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Experimental verification of design methodology for chatter suppression in tool swing–assisted parallel turning

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Abstract

Parallel turning has the potential in enhancing the machining productivity and consequently reducing total production costs. However, due to the complex interaction of tools and workpieces, the stability of the process against chatter vibration is often decreased; hence, a successful chatter avoidance/suppression must be achieved. Recently, our research group suppressed the chatter in the shred-surface parallel turning by oscillating two tools in the circumferential direction of a flexible workpiece while keeping the equal pitch. However, there are insufficient discussion and experimental verification surrounding the optimal design for the tool swing motion (TSM). This paper presents a design methodology for the tool swing parallel turning based on the analogy with the spindle speed variation (SSV) techniques. A series of experiments were conducted while varying TSM design parameters to support the proposed design method. In-depth discussions regarding the experimental results were also carried out. The results of this study provide adequate information for properly tuning the TSM process for effective chatter suppression in practical applications.

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Abbreviations

a t :

Acceleration of stage (m/s2)

GLPF(s):

Low-pass filter (-)

fc, ωc :

Chatter frequency (Hz) (ωc = 2πfc (rad/s))

F cut :

Cutting force (N)

Ffric, Tfric :

Friction force and torque (N, Nm)

F grav :

Gravity force (N)

fsw, ωsw :

Tool swing frequency (Hz), (ωsw = 2πfsw (rad/s))

\( {I}_a^{\mathrm{ref}} \) :

Motor current reference (A)

J r :

Total inertia of motor, coupling, and ball screw (kgm2)

k :

Chatter lobe number (-)

K t :

Torque coefficient (Nm/A)

M t :

Movable mass (kg)

N :

Number of teeth/cutters (-)

R :

Transform coefficient for rotational to translational motion (mm/rad)

RVA :

Relative amplitude of spindle speed variation against the mean (nominal) spindle speed (-)

RVA opt :

Optimal value of RVA (-)

RVF :

Relative frequency of spindle speed variation against the mean (nominal) spindle speed (-)

RVF lim :

Lower limit value of RVF (-)

S :

Spindle speed (min-1)

S rel :

Relative spindle speed in TSM process (min-1)

t :

Process time (s)

α r :

Angular acceleration (rad/s2)

ε :

Chatter phase shift (rad)

θ :

Tool swing angle in TSM process (rad)

θ 0 :

Offset angle in TSM process (rad)

θ sw :

Amplitude of swing angle in TSM process (rad)

ρ :

Amplitude ratio of the expected and the real delay term representing the efficiency of TSM process (-)

τ :

Real delay in TSM process (s)

\( \overset{\sim }{\tau } \) :

Expected delay in TSM process (s)

\( \left(\hat{\mkern6mu}\right) \) :

Estimated value

()n :

Nominal value

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Acknowledgments

The authors thank Mr. Okuma and OMRON Corporation for their support and assistance for this research.

Funding

A part of this study was supported by SIP Innovative Design and Production Technology Project commissioned by the New Energy and Industrial Technology Development Organization (NEDO) and JSPS Grant-in-Aid for JSPS Fellows Grant Numbers JP19J13204.

Author information

Authors and Affiliations

  1. Department of System Design Engineering, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, Kanagawa, 223-8522, Japan

    Shuntaro Yamato & Yasuhiro Kakinuma

  2. Nakamura-Tome Precision Industry Co., Ltd., Ro 15 Netsuno, Hakusan, Ishikawa, 920-2195, Japan

    Kenichi Nakanishi

  3. Department of Mechanical Aerospace Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8603, Japan

    Norikazu Suzuki

Authors
  1. Shuntaro Yamato
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  2. Kenichi Nakanishi
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  4. Yasuhiro Kakinuma
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Correspondence to Shuntaro Yamato.

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Appendix

Appendix

In the TSM process, the process time delay is a time function. In the tool swing parallel turning, as two tools oscillate according to Eq. (5) while keeping the equal pitch, the following equation should hold:

$$ {\int}_{t-\tau (t)}^t\frac{2\pi {S}_n}{60} dt=\pi +{\theta}_{sw}\sin \left({\omega}_{sw}t\right)-{\theta}_{sw}\sin \left({\omega}_{sw}\left(t-\tau (t)\right)\right) $$
(10)

The delay satisfying Eq. (10) can be calculated by numerical calculations such as the Newton-Raphson method, once the cutting conditions and time-varying profile of TSM are determined.

On the other hand, the expected time-varying delay in the TSM process, straightforwardly derived from Eq. (6), is as follows:

$$ \kern2.75em {\displaystyle \begin{array}{c}\overset{\sim }{\tau }=\frac{60}{N{S}_{rel}}=\frac{60}{N{S}_n\left(1-\frac{60{\theta}_{sw}{\omega}_{sw}}{2\uppi {S}_n}\cdotp \cos \left({\omega}_{sw}t\right)\right)}\kern0.75em \\ {}=\frac{60}{N{S}_n\left(1- RVA\cdotp \cos \left({\omega}_{sw}t\right)\right)}\end{array}} $$
(11)

As a result, the amplitude ratio representing efficiency of TSM process can be defined as follows:

$$ \rho =\frac{\left\{\max \left(\tau (t)\right)-\min \left(\tau (t)\right)\right\}/2}{\left\{\max \left(\overset{\sim }{\tau }(t)\right)-\min \left(\overset{\sim }{\tau }(t)\right)\right\}/2}=\frac{A_{\tau }}{A_{\overset{\sim }{\tau }}} $$
(12)

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Yamato, S., Nakanishi, K., Suzuki, N. et al. Experimental verification of design methodology for chatter suppression in tool swing–assisted parallel turning. Int J Adv Manuf Technol 110, 1759–1771 (2020). https://doi.org/10.1007/s00170-020-05951-1

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