﻿ 大通径多关节矢量推进器喷口摆动特性研究
 舰船科学技术  2022, Vol. 44 Issue (8): 35-38    DOI: 10.3404/j.issn.1672-7649.2022.08.007 PDF

1. 华中科技大学 船舶与海洋工程学院，湖北 武汉 430074;
2. 武汉第二船舶设计研究所，湖北 武汉 430205

Research on swing characteristics of the large diameter multi-joint vectoring nozzle
SONG Shi-wei1, LI Wei-jia1, PAN Zhi2, JIA Zhi-chun2
1. School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan 430074, China;
2. Wuhan Second Ship Design and Research Institute, Wuhan 430205, China
Abstract: In order to meet the requirements for full-range operation of large-diameter vector nozzles for large underwater vehicles, a multi-joint serial mechanism with full range of swing capabilities is proposed. In order to address the characteristics of the redundant-degree-of-freedom of this mechanism, a "fit-and-solve" locally optimal algorithm is proposed for calculating joint angles with the range of joint rotation angles as the limit and the minimum joint angle increment as the objective. A set of parameters for a four-joint serial nozzle configuration with individual joint end face angles of 15°, −30°, 30° and −15° are used as an example, the control surface for each joint angle to achieve full range swing control of the nozzle is obtained based on this algorithm. The results of this paper can provide a theoretical basis and analysis method for the research and application of such mechanisms to large vector thrusters.
Key words: vector thruster     serial mechanism     kinematics     redundant-degree-of-freedom     joint angle control surface
0 引　言

1 机构运动学模型

 图 1 坐标系示意图 Fig. 1 Coordinate system diagram

 ${{\boldsymbol{Z}}_B} = \prod\nolimits_{i = 1}^N {{{\boldsymbol{T}}_i}({\theta _i})} \cdot {\boldsymbol{z}} = {{\text{[}}{b_1},{b_2},{b_3}]^{\text{T}}}。$ (1)

 图 2 喷口法矢量方向描述 Fig. 2 Description of the normal vector direction of the nozzle

 ${{\boldsymbol{Z}}_B} = {\boldsymbol{R}}({z_B},\alpha ) \cdot {\boldsymbol{R}}({x_B},\beta ) \cdot {\boldsymbol{z}} 。$ (2)

 ${{\boldsymbol{Z}}_B} = \prod\nolimits_{i = 1}^N {{{\boldsymbol{T}}_i}({\theta _i})} \cdot {\boldsymbol{z}} = {\boldsymbol{R}}({z_B},\alpha ) \cdot {\boldsymbol{R}}({x_B},\beta ) \cdot {\boldsymbol{z}} 。$ (3)

 ${\boldsymbol{F}}({\boldsymbol{\theta }}) = {[\alpha ,\beta ]^{\text{T}}} ，$ (4)

 $\left\{ \begin{gathered} \alpha = \arcsin ({{{b_1}} \mathord{\left/ {\vphantom {{{b_1}} {\sin \;\beta }}} \right. } {\sin \;\beta }}) ，\hfill \\ \beta = \arccos \;{b_3} 。\hfill \\ \end{gathered} \right.$ (5)

2 四关节式喷管关节角控制面的求解及分析

1）矢量推进器喷管的操纵控制，需要根据工作空间内喷口方向的连续变化轨迹，得到对应关节空间中连续变化的角度曲线，通过控制关节角的连续变化，实现喷口偏转角和方位角在任意位置向任意方向的变化。考虑实际操纵过程中各关节运动速度的限制，以相邻位置关节角增量最小为目标，实现关节角局部速度的最小，便于实现关节角的控制。

2）关节转动的驱动设备多为电机或液压马达，均接有供电线缆或液压油路，为防止管线的缠绕，各关节不能进行无限制的连续转动。因此，需要对各关节的旋转角度范围进行约束，避免关节角运动超限。

2.1 局部最优的运动学反解策略

 ${\varphi }^{(k\text+1)}={\varphi }^{(k)}-{J}^{-1}\{F({\theta }^{(k)})-{[\alpha ,\beta ]}^{\text{T}}\} 。$ (6)

 ${\boldsymbol{J}} = \left[ {\begin{array}{*{20}{c}} {{{\partial {f_1}({\boldsymbol{\theta }})} \mathord{\left/ {\vphantom {{\partial {f_1}({\boldsymbol{\theta }})} {\partial {\theta _m}}}} \right. } {\partial {\theta _m}}}}&{{{\partial {f_1}({\boldsymbol{\theta }})} \mathord{\left/ {\vphantom {{\partial {f_1}({\boldsymbol{\theta }})} {\partial {\theta _n}}}} \right. } {\partial {\theta _n}}}} \\ {{{\partial {f_2}({\boldsymbol{\theta }})} \mathord{\left/ {\vphantom {{\partial {f_2}({\boldsymbol{\theta }})} {\partial {\theta _m}}}} \right. } {\partial {\theta _m}}}}&{{{\partial {f_2}({\boldsymbol{\theta }})} \mathord{\left/ {\vphantom {{\partial {f_2}({\boldsymbol{\theta }})} {\partial {\theta _n}}}} \right. } {\partial {\theta _n}}}} \end{array}} \right] 。$ (7)

1）目标取为与方位对称位置的反解关节角度增量最小，保证关节角度的周期摆动。

2）对数据作曲线拟合，以距离拟合曲线最近为目标再次寻解，满足当前轨迹下关节角度变化的连续性。

3）对于不同偏转角下的转动，以相邻偏转角下的反解结果增量最小为目标寻解，对寻解结果再进行步骤2的计算，实现偏转角 $\beta$ 和方位角 $\alpha$ 变化时关节角度的连续变化，满足实际操纵需求。

2.2 关节角不超限的控制面实现

 图 3 关节角控制面 Fig. 3 Joint angle control surface

2.3 控制面效果验证

1）初始位置： ${\alpha _0} = 0^\circ$ ${\beta _0} = 10^\circ$ 。运动轨迹：偏转角 $\beta$ 保持恒定，方位角 $\alpha$ 作360°的连续变化。

2）初始位置： ${\alpha _0} = 10^\circ$ $\,{\beta _0} = 5^\circ$ 。运动轨迹：方位角 $\alpha$ 和偏转角 $\,\beta$ 按2∶1的比例变化到 ${\alpha _E} = 60^\circ$ ${\beta _E} =$ $30^\circ$ 的位置处。

 图 4 轨迹1关节角对应关系 Fig. 4 Joint angle correspondences for trajectory 1

 图 5 轨迹2关节角对应关系 Fig. 5 Joint angle correspondences for trajectory 2

3 结　语

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