﻿ 深海潜水器运动操纵仿真研究
 舰船科学技术  2022, Vol. 44 Issue (8): 69-72    DOI: 10.3404/j.issn.1672-7649.2022.08.014 PDF

Research on motion simulation of deep sea submersible
LI De-jun, ZHANG Wei, ZHAO Qiao-sheng, LI Wen-yue, HE Chun-rong, PENG Chao
State Key Laboratory of Deep-Sea Manned Vehicles, China Ship Scientific Research Center, Wuxi 214082, China
Abstract: In order to study the underwater motion characteristics of a deep-sea submersible, the underwater space motion of a deep-sea submersible is simulated in this paper. In this paper, the six degree of freedom motion equation of deep-sea submersible is given, the motion equation of deep-sea submersible is solved based on C++ self programming, the important parameters of deep-sea submersible are displayed in MFC dialog box, the development of deep-sea submersible motion simulation software is completed, and the rotary motion and rotary motion under fixed depth are simulated. The results show that the submersible has good spatial maneuverability and weak hydrodynamic characteristics upward due to the asymmetry of shape up and down. The rotary diameter in the fixed depth state is relatively small, which reflects the interference effect of vertical induced hydrodynamic force on the rotary diameter. The fixed depth control can ensure that the deep submersible can complete the horizontal rotary movement better.
Key words: deep sea submersible     calculation and simulation     motion manipulation     rotary motion
0 引　言

1 深海潜水器六自由度模型

 $\begin{split} \left\{ {\begin{array}{*{20}{c}} {m\left[ {\dot u - vr + wq - {x_G}\left( {{q^2} + {r^2}} \right) + {y_G}\left( {pq - \dot r} \right) + {z_G}\left( {pr + \dot q} \right)} \right] = \displaystyle\sum\limits_{{i}} {{X_i}} } ，\\ {m\left[ {\dot v - wp + ur - {y_G}\left( {{r^2} + {p^2}} \right) + {z_G}\left( {qr - \dot p} \right) + {x_G}\left( {qp + \dot r} \right)} \right] = \displaystyle\sum\limits_{{i}} {{Y_i}} } ，\\ {m\left[ {\dot w - uq + vp - {z_G}\left( {{p^2} + {q^2}} \right) + {x_G}\left( {rp - \dot q} \right) + {y_G}\left( {rq + \dot p} \right)} \right] = \displaystyle\sum\limits_{{i}} {{Z_i}} } ，\\ \begin{gathered} {I_x}\dot p + \left( {{I_z} - {I_y}} \right)qr + m\left[ {{y_G}\left( {\dot w + pv - qu} \right) - {z_G}\left( {\dot v + ru - pw} \right)} \right] - ，\\ \left( {\dot r + pq} \right){I_{xz}} + \left( {{r^2} - {q^2}} \right){I_{yz}} + \left( {pr - \dot q} \right){I_{xy}} = \sum\limits_{{i}} {{K_i}} ，\\ \end{gathered} \\ \begin{gathered} {I_y}\dot q + \left( {{I_x} - {I_z}} \right)rp + m\left[ {{z_G}\left( {\dot u + qw - rv} \right) - {x_G}\left( {\dot w + pv - qu} \right)} \right] - ，\\ \left( {\dot p + qr} \right){I_{xy}} + \left( {{p^2} - {r^2}} \right){I_{xz}} + \left( {qp - \dot r} \right){I_{yz}} = \sum\limits_{{i}} {{M_i}} ，\\ \end{gathered} \\ \begin{gathered} {I_z}\dot r + \left( {{I_y} - {I_x}} \right)pq + m\left[ {{x_G}\left( {\dot v + ru - pw} \right) - {y_G}\left( {\dot u + qw - rv} \right)} \right] - ，\\ \left( {\dot q + rp} \right){I_{yz}} + \left( {{q^2} - {p^2}} \right){I_{xy}} + \left( {rq - \dot p} \right){I_{xz}} = \sum\limits_{{i}} {{N_i}}。\end{gathered} \end{array}} \right. \end{split}$ (1)

 $\begin{split} \sum\limits_{{i}} {{X_i}} = &\frac{1}{2}\rho {L^4}\left[ {X_{qq}^{'}{q^2} + X_{rr}^{'}{r^2} + X_{pr}^{'}pr} \right] + \frac{1}{2}\rho {L^3}\left[ X_{\dot u}^{'}\dot u +\right.\\ &\left.X_{vr}^{'}vr + X_{wq}^{'}wq \right] + \frac{1}{2}\rho {L^2}\left[ X_{uu}^{'}{u^2} + X_{vv}^{'}{v^2} + \right.\\ &\left.X_{ww}^{'}{w^2} + X_{uw}^{'}uw \right] - \left( {W - B} \right)\sin \theta + {X_T}，\end{split}$ (2)
 $\begin{split} \sum\limits_{{i}} {{Y_i}} =& \frac{1}{2}\rho {L^4}\left[ {Y_{\dot r}^{'}\dot r + Y_{\dot p}^{'}\dot p + Y_{r\left| r \right|}^{'}r\left| r \right| + Y_{p\left| p \right|}^{'}p\left| p \right| + Y_{pq}^{'}pq + Y_{qr}^{'}qr} \right] + \\ & \frac{1}{2}\rho {L^3}\left[ {Y_{\dot v}^{'}\dot v + Y_p^{'}up + Y_r^{'}ur + Y_{vq}^{'}vq + Y_{wp}^{'}wp + Y_{wr}^{'}wr} \right] + \\ & \frac{1}{2}\rho {L^3}\left[ {Y_{v\left| r \right|}^{'}\frac{v}{{\left| v \right|}}\left| {{{\left( {{v^2} + {w^2}} \right)}^{{1 \mathord{\left/ {\vphantom {1 2}} \right. } 2}}}} \right|\left| r \right| + Y_{vww}^{'}v{w^2}} \right] +\\ &\frac{1}{2}\rho {L^2}\left[ {Y_0^{'}{u^2} + Y_v^{'}uv + Y_{vw}^{'}vw} \right] + \\ &\frac{1}{2}\rho {L^2}Y_{v\left| v \right|}^{'}v\left| {{{\left( {{v^2} + {w^2}} \right)}^{\frac{1}{2}}}} \right| + \\ & \left( {W - B} \right)\cos \theta \sin \phi + {Y_T} ，\\[-15pt] \end{split}$ (3)
 $\begin{split} \sum\limits_{{i}} {{Z_i}} = & \frac{1}{2}\rho {L^4}\left[ {Z_{\dot q}^{'}\dot q + Z_{q\left| q \right|}^{'}q\left| q \right| + Z_{pp}^{'}{p^2} + Z_{rr}^{'}{r^2} + Z_{rp}^{'}rp} \right] +\\[-3pt] &\frac{1}{2}\rho {L^3}\left[ {Z_{\dot w}^{'}\dot w + Z_{vr}^{'}vr + Z_{vp}^{'}vp + Z_q^{'}uq} \right] +\\ & \frac{1}{2}\rho {L^3}Z_{w\left| q \right|}^{'}\frac{w}{{\left| w \right|}}\left| {{{\left( {{v^2} + {w^2}} \right)}^{{1 \mathord{\left/ {\vphantom {1 2}} \right. } 2}}}} \right|\left| q \right| + \\ &\frac{1}{2}\rho {L^2}\left[ {Z_0^{'}{u^2} + Z_w^{'}uw + Z_{\left| w \right|}^{'}u\left| w \right| + Z_{vv}^{'}{v^2} + Z_{\left| v \right|w}^{'}\left| v \right|w} \right]+ \\ & \frac{1}{2}\rho {L^2}\left[ {Z_{ww}^{'}\left| {w{{\left( {{v^2} + {w^2}} \right)}^{{1 \mathord{\left/ {\vphantom {1 2}} \right. } 2}}}} \right| + Z_{w\left| w \right|}^{'}w\left| {{{\left( {{v^2} + {w^2}} \right)}^{{1 \mathord{\left/ {\vphantom {1 2}} \right. } 2}}}} \right|} \right] +\\ &\left( {W - B} \right)\cos \theta {s} \cos \phi + {Z_T} ，\\[-10pt] \end{split}$ (4)
 $\begin{split} \sum\limits_{{i}} {{K_i}} = &\frac{1}{2}\rho {L^5}\left[ K_{\dot r}^{'}\dot r + K_{\dot p}^{'}\dot p + K_{r\left| r \right|}^{'}r\left| r \right| + K_{p\left| p \right|}^{'}p\left| p \right| + K_{pq}^{'}pq +\right.\\[-3pt] &\left.Z_{qr}^{'}qr \right] + \frac{1}{2}\rho {L^4}\left[ {K_{\dot v}^{'}\dot v + K_{vq}^{'}vq + K_{wp}^{'}wp + K_{wr}^{'}wr} \right] + \\ &\frac{1}{2}\rho {L^4}\left[ {K_r^{'}ur + K_p^{'}up + K_{vww}^{'}v{w^2}} \right] + \frac{1}{2}\rho {L^3}\left[ K_0^{'}{u^2} +\right. \\ & \left.K_v^{'}uv + K_{v\left| v \right|}^{'}v\left| {{{\left( {{v^2} + {w^2}} \right)}^{{1 \mathord{\left/ {\vphantom {1 2}} \right. } 2}}}} \right| + K_{vw}^{'}vw \right] + ( {y_G}W -\\ & {y_C}B )\cos \theta \cos \phi -\left( {{z_G}W - {z_C}B} \right)\cos \theta \sin \phi + {K_T} ，\\[-10pt] \end{split}$ (5)
 $\begin{split} \sum\limits_{{i}} {{M_i}} = & \frac{1}{2}\rho {L^5}\left[ {M_{\dot q}^{'}\dot q + M_{q\left| q \right|}^{'}q\left| q \right| + M_{pp}^{'}{p^2} + M_{rr}^{'}{r^2} + M_{rp}^{'}rp} \right] +\\[-3pt] & \frac{1}{2}\rho {L^4}\left[ M_{\dot w}^{'}\dot w + M_{vr}^{'}vr + M_{vp}^{'}vp + M_q^{'}uq + \right.\\ &\left.M_{\left| w \right|q}^{'}{{\left( {{v^2} + {w^2}} \right)}^{{1 \mathord{\left/ {\vphantom {1 2}} \right. } 2}}}q \right] + \frac{1}{2}\rho {L^3}\left[ M_0^{'}{u^2} + M_w^{'}uw +\right.\\ &\left. M_{w\left| w \right|}^{'}w\left| {{{\left( {{v^2} + {w^2}} \right)}^{{1 \mathord{\left/ {\vphantom {1 2}} \right. } 2}}}} \right| +M_{vv}^{'}{v^2} + M_{\left| w \right|}^{'}u\left| w \right| \right] + \\ \begin{array}{*{20}{c}} \end{array} & \frac{1}{2}\rho {L^3}M_{ww}^{'}\left| {w{{\left( {{v^2} + {w^2}} \right)}^{{1 \mathord{\left/ {\vphantom {1 2}} \right. } 2}}}} \right| - \left( {x_G}W -\right.\\ &\left. {x_C}B \right)\cos \theta \cos \phi - \left( {z_G}W - {z_C}B \right)\sin \theta + {M_T} ，\\[-15pt] \end{split}$ (6)
 $\begin{split} \sum\limits_{{i}} {{N_i}} =& \frac{1}{2}\rho {L^5}\left[ {N_{\dot r}^{'}\dot r + N_{\dot p}^{'}\dot p + N_{pq}^{'}pq + N_{qr}^{'}qr} \right] + \\[-3pt] &\frac{1}{2}\rho {L^5}\left[ {N_{r\left| r \right|}^{'}r\left| r \right| + N_{p\left| p \right|}^{'}p\left| p \right|} \right]+ \frac{1}{2}\rho {L^4}\left[ N_{\dot v}^{'}\dot v + \right.\\ &\left. N_{wr}^{'}wr + N_{wp}^{'}wp + N_{vq}^{'}vq + N_{vww}^{'}v{w^2} + N_r^{'}ur + N_p^{'}up \right] + \\ & \frac{1}{2}\rho {L^4}N_{\left| v \right|r}^{'}\left| {{{\left( {{v^2} + {w^2}} \right)}^{{1 \mathord{\left/ {\vphantom {1 2}} \right. } 2}}}} \right|r + \frac{1}{2}\rho {L^3}\left[ N_0^{'}{u^2} + N_v^{'}uv +\right.\\ &\left.N_{v\left| v \right|}^{'}v\left| {{{\left( {{v^2} + {w^2}} \right)}^{{1 \mathord{\left/ {\vphantom {1 2}} \right. } 2}}}} \right| + N_{vw}^{'}vw \right]+ \left( {x_G}W -\right. \\ &\left. {x_C}B \right)\cos \theta \sin \phi + \left( {{y_G}W - {y_C}B} \right)\sin \theta + {N_T} 。\\[-10pt] \end{split}$ (7)

2 深海潜水器运动仿真软件

3 运动仿真研究 3.1 空间回转运动仿真

 图 1 空间回转轨迹 Fig. 1 Spatial rotation trajectory

 图 2 水平面投影 Fig. 2 Horizontal plane projection

 图 3 空间回转u-t Fig. 3 Spatial rotation u-t

 图 4 空间回转v-t Fig. 4 Spatial rotation v-t

 图 5 空间回转w-t Fig. 5 Spatial rotation w-t

 图 6 空间回转ϕ-t Fig. 6 Spatial rotation ϕ-t

 图 7 空间回转θ-t Fig. 7 Spatial rotation θ-t

 图 8 空间回转ψ-t Fig. 8 Spatial rotation ψ-t

 图 9 潜器垂向水动力 Fig. 9 Vertical hydrodynamic force of submersible
3.2 自动定深下的回转运动仿真

 图 10 定深下的回转轨迹 Fig. 10 Rotation track under fixed depth control

 图 11 水平面投影 Fig. 11 Horizontal projection

3.3 结果分析
 图 12 垂直面投影对比图 Fig. 12 Comparison of vertical plane projection

1）深潜器回转时，做空间运动，在轨迹上看作为螺旋运动。由于潜器上下不对称导致产生向上的微小水动力，而且垂向水动力具有很强的非线性，导致做空间回转运动。

2）该深潜器回转运动运动半径不大，反映深潜器的机动性很好。同时，定深状态下的回转半径相对较小，反映出垂向诱导水动力对回转半径的干扰影响。

3）通过自动定深控制，深潜器能够较好地完成水平面回转运动作业。

4 结　语

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