two additive components: one due to diffaction and a second one due to esidual spheical abeation [ ]: d spot total = dspot difactional + dspot abeational () whee: 4λM dspot difactional =, () π 3 k d =. (3) spot abeational In elations () and (3) λ epesents the wavelength [μm], M modal paamete of the beam (fo most applications equal to the unit) [-], f effective focal length of the objective [mm], apetue of the objective [mm], k non-dimensional coefficient depending on the efactive index [-]. The spot size is stongly dependent on the f-numbe of the objective: f /# =. (4) Pactically, the design input data equies both the focal length and the apetue. The liteatue [ ] ecommends estimation elations fo one of them in case the othe one is given. If the focal length is fixed, the optimum apetue is: 3 4λM f = 4. (5) 3πk If the apetue is fixed, the ecommendation fo the focal length is: 4 πk = 3. (6) λm Usually, the apetue is fixed because it is imposed by the expanded beam diamete of the adiation emitted fom the lase souce.

3 The expansion esults accodingly to mateials admitted powe density the spot abscissa and the depth of focus ae coelated and depend on the spot size. The optical system quality is essential. The spot abscissa is adjustable by defocusing. It is quite easy to achieve defocusing by mechanical micometic devices. efocusing is necessay because the minimum spot size in not always neaby the paaxial focus. The moe difficult issue is the depth of the focus (OF). This must be as long as possible fo a pecise cutting. Empiically, the OF can be estimated as : 8λM OF = ρ, (7) π whee ρ is a toleance facto (fo instance ρ=.05 signifies a gowth of 5% of the spot diamete). OF shows the height of the piece which can be cut fo a pecision of (ρ-) %.. ALGORITHMS FOR EXPANER AN OBJECTIVE ESIGN. SYNTHEZIS OF LENSES The input data ae: expansion, Γ. Its value is not totally independent at choice. It is imposed by the maximum admitted powe density of the mateials available o chosen fom a catalogue appoximate desied length of the optical system, L apetue of the beam emitted fom the souce,. The focal lengths of the expande s lenses and the objective apetue ae given by the following fomulas: L =, (8) Γ LΓ =, (9) Γ = Γ ', (0) whee f is the effective focal length of the divegent lens, f the effective focal length of the convegent lens, the apetue of the convegent lens (valid fo both the last expande lens and the objective lens). The fomulas (6) and (7) complete the geneal design. The synthesis of each lens needs to be woked out. Figue illustates the geomety of a lens. Each element must be computed o chosen. f+ Δ f t / Δ d u t Fig. Geometical chaacteistics of a single lens The total diamete t is a sum of two tems: the active apetue u and an additional size needed fo mounting. The adii calculus assumes the thin lens hypothesis, fo which the thickness is neglected. The optical powe of a thin lens is: Φ ' = = ( n ) ( n )( c c ) = ( n )c =, () = whee c, ae the lens cuvatues (evese of adii) and c=c -c is the total cuvatue of the lens. The fomula () contains two degees of feedom (two adii) which ae used fo imposing two conditions. One of them is always the optical powe (focal length). The second condition is imposed to coect an abeation. In the pesent case, the abeation is the spheical one. The pimay spheical abeation, as a sum of contibution egading the two sufaces is given in liteatue [ ], [ 3 ]. The lens with minimum spheical abeation is called best shape lens. Its cuvatues satisfy the equation (): G c + G 4cc G5c = 0 () s this gives the solution:

4 c G c + G p 5 =, (3) G 4 whee p=/s (s object abscissa), G = ( n + )( n ), (4) G 4 = ( n + )( n ), (5) n ( n ) G5 =, (6) n n efactive index of glass. Fo the fequent case of infinite object distance the expessions () and (3) lead to specific foms: ( n + ) ( n + ) n c c = s =. (7) n n 4 c = c n( n + ) It is obvious that the best shape of the lens can be bi-convex, plano-convex o meniscus, depending on the efactive index value. The plano-convex shape occus fo n= As the IR optical mateials get high efactive indexes ( 4) one can expect the most of the lenses to be meniscus shaped. Knowing the adii and the total diamete allows the computation of thickness. Moe efficient educing of spheical abeation is possible by using aspheic evolution sufaces. Among the special aspheic lenses used to educe spheical abeation thee is the hypebolic plano-convex lens (fig. 3) [ 4 ]. b k =, (9) a is the eccenticity and o the adius of the tangent cicle at the vetex of the suface. 3. SOFTWARE FOR THE ESIGN OF AN OPTICAL SYSTEM FOR LASER CUTTING MACHINES The pesent application s goal is to design the optical system included in the scheme of a lase cutting machine. The adiation souce is a CO lase (λ=0.6μm), emitting a mm diamete beam, at an adjustable powe up to 000W. Cutting the polycabonate, which pieces ae made of needs a powe P=500 W. The entie calculus is accomplished with oiginal softwae, witten as VB application. The following figues show captues of gaphical inteface pesenting its main fames: input data and estimated values (fig. 4), mateials choice and powe density checking (fig.5), solution fo the expande and solutions fo the focusing objective (fig, 6). Fig. 4. Input data and estimated paametes H H' F' f' Fig. 3. Plano-convex hypebolic lens Its eccenticity is k= - n. The geomety and optical chaacteistics ae given by the elationships: o = ( n ) k= -n, (8) whee: Fig. 5. Mateials choice and powe density

5 able to wok with a spot size of about 300 μm. A simple study shows that a small decease of incidence height (down to 7mm) bings the system to diffaction limited quality. So, only a shot maginal zone is out of the best chaacteistics. In ode to extend the system s quality ove the entie apetue, the second solution consisting in an aspheic objective is appopiate. Quality paametes ae: RMS OP = and Stehl Ratio = Thei values qualify the system almost ideal. The esidual spheical abeation is almost entiely eliminated (fig. 9). Fig. 6. Solutions fo the expande and the focusing objective The analysis of the optical systems got, was accomplished with the pogam OSLO LT. Quality paametes of the spheical objective solution ae: RMS OP = 0.64 and Stehl Ratio = The system is not diffaction limited. The esidual spheical abeation is still too lage (fig. 7), even though each lens was designed fo its best shape. Howeve, the cumulative effect is obvious. Fig. 7. Residual spheical abeation of the system with spheical objective The spot diagams analysis shows that whateve the defocusing plane is chosen, the spot is lage than the Aiy cicle. Howeve, the system is quite good, as it is Fig. 3. Residual spheical abeation of the system with aspheic objective The spot size and OF can be evaluated by the study of spot diagams at diffeent defocusing. Table contains numeical data got fom the spot diagams. The last column indicates the diamete of Aiy cicle, to which the eal diffusion spots compae. Table. Spot size fo defocusing within the ange of ± mm Aiy efocusing Spot diamete cicle [mm] [μm] [μm]

6 The spot size is aound 50 [μm] fo a ±.5 mm distance, which expesses, in fact, the OF. Both chaacteistics ae fully convenient, so the oiginal system designed can be qualified as vey good. 4. CONCLUSIONS The optical systems used in lase applications featue specific chaacteistics pointing to special mateials, optical schemes, and enegetic issues. The design of such a system, which is a non-imaging one, needs special algoithms, aiming the educing of esidual spheical abeation. The oiginal algoithms and softwae descibed above diected to vey good solutions egading the spot size and the depth of focus, which detemine the pecision in lase cutting. One solution uses a spheical objective, consisting in a single meniscus lens. The second solution uses a plano-convex objective, the convex suface being hypebolic. The aspheic objective ensues best quality of the entie system (expande and objective). 5. REFERENCES. fomulas.html, last on-line access Smith, W.J. Moden Optical Engineeing, McGaw Hill NY, Guescu, C., Nicoaă, I. Analiza şi sinteza sistemelo optice lenticulae. Ed. Politehnica Timişoaa, Naumann, A., Schode, G. Bauelemente de Optik. Taschenbuch de technischen Optik. Cal Hanse Velag München Wien, AITIONAL ATA ABOUT AUTHORS Authos: GRUESCU Coina Mihaela, Ph.. eng., signo lectue IONESCU, Cosmin eng., eseache NICOARA Ioan, Ph.. eng., pofesso BREABAN, Floin, Ph.. eng, pofesso Full Addess of all authos: Ph.. signo lectue GRUESCU Coina Mihaela Timisoaa, RO 300 Mihai Viteazu, Timisoaa, coina_guescu@yahoo.com home page: phone: , fax: eng. IONESCU Cosmin Timisoaa, RO 300 Mihai Viteazu, Timisoaa, cosminlauentiu@yahoo.com home page: phone: fax: Ph.. pofesso NICOARA Ioan Timisoaa, RO 300 Mihai Viteazu, Timisoaa, inicoaa@mec.upt.o home page: phone: fax: Ph.. pofesso BREABAN Floin Univesite d Atois, Fance ue de l univesite BP 89 FR 6408 Bethune cedex, Fance gfbeaban@yahoo.f home page: phone: fax: Coesponding Autho: GRUESCU Coina Mihaela Timisoaa, RO 300 Mihai Viteazu, Timisoaa, coina_guescu@yahoo.com