PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

Wibrostabilność skrawania wieloostrzowymi narzędziami obrotowymi

Autorzy
Identyfikatory
Warianty tytułu
EN
Vibrostability of cutting process using rotational multi-edge cutting tools
Języki publikacji
PL
Abstrakty
PL
Pierwszym i głównym celem pracy jest stworzenie uniwersalnej metodyki modelowania procesu skrawania narzędziami wieloostrzowymi z zastosowaniem techniki NURBS, możliwej do wykorzystania w przypadku szerokiej klasy narzędzi wieloostrzowych pracujących w różnorodnych konfiguracjach technologicznych, a w szczególności podczas obróbki w pięciu osiach.
EN
The present monograph gives the reader a summary of the author's earlier research into modeling cutting process with rotational multi-edge tools in order to analyze the vibrostability of machine tool-cutting process (MT-CP) system. Vibrostability, i.e. the resistance of a system to self-excited vibrations, is one of the basic dynamic properties of machine tool. Self-excited vibrations heavily affect the process of machining, the quality of machined surface and the tool and machine's life. Following the recent quick development of machine building and control techniques a modern type of CNC (computer numerical control) machine tools, which can be controlled in five axes, as well as machine tools with parallel kinematics (also called hexapods) came into use. These types of machine tools can perform many complex operations of the machine tool versus the work piece and consequently they enable to machine surfaces with complex topology. In this case, using standard models of the machine cutting process to predict the vibrostability of MT-CP (machine tool-cutting process) system proved to be inadequate. Therefore, there was a need to further develop these models using new techniques of geometric modeling applied in advanced CAD systems. The precision of vibrostability forecasting depends on the precision of both numerical models of mass-damping-spring (MDS) system and models of processes taking place in the machine tool. The work presents a concise description of the ways of MDS modeling using the finite (rigid, deformable and hybrid) element method, modal method and the methods of describing the kinematics of a system by means of homogeneous transformations. The basic operation of a machine tool is machine cutting. Two aspects of machine cutting process can be singled out: a model describing the geometry of the machined layer's cross- section and the so-called elementary model of the machine cutting process. The monograph presents a simplified method of describing the geometry of the machined layer's cross-section applied to modeling the machining of planes and holes, in which the machine tool performs a rectilinear advance movement. If this is the case, the cross-section of the machined layer is fixed and can be given using simple geometrical relations. The machining of complex spatial surfaces on five-axis machine tools using modern tools such as toroidal and spherical cutters is an example of a process, which is difficult to model using simple geometrical relations. The present work suggests an original method of describing the geometry of the cross-section to be machined using NURBS technique (rational B-spline curves and surfaces). The method seems to be very universal and also it makes it possible to apply a uniform mathematical method to build geometrical models of the cutting process. Moreover, the method can be used with a majority of rotational multi-edge tools (such as face milling cutters, spherical and toroidal cutters, drills, reamers, boring bars, etc.). These kinds of models can also be well applied to model five-axis machining. The monograph also contains a synthetic review of elementary models of the machine cutting process, which describe dynamic phenomena taking place at the cutting zone and directly at the cutter. These models, combined with a geometrical model, are used to describe the dynamics of cutting with a rotational, multi-edge tool as well as to analyze the vibrostability of MT-CP (machine tool-cutting process) system. There are many models of the machine cutting process and methods of forecasting the vibrostability that significantly differ one from the other. Their usefulness depends to a large degree on the aim, the constructor - designer has in mind. The work lists the main guidelines used in the selection process of choosing a geometrical model of the cutting layer, an elementary model of the cutting process and criteria of assessing vibrostability. Theoretical reasoning presented in the monograph is illustrated with many examples of practical applications and it is also experimentally verified. The work contains many results of simulations, measurements of real cutting forces, forecasting and experiments on vibrostability of both conventional and parallel kinematics machine tools. The results of experiments and tests are in good agreement with the results of numerical simulations and therefore confirm the usefulness of the presented computational methods. In the summary, the author suggests some future directions of further research in the fields of modeling of the process of cutting with rotational, multi-edge tools and in forecasting vibrostability of MT-CP system.
Rocznik
Strony
3--190
Opis fizyczny
Bibliogr. 233 poz., rys., tab.
Twórcy
autor
  • Instytut Technologii Mechanicznej Politechniki Szczecińskiej
Bibliografia
  • [1] Abrari F., Elbestawi M. A.: Closed form formulation of cutting forces for bal land flat end mills, Int. J. Mach, Tools Manufact., 1997, vol. 37, no. 1, s. 17—37.
  • [2] Abrari F., Elbestawi M. A., Spence A. D.: On the dynamics of ball end milling: modeling of cutting forces and stability analysis, International Journal of Machine Tools & Manufacture, 1998, no. 38, s. 215—237.
  • [3] Adolfsson C., Stahl j-E.: Cutting force model for multi-toothed cutting processes and force measuring equipment for face milling, Int. J. Mach. Tools Manufact., 1995. vol. 35, no. 12. s. 1715 - 1728.
  • [4] Ahn T. Y., Eman K. F., Wu S. M.: Determination of inner and outer modulation dynamics in orthogonal cutting, Transactions of the ASME, Journal of Engineering for Industry, February 1987, vol. 109, s.275—280.
  • [5] Albrecht P.: Dynamics of the metal cutting process, ASME Journal of Engineering for Industry, 1965, vol. 87, s. 429—441.
  • [6] Al-Regib E., Ni J., Lee S.-H.: Programming spindle speed vibration for machine tool chatter suppression, International Journal of Machine Tools & Manufacture, 2003, no. 43, s. 1229—1240.
  • [7] Altintas Y., Budak E.: Analytical prediction of stability lobes in milling. Annals of the CIRP, 1995, vol. 44(1), s. 357—362.
  • [8] Altintas Y., Engin S.: Generalized modeling of mechanics and dynamics of milling cutters, Annals of the CIRP, 2001, vol. 50(1), s. 25—30.
  • [9] Altintas Y., Lee P.: Mechanics and dynamics of ball end milling, Transactions of the ASME, Journal of Manufacturing Science and Engineering, November 1998, vol. 120, s. 684—692.
  • [10] Arcona C., Dow T. A.: An empirical tool force model for precision machining, Transactions of the ASME, Journal of Manufacturing Science and Engineering, November 1998, vol. 120, s. 700—707.
  • [11] Arsecularatine J. A., Fowle R. F., Mathew P.: Nose radius oblique tool: cutting force and built-up edge prediction. Int. J. Mach. Tools Manufact., 1996, vol. 36, no. 5, s. 585—595.
  • [12] Azeem A., Feng H.-Y., Wang L.: Simplified and efficient calibration of a mechanistic cutting force model for ball-end milling. International Journal of Machine Tools & Manufacture, 2004, no. 44, s.291—298.
  • [13] Baker H.: Computer graphics, USA, Pearson Education International 2004.
  • [14] Bandyopadhyay B. P., Bhatacharya R. K.: Chatter reduction in machine tools, in: 42nd Earthmoving Industry Conference, Aprill 9—10 Peorla, Illinois, USA 1991, s.l—8.
  • [15] Bayly P. V., Lamar M. T., Calvert S. G.: Low-frequency regenerative vibration and the formation of lobed holes in drilling. Transactions of ASME. Journal of Manufacturing Science and Engineering, May 2002, vol. 124, s. 275—285.
  • [16] Bayly P. V., Metzier S. A., Schaut A. J., Young K. A.: Theory of torsional chatter in twist drills: model, stability analysis and composition to test, Transactions of ASME. Journal of Manufacturing Science and Engineering, November 2001, vol. 123, s. 552—561.
  • [17] Berczyński S., Pajor M., Gutowski P.: Shaping dynamic properties of machine tools to improve their vibrostability. Part I. Methodology of computations, Postępy Technologii Maszyn i Urządzeń, 1998, vol. 22, nr 2, s. 5—20.
  • [18] Berczyński S., Pajor M., Lachowicz M.: Algorytm redukcji danych opisujących częstotliwościowe charakterystyki dynamiczne obrabiarki. Postępy Technologii Maszyn i Urządzeń, 1996, vol. 20. nr 2, s. 11 - 21.
  • [19] Bodnar A.: Diagnostyka drgań samowzbudnych w systemie obrabiarka-proces skrawania, Prace Naukowe Politechniki Szczecińskiej, 2006, nr 595, Instytut Technologii Mechanicznej, nr 18.
  • [20] Budak E., Altintas Y.: Modeling and avoidance of static form errors in peripheral milling of plates, Int. J. Mach. Tools Manufact., 1995, vol. 35, no. 3, s. 459—476.
  • [21] Campomanes M. L., Altintas Y.: An improved time domain simulation for dynamic milling at small radial immersions, Transactions of ASME. Journal of Manufacturing Science and Engineering, August 2003, vol. 125, s. 416—422.
  • [22] Carlsson T., Stjernstoft T.: A model for calculation of the geometrical shape of cutting tool-work piece interface, Annals of the CIRP, 2001, vol. 50( 1), s. 41—44.
  • [23] CATIA: http://www.3ds.com.
  • [24] Chandrasekharan V., Kapoor S. G., DrVor R. E.: A mechanistic approach to predicting the cutting forces in drilling: with application to fiber-reinforced composite materials, Transactions of the ASME, Journal of Engineering for Industry. November 1995, vol. 117, s. 559—570.
  • [25] Chang H. C., Sadek M. M., Tobias S. A.: Relative assessment of the dynamic behavior and cutting performance of a bonded and a cast-iron horizontal milling machine. Transactions of the ASME, Journal of Engineering for Industry, August 1983, vol. 105, s. 187 - 196.
  • [26] Chen S. G., Ulsoy A. G., Koren Y.: Computational stability analysis of chatter in turning. in: ASME Symposium in Mechatronics, New Orleans 1993, DSC-vol. 50/PED-vol. 63, s. 107—111.
  • [27] Chiou C.-H., Hong M.-S., Ehmann K. F.: The feasibility of eigenstructure assignment for machining chatter control, International Journal of Machine Tools & Manufacture, 2003, no. 43, s. 1603—1620.
  • [28] Chiou R. Y., Liang S. Y.: Chatter stability of a slender cutting tool in turning with tool wear effect, Int. J. Mach. Tools Manufact., 1998, vol. 38, no. 4, s. 315—327.
  • [29] Chodźko M.: Zwiększenie wibrostabilności systemu obrabiarka-proces-skrawania, przez zastosowanie eliminatora drgań, rozprawa doktorska, Politechnika Szczecińska, Szczecin 2006, maszynopis.
  • [30] Cook N. H.: Manufacturing analysis, Massachusetts, Addison Wesley Publishing Co., Reading 1966.
  • [31] Craig J. J.: Wprowadzenie do robotyki: mechanika i sterowanie, Warszawa, WNT 1993.
  • [32] Croitoru C., Severincu M., Belous V.: Determination method of a mathematical model for the coefficient of longitudinal chip contraction, in: Proceedings of the 10th International DAAAM Symposium, Wiedeń 1999, s. 105 — 106.
  • [33] Das M. K. i inni: A critical assessment of cutting force models in the analysis of machine tool instability, in: Proc. of 11 MTDR Conference, University of Birmingham 1970, s. 87—98.
  • [34] Das M. K., Tobias S. A.: The relation between the static and the dynamic cutting of metals. International Journal of Machine Tool Design and Research, 1967, no. 2.
  • [35] Davies M. A., Prat J. R., Dutterer B.: Stability prediction for low radial immersion milling. Transactions of ASME. Journal of Manufacturing Science and Engineering, May 2002, vol. 124, s. 217—225.
  • [36] De Boor C.: A practical guide to spline, Berlin, Springer-Verlag 1978.
  • [37] Denavit J., Hartenberg R. S.: A kinematic notation for low-pair mechanisms based on matrices, Journal of Applied Mechanics, June 1955, s. 215—221.
  • [38] Dohner J. L., Lauffer J. P., Hinnerichs T. D. i inni: Mitigation of chatter instabilities in milling by active structural control, Journal of Sound and Vibration, 2004. no. 269, s. 197—211.
  • [39] Doi M., Ohhashi M.: A study on parametric vibration in machining of hard cutting metals. Inr. J. Japan Soc Prec. Bug., 1992, vol. 26, no. 3, s. 195—200.
  • [40] Ehmann K. F., Kapoor S. G., DeVor R. E., Lazoglu I.: Machining process modeling: a review. Transactions of the ASME, Journal of Manufacturing Science and Engineering. November 1997, vol. 119, s. 655—663.
  • [41] El Baradi M. A.: Statistical analysis of the dynamic cutting coefficients and machine tool stability, Transactions of the ASME, Journal of Engineering for Industry, May 1993, vol. 115, s. 205—215.
  • [42] Elhachimi M., Torbaty S., .Joyot P.: Mechanical modeling of high speed drilling. 1: Predicting torque and thrust. International Journal of Machine Tools & Manufacture, 1999, no. 39, s. 553—568.
  • [43] Elhachimi M., Torbaty S., Joyot P.: Mechanical modeling of high speed drilling. 2: Predicted and experimental results, International Journal of Machine Tools & Manufacture, 1999, no. 39, s. 569—581.
  • [44] Eman K., Wu S. M.: A fessibility study of on-line identification of chatter in turning operations. Transactions of the ASME, Journal of Engineering for Industry, November 1980, vol. 102, s. 315—321.
  • [45] Engin S., Altintas Y.: Generalized modeling of milling mechanics and dynamics. Part I. Helical end mills. Machining Science and Technology, 1999, no. 3(2), s. 131 —139.
  • [46] Engin S., Altintas Y.: Mechanics and dynamics of general milling cutters. Part I. Helical end mills, International Journal of Machine Tools & Manufacture, 2001, no. 41, s. 2195 -2212.
  • [47] Engin S., Altintas Y.: Mechanics and dynamics of general milling cutters. Part II. Inserted cutters. International Journal of Machine Tools & Manufacture, 2001. no. 41, s. 2213-2231.
  • [48] Ewins D. J.: Modal testing: theory and practice, Taunton, England, Research Studies Press Ltd 1984.
  • [49] Fasen K., Junyi Y., Xiaoqin Z.: Analysis of fuzzy dynamic characteristics of machine cutting process: fuzzy stability analysis in regenerative-type-chatter. International Journal of Machine Tools & Manufacture, 1999, no. 39, s .1299—1309.
  • [50] Feng H-Y., Su N.: A mechanistic cutting force model for 3D ball-end milling. Transactions of ASME. Journal of Manufacturing Science and Engineering, February 2001, vol. 123, s. 23—29.
  • [51] Fuh K.-H., Chang C.-H.: Prediction of the cutting forces for chamfered main cutting edge tools, Int. J. Mach Tools Manufact., 1995, vol. 35, no. 11, s. 1559—1586.
  • [52] Fuh K.-H., Hwang R.-M.: A predicted milling force model for high-speed end milling operation, Int. J. Mach. Tools Manufact., 1997, vol. 37, no. 1, s. 969—929.
  • [53] Fussell B. K., Jerard R. B., Hemmett J. G.: Modeling of cutting geometry and forces for 5-axis sculptured surface machining, Computer-Aided Design, 2003, vol. 35, s. 333—346.
  • [54] Fussell B. K., Jerard R. B., Hemmett J. G.: Robuste feedrate selection for 3-axis NC machining using discrete models. Transactions of ASME. Journal of Manufacturing Science and Engineering, May 2001, vol. 123, s. 214—224.
  • [55] Gente A., Hoffmeister H.-W.: Chip formation in machining Ti6A14V at extremely high cutting speeds, Annals of the C1RP, 2001, vol. 50(1), s. 49—52.
  • [56] Gong Y., Ehmann K. F.: Mechanistic model for dynamic forces in micro-drilling, New York, Proc. IMECE 200l, s. 131 — 141.
  • [57] Grabec I.: Chaotic dynamics of cutting process, Int. J. Mach. Tools Manufact., 1988, vol. 28, no. l, s. 19—32.
  • [58] Gurney J. P., Tobias S. A.: A grafical analysis of regenerative machnie tool instability. Transactions of the ASME, Journal of Engineering for Industry, February 1962, s. 103—112
  • [59] Gutowski P.: Identyfikacja parametrów modeli dynamicznych układów nośnych obrabiarek, Prace Naukowe Politechniki Szczecińskiej, 2003, nr 574, Wydział Mechaniczny, nr 1.
  • [60] Gutowski P., Berczyński S., Marchelek K.: Rozwój metod identyfikacji modeli dynamicznych układów nośnych obrabiarek. raport końcowy z projektu KBN nr 7S101 052 04, Politechnika Szczecińska, Szczecin 1995, maszynopis.
  • [61] Hahn W.: On difference differential equations with periodic coefficients. Journal of Mathematical Analysis and Applications, 1961, no. 3, s. 70—101.
  • [62] Hanna N. H., Tobias S. A.: A theory of nonlinear regenerative chatter, ASME Journal of Engineering for Industry, 1974, vol. 96, s. 247—253.
  • [63] Hashimoto M., Maru E., Kato S.: Experimental research on cutting force variation during primary chatter vibration occurring in plain milling operation. Int. J. Mach. Tools Manufact., 1996, vol. 36, no. 2, s. 183—201.
  • [64] Heisel U., Meliberg J.: Vibrations and surface generation in slab milling. Annals of the CIRP, 1994, vol. 43(1), s. 337—340.
  • [65] Hohn R. E., Sridhar R., Long G. W.: A stability algorithm for a special case of the milling process, Transactions of ASME. Journal of Engineering for Industry, May 1968, s. 325—329.
  • [66] Hoon Ko j., Clio D-W.: 3D ball-end milling force model using instantaneous cutting force coefficients, Transactions of ASME. Journal of Manufacturing Science and Engineering. February 2005, vol. 127, s. 1 —12.
  • [67] Huang D., Te-Yen, Lee, Jyh-Jon: On obtaining machine tool stiffness by CAE techniques, International Journal of Machine Tool Design and Research, 2001, vol. 41, s. 1149—1163.
  • [68] I-DEAS: http://www.ugs.pl/products/ideas/ideas.shtml.
  • [69] Imani B. M., Elbestawi M. A.: Geometric simulation of ball-end milling operations, Transactions of the ASME, Journal of Manufacturing Science and Engineering, May 2001, vol. 123, s. 177-184.
  • [70] Inamura T., Sata T.: Stability analysis of cutting under varying spindle speed, Annals of the CIRP, 1974, no. 23, s. 119—120.
  • [71] Insperger T., Gabor S.: Stability of the milling process, Periodica Polytechnica Ser. Mech. Eng, 2000, vol. 44, no. 1, s. 47—57.
  • [72] Insperger T., Mann B. P., Stepan G., Bayly P. V.: Stability of up-milling and down-milling. Part 1. Alternative analytical methods, International Journal of Machine Tools & Manufacture, 2003, no. 43, s. 25—34.
  • [73] Insperger T., Stepan G.: Stability of high-speed milling, in: Proceedings of Symposium on Nonlinear Dynamics and Stochastic Mechanics, AMD-vol. 241, Orlando 2000, s. 1—5.
  • [74] Insperger T., Stepan G.: Vibration frequencies in high-speed milling processes or a positive answer to Davies, Pratt, Dutterer and Burns, Transaction of ASME, Journal of Manufacturing and Engineering, August 2004, vol. 126, s. 481—487.
  • [75] Ismail F., Bastami A.: Improving stability of slender end mills against chatter, ASME Journal of Engineering for Industry, 1986, no. 108, s. 264—268.
  • [76] Ismail F., Soliman E.: A new method for the identification of stability lobes in machining. Int. J. Mach. Tools Manufact., 1997, vol. 37, no. 6, s. 763—774.
  • [77] Ismail F., Vadari V. R.: Machining chatter of end mills with unequal modes, Transactions of the ASME, Journal of Engineering for Industry, August 1990, vol. 112, s. 229—235.
  • [78] Ismail F., Ziaei R.: Chatter suppression in five-axis machining of flexible parts. International Journal of Machine Tools & Manufacture, 2002, no. 42, s. 115—122.
  • [79] Jabłoński W.: Modelling and verification of the cutting force, in: Proceedings of the 10th International DAAAM Symposium, Wiedeń 1999, s. 219—220.
  • [80] Jabłoński W.: The analysis of one-degree freedom model parameters, in: Proceedings of the 10th International DAAAM Symposium, Wiedeń 1999, s. 217—218.
  • [81] Jang D., Kim K., Jung J.: Voxel-based virtual multi-axis machining, Int. J. Advanced Manufacturing Technology, 2000, no. 16, s. 709—713.
  • [82] Jastrzębski D., Pawełko P., Szwengier G.: Modelowanie ślizgowego połączenia śruba pociągowa-nakrętka, XLIII Sympozjon PTMTS „Modelowanie w mechanice", Zeszyty Naukowe Politechniki Śląskiej, 2004, nr 23, s. 185—190.
  • [83] Jayaram S., Kapoor S. G., DeVor R. E.: Analytical stability analysis of variable spindle speed machining, Transactions of ASME. Journal of Manufacturing Science and Engineering, August 2000, vol. 122, s. 391—397.
  • [84] Jayaram S., Kapoor S. G., DeVor R. E.: Estimation of the specific cutting pressures for mechanistic cutting force models, International Journal of Machine Tools & Manufacture, 2001, no. 41, s. 265—281.
  • [85] Jemielniak K.: Modellin of dynamic cutting coefficients in three-dimensional cutting, Int. J. Mach. Tools Manufact., 1992, vol. 32, no. 4, s. 509—519.
  • [86] Jensen C., G., Red W. E., Pi J.: Tool section for five-axis curvature matched machining. Computer-Aided Design, 2002, no. 34, s. 251—266.
  • [87] Jiulian F., Zhejun Y., Yingxue Y.: A unified system model of cutting chatter and its transformation function, Int. J. Mach. Tools Manufact., 1989, vol. 29, no. 4, s. 601 - 609
  • [88] Junz Wang J.-J., Zheng C. M.: An analytical force model with shearing and ploughing mechanisms for end milling, International Journal of Machine Tools & Manufacture, 2002, no. 42, s. 761—771.
  • [89] Kaczorek T.: Teoria sterowania i systemów, Warszawa, Wydawnictwo Naukowe PWN 1993.
  • [90] Kaliński K.: A transient face milling process dynamics analysis. Machine Vibrations, 1995, no. 3, s. 217 — 224.
  • [91] Kaliński K.: An analysis of the dynamics of the nonlinear milling machine process. Machine Vibrations, 1995, no. 3, s. 209-216.
  • [92] Kaliński K.: Chatter vibration surveillance by the spindle speed optimal control. in: Third International Conference on Metal Cutting and High Speed Machining, Metz, Francja 2001, s. 237—240.
  • [93] Kaliński K.: Computer prediction of the tool-workpiece vibration surveillance in modern milling operations, in: II International Seminar on Improving Machine Tool Performance, Ref. A25, Ecole Centrale, La Baule, France 2000, s. 20.
  • [94] Kaliński K.: On one method of the tool-workpiece vibration control during cutting process, Postępy Technologii Maszyn i Urządzeń, 1999, vol. 23, nr 3, s. 17—42.
  • [95] Kaliński K., Kucharski T., Pawiak S.: A new method for suppression of chatter vibration by programmed spindle speed control, in: Third International Conference on Metal Cutting and High Speed Machining, Metz, Francja 2001, s. 241—250.
  • [96] Kamar-Nagy T., Moon F. C.: Mode-coupled regenerative machine tool vibrations. Nonlinear Dynamics of Production Systems, Weinheim, Wiley-VCH Verlag, 2004, s. 129—151.
  • [97] Karsai G.: Stability of periodically operating dynamic systems, Periodica Polytechnica Ser. Mech. Eng., 1996, vol. 10, no. 1, s. 45—57.
  • [98] Karube S., Hoshino W., Soutome T., Sato K.: The non-linear phenomena in vibration cutting system the establishment of dynamic model, International Journal of Non—Linear Mechanics, 2002, no. 37, s. 541— 564.
  • [99] Kasahara N., Sato H., Tani Y.: Phase characteristics of self-excited charter in cutting, Transactions of the ASME, Journal of Engineering for Industry, November 1992, vol. 114, s. 393—399.
  • [100] Kegg R. L.: Cutting dynamics in machine tool chatter — Research III, ASME Journal of Engineering for Industry, 1965, vol. 87, s. 464-470.
  • [101] Kiciak P.: Podstawy modelowania krzywych i powierzchni. Warszawa, WNT 2000.
  • [102] Kim K. J., Ha J. Y.: Suppression of machine tool chatter using a viscoelastic dynamic damper, Transactions of the ASME, Journal of Engineering for Industry, February 1987, vol. 109, s. 58—65.
  • [103] Kitajima K., Nakamae T., Sugimoto K., Momose K.: Suppression of charter vibration with cutting-off tool using damping alloy, Int. J. Japan Soc. Prec. Eng., 1994, vol. 28, no. 1, s. 41—42.
  • [104] Ko T. J., Kim H. S., Lee S. S.: Selection of machining inclination angle in high-speed ball end milling, Int. Journal of Advanced Manufacturing Technology, 2001, no. 17, s. 163—170.
  • [105] Kruszewski J. i inni: Metoda elementów skończonych w dynamice konstrukcji. Warszawa, Arkady 1984.
  • [106] Kruszewski J., Wittbrodt E., Walczyk Z.: Drgania układów mechanicznych w ujęciu komputerowym, tom 1, Warszawa, WNT 1993.
  • [107] Kruszewski J., Wittbrodt E., Walczyk Z.: Drgania układów mechanicznych w ujęciu komputerowym, tom 2, Warszawa, WNT 1994.
  • [108] Kudinov V. A.: Dinamičeskaja harakteristika rezanija, Stanki i Instrumenty-, 1963, nr 10.
  • [109] Kudinov V. A.: Dinamika stankov; Moskva, Mašinostroenie 1967.
  • [110] Lagö T. L., Olson S., Häkanson L., Claesson I.: Performance of a chatter control system for turning and boring applications, in: 4th GRACM Congress on Computational Mechanics, 27—29 June, Patras 2002, s. 1—8.
  • [111] Lai G. J., Chang J. Y.: Stability analysis of chatter vibration for a thin-wall cylindrical workpiece, Int. J. Mach. Tools Mamifact., 1995, vol. 35, no. 3, s. 431- -444.
  • [112] Lartigue C., Duc E., Affouard A.: Tool path deformation in 5-axis flank milling using envelope surface, Computer-Aided Design, 2003, no. 35, s. 375—382.
  • [113] Lee B. Y., Targ Y. S., Ma S. C.: Modeling of the process damping force in charter vibration, Int..J. Mach. Tools Manufact., 1995, vol. 35, no. 7, s. 951—962.
  • [114] Lee R. S., Lee J. N.: A new tool-path generation method using a cylindrical end mill for 5-axis machining of spatial cam with a conical meshing element, Int J Adv Manuf Technol, 2001, no. 18, s. 615—623.
  • [115] Lee S. H., Yang S. H.: CNC tool-path planning for high-speed high-resolution machining using a new tool-path calculation algorithm, Int. J. Advanced Mamufacturing Technology. 2002. no. 20, s. 326—333.
  • [116] Li H., Li X.: Modeling and simulation of charter in milling using a predictive force model, International Journal of Machine Tools & Manufacture, 2000, no. 40, s. 2047—2071.
  • [117] Lim E. M., Feng H.-Y., Meno C.-H., Lin Z.-H.: The prediction of dimensional error for sculptured surface productions using the ball-end milling process. Part 1. Chip geometry analysis and cutting force prediction, Int. J. Mach. Tools Manufact., 1995, vol. 35, no. 8, s. 1149— 1169.
  • [118] Lin A. C., Gian R.: A multiple-tool approach to rough machining of sculptured surfaces, Int. J. Advanced Manufacturing Technology, 1999, no. 15, s. 387—398.
  • [119] Lisewski W.: Metoda doświadczalnego poszukiwania słabych ogniw w układzie masowo-sprężystym obrabiarki ze względu na jej wibrostabilność, rozprawa doktorska. Politechnika Szczecińska, Szczecin 1991, maszynopis.
  • [120] Liu X. D., Lee L. C., Lam K. L.: A slip-line field model for the determination of chip curl radius, Transactions of the ASME, Journal of Engineering for Industry, May 1995, vol. 117, s. 266—271.
  • [121] Mann B. P., Bayly P. V., Davies M. A., Halley J. E.: Limit cycles, bifurcations, and accuracy of the milling process, Journal of Sound and Vibration, 2004, no. 227, s. 31—48.
  • [122] Mann B. P., Garg N. K., Young K. A., Helvey A. M.: Milling bifurcations from structural asymmetry and nonlinear regeneration, Nonlinear Dynamics, 2005, no. 42, s. 319—337.
  • [123] Mann B. P., Insperger T., Bayly P. V., Stepan G.: Stability of up-milling and down-milling. Part 2. Experimental verification, International Journal of Machine Tools & Manufacture. 2003, no. 43, s. 35—40.
  • [124] Marchelek K.: Dynamika obrabiarek. Warszawa, WNT 1991.
  • [125] Marciniak K., Putz B., Wojciechowski J.: Obróbka powierzchni krzywoliniowych na frezarkach sterowanych numerycznie. Warszawa, WNT 1998.
  • [126] Marui E., Hashimoto M., Kato S.: Regenerative chatter vibration occurring in turning with different side cutting edge angles, Transactions of the ASME, Journal of Engineering for Industry, November 1995, vol. 117, s. 551—558.
  • [127] Marui E., Kato S., Hashimoto M., Yamada T.: The mechanism of chatter vibration in spindle-workpiece system. Part 1. Properties of self-excited chatter vibration in spindle-workpiece-system, Transactions of the ASME, Journal of Engineering for Industry, August 1988, vol. 110, s. 236—241.
  • [128] Marui E., Kato S., Hashimoto M„ Yamada T.: The mechanism of chatter vibration in spindle-workpiece system. Part 2. Characteristics of dynamic cutting force and vibration energy. Transactions of the ASME, Journal of Engineering for Industry. August 1988, vol. 110, s. 242—247.
  • [129] Marui E., Kato S., Hashimoto M., Yamada T.: The mechanism of chatter vibration in spindle-workpiece system. Part 3. Analytical considerations, Transactions of the ASME, Journal of Engineering for Industry, August 1988, vol. 110, s. 248—253.
  • [130] MasterCAM: http://www.mastercam.com.
  • [131] Matsubara T., Yamamoto H., Mizumoto H.: Study on regenerative charter vibration in bering operations (1st report), Bull. Japan Soc. of Prec. Eng., 1989, vol. 23, no. 1, s. 42—46.
  • [132] Merritt H. E.: Theory of self-excited machine tool chatter-research I, ASME Journal of Engineering for Industry, 1965, vol. 17, s. 447—454.
  • [133] Milfelner M., Cus F.: Simulation of cutting forces in ball-end milling. Robotics and Computer Integrated Manufacturing, 2003, nr 19, s. 99—106.
  • [134] Minis E. I., Magrab E. B., Pandelidis I. O.: Improved methods for the prediction of chatter in turning. Part I. Determination of structural response parameters. Transactions of the ASME, Journal of Engineering for Industry, February 1990, vol. 112, s. 12—20.
  • [135] Minis E. I., Magrab E. B., Pandelidis I. O.: Improved methods for the prediction of chatter in turning. Part 2. Determination of cutting process parameters, Transactions of the ASME, Journal of Engineering for Industry, February 1990, vol. 112, s. 21—27.
  • [136] Minis E. I., Magrab E. B., Pandelidis I. O.: Improved methods fort he prediction of chatter in turning. Part 3. A generalized linear theory, Transactions of the ASME, Journal of Engineering for Industry, February 1990, vol. 112, s. 28—35.
  • [137] Minis I., Tembo A.: Experimental verification of a stability theory for periodic cutting operations, Transactions of the ASME, Journal of Engineering for Industry. February 1993, vol. 115, s. 9—14.
  • [138] Minis I., Yanushevsky R.: A new theoretical approach for the prediction of machine tool chatter in milling, Transactions of the ASME, Journal of Engineering for Industry, February 1993. vol. 115, s. 1—8.
  • [139] Miszczak W.: Model predykcyjny sił i momentu skrawania w procesie wiercenia, Prace Naukowe Katedry Budowy Muszyn Politechniki Śląskiej, 2005, nr 19.
  • [140] Mitsuishi M., Nagao T., Ohta T., Okabe H.: A practical machining condition determination strategy using multi-axis force information, Annals of the CIRP, 1996, vol. 45(1), s. 373—376.
  • [141] Moon F. C., Kalmar-Nagy T.: Nonlinear models for complex dynamics in cutting materials, The Royal Society, 2001, no. 359, s. 695—711.
  • [142] Movahhedy M. R., Mosaddegh P.: Prediction of chatter in high speed milling including gyroscopic effects, International Journal of Machine Tools & Manufacture, 2006. no. 46, s. 996—1001.
  • [143] Ng E.-G., Aspinwall D. K., Brazil D., Monaghan J.: Modeling of temperature and forces when orthogonal machining hardened steel, International Journal of Machine Tools & Manufacture, 1999, no. 39, s. 885—903.
  • [144] Nigm M. M., Sadek M. M., Tobias S. A.: Determination of dynamic cutting coefficients from steady state cutting data, Int. J of Machine Tools Des and Res, 1977, vol. 17, s. 19—27.
  • [145] Oczoś K., Pyrzycki J.: Szlifowanie, Warszawa, WNT 1986.
  • [146] Olgac N., Hosek M.: A new perspective and analysis for regenerative machine tool chatter, International Journal of Machine Tools & Manufacture, 1998, no. 38, s. 783—798.
  • [147] Osiński Z.: Tłumienie drgań mechanicznych. Warszawa, PWN 1986.
  • [148] Ozturk B., Lazoglu I.: Machining of free-form surfaces. Part I. Analytical chip load, International Journal of Machine Tools & Manufacture, 2006. no. 46, s. 728—735.
  • [149] Ozturk B., Lazoglu I., Erdim H.: Machining of free-form surfaces. Part II. Calibration and forces, International Journal of Machine Tools & Manufacture, 2006, no. 46, s. 736—746.
  • [150] Pajor M.: Prognozowanie wibrostabilności wielowymiarowego układu OUPN przy frezowaniu walcowo-czołowvm, rozprawa doktorska. Politechnika Szczecińska, Szczecin 1997, maszynopis.
  • [151] Pajor M. i inni: Wibrostabilność frezowania czołowego - prognozowanie i badania doświadczalne, raport końcowy z projektu KBN nr T07D 003 14, Politechnika Szczecińska, Szczecin 2001, maszynopis.
  • [152] Pajor M., Gutowski P., Berczyński S.: Shaping dynamic properties of machine tools to improve their vibrostability. Part III. Practical verification of the method. Postępy Technologii Maszyn i Urządzeń, 2002, vol. 22, nr 2, s. 5—20.
  • [153] Pajor M., Tomków J., Witek A.: Obliczenia wibrostabilności obrabiarek w systemie DOUNO, Archiwum Technologii Maszyn i Automatyzacji, 1993, z. 12, s. 301—321.
  • [154] Pakdemirli M., Ulsoy A. G.: Perturbation analysis of speed variation in machine tool chatter, Journal of Vibration and Control, 1997, no. 3, s. 261—278.
  • [155] Petko M. i inni: Aktywne kształtowanie sztywności konstrukcji wsporczych maszyn realizowanych w postaci manipulatorów równoległych, raport końcowy z projektu KBN nr 4 T07B 077 26, Akademia Górniczo-Hutnicza, Kraków 2006, maszynopis.
  • [156] Powałka B.: Metody kształtowania wibrostabilności systemu obrabiarka-proces skrawania, Prace Naukowe Politechniki Szczecińskiej, 2006, nr 586, Instytut Technologii Mechanicznej, (w druku).
  • [157] Rao C. B., Shin Y. C.: A comprehensive dynamic cutting force model for chatter prediction in turning, International Journal of Machine Tools & Manufacture, 1999, no. 39, s. 1631—1654.
  • [158] Reddy R. G., DeVor R. E., Kapoor S. G.: A mechanistic force model for combined axial-radial contour turning. International Journal of Machine Tools & Manufacture. 2001. no. 41, s. 1551—1572.
  • [159] Redonnet I. M. i inni: Optimissing tool positioning for end-mill machining of frez-form surfaces on 5-axis machines for both sami-finishing, Int J Adv Manuf Technol, 2001, no. 18, s 383—391.
  • [160] Richards N. D., Fussell B. K., Jerard R. B.: Efficient NC machining using off-line optimized feedrates and on-line adaptive control, in: Manufactiring Eng.Division: Symposium on Process Planing and Process Optimization 2002 IMECE, New Orlean 2002, s. 1—11.
  • [161] Rigal J.-F., Pupaza C., Bedrin C.: A model for simulation of vibrations during operations of complex surfaces, Annals of the CIRP, 1998, vol. 47( 1), s. 51—54.
  • [162] Roth D., Ismail F., Bedi S.: Mechanistic modeling of 5-axis milling using an adaptive depth buffor. Computer-Aided Design, 2003, vol. 35, s. 1287—1303.
  • [163] Rusiek R., Szablewski K., Warminski J.: Influence of the workpiece profile on the self-excited vibrations in a metal turning process. Nonlinear Dynamics of Production Systems, Weinheim, Wiley-VCH Verlag 2004, s. 154—167.
  • [164] Sandvik Coromant: Narzędzia skrawające firmy Sandvik Coromant, katalog główny, Szwecja 2006.
  • [165] Sandvik Coromant: Poradnik obróbki skrawaniem, podręcznik firmy Sandvik Coromant, Szwecja 2006.
  • [166] Sasahara H., Obikawa T., Shirakashi T.: FEM analysis on three dimensional cutting. Int. J. Japan Soc. Prec. Eng., 1994, vol. 28, no. 2, s. 123—128.
  • [167] Sastry S., Kapoor S. G. DeVor R. E.: Floquet theory based approach for stability analysis of the variable speed face-milling process, Transactions of ASME. Journal of Manufacturing Science and Engineering, February 2002, vol. 124, s. 10—17.
  • [168] Saxton J. S., Stone B. J.: The stability of machining with continuosly varing spindle speed, Annals of the CIRP, 1978, vol.27(1), s. 321—326.
  • [169] Shabana A., Thomas B.: Charter vibration of flexible multibody machine tool mechanisms. Mech. Mach. Theory, 1987, vol. 22, no. 4, s. 359—369.
  • [170] Shih A. J., Luo J., Lewis M. A., Strenkowski J. S.: Chip morfology and forces in end milling of elastomers, Transactions of ASME. Journal of Manufacturing Science and Engineering, February 2004, vol. 126, s. 124—130.
  • [171] Shin Y. C.: Bearing nonlinearity and stability analysis in high speed machining, Transactions of the ASME, Journal of Engineering for Industry, February 1992, vol. 114, s. 23—29.
  • [172] Shirase K., Altintas Y.: Cutting force and dimensional surface error generation in peripheral milling with variable pitch helical end mills, Int. J. Mach. Tools Manufact., 1996, vol. 36. no. 5, s. 567—584.
  • [173] Smith S., Tlusty J.: Current trends in high-speed machining, Transactions of ASME. Journal of Manufacturing Science and Engineering, November 1997, vol. 119, s. 664—666.
  • [174] Smith S., Tlusty J.: Efficient simulations programs for chatter in milling. Annals of the CIRP, 1993, vol. 42(1), s. 463—466.
  • [I75] Smith S., Tlusty J.: Stabilizing chatter by automatic spindle speed regulation. Annals of the CIRP, 1992. vol. 41(1), s. 433—436.
  • [176] Smith S., Tlusty J.: Update on high-speed milling dynamics, Transactions of the ASME, Journal of Engineering for Industry, May 1990, vol. 112, s. 142—149.
  • [177] Smithey D. W., Kapoor S. G., DeVor R. E.: A worn tool force model for three-dimensional cutting operations, International Journal of Machine Tools & Manufacture, 2000, no. 40, s. 1929—1950.
  • [178] SolidCAM: http://www.solidcam.info.
  • [179] Spence A. D., Abrari F., Elbestawi M. A.: Integrated solid modeler based solutions for machining, Computer-Aided Design, 2000, no. 32, s. 553—568.
  • [180] Sridhar R., Hohn R. E., Long G. W.: A stability algorithm for the general milling process, Transactions of ASME. Journal of Engineering for Industry, May 1968, s. 330—334.
  • [181] Srinivasan K., Nachtigal C. L.: Analysis and design of machine tool chatter control system using the regeneration spectrum, Transactions of the ASME, Journal of Dynamic Systems and Control, September 1978, vol. 100, s. 191—200.
  • [182] Srinivasan K., Nachtigal C. L.: Investigation of the cutting process dynamics in turning operations, Transactions of the ASME, Journal of Engineering for Industry, August 1978, vol. 100, s. 323—331.
  • [183] Stepan G., Szalai R., lnsperger T.: Nonlinear dynamics of high-speed milling subjected to regenerative effect, Nonlinear Dynamics of Production Systems, Weinheim, Wiley-VCH Verlag 2004, s. 111—128.
  • [184] Stone E., Ahmed S., Askari A., Tat H.: Investigations of process damping forces in metal cutting, Journal of Computational Methods in Science, February 2005, s. 1—27.
  • [185] Stone E., Askari A.: Nonlinear models of chatter in drilling processes, Dynamical System, 2002, no. 17(1), s. 65—85.
  • [186] Stone E., Askari A., Tat H.: Investigations of nonlinear forces in metal cutting, 2001, s. 1—25.
  • [187] Stori J. A., Wright P. K.: Parameter space decomposition for selection of the axial and radial depth of cut in endmilling, Transactions of ASME. Journal of Manufacturing Science and Engineering, November 2001, vol. 123, s. 654—664.
  • [188] Suh C. S., Khurjekar P. P., Yang B.: Characterisation and identification of dynamic istability in milling operation, Mechanical System and Signal Processing, 2002, no. 16(5), s. 853—872.
  • [189] Szwengier G.: Metoda korekcji obciążeń w projektowych obliczeniach połączeń stykowych elementów maszyn. Część I. Koncepcja metody. Część II. Modelowanie układów z połączeniami stykowymi. Część III. Efektywność metody, Archiwum Technologii Maszyn i Automatyzacji, 1993, z. 12, s. 423—481.
  • [190] Szwengier G.: Modelowanie i obliczenia układów prowadnicowych obrabiarek, Prace Naukowe Politechniki Szczecińskiej, 1994, nr 512, Instytut Technologii Mechanicznej, nr 13.
  • [191] Tansel I. N.: Simulation of turning operations, Int. J. Mach. Tools Manufact., 1990, vol. 30, no. 4, s. 535-547.
  • [192] Tansel I. N., Erkal C., Keramidas T.: The chaotic characteristics of three dimensional cutting, Int. J. Mach. Tools Manufact., 1992, vol. 32, no. 6, s. 811—827.
  • [193] Tarng Y. S., Kao J. Y., Lee E. C.: Chatter suppression in turning operations with a tuned vibration absorber, Journal of Materials Processing Technology, 2000, no. 105, s. 55—60.
  • [194] Tarng Y. S., Li T. C.: On-line monitoring and suppression of self-excited vibration in end milling, Mechanical System and Signal Processing, 1994, 8(5), s.597—606.
  • [195] Tarng Y. S., Young H. T., Lee B. Y.: An analytical model of chatter vibration in metal cutting, Int. J. Mach. Tools Manufact., 1994, vol. 34, no. 2, s. 183—197.
  • [196] Thompson R. A.: Chatter growth — tests to evaluate the theory, Transactions of the ASME, Journal of Engineering for Industry, November 1988, vol. 110, s. 344—351.
  • [197] Tian J., Hutton S. G.: Chatter instability in milling systems with flexible rotating spindles — a new theoretical approach, Transactions of ASME. Journal of Manufacturing Science and Engineering, February 2001, vol. 123, s. 1—9.
  • [198] Tlusty J.: Analysis of the state of research in cutting dynamic, Annals of the CIRP, 1978, vol. 27(2), s. 583—589.
  • [199] Tlusty J., Ismail F.: Basic non-linearity in machining chatter, Annals of the CIRP, 1981, vol. 30( 1), s. 299—304.
  • [200] Tlusty J., Polacek M.: The stability of the machine tool against self-excited vibration in machining, International Res. in Production Engineering, ASME, 1963, s. 465—474.
  • [201] Tlusty J., Polacek M., Danek C., Spacek J.: Selbsterregte Schwingungen on Werkzeugmaschinen, Berlin, VEB Verlag Technik 1962.
  • [202] Tlusty J., Zaton W., Ismail F.: Stability lobes in milling. Annals of the CIRP. 1983. vol. 32( 1), s. 309—313.
  • [203] Tobias S. A., Fishwick W.: The chatter of lathe tools under other cutting conditions, Transactions of ASME, 1958, vol. 80, s. 1079—1088.
  • [204] Tomków J.: Wibrostabilność obrabiarek. Komputerowe wspomaganie obliczeń i badania doświadczalne. Warszawa, WNT 1997.
  • [205] Tomków J., Skrodzewicz J.: Metody badania dynamicznych charakterystyk procesu skrawania przy toczeniu ortogonalnym, rozprawa doktorska. Politechnika Szczecińska, Szczecin 1980, maszynopis.
  • [206] Uhl T.: Wspomaganie komputerowe CAD CAM. Komputerowo wspomagana identyfikacja modeli konstrukcji mechanicznych. Warszawa, WNT 1997.
  • [207] Van de Wou N., Faassen R. P. H., Osterling J. A. J., Nijmeijer H.: Modeling of high-speed milling for prediction of regenerative chatter, Nonlinear Dynamics of Production Systems, Weinheim, Wiley-VCH Verlag 2004, s. 169—186.
  • [208] Venuvinod P. K., Jin W. L.: Three-dimensional cutting force analysis based on the lower boundary of the shear zone. Part 1. Single edge oblique cutting, Int. J. Mach. Tools Manufact.. 1996, vol. 36, no. 3, s. 307—323.
  • [209] Waldorf D. J., DeVor R. E., Kapoor S. G.: A slip-line field for ploughing during orthogonal cutting, Transactions of the ASME, Journal of Manufacturing Science and Engineering. November 1998, vol. 120, s. 693—699.
  • [210] Wang J., Mathew P.: Development of a general tool model for turning operations based on a variable flow stress theory, Int. J. Mach. Tools Manufact., 1995, vol. 35, no. 1, s. 71—90.
  • [211] Wang M., Renyuan F.: Chatter suppression based on nonlinear vibration characteristic of electrorheological fluids, International Journal of Machine Tools & Manufacture, 1999, no. 39, s. 1925—1934.
  • [212] Warkentin A., Ismail F., Bedi S.: Intersection approach to multi-point machining of sculptured surfaces, Computer Aided Geometric Design, 1998, no. 15, s. 567—584.
  • [213] Weck M., Petuelli G.: Verfahren zur Analyse des richtungsoientierten Schwingungsverhaltens spanender Werkzeugmaschinen, WT Zeitschrift für industrielle Fertigung, 1979, 69, s. 709—715.
  • [214] Werntze G.: Dynamische Schnittkraftkoeffizienten, Dr Ing. Dissertation, Technische Hohschule Achen 1973.
  • [215] Wiercigroch M., Krivtsov A. M.: Frictional chatter in orthogonal metal cutting, The Royal Society, 2001, no. 359, s. 713— 738.
  • [216] Wittbrodt E.: Dynamika układów o zmiennej w czasie konfiguracji z zastosowaniem metody elementów skończonych, Zeszyty Naukowe Politechniki Gdańskiej, 1983, nr 364, Mechanika, nr 46.
  • [217] Wright W. C., Kerlin T. W.: An efficient, computer-oriented method for stability analysis of large multivariable linear system, Transactions of the ASME, Journal of Basic Engineering, June 1970, s. 279—285.
  • [218] Wrotny L. T.: Projektowanie obrabiarek. Zagadnienia ogólne i przykłady obliczeń. Warszawa, WNT 1986.
  • [219] Wu D. W.: A new approach of formulating the transfer function for dynamic cutting processes, Transactions of the ASME, Journal of Engineering for Industry, February 1989, vol. 111, s. 37—47.
  • [220] Xiao M., Karube S., Soutome T., Sato K.: Analysis of chatter suppression in vibration cutting, International Journal of Machine Tools & Manufacture, 2002, no. 42, s. 1677—1685.
  • [221] Yang X. G., Chen W. J., Li S. Z., Eman K. F.: The theoretical stability chert of machine tools - a development of S. A. Tobias' theory, Int. J. Mach. Tools Manufact., 1989, vol. 29, no. 2, s. 267—274.
  • [222] Yilmaz A., AL-Regib E., Ni J.: Machine chatter suppression by multi-leval random spindle speed variation, Transactions of ASME. Journal of Manufacturing Science and Engineering, May 2002, vol. 124, s. 208—216.
  • [223] Yoon M. C., Kim Y. G.: Cutting dynamic force modeling of endmilling operation, Journal of Materials Processing Technology, 2004, no. 155—156, s. 1383—1389.
  • [224] Youn J-W., Yang M-Y.: A study on the relationships between static/dynamic cutting force components and tool wear, Transactions of ASME. Journal of Manufacturing Science and Engineering, May 2001, vol. 123, s. 196—205.
  • [225] Yu W., Xiaowei T.: Five-axix NC machining of sculptured surfaces, Int J Adv Manuf Technol. 1999, no. 15, s. 7—14.
  • [226] Yun W.-S., Cho D.-W.: Accurate 3-D cutting force prediction using cutting condition independent coefficients in end milling, International Journal of Machine Tools & Manufacture, 2001, no. 41, s. 463—478.
  • [227] Zars V. V.: Ustojcivost sistem s otstavaniem sily po skorosti rezanija, Voprosy Dynamiki i Pročnosti, 1967, nr 15.
  • [228] Zars V. V.: Vlijanie otstavanija na vozbuzdajuščuju sposobnost sily rezanija, Voprosy Dynamiki i Procnosti, 1967, nr 14.
  • [229] Zars V. V.: Voprosy ustojcivosti rezanija na metallorezuščih stankah, rozprawa doktorska, Riga 1971.
  • [230] Zars V. V.: Wybrane zagadnienia wyznaczania granicy stabilności obrabiarek do metali, Prace Naukowe Politechniki Szczecińskiej, 1978, nr 96.
  • [231] Zeid I.: Mastering CAD/CAM, New York, MacGraw Hill 2005.
  • [232] Zheng H. Q., Li X. P., Wong Y. S., Nee A. Y. C.: Theoretical modeling and simulation of cutting face milling with cutter runout, International Journal of Machine Tools & Manufacture, 1999, no. 39, s. 2003—2018.
  • [233] Zienkiewicz O. C.: Metoda elementów skończonych, Warszawa, Arkady 1972.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPS2-0042-0027
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.