Skip to main content
SpringerLink
Log in

Turning Dynamics

  • Chapter
  • First Online:
Machining Dynamics

  • 2230 Accesses

Abstract

Chapter 3 describes regenerative chatter in turning. To predict turning behavior, both analytical and numerical analyses are presented. The analytical, frequency domain stability lobe diagram is derived that describes the limiting stable chip width as a function of spindle speed. A time domain simulation is detailed that determines the dynamic cutting force and tool displacement in turning by numerical integration. The simulation is then used to identify stable and unstable cutting conditions. Finally, the specific application of modulated tool path turning and the effect of process damping on turning stability at low speeds are presented.

Make everything as simple as possible, but not simpler.

—Albert Einstein

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 129.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    We represent \( \overrightarrow{y}(t) \) and \( \overrightarrow{y}\left(t-\tau \right) \) as vectors because they have both a magnitude and phase relative to the force, Fn. The force and both displacement vectors are displayed in Fig. 3.10.

    Fig. 3.10
    figure 10

    Vector representation of unit normal force and tool deflections (current and previous revolutions) for limit of stability

    Full size image
  2. 2.

    In other words, the ratio of the chatter frequency to forcing frequency cannot be expressed as a ratio of whole numbers.

  3. 3.

    T. Schmitz recognizes the significant contributions of R. Copenhaver and M. Rubeo to the experimental setup.

  4. 4.

    T. Schmitz recognizes the significant contributions of C. Tyler to this section.

References

  1. Trent, E., & Wright, P. (2000). Metal cutting (4th ed.). Boston, MA: Butterworth-Heinemann.

    Google Scholar 

  2. Tlusty, G. (2000). Manufacturing equipment and processes. Upper Saddle River, NJ: Prentice-Hall.

    Google Scholar 

  3. Altintas, Y. (2000). Manufacturing automation: Metal cutting mechanics, machine tool vibrations, and CNC design. Cambridge: Cambridge University Press.

    Google Scholar 

  4. Stephenson, D., & Agapiou, J. (1997). Metal cutting theory and practice. New York, NY: Marcel Dekker, Inc.

    Google Scholar 

  5. Schmitz, T. (2015). The microphone feedback analogy for chatter in machining. Shock and Vibration, 2015, 976819.

    Article  Google Scholar 

  6. Zhang, Y. Z. (1980). Chip curl, chip breaking, and chip control of difficult-to-cut materials. Annals of the CIRP, 29(1), 79–83.

    Article  Google Scholar 

  7. Adams, D. (2008) Chip breaking in turning operations using CNC toolpaths. MS thesis, UNC Charlotte, Charlotte, NC.

    Google Scholar 

  8. Assaid, T. S. (2010). Generation, measurement, and assessment of modulated tool-path chip breaking in CNC turning processes. MS thesis, UNC Charlotte, Charlotte, NC.

    Google Scholar 

  9. Tursky, D. (2010). Chip breaking through oscillating CNC toolpaths and its effect on chip length, tool wear and machine dynamics. MS thesis, UNC Charlotte, Charlotte, NC.

    Google Scholar 

  10. Berglind, L., & Zeigert, J. (2013). Chip breaking parameter selection for constant surface speed machining. In: ASME 2013 international mechanical engineering congress and exposition. Vol. 2B: Advanced manufacturing, San Diego, CA.

    Google Scholar 

  11. Berglind, L., & Zeigert, J. (2015). Modulated tool path (MTP) machining for threading applications. Procedia Manufacturing, 1, 546–555.

    Article  Google Scholar 

  12. Copenhaver, R., Rubeo, M., Guzorek, S., Landge, S., Smith, K. S., Ziegert, J., & Schmitz, T. (2017). A fundamental investigation of modulated tool path turning mechanics. Procedia Manufacturing, 10, 159–170.

    Article  Google Scholar 

  13. Rubeo, M., Copenhaver, R., Landge, S., & Schmitz, T. (2016). Experimental platform for in-process metrology during orthogonal turning, American Society for Precision Engineering Annual Meeting, October 23–28, Portland, OR.

    Google Scholar 

  14. Schmitz, T., & Smith, K. S. (2012). Mechanical vibrations: Modeling and measurement. New York, NY: Springer.

    Book  Google Scholar 

  15. Delio, T., Tlusty, J., & Smith, S. (1992). Use of audio signals for chatter detection and control. Journal of Engineering for Industry, 114, 146–157.

    Google Scholar 

  16. Honeycutt, A., & Schmitz, T. (2016). A new metric for automated stability identification in time domain milling simulation. Journal of Manufacturing Science and Engineering, 138(7), 074501.

    Article  Google Scholar 

  17. Honeycutt, A., & Schmitz, T. (2017). Milling stability interrogation by subharmonic sampling. Journal of Manufacturing Science and Engineering, 139(4), 041009.

    Article  Google Scholar 

  18. Smith, S. T. (2000). Flexures: elements of elastic mechanisms. Boca Raton, FL: CRC Press.

    Google Scholar 

  19. Wallace, P. W., & Andrew, C. (1965). Machining forces: Some effects of tool vibration. Journal of Mechanical Engineering Science, 7, 152–162.

    Article  Google Scholar 

  20. Sisson, T. R., & Kegg, R. L. (1969). An explanation of low-speed chatter effects. Journal of Engineering for Industry, 91, 951–958.

    Article  Google Scholar 

  21. Peters, J., Vanherck, P., & Van Brussel, H. (1971). The measurement of the dynamic cutting coefficient. Annals of the CIRP, 21(2), 129–136.

    Google Scholar 

  22. Tlusty, J. (1978). Analysis of the state of research in cutting dynamics. Annals of the CIRP, 27(2), 583–589.

    Google Scholar 

  23. Wu, D. W. (1989). A new approach of formulating the transfer function for dynamic cutting processes. Journal of Engineering for Industry, 111, 37–47.

    Article  Google Scholar 

  24. Elbestawi, M. A., Ismail, F., Du, R., & Ullagaddi, B. C. (1994). Modelling machining dynamics damping in the tool-workpiece interface. Journal of Engineering for Industry, 116, 435–439.

    Article  Google Scholar 

  25. Lee, B. Y., Trang, Y. S., & Ma, S. C. (1995). Modeling of the process damping force in chatter vibration. International Journal of Machine Tools and Manufacture, 35, 951–962.

    Article  Google Scholar 

  26. Abraria, F., Elbestawi, M. A., & Spencea, A. D. (1998). On the dynamics of ball end milling: Modeling of cutting forces and stability analysis. International Journal of Machine Tools and Manufacture, 38, 215–237.

    Article  Google Scholar 

  27. Ahmadi, K., & Ismail, F. (2010). Machining chatter in flank milling. International Journal of Machine Tools and Manufacture, 50, 75–85.

    Article  Google Scholar 

  28. Huang, C. Y., & Wang, J. J. (2007). Mechanistic modeling of process damping in peripheral milling. Journal of Manufacturing Science and Engineering, 129, 12–20.

    Article  Google Scholar 

  29. Chiou, Y. S., Chung, E. S., & Liang, S. Y. (1995). Analysis of tool wear effect on chatter stability in turning. International Journal of Mechanical Sciences, 37, 391–404.

    Article  Google Scholar 

  30. Chiou, R. Y., & Liang, S. Y. (1998). Chatter stability of a slender cutting tool in turning with tool wear effect. International Journal of Machine Tools and Manufacture, 38, 315–327.

    Article  Google Scholar 

  31. Chandiramani, N. K., & Pothala, T. (2006). Dynamics of 2-dof regenerative chatter during turning. Journal of Sound and Vibration, 290, 448–464.

    Article  Google Scholar 

  32. Jemielniak, K., & Widota, A. (1989). Numerical simulation of non-linear chatter vibration in turning. International Journal of Machine Tools and Manufacture, 29, 239–247.

    Article  Google Scholar 

  33. Ahmadi, K., & Ismail, F. (2010). Experimental investigation of process damping nonlinearity in machining chatter. International Journal of Machine Tools and Manufacture, 50, 1006–1014.

    Article  Google Scholar 

  34. Budak, E., & Tunc, L. T. (2009). A new method for identification and modeling of process damping in machining. Journal of Manufacturing Science and Engineering, 131(051019), 1–10.

    Google Scholar 

  35. Altintas, Y., Eynian, M., & Onozuka, H. (2008). Identification of dynamic cutting force coefficients and chatter stability with process damping. Annals of the CIRP, 57(1), 371–374.

    Article  Google Scholar 

  36. Tyler, C., & Schmitz, T. (2012). Process damping analytical stability analysis and validation. Transactions of the NAMRI/SME, 40, 37–47.

    Google Scholar 

  37. Tyler, C., & Schmitz, T. (2013). Analytical process damping stability prediction. Journal of Manufacturing Processes, 15, 69–76.

    Article  Google Scholar 

  38. Tyler, C., Karandikar, J., & Schmitz, T. (2013). Process damping coefficient identification using Bayesian inference. Transactions of the NAMRI/SME, 41, 1–8.

    Google Scholar 

  39. Tyler, C., & Schmitz, T. (2014). Process damping milling model database. Transactions of the NAMRI/SME, 42, 1–10.

    Google Scholar 

  40. Tyler, C., Troutman, J., & Schmitz, T. (2015). Radial depth of cut stability lobe diagrams with process damping effects. Precision Engineering, 40, 318–324.

    Article  Google Scholar 

  41. Tyler, C., Troutman, J., & Schmitz, T. (2016). A coupled dynamics, multiple degree of freedom process damping model, Part 1: Turning. Precision Engineering, 46, 65–72.

    Article  Google Scholar 

  42. Tyler, C., Troutman, J., & Schmitz, T. (2016). A coupled dynamics, multiple degree of freedom process damping model, Part 2: Milling. Precision Engineering, 46, 73–80.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering and Engineering Science, University of North Carolina at Charlotte, Charlotte, NC, USA

    Tony L. Schmitz & K. Scott Smith

Authors
  1. Tony L. Schmitz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. Scott Smith
    View author publications

    You can also search for this author in PubMed Google Scholar

Exercises

Exercises

  1. 1.

    For the turning schematic shown in Fig. 3.69, complete parts (a) through (f). For the single degree of freedom dynamics, the mass is 2 kg, the damping ratio is 0.05, and the stiffness is 2 × 107 N/m. The u direction is oriented at an angle, α, of 35 deg relative to the surface normal, y. The force model parameters are Ks = 1500 N/mm2 and β = 70 deg.

    1. (a)

      Calculate the directional orientation factor. Using this value, compute and plot the real and imaginary parts (in m/N) of the oriented frequency response function versus frequency (in Hz).

    2. (b)

      Determine the minimum value of the real part of the oriented frequency response function and the corresponding chatter frequency. Calculate blim,crit.

    3. (c)

      Determine the spindle speed (in rpm) corresponding to the stability peak defined by the intersection of the N = 0 and N = 1 stability lobes.

    4. (d)

      Find the spindle speed (in rpm) corresponding to the minimum stability limit for the N = 0 lobe.

    5. (e)

      Determine the spindle speed (in rpm) corresponding to the stability peak defined by the intersection of the N = 3 and N = 4 stability lobes.

    6. (f)

      Plot the first four stability lobes (N = 0 to 3) for this system. Use blim units of mm and spindle speed units of rpm.

  2. 2.

    Using the turning schematic shown in Fig. 3.70, complete parts (a) through (d). For the u1 direction, the mass is 10 kg, the damping is 170 N s/m, and the stiffness is 7 × 106 N/m. The u1 direction is oriented at an angle, α1, of 60 deg relative to the surface normal, y. For the u2 direction, the mass is 12 kg, the damping is 1700 N s/m, and the stiffness is 5 × 107 N/m. The u2 direction is oriented at an angle, α2, of 30 deg relative to the y direction. The force model parameters are Ks = 2000 N/mm2 and β = 60 deg.

    1. (a)

      Compute the directional orientation factors, μ1 and μ2. Plot the real and imaginary parts (in m/N) of the oriented frequency response function versus frequency (in Hz).

    2. (b)

      Determine the minimum value of the real part of the oriented frequency response function and the corresponding chatter frequency. Calculate blim,crit.

    3. (c)

      Find the spindle speed (in rpm) corresponding to the minimum stability limit for the N = 2 lobe.

    4. (d)

      Plot the first five stability lobes (N = 0 to 4) for this system. Use blim units of mm and spindle speed units of rpm.

  3. 3.

    Considering the turning model shown in Fig. 3.71, determine the critical stability limit if Ks = 750 N/mm2. For both lumped parameter degrees of freedom, the mass is 1 kg, the stiffness is 7 × 106 N/m, and the damping is 200 N s/m.

  4. 4.

    Complete time domain simulations for the turning model described in Exercise 2. Evaluate the following points for stable or unstable behavior. Use a mean chip thickness (feed per revolution) of 0.15 mm and carry out your simulations for 25 revolutions.

    Ω (rpm)

    b (mm)

    2150

    0.1

    2150

    0.5

    2500

    0.1

    2500

    0.5

    2930

    0.1

    2930

    0.5

    3750

    0.1

    3750

    0.5

    4600

    0.1

    4600

    0.5

    Superimpose your results on the stability lobe diagram from Exercise 2, part (d). Use a circle for stable operating points and an “x” for unstable points.

  5. 5.

    For the facing (turning) operation shown in Fig. 3.72, identify all items on the picture:

    • The direction the spindle rotates

    • The chip width, b

    • The tangential, Ft, and normal, Fn, direction cutting force components that act on the insert/holder

    • The resultant cutting force, F

    • The force angle, β

    • The surface normal direction (for chip thickness variations)

  6. 6.

    For the SDOF turning model shown in Fig. 3.73 with the following parameters, complete parts (a) through (c).

    • k = 2 × 106 N/m

    • m = 2 kg

    • c = 120 N s/m

    • α = 20 deg

    • β = 60 deg

    • Ks = 750 N/mm2 (aluminum alloy)

    • hm = 0.2 mm/rev

    1. (a)

      Compute blim,crit (in mm).

    2. (b)

      Compute the best spindle speed (in rpm) for the N = 3 stability lobe.

    3. (c)

      Compute the approximate chatter frequency (in Hz) at the worst speed for the N = 4 stability lobe.

Fig. 3.69
figure 69

Turning model with flexible tool

Full size image
Fig. 3.70
figure 70

Turning model with a single degree of freedom in both the u1 and u2 directions

Full size image
Fig. 3.71
figure 71

Two degree of freedom turning model

Full size image
Fig. 3.72
figure 72

Facing operation schematic

Full size image
Fig. 3.73
figure 73

Turning model with a single degree of freedom in the u direction

Full size image

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer International Publishing AG, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Schmitz, T.L., Smith, K.S. (2019). Turning Dynamics. In: Machining Dynamics. Springer, Cham. https://doi.org/10.1007/978-3-319-93707-6_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-93707-6_3

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-93706-9

  • Online ISBN: 978-3-319-93707-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation