2017
DOI: 10.21595/vp.2017.18461
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On the question of the relationship between longitudinal and torsional vibrations in the manufacture of holes in the details

Abstract: Abstract. The article describes the features of the interaction between the cutting part of the tool and the part when processing deep holes. The description of the motion of the executive body is based on the second-order Lagrange equation. The differential equations of motion for five generalized coordinates derived. At the first stage of the study, only longitudinal and torsional oscillations were considered. With the use of Laplace images, a transfer function is obtained, taking into account the relationsh… Show more

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Cited by 8 publications
(3 citation statements)
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“…These result in a loss of accuracy of hole manufacture, facet-type defects and considerable deviations (run-outs) of the cutting tool, etc. [6][7][8].…”
Section: Development and Rationale For Choosing The Specimensmentioning
confidence: 99%
“…These result in a loss of accuracy of hole manufacture, facet-type defects and considerable deviations (run-outs) of the cutting tool, etc. [6][7][8].…”
Section: Development and Rationale For Choosing The Specimensmentioning
confidence: 99%
“…Many studies of dynamic systems, adapted to specific technological processes, include various approaches to the construction of a mathematical model. For example, in [2][3][4][5], modeling of complex technological objects was carried out on the basis of the method using the well-known equations of the momentum in differential form for longitudinal and torsional vibrations. This approach made it possible to relate the fluctuations in the velocities and stresses in rather complex systems with both distributed parameters and significant nonlinearities.…”
Section: Statement Of the Problemmentioning
confidence: 99%
“…Gopalkrishna et al studied the optimal stable rest number of gun drilling rigs by establishing an empirical relationship between the maximum amplitude of resonance frequency and the length and diameter of the borehole 10 . Kondratenko et al established a differential equation for drill pipe vibration based on the Lagrange equation and studied the variation of drill pipe drilling speed and stress at different lengths 11 . Wang et al established a rigid flexible coupling dynamic model of the horizontal drilling rig drill pipe hole wall system based on the second type of Lagrange equation and the Newton Euler method, and found that the drilling depth has a greater impact on the system 12 .…”
mentioning
confidence: 99%