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A sensorless method for predicting force-induced deformation and surface waviness in robotic milling

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Abstract

Process monitoring is essential to enable process parameter optimization, deformation prediction, and fault diagnosis in robotic milling. However, expensive costs and installation requirements limit the use of industrial sensors in machining process. This paper proposed a sensorless method to predict force-induced deformation and surface waviness. First, the tracking errors of tooltip was calculated based on the robot joint tracking errors and the robot kinematic model. Subsequently, the idle running and cutting process signals monitored by the robot controller were used to calculate the cutting force acting on tooltip based on Kalman filter and robot static model. On this base, the force-induced deformation, considering the posture error of the robot flange coordinate system, was calculated using the estimated milling force and the flexible model. Finally, the effectiveness of the proposed method was verified by a series of cutting experiments.

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Data availability

The publication-related datasets are available from the corresponding author on reasonable request.

Abbreviations

\({T}_{\textrm{fl}}^{\textrm{base}}\) :

The transformation from RBCS to RFCS

θ i :

Joint angle around z-axis

a i :

The angle measured around the x-axis

d i :

Slide distance along the z-axis

a i :

The distance along the x-axis

\({T}_{\textrm{wp}}^{\textrm{base}}\) :

The transformation from RBCS to WCS

\({P}_{\textrm{tool}}^{\textrm{fl}}\) :

The coordinate value of TCP in the RFCS

M(q):

The inertia matrix of the robot

G(q):

The gravity matrix of the robot

\(C\left(q,\dot{q}\right)\) :

The centrifugal and Coriolis effects

τm :

The total joint torque during milling process

τf :

Joint torque caused by friction

τ ext :

Joint torque caused by cutting force (cutting torque)

\(\overline{\tau}\) :

The total joint torque of idle running

x(t):

State vector

y(t):

Output vector, estimated cutting torque

u(t):

Input vector, measured cutting torque

L :

Kalman gain matrix

P :

Covariance matrix

Q :

The covariance of process noise

R :

The covariance of measurement noise

J :

Jacobi matrix of the robot

F fl :

The external force acting in RFCS

F tool :

The cutting force acting on tooltip

\({R}_{\textrm{tool}}^{\textrm{fl}}\) :

The transformation from RFCS to TCS

PI i :

The observability index of the ith joint

τ cut, i :

The cutting torque of the ith joint

τ move, i :

The idle-running torque of the ith joint

τ ext, m :

The n × 1 (n ≥ 3) joint cutting torque matrix

\({J}_{\textrm{m}}^T\) :

The n × 6 generalized Jacobi matrix

δ fcp :

The force-induced deformation in the RFCS

C θ :

The robot joint flexibility matrix

K θ :

The robot joint stiffness matrix

δ tool :

The deformation of tooltip

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Funding

This work was supported by National Key Research and Development Project of China (2018YFB1306803).

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Authors and Affiliations

  1. School of Mechatronic Engineering, Harbin Institute of Technology, Harbin, 150001, China

    Kenan Deng, Dong Gao & Yong Lu

  2. Department of Mechanical Engineering, The University of Hong Kong, Pokfulam, Hong Kong

    Chang Zhao

Authors
  1. Kenan Deng
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Contributions

K. N. D., Y. L., and D. G. conceived and designed the study. K. N. D. and S. D. M. performed the experiments. K. N. D. and C. Z. wrote the paper. K. N. D., Y. L., and D. G. reviewed and edited the manuscript. All authors read and approved the manuscript.

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Correspondence to Chang Zhao or Yong Lu.

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Deng, K., Gao, D., Zhao, C. et al. A sensorless method for predicting force-induced deformation and surface waviness in robotic milling. Int J Adv Manuf Technol 127, 831–844 (2023). https://doi.org/10.1007/s00170-023-11559-y

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