Dynamic behavior of micromachining systems

Predmet istraživanja prikazanih u okviru doktorske diseracije su samopobudne vibracije pri obradi glodanjem. Na osnovu detaljne analize zakonitosti nastanka samopobudnih vibracija uspostavljena je određena paralela između glodanja i mikrogkodanja, za slučajeve kada je dubina rezanja veća od radijusa rezne ivice alata. Za tako usvojene pretpostavke, razvijeni su modeli unapređene numeričke simulacije procesa glodanja i mikroglodanja. Razvijeni modeli su svestrano verifikovani, s jedne strane, u segmentima gde postoje podaci u literaturi; poređenjem sa rezultatima drugih autora, a sa druge strane poređenjem sa sopstvenim eksperimentalnim ispitivanjima. Za eksperimentalno definisanje granične dubine rezanja pri glodanju predložena je inovativna metoda tangenti, a pri mikroglodanju, imajući u vidu raspoloživu mernu opremu, metoda hrapavosti obrađene površine. Matematički modeli i eksperimentalne metode su verifikovani pri obradi tri karakteristične vrste materijala i na dva obradna sistema pri glodanju, odnosno jednom materijalu i jednom obradnom sistemu pri mikroglodanju. Rezultati istraživanja su prezentovani kroz dvanaest poglavlja čiji sadržaj se navodi u nastavku. U prvom, uvodnom poglavlju, ukazano je na značaj istraživanja samopobudnih vibracija pri makro i mikroglodanju. Prikazana je i aktuelnost istraživanja analizom broja naučnih radova koji se bave problematikom samopobudnih vibracija u periodu od poslednjih dvadeset pet godina. Kroz drugo poglavlje detaljno su prikazana dosadašnja istraživanja samopobudnih vibracija pri makroglodanju, dok su u trećem poglavlju prikazana istraživanja samopobudnih vibracija pri mikroglodanju. Izvršena je analiza uticajnih parametri na graničnu dubinu rezanja, koja predstavlja osnovni pokazatelj dinamičke stabilnosti kako makro, tako i mikroobradnih sistema. Na osnovu saznanja prikazanih u okviru drugog i trećeg poglavlja u četvrtom poglavlju su definisani ciljevi i hipoteze istraživanja. Matematičke metode za definisanje karte stabilnosti obradnog sistema, prikazane su u petom poglavlju. Prikazana su dva matematička modela za definisanje karte stabilnosti pri makroglodanju, model srednjeg ugla kontakta alata u zahvatu i model Furijeovih redova. Prezentovana je numerička simulacija procesa obrade glodanjem, namenjena prvenstveno za simulaciju sila rezanja. Polazeći od prethodno prikazane ideje u okviru ovog poglavlja je razvijena nova matematička metoda predikcije granične dubine rezanja - unapređena numerička simulacija procesa glodanja. U okviru šestog poglavlja prikazane su eksperimentalne metode identifikacije vibracija mašina alatki, odnosno eksperimentalno određivanje modalnih parametara obradnih sistema kao i metode detekcije samopobudnih vibracija pri glodanju. U cilju definisanja granične dubine rezanja, prikazana je metoda frekventne analize vibracija pri glodanju, kao metoda koja se često koristi u savremenim eksperimentalnim istraživanjima. Međutim, i matematičke i eksperimentalne metode analize vibracija pri glodanju imaju određena ograničenja. Polazeći od prethodnog, razvijena je inovativna metoda tangenti, bazirana na ranije korišćenoj metodi u okviru Laboratorije za mašine alatke Instituta za proizvodno mašinstvo FTN u Novom Sadu, i primeni savremenih mernih sistema. Pored toga, u ovom poglavlju je eksperimentalno potvrđen uticaj samopobudnih vibracija na kvalitet obrađene površine i geometrijsku tačnost obratka. Metodologija sprezanja matematički i eksperimentalno definisanih funkcija frekventnog odziva elemenata mašine alatke prikazana je u sedmom poglavlju. Prezentovane su jednačine sprezanja pomerajnih odziva matematmički definisanih funkcija frekventnog odziva alata i držača alata, bazirane na Ojlerovoj teoriji grede, sa eksperimentalno definisanom funkcijom frekventnog odziva sklopa glavnog vretena mašine alatke. U okviru osmog poglavlja razvijen je matematički model sila rezanja pri mikroglodanju. Predloženi model sila rezanja, koji uzima u obzir silu trenja između leđne površine alata i obrađene površine, implementiran je u unapređenu numeričku simulaciju glodanja čime je omogućena njena primena za definisanje graničnih dubina rezanja pri mikroglodanju. Verifikacija razvijenih numeričkih i eksperimentalnih metoda za ispitivanje vibracija pri makroglodanju je prikazana u devetom poglavlju. Sproveden je niz eksperimentalnih ispitivanja, pri kojima su određivane granične dubine glodanja pri obradi tri različita materijala obratka (Al7075, 42CrMo4 i Ti-6Al-4V) na dva obradna sistema. Na osnovu ovih ispitivanjima izvršena je verifikacija unapređene numeričke simulacije glodanja i inovativne metode tangenti. U desetom poglavlju prikazana je verifikacija metoda analize samopobudnih vibracija pri mikroglodanju. Primenom metodologije sprezanja pomerajnih odziva, definisani su modalni parametri obradnog sistema za mikroobradu, potrebni za definisanje graničnih dubina rezanja, tj. karte stabilnosti, unapređenom numeričkom simulacijom mikroglodanja. Karta stabilnosti definisana razvijenom unapređenom numeričkom simulacijom, verifikovana je eksperimentalno i poređenjem sa literaturnim izvorima. U jedanaestom poglavlju data su zaključna razmatranja, kritički osvrt na ostvarene rezultate, i pravci budućih istraživanja. Dvanaesto poglavlje prikazuje pregled korišćene literature, koju čini 218 referenci većim delom citirane u samom radu, a u zasebnom poglavlju dati su prilozi.The subject of research presented in the doctoral dissertation are self-excited vibrations in milling. Based on a detailed analysis of the self-excited vibrations occurrence, a certain parallel has been established between macro and micromilling, for cases when the depth of cut is greater than the cutting edge radius of the tool. For such adopted assumptions, models of advanced numerical simulation of macro and micromilling processes were developed. The developed models were comprehensively verified, on the one hand, by comparison with the results of other authors, and on the other hand by comparison with own experimental results. An innovative tangent method has been proposed for the experimental definition of the cutting depth limit in milling, and the method of machined surface roughness has been proposed for micromilling, having in mind the available measuring equipment. Mathematical models and experimental methods were verified by machining three characteristic types of materials on two machining systems in macromilling, and one material on one machining system in micromilling. The results of the research are presented through twelve chapters, the content of which is listed below. In the first, introductory chapter, the importance of the research of self - excited vibrations in macro and micromilling is pointed out. The topicality of the research is also presented by analyzing the number of scientific papers dealing with the issue of self - excited vibrations in the period of the last twenty - five years. The second chapter presents in detail the previous research on self-excited vibrations during macromilling, while the third chapter presents research on self-excited vibrations during micromilling. An analysis of the influential parameters on the cutting depth limit was performed, which is a basic indicator of the dynamic stability of both macro and micromachining systems. Based on the findings presented in the second and third chapters, the fourth chapter defines the goals and hypotheses of the research. Mathematical methods for defining the stability lobe diagram of the machining system are presented in the fifth chapter. Two mathematical models for defining the stability lobe diagram for macromachining are presented, the model of the tool’s mean contact angle and the model of Fourier series. Numerical simulation of the milling process is presented, intended primarily for the simulation of cutting forces. Starting from the previously presented idea, a new mathematical method for predicting the cutting depth limit has been developed within this chapter - an improved numerical simulation of the milling process. In the sixth chapter, experimental methods of machine tools vibration identification are presented, ie experimental determination of machining systems modal parameters as well as methods of self - excited vibrations detection during milling. In order to define the cutting depth limit, the method of vibrations frequency analysis during milling is presented, as a method that is often used in modern experimental research. However, both mathematical and experimental methods of milling vibration analysis have certain limitations. Starting from the previous one, an innovative tangent method was developed, based on the previously developed method, used within the Laboratory for Machine Tools, Institute of Production Engineering Facultz of Technical Sciences in Novi Sad, and the application of modern measuring systems. In addition, in this chapter, the influence of self - excited vibrations on the machined surface quality and the geometric accuracy of the workpiece is experimentally confirmed. The methodology of machine tool elements mathematically and experimentally defined frequency response functions coupling is presented in the seventh chapter. The displacement responses coupling equations of mathematically defined tools and tool holders FRF's (based on Euler 's beam theory) with the experimentally defined FRF of the machine tool main spindle assembly are presented. Within the eighth chapter, a mathematical model of cutting forces in micromilling was developed. The proposed cutting forces model, which takes into account the friction force between the reliefe tool surface and the machined surface, is implemented in an advanced numerical micromilling simulation, which enables its application to define cutting depth limit in micromilling. Verification of the developed numerical and experimental methods for vibrations analysis during macromachining is presented in the ninth chapter. A series of experimental tests were performed, during which the cutting depth limits were determined during the milling of three different workpiece materials (Al7075, 42CrMo4 and Ti-6Al-4V) on two machining systems. In the tenth chapter, the verification of the methods of analysis of self-excited vibrations during micromilling is presented. Using the methodology of coupling displacement responses, the modal parameters of the machining system for micromachining are defined, needed to define the cutting depth limits, ie. stability lobe diagram, by advanced numerical micromilling simulation The stability lobe diagram, defined by the developed advanced numerical simulation, was verified experimentally and by comparison with literature sources. The eleventh chapter provides concluding remarks, a critical review of the achieved results, and directions for future research. The twelfth chapter presents an overview of the used literature, which consists of 218 references, mostly cited in the paper itself