Abstract
The stability and synchronous rotation of oscillators is a key technology of the sonic drilling rigs, vibratory breakers and pile sinkers. This paper studies the stability and synchronization properties of two oscillators in a solid–liquid coupling system. The system mainly comprises two oscillators, two hydraulic motors and a gear pair. Since each oscillator is driven by a hydraulic motor and the hydraulic motors are connected in parallel, a new dynamic model of the two oscillators is established. In this model, we consider both the nonlinearity of the gear pair and the hydraulic factors. According to the numerical results, the new method improves the stability of the system. The rotational angle and speed deviations indicate that the system can guarantee the synchronization of the two oscillators when the meshing stiffness and meshing damping ratio of the gear system are varied. The synchronization accuracy is excellent. Additionally, the numerical results are validated by simulation in AMESIM software.
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Abbreviations
- Q Tin :
-
Inlet volume flux of the system.
- Q Tout :
-
Outlet volume flux of the system.
- Q ti :
-
Load volume flux of the hydraulic motor (HM) i, i = 1,2. (the same below)
- Q in ti :
-
Inlet volume flux of the HM i.
- Q out ti :
-
Outlet volume flux of the HM i.
- p t :
-
Inlet pressure of the system.
- p Li :
-
Load pressure of the HM i.
- p in i :
-
Inlet pressure of the HM i.
- p out i :
-
Outlet pressure of the HM i.
- C tmi :
-
Internal leakage coefficient of the HM i.
- J mi :
-
Rotational inertia of the HM i.
- J oi :
-
Rotational inertia of the oscillator i.
- J gi :
-
Rotational inertia of the gear i.
- B mi :
-
Rotational damping coefficient of the HM i.
- B oi :
-
Rotational damping coefficient of the oscillator i.
- B gi :
-
Rotational damping coefficient of the gear i.
- K vi :
-
Torsional stiffness of the connector i.
- θ mi :
-
Rotational angle of the HM i.
- θ oi :
-
Rotational angle of the oscillator i.
- θ gi :
-
Rotational angle of the gear i.
- ω mi :
-
Rotational speed of the HM i.
- ω oi :
-
Rotational speed of the oscillator i.
- ω gi :
-
Rotational speed of the gear i.
- ω h :
-
Meshing speed of the gear pair.
- φ 0 :
-
Initial phase error of the gear pair.
- e g :
-
Comprehensive transmission error
- C g :
-
Meshing damping
- K g :
-
Meshing stiffness
- b c :
-
Backlash
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Funding
This work is supported by the National Key R&D Program of China (No.2018YFC1802404) and the National Natural Science Foundation of China (No. 42172343).
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Hao Wu and Yu Wang conceived and designed the structure; Lingrong Kong performed the numerical calculation; Yunwang Sun and Jun Qu performed the simulation analysis; Jiong Li analysed the data and wrote the paper.
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Li, J., Wang, Y., Kong, L. et al. Investigation of stability and synchronization properties of two oscillators in a solid–liquid coupling system. Int J Mech Mater Des 18, 823–836 (2022). https://doi.org/10.1007/s10999-022-09606-9
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DOI: https://doi.org/10.1007/s10999-022-09606-9