Abstract
This paper deals with the modeling and analysis of the cutting tool's global dynamics in the orthogonal cutting process of turning operations considering the effect of state dependency and fly-over in one model. In particular, the one-degree-of-freedom non-smooth model, presented by Wahi and Chatterjee in 2008, is extended by the consideration of vibrations in the direction perpendicular to the feed velocity. This results in the statedependency of the model and gives an additional direction in which fly-over can occur. The constructed mathematical model consists of a nonlinear PDE, which describes the evolution of the surface height of the workpiece and a two-degree-of-freedom ODE, which governs the motion of the tool. The PDE is connected to the solution of the ODE by a non-local, non-smooth boundary condition. For the case when the tool is within the cut, this model gives the conventional model of turning governed by delay-differential equations with state-dependent delays. In order to study the effect of vibrations in the tangential direction numerical simulations are carried out and their results are compared to the model presented by Wahi and Chatterjee (2008).
| Original language | English |
|---|---|
| Title of host publication | 11th International Conference on Multibody Systems, Nonlinear Dynamics, and Control |
| Publisher | American Society of Mechanical Engineers (ASME) |
| Volume | 6 |
| ISBN (Electronic) | 9780791857168 |
| DOIs | |
| Publication status | Published - 2015 |
| Event | ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2015 - Boston, United States Duration: Aug 2 2015 → Aug 5 2015 |
Other
| Other | ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2015 |
|---|---|
| Country | United States |
| City | Boston |
| Period | 8/2/15 → 8/5/15 |
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ASJC Scopus subject areas
- Mechanical Engineering
- Computer Graphics and Computer-Aided Design
- Computer Science Applications
- Modelling and Simulation
Cite this
State-dependent, non-smooth model of chatter vibrations in turning. / Lehotzky, Dávid; Insperger, T.; Stépán, G.
11th International Conference on Multibody Systems, Nonlinear Dynamics, and Control. Vol. 6 American Society of Mechanical Engineers (ASME), 2015.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - State-dependent, non-smooth model of chatter vibrations in turning
AU - Lehotzky, Dávid
AU - Insperger, T.
AU - Stépán, G.
PY - 2015
Y1 - 2015
N2 - This paper deals with the modeling and analysis of the cutting tool's global dynamics in the orthogonal cutting process of turning operations considering the effect of state dependency and fly-over in one model. In particular, the one-degree-of-freedom non-smooth model, presented by Wahi and Chatterjee in 2008, is extended by the consideration of vibrations in the direction perpendicular to the feed velocity. This results in the statedependency of the model and gives an additional direction in which fly-over can occur. The constructed mathematical model consists of a nonlinear PDE, which describes the evolution of the surface height of the workpiece and a two-degree-of-freedom ODE, which governs the motion of the tool. The PDE is connected to the solution of the ODE by a non-local, non-smooth boundary condition. For the case when the tool is within the cut, this model gives the conventional model of turning governed by delay-differential equations with state-dependent delays. In order to study the effect of vibrations in the tangential direction numerical simulations are carried out and their results are compared to the model presented by Wahi and Chatterjee (2008).
AB - This paper deals with the modeling and analysis of the cutting tool's global dynamics in the orthogonal cutting process of turning operations considering the effect of state dependency and fly-over in one model. In particular, the one-degree-of-freedom non-smooth model, presented by Wahi and Chatterjee in 2008, is extended by the consideration of vibrations in the direction perpendicular to the feed velocity. This results in the statedependency of the model and gives an additional direction in which fly-over can occur. The constructed mathematical model consists of a nonlinear PDE, which describes the evolution of the surface height of the workpiece and a two-degree-of-freedom ODE, which governs the motion of the tool. The PDE is connected to the solution of the ODE by a non-local, non-smooth boundary condition. For the case when the tool is within the cut, this model gives the conventional model of turning governed by delay-differential equations with state-dependent delays. In order to study the effect of vibrations in the tangential direction numerical simulations are carried out and their results are compared to the model presented by Wahi and Chatterjee (2008).
UR - http://www.scopus.com/inward/record.url?scp=84982171465&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84982171465&partnerID=8YFLogxK
U2 - 10.1115/DETC2015-46748
DO - 10.1115/DETC2015-46748
M3 - Conference contribution
AN - SCOPUS:84982171465
VL - 6
BT - 11th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
PB - American Society of Mechanical Engineers (ASME)
ER -