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


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.


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



Axial depth of cut


Acceleration of table


Viscous damping coefficient of translational element


Diameter of screw shaft


Viscous damping coefficient of rotational element


Young’s module of screw shaft


Cutting force


Friction force


Low-pass filter


Motor current


Total inertia of motor, coupling, and ball-screw


Axial stiffness of bearing


Summation of Kb and Ks


Axial stiffness of motor side bearing


Axial stiffness of anti-motor side bearing


Axial stiffness of nut


Axial stiffness of feed drive system


Axial stiffness of screw shaft


Torque coefficient


Pitch length of ball-screw


Length of ball-screw shaft


Movable mass


Number of data corresponding to window length


Absolute stage position from the motor side bearing


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


Friction torque


Relative displacement between motor and stage


Displacement of table


Velocity of table


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


Constant for proportional damping


Angular acceleration of motor


Residual sum of squares


Angle of motor


Standard deviation of relative displacement xr


Angular velocity of motor


Estimated value


Identified value



Difference between values identified by moving and fixed identification tests


Value identified by fixed identification tests


Index number of data inside calculation window


Value in load-side disturbance observer


Value in multi-encoder-based disturbance observer


Value identified by moving identification tests


Nominal value


Value in vibration mode



Reference value


Response value


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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