基于旋量的测力台架模型分析和推力定位

李东; 张磊乐; 郑国良; 邢彦昌; 游广飞

doi:10.13224/j.cnki.jasp.20220960

基于旋量的测力台架模型分析和推力定位

doi: 10.13224/j.cnki.jasp.20220960

李东^1,,
张磊乐^1,*, ,,
郑国良¹,
邢彦昌²,
游广飞¹

1.
中国机械科学研究总院郑州机械研究所有限公司，郑州 450001
2.
中国空气动力研究与发展中心超高速空气动力研究所，四川绵阳 621000

详细信息

作者简介:
李东（1998-），男，硕士生，主要研究方向为非标设备的力学分析与优化创新

通讯作者:
张磊乐（1979-），男，研究员级高级工程师，硕士，主要研究方向为非标设备设计。E-mail：99336093@qq.com

中图分类号: V216
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- 文章访问数: 500
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- 被引次数: 0
出版历程
- 收稿日期: 2022-12-16
- 网络出版日期: 2024-02-20

Thrust stand model analysis and thrust positioning based on screw algebra

1.
Zhengzhou Research Institute of Mechanical Engineering Company Limited，China Academy of Machiney Science and Technology Group，Zhengzhou 450001，China
2.
Hypervelocity Aerodynamics Institute，China Aerodynamics Research and Development Center，Mianyang Sichuan 621000，China

摘要

摘要:
基于旋量理论和变形位移协调关系，对八分支正交盒式测力台架进行了旋量建模、模型求解、误差补偿和推力定位方面的研究。从台架的载荷偏心和测力耦合两大特点出发，建立了台架的旋量模型，并结合分支变形约束关系推导出辅助模型求解的约束方程。数值算例和仿真表明，旋量模型及约束方程的最大相对误差为9.147‰。基于测力单元变形与台架位移之间的协调关系，建立了误差补偿模型。数值算例和仿真表明，分力的最小补偿量为78.03%。此外，针对矢量推力定位的不确定性问题，通过旋量理论的Poinsot中心轴定理明确了其原因，即忽略了合力中纯力偶的影响。解析法表明，质心偏移对矢量推力不确定的影响为线性。
- 测力台架 /
- 变形协调 /
- 旋量 /
- 台架设计 /
- 推力定位
Abstract:
The screw theory and coordination between deformation and displacement were applied to research the octagonal orthogonal box-type thrust stand in screw modeling, model solving, error compensation, and thrust positioning. Screw model of the stand was established based on the two major characteristics of load eccentricity and force coupling. And constraint equations for model solution were derived based on the branches deformation constraint relationship. Numerical examples and simulations showed that the maximum relative error of the screw model was 9.147‰. An error compensation model was established based on the coordinated relationship between the branches deformation and the stand displacement. Numerical examples and simulations showed that the minimum compensation for force was 78.03%. The Poinsot’s central axis theorem of the screw theory was used to clarify the uncertainty of vector thrust positioning, which was caused by ignoring the influence of pure couple in the resultant force. The analytic method indicated that the effect of mass center offset on vector thrust uncertainty was linear.
- thrust stand /
- deformation compatibility /
- screw algebra /
- stand design /
- thrust positioning

HTML

图 1 盒式测力台架示意图

1～4 y向测力单元； 5、6 x向测力单元； 7、8 z向测力单元；a 模型支架； b 动架； c 定架； d 模型； e 气流。

Figure 1. Box-type thrust stand

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图 2 变形协调示意图

Figure 2. Compatibility of deformations

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图 3 载荷和变形关系示意图

Figure 3. Relationship of load and deformation

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图 4 仿真示意图

1～4 y向测力单元； 5、6 x向测力单元；7、8 z向测力单元； A 载荷作用点。

Figure 4. Simulation diagram

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图 5 质心位置与合力关系图

Figure 5. Relationship between the position of the center of mass and the resultant force

下载: 全尺寸图片幻灯片

表 1 载荷信息表

Table 1. Load information table

分力	方向/m	作用点/m	分力数值
F_x/kN	（1, 0, 0）	（0, 3.36, 0）	150
F_y/kN	（0, 1, 0）	（0, 3.36, 0）	−100
F_z/kN	（0, 0, 1）	（0, 3.36, 0）	50
M_z/（kN·m）	（0, 0, 1）	（0, 3.36, 0）	−50

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表 2 重力信息表

Table 2. Gravity information table

结构	重力方向/m	重心坐标/m	质量/kg
模型	（0, −1, 0）	（0, 3.36, 0）	5000
支架	（0, −1, 0）	（0, 2, 0）	5000
动架	（0, −1, 0）	（0, 0.6, 0）	2000

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表 3 测力单元信息表

Table 3. Force cell information table

i	$ {{\boldsymbol{r}}_{{\mathrm{s}}i}} $/mm	$ {{\boldsymbol{t}}_{{\mathrm{s}}i}} $/ mm	$ {{\boldsymbol{s}}_{{\mathrm{s}}i}} $/m
1	（−1360, 100, −320）	（−1360, 635, −320）	（0, 1, 0）
2	（−1360, 100, 320）	（−1360, 635, 320）	（0, 1, 0）
3	（1360, 100, 320）	（1360, 635, 320）	（0, 1, 0）
4	（1360, 100, −320）	（1360, 635, −320）	（0, 1, 0）
5	（−470, 390, −300）	（−40, 390, −300）	（1, 0, 0）
6	（470, 390, 300）	（40, 390, 300）	（−1, 0, 0）
7	（−1100, 515, 180）	（−1100, 515, −180）	（0, 0, −1）
8	（1100, 515, −180）	（1100, 515, 180）	（0, 0, 1）

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表 4 测力模型计算结果

Table 4. Force measurement model calculation results

编号	力/N			相对误差/‰
编号	理论数值	仿真数值	差值	相对误差/‰
1	147817.37	−148159.50	−342.1259	2.309
2	−74448.25	74782.77	334.5158	4.473
3	−256617.37	256982.63	365.2618	1.421
4	−34351.75	34040.37	−311.3798	−9.147
5	75000.00	−75049.34	−49.3374	0.657
6	−75000.00	75044.18	44.1807	0.589
7	−25000.00	25175.27	175.2674	6.962
8	25000.00	−24892.22	107.7764	−4.330

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表 5 载荷测量结果

Table 5. Result of load measurement

$ {{\boldsymbol{W}}_{{\mathrm{lg}}}} $/N	$ （{{{\boldsymbol{G}}_{\mathrm{s}}}{{\boldsymbol{f}}_{\mathrm{s}}} - {{\boldsymbol{W}}_{{\mathrm{lg}}}}} ） $/N	$ （ {{\boldsymbol{G}}_{\mathrm{s}}'{\boldsymbol{f}} - {{\boldsymbol{W}}_{{\mathrm{lg}}}}} ） $/N	$ {\boldsymbol{E}} $
150000	−142.5034	31.2895	−0.2196
−100000	186.7216	2.4000	0.0129
50000	−118.4333	6.4352	−0.0543
169003.17	−47.0292	51.8225	−1.1019
1567.5947	331.7391	−59.6066	−0.1797
−554233.5	13.9714	−64.7990	−4.6380

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表 6 合力状态表

Table 6. State of resultant force

序号	合力	合力矩	力与力矩位置关系	刚体受力状况
1	≠0	=0		过原点纯力
2	=0	≠0		纯力偶
3	=0	=0		平衡
4	≠0	≠0	垂直	不过原点纯力
5	≠0	≠0	平行	螺旋状态
6	≠0	≠0	既不垂直也不平行	不过原点纯力和纯力偶

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