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Effects of pulse voltage on piezoelectric micro-jet for lubrication

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Abstract

A novel piezoelectric micro-jet for bearing lubrication is presented in this paper, and the micro-jet is working at the slap** mode. The micro-jet is embedded in the bearing system, and add little mass or volume of the system. In order to meet the different requirements for different applications and to improve the injection performance of the micro-jet, the trapezoidal wave is selected as the pulse voltage by analyzing the Fourier expansion of different pulse forms. And the influences of the parameters of the trapezoidal wave are analyzed by experiments. The injection status of the micro-jet and the mass of the droplet under single pulse voltage are obtained. The recommended exciting method for different requirements are given by analyzing the results.

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Acknowledgments

Project supported by the National Natural Science Foundation of China (51075082, 51375107).

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Authors and Affiliations

  1. State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin, 150001, China

    Kai Li, Jun-kao Liu & Wei-shan Chen

  2. AVIC, Harbin Dongan Engine Corporation LTD, Harbin, 150001, China

    Lu Zhang

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  1. Kai Li
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  2. Jun-kao Liu
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  3. Wei-shan Chen
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  4. Lu Zhang
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Corresponding author

Correspondence to Jun-kao Liu.

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Appendix: The coefficient of Eq. (6)

Appendix: The coefficient of Eq. (6)

$$\begin{aligned} a^{\prime}_{n} & = T_{f} \cos^{2} \left( {\frac{{T_{r} }}{T}n\pi } \right) - 2T_{r} \cos^{2} \left( {\frac{{T_{r} }}{T}n\pi } \right) - 2T_{r} \cos^{2} \left( {\frac{{T_{h} }}{T}n\pi } \right) - T_{r} \cos^{2} \left( {\frac{{T_{f} }}{T}n\pi } \right) \\ & \quad + 4T_{r} \cos^{2} \left( {\frac{{T_{r} }}{T}n\pi } \right)\cos^{2} \left( {\frac{{T_{h} }}{T}n\pi } \right)\sin^{2} \left( {\frac{{T_{f} }}{T}n\pi } \right) + 2T_{r} \cos^{2} \left( {\frac{{T_{r} }}{T}n\pi } \right)\cos^{2} \left( {\frac{{T_{f} }}{T}n\pi } \right) \\ & \quad + 2T_{r} \cos^{2} \left( {\frac{{T_{h} }}{T}n\pi } \right)\cos^{2} \left( {\frac{{T_{f} }}{T}n\pi } \right) - \frac{1}{2}T_{r} \sin \left( {\frac{{2T_{r} }}{T}n\pi } \right)\sin \left( {\frac{{2T_{f} }}{T}n\pi } \right) \\ & \quad - T_{r} \sin \left( {\frac{{2T_{r} }}{T}n\pi } \right)\sin \left( {\frac{{2T_{h} }}{T}n\pi } \right) - \frac{1}{2}T_{r} \sin \left( {\frac{{2T_{h} }}{T}n\pi } \right)\sin \left( {\frac{{2T_{f} }}{T}n\pi } \right) \\ & \quad + T_{r} \sin \left( {\frac{{2T_{r} }}{T}n\pi } \right)\sin \left( {\frac{{2T_{h} }}{T}n\pi } \right)\cos^{2} \left( {\frac{{T_{f} }}{T}n\pi } \right) + T_{r} \sin \left( {\frac{{2T_{h} }}{T}n\pi } \right)\sin \left( {\frac{{2T_{f} }}{T}n\pi } \right)\cos^{2} \left( {\frac{{T_{r} }}{T}n\pi } \right) \\ & \quad + T_{r} \sin \left( {\frac{{2T_{r} }}{T}n\pi } \right)\sin \left( {\frac{{2T_{f} }}{T}n\pi } \right)\cos^{2} \left( {\frac{{T_{h} }}{T}n\pi } \right) + T_{r} - T_{f} \\ \end{aligned}$$
$$\begin{aligned} b^{\prime}_{n} & = 2T_{r} \sin \left( {\frac{{2T_{r} }}{T}n\pi } \right)\cos^{2} \left( {\frac{{T_{h} }}{T}n\pi } \right) + 2T_{r} \sin \left( {\frac{{2T_{h} }}{T}n\pi } \right)\cos^{2} \left( {\frac{{T_{r} }}{T}n\pi } \right) + T_{r} \sin \left( {\frac{{2T_{r} }}{T}n\pi } \right)\cos^{2} \left( {\frac{{T_{f} }}{T}n\pi } \right) \\ & \quad + T_{r} \sin \left( {\frac{{2T_{f} }}{T}n\pi } \right)\cos^{2} \left( {\frac{{T_{r} }}{T}n\pi } \right) + T_{r} \sin \left( {\frac{{2T_{h} }}{T}n\pi } \right)\cos^{2} \left( {\frac{{T_{f} }}{T}n\pi } \right) + T_{r} \sin \left( {\frac{{2T_{f} }}{T}n\pi } \right)\cos^{2} \left( {\frac{{T_{h} }}{T}n\pi } \right) \\ & \quad - 2T_{r} \sin \left( {\frac{{2T_{r} }}{T}n\pi } \right)\cos^{2} \left( {\frac{{T_{h} }}{T}n\pi } \right)\cos^{2} \left( {\frac{{T_{f} }}{T}n\pi } \right) - 2T_{r} \sin \left( {\frac{{2T_{h} }}{T}n\pi } \right)\cos^{2} \left( {\frac{{T_{r} }}{T}n\pi } \right)\cos^{2} \left( {\frac{{T_{f} }}{T}n\pi } \right) \\ & \quad - 2T_{r} \sin \left( {\frac{{2T_{f} }}{T}n\pi } \right)\cos^{2} \left( {\frac{{T_{r} }}{T}n\pi } \right)\cos^{2} \left( {\frac{{T_{h} }}{T}n\pi } \right) + \frac{1}{2}T_{f} \sin \left( {\frac{{2T_{r} }}{T}n\pi } \right) - T_{r} \sin \left( {\frac{{2T_{r} }}{T}n\pi } \right) \\ & \quad - T_{r} \sin \left( {\frac{{2T_{h} }}{T}n\pi } \right) - \frac{1}{2}T_{r} \sin \left( {\frac{{2T_{f} }}{T}n\pi } \right) + \frac{1}{2}T_{r} \sin \left( {\frac{{2T_{r} }}{T}n\pi } \right)\sin \left( {\frac{{2T_{h} }}{T}n\pi } \right)\sin \left( {\frac{{2T_{f} }}{T}n\pi } \right) \\ \end{aligned}$$

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Li, K., Liu, Jk., Chen, Ws. et al. Effects of pulse voltage on piezoelectric micro-jet for lubrication. Microsyst Technol 23, 3081–3089 (2017). https://doi.org/10.1007/s00542-016-3080-3

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