A Dynamic Model for a Drill in the Drilling Process
The dynamic model of a drill in drilling process was
proposed and investigated in this study. To assure a good drilling quality, the vibration variation on the drill tips during high speed
drilling is needed to be investigated. A pre-twisted beam is used to
simulate the drill. The moving Winkler-Type elastic foundation is used to characterize the tip boundary variation in drilling. Due to the
variation of the drill depth, a time dependent dynamic model for the drill is proposed. Results simulated from this proposed model indicate that an abrupt natural frequencies drop are experienced as the drill tip
tough the workpiece, and a severe vibration is induced. The effects of parameters, e.g. drilling speed, depth, drill size and thrust force on the
drill tip responses studied.
[1] D. D. Rosard, "Natural Frequency of Twisted Cantilever Beams," in 1952
Pro. ASME Paper No. 52-A-15,
[2] G. W. Jarrett and P. C. Warner, "The Vibration of Rotating Tapered Twisted Beam," ASME, Journal of Applied Mechanics, pp. 381-389,1953.
[3] O. Tekinalp and A. G. Ulsoy, "Modeling and Finite Element Analysis of
Drill Bit Vibration," ASME, Journal of Vibration, Acoustics, Stress, and
Reliability in Design, vol. 111, pp. 148-155, 1989.
[4] O. Tekinalp and A. G. Ulsoy, "Effect of Geometric and Process Parameters in Drill Transverse Vibration," ASME, Journal of Engineering
for Industry, vol. 112, pp. 189-194, 1990.
[5] C. L. Liao, and Y. H. Dang, "Structural Characteristics of Spinning Pretwisted Orthotropic Beams," Computer & Structures, vol. 45, no. 4, pp. 715-731, 1992.
[6] C. L. Liao and B. W. Huang, "Parametric Instability of a Pretwisted Beam
under Periodic Axial Force," International Journal of Mechanical Science, vol. 37, no. 4, pp. 423-439, 1995.
[7] E. Magrab and D. E. Gilsinn, "Bucking loads and natural frequency of
twist drills," Transactions of ASME, vol. 106, pp. 196-204, 1984.
[8] A. G. Ulsoy, "A lumped parameter model for the transverse vibration of
drill bit," in 1989 Proc. Control of Manufacturing Processes and Robotic System, pp. 15-25.
[9] H. Fuji, E. Marui and S. Ema, "Whirling Vibration in drilling part 3: Vibration analysis in Drilling Workpiece with a Pilot Hole," ASME, Journal of engineering for Industry, vol. 110, pp. 315-321, 1988.
[10] D. M. Rincon and A. G. Ulsoy, "Complex Geometry, Rotary Inertia and
Gyroscopic Moment Effects on Drill Vibrations," Journal of Sound and Vibration, vol. 188, no. 5, pp. 701-715, 1995.
[11] T. Iwastsubo, Y. Sugiyama and K. Ishihara, "Stability and Stationary
Vibrations of Columns under Periodic Loads," Journal of Sound and Vibration, vol. 23, pp. 245-257, 1972.
[12] H. P. Lee, "Buckling and Dynamic Stability of Spinning Pre-twisted Beams under Compressive Axial Loads," International Journal of Mechanical Sciences, vol. 36, no. 11, pp. 1011-1026, 1994.
[13] H. P. Lee, "Dynamic Response of a Beam with a Moving Mass," Journal
of Sound and Vibration, vol. 192, no. 2, pp. 289-294,1996.
[14] Y. M. Ram and J. Caldwell, "Free Vibration of a string with Moving
Boundary Conditions by The Method of Distorted Images," Journal of Sound and Vibration, vol. 194, no. 1, pp. 35-47, 1996.
[15] R. F. Fung, J. S. Huang and J. J. Chu, "Dynamic Stability of an Axially
Travelling String/Slider Coupling System with Moving Boundary,"
Journal of Sound and Vibration, vol. 211, no.4, pp. 689-701, 1998.
[16] S. S. Law and X. Q. Zhu, "Study on Different Beam Models in Moving
Force Identification," Journal of Sound and Vibration, vol. 234, no.4, pp. 661-679, 2000.
[17] J. S. Wu and D. W. Chen, "Dynamic Analysis of a Uniform Cantilever
Beam Carrying a Number of Elastically Mounted Point Masses with Dampers," Journal of Sound and Vibration, vol. 229, no. 3, pp. 549-578, 2000.
[18] H. P. Lee, "Dynamic stability of a tapered cantilever beam on an elastic
foundation subjected to a follower force," International Journal of Solid and Structure, vol. 33, no. 10, pp. 1409-1424, 1996.
[19] B. W. Huang and J. H. Kuang, , "The Parametric Resonance Instability in
a Drilling Process," ASME, Journal of Applied Mechanics, vol. 74, no. 5, pp. 958-964, 2007.
[1] D. D. Rosard, "Natural Frequency of Twisted Cantilever Beams," in 1952
Pro. ASME Paper No. 52-A-15,
[2] G. W. Jarrett and P. C. Warner, "The Vibration of Rotating Tapered Twisted Beam," ASME, Journal of Applied Mechanics, pp. 381-389,1953.
[3] O. Tekinalp and A. G. Ulsoy, "Modeling and Finite Element Analysis of
Drill Bit Vibration," ASME, Journal of Vibration, Acoustics, Stress, and
Reliability in Design, vol. 111, pp. 148-155, 1989.
[4] O. Tekinalp and A. G. Ulsoy, "Effect of Geometric and Process Parameters in Drill Transverse Vibration," ASME, Journal of Engineering
for Industry, vol. 112, pp. 189-194, 1990.
[5] C. L. Liao, and Y. H. Dang, "Structural Characteristics of Spinning Pretwisted Orthotropic Beams," Computer & Structures, vol. 45, no. 4, pp. 715-731, 1992.
[6] C. L. Liao and B. W. Huang, "Parametric Instability of a Pretwisted Beam
under Periodic Axial Force," International Journal of Mechanical Science, vol. 37, no. 4, pp. 423-439, 1995.
[7] E. Magrab and D. E. Gilsinn, "Bucking loads and natural frequency of
twist drills," Transactions of ASME, vol. 106, pp. 196-204, 1984.
[8] A. G. Ulsoy, "A lumped parameter model for the transverse vibration of
drill bit," in 1989 Proc. Control of Manufacturing Processes and Robotic System, pp. 15-25.
[9] H. Fuji, E. Marui and S. Ema, "Whirling Vibration in drilling part 3: Vibration analysis in Drilling Workpiece with a Pilot Hole," ASME, Journal of engineering for Industry, vol. 110, pp. 315-321, 1988.
[10] D. M. Rincon and A. G. Ulsoy, "Complex Geometry, Rotary Inertia and
Gyroscopic Moment Effects on Drill Vibrations," Journal of Sound and Vibration, vol. 188, no. 5, pp. 701-715, 1995.
[11] T. Iwastsubo, Y. Sugiyama and K. Ishihara, "Stability and Stationary
Vibrations of Columns under Periodic Loads," Journal of Sound and Vibration, vol. 23, pp. 245-257, 1972.
[12] H. P. Lee, "Buckling and Dynamic Stability of Spinning Pre-twisted Beams under Compressive Axial Loads," International Journal of Mechanical Sciences, vol. 36, no. 11, pp. 1011-1026, 1994.
[13] H. P. Lee, "Dynamic Response of a Beam with a Moving Mass," Journal
of Sound and Vibration, vol. 192, no. 2, pp. 289-294,1996.
[14] Y. M. Ram and J. Caldwell, "Free Vibration of a string with Moving
Boundary Conditions by The Method of Distorted Images," Journal of Sound and Vibration, vol. 194, no. 1, pp. 35-47, 1996.
[15] R. F. Fung, J. S. Huang and J. J. Chu, "Dynamic Stability of an Axially
Travelling String/Slider Coupling System with Moving Boundary,"
Journal of Sound and Vibration, vol. 211, no.4, pp. 689-701, 1998.
[16] S. S. Law and X. Q. Zhu, "Study on Different Beam Models in Moving
Force Identification," Journal of Sound and Vibration, vol. 234, no.4, pp. 661-679, 2000.
[17] J. S. Wu and D. W. Chen, "Dynamic Analysis of a Uniform Cantilever
Beam Carrying a Number of Elastically Mounted Point Masses with Dampers," Journal of Sound and Vibration, vol. 229, no. 3, pp. 549-578, 2000.
[18] H. P. Lee, "Dynamic stability of a tapered cantilever beam on an elastic
foundation subjected to a follower force," International Journal of Solid and Structure, vol. 33, no. 10, pp. 1409-1424, 1996.
[19] B. W. Huang and J. H. Kuang, , "The Parametric Resonance Instability in
a Drilling Process," ASME, Journal of Applied Mechanics, vol. 74, no. 5, pp. 958-964, 2007.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:61136", author = "Bo Wun Huang and Ah Der Lin and Yung Chuan Chen and Jao Hwa Kuang", title = "A Dynamic Model for a Drill in the Drilling Process", abstract = "The dynamic model of a drill in drilling process was
proposed and investigated in this study. To assure a good drilling quality, the vibration variation on the drill tips during high speed
drilling is needed to be investigated. A pre-twisted beam is used to
simulate the drill. The moving Winkler-Type elastic foundation is used to characterize the tip boundary variation in drilling. Due to the
variation of the drill depth, a time dependent dynamic model for the drill is proposed. Results simulated from this proposed model indicate that an abrupt natural frequencies drop are experienced as the drill tip
tough the workpiece, and a severe vibration is induced. The effects of parameters, e.g. drilling speed, depth, drill size and thrust force on the
drill tip responses studied.", keywords = "Drilling, vibration of drill, twisted beam", volume = "2", number = "5", pages = "732-7", }
