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Generalized cutting loads decomposition model of five-axis serial machine tools based on the screw theory

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Abstract

There are large volume of existing literatures focused on cutting force modeling, but so far only few research has been reported on cutting loads decomposition model to calculate cutting loads components acted on five axes of the machine, which, however, directly affect five-axis tracking accuracy. To this end, a generalized cutting loads decomposition model of five-axis serial machine tools is proposed, which provides a mathematical basis to evaluate the cutting loads components. A cutting loads decomposition model is first developed based on kinematics and virtual work analysis, then a generalized cutting loads decomposition model is established by differentiating the forward kinematics model based on the screw theory. Kinematic factors that affect the cutting load components on translational and rotary axes are also analyzed, which provides a guidance to optimize the workpiece setup location to reduce the cutting loads components acted on rotary axes. Experiments and simulations on a table-tilting five-axis machine tool verify the effectiveness of the proposed model.

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Abbreviations

\(\boldsymbol {F}=\left [F_{x}, F_{y}, F_{z}, n_{x}, n_{y}, n_{z} \right ]^{\text {T}}\) :

Cutting loads acted on the workpiece

\(\boldsymbol {\tau }=\left [f_{x}, f_{y}, f_{z}, \tau _{p}, \tau _{s} \right ]^{\text {T}}\) :

Cutting loads components acted on five axes

\(\boldsymbol {P}=\left [P_{x},P_{y},P_{z} \right ]^{\text {T}}\) :

Tool tip position

\(\boldsymbol {O}=\left [O_{i},O_{j},O_{k} \right ]^{\text {T}}\) :

Tool orientation

\(\boldsymbol {q}=\left [x,y,z,\theta _{p},\theta _{s} \right ]^{\text {T}}\) :

Axis displacements in machine coordinates

J :

Tool pose Jacobian matrix

\(\left [g_{wt}\right ]\) :

Forward kinematics transfer matrix

\(\left [g_{bw}\right ],~\left [g_{bt}\right ]\) :

Transfer matrix of the workpiece and tool frame relative to the foundation frame

r p t , r o t :

Cutter position and orientation vectors relative to the tool frame

\(\left (\boldsymbol {\xi }_{x},~\boldsymbol {\xi }_{y},~\boldsymbol {\xi }_{z} \right ),\left (\boldsymbol {\xi }_{p},~\boldsymbol {\xi }_{s}\right )\) :

Twist coordinates of translational and rotary axes

\(\left (\boldsymbol {v}_{x},\boldsymbol {v}_{y},\boldsymbol {v}_{z}\right ),~\left (\boldsymbol {\omega }_{p},\boldsymbol {\omega }_{s}\right )\) :

Unit vectors of translational and rotary axes

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Authors and Affiliations

  1. School of Automation, Key Laboratory of Image Processing and Intelligent Control, Huazhong University of Science and Technology, Wuhan, 430074, People’s Republic of China

    Jixiang Yang & Hai-Tao Zhang

  2. School of Mechanical Science and Engineering, State Key Laboratory of Digital Manufacturing Equipments and Technology, Huazhong University of Science and Technology, Wuhan, 430074, People’s Republic of China

    Jixiang Yang, Tao Huang, Ming Yang & Han Ding

Authors
  1. Jixiang Yang
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  2. Tao Huang
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  3. Ming Yang
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  4. Han Ding
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  5. Hai-Tao Zhang
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Correspondence to Hai-Tao Zhang.

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Yang, J., Huang, T., Yang, M. et al. Generalized cutting loads decomposition model of five-axis serial machine tools based on the screw theory. Int J Adv Manuf Technol 91, 399–410 (2017). https://doi.org/10.1007/s00170-016-9745-3

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  • DOI: https://doi.org/10.1007/s00170-016-9745-3

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