0
Research Papers

Probabilistic Sequential Prediction of Cutting Force Using Kienzle Model in Orthogonal Turning Process

[+] Author and Article Information
M. Salehi

Department of Mechanical Engineering,
Institute for Information Management
in Engineering,
Karlsruhe Institute of Technology,
Kaiserstr. 12,
Karlsruhe 76131, Germany;
Department of Mechanical Engineering
and Mechatronic,
Institute of Materials and Processes,
Karlsruhe University of Applied Science,
Moltkestr.30,
Karlsruhe 76133, Germany
e-mail: mehdi.salehi@hs-karlsruhe.de

T. L. Schmitz, R. Copenhaver

Department of Mechanical Engineering and
Engineering Science,
University of North Carolina at Charlotte,
Charlotte, NC 28223

R. Haas

Department of Mechanical Engineering
and Mechatronic,
Institute of Materials and Processes,
Karlsruhe University of Applied Science,
Moltkestr.30,
Karlsruhe 76133, Germany

J. Ovtcharova

Department of Mechanical Engineering,
Institute for Information Management in
Engineering,
Karlsruhe Institute of Technology,
Kaiserstr. 12,
Karlsruhe 76131, Germany

1Corresponding author.

Manuscript received June 4, 2018; final manuscript received October 4, 2018; published online November 8, 2018. Assoc. Editor: Laine Mears.

J. Manuf. Sci. Eng 141(1), 011009 (Nov 08, 2018) (12 pages) Paper No: MANU-18-1383; doi: 10.1115/1.4041710 History: Received June 04, 2018; Revised October 04, 2018

Probabilistic sequential prediction of cutting forces is performed applying Bayesian inference to Kienzle force model. The model uncertainties are quantified using the Metropolis algorithm of the Markov chain Monte Carlo (MCMC) approach. Prior probabilities are established and posteriors of the models parameters and force predictions are completed using the results of orthogonal turning experiments. Two types of tools with chamfer (rake) angles of 0 deg and −10 deg are tested under various cutting speed and feed per revolution values. First, Bayesian inference is applied to two force models, Merchant and Kienzle, to investigate the cutting force prediction at the low feed values for the 0 deg rake angle tool. Second, the results of the posteriors of the Kienzle model parameters are used as prior probabilities of the −10 deg rake angle tool. The simulation results of the 0 deg and −10 deg tool rake angle are compared with the experiments which are obtained under other cutting conditions for model verification. Maximum prediction errors of 7% and 9% are reported for the tangential and feed forces, respectively. This indicates a good capability of the Bayesian inference for model parameter identification and cutting force prediction considering the inherent uncertainty and minimum input experimental data.

Copyright © 2019 by ASME
Topics: Cutting , Uncertainty , Chain
Your Session has timed out. Please sign back in to continue.

References

Merchant, M. E. , 1945, “ Mechanics of the Metal Cutting Process—II: Plasticity Conditions in Orthogonal Cutting,” J. Appl. Phys., 16(6), pp. 318–324. [CrossRef]
Shamoto, E. , and Altıntas, Y. , 1999, “ Prediction of Shear Angle in Oblique Cutting With Maximum Shear Stress and Minimum Energy Principles,” J. Manuf. Sci. Eng. 121(3), pp. 399–407.
Smithey, D. W. , Kapoor, S. G. , and DeVor, R. E. , 2001, “ A New Mechanistic Model for Predicting Worn Tool Cutting Forces,” Mach. Sci. Technol., 5(1), pp. 23–42.
Schmitz, T. L. , Smith, K. S. , and Dynamics, M. , 2009, “ Milling Dynamics,” Milling, Springer US, Boston, MA.
Karandikar, J. M. , 2013, The Fundamental Application of Decision Analysis to Manufacturing, University of North Carolina at Charlotte, Charlotte, NC.
Karandikar, J. M. , Abbas, A. E. , and Schmitz, T. L. , 2014, “ Tool Life Prediction Using Bayesian Updating. Part 1: Milling Tool Life Model Using a Discrete Grid Method,” Precis. Eng., 38(1), pp. 9–17. [CrossRef]
Karandikar, J. M. , Abbas, A. E. , and Schmitz, T. L. , 2014, “ Tool Life Prediction Using Bayesian Updating. Part 2: Turning Tool Life Using a Markov Chain Monte Carlo Approach,” Precis. Eng., 38(1), pp. 18–27. [CrossRef]
Metropolis, N. , Rosenbluth, A. W. , Rosenbluth, M. N. , Teller, A. H. , and Teller, E. , 1953, “ Equation of State Calculations by Fast Computing Machines,” J. Chem. Phys., 21(6), pp. 1087–1092. [CrossRef]
Niaki, A. F. , Ulutan, D. , and Mears, L. , 2016, “ Parameter Inference Under Uncertainty in End-Milling γ′-Strengthened Difficult-to-Machine Alloy,” ASME J. Manuf. Sci. Eng., 138(6), p. 061014. [CrossRef]
Niaki, F. A. , Ulutan, D. , and Mears, L. , 2015, “ Parameter Estimation Using Markov Chain Monte Carlo Method in Mechanistic Modeling of Tool Wear During Milling,” ASME Paper No. MSEC2015-9357.
Gözü, E. , and Karpat, Y. , 2017, “ Uncertainty Analysis of Force Coefficients During Micromilling of Titanium Alloy,” Int. J. Adv. Manuf. Technol., 93(1–4), pp. 839–855. [CrossRef]
Schmitz, T. L. , Karandikar, J. , Ho Kim, N. , and Abbas, A. , 2011, “ Uncertainty in Machining: Workshop Summary and Contributions,” ASME J. Manuf. Sci. Eng., 133(5), p. 051009. [CrossRef]
Mehta, P. , Kuttolamadom, M. , and Mears, L. , 2017, “ Mechanistic Force Model for Machining Process—Theory and Application of Bayesian Inference,” Int. J. Adv. Manuf. Technol., 91(9–12), pp. 3673–3682. [CrossRef]
Weber, M. , Hochrainer, T. , Gumbsch, P. , Autenrieth, H. , Delonnoy, L. , Schulze, V. , Löhe, D. , Kotschenreuther, J. , and Fleischer, J. , 2007, “ Investigation of Size-Effects in Machining With Geometrically Defined Cutting Edges,” Mach. Sci. Technol., 11(4), pp. 447–473. [CrossRef]
Vollertsen, F. , Biermann, D. , Hansen, H. N. , Jawahir, I. S. , and Kuzman, K. , 2009, “ Size Effects in Manufacturing of Metallic Components,” CIRP Ann.-Manuf. Technol., 58(2), pp. 566–587. [CrossRef]
Altintas, Y. , and Ber, A. , 2001, Manufacturing Automation: Metal Cutting Mechanics, Machine Tool Vibrations, and CNC Design, Cambridge University Press, Cambridge, UK.
Klocke, F. , Adams, O. , Auerbach, T. , Gierlings, S. , Kamps, S. , Rekers, S. , Veselovac, D. , Eckstein, M. , Kirchheim, A. , Blattner, M. , Thiel, R. , and Kohler, D. , 2015, “ New Concepts of Force Measurement Systems for Specific Machining Processes in Aeronautic Industry,” CIRP J. Manuf. Sci. Technol., 9, pp. 31–38.
Andrieu, C. , De Freitas, N. , Doucet, A. , and Jordan, M. I. , 2003, “ An Introduction to MCMC for Machine Learning,” Mach. Learn., 50(1/2), pp. 5–43. [CrossRef]
Roberts, G. O. , and Rosenthal, J. S. , 2001, “ Optimal Scaling for Various Metropolis-Hastings Algorithms,” Stat. Sci., 16(4), pp. 351–367. [CrossRef]
Hoff, P. D. , 2009, A First Course in Bayesian Statistical Methods, Springer, New York.
Niaki, F. A. , 2016, A Probabilistic-Based Approach to Monitoring Tool Wear State and Assessing Its Effect on Workpiece Quality in Nickel-Based Alloys, Clemson University, Clemson, SC.
Geweke, J. , 1992, “ Evaluating the Accuracy of Sampling-Based Approaches to the Calculation of Posterior Moments,” Bayesian Stat., 4, pp. 169–193.
Schimmel, R. J. , Endres, W. J. , and Stevenson, R. , 2002, “ Application of an Internally Consistent Material Model to Determine the Effect of Tool Edge Geometry in Orthogonal Machining,” ASME J. Manuf. Sci. Eng., 124(3), p. 536. [CrossRef]
Denkena, B. , and Tönshoff, H. K. , 2011, Spanen: Grundlagen, Springer, Berlin.

Figures

Grahic Jump Location
Fig. 5

Mean and one standard deviation of the cut chip thickness using the 0 deg rake angle tool

Grahic Jump Location
Fig. 1

Merchant cutting force diagram

Grahic Jump Location
Fig. 4

Tangential and feed force components for training of the priors using tool rake angle −10 deg

Grahic Jump Location
Fig. 3

Tangential and feed force components for training of the priors using tool rake angle 0 deg

Grahic Jump Location
Fig. 2

Machining experiments setup and the cutting forces directions

Grahic Jump Location
Fig. 6

Prior distribution of ϕc

Grahic Jump Location
Fig. 7

Joint distribution of βa and τs

Grahic Jump Location
Fig. 8

Prior function of tangential cutting force with ±2σ standard deviation uncertainty intervals

Grahic Jump Location
Fig. 9

Comparison of prior and posterior distributions of ϕc after three updates

Grahic Jump Location
Fig. 17

Posterior functions for prediction of tangential (left) and feed (right) forces with ±2σ standard deviation uncertainty intervals for the tool rake angle 0 deg

Grahic Jump Location
Fig. 18

Sequential training and prediction of cutting forces using Bayesian updating for different tool rake angles

Grahic Jump Location
Fig. 10

Joint PDF of βa and τs after three updates

Grahic Jump Location
Fig. 11

Comparison of prior and posterior distributions of the Kt, after three updates

Grahic Jump Location
Fig. 21

Posterior functions of tangential (left) and feed (right) forces with ±2σ standard deviation uncertainty intervals for the tool rake angle −10 deg

Grahic Jump Location
Fig. 22

Posterior functions for prediction of tangential (left) and feed (right) forces with ±2σ standard deviation uncertainty intervals for the tool rake angle −10 deg

Grahic Jump Location
Fig. 13

Joint Gaussian prior distributions of Ktt and ctt (left), and Kff and cf (right) for the tool rake angle 0 deg

Grahic Jump Location
Fig. 14

Prior functions of the tangential forces (left) and feed force (right) with ±2σ standard deviation uncertainty intervals for the tool rake angle 0 deg

Grahic Jump Location
Fig. 15

Joint posterior distributions of Ktt and ctt (left), and Kff and cf (right), for the tool rake angle 0 deg

Grahic Jump Location
Fig. 19

Prior functions of the tangential forces (left) and feed force (right) with ±2σ standard deviation uncertainty intervals for the tool rake angle −10 deg

Grahic Jump Location
Fig. 20

Joint posterior distributions of Ktt and ctt (left), and Kff and cf (right) for the tool rake angle −10 deg

Grahic Jump Location
Fig. 12

Posterior function of tangential cutting force with ±2σ standard deviation uncertainty intervals

Grahic Jump Location
Fig. 16

Posterior functions of tangential (left) and feed (right) force with ±2σ standard deviation uncertainty intervals for the tool rake angle 0 deg

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In