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Energy Optimisation For End Face Turning With Variable Material Removal Rate Considering the Spindle Speed Changes

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Abstract

Many studies have approved that optimising the cutting parameters is effective for reducing the energy consumption of machining operations of machine tools. However, this technique to reduce the end face turning energy consumption (EFTEC), where the material removal rate is variable, has not received attention. Besides, the energy consumed for the spindle speed changes was ignored in previous research. Aiming to fill these gaps, an integrated EFTEC model is developed considering the spindle speed changes. In terms of optimisation, the EFTEC model is discretised according to the allowable accuracy of the machine tool. Simulated annealing is adopted to search for the optimal values of cutting parameters that lead to the minimum EFTEC. In the case study, nine parts with changing diameters and cutting depths are machined by a lathe (CK6153i). According to the experiments, simulated annealing has more than 96% probability of obtaining the global optima. The optimum achieves a 14.03% EFTEC reduction for a case. The relationship between the design parameters and the optimal cutting parameters is discussed. A case shows that 2.43% of the machining time increases suffer from the EFTEC optimisation.

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Abbreviations

EC:

Energy consumption [J]

EFTEC:

End face turning energy consumption [J]

SA:

Simulated annealing

SRS:

Spindle rotation speed [rpm]

MRR:

Material removal rate [cm3/s]

\(\alpha_{A}\) :

Spindle’s angular acceleration [rad/s2]

\(\alpha_{D}\) :

Spindle’s angular deceleration [rad/s2]

\(A_{1} ,\,A_{2} ,\,A_{3}\) :

First, second, and third feeding activities

\(C_{1}\) :

Spindle acceleration from 0 to \(n\)

\(C_{2}\) :

Spindle deceleration from n to 0

\(C_{L}\) :

Coefficient in the tool life model

\(d\) :

Required cutting depth [mm]

\(d\left( t \right)\) :

Function of cutting depth against time [mm]

\(D_{0}\) :

Diameter of the part [mm]

\(E_{\text{eft}}\) :

Total EFTEC for single-pass end face turning [J]

\(E_{\text{fa}}\) :

EC for feeding activities in single-pass end face turning [J]

\(E_{\text{fa}}^{j}\) :

EC for the \(j\)-th feeding activity [J]

\(E_{\text{mc}}\) :

Material-cutting EC in single-pass end face turning [J]

\(E_{\text{sc}}\) :

EC for spindle speed changes in single-pass end face turning [J]

\(f\) :

Feed rate [mm/r]

\(f_{L} ,f_{U}\) :

Lower and upper bounds of feed rates in material-cutting [mm/r]

\(F_{\text{cut}}\) :

Material-cutting force when the fully cutting begins [N]

\(F_{U}\) :

Maximum allowable cutting force [N]

\(j\) :

Index for a feeding activity

\(k\) :

Index for the iteration

\(K\) :

Main angle of the cutter [°]

\(n\) :

Spindle rotation speed in material-cutting [rpm]

n max :

Maximum allowable SRS of the machine tool [rpm]

\(N_{L}\) :

Minimum required passes of end face turning within one tool life

\(P_{0}\) :

Basic power of the machine tool [W]

\(P_{\text{cut}}\) :

Machine tool power when the fully cutting begins [W]

\(P_{CS}\) :

Coolant spray power [W]

\(P_{\text{mc}} \left( t \right)\) :

Function of material-cutting power against time [W]

\(P_{SR}\) :

Spindle rotation power [W]

\(P_{U}\) :

Maximum available machine tool power [W]

\(P_{\text{XF}}^{2}\) :

X-axial feeding power for the second feeding activity [W]

\(P_{\text{XR}}\) :

X-axial rapid feeding power [W]

\(R_{N}\) :

Nose radius of the cutter [mm]

\(t\) :

Time variable [s]

\(t_{0}\) :

Moment when the material-cutting begins

\(t_{ce}\) :

Cutter entering duration in material-cutting [s]

\(t_{\text{fc}}\) :

Fully cutting duration in material-cutting [s]

\(t_{j}\) :

Time consumption of the machine tool for the \(j\)-th feeding activity [s]

\(t_{\text{mc}}\) :

Total material-cutting duration for the end face turning [s]

\(t_{\text{XR}}^{j}\) :

X-axial rapid feeding time for the \(j\)-th feeding activity [s]

\(t_{\text{ZR}}^{j}\) :

Z-axial rapid feeding time for the \(j\)-th feeding activity [s]

\(T_{L}\) :

Tool life model for end face turning [s]

\(T_{s}\) :

Spindle’s acceleration torque [N m]

\(v\left( t \right)\) :

Function of cutting speed against time [m/min]

\(v_{L} ,v_{U}\) :

Lower and upper bounds of cutting speeds in the beginning of material-cutting [m/min]

\(v_{XR}\) :

X-axial rapid feeding speed [m/min]

\(v_{ZR}\) :

Z-axial rapid feeding speed [m/min]

\(w_{L} ,y_{L} ,x_{L}\) :

Exponents in the tool life model

\(w_{M} ,y_{M} ,x_{M}\) :

Exponents in the model of material-cutting power

\(w_{Q} ,y_{Q} ,x_{Q}\) :

Exponents in the model of material-cutting force

\(\Delta X_{j}\) :

Relative distance between the start and the end of the \(j\)-th feeding activity in X-axis [mm]

\(\Delta Z_{j}\) :

Relative distance between the start and the end of the \(j\)-th feeding activity in Z-axis [mm]

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Acknowledgements

This research is supported by the National Natural Science Foundation of China (Grant No. 51805479), the Research Committee of UM (Grant No. MYRG2018-00087-FBA), Zhejiang Postdoctoral Foundation (Grant No. zj2019026), and the SDUST Research Fund (Grant No. 2018YQJH103).

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Authors and Affiliations

  1. Key Laboratory of Advanced Manufacturing Technology of Zhejiang Province, State Key Laboratory of Fluid Power and Mechatronic Systems, School of Mechanical Engineering, Zhejiang University, Hangzhou, 310027, China

    Luoke Hu & Hao Zheng

  2. College of Engineering and Technology, Southwest University, Chongqing, 400715, China

    Wei Cai

  3. Faculty of Business Administration, University of Macau, Macau, 999078, China

    Lianjie Shu

  4. School of Electromechanical Engineering, Guangdong University of Technology, Guangzhou, 510006, China

    Kangkang Xu

  5. Department of Industrial Engineering, Shandong University of Science and Technology, Qingdao, 266590, China

    Shun Jia

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  1. Luoke Hu
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Hu, L., Cai, W., Shu, L. et al. Energy Optimisation For End Face Turning With Variable Material Removal Rate Considering the Spindle Speed Changes. Int. J. of Precis. Eng. and Manuf.-Green Tech. 8, 625–638 (2021). https://doi.org/10.1007/s40684-020-00210-w

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