slide1 n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Identification of nonlinear characteristics based on bistability in delayed model of cutting PowerPoint Presentation
Download Presentation
Identification of nonlinear characteristics based on bistability in delayed model of cutting

Loading in 2 Seconds...

play fullscreen
1 / 29

Identification of nonlinear characteristics based on bistability in delayed model of cutting - PowerPoint PPT Presentation


  • 88 Views
  • Uploaded on

Identification of nonlinear characteristics based on bistability in delayed model of cutting. G Stepan , Z Dombovari Department of Applied Mechanics Budapest University of Technology and Economics J Munoa Ideko Research Alliance IK4, Danobat Group. Introduction to cutting.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Identification of nonlinear characteristics based on bistability in delayed model of cutting' - paki-peters


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
slide1

Identification of nonlinear

characteristics based on bistability

in delayed model of cutting

G Stepan, Z Dombovari

Department of Applied Mechanics

Budapest University of Technology and Economics

J Munoa

Ideko Research Alliance IK4, Danobat Group

introduction to cutting
Introduction to cutting

Specific amount of material cut within a certain time

where

w – chip width

h – chip thickness

v – cutting speed

Ω~cutting speed

Cutting force

introduction to milling
Introduction to milling

Number of cutting edgesin contact varies periodically with periodequal to the delay between two subsequent cutting edges.

Thus, the resultant cutting force also varies with the same period.

cutting force characteristics
Cutting force characteristics

How to measure/identify?

{

}

nonlinearities?

Linear (Taylor):

}

Shifted lin. (Altintas):

uniqueness?

Power (Kienzle):

Exponential (Endres):

Cubic pol. (Tobias):

slide6

Preliminaries

  • Classical experiment (Tobias, Shi, 1984)
  • cutting process is sensitive tolarge perturbations
  • self excited vibrations (chatter) “around” stable cutting
  • important effect of chip thicknesson size of unsafe zone

2/17

mechanical model of turning
Mechanical model of turning

τ – time period of revolution

slide8
A pair of complex conjugate roots at stability limit

Transversality condition

Linear stability & Hopf Bifurcation

18/27

subcritical hopf bifurcation
Centre manifold reduction, and

calculation of Poincare-Ljapunov constant (PLC)

since

and

Subcritical Hopf bifurcation

19/27

fly over
Fly-over
  • Dombovari, Barton, Wilson
  • Stepan, 2010
model of milling
Model of milling

Mechanical model:

- number of cutting edgesin contact varies periodically with periodequal to the delay

high s peed m illing
High-speedmilling

Theory &experiments:

stability chart (Insperger,Mann, Stepan,Bayly, 2004,

also groupsin Dortmund,Ljubljana,…)

slide16

Turning

(Tobias, Tlusty, 1960)

slide17

Newtonian impact theory

and regenerative effect

(Davies, Burns, Dutterer, Pratt,…Insperger, Stépán, 2001 Szalay, Stépán, 2002 – subcr, flip)

slide18

Semi-discretization method – Insperger, Stépán

Multi-frequency method – Merdol, Altintas

Time Finite Element method – Bayly, Mann,…

Full discretization – Altintas, Balachandran,…

Period-doubling(Corpus, Endres)

slide19

= 0.05…

0.1 …

0.2

Characteristic matrices(Szalai, 2006)

Experiments on

lenses/islands

(Zatarian, Mann, 2008)

slide20

Time averaging (basic Fourier component)

provides satisfactory stability limits, bifurcations

(Tobias, Tlusty, Minis,… 1965…1995,

Altintas, Budak – multi DoF, single frequency… 1998),

but the frequency content is rich (Insperger,... 2003)

differential equation of cutting force characteristics
Differential equation of cutting force characteristics

+ 2=

=

From the Hopf calculation:

where we can measure:

example size w of bistable zone does not depend on chip thickness h
Example: size w of bistable zone does not depend on chip thickness h

Eulerian-type diff. equ,

,

,

With the boundary conditions

, softening

With a typical measured value of

Typical power law

conclusion
Conclusion

The invers application of the results of the Hopf

bifurcation calculation in case of regenerative

machine tool vibrations makes it possible to

measure the nonlinear cutting force

characteristics with cheap accelerometers only

in a fast and accurate way.

Thank you for your attention!