DETERMINATION OF OSCILLATOR CIRCUIT PARAMETERS OF A MATHEMATICAL MODEL OF THE DYNAMICS OF THE CUTTING PROCESS WITH A METAL CUTTING TOOL

Objectives. The development of a mathematical dynamic system model is necessary for analysing vibrational motion during the metal  cutting processes. The mathematical model of the dynamic system is considered to be defined if the system parameters that  unambiguously determine its state are known and the alteration of  its state over time is specified. Considering the above mentioned, each study of vibrational motion must be preceded by a  determination of the parameters of the oscillator circuits of the  mathematical model. The working part of the metal cutting tool  consists in a shank having a complex profile, which makes such  calculations very difficult to carry out. There are no sufficiently rigorous and, at the same time, acceptable formulae for  engineering practice in the literature data. Therefore, data on the  characteristics of the metal cutting tool – in particular, its stiffness  and moment of inertia – scatter significantly. The aim of the study is to obtain calculated dependences that meet these requirements and  determine the limits of their applicability for different cutting tool  diameter ranges.

Methods. Approaches referring to the theory of elasticity are used for the calculations.

Results. Engineering formulae for the calculation of stiffness and  polar moment of inertia of the metal cutting tool are obtained; in  particular, three- and four-blade taps with straight flutes as well as  drills. It is established that to increase the dynamic stability of the  metal cutting tool, it is necessary to increase the moment of inertia  of the section. This can be achieved by increasing the diameter of  the core.As the flute helix angle increases, the stiffness of the tool  decreases significantly. High stiffness of the metal cutting tool can be achieved by employing a flute with a variable helix angle. 

Conclusion. The calculated dependences allow the parameters of  the Machine-Device-Tool-Part (MDTP) system to be set with an  acceptable accuracy when analysing metal processing dynamics  using metal cutting tools. The influence of the sharpening angles on  the moment of inertia is demonstrated; the account given for the  latter will significantly increase the reliability of the results of the  analysis of the process dynamics.

1. Arutyunyan N. Kh., Abromyan B.M. Kruchenieuprugikhtel. M.: GIFML, 1963. 688 s. [ArutyunyanN.Kh., AbromyanB.M. torsion of elastic bodies. M.: GIFML, 1963. 688 p. (In Russ.)]

2. Guseynov R.V. Intensifikatsiya tekhnologicheskikh protsessov obrabotki trudnoobrabatyvaemykh materialov putem upravleniya dinamicheskimi parametrami sistemy. Avtoreferat dissertatsii na soiskanie uchenoy stepeni dokt. tekhn. nauk. Sankt-Peterburg; 1998. [Guseynov R.V. Intensification of technological processing of the hardly processed materials by the management of system's dynamic parameters. Published summary of Doctor of Technical Sciences thesis. St. Petersburg; 1998. (In Russ.)]

3. Guseinov R.V., Rustamova M.R. Matematicheskayamodel' protsessaobrabotkiotverstiisverlaminaosnovenelineinoidinamiki. Ch.1. Postanovka zadachi. Vestnik Dagestanskogo gosudarstvennogo tekhnicheskogo universiteta. Tekhnicheskie nauki. 2011; 3(22):64-68. [Guseinov R.V., Rustamova M.R. Mathematical model of the holeprocessing with drills based on nonlinear dynamics. Part 1. Formulation of the problem. Herald of Daghestan State Technical University. Technical Sciences. 2011; 3(22):64-68. (In Russ.)]

4. Guseinov R.V., Rustamova M.R. Sovershenstvovanie obrabotki otverstii nebol'shogo diametra. Vestnikmashinostroeniya. 2012; 9:50-52. [Guseinov R.V., Rustamova M.R. The improvement of processing the holesof small diameter. Russian Engineering Research. 2012; 9:50-52. (In Russ.)]

5. Guseinov R.V., Rustamova M.R. Issledovanie protsessa obrabotki otverstii na osnove nelineinoi dinamiki. Vestnik Dagestanskogo gosudarstvennogo tekhnicheskogo universiteta. Tekhnicheskienauki. 2012; 26:77-80. [Guseinov R.V., Rustamova M.R. Investigation of the process of hole processing on the basis of nonlinear dynamics. Herald of Dahgestan State Technical University. Technical Sciences. 2012; 26:77-80. (In Russ.)]

6. Guseynova M.R., Guseynov R.V. Obosnovanie bazy dannykh dlya issledovaniya dinamicheskikh protsessov pri rezanii. Vestnik Dagestanskogo gosudarstvennogo tekhnicheskogo universiteta. Tekhnicheskie nauki. 2014; 4(35):36–44. [Guseynova M.R., Guseynov R.V. Justification of the database for the study of dynamic processes during cutting. Herald of Daghestan State Technical University. Technical Sciences. 2014; 4(35):36–44. (In Russ.)]

7. Denisenko V.I. Zhestkost' spiral'nykh sverl i ikh ekspluatatsionnye kharakteristiki. Vil'nyus: 1974. 14 s. [Denisenko V.I. Stiffness of twist drills and their performance characteristics. Vil'nyus: 1974. 14 p. (In Russ.)]

8. Emel'yanov D.V. Analiz prochnostnykh kharakteristik spiral'nykh sverl. Elektronnyi nauchno-prakticheskii zhurnal ―Sovremennaya tekhnika i tekhnologiya‖. 2015; 1(41):87-92. URL: http://technology.snauka.ru/2015/01/5617 (data obrashcheniya: 20.08.2017) [Emel'yanov D.V. Analysis of the strength characteristics of twist drills. Electronic Scientific & Practical Journal ―Modern Technics and Technologies‖. 2015; 1(41):87-92. URL: http://technology.snauka.ru/2015/01/5617 (accessdate: 20.08.2017) (In Russ.)

9. Kirsanov S.V. Vliyanie konstruktsi i razvertki na ogranku obrabotannykh otverstii. Stanki i instrument. 2000; 4:22-23. [Kirsanov S.V. Influence of the reamer design on the facet of the treated holes. Machines and Tooling. 2000; 4:22-23. (In Russ.)]

10. Kudinov V.A. Dinamika stankov. M.: Mashinostroenie; 1967. 357 s. [Kudinov V.A. Dynamics of machine tools. M.: Mashinostroenie; 1967. 357 p. (In Russ.)]

11. Malyshko I.A. Osnovy proektirovaniya osevykh kombinirovannykh instrumentov.Avtoreferat dissertatsii na soiskanie uchenoy stepeni dokt. tekhn. nauk. Kiev; 1996.430 s. [Malyshko I.A. Basics of design of axial combined tools. Published summary of Doctor of Technical Sciences thesis. Kiev; 1996. 430 p. (In Russ.)]

12. Muskhelishvili N.I. Nekotorye osnovnye zadachi matematicheskoi teorii uprugosti. M.: Nauka; 1966. 192 s. [Muskhelishvili N.I. Some basic problems of the mathematical theory of elasticity. M.: Nauka; 1966. 192 p. (In Russ.)]

13. Kholmogortsev Yu.P. Optimizatsiya protsessov obrabotki otverstii. M: Mashinostroenie; 1984. 128 s. [Kholmogortsev Yu.P. Optimisation of the holes processing. M: Mashinostroenie; 1984. 128 p. (In Russ.)]

14. Altintas Y. Manufacturing Automation. New York: Cambridge University Press; 2012. 366 p.

15. Badrawy S. Cutting Dynamics of High Speed Machining. Technology Update. 2001; 8(1):24-26.

16. Ema S., FujiiH., MaruiE. Whirling vibration in drilling. Part 3: Vibration analysis in drilling workpiece with a pilot hole. Journal of Engineering for Industry. 1998; 110:315-321.

17. Schmitz T.L., Smith K.S. Machining Dynamics. Frequency Response to Improved Productivity. Springer US; 2009. 303 p. DOI: 10.1007/978-0-387-09645-2.

18. Systeme doutilequilibre multi-fonctions. TraMetal; Revue techniquemensuelle du travail des metaux. 2000; 51:14–16.