The Method of Calculating Bridges when Milling

The article introduces the method of checking calculations for bridges that are used for clamping workpieces when they are milled on a CNC machine.  Functions are described for determining elastic deflections of the workpiece resulting from the suppleness of the bridges, and for calculating equivalent stresses in the bridges allowing their strength to be estimated.  The calculation is based on the premises that bridges are rectangular and malleable, while the workpiece, in comparison, is rigid. Stress concentrations in the corner of the bridge are ignored. The geometry of the manufactured part can be arbitrary but such that it can be described by analytical functions. Two examples of calculating bridges when milling are considered. Graphs of equivalent stresses and elastic deflections are presented. The proposed method can be used for selecting the right number of bridges and compensating for the errors that occur due to elastic deflections when a workpiece is machined. This is useful in the absence of special tools for clamping the workpiece when milling.

References

[1] Frolov V.K., Gladskii M.N. Analiticheskoe reshenie zadachi opredeleniia uprugikh deformatsii instrumenta pri konturnom frezerovanii kontsevymi frezami [The analytical solution of the problem of determining the elastic deformation of the tool during contour milling end mills]. Vestnik NTUU KPI. Ser. Mashinostroenie [Journal of Mechanical Engineering the National Technical University of Ukraine «Kyiv Polytechnic Institute»]. 2011, no. 63, pp. 171–174.

[2] Kiselev I.A. Modelirovanie dinamiki protsessa frezerovaniia tonkostennykh slozhnoprofil’nykh detalei. Diss. kand. tekhn. nauk [Modeling the dynamics of the milling process of thin-walled parts slozhnoprofilnyh. Cand. tech. sci. diss.]. Moscow, 2013. 16 p.

[3] Poduval’tsev V.V., Khlystunov M.S., Mogiliuk Zh.G. Metrologicheskie kharakteristiki chislennogo modelirovaniia i rascheta rezonansnykh chastot metodom konechnykh elementov [Metrological characteristics of resonant frequencies numerical modelling and calculation by the finite element method]. Nauka i obrazovanie. MGTU im. N.E. Baumana [Science and Education. Bauman MSTU]. 2011, no. 12. Available at: http://technomag.bmstu.ru/doc/252202.html (accessed 25 February 2016).

[4] Chertishchev V.V., Chertishchev V.V. Raschet polei temperatur i teplovykh potokov v nepodvizhnoi srede metodom konechnykh elementov [Calculating Temperature Fields and Heat Flows in Motionless Medium by Finite Element Method]. Izvestiia AltGU [News of Altai State University]. 2011, no. 1–2, pp. 176–180.

[5] Sagdeeva Iu.A., Kopysov S.P., Novikov A.K. Vvedenie v metod konechnykh elementov [Introduction to finite element method]. Izhevsk, Udmurtskii universitet publ., 2011. 44 p.

[6] Osipov A.A., Pershin V.F., Pershina S.V. Soprotivlenie materialov. Ch. 2 [Strength of materials. Pt. 2]. Tambov, TSTU publ., 2011. 80 p.

[7] Biletskii E.O., Gus’kov A.M., Riakhovskii O.A., Firsov E.P. Osobennosti proektirovaniia uprugoi kompensiruiushchei mufty. Ch. 1. Raschet uprugogo elementa pri soosnom raspolozhenii valov [Design features an elastic compensating coupling. Pt. 1. Calculation of the elastic element in the coaxial shafts]. Nauka i obrazovanie. MGTU im. N.E. Baumana [Science and Education. Bauman MSTU]. 2010, no. 12. Available at: http://technomag.bmstu.ru/doc/163921.html (accessed 25 February 2016).

[8] Fomin M.V. Planetarno-tsevochnye peredachi [Planetary transmission-lantern]. Moscow, Bauman Press, 2009. 64 p.

[9] Shchurov I.A., Boldyrev I.S. Modelirovanie protsessa rezaniia zagotovok iz kompozitnykh materialov s primeneniem metoda konechnykh elementov [Finite element method calculation of free orthogonal cutting of composite materials]. Vestnik IuUrGU. Ser. Mashinostroenie [Bulletin of the SUSU, Series «Mechanical engineering industry»]. 2012, no. 12 (271), pp. 143–147.

[10] Repetskii O.V., Do M.T. Matematicheskoe modelirovanie i chislennyi analiz kolebanii ideal’nykh tsiklicheski-simmetricheskikh sistem metodom konechnykh elementov [Mathematical modeling and numerical analysis of vibrations of ideal cyclic symmetric systems by finite element method]. Izvestiia IGEA [Izvestiya of Irkutsk State Economics Academy]. 2012, no. 3, pp. 149–153.

[11] Fokin V.G., Dmitriev V.A. Opredelenie metodom konechnykh elementov dopolnitel’nykh ostatochnykh napriazhenii pri razrezke detalei [Determination of the finite element method of additional residual stresses in cutting parts]. Vestnik Samarskogo gosudarstvennogo tekhnicheskogo universiteta. Ser. «Fiziko-matematicheskie nauki» [Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences]. 2009, no. 1 (18), pp. 95–100.

[12] Mikhailov V.A., Ivannikov S.N., Mokrinskaia A.Iu. Opredelenie kharakteristik rezhushchego instrumenta metodom konechnykh elementov [Capability Check of the Cutting Tool by Method of Final Elements]. Izvestiia MGTU «MAMI» [Proceedings of the MSTU «MAMI»]. 2010, no. 1, pp. 132–135.

[13] Kireev S.O. Teoreticheskie osnovy metodov analiza i sinteza planetarnykh mekhanizmov s vnetsentroidnym tsevochnym zatsepleniem. Diss. dokt. tekhn. nauk [Theoretical foundations of methods of analysis and synthesis of planetary mechanisms with non-centrode pin engagement. Dr. tech. sci. diss.]. Novocherkassk, 2002. 20 p.