An Experimental Study of the Effect of Screw Tightening on the Resonance Frequencies of a Cantilever Beam

The vibrations arising in the process of machining, have a significant effect on the accuracy of technological machines. When simulating the dynamic behavior of a machine, approaches based on simplified modeling of parts and assemblies do not yield reliable results, because they consider the contact of perfectly smooth surfaces, while detailed simulation of the contact layer involves large computational costs and is difficult to perform for most engineering tasks. In this context, the approach based on modeling the contact layer as a third body, the parameters of which depend on many factors, such as the pressure in the contact layer, has become widely adopted. In this paper, the results of experiments to determine the effect of the tightening force of screws of a threaded joint on the resonant frequencies of a sample consisting of a base and a cantilever fitted beam are presented. The studies are performed on the assumption of a nonlinear dependence of the pliability of the contact layer on the contact pressures. As a result, the dependencies of the resonance frequency on the tightening forces for different cases of the contact area are obtained.

References

[1] Koloskova A.V., Kiselev I.A., Ivanov I.I. Modelirovanie dinamiki protsessa tocheniya s uchetom podatlivosti obrabatyvaemoy detali [Modeling of the turning process dynamics, taking into the account the compliance of the workpiece]. Internet-zhurnal «Naukovedenie» [Internet-journal «Science of science»]. 2017, vol. 9, no. 2, 70 p. Available at: https://naukovedenie.ru/PDF/36TVN217.pdf (accessed 15 April 2018).

[2] Ito Y. Modular design for machine tools. New York, McGraw Hill Professional, 2008. 504 p.

[3] Guo T., Li L., Cai L., Zhao Y. Alternative method for identification of the dynamic properties of bolted joints. Journal of Mechanical Science and Technology, 2012, no. 26 (10), pp. 3017–3027.

[4] Ahmadian H., Jalali H. Identification of bolted lap joints parameters in assembled structures. Mechanical Systems and Signal Processing, 2007, no. 21, pp. 1041–1050.

[5] Sokolov A.P., Shchetinin V.N., Pershin A.Yu., Sapelkin A.S. Reversivnaya mnogomassh¬tabnaya gomogenizatsiya fiziko-mekhanicheskih harakteristik geterogennyh mekhanicheskih sred s ispol’zovaniem grafoorientirovannogo programmnogo podhoda [Reversible multiscale homogenization of physical properties of heterogeneous medium using graph-based software engineering]. Kompozity i nanostruktury [Composites & nanostructures]. 2017, vol. 9, no. 3–4(35–36), pp. 142–155.

[6] Shchetinin V.N., Sokolov A.P. Reshenie zadachi identifikatsii uprugih harakteristik komponent izotropnyh kompozitnyh materialov [Solution of the problem of identification of elastic characteristics of components of isotropic composite materials]. Materialy 20 yubileynoy mezhdunarodnoy konferentsii po vychislitel’noy mekhanike i sovremennym prikladnym sistemam [Materials of the 20 anniversary international conference on computational mechanics and modern applied systems]. Alushta, 24–31 May, Moscow, MAI publ., 2017, pp. 665–666.

[7] Levina Z.M., Reshetov D.N. Kontaktnaya zhestkost’ mashin [Contact stiffness of machines]. Moscow, Mashinostroenie publ., 1971. 264 p.

[8] Ryzhov E.V. Kontaktnaya zhestkost’ detaley mashin [Contact stiffness of machine parts]. Moscow, Mashinostroenie publ., 1966. 196 p.

[9] Ivanov A.S., Izmaylov V.V. Raschet kontaktnoy deformatsii pri konstruirovanii mashin [Calculation of contact deformation in the design of machines]. Trenie i smazka v mashinah i mekhanizmah [Friction&Lubrication in Machines and Mechanisms]. 2006, no. 8, pp. 3–10.

[10] Ivanov A.S. Normal’naya, uglovaya i kasatel’naya kontaktnye zhestkosti ploskogo styka [Normal, angular and tangent contact stiffness of the flat joint]. Vestnik mashinostroeniya [Russian Engineering Research]. 2007, no. 7, pp. 34–37.

[11] Ivanov A.S., Rudnev S.K., Ermolaev M.M. Issledovaniya i raschet sobstvennyh chastot kolebaniy rez’bovyh soedineniy [Research and calculation of natural vibration frequencies of threaded connections]. Sovremennoe mashinostroenie. Nauka i obrazovanie [Modern mechanical engineering. Science and education]. 2014, no. 4, pp. 425–432.

[12] Ermolaev M.M. Taking account of the contact-layer pliability in end clip design. Russian engineering reserch, 2016, vol. 36, no. 5, pp. 355–359.

[13] Biderman V.L. Teoriya mekhanicheskih kolebaniy [Theory of mechanical oscillations]. Moscow, Lenand publ., 2017. 416 p.

[14] Voronov S.A., Kiselev I.A. Nelineynye zadachi dinamiki protsessov rezaniya [Nonlinear Problems of Cutting Process Dynamics]. Mashinostroenie i inzhenernoe obrazovanie [Mechanical engineering and engineering education]. 2017, no. 2(51), pp. 9–23.

[15] Nikolaev S., Voronov S., Kiselev I. Estimation of damping model correctness using experimental modal analysis. Vibroengineering Procedia, 2014, vol. 3, pp. 50–54.

[16] Ewins D.J. Modal testing: theory, practice and application. John Wiley & Sons, 2009. 576 p.

[17] Dunaev P.F., Lelikov O.P. Konstruirovanie uzlov i detaley mashin [Design of units and machine parts]. Moscow, Bauman Press, 2017. 569 p.

[18] Detali mashin [Details of machines]. Ed. Ryahovskiy O.A. Moscow, Bauman Press, 2014. 472 p.