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Enhancement of cutting force observer by identification of position and force-amplitude dependent model parameters

  • Shuntaro YamatoEmail author
  • Akihiro Sugiyama
  • Norikazu Suzuki
  • Naruhiro Irino
  • Yasuhiro Imabeppu
  • Yasuhiro Kakinuma
ORIGINAL ARTICLE
  • 83 Downloads

Abstract

External sensor-less cutting force estimation has good potential in terms of its sustainability. However, its accuracy will deteriorate due to variation of machine dynamics depending on the stage position and cutting force amplitude. In the conventional methods, the physical model parameters such as the axial stiffness and viscous damping coefficient are regarded as constant values identified at a certain condition. As a result, the estimation accuracy decreases because the above parameter variation is not considered. To tackle this issue, a simple parameter identification method in time domain by employing the least-squares method (LSM) and a cutting force estimation by a load-side disturbance observer (LDOB) are proposed for a full-closed controlled ball-screw-driven stage. A series of excitation tests were conducted at different stage positions and various excitation amplitudes in order to capture the position and force-amplitude dependent model parameters. The difference of model behavior in the moving and stopped condition of the stage was also investigated. The position and force-amplitude dependent model parameters captured by the proposed method are installed into the observer. The validity of the proposed method was evaluated through end-milling tests. The experimental results clearly showed that the estimation accuracy of cutting force can be greatly improved in both feed and cross-feed directions by taking into account the position and force-amplitude dependency of physical model parameters.

Keywords

Process monitoring Ball-screw-driven stage Sensor-less Disturbance observer Parameter identification 

Nomenclature

ap

Axial depth of cut

at

Acceleration of table

Ct

Viscous damping coefficient of translational element

d

Diameter of screw shaft

Dm

Viscous damping coefficient of rotational element

Es

Young’s module of screw shaft

Fcut

Cutting force

Ffric

Friction force

GLPF

Low-pass filter

Ia

Motor current

Jm

Total inertia of motor, coupling, and ball-screw

Kb

Axial stiffness of bearing

Kbs

Summation of Kb and Ks

Kb1

Axial stiffness of motor side bearing

Kb2

Axial stiffness of anti-motor side bearing

Kn

Axial stiffness of nut

Kr

Axial stiffness of feed drive system

Ks

Axial stiffness of screw shaft

Ktq

Torque coefficient

l

Pitch length of ball-screw

L

Length of ball-screw shaft

Mt

Movable mass

N

Number of data corresponding to window length

p

Absolute stage position from the motor side bearing

R

Transform coefficient for rotational to translational motion (=l/2π)

Tfric

Friction torque

xr

Relative displacement between motor and stage

xt

Displacement of table

vt

Velocity of table

α 

Inertia ratio of dual-inertia ball-screw-driven stage

αc

Constant for proportional damping

αm

Angular acceleration of motor

ϵ

Residual sum of squares

θm

Angle of motor

σxr

Standard deviation of relative displacement xr

ωm

Angular velocity of motor

^(hat)

Estimated value

~(tilde)

Identified value

Subscript

diff

Difference between values identified by moving and fixed identification tests

fix

Value identified by fixed identification tests

i

Index number of data inside calculation window

LDOB

Value in load-side disturbance observer

MEDOB

Value in multi-encoder-based disturbance observer

move

Value identified by moving identification tests

n

Nominal value

vib

Value in vibration mode

Superscript

ref

Reference value

res

Response value

Notes

Funding information

This work was supported by JSPS KAKENHI, Grant Number 18H01353.

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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  • Shuntaro Yamato
    • 1
    Email author
  • Akihiro Sugiyama
    • 1
  • Norikazu Suzuki
    • 2
  • Naruhiro Irino
    • 3
  • Yasuhiro Imabeppu
    • 3
  • Yasuhiro Kakinuma
    • 1
  1. 1.Department of System Design EngineeringKeio UniversityYokohamaJapan
  2. 2.Department of Mechanical and Aerospace EngineeringNagoya UniversityNagoyaJapan
  3. 3.DMG MORI Co., Ltd.IgaJapan

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