CN118182875A - Synchronous unfolding design method and system for sailboard of flat-plate satellite - Google Patents
Synchronous unfolding design method and system for sailboard of flat-plate satellite Download PDFInfo
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Abstract
本公开实施例公开了一种用于平板式卫星的帆板的同步展开设计方法及系统,涉及卫星结构技术领域;该同步展开设计方法包括:在第一子帆板、第二子帆板以及第三子帆板的展开过程中,获取第一子帆板、第二子帆板以及第三子帆板各自的第一展开角度分别与对应的扭簧的刚度系数之间的第一对应关系;当第一展开角度为第一子帆板、第二子帆板以及第三子帆板同步展开时的第二展开角度时,基于第一对应关系,获取第一子帆板、第二子帆板以及第三子帆板对应的扭簧的刚度系数。通过本公开实施例提供的同步展开设计方法能够实现第一子帆板、第二子帆板以及第三子帆板同步展开。
The disclosed embodiment discloses a synchronous deployment design method and system for a sailboard of a flat-panel satellite, which relates to the field of satellite structure technology; the synchronous deployment design method includes: in the deployment process of the first sub-sailboard, the second sub-sailboard and the third sub-sailboard, obtaining the first corresponding relationship between the first deployment angle of each of the first sub-sailboard, the second sub-sailboard and the third sub-sailboard and the stiffness coefficient of the corresponding torsion spring; when the first deployment angle is the second deployment angle when the first sub-sailboard, the second sub-sailboard and the third sub-sailboard are synchronously deployed, based on the first corresponding relationship, obtaining the stiffness coefficient of the torsion spring corresponding to the first sub-sailboard, the second sub-sailboard and the third sub-sailboard. The synchronous deployment design method provided by the disclosed embodiment can realize the synchronous deployment of the first sub-sailboard, the second sub-sailboard and the third sub-sailboard.
Description
技术领域Technical Field
本公开实施例涉及卫星结构技术领域,尤其涉及一种用于平板式卫星的帆板的同步展开设计方法及系统。The disclosed embodiments relate to the field of satellite structure technology, and more particularly to a method and system for designing the synchronous deployment of sailboards for flat-panel satellites.
背景技术Background technique
平板式卫星通常带有大型的太阳能帆板(以下简称为“帆板”),考虑到运载工具中的空间的限制以及在发射过程中需要承受较大的过载,因此在发射阶段平板式卫星的帆板一般呈收拢状态,直至平板式卫星与运载工具分离后,帆板方可解锁展开。Flat-panel satellites usually carry large solar panels (hereinafter referred to as "panels"). Considering the space limitations in the carrier and the need to withstand large overloads during the launch process, the panels of flat-panel satellites are generally in a folded state during the launch phase. The panels can only be unlocked and unfolded after the flat-panel satellite is separated from the carrier.
一般来说,为了保证帆板中的各子帆板均能够按照预定轨迹运动并同步展开,帆板上通常都需要加入同步展开机构以保证各子帆板的同步展开。但是,目前使用的展开控制机构质量大,不仅不利于帆板的轻量化设计,而且降低了平板式卫星上的有效载荷的质量。Generally speaking, in order to ensure that each sub-board in a sailboard can move according to a predetermined trajectory and be deployed synchronously, a synchronous deployment mechanism is usually added to the sailboard to ensure the synchronous deployment of each sub-board. However, the currently used deployment control mechanism has a large mass, which is not only not conducive to the lightweight design of the sailboard, but also reduces the mass of the payload on the flat-panel satellite.
发明内容Summary of the invention
有鉴于此,本公开实施例期望提供一种用于平板式卫星的帆板的同步展开设计方法及系统;能够在保证帆板中的各子帆板同步展开的同时实现帆板的轻量化设计。In view of this, the embodiments of the present disclosure are intended to provide a method and system for designing the synchronous deployment of a sailboard for a flat-panel satellite, which can achieve a lightweight design of the sailboard while ensuring the synchronous deployment of each sub-sailboard in the sailboard.
本公开实施例的技术方案是这样实现的:The technical solution of the embodiment of the present disclosure is implemented as follows:
第一方面,本公开实施例提供了一种用于平板式卫星的帆板的同步展开设计方法,所述帆板包括第一子帆板、第二子帆板以及第三子帆板,并且所述平板式卫星的主体、所述第一子帆板、所述第二子帆板以及所述第三子帆板依次通过带有扭簧的铰链组件连接,所述同步展开设计方法包括:In a first aspect, an embodiment of the present disclosure provides a synchronous deployment design method for a sailboard of a flat-panel satellite, wherein the sailboard includes a first sub-sailboard, a second sub-sailboard, and a third sub-sailboard, and a main body of the flat-panel satellite, the first sub-sailboard, the second sub-sailboard, and the third sub-sailboard are sequentially connected by a hinge assembly with a torsion spring, and the synchronous deployment design method includes:
在所述第一子帆板、所述第二子帆板以及所述第三子帆板的展开过程中,获取所述第一子帆板、所述第二子帆板以及所述第三子帆板各自的第一展开角度分别与对应的所述扭簧的刚度系数之间的第一对应关系;During the deployment of the first sub-sailboard, the second sub-sailboard and the third sub-sailboard, obtaining a first corresponding relationship between the first deployment angles of the first sub-sailboard, the second sub-sailboard and the third sub-sailboard and the stiffness coefficients of the corresponding torsion springs;
当所述第一展开角度为所述第一子帆板、所述第二子帆板以及所述第三子帆板同步展开时的第二展开角度时,基于所述第一对应关系,分别获取所述第一子帆板、所述第二子帆板以及所述第三子帆板对应的扭簧的刚度系数;When the first deployment angle is the second deployment angle when the first sub-sail board, the second sub-sail board and the third sub-sail board are deployed synchronously, based on the first corresponding relationship, the stiffness coefficients of the torsion springs corresponding to the first sub-sail board, the second sub-sail board and the third sub-sail board are respectively obtained;
其中,分别获取的所述第一子帆板、所述第二子帆板以及所述第三子帆板对应的扭簧的刚度系数能够使得所述第一子帆板、所述第二子帆板以及所述第三子帆板同步展开。The respectively acquired stiffness coefficients of the torsion springs corresponding to the first sub-sailboard, the second sub-sailboard and the third sub-sailboard can enable the first sub-sailboard, the second sub-sailboard and the third sub-sailboard to be deployed synchronously.
第二方面,本公开实施例提供了一种用于平板式卫星的帆板的同步展开设计系统,所述同步展开设计系统用于包含平板式卫星的主体、第一子帆板、第二子帆板以及第三子帆板的平板式卫星,所述同步展开设计系统包括:第一获取部与第二获取部;其中,In a second aspect, an embodiment of the present disclosure provides a synchronous deployment design system for a sailboard of a flat-panel satellite, wherein the synchronous deployment design system is used for a flat-panel satellite including a main body of the flat-panel satellite, a first sub-sailboard, a second sub-sailboard, and a third sub-sailboard, and the synchronous deployment design system includes: a first acquisition unit and a second acquisition unit; wherein,
所述第一获取部,被配置为在所述第一子帆板、所述第二子帆板以及所述第三子帆板的展开过程中,获取所述第一子帆板、所述第二子帆板以及所述第三子帆板各自的第一展开角度分别与对应的扭簧的刚度系数之间的第一对应关系;The first acquisition unit is configured to acquire a first corresponding relationship between the first deployment angles of the first sub-sailboard, the second sub-sailboard and the third sub-sailboard and the stiffness coefficients of the corresponding torsion springs during the deployment of the first sub-sailboard, the second sub-sailboard and the third sub-sailboard;
所述第二获取部,被配置为当所述第一展开角度为所述第一子帆板、所述第二子帆板以及所述第三子帆板同步展开时的第二展开角度时,基于所述第一对应关系,分别获取所述第一子帆板、所述第二子帆板以及所述第三子帆板对应的扭簧的刚度系数;The second acquisition unit is configured to respectively acquire stiffness coefficients of torsion springs corresponding to the first sub-sail board, the second sub-sail board, and the third sub-sail board based on the first corresponding relationship when the first deployment angle is a second deployment angle when the first sub-sail board, the second sub-sail board, and the third sub-sail board are deployed synchronously;
其中,分别获取的所述第一子帆板、所述第二子帆板以及所述第三子帆板对应的扭簧的刚度系数能够使得所述第一子帆板、所述第二子帆板以及所述第三子帆板同步展开。The respectively acquired stiffness coefficients of the torsion springs corresponding to the first sub-sailboard, the second sub-sailboard and the third sub-sailboard can enable the first sub-sailboard, the second sub-sailboard and the third sub-sailboard to be deployed synchronously.
本公开实施例提供了一种用于平板式卫星的帆板的同步展开设计方法及系统;平板式卫星的主体、第一子帆板、第二子帆板以及第三子帆板依次通过带有扭簧的铰链组件连接,降低了帆板的质量,实现了帆板的轻量化设计。此外,通过在第一子帆板、第二子帆板以及第三子帆板的展开过程中,获取第一子帆板、第二子帆板以及第三子帆板各自的第一展开角度分别与对应的扭簧的刚度系数之间的第一对应关系;并且当第一展开角度均为第一子帆板、第二子帆板以及第三子帆板同步展开时的第二展开角度时,基于第一对应关系,获取各子帆板对应的扭簧的刚度系数,从而实现第一子帆板、第二子帆板以及第三子帆板同步展开。The disclosed embodiment provides a synchronous deployment design method and system for a sailboard of a flat-panel satellite; the main body of the flat-panel satellite, the first sub-sailboard, the second sub-sailboard and the third sub-sailboard are sequentially connected by a hinge assembly with a torsion spring, which reduces the mass of the sailboard and realizes a lightweight design of the sailboard. In addition, during the deployment of the first sub-sailboard, the second sub-sailboard and the third sub-sailboard, the first corresponding relationship between the first deployment angle of each of the first sub-sailboard, the second sub-sailboard and the third sub-sailboard and the stiffness coefficient of the corresponding torsion spring is obtained; and when the first deployment angle is the second deployment angle when the first sub-sailboard, the second sub-sailboard and the third sub-sailboard are synchronously deployed, based on the first corresponding relationship, the stiffness coefficient of the torsion spring corresponding to each sub-sailboard is obtained, thereby realizing the synchronous deployment of the first sub-sailboard, the second sub-sailboard and the third sub-sailboard.
附图说明BRIEF DESCRIPTION OF THE DRAWINGS
图1为相关技术中帆板中的各子帆板采用绳索联动机构连接的示意图;FIG1 is a schematic diagram showing the connection of sub-sailboards in a sailboard using a rope linkage mechanism in the related art;
图2为绳索联动机构的结构示意图;FIG2 is a schematic structural diagram of a rope linkage mechanism;
图3为本公开实施例提供的铰链组件的结构示意图;FIG3 is a schematic structural diagram of a hinge assembly provided in an embodiment of the present disclosure;
图4为本公开实施例提供的一种用于平板式卫星的帆板的同步展开设计方法流程示意图;FIG4 is a schematic flow chart of a synchronous deployment design method for a flat-panel satellite provided by an embodiment of the present disclosure;
图5为本公开实施例提供的不带有同步展开机构的帆板的简化模型示意图;FIG5 is a simplified model schematic diagram of a sailboard without a synchronous unfolding mechanism provided by an embodiment of the present disclosure;
图6为本公开实施例提供的带有同步展开机构的帆板的简化模型示意图;FIG6 is a simplified model schematic diagram of a sailboard with a synchronous unfolding mechanism provided by an embodiment of the present disclosure;
图7为本公开实施例提供的平板式卫星对第一子帆板的约束示意图;FIG7 is a schematic diagram of the constraint of the first sub-sailboard by the flat-panel satellite provided in an embodiment of the present disclosure;
图8为本公开实施例提供的第一子帆板对第二子帆板的约束示意图;FIG8 is a schematic diagram of the constraint of the first sub-sailboard on the second sub-sailboard provided by an embodiment of the present disclosure;
图9为本公开实施例提供的第二子帆板对第三子帆板的约束示意图;FIG9 is a schematic diagram of the constraint of the third sub-sailboard by the second sub-sailboard provided by an embodiment of the present disclosure;
图10为本公开实施例提供的第一子帆板与平板式卫星的碰撞锁定示意图;FIG10 is a schematic diagram of collision locking between a first sub-sailboard and a flat-panel satellite provided by an embodiment of the present disclosure;
图11为本公开实施例提供的第二子帆板与第一子帆板的碰撞锁定示意图;FIG11 is a schematic diagram of collision locking between the second sub-sailboard and the first sub-sailboard provided by an embodiment of the present disclosure;
图12为本公开实施例提供的第三子帆板与第二子帆板的碰撞锁定示意图;FIG12 is a schematic diagram of collision locking between the third sub-sailboard and the second sub-sailboard provided by an embodiment of the present disclosure;
图13为本公开实施例提供的第一子帆板的力学分析示意图;FIG13 is a schematic diagram of mechanical analysis of the first sub-sailboard provided by an embodiment of the present disclosure;
图14为本公开实施例提供的第二子帆板的力学分析示意图;FIG14 is a schematic diagram of mechanical analysis of a second sub-sailboard provided by an embodiment of the present disclosure;
图15为本公开实施例提供的第三子帆板的力学分析示意图;FIG15 is a schematic diagram of mechanical analysis of the third sub-sailboard provided by an embodiment of the present disclosure;
图16为本公开实施例提供的第三子帆板的运动约束示意图;FIG16 is a schematic diagram of motion constraint of a third sub-windsurface provided in an embodiment of the present disclosure;
图17为本公开实施例提供的第二子帆板的运动约束示意图;FIG17 is a schematic diagram of motion constraints of a second sub-windsurfing board provided by an embodiment of the present disclosure;
图18为本公开实施例提供的平板式卫星的力学分析示意图;FIG18 is a schematic diagram of mechanical analysis of a flat-panel satellite provided by an embodiment of the present disclosure;
图19为本公开实施例提供的一种用于平板式卫星的帆板的同步展开设计系统组成示意图;FIG19 is a schematic diagram of a synchronous deployment design system for a flat-panel satellite provided by an embodiment of the present disclosure;
图20为本公开实施例提供的各子帆板同步展开的角度变化曲线图;FIG20 is a curve diagram of angle variation of synchronous deployment of each sub-sailboard provided by an embodiment of the present disclosure;
图21为本公开实施例提供的各子帆板同步展开的角速度变化曲线图;FIG21 is a curve diagram of angular velocity variation of each sub-sailboard synchronously deployed according to an embodiment of the present disclosure;
图22为本公开实施例提供的各子帆板对应的扭簧的刚度系数变化曲线图;FIG22 is a graph showing a change in stiffness coefficient of a torsion spring corresponding to each sub-sailboard according to an embodiment of the present disclosure;
图23为本公开实施例提供的第一子帆板未展开到位,第二子帆板和第三子帆板展开到位的示意图;FIG23 is a schematic diagram of a first sub-sailboard provided by an embodiment of the present disclosure, in which the second sub-sailboard and the third sub-sailboard are deployed;
图24为图23示出的情况下的各子帆板的展开角度变化曲线图;FIG24 is a curve diagram showing the variation of the deployment angles of the sub-sailboards in the case shown in FIG23;
图25为本公开实施例提供的第一子帆板和第三子帆板展开到位,第二子帆板未展开到位的示意图;FIG25 is a schematic diagram of a first sub-sailboard and a third sub-sailboard provided by an embodiment of the present disclosure, in which the second sub-sailboard is not deployed;
图26为图25示出的情况下的各子帆板的展开角度变化曲线图;FIG26 is a curve diagram showing the variation of the deployment angles of the sub-sailboards in the case shown in FIG25;
图27为本公开实施例提供的第一子帆板和第二子帆板展开到位,第三子帆板未展开到位的示意图;FIG27 is a schematic diagram of a first sub-sailboard and a second sub-sailboard provided by an embodiment of the present disclosure deployed in place, while a third sub-sailboard is not deployed in place;
图28为图27示出的情况下的各子帆板的展开角度变化曲线图;FIG28 is a curve diagram showing the variation of the deployment angles of the sub-sailboards in the case shown in FIG27;
图29为本公开实施例提供的单级铰链组件的同步展开仿真结果图;FIG29 is a diagram showing a simulation result of synchronous deployment of a single-stage hinge assembly provided by an embodiment of the present disclosure;
图30为本公开实施例提供的第一级刚度系数对应的同步展开仿真结果图;FIG30 is a diagram of synchronous deployment simulation results corresponding to the first-level stiffness coefficient provided by an embodiment of the present disclosure;
图31为本公开实施例提供的添加第二级刚度系数后的同步展开仿真结果图;FIG31 is a diagram of a synchronous deployment simulation result after adding a second-level stiffness coefficient according to an embodiment of the present disclosure;
图32为本公开实施例提供的第二子帆板与第三子帆板分别相对于第一子帆板展开过程中的同步偏差角度的仿真结果图。FIG. 32 is a diagram showing simulation results of the synchronization deviation angles of the second sub-sailboard and the third sub-sailboard during the deployment process relative to the first sub-sailboard provided by an embodiment of the present disclosure.
附图标记列表:List of reference numerals:
1:平板式卫星;10:平板式卫星的主体;20:帆板;201:第一子帆板;202:第二子帆板;203:第三子帆板;2:绳索联动机构;21:导索环;22:软钢索;3:铰链组件;31扭簧;32:第一连接部;33:第二连接部;34:枢轴;35:限位件。1: flat-panel satellite; 10: main body of the flat-panel satellite; 20: sailboard; 201: first sub-sailboard; 202: second sub-sailboard; 203: third sub-sailboard; 2: rope linkage mechanism; 21: guide ring; 22: soft steel cable; 3: hinge assembly; 31 torsion spring; 32: first connecting part; 33: second connecting part; 34: pivot; 35: limiter.
具体实施方式Detailed ways
下面将结合本公开实施例中的附图,对本公开实施例中的技术方案进行清楚、完整地描述。The technical solutions in the embodiments of the present disclosure will be clearly and completely described below in conjunction with the drawings in the embodiments of the present disclosure.
参见图1,其示例性地示出了平板式卫星1的结构示意图。如图1所示,该平板式卫星1包括平板式卫星的主体10以及帆板20。该帆板20包括第一子帆板201、第二子帆板202以及第三子帆板203。在相关技术中为了使得第一子帆板201、第二子帆板202以及第三子帆板203同步展开,平板式卫星1的主体10、第一子帆板201、第二子帆板202以及第三子帆板203依次通过图2所示的绳索联动机构2以及图3所示的铰链组件3连接。该绳索联动机构2作为同步展开机构,用于各子帆板的展开过程中控制各子帆板同步地移动。该铰链组件3用于驱动各子帆板朝向目标位置展开。也就是说在相关技术中,为了确保各子帆板能够同步展开需要对应的绳索联动机构2以及铰链组件3共同作用。在一些示例中,如图2所示,该绳索联动机构2由导索环21、以导索环21导向和支撑的软钢索22组成。其中,该导索环21与对应的子帆板固定连接。在一些示例中,如图3所示,该铰链组件3包括扭簧31、第一连接部32、第二连接部33以及枢轴34。该第一连接部32和第二连接部33能够绕枢轴34转动。在另一示例中,扭簧31安装在枢轴34上。Referring to FIG. 1 , a schematic diagram of the structure of a flat-panel satellite 1 is exemplarily shown. As shown in FIG. 1 , the flat-panel satellite 1 includes a main body 10 of the flat-panel satellite and a sailboard 20. The sailboard 20 includes a first sub-sailboard 201, a second sub-sailboard 202, and a third sub-sailboard 203. In the related art, in order to enable the first sub-sailboard 201, the second sub-sailboard 202, and the third sub-sailboard 203 to be deployed synchronously, the main body 10 of the flat-panel satellite 1, the first sub-sailboard 201, the second sub-sailboard 202, and the third sub-sailboard 203 are sequentially connected by a rope linkage mechanism 2 shown in FIG. 2 and a hinge assembly 3 shown in FIG. 3. The rope linkage mechanism 2 is used as a synchronous deployment mechanism to control each sub-sailboard to move synchronously during the deployment process of each sub-sailboard. The hinge assembly 3 is used to drive each sub-sailboard to deploy toward a target position. That is to say, in the related art, in order to ensure that each sub-sailboard can be deployed synchronously, the corresponding rope linkage mechanism 2 and the hinge assembly 3 need to work together. In some examples, as shown in FIG2 , the rope linkage mechanism 2 is composed of a guide ring 21 and a soft steel rope 22 guided and supported by the guide ring 21. The guide ring 21 is fixedly connected to the corresponding sub-sail board. In some examples, as shown in FIG3 , the hinge assembly 3 includes a torsion spring 31, a first connection part 32, a second connection part 33 and a pivot 34. The first connection part 32 and the second connection part 33 can rotate around the pivot 34. In another example, the torsion spring 31 is installed on the pivot 34.
上述的同步展开指的是在各子帆板的展开过程中,各子帆板在任意相同的时间点对应的展开角度相同。The synchronous deployment mentioned above means that during the deployment process of each sub-sail board, the deployment angles corresponding to each sub-sail board at any same time point are the same.
需要说明的是,如图1和图2所示,与平板式卫星1的主体10(图中填充阴影的矩形区域所示)连接的第一子帆板201通常称为内帆板,处于最外侧的第三子帆板203通常称为外帆板,处于第一子帆板201和第三子帆板203之间的第二子帆板202通常称为中间帆板。It should be noted that, as shown in Figures 1 and 2, the first sub-sail panel 201 connected to the main body 10 of the flat-panel satellite 1 (as shown in the shaded rectangular area in the figure) is generally called an inner sail panel, the outermost third sub-sail panel 203 is generally called an outer sail panel, and the second sub-sail panel 202 between the first sub-sail panel 201 and the third sub-sail panel 203 is generally called an intermediate sail panel.
在一些示例中,本公开实施例的技术方案也能够应用于其他的卫星,例如圆柱形卫星等。In some examples, the technical solutions of the embodiments of the present disclosure can also be applied to other satellites, such as cylindrical satellites.
在一些示例中,该平板式卫星1除了包括主体10以及帆板20以外,还可以包括有效载荷等。In some examples, the flat-panel satellite 1 may include a payload, etc. in addition to the main body 10 and the sailboard 20 .
由图1和图2可以看出,第一子帆板201与平板式卫星的主体10、第一子帆板201与第二子帆板202,以及第三子帆板203与第二子帆板202均需要安装绳索联动机构2以确保第一子帆板201、第二子帆板202以及第三子帆板203能够同步展开。这些绳索联动机构2增加了帆板20的质量,进而增加了整个系统的质量,不仅会增加发射成本,而且会限制整个系统的灵活性以及限制有效载荷的质量。As can be seen from Figures 1 and 2, the first sub-sailboard 201 and the main body 10 of the flat-panel satellite, the first sub-sailboard 201 and the second sub-sailboard 202, and the third sub-sailboard 203 and the second sub-sailboard 202 all need to be equipped with a rope linkage mechanism 2 to ensure that the first sub-sailboard 201, the second sub-sailboard 202 and the third sub-sailboard 203 can be deployed synchronously. These rope linkage mechanisms 2 increase the mass of the sailboard 20, and then increase the mass of the entire system, which not only increases the launch cost, but also limits the flexibility of the entire system and the mass of the payload.
基于此,对于图1所示的包含有3个子帆板的平板式卫星1,本公开实施例期望能够提供一种既能够实现轻量化又能够实现各子帆板同步展开的技术方案。发明人注意到,对于图1所示的平板式卫星1在不安装绳索联动机构2的情况下仅通过铰链组件3也能够实现各子帆板的同步展开。因此在本公开实施例中,平板式卫星1的主体10、第一子帆板201、第二子帆板202以及第三子帆板203依次通过如图3所示的带有扭簧31的铰链组件3连接。需要说明的是,在本公开实施例中,第一子帆板201对应的铰链组件3用于连接第一子帆板201与平板式卫星的主体10、第二子帆板202对应的铰链组件3用于连接第一子帆板201与第二子帆板202,以及第三子帆板203对应的铰链组件3用于连接第三子帆板203与第二子帆板202。Based on this, for the flat-panel satellite 1 including three sub-sailboards shown in FIG. 1, the embodiment of the present disclosure is expected to provide a technical solution that can achieve both lightweight and synchronous deployment of each sub-sailboard. The inventor noted that for the flat-panel satellite 1 shown in FIG. 1, the synchronous deployment of each sub-sailboard can be achieved only by the hinge assembly 3 without installing the rope linkage mechanism 2. Therefore, in the embodiment of the present disclosure, the main body 10 of the flat-panel satellite 1, the first sub-sailboard 201, the second sub-sailboard 202 and the third sub-sailboard 203 are sequentially connected by the hinge assembly 3 with the torsion spring 31 as shown in FIG. 3. It should be noted that in the embodiment of the present disclosure, the hinge assembly 3 corresponding to the first sub-sailboard 201 is used to connect the first sub-sailboard 201 with the main body 10 of the flat-panel satellite, the hinge assembly 3 corresponding to the second sub-sailboard 202 is used to connect the first sub-sailboard 201 with the second sub-sailboard 202, and the hinge assembly 3 corresponding to the third sub-sailboard 203 is used to connect the third sub-sailboard 203 with the second sub-sailboard 202.
发明人还注意到,当各子帆板呈收拢状态时,各铰链组件中的扭簧31均被压缩且产生驱动力矩。当各子帆板展开时,该驱动力矩驱动对应的子帆板展开。当各子帆板展开到位后,由于各铰链组件中的扭簧31仍然保持有一定的压缩量,因此该压缩量对应的预紧力能够将对应的各子帆板锁定。当然,在一些示例中,该铰链组件3还包括限位件35,在各子帆板展开到位后,对应的铰链组件中的扭簧31产生的预紧力能够将对应的子帆板压紧在该限位件35上以实现对应的子帆板的锁定。The inventors also noticed that when each sub-sail board is in a folded state, the torsion spring 31 in each hinge assembly is compressed and generates a driving torque. When each sub-sail board is unfolded, the driving torque drives the corresponding sub-sail board to unfold. After each sub-sail board is unfolded into place, since the torsion spring 31 in each hinge assembly still maintains a certain amount of compression, the pre-tightening force corresponding to the compression amount can lock the corresponding sub-sail board. Of course, in some examples, the hinge assembly 3 also includes a limiter 35. After each sub-sail board is unfolded into place, the pre-tightening force generated by the torsion spring 31 in the corresponding hinge assembly can press the corresponding sub-sail board against the limiter 35 to achieve the locking of the corresponding sub-sail board.
在本公开实施例中,帆板20中并没有设置绳索联动机构2来实现各子帆板的同步展开,而是采用铰链组件3实现各子帆板的同步展开,减小了帆板20的质量,实现了帆板20的轻量化设计。In the disclosed embodiment, the sailboard 20 does not have a rope linkage mechanism 2 to achieve the synchronous deployment of each sub-sailboard. Instead, a hinge assembly 3 is used to achieve the synchronous deployment of each sub-sailboard, which reduces the weight of the sailboard 20 and achieves a lightweight design of the sailboard 20.
基于上述内容,参见图4,其示出了本公开实施例提供的一种用于平板式卫星的帆板的同步展开设计方法,该同步展开设计方法包括以下步骤。Based on the above content, referring to FIG. 4 , a synchronous deployment design method for a sailboard of a flat-panel satellite provided by an embodiment of the present disclosure is shown. The synchronous deployment design method includes the following steps.
在步骤S401中,在第一子帆板、第二子帆板以及第三子帆板的展开过程中,获取第一子帆板、第二子帆板以及第三子帆板各自的第一展开角度分别与对应的扭簧的刚度系数之间的第一对应关系。In step S401, during the deployment of the first sub-board, the second sub-board and the third sub-board, a first corresponding relationship between the first deployment angles of the first sub-board, the second sub-board and the third sub-board and the stiffness coefficients of the corresponding torsion springs is obtained.
在一些示例中,对本公开实施例提供的各子帆板仅通过铰链组件3连接的帆板20建立简化模型,具体如图5所示。需要说明的是,由于图5所示的帆板20中不带有同步展开机构,因此在展开过程中各子帆板的第一展开角度,第一展开角速度,第一展开角加速度均不相等,进而在图5所示的简化模型中具有三个自由度,并用三个广义坐标参数(α、θ、β)来建立帆板20的位形坐标。需要说明的是,图5中的坐标系的原点位于第一子帆板201对应的铰链组件3的轴心,x轴垂直于帆板20呈收拢状态时所在的平面,并指向平板式卫星的主体10的外侧,y轴垂直于帆板20展开后所在的平面。In some examples, a simplified model is established for the sailboard 20 provided by the embodiment of the present disclosure, in which each sub-sailboard is connected only by the hinge assembly 3, as shown in FIG5. It should be noted that since the sailboard 20 shown in FIG5 does not have a synchronous deployment mechanism, the first deployment angle, the first deployment angular velocity, and the first deployment angular acceleration of each sub-sailboard are not equal during the deployment process, and thus there are three degrees of freedom in the simplified model shown in FIG5, and three generalized coordinate parameters ( α , θ , β ) are used to establish the configuration coordinates of the sailboard 20. It should be noted that the origin of the coordinate system in FIG5 is located at the axis of the hinge assembly 3 corresponding to the first sub-sailboard 201, the x-axis is perpendicular to the plane where the sailboard 20 is in a folded state, and points to the outside of the main body 10 of the flat-panel satellite, and the y-axis is perpendicular to the plane where the sailboard 20 is deployed.
具体来说,第一子帆板201的第一展开角度表示第一子帆板201相对惯性系的y轴负方向的角度,即图5中的角度α;第二子帆板202的第一展开角度表示第二子帆板202相对惯性系的y轴正方向的角度,即图5中的角度θ;第三子帆板203的第一展开角度表示第三子帆板203相对惯性系的y轴负方向的角度,即图5中的角度β。Specifically, the first deployment angle of the first sub-sail board 201 represents the angle of the first sub-sail board 201 relative to the negative direction of the y-axis of the inertial system, that is, the angle α in Figure 5; the first deployment angle of the second sub-sail board 202 represents the angle of the second sub-sail board 202 relative to the positive direction of the y-axis of the inertial system, that is, the angle θ in Figure 5; the first deployment angle of the third sub-sail board 203 represents the angle of the third sub-sail board 203 relative to the negative direction of the y-axis of the inertial system, that is, the angle β in Figure 5.
在步骤S402中,当第一展开角度为第一子帆板、第二子帆板以及第三子帆板同步展开时的第二展开角度时,基于第一对应关系,分别获取第一子帆板、第二子帆板以及第三子帆板对应的扭簧的刚度系数;In step S402, when the first deployment angle is the second deployment angle when the first sub-sail board, the second sub-sail board and the third sub-sail board are deployed synchronously, based on the first corresponding relationship, the stiffness coefficients of the torsion springs corresponding to the first sub-sail board, the second sub-sail board and the third sub-sail board are respectively obtained;
其中,分别获取的第一子帆板、第二子帆板以及第三子帆板对应的扭簧的刚度系数能够使得第一子帆板、第二子帆板以及第三子帆板同步展开。The stiffness coefficients of the torsion springs corresponding to the first sub-sailboard, the second sub-sailboard and the third sub-sailboard respectively obtained can enable the first sub-sailboard, the second sub-sailboard and the third sub-sailboard to be deployed synchronously.
上述的第二展开角度指的是当平板式卫星1中设置有同步展开机构,例如绳索联动机构2来驱动第一子帆板201、第二子帆板202以及第三子帆板203同步展开时各子帆板的展开角度。可以理解地,当第一子帆板201、第二子帆板202以及第三子帆板203同步展开时,其各自的第二展开角度相同、第二展开角速度以及第二展开角加速度也均相同。The second deployment angle mentioned above refers to the deployment angle of each sub-sailboard when a synchronous deployment mechanism, such as a rope linkage mechanism 2, is provided in the flat-panel satellite 1 to drive the first sub-sailboard 201, the second sub-sailboard 202, and the third sub-sailboard 203 to be deployed synchronously. It can be understood that when the first sub-sailboard 201, the second sub-sailboard 202, and the third sub-sailboard 203 are deployed synchronously, their respective second deployment angles, second deployment angular velocities, and second deployment angular accelerations are also the same.
因此,当已知第一子帆板201、第二子帆板202以及第三子帆板203各自的第一展开角度分别与对应的扭簧的刚度系数之间的第一对应关系时,在设定第一子帆板201、第二子帆板202以及第三子帆板203的第一展开角度为第一子帆板201、第二子帆板202以及第三子帆板203同步展开时的第二展开角度的情况下,能够获得各子帆板对应的铰链组件中扭簧的刚度系数。由于在本公开实施例中通过铰链组件3中扭簧31驱动对应的子帆板展开,因此基于上述获取得到的各子帆板对应的铰链组件3中扭簧31的刚度系数能够实现第一子帆板201、第二子帆板202以及第三子帆板203同步展开。Therefore, when the first corresponding relationship between the first deployment angles of the first sub-sailboard 201, the second sub-sailboard 202 and the third sub-sailboard 203 and the stiffness coefficients of the corresponding torsion springs are known, the stiffness coefficients of the torsion springs in the hinge assembly corresponding to each sub-sailboard can be obtained by setting the first deployment angles of the first sub-sailboard 201, the second sub-sailboard 202 and the third sub-sailboard 203 as the second deployment angles when the first sub-sailboard 201, the second sub-sailboard 202 and the third sub-sailboard 203 are deployed synchronously. Since the torsion springs 31 in the hinge assembly 3 drive the corresponding sub-sailboards to be deployed in the embodiment of the present disclosure, the first sub-sailboard 201, the second sub-sailboard 202 and the third sub-sailboard 203 can be deployed synchronously based on the stiffness coefficients of the torsion springs 31 in the hinge assembly 3 corresponding to each sub-sailboard obtained as above.
对于图4所示的技术方案,平板式卫星的主体10、第一子帆板201、第二子帆板202以及第三子帆板203依次通过带有扭簧的铰链组件连接,降低了帆板20的质量,实现了帆板20的轻量化设计。此外,通过在第一子帆板201、第二子帆板202以及第三子帆板203的展开过程中,获取第一子帆板201、第二子帆板202以及第三子帆板203各自的第一展开角度分别与对应的铰链组件中扭簧的刚度系数之间的第一对应关系;并且当第一展开角度均为第一子帆板201、第二子帆板202以及第三子帆板203同步展开时的第二展开角度时,基于第一对应关系,获取各子帆板对应的铰链组件中扭簧的刚度系数,从而实现第一子帆板201、第二子帆板202以及第三子帆板203同步展开。For the technical solution shown in FIG4 , the main body 10 of the flat-panel satellite, the first sub-sailboard 201, the second sub-sailboard 202 and the third sub-sailboard 203 are sequentially connected by a hinge assembly with a torsion spring, which reduces the mass of the sailboard 20 and realizes a lightweight design of the sailboard 20. In addition, during the unfolding process of the first sub-sailboard 201, the second sub-sailboard 202 and the third sub-sailboard 203, the first corresponding relationship between the first unfolding angles of the first sub-sailboard 201, the second sub-sailboard 202 and the third sub-sailboard 203 and the stiffness coefficient of the torsion spring in the corresponding hinge assembly is obtained; and when the first unfolding angles are all the second unfolding angles when the first sub-sailboard 201, the second sub-sailboard 202 and the third sub-sailboard 203 are unfolded synchronously, based on the first corresponding relationship, the stiffness coefficient of the torsion spring in the hinge assembly corresponding to each sub-sailboard is obtained, so as to realize the synchronous unfolding of the first sub-sailboard 201, the second sub-sailboard 202 and the third sub-sailboard 203.
对于图4所示的技术方案,在一些可能的实施方式中,在获取第一对应关系之前,该同步展开设计方法还包括:For the technical solution shown in FIG. 4 , in some possible implementations, before obtaining the first corresponding relationship, the synchronous deployment design method further includes:
基于设定的同步展开模型,在第一子帆板、第二子帆板以及第三子帆板同步展开过程中,分别根据第一子帆板、第二子帆板以及第三子帆板的长度、质量以及绕质心的惯性半径,获取第一子帆板、第二子帆板以及第三子帆板的惯性力和惯性力矩;Based on the set synchronous deployment model, during the synchronous deployment process of the first sub-sailboard, the second sub-sailboard and the third sub-sailboard, the inertia force and inertia moment of the first sub-sailboard, the second sub-sailboard and the third sub-sailboard are obtained according to the length, mass and inertia radius around the center of mass of the first sub-sailboard, the second sub-sailboard and the third sub-sailboard respectively;
基于达朗贝尔原理,确定惯性力和惯性力矩以及第二展开角度之间的第二对应关系;Based on the D'Alembert principle, a second corresponding relationship between the inertial force and the inertial moment and the second deployment angle is determined;
基于惯性力和惯性力矩以及第二对应关系,获取第二展开角度。A second deployment angle is acquired based on the inertial force and the inertial moment and the second corresponding relationship.
在一些示例中,上述设定的同步展开模型为对图1所示的带有绳索联动机构2的帆板20建立简化模型,具体如图6所示。可以理解的是,在图6所示的模型中,第一子帆板201、第二子帆板202以及第三子帆板203能够在对应的绳索联动机构2的驱动下同步展开。上述的第二展开角度指的是各子帆相对惯性系的y轴之间的角度,即图6中的角度的余角。如图6所示,本公开实施例中设定第一子帆板201的长度为/>,第一子帆板201的质心偏心距为,第二子帆板202的长度为/>以及第三子帆板的长度为/>,第一子帆板201中的端部A距第一子帆板201的质心的距离为/>,第一子帆板201中的端部B距第一子帆板201的质心的距离为/>。第二子帆板202中的端部B距第二子帆板202的质心的距离为/>,第二子帆板202中的端部C距第二子帆板202的质心的距离为/>。第三子帆板203中的端部C距第三子帆板203的质心的距离为/>,第三子帆板203中的端部D点距第三子帆板203的质心的距离为/>。In some examples, the synchronous deployment model set above is to establish a simplified model for the sailboard 20 with the rope linkage mechanism 2 shown in FIG1, as shown in FIG6. It can be understood that in the model shown in FIG6, the first sub-sailboard 201, the second sub-sailboard 202 and the third sub-sailboard 203 can be synchronously deployed under the drive of the corresponding rope linkage mechanism 2. The second deployment angle mentioned above refers to the angle between each sub-sail relative to the y-axis of the inertial system, that is, the angle in FIG6 As shown in FIG6 , in the embodiment of the present disclosure, the length of the first sub-sailboard 201 is set to / , the mass center eccentricity of the first sub-windboard 201 is , the length of the second sub-sailboard 202 is/> And the length of the third sub-board is/> , the distance between the end A of the first sub-sailboard 201 and the center of mass of the first sub-sailboard 201 is / > , the distance between the end B of the first sub-sailboard 201 and the center of mass of the first sub-sailboard 201 is / > The distance between the end B of the second sub-sailboard 202 and the center of mass of the second sub-sailboard 202 is / > , the distance between the end C of the second sub-sailboard 202 and the center of mass of the second sub-sailboard 202 is / > The distance between the end C of the third sub-sailboard 203 and the mass center of the third sub-sailboard 203 is / > , the distance between the end point D of the third sub-sailboard 203 and the mass center of the third sub-sailboard 203 is / > .
需要说明的是,在图5和图6中示例性地示出了第二子帆板202以及第三子帆板203的质心位于x轴上,但是在具体实施过程中第二子帆板202以及第三子帆板203的质心的纵坐标仍需要通过前述技术方案的计算方法进行计算得到。It should be noted that, in Figures 5 and 6, it is exemplarily shown that the center of mass of the second sub-sail panel 202 and the third sub-sail panel 203 are located on the x-axis, but in the specific implementation process, the vertical coordinates of the center of mass of the second sub-sail panel 202 and the third sub-sail panel 203 still need to be calculated by the calculation method of the aforementioned technical solution.
在一些示例中,根据第一子帆板201的长度、质心偏心距以及第二展开角度的余角,能够计算得到第一子帆板201的质心坐标。具体可以根据式(1)进行计算:In some examples, according to the length of the first sub-windsurface 201, the mass center eccentricity and the complementary angle of the second deployment angle , the coordinates of the center of mass of the first sub-sailboard 201 can be calculated. Specifically, the calculation can be performed according to formula (1):
(1) (1)
其中,x 01表示第一子帆板201的质心的横坐标,y 01表示第一子帆板201的质心的纵坐标。Wherein, x01 represents the abscissa of the center of mass of the first sub-sailboard 201, and y01 represents the ordinate of the center of mass of the first sub-sailboard 201.
需要说明的是,在式(1)中,。It should be noted that in formula (1), .
在另一些示例中,根据第二子帆板202和第三子帆板203的长度以及第二展开角度的余角,能够分别计算得到第二子帆板202和第三子帆板203的质心坐标。具体可以根据式(2)进行计算:In other examples, according to the length of the second sub-sailboard 202 and the third sub-sailboard 203 and the complementary angle of the second deployment angle, the centroid coordinates of the second sub-sailboard 202 and the third sub-sailboard 203 can be calculated respectively. Specifically, the calculation can be performed according to formula (2):
(2) (2)
其中,当i=2时,根据式(2)计算得到的是BC段所示的第二子帆板202的质心坐标,当i=3时,根据式(2)计算得到的是CD段所示的第三子帆板203的质心坐标。When i = 2, the coordinates of the center of mass of the second sub-sailboard 202 shown in the BC segment are calculated according to formula (2), and when i = 3, the coordinates of the center of mass of the third sub-sailboard 203 shown in the CD segment are calculated according to formula (2).
需要说明的是,在式(2)中,。It should be noted that in formula (2), .
可以理解地,在本公开的技术方案是基于第二子帆板202与第三子帆板203的长度相同的情况进行详细阐述的。但是在一些示例中,基于本公开的技术方案也能够对第一子帆板201、第二子帆板202以及第三子帆板203各自的长度不相同的情况进行同步展开设计。It can be understood that the technical solution of the present disclosure is described in detail based on the case where the lengths of the second sub-sailboard 202 and the third sub-sailboard 203 are the same. However, in some examples, the technical solution of the present disclosure can also be used to perform synchronous deployment design when the lengths of the first sub-sailboard 201, the second sub-sailboard 202, and the third sub-sailboard 203 are different.
在本公开实施例中,每个子帆板的惯性力和惯性力矩与对应的质心坐标对时间的二次微分结果有关。因此基于式(1)和式(2)分别对时间t作一次微分,可得:In the disclosed embodiment, the inertial force and inertial moment of each sub-board are related to the second derivative of the corresponding center of mass coordinate with respect to time. Therefore, based on equations (1) and (2), first derivatives are made with respect to time t, respectively, to obtain:
(3) (3)
(4) (4)
接着,基于式(3)和式(4)分别对时间t再作一次微分,可得:Next, based on equations (3) and (4), we differentiate the time t again and obtain:
(5) (5)
由此,基于每个子帆板的质心坐标对时间t的二次微分结果,通过达朗贝尔原理能够获得每个子帆板的惯性力和惯性力矩。Therefore, based on the quadratic differential result of the center of mass coordinates of each sub-sail board with respect to time t, the inertial force and inertial moment of each sub-sail board can be obtained through the D'Alembert principle.
(6) (6)
其中,F x1表示第一子帆板在x方向的惯性力;F y1表示第一子帆板在y方向的惯性力;M 1表示第一子帆板的惯性力矩;表示第一子帆板绕其质心的惯性半径;当i=2时,/>表示第二子帆板绕其质心的惯性半径,F xi表示第二子帆板在x方向的惯性力,F yi表示第二子帆板在y方向的惯性力,M i表示第二子帆板的惯性力矩;当i=3时,/>表示第三子帆板绕其质心的惯性半径,F xi表示第三子帆板在x方向的惯性力,F yi表示第三子帆板在y方向的惯性力,M i表示第三子帆板的惯性力矩。Wherein, Fx1 represents the inertia force of the first sub-board in the x direction ; Fy1 represents the inertia force of the first sub-board in the y direction; M1 represents the inertia moment of the first sub-board; represents the radius of inertia of the first sub-board around its center of mass; when i = 2, /> represents the radius of inertia of the second sub- board around its mass center, F xi represents the inertia force of the second sub-board in the x direction, F yi represents the inertia force of the second sub-board in the y direction, Mi represents the inertia moment of the second sub-board; when i = 3,/> represents the radius of inertia of the third sub-sailboard around its mass center, F xi represents the inertia force of the third sub-sailboard in the x direction, F yi represents the inertia force of the third sub-sailboard in the y direction, and Mi represents the inertia moment of the third sub-sailboard.
对于图6所示的简化模型,基于达朗贝尔原理,可以得到:For the simplified model shown in Figure 6, based on the D'Alembert principle, we can get:
(7) (7)
其中,表示第一子帆板、第二子帆板以及第三子帆板同步展开时第一子帆板对应的铰链组件中扭簧的驱动力矩;/>表示第一子帆板、第二子帆板以及第三子帆板同步展开时第一子帆板对应的铰链组件的阻力矩;/>表示虚位移;/>表示第i子帆板的质心在x方向的虚位移;/>表示第i子帆板的质心在y方向的虚位移;当i=2时,/>表示第一子帆板、第二子帆板以及第三子帆板同步展开时第二子帆板对应的铰链组件中扭簧的驱动力矩,表示第一子帆板、第二子帆板以及第三子帆板同步展开时第二子帆板对应的铰链组件的阻力矩;当i=3时,/>表示第一子帆板、第二子帆板以及第三子帆板同步展开时第三子帆板对应的铰链组件中扭簧的驱动力矩,/>表示第一子帆板、第二子帆板以及第三子帆板同步展开时第三子帆板对应的铰链组件的阻力矩。in, Indicates the driving torque of the torsion spring in the hinge assembly corresponding to the first sub-sailboard when the first sub-sailboard, the second sub-sailboard and the third sub-sailboard are synchronously unfolded; /> Indicates the resistance moment of the hinge assembly corresponding to the first sub-sailboard when the first sub-sailboard, the second sub-sailboard and the third sub-sailboard are deployed synchronously; /> represents virtual displacement; /> represents the virtual displacement of the center of mass of the ith sub-board in the x direction; /> represents the virtual displacement of the mass center of the ith sub-board in the y direction; when i = 2, /> represents the driving torque of the torsion spring in the hinge assembly corresponding to the second sub-sailboard when the first sub-sailboard, the second sub-sailboard and the third sub-sailboard are synchronously deployed, represents the resistance moment of the hinge assembly corresponding to the second sub-board when the first sub-board, the second sub-board and the third sub-board are deployed synchronously; when i = 3, /> represents the driving torque of the torsion spring in the hinge assembly corresponding to the third sub-sailboard when the first sub-sailboard, the second sub-sailboard and the third sub-sailboard are deployed synchronously, /> It represents the resistance moment of the hinge assembly corresponding to the third sub-sail board when the first sub-sail board, the second sub-sail board and the third sub-sail board are synchronously unfolded.
需要说明的是,在图6所示的模型中,第一子帆板201、第二子帆板202以及第三子帆板203对应的虚位移均相等。It should be noted that, in the model shown in FIG6 , the virtual displacements corresponding to the first sub-sailboard 201 , the second sub-sailboard 202 and the third sub-sailboard 203 are all equal.
可以理解地,式(7)用于表征惯性力和惯性力矩以及第二展开角度之间的第二对应关系。It can be understood that formula (7) is used to characterize the second corresponding relationship between the inertia force and the inertia moment and the second deployment angle.
在式(7)中:In formula (7):
其中,i=2,3(8) Where, i = 2, 3 (8)
将式(8)代入(7)可得:Substituting equation (8) into equation (7), we can obtain:
(9) (9)
其中,in,
(10) (10)
其中,表示第一子帆板、第二子帆板以及第三子帆板同步展开时第一子帆板对应的铰链组件中的扭簧的刚度系数;/>表示第一子帆板、第二子帆板以及第三子帆板同步展开时第一子帆板对应的铰链组件的阻力系数;当i=2时,/>表示第一子帆板、第二子帆板以及第三子帆板同步展开时第二子帆板对应的铰链组件中扭簧的刚度系数;/>表示第一子帆板、第二子帆板以及第三子帆板同步展开时第二子帆板对应的铰链组件的阻力系数;当i=3时,/>表示第一子帆板、第二子帆板以及第三子帆板同步展开时第三子帆板对应的铰链组件中扭簧的刚度系数;/>表示第一子帆板、第二子帆板以及第三子帆板同步展开时第三子帆板对应的铰链组件的阻力系数。in, Indicates the stiffness coefficient of the torsion spring in the hinge assembly corresponding to the first sub-sailboard when the first sub-sailboard, the second sub-sailboard and the third sub-sailboard are synchronously unfolded; /> represents the drag coefficient of the hinge assembly corresponding to the first sub-sailboard when the first sub-sailboard, the second sub-sailboard and the third sub-sailboard are deployed synchronously; when i = 2, /> Indicates the stiffness coefficient of the torsion spring in the hinge assembly corresponding to the second sub-sailboard when the first sub-sailboard, the second sub-sailboard and the third sub-sailboard are synchronously unfolded; /> represents the drag coefficient of the hinge assembly corresponding to the second sub-sailboard when the first sub-sailboard, the second sub-sailboard and the third sub-sailboard are deployed synchronously; when i = 3, /> Indicates the stiffness coefficient of the torsion spring in the hinge assembly corresponding to the third sub-sailboard when the first sub-sailboard, the second sub-sailboard and the third sub-sailboard are deployed synchronously; /> It represents the drag coefficient of the hinge assembly corresponding to the third sub-sail board when the first sub-sail board, the second sub-sail board and the third sub-sail board are synchronously unfolded.
可以理解地,在具体实施过程中,对于图6所示的模型,当已知各子帆板对应的式(10)中的各参数时,通过式(9)能够获得关于各子帆板同步展开时的第二展开角度的余角φ,进而能够获得第二展开角度。It can be understood that, in a specific implementation process, for the model shown in FIG6 , when the parameters in formula (10) corresponding to each sub-sail board are known, the complementary angle φ of the second deployment angle when each sub-sail board is synchronously deployed can be obtained by formula (9), and then the second deployment angle can be obtained.
对图4所示的技术方案,在一些可能的实施方式中,在第一子帆板、第二子帆板以及第三子帆板的展开过程中,分别获取第一子帆板、第二子帆板以及第三子帆板的第一展开角度与对应的扭簧的刚度系数之间的第一对应关系,包括:For the technical solution shown in FIG. 4 , in some possible implementations, during the deployment of the first sub-sailboard, the second sub-sailboard, and the third sub-sailboard, respectively obtaining a first corresponding relationship between the first deployment angles of the first sub-sailboard, the second sub-sailboard, and the third sub-sailboard and the stiffness coefficients of the corresponding torsion springs includes:
在第一子帆板、第二子帆板以及第三子帆板的展开过程中,确定帆板的动能方程如下所示:During the deployment of the first sub-sailboard, the second sub-sailboard and the third sub-sailboard, the equation for determining the kinetic energy of the sailboard is as follows:
其中,,/>,,/>,/>,/>;m 1表示第一子帆板的质量;m 2表示第二子帆板的质量;m 3表示第三子帆板的质量;α表示第一子帆板的第一展开角度;/>表示第一子帆板的第一展开角速度;θ表示第二子帆板的第一展开角度;/>表示第二子帆板的第一展开角速度;β表示第三子帆板的第一展开角度;/>表示第三子帆板的第一展开角速度;/>表示第一子帆板的长度;/>表示第二子帆板的长度;/>表示第三子帆板的长度;/>表示第二子帆板中的与第一子帆板连接的端部与第二子帆板的质心之间的距离;/>表示第三子帆板中的与第二子帆板连接的端部与第三子帆板的质心之间的距离;in, ,/> , ,/> ,/> ,/> ; m1 represents the mass of the first sub - sailboard; m2 represents the mass of the second sub - sailboard; m3 represents the mass of the third sub - sailboard; α represents the first deployment angle of the first sub-sailboard; /> represents the first deployment angular velocity of the first sub-sailboard; θ represents the first deployment angle of the second sub-sailboard; /> represents the first deployment angular velocity of the second sub-sailboard; β represents the first deployment angle of the third sub-sailboard; /> represents the first deployment angular velocity of the third sub-sailboard; /> Indicates the length of the first sub-board; /> Indicates the length of the second sub-board; /> Indicates the length of the third sub-board; /> represents the distance between the end of the second sub-sailboard connected to the first sub-sailboard and the mass center of the second sub-sailboard; /> represents the distance between the end of the third sub-sailboard connected to the second sub-sailboard and the mass center of the third sub-sailboard;
基于第一子帆板、第二子帆板以及第三子帆板对应扭簧的驱动力矩,获得帆板的势能方程如下所示:Based on the driving torque of the torsion springs corresponding to the first sub-sailboard, the second sub-sailboard and the third sub-sailboard, the potential energy equation of the sailboard is obtained as follows:
其中,表示第一子帆板对应的铰链组件中扭簧的驱动力矩;/>表示第一子帆板对应的铰链组件中扭簧的刚度系数;/>表示第二子帆板对应的铰链组件中扭簧的驱动力矩;/>表示第二子帆板对应的铰链组件中扭簧的刚度系数;/>表示第三子帆板对应的铰链组件中扭簧的驱动力矩;/>表示第三子帆板对应的铰链组件中扭簧的刚度系数;in, represents the driving torque of the torsion spring in the hinge assembly corresponding to the first sub-sailboard; /> represents the stiffness coefficient of the torsion spring in the hinge assembly corresponding to the first sub-sailboard;/> represents the driving torque of the torsion spring in the hinge assembly corresponding to the second sub-sailboard; /> represents the stiffness coefficient of the torsion spring in the hinge assembly corresponding to the second sub-sailboard;/> represents the driving torque of the torsion spring in the hinge assembly corresponding to the third sub-sailboard; /> represents the stiffness coefficient of the torsion spring in the hinge assembly corresponding to the third sub-sailboard;
基于动能方程与势能方程,利用第二类拉格朗日方程获得第一对应关系如下所示:Based on the kinetic energy equation and the potential energy equation, the first corresponding relationship is obtained using the second-kind Lagrange equation as follows:
其中,表示第一子帆板的第一角加速度;/>表示第二子帆板的第一角加速度;/>表示第三子帆板的第一角加速度。in, represents the first angular acceleration of the first sub-board; /> represents the first angular acceleration of the second sub-board; /> represents the first angular acceleration of the third sub-board.
在一些示例中,如图5所示,设定每个子帆板的质心均位于其各自的几何中心,因此该三个子帆板的质心坐标可用广义坐标表示为:In some examples, as shown in FIG5 , the center of mass of each sub-sail panel is assumed to be located at its respective geometric center, so the center of mass coordinates of the three sub-sail panels can be expressed in generalized coordinates as follows:
(11) (11)
(12) (12)
其中,表示第一子帆板201的质心的横坐标;/>表示第一子帆板201的质心的纵坐标;/>表示第二子帆板202的质心的横坐标;/>表示第二子帆板202的质心的纵坐标;/>表示第三子帆板203的质心的横坐标;/>表示第三子帆板203的质心的纵坐标。in, The horizontal coordinate representing the center of mass of the first sub-windsurface panel 201; /> The ordinate representing the center of mass of the first sub-windsurfing board 201; /> The horizontal coordinate representing the mass center of the second sub-windsurface panel 202; /> The ordinate representing the center of mass of the second sub-windsurfing board 202; /> The horizontal coordinate representing the mass center of the third sub-windsurface panel 203; /> The ordinate represents the center of mass of the third sub-windsurfing panel 203 .
在一些示例中,对上式求一阶导得到各子帆板的质心的广义速度:In some examples, the first-order derivative of the above equation is taken to obtain the generalized velocity of the center of mass of each sub-board:
(13) (13)
(14) (14)
由此可得帆板的动能方程如下所示:The kinetic energy equation of the sailboard is as follows:
(15) (15)
在一些示例中,通过铰链组件的扭簧驱动对应的子帆板展开的过程中,该扭簧产生的驱动力矩用数学形式可以表示为:In some examples, when the torsion spring of the hinge assembly drives the corresponding sub-sail panel to unfold, the driving torque generated by the torsion spring can be expressed in mathematical form as follows:
其中,表示扭簧的驱动力矩;/>表示当帆板20展开后的扭簧所剩余的预紧力;/>表示扭簧的刚度系数;λ表示铰链组件呈折叠状态时对应的角度,且λ=2φ。in, Indicates the driving torque of the torsion spring; /> Indicates the remaining preload of the torsion spring after the sailboard 20 is deployed; /> represents the stiffness coefficient of the torsion spring; λ represents the angle corresponding to the hinge assembly in the folded state, and λ= 2 φ .
扭簧的势函数V q用数学形式可以表示为:The potential function Vq of the torsion spring can be expressed in mathematical form as follows:
因此图5所示的简化模型的势能方程可用以下势函数表示:Therefore, the potential energy equation of the simplified model shown in Figure 5 can be expressed by the following potential function:
。 .
利用第二类拉格朗日方程求解得到图5所示的简化模型的动力学微分方程组。The second kind of Lagrangian equation is used to solve the dynamic differential equation group of the simplified model shown in Figure 5.
将上述计算得到的动能方程Q、势能方程V的表达式代入第二类拉格朗日方程:Substitute the expressions of the kinetic energy equation Q and the potential energy equation V calculated above into the second kind of Lagrangian equation:
其中,;q k表示上述的广义坐标(α,θ,β)。in, ; q k represents the generalized coordinates ( α , θ , β ) mentioned above.
进而得到如下所示的动力学方程:Then the kinetic equation is obtained as follows:
(16) (16)
在具体实施过程中,上述的动力学方程式(16)用于表征第一子帆板、第二子帆板以及第三子帆板的第一展开角度与对应的铰链组件中扭簧的刚度系数之间的第一对应关系。In a specific implementation process, the above dynamic equation (16) is used to characterize the first corresponding relationship between the first deployment angles of the first sub-sailboard, the second sub-sailboard and the third sub-sailboard and the stiffness coefficients of the torsion springs in the corresponding hinge assemblies.
对于图4所示的技术方案,在一些可能的实施方式中,当第一展开角度为第一子帆板、第二子帆板以及第三子帆板同步展开时的第二展开角度时,基于第一对应关系,分别获取第一子帆板、第二子帆板以及第三子帆板对应的扭簧的刚度系数,包括:For the technical solution shown in FIG4 , in some possible implementations, when the first deployment angle is the second deployment angle when the first sub-sail board, the second sub-sail board and the third sub-sail board are synchronously deployed, based on the first corresponding relationship, the stiffness coefficients of the torsion springs corresponding to the first sub-sail board, the second sub-sail board and the third sub-sail board are respectively obtained, including:
当第一展开角度为第二展开角度时,根据第二展开角度的余角以及第一对应关系,分别获取第一子帆板、第二子帆板以及第三子帆板对应的扭簧的刚度系数如下所示:When the first deployment angle is the second deployment angle, according to the complementary angle of the second deployment angle and the first corresponding relationship, the stiffness coefficients of the torsion springs corresponding to the first sub-sailboard, the second sub-sailboard and the third sub-sailboard are respectively obtained as follows:
(17) (17)
其中,表示第一子帆板、第二子帆板以及第三子帆板同步展开时第二展开角度的余角;/>表示第一子帆板、第二子帆板以及第三子帆板同步展开时的第二展开角速度;/>表示第一子帆板、第二子帆板以及第三子帆板同步展开时的第二展开角加速度;并且in, Indicates the complementary angle of the second deployment angle when the first sub-sailboard, the second sub-sailboard and the third sub-sailboard are deployed synchronously; /> represents the second deployment angular velocity when the first sub-sailboard, the second sub-sailboard and the third sub-sailboard are deployed synchronously; /> represents a second deployment angular acceleration when the first sub-sailboard, the second sub-sailboard and the third sub-sailboard are deployed synchronously; and
; ;
; ;
表示第一子帆板绕其质心的转动惯量;/>表示第二子帆板绕其质心的转动惯量;/>表示第三子帆板绕其质心的转动惯量;m 1表示第一子帆板的质量;m 2表示第二子帆板的质量;m 3表示第三子帆板的质量;/>表示第一子帆板的长度;/>表示第二子帆板的长度;/>表示第二子帆板中的与第三子帆板连接的端部与第二子帆板的质心之间的距离;/>表示第二子帆板中的与第一子帆板连接的端部与第二子帆板的质心之间的距离;/>表示第三子帆板中的与第二子帆板连接的端部与第三子帆板的质心之间的距离。 represents the moment of inertia of the first sub-board around its center of mass; /> represents the moment of inertia of the second sub-board around its center of mass; /> represents the moment of inertia of the third sub-board around its mass center; m1 represents the mass of the first sub-board ; m2 represents the mass of the second sub-board ; m3 represents the mass of the third sub-board; /> Indicates the length of the first sub-board; /> Indicates the length of the second sub-board; /> represents the distance between the end of the second sub-sailboard connected to the third sub-sailboard and the mass center of the second sub-sailboard; /> represents the distance between the end of the second sub-sailboard connected to the first sub-sailboard and the mass center of the second sub-sailboard; /> It represents the distance between the end of the third sub-sailboard connected to the second sub-sailboard and the mass center of the third sub-sailboard.
可以理解的是,当图5所示的模型中的各子帆板实现同步展开后,其各子帆板的第一展开角度相同,且其各子帆板的第一展开角度均为第二展开角度。因此,设定上式(16)中的各子帆板的第一展开角度α、θ、β均等于第二展开角度,进而能够获得各子帆板同步展开时各子帆板对应的铰链组件中扭簧的刚度系数。It can be understood that when the sub-sail panels in the model shown in FIG5 are synchronously deployed, the first deployment angles of the sub-sail panels are the same, and the first deployment angles of the sub-sail panels are all the second deployment angles. Therefore, the first deployment angles α , θ , β of the sub-sail panels in the above formula (16) are set to be equal to the second deployment angle, and then the stiffness coefficients of the torsion springs in the hinge assemblies corresponding to the sub-sail panels when the sub-sail panels are synchronously deployed can be obtained.
具体地,各子帆板对应的铰链组件中扭簧的刚度系数与各参数的关系方程如下所示:Specifically, the relationship equation between the stiffness coefficient of the torsion spring in the hinge assembly corresponding to each sub-sail board and each parameter is as follows:
。 .
基于此,当第一子帆板、第二子帆板以及第三子帆板依次通过铰链组件连接且展开时,通过设置各子帆板对应的铰链组件中扭簧的刚度系数为式(17)中计算得到的数值,就能够实现第一子帆板、第二子帆板以及第三子帆板同步展开。Based on this, when the first sub-sail board, the second sub-sail board and the third sub-sail board are connected and unfolded in sequence through the hinge assembly, by setting the stiffness coefficient of the torsion spring in the hinge assembly corresponding to each sub-sail board to the value calculated in formula (17), the first sub-sail board, the second sub-sail board and the third sub-sail board can be unfolded synchronously.
对于图4所示的技术方案,在一些可能的实施方式中,该同步展开设计方法还包括:For the technical solution shown in FIG4 , in some possible implementations, the synchronous deployment design method further includes:
根据第一子帆板、第二子帆板以及第三子帆板的展开顺序,建立第一子帆板、第二子帆板以及第三子帆板之间的第一约束反力矩数学模型;According to the deployment sequence of the first sub-sailboard, the second sub-sailboard and the third sub-sailboard, a first constraint counter-torque mathematical model between the first sub-sailboard, the second sub-sailboard and the third sub-sailboard is established;
根据第一子帆板、第二子帆板以及第三子帆板的第一展开角度,建立第一子帆板、第二子帆板以及第三子帆板之间的第二约束反力矩数学模型;According to the first deployment angles of the first sub-sailboard, the second sub-sailboard and the third sub-sailboard, a second constraint counter-torque mathematical model between the first sub-sailboard, the second sub-sailboard and the third sub-sailboard is established;
基于第一约束反力矩数学模型和第二约束反力矩数学模型,在第一子帆板、第二子帆板以及第三子帆板的展开过程中修正第一子帆板、第二子帆板以及第三子帆板对应的扭簧的刚度系数。Based on the first constraint counter-torque mathematical model and the second constraint counter-torque mathematical model, the stiffness coefficients of the torsion springs corresponding to the first sub-sailboard, the second sub-sailboard and the third sub-sailboard are corrected during the deployment of the first sub-sailboard, the second sub-sailboard and the third sub-sailboard.
需要说明的是,利用第一约束反力矩数学模型和第二约束反力矩数学模型能够辅助修正第一子帆板、第二子帆板以及第三子帆板对应的扭簧的刚度系数,进而以确保图5所示的模型在帆板20展开的开始与结束临界点的连续性。It should be noted that the use of the first constraint counter-torque mathematical model and the second constraint counter-torque mathematical model can assist in correcting the stiffness coefficients of the torsion springs corresponding to the first sub-sail board, the second sub-sail board and the third sub-sail board, thereby ensuring the continuity of the model shown in Figure 5 at the start and end critical points of the deployment of the sailboard 20.
对于上述的实施方式,在一些示例中,根据第一子帆板、第二子帆板以及第三子帆板的展开顺序,建立第一子帆板、第二子帆板以及第三子帆板之间的第一约束反力矩数学模型,包括:For the above implementation, in some examples, according to the deployment order of the first sub-sailboard, the second sub-sailboard and the third sub-sailboard, a first constraint counter-torque mathematical model between the first sub-sailboard, the second sub-sailboard and the third sub-sailboard is established, including:
当第二子帆板先于第一子帆板展开时,第一子帆板受到平板式卫星的主体的第一约束反力矩数学模型为:When the second sub-sailboard is deployed before the first sub-sailboard, the mathematical model of the first constraint counter-torque of the main body of the flat-panel satellite on the first sub-sailboard is:
其中,G 1表示第一子帆板受到平板式卫星的主体的第一约束反力矩;α表示第一子帆板的第一展开角度;表示第一子帆板与平板式卫星的主体之间的挤压弹性系数;Wherein, G1 represents the first constraint reaction moment of the first sub-sailboard subjected to the main body of the flat-panel satellite; α represents the first deployment angle of the first sub-sailboard; represents the extrusion elastic coefficient between the first sub-sailboard and the main body of the flat-panel satellite;
当第一子帆板先于第二子帆板展开时,第二子帆板受到第一子帆板的第一约束反力矩数学模型为:When the first sub-board is deployed before the second sub-board, the mathematical model of the first constraint counter-torque of the second sub-board on the first sub-board is:
其中,G 2表示第二子帆板受到第一子帆板的第一约束反力矩;表示第一子帆板的第一展开角速度;/>表示第二子帆板的第一展开角速度;/>表示第一子帆板与第二子帆板之间的挤压弹性系数;Wherein , G2 represents the first constraint reaction moment of the first sub-sailboard on the second sub-sailboard; represents the first deployment angular velocity of the first sub-sailboard; /> represents the first deployment angular velocity of the second sub-sailboard; /> represents the extrusion elastic coefficient between the first sub-sail board and the second sub-sail board;
当第二子帆板先于第三子帆板展开时,第三子帆板受到第二子帆板的第一约束反力矩数学模型为:When the second sub-board is deployed before the third sub-board, the mathematical model of the first constraint counter-torque of the third sub-board subjected to the second sub-board is:
其中,G 3表示第三子帆板受到第二子帆板的第一约束反力矩;表示第三子帆板的第一展开角速度;/>表示第二子帆板与第三子帆板之间的挤压弹性系数。Wherein, G 3 represents the first constraint reaction moment of the third sub-sailboard subjected to the second sub-sailboard; represents the first deployment angular velocity of the third sub-sailboard; /> It represents the extrusion elastic coefficient between the second sub-sail panel and the third sub-sail panel.
具体参见图7至图9,其示出了第一子帆板201、第二子帆板202以及第三子帆板203在展开过程中的约束情况。7 to 9 , which illustrate the constraints of the first sub-sailboard 201 , the second sub-sailboard 202 and the third sub-sailboard 203 during the deployment process.
在一些示例中,如图7所示,当第二子帆板202先于第一子帆板201展开时,由于第一子帆板201受到平板式卫星的主体(图7中未示出)的约束,因此第一子帆板201不能朝向平板式卫星的主体的方向展开,即第一子帆板201的第一展开角度不可能小于0度,因此此时第一子帆板201受到平板式卫星的主体的约束反力(图7中的点划线箭头所示),以阻止第一子帆板201朝向平板式卫星的主体的方向展开。In some examples, as shown in FIG7 , when the second sub-sail panel 202 is deployed before the first sub-sail panel 201, since the first sub-sail panel 201 is constrained by the main body of the flat-panel satellite (not shown in FIG7 ), the first sub-sail panel 201 cannot be deployed in the direction of the main body of the flat-panel satellite, that is, the first deployment angle of the first sub-sail panel 201 cannot be less than 0 degrees. Therefore, at this time, the first sub-sail panel 201 is subject to the constrained reaction force of the main body of the flat-panel satellite (indicated by the dotted arrow in FIG7 ) to prevent the first sub-sail panel 201 from being deployed in the direction of the main body of the flat-panel satellite.
在这种情况下,第一子帆板201受到平板式卫星的主体的约束反力矩可表示为:In this case, the constraint reaction moment of the first sub-sailboard 201 by the main body of the flat-panel satellite can be expressed as:
。 .
在另一些示例中,如图8所示,当第一子帆板201先于第二子帆板202展开时,由于第二子帆板202受到第一子帆板201的约束,因此不能反方向展开以避免第二子帆板202穿过第一子帆板201,即第二子帆板202反方向的第一展开角度不可能大于第一子帆板201的第一展开角度,因此此时第二子帆板202受到第一子帆板201的约束反力(图8中的点划线箭头所示),以阻止第二子帆板202反方向展开从而穿过第一子帆板201。In other examples, as shown in FIG8 , when the first sub-sail board 201 is deployed before the second sub-sail board 202, since the second sub-sail board 202 is constrained by the first sub-sail board 201, it cannot be deployed in the opposite direction to prevent the second sub-sail board 202 from passing through the first sub-sail board 201, that is, the first deployment angle of the second sub-sail board 202 in the opposite direction cannot be greater than the first deployment angle of the first sub-sail board 201. Therefore, at this time, the second sub-sail board 202 is subject to the constrained reaction force of the first sub-sail board 201 (indicated by the dotted arrow in FIG8 ) to prevent the second sub-sail board 202 from deploying in the opposite direction and passing through the first sub-sail board 201.
在这种情况下,第二子帆板202受到第一子帆板201的约束反力矩可表示为:In this case, the restraint reaction moment of the second sub-windboard 202 subjected to the first sub-windboard 201 can be expressed as:
。 .
在又一些示例中,如图9所示,当第二子帆板202先于第三子帆板203展开时,由于第三子帆板203受到第二子帆板202的约束,不能反方向展开以避免第三子帆板203穿过第二子帆板202,即第三子帆板203反方向的第一展开角度不可能大于第二子帆板202的第一展开角度,因此此时第三子帆板203受到第二子帆板202的约束反力(图9中的点划线箭头所示),以阻止第三子帆板203反方向展开穿过第二子帆板202。In some other examples, as shown in FIG9 , when the second sub-sail panel 202 is deployed before the third sub-sail panel 203, since the third sub-sail panel 203 is constrained by the second sub-sail panel 202, it cannot be deployed in the opposite direction to prevent the third sub-sail panel 203 from passing through the second sub-sail panel 202, that is, the first deployment angle of the third sub-sail panel 203 in the opposite direction cannot be greater than the first deployment angle of the second sub-sail panel 202. Therefore, at this time, the third sub-sail panel 203 is subject to the constrained reaction force of the second sub-sail panel 202 (indicated by the dotted arrow in FIG9 ) to prevent the third sub-sail panel 203 from deploying in the opposite direction and passing through the second sub-sail panel 202.
在这种情况下,第三子帆板203受到第二子帆板202的约束反力矩可表示为:In this case, the constraint reaction moment of the third sub-sailboard 203 subjected to the second sub-sailboard 202 can be expressed as:
。 .
对于上述的实施方式,在一些示例中,根据第一子帆板、第二子帆板以及第三子帆板的第一展开角度,建立第一子帆板、第二子帆板以及第三子帆板之间的第二约束反力矩数学模型,包括:For the above implementation, in some examples, according to the first deployment angles of the first sub-sailboard, the second sub-sailboard and the third sub-sailboard, a second constraint counter-torque mathematical model between the first sub-sailboard, the second sub-sailboard and the third sub-sailboard is established, including:
当第一子帆板的第一展开角度大于90度时,第一子帆板受到对应的铰链组件中的限位件的第二约束反力矩数学模型为:When the first deployment angle of the first sub-sailboard is greater than 90 degrees, the mathematical model of the second constraint counter-torque of the first sub-sailboard subjected to the corresponding limiter in the hinge assembly is:
其中,S 1表示第一子帆板受到限位件的第二约束反力矩;表示第一子帆板的第一展开角速度;/>表示第一子帆板与平板式卫星的主体之间的碰撞弹性系数;Wherein, S1 represents the second constraint reaction moment of the first sub-sailboard subjected to the limiter; represents the first deployment angular velocity of the first sub-sailboard; /> represents the collision elastic coefficient between the first sub-sailboard and the main body of the flat-panel satellite;
当第一子帆板的第一展开角度与第二子帆板的第一展开角度之和大于180度时,第二子帆板受到第一子帆板的第二约束反力矩数学模型为:When the sum of the first deployment angle of the first sub-sailboard and the first deployment angle of the second sub-sailboard is greater than 180 degrees, the mathematical model of the second constraint counter-torque of the first sub-sailboard on the second sub-sailboard is:
其中,S 2表示第二子帆板受到第一子帆板的第二约束反力矩;表示第二子帆板的第一展开角速度;/>表示第二子帆板与第一子帆板之间的碰撞弹性系数;Wherein , S2 represents the second constraint reaction moment of the first sub-sailboard on the second sub-sailboard; represents the first deployment angular velocity of the second sub-sailboard; /> represents the collision elastic coefficient between the second sub-sailboard and the first sub-sailboard;
当第三子帆板的第一展开角度与第二子帆板的第一展开角度之和大于180度时,第三子帆板受到第二子帆板的第二约束反力矩数学模型为:When the sum of the first deployment angle of the third sub-sailboard and the first deployment angle of the second sub-sailboard is greater than 180 degrees, the mathematical model of the second constraint counter-torque of the third sub-sailboard subjected to the second sub-sailboard is:
其中,S 3表示第三子帆板受到第二子帆板的第二约束反力矩;表示第三子帆板的第一展开角速度;/>表示第三子帆板与第二子帆板之间的碰撞弹性系数。Wherein, S 3 represents the second constraint reaction moment of the third sub-sailboard subjected to the second sub-sailboard; represents the first deployment angular velocity of the third sub-sailboard; /> It represents the collision elastic coefficient between the third sub-sailboard and the second sub-sailboard.
在一些示例中,如图10所示,由于受到对应的铰链组件3中的限位件35的约束,第一子帆板201的第一展开角度不能超过90度。因此当第一子帆板201的第一展开角度为90度时,第一子帆板201若继续展开则会与对应的铰链组件中的限位件35发生碰撞,因此第一子帆板201受到限位件35的约束反力矩(图10中的点划线箭头所示),以阻止第一子帆板201的第一展开角度过大,进而使得第一子帆板201被锁定至其第一展开角度为90度的位置处,也就是图10中示出的第一子帆板201所处的位置。In some examples, as shown in FIG10 , due to the constraint of the stopper 35 in the corresponding hinge assembly 3, the first deployment angle of the first sub-sailboard 201 cannot exceed 90 degrees. Therefore, when the first deployment angle of the first sub-sailboard 201 is 90 degrees, if the first sub-sailboard 201 continues to be deployed, it will collide with the stopper 35 in the corresponding hinge assembly. Therefore, the first sub-sailboard 201 is subject to the constraint reaction moment of the stopper 35 (as shown by the dotted arrow in FIG10 ) to prevent the first deployment angle of the first sub-sailboard 201 from being too large, thereby locking the first sub-sailboard 201 to the position where its first deployment angle is 90 degrees, that is, the position of the first sub-sailboard 201 shown in FIG10 .
在这种情况下,第一子帆板受到对应的铰链组件中的限位件的约束反力矩可表示为:In this case, the restraint reaction moment of the first sub-windboard subjected to the corresponding limiter in the hinge assembly can be expressed as:
。 .
在另一些示例中,如图11所示,由于各子帆板相互之间也存在对应的限位件的约束,因此第二子帆板202展开至与第一子帆板201平行时就不能够再继续展开,即第一子帆板201的第一展开角度和第二子帆板202的第一展开角度之和不能超过180度,以避免第二子帆板202继续展开时与第一子帆板201发生碰撞。基于此,第二子帆板202将受到第一子帆板201的约束反力矩(图11中的点划线箭头所示)。但是由于第一子帆板201和第二子帆板202之间的相互作用,第一子帆板201也将受到第二子帆板202的约束反力矩(图11中的双点划线箭头所示),从而阻止第二子帆板202继续展开,最终使得第二子帆板202被锁定至与第一子帆板201相互平行的位置处,并与第一子帆板201共同运动。In other examples, as shown in FIG11, since each sub-sailboard is also constrained by a corresponding stopper, the second sub-sailboard 202 cannot be further deployed when it is deployed to be parallel to the first sub-sailboard 201, that is, the sum of the first deployment angle of the first sub-sailboard 201 and the first deployment angle of the second sub-sailboard 202 cannot exceed 180 degrees, so as to avoid the second sub-sailboard 202 from colliding with the first sub-sailboard 201 when it continues to be deployed. Based on this, the second sub-sailboard 202 will be subject to the constraint reaction moment of the first sub-sailboard 201 (as shown by the dotted line arrow in FIG11). However, due to the interaction between the first sub-sailboard 201 and the second sub-sailboard 202, the first sub-sailboard 201 will also be subject to the constraint reaction moment of the second sub-sailboard 202 (as shown by the double dotted line arrow in FIG11), thereby preventing the second sub-sailboard 202 from continuing to be deployed, and finally causing the second sub-sailboard 202 to be locked to a position parallel to the first sub-sailboard 201 and move together with the first sub-sailboard 201.
在这种情况下,第二子帆板202受到第一子帆板201的约束反力矩可表示为:In this case, the restraint reaction moment of the second sub-windboard 202 subjected to the first sub-windboard 201 can be expressed as:
。 .
在又一些示例中,如图12所示,在具体实施过程中,第三子帆板203展开至与第二子帆板202平行时就不能够再继续展开,即第三子帆板203的第一展开角度和第二子帆板202的第一展开角度之和不能超过180度,以避免第三子帆板203继续展开时与第二子帆板202发生碰撞。基于此,第三子帆板203将受到第二子帆板202的约束反力矩(图12中的点划线箭头所示)。但是由于第三子帆板203和第二子帆板202之间的相互作用,第二子帆板202也将受到第三子帆板203的约束反力矩(图12中的双点划线箭头所示),从而阻止第三子帆板203继续展开,最终使得第三子帆板203被锁定至与第二子帆板202相互平行的位置处,并与第二子帆板202共同运动。In some other examples, as shown in FIG12, in a specific implementation process, when the third sub-sailboard 203 is unfolded to be parallel to the second sub-sailboard 202, it cannot be further unfolded, that is, the sum of the first unfolding angle of the third sub-sailboard 203 and the first unfolding angle of the second sub-sailboard 202 cannot exceed 180 degrees, so as to avoid the third sub-sailboard 203 from colliding with the second sub-sailboard 202 when it continues to unfold. Based on this, the third sub-sailboard 203 will be subject to the constraint counter-torque of the second sub-sailboard 202 (as shown by the dotted line arrow in FIG12). However, due to the interaction between the third sub-sailboard 203 and the second sub-sailboard 202, the second sub-sailboard 202 will also be subject to the constraint counter-torque of the third sub-sailboard 203 (as shown by the double dotted line arrow in FIG12), thereby preventing the third sub-sailboard 203 from continuing to unfold, and finally causing the third sub-sailboard 203 to be locked to a position parallel to the second sub-sailboard 202 and move together with the second sub-sailboard 202.
在这种情况下,第三子帆板203受到第二子帆板202的约束反力矩可表示为:In this case, the constraint reaction moment of the third sub-sailboard 203 subjected to the second sub-sailboard 202 can be expressed as:
。 .
对于图4所示的技术方案,在一些可能的实施方式中,该同步展开设计方法还包括:For the technical solution shown in FIG4 , in some possible implementations, the synchronous deployment design method further includes:
对第一子帆板、第二子帆板以及第三子帆板分别进行力学分析,获得第一子帆板、第二子帆板以及第三子帆板分别对应的动力学方程;Performing mechanical analysis on the first sub-sailboard, the second sub-sailboard and the third sub-sailboard respectively, and obtaining dynamic equations corresponding to the first sub-sailboard, the second sub-sailboard and the third sub-sailboard respectively;
基于动力学方程,获得第一子帆板对应的铰链组件的支撑力如下所示:Based on the dynamic equation, the support force of the hinge assembly corresponding to the first sub-sailboard is obtained as follows:
其中,;/>;/>;m 1表示第一子帆板的质量;m 2表示第二子帆板的质量;m 3表示第三子帆板的质量;/>表示第一子帆板的长度;/>表示第二子帆板的长度;/>表示第一子帆板中的与平板式卫星的主体连接的端部与第一子帆板的质心之间的距离;/>表示第二子帆板中的与第三子帆板连接的端部与第二子帆板的质心之间的距离;/>表示第三子帆板中的与第二子帆板连接的端部与第三子帆板的质心之间的距离;/>表示第一子帆板对应的铰链组件的支撑力在x方向的分力;/>表示第一子帆板对应的铰链组件的支撑力在y方向的分力;in, ; /> ; /> ; m1 represents the mass of the first sub-sailboard; m2 represents the mass of the second sub - sailboard ; m3 represents the mass of the third sub - sailboard; /> Indicates the length of the first sub-board; /> Indicates the length of the second sub-board; /> represents the distance between the end of the first sub-sail panel connected to the main body of the flat-panel satellite and the mass center of the first sub-sail panel; /> represents the distance between the end of the second sub-sailboard connected to the third sub-sailboard and the mass center of the second sub-sailboard; /> represents the distance between the end of the third sub-sailboard connected to the second sub-sailboard and the mass center of the third sub-sailboard; /> Indicates the component of the support force of the hinge assembly corresponding to the first sub-sailboard in the x direction; /> represents the component of the support force of the hinge assembly corresponding to the first sub-sailboard in the y direction;
其中,第一子帆板对应的铰链组件的支撑力用于表征第一子帆板展开时对平板式卫星的主体的扰动性能。The supporting force of the hinge assembly corresponding to the first sub-sail panel is used to characterize the disturbance performance of the main body of the flat-panel satellite when the first sub-sail panel is unfolded.
具体来说,如图13所示,对第一子帆板201进行力学分析。第一子帆板在端部A、端部B处分别受到扭簧的扭矩和/>的作用,并且在端部A处受到平板式卫星的主体的支撑力作用,在端部B处受到第二子帆板202的作用力。Specifically, as shown in FIG13 , a mechanical analysis is performed on the first sub-sailboard 201. The first sub-sailboard is subjected to torque of the torsion spring at the end A and the end B respectively. and/> , and at end A it is acted upon by the supporting force of the main body of the flat-panel satellite, and at end B it is acted upon by the force of the second sub-sailboard 202.
基于上述阐述,可得第一子帆板201的动力学方程如下所示:Based on the above description, the dynamic equation of the first sub-windboard 201 is as follows:
其中,表示第一子帆板201绕端部A的转动惯量。in, represents the moment of inertia of the first sub-windboard 201 around the end A.
如图14所示,对第二子帆板202进行力学分析。第二子帆板202在端部B、端部C处分别受到扭簧的扭矩和/>的作用,并且在端部B处受到第一子帆板201的支撑力作用,在端部C处受到第三子帆板203的作用力。As shown in FIG14 , a mechanical analysis is performed on the second sub-sailboard 202. The second sub-sailboard 202 is subjected to torques of the torsion springs at the end B and the end C, respectively. and/> , and at end B it is acted upon by the support force of the first sub-sailboard 201 , and at end C it is acted upon by the force of the third sub-sailboard 203 .
基于上述阐述,可得第二子帆板202对应的动力学方程如下所示:Based on the above description, the dynamic equation corresponding to the second sub-windboard 202 is as follows:
其中,表示第二子帆板绕其质心的转动惯量。in, represents the moment of inertia of the second sub-board around its center of mass.
如图15所示,对第三子帆板203进行力学分析。第三子帆板203在端部C处受到扭簧的扭矩的作用,在端部C处受到第二子帆板202的支撑力。As shown in FIG15 , a mechanical analysis is performed on the third sub-sailboard 203. The third sub-sailboard 203 is subjected to a torque of a torsion spring at the end C. , and receives the support force of the second sub-sail board 202 at the end C.
基于上述阐述,可得第三子帆板203对应的动力学方程如下所示:Based on the above description, the dynamic equation corresponding to the third sub-windboard 203 is as follows:
其中,表示第三子帆板绕其质心的转动惯量。in, represents the moment of inertia of the third sub-board around its center of mass.
此外,在帆板的展开过程中,第一子帆板201在端部A处与平板式卫星的主体连接产生约束,第一子帆板201与第二子帆板202在端部B处连接产生约束,第二子帆板202与第三子帆板203在端部C处连接产生约束。In addition, during the unfolding process of the sailboard, the first sub-sailboard 201 is connected to the main body of the flat-panel satellite at end A to generate a constraint, the first sub-sailboard 201 is connected to the second sub-sailboard 202 at end B to generate a constraint, and the second sub-sailboard 202 is connected to the third sub-sailboard 203 at end C to generate a constraint.
由图16和图17所示的约束关系可以得到以下约束方程组:The following constraint equations can be obtained from the constraint relationships shown in Figures 16 and 17:
进而可得第一子帆板对应的铰链组件的支撑力:Then the support force of the hinge assembly corresponding to the first sub-sailboard can be obtained:
其中,;/>;/>。in, ; /> ; /> .
需要说明的是,上述的第一子帆板对应的铰链组件的支撑力指的是与平板式卫星的主体连接的第一子帆板201的端部所受到的力,也即图5中的端部A处的力,也称为“根部铰链支撑力”。It should be noted that the support force of the hinge assembly corresponding to the first sub-sail panel refers to the force exerted on the end of the first sub-sail panel 201 connected to the main body of the flat-panel satellite, that is, the force at the end A in Figure 5, also known as the "root hinge support force".
对于图4所示的技术方案,在一些可能的实施方式中,该同步展开设计方法还包括:For the technical solution shown in FIG4 , in some possible implementations, the synchronous deployment design method further includes:
在获得第一子帆板对应的铰链组件的支撑力的情况下,对平板式卫星的主体进行力学分析以获取平板式卫星的主体对应的动力学方程;When the support force of the hinge assembly corresponding to the first sub-sailboard is obtained, a mechanical analysis is performed on the main body of the flat-panel satellite to obtain a dynamic equation corresponding to the main body of the flat-panel satellite;
基于平板式卫星的主体对应的动力学方程,对平板式卫星的主体进行扰动分析。Based on the dynamic equation corresponding to the main body of the flat-panel satellite, a disturbance analysis of the main body of the flat-panel satellite is performed.
在具体实施过程中,如图18所示,将与平板式卫星的主体的两侧连接的子帆板与平板式卫星的主体耦合后展开,并分析位于平板式卫星的主体的两侧的子帆板的铰链组件对平板式卫星的主体产生的力与力矩。在一些示例中,平板式卫星的主体受到两侧的子帆板的铰链组件在x′方向和y′方向的力与力矩。如果两侧的子帆板不同步展开,则平板式卫星的主体的两侧受到的力在同一时刻并不相同,进而造成平板式卫星的主体将分别产生沿x′方向和y′方向的加速度,同时还会产生角加速度,影响平板式卫星的主体的姿态。在具体实施过程中,两侧子帆板关于平板式卫星的主体的质心对称安装,且x′方向的力均通过质心,所以两侧的子帆板的铰链组件在x′方向的力不产生使平板式卫星的主体姿态扰动的力矩。In the specific implementation process, as shown in FIG18, the sub-sail panels connected to the two sides of the main body of the flat-panel satellite are coupled with the main body of the flat-panel satellite and then deployed, and the forces and moments generated by the hinge components of the sub-sail panels on both sides of the main body of the flat-panel satellite on the main body of the flat-panel satellite are analyzed. In some examples, the main body of the flat-panel satellite is subjected to forces and moments in the x' and y' directions by the hinge components of the sub-sail panels on both sides. If the sub-sail panels on both sides are not deployed synchronously, the forces on both sides of the main body of the flat-panel satellite are not the same at the same time, which causes the main body of the flat-panel satellite to generate accelerations in the x' and y' directions respectively, and angular acceleration is also generated, affecting the attitude of the main body of the flat-panel satellite. In the specific implementation process, the sub-sail panels on both sides are symmetrically installed about the center of mass of the main body of the flat-panel satellite, and the forces in the x' direction pass through the center of mass, so the forces of the hinge components of the sub-sail panels on both sides in the x' direction do not generate moments that disturb the attitude of the main body of the flat-panel satellite.
由此,基于图18所示的简化模型可以得到以下动力学方程:Therefore, based on the simplified model shown in Figure 18, the following kinetic equation can be obtained:
其中,m表示平板式卫星的主体的质量;J表示平板式卫星的主体绕其质心的转动惯量;表示两侧的子帆板分别与平板式卫星的主体之间的距离;/>表示平板式卫星的主体以y′轴正方向起始转动的角度;/>表示位于平板式卫星的主体的右侧的第一子帆板对应的铰链组件的支撑力在x′方向的分力;/>表示位于平板式卫星的主体的右侧的第一子帆板对应的铰链组件的支撑力在y′方向的分力;/>表示位于平板式卫星的主体的左侧的第一子帆板对应的铰链组件的支撑力在x′方向的分力;/>表示位于平板式卫星的主体的左侧的第一子帆板对应的铰链组件的支撑力在y′方向的分力;/>表示位于平板式卫星的主体的右侧的第一子帆板对平板式卫星的主体产生的扭矩;/>表示位于平板式卫星的主体的左侧的第一子帆板对平板式卫星的主体产生的扭矩。Wherein, m represents the mass of the main body of the flat-panel satellite; J represents the moment of inertia of the main body of the flat-panel satellite about its center of mass; Indicates the distances between the sub-sail panels on both sides and the main body of the flat-panel satellite; /> Indicates the angle at which the main body of the flat-panel satellite starts to rotate in the positive direction of the y′ axis; /> Indicates the component of the support force of the hinge assembly corresponding to the first sub-sailboard located on the right side of the main body of the flat-panel satellite in the x'direction;/> Indicates the component of the support force of the hinge assembly corresponding to the first sub-sailboard located on the right side of the main body of the flat-panel satellite in the y′ direction; /> represents the component of the support force of the hinge assembly corresponding to the first sub-sailboard located on the left side of the main body of the flat-panel satellite in the x'direction;/> Indicates the component of the support force of the hinge assembly corresponding to the first sub-sailboard located on the left side of the main body of the flat-panel satellite in the y′ direction; /> Indicates the torque generated by the first sub-sailboard located on the right side of the main body of the flat-panel satellite on the main body of the flat-panel satellite; /> It represents the torque generated by the first sub-sailboard located on the left side of the main body of the flat-panel satellite on the main body of the flat-panel satellite.
需要说明的是,图18中的坐标系的原点位于平板式卫星的主体的质心位置处,x′轴垂直于帆板20呈收拢状态时所在的平面,并指向平板式卫星的主体10的外侧,y′轴垂直于帆板20展开后所在的平面。It should be noted that the origin of the coordinate system in Figure 18 is located at the center of mass of the main body of the flat-panel satellite, the x′ axis is perpendicular to the plane where the sailboard 20 is in a folded state and points to the outside of the main body 10 of the flat-panel satellite, and the y′ axis is perpendicular to the plane where the sailboard 20 is unfolded.
此外,需要说明的是,在具体实施过程中,平板式卫星的主体10的两侧对称地安装有帆板20。In addition, it should be noted that, in a specific implementation process, sailboards 20 are symmetrically installed on both sides of the main body 10 of the flat-panel satellite.
最后,参见图19,本公开实施例还提供了一种用于平板式卫星的帆板的同步展开设计系统190,该同步展开设计系统190包括:第一获取部1901与第二获取部1902;其中,Finally, referring to FIG. 19 , the embodiment of the present disclosure further provides a synchronous deployment design system 190 for a sailboard of a flat-panel satellite, the synchronous deployment design system 190 comprising: a first acquisition unit 1901 and a second acquisition unit 1902; wherein,
该第一获取部1901,被配置为在第一子帆板、第二子帆板以及第三子帆板的展开过程中,获取第一子帆板、第二子帆板以及第三子帆板各自的第一展开角度分别与对应的扭簧的刚度系数之间的第一对应关系;The first acquisition unit 1901 is configured to acquire a first corresponding relationship between the first deployment angles of the first sub-sailboard, the second sub-sailboard and the third sub-sailboard and the stiffness coefficients of the corresponding torsion springs during the deployment of the first sub-sailboard, the second sub-sailboard and the third sub-sailboard;
该第二获取部1902,被配置为当第一展开角度为第一子帆板、第二子帆板以及第三子帆板同步展开时的第二展开角度时,基于第一对应关系,分别获取第一子帆板、第二子帆板以及第三子帆板对应的扭簧的刚度系数;The second acquisition unit 1902 is configured to respectively acquire stiffness coefficients of torsion springs corresponding to the first sub-sail board, the second sub-sail board and the third sub-sail board based on the first corresponding relationship when the first deployment angle is the second deployment angle when the first sub-sail board, the second sub-sail board and the third sub-sail board are deployed synchronously;
其中,分别获取的第一子帆板、第二子帆板以及第三子帆板对应的扭簧的刚度系数能够使得第一子帆板、第二子帆板以及第三子帆板同步展开。The stiffness coefficients of the torsion springs corresponding to the first sub-sailboard, the second sub-sailboard and the third sub-sailboard respectively obtained can enable the first sub-sailboard, the second sub-sailboard and the third sub-sailboard to be deployed synchronously.
下面通过仿真分析示例对本公开实施例提供的技术方案进行详细地阐述。The technical solution provided by the embodiment of the present disclosure is described in detail below through a simulation analysis example.
参见表1,其示出了帆板20的具体参数。See Table 1, which shows specific parameters of the windsurfing board 20.
表1Table 1
经过仿真分析得到图6所示的带有绳索联动机构2的帆板20的角度变化以及角速度变化曲线,具体参见图20和图21。将图20和图21所示的第一子帆板、第二子帆板以及第三子帆板的第二展开角度变化以及第二展开角速度变化曲线导入前述技术方案所述的式(17)中,并输入表1中的各项参数,可以得到图5所示的模型中的各子帆板对应的扭簧的刚度系数变化曲线,具体如图22所示。根据图22所示的各子帆板对应的扭簧的刚度系数变化曲线能够拟合得到各子帆板对应的扭簧的大致的刚度系数,若每个扭簧仅拟合单值的刚度系数,则为单级铰链组件,若将图22所示的各子帆板对应的扭簧的刚度系数变化曲线分段拟合,每个扭簧拟合出多值组合的刚度系数,则为多级铰链组件。After simulation analysis, the angle change and angular velocity change curves of the sailboard 20 with the rope linkage mechanism 2 shown in FIG6 are obtained, specifically referring to FIG20 and FIG21. The second deployment angle change and second deployment angular velocity change curves of the first sub-sailboard, the second sub-sailboard and the third sub-sailboard shown in FIG20 and FIG21 are introduced into the formula (17) described in the aforementioned technical solution, and the parameters in Table 1 are input, and the stiffness coefficient change curves of the torsion springs corresponding to each sub-sailboard in the model shown in FIG5 can be obtained, as shown in FIG22. According to the stiffness coefficient change curves of the torsion springs corresponding to each sub-sailboard shown in FIG22, the approximate stiffness coefficients of the torsion springs corresponding to each sub-sailboard can be fitted. If each torsion spring only fits a single-value stiffness coefficient, it is a single-stage hinge assembly. If the stiffness coefficient change curves of the torsion springs corresponding to each sub-sailboard shown in FIG22 are segmented, and each torsion spring fits a multi-value combination of stiffness coefficients, it is a multi-stage hinge assembly.
对于单级铰链组件连接的帆板展开过程进行仿真,具体如下:The unfolding process of the sailboard connected by a single-stage hinge assembly is simulated as follows:
在一些示例中,若第一子帆板对应的铰链组件中扭簧的驱动力矩较小,第二子帆板与第三子帆板对应的铰链组件中扭簧的驱动力矩相对较大,则会出现图23所示的情况,也就是第二子帆板和第三子帆板均已展开到位,但是第一子帆板还没有展开到位。在这种情况下,第二子帆板和第三子帆板已锁定,且与第一子帆板共同在第一子帆板对应的铰链组件中扭簧的驱动下一起转动(图23中的虚线箭头所示)。如图24所示,在5.2秒左右第二子帆板展开到位,随后在5.6秒左右第三子帆板展开到位。然后第二子帆板和第三子帆板以相同的第一角速度与第一子帆板转动到目标位置。此时,需要增大第一子帆板对应的铰链组件中扭簧的驱动力矩,并分别调整第二子帆板和第三子帆板对应的铰链组件中扭簧的驱动力矩,以使得第一子帆板、第二子帆板以及第三子帆板同步展开。In some examples, if the driving torque of the torsion spring in the hinge assembly corresponding to the first sub-sailboard is small, and the driving torque of the torsion spring in the hinge assembly corresponding to the second sub-sailboard and the third sub-sailboard is relatively large, the situation shown in Figure 23 will appear, that is, the second sub-sailboard and the third sub-sailboard are both deployed in place, but the first sub-sailboard has not yet been deployed in place. In this case, the second sub-sailboard and the third sub-sailboard are locked, and rotate together with the first sub-sailboard under the drive of the torsion spring in the hinge assembly corresponding to the first sub-sailboard (as shown by the dotted arrow in Figure 23). As shown in Figure 24, the second sub-sailboard is deployed in place at about 5.2 seconds, and then the third sub-sailboard is deployed in place at about 5.6 seconds. Then the second sub-sailboard and the third sub-sailboard rotate to the target position with the first sub-sailboard at the same first angular velocity. At this time, it is necessary to increase the driving torque of the torsion spring in the hinge assembly corresponding to the first sub-sailboard, and adjust the driving torque of the torsion spring in the hinge assembly corresponding to the second sub-sailboard and the third sub-sailboard respectively, so that the first sub-sailboard, the second sub-sailboard and the third sub-sailboard are deployed synchronously.
在碰撞顺序上,首先是第二子帆板与第一子帆板碰撞,使得第二子帆板与第一子帆板的第一角速度均减小,之后第三子帆板与第一角速度减小后的第二子帆板碰撞,此时第二子帆板的第一角速度反向增大,第三子帆板的第一角速度减小,最终第一子帆板、第二子帆板以及第三子帆板以相同的第一角速度转动至目标位置,最后是第一子帆板与平板式卫星的主体发生碰撞后锁定。In terms of the collision sequence, the second sub-sail panel collides with the first sub-sail panel first, causing the first angular velocities of the second sub-sail panel and the first sub-sail panel to decrease. Then the third sub-sail panel collides with the second sub-sail panel after the first angular velocity is reduced. At this time, the first angular velocity of the second sub-sail panel increases in the opposite direction, and the first angular velocity of the third sub-sail panel decreases. Finally, the first sub-sail panel, the second sub-sail panel and the third sub-sail panel rotate to the target position at the same first angular velocity. Finally, the first sub-sail panel collides with the main body of the flat-panel satellite and is locked.
在另一些示例中,若第二子帆板对应的铰链组件中扭簧的驱动力矩相对较小,则会出现图25所示的情况,也就是第一子帆板和第三帆板均已展开到位,但是第二子帆板还没有展开到位。在这种情况下,第一子帆板与平板式卫星的主体锁定,第三子帆板与第二帆板锁定并与第二子帆板共同在第二子帆板对应的铰链组件扭簧的驱动下一同转动(图25中的虚线箭头所示)。如图26所示,在5.4秒左右第一子帆板展开到位,随后在5.6秒左右第三子帆板展开到位,然后第一子帆板与第三子帆板以相同的第一角速度与第二子帆板转动到目标位置。此时,需要增大第二子帆板对应的铰链组件中扭簧的驱动力矩,并相应地减小第三子帆板对应的铰链组件中扭簧的驱动力矩,以使得第一子帆板、第二子帆板以及第三子帆板同步展开。In other examples, if the driving torque of the torsion spring in the hinge assembly corresponding to the second sub-sailboard is relatively small, the situation shown in Figure 25 will occur, that is, the first sub-sailboard and the third sailboard have been deployed in place, but the second sub-sailboard has not yet been deployed in place. In this case, the first sub-sailboard is locked with the main body of the flat-panel satellite, and the third sub-sailboard is locked with the second sailboard and rotates together with the second sub-sailboard under the drive of the torsion spring of the hinge assembly corresponding to the second sub-sailboard (as shown by the dotted arrow in Figure 25). As shown in Figure 26, the first sub-sailboard is deployed in place at about 5.4 seconds, and then the third sub-sailboard is deployed in place at about 5.6 seconds, and then the first sub-sailboard and the third sub-sailboard rotate to the target position with the second sub-sailboard at the same first angular velocity. At this time, it is necessary to increase the driving torque of the torsion spring in the hinge assembly corresponding to the second sub-sailboard, and correspondingly reduce the driving torque of the torsion spring in the hinge assembly corresponding to the third sub-sailboard, so that the first sub-sailboard, the second sub-sailboard and the third sub-sailboard are deployed synchronously.
在碰撞顺序上,首先是第一子帆板与平板式卫星的主体碰撞,以锁定第一子帆板,然后是第三子帆板与第二子帆板碰撞,第三子帆板与第二子帆板碰撞后第一角速度均减小,最后第三子帆板与第二子帆板以相同的第一角速度转到目标位置,第二子帆板与第一子帆板碰撞,由于此时第二子帆板的第一角速度较小,因此不会对第一子帆板造成太大位置偏移。In terms of the collision sequence, the first sub-sail panel collides with the main body of the flat-panel satellite first to lock the first sub-sail panel, and then the third sub-sail panel collides with the second sub-sail panel. After the third sub-sail panel collides with the second sub-sail panel, the first angular velocity of both sub-sail panels decreases. Finally, the third sub-sail panel and the second sub-sail panel rotate to the target position at the same first angular velocity, and the second sub-sail panel collides with the first sub-sail panel. Since the first angular velocity of the second sub-sail panel is smaller at this time, it will not cause too much position displacement to the first sub-sail panel.
在又一些示例中,若第三子帆板对应的铰链组件中扭簧的驱动力矩相对较小,则会出现图27所示的情况,也就是第一子帆板和第二子帆板均已展开到位,但是第三子帆板还没有展开到位。在这种情况下第一子帆板与平板式卫星的主体锁定,第二子帆板与第一子帆板锁定,第三子帆板继续展开(图27中的虚线箭头所示)。如图28所示,在5.2秒左右第二子帆板展开到位,随后在6.2秒左右第一子帆板展开到位。在这种情况下第三子帆板也展开到位,但是第二子帆板被第三子帆板撞离锁定位置,然后第三子帆板再随第二子帆板转动至目标位置。此时,需要增大第二子帆板对应的铰链组件中扭簧的驱动力矩,并相应地减小第三子帆板对应的铰链组件中扭簧的驱动力矩,以使得第一子帆板、第二子帆板以及第三子帆板同步展开。In some other examples, if the driving torque of the torsion spring in the hinge assembly corresponding to the third sub-sailboard is relatively small, the situation shown in Figure 27 will occur, that is, the first sub-sailboard and the second sub-sailboard are both deployed in place, but the third sub-sailboard has not yet been deployed in place. In this case, the first sub-sailboard is locked with the main body of the flat-panel satellite, the second sub-sailboard is locked with the first sub-sailboard, and the third sub-sailboard continues to be deployed (as shown by the dotted arrow in Figure 27). As shown in Figure 28, the second sub-sailboard is deployed in place at about 5.2 seconds, and then the first sub-sailboard is deployed in place at about 6.2 seconds. In this case, the third sub-sailboard is also deployed in place, but the second sub-sailboard is knocked out of the locked position by the third sub-sailboard, and then the third sub-sailboard rotates to the target position with the second sub-sailboard. At this time, it is necessary to increase the driving torque of the torsion spring in the hinge assembly corresponding to the second sub-sailboard, and correspondingly reduce the driving torque of the torsion spring in the hinge assembly corresponding to the third sub-sailboard, so that the first sub-sailboard, the second sub-sailboard and the third sub-sailboard are deployed synchronously.
在碰撞顺序上,首先是第二子帆板与第一子帆板碰撞,且第二子帆板已锁定,并随第一子帆板转移到至目标位置。然后第一子帆板与平板式卫星的主体碰撞已完成锁定。最后第三子帆板展开到位,与第二子帆板碰撞。但是此时第三子帆板具有较大的第一角速度,与第二子帆板碰撞后导致第二子帆板偏离了原来的锁定位置,形成了较大的偏移,最后第三子帆板与第二子帆板花费3秒才重新转动至目标位置。In the collision sequence, the second sub-sailboard collides with the first sub-sailboard first, and the second sub-sailboard is locked and transferred to the target position with the first sub-sailboard. Then the first sub-sailboard collides with the main body of the flat-panel satellite and is locked. Finally, the third sub-sailboard is deployed and collides with the second sub-sailboard. However, the third sub-sailboard has a large first angular velocity at this time, and after colliding with the second sub-sailboard, the second sub-sailboard deviates from the original locked position, forming a large offset. Finally, it takes 3 seconds for the third sub-sailboard and the second sub-sailboard to rotate to the target position again.
基于上述阐述,通过调整各子帆板对应的铰链组件的参数,基本可以实现各子帆板的同步展开。但是为了避免在展开到位时的碰撞对已展开到位的子帆板造成位置偏移,需要微调对应的铰链组件中扭簧的驱动力矩,以保证碰撞次序。Based on the above description, by adjusting the parameters of the hinge assembly corresponding to each sub-sail board, the synchronous deployment of each sub-sail board can be basically achieved. However, in order to avoid the position displacement of the deployed sub-sail board caused by the collision when deployed, it is necessary to fine-tune the driving torque of the torsion spring in the corresponding hinge assembly to ensure the collision order.
在对铰链组件中扭簧的驱动力矩优化后,初步得到的仿真结果如图29所示。由图29可以看出,第一子帆板、第二子帆板以及第三子帆板在6.2秒时同时展开至90度,即第一子帆板、第二子帆板以及第三子帆板同步展开到位。具体来说,在前两秒,第二子帆板率先展开,第一子帆板由于平板式卫星的主体的约束保持在0度不动,而第三子帆板由于第二子帆板的约束,跟随第二子帆板逐渐地展开。在两秒以后,第一子帆板也开始展开,第三子帆板仍然紧贴第二子帆板,跟随反向展开。在三秒之后,第三子帆板开始正向展开。第一子帆板、第二子帆板以及第三子帆板此时都沿正向展开。第二子帆板展开速度先快后慢,第一子帆板匀速地展开,第三子帆板先反向展开之后再正向加速展开。最终第一子帆板、第二子帆板以及第三子帆板在6.2秒时同时展开至90度。After optimizing the driving torque of the torsion spring in the hinge assembly, the preliminary simulation results are shown in Figure 29. As can be seen from Figure 29, the first sub-sailboard, the second sub-sailboard and the third sub-sailboard are simultaneously deployed to 90 degrees at 6.2 seconds, that is, the first sub-sailboard, the second sub-sailboard and the third sub-sailboard are deployed in place synchronously. Specifically, in the first two seconds, the second sub-sailboard is deployed first, the first sub-sailboard is kept at 0 degrees due to the constraint of the main body of the flat-panel satellite, and the third sub-sailboard is gradually deployed following the second sub-sailboard due to the constraint of the second sub-sailboard. After two seconds, the first sub-sailboard also begins to deploy, and the third sub-sailboard is still close to the second sub-sailboard and follows the reverse deployment. After three seconds, the third sub-sailboard begins to deploy forward. The first sub-sailboard, the second sub-sailboard and the third sub-sailboard are all deployed in the forward direction at this time. The deployment speed of the second sub-sailboard is fast at first and then slow, the first sub-sailboard is deployed at a uniform speed, and the third sub-sailboard is first deployed in the reverse direction and then accelerated in the forward direction. Finally, the first sub-sailboard, the second sub-sailboard and the third sub-sailboard were simultaneously deployed to 90 degrees at 6.2 seconds.
需要说明的是,上述的子帆板反向展开指的是子帆板沿远离目标位置的方向转动,正向展开则指的是子帆板沿靠近目标位置的方向转动。It should be noted that the reverse deployment of the sub-sail board mentioned above refers to the sub-sail board rotating in a direction away from the target position, and the forward deployment refers to the sub-sail board rotating in a direction close to the target position.
对于二级铰链组件连接的帆板展开过程进行仿真,具体如下:The unfolding process of the sailboard connected by the secondary hinge assembly is simulated as follows:
二级铰链组件的仿真优化是在单级铰链组件的仿真基础上进行的。首先根据图22所示的各子帆板对应的扭簧的刚度系数变化曲线拟合出第一级刚度系数使得各子帆板在初始展开过程中实现同步展开,然后当各子帆板出现不同步展开的情况时,根据图22所示的各子帆板对应的扭簧的刚度系数变化曲线进行第二级刚度系数的拟合,使得各子帆板在后续展开过程中实现同步展开,然后再对第一级刚度系数和第二级刚度系数进行调整,进一步优化各子帆板的同步展开过程。The simulation optimization of the secondary hinge assembly is carried out on the basis of the simulation of the single-stage hinge assembly. First, the first-stage stiffness coefficient is fitted according to the stiffness coefficient variation curve of the torsion spring corresponding to each sub-sail board shown in FIG22, so that each sub-sail board can be deployed synchronously during the initial deployment process. Then, when each sub-sail board is deployed asynchronously, the second-stage stiffness coefficient is fitted according to the stiffness coefficient variation curve of the torsion spring corresponding to each sub-sail board shown in FIG22, so that each sub-sail board can be deployed synchronously during the subsequent deployment process. Then, the first-stage stiffness coefficient and the second-stage stiffness coefficient are adjusted to further optimize the synchronous deployment process of each sub-sail board.
在一些示例中,首先拟合得到第一级刚度系数使得各子帆板在初始展开过程中实现同步展开,图30示出了各子帆板的展开曲线图。由图30可以看出,在2.5秒前,各子帆板基本可以实现每个时间点均同步展开。在2.5秒后,第二子帆板展开滞后,而第一子帆板与第三子帆板仍然保持同步展开。在3.5秒后,第三子帆板相较于第一帆板超前展开。由图30看出在第二子帆板对应的铰链组件以第一级刚度系数展开的弧度达到0.8rad时需要较大的第二级刚度系数,以避免第二子帆板滞后展开。而在第三子帆板对应的铰链组件以第一级刚度系数展开的弧度达到2.2rad时需要较小的第二级刚度系数,以避免第三子帆板超前展开。图31为添加第二级刚度系数后各子帆板的展开曲线图。In some examples, the first-level stiffness coefficient is first fitted so that each sub-sailboard can be synchronously deployed during the initial deployment process. Figure 30 shows the deployment curve of each sub-sailboard. It can be seen from Figure 30 that before 2.5 seconds, each sub-sailboard can basically achieve synchronous deployment at each time point. After 2.5 seconds, the second sub-sailboard is deployed with a lag, while the first sub-sailboard and the third sub-sailboard are still deployed synchronously. After 3.5 seconds, the third sub-sailboard is deployed ahead of the first sailboard. It can be seen from Figure 30 that when the arc of the hinge assembly corresponding to the second sub-sailboard with the first-level stiffness coefficient reaches 0.8rad, a larger second-level stiffness coefficient is required to avoid the second sub-sailboard from lagging behind. When the arc of the hinge assembly corresponding to the third sub-sailboard with the first-level stiffness coefficient reaches 2.2rad, a smaller second-level stiffness coefficient is required to avoid the third sub-sailboard from being deployed ahead of time. Figure 31 is the deployment curve of each sub-sailboard after adding the second-level stiffness coefficient.
由图31可以看出,相较于单级铰链组件的同步展开过程,二级铰链组件的同步展开过程中不仅可以保证第一子帆板、第二子帆板以及第三子帆板同一时间到达目标位置,而且在展开过程中能够使得第一子帆板、第二子帆板以及第三子帆板保持较好的同步性。It can be seen from Figure 31 that compared with the synchronous deployment process of the single-stage hinge assembly, the synchronous deployment process of the secondary hinge assembly can not only ensure that the first sub-sail panel, the second sub-sail panel and the third sub-sail panel reach the target position at the same time, but also enable the first sub-sail panel, the second sub-sail panel and the third sub-sail panel to maintain good synchronization during the deployment process.
图32示出了第二子帆板与第三子帆板分别相对于第一子帆板展开过程中的同步偏差角度。由图32可以看出,第二子帆板展开过程中相较于第一子帆板的最大同步偏差角度为0.14rad左右,第三子帆板展开过程中相较于第一子帆板的最大同步偏差角度为0.17rad左右,第二子帆板和第三子帆板分别相对于第一子帆板展开过程中的最大同步偏差角度移量均较小,表明采用二级铰链组件实现了第一子帆板、第二子帆板以及第三子帆板同步展开。Figure 32 shows the synchronous deviation angles of the second sub-sailboard and the third sub-sailboard respectively relative to the first sub-sailboard during the deployment process. It can be seen from Figure 32 that the maximum synchronous deviation angle of the second sub-sailboard relative to the first sub-sailboard during the deployment process is about 0.14 rad, and the maximum synchronous deviation angle of the third sub-sailboard relative to the first sub-sailboard during the deployment process is about 0.17 rad. The maximum synchronous deviation angle displacements of the second sub-sailboard and the third sub-sailboard relative to the first sub-sailboard during the deployment process are both small, indicating that the use of the secondary hinge assembly realizes the synchronous deployment of the first sub-sailboard, the second sub-sailboard and the third sub-sailboard.
需要说明的是:本公开实施例所记载的技术方案之间,在不冲突的情况下,可以任意组合。It should be noted that the technical solutions described in the embodiments of the present disclosure can be combined arbitrarily without conflict.
以上所述,仅为本公开的具体实施方式,但本公开的保护范围并不局限于此,任何熟悉本技术领域的技术人员在本公开揭露的技术范围内,可轻易想到变化或替换,都应涵盖在本公开的保护范围之内。因此,本公开的保护范围应以所述权利要求的保护范围为准。The above is only a specific embodiment of the present disclosure, but the protection scope of the present disclosure is not limited thereto. Any person skilled in the art who is familiar with the technical field can easily think of changes or substitutions within the technical scope disclosed in the present disclosure, which should be included in the protection scope of the present disclosure. Therefore, the protection scope of the present disclosure should be based on the protection scope of the claims.
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