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An evolutionary framework in modelling of multi-output characteristics of the bone drilling process

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Abstract

For the improvement of economic and environmental performance of bone drilling operations, the optimum value of the spindle speed and feed rate must be known. This is because the input spindle speed is an important factor of energy consumption and with its approximate value known in optimization of output characteristics of bone drilling operations may result in significant energy savings. Optimization of multi-output characteristics of the bone drilling process is possible, if the relationships between the outputs and the inputs are known. Therefore, this study forms the strong basis for development of the models for the three output characteristics (maximum temperature, maximum force and maximum average surface roughness) for the bone drilling operation performed on the bovine bone. Experimental studies are conducted to measure these three outputs based on the spindle speed and feed rate. The validation of the formulated models is done based on the root-mean-square error, coefficient of determination, relative error, multi-objective error and mean absolute percentage error. The relationships between the three outputs and the inputs are further revealed by the 2-D analysis on the models. The findings from these relationships can be used for the predictive monitoring the bone drilling operation. The work concludes with discussion of environmental implications arising from the current study.

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Acknowledgements

This study was supported by Shantou University Scientific Research Funded Project (Grant No. NTF 16002). This project is also supported by National Natural Science Foundation of China (61502291), the Cultivation Project for Outstanding Young Teachers in Higher Education Institutions of Guangdong Province (YQ2015070) and the Characteristic Innovation Project in Higher Education Institutions of Guangdong Province (2015GXJK037, 2015KTSCX039).

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Authors and Affiliations

  1. Department of Mechatronics Engineering, Shantou University, Shantou, 515063, China

    Akhil Garg

  2. Department of Mechanical Engineering, Kalinga Institute of Industrial Technology, Bhubaneswar, 751024, India

    K. Shankhwar

  3. Department of Computer Science, Shantou University, Shantou, 515063, China

    Dazhi Jiang

  4. School of Engineering, Monash University Malaysia, 47500, Bandar Sunway, Selangor Darul Ehsan, Malaysia

    V. Vijayaraghavan

  5. IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1040-001, Lisbon, Portugal

    B. N. Panda

  6. Department of Mechanical Engineering, Indian Institute of Technology, Patna, 800013, India

    Sudhansu Sekhar Panda

Authors
  1. Akhil Garg
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  2. K. Shankhwar
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  3. Dazhi Jiang
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  4. V. Vijayaraghavan
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  5. B. N. Panda
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  6. Sudhansu Sekhar Panda
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Corresponding author

Correspondence to B. N. Panda.

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Appendix

Appendix

$$\begin{aligned} &{\text{Maximum temperature}}_{\text{GP}} = 55.1011 + \left( {2.4727} \right)*\left( {{ \tan }\left( {{ \cos }\left( {x_{2} } \right)} \right)} \right) \\ & \quad + \left( { - 2.525} \right)*\left( {{ \cos }\left( {\left( {\left( {x_{1} } \right) + \left( {\left( {7.744684} \right)} \right)} \right) + \left( {x_{1} } \right)} \right)} \right) \\ & \quad + \left( { - 0.26165} \right)*\left( {{ \sin }\left( {{ \tanh }\left( {{ \sin }\left( {\left( {{ \cos }\left( {x_{2} } \right)} \right) + \left( {{ \cos }\left( {x_{2} } \right)} \right)} \right)} \right)} \right)} \right) + \left( { - 0.013513} \right) \\ & \quad *\left( {\left( {\left( {{ \sin }\left( {{ \cos }\left( {x_{2} } \right)} \right)} \right) + \left( {\left( {\left( {{ \cos }\left( {x_{1} } \right)} \right) + \left( {\left( {7.744684} \right)} \right)} \right) + \left( {x_{1} } \right)} \right)} \right)*\left( {{ \sin }\left( {\left( {x_{2} } \right) + \left( {{ \cos }\left( {x_{2} } \right)} \right)} \right)} \right)} \right) \\ & \quad + \left( {0.68269} \right)*\left( {{ \tanh }\left( {\left( {{ \tanh }\left( {{ \sin }\left( {x_{1} } \right)} \right)} \right) + \left( {{ \cos }\left( {\left( {x_{1} } \right) + \left( {x_{2} } \right)} \right)} \right)} \right)} \right) \\ & \quad + \left( { - 0.11163} \right)*\left( {\left( {{ \sin }\left( {\left( {x_{1} } \right) + \left( {{ \tan }\left( {{ \cos }\left( {x_{2} } \right)} \right)} \right)} \right)} \right) + \left( {x_{1} } \right)} \right) \\ \end{aligned}$$
(6)
$$\begin{aligned} &{\text{Maximum thrust force}}_{\text{GP}} = - 26.7024 + \left( {0.35454} \right)*\left( {\left( {\tan \left( {x_{1} } \right)} \right)*\left( {\tanh \left( {x_{1} } \right)} \right)} \right) \\ & \quad + \left( {0.011571} \right)*\left( {\left( {\left( {\left( {x_{1} } \right)*\left( {\cos \left( {x_{2} } \right)} \right)} \right) + \left( {\left( {\tanh \left( {\sin \left( {\left( {8.500942} \right)} \right)} \right)} \right) - \left( {x_{2} } \right)} \right)} \right)*\left( {\cos \left( {x_{1} } \right)} \right)} \right) \\ & \quad + \left( { - 0.59937} \right)*\left( {\left( {\left( {8.500942} \right)} \right)*\left( {\cos \left( {x_{2} } \right)} \right)} \right) \\ & \quad + \left( {0.87393} \right)*\left( {x_{1} } \right) + \left( { - 0.0001998} \right)*\left( {\left( {x_{1} } \right)*\left( {\left( {\left( {\tanh \left( {x_{1} } \right)} \right) - \left( {\left( {x_{2} } \right) - \left( {x_{1} } \right)} \right)} \right)*\left( {\cos \left( {x_{1} } \right)} \right)} \right)} \right) \\ & \quad + \left( { - 0.1258} \right)*\left( {\tan \left( {\left( {x_{1} } \right)*\left( {\left( {x_{2} } \right)*\left( {\cos \left( {x_{1} } \right)} \right)} \right)} \right)} \right) \\ \end{aligned}$$
(7)
$$\begin{aligned}& {\text{Maximum average surface roughness}} _{\text{GP}} = 1.2153 + \left( { - 0.016092} \right) \\ & \quad *\left( {\left( {\left( {\tan \left( {\tan \left( {\left( {x_{2} } \right) - \left( {\left( {5.304303} \right)} \right)} \right)} \right)} \right) - \left( {\cos \left( {\left( {\left( {x_{2} } \right) + \left( {\left( { - 5.107464} \right)} \right)} \right) + \left( {x_{2} } \right)} \right)} \right)} \right)} \right. \\ & \quad \left. { - \left( {\cos \left( {\left( {x_{2} } \right) - \left( {\left( {\left( {x_{2} } \right) - \left( {\left( {5.304303} \right)} \right)} \right)*\left( {\sin \left( {x_{1} } \right)} \right)} \right)} \right)} \right)} \right) \\ & \quad + \left( {0.36557} \right)*\left( {\sin \left( {\cos \left( {\left( {x_{2} } \right) - \left( {\left( {5.304303} \right)} \right)} \right)} \right)} \right) + \left( { - 0.00069953} \right) \\ & \quad *\left( {\left( {x_{1} } \right)*\left( {\tan \left( {x_{2} } \right)} \right)} \right) + \left( { - 3.6113e - 005} \right) \\ & \quad *\left( {\left( {\left( {x_{1} } \right) - \left( {\left( {x_{2} } \right) - \left( {\cos \left( {\left( {x_{2} } \right) - \left( {\left( {5.304303} \right)} \right)} \right)} \right)} \right)} \right) - \left( {\left( {5.304303} \right)} \right)} \right) \\ & \quad + \left( { - 0.0056038} \right)*\left( {\left( {x_{1} } \right)*\left( {\sin \left( {\cos \left( {\left( {x_{1} } \right) + \left( {\left( { - 1.501624} \right)} \right)} \right)} \right)} \right)} \right) + \left( {0.02242} \right)*\left( {\tan \left( {x_{2} } \right)} \right) \\ \end{aligned}$$
(8)

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Garg, A., Shankhwar, K., Jiang, D. et al. An evolutionary framework in modelling of multi-output characteristics of the bone drilling process. Neural Comput & Applic 29, 1233–1241 (2018). https://doi.org/10.1007/s00521-016-2632-x

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